Microelectronic Circuits 6th Edition

PART I

Devices and Basic Circuits CHAPTER 1

Signals and Amplifiers

4

CHAPTER 2

Operational Amplifiers

52

CHAPTER 3

Semiconductors

124

CHAPTER 4

Diodes

164

CHAPTER 5

MOS Field-Effect Transistors (MOSFETs) CHAPTER 6

Bipolar Junction Transistors (BJTs)

350

230

P

art I, Devices and Basic Circuits, includes the most fundamental and essential topics for the study of electronic circuits. At the same time, it constitutes a complete package for a first course on the subject. The heart of Part I is the study of the three basic semiconductor devices: the diode (Chapter 4); the MOS transistor (Chapter 5); and the bipolar transistor (Chapter 6). In each case, we study the device operation, its characterization, and its basic circuit applications. For those who have not had a prior course on device physics, Chapter 3 provides an overview of semiconductor concepts at a level sufficient for the study of electronic circuits. A review of Chapter 3 should prove useful even for those with prior knowledge of semiconductors. Since the purpose of electronic circuits is the processing of signals, an understanding is essential of signals, their characterization in the time and frequency domains, and their analog and digital representations. This is provided in Chapter 1, which also introduces the most common signal-processing function, amplification, and the characterization and types of amplifiers. Besides diodes and transistors, the basic electronic devices, the op amp is studied in Part I. Although not an electronic device in the most fundamental sense, the op amp is commercially available as an integrated circuit (IC) package and has well-defined terminal characteristics. Thus, despite the fact that the op amp’s internal circuit is complex, typically incorporating 20 or more transistors, its almost-ideal terminal behavior makes it possible to treat the op amp as a circuit element and to use it in the design of powerful circuits, as we do in Chapter 2, without any knowledge of its internal construction. We should mention, however, that the study of op amps can be delayed to a later point, and Chapter 2 can be skipped with no loss of continuity. The foundation of this book, and of any electronics course, is the study of the two transistor types in use today: the MOS transistor in Chapter 5 and the bipolar transistor in Chapter 6. These two chapters have been written to be completely independent of one another and thus can be studied in either order as desired. Furthermore, the two chapters have the same structure, making it easier and faster to study the second device, as well as to draw comparisons between the two device types. After the study of Part I, the reader will be fully prepared to undertake the study of either integrated-circuit amplifiers in Part II or digital integrated circuits in Part III.

3

CHAPTER 1

Signals and Amplifiers Introduction 5

1.5

Circuit Models for Amplifiers 21

1.1

Signals 6

1.6

Frequency Response of Amplifiers 30

1.2

Frequency Spectrum of Signals 9

Summary 41

1.3

Analog and Digital Signals 11

Problems 42

1.4 Amplifiers 14

IN THIS CHAPTER YOU WILL LEARN 1. That electronic circuits process signals, and thus understanding electrical signals is essential to appreciating the material in this book. 2. The Thévenin and Norton representations of signal sources. 3. The representation of a signal as the sum of sine waves. 4. The analog and digital representations of a signal. 5. The most basic and pervasive signal-processing function: signal amplification, and correspondingly, the signal amplifier. 6. How amplifiers are characterized (modeled) as circuit building blocks independent of their internal circuitry. 7. How the frequency response of an amplifier is measured, and how it is calculated, especially in the simple but common case of a single-timeconstant (STC) type response.

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5

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7

8 Chapter 1 Signals and Amplifiers

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1.2 Frequency Spectrum of Signals 9

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10 Chapter 1 Signals and Amplifiers

Figure 1.5 L$%>//#*1-)53$%G&51#965E#$%-8253$+,$5/?3-*&0#$)7

6"#1#$)$-%$*"#$5/?3-*&0#$+,$*"#$%G&51#$65E#$520$ω A $S$B π ⁄ , $:,$-%$*"#$?#1-+0$+,$*"#$%G&51# 65E#=$ -%$ )533#0$ *"#$ 90*13!'*)3(, 9$':0'*#;7$ O+*#$ *"5*$ '#)5&%#$ *"#$ 5/?3-*&0#%$ +,$ *"# "51/+2-)%$ ?1+81#%%-E#3>$ 0#)1#5%#4$ *"#$ -2,-2-*#$ %#1-#%$ )52$ '#$ *1&2)5*#04$ 6-*"$ *"#$ *1&2)5*#0 %#1-#%$?1+E-0-28$52$5??1+D-/5*-+2$*+$*"#$%G&51#$65E#,+1/7 !"#$%-2&%+-053$)+/?+2#2*%$-2$*"#$%#1-#%$+,$JG7$:@7B=$)+2%*-*&*#$*"#$,1#G)>$%?#)*1&/$+, *"#$%G&51#965E#$%-82537$I&)"$5$%?#)*1&/$)52$'#$815?"-)533>$1#?1#%#2*#0$5%$-2$K-87$@7b4$6"#1# *"#$"+1-T+2*53$5D-%$1#?1#%#2*%$*"#$528&351$,1#G)>$ω$-2$150-52%$?#1$%#)+207$ !"#$ K+&1-#1$ *152%,+1/$ )52$ '#$ 5??3-#0$ *+$ 5$ 2+2?#1-+0-)$ ,&2)*-+2$ +,$ *-/#4$ %&)"$ 5%$ *"5* 0#?-)*#0$-2$K-87$@7U4$520$?1+E-0#%$-*%$,1#G)>$%?#)*1&/$5%$5$)+2*-2&+&%$,&2)*-+2$+,$,1#9 G)>4$5%$-20-)5*#0$-2$K-87$@7c7$d23-.#$*"#$)5%#$+,$?#1-+0-)$%-8253%4$6"#1#$*"#$%?#)*1&/$)+29 %-%*%$+,$0-%)1#*#$,1#G)-#%$:5*$ ω A$520$-*%$"51/+2-)%=4$*"#$%?#)*1&/$+,$5$2+2?#1-+0-)$%-8253 )+2*5-2%$-2$8#2#153$533$?+%%-'3#$,1#G)-#%7$O#E#1*"#3#%%4$*"#$#%%#2*-53$?51*%$+,$*"#$%?#)*15 +,$?15)*-)53$%-8253%$51#$&%&533>$)+2,-2#0$*+$1#35*-E#3>$%"+1*$%#8/#2*%$+,$*"#$,1#G)>$ -ω. 5D-%e52$+'%#1E5*-+2$*"5*$-%$E#1>$&%#,&3$-2$*"#$?1+)#%%-28$+,$%&)"$%-8253%7$K+1$-2%*52)#4$*"# %?#)*1&/$+,$5&0-'3#$%+&20%$%&)"$5%$%?##)"$520$ /&%-)$#D*#20%$,1+/$5'+&*$BA$aT$*+$5'+&* BA .aTe5$,1#G)>$1528#$.2+62$5%$*"#$301"%,83*17$a#1#$6#$%"+&30$2+*#$*"5*$53*"+&8" %+/#$/&%-)53$*+2#%$"5E#$,1#G)-#%$5'+E#$BA$.aT4$*"#$"&/52$#51$-%$-2)5?5'3#$+,$"#51-28 ,1#G)-#%$ *"5*$ 51#$ /&)"$ 5'+E#$ BA$ .aT7$ L%$ 52+*"#1$ #D5/?3#4$ 5253+8$ E-0#+$ %-8253%$ "5E# *"#-1$%?#)*15$-2$*"#$1528#$+,$A$_aT$*+$^7]$_aT7$$$$

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1.3 Analog and Digital Signals 11

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EXERCISES 1.5 K-20$*"#$,1#G)-#%$*$520$ω$+,$5$%-2#965E#$%-8253$6-*"$5$?#1-+0$+,$@$/%7 U Ans. *$= @AAA$aTM$ ω = B π × @A $150`% 1.6 F"5*$-%$*"#$?#1-+0$,$+,$%-2#$65E#,+1/%$)"515)*#1-T#0$'>$,1#G)-#%$+,$:5=$*+=$bA$aTX$:'=$*+=$@A−U$aTX :)=$*+=$@$_aTX$$ Ans. @b7c$/%M$@AAA$%M$@$µ% 1.7 !"#$daK$:&3*15$"-8"$,1#G)>=$*#3#E-%-+2$'1+50)5%*$'520$'#8-2%$6-*"$)"522#3$@^$520$#D*#20%$,1+/ ^cA$_aT$*+$ZAb$_aT7$;,$b$_aT$-%$533+)5*#0$,+1$#5)"$)"522#34$"+6$/52>$)"522#3%$)52$*"-%$'520 5))+//+05*#X Ans. ]bM$)"522#3%$@^$*+$b\ 1.8 F"#2$*"#$%G&51#965E#$%-8253$+,$K-87$@7]4$6"+%#$K+&1-#1$%#1-#%$-%$8-E#2$-2$JG7$:@7B=4$-%$5??3-#0$*+$5$1#%-%9 , *+14$*"#$*+*53$?+6#1$0-%%-?5*#0$/5>$'#$)53)&35*#0$0-1#)*3>$&%-28$*"#$1#35*-+2%"-?$ - = @ ⁄ , A ( v B ⁄ # ) ." +1$-20-1#)*3>$'>$%&//-28$*"#$)+2*1-'&*-+2$+,$#5)"$+,$*"#$"51/+2-)$)+/?+2#2*%4$*"5*$-%4$-$S$-@$f$-U$f -] f$g4$6"-)"$/5>$'#$,+&20$0-1#)*3>$,1+/$1/%$E53&#%7$Y#1-,>$*"5*$*"#$*6+$5??1+5)"#%$51#$#G&-E53#2*7 F"5*$,15)*-+2$+,$*"#$#2#18>$+,$5$%G&51#$65E#$-%$-2$-*%$,&205/#2*53X$;2$-*%$,-1%*$,-E#$"51/+2-)%X$;2$-*%$,-1%* %#E#2X$K-1%*$2-2#X$;2$6"5*$2&/'#1$+,$"51/+2-)%$-%$\A[$+,$*"#$#2#18>X$:O+*#$*"5*$-2$)+&2*-28$"51/+2-)%4 *"#$,&205/#2*53$5*$ω A$-%$*"#$,-1%*4$*"#$+2#$5*$Bω A$-%$*"#$%#)+204$#*)7= Ans. A7Z@M$A7\UM$A7\]M$A7\bM$U

1.3 Analog and Digital Signals !"#$E+3*58#$%-8253$0#?-)*#0$-2$K-87$@7U$-%$)533#0$52$3*3(%2,+"2*3(7$!"#$25/#$0#1-E#%$,1+/ *"#$,5)*$*"5*$%&)"$5$%-8253$-%$5253+8+&%$*+$*"#$?">%-)53$%-8253$*"5*$-*$1#?1#%#2*%7$!"#$/582-9 *&0#$+,$52$5253+8$%-8253$)52$*5.#$+2$52>$E53&#M$*"5*$-%4$*"#$5/?3-*&0#$+,$52$5253+8$%-8253 #D"-'-*%$5$)+2*-2&+&%$E51-5*-+2$+E#1$-*%$1528#$+,$5)*-E-*>7$!"#$E5%*$/5(+1-*>$+,$%-8253%$-2$*"#

12 Chapter 1 Signals and Amplifiers 6+130$51+&20$&%$51#$5253+87$J3#)*1+2-)$)-1)&-*%$*"5*$?1+)#%%$%&)"$%-8253%$51#$.2+62$5%$3*3& (%2,#"$#0")+7$L$E51-#*>$+,$5253+8$)-1)&-*%$6-33$'#$%*&0-#0$-2$*"-%$'++.7 L2$53*#125*-E#$,+1/$+,$%-8253$1#?1#%#2*5*-+2$-%$*"5*$+,$5$%#G)#$+,$2&/'#1%4$#5)"$2&/9 '#1$1#?1#%#2*-28$*"#$%-8253$/582-*&0#$5*$52$-2%*52*$+,$*-/#7$!"#$1#%&3*-28$%-8253$-%$)533#0$5 1"2")3(,+"2*3(7,!+$%##$"+6$5$%-8253$)52$'#$1#?1#%#2*#0$-2$*"-%$,+1/e*"5*$-%4$"+6$%-8253%$)52 '#$)+2E#1*#0$,1+/$5253+8$*+$0-8-*53$,+1/e)+2%-0#1$K-87$@7Z:5=7$a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a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1.3 Analog and Digital Signals 13

v (t)

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Logic values

0

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14 Chapter 1 Signals and Amplifiers *+$'#$A$+1$@4$1#%?#)*-E#3>7$!"#$0&53$)-1)&-*$+,$*"#$LQ<$-%$*"#$1"2")3(&)%&3*3(%2,#%*B'$)'$$:EDC$+1 EC6=7$;*$)+2E#1*%$52$/9'-*$0-8-*53$-2?&*$*+$52$5253+8$+&*?&*$E+3*58#7 C2)#$*"#$%-8253$-%$-2$0-8-*53$,+1/4$-*$)52$'#$?1+)#%%#0$&%-28$1"2")3(,#"$#0")+>$C,$)+&1%# 0-8-*53$)-1)&-*%$)52$0#53$53%+$6-*"$%-8253%$*"5*$0+$2+*$"5E#$52$5253+8$+1-8-24$%&)"$5%$*"#$%-89 253%$*"5*$1#?1#%#2*$*"#$E51-+&%$-2%*1&)*-+2%$+,$5$0-8-*53$)+/?&*#17 I-2)#$0-8-*53$)-1)&-*%$0#53$#D)3&%-E#3>$6-*"$'-251>$%-8253%4$*"#-1$0#%-82$-%$%-/?3#1$*"52$*"5*$+, 5253+8$ )-1)&-*%7$ K&1*"#1/+1#4$ 0-8-*53$ %>%*#/%$ )52$ '#$ 0#%-82#0$ &%-28$ 5$ 1#35*-E#3>$ ,#6$ 0-,,#1#2* .-20%$+,$0-8-*53$)-1)&-*$'3+).%7$a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

EXERCISE 1.9$ <+2%-0#1$5$^9'-*$0-8-*53$6+10$1$S$0U0B0@0A$:%##$JG7$@7U=$&%#0$*+$1#?1#%#2*$52$5253+8$%-8253$v8$*"5*$E51-#% '#*6##2$A$Y$520$+@]$Y7 :5= j-E#$1$)+11#%?+20-28$*+$v8$S$A$Y4$@$Y4$B$Y4$520$@]$Y7 :'= F"5*$)"528#$-2$v8$)5&%#%$5$)"528#$,1+/$A$*+$@$-2$:-=$0A4$:--=$0@4$:---=$0B4$520$:-E=$0UX :)= ;,$v8$S$]7B$Y4$6"5*$0+$>+&$#D?#)*$1$*+$'#X$F"5*$-%$*"#$1#%&3*-28$#11+1$-2$1#?1#%#2*5*-+2X Ans. :5= AAAA4$AAA@4$AA@A4$@@@@M :'= +@$Y4$+B$Y4$+^$Y4$+Z$YM :)= A@A@4$h^[

1.4 Amplifiers ;2$*"-%$%#)*-+24$6#$%"533$-2*1+0&)#$*"#$/+%*$,&205/#2*53$%-82539?1+)#%%-28$,&2)*-+24$+2#$*"5* -%$#/?3+>#0$-2$%+/#$,+1/$-2$53/+%*$#E#1>$#3#)*1+2-)$%>%*#/4$25/#3>4$%-8253$5/?3-,-)5*-+27 F#$%"533$%*&0>$*"#$5/?3-,-#1$5%$5$)-1)&-*$'&-30-289'3+).M$*"5*$-%4$6#$%"533$)+2%-0#1$-*%$#D*#1253 )"515)*#1-%*-)%$520$3#5E#$*"#$0#%-82$+,$-*%$-2*#1253$)-1)&-*$*+$35*#1$)"5?*#1%7

1.4.1 Signal Amplification K1+/$5$)+2)#?*&53$?+-2*$+,$E-#6$*"#$%-/?3#%*$%-82539?1+)#%%-28$*5%.$-%$*"5*$+,$+"2*3(,3!/("9"#3& )"%*7$!"#$2##0$,+1$5/?3-,-)5*-+2$51-%#%$'#)5&%#$*152%0&)#1%$?1+E-0#$%-8253%$*"5*$51#$%5-0$*+$'# V6#5.4W$*"5*$-%4$-2$*"#$/-)1+E+3*$:µY=$+1$/-33-E+3*$:/Y=$1528#$520$?+%%#%%-28$3-**3#$#2#18>7$I&)"

1.4 Amplifiers

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16 Chapter 1 Signals and Amplifiers

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8 ; = 8v 8 $

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1.4.5 Expressing Gain in Decibels !"#$5/?3-,-#1$85-2%$0#,-2#0$5'+E#$51#$15*-+%$+,$%-/-3513>$0-/#2%-+2#0$G&52*-*-#%7$!"&%$*"#> 6-33$'#$#D?1#%%#0$#-*"#1$5%$0-/#2%-+23#%%$2&/'#1%$+14$,+1$#/?"5%-%4$5%$Y`Y$,+1$*"#$E+3*58# 85-24$L`L$,+1$*"#$)&11#2*$85-24$520$F`F$,+1$*"#$?+6#1$85-27$L3*#125*-E#3>4$,+1$5$2&/'#1$+, 1#5%+2%4$%+/#$+,$*"#/$"-%*+1-)4$#3#)*1+2-)%$#28-2##1%$#D?1#%%$5/?3-,-#1$85-2$6-*"$5$3+851-*"9 /-)$/#5%&1#7$I?#)-,-)533>$*"#$E+3*58#$85-2$8v$)52$'#$#D?1#%%#0$5%

Y+3*58#$85-2$-2$0#)-'#3% " BA$3+8 8v

0i

520$*"#$)&11#2*$85-2$8$$)52$'#$#D?1#%%#0$5%

<&11#2*$85-2$-2$0#)-'#3% = BA$3+8 8 $

0i

I-2)#$?+6#1$-%$1#35*#0$*+$E+3*58#$:+1$)&11#2*=$%G&51#04$*"#$?+6#1$85-2$8;$)52$'#$#D?1#%%#0$-2 0#)-'#3%$5%

l+6#1$85-2$-2$0#)-'#3% = @A$3+8 8 ;

0i

!"#$5'%+3&*#$E53&#%$+,$*"#$E+3*58#$520$)&11#2*$85-2%$51#$&%#0$'#)5&%#$-2$%+/#$)5%#%$8v$+1 8$$6-33$'#$5$2#85*-E#$2&/'#17$L$2#85*-E#$85-2$8v$%-/?3>$/#52%$*"5*$*"#1#$-%$5$@ZA°$?"5%#$0-,9 ,#1#2)#$'#*6##2$-2?&*$520$+&*?&*$%-8253%M$-*$0+#%$2+*$-/?3>$*"5*$*"#$5/?3-,-#1$-%$3))'*03)"*2 *"#$%-82537$C2$*"#$+*"#1$"5204$52$5/?3-,-#1$6"+%#$E+3*58#$85-2$-%4$%5>4$hBA$0i$-%$-2$,5)*$5**#29 &5*-28$*"#$-2?&*$%-8253$'>$5$,5)*+1$+,$@A$:-7#74$8v$=$A7@$Y`Y=7

1.4.6 The Amplifier Power Supplies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f$520$) >4$,+1$)+22#)9 *-+2$*+$*"#$0)$%&??3-#%7$K+1$*"#$5/?3-,-#1$*+$+?#15*#4$*"#$*#1/-253$35'#3#0$) f$"5%$*+$'#$)+29 2#)*#0$ *+$ *"#$ ?+%-*-E#$ %-0#$ +,$ 5$ 0)$ %+&1)#$ 6"+%#$ E+3*58#$ -%$ )<<$ 520$ 6"+%#$ 2#85*-E#$ %-0#$ -% )+22#)*#0$*+$*"#$)-1)&-*$81+&207$L3%+4$*"#$*#1/-253$35'#3#0$) >$"5%$*+$'#$)+22#)*#0$*+$*"#$2#859 *-E#$%-0#$+,$5$0)$%+&1)#$6"+%#$E+3*58#$-%$)==$520$6"+%#$?+%-*-E#$%-0#$-%$)+22#)*#0$*+$*"#$)-1)&-* 81+&207$O+64$-,$*"#$)&11#2*$01562$,1+/$*"#$?+%-*-E#$%&??3>$-%$0#2+*#0$9<<$520$*"5*$,1+/$*"# 2#85*-E#$%&??3>$-%$9==$:%##$K-87$@7@U5=4$*"#2$*"#$0)$?+6#1$0#3-E#1#0$*+$*"#$5/?3-,-#1$-%

17

18 Chapter 1 Signals and Amplifiers - .' " ) << 9 << ! ) == 9 ==

;,$*"#$?+6#1$0-%%-?5*#0$-2$*"#$5/?3-,-#1$)-1)&-*$-%$0#2+*#0 -0-%%-?5*#04 *"#$?+6#19'5352)#$#G&59 *-+2$,+1$*"#$5/?3-,-#1$)52$'#$61-**#2$5%

- 0) + - 9 = - % + - 0-%%-?5*#0 6"#1#$-9$-%$*"#$?+6#1$01562$,1+/$*"#$%-8253$%+&1)#$520$-%$-%$*"#$?+6#1$0#3-E#1#0$*+$*"#$3+507 I-2)#$ *"#$ ?+6#1$ 01562$ ,1+/$ *"#$ %-8253$ %+&1)#$ -%$ &%&533>$ %/5334$ *"#$ 5/?3-,-#1$ ?+6#1$ '99"& #"'*#;,-%$0#,-2#0$5%

η $≡$ 999999%9 × @AA - 0)

-($(*.

!"#$?+6#1$#,,-)-#2)>$-%$52$-/?+1*52*$?#1,+1/52)#$?515/#*#1$,+1$5/?3-,-#1%$*"5*$"5203#$3518# 5/+&2*%$+,$?+6#17$I&)"$5/?3-,-#1%4$)533#0$?+6#1$5/?3-,-#1%4$51#$&%#04$,+1$#D5/?3#4$5%$+&*9 ?&*$5/?3-,-#1%$+,$%*#1#+$%>%*#/%7 ;2$+10#1$*+$%-/?3-,>$)-1)&-*$0-5815/%4$6#$%"533$50+?*$*"#$)+2E#2*-+2$-33&%*15*#0$-2$K-87 @7@U:'=7 a#1#$*"#$) ?$*#1/-253$-%$%"+62$)+22#)*#0$*+$52$511+6"#50$?+-2*-28$&?6510$520$*"#$) >$*#1/-253 *+$52$511+6"#50$?+-2*-28$0+6265107$!"#$)+11#%?+20-28$E+3*58#$-%$-20-)5*#0$2#D*$*+$#5)"$511+69 "#507$O+*#$*"5*$-2$/52>$)5%#%$6#$6-33$2+*$#D?3-)-*3>$%"+6$*"#$)+22#)*-+2%$+,$*"#$5/?3-,-#1$*+$*"# 0)$?+6#1$%+&1)#%7$K-2533>4$6#$2+*#$*"5*$%+/#$5/?3-,-#1%$1#G&-1#$+23>$+2#$?+6#1$%&??3>7 ICC

VCC ICC VCC IEE

IEE

(a)

VEE

VEE

(b)

Figure 1.13 L2$5/?3-,-#1$*"5*$1#G&-1#%$*6+$0)$%&??3-#%$:%"+62$5%$'5**#1-#%=$,+1$+?#15*-+27

Example 1.2 <+2%-0#1$52$5/?3-,-#1$+?#15*-28$,1+/$±@A9Y$?+6#1$%&??3-#%7$;*$-%$,#0$6-*"$5$%-2&%+-053$E+3*58#$"5E-28$@$Y ?#5.$520$0#3-E#1%$5$%-2&%+-053$E+3*58#$+&*?&*$+,$\$Y$?#5.$*+$5$@9.Ω$3+507$!"#$5/?3-,-#1$0156%$5$)&11#2*$+, \7]$/L$,1+/$#5)"$+,$-*%$*6+$?+6#1$%&??3-#%7$!"#$-2?&*$)&11#2*$+,$*"#$5/?3-,-#1$-%$,+&20$*+$'#$%-2&%+-053 6-*"$A7@$/L$?#5.7$K-20$*"#$E+3*58#$85-24$*"#$)&11#2*$85-24$*"#$?+6#1$85-24$*"#$?+6#1$01562$,1+/$*"#$0) %&??3-#%4$*"#$?+6#1$0-%%-?5*#0$-2$*"#$5/?3-,-#14$520$*"# 5/?3-,-#1$#,,-)-#2)>7

Solution

\ 8v = 999 = \$Y`Y @

1.4 Amplifiers 19

+1 8 v = BA$3+8$\ = @\7@$0i

+1

\$Y 9k& = 999999999999 = \$/L @$.Ω 9k \ 8 $ = 999&9 = 9999999 = \A$L`L A7@ 9k$ 8 $ = BA$3+8$\A = U\7@$0i \ \ - % = ) &1/% 9 & 1/% = 9999999 9999999 = ^A7]$/F B B @ A7@ - 9 = ) $1/% 9 $1/% = 9999999 9999999 = A7A]$/F B B -% ^A7] 8 ; = 999999 = 9999999999 = Z@A$F`F -9 A7A]

+1 8 ; = @A$3+8$Z@A = B\7@$0i - 0) = @A × \7] + @A × \7] = @\A$/F - 0-%%-?5*#0 = - 0) + - 9 4 - % = @\A + A7A] 4 ^A7] = @^\7b$/F η = 999999%9 × @AA = B@7U[ - 0)

K1+/$ *"#$ 5'+E#$ #D5/?3#$ 6#$ +'%#1E#$ *"5*$ *"#$ 5/?3-,-#1$ )+2E#1*%$ %+/#$ +,$ *"#$ 0)$ ?+6#1$ -* 0156%$,1+/$*"#$?+6#1$%&??3-#%$*+$%-8253$?+6#1$*"5*$-*$0#3-E#1%$*+$*"#$3+507

1.4.7 Amplifier Saturation l15)*-)533>$ %?#5.-284$ *"#$ 5/?3-,-#1$ *152%,#1$ )"515)*#1-%*-)$ 1#/5-2%$ 3-2#51$ +E#1$ +23>$ 5$ 3-/-*#0 1528#$+,$-2?&*$520$+&*?&*$E+3*58#%7$K+1$52$5/?3-,-#1$+?#15*#0$,1+/$*6+$?+6#1$%&??3-#%$*"#$+&*9 ?&*$E+3*58#$)522+*$#D)##0$5$%?#)-,-#0$?+%-*-E#$3-/-*$520$)522+*$0#)1#5%#$'#3+6$5$%?#)-,-#0$2#89 5*-E#$ 3-/-*7$ !"#$ 1#%&3*-28$ *152%,#1$ )"515)*#1-%*-)$ -%$ %"+62$ -2$ K-87$ @7@^4$ 6-*"$ *"#$ ?+%-*-E#$ 520 2#85*-E#$%5*&15*-+2$3#E#3%$0#2+*#0$%f$520$%h 4$1#%?#)*-E#3>7$J5)"$+,$*"#$*6+$%5*&15*-+2$3#E#3%$-% &%&533>$6-*"-2$5$,15)*-+2$+,$5$E+3*$+,$*"#$E+3*58#$+,$*"#$)+11#%?+20-28$?+6#1$%&??3>7 C'E-+&%3>4$-2$+10#1$*+$5E+-0$0-%*+1*-28$*"#$+&*?&*$%-8253$65E#,+1/4$*"#$-2?&*$%-8253$%6-28 /&%*$'#$.#?*$6-*"-2$*"#$3-2#51$1528#$+,$+?#15*-+24

% % 9999−9 $ ≤ $v 9$ ≤ $ 9999+9 8v 8v ;2$K-87$@7@^4$6"-)"$%"+6%$*6+$-2?&*$65E#,+1/%$520$*"#$)+11#%?+20-28$+&*?&*$65E#,+1/%4 *"#$?#5.%$+,$*"#$3518#1$65E#,+1/$"5E#$'##2$)3-??#0$+,,$'#)5&%#$+,$5/?3-,-#1$%5*&15*-+27

20 Chapter 1 Signals and Amplifiers

Figure 1.14 L2$5/?3-,-#1$*152%,#1$)"515)*#1-%*-)$*"5*$-%$3-2#51$#D)#?*$,+1$+&*?&*$%5*&15*-+27

1.4.8 Symbol Convention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

-($((.

6"#1#$*"#$%-8253$)&11#2*$-%$8-E#2$'> $ ' ( " ) " 9 ' %-2 ω"

!"&%4$6#$%*5*#$%+/#$)+2E#2*-+2%H$!+*53$-2%*52*52#+&%$G&52*-*-#%$51#$0#2+*#0$'>$5$3+6#1)5%# %>/'+3$6-*"$&??#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#4$$< :"=4$v1@ :"=7$Q-1#)*9)&11#2*$:0)=$G&52*-*-#%$51# 0#2+*#0$'>$52$&??#1)5%#$%>/'+3$6-*"$&??#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#$9< 4$V1@ 7$;2)1#/#2*53

1.5 Circuit Models for Amplifiers 21

iC

ic

Ic

iC IC

0

t

Figure 1.15 I>/'+3$)+2E#2*-+2$#/?3+>#0$*"1+&8"+&*$*"#$'++.7

%-8253$G&52*-*-#%$51#$0#2+*#0$'>$5$3+6#1)5%#$%>/'+3$6-*"$3+6#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#4 $':"=4$vA!:"=7$;,$*"#$%-8253$-%$5$%-2#$65E#4$*"#2$-*%$5/?3-*&0#$-%$0#2+*#0$'>$52$&??#1)5%#$%>/'+3 6-*"$3+6#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#$9' 4$)A!7$K-2533>4$53*"+&8"$2+*$%"+62$-2$K-87$@7@]4$0) ?+6#1$%&??3-#%$51#$0#2+*#0$'>$52$&??#1)5%#$3#**#1$6-*"$5$0+&'3#93#**#1$&??#1)5%#$%&'%)1-?*4$,+1 #D5/?3#4$)<< 4$)117$L$%-/-351$2+*5*-+2$-%$&%#0$,+1$*"#$0)$)&11#2*$01562$,1+/$*"#$?+6#1$%&??3>4 ,+1$#D5/?3#4$9<< 4$9117$

EXERCISES 1.10 L2$5/?3-,-#1$"5%$5$E+3*58#$85-2$+,$@AA$Y`Y$520$5$)&11#2*$85-2$+,$@AAA$L`L7$JD?1#%%$*"#$E+3*58#$520 )&11#2*$85-2%$-2$0#)-'#3%$520$,-20$*"#$?+6#1$85-27 Ans. ^A$0iM$bA$0iM$]A$0i 1.11 L2$5/?3-,-#1$+?#15*-28$,1+/$5$%-283#$@]9Y$%&??3>$?1+E-0#%$5$@B9Y$?#5.9*+9?#5.$%-2#965E#$%-8253 *+$5$@9.Ω$3+50$520$0156%$2#83-8-'3#$-2?&*$)&11#2*$,1+/$*"#$%-8253$%+&1)#7$!"#$0)$)&11#2*$01562$,1+/$*"# @]9Y$%&??3>$-%$Z$/L7$F"5*$-%$*"#$?+6#1$0-%%-?5*#0$-2$*"#$5/?3-,-#14$520$6"5*$-%$*"#$5/?3-,-#1$#,,-)-#2)>X Ans. @AB$/FM$@][

1.5 Circuit Models for Amplifiers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

22 Chapter 1 Signals and Amplifiers

1.5.1 Voltage Amplifiers K-8&1#$@7@b:5=$%"+6%$5$)-1)&-*$/+0#3$,+1$*"#$E+3*58#$5/?3-,-#17$!"#$/+0#3$)+2%-%*%$+,$5$E+3*9 58#9)+2*1+33#0$E+3*58#$%+&1)#$"5E-28$5$85-2$,5)*+1$ 8 v&4$52$-2?&*$1#%-%*52)#$#$$*"5*$5))+&2*% ,+1$*"#$,5)*$*"5*$*"#$5/?3-,-#1$0156%$52$-2?&*$)&11#2*$,1+/$*"#$%-8253$%+&1)#4$520$52$+&*?&* 1#%-%*52)#$#&$*"5*$5))+&2*%$,+1$*"#$)"528#$-2$+&*?&*$E+3*58#$5%$*"#$5/?3-,-#1$-%$)533#0$&?+2$*+ %&??3>$+&*?&*$)&11#2*$*+$5$3+507$!+$'#$%?#)-,-)4$6#$%"+6$-2$K-87$@7@b:'=$*"#$5/?3-,-#1$/+0#3 ,#0$6-*"$5$%-8253$E+3*58#$%+&1)#$v!$"5E-28$5$1#%-%*52)#$#!$520$)+22#)*#0$5*$*"#$+&*?&*$*+$5 3+50$ 1#%-%*52)#$ #%7$ !"#$ 2+2T#1+$ +&*?&*$ 1#%-%*52)#$ #&$ )5&%#%$ +23>$ 5$ ,15)*-+2$ +,$ 8 v& v $ $ *+ 5??#51$5)1+%%$*"#$+&*?&*7$d%-28$*"#$E+3*58#90-E-0#1$1&3#$6#$+'*5-2

#% #% + #&

v & = 8 v& v $ 999999999999999999 !"&%$*"#$E+3*58#$85-2$-%$8-E#2$'> v #% 9 8 v ≡ 9999& = 8 v& 99999999999999999 v$ #% + #&

-($(+.

;*$,+33+6%$*"5*$-2$+10#1$2+*$*+$3+%#$85-2$-2$)+&?3-28$*"#$5/?3-,-#1$+&*?&*$*+$5$3+504$*"#$+&*9 ?&*$1#%-%*52)#$#&$%"+&30$'#$/&)"$%/533#1$*"52$*"#$3+50$1#%-%*52)#$#%7$;2$+*"#1$6+10%4$,+1 5$8-E#2$#%$+2#$/&%*$0#%-82$*"#$5/?3-,-#1$%+$*"5*$-*%$#&$-%$/&)"$%/533#1$*"52$#%7$K&1*"#19 /+1#4$*"#1#$51#$5??3-)5*-+2%$-2$6"-)"$#%$-%$.2+62$*+$E51>$+E#1$5$)#1*5-2$1528#7$;2$+10#1$*+ .##?$*"#$+&*?&*$E+3*58#$v&$5%$)+2%*52*$5%$?+%%-'3#4$*"#$5/?3-,-#1$-%$0#%-82#0$6-*"$#&$/&)" %/533#1$*"52$*"#$3+6#%*$E53&#$+,$#%7$L2$-0#53$E+3*58#$5/?3-,-#1$-%$+2#$6-*"$#&$=$A7$JG&59 *-+2$:@7@B=$-20-)5*#%$53%+$*"5*$,+1$#%$=$∞4$ 8 v = 8 v&7$!"&%$ 8 v& $-%$*"#$E+3*58#$85-2$+,$*"# &23+50#0$5/?3-,-#14$+1$*"#$%/'*&#"$#0"),B%()32',23"*7$;*$%"+&30$53%+$'#$)3#51$*"5*$-2$%?#)9 -,>-28$*"#$E+3*58#$85-2$+,$52$5/?3-,-#14$+2#$/&%*$53%+$%?#)-,>$*"#$E53&#$+,$3+50$1#%-%*52)#

1 vo 2

(a) ii

io " vo

vs

!

(b) Figure 1.16 437$<-1)&-*$/+0#3$,+1$*"#$E+3*58#$5/?3-,-#17$487$!"#$E+3*58#$5/?3-,-#1$6-*"$-2?&*$%-8253$%+&1)# 520$3+507

1.5 Circuit Models for Amplifiers 23

5*$6"-)"$*"-%$85-2$-%$/#5%&1#0$+1$)53)&35*#07$;,$5$3+50$1#%-%*52)#$-%$2+*$%?#)-,-#04$-*$-%$2+19 /533>$5%%&/#0$*"5*$*"#$8-E#2$E+3*58#$85-2$-%$*"#$+?#29)-1)&-*$85-2$ 8 v& 7 !"#$,-2-*#$-2?&*$1#%-%*52)#$#$$-2*1+0&)#%$52+*"#1$E+3*58#90-E-0#1$5)*-+2$5*$*"#$-2?&*4$6-*" *"#$1#%&3*$*"5*$+23>$5$,15)*-+2$+,$*"#$%+&1)#$%-8253$v!$5)*&533>$1#5)"#%$*"#$-2?&*$*#1/-253%$+,$*"# 5/?3-,-#1M$*"5*$-%4

#$ #$ + #!

v $ = v ! 9999999999999999

-($(/.

;*$,+33+6%$*"5*$-2$+10#1$2+*$*+$3+%#$5$%-82-,-)52*$?+1*-+2$+,$*"#$-2?&*$%-8253$-2$)+&?3-28$*"# %-8253$%+&1)#$*+$*"#$5/?3-,-#1$-2?&*4$*"#$5/?3-,-#1$/&%*$'#$0#%-82#0$*+$"5E#$52$-2?&*$1#%-%9 m *52)#$#$$/&)"$81#5*#1$*"52$*"#$1#%-%*52)#$+,$*"#$%-8253$%+&1)#4$ # $ $ # !7$K&1*"#1/+1#4$*"#1# 51#$ 5??3-)5*-+2%$ -2$ 6"-)"$*"#$%+&1)#$1#%-%*52)#$-%$.2+62$ *+$ E51>$+E#1$5$ )#1*5-2$1528#7$!+ /-2-/-T#$*"#$#,,#)*$+,$*"-%$E51-5*-+2$+2$*"#$E53&#$+,$*"#$%-8253$*"5*$5??#51%$5*$*"#$-2?&*$+,$*"# 5/?3-,-#14$*"#$0#%-82$#2%&1#%$*"5*$#$$-%$/&)"$81#5*#1$*"52$*"#$3518#%*$E53&#$+,$#!7$L2$-0#53 E+3*58#$5/?3-,-#1$-%$+2#$6-*"$#$$=$∞7$;2$*"-%$-0#53$)5%#$'+*"$*"#$)&11#2*$85-2$520$?+6#1$85-2 '#)+/#$-2,-2-*#7 !"#$+E#1533$E+3*58#$85-2$:v& /v!=$)52$'#$,+&20$'>$)+/'-2-28$JG%7$:@7@B=$520$:@7@U=4

#$ #% v& 9 99999999999999999 9 9999 " 8 v& 999999999999999 # + # # v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

EXERCISES 1.12 L$*152%0&)#1$)"515)*#1-T#0$'>$5$E+3*58#$+,$@$Y$1/%$520$5$1#%-%*52)#$+,$@$_Ω$-%$5E5-35'3#$*+$01-E# 5$@A9Ω$3+507$;,$)+22#)*#0$0-1#)*3>4$6"5*$E+3*58#$520$?+6#1$3#E#3%$1#%&3*$5*$*"#$3+50X$;,$5$&2-*>985-2$:-7#74 8 v& " @=$'&,,#1$5/?3-,-#1$6-*"$@9_Ω$-2?&*$1#%-%*52)#$520$@A9Ω$+&*?&*$1#%-%*52)#$-%$-2*#1?+%#0$'#*6##2 %+&1)#$520$3+504$6"5*$0+$*"#$+&*?&*$E+3*58#$520$?+6#1$3#E#3%$'#)+/#X$K+1$*"#$2#6 511528#/#2*4$,-20 *"#$E+3*58#$85-2$,1+/$%+&1)#$*+$3+504$520$*"#$?+6#1$85-2$:'+*"$#D?1#%%#0$-2$0#)-'#3%=7 Ans. @A$µY$1/%M$@A−@@$FM$A7B]$YM$b7B]$/FM$−@B$0iM$^^$0i 1.13 !"#$+&*?&*$E+3*58#$+,$5$E+3*58#$5/?3-,-#1$"5%$'##2$,+&20$*+$0#)1#5%#$'>$BA[$6"#2$5$3+50$1#%-%*52)# +,$@$.Ω$-%$)+22#)*#07$F"5*$-%$*"#$E53&#$+,$*"#$5/?3-,-#1$+&*?&*$1#%-%*52)#X Ans. B]A$Ω 1.14 L2$5/?3-,-#1$6-*"$5$E+3*58#$85-2$+,$+^A$0i4$52$-2?&*$1#%-%*52)#$+,$@A$.Ω4$520$52$+&*?&*$1#%-%*52)# +, @ .Ω$-%$&%#0$*+$01-E#$5$@9.Ω$3+507$F"5*$-%$*"#$E53&#$+,$ 8 v& X$K-20$*"#$E53&#$+,$*"#$?+6#1$85-2$-2 0#)-'#3%7 Ans. @AA$Y`YM$^^$0i$

24 Chapter 1 Signals and Amplifiers

1.5.2 Cascaded Amplifiers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

Example 1.3 K-8&1#$@7@c$0#?-)*%$52$5/?3-,-#1$)+/?+%#0$+,$5$)5%)50#$+,$*"1##$%*58#%7$!"#$5/?3-,-#1$-%$,#0$'>$5$%-8253 %+&1)#$6-*"$5$%+&1)#$1#%-%*52)#$+,$@AA$.Ω$520$0#3-E#1%$-*%$+&*?&*$-2*+$5$3+50$1#%-%*52)#$+,$@AA$Ω7$!"#$,-1%* %*58#$"5%$5$1#35*-E#3>$"-8"$-2?&*$1#%-%*52)#$520$5$/+0#%*$85-2$,5)*+1$+,$@A7$!"#$%#)+20$%*58#$"5%$5$"-8"#1$85-2 ,5)*+1$'&*$3+6#1$-2?&*$1#%-%*52)#7$K-2533>4$*"#$35%*4$+1$+&*?&*4$%*58#$"5%$&2-*>$85-2$'&*$5$3+6$+&*?&*$1#%-%*52)#7 F#$6-%"$*+$#E53&5*#$*"#$+E#1533$E+3*58#$85-24$*"5*$-%4$v%/v!4$*"#$)&11#2*$85-24$520$*"#$?+6#1$85-27

Figure 1.17 !"1##9%*58#$5/?3-,-#1$,+1$JD5/?3#$@7U7

Solution !"#$,15)*-+2$+,$%+&1)#$%-8253$5??#51-28$5*$*"#$-2?&*$*#1/-253%$+,$*"#$5/?3-,-#1$-%$+'*5-2#0$&%-28$*"#$E+3*9 58#90-E-0#1$1&3#$5*$*"#$-2?&*4$5%$,+33+6%H

v $@ @$_Ω 999999 = 999999999999999999999999999999999999999 9 = A7\A\$Y`Y @$_Ω + @AA$.Ω v! !"#$E+3*58#$85-2$+,$*"#$,-1%*$%*58#$-%$+'*5-2#0$'>$)+2%-0#1-28$*"#$-2?&*$1#%-%*52)#$+,$*"#$%#)+20$%*58#$*+$'# *"#$3+50$+,$*"#$,-1%*$%*58#M$*"5*$-%4

v @AA$.Ω 8 v@ ≡ 99999$B9 = @A 9999999999999999999999999999999999999 = \7\$Y`Y @AA$.Ω + @$.Ω v $@ I-/-3513>4$*"#$E+3*58#$85-2$+,$*"#$%#)+20$%*58#$-%$+'*5-2#0$'>$)+2%-0#1-28$*"#$-2?&*$1#%-%*52)#$+,$*"#$*"-10 %*58#$*+$'#$*"#$3+50$+,$*"#$%#)+20$%*58#4

v @A$.Ω 8 vB ≡ 99999$U9 = @AA 9999999999999999999999999999999999 = \A7\$Y`Y @A$.Ω + @$.Ω v $B

1.5 Circuit Models for Amplifiers

K-2533>4$*"#$E+3*58#$85-2$+,$*"#$+&*?&*$%*58#$-%$5%$,+33+6%H

v @AA$Ω 8 vU ≡ 99999%9 = @ 9999999999999999999999999999999999 = A7\A\$Y`Y @AA$Ω + @A$Ω v $U !"#$*+*53$85-2$+,$*"#$*"1##$%*58#%$-2$)5%)50#$)52$'#$2+6$,+&20$,1+/

v v $@

8 v ≡ 99999%9 = 8 v@ 8 vB 8 vU = Z@Z$Y`Y +1$]Z7U$0i7 !+$,-20$*"#$E+3*58#$85-2$,1+/$%+&1)#$*+$3+504$6#$/&3*-?3>$8v$'>$*"#$,5)*+1$1#?1#%#2*-28$*"#$3+%%$+,$85-2$5* *"#$-2?&*M$*"5*$-%4

v% v v v 99999 = 99999%9 99999$@9 = 8 v 99999$@9 v! v $@ v ! v! = Z@Z × A7\A\ = c^U7b$Y`Y +1$]c7^$0i7 !"#$)&11#2*$85-2$-%$,+&20$5%$,+33+6%H $ v % / @AA$Ω 9 8 $ ≡ 999& = 9999999999999999999999999 v $@ ⁄ @$_Ω $$ ^ b = @A × 8 v = Z7@Z × @A $L`L +1$@UZ7U$0i7 !"#$?+6#1$85-2$-%$,+&20$,1+/ 8 ; ≡ 99999%9 = -9 =

v% $& 999999999 9 v $@ $ $ b Z 8 v 8 $ = Z@Z × Z7@Z × @A = bb7\ × @A $F`F

+1$\Z7U$0i7$O+*#$*"5* 8 ; ( 0i ) = @99B9 [ 8 v ( 0i ) + 8 $ ( 0i ) ]

L$,#6$)+//#2*%$+2$*"#$)5%)50#$5/?3-,-#1$-2$*"#$5'+E#$#D5/?3#$51#$-2$+10#17$!+$5E+-0$3+%-28 %-8253$ %*1#28*"$ 5*$ *"#$ 5/?3-,-#1$ -2?&*$ 6"#1#$ *"#$ %-8253$ -%$ &%&533>$ E#1>$ %/5334$ *"#$ ,-1%*$ %*58#$ -% 0#%-82#0$*+$"5E#$5$1#35*-E#3>$3518#$-2?&*$1#%-%*52)#$:@$_Ω=4$6"-)"$-%$/&)"$3518#1$*"52$*"#$%+&1)# 1#%-%*52)#7$!"#$*150#9+,,$5??#51%$*+$'#$5$/+0#15*#$E+3*58#$85-2$:@A$Y`Y=7$!"#$%#)+20$%*58#$0+#% 2+*$ 2##0$ *+$ "5E#$ %&)"$ 5$ "-8"$ -2?&*$ 1#%-%*52)#M$ 15*"#14$ "#1#$ 6#$ 2##0$ *+$ 1#53-T#$ *"#$ '&3.$ +,$ *"# 1#G&-1#0$E+3*58#$85-27$!"#$*"-10$520$,-2534$+1$+&*?&*4$%*58#$-%$2+*$5%.#0$*+$?1+E-0#$52>$E+3*58#$85-2M 15*"#14$-*$,&2)*-+2%$5%$5$'&,,#1$5/?3-,-#14$?1+E-0-28$5$1#35*-E#3>$3518#$-2?&*$1#%-%*52)#$520$5$3+6$+&*9 ?&*$1#%-%*52)#4$/&)"$3+6#1$*"52$#%7$;*$-%$*"-%$%*58#$*"5*$#25'3#%$)+22#)*-28$*"#$5/?3-,-#1$*+$*"#$@A9 Ω$3+507$!"#%#$?+-2*%$)52$'#$/50#$/+1#$)+2)1#*#$'>$%+3E-28$*"#$,+33+6-28$#D#1)-%#%7$;2$%+$0+-284 +'%#1E#$*"5*$-2$,-20-28$*"#$85-2$+,$52$5/?3-,-#1$%*58#$-2$5$)5%)50#$5/?3-,-#14$*"#$3+50-28$#,,#)*$+, *"#$%&))##0-28$5/?3-,-#1$%*58#$/&%*$'#$*5.#2$-2*+$5))+&2*$5%$6#$"5E#$0+2#$-2$*"#$5'+E#$#D5/?3#7

25

26 Chapter 1 Signals and Amplifiers

EXERCISES 1.15 F"5*$6+&30$*"#$+E#1533$E+3*58#$85-2$+,$*"#$)5%)50#$5/?3-,-#1$-2$JD5/?3#$@7U$'#$6-*"+&*$%*58#$UX Ans. Z@7Z$Y`Y 1.16 K+1$*"#$)5%)50#$5/?3-,-#1$+,$JD5/?3#$@7U4$3#*$v!$'#$@$/Y7$K-20$v$@4$v$B4$v$U4$520$v%7 Ans. A7\@$/YM$\$/YM$Z@Z$/YM$c^^$/Y 1.17 :5=$_+0#3$*"#$*"1##9%*58#$5/?3-,-#1$+,$JD5/?3#$@7U$:6-*"+&*$*"#$%+&1)#$520$3+50=4$&%-28$*"#$E+3*58# 5/?3-,-#1$/+0#37$F"5*$51#$*"#$E53&#%$+,$#$4$8v &4$520$#&X :'=$;,$#%$E51-#%$-2$*"#$1528#$@A$Ω$*+$@AAA$Ω4$,-20$*"#$)+11#%?+20-28$1528#$+,$*"#$+E#1533$E+3*58#$85-24$ v& `v!7 Ans. @$_Ω4$\AA$Y`Y4$@A$ΩM$^A\$Y`Y$*+$Z@A$Y`Y

1.5.3 Other Amplifier Types ;2$*"#$0#%-82$+,$52$#3#)*1+2-)$%>%*#/4$*"#$%-8253$+,$-2*#1#%*e6"#*"#1$5*$*"#$%>%*#/$-2?&*4$5*$52 -2*#1/#0-5*#$%*58#4$+1$5*$*"#$+&*?&*e)52$'#$#-*"#1$5$E+3*58#$+1$5$)&11#2*7$K+1$-2%*52)#4$%+/#$*152%9 0&)#1%$ "5E#$ E#1>$ "-8"$ +&*?&*$ 1#%-%*52)#%$ 520$ )52$ '#$ /+1#$ 5??1+?1-5*#3>$ /+0#3#0$ 5%$ )&11#2* %+&1)#%7$I-/-3513>4$*"#1#$51#$5??3-)5*-+2%$-2$6"-)"$*"#$+&*?&*$)&11#2*$15*"#1$*"52$*"#$E+3*58#$-%$+, Table 1.1 The Four Amplifier Types $$$$$$$$$$$$$!>?#

$$$$$$$$$$$$$$$$$$$$<-1)&-*$_+0#3

$$Y+3*58#$L/?3-,-#1

Ri

" !

" vo !

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ii

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$$!152%)+20&)*52)#$ $$L/?3-,-#1 Gmvi

Ri

ii

Ro Ri

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" vo !

Ro

( Y`Y ) $ & =A

$ 8 $! ≡ 999& $$

( L`L ) v & =A

I"+1*9<-1)&-* !152%)+20&)*52)#

io " vi !

v v$

& $$$ 8 v& ≡ 99999

I"+1*9<-1)&-*$<&11#2*$j5-2

io

Ri

$$!152%1#%-%*52)# $$L/?3-,-#1

C?#29<-1)&-*$Y+3*58#$j5-2

io

Ro " vi !

$$<&11#2*$L/?3-,-#1

$$$$$$$$j5-2$l515/#*#1

$ B C ≡ 999&9

v$

( L`Y )

v

" vo !

# C ≡ 9999&9 $$

#$$=$∞$ #& =$A

#$$=$A$ #& =$∞

#$ =$∞ #& =$∞

v & =A

C?#29<-1)&-*$!152%1#%-%*52)#

io

;0#53$$<"515)*#1-%*-)%

( Y`L ) $ & =A

#$$=$A #& =$A

1.5 Circuit Models for Amplifiers

-2*#1#%*7$!"&%4$53*"+&8"$-*$-%$*"#$/+%*$?+?&3514$*"#$E+3*58#$5/?3-,-#1$)+2%-0#1#0$5'+E#$-%$(&%*$+2#$+, ,+&1$?+%%-'3#$5/?3-,-#1$*>?#%7$!"#$+*"#1$*"1##$51#$*"#$)&11#2*$5/?3-,-#14$*"#$*152%)+20&)*52)#$5/?3-9 ,-#14$520$*"#$*152%1#%-%*52)#$5/?3-,-#17$!5'3#$@7@$%"+6%$*"#$,+&1$5/?3-,-#1$*>?#%4$*"#-1$)-1)&-*$/+09 #3%4$*"#$0#,-2-*-+2$+,$*"#-1$85-2$?515/#*#1%4$520$*"#$-0#53$E53&#%$+,$*"#-1$-2?&*$520$+&*?&*$1#%-%*52)#%7

1.5.4 Relationships between the Four Amplifier Models L3*"+&8"$,+1$5$8-E#2$5/?3-,-#1$5$?51*-)&351$+2#$+,$*"#$,+&1$/+0#3%$-2$!5'3#$@7@$-%$/+%*$?1#,9 #15'3#4$(4D+&*+"E6+*&37+'(4+06+3!6.+"&+C&.6F+(4D+(C;F$*$67G$;2$,5)*4$%-/?3#$1#35*-+2%"-?%$)52 '#$0#1-E#0$*+$1#35*#$*"#$?515/#*#1%$+,$*"#$E51-+&%$/+0#3%7$K+1$-2%*52)#4$*"#$+?#29)-1)&-*$E+3*9 58#$85-2$8v &$)52$'#$1#35*#0$*+$*"#$%"+1*9)-1)&-*$)&11#2*$85-2$8$!$5%$,+33+6%H$!"#$+?#29)-1)&-* +&*?&*$E+3*58#$8-E#2$'>$*"#$E+3*58#$5/?3-,-#1$/+0#3$+,$!5'3#$@7@$-%$8v &v$7$!"#$)&11#2*$5/?3-9 ,-#1$/+0#3$-2$*"#$%5/#$*5'3#$8-E#%$52$+?#29)-1)&-*$+&*?&*$E+3*58#$+,$8$!$$ #&7$JG&5*-28$*"#%# *6+$E53&#%$520$2+*-28$*"5*$$$$=$v$ /#$$8-E#%

# 8 v& = 8 $! 99999& #$ I-/-3513>4$6#$)52$%"+6$*"5*

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-($(0.

8 v& = B C # &

-($().

# 8 v& = 99999C9 #$

-($(1.

520

!"#$#D?1#%%-+2%$-2$JG%7$:@7@^=$*+$:@7@b=$)52$'#$&%#0$*+$1#35*#$52>$*6+$+,$*"#$85-2$?515/#*#1% 8v&4$8$!4$BC4$520$#C7

1.5.5 Determining Ri and Ro K1+/$*"#$5/?3-,-#1$)-1)&-*$/+0#3%$8-E#2$-2$!5'3#$@7@4$6#$+'%#1E#$*"5*$*"#$-2?&*$1#%-%*52)#$#$$+, *"#$5/?3-,-#1$)52$'#$0#*#1/-2#0$'>$5??3>-28$52$-2?&*$E+3*58#$v$$520$/#5%&1-28$:+1$)53)&35*-28= *"#$-2?&*$)&11#2*$$$M$*"5*$-%4$#$+=+v$ /$$7$!"#$+&*?&*$1#%-%*52)#$-%$,+&20$5%$*"#$15*-+$+,$*"#$+?#29 )-1)&-*$+&*?&*$ E+3*58#$ *+$*"#$%"+1*9)-1)&-*$+&*?&*$)&11#2*7$ L3*#125*-E#3>4$*"#$+&*?&*$1#%-%*52)# )52$'#$,+&20$'>$#3-/-25*-28$*"#$-2?&*$%-8253$%+&1)#$:*"#2$$$$520$v$$6-33$'+*"$'#$T#1+=$520$5??3>9 -28$5$E+3*58#$%-8253$vH$*+$*"#$+&*?&*$+,$*"#$5/?3-,-#14$5%$%"+62$-2$K-87$@7@Z7$;,$6#$0#2+*#$*"# )&11#2*$01562$,1+/$vH$$4"&$*"#$+&*?&*$*#1/-253%$5%$$H$:2+*#$*"5*$$H$-%$+??+%-*#$-2$0-1#)*-+2$*+$$&=4 *"#2$ #&+ =+ vH /$H7$ L3*"+&8"$ *"#%#$ *#)"2-G&#%$ 51#$ )+2)#?*&533>$ )+11#)*4$ -2$ 5)*&53$ ?15)*-)#$ /+1# 1#,-2#0$/#*"+0%$51#$#/?3+>#0$-2$/#5%&1-28$#$$520$#&7 ix

" !

Ro "

vx ix

vx

Figure 1.18 Q#*#1/-2-28$*"#$+&*?&*$1#%-%*52)#7

27

28 Chapter 1 Signals and Amplifiers

1.5.6 Unilateral Models !"#$5/?3-,-#1$/+0#3%$)+2%-0#1#0$5'+E#$51#$0*"(3)'$3(M,*"5*$-%4$%-8253$,3+6$-%$&2-0-1#)*-+2534 ,1+/$-2?&*$*+$+&*?&*7$_+%*$1#53$5/?3-,-#1%$%"+6$%+/#$1#E#1%#$*152%/-%%-+24$6"-)"$-%$&%&533> &20#%-15'3#$'&*$/&%*$2+2#*"#3#%%$'#$/+0#3#07$F#$%"533$2+*$?&1%&#$*"-%$?+-2*$,&1*"#1$5*$*"-% *-/#$#D)#?*$*+$/#2*-+2$*"5*$/+1#$)+/?3#*#$/+0#3%$,+1$3-2#51$*6+9?+1*$2#*6+1.%$51#$8-E#2$-2 L??#20-D$<7$L3%+4$-2$35*#1$)"5?*#1%4$6#$6-33$,-20$-*$2#)#%%51>$-2$)#1*5-2$)5%#%$*+$5&8/#2*$*"# /+0#3%$+,$!5'3#$@7@$*+$*5.#$-2*+$5))+&2*$*"#$2+2&2-35*#153$25*&1#$+,$%+/#$*152%-%*+1$5/?3-,-#1%7

Example 1.4 !"#$8"/%(3$,H0*#)"%*,)$3*+"+)%$,4AIJ74$6"-)"$6-33$'#$%*&0-#0$-2$<"5?*#1$b4$-%$5$*"1##9*#1/-253$0#E-)# *"5*$6"#2$?+6#1#09&?$'>$5$0)$%+&1)#$:'5**#1>=$520$+?#15*#0$6-*"$%/533$%-8253%$)52$'#$/+0#3#0$'>$*"#$3-29 #51$)-1)&-*$%"+62$-2$K-87$@7@\:5=7$!"#$*"1##$*#1/-253%$51#$*"#$83+',4A74$*"#$'!"))'$,4K74$520$*"#$#%(('#)%$ 4677$!"#$"#51*$+,$*"#$/+0#3$-%$5$*152%)+20&)*52)#$5/?3-,-#1$1#?1#%#2*#0$'>$52$-2?&*$1#%-%*52)#$'#*6##2$i 520$J$:0#2+*#0$7π =4$5$%"+1*9)-1)&-*$*152%)+20&)*52)#$AC4$520$52$+&*?&*$1#%-%*52)#$7&7 B

Rs

C " vbe

rp

ro

gmvbe

!

B

C 1 vbe

vs 1 2

rp

gmvbe

2

E

ro

RL

E (a)

(b) B ib 1 vbe

C

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2 E (c)

Figure 1.19 437$ I/5339%-8253$ )-1)&-*$ /+0#3$ ,+1$ 5$'-?+351$ (&2)*-+2$ *152%-%*+1$ :in!=7$ 487, !"#$ in!$ )+22#)*#0$5%$52 5/?3-,-#1$6-*"$*"#$#/-**#1$5%$5$)+//+2$*#1/-253$'#*6##2$-2?&*$520$+&*?&*$:)533#0$5$)+//+29#/-**#1$5/?3-,-#1=7$ 4#7$L2$53*#125*-E#$%/5339%-8253$)-1)&-*$/+0#3$,+1$*"#$in!7

:5= F-*"$*"#$#/-**#1$&%#0$5%$5$)+//+2$*#1/-253$'#*6##2$-2?&*$520$+&*?&*4$K-87$@7@\:'=$%"+6%$5$*1529 %-%*+1$5/?3-,-#1$.2+62$5%$5$#%!!%*&'!"))'$$+1$2$%0*1'1&'!"))'$$)-1)&-*7$Q#1-E#$52$#D?1#%%-+2$,+1$*"# E+3*58#$85-2$ v& /v!4$520$#E53&5*#$-*%$/582-*&0#$,+1$*"#$)5%#$#!$=$]$.Ω4$7π$=$B7]$.Ω4$AC$= ^A$/L`Y4 7& = @AA$.Ω,$520$#%$= ]$.Ω7$F"5*$6+&30$*"#$85-2$E53&#$'#$-,$*"#$#,,#)*$+,$7&$6#1#$2#83#)*#0X :'= L2$53*#125*-E#$/+0#3$,+1$*"#$*152%-%*+1$-2$6"-)"$5$)&11#2*$5/?3-,-#1$15*"#1$*"52$5$*152%)+20&)*52)#$5/9 ?3-,-#1$-%$&*-3-T#0$-%$%"+62$-2$K-87$@7@\:)=7$F"5*$/&%*$*"#$%"+1*9)-1)&-*$)&11#2*$85-2$β$'#X$j-E#$'+*"$52 #D?1#%%-+2$520$5$E53

1 vo 2

1.5 Circuit Models for Amplifiers 29

Solution :5=$R#,#1$*+$K-87$@7@\:'=7$F#$&%#$*"#$E+3*58#90-E-0#1$1&3#$*+$0#*#1/-2#$*"#$,15)*-+2$+,$-2?&*$%-8253$*"5* 5??#51%$5*$*"#$5/?3-,-#1$-2?&*$5% 7π 9 v 06 = v ! 999999999999999 7π + #!

-($(2.

O#D*$6#$0#*#1/-2#$*"#$+&*?&*$E+3*58#$v&$'>$/&3*-?3>-28$*"#$)&11#2*$:ACv06=$'>$*"#$1#%-%*52)#$:#%$oo$7&=4

v & = 4 A C v 06 ( # % || 7 & )

-($(3.

I&'%*-*&*-28$,+1$v06$,1+/$JG7$:@7@c=$>-#30%$*"#$E+3*58#985-2$#D?1#%%-+2 7π v& 99999 = 4 999999999999999 9 A ( # || 7 ) 7π + #! C % & v!

-($(#.

C'%#1E#$*"5*$*"#$85-2$-%$2#85*-E#4$-20-)5*-28$*"5*$*"-%$5/?3-,-#1$-%$-2E#1*-287$K+1$*"#$8-E#2$)+/?+2#2*$E53&#%4

v& B7] 99999 = 4 9999999999999999 × ^A × ( ] || @AA ) B7] + ] v! = 4 bU7]$Y`Y O#83#)*-28$*"#$#,,#)*$+,$7&4$6#$+'*5-2

v& B7] 99999 ! 4 9999999999999999 × ^A × ] B7] + ] v! = 4 bb7c$Y`Y 6"-)"$-%$G&-*#$)3+%#$*+$*"#$E53&#$+'*5-2#0$-2)3&0-28$7&7$!"-%$-%$2+*$%&1?1-%-284$%-2)#$ 7 & $ # %7 -6.%789%:;<%=8>
β $0+ =+AC v06 i&*$ $ 0 = v 06 ⁄ 7 π M$*"&%4 K+1$*"#$E53&#%$8-E#24

β$ =$AC7π β$ =$^A$/L`Y$×$B7]$.Ω S$@AA$L`L

EXERCISES 1.18 <+2%-0#1$5$)&11#2*$5/?3-,-#1$"5E-28$*"#$/+0#3$%"+62$-2$*"#$%#)+20$1+6$+,$!5'3#$@7@7$p#*$*"#$5/?3-9 ,-#1$'#$,#0$6-*"$5$%-8253$)&11#2*9%+&1)#$$!$"5E-28$5$1#%-%*52)#$#!4$520$3#*$*"#$+&*?&*$'#$)+22#)*#0$*+$5 3+50$1#%-%*52)#$#%7$I"+6$*"5*$*"#$+E#1533$)&11#2*$85-2$-%$8-E#2$'> $& #! #& 999 = 8 $! 9999999999999999 99999999999999999 9 $! #! + #$ #& + #% 1.19 <+2%-0#1$*"#$*152%)+20&)*52)#$5/?3-,-#1$6"+%#$/+0#3$-%$%"+62$-2$*"#$*"-10$1+6$+,$!5'3#$@7@7$p#*$5 E+3*58#$%-8253$%+&1)#$v!$6-*"$5$%+&1)#$1#%-%*52)#$#!$'#$)+22#)*#0$*+$*"#$-2?&*$520$5$3+50$1#%-%*52)#$#% '#$)+22#)*#0$*+$*"#$+&*?&*7$I"+6$*"5*$*"#$+E#1533$E+3*58#985-2$-%$8-E#2$'> #$ v& 99999 = B C 9999999999999999 ( # & || # % ) # v! $ + #!

30 Chapter 1 Signals and Amplifiers 1.20 <+2%-0#1$5$*152%1#%-%*52)#$5/?3-,-#1$"5E-28$*"#$/+0#3$%"+62$-2$*"#$,+&1*"$1+6$+,$!5'3#$@7@7$p#*$*"# 5/?3-,-#1$'#$,#0$6-*"$5$%-8253$)&11#2*9%+&1)#$$!$"5E-28$5$1#%-%*52)#$#!4$520$3#*$*"#$+&*?&*$'#$)+22#)*#0 *+$5$3+50$1#%-%*52)#$#%7$I"+6$*"5*$*"#$+E#1533$85-2$-%$8-E#2$'> #! #% v& 99999 = # C 9999999999999999 9 $ 99999999999999999 $! #! + #$ #% + #& 1.21$ K-20$*"#$-2?&*$1#%-%*52)#$'#*6##2$*#1/-253%$i$520$j$-2$*"#$)-1)&-*$%"+62$-2$K-87$J@7B@7$!"#$E+3*58# vH$-%$5$*#%*$E+3*58#$6-*"$*"#$-2?&*$1#%-%*52)#$#-2$0#,-2#0$5%$#-2 ≡+ vH / $HG ix

Rin

Figure E1.21

Ans. #-2+=+7π+++:β+++@=#6

1.6 Frequency Response of Amplifiers2 K1+/$I#)*-+2$@7B$6#$.2+6$*"5*$*"#$-2?&*$%-8253$*+$52$5/?3-,-#1$)52$5365>%$'#$#D?1#%%#0$5% *"#$%&/$+,$%-2&%+-053$%-8253%7$;*$,+33+6%$*"5*$52$-/?+1*52*$)"515)*#1-T5*-+2$+,$52$5/?3-,-#1$-% -2$*#1/%$+,$-*%$1#%?+2%#$*+$-2?&*$%-2&%+-0%$+,$0-,,#1#2*$,1#G)-#%7$I&)"$5$)"515)*#1-T5*-+2$+, 5/?3-,-#1$?#1,+1/52)#$-%$.2+62$5%$*"#$5/?3-,-#1$,1#G)>$1#%?+2%#7

1.6.1 Measuring the Amplifier Frequency Response F#$%"533$-2*1+0&)#$*"#$%&'(#)*$+,$5/?3-,-#1$,1#G)>$1#%?+2%#$'>$%"+6-28$"+6$-*$)52$'# /#5%&1#07$K-8&1#$@7BA$0#?-)*%$5$3-2#51$E+3*58#$5/?3-,-#1$,#0$5*$-*%$-2?&*$6-*"$5$%-2#965E# %-8253$+,$5/?3-*&0#$)$$520$,1#G)>$ ω7$L%$*"#$,-8&1#$-20-)5*#%4$*"#$%-8253$/#5%&1#0$5*$*"# 5/?3-,-#1$+&*?&*$53%+$-%$%-2&%+-053$6-*"$#D5)*3>$*"#$%5/#$,1#G)>$ ω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ω7$L3%+4$*"#$5283#$ φ$-%$*"#$?"5%#$+,$*"#$5/?3-,-#1$*152%/-%%-+2$5*$*"#$*#%*$,1#G)> ω7$;,$6#$0#2+*#$*"#$3!/("9"'$,)$3*+!"++"%*4$+1$)$3*+9'$,90*#)"%*$5%$-*$-%$/+1#$)+//+23> B

JD)#?*$,+1$-*%$&%#$-2$*"#$%*&0>$+,$*"#$,1#G)>$1#%?+2%#$+,$+?95/?$)-1)&-*%$-2$I#)*-+2%$B7]$520$B7c4$*"#$ /5*#1-53$-2$*"-%$%#)*-+2$6-33$2+*$'#$2##0#0$-2$5$%&'%*52*-53$/522#1$&2*-3$<"5?*#1$\7$

1.6 Frequency Response of Amplifiers 31

Linear amplifier " vi % Vi sin & t

" !

vo % Vo sin (& t " ' ) !

Figure 1.20 _#5%&1-28$*"#$,1#G)>$1#%?+2%#$+,$5$3-2#51$5/?3-,-#1H$L*$*"#$*#%*$,1#G)>$ ω4$*"#$5/?3-,-#1 85-2$-%$)"515)*#1-T#0$'>$-*%$/582-*&0#$:)& /)$=$520$?"5%#$φ7

.2+624$'>$,:ω=4$*"#2 ) , ( ω ) = 99999& )$

∠, ( ω ) = φ !"#$1#%?+2%#$+,$*"#$5/?3-,-#1$*+$5$%-2&%+-0$+,$,1#G)>$ω$-%$)+/?3#*#3>$0#%)1-'#0$'>$o,:ω=o 520$ ∠,:ω=7$ O+64$ *+$ +'*5-2$ *"#$ )+/?3#*#$ ,1#G)>$ 1#%?+2%#$ +,$ *"#$ 5/?3-,-#1$ 6#$ %-/?3> )"528#$*"#$,1#G)>$+,$*"#$-2?&*$%-2&%+-0$520$/#5%&1#$*"#$2#6$E53&#$,+1$o, o$520$∠,7$!"# #20$ 1#%&3*$6-33$'#$5$*5'3#$520`+1$815?"$+,$85-2$/582-*&0#$qo,:ω=or$ E#1%&%$,1#G)>$ 520$5 *5'3#$ 520`+1$ 815?"$ +,$ ?"5%#$ 5283#$ q∠,:ω=r$ E#1%&%$ ,1#G)>7$ !"#%#$ *6+$ ?3+*%$ *+8#*"#1 )+2%*-*&*#$*"#$,1#G)>$1#%?+2%#$+,$*"#$5/?3-,-#1M$*"#$,-1%*$-%$.2+62$5%$*"#$!32*")01'$+1 3!/(")01',$'+/%*+'4$520$*"#$%#)+20$-%$*"#$/.3+',$'+/%*+'7$K-2533>4$6#$%"+&30$/#2*-+2$*"5* -*$-%$5$)+//+2$?15)*-)#$*+$#D?1#%%$*"#$/582-*&0#$+,$*152%/-%%-+2$-2$0#)-'#3%$520$*"&%$?3+* BA$3+8$o,:ω=o$E#1%&%$,1#G)>7

1.6.2 Amplifier Bandwidth K-8&1#$@7B@$%"+6%$*"#$/582-*&0#$1#%?+2%#$+,$52$5/?3-,-#17$;*$-20-)5*#%$*"5*$*"#$85-2$-%$53/+%* )+2%*52*$+E#1$5$6-0#$,1#G)>$1528#4$1+&8"3>$'#*6##2$ω@$520$ωB7$I-8253%$6"+%#$,1#G)-#% 51#$'#3+6$ ω@$+1$5'+E#$ ωB$6-33$#D?#1-#2)#$3+6#1$85-24$6-*"$*"#$85-2$0#)1#5%-28$5%$6#$/+E# ,51*"#1$565>$,1+/$ω@$520$ωB7$!"#$'520$+,$,1#G)-#%$+E#1$6"-)"$*"#$85-2$+,$*"#$5/?3-,-#1$-% 53/+%*$)+2%*52*4$*+$6-*"-2$5$)#1*5-2$2&/'#1$+,$0#)-'#3%$:&%&533>$U$0i=4$-%$)533#0$*"#$3!/("9"'$ 83*1G"1).7$ O+1/533>$ *"#$ 5/?3-,-#1$ -%$ 0#%-82#0$ %+$ *"5*$ -*%$ '5206-0*"$ )+-2)-0#%$ 6-*"$ *"# %?#)*1&/$ +,$ *"#$ %-8253%$ -*$ -%$ 1#G&-1#0$ *+$ 5/?3-,>7$ ;,$ *"-%$ 6#1#$ 2+*$ *"#$ )5%#4$ *"#$ 5/?3-,-#1 6+&30$.$!"&7"$*"#$,1#G)>$%?#)*1&/$+,$*"#$-2?&*$%-82534$6-*"$0-,,#1#2*$)+/?+2#2*%$+,$*"# -2?&*$%-8253$'#-28$5/?3-,-#0$'>$0-,,#1#2*$5/+&2*%7

1.6.3 Evaluating the Frequency Response of Amplifiers L'+E#4$6#$0#%)1-'#0$*"#$/#*"+0$&%#0$*+$/#5%&1#$*"#$,1#G)>$1#%?+2%#$+,$52$5/?3-,-#17 F#$ 2+6$ '1-#,3>$ 0-%)&%%$ *"#$ /#*"+0$ ,+1$ 5253>*-)533>$ +'*5-2-28$ 52$ #D?1#%%-+2$ ,+1$ *"#$ ,1#9 G)>$1#%?+2%#7$F"5*$6#$51#$5'+&*$*+$%5>$-%$(&%*$5$?1#E-#6$+,$*"-%$-/?+1*52*$%&'(#)*4$6"+%# 0#*5-3#0$%*&0>$-%$-2$<"5?*#1$\7

32 Chapter 1 Signals and Amplifiers

Figure 1.21 !>?-)53$/582-*&0#$1#%?+2%#$+,$52$5/?3-,-#1H$o,:ω=o$-%$*"#$/582-*&0#$+,$*"#$5/?3-,-#1$*152%,#1 ,&2)*-+2e*"5*$-%4$*"#$15*-+$+,$*"#$+&*?&*$)&:ω=$*+$*"#$-2?&*$)$ :ω=7

!+$ #E53&5*#$ *"#$ ,1#G)>$ 1#%?+2%#$ +,$ 52$ 5/?3-,-#14$ +2#$ "5%$ *+$ 5253>T#$ *"#$ 5/?3-,-#1 #G&-E53#2*$ )-1)&-*$ /+0#34$ *5.-28$ -2*+$ 5))+&2*$ 533$ 1#5)*-E#$ )+/?+2#2*%7U$ <-1)&-*$ 5253>%-% ?1+)##0%$ -2$ *"#$ &%&53$ ,5%"-+2$ '&*$ 6-*"$ -20&)*52)#%$ 520$ )5?5)-*52)#%$ 1#?1#%#2*#0$ '>$ *"#-1 1#5)*52)#%7$L2$-20&)*52)#$%$"5%$5$1#5)*52)#$+1$-/?#052)#$Nω%4$520$5$)5?5)-*52)#$<$"5%$5 1#5)*52)#$+1$-/?#052)#$@ ⁄ N ω < $+14$#G&-E53#2*3>4$5$%&%)#?*52)#$+1$50/-**52)#$Nω<7$!"&%$-2$5 *762364'DK.&C($4$5253>%-%$6#$0#53$6-*"$-/?#052)#%$520/+1$50/-**52)#%7$!"#$1#%&3*$+,$*"# 5253>%-%$-%$*"#$5/?3-,-#1$*152%,#1$,&2)*-+2$,:ω=

)& ( ω ) 9 , ( ω ) = 99999999999999 )$ ( ω ) 6"#1#$)$:ω=$520$)&:ω=$0#2+*#$*"#$-2?&*$520$+&*?&*$%-8253%4$1#%?#)*-E#3>7$,:ω=$-%$8#2#1533>$5 )+/?3#D$,&2)*-+2$6"+%#$/582-*&0#$o,:ω=o$8-E#%$*"#$/582-*&0#$+,$*152%/-%%-+2$+1$*"#$/589 2-*&0#$1#%?+2%#$+,$*"#$5/?3-,-#17$!"#$?"5%#$+,$,:ω=$8-E#%$*"#$?"5%#$1#%?+2%#$+,$*"#$5/?3-9 ,-#17 ;2$*"#$5253>%-%$+,$5$)-1)&-*$*+$0#*#1/-2#$-*%$,1#G)>$1#%?+2%#4$*"#$538#'15-)$/52-?&35*-+2% )52$'#$)+2%-0#15'3>$%-/?3-,-#0$'>$&%-28$*"#$#%!/('F,9$':0'*#;,B3$"38('$!7$;2$*#1/%$+,$!4$*"# -/?#052)#$+,$52$-20&)*52)#$%$-%$!%$520$*"5*$+,$5$)5?5)-*52)#$<$-%$@ ⁄ !<7$R#?35)-28$*"#$1#5)*-E# #3#/#2*%$6-*"$*"#-1$-/?#052)#%$520$?#1,+1/-28$%*520510$)-1)&-*$5253>%-%4$6#$+'*5-2$*"#$*152%,#1 ,&2)*-+2+,:!=$5%

)& ( ! ) 9 , ( ! ) ≡ 999999999999 )$ ( ! ) I&'%#G*3>4$6#$1#?35)#$!$'>$Nω$*+$0#*#1/-2#$*"#$*152%,#1$,&2)*-+2$,+1$/.;+"#3(,9$':0'*& #"'+4$,: Nω=7$O+*#$*"5*$,: Nω=$-%$*"#$%5/#$,&2)*-+2$6#$)533#0$,:ω=$5'+E#^M$*"#$500-*-+253$N$-% -2)3&0#0$-2$+10#1$*+$#/?"5%-T#$*"5*$,: Nω=$-%$+'*5-2#0$,1+/$,:!=$'>$1#?35)-28$!$6-*"$Nω7

U

O+*#$*"5*$-2$*"#$/+0#3%$)+2%-0#1#0$-2$?1#E-+&%$%#)*-+2%$2+$1#5)*-E#$)+/?+2#2*%$6#1#$-2)3&0#07$!"#%#$ 6#1#$%-/?3-,-#0$/+0#3%$520$)522+*$'#$&%#0$53+2#$*+$?1#0-)*$*"#$5/?3-,-#1$,1#G)>$1#%?+2%#7 ^ L*$*"-%$%*58#4$6#$51#$&%-28$!$%-/?3>$5%$5$%"+1*"520$,+1$Nω7$F#$%"533$2+*$1#G&-1#$0#*5-3#0$.2+63#08#$+,$ !9?352#$)+2)#?*%$&2*-3$<"5?*#1$\7$L$'1-#,$1#E-#6$+,$!9?352#$5253>%-%$-%$?1#%#2*#0$-2$L??#20-D$K7

1.6 Frequency Response of Amplifiers 33

1.6.4 Single-Time-Constant Networks ;2$5253>T-28$5/?3-,-#1$)-1)&-*%$*+$0#*#1/-2#$*"#-1$,1#G)>$1#%?+2%#4$+2#$-%$81#5*3>$5-0#0$'> .2+63#08#$+,$*"#$,1#G)>91#%?+2%#$)"515)*#1-%*-)%$+,$%-283#9*-/#9)+2%*52*$:I!<=$2#*6+1.%7 L2$I!<$2#*6+1.$-%$+2#$*"5*$-%$)+/?+%#0$+,4$+1$)52$'#$1#0&)#0$*+4$+2#$1#5)*-E#$)+/?+2#2* :-20&)*52)#$+1$)5?5)-*52)#=$520$+2#$1#%-%*52)#7$JD5/?3#%$51#$%"+62$-2$K-87$@7BB7$L2$I!< 2#*6+1.$,+1/#0$+,$52$-20&)*52)#$%$520$5$1#%-%*52)#$#$"5%$5$*-/#$)+2%*52*$τ " % ⁄ # 7$!"# *-/#$)+2%*52*$τ$+,$52$I!<$2#*6+1.$)+/?+%#0$+,$5$)5?5)-*52)#$<$520$5$1#%-%*52)#$#$-%$8-E#2 '>$τ =$<#7 L??#20-D$J$?1#%#2*%$5$%*&0>$+,$I!<$2#*6+1.%$520$*"#-1$1#%?+2%#%$*+$%-2&%+-0534$%*#?4$520 ?&3%#$-2?&*%7$s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⁄ N ω < =4$-*$-%$#5%>$*+$%##$*"5*$*"#$*152%/-%%-+2$+,$*"# )-1)&-*$-2$K-87$@7BB:5=$6-33$0#)1#5%#$6-*"$,1#G)>$520$5??1+5)"$T#1+$5%$ω$5??1+5)"#%$∞7$!"&% *"#$)-1)&-*$+,$K-87$@7BB:5=$5)*%,5%,5,(%G&/3++,9"()'$bM$-*$?5%%#%$3+69,1#G)>4$%-2#965E#$-2?&*% 6-*"$3-**3#$+1$2+$5**#2&5*-+2$:5*$ω$=$A4$*"#$*152%/-%%-+2$-%$&2-*>=$520$5**#2&5*#%$"-8"9,1#G)> -2?&*$%-2&%+-0%7$!"#$)-1)&-*$+,$K-87$@7BB:'=$0+#%$*"#$+??+%-*#M$-*%$*152%/-%%-+2$-%$&2-*>$5*$ω$=$∞ 520$0#)1#5%#%$5%$ω$-%$1#0&)#04$1#5)"-28$A$,+1$ω$=$A7$!"#$35**#1$)-1)&-*4$*"#1#,+1#4$?#1,+1/%$5%$5 ."2.&/3++,9"()'$7 !5'3#$ @7B$ ?1+E-0#%$ 5$ %&//51>$ +,$ *"#$ ,1#G)>91#%?+2%#$ 1#%&3*%$ ,+1$ I!<$ 2#*6+1.%$ +, '+*"$*>?#%7c$L3%+4$%.#*)"#%$+,$*"#$/582-*&0#$520$?"5%#$1#%?+2%#%$51#$8-E#2$-2$K-8%7$@7BU$520 @7B^7$!"#%#$,1#G)>91#%?+2%#$0-5815/%$51#$.2+62$5%$A%1',/(%)+$520$*"#$N&1A,9$':0'*#;

C

R Vi

" !

C

(a)

]

" Vo !

Vi

" !

R

(b)

" Vo !

Figure 1.22 !6+$#D5/?3#%$+,$I!< 2#*6+1.%H$437$5$3+69?5%%$2#*6+1.$520 487$5$"-8"9?5%%$2#*6+1.7

L2$-/?+1*52*$#D)#?*-+2$-%$*"#$3((&/3++$I!<$2#*6+1.$%*&0-#0$-2$<"5?*#1$@b7 L$,-3*#1$-%$5$)-1)&-*$*"5*$?5%%#%$%-8253%$-2$5$%?#)-,-#0$,1#G)>$'520$:*"#$,-3*#1$?5%%'520=$520$%*+?%$+1$ %#E#1#3>$5**#2&5*#%$:,-3*#1%$+&*=$%-8253%$-2$52+*"#1$,1#G)>$'520$:*"#$,-3*#1$%*+?'520=7$K-3*#1%$6-33$'#$ %*&0-#0$-2$<"5?*#1$@b7 c !"#$*152%,#1$,&2)*-+2%$-2$!5'3#$@7B$51#$8-E#2$-2$8#2#153$,+1/7$K+1$*"#$)-1)&-*%$+,$K-87$@7BB4$O$=$@$520$ ω A$= @/<#7 b

34 Chapter 1 Signals and Amplifiers

Table 1.2 Frequency Response of STC Networks p+69l5%%$:pl=

a-8"9l5%%$:al=

!152%,#1$K&2)*-+2$,:!=

O 99999999999999999999999999 @ + ( ! ⁄ ωA )

O! 99999999999999 ! + ωA

!152%,#1$K&2)*-+2$:,+1$?">%-)53 ,1#G)-#%=$,: Nω=

O 999999999999999999999999999999 @ + N ( ω ⁄ ωA )

O 99999999999999999999999999999 9 @ 4 N ( ωA ⁄ ω )

_582-*&0#$R#%?+2%#$|,: Nω=|

O 99999999999999999999999999999999999 B @ + ( ω ⁄ ωA )

O 99999999999999999999999999999999999 B @ + ( ωA ⁄ ω )

l"5%#$R#%?+2%#$∠,: Nω=

4 *52 ( ω ⁄ ω A )

*52 ( ω A ⁄ ω )

O

A

A

O

!152%/-%%-+2$5*$ω$=$A !152%/-%%-+2$5*$ω$=$∞

4@

:0)=

ω A+=+@/τ M+τ++≡+*-/#$)+2%*52* τ++=+<#++1+%/#

U90i$K1#G)> i+0#$l3+*%

4@

-2$K-87$@7BU

-2$K-87$@7B^

(a)

(b) Figure 1.23 437$_582-*&0#$520$487$?"5%#$1#%?+2%#$+,$I!<$2#*6+1.%$+,$*"#$3+69?5%%$*>?#7

1.6 Frequency Response of Amplifiers 35

(a)

(b) Figure 1.24 437$_582-*&0#$520$487$?"5%#$1#%?+2%#$+,$I!<$2#*6+1.%$+,$$*"#$"-8"9?5%%$*>?#7

:ω A=$ -%$ 53%+$ .2+62$ 5%$ *"#$ #%$*'$, 9$':0'*#;4$ 8$'3O, 9$':0'*#;4, +1, /%(', 9$':0'*#;7$ !"# 1#50#1$-%$&18#0$*+$'#)+/#$,5/-3-51$6-*"$*"-%$-2,+1/5*-+2$520$*+$)+2%&3*$L??#20-D$J$-,$,&1*"#1 )351-,-)5*-+2%$ 51#$ 2##0#07$ ;2$ ?51*-)&3514$ -*$ -%$ -/?+1*52*$ *+$ 0#E#3+?$ 5$ ,5)-3-*>$ ,+1$ *"#$ 15?-0 0#*#1/-25*-+2$+,$*"#$*-/#$)+2%*52*$ τ$+,$52$I!<$)-1)&-*7$!"#$?1+)#%%$-%$E#1>$%-/?3#H$I#*$*"# -20#?#20#2*$E+3*8#$+1$)&11#2*$%+&1)#$*+$T#1+M$V815'$"+30W$+,$*"#$*6+$*#1/-253%$+,$*"#$1#5)*-E# #3#/#2*$:)5?5)-*+1$<$+1$-20&)*+1$%=M$520$0#*#1/-2#$*"#$#G&-E53#2*$1#%-%*52)#$#$*"5*$5??#51% '#*6##2$*"#%#$*6+$*#1/-253%7$!"#$*-/#9)+2%*52*$-%$*"#2$<#$+1$%`#7

36 Chapter 1 Signals and Amplifiers

Example 1.5 K-8&1#$@7B]$%"+6%$5$E+3*58#$5/?3-,-#1$"5E-28$52$-2?&*$1#%-%*52)#$#$ 4$52$-2?&*$)5?5)-*52)#$<$ 4$5$85-2$,5)*+1 µ4$520$52$+&*?&*$1#%-%*52)#$#&7$!"#$5/?3-,-#1$-%$,#0$6-*"$5$E+3*58#$%+&1)#$)!$"5E-28$5 %+&1)#$1#%-%*52)#$#!4 520$5$3+50$+,$1#%-%*52)#$#%$-%$)+22#)*#0$*+$*"#$+&*?&*7 Rs

Ro "

Vs

" !

Vi

" Ri

" !

Ci

( Vi

!

RL

Vo !

Figure 1.25 <-1)&-*$,+1$JD5/?3#$@7]7

:5= Q#1-E#$52$#D?1#%%-+2$,+1$*"#$5/?3-,-#1$E+3*58#$85-2$ )& ⁄ )!$5%$5$,&2)*-+2$+,$,1#G)>7$K1+/$*"-%$,-20 #D?1#%%-+2%$,+1$*"#$0)$85-2$520$*"#$U90i$,1#G)>7 :'= <53)&35*#$*"#$E53&#%$+,$*"#$0)$85-24$*"#$U90i$,1#G)>4$520$*"#$,1#G)>$5*$6"-)"$*"#$85-2$'#)+/#% A$0i$:-7#74$&2-*>=$,+1$*"#$)5%#$#!$=$BA$.Ω4$#$$=$@AA$.Ω4$<$$=$bA$?K4$ µ " @^^$Y`Y4 +#&$=$BAA$Ω4$520$#% =$@$.Ω7 :)= K-20$v&:"=$,+1$#5)"$+,$*"#$,+33+6-28$-2?&*%H :-= v$$=$A7@$%-2$@AB$"4$Y :--= v$$=$A7@$%-2$@A]$"4$Y :---= v$$=$A7@$%-2$@Ab$"4$Y :-E= v$$=$A7@$%-2$@AZ$"4$Y

Solution -G.%H:@?@I@AB%:;<%F8?:GB@F@><9%9E?<5%K<%CGA% #5%-#1$*+$6+1.$-2$*#1/%$+,$ Q $ = @ ⁄ P $ 7$!+6510$*"5*$#20$6#$0-E-0#$*"#$2&/#15*+1$520$0#2+/-25*+1$'>$P$ 4 *"&%$+'*5-2-28 @ ) $ = ) ! 9999999999999999999 @ + #! Q$ @ = ) ! 999999999999999999999999999999999999999999999999999 @ + # ! [ ( @ ⁄ # $ ) ! !< $ ] !"&%4 ) @ 99999$ = 999999999999999999999999999999999999999999999999 @ + ( # ! ⁄ # $ ) + !< $ # ! )!

1.6 Frequency Response of Amplifiers

!"-%$#D?1#%%-+2$)52$'#$?&*$-2$*"#$%*520510$,+1/$,+1$5$3+69?5%%$I!<$2#*6+1.$:%##$*"#$*+?$3-2#$+,$!5'3#$@7B= '>$#D*15)*-28$[ @ ! ( # ! ⁄ # $ ) ]$,1+/$*"#$0#2+/-25*+1M$*"&%$6#$"5E# ) @ @ 99999$ = 999999999999999999999999999 9 999999999999999999999999999999999999999999999999999999999999999 9 )! @ + ( # ! ⁄ # $ ) @ + !< $ [ ( # ! # $ ) ⁄ ( # ! + # $ ) ]

-($+*.

&:%:;<%8E:ME:%N@><%8O%:;<%G=M?@O@<9%K<%CGA%EN<%:;<%F8?:GB@F@><9%9E?<%:8%K9@:< #% 9 ) & = µ ) $ 99999999999999999 #% + #& P;@N%%K@:;%QD$%-($+*.%:8%86:G@A%:;<%G=M?@O@<9%:9GANO<9%OEAC:@8A%GN ) @ @ @ 99999& = µ 9999999999999999999999999999 99999999999999999999999999999 9 9999999999999999999999999999999999999999999999999999999999999999 @ + ( # ! ⁄ # $ ) @ + ( # & ⁄ # % ) @ + !< $ [ ( # ! # $ ) ⁄ ( # ! + # $ ) ] )!

-($+(.

F#$2+*#$*"5*$+23>$*"#$35%*$,5)*+1$-2$*"-%$#D?1#%%-+2$-%$2#6$:)+/?51#0$6-*"$*"#$#D?1#%%-+2$0#1-E#0$-2$*"# 35%*$%#)*-+2=7$!"-%$,5)*+1$-%$5$1#%&3*$+,$*"#$-2?&*$)5?5)-*52)#$<$4$6-*"$*"#$*-/#$)+2%*52*$'#-28 ## #! + #$

! $ τ = < $ 9999999999999999

-($++.

$ = < $ ( # ! oo # $ ) F#$)+&30$"5E#$+'*5-2#0$*"-%$1#%&3*$'>$-2%?#)*-+2H$K1+/$K-87$@7B]$6#$%##$*"5*$*"#$-2?&*$)-1)&-*$-%$52$I!< 2#*6+1.$520$*"5*$-*%$*-/#$)+2%*52*$)52$'#$,+&20$'>$1#0&)-28$)!$*+$T#1+4$6-*"$*"#$1#%&3*$*"5*$*"#$1#%-%*52)# %##2$'>$<$$-%$#$$-2$?51533#3$6-*"$#!7$!"#$*152%,#1$,&2)*-+2$-2$JG7$:@7B@=$-%$+,$*"#$,+1/$ O ⁄ ( @ + ( ! ⁄ ω A ) ) 4 6"-)"$)+11#%?+20%$*+$5$3+69?5%%$I!<$2#*6+1.7$!"#$0)$85-2$-%$,+&20$5% ) @ @ O ≡ 99999& ( ! = A ) = µ 9999999999999999999999999999 999999999999999999999999999999 @ + ( #! ⁄ #$ ) @ + ( #& ⁄ #% ) )!

-($+/.

!"#$U90i$,1#G)>$ωA$)52$'#$,+&20$,1+/ @ @ ω A = 999 = 999999999999999999999999999 < $ ( # ! $oo$# $ ) τ

-($+0.

I-2)#$*"#$,1#G)>$1#%?+2%#$+,$*"-%$5/?3-,-#1$-%$+,$*"#$3+69?5%%$I!<$*>?#4$*"#$i+0#$?3+*%$,+1$*"#$85-2 /582-*&0#$520$?"5%#$6-33$*5.#$*"#$,+1/$%"+62$-2$K-87$@7BU4$6"#1#$O$-%$8-E#2$'>$JG7$:@7BU=$520$ωA$-%$8-E#2 '>$JG7$:@7B^=7 :'=$I&'%*-*&*-28$*"#$2&/#1-)53$E53&#%$8-E#2$-2*+$JG7$:@7BU=$1#%&3*%$-2 @ @ O = @^^ 999999999999999999999999999999999 999999999999999999999999999999999999999 = @AA$Y`Y @ + ( BA ⁄ @AA ) @ + ( BAA ⁄ @AAA ) !"&%$*"#$5/?3-,-#1$"5%$5$0)$85-2$+,$^A$0i7$I&'%*-*&*-28$*"#$2&/#1-)53$E53&#%$-2*+$JG7$:@7B^=$8-E#%$*"#$U90i ,1#G)> @ ω A $= 999999999999999999999999999999999999999999999999999999999999999

bA$?K × ( BA$.Ω``@AA$.Ω ) @ 9 = @A b $150`% = 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 4 @B U bA × @A × ( BA × @AA ⁄ ( BA ! @AA ) ) × @A

37

38 Chapter 1 Signals and Amplifiers

Example 1.5 continued

!"&%4

b

@A * A = 99999999 = @]\7B$.aT Bπ I-2)#$*"#$85-2$,533%$+,,$5*$*"#$15*#$+,$hBA$0i/0#)50#4$%*51*-28$5*$ω A$:%##$K-87$@7BU5=$*"#$85-2$6-33$1#5)"$A$0i -2$*6+$0#)50#%$:5$,5)*+1$+,$@AA=M$*"&%$6#$"5E# Z

d2-*>985-2$,1#G)> " @AA × ω A " @A $150`% +1 @]7\B$_aT :)=$!+$,-20$v&:"=$6#$2##0$*+$0#*#1/-2#$*"#$85-2$/582-*&0#$520$?"5%#$5*$@AB4$@A]4$@Ab4$520$@AZ$150/%7$!"-%$)52 '#$0+2#$#-*"#1$5??1+D-/5*#3>$&*-3-T-28$*"#$i+0#$?3+*%$+,$K-87$@7BU$+1$#D5)*3>$&*-3-T-28$*"#$#D?1#%%-+2$,+1 *"#$5/?3-,-#1$*152%,#1$,&2)*-+24 ) @AA , ( N ω ) ≡ 99999& ( N ω ) " 9999999999999999999999999999999 9 b )! @ ! N ( ω ⁄ @A ) F#$%"533$0+$'+*"H ^ :-=$K+1$ ω$ =$@AB$150/%4$6"-)"$-%$ ( ω A ⁄ @A )4$*"#$i+0#$?3+*%$+,$K-87$@7BU$%&88#%*$*"5*$o, o$=$O$=$@AA$520 φ$=$A°7$!"#$*152%,#1$,&2)*-+2$#D?1#%%-+2$8-E#%$o, o$!$@AA$520$φ$=$h*52h@$@Ah^$!$A°7$!"&%4 v&:"=$=$@A$%-2$@AB"4$Y :--=$K+1$ω$ =$@A]$150/%4$6"-)"$-%$ ( ω A ⁄ @A )4$*"#$i+0#$?3+*%$+,$K-87$@7BU$%&88#%*$*"5*$o, o$!$O$=$@AA$520 φ$=$−]7c°7$!"#$*152%,#1$,&2)*-+2$#D?1#%%-+2$8-E#%$o, o$=$\\7]$520$φ$=$−*52−@$A7@$=$−]7c°7$!"&%4 v&:"=$=$\7\]$%-2:@A]"$h$]7c°=4$Y -@@@.%789%ω%=%(*1%9G>/N%=%ω *5% , = @AA ⁄ B = cA7c$Y`Y 89%/2%>R%GA>%φ%=%−0)°$%P;EN5 v&:"=$=$c7Ac$%-2:@Ab"$−$^]°=4$Y :-E=$K+1$ ω$=$@AZ$150/%4$6"-)"$-%$:@AAω A=4$*"#$i+0#$?3+*%$%&88#%*$*"5*$o,o$=$@$520$ φ =$h\A°7$!"#$*152%,#1 ,&2)*-+2$#D?1#%%-+2$8-E#% o, o$!$@

520 φ = −*52h@$@AA = −Z\7^°

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v&:"=$=$A7@$%-2:@AZ"$−$Z\7^°=4$Y

1.6.5 Classification of Amplifiers Based on Frequency Response L/?3-,-#1%$)52$'#$)35%%-,-#0$'5%#0$+2$*"#$%"5?#$+,$*"#-1$/582-*&0#91#%?+2%#$)&1E#7$K-8&1#$@7Bb %"+6%$*>?-)53$,1#G)>91#%?+2%#$)&1E#%$,+1$E51-+&%$5/?3-,-#1$*>?#%7$;2$K-87$@7Bb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c7$!"-%$?15)*-)#$-%$&%&9 533>$50+?*#0$*+$%-/?3-,>$*"#$0#%-82$?1+)#%%$+,$*"#$0-,,#1#2*$%*58#%7$!"#$)+&?3-28$)5?5)-*+1%

1.6 Frequency Response of Amplifiers 39

(a)

(b)

(c) Figure 1.26 K1#G)>$1#%?+2%#$,+1$437$5$)5?5)-*-E#3>$)+&?3#0$5/?3-,-#14$487$5$0-1#)*9)+&?3#0$5/?3-,-#14 520$4#7$5$*&2#0$+1$'520?5%%$5/?3-,-#17

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40 Chapter 1 Signals and Amplifiers K-87$@7Bc$6#$+'%#1E#$*"5*$*"#$)+&?3-28$)5?5)-*+14$5)*-28$*+8#*"#1$6-*"$*"#$-2?&*$1#%-%*52)#$+, *"#$ %&'%#G*$ %*58#4$ ,+1/%$ 5$ "-8"9?5%%$ I!<$ )-1)&-*7$ ;*$ -%$ *"#$ ,1#G)>$ 1#%?+2%#$ +,$ *"-% "-8"9?5%%$ )-1)&-*$ *"5*$ 5))+&2*%$ ,+1$ *"#$ %"5?#$ +,$ *"#$ 5/?3-,-#1$ ,1#G)>$ 1#%?+2%#$ -2$ K-87 @7Bb:5=$5*$*"#$3+69,1#G)>$#207 !"#1#$51#$/52>$5??3-)5*-+2%$-2$6"-)"$-*$-%$-/?+1*52*$*"5*$*"#$5/?3-,-#1$/5-2*5-2$-*%$85-2$5* 3+6$ ,1#G)-#%$ 0+62$ *+$ 0)7$ K&1*"#1/+1#4$ /+2+3-*"-)$ -2*#815*#09)-1)&-*$ :;<=$ *#)"2+3+8> 0+#%$2+*$533+6$*"#$,5'1-)5*-+2$+,$3518#$)+&?3-28$)5?5)-*+1%7$!"&%$;<$5/?3-,-#1%$51#$&%&533> 0#%-82#0$ 5%$ 1"$'#)(;, #%0/('1$ +1$ 1#, 3!/("9"'$+$ :5%$ +??+%#0$ *+$ #3/3#")"B'(;, #%0/('14$ +1 3# 3!/("9"'$+=7$K-8&1#$@7Bb:'=$%"+6%$*"#$,1#G)>$1#%?+2%#$+,$5$0)$5/?3-,-#17$I&)"$5$,1#G)> 1#%?+2%#$)"515)*#1-T#%$6"5*$-%$1#,#11#0$*+$5%$5$(%G&/3++,3!/("9"'$7 ;2$5$2&/'#1$+,$5??3-)5*-+2%4$%&)"$5%$-2$*"#$0#%-82$+,$150-+$520$!Y$1#)#-E#1%4$*"#$2##0$51-%#% ,+1$52$5/?3-,-#1$6"+%#$,1#G)>$1#%?+2%#$?#5.%$51+&20$5$)#1*5-2$,1#G)>$:)533#0$*"#$#'*)'$ 9$':0'*#;=$520$,533%$+,,$+2$'+*"$%-0#%$+,$*"-%$,1#G)>4$5%$%"+62$-2$K-87$@7Bb:)=7$L/?3-,-#1% 6-*"$%&)"$5$1#%?+2%#$51#$)533#0$)0*'1,3!/("9"'$+4,83*1/3++,3!/("9"'$+4$+1$83*1/3++,9"()'$+7 L$*&2#0$5/?3-,-#1$,+1/%$*"#$"#51*$+,$*"#$,1+2*9#20$+1$*&2#1$+,$5$)+//&2-)5*-+2$1#)#-E#1M$'> 50(&%*-28$ -*%$ )#2*#1$ ,1#G)>$ *+$ )+-2)-0#$ 6-*"$ *"#$ ,1#G)>$ +,$ 5$ 0#%-1#0$ )+//&2-)5*-+2% )"522#3$:#7874$5$150-+$%*5*-+2=4$*"#$%-8253$+,$*"-%$?51*-)&351$)"522#3$)52$'#$1#)#-E#0$6"-3#$*"+%# +,$+*"#1$)"522#3%$51#$5**#2&5*#0$+1$,-3*#1#0$+&*7

EXERCISES 1.22 <+2%-0#1$5$E+3*58#$5/?3-,-#1$"5E-28$5$,1#G)>$1#%?+2%#$+,$*"#$3+69?5%%$I!<$*>?#$6-*"$5$0) 85-2$+,$bA$0i$520$5$U90i$,1#G)>$+,$@AAA$aT7$K-20$*"#$85-2$-2$0i$5*$*$=$@A$aT4$@A$.aT4$@AA .aT4$520$@$_aT7 Ans. bA$0iM$^A$0iM$BA$0iM$A$0i D1.23 <+2%-0#1$5$*152%)+20&)*52)#$5/?3-,-#1$"5E-28$*"#$/+0#3$%"+62$-2$!5'3#$@7@$6-*"$#$$=$]$.Ω4$#&$=$]A .Ω4$520$BC$=$@A$/L/Y7$;,$*"#$5/?3-,-#1$3+50$)+2%-%*%$+,$5$1#%-%*52)#$#%$-2$?51533#3$6-*"$5$)5?5)-9 *52)#$<%4$)+2E-2)#$>+&1%#3,$*"5*$*"#$E+3*58#$*152%,#1$,&2)*-+2$1#53-T#04$)&/)$4$-%$+,$*"#$3+69?5%% I!<$*>?#7$F"5*$-%$*"#$3+6#%*$E53&#$*"5*$#%$)52$"5E#$6"-3#$5$0)$85-2$+,$5*$3#5%*$^A$0i$-%$+'*5-2#0X F-*"$*"-%$E53&#$+,$#%$)+22#)*#04$,-20$*"#$"-8"#%*$E53&#$*"5*$<%$)52$"5E#$6"-3#$5$U90i$'5206-0*" +,$5*$3#5%*$@AA$.aT$-%$+'*5-2#07 Ans. @B7]$.ΩM$@]\7B$?K D1.24 <+2%-0#1$*"#$%-*&5*-+2$-33&%*15*#0$-2$K-87$@7Bc7$p#*$*"#$+&*?&*$1#%-%*52)#$+,$*"#$,-1%*$E+3*58#$5/?3-9 ,-#1$'#$@$.Ω$520$*"#$-2?&*$1#%-%*52)#$+,$*"#$%#)+20$E+3*58#$5/?3-,-#1$:-2)3&0-28$*"#$1#%-%*+1$%"+62= '#$\$.Ω7$!"#$1#%&3*-28$#G&-E53#2*$)-1)&-*$-%$%"+62$-2$K-87$J@7B^$6"#1#$)!$520$#!$51#$*"#$+&*?&* E+3*58#$520$+&*?&*$1#%-%*52)#$+,$*"#$,-1%*$5/?3-,-#14$<$-%$5$)+&?3-28$)5?5)-*+14$520$#$$-%$*"#$-2?&* 1#%-%*52)#$+,$*"#$%#)+20$5/?3-,-#17$<+2E-2)#$>+&1%#3,$*"5*$)B/)!$-%$5$"-8"9?5%%$I!<$,&2)*-+27$F"5* -%$*"#$%/533#%*$E53&#$,+1$<$*"5*$6-33$#2%&1#$*"5*$*"#$U90i$,1#G)>$-%$2+*$"-8"#1$*"52$@AA$aTX Ans. A7@b$µK Rs % 1 k)

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1.6 Frequency Response of Amplifiers 41

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Problems 43

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CHAPTER 1 P R O B L E M S

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CHAPTER 1 P R O B L E M S

44 Chapter 1 Signals and Amplifiers -G. UE99% 9+% @A% #(% GA>% #+5 9%N8?F<%:;<=$ -6. S8?:GB<%F8?:GB<%)%G:%:;<%C8==8A%A8><' @>%N8?F<%@:$ F"-)"$/#*"+0$0+$>+&$?1#,#1X$F">X

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R2 1 kV

1 kV

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Figure P1.18

AC Circuits Figure P1.16

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Problems 45

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Section 1.2: Frequency Spectrum of Signals 1.27 !+$ ,5/-3-51-T#$ >+&1%#3,$ 6-*"$ *>?-)53$ E53&#%$ +,$ 528&351 ,1#G)>$ ω 4$ )+2E#2*-+253$ ,1#G)>$ *4$ 520$ ?#1-+0$ ,4$ )+/9 ?3#*#$*"#$#2*1-#%$-2$*"#$,+33+6-28$*5'3#H Case G 6 C > < O

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Section 1.3: Analog and Digital Signals 1.34 j-E#$*"#$'-251>$1#?1#%#2*5*-+2$+,$*"#$,+33+6-28$0#)-/53 2&/'#1%H$A4$]4$Z4$B]4$520$]c7 1.35 <+2%-0#1$5$^9'-*$0-8-*53$6+10$0U0B0@0A$-2$5$,+1/5*$)533#0 %-82#09/582-*&0#4$ -2$ 6"-)"$ *"#$ /+%*$ %-82-,-)52*$ '-*4$ 0U4$ -% -2*#1?1#*#0$5%$5$%-82$'-*eA$,+1$?+%-*-E#$520$@$,+1$2#85*-E#$E539 &#%7$ p-%*$ *"#$ E53&#%$ *"5*$ )52$ '#$ 1#?1#%#2*#0$ '>$ *"-%$ %)"#/#7 F"5*$-%$?#)&3-51$5'+&*$*"#$1#?1#%#2*5*-+2$+,$T#1+X$K+1$5$?519 *-)&351$5253+89*+90-8-*53$)+2E#1*#1$:LQ<=4$#5)"$)"528#$-2$0A )+11#%?+20%$*+$5$A7]9Y$)"528#$-2$*"#$5253+8$-2?&*7$F"5*$-%$*"# ,&33$1528#$+,$*"#$5253+8$%-8253$*"5*$)52$'#$1#?1#%#2*#0X$F"5* %-82#09/582-*&0#$0-8-*53$)+0#$1#%&3*%$,+1$52$-2?&*$+,$+B7]$YX K+1$−U7A$YX$K+1$+B7c$YX$K+1$−B7Z$YX

CHAPTER 1 P R O B L E M S

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CHAPTER 1 P R O B L E M S

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CHAPTER 1 P R O B L E M S

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47

CHAPTER 1 P R O B L E M S

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Problems

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Figure P1.64

Section 1.6: Frequency Response of Amplifiers

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49

CHAPTER 1 P R O B L E M S

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CHAPTER 2

Operational Amplifiers Introduction 2.1

2.6 DC Imperfections

53

2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance 97

The Ideal Op Amp 54

2.2 The Inverting Configuration

58

2.3 The Noninverting Configuration 2.4 Difference Amplifiers

67

71

2.5 Integrators and Differentiators

88

80

2.8 Large-Signal Operation of Op Amps 102 Summary

107

Problems

108

IN THIS CHAPTER YOU WILL LEARN 1. The terminal characteristics of the ideal op amp. 2. How to analyze circuits containing op amps, resistors, and capacitors. 3. How to use op amps to design amplifiers having precise characteristics. 4. How to design more sophisticated op-amp circuits, including summing amplifiers, instrumentation amplifiers, integrators, and differentiators. 5. Important nonideal characteristics of op amps and how these limit the performance of basic op-amp circuits.

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2.1.2 Function and Characteristics of the Ideal Op Amp Y)'%26'.2%-$+)*'39)'.$*.7$3'17%.3$2%'21'39)'20'"/0>';9)'20'"/0'$-'+)-$&%)+'32'-)%-)'39)'+$1B 1)*)%.)',)36))%'39)'#2(3"&)'-$&%"(-'"00($)+'"3'$3-'362'$%073'3)*/$%"(-'<$>)>5'39)'K7"%3$34'vQ'− vC=5'/7(3$0(4'39$-',4'"'%7/,)*'$5'"%+'."7-)'39)'*)-7(3$%&'#2(3"&)'$';97-'vT%Z%$'!)*)'$3'-927(+',)')/09"-$[)+'39"3'69)%'6)'3"(8'",273 39)' #2(3"&)' "3' "' 3)*/$%"(' 6)' /)"%' 39)' #2(3"&)' ,)36))%' 39"3' 3)*/$%"(' "%+' &*27%+X' 397-' v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vQ'"%+'$-'273'21'09"-) 6$39'<9"-'39)'2002-$3)'-$&%'21='vC>'S2*'39$-'*)"-2%5'$%073'3)*/$%"('C'$-'."(()+'39)'!"#$%&!"' !"()&*&$%+!",-'"%+'$-'+$-3$%&7$-9)+',4'"'^−_'-$&%5'69$()'$%073'3)*/$%"('Q'$-'."(()+'39)'"."!"/ #$%&!"'*!"()&*&$%+!",-'"%+'$-'+$-3$%&7$-9)+',4'"'^+_'-$&%>''' H-'."%',)'-))%'1*2/'39)'",2#)'+)-.*$03$2%5'39)'20'"/0'*)-02%+-'2%(4'32'39)'.)22(8(*0( -$&%"('vQ'−'vC'"%+'9)%.)'$&%2*)-'"%4'-$&%"('01--1*'32',239'$%073->';9"3'$-5'$1'vC'='vQ'='C'`5 39)%'39)'273073'6$(('<$+)"((4=',)'[)*2>'Y)'."(('39$-'0*20)*34'0.++."/+.1$*%$2$0&!."5'"%+'6) .2%.(7+)'39"3'"%'$+)"('20'"/0'9"-'[)*2'.2//2%B/2+)'&"$%'2*5')K7$#"()%3(45'$%1$%$3)'.2/B /2%B/2+)'*)W).3$2%>'Y)'6$(('9"#)'/2*)'32'-"4'",273'39$-'02$%3'("3)*>'S2*'39)'3$/)',)$%& %23)'39"3'39)'20'"/0'$-'"'1!33$%$"&!,-/!"()&5*4!"'-$/$"1$1/.)&()&'"/0($1$)*5'6$39 39)'("3B 3)*' 3)*/' *)1)**$%&' 32' 39)' 1".3' 39"3' 39)' 273073' "00)"*-' ,)36))%' 3)*/$%"(' T' "%+' &*27%+>C C

L2/)'20'"/0-'"*)'+)-$&%)+'32'9"#)'+$11)*)%3$"('273073->';9$-'320$.'6$(('%23',)'+$-.7--)+'$%'39$-',228>' O"39)*5'6)'.2%1$%)'27*-)(#)-'9)*)'32'-$%&()B)%+)+B273073'20'"/0-5'69$.9'.2%-3$373)'39)'#"-3'/"W2*$34' 21'.2//)*.$"((4'"#"$(",()'20'"/0->

55

56 Chapter 2 Operational Amplifiers Inverting input

Output

Noninverting input Figure 2.3 @K7$#"()%3'.$*.7$3'21'39)'$+)"('20'"/0>

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a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able 2.1 Characteristics of the Ideal Op Amp C> A%1$%$3)'$%073'$/0)+"%.) Q> b)*2'273073'$/0)+"%.) T> b)*2'.2//2%B/2+)'&"$%'2*5')K7$#"()%3(45'$%1$%$3)'.2//2%B/2+)'*)W).3$2% U> A%1$%$3)'20)%B(220'&"$%'$ V> A%1$%$3)',"%+6$+39

2.1 The Ideal Op Amp

2.1.3 Differential and Common-Mode Signals ;9)'+$11)*)%3$"('$%073'-$&%"('v>.'$-'-$/0(4'39)'+$11)*)%.)',)36))%'39)'362'$%073'-$&%"(vC'"%+'vQX'39"3'$-5

v >. = v Q ! v C

C=

;9)' .2//2%B/2+)' $%073' -$&%"(' v>0-' $-' 39)' "#)*"&)' 21' 39)' 362' $%073' -$&%"(-' vC' "%+' vQX %"/)(45

v >0- = CBBQB ( v C + v Q )

Q=

@K7"3$2%-'C='"%+'Q='."%',)'7-)+'32')M0*)--'39)'$%073'-$&%"(-'vC'"%+'vQ'$%'3)*/-'21'39)$* +$11)*)%3$"('"%+'.2//2%B/2+)'.2/02%)%3-'"-'12((26-:

v C = v >0- ! v >. ⁄ Q

T=

v Q = v >0- + v >. ⁄ Q

'U=

"%+

;9)-)')K7"3$2%-'."%'$%'37*%'()"+'32'39)'0$.32*$"('*)0*)-)%3"3$2%'$%'S$&>'Q>U>'''''' 1

1

v1 " !

vIcm 2

" !

! "

vId #2

! "

vId #2 2

v2 " !

Figure 2.4 O)0*)-)%3"3$2%'21'39)'-$&%"('-27*.)-'vC'"%+'vQ'$%'3)*/-'21'39)$*'+$11)*)%3$"('"%+'.2//2%B/2+)' .2/02%)%3->

EXERCISES 2.2' G2%-$+)*'"%'20'"/0'39"3'$-'$+)"(')M.)03'39"3'$3-'20)%B(220'&"$%'$'='CFT>';9)'20'"/0'$-'7-)+'$%'"'1))+B ,".8'.$*.7$35'"%+'39)'#2(3"&)-'"00)"*$%&'"3'362'21'$3-'39*))'-$&%"('3)*/$%"(-'"*)'/)"-7*)+>'A%')".9'21 39)'12((26$%&'."-)-5'7-)'39)'/)"-7*)+'#"(7)-'32'1$%+'39)')M0).3)+'#"(7)'21'39)'#2(3"&)'"3'39)'39$*+'3)*B /$%"(>'H(-2'&$#)'39)'+$11)*)%3$"('"%+'.2//2%B/2+)'$%073'-$&%"(-'$%')".9'."-)>'<"='vQ'='F'`'"%+'vT'= Q `X'<,='vQ'='+V'`'"%+'vT'='−CF'`X'<.='vC'='C>FFQ'`'"%+'vQ'='F>DDc'`X'<+='vC'='−T>E'`'"%+'vT'='−T>E'`> Ans. <"='vC'='−F>FFQ'`5'v>.'='Q'/`5'v>0-'Z'−C'/`X'<,='vC'='+V>FC'`5'v>.'='−CF'/`5'v>0-'='V>FFV'!'V `X <.= vT'='−U'`5%v>.'='−U'/`5'v>0-'= C'`X'<+='vQ'='−T>EFTE'`5'v>.'='−T>E'/`5'v>0-'!'−T>E'`

57

58 Chapter 2 Operational Amplifiers 2.3' ;9)'$%3)*%"('.$*.7$3'21'"'0"*3$.7("*'20'"/0'."%',)'/2+)()+',4'39)'.$*.7$3'-926%'$%'S$&>'@Q>T>'@M0*)-vT'"-'"'17%.3$2%'21'vC'"%+'vQ>'S2*'39)'."-)'A-'='CF'/Hd`5'?'='CF'8Ω5'"%+' µ'='CFF5'1$%+'39)'#"(7)'21 39)'20)%B(220'&"$%'$> Ans. vT'= µA-?
Figure E2.3

2.2 The Inverting Configuration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v>>' ;9)' 273073' 21' 39)' 2#)*"((' .$*.7$3' $-' 3"8)%' "3' 3)*/$%"(' T' <$>)>5 ,)36))%' 3)*/$%"(' T' "%+

2.2 The Inverting Configuration

Figure 2.5 ;9)'$%#)*3$%&'.(2-)+B(220 .2%1$&7*"3$2%>

&*27%+=>';)*/$%"('T'$-5'21'.27*-)5'"'.2%#)%$)%3'02$%3'1*2/'69$.9'32'3"8)'39)'2730735'-$%.)'39) $/0)+"%.)'()#)('39)*)'$-'$+)"((4'[)*2>';97-'39)'#2(3"&)'vB'6$(('%23'+)0)%+'2%'39)'#"(7)'21'39)'.7*B *)%3'39"3'/$&93',)'-700($)+'32'"'(2"+'$/0)+"%.)'.2%%).3)+',)36))%'3)*/$%"('T'"%+'&*27%+>

2.2.1 The Closed-Loop Gain Y)'%26'6$-9'32'"%"(4[)'39)'.$*.7$3'$%'S$&>'Q>V'32'+)3)*/$%)'39)'0-.4$1/-..(*',!"*A5'+)1$%)+'"-

v A ≡ BBBBBB v> Y)'6$(('+2'-2'"--7/$%&'39)'20'"/0'32',)'$+)"(>'S$&7*)'Q>E<"='-926-'39)')K7$#"()%3'.$*.7$35 "%+'39)'"%"(4-$-'0*2.))+-'"-'12((26-:';9)'&"$%'$'$-'#)*4'("*&)'<$+)"((4'$%1$%$3)=>'A1'6)'"--7/) 39"3' 39)' .$*.7$3' $-' ^62*8$%&_' "%+' 0*2+7.$%&' "' 1$%$3)' 273073' #2(3"&)' "3' 3)*/$%"(' T5' 39)%' 39) #2(3"&)' ,)36))%' 39)' 20B"/0' $%073' 3)*/$%"(-' -927(+' ,)' %)&($&$,(4' -/"((' "%+' $+)"((4' [)*2> L0).$1$."((45'$1'6)'."(('39)'273073'#2(3"&)'vB5'39)%5',4'+)1$%$3$2%5

v v Q ! v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e73'3)*/$%"('Q'9"00)%-'32',)'.2%B %).3)+'32'&*27%+X'397-'vQ'='F'"%+'vC'='F>'Y)'-0)"8'21'3)*/$%"('C'"-',)$%&'"'#!%&),-*'%.)"1f 39"3'$-5'9"#$%&'[)*2'#2(3"&)',73'%23'094-$."((4'.2%%).3)+'32'&*27%+>' P26'39"3'6)'9"#)'+)3)*/$%)+'vC'6)'"*)'$%'"'02-$3$2%'32'"00(4'?9/J-'("6'"%+'1$%+'39) .7**)%3')C'39*27&9'?C'<-))'S$&>'Q>E='"-'12((26-:

v> ! vC v> ! F v B = BBBBBBBBBBBB B = BBBBB> ) C = BBBBBBBBBBBBBB ?C ?C ?C Y9)*)'6$(('39$-'.7**)%3'&2\'A3'."%%23'&2'$%32'39)'20'"/05'-$%.)'39)'$+)"('20'"/0'9"-'"%'$%1$%$3) $%073'$/0)+"%.)'"%+'9)%.)'+*"6-'[)*2'.7**)%3>'A3'12((26-'39"3')C'6$(('9"#)'32'1(26'39*27&9'?Q'32 39)'(26B$/0)+"%.)'3)*/$%"('T>'Y)'."%'39)%'"00(4'?9/J-'("6'32'?Q'"%+'+)3)*/$%)'vBX'39"3'$-5

;97-5

vB = vC ! )C ?Q v = F ! BBBBB> ? Q ?C v ? BBBBBB = ! BBBBBQ v> ?C

59

60 Chapter 2 Operational Amplifiers

5 3

4 ! 1

" 6

2

Figure 2.6 H%"(4-$-'21'39)'$%#)*3$%&'.2%1$&7*"3$2%>';9)'.$*.()+'%7/,)*-'$%+$."3)'39)'2*+)*'21'39)'"%"(4-$-' -3)0->

69$.9'$-'39)'*)K7$*)+'.(2-)+B(220'&"$%>'S$&7*)'Q>E<,=%$((7-3*"3)-'39)-)'-3)0-'"%+'$%+$."3)-',4 39)'.$*.()+'%7/,)*-'39)'2*+)*'$%'69$.9'39)'"%"(4-$-'$-'0)*12*/)+> Y)'397-'-))'39"3'39)'.(2-)+B(220'&"$%'$-'-$/0(4'39)'*"3$2'21'39)'362'*)-$-3"%.)-'?Q'"%+'?C> ;9)' /$%7-' -$&%' /)"%-' 39"3' 39)' .(2-)+B(220' "/0($1$)*' 0*2#$+)-' -$&%"(' $%#)*-$2%>' ;97-' $1 ? Q ⁄ ? C = CF '"%+'6)'"00(4'"3'39)'$%073''e)."7-)'21'39)'/$%7-'-$&%'"--2.$"3)+'6$39'39)'.(2-)+B(220'&"$%5'39$-'.2%1$&B 7*"3$2%'$-'."(()+'39)'!"#$%&!"'*0."3!')%,&!.">

2.2 The Inverting Configuration

;9)' 1".3' 39"3' 39)' .(2-)+B(220' &"$%' +)0)%+-' )%3$*)(4' 2%' )M3)*%"(' 0"--$#)' .2/02%)%3<*)-$-32*-'?C'"%+'?Q='$-'#)*4'-$&%$1$."%3>'A3'/)"%-'39"3'6)'."%'/"8)'39)'.(2-)+B(220'&"$%'""..7*"3)' "-' 6)' 6"%3' ,4' -)().3$%&' 0"--$#)' .2/02%)%3-' 21' "00*20*$"3)' "..7*".4>' A3' "(-2 /)"%-'39"3'39)'.(2-)+B(220'&"$%'$-'<$+)"((4='$%+)0)%+)%3'21'39)'20B"/0'&"$%>';9$-'$-'"'+*"B /"3$.'$((7-3*"3$2%'21'%)&"3$#)'1))+,".8:'Y)'-3"*3)+'273'6$39'"%'"/0($1$)*'9"#$%&'#)*4'("*&) &"$%' $5' "%+' 39*27&9' "00(4$%&' %)&"3$#)' 1))+,".8' 6)' 9"#)' 2,3"$%)+' "' .(2-)+B(220' &"$% ? Q ⁄ ? C'39"3'$-'/7.9'-/"(()*'39"%'$',73'$-'-3",()'"%+'0*)+$.3",()>';9"3'$-5'6)'"*)'3*"+$%&'&"$% 12*'"..7*".4>

2.2.2 Effect of Finite Open-Loop Gain ;9)'02$%3-'W7-3'/"+)'"*)'/2*)'.()"*(4'$((7-3*"3)+',4'+)*$#$%&'"%')M0*)--$2%'12*'39)'.(2-)+B (220'&"$%'7%+)*'39)'"--7/03$2%'39"3'39)'20B"/0'20)%B(220'&"$%'$'$-'1$%$3)>'S$&7*)'Q>I'-92639)' "%"(4-$->' A1' 6)' +)%23)' 39)' 273073' #2(3"&)' vB5' 39)%' 39)' #2(3"&)' ,)36))%' 39)' 362' $%073 3)*/$%"(-'21'39)'20'"/0'6$((',)' v B ⁄ $>'L$%.)'39)'02-$3$#)'$%073'3)*/$%"('$-'&*27%+)+5'39) #2(3"&)'"3'39)'%)&"3$#)'$%073'3)*/$%"('/7-3',)' ! v B ⁄ $> ';9)'.7**)%3')C'39*27&9'?C'."%'%26',) 127%+'1*2/

v> ! ( !vB ⁄ $ ) v> + vB ⁄ $ B ) C = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB = BBBBBBBBBBBBBBBBBBBBBBB ?C ?C

Figure 2.7 H%"(4-$-' 21' 39)' $%#)*3$%& .2%1$&7*"3$2%'3"8$%&'$%32'"..27%3'39)'1$%$3) 20)%B(220'&"$%'21'39)'20'"/0>

;9)'$%1$%$3)'$%073'$/0)+"%.)'21'39)'20'"/0'12*.)-'39)'.7**)%3')C'32'1(26')%3$*)(4'39*27&9 ?Q>';9)'273073'#2(3"&)'vB'."%'397-',)'+)3)*/$%)+'1*2/

v v B = ! BBBBBB ! ) C ? Q $ vB v> + vB ⁄ $ B ?Q = ! BBBBB ' ! ' BBBBBBBBBBBBBBBBBBBBBBB ?C $ G2(().3$%&'3)*/-5'39)'.(2-)+B(220'&"$%'A'$-'127%+'"-

v !?Q ⁄ ?C B A ≡ BBBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB C + ( C + ?Q ⁄ ?C ) ⁄ $ v>

V=

Y)'%23)'39"3'"-'$'"00*2".9)-'∞5'A'"00*2".9)-'39)'$+)"('#"(7)'21' ! ? Q ⁄ ? C > 'H(-25'1*2/'S$&>'Q>I 6)'-))'39"3'"-'$'"00*2".9)-'∞5'39)'#2(3"&)'"3'39)'$%#)*3$%&'$%073'3)*/$%"('"00*2".9)-'[)*2> ;9$-'$-'39)'#$*37"(B&*27%+'"--7/03$2%'6)'7-)+'$%'27*')"*($)*'"%"(4-$-'69)%'39)'20'"/0'6"-

61

62 Chapter 2 Operational Amplifiers "--7/)+' 32' ,)' $+)"(>' S$%"((45' %23)' 39"3' @K>' V=' $%' 1".3' $%+$."3)-' 39"3' 32' /$%$/$[) 39) +)0)%+)%.)'21'39)' .(2-)+B(220' &"$%' A'2%' 39)'#"(7)'21'39)' 20)%B(220' &"$%'$5'6)' -927(+ /"8)

? C + BBBBBQ '$'$ ?C

Example 2.1 G2%-$+)*'39)'$%#)*3$%&'.2%1$&7*"3$2%'6$39'?C'='C'8Ω'"%+'?Q'='CFF'8Ω> <"= S$%+'39)'.(2-)+B(220'&"$%'12*'39)'."-)-'$'='CFT5'CFU5'"%+'CFV>'A%')".9'."-)'+)3)*/$%)'39)'0)*.)%3"&) )**2*'$%'39)'/"&%$37+)'21'A'*)("3$#)'32'39)'$+)"('#"(7)'21' ? Q ⁄ ? C '<2,3"$%)+'6$39'$'='∞=>'H(-2'+)3)*B /$%)'39)'#2(3"&)'vC'39"3'"00)"*-'"3'39)'$%#)*3$%&'$%073'3)*/$%"('69)%'v>'='F>C'`> <,= A1'39)'20)%B(220'&"$%'$'.9"%&)-'1*2/'CFF5FFF'32'VF5FFF'<$>)>5'+*20-',4'VFg=5'69"3'$-'39)'.2**)-02%+B $%&'0)*.)%3"&)'.9"%&)'$%'39)'/"&%$37+)'21'39)'.(2-)+B(220'&"$%'A\

Solution <"= L7,-3$373$%&'39)'&$#)%'#"(7)-'$%'@K>'V=5'6)'2,3"$%'39)'#"(7)-'&$#)%'$%'39)'12((26$%&'3",()5'69)*)'39) 0)*.)%3"&)')**2*'ε'$-'+)1$%)+'"A ! (? ⁄ ? ) ( ?Q ⁄ ?C )

Q C B × CFF ε ≡ BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

;9)'#"(7)-'21'vC'"*)'2,3"$%)+'1*2/' v C = ! v B ⁄ $ = Av > ⁄ $ '6$39'v>'='F>C'`> A

|G|

CFT CFU CFV

'DF>cT DD>FF DD>DF

ε −D>CIg −C>FFg −F>CFg

v1 −D>Fc'/` −F>DD'/` −F>CF'/`

<,= a-$%&'@K>'V=5'6)'1$%+'39"3'12*'$'='VF5FFF5'|A|'='DD>cF>';97-'"'−VFg'.9"%&)'$%'39)'20)%B(220'&"$% *)-7(3-'$%'"'.9"%&)'21'2%(4'−F>Cg'$%'39)'.(2-)+B(220'&"$%N

2.2.3 Input and Output Resistances H--7/$%&'"%'$+)"('20'"/0'6$39'$%1$%$3)'20)%B(220'&"$%5'39)'$%073'*)-$-3"%.)'21'39)'.(2-)+B(220 $%#)*3$%&'"/0($1$)*'21'S$&>'Q>V'$-'-$/0(4')K7"('32'?C>';9$-'."%',)'-))%'1*2/'S$&>'Q>E<,=5'69)*)

v v> B = ?C ? ) ≡ BBBB> = BBBBBBBBBBBBB )C v> ⁄ ?C P26'*)."(('39"3'$%'L).3$2%'C>V'6)'()"*%)+'39"3'39)'"/0($1$)*'$%073'*)-$-3"%.)'12*/-'"'#2(3"&) +$#$+)*'6$39'39)'*)-$-3"%.)'21'39)'-27*.)'39"3'1))+-'39)'"/0($1$)*>';97-5'32'"#2$+'39)'(2--'21'-$&%"( -3*)%&395'#2(3"&)'"/0($1$)*-'"*)'*)K7$*)+'32'9"#)'9$&9'$%073'*)-$-3"%.)>'A%'39)'."-)'21'39)'$%#)*3B $%&'20B"/0'.2%1$&7*"3$2%'6)'"*)'-37+4$%&5'32'/"8)'?)'9$&9'6)'-927(+'-)().3'"'9$&9'#"(7)'12*'?C> !26)#)*5'$1'39)'*)K7$*)+'&"$%' ? Q ⁄ ? C $-'"(-2'9$&95'39)%'?Q'.27(+',).2/)'$/0*".3$."((4'("*&) <)>&>5'&*)"3)*'39"%'"'1)6'/)&29/-=>'Y)'/"4'.2%.(7+)'39"3'39)'$%#)*3$%&'.2%1$&7*"3$2%'-711)*1*2/'"'(26'$%073'*)-$-3"%.)>'H'-2(73$2%'32'39$-'0*2,()/'$-'+$-.7--)+'$%'@M"/0()'Q>Q',)(26>'

2.2 The Inverting Configuration

L$%.)'39)'273073'21'39)'$%#)*3$%&'.2%1$&7*"3$2%'$-'3"8)%'"3'39)'3)*/$%"(-'21'39)'$+)"('#2(3"&) -27*.)'$'Q>E"=5'$3'12((26-'39"3'39)'273073'*)-$-3"%.)'21'39)'.(2-)+B(220'"/0($B 1$)*'$-'[)*2>

Example 2.2 H--7/$%&'39)'20'"/0'32',)'$+)"(5'+)*$#)'"%')M0*)--$2%'12*'39)'.(2-)+B(220'&"$%' v B ⁄ v > '21'39)'.$*.7$3 -926%'$%'S$&>'Q>c>'a-)'39$-'.$*.7$3'32'+)-$&%'"%'$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'CFF'"%+'"%'$%073 *)-$-3"%.)'21'C'RΩ>'H--7/)'39"3'12*'0*".3$."('*)"-2%-'$3'$-'*)K7$*)+'%23'32'7-)'*)-$-32*-'&*)"3)*'39"% C'RΩ>'G2/0"*)'427*'+)-$&%'6$39'39"3',"-)+'2%'39)'$%#)*3$%&'.2%1$&7*"3$2%'21'S$&>'Q>V>

5 4

vx

7

x 6 3

2

! 1

" 8

Figure 2.8 G$*.7$3'12*'@M"/0()'Q>Q>';9)'.$*.()+'%7/,)*-'$%+$."3)'39)'-)K7)%.)'21'39)'-3)0-'$%'39)'"%"(4-$->

Solution ;9)'"%"(4-$-',)&$%-'"3'39)'$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/05'69)*)'39)'#2(3"&)'$!v !v v C = BBBBBBBBBB = BBBBBBBBBB = F $ ∞

!)*)'6)'9"#)'"--7/)+'39"3'39)'.$*.7$3'$-'^62*8$%&_'"%+'0*2+7.$%&'"'1$%$3)'273073'#2(3"&)'vB>'h%26B $%&'vC5'6)'."%'+)3)*/$%)'39)'.7**)%3')C'"-'12((26-: v> ! F v v> ! vC B = BBBBBBBBBBBB B = BBBBB> ) C = BBBBBBBBBBBBBB ?C ?C ?C

L$%.)'[)*2'.7**)%3'1(26-'$%32'39)'$%#)*3$%&'$%073'3)*/$%"(5'"(('21')C'6$(('1(26'39*27&9'?Q5'"%+'397v ) Q = ) C = BBBBB> ?C

P26'6)'."%'+)3)*/$%)'39)'#2(3"&)'"3'%2+)'C: ? v v C = v C ! ) Q ? Q = F' ! ' BBBBB> ? Q = ! BBBBBQ v > ?C ?C

63

64 Chapter 2 Operational Amplifiers Example 2.2 continued

;9$-'$%'37*%')%",()-'7-'32'1$%+'39)'.7**)%3')T: ?Q F!v Bv ) T = BBBBBBBBBBBBBC = BBBBBBBBBBB ?T ?C ?T > P)M35'"'%2+)')K7"3$2%'"3'C'4$)(+-')U: ?Q v Bv ) U = ) Q + ) T = BBBBB> + BBBBBBBBBBB ?C ?C ?T > S$%"((45'6)'."%'+)3)*/$%)'vB'1*2/ vB = vC ! )U ?U ?Q ? v Bv ? = ! BBBBBQ v > ! BBBBB> + BBBBBBBBBBB ?C ?C ?C ?T > U ;97-'39)'#2(3"&)'&"$%'$-'&$#)%',4 vB ? ? ? BBBBBB = ! BBBBBQ + BBBBBU C + BBBBBQB v> ?C ?C ?T 69$.9'."%',)'6*$33)%'$%'39)'12*/ ? ? ? vB BBBBBB = ! BBBBBQ C + BBBBBU + BBBBBU v> ?C ?Q ?T

P265'-$%.)'"%'$%073'*)-$-3"%.)'21'C'RΩ'$-'*)K7$*)+5'6)'-)().3'?C'='C'RΩ>';9)%5'6$39'39)'($/$3"B 3$2%'21'7-$%&'*)-$-32*-'%2'&*)"3)*'39"%'C'RΩ5'39)'/"M$/7/'#"(7)'02--$,()'12*'39)'1$*-3'1".32*'$%'39) &"$%')M0*)--$2%'$-'C'"%+'$-'2,3"$%)+',4'-)().3$%&'?Q'='C'RΩ>';2'2,3"$%'"'&"$%'21'−CFF5'?T'"%+'?U /7-3',)'-)().3)+'-2'39"3'39)'-).2%+'1".32*'$%'39)'&"$%')M0*)--$2%'$-'CFF>'A1'6)'-)().3'39)'/"M$/7/ "((26)+'<$%'39$-')M"/0()='#"(7)'21'C'RΩ'12*'?U5'39)%'39)'*)K7$*)+'#"(7)'21'?T'."%',)'."(.7("3)+'32 ,)'CF>Q'8Ω>';97-'39$-'.$*.7$3'73$($[)-'39*))'CBRΩ'*)-$-32*-'"%+'"'CF>QB8Ω'*)-$-32*>'A%'.2/0"*$-2%5 $1'39)'$%#)*3$%&'.2%1$&7*"3$2%'6)*)'7-)+'6$39'?C'='C'RΩ'6)'627(+'9"#)'*)K7$*)+'"'1))+,".8'*)-$-B 32*'21'CFF'RΩ5'"%'$/0*".3$."((4'("*&)'#"(7)N e)12*)'()"#$%&'39$-')M"/0()'$3'$-'$%-$&9317('32'$%K7$*)'$%32'39)'/).9"%$-/',4'69$.9'39)'.$*.7$3'$",()'32'*)"($[)'"'("*&)'#2(3"&)'&"$%'6$39273'7-$%&'("*&)'*)-$-3"%.)-'$%'39)'1))+,".8'0"39>';26"*+'39"3 )%+5'2,-)*#)'39"3',)."7-)'21'39)'#$*37"('&*27%+'"3'39)'$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/05'?Q'"%+%?T "*)'$%')11).3'$%'0"*"(()(>';97-5',4'/"8$%&'?T'(26)*'39"%'?Q',45'-"45'"'1".32*'@'<$>)>5''69)*)'@'>'C=5'?T'$12*.)+'32'."**4'"'.7**)%3'@B3$/)-'39"3'$%'?Q>';97-5'69$()')Q'=')C5')T ='@)C%"%+')U'='<@'+'C=)C>'A3'$-'39)'.7**)%3 /7(3$0($."3$2%',4'"'1".32*'21'<@'+'C='39"3')%",()-'"'("*&)'#2(3"&)'+*20'32'+)#)(20'".*2--'?U'"%+'9)%.)'" ("*&)'vB'6$39273'7-$%&'"'("*&)'#"(7)'12*'?U>'P23$.)'"(-2'39"3'39)'.7**)%3'39*27&9'?U'$-'$%+)0)%+)%3'21'39) #"(7)'21'?U>'A3'12((26-'39"3'39)'.$*.7$3'."%',)'7-)+'"-'"'.7**)%3'"/0($1$)*'"-'-926%'$%'S$&>'Q>D>' i2 % iI

i4

R2

R4

R3 v1 % 0 iI

R2 i3 % i R3 I ! "

"

i4 % 1 "

#

R2 i R3 I

Figure 2.9 H'.7**)%3'"/0($1$)*',"-)+'2%'39) .$*.7$3' 21' S$&>' Q>c>' ;9)' "/0($1$)*' +)($#)*-' $3273073' .7**)%3' 32' ?U>' A3' 9"-' "' .7**)%3' &"$%' 21 ';9)'(2"+')>5'%)$39)*'21'$3-'362'3)*/$B %"(-'."%',)'.2%%).3)+'32'&*27%+=>

2.2 The Inverting Configuration

EXERCISES D2.4' a-)'39)'.$*.7$3'21'S$&>'Q>V'32'+)-$&%'"%'$%#)*3$%&'"/0($1$)*'9"#$%&'"'&"$%'21'−CF'"%+'"%'$%073'*)-$-3B "%.)'21'CFF'8Ω>'i$#)'39)'#"(7)-'21'?C%"%+'?Q> Ans. ?C'='CFF'8ΩX'?Q'Z'C'RΩ 2.5' ;9)'.$*.7$3'-926%'$%'S$&>'@Q>V<"='."%',)'7-)+'32'$/0()/)%3'"'3*"%-*)-$-3"%.)'"/0($1$)*'<-))';",() C>C'$%'L).3$2%'C>V=>'S$%+'39)'#"(7)'21'39)'$%073'*)-$-3"%.)'?)5'39)'3*"%-*)-$-3"%.)'?-5'"%+'39)'273073 *)-$-3"%.)'?1'21'39)'3*"%-*)-$-3"%.)'"/0($1$)*>'A1'39)'-$&%"('-27*.)'-926%'$%'S$&>'@Q>V<,='$-'.2%%).3)+ 32'39)'$%073'21'39)'3*"%-*)-$-3"%.)'"/0($1$)*5'1$%+'$3-'273073'#2(3"&)> Ans. ?)'='FX'?-'= −CF'8ΩX'?1'='FX'vB'Z'−V'`

Figure E2.5

2.6' S2*'39)'.$*.7$3'$%'S$&>'@Q>E'+)3)*/$%)'39)'#"(7)-'21'vC5')C5')Q5'vB5')D5'"%+')B>'H(-2'+)3)*/$%)'39)'#2(3"&) &"$%' v B ⁄ v > 5 '.7**)%3'&"$%' ) D ⁄ ) > 5 '"%+'026)*'&"$%' E B ⁄ E > > Ans. F'`X'C'/HX'C'/HX'−CF'`X'−CF'/HX'−CC'/HX'−CF'`d`'
1 k& v1

1V

" !

10 k&

! "

iO iL

vO

1 k&

Figure E2.6

2.2.4 An Important Application—The Weighted Summer H'#)*4'$/02*3"%3'"00($."3$2%'21'39)'$%#)*3$%&'.2%1$&7*"3$2%'$-'39)'6)$&93)+B-7//)*'.$*B .7$3'-926%'$%'S$&>'Q>CF>'!)*)'6)'9"#)'"'*)-$-3"%.)'?2'$%'39)'%)&"3$#)B1))+,".8'0"39'<",)12*)=X',73'6)'9"#)'"'%7/,)*'21'$%073'-$&%"(-'vC5'vQ5'>'>'>'5' v*')".9'"00($)+'32'"'.2**)B -02%+$%&'*)-$-32*'?C5'?Q5'>'>'>'5'?*5'69$.9'"*)'.2%%).3)+'32'39)'$%#)*3$%&'3)*/$%"('21'39)'20 "/0>'S*2/'27*'0*)#$27-'+$-.7--$2%5'39)'$+)"('20'"/0'6$(('9"#)'"'#$*37"('&*27%+'"00)"*$%&

65

66 Chapter 2 Operational Amplifiers "3' $3-' %)&"3$#)' $%073' 3)*/$%"(>' ?9/J-' ("6' 39)%' 3)((-' 7-' 39"3' 39)' .7**)%3-' )C5' )Q5' >' >' >' 5' )*' "*) &$#)% ,4

v ) Q = BBBBQB, ?Q

v ) C = BBBBCB, ?C

>'>'>',

v ) * = BBBB*B ?*

0

Figure 2.10 H'6)$&93)+'-7//)*>

H(('39)-)'.7**)%3-'-7/'32&)39)*'32'0*2+7.)'39)'.7**)%3')X'39"3'$-5

) = )C + )Q + … + )*

E=

6$((',)'12*.)+'32'1(26'39*27&9'?2'<-$%.)'%2'.7**)%3'1(26-'$%32'39)'$%073'3)*/$%"(-'21'"%'$+)"('20 "/0=>';9)'273073'#2(3"&)'vB'/"4'%26',)'+)3)*/$%)+',4'"%239)*'"00($."3$2%'21'?9/J-'("65

v B = F ! )? 2 = ! )? 2 ;97-5

?2 ?2 ?2 v B = ! ' BBBBB v C + BBBBB v Q + … + BBBBB v * ' ?C ?Q ?*

'I=

;9"3'$-5'39)'273073'#2(3"&)'$-'"'6)$&93)+'-7/'21'39)'$%073'-$&%"(-'vC5'vQ5'>'>'>'5'v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

? v B = v C BBBBB/ ?C

? ? BBBBB0 + v Q BBBBB/ ?5 ?Q

? ? ? BBBBB0 ! v T BBBBB0 ! v U BBBBB0 ?5 ?T ?U

'''' ''

c=

2.3 The Noninverting Configuration

Rc

Ra

v1 v2

R1 !

Rb

"

R3

!

R2

v3

vO

"

R4

v4

Figure 2.11 H'6)$&93)+'-7//)*'."0",()'21'$/0()/)%3$%&'-7//$%&'.2)11$.$)%3-'21',239'-$&%->

EXERCISES D2.7' j)-$&%' "%' $%#)*3$%&' 20B"/0' .$*.7$3' 32' 12*/' 39)' 6)$&93)+' -7/' vB' 21' 362' $%073-' vC' "%+' vQ>' A3' $*)K7$*)+'39"3'vB'= − 'G922-)'#"(7)-'12*'?C5'?Q5'"%+'?2''-2'39"3'12*'"'/"M$/7/'273073'#2(3B "&)'21'CF'`'39)'.7**)%3'$%'39)'1))+,".8'*)-$-32*'6$(('%23')M.))+'C'/H> Ans. H'02--$,()'.92$.):'?C'='CF'8Ω5'?Q'='Q'8Ω5'"%+'?2''='CF'8Ω D2.8' a-)'39)'$+)"'0*)-)%3)+'$%'S$&>'Q>CC'32'+)-$&%'"'6)$&93)+'-7//)*'39"3'0*2#$+)v B = Qv C + v Q ! Uv T Ans. H'02--$,()'.92$.):'?C'='V'8Ω5'?Q'='CF'8Ω5'?/%='CF'8Ω5'?5'='CF'8Ω5'?T'='Q>V'8Ω5 ?0'='CF'8Ω>''

2.3 The Noninverting Configuration ;9)'-).2%+'.(2-)+B(220'.2%1$&7*"3$2%'6)'-9"(('-37+4'$-'-926%'$%'S$&>'Q>CQ>'!)*)'39)'$%073 -$&%"('v>'$-'"00($)+'+$*).3(4'32'39)'02-$3$#)'$%073'3)*/$%"('21'39)'20'"/0'69$()'2%)'3)*/$%"('21 ?C'$-'.2%%).3)+'32'&*27%+>''

2.3.1 The Closed-Loop Gain H%"(4-$-'21'39)'%2%$%#)*3$%&'.$*.7$3'32'+)3)*/$%)'$3-'.(2-)+B(220'&"$%' ( v B ⁄ v > ) '$-'$((7-3*"3)+ $%' S$&>' Q>CT>' H&"$%' 39)' 2*+)*' 21' 39)' -3)0-' $%' 39)' "%"(4-$-' $-' $%+$."3)+' ,4' .$*.()+' %7/,)*-> H--7/$%&'39"3'39)'20'"/0'$-'$+)"('6$39'$%1$%$3)'&"$%5'"'#$*37"('-92*3'.$*.7$3')M$-3-',)36))%'$3362'$%073'3)*/$%"(->'!)%.)'39)'+$11)*)%.)'$%073'-$&%"('$-

v v >. = BBBBBB = F $

12*'$ = ∞ '

;97-'39)'#2(3"&)'"3'39)'$%#)*3$%&'$%073'3)*/$%"('6$((',)')K7"('32'39"3'"3'39)'%2%$%#)*3$%&'$%073 3)*/$%"(5'69$.9'$-'39)'"00($)+'#2(3"&)'v>>';9)'.7**)%3'39*27&9'?C'."%'39)%',)'+)3)*/$%)+'"v > ⁄ ? C>'e)."7-)'21'39)'$%1$%$3)'$%073'$/0)+"%.)'21'39)'20'"/05'39$-'.7**)%3'6$(('1(26'39*27&9 ?Q5'"-'-926%'$%'S$&>'Q>CT>'P26'39)'273073'#2(3"&)'."%',)'+)3)*/$%)+'1*2/

v v B = v > + BBBBB> ? Q ?C

67

68 Chapter 2 Operational Amplifiers

Figure 2.12 ;9)'%2%$%#)*3$%&'.2%1$&7*"3$2%>

5 3

vI R1

vI R1

2v I

R1

! 0 1 vId % 0 V 4 " " vI !

R2 vO % vI "

!

"

R vI R % vI 1 " 2 R1 2 R1

6

" vO !

Figure 2.13 H%"(4-$-'21'39)'%2%$%#)*3$%&'.$*.7$3>';9)'-)K7)%.)'21'39)'-3)0-'$%'39)'"%"(4-$-'$-'$%+$."3)+',4' 39)'.$*.()+'%7/,)*->

69$.9'4$)(+-

vB ? BBBBB = C + BBBBBQ ' v> ?C

D=

S7*39)*'$%-$&93'$%32'39)'20)*"3$2%'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'."%',)'2,3"$%)+',4 .2%-$+)*$%&'39)'12((26$%&:'L$%.)'39)'.7**)%3'$%32'39)'20B"/0'$%#)*3$%&'$%073'$-'[)*25'39)'.$*B .7$3'.2/02-)+'21'?C'"%+'?Q'".3-'$%')11).3'"-'"'#2(3"&)'+$#$+)*'1))+$%&'"'1*".3$2%'21'39)'273073 #2(3"&)',".8'32'39)'$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/0X'39"3'$-5

?C B v C = v B BBBBBBBBBBBBBBBB ?C + ?Q

'CF=

;9)%'39)'$%1$%$3)'20B"/0'&"$%'"%+'39)'*)-7(3$%&'#$*37"('-92*3'.$*.7$3',)36))%'39)'362'$%073'3)*/$B %"(-'21'39)'20'"/0'12*.)-'39$-'#2(3"&)'32',)')K7"('32'39"3'"00($)+'"3'39)'02-$3$#)'$%073'3)*/$%"(X'397-5

?C v B BBBBBBBBBBBBBBBBB ?C + ?Q

= v>

69$.9'4$)(+-'39)'&"$%')M0*)--$2%'&$#)%'$%'@K>'D=> ;9$-'$-'"%'"00*20*$"3)'02$%3'32'*)1().3'17*39)*'2%'39)'".3$2%'21'39)'%)&"3$#)'1))+,".8'0*)-)%3 $%' 39)' %2%$%#)*3$%&' .$*.7$3' 21' S$&>' Q>CQ>' k)3' v>' $%.*)"-)>' L7.9' "' .9"%&)' $%' v>' 6$((' ."7-)' v>.' 32 $%.*)"-)5'"%+'vB'6$(('.2**)-02%+$%&(4'$%.*)"-)'"-'"'*)-7(3'21'39)'9$&9'<$+)"((4'$%1$%$3)='&"$%'21'39) 20'"/0>'!26)#)*5'"'1*".3$2%'21'39)'$%.*)"-)'$%'vB%6$((',)'1)+',".8'32'39)'$%#)*3$%&'$%073'3)*/$%"( 21'39)'20'"/0'39*27&9'39)'';9)'*)-7(3'21'39$-'1))+,".8'6$((',)'32'.27%3)*B ".3'39)'$%.*)"-)'$%'v>. 5'+*$#$%&'v>.',".8'32'[)*25'"(,)$3'"3'"'9$&9)*'#"(7)'21'vB'39"3'.2**)-02%+-'32 39)'$%.*)"-)+'#"(7)'21'v> >';9$-'.(<(*(8/&);('".3$2%'21'%)&"3$#)'1))+,".8'&$#)-'$3'39)'"(3)*%"3$#) %"/)'1$'$"$%,&!#$*3$$15,06>'S$%"((45'%23)'39"3'39)'"*&7/)%3'",2#)'"00($)-')K7"((4'6)(('$1'v> +).*)"-)->'H'12*/"('"%+'+)3"$()+'-37+4'21'1))+,".8'$-'0*)-)%3)+'$%'G9"03)*'CF>'

2.3 The Noninverting Configuration

2.3.2 Effect of Finite Open-Loop Gain H-'6)'9"#)'+2%)'12*'39)'$%#)*3$%&'.2%1$&7*"3$2%5'6)'%26'.2%-$+)*'39)')11).3'21'39)'1$%$3) 20B"/0'20)%B(220'&"$%'$'2%'39)'&"$%'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%>'H--7/$%&'39)'20'"/0 32',)'$+)"(')M.)03'12*'9"#$%&'"'1$%$3)'20)%B(220'&"$%'$5'$3'."%',)'-926%'39"3'39)'.(2-)+B(220 &"$%'21'39)'%2%$%#)*3$%&'"/0($1$)*'.$*.7$3'21'S$&>'Q>CQ'$-'&$#)%',4

v C 2 ( ?Q ⁄ ?C ) A ≡ BBBBBB 3 BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B v> C 2 ( ?Q ⁄ ?C ) C 2 BBBBBBBBBBBBBBBBBBBBBBBBBBBBB $

"#$%%&

?,-)*#)'39"3'39)'+)%2/$%"32*'$-'$+)%3$."('32'39"3'12*'39)'."-)'21'39)'$%#)*3$%&'.2%1$&7*"3$2% <@K>'Q>V=>';9$-'$-'%2'.2$%.$+)%.)X'$3'$-'"'*)-7(3'21'39)'1".3'39"3',239'39)'$%#)*3$%&'"%+'39)'%2%B $%#)*3$%&'.2%1$&7*"3$2%-'9"#)'39)'-"/)'1))+,".8'(2205'69$.9'."%',)'*)"+$(4'-))%'$1'39)'$%073 -$&%"('-27*.)'$-')($/$%"3)+'<$>)>5'-92*3B.$*.7$3)+=>';9)'%7/)*"32*-5'926)#)*5'"*)'+$11)*)%35'12* 39)'%7/)*"32*'&$#)-'39)'$+)"('2*'%2/$%"('.(2-)+B(220'&"$%'< ! ? Q ⁄ ? C '12*'39)'$%#)*3$%&'.2%B 1$&7*"3$2%5'"%+' C 2 ? Q ⁄ ? C 12*'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%=>'S$%"((45'6)'%23)'<6$39'*)"-B -7*"%.)='39"3'39)'&"$%')M0*)--$2%'$%'@K>'CC='*)+7.)-'32'39)'$+)"('#"(7)'12*'$'='∞>'A%'1".35'$3 "00*2M$/"3)-'39)'$+)"('#"(7)'12*

?Q l C 2 BBBBB $> l ?C ;9$-'$-'39)'-"/)'.2%+$3$2%'"-'$%'39)'$%#)*3$%&'.2%1$&7*"3$2%5')M.)03'39"3'9)*)'39)'K7"%3$34'2% 39)'*$&93B9"%+'-$+)'$-'39)'%2/$%"('.(2-)+B(220'&"$%>;9)')M0*)--$2%-'12*'39)'".37"('"%+'$+)"( #"(7)-'21'39)'.(2-)+B(220'&"$%'A'$%'@K->'CC='"%+'D=5'*)-0).3$#)(45'."%',)'7-)+'32'+)3)*B /$%)'39)'0)*.)%3"&)')**2*'$%'A'*)-7(3$%&'1*2/'39)'1$%$3)'20B"/0'&"$%'$'"C 2 ( ?Q ⁄ ?C ) B × CFF '()*(+,-./0+-())1)- 3 ! BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB $ 2 C 2 ( ?Q ⁄ ?C )

"#$%#&

;97-5'"-'"%')M"/0()5'$1'"%'20'"/0'6$39'"%'20)%B(220'&"$%'21'CFFF'$-'7-)+'32'+)-$&%'"'%2%$%B #)*3$%&'"/0($1$)*'6$39'"'%2/$%"('.(2-)+B(220'&"$%'21'CF5'6)'627(+')M0).3'39)'.(2-)+B(220 &"$%'32',)'",273'Cg',)(26'39)'%2/$%"('#"(7)>

2.3.3 Input and Output Resistance ;9)'&"$%'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'$-'02-$3$#)f9)%.)'39)'%"/)'*1*)*;(8&)*<>';9) $%073'$/0)+"%.)'21'39$-'.(2-)+B(220'"/0($1$)*'$-'$+)"((4'$%1$%$3)5'-$%.)'%2'.7**)%3'1(26-'$%32 39)'02-$3$#)'$%073'3)*/$%"('21'39)'20'"/0>';9)'273073'21'39)'%2%$%#)*3$%&'"/0($1$)*'$-'3"8)% "3'39)'3)*/$%"(-'21'39)'$+)"('#2(3"&)'-27*.)'$'Q>T=5'397-'39)'273073'*)-$-3"%.)'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'$-'[)*2>

2.3.4 The Voltage Follower ;9)'0*20)*34'21'9$&9'$%073'$/0)+"%.)'$-'"'#)*4'+)-$*",()'1)"37*)'21'39)'%2%$%#)*3$%&'.2%1$&7*"B 3$2%>'A3')%",()-'7-$%&'39$-'.$*.7$3'"-'"',711)*'"/0($1$)*'32'.2%%).3'"'-27*.)'6$39'"'9$&9'$/0)+B "%.)'32'"'(26B$/0)+"%.)'(2"+>'Y)'9"#)'+$-.7--)+'39)'%))+'12*',711)*'"/0($1$)*-'$%'L).3$2%'C>V> A%'/"%4'"00($."3$2%-'39)',711)*'"/0($1$)*'$-'%23'*)K7$*)+'32'0*2#$+)'"%4'#2(3"&)'&"$%X'*"39)*5'$3 $-'7-)+'/"$%(4'"-'"%'$/0)+"%.)'3*"%-12*/)*'2*'"'026)*'"/0($1$)*>'A%'-7.9'."-)-'6)'/"4'/"8) ?Q'='F'"%+'?C'='∞'32'2,3"$%'39)')"!&9/',!"*,+(-!3!$%'-926%'$%'S$&> Q>CU<"=>';9$-'.$*.7$3'$.2//2%(4'*)1)**)+'32'"-'"'#.-&,'$*3.--.8$%5'-$%.)'39)'273073'^12((26-_'39)'$%073>'A%'39)'$+)"( ."-)5'vB'= v> 5'?$%'='∞5'?273'='F5'"%+'39)'12((26)*'9"-'39)')K7$#"()%3'.$*.7$3'-926%'$%'S$&>'Q>CU<,=>'

69

70 Chapter 2 Operational Amplifiers

!

" vI

" vO % vI

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vI

1 ' vI

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Figure 2.14 :,;';9)'7%$34B&"$%',711)*'2*'12((26)*'"/0($1$)*>':5;'A3-')K7$#"()%3'.$*.7$3'/2+)(>

L$%.)'$%'39)'#2(3"&)B12((26)*'.$*.7$3'39)')%3$*)'273073'$-'1)+',".8'32'39)'$%#)*3$%&'$%0735 39)'.$*.7$3'$-'-"$+'32'9"#)'CFFg'%)&"3$#)'1))+,".8>';9)'$%1$%$3)'&"$%'21'39)'20'"/0'39)%'".332'/"8)'v>.'='F'"%+'9)%.)'vB'='v>>'?,-)*#)'39"3'39)'.$*.7$3'$-')()&"%3'$%'$3-'-$/0($.$34N' L$%.)'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'9"-'"'&"$%'&*)"3)*'39"%'2*')K7"('32'7%$345'+)0)%+$%& 2%'39)'.92$.)'21' ? Q ⁄ ? C5'-2/)'0*)1)*'32'."(('$3'^"'12((26)*'6$39'&"$%>_'''

EXERCISES 2.9' a-)'39)'-70)*02-$3$2%'0*$%.$0()'32'1$%+'39)'273073'#2(3"&)'21'39)'.$*.7$3'-926%'$%'S$&>'@Q>D> Ans. vB'='EvC'+'UvQ

Figure E2.9

2.10' A1'$%'39)'.$*.7$3'21'S$&>'@Q>D'39)'CB8Ω'*)-$-32*'$-'+$-.2%%).3)+'1*2/'&*27%+'"%+'.2%%).3)+'32'"'39$*+ -$&%"('-27*.)'vT5'7-)'-70)*02-$3$2%'32'+)3)*/$%)'vB'$%'3)*/-'21'vC5'vQ5'"%+'vT> Ans. vB'='EvC'+'UvQ'−'DvT' D2.11 j)-$&%'"'%2%$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'Q>'H3'39)'/"M$/7/'273073'#2(3"&)'21'CF'`'39)'.7*B *)%3'$%'39)'#2(3"&)'+$#$+)*'$-'32',)'CF'µH> Ans. ?C'='?Q'='F>V'RΩ 2.12' <"='L926'39"3'$1'39)'20'"/0'$%'39)'.$*.7$3'21'S$&>'Q>CQ'9"-'"'1$%$3)'20)%B(220'&"$%'$5'39)%'39)'.(2-)+B (220'&"$%'$-'&$#)%',4'@K>'CC=>'<,='S2*'?C'='C'8Ω'"%+'?Q'='D'8Ω'1$%+'39)'0)*.)%3"&)'+)#$"3$2%'ε 21'39)'.(2-)+B(220'&"$%'1*2/'39)'$+)"('#"(7)'21' ( C 2 ? Q ⁄ ? C ) '12*'39)'."-)-'$'='CFT5'CFU5'"%+'CFV> S2*'v>'='C'`5'1$%+'$%')".9'."-)'39)'#2(3"&)',)36))%'39)'362'$%073'3)*/$%"(-'21'39)'20'"/0> Ans. ε'='−Cg5'− F>Cg5 − F>FCgX'vQ'−'vC'='D>D'/`5'C'/`5'F>C'/`

2.4 Difference Amplifiers

2.13' S2*'39)'.$*.7$3'$%'S$&>'@Q>CT'1$%+'39)'#"(7)-'21')>5'vC5')C5')Q5'vB5%)D5'"%+')B>'H(-2'1$%+'39)'#2(3"&)'&"$% v B ⁄ v > 5 '39)'.7**)%3'&"$%' ) D ⁄ ) > 5 '"%+'39)'026)*'&"$%' E D ⁄ E > > Ans. FX'C'`X'C'/HX'C'/HX'CF'`X'CF'/HX'CC'/HX'CF'`d`'
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2.14' A3'$-'*)K7$*)+'32'.2%%).3'"'3*"%-+7.)*'9"#$%&'"%'20)%B.$*.7$3'#2(3"&)'21'C'`'"%+'"'-27*.)'*)-$-3"%.) 21'C RΩ'32'"'(2"+'21'CB8Ω'*)-$-3"%.)>'S$%+'39)'(2"+'#2(3"&)'$1'39)'.2%%).3$2%'$-'+2%)'<"='+$*).3(4'"%+ <,= 39*27&9'"'7%$34B&"$%'#2(3"&)'12((26)*> Ans. <"='C'/`X'<,='C'`

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v B = $ . v >. + $ 0- v >0-

CT=

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$. B GROO = QF'(2& BBBBBBBBBBB $ 0Q

CU=

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71

72 Chapter 2 Operational Amplifiers vI1 % vIcm ! vId #2 ! "

vId #2 vId % vI2 ! vI1 1 2

vIcm % (vI1 " vI2) vIcm

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vId #2 vI2 % vIcm " vId #2

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?U ? ? BBBBBBBBBBBBBBBBB C + BBBBBQ = BBBBBQ ?U + ?T ?C ?C 69$.9'."%',)'073'$%'39)'12*/

?U ?Q BBBBBBBBBBBBBBBBB = BBBBBBBBBBBBBBBBB ?U + ?T ?Q + ?C ;9$-'.2%+$3$2%'$-'-"3$-1$)+',4'-)().3$%&

? ? BBBBBU = BBBBBQ ?T ?C

CV=

2.4 Difference Amplifiers

vI 1 vI 2

Figure 2.16 H'+$11)*)%.)'"/0($1$)*>

;9$-'.2/0()3)-'27*'62*8>'!26)#)*5'6)'9"#)'0)*9"0-'0*2.))+)+'"'($33()'322'1"-3N'k)3J-'-3)0 ,".8'"%+'#)*$14'39"3'39)'.$*.7$3'$%'S$&>'Q>CE'6$39'?T'"%+'?U'-)().3)+'"..2*+$%&'32'@K>'CV= +2)-'$%'1".3'17%.3$2%'"-'"'+$11)*)%.)'"/0($1$)*>'L0).$1$."((45'6)'6$-9'32'+)3)*/$%)'39)'273073 #2(3"&)'vB'$%'3)*/-'21'v>C'"%+'v> Q>';26"*+'39"3')%+5'6)'2,-)*#)'39"3'39)'.$*.7$3'$-'($%)"*5'"%+ 397-'6)'."%'7-)'-70)*02-$3$2%> ;2' "00(4' -70)*02-$3$2%5' 6)' 1$*-3' *)+7.)' v> Q' 32' [)*2⎯39"3' $-5' &*27%+' 39)' 3)*/$%"(' 32 69$.9' v>Q' $-' "00($)+⎯"%+' 39)%' 1$%+' 39)' .2**)-02%+$%&' 273073' #2(3"&)5' 69$.9' 6$((' ,)' +7) )%3$*)(4'32'v>C>'Y)'+)%23)'39$-'273073'#2(3"&)'vBC>'A3-'#"(7)'/"4',)'127%+'1*2/'39)'.$*.7$3'$% S$&>'Q>CI<"=5'69$.9'6)'*).2&%$[)'"-'39"3'21'39)'$%#)*3$%&'.2%1$&7*"3$2%>';9)')M$-3)%.)'21'?T "%+'?U'+2)-'%23'"11).3'39)'&"$%')M0*)--$2%5'-$%.)'%2'.7**)%3'1(26-'39*27&9')$39)*'21'39)/> ;97-5

? v BC 3 ! BBBBBQ v >C ?C P)M35'6)'*)+7.)'v>C'32'[)*2'"%+')#"(7"3)'39)'.2**)-02%+$%&'273073'#2(3"&)'vBQ>';9)'.$*.7$3 6$(('%26'3"8)'39)'12*/'-926%'$%'S$&>'Q>CI<,=5'69$.9'6)'*).2&%$[)'"-'39)'%2%$%#)*3$%&'.2%B 1$&7*"3$2%'6$39'"%'"++$3$2%"('#2(3"&)'+$#$+)*5'/"+)'70'21'?T'"%+'?U5'.2%%).3)+'32'39)'$%073 v>Q>';9)'273073'#2(3"&)'vBQ'$-'39)*)12*)'&$#)%',4

?U ? ? B C + BBBBBQ = BBBBBQ v >Q v BQ = v >Q BBBBBBBBBBBBBBBB ?T + ?U ?C ?C 69)*)'6)'9"#)'73$($[)+'@K>'CV=> ;9)'-70)*02-$3$2%'0*$%.$0()'3)((-'7-'39"3'39)'273073'#2(3"&)'vB'$-')K7"('32'39)'-7/'21'vBC "%+'vBQ>';97-'6)'9"#)

? ?C

? ?C

'v B = BBBBBQ ( v >Q ! v >C )' = BBBBBQ v >. ''''

CE=

;97-5'"-')M0).3)+5'39)'.$*.7$3'".3-'"-'"'+$11)*)%.)'"/0($1$)*'6$39'"'+$11)*)%3$"('&"$%'$.'21

? $ . = BBBBBQ ?C

CI=

?1'.27*-)'39$-'$-'0*)+$."3)+'2%'39)'20'"/0',)$%&'$+)"('"%+'17*39)*/2*)'2%'39)'-)().3$2%'21'?T "%+' ?U' -2' 39"3' 39)$*' *"3$2' /"3.9)-' 39"3' 21' ?C' "%+' ?Q' <@K>' Q>CV=>' ;2' /"8)' 39$-' /"3.9$%& *)K7$*)/)%3'"'($33()')"-$)*'32'-"3$-145'6)'7-7"((4'-)().3

73

74 Chapter 2 Operational Amplifiers

vI1 vI 2

Figure 2.17 H00($."3$2%'21'-70)*02-$3$2%'32'39)'"%"(4-$-'21'39)'.$*.7$3'21'S$&>'Q>CE>

?T = ?C

"%+

?U = ?Q

k)3J-' %)M3' .2%-$+)*' 39)' .$*.7$3' 6$39' 2%(4' "' .2//2%B/2+)' -$&%"(' "00($)+' "3' 39)' $%0735' "-926%'$%'S$&>'Q>Cc>';9)'1$&7*)'"(-2'-926-'-2/)'21'39)'"%"(4-$-'-3)0->';97-5

?U C Bv ) C = BBBBB v >0- ! BBBBBBBBBBBBBBBB ? U + ? T >0?C ?T C BBBBB = v >0- BBBBBBBBBBBBBBBBB ?U + ?T ?C

Cc=

;9)'273073'#2(3"&)'."%'%26',)'127%+'1*2/'

?U Bv ! ) ? v B = BBBBBBBBBBBBBBBB ? U + ? T >0- Q Q L7,-3$373$%&')Q'=')C'"%+'12*')C'1*2/'@K>'Cc=5

? ? ? ?U + ?T ?C ?U + ?T ?U ?Q ?T = BBBBBBBBBBBBBBBBB C ! BBBBB ' BBBBB v >0?U + ?T ?C ?U

U T B v >0- ! BBBBBQ BBBBBBBBBBBBBBBB B v >0' v B = BBBBBBBBBBBBBBBB

;97-5

vB ?U ? ? B C ! BBBBBQ ' BBBBBT $ 0- ≡ BBBBBBBB = BBBBBBBBBBBBBBBB v >0?U + ?T ?C ?U

CD=

S2*'39)'+)-$&%'6$39'39)'*)-$-32*'*"3$2-'-)().3)+'"..2*+$%&'32'@K>'CV=5'6)'2,3"

%$$ 0- = F "-')M0).3)+>'P23)5'926)#)*5'39"3'"%4'/$-/"3.9'$%'39)'*)-$-3"%.)'*"3$2-'."%'/"8)'$0-'%2%[)*25 "%+'9)%.)'GROO'1$%$3)>'' A%'"++$3$2%'32'*)W).3$%&'.2//2%B/2+)'-$&%"(-5'"'+$11)*)%.)'"/0($1$)*'$-'7-7"((4'*)K7$*)+ 32'9"#)'"'9$&9'$%073'*)-$-3"%.)>';2'1$%+'39)'$%073'*)-$-3"%.)',)36))%'39)'362'$%073'3)*/$%"(-

2.4 Difference Amplifiers

i2 i1

R2

R1 ! vO "

R3 vIcm

" !

"

#

R4

R4 v R4 " R3 Icm

Figure 2.18 H%"(4-$-'21'39)'+$11)*)%.)'"/0($1$)*'32'+)3)*/$%)'$3-'.2//2%B/2+)'&"$%' $ 0- ≡ v B ⁄ v >0- > '

<$>)>5'39)'*)-$-3"%.)'-))%',4'v>.=5'."(()+'39)'1!33$%$"&!,-*!"()&*%$4!4&,"0$'?). 5'.2%-$+)*'S$&>'Q>CD> !)*)'6)'9"#)'"--7/)+'39"3'39)'*)-$-32*-'"*)'-)().3)+'-2'39"3

?T = ?C

"%+

?U = ?Q

P26

v ? ). ≡ BBBBB>.B )> L$%.)'39)'362'$%073'3)*/$%"(-'21'39)'20'"/0'3*".8')".9'239)*'$%'023)%3$"(5'6)'/"4'6*$3)'" (220')K7"3$2%'"%+'2,3"

%$v >. = ? C ) > + F + ? C ) > ;97-5

? ). = Q? C

QF=

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I

vId

Rid

I

Figure 2.19 S$%+$%&'39)'$%073'*)-$-B 3"%.)' 21' 39)' +$11)*)%.)' "/0($1$)*' 12* 39)'."-)'?T'='?C'"%+'?U'='?Q>

75

76 Chapter 2 Operational Amplifiers

EXERCISES 2.15 G2%-$+)*'39)'+$11)*)%.)B"/0($1$)*'.$*.7$3'21'S$&>'Q>CE'12*'39)'."-)'?C'='?T'='Q'8Ω'"%+'?Q'='?U'=

QFF 8Ω>'<"='S$%+'39)'#"(7)'21'39)'+$11)*)%3$"('&"$%'$.>'<,='S$%+'39)'#"(7)'21'39)'+$11)*)%3$"('$%073 *)-$-3"%.)'?).'"%+'39)'273073'*)-$-3"%.)'?1>'<.='A1'39)'*)-$-32*-'9"#)'Cg'32()*"%.)'<$>)>5')".9'."%',) 6$39$%'±Cg'21'$3-'%2/$%"('#"(7)=5'7-)'@K>'CD='32'1$%+'39)'62*-3B."-)'.2//2%B/2+)'&"$%'$0"%+'9)%.)'39)'.2**)-02%+$%&'#"(7)'21'GROO> Ans. <"='CFF'`d`'FU'`d`5'Ec'+e

D2.16 S$%+'#"(7)-'12*'39)'*)-$-3"%.)-'$%'39)'.$*.7$3'21'S$&>'Q>CE'-2'39"3'39)'.$*.7$3',)9"#)-'"-'"'+$11)*)%.)

"/0($1$)*'6$39'"%'$%073'*)-$-3"%.)'21'QF'8Ω'"%+'"'&"$%'21'CF> Ans. ?C'='?T'='CF'8ΩX'?Q'='?U'='CFF'8Ω

2.4.2 A Superior Circuit—The Instrumentation Amplifier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

"1 " RR # v 2

vI1

" A1 ! R2

1

I1

R4

R1

R3

! A3 "

X R1

R3

R2

R4

" vO !

vI2

! A2 "

"1 " RR # v 2 1

I2

(a) Figure 2.20 H'0207("*'.$*.7$3'12*'"%'$%-3*7/)%3"3$2%'"/0($1$)*>':,;'A%$3$"('"00*2".9'32'39)'.$*.7$3':5;';9) .$*.7$3'$%':,;'6$39'39)'.2%%).3$2%',)36))%'%2+)'m'"%+'&*27%+'*)/2#)+'"%+'39)'362'*)-$-32*-'?C'"%+'?C'(7/0)+ 32&)39)*>' ;9$-' -$/0()' 6$*$%&' .9"%&)' +*"/"3$."((4' $/0*2#)-' 0)*12*/"%.)>' :0;' H%"(4-$-' 21' 39)' .$*.7$3' $% :5; "--7/$%&'$+)"('20'"/0->

2.4 Difference Amplifiers

vI1

" A1 !

R4

R2

R3 !

2R1 !

A3

R3

"

R2

vO

R4

A2

vI2

"

!

" (b)

vI1

"

"

0

vI1

! R 2

R4 R3

vId /2R1

! (vI2 ! vI1) % vId " vI2

vI2

vO1

A1

0V !

2R1

! 0V "

! 2R2 vId 1 " 2R1 "

vId 2R1 vId /2R1

0 !

A3 " R3 R4

R2 A2

! " vO %

R4 R 1" 2 R3 R1

vId

! vO2

" (c )

Figure 2.20 <"1*&)*,(.=

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⁄ ? C )>'A3'12((26-'39"3')".9'21'v>C'"%+'v>Q'$-'"/0($1$)+',4 39$-'1".32*5'"%+'39)'*)-7(3$%&'"/0($1$)+'-$&%"(-'"00)"*'"3'39)'273073-'21'$C'"%+'$Q5'*)-0).3$#)(4> ;9)' +$11)*)%.)' "/0($1$)*' $%' 39)' -).2%+' -3"&)' 20)*"3)-' 2%' 39)' +$11)*)%.)' -$&%"( ( C + ? Q ⁄ ? C ) ( v >Q ! v >C ) =' ( C + ? Q ⁄ ? C )v >. '"%+'0*2#$+)-'"3'$3-'273073

? ? v B = BBBBBU C + BBBBBQ v >. ?T ?C ;97-'39)'+$11)*)%3$"('&"$%'*)"($[)+'$-

? ? $ . = BBBBBU C + BBBBBQ ?T ?C

QC=

77

78 Chapter 2 Operational Amplifiers ;9)'.2//2%B/2+)'&"$%'6$((',)'[)*2',)."7-)'21'39)'+$11)*)%.$%&'".3$2%'21'39)'-).2%+B-3"&) "/0($1$)*> ;9)'.$*.7$3'$%'S$&>'Q>QF<"='9"-'39)'"+#"%3"&)'21'#)*4'9$&9'<$+)"((4'$%1$%$3)='$%073'*)-$-B 3"%.)'"%+'9$&9'+$11)*)%3$"('&"$%>'H(-25'0*2#$+)+'$C'"%+'$Q'"%+'39)$*'.2**)-02%+$%&'*)-$-32*"*)'/"3.9)+5'39)'362'-$&%"('0"39-'"*)'-4//)3*$.⎯"'+)1$%$3)'"+#"%3"&)'$%'39)'+)-$&%'21'"'+$1B 1)*)%3$"('"/0($1$)*>';9)'.$*.7$35'926)#)*5'9"-'39*))'/"W2*'+$-"+#"%3"&)-: 1. ;9)'$%073'.2//2%B/2+)'-$&%"('v>0-'$-'"/0($1$)+'$%'39)'1$*-3'-3"&)',4'"'&"$%')K7"('32 39"3')M0)*$)%.)+',4'39)'+$11)*)%3$"('-$&%"('v>.>';9$-'$-'"'#)*4'-)*$27-'$--7)5'12*'$3'.27(+ *)-7(3'$%'39)'-$&%"(-'"3'39)'273073-'21'$C'"%+'$T',)$%&'21'-7.9'("*&)'/"&%$37+)-'39"3'39) 20'"/0-'-"37*"3)'c=>'e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m5'1*2/'&*27%+>';9)'.$*.7$3'6$39'39$-'-/"(( ,73'17%.3$2%"((4'0*2127%+'.9"%&)'$-'*)+*"6%'$%'S$&>'Q>QF<,=5'69)*)'6)'9"#)'(7/0)+'39)'362 *)-$-32*-' H%"(4-$-'21'39)'.$*.7$3'$%'S$&>'Q>QF<,=5'"--7/$%&'$+)"('20'"/0-5'$-'-3*"$&9312*6"*+5'"-'$$((7-3*"3)+'$%'S$&>'Q>QF<.=>';9)'8)4'02$%3'$-'39"3'39)'#$*37"('-92*3'.$*.7$3-'"3'39)'$%073-'21'20 "/0-'$C'"%+'$Q'."7-)'39)'$%073'#2(3"&)-'v>C'"%+'v>Q'32'"00)"*'"3'39)'362'3)*/$%"(-'21'*)-$-32* ';97-'39)'+$11)*)%3$"('$%073'#2(3"&)'v>Q'−'v>C'≡'v>.'"00)"*-'".*2--'Q?C'"%+'."7-)-'"'.7**)%3 ) = v >. ⁄ Q? C%32'1(26'39*27&9'Q?C'"%+'39)'362'*)-$-32*-'(",)()+'?Q>';9$-'.7**)%3'$%'37*%'0*2B +7.)-'"'#2(3"&)'+$11)*)%.)',)36))%'39)'273073'3)*/$%"(-'21'$C'"%+'$Q'&$#)%',4

Q? v BQ ! v BC = C + BBBBBBBBQB v >. Q? C ;9)'+$11)*)%.)'"/0($1$)*'12*/)+',4'20'"/0'$T'"%+'$3-'"--2.$"3)+'*)-$-32*-'-)%-)-'39)'#2(3"&) +$11)*)%.)'
? v B = BBBBBU ( v BQ ! v BC ) ?T ?U ? = BBBBB C + BBBBBQB v >. ?T ?C ;97-'39)'2#)*"(('+$11)*)%3$"('#2(3"&)B&"$%'$-'&$#)%',4

v ? ? $ . ≡ BBBBBBB = BBBBBU C + BBBBBQB v >. ?T ?C

QQ=

?,-)*#)'39"3'0*20)*'+$11)*)%3$"('20)*"3$2%'+2)-'*1&'+)0)%+'2%'39)'/"3.9$%&'21'39)'362'*)-$-32*(",)()+'?Q>'A%+))+5'$1'2%)'21'39)'362'$-'21'+$11)*)%3'#"(7)5'-"4'?Q′5 39)')M0*)--$2%'12*'$.',).2/)-

? Q + ?′Q ? B $ . = BBBBBU C + BBBBBBBBBBBBBBBBBB Q? C ?T

QT=

2.4 Difference Amplifiers

G2%-$+)*'%)M3'69"3'9"00)%-'69)%'39)'362'$%073'3)*/$%"(-'"*)'.2%%).3)+'32&)39)*'32'"'.2//2%B /2+)'$%073'#2(3"&)'v>0->'A3'$-')"-4'32'-))'39"3'"%')K7"('#2(3"&)'"00)"*-'"3'39)'%)&"3$#)'$%073'3)*/$%"(21'$C'"%+'$Q5'."7-$%&'39)'.7**)%3'39*27&9'Q?C'32',)'[)*2>';97-'39)*)'6$((',)'%2'.7**)%3'1(26$%&'$%'39) ?Q'*)-$-32*-5'"%+'39)'#2(3"&)-'"3'39)'273073'3)*/$%"(-'21'$C'"%+'$Q'6$((',)')K7"('32'39)'$%073'<$>)>5'v>0-=> ;97-'39)'1$*-3'-3"&)'%2'(2%&)*'"/0($1$)-'v>0-X'$3'-$/0(4'0*20"&"3)-'v>0-'32'$3-'362'273073'3)*/$%"(-5 69)*)'39)4'"*)'-7,3*".3)+'32'0*2+7.)'"'[)*2'.2//2%B/2+)'273073',4'$T>';9)'+$11)*)%.)'"/0($1$)* $%'39)'-).2%+'-3"&)5'926)#)*5'%26'9"-'"'/7.9'$/0*2#)+'-$37"3$2%'"3'$3-'$%073:';9)'+$11)*)%.)'-$&%"( 9"-',))%'"/0($1$)+',4'( C + ? Q ⁄ ? C )'69$()'39)'.2//2%B/2+)'#2(3"&)'*)/"$%)+'7%.9"%&)+> S$%"((45' 6)' 2,-)*#)' 1*2/' 39)' )M0*)--$2%' $%' @K>' QQ=' 39"3' 39)' &"$%' ."%' ,)' #"*$)+' ,4 .9"%&$%&'2%(4'2%)'*)-$-32*5'Q?C>'Y)'.2%.(7+)'39"3'39$-'$-'"%')M.)(()%3'+$11)*)%3$"('"/0($1$)* .$*.7$3'"%+'$-'6$+)(4')/0(24)+'"-'"%'$%-3*7/)%3"3$2%'"/0($1$)*X'39"3'$-5'"-'39)'$%073'"/0($1$)* 7-)+'$%'"'#"*$)34'21')().3*2%$.'$%-3*7/)%3->

Example 2.3 j)-$&%'39)'$%-3*7/)%3"3$2%'"/0($1$)*'.$*.7$3'$%'S$&>'Q>QF<,='32'0*2#$+)'"'&"$%'39"3'."%',)'#"*$)+'2#)* 39)'*"%&)'21'Q'32'CFFF'73$($[$%&'"'CFFB8Ω'#"*$",()'*)-$-3"%.)'<"'023)%3$2/)3)*5'2*'^023_'12*'-92*3=> Solution A3'$-'7-7"((4'0*)1)*",()'32'2,3"$%'"(('39)'*)K7$*)+'&"$%'$%'39)'1$*-3'-3"&)5'()"#$%&'39)'-).2%+'-3"&)'32 0)*12*/'39)'3"-8'21'3"8$%&'39)'+$11)*)%.)',)36))%'39)'273073-'21'39)'1$*-3'-3"&)'"%+'39)*),4'*)W).3$%&'39) .2//2%B/2+)'-$&%"(>'A%'239)*'62*+-5'39)'-).2%+'-3"&)'$-'7-7"((4'+)-$&%)+'12*'"'&"$%'21'C>'H+203$%& 39$-'"00*2".95'6)'-)().3'"(('39)'-).2%+B-3"&)'*)-$-32*-'32',)')K7"('32'"'0*".3$."((4'.2%#)%$)%3'#"(7)5 -"4'CF'8Ω>';9)'0*2,()/'39)%'*)+7.)-'32'+)-$&%$%&'39)'1$*-3'-3"&)'32'*)"($[)'"'&"$%'"+W7-3",()'2#)*'39) *"%&)'21'Q'32'CFFF>'A/0()/)%3$%&'Q?C'"-'39)'-)*$)-'.2/,$%"3$2%'21'"'1$M)+'*)-$-32*'?C2'"%+'39)'#"*$B ",()'*)-$-32*'?Cv'2,3"$%)+'7-$%&'39)'CFFB8Ω'023''Q>QC=5'6)'."%'6*$3) Q? Q C + BBBBBBBBBBBBBBBBBBBBB = Q'32'CFFF ? C2 + ? Cv

;97-5 Q? C + BBBBBBBBQB = CFFF ? C2

"%+ Q? Q B = Q C + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB ? C2 + CFF'8Ω

;9)-)' 362' )K7"3$2%-' 4$)(+' ?C2' =' CFF>Q' Ω' "%+' ?Q' =' VF>FVF' 8Ω>' ?39)*' 0*".3$."(' #"(7)-' /"4' ,) -)().3)+X' 12*' $%-3"%.)5' ?C2' =' CFF' Ω' "%+' ?Q' =' UD>D' 8Ω' <,239' #"(7)-' "*)' "#"$(",()' "-' -3"%+"*+' CgB 32()*"%.)' /)3"(B1$(/' *)-$-32*-X' -))' H00)%+$M' !=' *)-7(3-' $%' "' &"$%' .2#)*$%&' "00*2M$/"3)(4' 39) *)K7$*)+'*"%&)>

R1f 2R1

100 k& pot

R1v

Figure 2.21 ;2'/"8)'39)'&"$%'21'39)'.$*.7$3'$%'S$&>'Q>QF<,='#"*$",()5'Q?C'$$/0()/)%3)+'"-'39)'-)*$)-'.2/,$%"3$2%'21'"'1$M)+'*)-$-32*'?C2 "%+'"'#"*$",() *)-$-32*'?Cv>'O)-$-32*'?C2' )%-7*)-'39"3'39)'/"M$/7/'"#"$(",()'&"$%'$-'($/$3)+>

79

80 Chapter 2 Operational Amplifiers

EXERCISE 2.17' G2%-$+)*'39)'$%-3*7/)%3"3$2%'"/0($1$)*'21'S$&>'Q>QF<,='6$39'"'.2//2%B/2+)'$%073'#2(3"&)'21'+V'` <+.='"%+'"'+$11)*)%3$"('$%073'-$&%"('21'CFB/`B0)"8'-$%)'6"#)>'k)3'V'RΩ5'"%+ ?T'='?U'='CF'8Ω>'S$%+'39)'#2(3"&)'"3')#)*4'%2+)'$%'39)'.$*.7$3> Ans. v>C'='V'−'F>FFV'-$%'ω &X v>Q'='V'+'F>FFV'-$%'ω &X vn'<20'"/0'$C='='V'−'F>FFV'-$%'ω &X'vn'<20'"/0 $Q='='V'+'F>FFV'-$%'ω &X vBC'='V'−'V>FFV'-$%'ω &X' vBQ'='V'+'V>FFV'-$%'ω &X vn'<$T='='v +'<$T='='Q>V'+'Q>VFQV -$%'ω &X%vB'='CF>FC'-$%'ω &%<"(('$%'#2(3-=

2.5 Integrators and Differentiators ;9)' 20B"/0' .$*.7$3' "00($."3$2%-' 6)' 9"#)' -37+$)+' 397-' 1"*' 73$($[)+' *)-$-32*-' $%' 39)' 20B"/0 1))+,".8'0"39'"%+'$%'.2%%).3$%&'39)'-$&%"('-27*.)'32'39)'.$*.7$35'39"3'$-5'$%'39)'1))+B$%'0"39> H-'"'*)-7(35'.$*.7$3'20)*"3$2%'9"-',))%'<$+)"((4='$%+)0)%+)%3'21'1*)K7)%.4>'e4'"((26$%&'39) 7-)'21' ."0".$32*-' 32&)39)*' 6$39' *)-$-32*-' $%' 39)'1))+,".8'"%+' 1))+B$%' 0"39-' 21' 20B"/0' .$*B .7$3-5'6)'20)%'39)'+22*'32'"'#)*4'6$+)'*"%&)'21'7-)17('"%+')M.$3$%&'"00($."3$2%-'21'39)'20 "/0>' Y)' ,)&$%' 27*' -37+4' 21' 20B"/0n?"' .$*.7$3-' ,4' .2%-$+)*$%&' 362' ,"-$.' "00($."3$2%-5 %"/)(45'-$&%"('$%3)&*"32*-'"%+'+$11)*)%3$"32*->

2.5.1 The Inverting Configuration with General Impedances ;2',)&$%'6$395'.2%-$+)*'39)'$%#)*3$%&'.(2-)+B(220'.2%1$&7*"3$2%'6$39'$/0)+"%.)-'FC<4='"%+ FQ <4='*)0(".$%&'*)-$-32*-'?C'"%+'?Q5'*)-0).3$#)(4>';9)'*)-7(3$%&'.$*.7$3'$-'-926%'$%'S$&>'Q>QQ "%+5'12*'"%'$+)"('20'"/05'9"-'39)'.(2-)+B(220'&"$%'2*5'/2*)'"00*20*$"3)(45'39)'.(2-)+B(220 3*"%-1)*'17%.3$2%

!1 ( 4 ) FQ ( 4 ) BBBBBBBBBBBB B = − BBBBBBBBBBBB !) ( 4 ) FC ( 4 )

QU=

H-')M0("$%)+'$%'L).3$2%'C>E5'*)0(".$%&'4',4'Gω'0*2#$+)-'39)'3*"%-1)*'17%.3$2%'12*'094-$."('1*)B K7)%.$)-' ω5'39"3'$-5'39)'3*"%-/$--$2%'/"&%$37+)'"%+'09"-)'12*'"'-$%7-2$+"('$%073'-$&%"('21 1*)K7)%.4'ω>''

Figure 2.22 ;9)'$%#)*3$%&'.2%1$&7*"3$2%'6$39'&)%)*"('$/0)+"%.)-'$%'39)'1))+,".8'"%+'39)'1))+B$%'0"39->

2.5 Integrators and Differentiators

Example 2.4 S2*'39)'.$*.7$3'$%'S$&>'Q>QT5'+)*$#)'"%')M0*)--$2%'12*'39)'3*"%-1)*'17%.3$2%' !1 ( 4 ) ⁄ !) ( 4 )>'L926'39"3'39) 3*"%-1)*'17%.3$2%'$-'39"3'21'"'(26B0"--'L;G'.$*.7$3>'e4')M0*)--$%&'39)'3*"%-1)*'17%.3$2%'$%'39)'-3"%B +"*+'12*/'-926%'$%';",()'C>Q'2%'0"&)'TU5'1$%+'39)'+.'&"$%'"%+'39)'TB+e'1*)K7)%.4>'j)-$&%'39)'.$*.7$3 32'2,3"$%'"'+.'&"$%'21'UF'+e5'"'TB+e'1*)K7)%.4'21'C'8![5'"%+'"%'$%073'*)-$-3"%.)'21'C'8Ω>'H3'69"3'1*)B K7)%.4' +2)-' 39)' /"&%$37+)' 21' 3*"%-/$--$2%' ,).2/)' 7%$34\' Y9"3' $-' 39)' 09"-)' "%&()' "3' 39$1*)K7)%.4\

Figure 2.23 G$*.7$3'12*'@M"/0()'Q>U>

Solution ;2'2,3"$%'39)'3*"%-1)*'17%.3$2%'21'39)'.$*.7$3'$%'S$&>'Q>QT5'6)'-7,-3$373)'$%'@K>'QU=5'FC'='?C'"%+ F Q = ? Q || ( C ⁄ 4" Q )>'L$%.)'FQ'$-'39)'0"*"(()('.2%%).3$2%'21'362'.2/02%)%3-5'$3'$-'/2*)'.2%#)%$)%3'32 62*8'$%'3)*/-'21'HQX'39"3'$-5'6)'7-)'39)'12((26$%&'"(3)*%"3$#)'12*/'21'39)'3*"%-1)*'17%.3$2%: !1 ( 4 ) C BBBBBBBBBBBB B = ! BBBBBBBBBBBBBBBBBBBBBBBBB B !) ( 4 ) F C ( 4 )H Q ( 4 )

"%+'-7,-3$373)'FC'='?C'"%+' H Q ( 4 ) = ( C ⁄ ? Q ) + 4" Q '32'2,3"$% !1 ( 4 ) C B BBBBBBBBBBBB B = ! BBBBBBBBBBBBBBBBBBBBBBBBBB !) ( 4 ) ?C BBBBB + 4" Q ? C ?Q

;9$-'3*"%-1)*'17%.3$2%'$-'21'1$*-3'2*+)*5'9"-'"'1$%$3)'+.'&"$%' ( "3'4 = F, !1 ⁄ !) = ! ? Q ⁄ ? C )5'"%+'9"-'[)*2 &"$%'"3'$%1$%$3)'1*)K7)%.4>';97-'$3'$-'39)'3*"%-1)*'17%.3$2%'21'"'(26B0"--'L;G'%)362*8'"%+'."%',) )M0*)--)+'$%'39)'-3"%+"*+'12*/'21';",()'C>Q'"-'12((26-: !1 ( 4 ) ! ?Q ⁄ ?C BBBBBBBBBBBB B = BBBBBBBBBBBBBBBBBBBBBBB B !) ( 4 ) C + 4" Q ? Q

1*2/'69$.9'6)'1$%+'39)'+.'&"$%'I'32',) ? I = ! BBBBBQ ?C

81

82 Chapter 2 Operational Amplifiers

Example 2.4 continued

"%+'39)'TB+e'1*)K7)%.4'ω F'"C ω F = BBBBBBBBBBBB

"Q ?Q Y)'.27(+'9"#)'127%+'"(('39$-'1*2/'39)'.$*.7$3'$%'S$&>'Q>QT',4'$%-0).3$2%>'L0).$1$."((45'%23)'39"3'39) ."0".$32*' ,)9"#)-' "-' "%' 20)%' .$*.7$3' "3' +.X' 397-' "3' +.' 39)' &"$%' $-' -$/0(4' ( ! ? Q ⁄ ? C )>' S7*39)*/2*)5 ,)."7-)'39)*)'$-'"'#$*37"('&*27%+'"3'39)'$%#)*3$%&'$%073'3)*/$%"(5'39)'*)-$-3"%.)'-))%',4'39)'."0".$32* $-'?Q5'"%+'397-'39)'3$/)'.2%-3"%3'21'39)'L;G'%)362*8'$-'"Q?Q> P26'32'2,3"$%'"'+.'&"$%'21'UF'+e5'39"3'$-5'CFF'`d`5'6)'-)().3' ? Q ⁄ ? C = CFF> 'S2*'"%'$%073'*)-$-B 3"%.)'21'C'8Ω5'6)'-)().3'?C'='C'8Ω5'"%+'397-'?Q'='CFF'8Ω>'S$%"((45'12*'"'TB+e'1*)K7)%.4'2F'='C 8![5 6)'-)().3'"Q'1*2/ C T Q π × C × CF = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBTB " Q × CFF × CF

69$.9'4$)(+-'"Q'='C>VD'%S> ;9)'.$*.7$3'9"-'&"$%'"%+'09"-)'e2+)'0(23-'21'39)'-3"%+"*+'12*/'$%'S$&>'C>QT>'H-'39)'&"$%'1"((-'211'"3'39) *"3)' 21' nQF'+e/+)."+)5' $3' 6$(('*)".9' F' +e' $%'362' +)."+)-5' 39"3' $-5' "3'2' =' CFF2F' =' CFF' 8![>' H-' S$&> C>QT<,='$%+$."3)-5'"3'-7.9'"'1*)K7)%.4'69$.9'$-'/7.9'&*)"3)*'39"%'2F5'39)'09"-)'$-'"00*2M$/"3)(4'−DF°> ;2'39$-5'926)#)*5'6)'/7-3'"++'39)'CcF°'"*$-$%&'1*2/'39)'$%#)*3$%&'%"37*)'21'39)'"/0($1$)*'<$>)>5'39) %)&"3$#)'-$&%'$%'39)'3*"%-1)*'17%.3$2%')M0*)--$2%=>';97-'"3'CFF'8![5'39)'323"('09"-)'-9$13'6$((',)'−QIF° 2*5')K7$#"()%3(45'+DF°>

2.5.2 The Inverting Integrator e4'0(".$%&'"'."0".$32*'$%'39)'1))+,".8'0"39'<$>)>5'$%'0(".)'21'FQ'$%'S$&>'Q>QQ='"%+'"'*)-$-32*'"3 39)'$%073'<$%'0(".)'21'FC=5'6)'2,3"$%'39)'.$*.7$3'21'S$&>'Q>QU<"=>'Y)'-9"(('%26'-926'39"3'39$.$*.7$3' *)"($[)-' 39)' /"39)/"3$."(' 20)*"3$2%' 21' $%3)&*"3$2%>' k)3' 39)' $%073',)' "' 3$/)B#"*4$%& 17%.3$2%' v> <&=>' ;9)' #$*37"(' &*27%+' "3' 39)' $%#)*3$%&' 20B"/0' $%073' ."7-)-' v> <&=' 32' "00)"*' $% )11).3'".*2--'?5'"%+'397-'39)'.7**)%3')C<&='6$((',)' v > ( & ) ⁄ ?> ';9$-'.7**)%3'1(26-'39*27&9'39) ."0".$32*'"5'."7-$%&'.9"*&)'32'"..7/7("3)'2%'">'A1'6)'"--7/)'39"3'39)'.$*.7$3',)&$%-'20)*"B 3$2%' "3' 3$/)' &' =' F5' 39)%' "3' "%' "*,$3*"*4' 3$/)' &' 39)' .7**)%3' )C<&=' 6$((' 9"#)' +)02-$3)+' 2%' "' " & & .9"*&)')K7"('32' F ) C ( & ) .&> ';97-'39)'."0".$32*'#2(3"&)'v"<&='6$(('.9"%&)',4' BBB"CB F ) C ( & ) .&> 'A1 39)'$%$3$"('#2(3"&)'2%'"'<"3'&'='F='$-'+)%23)+'!" 5'39)%

C & v " ( & ) = !" + BBBB ) C ( & ) .& " F P26'39)'273073'#2(3"&)'vB<&='='−v"<&=X'397-5'

C v B ( & ) = ! BBBBBBBB "?

&

v > ( & ) .& ! !"

QV=

F

;97-'39)'.$*.7$3'0*2#$+)-'"%'273073'#2(3"&)'39"3'$-'0*202*3$2%"('32'39)'3$/)'$%3)&*"('21'39) $%0735'6$39'!"',)$%&'39)'$%$3$"('.2%+$3$2%'21'$%3)&*"3$2%'"%+'"?'39)'!"&$'%,&.%*&!+$*0."4&,"&> P23)'39"35'"-')M0).3)+5'39)*)'$-'"'%)&"3$#)'-$&%'"33".9)+'32'39)'273073'#2(3"&)5'"%+'397-'39$-

2.5 Integrators and Differentiators

" vC ! i1 i1 " vI (t)

R

0 0V

vO(t) % !

C ! " vO(t) !

"

!

1 CR

t

$ v (t) dt!V 0

I

C

Vo 1 %! Vi sCR

(a)

(b) Figure 2.24 :,;';9)'R$(()*'2*'$%#)*3$%&'$%3)&*"32*>':5;'S*)K7)%.4'*)-02%-)'21'39)'$%3)&*"32*>

$%3)&*"32*'.$*.7$3'$-'-"$+'32',)'"%'!"#$%&!"'*!"&$'%,&.%>'A3'$-'"(-2'8%26%'"-'"'=!--$%*!"&$'%,/ &.%'"13)*'"%')"*(4'62*8)*'$%'39$-'1$)(+> ;9)'20)*"3$2%'21'39)'$%3)&*"32*'.$*.7$3'."%',)'+)-.*$,)+'"(3)*%"3$#)(4'$%'39)'1*)K7)%.4 +2/"$%',4'-7,-3$373$%&'FC<4='='?'"%+' F Q ( 4 ) = C ⁄ 4" '$%'@K>'QU='32'2,3"$%'39)'3*"%-1)* 17%.3$2%

!1 ( 4 ) C BBBBBBBBBBBB B = ! BBBBBBBBBB !) ( 4 ) 4"?

QE=

!1 ( G ω ) C BBBBBBBBBBBBBBBBB B = ! BBBBBBBBBBBBBB !) ( G ω ) G ω "?

QI=

S2*'094-$."('1*)K7)%.$)-5'4'='Gω'"%+

;97-'39)'$%3)&*"32*'3*"%-1)*'17%.3$2%'9"-'/"&%$37+)

C !1 = BBBBBBBBBBB B BBBBB ω "? !)

Qc=

83

84 Chapter 2 Operational Amplifiers "%+'09"-)

φ = +DF°

QD=

;9)'e2+)'0(23'12*'39)'$%3)&*"32*'/"&%$37+)'*)-02%-)'."%',)'2,3"$%)+',4'%23$%&'1*2/'@K>'Qc= 39"3'"-' ω'+27,()-'<$%.*)"-)-',4'"%'2.3"#)='39)'/"&%$37+)'$-'9"(#)+'<+).*)"-)+',4'E'+e=> ;97-' 39)' e2+)' 0(23' $-' "' -3*"$&93' ($%)' 21' -(20)' nE' +e/2.3"#)' <2*5' )K7$#"()%3(45' nQF' +e/ +)."+)=>';9$-'($%)'<-926%'$%'S$&>'Q>QU,='$%3)*.)03-'39)'FB+e'($%)'"3'39)'1*)K7)%.4'39"3'/"8)!1 ⁄ !) = C5 '69$.9'1*2/'@K>'Qc='$-

C ω )*& = BBBBBBBB ' "?

TF=

;9)'1*)K7)%.4' ω)*&'$-'8%26%'"-'39)'!"&$'%,&.%*3%$?)$"09'"%+'$-'-$/0(4'39)'$%#)*-)'21'39) $%3)&*"32*'3$/)'.2%-3"%3> G2/0"*$-2%'21'39)'1*)K7)%.4'*)-02%-)'21'39)'$%3)&*"32*'32'39"3'21'"%'L;G'(26B0"--'%)3B 62*8'$%+$."3)-'39"3'39)'$%3)&*"32*',)9"#)-'"-'"'(26B0"--'1$(3)*'6$39'"'.2*%)*'1*)K7)%.4'21'[)*2> ?,-)*#)'"(-2'39"3'"3' ω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n?J d? *"39)*'39"%'$%1$%$3)>'L7.9'"'*)-$-32*'0*2#$+)-'"'+.'1))+,".8'0"39>'a%12*37%"3)(45'926)#)*5'39) $%3)&*"3$2%'$-'%2'(2%&)*'$+)"(5'"%+'39)'(26)*'39)'#"(7)'21'?J 5'39)'()--'$+)"('39)'$%3)&*"32*'.$*.7$3 ,).2/)->';9$-'$-',)."7-)'?J'."7-)-'39)'1*)K7)%.4'21'39)'$%3)&*"32*'02()'32'/2#)'1*2/'$3-'$+)"( (2."3$2%'"3'ω'='F'32'2%)'+)3)*/$%)+',4'39)'.2*%)*'1*)K7)%.4'21'39)'L;G'%)362*8''L0)B .$1$."((45'39)'$%3)&*"32*'3*"%-1)*'17%.3$2%',).2/)-

!1 ( 4 ) ?J ⁄ ? BBBBBBBBBBBB B = ! BBBBBBBBBBBBBBBBBBBBB B !) ( 4 ) C + 4"? J

RF C R ! " v I (t) !

"

" vO (t) !

Figure 2.25 ;9)'R$(()*'$%3)&*"32*'6$39'"'("*&)'*)-$-3"%.)'?J .2%%).3)+'$%'0"*"(()('6$39'"'$%'2*+)*'32'0*2#$+)'%)&"3$#)'1))+B ,".8'"%+'9)%.)'1$%$3)'&"$%'"3'+.>

2.5 Integrators and Differentiators

"-' 2002-)+' 32' 39)' $+)"(' 17%.3$2%' 21' ! C ⁄ 4"? >' ;9)' (26)*' 39)' #"(7)' 6)' -)().3' 12*' ?J 5' 39) 9$&9)*' 39)' .2*%)*' 1*)K7)%.4' ( C ⁄ "? J ) ' 6$((' ,)' "%+' 39)' /2*)' %2%$+)"(' 39)' $%3)&*"32* ,).2/)->' ;97-'-)().3$%&'"'#"(7)'12*'?J'0*)-)%3-'39)'+)-$&%)*'6$39'"'3*"+)B211',)36))%'+. 0)*12*/"%.)'"%+'-$&%"('0)*12*/"%.)>';9)')11).3'21'?J'2%'$%3)&*"32*'0)*12*/"%.)'$-'$%#)-3$B &"3)+'17*39)*'$%'39)'@M"/0()'Q>V>

Example 2.5 S$%+'39)'273073'0*2+7.)+',4'"'R$(()*'$%3)&*"32*'$%'*)-02%-)'32'"%'$%073'07(-)'21'CB`'9)$&93'"%+'CB/6$+39'oS$&>'Q>QE<"=p>'k)3'?'='CF'8Ω'"%+'"'='CF'%S>'A1'39)'$%3)&*"32*'."0".$32*'$-'-97%3)+',4'"'CBRΩ *)-$-32*5'926'6$(('39)'*)-02%-)',)'/2+$1$)+\';9)'20'"/0'$-'-0).$1$)+'32'-"37*"3)'"3'±CT'`> Solution A%'*)-02%-)'32'"'CB`5'CB/-'$%073'07(-)5'39)'$%3)&*"32*'273073'6$((',) & C v B ( & ) = ! BBBBBBBB C .&5 F ≤ & ≤ C'/- '''' "? F 69)*)'6)'9"#)'"--7/)+'39"3'39)'$%$3$"('#2(3"&)'2%'39)'$%3)&*"32*'."0".$32*'$-'F>'S2*'"'='CF'%S'"%+ ?'='CF'8Ω5'"?'='F>C'/-5'"%+ v B ( & ) = ! CF&5

F ≤ & ≤ C'/-

69$.9'$-'39)'($%)"*'*"/0'-926%'$%'S$&>'Q>QE<,=>'A3'*)".9)-'"'/"&%$37+)'21' −CF'`'"3'&'='C'/-'"%+ *)/"$%-'.2%-3"%3'39)*)"13)*> ;9"3'39)'273073'$-'"'($%)"*'*"/0'-927(+'"(-2',)'2,#$27-'1*2/'39)'1".3'39"3'39)'CB`'$%073'07(-) 0*2+7.)-'"'.2%-3"%3'.7**)%3'39*27&9'39)'."0".$32*'21' C'` ⁄ CF'8Ω = F>C'/H>';9$-'.2%-3"%3'.7**)%3 > ='F>C'/H'-700($)-'39)'."0".$32*'6$39'"'.9"*&)' >&5 "%+'397-'39)'."0".$32*'#2(3"&)'.9"%&)-'($%)"*(4 "-' ( >& ⁄ " )5 '*)-7(3$%&'$%' v B = ! ( > ⁄ " )& > 'A3'$-'62*39'*)/)/,)*$%&'39"3'.9"*&$%&'"'."0".$32*'6$39'" .2%-3"%3'.7**)%3'0*2+7.)-'"'($%)"*'#2(3"&)'".*2--'$3> P)M3'.2%-$+)*'39)'-$37"3$2%'6$39'*)-$-32*' ? J = C'RΩ '.2%%).3)+'".*2--'">'H-',)12*)5'39)'CB` 07(-)'6$(('0*2#$+)'"'.2%-3"%3'.7**)%3'>%='F>C'/H>'P265'926)#)*5'39$-'.7**)%3'$-'-700($)+'32'"%'L;G %)362*8'.2/02-)+'21'?J'$%'0"*"(()('6$39'">';97-5'39)'273073'6$((',)'"%')M02%)%3$"('9)"+$%&'326"*+ −CFF'`'6$39'"'3$/)'.2%-3"%3'21'"?J'= CF ' CF−D'' C ''CFE = CF'/-5 v B ( & ) = ! CFF ( C ! (

! & ⁄ CF

)5

F ≤ & ≤ C'/-

?1'.27*-)5'39)')M02%)%3$"('6$((',)'$%3)**703)+'"3'39)')%+'21'39)'07(-)5'39"3'$-5'"3'&%='C'/-5'"%+'39)'273B 073'6$(('*)".9'39)'#"(7) v B ( C'/- ) = ! CFF ( C ! (

! C ⁄ CF

) = ! D>V'`

;9)'273073'6"#)12*/'$-'-926%'$%'S$&>'Q>QE<.=5'1*2/'69$.9'6)'-))'39"3'$%.(7+$%&'?J'."7-)-'39)'*"/0'32 ,)'-($&93(4'*27%+)+'-7.9'39"3'39)'273073'*)".9)-'2%(4'−D>V'`5'F>V'`'-92*3'21'39)'$+)"('#"(7)'21'−CF'`> S7*39)*/2*)5'12*'&%>'C'/-5'39)'."0".$32*'+$-.9"*&)-'39*27&9'?J'6$39'39)'*)("3$#)(4'(2%&'3$/)B.2%-3"%3'21 CF'/->'S$%"((45'6)'%23)'39"3'20'"/0'-"37*"3$2%5'-0).$1$)+'32'2..7*'"3'±CT'`5'9"-'%2')11).3'2%'39)'20)*"B 3$2%'21'39$-'.$*.7$3>

85

86 Chapter 2 Operational Amplifiers >

Example 2.5 continued

vI (t)

1V 0 0

t

1 ms (a)

vO (t)

0

t

1 ms

!10 V (b) vO (t)

0

t

1 ms to 0 V

!9.5 V

Exponentials with time constant of 10 ms to !100 V (c)

Figure 2.26 Y"#)12*/-'12*'@M"/0()'Q>V:':,;'A%073'07(-)>':5;'?73073'($%)"*'*"/0'21'$+)"('$%3)&*"32*'6$39'3$/)'.2%B -3"%3'21'F>C'/->':0;'?73073')M02%)%3$"('*"/0'6$39'*)-$-32*'?J'.2%%).3)+'".*2--'$%3)&*"32*'."0".$32*>

;9)'0*).)+$%&')M"/0()'9$%3-'"3'"%'$/02*3"%3'"00($."3$2%'21'$%3)&*"32*-5'%"/)(45'39)$*'7-) $%' 0*2#$+$%&' 3*$"%&7("*' 6"#)12*/-' $%' *)-02%-)' 32' -K7"*)B6"#)' $%073->' ;9$-' "00($."3$2%' $)M0(2*)+'$%'@M)*.$-)'Q>Cc>'A%3)&*"32*-'9"#)'/"%4'239)*'"00($."3$2%-5'$%.(7+$%&'39)$*'7-)'$%'39) +)-$&%'21'1$(3)*-'

2.5 Integrators and Differentiators

2.5.3 The Op-Amp Differentiator A%3)*.9"%&$%&' 39)' (2."3$2%' 21' 39)' ."0".$32*' "%+' 39)' *)-$-32*' 21' 39)' $%3)&*"32*' .$*.7$3 *)-7(3-'$%'39)'.$*.7$3'$%'S$&>'Q>QI<"=5'69$.9'0)*12*/-'39)'/"39)/"3$."('17%.3$2%'21'+$11)*B )%3$"3$2%>';2'-))'926'39$-'.2/)-'",2735'()3'39)'$%073',)'39)'3$/)B#"*4$%&'17%.3$2%' v > ( & )5 "%+' %23)' 39"3' 39)' #$*37"(' &*27%+' "3' 39)' $%#)*3$%&' $%073' 3)*/$%"(' 21' 39)' 20' "/0' ."7-)v > ( & ) ' 32' "00)"*' $%' )11).3' ".*2--' 39)' ."0".$32*' ">' ;97-' 39)' .7**)%3' 39*27&9' "' 6$((' ,) " ( .v > ⁄ .& )5 ' "%+' 39$-' .7**)%3' 1(26-' 39*27&9' 39)' 1))+,".8' *)-$-32*' ?' 0*2#$+$%&' "3' 39) 20B"/0'273073'"'#2(3"&)' v B ( & )5

.v > ( & ) B v B ( & ) = ! "? BBBBBBBBBBBBB .&

TC=

;9)'1*)K7)%.4B+2/"$%'3*"%-1)*'17%.3$2%'21'39)'+$11)*)%3$"32*'.$*.7$3'."%',)'127%+',4'-7,-3$B 373$%&'$%'@K>'QU=5' F C ( 4 ) = C ⁄ 4" '"%+' F Q ( 4 ) = ? '32'2,3"

%$!1 ( 4 ) BBBBBBBBBBBB B = ! 4"? !) ( 4 )

TQ=

69$.9'12*'094-$."('1*)K7)%.$)-' 4 = G ω '4$)(+-

!1 ( G ω ) BBBBBBBBBBBBBBBBB B = ! G ω "? !) ( G ω ) i i

C

R

0

dvI (t) dt dv (t) vO (t) % !CR I dt Vo % !sCR Vi

i (t) % C

! " vI (t) !

TT=

" vO (t) !

" 0V (a)

Vo (dB) Vi

"6 dB/octave 0

( (log scale)

1 CR (b)

Figure 2.27 :,;*H'+$11)*)%3$"32*>':5;'S*)K7)%.4'*)-02%-)'21'"'+$11)*)%3$"32*'6$39'"'3$/)B.2%-3"%3'"?>'

87

88 Chapter 2 Operational Amplifiers ;97-'39)'3*"%-1)*'17%.3$2%'9"-'/"&%$37+)

!1 BBBBB = ω "? !)

TU=

φ = ! DF°

TV=

"%+'09"-)

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EXERCISES 2.18 G2%-$+)*'"'-4//)3*$."('-K7"*)'6"#)'21'QFB`'0)"8B32B0)"85'F'"#)*"&)5'"%+'QB/-'0)*$2+'"00($)+ 32'"'R$(()*'$%3)&*"32*>'S$%+'39)'#"(7)'21'39)'3$/)'.2%-3"%3'"?'-7.9'39"3'39)'3*$"%&7("*'6"#)12*/'"3 39)'273073'9"-'"'QFB`'0)"8B32B0)"8'"/0($37+)> Ans. F>V'/D2.19 a-)'"%'$+)"('20'"/0'32'+)-$&%'"%'$%#)*3$%&'$%3)&*"32*'6$39'"%'$%073'*)-$-3"%.)'21'CF'8Ω'"%+'"% $%3)&*"3$2%'3$/)'.2%-3"%3'21'CF−T'->'Y9"3'$-'39)'&"$%'/"&%$37+)'"%+'09"-)'"%&()'21'39$-'.$*.7$3'"3 CF'*"+d-'"%+'"3'C'*"+d-\'Y9"3'$-'39)'1*)K7)%.4'"3'69$.9'39)'&"$%'/"&%$37+)'$-'7%$34\ Ans. ?'='CF'8Ω, "'='F>C'µSX'"3'ω''='CF'*"+d-:' !1 ⁄ !) = CFF `d`'"%+'φ'='+DF°X'"3'ω ='C'*"+d-: ! 1 ⁄ ! ) = 'C5FFF'`d`'"%+'φ ='+DF°; 1000'*"+dD2.20 j)-$&%'"'+$11)*)%3$"32*'32'9"#)'"'3$/)'.2%-3"%3'21'CF−Q'-'"%+'"%'$%073'."0".$3"%.)'21'F>FC'µS>'Y9"3 $-'39)'&"$%'/"&%$37+)'"%+'09"-)'21'39$-'.$*.7$3'"3'CF'*"+d-5'"%+'"3'CFT'*"+d-\'A%'2*+)*'32'($/$3'39) 9$&9B1*)K7)%.4'&"$%'21'39)'+$11)*)%3$"32*'.$*.7$3'32'CFF5'"'*)-$-32*'$-'"++)+'$%'-)*$)-'6$39'39)'."B 0".$32*>'S$%+'39)'*)K7$*)+'*)-$-32*'#"(7)> Ans. "'='F>FC'µSX ?'='C'RΩX'"3'ω''='CF'*"+d-:' !1 ⁄ !) = F>C `d`'"%+'φ'='−DF°X'"3'ω'='CFFF'*"+d-: !1 ⁄ !) = CF `d`'"%+'φ ='−DF°; 10'8Ω

2.6 DC Imperfections ;97-'1"*'6)'9"#)'.2%-$+)*)+'39)'20'"/0'32',)'$+)"(>';9)'2%(4')M.)03$2%'9"-',))%'"',*$)1'+$-B .7--$2%'21'39)')11).3'21'39)'20B"/0'1$%$3)'&"$%'$'2%'39)'.(2-)+B(220'&"$%'21'39)'$%#)*3$%&'"%+ %2%$%#)*3$%&' .2%1$&7*"3$2%->' H(3927&9' $%' /"%4' "00($."3$2%-' 39)' "--7/03$2%' 21' "%' $+)"(' 20

2.6 DC Imperfections

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89

90 Chapter 2 Operational Amplifiers +.'-27*.)'21'#"(7)'!BK'0(".)+'$%'-)*$)-'6$39'39)'02-$3$#)'$%073'()"+'21'"%'211-)3B1*))'20'"/0> ;9)'W7-3$1$."3$2%'12*'39$-'/2+)('12((26-'1*2/'39)'+)-.*$03$2%'",2#)>'

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? !B = !BK C + BBBBBQ ?C

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2.6 DC Imperfections

R2 R1 !"

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R2 VO % VOS 1 " R 1

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To rest of circuit

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91

92 Chapter 2 Operational Amplifiers

R2

! !" VOS (a)

VO % VOS

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Figure 2.31 :,;'H'."0".$3$#)(4'.270()+'$%#)*3$%&'"/0($1$)*>':5;';9)')K7$#"()%3'.$*.7$3'12*'+)3)*/$%$%&'$3-' +.'273073'211-)3'#2(3"&)'!B>

#2(3"&)'*)-7(3$%&'1*2/'39)'20B"/0'$%073'211-)3'#2(3"&)%!BK'6$((',)'39"3'-926%'$%'S$&>'Q>TC<,=> ;97-'!BK'-))-'$%')11).3'"'7%$34B&"$%'#2(3"&)'12((26)*5'"%+'39)'+.'273073'#2(3"&)' !B'6$((',) )K7"('32'!BK'*"39)*'39"%'!BK ( C + ? Q ⁄ ? C )5'69$.9'$-'39)'."-)'6$39273'39)'.270($%&'."0".$32*> H-'1"*'"-'$%073'-$&%"(-'"*)'.2%.)*%)+5'39)'.270($%&'."0".$32*'"'12*/-'32&)39)*'6$39'?C'"%'L;G 9$&9B0"--'.$*.7$3'6$39'"'.2*%)*'1*)K7)%.4'21'ω F = C ⁄ "? C >';97-'39)'&"$%'21'39)'."0".$3$#)(4 .270()+'"/0($1$)*'6$(('1"(('211'"3'39)'(26B1*)K7)%.4')%+'o1*2/'"'/"&%$37+)'21'( C + ? Q ⁄ ? C )'"3 9$&9'1*)K7)%.$)-p'"%+'6$((',)'T'+e'+26%'"3'ω F>

EXERCISES 2.22 G2%-$+)*'"%'$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'CFFF'.2%-3*7.3)+'1*2/'"%'20'"/0'6$39'"% $%073'211-)3'#2(3"&)'21'T'/`'"%+'6$39'273073'-"37*"3$2%'()#)(-'21'±CF'`>'<"='Y9"3'$-'<"00*2M$/"3)(4= 39)'0)"8'-$%)B6"#)'$%073'-$&%"('39"3'."%',)'"00($)+'6$39273'273073'.($00$%&\'<,='A1'39)')11).3'21'!BK $-'%7(()+'"3'*22/'3)/0)*"37*)'V'/` 2.23 G2%-$+)*'39)'-"/)'"/0($1$)*'"-'$%'@M)*.$-)'Q>QQf39"3'$-5'"%'$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$% 21'CFFF'.2%-3*7.3)+'1*2/'"%'20'"/0'6$39'"%'$%073'211-)3'#2(3"&)'21'T'/`'"%+'6$39'273073'-"37*"3$2% ()#)(-'21'±CF'`f)M.)03'9)*)'()3'39)'"/0($1$)*',)'."0".$3$#)(4'.270()+'"-'$%'S$&>'Q>TC<"=>'<"='Y9"3 $-'39)'+.'211-)3'#2(3"&)'"3'39)'2730735'"%+'69"3'<"00*2M$/"3)(4='$-'39)'0)"8'-$%)B6"#)'-$&%"('39"3'."% ,)'"00($)+'"3'39)'$%073'6$39273'273073'.($00$%&\'A-'39)*)'"'%))+'12*'211-)3'3*$//$%&\'<,='A1'?C'='C'8Ω "%+'?Q'='C RΩ5'1$%+'39)'#"(7)'21'39)'.270($%&'."0".$32*'"C'39"3'6$((')%-7*)'39"3'39)'&"$%'6$((',)'&*)"3)* 39"%'VI'+e'+26%'32'CFF'![> Ans. <"='T'/`5'CF'/`5'%2'%))+'12*'211-)3'3*$//$%&X'<,='C>E'µS

2.6 DC Imperfections

2.6.2 Input Bias and Offset Currents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

>LC + >LQ B >L = BBBBBBBBBBBBBBBBBB Q "%+'39)'+$11)*)%.)'$-'."(()+'39)'!"()&*.334$&*0)%%$"&'"%+'$-'&$#)%',4

>BK = >LC − >LQ ;40$."('#"(7)-'12*'&)%)*"(B07*02-)'20'"/0-'39"3'7-)',$02("*'3*"%-$-32*-'"*)'>L'= CFF'%H'"%+ >BK'= CF'%H> Y)' %26' 6$-9' 32' 1$%+' 39)' +.' 273073' #2(3"&)' 21' 39)' .(2-)+B(220' "/0($1$)*' +7)' 32' 39) $%073',$"-'.7**)%3->';2'+2'39$-'6)'&*27%+'39)'-$&%"('-27*.)'"%+'2,3"$%'39)'.$*.7$3'-926%'$% S$&> Q>TT'12*',239'39)'$%#)*3$%&'"%+'%2%$%#)*3$%&'.2%1$&7*"3$2%->'H-'-926%'$%'S$&>'Q>TT5'39) 273073'+.'#2(3"&)'$-'&$#)%',4

!B = >LC ? Q ! > L ? Q

TI=

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Figure 2.32 ;9)'20B"/0'$%073',$"-'.7**)%3-' *)0*)-)%3)+',4'362'.7**)%3'-27*.)-'>LC'"%+'>LQ>

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93

94 Chapter 2 Operational Amplifiers

Figure 2.33 H%"(4-$-'21'39)'.(2-)+B(220'"/0($1$)*5'3"8$%&'$%32'"..27%3'39)'$%073',$"-'.7**)%3->

Figure 2.34 O)+7.$%&'39)')11).3'21'39)'$%073',$"-'.7**)%3-',4'$%3*2+7.$%&'"'*)-$-32*'?T>

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!B = − >LQ ? T + ? Q ( >LC ! >LQ ? T ⁄ ? C ) G2%-$+)*'1$*-3'39)'."-)'>LC'='>LQ'='>L5'69$.9'*)-7(3-'

%$!B = >L [ ? Q ! ? T ( C + ? Q ⁄ ? C ) ]

Tc=

2.6 DC Imperfections

;97-'6)'."%'*)+7.)'!B'32'[)*2',4'-)().3$%&'?T'-7.9'39"3

?Q ?C ?Q B ? T = BBBBBBBBBBBBBBBBBBBBBBBB = BBBBBBBBBBBBBBBB C + ?Q ⁄ ?C ?C + ?Q

TD=

;9"3'$-5'?T'-927(+',)'/"+)')K7"('32'39)'0"*"(()(')K7$#"()%3'21'?C'"%+'?Q>'' !"#$%&'-)().3)+'?T'"-'",2#)5'()3'7-')#"(7"3)'39)')11).3'21'"'1$%$3)'211-)3'.7**)%3'>BK>'k)3 >LC = >L + >BK ⁄ Q '"%+' >LQ = >L ! >BK ⁄ Q 5 '"%+'-7,-3$373)'$%'@K>'Tc=>';9)'*)-7(3'$-

!B = >BK ? Q

UF=

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a%12*37%"3)(45'$%.(7+$%&'?T'(26)*-'.2%-$+)*",(4'39)'$%073'*)-$-3"%.)'21'39)'.(2-)+B(220 "/0($1$)*>''

Figure 2.35 A%'"%'".B.270()+'"/0($1$)*'39)'+.'*)-$-3"%.)'-))%',4'39)'$%#)*3$%&'3)*/$%"('$-'?QX'9)%.) ?T'$-'.92-)%')K7"('32'?Q>

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95

96 Chapter 2 Operational Amplifiers

EXERCISE 2.24 G2%-$+)*'"%'$%#)*3$%&'"/0($1$)*'.$*.7$3'+)-$&%)+'7-$%&'"%'20'"/0'"%+'362'*)-$-32*-5'?C'='CF'8Ω'"%+ ?Q ='C'RΩ>'A1'39)'20'"/0'$-'-0).$1$)+'32'9"#)'"%'$%073',$"-'.7**)%3'21'CFF'%H'"%+'"%'$%073'211-)3 .7**)%3'21'CF'%H5'1$%+'39)'273073'+.'211-)3'#2(3"&)'*)-7(3$%&'"%+'39)'#"(7)'21'"'*)-$-32*'?T'32',)'0(".)+ $%'-)*$)-'6$39'39)'02-$3$#)'$%073'()"+'$%'2*+)*'32'/$%$/$[)'39)'273073'211-)3'#2(3"&)>'Y9"3'$-'39)'%)6 #"(7)'21%!B\ Ans. F>C'`X'D>D'8Ω'FC'`

2.6.3 Effect of VOS and IOS on the Operation of the Inverting Integrator ?7*'+$-.7--$2%'21'39)'$%#)*3$%&'$%3)&*"32*'.$*.7$3'$%'L).3$2%'Q>V>Q'/)%3$2%)+'39)'-7-.)03$,$($34 21' 39$-' .$*.7$3' 32' -"37*"3$2%' $%' 39)' 0*)-)%.)' 21' -/"((' +.' #2(3"&)-' 2*' .7**)%3->' A3' ,)922#)-' 739)*)12*)'32'.2%-$+)*'39)')11).3'21'39)'20B"/0'+.'211-)3-'2%'$3-'20)*"3$2%>'H-'6$((',)'-))%5'39)-) )11).3-'."%',)'K7$3)'+*"/"3$.> ;2'-))'39)')11).3'21'39)'$%073'+.'211-)3'#2(3"&)'!BK 5'.2%-$+)*'39)'$%3)&*"32*'.$*.7$3'$%'S$&> Q>Tc5'69)*)'12*'-$/0($.$34'6)'9"#)'-92*3B.$*.7$3)+'39)'$%073'-$&%"('-27*.)>'H%"(4-$-'21'39) .$*.7$3'$-'-3*"$&9312*6"*+'"%+'$-'-926%'$%'S$&>'Q>TI>'H--7/$%&'12*'-$/0($.$34'39"3'"3'3$/)'&'='F 39)'#2(3"&)'".*2--'39)'."0".$32*'$-'[)*25'39)'273073'#2(3"&)'"-'"'17%.3$2%'21'3$/)'$-'&$#)%',4'''

!BK B &' v B = !BK + BBBBBBB "?

UC=

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2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance

L7.9' "' *)-$-32*' 0*2#$+)-' "' +.' 0"39' 39*27&9' 69$.9' 39)' +.' .7**)%3-' BK' ."% 1(265' 6$39' 39)' *)-7(3' 39"3' vB' 6$((' %26' 9"#)' "' +.' .2/02%)%3' o!BK ( C + ? J ⁄ ? ) + > BK ? J p $%-3)"+'21'*$-$%&'($%)"*(4>';2'8))0'39)'+.'211-)3'"3'39)'273073'-/"((5'2%)'627(+'-)().3'" (26'#"(7)'12*'?J>'a%12*37%"3)(45'926)#)*5'39)'(26)*'39)'#"(7)'21'?J5'39)'()--'$+)"('39) $%3)&*"32*'.$*.7$3',).2/)->''' C

(IB1 ! IB2) % IOS IB2R#R % IB2

R

IB1 ! IB2

R !IB2R

"

vO vO % !IB2R "

Figure 2.38 @11).3'21'39)'20B"/0'

IOS $%073',$"-'"%+'211-)3'.7**)%3-'2%'39)' t C 0)*12*/"%.)'21'39)'R$(()*'$%3)&*"32*' .$*.7$3>

EXERCISE 2.25'G2%-$+)*'"'R$(()*'$%3)&*"32*'6$39'"'3$/)'.2%-3"%3'21'C'/-'"%+'"%'$%073'*)-$-3"%.)'21'CF'8Ω>'k)3'39) 20'"/0'9"#)'!BK'='Q'/`'"%+'273073'-"37*"3$2%'#2(3"&)-'21''±CQ'`>'<"='H--7/$%&'39"3'69)%'39) 026)*'-700(4'$-'37*%)+'2%'39)'."0".$32*'#2(3"&)'$-'[)*25'926'(2%&'+2)-'$3'3"8)'12*'39)'"/0($1$)*'32 -"37*"3)\'<,='L)().3'39)'("*&)-3'02--$,()'#"(7)'12*'"'1))+,".8'*)-$-32*'?J'-2'39"3'"3'()"-3'±10'`'21 273073' -$&%"(' -6$%&'*)/"$%-' "#"$(",()>' Y9"3'$-' 39)' .2*%)*' 1*)K7)%.4' 21' 39)'*)-7(3$%&' L;G'%)3B 62*8\ Ans. <"='E'-X'<,='CF'RΩ5'F>CE'!['

2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance 2.7.1 Frequency Dependence of the Open-Loop Gain ;9)'+$11)*)%3$"('20)%B(220'&"$%'$%21'"%'20'"/0'$-'%23'$%1$%$3)X'*"39)*5'$3'$-'1$%$3)'"%+'+).*)"-)6$39'1*)K7)%.4>'S$&7*)'Q>TD'-926-'"'0(23'12*' $ 5'6$39'39)'%7/,)*-'340$."('21'-2/)'.2//)*B .$"((4'"#"$(",()'&)%)*"(B07*02-)'20'"/0-'<-7.9'"-'39)'0207("*'IUCB340)'20'"/05'"#"$(",()'1*2/ /"%4'-)/$.2%+7.32*'/"%71".37*)*-X'$3-'$%3)*%"('.$*.7$3'$-'-37+$)+'$%'G9"03)*'CQ=> P23)'39"3'"(3927&9'39)'&"$%'$-'K7$3)'9$&9'"3'+.'"%+'(26'1*)K7)%.$)-5'$3'-3"*3-'32'1"(('211 "3'"'*"39)*'(26'1*)K7)%.4'';9)'7%$12*/'nQFB+ed+)."+)'&"$%'*2((211 -926%'$-'340$."('21'!"&$%",--9*0.+($"4,&$1'20'"/0->';9)-)'"*)'7%$3-'39"3'9"#)'"'%)362*8 <7-7"((4'"'-$%&()'."0".$32*='$%.(7+)+'6$39$%'39)'-"/)'AG'.9$0'692-)'17%.3$2%'$-'32'."7-) 39)' 20B"/0' &"$%'32' 9"#)'39)'-$%&()B3$/)B.2%-3"%3' ' ;9$-

97

98 Chapter 2 Operational Amplifiers

Figure 2.39 ?0)%B(220'&"$%'21'"'340$."('&)%)*"(B07*02-)'$%3)*%"((4'.2/0)%-"3)+'20'"/0>

0*2.)--' 21' /2+$14$%&' 39)' 20)%B(220' &"$%' $-' 3)*/)+' 3%$?)$"09* 0.+($"4,&!."5' "%+' $307*02-)'$-'32')%-7*)'39"3'20B"/0'.$*.7$3-'6$((' ,)'-3",()'<"-'2002-)+'32'2-.$(("32*4=>';9) -7,W).3'21'-3",$($34'21'20B"/0'.$*.7$3-f2*5'/2*)'&)%)*"((45'21'1))+,".8'"/0($1$)*-f6$(( ,)'-37+$)+'$%'G9"03)*'CF> e4' "%"(2&4' 32' 39)' *)-02%-)' 21' (26B0"--' L;G' .$*.7$3-' <-))' L).3$2%' C>E' "%+5' 12*' /2*) +)3"$(5'H00)%+$M'@=5'39)'&"$%'$<4='21'"%'$%3)*%"((4'.2/0)%-"3)+'20'"/0'/"4',)')M0*)--)+'"-

$F $ ( 4 ) = BBBBBBBBBBBBBBBBBBBBB C + 4 ⁄ ω5

UQ=

69$.9'12*'094-$."('1*)K7)%.$)-5'4'='Gω5',).2/)-

$F B $ ( G ω ) = BBBBBBBBBBBBBBBBBBBBBBBB C + G ω ⁄ ω5

UT=

69)*)'$F'+)%23)-'39)'+.'&"$%'"%+'ω5'$-'39)'TB+e'1*)K7)%.4'<.2*%)*'1*)K7)%.4'2*'^,*)"8_'1*)B K7)%.4=>'S2*'39)')M"/0()'-926%'$%'S$&>'Q>TD5'$F'='CFV'"%+'ω5'='Qπ '×'CF'*"+d->'S2*'1*)K7)%.$)-' ω')'ω5'<",273'CF'3$/)-'"%+'9$&9)*='@K>'UT='/"4',)'"00*2M$/"3)+',4

$F ω5 B $ ( G ω )'!' BBBBBBBBBBB Gω

UU=

$F ω5 B $ ( G ω ) ' = BBBBBBBBBBB

UV=

;97-5

ω

1*2/'69$.9'$3'."%',)'-))%'39"3'39)'&"$%'r$r'*)".9)-'7%$34'
ω& 3 $F ω5

UE=

2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance

L7,-3$373$%&'$%'@K>'UU='&$#)-

ω

$ ( G ω )'!' BBBBBB& Gω

UI=

;9)'1*)K7)%.4' 2 & = ω & ⁄ Q π '$-'7-7"((4'-0).$1$)+'2%'39)'+"3"'-9))3-'21'.2//)*.$"((4'"#"$(",() 20'"/0-'"%+'$-'8%26%'"-'39)')"!&9/',!"*5,"18!1&7>V'H(-2'%23)'39"3'12*' ω')' ω5'39)'20)%B (220'&"$%'$%'@K>'UQ=',).2/)-

ω

$ ( 4 )'!' BBBBB& 4

Uc=

;9)'&"$%'/"&%$37+)'."%',)'2,3"$%)+'1*2/'@K>'UI='"-

ω 2 $ ( G ω ) ! BBBBB& = BB& ω 2

UD=

;97-'$1'2&'$-'8%26%'' S7*39)*/2*)5' 2,-)*#)'39"3' 39$-' *)("3$2%-9$0' .2**)("3)6$39'39)'e2+)'0(23'$%'S$&>'Q>TD>'L0).$1$."((45'12*'2')'255%+27,($%&'2'<"%'2.3"#)'$%.*)"-)='*)-7(3$%' 9"(#$%&' 39)' &"$%' <"' EB+e' *)+7.3$2%=>' L$/$("*(45' $%.*)"-$%&% 2' ,4' "' 1".32*' 21' CF' <"' +)."+) $%.*)"-)='*)-7(3-'$%'*)+7.$%&'r$r',4'"'1".32*'21'CF' H-'"'/"33)*'21'0*".3$."('$/02*3"%.)5'6)'%23)'39"3'39)'0*2+7.3$2%'-0*)"+'$%'39)'#"(7)'21'2& ,)36))%'20B"/0'7%$3-'21'39)'-"/)'340)'$-'7-7"((4'/7.9'-/"(()*'39"%'39"3'2,-)*#)+'12*'$F'"%+ 25>'S2*'39$-'*)"-2%'2&'$-'0*)1)**)+'"-'"'-0).$1$."3$2%'0"*"/)3)*>'S$%"((45'$3'-927(+',)'/)%3$2%)+ 39"3' "%' 20' "/0' 9"#$%&' 39$-' 7%$12*/' nEB+ed2.3"#)' <2*' )K7$#"()%3(4' nQFB+ed+)."+)=' &"$% *2((211'$-'-"$+'32'9"#)'"'4!"'-$/(.-$*+.1$->'H(-25'-$%.)'39$-'-$%&()'02()'.1-)*/&(4'39)'"/0($B 1$)*'1*)K7)%.4'*)-02%-)5'$3'$-'."(()+'"'.1-)*/*&%+13(>*S2*'/2*)'2%'02()-'<"%+'[)*2-=5'39)'*)"+)* /"4'6$-9'32'.2%-7(3'H00)%+$M'S>

EXERCISE 2.26 H%'$%3)*%"((4'.2/0)%-"3)+'20'"/0'$-'-0).$1$)+'32'9"#)'"%'20)%B(220'+.'&"$%'21'CFE'+e'"%+'"'7%$34B &"$%',"%+6$+39'21'T'R![>'S$%+'25'"%+'39)'20)%B(220'&"$%'<$%'+e='"3'255'TFF'![5'T'8![5'CQ'8![5'"%+ EF'8![> Ans. CV'![X'CFT'+eX'cF'+eX'EF'+eX'Uc'+eX'TU'+e

2.7.2 Frequency Response of Closed-Loop Amplifiers Y)'%)M3'.2%-$+)*'39)')11).3'21'($/$3)+'20B"/0'&"$%'"%+',"%+6$+39'2%'39)'.(2-)+B(220'3*"%-1)* 17%.3$2%-'21'39)'362',"-$.'.2%1$&7*"3$2%-:'39)'$%#)*3$%&'.$*.7$3'21'S$&>'Q>V'"%+'39)'%2%$%#)*3$%& .$*.7$3'21'S$&>'Q>CQ>';9)'.(2-)+B(220'&"$%'21'39)'$%#)*3$%&'"/0($1$)*5'"--7/$%&'"'1$%$3)'20B"/0 20)%B(220'&"$%'$5'6"-'+)*$#)+'$%'L).3$2%'Q>Q'"%+'&$#)%'$%'@K>'V=5'69$.9'6)'*)0)"3'9)*)'"-

!1 !?Q ⁄ ?C BBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B C + ( C + ?Q ⁄ ?C ) ⁄ $ !)

VF=

L$%.)'2&'$-'39)'0*2+7.3'21'39)'+.'&"$%'$F'"%+'39)'TB+e',"%+6$+39'25'<69)*)'25 = ω5 /Qπ=5'$3'$-'"(-2'8%26% "-'39)'',!"@5,"18!1&7*(%.1)0&'';9)'*)"+)*'$-'."73$2%)+5'926)#)*5'39"3'$%'-2/)'"/0($1$)*-5'39) 7%$34B&"$%'1*)K7)%.4'"%+'39)'&"$%B,"%+6$+39'0*2+7.3'"*)'*1&')K7"(> V

99

100 Chapter 2 Operational Amplifiers L7,-3$373$%&'12*'$'1*2/'@K>'UQ='"%+'7-$%&'@K>'UE='&$#)-

!1 ( 4 ) !?Q ⁄ ?C BBBBBBBBBBBB B = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B !) ( 4 ) ?Q C 4 BBBB B BBBBB B BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B C+ C+ + ?C ω& ⁄ ( C + ?Q ⁄ ?C ) $F

VC=

l C + ? Q ⁄ ? C 5 '69$.9'$-'7-7"((4'39)'."-)5 S2*' $ F s l

!1 ( 4 ) !?Q ⁄ ?C BBBBBBBBBBBB B ≈ BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B !) ( 4 ) 4 C + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB ω& ⁄ ( C + ?Q ⁄ ?C )

VQ=

69$.9'$-'21'39)'-"/)'12*/'"-'39"3'12*'"'(26B0"--'L;G'%)362*8'<-))';",()'C>Q5'0"&)'TU=>';9739)'$%#)*3$%&'"/0($1$)*'9"-'"%'L;G'(26B0"--'*)-02%-)'6$39'"'+.'&"$%'21'/"&%$37+)')K7"('32 ?Q /?C>';9)'.(2-)+B(220'&"$%'*2((-'211'"3'"'7%$12*/'nQFB+ed+)."+)'-(20)'6$39'"'.2*%)*'1*)B K7)%.4'
ω& ω T+e = BBBBBBBBBBBBBBBBBBBBBBBB C + ?Q ⁄ ?C

VT=

L$/$("*(45'"%"(4-$-'21'39)'%2%$%#)*3$%&'"/0($1$)*'21'S$&>'Q>CQ5'"--7/$%&'"'1$%$3)'20)%B(220 &"$%'$5'4$)(+-'39)'.(2-)+B(220'3*"%-1)*'17%.3$2%

!1 C + ?Q ⁄ ?C BBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B !) C + ( C + ?Q ⁄ ?C ) ⁄ $

VU=

l C + ? Q ⁄ ? C'*)-7(3-'$% L7,-3$373$%&'12*'$'1*2/'@K>'UQ='"%+'/"8$%&'39)'"00*2M$/"3$2%' $ F s l

!1 ( 4 ) C + ?Q ⁄ ?C BBBBBBBBBBBB B ! BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB B !) ( 4 ) 4 C + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB ω& ⁄ ( C + ?Q ⁄ ?C )

VV=

;97-'39)'%2%$%#)*3$%&'"/0($1$)*'9"-'"%'L;G'(26B0"--'*)-02%-)'6$39'"'+.'&"$%'21'( C + ? Q ⁄ ? C ) "%+'"'TB+e'1*)K7)%.4'&$#)%'"(-2',4'@K>'VT=>

Example 2.6 G2%-$+)*'"%'20'"/0'6$39'2& = C'R![>'S$%+'39)'TB+e'1*)K7)%.4'21'.(2-)+B(220'"/0($1$)*-'6$39'%2/$B %"(' &"$%-' 21' +CFFF5' +CFF5' +CF5' +C5' −C5' −CF5' −CFF5' "%+' −CFFF>' L8)3.9' 39)' /"&%$37+)' 1*)K7)%.4 *)-02%-)'12*'39)'"/0($1$)*-'6$39'.(2-)+B(220'&"$%-'21'+CF'"%+'nCF> Solution Y)'7-)'@K>'VT='32'2,3"$%'39)'*)-7(3-'&$#)%'$%'39)'12((26$%&'3",()> Closed-Loop Gain

+CFFF +CFF +CF +C −C −CF −CFF −CFFF

R2 ⁄ R1

'''''''''''''''''''DDD '''''''''''''DD D F C CF CFF CFFF

f3 dB = ft / (1 + R2 ⁄R1)

C'8![ CF'8![ CFF'8![ ''C'R![ F>V'R![ DF>D'8![ D>D'8![ !C'8![

2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance

S$&7*)'Q>UF'-926-'39)'1*)K7)%.4'*)-02%-)'12*'39)'"/0($1$)*'692-)'%2/$%"('+.'&"$%'$-'tCF 'Q>UC'-926-'39)'1*)K7)%.4'*)-02%-)'12*'39)'nCF'<"(-2'QF'+e='."-)>'H%'$%3)*)-3B $%&'2,-)*#"3$2%'12((26-'1*2/'39)'3",()'",2#):';9)'7%$34B&"$%'$%#)*3$%&'"/0($1$)*'9"-'"'TB+e'1*)B K7)%.4'21'2& dQ'"-'.2/0"*)+'32'2&'12*'39)'7%$34B&"$%'%2%$%#)*3$%&'"/0($1$)*'<39)'7%$34B&"$%'#2(3"&) 12((26)*=>''''

Figure 2.40 S*)K7)%.4'*)-02%-)'21'"%'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'+CF'`d`>

Figure 2.41 S*)K7)%.4'*)-02%-)'21'"%'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'−CF'`d`>

;9)'3",()'$%'@M"/0()'Q>E'",2#)'.()"*(4'$((7-3*"3)-'39)'3*"+)B211',)36))%'&"$%'"%+',"%+B 6$+39:'S2*'"'&$#)%'20'"/05'39)'(26)*'39)'.(2-)+B(220'&"$%'*)K7$*)+5'39)'6$+)*'39)',"%+6$+39 ".9$)#)+>'A%+))+5'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%')M9$,$3-'"'.2%-3"%3'',!"@5,"18!1&7*(%.1)0& )K7"('32'2&'21'39)'20'"/0>'H%'$%3)*0*)3"3$2%'21'39)-)'*)-7(3-'$%'3)*/-'21'1))+,".8'39)2*4'6$((',) &$#)%'$%'G9"03)*'CF>

101

102 Chapter 2 Operational Amplifiers

EXERCISES 2.27 H%'$%3)*%"((4'.2/0)%-"3)+'20'"/0'9"-'"'+.'20)%B(220'&"$%'21'CFE'`d`'"%+'"%'".'20)%B(220'&"$%'21'UF +e'"3'CF'8![>'@-3$/"3)'$3-'TB+e'1*)K7)%.45'$3-'7%$34B&"$%'1*)K7)%.45'$3-'&"$%n,"%+6$+39'0*2+7.35 "%+'$3-')M0).3)+'&"$%'"3'C'8![> Ans. C'![X'C'R![X'C'R![X'EF'+e 2.28 H%'20'"/0'9"#$%&'"'CFEB+e'&"$%'"3'+.'"%+'"'-$%&()B02()'1*)K7)%.4'*)-02%-)'6$39'2&'Z'Q'R!['$7-)+'32'+)-$&%'"'%2%$%#)*3$%&'"/0($1$)*'6$39'%2/$%"('+.'&"$%'21'CFF>'S$%+'39)'TB+e'1*)K7)%.4'21 39)'.(2-)+B(220'&"$%> Ans. QF'8![

2.8 Large-Signal Operation of Op Amps A%'39$-'-).3$2%5'6)'-37+4'39)'($/$3"3$2%-'2%'39)'0)*12*/"%.)'21'20B"/0'.$*.7$3-'69)%'("*&) 273073'-$&%"(-'"*)'0*)-)%3>

2.8.1 Output Voltage Saturation L$/$("*'32'"(('239)*'"/0($1$)*-5'20'"/0-'20)*"3)'($%)"*(4'2#)*'"'($/$3)+'*"%&)'21'273073'#2(3B "&)->'L0).$1$."((45'39)'20B"/0'273073'-"37*"3)-'$%'39)'/"%%)*'-926%'$%'S$&>'C>CU'6$39'Dt'"%+ Dn'6$39$%'C'`'2*'-2'21'39)'02-$3$#)'"%+'%)&"3$#)'026)*'-700($)-5'*)-0).3$#)(4>';97-5'"%'20 "/0' 39"3' $-' 20)*"3$%&' 1*2/' ±CVB`' -700($)-' 6$((' -"37*"3)' 69)%' 39)' 273073' #2(3"&)' *)".9)",273'+CT'`'$%'39)'02-$3$#)'+$*).3$2%'"%+'nCT'`'$%'39)'%)&"3$#)'+$*).3$2%>'S2*'39$-'0"*3$.7("* 20'"/0'39)'%,&$1*.)&()&*#.-&,'$'$-'-"$+'32',)'±CT'`>';2'"#2$+'.($00$%&'211'39)'0)"8-'21'39) 273073'6"#)12*/5'"%+'39)'*)-7(3$%&'6"#)12*/'+$-32*3$2%5'39)'$%073'-$&%"('/7-3',)'8)03'.2**)B -02%+$%&(4'-/"((>

2.8.2 Output Current Limits H%239)*' ($/$3"3$2%'2%'39)' 20)*"3$2%'21'20'"/0-'$-'39"3' 39)$*'273073'.7**)%3'$-'($/$3)+'32'" -0).$1$)+'/"M$/7/>'S2*'$%-3"%.)5'39)'0207("*'IUC'20'"/0'$-'-0).$1$)+'32'9"#)'"'/"M$/7/ 273073' .7**)%3' 21' ±QF' /H>' ;97-5' $%' +)-$&%$%&' .(2-)+B(220' .$*.7$3-' 73$($[$%&' 39)' IUC5' 39) +)-$&%)*'9"-'32')%-7*)'39"3'7%+)*'%2'.2%+$3$2%'6$(('39)'20'"/0',)'*)K7$*)+'32'-700(4'"%'273B 073'.7**)%35'$%')$39)*'+$*).3$2%5')M.))+$%&'QF'/H>';9$-5'21'.27*-)5'9"-'32'$%.(7+)',239'39) .7**)%3'$%'39)'1))+,".8'.$*.7$3'"-'6)(('"-'39)'.7**)%3'-700($)+'32'"'(2"+'*)-$-32*>'A1'39)'.$*.7$3 *)K7$*)-'"'("*&)*'.7**)%35'39)'20B"/0'273073'#2(3"&)'6$(('-"37*"3)'"3'39)'()#)('.2**)-02%+$%& 32'39)'/"M$/7/'"((26)+'273073'.7**)%3>

103

2.8 Large-Signal Operation of Op Amps

Example 2.7 G2%-$+)*'39)'%2%$%#)*3$%&'"/0($1$)*'.$*.7$3'-926%'$%'S$&>'Q>UQ>'H-'-926%5'39)'.$*.7$3'$-'+)-$&%)+'12* "'%2/$%"('&"$%' ( C + ? Q ⁄ ? C ) = CF'`d`>'A3'$-'1)+'6$39'"'(26B1*)K7)%.4'-$%)B6"#)'-$&%"('21'0)"8'#2(3"&) !+'"%+'$-'.2%%).3)+'32'"'(2"+'*)-$-32*'?D>';9)'20'"/0'$-'-0).$1$)+'32'9"#)'273073'-"37*"3$2%'#2(3"&)21'±CT'`'"%+'273073'.7**)%3'($/$3-'21'±QF'/H> <"= S2*'!+'='C'`'"%+'?D'='C'8Ω, -0).$14'39)'-$&%"('*)-7(3$%&'"3'39)'273073'21'39)'"/0($1$)*> <,= S2*'!+'='C>V'`'"%+'?D'='C'8Ω5'-0).$14'39)'-$&%"('*)-7(3$%&'"3'39)'273073'21'39)'"/0($1$)*> <.= S2*'?D' ='C'8Ω5'69"3'$-'39)'/"M$/7/'#"(7)'21'!+'12*'69$.9'"%'7%+$-32*3)+'-$%)B6"#)'273073'$2,3"$%)+\ <+= S2*' !+' =' C' `5' 69"3' $-' 39)' (26)-3' #"(7)' 21' ?D' 12*' 69$.9' "%' 7%+$-32*3)+' -$%)B6"#)' 273073' $2,3"$%)+\ vO

15 V

R2 % 9 k& 1 k& !

R1

" Vp

0

t

vI

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vO RL

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iL !13 V !15 V

(a)

(b)

Figure 2.42 :,;'H'%2%$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'CF `d`'+)-$&%)+'7-$%&'"%'20'"/0'39"3'-"37*"3)-'"3 ±CTB`'273073'#2(3"&)'"%+'9"-'±QFB/H'273073'.7**)%3'($/$3->':5;*Y9)%'39)'$%073'-$%)'6"#)'9"-'"'0)"8'21'C>V `5'39) 273073'$-'.($00)+'211'"3'±CT'`>

Solution <"= S2*'!+'='C'`'"%+'?D'='C'8Ω5'39)'273073'6$((',)'"'-$%)'6"#)'6$39'0)"8'#"(7)'21'CF'`>';9$-'$(26)*'39"%'273073'-"37*"3$2%'()#)(-'21'±CT'`5'"%+'397-'39)'"/0($1$)*'$-'%23'($/$3)+'39"3'6"4>'H(-25 69)%'39)'273073'$-'"3'$3-'0)"8' <,= P26'$1'!+'$-'$%.*)"-)+'32'C>V'`5'$+)"((4'39)'273073'627(+',)'"'-$%)'6"#)'21'CVB`'0)"8>';9)'20 "/05'926)#)*5'6$(('-"37*"3)'"3'±CT'`5'397-'.($00$%&'39)'-$%)B6"#)'273073'"3'39)-)'()#)(->'k)3J%)M3'.9).8'2%'39)'20B"/0'273073'.7**)%3:'H3'CTB`'273073'"%+'?D'='C'8Ω5')D'='CT'/H'"%+')J'= C>T'/HX'397-')B'='CU>T'/H5'"&"$%'7%+)*'39)'QFB/H'($/$3>';97-'39)'273073'6$((',)'"'-$%)'6"#) 6$39'$3-'0)"8-'.($00)+'211'"3'±CT'`5'"-'-926%'$%'S$&>'Q>UQ<,=>

104 Chapter 2 Operational Amplifiers

Example 2.7 continued

<.= S2*'?D'='C'8Ω5'39)'/"M$/7/'#"(7)'21'!+'12*'7%+$-32*3)+'-$%)B6"#)'273073'$-'C>T'`>';9)'273073 6$((',)'"'CTB`'0)"8'-$%)'6"#)5'"%+'39)'20B"/0'273073'.7**)%3'"3'39)'0)"8-'6$((',)'CU>T'/H> <+= S2*'!+'='C'`'"%+'?D'*)+7.)+5'39)'(26)-3'#"(7)'02--$,()'12*'?D'69$()'39)'273073'$-'*)/"$%$%&'"% 7%+$-32*3)+'-$%)'6"#)'21'CFB`'0)"8'."%',)'127%+'1*2/ CF'` CF'` ) B/"M = QF'/H = BBBBBBBBBBBB + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB ? D/$% D'8Ω + C'8Ω

69$.9'*)-7(3-'$% ? D/$% = VQE'Ω

2.8.3 Slew Rate H%239)*' 09)%2/)%2%' 39"3' ."%' ."7-)' %2%($%)"*' +$-32*3$2%' 69)%' ("*&)' 273073' -$&%"(-' "*) 0*)-)%3'$-'-()6B*"3)'($/$3$%&>';9)'%"/)'*)1)*-'32'39)'1".3'39"3'39)*)'$-'"'-0).$1$.'-/C)-,8/&(%12%0'/*<('02--$,()'"3'39)'273073'21'"'*)"('20'"/0>';9$-'/"M$/7/'$-'8%26%'"-'39)'4-$8 %,&$'
.v B LO = BBBBBBBB B .&

VE= /"M

"%+'$-'7-7"((4'-0).$1$)+'2%'39)'20B"/0'+"3"'-9))3'$%'7%$3-'21'`dµ->' A3'12((26-'39"3'$1'39)'$%073 -$&%"('"00($)+'32'"%'20B"/0'.$*.7$3'$-'-7.9'39"3'$3'+)/"%+-'"%'273073'*)-02%-)'39"3'$-'1"-3)* 39"%'39)'-0).$1$)+'#"(7)'21'LO5'39)'20'"/0'6$(('%23'.2/0(4>'O"39)*5'$3-'273073'6$(('.9"%&)'"3 39)'/"M$/7/'02--$,()'*"3)5'69$.9'$-')K7"('32'$3-'LO>'H-'"%')M"/0()5'.2%-$+)*'"%'20'"/0 .2%%).3)+'$%'39)'7%$34B&"$%'#2(3"&)B12((26)*'.2%1$&7*"3$2%'-926%'$%'S$&>'Q>UT<"=5'"%+'()3'39) $%073'-$&%"(',)'39)'-3)0'#2(3"&)'-926%'$%'S$&>'Q>UT<,=>';9)'273073'21'39)'20'"/0'6$(('%23',) ",()'32'*$-)'$%-3"%3"%)27-(4'32'39)'$+)"('#"(7)'!X'*"39)*5'39)'273073'6$((',)'39)'($%)"*'*"/0'21 -(20)')K7"('32'LO5'-926%'$%'S$&>'Q>UT<.=>';9)'"/0($1$)*'$-'39)%'-"$+'32',)'4-$8!"'5'"%+'$3273073'$-'4-$8/%,&$*-!+!&$1> A%'2*+)*'32'7%+)*-3"%+'39)'2*$&$%'21'39)'-()6B*"3)'09)%2/)%2%5'6)'%))+'32'8%26'",273 39)'$%3)*%"('.$*.7$3'21'39)'20'"/05'"%+'6)'6$(('-37+4'$3'$%'G9"03)*'CQ>'S2*'39)'3$/)',)$%&5 926)#)*5'$3'$-'-711$.$)%3'32'8%26'",273'39)'09)%2/)%2%'"%+'32'%23)'39"3'$3'$-'+$-3$%.3'1*2/ 39)'1$%$3)'20B"/0',"%+6$+39'39"3'($/$3-'39)'1*)K7)%.4'*)-02%-)'21'39)'.(2-)+B(220'"/0($1$B )*-5' -37+$)+' $%' 39)' 0*)#$27-' -).3$2%>' ;9)' ($/$3)+' ,"%+6$+39' $-' "' ($%)"*' 09)%2/)%2%' "%+ +2)-'%23'*)-7(3'$%'"'.9"%&)'$%'39)'-9"0)'21'"%'$%073'-$%7-2$+X'39"3'$-5'$3'+2)-'%23'()"+'32'%2%B ($%)"*'+$-32*3$2%>';9)'-()6B*"3)'($/$3"3$2%5'2%'39)'239)*'9"%+5'."%'."7-)'%2%($%)"*'+$-32*3$2% 32' "%' $%073' -$%7-2$+"(' -$&%"(' 69)%' $3-' 1*)K7)%.4' "%+' "/0($37+)' "*)' -7.9' 39"3' 39)' .2**)B -02%+$%&'$+)"('273073'627(+'*)K7$*)'vB'32'.9"%&)'"3'"'*"3)'&*)"3)*'39"%'LO>';9$-'$-'39)'2*$B &$%'21'"%239)*'*)("3)+'20B"/0'-0).$1$."3$2%5'$3-'17((B026)*',"%+6$+395'32',)')M0("$%)+'("3)*> e)12*)'()"#$%&'39)')M"/0()'$%'S$&>'Q>UT5'926)#)*5'6)'-927(+'02$%3'273'39"3'$1'39)'-3)0 $%073'#2(3"&)'!'$-'-711$.$)%3(4'-/"((5'39)'273073'."%',)'39)')M02%)%3$"((4'*$-$%&'*"/0'-926%'$% S$&>'Q>UT<+=>'L7.9'"%'273073'627(+',)')M0).3)+'1*2/'39)'12((26)*'$1'39)'2%(4'($/$3"3$2%'2%'$3+4%"/$.'0)*12*/"%.)'6)*)'39)'1$%$3)'20B"/0',"%+6$+39>'L0).$1$."((45'39)'3*"%-1)*'17%.3$2%'21 39)'12((26)*'."%',)'127%+',4'-7,-3$373$%&'?C'='∞'"%+'?Q'='F'$%'@K>'VV='32'2,3"

%$!1 C BBBBB = BBBBBBBBBBBBBBBBBBBBB !) C + 4 ⁄ ω&

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2.8 Large-Signal Operation of Op Amps

v1

V 0

t (b) vO

Slope % SR

V 0

t (c)

vO

Slope % ( tV * SR V 0

t (d)

Figure 2.43 :,;' a%$34B&"$%' 12((26)*>' :5;' A%073' -3)0' 6"#)12*/>' :0;' k$%)"*(4' *$-$%&' 273073' 6"#)12*/ 2,3"$%)+'69)%'39)'"/0($1$)*'$-'-()6B*"3)'($/$3)+>':1;'@M02%)%3$"((4'*$-$%&'273073'6"#)12*/'2,3"$%)+'69)% ! $-'-711$.$)%3(4'-/"(('-2'39"3'39)'$%$3$"('-(20)'<ω&!='$-'-/"(()*'39"%'2*')K7"('32'LO>

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v B ( & ) = ! ( C ! ( !ω& & )

Vc=

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EXERCISE 2.29 H%'20'"/0'39"3'9"-'"'-()6'*"3)'21'C'`dµ-'"%+'"'7%$34B&"$%',"%+6$+39'2&'21'C'R!['$-'.2%%).3)+'$%'39) 7%$34B&"$%'12((26)*'.2%1$&7*"3$2%>'S$%+'39)'("*&)-3'02--$,()'$%073'#2(3"&)'-3)0'12*'69$.9'39)'273073 6"#)12*/'6$(('-3$((',)'&$#)%',4'39)')M02%)%3$"('*"/0'21'@K>'Vc=>'S2*'39$-'$%073'#2(3"&)5'69"3'$39)'CFg'32'DFg'*$-)'3$/)'21'39)'273073'6"#)12*/\'A1'"%'$%073'-3)0'CF'3$/)-'"-'("*&)'$-'"00($)+5'1$%+ 39)'CFg'32'DFg'*$-)'3$/)'21'39)'273073'6"#)12*/> Ans. F>CE'`X'F>TV'µ-X'C>Qc'µ-

105

106 Chapter 2 Operational Amplifiers

2.8.4 Full-Power Bandwidth ?0B"/0'-()6B*"3)'($/$3$%&'."%'."7-)'%2%($%)"*'+$-32*3$2%'$%'-$%7-2$+"('6"#)12*/->'G2%-$+)* 2%.)'/2*)'39)'7%$34B&"$%'12((26)*'6$39'"'-$%)B6"#)'$%073'&$#)%',4

v > = !u) -$% ω & ;9)'*"3)'21'.9"%&)'21'39$-'6"#)12*/'$-'&$#)%',4

.v BBBBBBB> = ω !u) .2- ω & .& 6$39' "' /"M$/7/' #"(7)'21' ω!u) >';9$-'/"M$/7/'2..7*-'"3'39)'[)*2'.*2--$%&-' 21'39)'$%073 -$%7-2$+>' P26' $1' ω!u) ' )M.))+-' 39)' -()6' *"3)' 21' 39)' 20' "/05' 39)' 273073' 6"#)12*/' 6$((' ,) +$-32*3)+'$%'39)'/"%%)*'-926%'$%'S$&>'Q>UU>'?,-)*#)'39"3'39)'273073'."%%23'8))0'70'6$39'39) ("*&)'*"3)'21'.9"%&)'21'39)'-$%7-2$+'"3'$3-'[)*2'.*2--$%&-5'"%+'39)'20'"/0'-()6->' ;9)'20B"/0'+"3"'-9))3-'7-7"((4'-0).$14'"'1*)K7)%.4'2N'."(()+'39)'3)--/(.8$%*5,"18!1&7> A3'$-'39)'1*)K7)%.4'"3'69$.9'"%'273073'-$%7-2$+'6$39'"/0($37+)')K7"('32'39)'*"3)+'273073'#2(3B "&)'21'39)'20'"/0',)&$%-'32'-926'+$-32*3$2%'+7)'32'-()6B*"3)'($/$3$%&>'A1'6)'+)%23)'39)'*"3)+ 273073'#2(3"&)'!1/"M 5'39)%'2N'$-'*)("3)+'32'LO'"-'12((26-:

ω N !1/"M = LO ;97-5

LO 2N = BBBBBBBBBBBBBBBBBBB Q π !1/"M

VD=

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ω ω

!1 = !1/"M BBBBBBNB '

Figure 2.44 @11).3'21'-()6B*"3)'($/$3$%&'2%'273073'-$%7-2$+"('6"#)12*/->

EF=

2.8 Large-Signal Operation of Op Amps

107

EXERCISE 2.30' H%'20'"/0'9"-'"'*"3)+'273073'#2(3"&)'21'±CF'`'"%+'"'-()6'*"3)'21'C'`dµ->'Y9"3'$-'$3-'17((B026)* ,"%+6$+39\'A1'"%'$%073'-$%7-2$+'6$39'1*)K7)%.4'2'='V2N'$-'"00($)+'32'"'7%$34B&"$%'12((26)*'.2%B -3*7.3)+'7-$%&'39$-'20'"/05'69"3'$-'39)'/"M$/7/'02--$,()'"/0($37+)'39"3'."%',)'"..2//2+"3)+ "3'39)'273073'6$39273'$%.7**$%&'LO'+$-32*3$2%\ Ans. CV>D'8![X'Q'`'<0)"8=

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PROBLEMS

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CHAPTER 2

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CHAPTER 2

PROBLEMS

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CHAPTER 2

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CHAPTER 3

Semiconductors

Introduction 3.1

3.5 The pn!Junction with Applied Voltage 145

125

Intrinsic Semiconductors

3.2 Doped Semiconductors

126

3.6 Capacitive Effects in the pn Junction 154

129

3.3 Current Flow in Semiconductors

132

3.4 The pn!Junction with Open-Circuit Terminals (Equilibrium) 138

Summary

157

Problems

159

IN THIS CHAPTER YOU WILL LEARN 1. The basic properties of semiconductors and in particular silicon, which is the material used to make most of today’s electronic circuits. 2. How doping a pure silicon crystal dramatically changes its electrical conductivity, which is the fundamental idea underlying the use of semiconductors in the implementation of electronic devices. 3. The two mechanisms by which current flows in semiconductors: drift and diffusion of charge carriers. 4. The structure and operation of the "#!junction; a basic semiconductor structure that implements the diode and plays a dominant role in transistors.

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125

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! "4 ! !

!

Hole

Silicon atoms

Figure 3.2 G.%(116%.*67*('.#(*3%$16*%1&%."*%01+'-*2.%412,$%'(*%4(19*2%45%."*(6'-%8*2*('./12:%O'0"%4(1? 9*2%412,%8/+*$%(/$*%.1%'%&(**%*-*0.(12%'2,%'%"1-*3%41."%1&%)"/0"%4*016*%'+'/-'4-*%&1(%0#((*2.%012,#0./12:

!"*(6'-%8*2*('./12%(*$#-.$%/2%&(**%*-*0.(12$%'2,%"1-*$%/2%*V#'-%2#64*($%'2,%"*20*%*V#'0120*2.('./12$3%)"*(*%0120*2.('./12%(*&*($%.1%."*%2#64*(%1&%0"'(8*%0'((/*($%7*(%#2/.%+1-#6* A06KC:%!"*%&(**%*-*0.(12$%'2,%"1-*$%61+*%('2,16-5%."(1#8"%."*%$/-/012%0(5$.'-%$.(#0.#(*3%'2, /2%."*%7(10*$$%$16*%*-*0.(12$%6'5%&/--%$16*%1&%."*%"1-*$:%!"/$%7(10*$$3%0'--*,%&$*-,2!"'#!-"3 (*$#-.$% /2% ."*% ,/$'77*'('20*% 1&% &(**% *-*0.(12$% '2,% "1-*$:% !"*% (*0164/2'./12% ('.*% /$

127

128 Chapter 3 Semiconductors 7(171(./12'-%.1%."*%2#64*(%1&% &(**%*-*0.(12$%'2,%"1-*$3%)"/0"%/2%.#(2%/$%,*.*(6/2*,%45%."* ."*(6'-%%$"$&'#!-")('.*:%!"*%-'..*(%/$%'%$.(128%./12%1&%.*67*('.#(*:%>2%."*(6'-%*V#/-/4? (/#63%."*%(*0164/2'./12%('.*%/$%*V#'-%.1%."*%8*2*('./12%('.*3%'2,%12*%0'2%0120-#,*%."'.%."* 0120*2.('./12%1&%&(**%*-*0.(12$%#%/$%*V#'-%.1%."*%0120*2.('./12%1&%"1-*$%"3% AK:SC

# ! " ! #+

)"*(*% # + %,*21.*$%."*%2#64*(%1&%&(**%*-*0.(12$%'2,%"1-*$%/2%'%#2/.%+1-#6*%A06KC%1&%/2.(/2$/0 $/-/012%'.%'%8/+*2%.*67*('.#(*:%_*$#-.$%&(16%$*6/012,#0.1(%7"5$/0$%8/+*$% # + %'$ # + ! *)

K ⁄ = ]&'`=()

%

AK:=C SD

"K

"K ⁄ =

)"*(*% *% /$% '% 6'.*(/'-?,*7*2,*2.% 7'('6*.*(% ."'.% /$% b:K × SU 06 Y % &1(% $/-/012L% &' 3% ' 7'('6*.*(%921)2%'$%."*% 2'"(%'0)$"$&%43%/$%S:S=%*-*0.(12%+1-.%A*PC%&1(%$/-/012=L%'2,% (%/$ M1-.X6'22W$%012$.'2.%A c:E= × SU "D %*P`YC:%>.%/$%/2.*(*$./28%.1%921)%."'.%."*%4'2,8'7%*2*(85 &'%/$%."*%6/2/6#6%*2*(85%(*V#/(*,%.1%4(*'9%'%01+'-*2.%412,%'2,%."#$%8*2*('.*%'2%*-*0.(12? "1-*%7'/(:%

Example 3.1 <'-0#-'.*%."*%+'-#*%1&% # + %&1(%$/-/012%'.%(116%.*67*('.#(*%A) ! KUU%YC:

Solution J#4$./.#./28%."*%+'-#*$%8/+*2%'41+*%/2%OV:%AK:SC%7(1+/,*$% SD

# + ! b:K × SU ( KUU ) SU

K ⁄ = " S:S= ⁄ ( = × c:E= × SU

%

! S:D × SU 0'((/*($ ⁄ 06

"D

× KUU )

K ==

G-."1#8"%."/$%2#64*(%$**6$%-'(8*3%.1%7-'0*%/.%/2.1%012.*@.%21.*%."'.%$/-/012%"'$% D × SU %'.16$`06K:%!"#$ S= '.%(116%.*67*('.#(*%12-5%12*%/2%'41#.% D × SU %'.16$%/$%/12/X*,%'2,%012.(/4#./28%'%&(**%*-*0.(12%'2,%' "1-*d

;/2'--53%/.%/$%#$*&#-%&1(%&#.#(*%7#(71$*$%.1%*@7(*$$%."*%7(1,#0.%1&%."*%"1-*%'2,%&(**?*-*0.(12 0120*2.('./12%'$ =

AK:KC

"# ! # +

SU

K

)"*(*% &1(% $/-/012% '.% (116% .*67*('.#(*3% # + ! S:D × SU ⁄ 06 :% G$% )/--% 4*% $**2% $"1(.-53% ."/$ (*-'./12$"/7%*@.*2,$%.1%*@.(/2$/0%1(%,17*,%$/-/012%'$%)*--:

a1.*%."'.%S%*P% ! S:E × SU

=%

" ST

%N:

3.2 Doped Semiconductors 129

EXERCISE 3.1 <'-0#-'.*%."*%/2.(/2$/0%0'((/*(%,*2$/.5% # + %&1(%$/-/012%'.%)%e%DU%Y%'2,%KDU%Y: " KT K K Ans. T:E × SU ⁄ 06 L% B:SD × SU SS ⁄ 06

3.2 Doped Semiconductors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ovalent bonds

Valence electrons !

!

!

! "4 ! !

! "4 ! !

! "4 ! !

!

!

!

! "4 ! !

! "5 ! !

! "4 ! !

!

!

!

! "4 ! !

! "4 ! !

! "4 ! !

!

Free electron donated by impurity atom Pentavalent impurity atom (donor)

Silicon atoms

Figure 3.3 G%$/-/012%0(5$.'-%,17*,%45%'%7*2.'+'-*2.%*-*6*2.:%O'0"%,17'2.%'.16%,12'.*$%'%&(**%*-*0.(12 '2,%/$%."#$%0'--*,%'%,121(:%!"*%,17*,%$*6/012,#0.1(%4*016*$%#%.57*:

130 Chapter 3 Semiconductors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

AK:BC

)"*(*%."*%$#4$0(/7.%#!,*21.*$%#?.57*%$/-/012:%!"#$% # # %/$%,*.*(6/2*,%45%."*%,17/28%0120*2? .('./12%'2,%21.%45%.*67*('.#(*:%!"/$%/$%21.%."*%0'$*3%"1)*+*(3%&1(%."*%"1-*%0120*2.('./12:%G-."*%"1-*$%/2%."*%#?.57*%$/-/012%'(*%."1$*%8*2*('.*,%45%."*(6'-%/12/X'./12:%!"*/(%0120*2.('./12 " # %0'2%4*%&1#2,%45%21./28%."'.%."*%(*-'./12$"/7%/2%OV:%AK:KC%'77-/*$%*V#'--5%)*--%&1(%,17*, $/-/0123%7(1+/,*,%."*(6'-%*V#/-/4(/#6%/$%'0"/*+*,:%!"#$%&1(%#?.57*%$/-/012 =

"# ## % ! #+

J#4$./.#./28%&1(% # # %&(16%OV:%AK:BC3%)*%14.'/2%&1(% " # =

# " # ! ??????+? 12

AK:DC =

!"#$% " # %)/--%"'+*%."*%$'6*%,*7*2,*20*%12%.*67*('.#(*%'$%."'.%1&% # + :%;/2'--53%)*%21.* ."'.%/2%#?.57*%$/-/012%."*%0120*2.('./12%1&%&(**%*-*0.(12$% # # %)/--%4*%6#0"%-'(8*(%."'2%."'.%1& "1-*$:% f*20*% *-*0.(12$% '(*% $'/,% .1% 4*% ."*% ,'6-&!#4% 0"'(8*% 0'((/*($% '2,% "1-*$% ."*% ,!"-&!#4 0"'(8*%0'((/*($%/2%#?.57*%$/-/012: !1%14.'/2%"?.57*%$/-/012%/2%)"/0"%"1-*$%'(*%."*%6'F1(/.5%0"'(8*%0'((/*($3%'%.(/+'-*2.%/67#? (/.5%$#0"%'$%41(12%/$%#$*,:%;/8#(*%K:B%$"1)$%'%$/-/012%0(5$.'-%,17*,%)/."%41(12:%a1.*%."'.%."* 41(12% '.16$% (*7-'0*% $16*% 1&% ."*% $/-/012% '.16$% /2% ."*% $/-/012% 0(5$.'-% $.(#0.#(*:% J/20*% *'0" Covalent bonds

Valence electrons

Silicon atom !

!

!

! "4 ! !

! "4 ! !

! "4 ! !

!

!

!

! "4 ! !

! "3 ! !

! "4 ! !

!

!

"

! "4 ! !

! "4 ! !

! "4 ! !

Trivalent impurity atom (acceptor)

Electron accepted from this atom, thus creating a hole

Figure 3.4 G%$/-/012%0(5$.'-%,17*,%)/."%'%.(/+'-*2.%/67#(/.5:%O'0"%,17'2.%'.16%8/+*$%(/$*%.1%'%"1-*3%'2, ."*%$*6/012,#0.1(%4*016*$%"%.57*:

3.2 Doped Semiconductors

41(12%'.16%"'$%."(**%*-*0.(12$%/2%/.$%1#.*(%$"*--3%/.%'**$0#5%'2%*-*0.(12%&(16%'%2*/8"41(/28 '.163%."#$%&1(6/28%01+'-*2.%412,$:%!"*%(*$#-.%/$%'%"1-*%/2%."*%2*/8"41(/28%'.16%'2,%'%41#2, 2*8'./+*%0"'(8*%'.%."*%'**$0#-&%A41(12C%'.16:%>.%&1--1)$%."'.%*'0"%'00*7.1(%'.16%7(1+/,*$%' "1-*:% >&% ."*% '00*7.1(% ,17/28% 0120*2.('./12% /$% 1 3 3% )"*(*% 1 3 # # + L % ."*% "1-*% 0120*2.('./12 4*016*$ AK:EC

" " %! 1 3

)"*(*%."*%$#4$0(/7.%"!,*21.*$%"?.57*%$/-/012:%!"#$3%"*(*%."*%6'F1(/.5%0'((/*($%'(*%"1-*$%'2, ."*/(% 0120*2.('./12% /$% ,*.*(6/2*,% 45% 13:% !"*% 0120*2.('./12% 1&% 6/21(/.5% *-*0.(12$% 0'2% 4* &1#2,%45%#$/28%."*%(*-'./12$"/7% =

"" #" % ! #+

'2,%$#4$./.#./28%&1(% " " %&(16%OV:%AK:EC3 =

# # " ! ?????+? 13

AK:bC

!"#$3% ."*% 0120*2.('./12% 1&% ."*% 6/21(/.5% *-*0.(12$% )/--% "'+*% ."*% $'6*% .*67*('.#(*% ,*7*2? = ,*20*%'$%."'.%1&% # + : >.%$"1#-,%4*%*67"'$/X*,%."'.%'%7/*0*%1&%#?.57*%1(%"?.57*%$/-/012%/$%*-*0.(/0'--5%2*#.('-L%."* 0"'(8*%1&%."*%6'F1(/.5%&(**%0'((/*($%A*-*0.(12$%/2%."*%#?.57*%'2,%"1-*$%/2%."*%"?.57*%$/-/012C%'(* 2*#.('-/X*,%45%."*%41#2,%0"'(8*$%'$$10/'.*,%)/."%."*%/67#(/.5%'.16$:

Example 3.2 Sb

K

<12$/,*(% '2%#?.57*% $/-/012% &1(% )"/0"% ."*% ,17'2.% 0120*2.('./12% 1 2 ! SU ⁄ 06 :% ;/2,% ."*% *-*0.(12% '2, "1-*%0120*2.('./12$%'.%)%%e%KUU%Y:

Solution !"*%0120*2.('./12%1&%."*%6'F1(/.5%*-*0.(12$%/$ Sb

# # ! 1 2 ! SU ⁄ 06

K

!"*%0120*2.('./12%1&%."*%6/21(/.5%"1-*$%/$ =

# " # ! ??????+? 12 SU

K

>2%O@'67-*%K:S%)*%&1#2,%."'.%'.%)%e%KUU%Y3% # + ! S:D × SU ⁄ 06 :%!"#$3 SU =

S:D × SU ) " # ! (?????????????????????????????? ? Sb SU K

! =:=D × SU ⁄ 06 R4$*(+*%."'.% # # # # + %'2,%."'.% # # %/$%+'$.-5%"/8"*(%."'2% " #:

K

131

132 Chapter 3 Semiconductors

EXERCISES 3.2 ;1(%."*%$/.#'./12%/2%O@'67-*%K:=3%&/2,%."*%*-*0.(12%'2,%"1-*%0120*2.('./12$%'.%KDU%Y:%g1#%6'5%#$* ."*%+'-#*%1&% # + %'.%)!e%KDU%Y%&1#2,%/2%O@*(0/$*%K:S: Sb K E K Ans. # # ! SU ⁄ 063 % " # ! S:b= × SU ⁄ 06 3.3 ;1(%'%$/-/012%0(5$.'-%,17*,%)/."%41(123%)"'.%6#$.% 1 3 %4*%/&%'.%)%e%KUU%Y%."*%*-*0.(12%0120*2.('./12 E ,(17$%4*-1)%."*%/2.(/2$/0%-*+*-%45%'%&'0.1(%1&% SU h SE K Ans. 1 3 ! S:D × SU ⁄ 06

3.3 Current Flow in Semiconductors !"*(*% '(*% .)1% ,/$./20.-5% ,/&&*(*2.% 6*0"'2/$6$% &1(% ."*% 61+*6*2.% 1&% 0"'(8*% 0'((/*($% '2, "*20*%&1(%0#((*2.%&-1)%/2%$*6/012,#0.1($H%,(/&.%'2,%,/&&#$/12:

3.3.1 Drift Current \"*2%'2%*-*0.(/0'-%&/*-,%&%/$%*$.'4-/$"*,%/2%'%$*6/012,#0.1(%0(5$.'-3%"1-*$%'(*%'00*-*('.*,%/2 ."*%,/(*0./12%1&%&3%'2,%&(**%*-*0.(12$%'(*%'00*-*('.*,%/2%."*%,/(*0./12%1771$/.*%.1%."'.%1&%&: !"/$%$/.#'./12%/$%/--#$.('.*,%/2%;/8:%K:D:%!"*%"1-*$%'0V#/(*%'%+*-10/.5%4"?,(/&.%8/+*2%45 4"?,(/&.%e%µ"&

AK:cC

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AK:TC

)"*(*%."*%(*$#-.%/$%2*8'./+*%4*0'#$*%."*%*-*0.(12$%61+*%/2%."*%,/(*0./12%1771$/.*%.1%&:%f*(* µ # %/$%."*%$.$*#&-"),-2!.!#43%)"/0"%&1(%/2.(/2$/0%$/-/012%/$%'41#.%SKDU%06=`P:$:%a1.*%."'.% µ # /$%'41#.%=:D%./6*$%µ" 3%$/82/&5/28%."'.%*-*0.(12$%61+*%)/."%6#0"%8(*'.*(%*'$*%."(1#8"%."*%$/-? /012%0(5$.'-%."'2%,1%"1-*$: E

Holes Electrons

" !

x

V

Figure 3.5 G2% *-*0.(/0% &/*-,% &% *$.'4-/$"*,% /2% ' 4'(%1&%$/-/012%0'#$*$%."*%"1-*$%.1%,(/&.%/2%."*%,/(*0? ./12%1&%&%'2,%."*%&(**%*-*0.(12$%.1%,(/&.%/2%."*%1771? $/.*% ,/(*0./12:% M1."% ."*% "1-*% '2,% *-*0.(12% ,(/&. 0#((*2.$%'(*%/2%."*%,/(*0./12%1&%&:

3.3 Current Flow in Semiconductors

Q*.W$%21)%(*.#(2%.1%."*%$/28-*?0(5$.'-%$/-/012%4'(%$"1)2%/2%;/8:%K:D:%Q*.%."*%0120*2.('./12 1&%"1-*$%4*%"!'2,%."'.%1&%&(**%*-*0.(12$%#:%\*%)/$"%.1%0'-0#-'.*%."*%0#((*2.%016712*2.%,#*%.1 ."*%&-1)%1&%"1-*$:%<12$/,*(%'%7-'2*%7*(7*2,/0#-'(%.1%."*%5%,/(*0./12:%>2%12*%$*012,3%."*%"1-* 0"'(8*% ."'.% 0(1$$*$% ."'.% 7-'2*% )/--% 4*% A3$"v"?,(/&.C% 01#-164$3% )"*(*% 3% /$% ."*% 0(1$$?$*0./12''(*'%1&%."*%$/-/012%4'(%'2,%$!/$%."*%6'82/.#,*%1&%*-*0.(12%0"'(8*:%!"/$%."*2%6#$.%4*%."*%"1-* 016712*2.%1&%."*%,(/&.%0#((*2.%&-1)/28%."(1#8"%."*%4'(3 6"% e% 3$"4"?,7+8/

AK:SUC

J#4$./.#./28%&1(%v"?,(/&.%&(16%OV:%AK:TC3%)*%14.'/2 6 " ! 3$" µ " &

\*% '(*% #$#'--5% /2.*(*$.*,% /2% ."*% 0#((*2.% ,*2$/.5% 9" 3% )"/0"% /$% ."*% 0#((*2.% 7*(% #2/.% 0(1$$? $*0./12'-%'(*'3 6" 9 " ! ???? ! $" µ " & AK:SSC 3 !"*% 0#((*2.% 016712*2.% ,#*% .1% ."*% ,(/&.% 1&%&(**%*-*0.(12$% 0'2% 4*%&1#2,% /2% '% $/6/-'(% 6'22*(: a1.*3%"1)*+*(3%."'.%*-*0.(12$%,(/&./28%&(16%(/8".%.1%-*&.%(*$#-.%/2%'%0#((*2.%016712*2.%&(16%-*&. .1%(/8".:%!"/$%/$%4*0'#$*%1&%."*%012+*2./12%1&%.'9/28%."*%,/(*0./12%1&%0#((*2.%&-1)%'$%."*%,/(*0? ./12%1&%&-1)%1&%71$/./+*%0"'(8*%'2,%1771$/.*%.1%."*%,/(*0./12%1&%&-1)%1&%2*8'./+*%0"'(8*:%!"#$3 6#% e% ]3$#4#?,(/&. J#4$./.#./28%&1(%v#?,(/&.%&(16%OV:%AK:TC3%)*%14.'/2%."*%0#((*2.%,*2$/.5% 9 # ! 6 # ⁄ 3 %'$% 9 # ! $# µ # &

AK:S=C

!"*%.1.'-%,(/&.%0#((*2.%,*2$/.5%0'2%21)%4*%&1#2,%45%$#66/28% 9 " %'2,% 9 # %&(16%OV$:%AK:SSC '2,%AK:S=C3 9 ! 9 " # 9 # ! $ ( " µ : # # µ # )&

AK:SKC

!"/$%(*-'./12$"/7%0'2%4*%)(/..*2%'$ 9 ! σ&

AK:SBC

9 ! &⁄ρ

AK:SDC

σ ! $ ( " µ" # # µ# )

AK:SEC

S S ? ρ ≡ ??? ! ??????????????????????????????? σ $ ( " µ" # # µ# )

AK:SbC

1(

)"*(*%."*%*-"(+*#!1!#4% σ %/$%8/+*2%45

'2,%."*%&$5!5#!1!#4% ρ %/$%8/+*2%45

R4$*(+*%."'.%OV:%AK:SDC%/$%'%&1(6%1&%R"6W$%-')%'2,%0'2%4*%)(/..*2%'-.*(2'.*-5%'$% ρ ! & ??? 9

P ⁄ 06 : !"#$%."*%#2/.$%1&%ρ%'(*%1"6:0*2./6*.*($% Ω ⋅ 06 ! ????????????????? = G ⁄ 06

AK:ScC

133

134 Chapter 3 Semiconductors

Example 3.3 SE

K

;/2,% ."*% (*$/$./+/.5% 1&% A'C% /2.(/2$/0% $/-/012% '2,% A4C% "?.57*% $/-/012% )/."% 1 3 % ! SU ⁄ 06 :% i$* SU = # + % ! S:D × SU ⁄ 06 K3% '2,% '$$#6*% ."'.% &1(% /2.(/2$/0% $/-/012% µ # % ! SKDU 06 ⁄ P : $% '2, = = = µ " % ! BcU 06 ⁄ P : $3% '2,% &1(% ."*% ,17*,% $/-/012% µ # % ! SSSU 06 ⁄ P : $% '2,% µ " % ! BUU 06 ⁄ P : $: Aa1.*%."'.%,17/28%(*$#-.$%/2%(*,#0*,%0'((/*(%614/-/./*$C: Solution A'C%;1(%/2.(/2$/0%$/-/0123 SU

" ! # ! # + ! S:D × SU ⁄ 06

K

!"#$3 S ρ ! ??????????????????????????????? ? $ ( " µ" # # µ# ) S ρ ! ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? " ST SU SU S:E × SU ( S:D × SU × BcU # S:D × SU × SKDU ) D

! =:=c × SU Ω :%%06 A4C%;1(%."*%"?.57*%$/-/012 SE

" " ! 1 3 ! SU ⁄ 06

K

=

SU = # S:D × SU ) # " ! ?????+? ! (?????????????????????????????? ? ! =:=D × SUB `06K SE 13 SU

!"#$3 S ρ ! ??????????????????????????????? ? $ ( " µ" # # µ# ) S ! ?????????????????????????????????????????????????????????????????????????????????????????????????????????? ? " ST SE B S:E × SU ( SU × BUU # =:=D × SU × SSSU ) S ? ! S:DE Ω :%%06 ! ????????????????????????????????????????????????????????? " ST SE S:E × SU × SU × BUU

R4$*(+*%."'.%."*%(*$/$./+/.5%1&%."*%"?.57*%$/-/012%/$%,*.*(6/2*,%'-61$.%*2./(*-5%45%."*%,17/28%0120*2? D .('./12:%G-$1%14$*(+*%."'.%,17/28%."*%$/-/012%(*,#0*$%/.$%(*$/$./+/.5%45%'%&'0.1(%1&%'41#.% SU 3%'%.(#-5 (*6'(9'4-*%0"'28*:

3.3 Current Flow in Semiconductors 135

EXERCISE 3.4 G% #2/&1(6% 4'(% 1&% #?.57*% $/-/012% 1&% =% µ6% -*28."% "'$% '% +1-.'8*% 1&% S% P% '77-/*,% '0(1$$% /.:% >& SE K = 1 2 ! SU ⁄ 06 %'2,% µ # ! SKDU 06 ⁄ P :$3%&/2,%A'C%."*%*-*0.(12%,(/&.%+*-10/.53%A4C%."*%./6*%/.%.'9*$%'2 *-*0.(12%.1%0(1$$%."*%=?µ6%-*28."3%A0C%."*%,(/&.?0#((*2.%,*2$/.53%'2,%A,C%."*%,(/&.%0#((*2.%/2%."*%0'$* = ."*%$/-/012%4'(%"'$%'%0(1$$%$*0./12'-%'(*'%1&% U:=D µ6 : E B = Ans. E:bD × SU %06`$L%KU%7$L%S:Uc × SU G ⁄ 06 L%=b%µG

3.3.2 Diffusion Current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

Hole injection

AK:STC

" "" " " " " " " " "" " " " " " " " " " " " " " " " " " " " "

(a)

x

Hole concentration, p

Hole diffusion Hole current

x

0 (b)

Figure 3.6 G% 4'(% 1&% $/-/012) 7'8% /2.1 )"/0"% "1-*$% '(*% /2F*0.*,3% ."#$% 0(*'./28% ."* "1-*%0120*2.('./12%7(1&/-*%'-128%."*%5%'@/$3 $"1)2%/2%728:%!"*%"1-*$%,/&&#$*%/2%."*%71$/? ./+*% ,/(*0./12% 1&% 5% '2,% 8/+*% (/$*% .1% '% "1-*? ,/&&#$/12% 0#((*2.% /2% ."*% $'6*% ,/(*0./12: a1.*%."'.%)*%'(*%21.%$"1)/28%."*%0/(0#/.%.1 )"/0"%."*%$/-/012%4'(%/$%0122*0.*,:

136 Chapter 3 Semiconductors =

)"*(*% 9 "%/$%."*%"1-*?0#((*2.%,*2$/.5%A G ⁄ 06 C3%$%/$%."*%6'82/.#,*%1&%*-*0.(12%0"'(8*3% 2 "%/$%' 012$.'2.% 0'--*,% ."*% (!33+5!-") *-"5#'"#% 1(% (!33+5!1!#4% 1&% "1-*$L% '2,% " ( 5 )% /$% ."*% "1-* 0120*2.('./12%'.%71/2.%5:%a1.*%."'.%."*%8(',/*2.% ( ," ⁄ ,5 ) %/$%2*8'./+*3%(*$#-./28%/2%'%71$/./+* 0#((*2.%/2%."*%5%,/(*0./123%'$%$"1#-,%4*%*@7*0.*,: >2%."*%0'$*%1&%*-*0.(12%,/&&#$/12%(*$#-./28%&(16%'2%*-*0.(12%0120*2.('./12%8(',/*2.%A$** ;/8:%K:bC3%'%$/6/-'(%(*-'./12$"/7%'77-/*$3%8/+/28%."*%*-*0.(12?0#((*2.%,*2$/.53 ,# ( 5 ) 9 # ! $2 # ?????????????? ,5

AK:=UC

)"*(*% 2 # %/$%."*%,/&&#$/12%012$.'2.%1(%,/&&#$/+/.5%1&%*-*0.(12$:%R4$*(+*%."'.%'%2*8'./+*%A,#`,5C 8/+*$%(/$*%.1%'%2*8'./+*%0#((*2.3%'%(*$#-.%1&%."*%012+*2./12%."'.%."*%71$/./+*%,/(*0./12%1&%0#((*2. /$%.'9*2%.1%4*%."'.%1&%."*%&-1)%1&%71$/./+*%0"'(8*%A'2,%1771$/.*%.1%."'.%1&%."*%&-1)%1&%2*8'./+* 0"'(8*C:%;1(%"1-*$%'2,%*-*0.(12$%,/&&#$/28%/2%/2.(/2$/0%$/-/0123%.57/0'-%+'-#*$%&1(%."*%,/&&#$/12 012$.'2.$%'(*%2"%e%S=%06=`$%%'2,%2#%e%KD%06=`$: G.%."/$%71/2.%."*%(*',*(%/$%7(14'4-5%)12,*(/28%)"*(*%."*%,/&&#$/12%0#((*2.%/2%."*%$/-/012 4'(%/2%;/8:%K:EA'C%81*$:%G%811,%V#*$./12%'$%)*%'(*%21.%$"1)/28%"1)%."*%(/8".?$/,*%*2,%1&%."* 4'(%/$%0122*0.*,%.1%."*%(*$.%1&%."*%0/(0#/.:%\*%)/--%',,(*$$%."/$%'2,%(*-'.*,%V#*$./12$%/2%,*.'//2%1#(%,/$0#$$/12%1&%."*%"#%F#20./12%/2%-'.*(%$*0./12$:%

Electron concentration, n

Electron diffusion Electron current

x

0

Figure 3.7 >&%."*%*-*0.(12?0120*2.('./12%7(1&/-* $"1)2%/$%*$.'4-/$"*,%/2%'%4'(%1&%$/-/0123%*-*0.(12$ ,/&&#$*%/2%."*%5%,/(*0./123%8/+/28%(/$*%.1%'2%*-*0.(12? ,/&&#$/12%0#((*2.%/2%."*%2*8'./+*%?5%,/(*0./12:

Example 3.4 <12$/,*(%'%4'(%1&%$/-/012%/2%)"/0"%'%"1-*%0120*2.('./12%7(1&/-*%,*$0(/4*,%45 " ( 5 ) ! "U %

"5 ⁄ ;: SE

K

/$%*$.'4-/$"*,:%;/2,%."*%"1-*?0#((*2.%,*2$/.5%'.%5!e%U:%Q*.% " U ! SU ⁄ 06 %'2,% ; " ! S % µ6:%>&%."* 0(1$$?$*0./12'-%'(*'%1&%."*%4'(%/$%SUU%µ6=3%&/2,%."*%0#((*2.%6":

3.3 Current Flow in Semiconductors

Solution ," ( 5 ) 9 " % ! " $2 " ?????????????? ,5 "5 ⁄ ;: , ! " $2 " ?????? [ " U % ] ,5

!"#$3 2" 9 " ( U )% ! $ ?????? " U ;" ! S:E × SU

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S= ? × SU SE × ?????????????????? "B S × SU

! ST= G ⁄ 06

=

!"*%0#((*2.%6 "%0'2%4*%&1#2,%&(16 6" % ! 9" × 3 ! ST= × SUU × SU

"c

e%ST=%%µG

EXERCISE 3.5 !"*%-/2*'(%*-*0.(12?0120*2.('./12%7(1&/-*%$"1)2%/2%;/8:%OK:D%"'$%4**2%*$.'4-/$"*,%/2%'%7/*0*%1&%$/-/? Sb K 012:% >&% # U ! SU ⁄ 06 % '2,% <% e% S% µ63% &/2,% ."*% *-*0.(12?0#((*2.% ,*2$/.5% /2% 6/0(1% '67*(*$% 7*( 6/0(12%$V#'(*,%AµG`µ6=C:%>&%'%,/&&#$/12%0#((*2.%1&%S%6G%/$%(*V#/(*,%)"'.%6#$.%."*%0(1$$?$*0./12''(*'%7/2%'%,/(*0./12%7*(7*2,/0#-'(%.1%."*%7'8*C%4*h n(x) n0

0

Ans. $%&µ'(µ)*+&,-&µ)*

W

x

Figure E3.5

137

138 Chapter 3 Semiconductors

3.3.3 Relationship between D and m G%$/67-*%4#.%71)*(&#-%(*-'./12$"/7%./*$%."*%,/&&#$/12%012$.'2.%)/."%."*%614/-/.53 2" 2# ?????? ! ?????? ! = )

µ#

AK:=SC

µ"

)"*(*% = ) ! () ⁄ $ :%!"*%7'('6*.*(% = ) %/$%921)2%'$%."*%#/$&,'.)1-.#'%$:%G.%(116%.*67*('? .#(*3%) ! KUU%Y%'2,% = ) %%e%=D:T %6P:%\*%)/--%*201#2.*(% = ) %(*7*'.*,-5%."(1#8"1#.%."/$%4119: !"*%(*-'./12$"/7%/2%OV:%AK:=SC%/$%921)2%'$%."*%9!"5#$!")&$.'#!-"5/!0:

EXERCISE =

3.6 i$*%."*% O/2$.*/2% (*-'./12$"/7%.1%&/2,% 2 # %'2,% 2 " %&1(%/2.(/2$/0%$/-/012%#$/28% µ # ! SKDU%06 ⁄ P⋅ $ = '2,% µ " ! BcU%06 ⁄ P ⋅ $ : = Ans. KD%06 `$L%S=:B%06= `$

3.4 The pn Junction with Open-Circuit Terminals (Equilibrium) f'+/28%-*'(2*,%/671(.'2.%$*6/012,#0.1(%0120*7.$3%)*%'(*%21)%(*',5%.1%012$/,*(%1#(%&/($. 7('0./0'-%$*6/012,#0.1(%$.(#0.#(*j."*%"#%F#20./12:%G$%6*2./12*,%7(*+/1#$-53%."*%"#%F#20? ./12%/67-*6*2.$%."*%,/1,*%A<"'7.*(%BC%'2,%7-'5$%."*%,16/2'2.%(1-*%/2%."*%$.(#0.#(*%'2,%17*(? './12%1&%."*%4/71-'(%F#20./12%.('2$/$.1(%AMN!C:%G$%)*--3%#2,*($.'2,/28% "#%F#20./12$%/$%+*(5 /671(.'2.%.1%."*%$.#,5%1&%."*%kRJ;O!%17*('./12%A<"'7.*(%DC:

3.4.1 Physical Structure ;/8#(*% K:c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c3%*@.*(2'-%)/(* 0122*0./12$%'(*%6',*%.1%."*%"%'2,%#%(*8/12$%."(1#8"%6*.'-%A'-#6/2#6C%012.'0.$:%>&%."*%"# F#20./12% /$% #$*,% '$% '% ,/1,*3% ."*$*% 012$./.#.*% ."*% ,/1,*% .*(6/2'-$% '2,% '(*% ."*(*&1(*% -'4*-*, Z'21,*[%'2,%Z0'."1,*[%/2%9**7/28%)/."%,/1,*%.*(6/21-185:K

K

!"/$%.*(6/21-185%/2%&'0.%/$%'%0'((51+*(%&(16%."'.%#$*,%)/."%+'0##6?.#4*%.*0"21-1853%)"/0"%)'$%."* .*0"21-185%&1(%6'9/28%,/1,*$%'2,%1."*(%*-*0.(12/0%,*+/0*$%#2./-%."*%/2+*2./12%1&%."*%.('2$/$.1(%/2%STBb: !"/$%*+*2.%#$"*(*,%/2%."*%*('%1&%$1-/,?$.'.*%*-*0.(12/0$3%)"/0"%0"'28*,%21.%12-5%*-*0.(12/0$3%0166#2/? 0'./12$3%'2,%0167#.*($%4#.%/2,**,%."*%)1(-,d

3.5 The pn Junction with an Applied Voltage

Metal contact

Anode

Metal contact

p-type silicon

n-type silicon

Cathode

Figure 3.8 J/67-/&/*,%7"5$/0'-%$.(#0.#(*%1&%."*%"#%F#20./12:%AG0.#'-%8*16*.(/*$%'(*%8/+*2%/2%G77*2,/@%G:C G$%."*!"#%F#20./12%/67-*6*2.$%."*%F#20./12%,/1,*3%/.$%.*(6/2'-$%'(*%-'4*-*,%'21,*%'2,%0'."1,*:

3.4.2 Operation with Open-Circuit Terminals ;/8#(*%K:T%$"1)$%'%"#%F#20./12%#2,*(%17*2?0/(0#/.%012,/./12$j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f*(*%'-$13%."* 41#2,%71$/./+*%0"'(8*3%)"/0"%2*#.('-/X*$%."*%0"'(8*%1&%."*%6'F1(/.5%*-*0.(12$3%/$%21.%$"1)2 /2%1(,*(%.1%9**7%."*%,/'8('6%$/67-*:%!"*%#?.57*%6'.*(/'-%'-$1%012.'/2$%6/21(/.5%"1-*$%8*2*(? '.*,%45%."*(6'-%/12/X'./12%4#.%21.%$"1)2%/2%."*%,/'8('6: The Diffusion Current ID M*0'#$*%."*%0120*2.('./12%1&%"1-*$%/$%"/8"%/2%."*%"%(*8/12%'2, -1)%/2%."*%#%(*8/123%"1-*$%,/&&#$*%'0(1$$%."*%F#20./12%&(16%."*%"%$/,*%.1%."*%#%$/,*L%$/6/-'(-53 *-*0.(12$%,/&&#$*%'0(1$$%."*%F#20./12%&(16%."*%#%$/,*%.1%."*%"%$/,*:%!"*$*%.)1%0#((*2.%01671? 2*2.$%',,%.18*."*(%.1%&1(6%."*%,/&&#$/12%0#((*2.%62 3%)"1$*%,/(*0./12%/$%&(16%."*%"%$/,*%.1%."* #%$/,*3%'$%/2,/0'.*,%/2%;/8:%K:T: The Depletion Region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j1(3%$/67-53%($0.$#!-")&$%!-"j/$%'-$1%0'--*,%."*%50'*$:*/'&%$ &$%!-":% !"*% 0"'(8*$% 12% 41."% $/,*$% 1&% ."*% ,*7-*./12% (*8/12% 0'#$*% '2% *-*0.(/0% &/*-,% &% .1% 4*

139

140 Chapter 3 Semiconductors

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(b) Figure 3.9 7'8%!"*%"#%F#20./12%)/."%21%'77-/*,%+1-.'8*%A17*2?0/(0#/.*,%.*(6/2'-$C:%728%!"*%71.*2./'-%,/$.(/? 4#./12%'-128%'2%'@/$%7*(7*2,/0#-'(%.1%."*%F#20./12:

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3.5 The pn Junction with an Applied Voltage 141

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62 = 6A B

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142 Chapter 3 Semiconductors

ID IS " " " " " "

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3.5 The pn Junction with an Applied Voltage 143

,*7-*./12%(*8/12%/2%."*%"%$/,*%45% 5 " %'2,%/2%."*%#%$/,*%45%5#3%)*%0'2%*@7(*$$%."*%6'82/.#,*%1& ."*%0"'(8*%12%."*%#%$/,*%1&%."*%F#20./12%'$ AK:=KC

B l % ! $35 # 1 2

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144 Chapter 3 Semiconductors

Example 3.5 <12$/,*(%'%"#%F#20./12%/2%*V#/-/4(/#6%'.%(116%.*67*('.#(*%A)%e%KUU%YC%&1(%)"/0"%."*%,17/28%0120*2? Sc K SE K .('./12$%'(*% 1 3 % ! SU ⁄ 06 %'2,% 1 2 % ! SU ⁄ 06 %'2,%."*%0(1$$?$*0./12'-%'(*'%3%e%SU]B%06=:%<'-0#-'.* SU K "" 3% #"U3% ## 3% "#U3% =U3%<3% 5#3% 5" 3%'2,% B 9 :%i$*% # + % ! S:D × SU ⁄ 06 : Solution

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3.5 The pn Junction with an Applied Voltage 145

EXERCISES 3.7 J"1)%."'. S $ = U % ! ??? ???? = ε0

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(c) Forward Bias

(V0 ! VF)

ID

VF

n

146 Chapter 3 Semiconductors

3.5 The pn Junction with an Applied Voltage

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

S S =ε 0 ????? ??????? ? # ??????? ( = U # = E ) $ 13 12

AK:KSC

'2,%."*%6'82/.#,*%1&%."*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1&%."*%,*7-*./12%(*8/12%0'2%4*%,*.*(? 6/2*,%45%(*7-'0/28% = U %/2%OV:%AK:KUC%45% ( = U # = E )3 13 12 ? ( =U # =E ) B 9 % ! 3 =ε 0 $ ??????????????????? 13 # 12

AK:K=C

\*%2*@.%012$/,*(%."*%&1()'(,?4/'$%0'$*%$"1)2%/2%;/8:%K:SSA0C:%f*(*%."*%'77-/*,%+1-.'8*%=F %/$ /2%."*%,/(*0./12%."'.%$#4.('0.$%&(16%."*%4#/-.?/2%+1-.'8*% =U3%(*$#-./28%/2%'%(*,#0*,%4'((/*(%+1-.? '8*% ( =U " =F ) %'0(1$$%."*%,*7-*./12%(*8/12:%!"/$%(*,#0*,%4'((/*(%+1-.'8*%)/--%4*%'00167'2/*, 45% (*,#0*,% ,*7-*./12?(*8/12% 0"'(8*% '2,% 01((*$712,/28-5% 2'((1)*(% ,*7-*./12?(*8/12% )/,." <:%k1$.%/671(.'2.-53%."*%-1)*(/28%1&%."*%4'((/*(%+1-.'8*%)/--%*2'4-*%61(*%"1-*$%.1%,/&&#$* &(16% "% .1% #! '2,% 61(*% *-*0.(12$% .1% ,/&&#$*% &(16% #% .1% ":% !"#$% ."*% ,/&&#$/12% 0#((*2.% 6 2 /20(*'$*$%$#4$.'2./'--5%'2,3%'$%)/--%4*%$**2%$"1(.-53%0'2%4*016*%6'25%1(,*($%1&%6'82/.#,* -'(8*(%."'2%."*%,(/&.%0#((*2.% 6 A : %!"*%0#((*2.%6%/2%."*%*@.*(2'-%0/(0#/.%/$%1&%01#($*%."*%,/&&*(*20* 4*.)**2% 6 2 %'2,% 6 A 3 6%% ! 6 2 " 6 A

'2,%/.%&-1)$%/2%."*%&1()'(,%,/(*0./12%1&%."*%F#20./123%&(16%"%.1%#:%\*%."#$%0120-#,*%."'.%."* "#%F#20./12%0'2%012,#0.%'%$#4$.'2./'-%0#((*2.%/2%."*%&1()'(,?4/'$%(*8/12%'2,%."'.%0#((*2.%/$ 61$.-5%'%,/&&#$/12%0#((*2.%)"1$*%+'-#*%/$%,*.*(6/2*,%45%."*%&1()'(,?4/'$%+1-.'8*% =F :

3.5.2 The Current–Voltage Relationship of the Junction \*%'(*%21)%(*',5%.1%&/2,%'2%'2'-5./0'-%*@7(*$$/12%."'.%,*$0(/4*$%."*%0#((*2.]+1-.'8*%(*-'? ./12$"/7% 1&% ."*% "#% F#20./12:% >2% ."*% &1--1)/28% )*% 012$/,*(% '% F#20./12% 17*('./28% )/."% '

147

148 Chapter 3 Semiconductors &1()'(,%'77-/*,%+1-.'8*%=!'2,%,*(/+*%'2%*@7(*$$/12%&1(%."*%0#((*2.%6!."'.%&-1)$%/2%."*%&1(? )'(,%,/(*0./12%A&(16%"%.1%#C:%f1)*+*(3%1#(%,*(/+'./12%/$%8*2*('-%'2,%)/--%4*%$**2%.1%5/*-, ."*%(*+*($*%0#((*2.%)"*2%."*%'77-/*,%+1-.'8*%=%/$%6',*%2*8'./+*: ;(16%."*%V#'-/.'./+*%,*$0(/7./12%'41+*%)*%921)%."'.%'%&1()'(,?4/'$%+1-.'8*%=%$#4.('0.$ &(16%."*%4#/-.?/2%+1-.'8*%= U 3%."#$%(*$#-./28%/2%'%-1)*(%4'((/*(%+1-.'8*% ( = U " = ):%!"*%-1)*(*, 4'((/*(%/2%.#(2%6'9*$%/.%71$$/4-*%&1(%'%8(*'.*(%2#64*(%1&%"1-*$%.1%1+*(016*%."*%4'((/*(%'2,%,/&? &#$*%/2.1%."*%#%(*8/12:%G%$/6/-'(%$.'.*6*2.%0'2%4*%6',*%'41#.%*-*0.(12$%&(16%."*%#!(*8/12%,/&? &#$/28%/2.1%."*%"%(*8/12:% Q*.%#$%21)%012$/,*(%."*%"1-*$%/2F*0.*,%/2.1%."*%#%(*8/12:%!"*%0120*2.('./12%1&%"1-*$%/2 ."*%#%(*8/12%'.%."*%*,8*%1&%."*%,*7-*./12%(*8/12%)/--%/20(*'$*%012$/,*('4-5:%>2%&'0.3%'2%/671(? .'2.%(*$#-.%&(16%,*+/0*%7"5$/0$%$"1)$%."'.%."*%$.*',5?$.'.*%0120*2.('./12%'.%."*%*,8*%1&%."* ,*7-*./12%(*8/12%)/--%4*% " # ( 5 # )% ! " #U %

= ⁄ =)

AK:KKC

!"'.%/$3%."*%0120*2.('./12%1&%."*%6/21(/.5%"1-*$%/20(*'$*$%&(16%."*%*V#/-/4(/#6%+'-#*%1&% " #U A$**%;/8:%K:SUC%.1%."*%6#0"%-'(8*(%+'-#*%,*.*(6/2*,%45%."*%+'-#*%1&%=3%8/+*2%45%OV:%AK:KKC: \*%,*$0(/4*%."/$%$/.#'./12%'$%&1--1)$H%!"*%&1()'(,?4/'$%+1-.'8*!=%(*$#-.$%/2%'2%$;*$55 *-"*$"#&'#!-"%1&%6/21(/.5%"1-*$%'.% 5%%! 5 # 3 %8/+*2%45 O@0*$$%0120*2.('./12%e% " #U % %

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! " #U ( %

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AK:KBC

!"*%/20(*'$*%/2%6/21(/.5%0'((/*(%0120*2.('./12%/2%OV$:%AK:KKC%'2,%AK:KBC%100#($%'.%."*%*,8*%1& ."*%,*7-*./12%(*8/12% ( 5% ! 5 # ):%G$%."*%/2F*0.*,%"1-*$%,/&&#$*%/2.1%."*%#%6'.*(/'-3%$16*%)/-(*0164/2*%)/."%."*%6'F1(/.5%*-*0.(12$%'2,%,/$'77*'(:%!"#$3%."*%*@0*$$%"1-*%0120*2.('./12 )/--%,*0'5%*@712*2./'--5%)/."%,/$.'20*:%G$%'%(*$#-.3%/2%."*%.1.'-%"1-*%0120*2.('./12%/2%."*%# 6'.*(/'-%)/--%4*%8/+*2%45% " # ( 5 )% ! " #U # ( O@0*$$%0120*2.('./12 )%

"( 5 " 5# ) ⁄ ;"

J#4$./.#./28%&1(%."*%ZO@0*$$%0120*2.('./12[%&(16%OV:%AK:KBC%8/+*$ " # ( 5 ) ! " #U # " #U ( %

= ⁄ =)

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"( 5 " 5# ) ⁄ ;"

AK:KDC

!"*%*@712*2./'-%,*0'5%/$%0"'('0.*(/X*,%45%."*%012$.'2.%;"3%)"/0"%/$%0'--*,%."*%(!33+5!-").$"%#/%1& "1-*$%/2%."*%#%6'.*(/'-:%!"*%$6'--*(%."*%+'-#*%1&%;"3%."*%&'$.*(%."*%/2F*0.*,%"1-*$%)/--%(*0164/2* )/."%."*%6'F1(/.5%*-*0.(12$3%(*$#-./28%/2%'%$.**7*(%,*0'5%1&%6/21(/.5%0'((/*(%0120*2.('./12: ;/8#(*%K:S=%$"1)$%."*%$.*',5?$.'.*%6/21(/.5%0'((/*(%0120*2.('./12%7(1&/-*$%12%41."%$/,*$%1&%'%"# F#20./12%/2%)"/0"% 1 3 # 1 2 :%Q*.W$%$.'5%'%-/..-*%-128*(%)/."%."*%,/&&#$/12%1&%"1-*$%/2.1%."*%#!(*8/12: a1.*%."'.%."*%$"',*,%(*8/12%#2,*(%."*%*@712*2./'-%(*7(*$*2.$%."*%*@0*$$%6/21(/.5%0'((/*($%A"1-*$C: ;(16%1#(%$.#,5%1&%,/&&#$/12%/2%J*0./12%K:K3%)*%921)%."'.%."*%*$.'4-/$"6*2.%1&%'%0'((/*(%0120*2.('? ./12%7(1&/-*%$#0"%'$%."'.%/2%;/8:%K:S=%/$%*$$*2./'-%.1%$#771(.%'%$.*',5?$.'.*%,/&&#$/12%0#((*2.:%>2%&'0.3 )*%0'2%21)%&/2,%."*%+'-#*%1&%."*%"1-*],/&&#$/12%0#((*2.%,*2$/.5%45%'77-5/28%OV:%AK:STC3 ," # ( 5 ) ? 9 " ( 5 )% ! " $2 " ??????????????? ,5 J#4$./.#./28%&1(% " # ( 5 ) %&(16%OV:%AK:KDC%8/+*$ 2" = ⁄ =) "( 5 " 5# ) ⁄ ;: 9 " ( 5 )% ! $ ?????? " #U ( % " S )% ;:

AK:KEC

3.5 The pn Junction with an Applied Voltage

pn , np p region

Depletion region

pn (xn)

n region

Excess concentration pn (x) np (!xp) np(x)

pn0 Thermal equilibrium value

np0 !xp 0

xn

x

Figure 3.12 k/21(/.5?0'((/*(%,/$.(/4#./12%/2%'%&1()'(,?4/'$*,%"#%F#20./12:%>.%/$%'$$#6*,%."'.%."*%"%(*8/12% /$%61(*%"*'+/-5%,17*,%."'2%."*%#%(*8/12L%13%#%12:

G$%*@7*0.*,3% 9 " ( 5 ) %/$%"/8"*$.%'.% 5 ! 5 #3 2 = ⁄ =) 9 " ( 5 # ) ! $ ?????"? " #U ( % " S) ;"

AK:KbC

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bC: G2%*@'0.-5%7'('--*-%,*+*-176*2.%0'2%4*%'77-/*,%.1%."*%*-*0.(12$%."'.%'(*%/2F*0.*,%&(16%."*%# .1% ."*% "% (*8/123% (*$#-./28% /2% '2% *-*0.(12% ,/&&#$/12% 0#((*2.% 8/+*2% 45% '% $/67-*% ','7.'./12% 1&% OV: AK:KbC3 2 = ⁄ =) AK:KcC " S) 9 # ( " 5 " ) ! $ ?????#? # "U ( % ;# a1)3%'-."1#8"%."*%0#((*2.$%/2%OV$:%AK:KbC%'2,%AK:KcC%'(*%&1#2,%'.%."*%.)1%*,8*$%1&%."*%,*7-*? ./12%(*8/123%."*/(%+'-#*$%,1%21.%0"'28*%/2%."*%,*7-*./12%(*8/12:%!"#$%)*%0'2%,(17%."*%-10'./12 ,*$0(/7.1($% ( 5 # )3% ( " 5 " )3%',,%."*%.)1%0#((*2.%,*2$/./*$3%'2,%6#-./7-5%45%."*%F#20./12%'(*'%3%.1 14.'/2%."*%.1.'-%0#((*2.%6!'$% 6 ! 3 ( 9" # 9# ) 2 2 = ⁄ =) " S) 6 ! 3$ ?????"? " #U # ?????#? # :U ( % ;" ;#

149

150 Chapter 3 Semiconductors =

=

J#4$./.#./28%&1(% " #U % ! # + ⁄ 1 2 %'2,%&1(% # "U ! # + ⁄ 1 3 %8/+*$ 2# 2" = ⁄ =) = " S) 6 ! 3$# + ????????????? # ???????????? ( % ;" 12 ;# 13

AK:KTC

;(16%."/$%*V#'./12%)*%21.*%."'.%&1(%'%2*8'./+*%=%A(*+*($*%4/'$C%)/."%'%6'82/.#,*%1&%'%&*) ./6*$% = ) %A=D:T%6PC3%."*%*@712*2./'-%.*(6%4*016*$%*$$*2./'--5%X*(13%'2,%."*%0#((*2.%'0(1$$ ."*% F#20./12% 4*016*$% 2*8'./+*% '2,% 012$.'2.:% ;(16% 1#(% V#'-/.'./+*% ,*$0(/7./12% /2% J*0./12 K:D:S3%)*%921)%."'.%."/$%0#((*2.%6#$.%4*% 6 A : %!"#$3 6% ! 6 A ( %

= ⁄ =)

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AK:BUC

)"*(* 2# 2" = 6 A% % ! 3$# + ????????????? # ???????????? ;" 12 ;# 13

AK:BSC

;/8#(*%AK:SKC%$"1)$%."*%6G=%0"'('0.*(/$./0%1&%."*%"#%F#20./12%AOV:%K:BUC:%R4$*(+*%."'.%/2 ."*%(*+*($*%,/(*0./12%."*%0#((*2.%$'.#('.*$%'.%'%+'-#*%*V#'-%.1%G6A:%;1(%."/$%(*'$123% 6 A %/$%8/+*2 ."*%2'6*%5'#+&'#!-")*+&&$"#:%;(16%OV:%AK:BSC%)*%$**%."'.%6A%/$%,/(*0.-5%7(171(./12'-%.1%."* 0(1$$?$*0./12'-%'(*'%3%1&%."*%F#20./12:%!"#$3%'21."*(%2'6*%&1(%6A 3%12*%)*%7(*&*(%.1%#$*%/2%."/$ 41193%/$%."*%F#20./12)5*'.$)*+&&$"#:%!57/0'-%+'-#*$%&1(%6A 3%&1(%F#20./12$%1&%+'(/1#$%'(*'$3%('28* " Sc " S= &(16% SU %.1% SU %G:% M*$/,*$% 4*/28% 7(171(./12'-% .1% ."*% F#20./12% '(*'% 33% ."*% *@7(*$$/12% &1(% 6 A % /2% OV:% AK:BSC = /2,/0'.*$%."'.% 6 A %/$% 7(171(./12'-%.1% # + %)"/0"%/$%'%+*(5%$.(128% ./12%1&% .*67*('.#(*%A$** OV: K:=C:

I

0 IS

Figure 3.13 !"*%"#%F#20./12%6G=%0"'('0.*(/$./0:

V

3.5 The pn Junction with an Applied Voltage

Example 3.6 Sc

K

SE

K

;1(% ."*% "#! F#20./12% 012$/,*(*,% /2% O@'67-*% K:D% &1(% )"/0"% 1 3 % ! SU ⁄ 06 3% 1 2 % ! SU ⁄ 06 3 "B = SU K = 3% ! SU 06 3% # + % ! S:D × SU ⁄ 06 3%-*.% ; " % ! D %µ63% ; # ! SU %µ63% 2 " %A/2%."*%#%(*8/12C%e SU%06 ⁄ P : $3 = '2,% 2 # %A/2%."*%"%(*8/12C% ! Sc%06 ⁄ P: $:%!"*%"#%F#20./12%/$%&1()'(,%4/'$*,%'2,%012,#0./28%'%0#((*2. 6%e%U:S%6G:%<'-0#-'.*H%A'C% 6 A L%A4C%."*%&1()'(,?4/'$%+1-.'8*%=L%'2,%A0C%."*%016712*2.%1&%."*%0#((*2.%6 ,#*%.1%"1-*%/2F*0./12%'2,%."'.%,#*%.1%*-*0.(12%/2F*0./12%'0(1$$%."*%F#20./12: Solution A'C%i$/28%OV:%AK:BSC3%)*%&/2,% 6 A %'$% "B

SU =

" ST

× S:E × SU × ( S:D × SU ) × SU Sc ??????????????????????????????????? ? # ?????????????????????????????????????? ? "B SE "B Sc D × SU × SU SU × SU × SU

6 A% % ! SU

! b:K × SU

" SD

%G

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= ⁄ =)

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;1(%6!e%U:S%6G3

6 =% ! = ) %-2 ???? 6A "K

U:S × SU "K ? =% ! =D:T × SU %-2 ????????????????????????? " SD b:K × SU

e%U:EUD%P A0C%!"*%"1-*?/2F*0./12%016712*2.%1&%6!0'2%4*%&1#2,%#$/28%OV:%AK:KbC 2" = ⁄ =) 6 " % ! 3$ ?????? " #U ( % " S) ;" 2 " # = = ⁄ =) ! 3$ ?????? ??????+? ( % " S) ;" 12

J/6/-'(-5% 6 # %0'2%4*%&1#2,%#$/28%OV:%AK:KTC3%

=

2 # =⁄= 6 # ! 3$ ?????#? ?????+? ( % ) " S ) ;# 13

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1 ??????3? 12

Sc 6" SU ? = ???? % ! SU ?????? × SU ?????? × ????????? ! S:SS × SU ! SSS 6 # Sc D SU SE

151

152 Chapter 3 Semiconductors

Example 3.6 continued

!"#$%61$.%1&%."*%0#((*2.%/$%012,#0.*,%45%"1-*$%/2F*0.*,%/2.1%."*%#%(*8/12: J7*0/&/0'--53 SSS 6 " % ! ????????? × U:S ! U:UTTS %6G SS= S 6 # % ! ????????? × U:S ! U:UUUT %6G SS=

!"/$%$.'2,$%.1%(*'$123%$/20*%."*%"%6'.*(/'-%"'$%'%,17/28%0120*2.('./12%SUU%./6*$%."'.%1&%."*%#%6'.*(/'-:

EXERCISES 3.10 J"1)%."'.%/&% 1 3 # 1 2 3% = 2" ? 6 A% ! 3$# + ???????????? ;" 12

3.11 ;1(%."*%"#%F#20./12%/2%O@'67-*%K:E3%&/2,%."*%+'-#*%1&% 6 A %'2,%."'.%1&%."*%0#((*2.%6%'.%=%e%U:EUD%P%A$'6* +1-.'8*%&1#2,%/2%O@'67-*%K:E%'.%'%0#((*2.%6%e%U:S%6GC%/&% 1 2 %/$%(*,#0*,%45%'%&'0.1(%1&%=: " SB Ans. S:BE × SU %GL%U:=%6G 3.12 ;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E3%&/2,%."*%)/,."%1&%."*%,*7-*./12%(*8/12%<%01(? (*$712,/28%.1%."*%&1()'(,?4/'$%+1-.'8*%&1#2,%/2%O@'67-*%K:E:%AI+#/H%i$*%."*%&1(6#-'%/2%OV: AK:KSC )/."% = E %(*7-'0*,%)/."% " = F :C Ans. U:SEE%µ6 3.13 ;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E3%&/2,%."*%)/,."%1&%."*%,*7-*./12%(*8/12%<%'2, ."*%0"'(8*%$.1(*,%/2%."*%,*7-*./12%(*8/12% B 9 %)"*2%'%=?P%(*+*($*%4/'$%/$%'77-/*,:%G-$1%&/2,%."*%+'-#* 1&%."*%(*+*($*%0#((*2.%6: " SD Ans. U:EUc%µ6L%T:EK%7
3.5.3 Reverse Breakdown !"*% ,*$0(/7./12% 1&% ."*% 17*('./12% 1&% ."*% "#% F#20./12% /2% ."*% (*+*($*% ,/(*0./123% '2,% ."*% 6 " = (*-'./12$"/7% 1&% ."*% F#20./12% /2% OV:% AK:BUC3% /2,/0'.*% ."'.% '.% '% (*+*($*?4/'$% +1-.'8*% ]=3% )/." = # = ) 3%."*%(*+*($*%0#((*2.%."'.%&-1)$%'0(1$$%."*%F#20./12%/$%'77(1@/6'.*-5%*V#'-%.1% 6 A !'2, ."#$%/$% +*(5% $6'--:% f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

3.5 The pn Junction with an Applied Voltage 153

I

!VZ 0

V

Figure 3.14 !"*%6?=%0"'('0.*(/$./0%1&%."*%"#%F#20./12%$"1)/28%."*%('7/,%/20(*'$*%/2%(*+*($*%0#((*2.%/2%."* 4(*'9,1)2%(*8/12:

-/6/.*,%45%."*%*@.*(2'-%0/(0#/.%.1%'%Z$'&*[%+'-#*:%!"*%Z$'&*[%+'-#*%/$%12*%."'.%(*$#-.$%/2%."*%-/6/? .'./12%1&%."*%71)*(%,/$$/7'.*,%/2%."*%F#20./12%.1%'%$'&*3%'--1)'4-*%-*+*-: !"*(*%'(*%.)1%71$$/4-*%6*0"'2/$6$%&1(%"#%F#20./12%4(*'9,1)2H%."*%>$"$&)$33$*#b%'2,%."* '1'.'"*/$)$33$*#:%>&%'%"#%F#20./12%4(*'9$%,1)2%)/."%'%4(*'9,1)2%+1-.'8*% = H < D %P3%."*%4(*'9? ,1)2%6*0"'2/$6%/$%#$#'--5%."*%X*2*(%*&&*0.:%G+'-'20"*%4(*'9,1)2%100#($%)"*2% = H %/$%8(*'.*( ."'2%'77(1@/6'.*-5%b%P:%;1(%F#20./12$%."'.%4(*'9%,1)2%4*.)**2%D%P%'2,%b%P3%."*%4(*'9,1)2 6*0"'2/$6%0'2%4*%*/."*(%."*%X*2*(%1(%."*%'+'-'20"*%*&&*0.%1(%'%0164/2'./12%1&%."*%.)1: n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a'6*,%'&.*(%'2%*'(-5%)1(9*(%/2%."*%'(*':%a1.*%."'.%."*%$#4$0(/7.!H%/2%=H%,*21.*$%J%#%7:%\*%)/--%#$*%=H .1%,*21.*%."*%4(*'9,1)2%+1-.'8*%)"*."*(%."*%4(*'9,1)2%6*0"'2/$6%/$%."*%X*2*(%*&&*0.%1(%."*%'+'-'20"* *&&*0.: b%

154 Chapter 3 Semiconductors G$%)/--%4*%$**2%/2%<"'7.*(%B3%$16*%"#!F#20./12%,/1,*$%'(*%&'4(/0'.*,%.1%17*('.*%$7*0/&/? 0'--5%/2%."*%4(*'9,1)2%(*8/123%)"*(*%#$*%/$%6',*%1&%."*%2*'(-5%012$.'2.%+1-.'8*%=H:

3.6 Capacitive Effects in the pn Junction !"*(*%'(*%.)1%0"'(8*%$.1('8*%6*0"'2/$6$%/2%."*%"#%F#20./12:%R2*%/$%'$$10/'.*,%)/."%."*%0"'(8* $.1(*,% /2% ."*% ,*7-*./12% (*8/123% '2,% ."*% 1."*(% '$$10/'.*,% )/."% ."*% 6/21(/.5% 0'((/*(% 0"'(8* $.1(*,%/2%."*%#%'2,%"%6'.*(/'-$%'$%'%(*$#-.%1&%."*%0120*2.('./12%7(1&/-*$%*$.'4-/$"*,%45%%0'(? (/*(%/2F*0./12:%\"/-*%."*%&/($.%/$%*'$/*(%.1%$**%)"*2%."*%"#%F#20./12%/$%(*+*($*%4/'$*,3%."*%$*0? 12,%/$%/2%*&&*0.%12-5%)"*2%."*%F#20./12%/$%&1()'(,%4/'$*,:

3.6.1 Depletion or Junction Capacitance \"*2%'%"#%F#20./12%/$%(*+*($*%4/'$*,%)/."%'%+1-.'8*%=E 3%."*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1& ."*%,*7-*./12%(*8/12%/$%8/+*2%45%OV:%AK:K=C3 13 12 ? ( = # =E ) B 9 %% ! 3 =ε 0 $ ??????????????????? 13 # 12 U

!"#$3%&1(%'%8/+*2%"#%F#20./123 B9 ! α =U # =E

AK:B=C

13 12 ? α% ! 3 =ε 0 $ ??????????????????? 13 # 12

AK:BKC

Charge stored in depletion layer, QJ

)"*(*% α %/$%8/+*2%45

Slope $ CJ

Q Bias point

0

VQ

Reverse voltage,VR

Figure 3.15 !"*% 0"'(8*% $.1(*,% 12% */."*(% $/,*% 1&% ."*% ,*7-*./12% -'5*(% '$% '% ./12% 1&% ."*% (*+*($* +1-.'8* =E:

3.6 Capacitive Effects in the pn Junction 155

!"#$% B 9 %/$%212-/2*'(-5%(*-'.*,%.1%=E 3%'$%$"1)2%/2%;/8:%AK:SDC:%!"/$%212-/2*'(%(*-'./12$"/7 6'9*$%/.%,/&&/0#-.%.1%,*&/2*%'%0'7'0/.'20*%."'.%'001#2.$%&1(%."*%2**,%.1%0"'28*% B 9 %)"*2*+*( = E %/$%0"'28*,:%\*%0'23%"1)*+*(3%'$$#6*%."'.%."*%F#20./12%/$%17*('./28%'.%'%71/2.%$#0"%'$%B3 '$%/2,/0'.*,%/2%;/8:%K:SD3%'2,%,*&/2*%'%0'7'0/.'20*% L M %."'.%(*-'.*$%."*%0"'28*%/2%."*%0"'(8* B 9 %.1%'%0"'28*%/2%."*%+1-.'8*% = E 3 ,B L M%% ! ?????????9 ,= E

AK:BBC = E != B

!"/$% /20(*6*2.'-?0'7'0/.'20*% '77(1'0"% .#(2$% 1#.% .1% 4*% V#/.*% #$*&#-% /2% *-*0.(12/0% 0/(0#/. ,*$/823%'$%)*%$"'--%$**%."(1#8"1#.%."/$%4119: i$/28%OV:%AK:BBC%.18*."*(%)/."%OV:%AK:B=C%5/*-,$% α L M % ! ?????????????????????????? = =U # =E

AK:BDC

!"*%+'-#*%1&% L M %'.%X*(1%(*+*($*?4/'$%0'2%4*%14.'/2*,%&(16%OV: AK:BDC%'$ α ? L MU ! ???????????? = =U )"/0"%*2'4-*$%#$%.1%*@7(*$$% L M %'

%$L MU L M ! ???????????????????? = S # ?????E? =U

AK:BEC

AK:BbC

)"*(*% L MU %/$%8/+*2%45%OV:%AK:BEC%1(%'-.*(2'./+*-5%/&%)*%$#4$./.#.*%&1(% α %&(16%OV:%AK:BKC%45 L MU ! 3

ε0 $ ??????? =

13 12 ??????????????????? ? 13 # 12

S ?????? =U

AK:BcC

M*&1(*%-*'+/28%."*%$#4F*0.%1&%,*7-*./12?(*8/12%1(%F#20./12%0'7'0/.'20*%)*%71/2.%1#.%."'.%/2 ."*%"#%F#20./12%)*%"'+*%4**2%$.#,5/283%."*%,17/28%0120*2.('./12%/$%6',*%.1%0"'28*%'4(#7.-5 '.%."*%F#20./12%41#2,'(5:%J#0"%'%F#20./12%/$%921)2%'$%'2%'2&+0#)6+"*#!-":%!"*(*%/$%'21."*( .57*%1&%"#%F#20./12%/2%)"/0"%."*%0'((/*(%0120*2.('./12%/$%6',*%.1%0"'28*%8(',#'--5%&(16%12* $/,*%1&%."*%F#20./12%.1%."*%1."*(:%!1%'--1)%&1(%$#0"%'%%&'($()6+"*#!-"3%."*%&1(6#-'%&1(%."* F#20./12%0'7'0/.'20*%AOV:%K:BbC%0'2%4*%)(/..*2%/2%."*%61(*%8*2*('-%&1(6 L MU L M ! ???????????????????????? ? =E K S # ?????? =U

AK:BTC

)"*(*%K%/$%'%012$.'2.%0'--*,%."*%%&'(!"%)*-$33!*!$"#3%)"1$*%+'-#*%('28*$%&(16%S`K%.1%S`= ,*7*2,/28%12%."*%6'22*(%/2%)"/0"%."*%0120*2.('./12%0"'28*$%&(16%."*%"%.1%."*%#%$/,*:%

EXERCISE 3.12 ;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E3%&/2,% L MU %'2,% L M %'.% = E % ! = %P:%_*0'--%."'. Sc K SE K "B = = U % ! U:cSB %P3% 1 3 % ! SU ⁄ 06 3% 1 2 % ! SU ⁄ 06 %'2,% 3% ! SU 06 : Ans. K:=%7;L%S:b%7;

156 Chapter 3 Semiconductors

3.6.2 Diffusion Capacitance <12$/,*(% '% &1()'(,?4/'$*,% "#% F#20./12:% >2% $.*',5?$.'.*3% 6/21(/.5% 0'((/*(% ,/$.(/4#./12$% /2 ."*%"%'2,%#%6'.*(/'-$%'(*%*$.'4-/$"*,3%'$%$"1)2%/2%;/8:%K:S=:%!"#$%'%0*(.'/2%'61#2.%1&%*@0*$$ 6/21(/.5%0'((/*(%0"'(8*%/$%$.1(*,%/2%*'0"%1&%."*%"%'2,%#%4#-9%(*8/12$%A1#.$/,*%."*%,*7-*./12 (*8/12C:% >&% ."*% .*(6/2'-% +1-.'8*% =% 0"'28*$3% ."/$% 0"'(8*% )/--% "'+*% .1% 0"'28*% 4*&1(*% '% 2*) $.*',5%$.'.*%/$%'0"/*+*,:%!"/$%0"'(8*?$.1('8*%7"*216*212%8/+*$%(/$*%.1%'21."*(%0'7'0/./+* *&&*0.3%,/$./20.-5%,/&&*(*2.%&(16%."'.%,#*%.1%0"'(8*%$.1('8*%/2%."*%,*7-*./12%(*8/12: !1%0'-0#-'.*%."*%*@0*$$%6/21(/.5%0'((/*(%0"'(8*3%(*&*(%.1%;/8:%K:S=:%!"*%*@0*$$%"1-*%0"'(8* $.1(*,%/2%."*%#%(*8/12%0'2%4*%&1#2,%&(16%."*%$"',*,%'(*'%#2,*(%."*%*@712*2./'-%'$%&1--1)$Hc B " ! 3$ × $"',*,%'(*'%#2,*(%."*% " # ( 5 ) %0#(+* ! 3$ [ " # ( 5 # ) " " #U ]; "

$#4$./.#./28%&1(% " # ( 5 # ) %&(16%OV:%AK:KKC%'2,%#$/28%OV:%AK:KbC%*2'4-*$%#$%.1%*@7(*$$% B " %'$ =

;" B " % ! ?????? 6 " 2"

AK:DUC

=

!"*%&'0.1(% ( ; " ⁄ 2 " ) %."'.%(*-'.*$% B " %.1% 6 " %/$%'%#$*&#-%,*+/0*%7'('6*.*(%."'.%"'$%."*%,/6*2$/12 1&%./6*%A$C%'2,%/$%,*21.*,% τ " =

;" τ " % ! ?????? 2"

AK:DSC

B" ! τ" 6"

AK:D=C

!"#$3 !"*%./6*%012$.'2.% τ "%/$%921)2%'$%."*%*@0*$$%,!"-&!#4)*'&&!$&)7/-.$8).!3$#!,$:%6/!+0!/@% .4%7.'%!/+K%!+/!/.(%0!8-7!.!@->%!+#M%?/%,!+#/-!/@%!#!7%'+-#!/-!7%?-KD+#%!N+/@!.!K.M-7+/O!%>%?P /7-#:%!"/$%,*&/2/./12%1&% τ "%/67-/*$%."'.%."*%*2./(*%0"'(8*% B "%,/$'77*'($%'2,%"'$%.1%4*%(*7-*2? /$"*,%*+*(5%τ "%$*012,$:%!"*%0#((*2.%."'.%'00167-/$"*$%."*%(*7-*2/$"/28%/$% 6 " ! B " ⁄ τ " :%!"/$%/$ '2%'-.*(2'.*%,*(/+'./12%&1(%OV:%AK:D=C: G%(*-'./12$"/7%$/6/-'(%.1%."'.%/2%OV:%AK:D=C%0'2%4*%,*+*-17*,%&1(%."*%*-*0.(12%0"'(8*%$.1(*,%/2 ."*%"%(*8/123 B# % ! τ# 6#

AK:DKC

)"*(*% τ # %/$%."*%*-*0.(12%-/&*./6*%/2%."*%"%(*8/12:%!"*%.1.'-%*@0*$$%6/21(/.5%0'((/*(%0"'(8*%0'2 4*%14.'/2*,%45%',,/28%.18*."*(% B " %'2,% B # 3 B% ! τ " 6 " # τ # 6 #

AK:DBC

!"/$%0"'(8*%0'2%4*%*@7(*$$*,%/2%.*(6$%1&%."*%,/1,*%0#((*2.% 6% ! 6 " # 6 # %'$% B% ! τ ) 6

AK:DDC

)"*(*% τ ) %/$%0'--*,%."*%,$'")#&'"5!#)#!,$%1&%."*%F#20./12:%R4+/1#$-53% τ ) %/$%(*-'.*,%.1% τ " %'2, τ #:%;#(."*(61(*3%&1(%61$.%7('0./0'-%,*+/0*$3%12*%$/,*%1&%."*%F#20./12%/$%6#0"%61(*%"*'+/-5 ,17*,% ."'2% ."*% 1."*(:% ;1(% /2$.'20*3% /&% 1 3 # 1 2 3% 12*% 0'2% $"1)% ."'.% 6 " # 6 # 3% 6 ! 6 " 3 B " # B # 3%B ! B " 3%'2,%."#$% τ )% ! τ " :% _*0'--%."'.%."*%'(*'%#2,*(%'2%*@712*2./'-%0#(+*% 3%

c

"5 ⁄ *

%/$%*V#'-%.1%3*:

3.6 Capacitive Effects in the pn Junction 157

;1(% $6'--% 0"'28*$% '(1#2,% '% 4/'$% 71/2.3% )*% 0'2% ,*&/2*% '2% !"*&$,$"#'.) (!33+5!-" *'0'*!#'"*$% L , %'$% ,B AK:DEC L , % ! ??????? ,= '2,%0'2%$"1)%."'. τ L , % ! ??????)? 6 =)

AK:DbC

)"*(*%6!/$%."*%&1()'(,?4/'$%0#((*2.:%a1.*%."'.% L , %/$%,/(*0.-5%7(171(./12'-%.1%."*%&1()'(,%0#(? (*2.%6%'2,%."#$%/$%2*8-/8/4-5%$6'--%)"*2%."*%,/1,*%/$%(*+*($*%4/'$*,:%G-$1%21.*%."'.%.1%9**7 L , %$6'--3%."*%.('2$/.%./6*% τ ) %6#$.%4*%6',*%$6'--3%'2%/671(.'2.%(*V#/(*6*2.%&1(%'%"#!F#20? ./12%/2.*2,*,%&1(%"/8"?$7**,%1(%"/8"?&(*V#*205%17*('./12:

EXERCISES 3.15

i$*%."*%,*&/2/./12%1&% L , %/2%OV:%AK:DEC%.1%,*(/+*%."*%*@7(*$$/12%/2%OV:%AK:DbC%45%6*'2$%1&%OV$:%AK:DDC '2,%AK:BUC:

3.16

;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E%&1(%)"/0"% 2 " % ! SU%06 ⁄ P ⋅ $ 3%'2,% ; " ! D µ63%&/2,% τ " %'2,% L , %'.%'%&1()'(,?4/'$%0#((*2.%1&%U:S%6G:%_*0'--%."'.%&1(%."/$%F#20./123% 6 " ! 6 :

=

Ans. =D%2$L%TE:D%7;

158 Chapter 3 Semiconductors

Summary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f1)*+*(3% .)1% *V#'-% '2,

1771$/.*% 0#((*2.$3% 6 2%'2,% 6 A 3% &-1)% '0(1$$% ."*% F#20./123 '2,%*V#/-/4(/#6%/$%6'/2.'/2*,%45%'%4#/-.?/2%+1-.'8*% = U ."'.%,*+*-17$%'0(1$$%."*%F#20./123%)/."%."*%#%$/,*%71$/./+* (*-'./+*% .1% ."*% "% $/,*:% a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

3.6 Capacitive Effects in the pn Junction

159

Table 3.1 Summary of Important Equations P'-#*$%1&%<12$.'2.$%'2,%r'('6*.*($% A&1(%>2.(/2$/0%J/%'.%)%e%KUU%YC

q#'2./.5

_*-'./12$"/7

<'((/*(%0120*2.('./12%/2% /2.(/2$/0%$/-/012%A06]KC

# + = *)

I/&&#$/12%0#((*2.% ,*2$/.5%AG`06=C

," 9 " = " $2 " ?????? ,5

K`= " & ' ⁄ =()

%

,# 9 # = $2 # ?????? ,5

* = &' = ( = #+ =

"K

SD

b:K × SU 06 Y S:S=%*P "D c:E= × SU *P`Y SU K S:D × SU `06

$ = S:EU × SU

" ST

" K`=

%01#-164

=

2 " = S=%06 `$ =

2 # = KB%06 `$ =

I(/&.%0#((*2.%,*2$/.5% AG`06=C

9 ,7+8/ = $ ( " µ " + # µ # )&

_*$/$./+/.5%AΩ⋅06C

ρ = S ⁄ [ $ ( " µ" + # µ# ) ]

µ"%'2,%µ#%,*0(*'$*%)/."%."*%/20(*'$*

_*-'./12$"/7%4*.)**2% 614/-/.5%'2,%,/&&#$/+/.5

2 2# ?????? = ?????"? = = )

= ) = () ⁄ $ ! =D:c%6P

<'((/*(%0120*2.('./12%/2% #?.57*%$/-/012%A06%]K C

# #U %! 1 2

<'((/*(%0120*2.('./12%/2% "?.57*%$/-/012%A06%%]K C

" "U% ! 1 3

N#20./12%4#/-.?/2% +1-.'8*%APC

13 12 ? = U = = ) -2 ????????????? = #+

\/,."%1&%,*7-*./12% (*8/12%A06C

5# 1 ???? = ??????3? 5" 12

=

µ # = SKDU%06 `P⋅$

µ#

µ" =

=

# "U = # + ⁄ 1 3

=

;1()'(,%0#((*2.%AGC

/2%,17/28%0120*2.('./12

" #U = # + ⁄ 1 2

ε 0 = SS:b ε U

< = 5# + 5"

<"'(8*%$.1(*,%/2%,*7-*./12% -'5*(%A01#-164C

µ " = BcU%06 `P⋅$

= ε0 S S? ??????? ?????? + ?????? ( =U + =E ) $ 1 3 12

13 12 ? 3< B 9 = $ ??????????????????? 13 + 12 6 = 6" + 6# = ⁄ =) = 2" 6 " = 3$ # + ????????????? ( % " S) ;" 12 =⁄= = 2# ? (% ) " S) 6 # = 3$ # + ??????????? ;# 13

J'.#('./12%0#((*2.%AGC

2" 2# = ? + ??????????? ? 6 A = 3$ # + ???????????? ;" 12 ;# 13

6?=%_*-'./12$"/7

6 ! 6A ( %

= ⁄ =)

" S)

ε U = c:cDB% × SU

" SB

%;`06

160 Chapter 3 Semiconductors

Table 3.1 continued q#'2./.5

_*-'./12$"/7

k/21(/.5?0'((/*(% -/&*./6*%A$C

τ " = ;" ⁄ 2"

k/21(/.5?0'((/*(% 0"'(8*%$.1('8*% A01#-164C

B" = τ" 6"

I*7-*./12%0'7'0/.'20*%A;C

=

P'-#*$%1&%<12$.'2.$%'2,%r'('6*.*($% A&1(%>2.(/2$/0%J/%'.%)%e%KUU%YC B

τ ", τ # = S%2$%.1%SU %2$ B# = τ# 6#

B = B" + B# = τ) 6 L MU = 3

ε0 $ ??????? =

13 12 S ??????????????????? ? ????? 13 # 12 =U

= L M = L MU %% S + ?????E? =U I/&&#$/12% 0'7'0/.'20*%A;C

; ", ; # = S%µ6%.1%SUU%µ6

=

τ# = ;# ⁄ 2#

K

S S K = ??? %.1% ??? K =

τ

L , = ?????)? 6 =)

PROBLEMS

r(14-*6$%'(*%6'(9*,%)/."%'$.*(/$9$%.1%,*$0(/4*%."*/(%,*8(** 1&%,/&&/0#-.5:%I/&&/0#-.%7(14-*6$%'(*%6'(9*,%)/."%'2%'$.*(/$9 AsCL% 61(*% ,/&&/0#-.% 7(14-*6$% )/."% .)1% '$.*(/$9$% AssCL% '2, +*(5% 0"'--*28/28% '2,`1(% ./6*?012$#6/28% 7(14-*6$% )/." ."(**%'$.*(/$9$%AsssC:%G-$13%/&%/2%."*%&1--1)/28%7(14-*6$%."* 2**,% '(/$*$% &1(% ."*% +'-#*$% 1&% 7'(./0#-'(% 7'('6*.*($% 1( 7"5$/0'-% 012$.'2.$% ."'.% '(*% 21.% $.'.*,3% 7-*'$*% 012$#-. !'4-* K:S:

Section 3.1: Intrinsic Semiconductors 3.1 ;/2,% +'-#*$% 1&% ."*% /2.(/2$/0% 0'((/*(% 0120*2.('./12% # + &1(% $/-/012% '.% " bU°<3% U° <3% =U°<3% SUU°<3% '2,% S=D°<:% G. *'0"% .*67*('.#(*3% )"'.% &('0./12% 1&% ."*% '.16$% /$% /12/X*,h == _*0'--% ."'.% '% $/-/012% 0(5$.'-% "'$% '77(1@/6'.*-5% D × SU K '.16$`06 :% 3.2 <'-0#-'.*% ."*% +'-#*% 1&% # + % &1(% 8'--/#6% '($*2/,* SB A^'G$C% '.% )% e% KUU% Y:% !"*% 012$.'2.% *% ! K:DE × SU "K "K ⁄ = ( 06 Y )%'2,%."*%4'2,8'7%+1-.'8*%&' e S:B=%*P:

Section 3.2: Doped Semiconductors 3.3

;1(%'%"?.57*%$/-/012%/2%)"/0"%."*%,17'2.%0120*2.('./12

1 3 % ! SU Sc ⁄ 06 K3% &/2,% ."*% "1-*% '2,% *-*0.(12% 0120*2.('./12$

'.%)%e%KUU%Y:

3.4 ;1(% '% $/-/012% 0(5$.'-% ,17*,% )/."% 7"1$7"1(#$3% )"'. 6#$.% 1 2 % 4*% /&% '.% )% e% KUU% Y% ."*% "1-*% 0120*2.('./12% ,(17$ b 4*-1)%."*%/2.(/2$/0%-*+*-%45%'%&'0.1(%1&% SU h 3.5 >2% '% 7"1$7"1(#$?,17*,% $/-/012% -'5*(% )/."% /67#(/.5 SE K 0120*2.('./12% 1&%SU ⁄ 06 3% &/2,% ."*% "1-*% '2,% *-*0.(12% 012? 0*2.('./12$%'.% =b°< %'2,%S=D°<:

Section 3.3: Current Flow in Semiconductors 3.6 G% 51#28% ,*$/82*(3% '/6/28% .1% ,*+*-17% /2.#/./12% 012? 0*(2/28%012,#0./28%7'."$%)/."/2%'2%/2.*8('.*,%0/(0#/.3%*@'6? /2*$%."*%*2,?.1?*2,%(*$/$.'20*%1&%'%0122*0./28%4'(%SU%µ6 -1283%K%µ6%)/,*3%'2,%S%µ6%."/093%6',*%1&%+'(/1#$%6'.*(/'-$: !"*%,*$/82*(%012$/,*($H

Problems

SE

K

Sc

K

SE

K

A4C%#?,17*,%$/-/012%)/."% 1 2 ! SU ⁄ 06 A0C%#?,17*,%$/-/012%)/."% 1 2 ! SU ⁄ 06 A,C%"?,17*,%$/-/012%)/."% 1 3 ! SU ⁄ 06

pn(x)

108 pn0

CHAPTER 3 P R O B L E M S

A'C%/2.(/2$/0%$/-/012

161

n region

A*C%'-#6/2#6%)/."%(*$/$./+/.5%1&%=:c% µΩ : 06 ;/2,%."*%(*$/$.'20*%/2%*'0"%0'$*:%;1(%/2.(/2$/0%$/-/0123%#$*%."* ,'.'% /2% !'4-*% K:S:% ;1(% ,17*,% $/-/0123% '$$#6* = µ #% ! =:D µ " % ! S=UU%06 ⁄ P:$:%A_*0'--%."'.% E ! ρ ; ⁄ 3 C 3.7 <12.('$.%."*%*-*0.(12%'2,%"1-*%,(/&.%+*-10/./*$%."(1#8" '%SU?µ6%-'5*(%1&%/2.(/2$/0%$/-/012%'0(1$$%)"/0"%'%+1-.'8*%1& = D P% /$% /671$*,:% Q*.% µ # ! SKDU %06 ⁄ P:$% '2, = µ " ! BcU%06 ⁄ P:$: 3.8 ;/2,%."*%0#((*2.%."'.%&-1)$%/2%'%$/-/012%4'(%1&%SU?µ6 -*28."% "'+/28% '% D?µ6 × B?µ6 % 0(1$$% $*0./12% '2,% "'+/28 D K SD K &(**%*-*0.(12%'2,%"1-*%,*2$/./*$%1&% SU ⁄ %06 %'2,%SU ⁄ 06 3 (*$7*0./+*-53% )"*2% '% S% P% /$% '77-/*,% *2,?.1?*2,:% i$* = = µ # ! S=UU%06 ⁄ P:$%'2,% µ " ! DUU%06 ⁄ P:$: 3.9 >2% '% SU?µ6% -128% 4'(% 1&% ,121(?,17*,% $/-/0123% )"'. ,121(%0120*2.('./12%/$%2**,*,%.1%(*'-/X*%'%0#((*2.%,*2$/.5%1& = S%6G ⁄ µ6 %/2%(*$712$*%.1%'2%'77-/*,%+1-.'8*%1&%S%P:%A1-/%H G-."1#8"%."*%0'((/*(%614/-/./*$%0"'28*%)/."%,17/28%0120*2? .('./123% '$% '% &/($.% '77(1@/6'./12% 51#% 6'5% '$$#6*% µ # % .1% 4* 012$.'2.% '2,% #$*% ."*% +'-#*% &1(% /2.(/2$/0% $/-/0123 = SKDU%06 ⁄ P:$C: 3.10 f1-*$% '(*% 4*/28% $.*',/-5% /2F*0.*,% /2.1% '% (*8/12% 1&% #? .57*%$/-/012%A0122*0.*,%.1%1."*(%,*+/0*$3%."*%,*.'/-$%1&%)"/0" '(*%21.%/671(.'2.%&1(%."/$%V#*$./12C:%>2%."*%$.*',5%$.'.*3%."* *@0*$$?"1-*% 0120*2.('./12% 7(1&/-*% $"1)2% /2% ;/8:% rK:SU% /$ *$.'4-/$"*,% /2% ."*% #?.57*% $/-/012% (*8/12:% f*(*% Z*@0*$$[ 6*'2$% 1+*(% '2,% '41+*% ."*% ."*(6'-?*V#/-/4(/#6% 0120*2.('? ./12% A/2% ."*% '4$*20*% 1&% "1-*% /2F*0./12C3% ,*21.*,% " #U:% >& 1 2 ! SU SE ⁄ 06 K3% # + ! S:D × SU SU ⁄ 06 K 3% 2 # ! S=%06 = ⁄ $3 '2,%
Doping Concentration (carriers/cm3) >2.(/2$/0

SU

SE

SU

Sb

SU

Sc

Table P3.11

mn (cm2/V·s)

pn0

0

W

x

Figure P3.10

3.11 M1."%."*%0'((/*(% 614/-/.5% '2,% ,/&&#$/+/.5% ,*0(*'$*% '$ ."*% ,17/28% 0120*2.('./12% 1&% $/-/012% /$% /20(*'$*,:% !"*% .'4-* 4*-1)%7(1+/,*$%'%&*)%,'.'%71/2.$%&1(% µ #%'2,%µ "%+*($#$%,17? /28%0120*2.('./12:%i$*%."*%O/2$.*/2%(*-'./12$"/7%.1%14.'/2%."* 01((*$712,/28%+'-#*$%&1(% 2 # %'2,% 2 ":

Section 3.4: The pn Junction with Open-Circuit Terminals (Equilibrium) 3.12 <'-0#-'.*% ."*% 4#/-.?/2% +1-.'8*% 1&% '% F#20./12% /2% )"/0" SE ."*%"%'2,%#%(*8/12$%'(*%,17*,%*V#'--5%)/."% SU %'.16$`06K: SU K G$$#6*% # + % ! S:D × SU ⁄ 06 :%\/."%."*%.*(6/2'-$%-*&.%17*23 )"'.%/$%."*%)/,."%1&%."*%,*7-*./12%(*8/123%'2,%"1)%&'(%,1*$%/. *@.*2,%/2.1%."*%"%'2,%#%(*8/12$h%>&%."*%0(1$$?$*0./12'-%'(*'%1& ."*% F#20./12% /$% SUU% µ6=3% &/2,% ."*% 6'82/.#,*% 1&% ."*% 0"'(8* $.1(*,%12%*/."*(%$/,*%1&%."*%F#20./12: 3.13 >&3%&1(%'%7'(./0#-'(%F#20./123%."*%'00*7.1(%0120*2.('? ./12%/$% SU SE⁄ 06 K %'2,%."*%,121(%0120*2.('./12%/$%SU SD⁄ 06 K3 &/2,% ."*% F#20./12% 4#/-.?/2% +1-.'8*:% G$$#6*% #+ e SU K S:D × SU ⁄ 06 :% G-$13% &/2,% ."*% )/,."% 1&% ."*% ,*7-*./12 (*8/12% A
mp (cm2/V·s)

SKDU

BcU

SSUU

BUU

bUU

=EU

KEU

SDU

Dn (cm2/s)

Dp (cm2/s)

CHAPTER 3 P R O B L E M S

162 Chapter 3 Semiconductors 3.14 O$./6'.*%."*%.1.'-%0"'(8*%$.1(*,%/2%'%U:S?µ6%,*7-*./12 -'5*(%12%12*%$/,*%1&%'% SU?µ6 × SU?µ6 %F#20./12:%!"*%,17? SE K /28%0120*2.('./12%12%."'.%$/,*%1&%."*%F#20./12%/$% SU ⁄ 06 : 3.15 >2%'%"#%F#20./12%&1(%)"/0"% 1 3 # 1 2 3%'2,%."*%,*7-*? ./12%-'5*(%*@/$.$%61$.-5%12%."*%$"'--1)-5%,17*,%$/,*%)/."%<%e SE K U:K%µ63%&/2,% = U %/&% 1 2 ! SU ⁄ 06 :%G-$1%0'-0#-'.*% B 9 : 3.16 M5% "1)% 6#0"% ,1*$% = U % 0"'28*% /&% 1 3 % 1(% 1 2 % /$ /20(*'$*,%45%'%&'0.1(%1&%SUh

l

3.22 G% " # %F#20./12%/$%12*%/2%)"/0"%."*%,17/28%0120*2.('? ./12%/2%."*%"%(*8/12%/$%6#0"%8(*'.*(%."'2%."'.%/2%."*%#!(*8/12: >2%$#0"%'%F#20./123%."*%&1()'(,%0#((*2.%/$%61$.-5%,#*%.1%"1-* /2F*0./12%'0(1$$%."*%F#20./12:%J"1)%."'.% =⁄= = 2" ?(% ) " S) 6 ! 6 " ! 3$# + ???????????? ;" 12 SE

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Section 3.6: Capacitive Effects in the pn Junction

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CHAPTER 3 P R O B L E M S

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163

CHAPTER 4

Diodes

Introduction 4.1

4.5 Rectifier Circuits

165

The Ideal Diode

166

4.2 Terminal Characteristics of Junction Diodes 173 4.3 Modeling the Diode Forward Characteristic 179 4.4 Operation in the Reverse Breakdown Region—Zener Diodes 189

194

4.6 Limiting and Clamping Circuits 4.7 Special Diode Types Summary

215

Problems

216

213

207

IN THIS CHAPTER YOU WILL LEARN 1. The characteristics of the ideal diode and how to analyze and design circuits containing multiple ideal diodes together with resistors and dc sources to realize useful and interesting nonlinear functions. 2. The details of the !"v characteristic of the junction diode (which was derived in Chapter 3) and how to use it to analyze diode circuits operating in the various bias regions: forward, reverse, and breakdown. 3. A simple but effective model of the diode !"v characteristic in the forward direction; the constant-voltage-drop model. 4. A powerful technique for the application and modeling of the diode (and in later chapters, transistors): dc-biasing the diode and modeling its operation for small signals around the dc operating point by means of the small-signal model. 5. The use of a string of forward-biased diodes and of diodes operating in the breakdown region (zener diodes), to provide constant dc voltages (voltage regulators). 6. Application of the diode in the design of rectifier circuits, which convert ac voltages to dc as needed for powering electronic equipment. 7. A number of other practical and important applications of diodes.

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165

166 Chapter 4 Diodes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4.1 The Ideal Diode

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167

168 Chapter 4 Diodes -32-)#(2#9)#3-)&0=#R6*3"<#(%)#'2+3(3;)#%&0:?5450)+#2:#(%)#3"'6(#+3"6+23-8#(%)#'2+3(3;)#v-#/300#5&6+) 56**)"(#(2#:02/#(%*26<%#(%)#-32-)#3"#3(+#:2*/&*-#-3*)5(32"=#!(#:2002/+#(%&(#(%)#-32-)#;20(&<) v+# /300# 9)# ;)*4# +1&00W3-)&004# M)*2=# F%6+# (%)# 53*563(# /300# %&;)# (%)# )C63;&0)"(# +%2/"# 3" L3<=#P=OB5D8#&"-#(%)#26('6(#;20(&<)#v.#/300#9)#)C6&0#(2#(%)#3"'6(#;20(&<)#v-=#K"#(%)#2(%)* %&"-8#-6*3"<#(%)#")<&(3;)#%&0:?5450)+#2:# v- 8#(%)#-32-)#/300#"2(#52"-65(=#F%6+#(%)#53*563( /300#%&;)#(%)#)C63;&0)"(#+%2/"#3"#L3<=#P=OB-D8#&"-#v.#/300#9)#M)*2=#F%6+#(%)#26('6(#;20(&<) /300#%&;)#(%)#/&;):2*1#+%2/"#3"#L3<=#P=OB)D=#X2()#(%&(#/%30)#v-#&0()*"&()+#3"#'20&*3(4#&"%&+#&#M)*2#&;)*&<)#;&06)8#v.#3+#6"3-3*)5(32"&0#&"-#%&+#&#:3"3()#&;)*&<)#;&06)#2*#&#*/0/&1#&2 $3$4=#F%6+#(%)#53*563(#2:#L3<=#P=OB&D#!"*,'.'"$#(%)#+3<"&0#&"-#%)"5)#3+#5&00)-#&#!"*,'.'"!=#!( 5&"#9)#6+)-#(2#<)")*&()#-5#:*21#&5=#I)#/300#+(6-4#*)5(3:3)*#53*563(+#3"#Y)5(32"#P=Z=

D

(a)

(b)

vI $ 0

vI # 0

(c)

(d)

(e) Figure 4.3 5(6#[)5(3:3)*#53*563(=#5&6#!"'6(#/&;):2*1=#5*6#@C63;&0)"(#53*563(#/%)"# v-# ≥# S=#5)6#@C63;&0)"( 53*563(#/%)"#v-#≤#S=#5"6#K6('6(#/&;):2*1=

4.1 The Ideal Diode 169

EXERCISES 4.1# L2*#(%)#53*563(#3"#L3<=#P=OB&D8#+H)(5%#(%)#(*&"+:)*#5%&*&5()*3+(35#v.#;)*+6+#v-= Ans. Y))#L3<=#@P=,=

Figure E4.1

4.2# L2*#(%)#53*563(#3"#L3<=#P=OB&D8#+H)(5%#(%)#/&;):2*1#2:#v+= Ans. v+#\#v-#]#v. 8#*)+60(3"<#3"#(%)#/&;):2*1#3"#L3<=#@P=.

Figure E4.2

4.3# !"#(%)#53*563(#2:#L3<=#P=OB&D8#0)(#v-#%&;)#&#')&H#;&06)#2:#,S#T#&"-#,#=#,#HΩ=#L3"-#(%)#')&H#;&06)#2:#!+ &"-#(%)#-5#521'2")"(#2:#v.= Ans. ,S#1E7#O=,^#T

Example 4.1 L3<6*)#P=PB&D#+%2/+#5*563(#:2*#5%&*<3"<#&#,.?T#9&(()*4=#!:#v5#3+#&#+3"6+23-#/3(%#.P?T#')&H#&1'03? (6-)8#:3"-#(%)#:*&5(32"#2:#)&5%#5450)#-6*3"<#/%35%#(%)#-32-)#52"-65(+=#E0+28#:3"-#(%)#')&H#;&06)#2: (%)#-32-)#56**)"(#&"-#(%)#1&A3161#*);)*+)?93&+#;20(&<)#(%&(#&'')&*+#&5*2++#(%)#-32-)=

170 Chapter 4 Diodes Example 4.1 continued

(b)

(a) Figure 4.4 $3*563(#&"-#/&;):2*1+#:2*#@A&1'0)#P=,=

Solution F%)# -32-)# 52"-65(+# /%)"# v5# )A5))-+# ,.# T8# &+# +%2/"# 3"# L3<=# P=PB9D=# F%)# 52"-65(32"# &"<0)# 3+# .θ8 /%)*)#θ#3+#<3;)"#94 .P#52+ θ = ,.

F%6+#θ#=#`S°#&"-#(%)#52"-65(32"#&"<0)#3+#,.S°8#2*#2")?(%3*-#2:#ᕊ)= F%)#')&H#;&06)#2:#(%)#-32-)#56**)"(#3+#<3;)"#94 ! ,.? " S=,.#E - * " .P ????????????????? ,SS

F%)#1&A3161#*);)*+)#;20(&<)#&5*2++#(%)#-32-)#2556*+#/%)"#v5 3+#&(#3(+#")<&(3;)#')&H#&"-#3+#)C6&0#(2 .P#+#,.#=#O`#T=

4.1.3 Another Application: Diode Logic Gates R32-)+#(2<)(%)*#/3(%#*)+3+(2*+#5&"#9)#6+)-#(2#31'0)1)"(#-3<3(&0#02<35#:6"5(32"+=#L3<6*)#P=Z +%2/+#(/2#-32-)#02<35#<&()+=#F2#+))#%2/#(%)+)#53*563(+#:6"5(32"8#52"+3-)*#&#'2+3(3;)?02<35 +4+()1#3"#/%35%#;20(&<)#;&06)+#502+)#(2#S#T#52**)+'2"-#(2#02<35#S#B2*#02/D#&"-#;20(&<)#;&06)+ 502+)#(2#+Z#T#52**)+'2"-#(2#02<35#,#B2*#%3<%D=#F%)#53*563(#3"#L3<=#P=ZB&D#%&+#(%*))#3"'6(+8#v6 8 v78#&"-#v8=#!(#3+#)&+4#(2#+))#(%&(#-32-)+#52"")5()-#(2#+Z?T#3"'6(+#/300#52"-65(8#(%6+#50&1'3"< (%)# 26('6(# v9# (2# &# ;&06)# )C6&0# (2# +Z# T=# F%3+# '2+3(3;)# ;20(&<)# &(# (%)# 26('6(# /300# H))'# (%) -32-)+# /%2+)# 3"'6(+#&*)#02/#B&*26"-#S#TD#56(# 2::=#F%6+# 4:30&;4#;40(!<<0=30:!>:0!%0&$30&' 1&'30&%04:30!$#;4?0)'30:!>:=#F%)#53*563(#(%)*):2*)#31'0)1)"(+#(%)#4-7'*%89%.+1*,'-18#/%35% 3"#_220)&"#"2(&(32"#3+#)A'*)++)-#&+

9 = 6+7+8 Y3130&*048#(%)#*)&-)*#3+#)"526*&<)-#(2#+%2/#(%&(#6+3"<#(%)#+&1)#02<35#+4+()1#1)"(32")&92;)8#(%)#53*563(#2:#L3<=#P=ZB9D#31'0)1)"(+#(%)#4-7'*%:;<%.+1*,'-18 9 = 6⋅7⋅8

4.1 The Ideal Diode 171

(a)

(b)

Figure 4.5 R32-)#02<35#<&()+Q#5(6#K[#<&()7#5&6#EXR#<&()#B3"#&#'2+3(3;)?02<35#+4+()1D=

Example 4.2 E++613"<#(%)#-32-)+#(2#9)#3-)&08#:3"-#(%)#;&06)+#2:#-#&"-#@#3"#(%)#53*563(+#2:#L3<=#P=`=

D

D

(a)

D

D

(b)

Figure 4.6 $3*563(+#:2*#@A&1'0)#P=.=

Solution !"#(%)+)#53*563(+#3(#13<%(#"2(#9)#29;326+#&(#:3*+(#+3<%(#/%)(%)*#"2")8#2")8#2*#92(%#-32-)+#&*)#52"-65(3"<= !"#+65%#&+)8#(301)A30)0#<);?!=<30)??;1#4!&$B0#'&/33*0(!4:04:30)$)
172 Chapter 4 Diodes

Example 4.2 continued

,S ! S - +. = ??????????????? = ,#1E ,S I*3(3"<#&#"2-)#)C6&(32"#&(#_8 S ! ( ! ,S ) - + , = ??????????????????????? Z

*)+60(+#3"#-#=#,#1E=#F%6+#+,#3+#52"-65(3"<#&+#2*3<3"&004#&++61)-8#&"-#(%)#:3"&0#*)+60(#3+#-#= , 1E#&"-#@#=#S#T= L2*# (%)# 53*563(# 3"# L3<=# P=`B9D8# 3:# /)# &++61)# (%&(# 92(%# -32-)+# &*)# 52"-65(3"<8# (%)" @7 = S#&"-#@#=#S=#F%)#56**)"(#3"#+.#3+#29(&3")-#:*21 ,S ! S - +. = ??????????????? = .#1E Z F%)#"2-)#)C6&(32"#&(#_#3+ S ! ( ! ,S ) - + . = ??????????????????????? ,S /%35%#43)0-+#-0=#−,#1E=#Y3"5)#(%3+#3+#"2(#'2++390)8#26*#2*3<3"&0#&++61'(32"#3+#$&4#52**)5(=#I) +(&*(#&<&3"8#&++613"<#(%&(#+,#3+#2::#&"-#+.#3+#2"=#F%)#56**)"(#-+.#3+#<3;)"#94 ,S ! ( ! ,S ) - +. = ?????????????????????????? = ,=OO#1E ,Z &"-#(%)#;20(&<)#&(#"2-)#_#3+ @ 7 = ],S + ,S × ,=OO = +O=O#T

F%6+#+,#3+#*);)*+)#93&+)-#&+#&++61)-8#&"-#(%)#:3"&0#*)+60(#3+#-0=#S#&"-#@#=#O=O#T=

EXERCISES 4.4# L3"-#(%)#;&06)+#2:#-#&"-#@#3"#(%)#53*563(+#+%2/"#3"#L3<=#@P=P=

(a) Figure E4.4

(b)

(c)

(d)

4.2 Terminal Characteristics of Junction Diodes 173

(f)

(e) Figure E4.4 B$2"(3"6)-D

Ans. B&D#.#1E8#S#T7#B9D#S#1E8#Z#T7#B5D#S#1E8#Z#T7#B-D#.#1E8#S#T7#B)D#O#1E8#+O#T7#B:D#P#1E8#+,#T 4.5# L3<6*)#@P=Z#+%2/+#5*563(#:2*#&"#&5#;20(1)()*=#!(#6(303M)+#3"3#56**)"(#:02/3"<#(%*26<%#3(#3+#,#1E=#F%)#12;3"
Moving-coil meter Figure E4.5

L3"-# (%)# ;&06)# 2:# ,# (%&(# *)+60(+# 3"# (%)# 1)()*# 3"-35&(3"<# &# :600?+5&0)# *)&-3"<# /%)"# (%)# 3"'6(# +3")?/&;) ;20(&<)#vI#3+#.S#T#')&H?(2?')&H=#BE!$4F#F%)#&;)*&<)#;&06)#2:#%&0:?+3")#/&;)+#3+#@# aπ=D# Ans. #O=,OO#HΩ

4.2 Terminal Characteristics of Junction Diodes F%)#12+(#52112"#31'0)1)"(&(32"#2:#(%)#-32-)#6(303M)+#&##$#J6"5(32"=#I)#%&;)#+(6-3)-#(%) '%4+35+#2:#(%)##$#J6"5(32"#&"-#-)*3;)-#3(+#!]v#5%&*&5()*3+(35#3"#$%&'()*#O=#F%&(#(%)##$#J6"5? (32"#3+#6+)-#(2#31'0)1)"(#(%)#-32-)#:6"5(32"#+%260-#521)#&+#"2#+6*'*3+)Q#(%)##$#J6"5(32"#5&" 52"-65(# +69+(&"(3&0# 56**)"(# 3"# (%)# :2*/&*-# -3*)5(32"# &"-# &012+(# "2# 56**)"(# 3"# (%)# *);)*+) -3*)5(32"=#!"#(%3+#+)5(32"#/)#+(6-4#(%)#!]v#5%&*&5()*3+(35#2:#(%)##$#J6"5(32"#-32-)#3"#-)(&30#3" 2*-)*#(2#'*)'&*)#26*+)0;)+#:2*#-32-)#53*563(#&''035&(32"+= L3<6*)#P=N#+%2/+#(%)#!]v#5%&*&5()*3+(35#2:#&#+30352"#J6"5(32"#-32-)=#F%)#+&1)#5%&*&5()*3+? (35#3+#+%2/"#3"#L3<=#P=^#/3(%#+21)#+5&0)+#)A'&"-)-#&"-#2(%)*+#521'*)++)-#(2#*);)&0#-)(&30+= X2()#(%&(#(%)#+5&0)#5%&"<)+#%&;)#*)+60()-#3"#(%)#&''&*)"(#-3+52"(3"63(4#&(#(%)#2*3<3"=

174 Chapter 4 Diodes

Figure 4.7 F%)#!]v##5%&*&5()*3+(35#2:#&#+30352"#J6"5(32"#-32-)=

Figure 4.8 F%)# -32-)# !]v# # *)0&(32"+%3'# /3(%# +21)# +5&0)+# )A'&"-)-# &"-# 2(%)*+# 521'*)++)-# 3"# 2*-)*# (2 *);)&0#-)(&30+=

E+#3"-35&()-8#(%)#5%&*&5()*3+(35#56*;)#52"+3+(+#2:#(%*))#-3+(3"5(#*)<32"+Q 1. F%)#:2*/&*-?93&+#*)<32"8#-)()*13")-#94#v#b#S 2. F%)#*);)*+)?93&+#*)<32"8#-)()*13")-#94#v#c#S 3. F%)#9*)&H-2/"#*)<32"8#-)()*13")-#94#v#c#]@GH F%)+)#(%*))#*)<32"+#2:#2')*&(32"#&*)#-)+5*39)-#3"#(%)#:2002/3"<#+)5(32"+=

4.2 Terminal Characteristics of Junction Diodes 175

4.2.1 The Forward-Bias Region F%)# :2*/&*-?93&+W2*# +31'04# :2*/&*-W*)<32"# 2:# 2')*&(32"# 3+# )"()*)-# /%)"# (%)# ()*13"&0 ;20(&<)#v#3+#'2+3(3;)=#!"#(%)#:2*/&*-#*)<32"#(%)#!]v#*)0&(32"+%3'#3+#502+)04#&''*2A31&()-#94# v⁄@ BP=,D ! = -5 ( 3 I ! , ) !"#(%3+#)C6&(32",#-5#3+#4"+(&"(#:2*#&#<3;)"#-32-)#&(#&#<3;)"#()1')*&(6*)=#E#:2*160&#:2*#-5#3" ()*1+#2:#(%)#-32-)d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v=#L2*#e+1&00?+3<"&0f#-32-)+8#/%35%#&*)#+1&00?+3M)#-32-)+#3"()"-)-#:2*#02/?'2/)*#&''035&? (32"+8#-5#3+#2"#(%)#2*-)*#2:#,S],Z#E=#F%)#;&06)#2:#-5#3+8#%2/);)*8#&#;)*4#+(*2"<#:6"5(32"#2:#()1? ')*&(6*)=#E+#&#*60)#2:#(%6198#-5#-2690)+#3"#;&06)#:2*#);)*4#Z°$#*3+)#3"#()1')*&(6*)= F%)#;20(&<)#@I#3"#@C=#BP=,D#3+#4"+(&"(#5&00)-#(%)#,2"!=(4%#-4,(7"#&"-#3+#<3;)"#94

AI @I = ?????? J

BP=.D

/%)*) A0=#_20(M1&""d+#52"+(&"(#=#^=`.#× ,S]Z#)Tag#=#,=O^#× ,S].O#J260)+aH)0;3" I0=#(%)#&9+206()#()1')*&(6*)#3"#H)0;3"+#=#.NO#+#()1')*&(6*)#3"#°$ J#=#(%)#1&<"3(6-)#2:#)0)5(*2"35#5%&*<)#=#,=`S#×#,S],U#5260219# Y69+(3(6(3"<#A#\#^=`.#× ,S]Z#)Tag#3"(2#@C=#BP=.D#<3;)+

@I = S=S^`.I8 1@

BP=.&D

F%6+8#&(#*221#()1')*&(6*)#B.S°$D#(%)#;&06)#2:#@I#3+#.Z=O#1T=#!"#*&'3-#&''*2A31&()#53*563( &"&04+3+#/)#+%&00#6+)#@I#!#.Z#1T#&(#*221#()1')*&(6*)=. L2*#&''*)53&90)#56**)"(#!#3"#(%)#:2*/&*-#-3*)5(32"8#+')53:35&004#:2*#!#%#-5 8#@C=#BP=,D#5&"#9) &''*2A31&()-#94#(%)#)A'2")"(3&0#*)0&(32"+%3' !0! -5 3

vK @

I

BP=OD

F%3+#*)0&(32"+%3'#5&"#9)#)A'*)++)-#&0()*"&(3;)04#3"#(%)#02<&*3(%135#:2*1

! -5

v = @I 0" ????

BP=PD

/%)*)#0"#-)"2()+#(%)#"&(6*&0#B9&+)#3D#02<&*3(%1= ,

@C6&(32"#BP=,D8#(%)#-32-)#)C6&(32"8#3+#+21)(31)+#/*3(()"#(2#3"506-)#4"+(&"(#$#3"#(%)#)A'2")"(3&08 va$A4

#! \ -5 B3

],D

/3(%#$#%&;3"<#&#;&06)#9)(/))"#,#&"-#.8#-)')"-3"<#2"#(%)#1&()*3&0#&"-#(%)#'%4+35&0#+(*65(6*)#2:#(%)#-32-)= R32-)+#6+3"<#(%)#+(&"-&*-#3"()<*&()-?53*563(#:&9*35&(32"#'*25)++#)A%393(#$#\#,#/%)"#2')*&()-#6"-)*#"2*? 1&0#52"-3(32"+=#L2*#+31'0353(48#/)#+%&00#6+)#$#\#,#(%*26<%26(#(%3+#922H8#6"0)++#2(%)*/3+)#+')53:3)-= . E#+03<%(04#%3<%)*#&193)"(#()1')*&(6*)#B.Z°$#2*#+2D#3+#6+6&004#&++61)-#:2*#)0)5(*2"35#)C63'1)"(#2')*? &(3"<#3"+3-)#&93")(=#E(#(%3+#()1')*&(6*)8#@I##!#.Z=^#1T=#X);)*(%)0)++8#:2*#(%)#+&H)#2:#+31'0353(4#&"(2#'*212()#*&'3-#53*563(#&"&04+3+8#/)#+%&00#6+)#(%)#12*)#&*3(%1)(35&004#52";)"3)"(#;&06)#2:#@I#!#.Z#1T (%*26<%26(#(%3+#922H=

176 Chapter 4 Diodes F%)#)A'2")"(3&0#*)0&(32"+%3'#2:#(%)#56**)"(#!#(2#(%)#;20(&<)#v#%20-+#2;)*#1&"4#-)5&-)+#2: 56**)"(#B&#+'&"#2:#&+#1&"4#&+# +);)"#-)5&-)+W3=)=8#&#:&5(2*#2:#,SNW5&"#9)#:26"-D=#F%3+#3+ C63()#&#*)1&*H&90)#'*2')*(4#2:#J6"5(32"#-32-)+8#2")#(%&(#3+#&0+2#:26"-#3"#93'20&*#J6"5(32"#(*&"? +3+(2*+#&"-#(%&(#%&+#9))"#)A'023()-#3"#1&"4#3"()*)+(3"<#&''035&(32"+= V)(# 6+# 52"+3-)*# (%)# :2*/&*-# !"v0 *)0&(32"+%3'# 3"# @C=# BP=OD# &"-# );&06&()# (%)# 56**)"(# -, 52**)+'2"-3"<#(2#&#-32-)#;20(&<)#@,Q

-, = -5 3

@, ⁄ @I

Y3130&*048#3:#(%)#;20(&<)#3+#@.8#(%)#-32-)#56**)"(#-.#/300#9)

- . = -5 3

@. ⁄ @I

F%)+)#(/2#)C6&(32"+#5&"#9)#52193")-#(2#'*2-65) (@ ! @ ) ⁄ @ ????. = 3 . , I -,

/%35%#5&"#9)#*)/*3(()"#&+

@ . ! @ , = @ I 0" ????. -, 2*8#3"#()*1+#2:#9&+)?,S#02<&*3(%1+8

@ . ! @ , = .=O@I 02< ????. -,

BP=ZD

F%3+#)C6&(32"#+31'04#+(&()+#(%&(#:2*#&#-)5&-)#B:&5(2*#2:#,SD#5%&"<)#3"#56**)"(8#(%)#-32-)#;20(? &<)#-*2'#5%&"<)+#94#.=O@I 8#/%35%#3+#&''*2A31&()04#`S#1T=#F%3+#&0+2#+6<<)+(+#(%&(#(%)#-32-) !"v# *)0&(32"+%3'# 3+# 12+(# 52";)"3)"(04# '02(()-# 2"# +)1302<# '&')*=# h+3"<# (%)# ;)*(35&08# 03")&* &A3+#:2*#v#&"-#(%)#%2*3M2"(&08#02<#&A3+#:2*#!8#2")#29(&3"+#&#+(*&3<%(#03")#/3(%#&#+02')#2:#`S 1T ')*#-)5&-)#2:#56**)"(= E#<0&"5)#&(#(%)#!"v#5%&*&5()*3+(35#3"#(%)#:2*/&*-#*)<32"#BL3<=#P=^D#*);)&0+#(%&(#(%)#56**)"( 3+#")<03<3904#+1&00#:2*#v#+1&00)*#(%&"#&926(#S=Z#T=#F%3+#;&06)#3+#6+6&004#*):)**)-#(2#&+#(%)#*+,0 '1%#-4,(7"=#!(#+%260-#9)#)1'%&+3M)-8#%2/);)*8#(%&(#(%3+#&''&*)"(#(%*)+%20-#3"#(%)#5%&*&5()*3+? (35#3+#+31'04#4"+)C6)"5)#2:#(%)#)A'2")"(3&0#*)0&(32"+%3'=#E"2(%)*#52"+)C6)"5)#2:#(%3+#*)0&? (32"+%3'#3+#(%)#*&'3-#3"5*)&+)#2:#!=#F%6+8#:2*#&#e:6004#52"-65(3"
Example 4.3 E#+30352"#-32-)#+&3-#(2#9)#&#,?1E#-);35)#-3+'0&4+#&#:2*/&*-#;20(&<)#2:#S=N#T#&(#8**)"(#2:#,#1E= @;&06&()#(%)#J6"5(32"#+5&03"<#52"+(&"(#-5=#I%&(#+5&03"<#52"+(&"(+#/260-#&''04#:2*#&#,?E#-32-)#2:#(%) +&1)#1&"6:&5(6*)#(%&(#52"-65(+#,#E#&(#S=N#Ti

4.2 Terminal Characteristics of Junction Diodes 177

Solution Y3"5)# ! = -5 3

v ⁄ @I

(%)" - 5 = !3

!v ⁄ @I

L2*#(%)#,?1E#-32-)Q -5#=#,S−O3−NSSa.Z#=#`=U#×#,S−,`#E F%)#-32-)#52"-65(3"<#,#E#&(#S=N#T#52**)+'2"-+#(2#2")?(%26+&"-#,?1E#-32-)+#3"#'&*&00)0#/3(%#&#(2(&0 J6"5(32"#&*)&#,SSS#(31)+#<*)&()*=#F%6+#-5#3+#&0+2#,SSS#(31)+#<*)&()*8# -5#=##`=U#×#,S−,O#E Y3"5)#92(%#-5#&"-#@I#&*)#:6"5(32"+#2:#()1')*&(6*)8#(%)#:2*/&*-#!"v#5%&*&5()*3+(35#;&*3)+#/3(%#()1? ')*&(6*)8#&+#3006+(*&()-#3"#L3<=#P=U=#E(#&#<3;)"#52"+(&"(#-32-)#56**)"(8#(%)#;20(&<)#-*2'#&5*2++#(%)#-32-) -)5*)&+)+#94#&''*2A31&()04#.#1T#:2*#);)*4#,°$#3"5*)&+)#3"#()1')*&(6*)=#F%)#5%&"<)#3"#-32-)#;20(? &<)#/3(%#()1')*&(6*)#%&+#9))"#)A'023()-#3"#(%)#-)+3<"#2:#)0)5(*2"35#(%)*121)()*+=

Figure 4.9 F)1')*&(6*)# -)')"-)"5)# 2:# (%) -32-)# :2*/&*-# 5%&*&5()*3+(35=# E(# &# 52"+(&"( 56**)"(8#(%)#;20(&<)#-*2'#-)5*)&+)+#94#&''*2A3? 1&()04#.#1T#:2*#);)*4#,°$#3"5*)&+)#3"#()1')*&? (6*)=

EXERCISES 4.6# L3"-#(%)#5%&"<)#3"#-32-)#;20(&<)#3:#(%)#56**)"(#5%&"<)+#:*21#S=,#1E#(2#,S#1E= Ans. ,.S#1T 4.7# E#+30352"#J6"5(32"#-32-)#%&+#v#= #S=N#T#&(#!0=#,#1E=#L3"-#(%)#;20(&<)#-*2'#&(#!#=#S=,#1E#&"-# ! =#,S#1E= Ans. #S=`P#T7#S=N`#T 4.8# h+3"<#(%)#:&5(#(%&(#&#+30352"#-32-)#%&+#-5#=#,S−,P#E#&(#.Z°$#&"-#(%&(#-5#3"5*)&+)+#94#,Zj#')*#°$#*3+)#3" ()1')*&(6*)8#:3"-#(%)#;&06)#2:#-5#&(#,.Z°$=## Ans. ,=,N#×#,S−^#E

178 Chapter 4 Diodes

4.2.2 The Reverse-Bias Region F%)#*);)*+)?93&+#*)<32"#2:#2')*&(32"#3+#)"()*)-#/%)"#(%)#-32-)#;20(&<)#v#3+#1&-)#")<&(3;)=#@C6&? (32"#BP=,D#'*)-35(+#(%&(#3:#v#3+#")<&(3;)#&"-#&#:)/#(31)+#0&*<)*#(%&"#@I#B.Z#1TD#3"#1&<"3(6-)8#(%) )A'2")"(3&0#()*1#9)521)+#")<03<3904#+1&00#521'&*)-#(2#6"3(48#&"-#(%)#-32-)#56**)"(#9)521)+ !#! ]-5 F%&(#3+8#(%)#56**)"(#3"#(%)#*);)*+)#-3*)5(32"#3+#52"+(&"(#&"-#)C6&0#(2#-5=#F%3+#52"+(&"54#3+#(%) *)&+2"#9)%3"-#(%)#()*1#?)4;')4!&$0/;''3$4= [)&0#-32-)+#)A%393(#*);)*+)#56**)"(+#(%&(8#(%26<%#C63()#+1&008#&*)#165%#0&*<)*#(%&"#-5=#L2* 3"+(&"5)8#&#+1&00?+3<"&0#-32-)#/%2+)#-5#3+#2"#(%)#2*-)*#2:#,S−,P#E#(2#,S−,Z#E#5260-#+%2/#& *);)*+)#56**)"(#2"#(%)#2*-)*#2:#,#"E=#F%)#*);)*+)#56**)"(#&0+2#3"5*)&+)+#+21)/%&(#/3(%#(%) 3"5*)&+)#3"#1&<"3(6-)#2:#(%)#*);)*+)#;20(&<)=#X2()#(%&(#9)5&6+)#2:#(%)#;)*4#+1&00#1&<"3(6-) 2:#(%)#56**)"(8#(%)+)#-)(&30+#&*)#"2(#50)&*04#);3-)"(#2"#(%)#-32-)#!]v#5%&*&5()*3+(35#2:#L3<=#P=^=# E#0&*<)#'&*(#2:#(%)#*);)*+)#56**)"(#3+#-6)#(2#0)&H&<)#)::)5(+=#F%)+)#0)&H&<)#56**)"(+#&*) '*2'2*(32"&0#(2#(%)#J6"5(32"#&*)&8#J6+(#&+#-5#3+=#F%)3*#-)')"-)"5)#2"#()1')*&(6*)8#%2/);)*8#3+ -3::)*)"(#:*21#(%&(#2:#-5=#F%6+8#/%)*)&+#-5#-2690)+#:2*#);)*4#Z°$#*3+)#3"#()1')*&(6*)8#(%)#52**)? +'2"-3"<#*60)#2:#(%619#:2*#(%)#()1')*&(6*)#-)')"-)"5)#2:#(%)#*);)*+)#56**)"(#3+#(%&(#3(#-26? 90)+#:2*#);)*4#,S°$#*3+)#3"#()1')*&(6*)=

EXERCISE 4.9# F%)#-32-)#3"#(%)#53*563(#2:#L3<=#@P=U#3+#�&*<)#%3<%?56**)"(#-);35)#/%2+)#*);)*+)#0)&H&<)#3+#*)&+2"&904 3"-)')"-)"(#2:#;20(&<)=#!:#@#=#,#T#&(#.0°$8#:3"-#(%)#;&06)#2:#@#&(#PS°$#&"-#&(#S°$=

Figure E4.9

Ans. P#T7#S=.Z#T

4.2.3 The Breakdown Region F%)#(%3*-#-3+(3"5(#*)<32"#2:#-32-)#2')*&(32"#3+#(%)#9*)&H-2/"#*)<32"8#/%35%#5&"#9)#)&+304 3-)"(3:3)-#2"#(%)#-32-)#!]v#5%&*&5()*3+(35#3"#L3<=#P=^=#F%)#9*)&H-2/"#*)<32"#3+#)"()*)-#/%)"#(%) 1&<"3(6-)#2:#(%)#*);)*+)#;20(&<)#)A5))-+#&#(%*)+%20-#;&06)#(%&(#3+#+')53:35#(2#(%)#'&*(3560&*#-32-)8 5&00)-#(%)#&!"(>)-/1%#-4,(7"=#F%3+#3+#(%)#;20(&<)#&(#(%)#eH"))f#2:#(%)#!]v#56*;)#3"#L3<=#P=^#&"-#3+ -)"2()-#@GH8#/%)*)#(%)#+69+5*3'(#G#+(&"-+#:2*#M)")*#B+))#Y)5(32"#O=Z=OD#&"-#H#-)"2()+#H"))=

4.3 Modeling the Diode Forward Characteristic 179

E+#5&"#9)#+))"#:*21#L3<=#P=^8#3"#(%)#9*)&H-2/"#*)<32"#(%)#*);)*+)#56**)"(#3"5*)&+)+#*&'? 3-048#/3(%#(%)#&++253&()-#3"5*)&+)#3"#;20(&<)#-*2'#9)3"<#;)*4#+1&00=#R32-)#9*)&H-2/"#3+#"2*? 1&004# "2(# -)+(*65(3;)8# '*2;3-)-# (%)# '2/)*# -3++3'&()-# 3"# (%)# -32-)# 3+# 0313()-# 94# )A()*"&0 53*563(*4#(2#&#e+&:)f#0);)0=#F%3+#+&:)#;&06)#3+#"2*1&004#+')53:3)-#2"#(%)#-);35)#-&(&#+%))(+=#!( (%)*):2*)#3+#")5)++&*4#(2#0313(#(%)#*);)*+)#56**)"(#3"#(%)#9*)&H-2/"#*)<32"#(2#&#;&06)#52"+3+? ()"(#/3(%#(%)#')*13++390)#'2/)*#-3++3'&(32"= F%)#:&5(#(%&(#(%)#-32-)#!]v#5%&*&5()*3+(35#3"#9*)&H-2/"#3+#&012+(#&#;)*(35&0#03")#)"&90)+#3( (2#9)#6+)-#3"#;20(&<)#*)<60&(32"=#F%3+#+69J)5(#/300#9)#+(6-3)-#3"#Y)5(32"#P=Z=

4.3 Modeling the Diode Forward Characteristic >&;3"<#+(6-3)-#(%)#-32-)#()*13"&0#5%&*&5()*3+(35+#/)#&*)#"2/#*)&-4#(2#52"+3-)*#(%)#&"&04+3+#2: 53*563(+#)1'0243"<#:2*/&*-?52"-65(3"<#-32-)+=#L3<6*)#P=,S#+%2/+#+65%#5*563(=#!(#52"+3+(+#2:#& -5#+26*5)#@++8#&#*)+3+(2*#,8#&"-#&#-32-)=#I)#/3+%#(2#&"&04M)#(%3+#53*563(#(2#-)()*13")#(%)#-32-) ;20(&<)#@+#&"-#56**)"(#-+=#F2/&*-#(%&(#)"-#/)#52"+3-)*#-);)02'3"<#&#;&*3)(4#2:#12-)0+#:2*#(%) 2')*&(32"#2:#(%)#-32-)=#I)#&0*)&-4#H"2/#2:#(/2#+65%#12-)0+Q#(%)#3-)&0?-32-)#12-)08#&"-#(%) )A'2")"(3&0#12-)0=#!"#(%)#:2002/3"<#-3+56++32"#/)#+%&00#&++)++#(%)#+63(&9303(4#2:#(%)+)#(/2#12-? )0+#3"#;&*326+#&"&04+3+#+3(6&(32"+=#E0+28#/)#+%&00#-);)02'#&"-#5211)"(#2"#2(%)*#12-)0+=#F%3+ 1&()*3&08#9)+3-)+#9)3"<#6+):60#3"#(%)#&"&04+3+#&"-#-)+3<"#2:#-32-)#53*563(+8#)+(&903+%)+#&#:26"-&? (32"#:2*#(%)#12-)03"<#2:#(*&"+3+(2*#2')*&(32"#(%&(#/)#/300#+(6-4#3"#(%)#")A(#(/2#5%&'()*+=

4.3.1 The Exponential Model F%)#12+(#&556*&()#-)+5*3'(32"#2:#(%)#-32-)#2')*&(32"#3"#(%)#:2*/&*-#*)<32"#3+#'*2;3-)-#94 (%)# )A'2")"(3&0# 12-)0=# h":2*(6"&()048# %2/);)*8# 3(+# +);)*)04# "2"03")&*# "&(6*)# 1&H)+# (%3+ 12-)0#(%)#12+(#-3::3560(#(2#6+)=#F2#3006+(*&()8#0)(d+#&"&04M)#(%)#53*563(#3"#L3<=#P=,S#6+3"<#(%) )A'2")"(3&0#-32-)#12-)0= E++613"<#(%&(#@++#3+#<*)&()*#(%&"#S=Z#T#2*#+28#(%)#-32-)#56**)"(#/300#9)#165%#<*)&()*#(%&" -5 8#&"-#/)#5&"#*)'*)+)"(#(%)#-32-)#!]v#5%&*&5()*3+(35#94#(%)#)A'2")"(3&0#*)0&(32"+%3'8#*)+60(3"<#3"

-+ = -5 3

@+ ⁄ @I

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F%)# 2(%)*# )C6&(32"# (%&(# <2;)*"+# 53*563(# 2')*&(32"# 3+# 29(&3")-# 94# /*3(3"<# &# g3*5%%2::# 022' )C6&(32"8#*)+60(3"<#3"

@++ ! @+ -+ = ????????????????????? ,

BP=ND

E++613"<#(%&(#(%)#-32-)#'&*&1)()*#-5#3+#H"2/"8#@C+=#BP=`D#&"-#BP=ND#&*)#(/2#)C6&(32"+#3"#(%) (/2# 6"H"2/"# C6&"(3(3)+# -+# &"-# @+=# F/2# &0()*"&(3;)# /&4+# :2*# 29(&3"3"<# (%)# +206(32"# &*) <*&'%35&0#&"&04+3+#&"-#3()*&(3;)#&"&04+3+=

Figure 4.10 E#+31'0)#53*563(#6+)-#(2#3006+(*&()#(%)#&"&04+3+#2: 53*563(+#3"#/%35%#(%)#-32-)#3+#:2*/&*-#52"-65(3"<=

180 Chapter 4 Diodes

4.3.2 Graphical Analysis Using the Exponential Model k*&'%35&0#&"&04+3+#3+#')*:2*1)-#94#'02((3"<#(%)#*)0&(32"+%3'+#2:#@C+=#BP=`D#&"-#BP=ND#2"#(%) !]v#'0&")=#F%)#+206(32"#5&"#(%)"#9)#29(&3")-#&+#(%)#522*-3"&()+#2:#(%)#'23"(#2:#3"()*+)5(32"#2: (%)#(/2#<*&'%+=#E#+H)(5%#2:#(%)#<*&'%35&0#52"+(*65(32"#3+#+%2/"#3"#L3<=#P=,,=#F%)#56*;)#*)'? *)+)"(+#(%)#)A'2")"(3&0#-32-)#)C6&(32"#B@C=#P=`D8#&"-#(%)#+(*&3<%(#03")#*)'*)+)"(+#@C=#BP=ND= Y65%#&#+(*&3<%(#03")#3+#H"2/"#&+#(%)#4-()%4'1"8#&#"&1)#(%&(#/300#9)521)#12*)#1)&"3"<:60 3"#0&()*#5%&'()*+=#F%)#02&-#03")#3"()*+)5(+#(%)#-32-)#56*;)#&(#'23"(#L8#/%35%#*)'*)+)"(+#(%) -3"!(,'17%3-'1,#2:#(%)#53*563(=#!(+#522*-3"&()+#<3;)#(%)#;&06)+#2:#-+#&"-#@+= k*&'%35&0# &"&04+3+# &3-+# 3"# (%)# ;3+6&03M&(32"# 2:# 53*563(# 2')*&(32"=# >2/);)*8# (%)# )::2*( 3";20;)-#3"#')*:2*13"<#+65%#&"#&"&04+3+8#'&*(3560&*04#:2*#521'0)A#53*563(+8#3+#(22#<*)&(#(2#9)#J6+(3? :3)-#3"#'*&5(35)=

Figure 4.11 k*&'%35&0#&"&04+3+#2:#(%)#53*563(#3"#L3<=#P=,S#6+3"<#(%)#)A'2")"(3&0#-32-)#12-)0=

4.3.3 Iterative Analysis Using the Exponential Model @C6&(32"+#BP=`D#&"-#BP=ND#5&"#9)#+20;)-#6+3"<#&#+31'0)#3()*&(3;)#'*25)-6*)8#&+#3006+(*&()-#3" (%)#:2002/3"<#)A&1'0)=

Example 4.4 R)()*13")#(%)#56**)"(#-+#&"-#(%)#-32-)#;20(&<)#@+#:2*#(%)#53*563(#3"#L3<=#P=,S#/3(%#@++#=#Z#T#&"-# ,#=#,#HΩ=#E++61)#(%&(#(%)#-32-)#%&+#8**)"(#2:#,#1E#&(#&#;20(&<)#2:#S=N#T= Solution F2#9)<3"#(%)#3()*&(32"8#/)#&++61)#(%&(#@+#=#S=N#T#&"-#6+)#@C=#BP=ND#(2#-)()*13")#(%)#56**)"(8 @++ ! @+ ? -+ = ????????????????????? , Z ! S=N = ???????????????? = P=O#1E ,

4.3 Modeling the Diode Forward Characteristic 181

I)#(%)"#6+)#(%)#-32-)#)C6&(32"#(2#29(&3"# )(()*#)+(31&()#:2*#@+=#F%3+#5&"#9)#-2")#94#)1'0243"< @C=#BP=ZD8#"&1)048 @ . ! @ , = .=O@I 02< ???.? -,

Y69+3(6(3"<#.=O@I#=#`S#1T8#/)#%&;) @. = @ , + S=S` 02< ???.? -, Y69+(3(6(3"<#@,#=#S=N#T8#-,#=#,#1E8#&"-#-.#=#P=O#1E#*)+60(+#3"#@.#=#S=NO^#T=#F%6+#(%)#*)+60(+#2:#(%)#:3*+(#3()*? &(32"#&*)#-+#=#P=O#1E#&"-#@+#=#S=NO^#T=#F%)#+)52"-#3()*&(32"#'*25))-+#3"#&#+3130&*#1&"")*Q Z ! S=NO^ -+ = ?????????????????????? = P=.`.#1E , P=.`. @. = S=NO^ + S=S`#02< ????????????? P=O = S=NO^#T

F%6+#(%)#+)52"-#3()*&(32"#43)0-+#-+#=#P=.`.#1E#&"-#@+#=#S=NO^#T=#Y3"5)#(%)+)#;&06)+#&*)#;)*4#502+) (2#(%)#;&06)+#29(&3")-#&:()*#(%)#:3*+(#3()*&(32"8#"2#:6*(%)*#3()*&(32"+#&*)#")5)++&*48#&"-#(%)#+206(32"#3+ -+#=#P=.`.#1E#&"-#@+#=#S=NO^#T=

4.3.4 The Need for Rapid Analysis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ȉ'6()*#53*563(?&"&04+3+#'*2<*&1#+65%#&+#Yl!$@ B+))#E'')"-3A#_#&"-#(%)#-3+5D=#F%)#*)+60(+#2:#+65%#&"#&"&04+3+#5&"#(%)"#9)#6+)-#(2#:6*(%)* *):3")#2*#e:3")?(6")f#(%)#-)+3<"= F2#+'))-#6'#(%)#&"&04+3+#'*25)++8#/)#16+(#:3"-#&#+31'0)*#12-)0#:2*#(%)#-32-)#:2*/&*5%&*&5()*3+(35=

4.3.5 The Constant-Voltage-Drop Model F%)#+31'0)+(#&"-#12+(#/3-)04#6+)-#-32-)#12-)0#3+#(%)#52"+(&"(?;20(&<)?-*2'#12-)0=#F%3+ 12-)0#3+#9&+)-#2"#(%)#29+)*;&(32"#(%&(#&#:2*/&*-?52"-65(3"<#-32-)#%&+#&#;20(&<)#-*2'#(%&( ;&*3)+#3"#&#*)0&(3;)04#"&**2/#*&"<)8#+&4#S=`#(2#S=^#T=#F%)#12-)0#&++61)+#(%3+#;20(&<)#(2#9) 52"+(&"(#&(#&#;&06)8#+&48#S=N#T=#F%3+#-);)02'1)"(#3+#3006+(*&()-#3"#L3<=#P=,.=

182 Chapter 4 Diodes

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(b) i " vD ! i & 0, vD ' 0.7 V (c)

Figure 4.12 R);)02'1)"(#2:#(%)#-32-)#52"+(&"(?;20(&<)?-*2'#12-)0Q#5(6#(%)#)A'2")"(3&0#5%&*&5()*? +(357# 5&6# &''*2A31&(3"<# (%)# )A'2")"(3&0# 5%&*&5()*3+(35# 94# &# 52"+(&"(# ;20(&<)8# 6+6&004# &926(# S=N# T37 5*6 (%)#*)+60(3"<#12-)0#2:#(%)#:2/&*-]52"-65(3"<#-32-)+=

F%)#52"+(&"(?;20(&<)?-*2'#12-)0#3+#(%)#2")#12+(#:*)C6)"(04#)1'024)-#3"#(%)#3"3(3&0#'%&+)+ 2:#&"&04+3+#&"-#-)+3<"=#F%3+#3+#)+')53&004#(*6)#3:#&(#(%)+)#+(&<)+#2")#-2)+#"2(#%&;)#-)(&30)3":2*1&(32"#&926(#(%)#-32-)#5%&*&5()*3+(35+8#/%35%#3+#2:()"#(%)#5&+)= L3"&0048#"2()#(%&(#3:#/)#)1'024#(%)#52"+(&"(?;20(&<)?-*2'#12-)0#(2#+20;)#(%)#'*290)1#3" @A&1'0)#P=P8#/)#29(&3"

@+ = S=N#T &"-

@++ ! S=N ? - + = ????????????????????? , Z ! S=N = ???????????????? = P=O#1E , /%35%#&*)#"2(#;)*4#-3::)*)"(#:*21#(%)#;&06)+#29(&3")-#9):2*)#/3(%#(%)#12*)#)0&92*&()#)A'2? ")"(3&0#12-)0=

4.3 Modeling the Diode Forward Characteristic

4.3.6 The Ideal-Diode Model !"#&''035&(32"+#(%&(#3";20;)#;20(&<)+#165%#<*)&()*#(%&"#(%)#-32-)#;20(&<)#-*2'#BS=`#T]S=^#TD8 /)#1&4#")<0)5(#(%)#-32-)#;20(&<)#-*2'#&0(2<)(%)*#/%30)#5&0560&(3"<#(%)#-32-)#56**)"(=#F%)#*)+60( 3+# (%)# 3-)&0?-32-)# 12-)08# /%35%# /)# +(6-3)-# 3"# Y)5(32"# P=,=# L2*# (%)# 53*563(# 3"# @A&1'0)+# P=P B3=)=8 L3<=#P=,S#/3(%#@++#=#Z#T#&"-#,#=#,#HΩD8#6(303M&(32"#2:#(%)#3-)&0?-32-)#12-)0#0)&-+#(2#

@ + = S#T Z!S - + = ???????????? = Z#1E , /%35%#:2*#&#;)*4#C635H#&"&04+3+#/260-#"2(#9)#9&-#&+#&#<*2++#)+(31&()=#>2/);)*8#/3(%#&012+( "2#&--3(32"&0#/2*H8#(%)#S=N?T?-*2'#12-)0#43)0-+#165%#12*)#*)&03+(35#*)+60(+=#I)#"2()8#%2/? );)*8#(%&(#(%)#<*)&()+(#6(303(4#2:#(%)#3-)&0?-32-)#12-)0#3+#3"#-)()*13"3"<#/%35%#-32-)+#&*)#2" &"-#/%35%#&*)#2::#3"# (3-32-)#53*563(8#+65%#&+#(%2+)#52"+3-)*)-#3"#Y)5(32"#P=,=

EXERCISES 4.10#L2*#(%)#53*563(#3"#L3<=#P=,S8#:3"-#-+#&"-#@+#:2*#(%)#5&+)#@++#=#Z#T#&"-#,#=#,S#HΩ=#E++61)#(%&(#(%) -32-)#%&+#&#;20(&<)#2:#S=N#T#&(#,?1E#56**)"(=#h+)#B&D#3()*&(32"#&"-#B9D#(%)#52"+(&"(?;20(&<)?-*2' 12-)0#/3(%#@+#=#S=N#T= Ans. B&D#S=PO#1E8#S=`^#T7#B9D#S=PO#1E8#S=N#T D4.11#R)+3<"#(%)#53*563(#3"#L3<=#@P=,,#(2#'*2;3-)#&"#26('6(#;20(&<)#2:#.=P#T=#E++61)#(%&(#(%)#-32-)+#&;&30&90) %&;)#S=N?T#-*2'#&(#,#1E=

Figure E4.11

Ans. ,#=#,OU#Ω 4.12# [)')&(#@A)*53+)#P=P#6+3"<#(%)#S=N?T?-*2'#12-)0#(2#29(&3"#9)(()*#)+(31&()+#2:#-#&"-#@#(%&"#(%2+)#:26"3"#@A)*53+)#P=P#B6+3"<#(%)#3-)&0?-32-)#12-)0D= Ans. B&D#,=N.#1E8#S=N#T7#B9D#S#1E8#Z#T7#B5D#S#1E8#Z#T7#B-D#,=N.#1E8#S=N#T7#B)D#.=O#1E8#+.=O#T7# B:D#O=O#1E8#+,=N#T

183

184 Chapter 4 Diodes

4.3.7 The Small-Signal Model F%)*)#&*)#&''035&(32"+#3"#/%35%#&#-32-)#3+#93&+)-#(2#2')*&()#&(#&#'23"(#2"#(%)#:2*/&*-#!]v 5%&*&5()*3+(35#&"-#&#+1&00#&5#+3<"&0#3+#+6')*31'2+)-#2"#(%)#-5#C6&"(3(3)+=#L2*#(%3+#+3(6&(32"8 /)# :3*+(# %&;)# (2# -)()*13")# (%)# -5# 2')*&(3"<# '23"(# B@+# &"-# -+D# 2:# (%)# -32-)# 6+3"<# 2")# 2: (%) 12-)0+# -3+56++)-# &92;)=# m2+(# :*)C6)"(048# (%)# S=N?T?-*2'# 12-)0# 3+# 6(303M)-=# F%)"8# :2* +1&00?+3<"&0#2')*&(32"#&*26"-#(%)#-5#93&+#'23"(8#(%)#-32-)#3+#12-)0)-#94#&#*)+3+(&"5)#)C6&0#(2 (%)#3";)*+)#2:#(%)#+02')#2:#(%)#(&"<)"(#(2#(%)#)A'2")"(3&0#!]v#5%&*&5()*3+(35#&(#(%)#93&+#'23"(= F%)# ()5%"3C6)# 2:# 93&+3"<# &# "2"03")&*# -);35)# &"-# *)+(*35(3"<# +3<"&0# )A56*+32"# (2# &# +%2*(8 &012+(?03")&*#+)<1)"(#2:#3(+#5%&*&5()*3+(35#&*26"-#(%)#93&+#'23"(#3+#5)"(*&0#(2#-)+3<"3"<#03")&* &1'03:3)*+# 6+3"<# (*&"+3+(2*+8# &+# /300# 9)# +))"# 3"# (%)# ")A(# (/2# 5%&'()*+=# !"# (%3+# +)5(32"8# /) -);)02'#+65%#&#+1&00?+3<"&0#12-)0#:2*#(%)#J6"5(32"#-32-)#&"-#3006+(*&()#3(+#&''035&(32"=#

Figure 4.13 R);)02'1)"(#2:#(%)#-32-)#+1&00?+3<"&0#12-)0=

4.3 Modeling the Diode Forward Characteristic 185

$2"+3-)*#(%)#52"5)'(6&0#53*563(#3"#L3<=#P=,OB&D#&"-#(%)#52**)+'2"-3"<#<*&'%35&0#*)'*)+)"? (&(32"#3"#L3<=#P=,OB9D=#E#-5#;20(&<)#@+8#*)'*)+)"()-#94# &(()*48#3+#&''03)-#(2#(%)#-32-)8#&"-#& (31)?;&*43"<# +3<"&0# v* B4D8# &++61)-# B&*93(*&*304D# (2# %&;)# &# (*3&"<60&*# /&;):2*18# 3+ +6')*31'2+)-#2"#(%)#-5#;20(&<)#@+=#!"#(%)#&9+)"5)#2:#(%)#+3<"&0# v* B4D8#(%)#-32-)#;20(&<)#3+ )C6&0#(2#@+8#&"-#52**)+'2"-3"<048#(%)#-32-)#/300#52"-65(#&#-5#56**)"(#-+#<3;)"#94

-+ = -5 3

@+ ⁄ @I

BP=^D

I%)"#(%)#+3<"&0#v* B4D#3+#&''03)-8#(%)#(2(&0#3"+(&"(&")26+#-32-)#;20(&<)#v+ B4D#/300#9)#<3;)"#94 v + ( 4 ) = @+ + v * ( 4 ) $2**)+'2"-3"<048#(%)#(2(&0#3"+(&"(&")26+#-32-)#56**)"(#!+ B4D#/300#9) v+ ⁄ @I

!+ ( 4 ) = -5 3

BP=UD

BP=,SD

Y69+(3(6(3"<#:2*#v+#:*21#@C=#BP=UD#<3;)+

!+ ( 4 ) = -5 3

( @+ + v* ) ⁄ @I

BP=,,D

/%35%#5&"#9)#*)/*3(()"

!+ ( 4 ) = -5 3

@+ ⁄ @I

3

v* ⁄ @I

h+3"<#@C=#BP=^D#/)#29(&3"

!+ ( 4 ) = -+ 3

v* ⁄ @I

BP=,.D

X2/#3:#(%)#&1'03(6-)#2:#(%)#+3<"&0#v* B4D#3+#H)'(#+6::353)"(04#+1&00#+65%#(%&( v

?????* (, @I

BP=,OD

(%)"#/)#1&4#)A'&"-#(%)#)A'2")"(3&0#2:#@C=#BP=,.D#3"#&#+)*3)+#&"-#(*6"5&()#(%)#+)*3)+#&:()*#(%) :3*+(#(/2#()*1+#(2#29(&3"#(%)#&''*2A31&()#)A'*)++32" v

! + ( 4 )# ! #- + , + ?????* @I

BP=,PD

F%3+#3+#(%)#$=(440$'71(4%(33!-?'=(,'-1=#!(#3+#;&03-#:2*#+3<"&0+#/%2+)#&1'03(6-)+#&*)#+1&00)* (%&"#&926(#Z#1T#B+))#@C=#P=,O8#&"-#*)5&00#(%&(#@I#=#.Z 1TD=O L*21#@C=#BP=,PD#/)#%&;)

-+ ! + ( 4 ) = - + + ????? v @I *

BP=,ZD

F%6+8#+6')*31'2+)-#2"#(%)#-5#56**)"(#-+8#/)#%&;)#&#+3<"&0#56**)"(#521'2")"(#-3*)5(04#'*2? '2*(32"&0#(2#(%)#+3<"&0#;20(&<)#v*=#F%&(#3+8 /%)*)

!+ = -+ + !*

BP=,`D

-+ ! * = ????? v @I *

BP=,ND

L2*#v*#=#Z#1T8# v * ⁄ @ I = S=.=#F%6+#(%)#")A(#()*1#3"#(%)#+)*3)+#)A'&"+32"#2:#(%)#)A'2")"(3&0#/300#9)# ,??.? #× S=.. = S=S.8#&#:&5(2*#2:#,S#02/)*#(%&"#(%)#03")&*#()*1#/)#H)'(=

O

186 Chapter 4 Diodes F%)#C6&"(3(4#*)0&(3"<#(%)#+3<"&0#56**)"(#!*#(2#(%)#+3<"&0#;20(&<)#v*#%&+#(%)#-31)"+32"+#2:#52"? -65(&"5)8#1%2+#B )8#&"-#3+#5&00)-#(%)#)'-)"%$=(440$'71(4%*-1)+*,(1*"=#F%)#3";)*+)#2:#(%3+ '&*&1)()*#3+#(%)#)'-)"%$=(440$'71(4%!"$'$,(1*"8#2*#'1*!"="1,(4%!"$'$,(1*"8#'* 8 Ω

@ '* = ?????I -+

BP=,^D

X2()#(%&(#(%)#;&06)#2:#'*#3+#3";)*+)04#'*2'2*(32"&0#(2#(%)#93&+#56**)"(#-+= V)(#6+#*)(6*"#(2#(%)#<*&'%35&0#*)'*)+)"(&(32"#3"#L3<=#P=,OB9D=#!(#3+#)&+4#(2#+))#(%&(#6+3"<#(%) +1&00?+3<"&0#&''*2A31&(32"#3+#)C63;&0)"(#(2#&++613"<#(%&(#4:30?!>$)<0)1#04:30!]v#/;'D30!?013$4N F%)#+02')#2:#(%3+#+)<1)"(8#/%35%#3+#)C6&0#(2#(%)#+02')#2:#(%)#(&"<)"(#(2#(%)#!]v#56*;)#&(#(%) 2')*&(3"<# '23"(# L8# 3+# )C6&0# (2# (%)# +1&00?+3<"&0# 52"-65(&"5)=# F%)# *)&-)*# 3+# )"526*&<)-# (2 '*2;)#(%&(#(%)#+02')#2:#(%)#!]v#56*;)#&(#!#=#-+#3+#)C6&0#(2# - + ⁄ @ I 8 #/%35%#3+# , ⁄ ' * 7#(%&(#3+8#

∂! ' * = ,## ????????+? ∂ v+

! + =- +

BP=,UD

L*21#(%)#'*)5)-3"<#/)#52"506-)#(%&(#+6')*31'2+)-#2"#(%)#C6&"(3(3)+#@+#&"-#-+#(%&(#-):3") (%)#-5#93&+#'23"(8#2*#@+'"$*"1,%3-'1,8#2:#(%)#-32-)#/300#9)#(%)#+1&00?+3<"&0#C6&"(3(3)+#v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

Example 4.5 $2"+3-)*#(%)#53*563(#+%2/"#3"#L3<=#P=,PB&D#:2*#(%)#5&+)#3"#/%35%#,#=#,S#HΩ=#F%)#'2/)*#+6''04#@ +#%&+#&#-5 ;&06)#2:#,S#T#2"#/%35%#3+#+6')*31'2+)-#&#`S?>M#+3"6+23-#2:#,?T#')&H#&1'03(6-)=#BF%3+#e+3<"&0f#521'2? ")"(# 2:# (%)# '2/)*?+6''04# ;20(&<)# 3+# &"# 31')*:)5(32"# 3"# (%)# '2/)*?+6''04# -)+3<"=# !(# 3+# H"2/"# &+# (%) 3-/"!0$+334A%!'334"=#m2*)#2"#(%3+#0&()*=D#$&0560&()#92(%#(%)#-5#;20(&<)#2:#(%)#-32-)#&"-#(%)#&1'03(6-)#2: (%)#+3")?/&;)#+3<"&0#&'')&*3"<#&5*2++#3(=#E++61)#(%)#-32-)#(2#%&;)#&#S=N?T#-*2'#&(#,?1E#56**)"(= 10 V ID

R

R " VD

" vs

" !

rd

!

(a)

(b)

vd !

(c)

Figure 4.14 5(6# $3*563(# :2*# @A&1'0)# P=Z=# 5&6# $3*563(# :2*# 5&0560&(3"<# (%)# -5# 2')*&(3"<# '23"(=# 5*6# Y1&00?+3<"&0 )C63;&0)"(#53*563(=

4.3 Modeling the Diode Forward Characteristic

187

Solution $2"+3-)*3"<#-5#C6&"(3(3)+#2"048#/)#&++61)#@+#!#S=N#T#&"-#5&0560&()#(%)#-32-)#-5#56**)"( ,S ! S=N - + = ??????????????????? = S=UO#1E ,S Y3"5)#(%3+#;&06)#3+#;)*4#502+)#(2#,#1E8#(%)#-32-)#;20(&<)#/300#9)#;)*4#502+)#(2#(%)#&++61)-#;&06)#2: S=N#T=#E(#(%3+#2')*&(3"<#'23"(8#(%)#-32-)#3"5*)1)"(&0#*)+3+(&"5)#'*#3+# @ .Z ' * = ?????I? = ?????????? = .`=U#Ω S=UO -+ F%)# +3<"&0# ;20(&<)# &5*2++# (%)# -32-)# 5&"# 9)# :26"-# :*21# (%)# +1&00?+3<"&0# )C63;&0)"(# 53*563(# 3" L3<= P=,PB5D=# >)*)# v?# -)"2()+# (%)# `S?>M# ,?T# ')&H# +3"6+23-&0# 521'2")"(# 2:# @ +8# &"-# v*# 3+# (%)# 52*? *)+'2"-3"<#+3<"&0#&5*2++#(%)#-32-)=#h+3"<#(%)#;20(&<)?-3;3-)*#*60)#'*2;3-)+#(%)#')&H#&1'03(6-)#2:#v* &+#:2002/+Q '* ? v * # ( ')&H ) = @n? ????????????? , + '* S=S.`U = , ???????????????????????????? = .=`^ 1T # ,S + S=S.`U L3"&004#/)#"2()#(%&(#+3"5)#(%3+#;&06)#3+#C63()#+1&008#26*#6+)#2:#(%)#+1&00?+3<"&0#12-)0#2:#(%)#-32-)#3+ J6+(3:3)-=

L3"&0048#/)#"2()#(%&(#/%30)#'*#12-)0+#(%)#+1&00?+3<"&0#2')*&(32"#2:#(%)#-32-)#&(#02/#:*)C6)"? 53)+8#3(+#-4"&135#2')*&(32"#3+#12-)0)-#94#(%)#5&'&53(&"5)+#8O#&"-#8* 8#/%35%#/)#+(6-3)-#3"#Y)5? (32"#O=`#&"-#/%35%#&0+2#&*)#+1&00?+3<"&0#'&*&1)()*+=#E#521'0)()#12-)0#2:#(%)#-32-)#3"506-)+#8O &"-#8*03"#'&*&00)0#/3(%0'* =

4.3.8 Use of the Diode Forward Drop in Voltage Regulation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±,Sj#;&*3&(32"D8#(%) 52**)+'2"-3"<#*3''0)#3"#(%)#-32-)#;20(&<)#/&+#2"04#&926(#±.=N#1T#B&#±S=Pj#;&*3&(32"D=#[)<6? 0&()-#;20(&<)+#<*)&()*#(%&"#S=N#T#5&"#9)#29(&3")-#94#52"")5(3"<#&#"619)*#2:#-32-)+#3"#+)*3)+= L2*#)A&1'0)8#(%)#6+)#2:#(%*))#:2*/&*-?93&+)-#-32-)+#3"#+)*3)+#'*2;3-)+#&#;20(&<)#2:#&926(#.#T= K")#+65%#53*563(#3+#3";)+(3<&()-#3"#(%)#:2002/3"<#)A&1'0)8#/%35%#6(303M)+#(%)#-32-)#+1&00?+3<"&0 12-)0#(2#C6&"(3:4#(%)#)::35&54#2:#(%)#;20(&<)#*)<60&(2*#(%&(#3+#*)&03M)-=

188 Chapter 4 Diodes

Example 4.6 $2"+3-)*#(%)#53*563(#+%2/"#3"#L3<=#P=,Z=#E#+(*3"<#2:#(%*))#-32-)+#3+#6+)-#(2#'*2;3-)#4"+(&"(#;20(&<) 2:#&926(#.=,#T=#I)#/&"(#(2#5&0560&()#(%)#')*5)"(&<)#5%&"<)#3"#(%3+#*)<60&()-#;20(&<)#5&6+)-#94#B&D#& ±,Sj#5%&"<)#3"#(%)#'2/)*?+6''04#;20(&<)#&"-#B9D#52"")5(32"#2:#&#,?HΩ#02&-#*)+3+(&"5)= 10) 1 V R = 1 k* " vO

RL = 1 k*

! Figure 4.15 $3*563(#:2*#@A&1'0)#P=`=

Solution I3(%#"2#02&-8#(%)#"213"&0#;&06)#2:#(%)#56**)"(#3"#(%)#-32-)#+(*3"<#3+#<3;)"#94# ,S ! .=, - = ??????????????????? = N=U#1E ID , F%6+#)&5%#-32-)#/300#%&;)#&"#3"5*)1)"(&0#*)+3+(&"5)#2: @ ' * = ?????I? I D F%6+8 .Z ' * = ??????? = O=.#Ω N=U

F%)#(%*))#-32-)+#3"#+)*3)+#/300#%&;)#&#(2(&0#3"5*)1)"(&0#*)+3+(&"5)#2:# ' = O' * = U=`#Ω

F%3+#*)+3+(&"5)8#&02"<#/3(%#(%)#*)+3+(&"5)#,8#:2*1+#&#;20(&<)#-3;3-)*#/%2+)#*&(32#5&"#9)#6+)-#(2#5&0? 560&()#(%)#5%&"<)#3"#26('6(#;20(&<)#-6)#(2#&#±,Sj#B3=)=8#±,?TD#5%&"<)#3"#+6''04#;20(&<)=#F%6+#(%) ')&H?(2?')&H#5%&"<)#3"#26('6(#;20(&<)#/300#9)# ' S=SSU` this is ans to q cuz 3* ∆ v . = . ???????????? = . ????????????????????????? = ,U#1T ')&H?(2?')&H 0.7 voltage wont change '+, S=SSU` + , anyway

19mV /2 = 9.5

F%&(#3+8#52**)+'2"-3"<#(2#(%)#±,?T#B±,SjD#5%&"<)#3"#+6''04#;20(&<)8#(%)#26('6(#;20(&<)#/300#5%&"<) 94#±U=Z#1T#2*#±S=Zj=#Y3"5)#(%3+#31'03)+#%&"<)#2:#&926(#±O=.#1T#')*#-32-)8#26*#6+)#2:#(%)#+1&00? +3<"&0#12-)0#3+#J6+(3:3)-= I%)"# &# 02&-# *)+3+(&"5)# 2:# ,# HΩ# 3+# 52"")5()-# &5*2++# (%)# -32-)# +(*3"<8# 3(# -*&/+# &# 56**)"(# 2: &''*2A31&()04#.=,#1E=#F%6+#(%)#56**)"(#3"#(%)#-32-)+#-)5*)&+)+#94#.=,#1E8#*)+60(3"<#3"#&#-)5*)&+) 3"#;20(&<)#&5*2++#(%)#-32-)#+(*3"<#<3;)"#94 ∆ v . = ! .=, × ' = ! .=, × U=` = ! .S#1T

e x

4.4 Operation in the Reverse Breakdown Region—Zener Diodes

Y3"5)# (%3+# 31'03)+# (%&(# (%)# ;20(&<)# &5*2++# )&5%# -32-)# -)5*)&+)+# 94# &926(# `=N# 1T8# 26*# 6+)# 2:# (%) +1&00?+3<"&0# 12-)0# 3+# "2(# )"(3*)04# J6+(3:3)-=# X);)*(%)0)++8# &# -)(&30)-# 5&0560&(32"# 2:# (%)# ;20(&<) 5%&"<)#6+3"<#(%)#)A'2")"(3&0#12-)0#*)+60(+#3"# ∆ v . = ! .O#1T8 #/%35%#3+#"2(#(22#-3::)*)"(#:*21#(%) &''*2A31&()#;&06)#29(&3")-#6+3"<#(%)#3"5*)1)"(&0#12-)0=

EXERCISES 4.13# L3"-#(%)#;&06)#2:#(%)#-32-)#+1&00?+3<"&0#*)+3+(&"5)#'*#&(#93&+#56**)"(+#2:#S=,#1E8#,#1E8#&"-#,S#1E= Ans. .ZS#Ω7#.Z#Ω7#.=Z#Ω 4.14# $2"+3-)*#&#-32-)#93&+)-#&(#,#1E=#L3"-#(%)#5%&"<)#3"#56**)"(#&+#&#*)+60(#2:#5%&"<3"<#(%)#;20(&<) 94#B&D#−,S#1T8#B9D#−Z#1T8#B5D#+Z#1T8#&"-#B-D#+,S#1T=#!"#)&5%#5&+)8#-2#(%)#5&0560&(32"+#B3D#6+3"< (%)#+1&00?+3<"&0#12-)0#&"-#B33D#6+3"<#(%)#)A'2")"(3&0#12-)0= Ans. B&D#−S=PS8#−S=OO#1E; B9D#−S=.S8#−S=,^#1E; B5D#+S=.S8#+S=..#1E; B-D#+S=PS8#+S=PU#1E D4.15# R)+3<"#(%)#53*563(#2:#L3<=#@P=,Z#+2#(%&(#@.#=#O#T#/%)"#-P#=#S8#&"-#@.#5%&"<)+#94#.S#1T#')*#,#1E 2:#02&-#56**)"(=# B&D#h+)#(%)#+1&00?+3<"&0#12-)0#2:#(%)#-32-)#(2#:3"-#(%)#;&06)#2:#,= B9D#Y')53:4#(%)#;&06)#2:#-5002:#)&5%#2:#(%)#-32-)+= B5D#L2*#(%3+#-)+3<"8#6+)#(%)#-32-)#)A'2")"(3&0#12-)0#(2#-)()*13")#(%)#&5(6&0#5%&"<)#3"#@.#/%)"#& 56**)"(#-P#\#,#1E#3+#-*&/"#:*21#(%)#*)<60&(2*= "15 V

R VO IL

Figure E4.15

Ans. B&D%,#=#.=P#HΩ7#B9D%-5#\#P=N#+#,S!,`#E7%B5D%!..=O#1T%

4.4 Operation in the Reverse Breakdown Region—Zener Diodes F%)#;)*4#+())'#!]v#56*;)#(%&(#(%)#-32-)#)A%393(+#3"#(%)#9*)&H-2/"#*)<32"#BL3<=#P=^D#&"-#(%) &012+(?52"+(&"(#;20(&<)#-*2'#(%&(#(%3+#3"-35&()+8#+6<<)+(#(%&(#-32-)+#2')*&(3"<#3"#(%)#9*)&H-2/" *)<32"#5&"#9)#6+)-#3"#(%)#-)+3<"#2:#;20(&<)#*)<60&(2*+=#L*21#(%)#'*);326+#+)5(32"8#(%)#*)&-)*

189

190 Chapter 4 Diodes /300#*)5&00#(%&(#;20(&<)#*)<60&(2*+#&*)#53*563(+#(%&(#'*2;3-)#4"+(&"(#-5#26('6(#;20(&<)#3"#(%) :&5)#2:#5%&"<)+#3"#(%)3*#02&-#56**)"(#&"-#3"#(%)#+4+()1#'2/)*?+6''04#;20(&<)=#F%3+#3"#:&5(#(6*"+ 26(#(2#9)#&"#31'2*(&"(#&''035&(32"#2:#-32-)+#2')*&(3"<#3"#(%)#*);)*+)?9*)&H-2/"#*)<32"8#&"+')53&0#-32-)+#&*)#1&"6:&5(6*)-#(2#2')*&()#+')53:35&004#3"#(%)#9*)&H-2/"#*)<32"=#Y65%#-32-)+ &*)#5&00)-#&!"(>)-/1%)'-)"$#2*8#12*)#52112"048#&+#"2()-#)&*03)*8#B"1"!%)'-)"$= L3<6*)#P=,`#+%2/+#(%)#53*563(#+41920#2:#(%)#M)")*#-32-)=#!"#"2*1&0#&''035&(32"+#2:#M)")* -32-)+8#56**)"(#:02/+#3"(2#(%)#5&(%2-)8#&"-#(%)#5&(%2-)#3+#'2+3(3;)#/3(%#*)+')5(#(2#(%)#&"2-)= F%6+#-G#&"-#@G#3"#L3<=#P=,`#%&;)#'2+3(3;)#;&06)+= IZ

" VZ ! Figure 4.16 $3*563(# +41920# :2*# & M)")*#-32-)=

4.4.1 Specifying and Modeling the Zener Diode L3<6*)# P=,N# +%2/+# -)(&30+# 2:# (%)# -32-)# !]v# 5%&*&5()*3+(35# 3"# (%)# 9*)&H-2/"# *)<32"=# I) 29+)*;)#(%&(#:2*#56**)"(+#<*)&()*#(%&"#(%)#>1""%*+!!"1,#-GH#B+')53:3)-#2"#(%)#-&(&#+%))(#2: (%) M)")*# -32-)D8# (%)# !]v# 5%&*&5()*3+(35# 3+# &012+(# &# +(*&3<%(# 03")=# F%)# 1&"6:&5(6*)*# 6+6&004 +')53:3)+#(%)#;20(&<)#&5*2++#(%)#M)")*#-32-)#@G#&(#&#+')53:3)-#()+(#56**)"(8#-GI=#I)#%&;)#3"-3? 5&()-#(%)+)#'&*&1)()*+#3"#L3<=#P=,N#&+#(%)#522*-3"&()+#2:#(%)#'23"(#0&9)0)-#L=#F%6+#&#`=^?T i !VZ

!VZ 0

!VZK 0 !IZK

Slope '

,V

1 rz

Q

v

!IZT (test current)

,I

,V ' ,I rz Figure 4.17 F%)#-32-)#!]v#5%&*&5()*3+(35#/3(%#(%)#9*)&H-2/"#*)<32"#+%2/"#3"#+21)#-)(&30=

4.4 Operation in the Reverse Breakdown Region—Zener Diodes 191

M)")*#-32-)#/300#)A%393(#&#`=^?T#-*2'#&(#&#+')53:3)-#()+(#56**)"(#2:8#+&48#,S#1E=#E+#(%)#56*? *)"(# (%*26<%# (%)# M)")*# -);3&()+# :*21# -GI 8# (%)# ;20(&<)# &5*2++# 3(# /300# 5%&"<)8# (%26<%# 2"04 +03<%(04=#L3<6*)#P=,N#+%2/+#(%&(#52**)+'2"-3"<#(2#56**)"(#5%&"<)#∆-#(%)#M)")*#;20(&<)#5%&"<)+ 94#∆@8#/%35%#3+#*)0&()-#(2#∆-#94

∆@ = ' Q ∆/%)*)#'Q#3+#(%)#3";)*+)#2:#(%)#+02')#2:#(%)#&012+(?03")&*#!]v#56*;)#&(#'23"(#L=#[)+3+(&"5)#'Q#3+ (%)#'1*!"="1,(4%!"$'$,(1*"#2:#(%)#M)")*#-32-)#&(#2')*&(3"<#'23"(#L=#!(#3+#&0+2#H"2/"#&+#(%) )A1(='*%!"$'$,(1*"#2:#(%)#M)")*8#&"-#3(+#;&06)#3+#+')53:3)-#2"#(%)#-);35)#-&(&#+%))(=#F4'3? 5&0048#'Q#3+#3"#(%)#*&"<)#2:#&#:)/#2%1+#(2#&#:)/#()"+#2:#2%1+=#K9;326+048#(%)#02/)*#(%)#;&06) 2:#'Q#3+8#(%)#12*)#52"+(&"(#(%)#M)")*#;20(&<)#*)1&3"+#&+#3(+#56**)"(#;&*3)+8#&"-#(%6+#(%)#12*) 3-)&0#3(+#')*:2*1&"5)#9)521)+#3"#(%)#-)+3<"#2:#;20(&<)#*)<60&(2*+=#!"#(%3+#*)<&*-8#/)#29+)*;) :*21#L3<=#P=,N#(%&(#/%30)#'Q#*)1&3"+#02/#&"-#&012+(#52"+(&"(#2;)*#&#/3-)#*&"<)#2:#56**)"(8#3(+ ;&06)# 3"5*)&+)+# 52"+3-)*&904# 3"# (%)# ;353"3(4# 2:# (%)# H"))=# F%)*):2*)8# &+ &# <)")*&0# -)+3<" <63-)03")8#2")#+%260-#&;23-#2')*&(3"<#(%)#M)")*#3"#(%3+#02/?56**)"(#*)<32"= o)")*#-32-)+#&*)#:&9*35&()-#/3(%#;20(&<)+#@G#3"#(%)#*&"<)#2:#&#:)/#;20(+#(2#&#:)/#%6"-*);20(+=#!"#&--3(32"#(2#+')53:43"<#@G#B&(#&#'&*(3560&*#56**)"(#-GID8#'Q8#&"-#-GH8#(%)#1&"6:&5(6*)* &0+2#+')53:3)+#(%)#1&A3161#'2/)*#(%&(#(%)#-);35)#5&"#+&:)04#-3++3'&()=#F%6+#& S=Z?I8#`=^?T M)")*# -32-)# 5&"# 2')*&()# +&:)04# &(# 56**)"(+# 6'# (2# &# 1&A3161# 2:# &926(# NS 1E= F%)# &012+(?03")&*# !]v# 5%&*&5()*3+(35# 2:# (%)# M)")*# -32-)# +6<<)+(+# (%&(# (%)# -);35)# 5&"# 9) 12-)0)-#&+#3"-35&()-#3"#L3<=#P=,^=#>)*)#@G S#-)"2()+#(%)#'23"(#&(#/%35%#(%)#+(*&3<%(#03")#2: +02')#, ⁄ ' Q#3"()*+)5(+#(%)#;20(&<)#&A3+#B*):)*#(2#L3<=#P=,ND=#E0(%26<%#@GS#3+#+%2/"#3"#L3<= P=,N (2#9)#+03<%(04#-3::)*)"(#:*21#(%)#H"))#;20(&<)#@GH8#3"#'*&5(35)#(%)3*#;&06)+#&*)#&012+(#)C6&0= F%)#)C63;&0)"(#53*563(#12-)0#2:#L3<=#P=,^#5&"#9)#&"&04(35&004#-)+5*39)-#94

@ G = @ GS + ' Q - G

BP=.SD

&"-#3(#&''03)+#:2*#-G#>#-GH#&"-8#29;326+048#@G#>#@G S=

Figure 4.18 m2-)0#:2*#(%)#M)")*#-32-)=

4.4.2 Use of the Zener as a Shunt Regulator I)#"2/#3006+(*&()8#94#/&4#2:#&"#)A&1'0)8#(%)#6+)#2:#M)")*#-32-)+#3"#(%)#-)+3<"#2:#+%6"(#*)
192 Chapter 4 Diodes

Example 4.7 F%)# `=^?T# M)")*#-32-)#3"#(%)#53*563(#2:#L3<=#P=,UB&D#3+# +')53:3)-#(2#%&;)# @G#=#`=^#T#&(# -G#=#Z#1E8 'Q = .S#Ω8#&"-#-GH#=#S=.#1E=#F%)#+6''04#;20(&<)#@ +#3+#"213"&004#,S#T#96(#5&"#;&*4#94#±,#T= 1 V) I

IZ

6.8V Vz, ;IZ = 0.005mA; to calculate Vzo

"

IL

VO !

(b)

(a)

Figure 4.19 5(6#$3*563(#:2*#@A&1'0)#P=N=#5&6#F%)#53*563(#/3(%#(%)#M)")*#-32-)#*)'0&5)-#/3(%#3(+#)C63;&0)"(#53*563( 12-)0=

B&D L3"-#@.#/3(%#"2#02&-#&"-#/3(%#@ +#&(#3(+#"213"&0#;&06)= + B9D L3"-# (%)# 5%&"<)# 3"# @.# *)+60(3"<# :*21# (%)# ±,?T# 5%&"<)# 3"# @ +=# X2()# (%&(# ( ∆@ . ⁄ ∆ @ ) 8# 6+6&004 )A'*)++)-#3"#1T/T8#3+#H"2/"#&+#4'1"%!"7+4(,'-1= B5D L3"-#(%)#5%&"<)#3"#@.#*)+60(3"<#:*21#52"")5(3"<#&-#*)+3+(&"5)#,P#(%&(#-*&/+#8**)"(#-P#= , 1E8#&"-#%)"5)#:3"-#(%)#4-()%!"7+4(,'-1# ( ∆@ . ⁄ ∆- P ) #3"#1T/1E= B-D L3"-#(%)#5%&"<)#3"#@.#/%)"#,P#=#.#HΩ= B)D L3"-#(%)#;&06)#2:#@.#/%)"#,P#=#S=Z#HΩ= B:D I%&(#3+#(%)#13"3161#;&06)#2:#,P#:2*#/%35%#(%)#-32-)#+(300#2')*&()+#3"#(%)#9*)&H-2/"#*)<32"i Solution

Vz and IZ change depend on supply

L3*+(#/)#16+(#-)()*13")#(%)#;&06)#2:#(%)#'&*&1)()*#@G S#2:#(%)#M)")*#-32-)#12-)0=#Y69+(3(6(3"<#@G#= `=^#T8#-G#=#Z#1E8#&"-#'Q#=#.S#Ω#3"#@C=#BP=.SD#43)0-+# @ GS = `=N#T= #L3<6*)#P=,UB9D#+%2/+#(%)#53*563( /3(%#(%)#M)")*#-32-)#*)'0&5)-#/3(%#3(+#12-)0= B&D I3(%#"2#02&-#52"")5()-8#(%)#56**)"(#(%*26<%#(%)#M)")*#3+#<3;)"#94 + @ ! @ GS ? - G = - = ??????????????????? consider , + 'Q ,S ! `=N Text = ???????????????????????? = `=OZ#1E S=Z + S=S.

F%6+8 Vz=

@ . = @ GS + - G ' Q = `=N + `=OZ × S=S. = `=^O#T

this as ID in amp biais, even the rz exist already

4.4 Operation in the Reverse Breakdown Region—Zener Diodes 193

B9D L2*#&#±,?T#5%&"<)#3"#@ +8#(%)#5%&"<)#3"#26('6(#;20(&<)#5&"#9)#:26"-#:*21 + 'Q ? ∆@ . = ∆@ ????????????? , + 'Q .S = ± , × ????????????????????? = ± O^=Z#1T ZSS + .S

F%6+8 V3")#*)<60&(32"#=#O^=Z#1TaT

B5D I%)"#&-#*)+3+(&"5)#,P#(%&(#-*&/+#&-#56**)"(#-P#=#,#1E#3+#52"")5()-8#(%)#M)")*#56**)"( /300#-)5*)&+)#94#,#1E=#F%)#52**)+'2"-3"<#5%&"<)#3"#M)")*#;20(&<)#5&"#9)#:26"-#:*21 ∆@ . = ' Q ∆- G = .S × ! , = ! .S#1T

F%6+#(%)#02&-#*)<60&(32"#3+

e x a)

∆@ V2&-#*)<60&(32" ≡ ??????????. = ! .S#1Ta1E ∆- P

B-D I%)"# &# 02&-# *)+3+(&"5)# 2:# . HΩ# 3+# 52"")5()-8# (%)# 02&-# 56**)"(# /300# 9)# &''*2A31&()04 `=^ Ta. HΩ#=#O=P#1E=#F%6+#(%)#5%&"<)#3"#M)")*#56**)"(#/300#9)#∆-G#=#−O=P#1E8#&"-#(%)#52**)+'2"-? 3"<#5%&"<)#3"#M)")*#;20(&<)#B26('6(#;20(&<)D#/300#(%6+#9) ∆@ . = ' Q ∆- G

e x

e a) x

= .S × ! O=P = ! `^#1T

F%3+#5&0560&(32"8#%2/);)*8#3+#&''*2A31&()8#9)5&6+)#3(#")<0)5(+#(%)#5%&"<)#3"#(%)#56**)"(#-=#E#12*) &556*&()#)+(31&()#2:#∆@.#5&"#9)#29(&3")-#94#&"&04M3"<#(%)#53*563(#3"#L3<=#P=,UB9D=#F%)#*)+60(#2:#+65% &"#&"&04+3+#3+#∆@.#=#−NS#1T= B)D E"#,P#2:#S=Z#HΩ#/260-#-*&/#&-#56**)"(#2:# `=^ ⁄ S=Z#=#,O=`#1E=#F%3+#3+#"2(#'2++390)8#9)5&6+) (%)#56**)"(#-#+6''03)-#(%*26<%#,#3+#2"04#`=P#1E#B:2*#@ +#=#,S#TD=#F%)*):2*)8#(%)#M)")*#16+(#9)#56(#2::= !:#(%3+#3+#3"-))-#(%)#5&+)8#(%)"#@.#3+#-)()*13")-#94#(%)#;20(&<)#-3;3-)*#:2*1)-#94#,P#&"-#,#BL3<=#P=,U&D8

e x

!!!!!

+ ,P ? @ . = @ ??????????????? , + ,P

S=Z ? = Z#T = ,S ???????????????????? Text S=Z + S=Z

Y3"5)#(%3+#;20(&<)#3+#02/)*#(%&"#(%)#9*)&H-2/"#;20(&<)#2:#(%)#M)")*8#(%)#-32-)#3+#3"-))-#"2#02"<)* 2')*&(3"<#3"#(%)#9*)&H-2/"#*)<32"= B: D L2*#(%)#M)")*#(2#9)#&(#(%)#)-<)#2:#(%)#9*)&H-2/"#*)<32"8#-G#=#-GH#=#S=.#1E#&"-#@G#!#@GH#!#`=N T= E(#(%3+#'23"(#(%)#02/)+(#B/2*+(?5&+)D#56**)"(#+6''03)-#(%*26<%#,#3+#( U ! `=N ) ⁄ S=Z = P=`#1E8#&"-#(%6+ e (%)#02&-#56**)"(#3+#P=`#−#S=.#=#P=P#1E=#F%)#52**)+'2"-3"<#;&06)#2:#, P#3+

x

`=N , P = ??????? ! ,=Z#HΩ P=P

e x

should give diod 0.2 mA even after "drawn current by add RL"

e x

= Vzo!!!

or 9- vzo - izk*rz ok too (see prolem e set)

x

194 Chapter 4 Diodes

4.4.3 Temperature Effects F%)#-)')"-)"5)#2:#(%)#M)")*#;20(&<)#@G#2"#()1')*&(6*)#3+#+')53:3)-#3"#()*1+#2:#3(+#,"=3"!(0 ,+!"% *-"..'*'"1,%CD8#2*# ,"=*-#&+#3(# 3+#52112"04# H"2/"8#/%35%#3+# 6+6&004#)A'*)++)-#3" 1Ta°$=#F%)#;&06)#2:#F$#-)')"-+#2"#(%)#M)")*#;20(&<)8#&"-#:2*#&#<3;)"#-32-)#(%)#F$#;&*3)+ /3(%#(%)#2')*&(3"<#56**)"(=#o)")*#-32-)+#/%2+)#@G#&*)#02/)*#(%&"#&926(#Z#T#)A%393(#&#")<&? (3;)#F$=#K"#(%)#2(%)*#%&"-8#M)")*+#/3(%#%3<%)*#;20(&<)+#)A%393(#&#'2+3(3;)#F$=#F%)#F$#2:#& M)")*#-32-)#/3(%#&#@G#2:#&926(#Z#T#5&"#9)#1&-)#M)*2#94#2')*&(3"<#(%)#-32-)#&(#&#+')53:3)56**)"(=#E"2(%)*#52112"04#6+)-#()5%"3C6)#:2*#29(&3"3"<#&#*):)*)"5)#;20(&<)#/3(%#02/#()1? ')*&(6*)# 52)::353)"(# 3+# (2# 52"")5(# &# M)")*# -32-)# /3(%# &# '2+3(3;)# ()1')*&(6*)# 52)::353)"(# 2: &926(# .# 1Ta°$# 3"# +)*3)+# /3(%# &# :2*/&*-?52"-65(3"<# -32-)=# Y3"5)# (%)# :2*/&*-?52"-65(3"< -32-)#%&+#&#;20(&<)#-*2'#2:#!S=N#T#&"-#&#F$#2:#&926(#−.#1Ta°$8#(%)#+)*3)+#52193"&(32" /300#'*2;3-)#&#;20(&<)#2:#B@G#+#S=ND#/3(%#&#F$#2:#&926(#M)*2=

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4.5.3 The Bridge Rectifier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v5#3+#'2+3(3;)8#&"-#(%6+#56**)"(#3+#52"-65()-#(%*26<%#-32-)#+,8#*)+3+(2*#,8#&"-32-)#+.=#m)&"/%30)8#-32-)+#+O#&"-#+P#/300#9)#*);)*+)#93&+)-=#K9+)*;)#(%&(#(%)*)#&*)#(/2 -32-)+#3"#+)*3)+#3"#(%)#52"-65(32"#'&(%8#&"-#(%6+#v.#/300#9)#02/)*#(%&"#v5#94#(/2#-32-)#-*2'+ B521'&*)-#(2#2")#-*2'#3"#(%)#53*563(#'*);326+04#-3+56++)-D=#F%3+#3+#+21)/%&(#2:#&#-3+&-;&"? (&<)#2:#(%)#9*3-<)#*)5(3:3)*= " ! ac line voltage

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199

200 Chapter 4 Diodes X)A(8#52"+3-)*#(%)#+3(6&(32"#-6*3"<#(%)#")<&(3;)#%&0:?5450)+#2:#(%)#3"'6(#;20(&<)=#F%)#+)5? 2"-&*4#;20(&<)#v5#/300#9)#")<&(3;)8#&"-#(%6+#−v5#/300#9)#'2+3(3;)8#:2*53"<#56**)"(#(%*26<%#+O8 ,8#&"-#+P=#m)&"/%30)8#-32-)+#+,#&"-#+.#/300#9)#*);)*+)#93&+)-=#F%)#31'2*(&"(#'23"(#(2#"2()8 (%26<%8#3+#(%&(#-6*3"<#92(%#%&0:?5450)+8#56**)"(#:02/+#(%*26<%#,#3"#(%)#+&1)#-3*)5(32"#B:*21 *3<%(#(2#0):(D8#&"-#(%6+#v.#/300#&0/&4+#9)#'2+3(3;)8#&+#3"-35&()-#3"#L3<=#P=.OB9D= F2#-)()*13")#(%)#')&H#3";)*+)#;20(&<)#Bl!TD#2:#)&5%#-32-)8#52"+3-)*#(%)#53*563(#-6*3"< (%)# '2+3(3;)# %&0:?5450)+=# F%)# *);)*+)# ;20(&<)# &5*2++# +O# 5&"# 9)# -)()*13")-# :*21# (%)# 022' :2*1)-#94#+O8#,8#&"-#+.#&+ v +O # ( *);)*+) ) = v . + v +. # ( :2*/&*- ) F%6+#(%)#1&A3161#;&06)#2:#v+O#2556*+#&(#(%)#')&H#2:#v.#&"-#3+#<3;)"#94

l!T = @ ? ! .@ + + @ + = @ ? ! @ + K9+)*;)#(%&(#%)*)#(%)#l!T#3+#&926(#%&0:#(%)#;&06)#:2*#(%)#:600?/&;)#*)5(3:3)*#/3(%#)"()*? (&'')-#(*&"+:2*1)*=#F%3+#3+#&"2(%)*#&-;&"(&<)#2:#(%)#9*3-<)#*)5(3:3)*= p)(#2")#12*)#&-;&"(&<)#2:#(%)#9*3-<)#*)5(3:3)*#53*563(#2;)*#(%&(#6(303M3"<#)"()*?(&'')(*&"+:2*1)*#3+#(%&(#2"04#&926(#%&0:#&+#1&"4#(6*"+#&*)#*)C63*)-#:2*#(%)#+)52"-&*4#/3"-3"<#2:#(%) (*&"+:2*1)*=#E"2(%)*#/&4#2:#022H3"<#&(#(%3+#'23"(#5&"#9)#29(&3")-#94#29+)*;3"<#(%&(#)&5%#%&0:#2: (%)#+)52"-&*4#/3"-3"<#2:#(%)#5)"()*?(&'')-#(*&"+:2*1)*#3+#6(303M)-#:2*#2"04#%&0:#(%)#(31)=#F%)+) &-;&"(&<)+#%&;)#1&-)#(%)#9*3-<)#*)5(3:3)*#(%)#12+(#'2'60&*#*)5(3:3)*#53*563(#52":3<6*&(32"=

EXERCISE 4.21#L2*#(%)#9*3-<)#*)5(3:3)*#53*563(#2:#L3<=#P=.OB&D8#6+)#(%)#52"+(&"(?;20(&<)?-*2'#-32-)#12-)0#(2#+%2/#(%&(#B&D (%)# &;)*&<)# B2*# -5# 521'2")"(D# 2:# (%)# 26('6(# ;20(&<)# 3+# @ . # ! # ( . ⁄ π )@ ? ! .@ + # &"-# B9D# (%)# ')&H -32-)#56**)"(#3+#( @ ? ! .@ + ) ⁄ , )=#L3"-#"61)*35&0#;&06)+#:2*#(%)#C6&"(3(3)+#3"#B&D#&"-#B9D#&"-#(%)#l!T :2*#(%)#5&+)#3"#/%35%#v5#3+#&#,.?T#B*1+D#+3"6+23-8#@+#!#S=N#T8#&"-#,#=#,SS#Ω. Ans. U=P#T7#,Z`#1E7#,`=O#T

4.5.4 The Rectifier with a Filter Capacitor—The Peak Rectifier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v-#9)#&#+3"6+23-#/3(%#&#')&H#;&06)#@#8#&"-#&++61)#(%) -32-)#(2#9)#3-)&0=#E+#v-#<2)+#'2+3(3;)8#(%)#-32-)#52"-65(+#&"-#(%)#5&'&53(2*#3+#5%&*<)-#+2#(%&( v.# =# v-=# F%3+# +3(6&(32"# 52"(3"6)+# 6"(30# v-# *)&5%)+# 3(+# ')&H# ;&06)# @#=# _)42"-# (%)# ')&H8# &+# v-)5*)&+)+#(%)#-32-)#9)521)+#*);)*+)#93&+)-#&"-#(%)#26('6(#;20(&<)#*)1&3"+#52"+(&"(#&(#(%) ;&06)#@#=#!"#:&5(8#(%)2*)(35&004#+')&H3"<8#(%)#5&'&53(2*#/300#*)(&3"#3(+#5%&*<)#&"-#%)"5)#3(+#;20(? &<)#3"-):3"3()048#9)5&6+)#(%)*)#3+#"2#/&4#:2*#(%)#5&'&53(2*#(2#-3+5%&*<)=#F%6+#(%)#53*563(#'*2? ;3-)+#&#-5#;20(&<)#26('6(#)C6&0#(2#(%)#')&H#2:#(%)#3"'6(#+3")#/&;)=#F%3+#3+#&#;)*4#)"526*&<3"< *)+60(#3"#;3)/#2:#26*#-)+3*)#(2#'*2-65)#&#-5#26('6(=

4.5 Rectifier Circuits 201

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(b) Figure 4.24 5(6# E# +31'0)# 53*563(# 6+)-# (2# 3006+(*&()# (%)# )::)5(# 2:# &# :30()*# 5&'&53(2*=# 5&6# !"'6(# &"-# 26('6( /&;):2*1+#&++613"<#&"#3-)&0#-32-)=#X2()#(%&(#(%)#53*563(#'*2;3-)+#&#-5#;20(&<)#)C6&0#(2#(%)#')&H#2:#(%)#3"'6( +3")#/&;)=#F%)#53*563(#3+#(%)*):2*)#H"2/"#&+#&##3)A0'3/4!%!3'#2*#&##3)A0*343/4&'=

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!P = v. ⁄ ,

BP=.OD

&"-#2:#(%)#-32-)#56**)"(#B/%)"#3(#3+#52"-65(3"
!+ = !8 + !P *v = 8 ???????- + ! P *4

BP=.PD BP=.ZD

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4.5 Rectifier Circuits 203

R6*3"<# (%)# -32-)?2::# 3"()*;&08# (%)# 5&'&53(2*# 8# -3+5%&*<)+# (%*26<%# ,8# &"-# (%6+# v. -)5&4+# )A'2")"(3&004# /3(%# &# (31)# 52"+(&"(# 8,=# F%)# -3+5%&*<)# 3"()*;&0# 9)<3"+# J6+( '&+(#(%)#')&H#2:#v-=#E(#(%)#)"-#2:#(%)#-3+5%&*<)#3"()*;&08#/%35%#0&+(+#:2*#&012+(#(%) )"(3*)# ')*32-# I8# v.# =# @## −# @' 8# /%)*)# @'# 3+# (%)# ')&H?(2?')&H# *3''0)# ;20(&<)=# I%)" 8, %#I8#(%)#;&06)#2:#@'#3+#+1&00= 4. I%)"#@'#3+#+1&008#v.#3+#&012+(#52"+(&"(#&"-#)C6&0#(2#(%)#')&H#;&06)#2:#v-=#F%6+#(%)#-5 26('6(#;20(&<)#3+#&''*2A31&()04#)C6&0#(2#@#=#Y3130&*048#(%)#56**)"(#!P#3+#&012+(#52"? +(&"(8#&"-#3(+#-5#521'2")"(#-P#3+#<3;)"#94 3.

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@ . = @ # ! ,??.? @ '

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! 4 ⁄ 8,

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@ # ! @ ' # ! #@ # 3

! I ⁄ 8,

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! I ⁄ 8,

! , ! I ⁄ 8, (2#29(&3"

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@# @ ' = ?????????? %8,

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@ ' = ?????P? %8

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X2()#(%&(#&"#&0()*"&(3;)#3"()*'*)(&(32"#2:#(%)#&''*2A31&(32"#1&-)#&92;)#3+#(%&(#(%)#5&'&53(2* -3+5%&*<)+#94#1)&"+#2:#4"+(&"(#56**)"(# - P = @ # ⁄ ,=#F%3+#&''*2A31&(32"#3+#;&03-#&+#02"< &+#@' ( @#= E++613"<#(%&(#-32-)#52"-65(32"#5)&+)+#&012+(#&(#(%)#')&H#2:#v- 8#/)#5&"#-)()*13")#(%) *-1)+*,'-1%'1,"!#(4#∆4#:*21

@ # 52+ ( ω ∆4 ) = @ # ! @ ' /%)*)# ω = . π % = . π ⁄ I 3+#(%)#&"<60&*#:*)C6)"54#2:#v- =#Y3"5)#Bω ∆4D#3+#&#+1&00#&"<0)8#/) . 5&"#)1'024#(%)#&''*2A31&(32"# 52+ ( ω ∆4 ) ! , ! ,??.? ( ω ∆4 ) #(2#29(&3"

ω ∆4# ! .@ ' ⁄ @ # I)#"2()#(%&(#/%)"#@'#(#@#8#(%)#52"-65(32"#&"<0)#ω ∆4#/300#9)#+1&008#&+#&++61)-=

BP=OSD

204 Chapter 4 Diodes F2# -)()*13")# (%)# &;)*&<)# -32-)# 56**)"(# -6*3"<# 52"-65(32"8# !+&;8# /)# )C6&()# (%)# 5%&*<) (%&(#(%)#-32-)#+6''03)+#(2#(%)#5&'&53(2*8

L +6''03)- = ! 8&; ∆4 /%)*)#:*21#@C=#BP=.PD8

! 8&; = ! +&; ! - P

(2#(%)#5%&*<)#(%&(#(%)#5&'&53(2*#02+)+#-6*3"<#(%)#-3+5%&*<)#3"()*;&08

L 02+( = 8@ ' (2#29(&3"8#6+3"<#@C+=#BP=OSD#&"-#BP=.U&D8

! +&; = - P ( , + π .@ # ⁄ @ ' )

BP=O,D

K9+)*;)#(%&(#/%)"#@'#(#@#8#(%)#&;)*&<)#-32-)#56**)"(#-6*3"<#52"-65(32"#3+#165%# <*)&()* (%&"# (%)# -5# 02&-# 56**)"(=# F%3+# 3+# "2(# +6*'*3+3"<8# +3"5)# (%)# -32-)# 52"-65(+# :2*# &# ;)*4# +%2*( 3"()*;&0#&"-#16+(#*)'0)"3+%#(%)#5%&*<)#02+(#94#(%)#5&'&53(2*#-6*3"<#(%)#165%#02"<)*#3"()*;&0 3"#/%35%#3(#3+#-3+5%&*<)-#94#-P= F%)#')&H#;&06)#2:#(%)#-32-)#56**)"(8#!+1&A8#5&"#9)#-)()*13")-#94#);&06&(3"<#(%)#)A'*)+? +32"#3"#@C=#BP=.ZD#&(#(%)#2"+)(#2:#-32-)#52"-65(32"W(%&(#3+8#&(#4#=#4,#=#−∆4#B/%)*)#4#=#S#3+#&(#(%) ')&HD=#E++613"<#(%&(#!P#3+#&012+(#52"+(&"(#&(#(%)#;&06)#<3;)"#94#@C=#BP=.`D8#/)#29(&3"

! +1&A = - P ( , + . π .@ # ⁄ @ ' )

BP=O.D

L*21#@C+=#BP=O,D#&"-#BP=O.D8#/)#+))#(%&(#:2*#@'#(#@#8#!+1&A#!#.!+&;8#/%35%#52**)0&()+#/3(%#(%) :&5(#(%&(#(%)#/&;):2*1#2:#!+#3+#&012+(#&#*3<%(?&"<0)#(*3&"<0)#B+))#L3<=#P=.Z5D=

Example 4.8 $2"+3-)*#&#')&H#*)5(3:3)*#:)-#94#&#`S?>M#+3"6+23-#%&;3"<#&#')&H#;&06)#@##=#,SS#T=#V)(#(%)#02&-#*)+3+? (&"5)#,#=#,S#HΩ=#L3"-#(%)#;&06)#2:#(%)#5&'&53(&"5)#8#(%&(#/300#*)+60(#3"#&#')&H?(2?')&H#*3''0)#2:#.#T= E0+28#5&0560&()#(%)#:*&5(32"#2:#(%)#5450)#-6*3"<#/%35%#(%)#-32-)#3+#52"-65(3"<#&"-#(%)#&;)*&<)#&"')&H#;&06)+#2:#(%)#-32-)#56**)"(= Solution L*21#@C=#BP=.U&D#/)#29(&3"#(%)#;&06)#2:#8#&+ @# ,SS 8 = ???????????? = ?????????????????????????????????????????O? = ^O=O#µL @ ' %, . × `S × ,S × ,S F%)#52"-65(32"#&"<0)#ω#∆4#3+#:26"-#:*21#@C=#BP=OSD#&+

ω ∆4 =

. × . ⁄ ,SS = S=.#*&-

F%6+# (%)# -32-)# 52"-65(+# :2*# ( S=. ⁄ . π ) × ,SS = O=,^j 2:# (%)# 5450)=# F%)# &;)*&<)# -32-)# 56**)"(# 3+ 29(&3")-#:*21#@C=#BP=O,D8#/%)*)# - P = ,SS ⁄ ,S = ,S#1E8 &+ ! +&; = ,S ( , + π . × ,SS ⁄ . ) = O.P#1E

F%)#')&H#-32-)#56**)"(#3+#:26"-#6+3"<#@C=#BP=O.D8 ! +1&A = ,S ( , + . π . × ,SS ⁄ . ) = `O^#1E

4.5 Rectifier Circuits 205

Figure 4.26 I&;):2*1+#3"#(%)#:600?/&;)#')&H#*)5(3:3)*=

F%)#53*563(#2:#L3<=#P=.ZB&D#3+#H"2/"#&+#&#%&0:?/&;)#3"(>%!"*,'.'"!=#F%)#:600?/&;)#*)5(3? :3)*#53*563(+#2:#L3<+=#P=..B&D#&"-#P=.OB&D#5&"#9)#52";)*()-#(2#')&H#*)5(3:3)*+#94#3"506-3"<#& 5&'&53(2*# &5*2++# (%)# 02&-# *)+3+(2*=# E+# 3"# (%)# %&0:?/&;)# 5&+)8# (%)# 26('6(# -5# ;20(&<)# /300# 9) &012+(#)C6&0#(2#(%)#')&H#;&06)#2:#(%)#3"'6(#+3")#/&;)#BL3<=#P=.`D=#F%)#*3''0)#:*)C6)"548#%2/? );)*8#/300#9)#(/35)#(%&(#2:#(%)#3"'6(=#F%)#')&H?(2?')&H#*3''0)#;20(&<)8#:2*#(%3+#5&+)8#5&"#9) -)*3;)-#6+3"<#&#'*25)-6*)#3-)"(35&0#(2#(%&(#&92;)#96(#/3(%#(%)#-3+5%&*<)#')*32-#I#*)'0&5)-#94 I ⁄ . 8#*)+60(3"<#3"

@# @ ' = ????????????? .%8,

BP=OOD

I%30)#(%)#-32-)#52"-65(32"#3"()*;&08#∆48#/300#+(300#9)#<3;)"#94#@C=#BP=OSD8#(%)#&;)*&<)#&"')&H#56**)"(+#3"#)&5%#2:#(%)#-32-)+#/300#9)#<3;)"#94

! +&; = - P ( , + π @ # ⁄ .@ ' )

BP=OPD

! +1&A = - P ( , + . π @ # ⁄ .@ ' )

BP=OZD

$21'&*3"<#(%)+)#)A'*)++32"+#/3(%#(%)#52**)+'2"-3"<#2")+#:2*#(%)#%&0:?/&;)#5&+)8#/)#"2() (%&(#:2*#(%)#+&1)#;&06)+#2:#@#8#%8#,8#&"-#@'#B&"-#(%6+#(%)#+&1)#-PD8#/)#"))-#&'&53(2*#%&0:#(%) +3M)#2:#(%&(#*)C63*)-#3"#(%)#%&0:?/&;)#*)5(3:3)*=#E0+28#(%)#56**)"(#3"#)&5%#-32-)#3"#(%)#:600? /&;)#*)5(3:3)*#3+#&''*2A31&()04#%&0:#(%&(#/%35%#:02/+#3"#(%)#-32-)#2:#(%)#%&0:?/&;)#53*563(= F%)#&"&04+3+#&92;)#&++61)-#3-)&0#-32-)+=#F%)#&556*&54#2:#(%)#*)+60(+#5&"#9)#31'*2;)-#94 (&H3"<#(%)#-32-)#;20(&<)#-*2'#3"(2#&5526"(=#F%3+#5&"#9)#)&+304#-2")#94#*)'0&53"<#(%)#')&H ;20(&<) @##(2#/%35%#(%)#5&'&53(2*#5%&*<)+#/3(%#B@##−#@+D#:2*#(%)#%&0:?/&;)#53*563(#&"-#(%)#:600?/&;)#53*? 563(#6+3"<#)"()*?(&'')-#(*&"+:2*1)*#&"-#/3(%#B@##−#.@+D#:2*#(%)#9*3-<)?*)5(3:3)*#5&+)= I)#52"506-)#(%3+#+)5(32"#94#"2(3"<#(%&(#')&H?*)5(3:3)*#53*563(+#:3"-#&''035&(32"#3"#+3<"&0? '*25)++3"<#+4+()1+#/%)*)#3(#3+#*)C63*)-#(2#-)()5(#(%)#')&H#2:#&"#3"'6(#+3<"&0=#!"#+65%#&+)8 (%)#53*563(#3+#*):)**)-#(2#&+#"(>%)","*,-!=#E#'&*(3560&*04#'2'60&*#&''035&(32"#2:#(%)#')&H -)()5(2*#3+#3"#(%)#-)+3<"#2:#&#-)12-60&(2*#:2*#&1'03(6-)?12-60&()-#BEmD#+3<"&0+=#I)#+%&00 "2(#-3+56++#(%3+#&''035&(32"#:6*(%)*#%)*)=#

EXERCISES 4.22# R)*3;)#(%)#)A'*)++32"+#3"#@C+=#BP=OOD8#BP=OPD8#&"-#BP=OZD= 4.23# $2"+3-)*# *3-<)?*)5(3:3)*#53*563(#/3(%#&#:30()*#5&'&53(2*#8#'0&5)-#&5*2++#(%)#02&-#*)+3+(2*#,#:2*#(%)#5&+) 3"#/%35%#(%)#(*&"+:2*1)*#+)52"-&*4#-)03;)*+#&#+3"6+23-#2:#,.#T#B*1+D#%&;3"<#&#`S?>M#:*)C6)"54#&"-

206 Chapter 4 Diodes &++613"<#@+#=#S=^#T &"-#&-#*)+3+(&"5)#,#=#,SS#Ω=#L3"-#(%)#;&06)#2:#8#(%&(#*)+60(+#3"#&#*3''0) ;20(&<)#"2#0&*<)*#(%&"#,#T#')&H?(2?')&H=#I%&(#3+#(%)#-5#;20(&<)#&(#(%)#26('6(i#L3"-#(%)#02&-#56**)"(= L3"-#(%)#-32-)+d#52"-65(32"#&"<0)=#l*2;3-)#(%)#&;)*&<)#&"-#')&H#-32-)#56**)"(+#I%&(#3+#(%)#')&H *);)*+)#;20(&<)#&5*2++#)&5%#-32-)i#Y')53:4#(%)#-32-)#3"#()*1+#2:#3(+#')&H#56**)"(#&"-#3(+#l!T= Ans. ,.^,#µL7#,Z=P#T#2*#B )(()*#)+(31&()D#,P=U#T7#S=,Z#E7#S=O`#*&-#B.S=N°D7#,=PZ#E7#.=NP#E7 ,`=. T=#F%6+#+)0)5(#&#-32-)#/3(%#O=Z?E#(2#P?E#')&H#56**)"(#&"-#&#.S?T#l!T#*&(3"<=

4.5.5 Precision Half-Wave Rectifier—The Superdiode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*)#521'*)%)"? +3;)#+(6-4#2:#2'#&1']-32-)#53*563(+#(2#$%&'()*#,N= L3<6*)#P=.NB&D#+%2/+#&#'*)53+32"#%&0:?/&;)#*)5(3:3)*#53*563(#52"+3+(3"<#2:#&#-32-)#'0&5)3"#(%)#")<&(3;)?:))-9&5H#'&(%#2:#&"#2'#&1'8#/3(%#,#9)3"<#(%)#*)5(3:3)*#02&-#*)+3+(&"5)=#F%)#2' &1'8#2:#526*+)8#"))-+#'2/)*#+6''03)+#:2*#3(+#2')*&(32"=#L2*#+31'0353(48#(%)+)#&*)#"2(#+%2/"#3" (%)#53*563(#-3&<*&1=#F%)#53*563(#/2*H+#&+#:2002/+Q#!:#v-#<2)+#'2+3(3;)8#(%)#26('6(#;20(&<)#v6#2: (%)#2'#&1'#/300#<2#'2+3(3;)#&"-#(%)#-32-)#/300#52"-65(8#(%6+#)+(&903+%3"<#Ƕ+)-#:))-9&5H '&(%#9)(/))"#(%)#2'#&1'd+#26('6(#()*13"&0#&"-#(%)#")<&(3;)#3"'6(#()*13"&0=#F%3+#")<&(3;)? :))-9&5H#'&(%#/300#5&6+)#&#;3*(6&0#+%2*(#53*563(#(2#&'')&*#9)(/))"#(%)#(/2#3"'6(#()*13"&0+#2:

(a)

(b)

Figure 4.27 F%)# e+6')*-32-)f# '*)53+32"# %&0:?/&;)# *)5(3:3)*# &"-# 3(+# &012+(?3-)&0# (*&"+:)*# 5%&*&5()*3+(35= X2()#(%&(#/%)"#v - > S#&"-#(%)#-32-)#52"-65(+8#(%)#2'#&1'#+6''03)+#(%)#02&-#56**)"(8#&"-#(%)#+26*5)#3+#52";)? "3)"(04#96::)*)-8#&"#&--)-#&-;&"(&<)=#X2(#+%2/"#&*)#(%)#2'?&1'#'2/)*#+6''03)+=

P

F%3+#+)5(32"#*)C63*)+#H"2/0)-<)#2:#2')*&(32"&0#&1'03:3)*+#B$%&'()*#.D=

Limiting and Clamping Circuits 207

(%)#2'#&1'=#F%6+#(%)#;20(&<)#&(#(%)#")<&(3;)#3"'6(#()*13"&08#/%35%#3+#&0+2#(%)#26('6(#;20(&<) v. 8#/300#)C6&0#B(2#/3(%3"#&#:)/#13003;20(+D#(%&(#&(#(%)#'2+3(3;)#3"'6(#()*13"&08#/%35%#3+#(%) 3"'6(#;20(&<)#v- 8 v. = v-

v- ≥ S

X2()#(%&(#(%)#2::+)(#;20(&<)#B!S=N#TD#)A%393()-#3"#(%)#+31'0)#%&0:?/&;)#*)5(3:3)*#53*563(#2: L3<=#P=.,#3+#"2#02"<)*#'*)+)"(=#L2*#(%)#2'?&1'#53*563(#(2#+(&*(#2')*&(32"8#v-#%&+#(2#)A5))-#2"04 &#")<03<3904#+1&00#;20(&<)#)C6&0#(2#(%)#-32-)#-*2'#-3;3-)-#94#(%)#2'#&1'd+#2')"?022'#<&3"= !"#2(%)*#/2*-+8#(%)#+(*&3<%(?03")#(*&"+:)*#5%&*&5()*3+(35#v.]v-#&012+(#'&++)+#(%*26<%#(%)#2*3? <3"=#F%3+#1&H)+#(%3+#53*563(#+63(&90)#:2*#&''035&(32"+#3";20;3"<#;)*4#+1&00#+3<"&0+= $2"+3-)*#"2/#(%)#5&+)#/%)"#v-#<2)+#")<&(3;)=#F%)#2'#&1'd+#26('6(#;20(&<)#v6#/300#()"(2#:2002/#&"-#<2#")<&(3;)=#F%3+#/300#*);)*+)?93&+#(%)#-32-)8#&"-#"2#56**)"(#/300#:02/#(%*26<% *)+3+(&"5)#,8#5&6+3"<#v.#(2#*)1&3"#)C6&0#(2#S#T=#F%6+8#:2*#v-#<#S8#v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e+6')*-32-)=f#

EXERCISES 4.24# $2"+3-)*#(%)#-3"!(,'-1(4%!"*,'.'"!#2*#+6')*-32-)#53*563(#2:#L3<=#P=.NB&D8#/3(%#,#=#,#HΩ=#L2*#v-#=#,S 1T8 , T8#&"-#−,#T8#/%&(#&*)#(%)#;20(&<)+#(%&(#*)+60(#&(#(%)#*)5(3:3)*#26('6(#&"-#&(#(%)#26('6(#2:#(%)#2'#&1'i E++61)#(%&(#(%)#2'#&1'#3+#3-)&0#&"-#(%&(#3(+#26('6(#+&(6*&()+#&(#±,.#T=#F%)#-32-)#%&+#&#S=N?T#-*2'#&( ,?1E#56**)"(= Ans. ,S#1T8#S=ZU#T7#,#T8#,=N#T7#S#T8#−,.#T 4.25# !:#(%)#-32-)#3"#(%)#53*563(#2:#L3<=#P=.NB&D#3+#*);)*+)-8#:3"-#(%)#(*&"+:)*#5%&*&5()*3+(35#v.#&+#&#:6"5(32"#2:#v-= Ans. v . = S%:2*%v - ≥ S7% v . = v - #:2*%v - ≤ S

4.6 Limiting and Clamping Circuits !"#(%3+#+)5(32"8#/)#+%&00#'*)+)"(#&--3(32"&0#"2"03")&*#53*563(#&''035&(32"+#2:#-32-)+=

4.6.1 Limiter Circuits L3<6*)# P=.^# +%2/+# (%)# <)")*&0# (*&"+:)*# 5%&*&5()*3+(35# 2:# &# 0313()*# 53*563(=# E+# 3"-35&()-8# :2* 3"'6(+#3"#)*(&3"#*&"<)8# P − ⁄ H ≤ v - ≤ P + ⁄ H 8#(%)#0313()*#&5(+#&+#")&*#53*563(8#'*2;3-3"<#&" 26('6(#'*2'2*(32"&0#(2#(%)#3"'6(8#v.#=#Hv-=#E0(%26<%#3"#<)")*&0#H#5&"#9)#<*)&()*#(%&"#,8#(%)#53*? 563(+#-3+56++)-#3"#(%3+#+)5(32"#%&;)#H#≤#,#&"-#&*)#H"2/"#&+#3($$'#"%4'=',"!$=#B@A&1'0)+#2: &5(3;)#0313()*+#/300#9)#'*)+)"()-#3"#$%&'()*#,N=D#!:#v-#)A5))-+#(%)#6'')*#4:'3?:&<*# ( P + ⁄ H ) 8#(%) 26('6(#;20(&<)#3+#
208 Chapter 4 Diodes

Figure 4.28 k)")*&0# (*&"+:)*# 5%&*&5()*3+(35 :2*#Ĺ()*#53*563(=

Figure 4.29 E''043"<#&#+3")#/&;)#(2#Ĺ()*#5&"#*)+60(#3"#503''3"<#2::#3(+#(/2#')&H+=

*)-65)-# 9)02/#(%)# 02/)*# 0313(3"<# (%*)+%20-# ( P − ⁄ H )8# (%)# 26('6(# ;20(&<)#v.# 3+# 0313()-#(2# (%) 02/)*#0313(3"<#0);)0# P − = F%)# <)")*&0# (*&"+:)*# 5%&*&5()*3+(35# 2:# L3<=# P=.^# -)+5*39)+# &# )-+&4"% 4'=',"!W(%&(# 3+8# & 0313()*#(%&(#/2*H+#2"#92(%#(%)#'2+3(3;)#&"-#")<&(3;)#')&H+#2:#&"#3"'6(#/&;):2*1=#E'174"%4'=0 ',"!$8#2:#526*+)8#)A3+(=#L3"&0048#"2()#(%&(#3:#&"#3"'6(#/&;):2*1#+65%#&+#(%&(#+%2/"#3"#L3<=#P=.U 3+#:)-#(2#&#-2690)#0313()*8#3(+#(/2#')&H+#/300#9)#/
Limiting and Clamping Circuits 209

Figure 4.30 Y2:(#0313(3"<=

Figure 4.31 E#;&*3)(4#2:#9&+35#0313(3"<#53*563(+=

F%)#53*563(#3"#L3<=#P=O,B&D#3+#(%&(#2:#(%)#%&0:?/&;)#*)5(3:3)*#)A5)'(#(%&(#%)*)#(%)#26('6(#3+ (&H)"#&5*2++#(%)#-32-)=#L2*#v-#c#S=Z#T8#(%)#-32-)#3+#56(#2::8#"2#56**)"(#:02/+8#&"-#(%)#;20(&<) -*2'#&5*2++#,#3+#M)*27#(%6+#v.#=#v- =#E+#v-#)A5))-+#S=Z#T8#(%)#-32-)#(6*"+#2"8#);)"(6&004#0313(3"<

210 Chapter 4 Diodes v.# (2# 2")# -32-)# -*2'# BS=N# TD=# F%)# 53*563(# 2:# L3<=# P=O,B9D# 3+# +3130&*# (2# (%&(# 3"# L3<=# P=O,B&D )A5)'(#(%&(#(%)#-32-)#3+#*);)*+)-= R2690)#0313(3"<#5&"#9)#31'0)1)"()-#94#'0&53"<#(/2#-32-)+#2:#2''2+3()#'20&*3(4#3"#'&*&0? 0)08# &+# +%2/"# 3"# L3<=# P=O,B5D=# >)*)# (%)# 03")&*# *)<32"# 2:# (%)# 5%&*&5()*3+(35# 3+# 29(&3")-# :2* ! S=Z#T ≤ v - ≤ S=Z#T=#L2*#(%3+#*&"<)#2:#v-8#92(%#-32-)+#&*)#2::#&"-#v.#=#v- =#E+#v-#)A5))-+#S=Z#T8 +,#(6*"+#2"#&"-#);)"(6&004#0313(+#v.#(2#+ S=N#T=#Y3130&*048#&+#v-#<2)+#12*)#")<&(3;)#(%&"#]S=Z#T8 +.#(6*"+#2"#&"-#);)"(6&004#0313(+#v.#(2#]S=N#T= F%)#(%*)+%20-+#&"-#+&(6*&(32"#0);)0+#2:#-32-)#0313()*+#5&"#9)#52"(*200)-#94#6+3"<#+(*3"<+ 2:#-32-)+#&"-a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m2*)# :0)A390)# 0313()*# 53*563(+# &*)# '2++390)# 3:# 2'# &1'+# &*)# 52193")-# /3(%# -32-)+# &"*)+3+(2*+=#@A&1'0)+#2:#+65%#53*563(+#&*)#-3+56++)-#3"#$%&'()*#,N=

EXERCISE 4.26# E++613"<#(%)#-32-)+#(2#9)#3-)&08#-)+5*39)#(%)#(*&"+:)*#5%&*&5()*3+(35#2:#(%)#53*563(#+%2/"#3"#L3<=#@P=.`=

"

!

Figure E4.26

Ans. v . = v #############:2*# ! Z ≤ v - ≤ +Z v . = ??,.? v - ! .=Z :2*# v - ≤ ! Z v . = ??,.? v - + .=Z :2*# v - ≥ +Z

4.6.2 The Clamped Capacitor or DC Restorer !:#3"#(%)#9&+35#')&H?*)5(3:3)*#53*563(8#(%)#26('6(#3+#(&H)"#&5*2++#(%)#-32-)#*&(%)*#(%&"#&5*2++ (%)#5&'&53(2*8#&"#3"()*)+(3"<#53*563(#/3(%#31'2*(&"(#&''035&(32"+#*)+60(+=#F%)#53*563(8#5&00)-#& -5#*)+(2*)*8#3+#+%2/"#3"#L3<=#P=O.#:)-#/3(%#&#+C6&*)#/&;)=#_)5&6+)#2:#(%)#'20&*3(4#3"#/%35% (%)#-32-)#3+#52"")5()-8#(%)#5&'&53(2*#/300#5%&*<)#(2#&#;20(&<)#v8#/3(%#(%)#'20&*3(4#3"-35&()-#3" L3<=#P=O.#&"-#)C6&0#(2#(%)#1&<"3(6-)#2:#(%)#12+(#")<&(3;)#')&H#2:#(%)#3"'6(#+3<"&0=#Y69+)? C6)"(048#(%)#-32-)#(6*"+#2::#&"-#(%)#5&'&53(2*#*)(&3"+#3(+#;20(&<)#3"-):3"3()04=#!:8#:2*#3"+(&"5)8 (%)#3"'6(#+C6&*)#/&;)#%&+#(%)#&*93(*&*4#0);)0+#−`#T#&"-#+P#T8#(%)"#v8#/300#9)#)C6&0#(2#`#T= X2/8#+3"5)#(%)#26('6(#;20(&<)#v.#3+#<3;)"#94# v. = v- + v8 3(# :2002/+# (%&(# (%)# 26('6(# /&;):2*1# /300#9)# 3-)"(35&0# (2# (%&(# 2:# (%)# 3"'6(8# )A5)'(# (%&(# 3(# 3+ +%3:()-#6'/&*-#94#v8#;20(+=#!"#26*#)A&1'0)#(%)#26('6(#/300#(%6+#9)#&#+C6&*)#/&;)#/3(%#0);)0+ 2:#S T#&"-#+,S#T=

Limiting and Clamping Circuits 211

! vC "

(a)

(b)

(c)

Figure 4.32 F%)#50&1')-#5&'&53(2*#2*#-5#*)+(2*)*#/3(%#&#+C6&*)?/&;)#3"'6(#&"-#"2#02&-=

E"2(%)*#/&4#2:#;3+6&03M3"<#(%)#2')*&(32"#2:#(%)#53*563(#3"#L3<=#P=O.#3+#(2#"2()#(%&( 9)5&6+)#(%)#-32-)#3+#52"")5()-#&5*2++#(%)#26('6(#/3(%#(%)#'20&*3(4#+%2/"8#3(#'*);)"(+#(%) 26('6(#;20(&<)#:*21#<23"<#9)02/#S#T#B94#52"-65(3"<#&"-#5%&*<3"<#6'#(%)#5&'&53(2*8#(%6+ 5&6+3"<# (%)# 26('6(# (2# *3+)# (2# S# TD8# 96(# (%3+# 52"")5(32"# /300# "2(# 52"+(*&3"# (%)# '2+3(3;) )A56*+32"# 2:# v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−S=Z#TD=#F%)"8#&+#(%)#3"'6(#*3+)+#94#@)#;20(+#B&(#4.D8 (%)#26('6(#:2002/+8#&"-#(%)#5450)#*)')&(+#3(+)0:=#!"#(%)#+()&-4#+(&()#(%)#5%&*<)#02+(#94#(%)#5&'&5? 3(2*# -6*3"<# (%)# 3"()*;&0# 4S# (2# 4,# 3+# *)52;)*)-# -6*3"<# (%)# 3"()*;&0# 4,# (2# 4.=# F%3+# 5%&*<) )C63039*361#)"&90)+#6+#(2#5&0560&()#(%)#&;)*&<)#-32-)#56**)"(#&+#/)00#&+#(%)#-)(&30+#2:#(%) 26('6(#/&;):2*1=

Z F%)#-6(4#5450)#2:#&#'60+)#/&;):2*1#3+#(%)#'*2'2*(32"#2:#)&5%#5450)#2556'3)-#94#(%)#'60+)=#!"#2(%)* /2*-+8#3(#3+#(%)#'60+)#/3-(%#)A'*)++)-#&+#&#:*&5(32"#2:#(%)#'60+)#')*32-=

212 Chapter 4 Diodes

(b)

(a) (c) Figure 4.33 F%)#50&1')-#5&'&53(2*#/3(%#&-#*)+3+(&"5)#,=

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4.7 Special Diode Types

!"#$!%"&'%(')*+,"-$&.'!"'-/.'0,)*+"#1'!.0-"%#'+2%3"&.!'-/.'3%,-)1.'4)3.(%2*'!/%4#5 )!!$*"#1'"&.),'&"%&.!5'"#'6"17'8798:;<7'=%-.'-/)-'4/",.'-/.'+%!"-"3.'+.)>!')2.'0,)*+.& -%' ?' @5' -/.' #.1)-"3.' +.)>' 2.)0/.!' −A!"7' B#' 2.!+%#!.' -%' -/"!' 4)3.(%2*5' -/.' +.)>C &.-.0-%2'!.0-"%#'+2%3"&.!')02%!!'0)+)0"-%2'#A')'#.1)-"3.'&0'3%,-)1.'%('*)1#"-$&.'A!"7 D.0)$!.'-/.'%$-+$-'3%,-)1.'"!'&%$;,.'-/.'"#+$-'+.)>5'-/.'0"20$"-'"!'>#%4#')!')'3%,-)1. &%$;,.27'E/.'-.0/#"F$.'0)#';.'.G-.#&.&'-%'+2%3"&.'%$-+$-'&0'3%,-)1.!'-/)-')2.'/"1/.2 *$,-"+,.!'%('!"7

EXERCISE 4.27 B('-/.'&"%&.'"#'-/.'0"20$"-'%('6"17'879A'"!'2.3.2!.&5'4/)-'4",,'-/.'&0'0%*+%#.#-'%('v%';.0%*.U Ans.!−!"#

4.7 Special Diode Types B#'-/"!'!.0-"%#5'4.'&"!0$!!';2".(,H'!%*.'"*+%2-)#-'!+.0"),'-H+.!'%('&"%&.!7

4.7.1 The Schottky-Barrier Diode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

N+)2-' (2%*' R)N!' 0"20$"-!5' I0/%-->H' &"%&.!' ("#&' )++,"0)-"%#' "#' -/.' &.!"1#' %(' )' !+.0"), (%2*'%(';"+%,)2C-2)#!"!-%2',%1"0'0"20$"-!5'>#%4#')!'I0/%-->HCEET5'4/.2.'EET'!-)#&!'(%2 -2)#!"!-%2C-2)#!"!-%2',%1"07 D.(%2.',.)3"#1'-/.'!$;L.0-'%('I0/%-->HC;)22".2'&"%&.!5'"-'"!'"*+%2-)#-'-%'#%-.'-/)-'#%.3.2H'*.-),K!.*"0%#&$0-%2'0%#-)0-'"!')'&"%&.7'B#'()0-5'*.-),'"!'0%**%#,H'&.+%!"-.&'%# P'

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213

214 Chapter 4 Diodes (%)#+)1352"-65(2*#+6*:&5)#3"#2*-)*#(2#1&H)#()*13"&0+#:2*#(%)#+)1352"-65(2*#-);35)+#&"-#(2 52"")5(# -3::)*)"(# -);35)+# 3"# &"# 3"()<*&()-?53*563(# 5%3'=# Y65%# 1)(&0]+)1352"-65(2*# 52"(&5(+ &*)#H"2/"#&+#-2='*%*-1,(*,$#(2#-3+(3"<63+%#(%)1#:*21#(%)#*)5(3:43"<#52"(&5(+#(%&(#*)+60(#3" Y_R+=#K%135#52"(&5(+#&*)#6+6&004#1&-)#94#-)'2+3(3"<#1)(&0#2"#;)*4#%)&;304#-2')-#B&"-#(%6+ 02/?*)+3+(3;3(4D#+)1352"-65(2*#*)<32"+=#B[)5&00#(%&(#Y_R+#6+)#12-)*&()04#-2')-#1&()*3&0=D

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4.7.4 Light-Emitting Diodes (LEDs) F%)#03<%(?)13((3"<#-32-)#BV@RD#')*:2*1+#(%)#3";)*+)#2:#(%)#:6"5(32"#2:#(%)#'%2(2-32-)7#3( 52";)*(+#&#:2*/&*-#56**)"(#3"(2#03<%(=#F%)#*)&-)*#/300#*)5&00#:*21#$%&'()*#O#(%&(#3"#&#:2*/&*-? 93&+)-##$#J6"5(32"8#13"2*3(4#5&**3)*+#&*)#3"J)5()-#&5*2++#(%)#J6"5(32"#&"-#-3::6+)#3"(2#(%)## N

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4.7 Special Diode Types 215

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PROBLEMS Computer Simulation Problems

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CHAPTER 4 P R O B L E M S

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CHAPTER 4 P R O B L E M S

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Problems 229

CHAPTER 4 P R O B L E M S

(a)

(e) Figure P4.95

(b)

(f)

(c)

(g)

(d)

(h)

CHAPTER 5

MOS Field-Effect Transistors (MOSFETs) Introduction 5.1

5.6 Basic MOSFET Amplifier Configurations 291

231

Device Structure and Physical Operation 232

5.2 Current—Voltage Characteristics 5.3 MOSFET Circuits at DC

258

5.4 Applying the MOSFET in Amplifier Design 268 5.5 Small-Signal Operation and Models 276

5.7 Biasing in MOS Amplifier Circuits 247

5.8 Discrete-Circuit MOS Amplifiers 5.9 The Body Effect and Other Topics Summary

328

Problems

329

306 314 323

IN THIS CHAPTER YOU WILL LEARN 1. The physical structure of the MOS transistor and how it works. 2. How the voltage between two terminals of the transistor controls the current that flows through the third terminal, and the equations that describe these current–voltage characteristics. 3. How to analyze and design circuits that contain MOS transistors, resistors, and dc sources. 4. How the transistor can be used to make an amplifier, and how it can be used as a switch in digital circuits. 5. How to obtain linear amplification from the fundamentally nonlinear MOS transistor. 6. The three basic ways for connecting a MOSFET to construct amplifiers with different properties. 7. Practical circuits for MOS–transistor amplifiers that can be constructed using discrete components.

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231

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5.1 Device Structure and Physical Operation

S Metal G W D Oxide (SiO2 ) Source region

n!

L

p-type substrate (Body)

n! Channel region B Drain region (a)

Source (S)

Gate (G)

Oxide (SiO2) (thickness " tox)

n!

Drain (D) Metal

Channel region

n!

L p-type substrate (Body)

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233

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Gate electrode

! vGS # G

S Oxide (SiO2 )

n!

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D

n!

L

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240 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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Voltage

VGS Vt

vGD (VOV # 21 vDS)

VOV Source 0

% VOV

vDS

Voltage drop along the channel

L 2

Average = 21 vDS

L Drain

x

(a)

%(VOV # vDS)

Channel

Drain

Source (b)

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5.1 Device Structure and Physical Operation

iD

Triode (vDS ! VOV) Curve bends because the channel resistance increases with vDS

Saturation (vDS & VOV) Current saturates because the channel is pinched off at the drain end, and vDS no longer affects the channel.

Almost a straight line with slope proportional to VOV

vGS = Vt + VOV

0

VDS sat " VOV

vDS

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EW8@NK

241

242 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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VGS vGD = Vt

Vt 1 2

VOV vDS = VOV

VOV Source 0

Source

L 2 Voltage drop along the channel (a)

Channel

Average = 12 VOV

L Drain

x

Drain (b)

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5.1 Device Structure and Physical Operation

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Example 5.1 ?0%($+,6'"'<60/,(('),/-%070&;':06'2-$/-'&3$%'='Z8b'µ31'#$%'='d'%31'µ!'='bWZ'/3QcS⋅ (1'"%+'8#'='Z8f'S8 E"K I$%+'<$%'"%+' > !′ 8 E4K I06'"'FGHIJ9'2$)-' ' ⁄ & = d'µ3 ⁄ Z8d' µ31'/"7/*7"),')-,'#"7*,('0:'8:8 1'8*) 1'"%+'8()3$%'%,,+,+')0 0<,6"),')-,')6"%($()06'$%')-,'(")*6")$0%'6,&$0%'2$)-'"'+/'/*66,%)'?('='@ZZ'µA8 E/K I06')-,'+,#$/,'$%'E4K1':$%+')-,'#"7*,('0:'8:80"%+'8*)'6,O*$6,+')0'/"*(,')-,'+,#$/,')0'0<,6"),'"('"'@ZZZ5( 6,($()06':06'#,6;'(3"77'v() 8

Solution

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E"K

Q

Q

> !′ = µ ! < $% = bWZ ( /3 cS⋅( ) × b8CQ ( :Icµ3 ) d

Q

= bWZ × @Z ( µ3 cS⋅( ) × b8CQ × @Z 'N

= @[b × @Z ( IcS⋅( ) = @[b'µAcS

Q

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( Icµ3 )

243

244 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

Example 5.1 continued

9-*(1

8 *) = 8 # ' ( '8 :8 ' & @8ZQ 'S

"%+

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9-*(

@ 5 @ZZZ = 555555555555555555555555555555555555555555555555555555 'N @[b × @Z × '@Z × 8 :8

2-$/-';$,7+(

8 :8 = Z8WQ'S

9-*(1

8 *) = @8QQ'S

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5.1 Device Structure and Physical Operation

S

G

D

p+

p+ n-type substrate

B (a) ! vGS S

#

G iG = 0

iD

iD

p+

iD

D

! vDS #

p+

induced p channel n-type substrate

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%$245

246 Chapter 5 MOS Field-Effect Transistors (MOSFETs) 2-,6,'µ"'$(')-,'304$7$);'0:')-,'-07,('$%')-,'$%+*/,+'"'/-"%%,78'9;<$/"77;1 µ"'e'Z8QW'µ!')0'Z8W µ!0 "%+' $(' <60/,((' ),/-%070&;' +,<,%+,%)8' 9-,' )6"%($()06' )6"%(/0%+*/)"%/,' <"6"3,),6' > "' $( 04)"$%,+'4;'3*7)$<7;$%&'>′"'4;')-,'"(<,/)'6")$0''c&1' > " & >′" ( ' ⁄ & )

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5.1.8 Complementary MOS or CMOS A(')-,'%"3,'$3<7$,(1'/03<7,3,%)"6;'FGH'),/-%070&;',3<70;('FGH')6"%($()06('0:'40)<07"6$)$,(8' A7)-0*&-' ?FGH' /$6/*$)(' "6,' (03,2-")' 306,' +$::$/*7)' )0' :"46$/"),' )-"% `FGH1')-,'"#"$7"4$7$);'0:'/03<7,3,%)"6;'+,#$/,('3"P,('<0(($47,'3"%;'<02,6:*7'/$6/*$)'/0%5 :$&*6")$0%(8'=%+,,+1'")')-,'<6,(,%)')$3,'?FGH'$(')-,'30()'2$+,7;'*(,+'0:'"77')-,'=?'),/-5 %070&$,(8' 9-$(' ()"),3,%)' "<<7$,(' )0' 40)-' "%"70&' "%+' +$&$)"7' /$6/*$)(8' ?FGH' ),/-%070&; -"('#$6)*"77;'6,<7"/,+'+,($&%('4"(,+'0%'`FGH')6"%($()06('"70%,8'I*6)-,6306,1'4;'QZZ[ ?FGH'),/-%070&;'-"+')"P,%'0#,6' 3"%;'"<<7$/")$0%(')-")'.*()'"':,2';,"6(',"67$,6'2,6, <0(($47,' 0%7;' 2$)-' 4$<07"6' +,#$/,(8' 9-60*&-0*)' )-$(' 400P1' 2,' 2$77' ()*+;' 3"%;' ?FGH /$6/*$)'),/-%$O*,(8 I$&*6,' W8@Z' (-02(' "' /60((' (,/)$0%' 0:' "' ?FGH' /-$<' $77*()6")$%&' -02' )-,' _FGH' "%+ `FGH' )6"%($()06(' "6,' :"46$/"),+8' G4(,6#,' )-")' 2-$7,' )-,' `FGH' )6"%($()06' $(' $3<7,3,%),+ +$6,/)7;' $%' )-,' "5);<,' (*4()6"),1' )-,' _FGH' )6"%($()06' $(' :"46$/"),+' $%' "' (<,/$"77;' /6,"),+' ! 6,&$0%1'P%02%'"('"%'!'D&..8'9-,')20'+,#$/,('"6,'$(07"),+':603',"/-'0)-,6'4;'"')-$/P'6,&$0%'0: 0B$+,')-")':*%/)$0%('"('"%'$%(*7")068'`0)'(-02%'0%')-,'+$"&6"3'"6,')-,'/0%%,/)$0%('3"+,')0 )-,'"5);<,'40+;'"%+')0')-,'!'2,778'9-,'7")),6'/0%%,/)$0%'(,6#,('"(')-,'40+;'),63$%"7':06')-, _FGH')6"%($()068

5.1.9 Operating the MOS Transistor in the Subthreshold Region 9-,'"40#,'+,(/6$<)$0%'0:')-,'!5/-"%%,7'FGHIJ9'0<,6")$0%'$3<7$,(')-")':06'v*)'<'8# 1'%0'/*65 6,%)':702('"%+')-,'+,#$/,'$('/*)'0::8'9-$('$('%0)',%)$6,7;')6*,1':06'$)'-"('4,,%':0*%+')-")':06 #"7*,('0:'v*)'(3"77,6')-"%'4*)'/70(,')0'8# 1'"'(3"77'+6"$%'/*66,%)':702(8'=%')-$('!#/-9$&!9".' $&,)"*'0:'0<,6")$0%1')-,'+6"$%'/*66,%)'$(',B<0%,%)$"77;'6,7"),+')0'v*) 1'3*/-'7$P,')-,'+< VvA= 6,7")$0%(-$<'0:'"'LM91'"('2$77'4,'(-02%'$%')-,'%,B)'/-"<),68 A7)-0*&-'$%'30()'"<<7$/")$0%(')-,'FGH')6"%($()06'$('0<,6"),+'2$)-' v*)'>'8# 1')-,6,'"6, (<,/$"71'4*)'"'&602$%&'%*34,6'0:1'"<<7$/")$0%(')-")'3"P,'*(,'0:'(*4)-6,(-07+'0<,6")$0%8'=% ?-"<),6'@C1'2,'2$77'46$,:7;'/0%($+,6'(*4)-6,(-07+'0<,6")$0%8

5.2 Current–Voltage Characteristics

NMOS S SiO2

PMOS D

G

Gate oxide

D

G

S

Polysilicon Thick SiO2 (isolation) n!

n!

SiO2 p!

p! n well

p-type body

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5.2 Current–Voltage Characteristics L*$7+$%&'0%')-,'<-;($/"7':0*%+")$0%',()"47$(-,+'$%')-,'<6,#$0*('(,/)$0%':06')-,'0<,6")$0%'0: )-,' ,%-"%/,3,%)' FGH' )6"%($()061' $%' )-$(' (,/)$0%' 2,' <6,(,%)' $)(' /03<7,),' /*66,%)V#07)"&, /-"6"/),6$()$/(8'9-,(,'/-"6"/),6$()$/('/"%'4,'3,"(*6,+'")'+/'06'")'702':6,O*,%/$,('"%+')-*( "6,'/"77,+'()")$/'/-"6"/),6$()$/(8'9-,'+;%"3$/',::,/)(')-")'7$3$)')-,'0<,6")$0%'0:')-,'FGHIJ9 ")'-$&-':6,O*,%/$,('"%+'-$&-'(2$)/-$%&'(<,,+('2$77'4,'+$(/*((,+'$%'?-"<),6'[8

5.2.1 Circuit Symbol I$&*6,' W8@@E"K' (-02(' )-,' /$6/*$)' (;3407' :06' )-,' !5/-"%%,7' ,%-"%/,3,%)5);<,' FGHIJ98 G4(,6#,')-")')-,'(<"/$%&'4,)2,,%')-,')20'#,6)$/"7'7$%,(')-")'6,<6,(,%)')-,'&"),'"%+')-,'/-"%5 %,7'$%+$/"),(')-,':"/)')-")')-,'&"),',7,/)60+,'$('$%(*7"),+':603')-,'40+;'0:')-,'+,#$/,8'9-, <07"6$);'0:')-,'"5);<,'(*4()6"),'E40+;K'"%+')-,'!'/-"%%,7'$('$%+$/"),+'4;')-,'"6602-,"+'0%')-, D

D

B

G

B

G

G

S

S (a)

D

(b)

S (c)

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247

248 Chapter 5 MOS Field-Effect Transistors (MOSFETs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a' #B/0 ,62+!0 +10 23C241 "$1+#+5/06/32#+5/0#$0#B/01$-6./0+!02!0!D.B2!!/30E=98 =%'"<<7$/")$0%('2-,6,')-,'(0*6/,'$('/0%%,/),+')0')-,'40+;'0:')-,'+,#$/,1'"':*6)-,6'($3<7$:$/"5 )$0%'0:')-,'/$6/*$)'(;3407'$('<0(($47,1'"('$%+$/"),+'$%'I$&8'W8@@E/K8'9-$('(;3407'$('"7(0'*(,+'$%'"<<7$5 /")$0%('2-,%')-,',::,/)'0:')-,'40+;'0%'/$6/*$)'0<,6")$0%'$('%0)'$3<06)"%)1'"('2$77'4,'(,,%'7"),68

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5.2 Current–Voltage Characteristics

Table 5.1 Regions of Operation of the Enhancement NMOS Transistor

iD +

vGD

−

+

iD

Saturation vDS ≥ vOV

( ) v 2OV

vDS

+

Triode vDS < vOV

1 ) W k 2 n L

vGS = Vtn + vOV

vGS −

−

Cut-off vGS < Vtn

Slope = gDS = r1 DS

0 v = kn) ( W L ) OV

vOV

vDS

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v *( > 8 #!

v *( * 8 #!

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06',O*$#"7,%)7;D

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v () ' v :8

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VOV

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249

250 Chapter 5 MOS Field-Effect Transistors (MOSFETs) iD 1 2

kn) ( WL ) VO2V4

vDS $ vOV Triode region

vDS " vOV Saturation region vGS = V t + VOV4 vDS = vOV 2 iD = 12 kn ( WL ) vDS

1 2

kn) ( WL ) VO2V3

vGS = Vt + VOV3

1 2

kn) ( WL ) VO2V2

vGS = V t + VOV2

1 2

kn) ( WL ) VO2V1

vGS = V t + VOV1 0 VOV1 VOV2 VOV3 VOV4

vGS $ Vt (Cutoff)

vDS

Figure 5.13 9-,'+(V v () '/-"6"/),6$()$/(':06'"%',%-"%/,3,%)5);<,'`FGH')6"%($()068

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251

252 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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253

254 Chapter 5 MOS Field-Effect Transistors (MOSFETs) Source

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257 06',O*$#"7,%)7; v )( @ ' Q + ( & 555 > "′ 55555 ( v )* ' 8 #" ) @ ( 55555555 5 Q & 8G

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2-,6,' λ ' "%+' 8 G' E)-,' J"67;' #07)"&,' :06' )-,' _FGH' )6"%($()06K' "6,' 4;' /0%#,%)$0%' %,&")$#, O*"%)$)$,(1'-,%/,'2,'*(,' λ '"%+' 8 G 8 I$%"77;1'2,'(-0*7+'%0),')-")':06'"'&$#,%'?FGH':"46$/")$0%'<60/,(('λ !'"%+' λ " '"6,'&,%,65 "77;'%0)',O*"71'"%+'($3$7"67;':06'8 G!'"%+' 8 G" 8 90'6,/"<1')0')*6%'"'_FGH')6"%($()06'0%1')-,'&"),'#07)"&,'-"(')0'4,'3"+,'702,6')-"%')-") 0:')-,'(0*6/,'4;'")'7,"()' 8 #" 8'90'0<,6"),'$%')-,')6$0+,'6,&$0%1')-,'+6"$%'#07)"&,'-"(')0',B/,,+ )-")'0:')-,'&"),'4;'")'7,"()' 8 #" a'0)-,62$(,1')-,'_FGH'0<,6"),('$%'(")*6")$0%8'I$%"77;1'I$&8'W8QZ <60#$+,('"'<$/)06$"7'6,<6,(,%)")$0%'0:')-,(,'0<,6")$%&'/0%+$)$0%(8'

Table 5.2 Regions of Operation of the Enhancement PMOS Transistor + −

iD

+

vSG

( ) v 2OV

vDG

iD

+

Saturation vSD ≥ |vOV|

1 ) W k 2 p L

vSD

−

Triode vSD < |vOV|

vSG = |Vtp| + |vOV| Cut-off vSG < |Vtp|

−

Slope = gDS = r1 0

|v OV|

DS

|v | = k p) ( W L ) OV

v SD

v )* < 8 #" D'%0'/-"%%,7a')6"%($()06'$%'/*)50::a' + ( & Z v )* & 8 #" ( v :8 D'"'/-"%%,7'$('$%+*/,+a')6"%($()06'0<,6"),('$%')-,')6$0+,'6,&$0%'06'$%')-,'(")*6")$0%'6,&$0% +,<,%+$%&'0%'2-,)-,6')-,'/-"%%,7'$('/0%)$%*0*('06'<$%/-,+50::'")')-,'+6"$%',%+a

96+$,/0F/7+$!

)2#-62#+$!0F/7+$!

?0%)$%*0*('/-"%%,71'04)"$%,+'4;D

_$%/-,+50::'/-"%%,71'04)"$%,+'4;D

v (* > 8 #"

v (* * 8 #"

06',O*$#"7,%)7;D

06',O*$#"7,%)7;

v )( < v :8

v )( ' v :8

9-,%1

9-,%

' + ( & > "′ 55555 &

@ Q

06',O*$#"7,%)7; +(

Q

( v )* ' 8 #" ) v )( ' 555 v )(

' & > "′ 55555 &

Q @ ' + ( & 555 > "′ 55555 ( v )* ' 8 #" )

Q

&

06',O*$#"7,%)7; v :8

@ ' 555 v )( v )( Q

@ ' + ( & 555 > "′ 55555 v Q:8 Q

&

258 Chapter 5 MOS Field-Effect Transistors (MOSFETs) Voltage

S Threshold

Vtp

G Overdrive voltage

Triode VOV Vtp Saturation

D Figure 5.20 9-,'6,7")$#,'7,#,7('0:')-,'),63$%"7' #07)"&,('0:')-,',%-"%/,3,%)5);<,'_FGH')6"%($(5 )06':06'0<,6")$0%'$%')-,')6$0+,'6,&$0%'"%+'$%')-,' (")*6")$0%'6,&$0%8

EXERCISE Q

5.7' 9-,'_FGH')6"%($()06'(-02%'$%'I$&8'JW8f'-"(' 8 #" = ' @'S1'>′" = NZ'µAc S 1 "%+' ' ⁄ & = @Z8 E"K'I$%+')-,'6"%&,'0:'8*':06'2-$/-')-,')6"%($()06'/0%+*/)(8' E4K'=%'),63('0:08*1':$%+')-,'6"%&,'0:'8(':06'2-$/-')-,')6"%($()06'0<,6"),('$%')-,')6$0+,'6,&$0%8' E/K'=%'),63('0:'8*1':$%+')-,'6"%&,'0:'8(':06'2-$/-')-,')6"%($()06'0<,6"),('$%'(")*6")$0%8' E+K'`,&7,/)$%&'/-"%%,757,%&)-'30+*7")$0%'E$8,81'"((*3$%&'λ'='ZK1':$%+')-,'#"7*,('0: 8:8 '"%+'8*' "%+')-,'/066,(<0%+$%&'6"%&,'0:'8(')0'0<,6"),')-,')6"%($()06'$%')-,'(")*6")$0%'30+,'2$)-'?( ='fW'µA8' E,K'=:'λ'='−Z8ZQ'S−@1':$%+')-,'#"7*,'0:'6$'/066,(<0%+$%&')0')-,'0#,6+6$#,'#07)"&,'+,),63$%,+'$% E+K8'' E:K'I06'λ'='−Z8ZQ'S−@'"%+':06')-,'#"7*,'0:'8:8'+,),63$%,+'$%'E+K1':$%+'?('")'8(0= +C'S'"%+'")'8('='Z Sa -,%/,1'/"7/*7"),')-,'#"7*,'0:')-,'"<<"6,%)'0*)<*)'6,($()"%/,'$%'(")*6")$0%8'?03<"6,')0')-,'#"7*,':0*%+ $% E,K8 !5 V

VG ID VD

Figure E5.7

Ans. E"K'8 * ≤ '+b'Sa'E4K'8 ( ≥ 8 * + @a'E/K'8 ( ≤ 8 * + @a'E+K'Z8W'S1'C8W'S1' ≤ b8W'Sa'E,K'Z8Nf'FΩa E:K fd'µA1'dQ8W'µA1'Z8Nf'FΩ'E("3,K

5.3 MOSFET Circuits at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a')-")'$(1 2,'2$77'"((*3,'λ'='Z8'U,'2$77':$%+'$)'/0%#,%$,%)')0'206P'$%'),63('0:')-,'0#,6+6$#,'#07)"&,a 8:8 '='8*) − 8#!':06'`FGH'"%+' 8 :8 & 8 )* ' 8 #" ':06'_FGH8

5.3 MOSFET Circuits at DC

Example 5.3 ^,($&%')-,'/$6/*$)'0:'I$&8'W8Q@1')-")'$(1'+,),63$%,')-,'#"7*,('0:' F ('"%+' F )1''(0')-")')-,')6"%($()06'0<,6"),( ")'?('='Z8b'3A'"%+'8('='+Z8W'S8'9-,'`FGH')6"%($()06'-"('8#'='Z8f'S1'µ!<$%'='@ZZ'µAcSQ1'&'='@'µ31'"%+ ''='CQ'µ38'`,&7,/)')-,'/-"%%,757,%&)-'30+*7")$0%',::,/)'E$8,81'"((*3,')-")'λ'='ZK8'

VDD " !2.5 V

VSS " #2.5 V

Figure 5.21 ?$6/*$)':06'JB"3<7,'W8C8

Solution 90',()"47$(-'"'+/'#07)"&,'0:'+Z8W'S'")')-,'+6"$%1'2,'3*()'(,7,/)'F('"(':07702(D 8 (( ' 8 ( 5 F ( = 5555555555555555555555 ?( Q8W ' Z8W = 555555555555555555555 = W'PΩ Z8b 90'+,),63$%,')-,'#"7*,'6,O*$6,+':06' F ) 1'2,'%,,+')0'P%02')-,'#07)"&,'")')-,'(0*6/,1'2-$/-'/"%'4,',"($7; :0*%+'$:'2,'P%02'8 *)8'9-$('$%')*6%'/"%'4,'+,),63$%,+':603'8 :8 8'902"6+')-")',%+1'2,'%0),')-")'($%/,'8('= Z8W'S'$('&6,"),6')-"%'8* 1')-,'`FGH')6"%($()06'$('0<,6")$%&'$%')-,'(")*6")$0%'6,&$0%1'"%+'2,'/"%'*(,')-,'(")5 *6")$0%56,&$0%',B<6,(($0%'0:'+(')0'+,),63$%,')-,'6,O*$6,+'#"7*,'0:'8:8 1 @ ' Q ? ( = 555 µ ! < $% 55555 8 :8 Q & 9-,%'(*4()$)*)$%&'?('='Z8b'3A'='bZZ'µA1'µ!<$%'='@ZZ'µAcSQ1'"%+ ' ⁄ & = CQ ⁄ @ '&$#,(

2-$/-'6,(*7)('$%' 9-*(1

@ CQ Q bZZ = 555 × @ZZ × 555555 8 :8 Q @ 8 :8 = Z8W'S 8 *) = 8 # + 8 :8 = Z8f + Z8W = @8Q'S

i,:,66$%&')0'I$&8'W8Q@1'2,'%0),')-")')-,'&"),'$('")'&60*%+'<0),%)$"78'9-*(1')-,'(0*6/,'3*()'4,'")'−@8Q'S1'"%+')-, 6,O*$6,+'#"7*,'0:'F)'/"%'4,'+,),63$%,+':603 8 ) ' 8 )) 5 F ) = 5555555555555555555 ?( −@8Q' ' ' ( ' Q8W ) = 5555555555555555555555555555555555 = C8QW'PΩ Z8b

259

260 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

EXERCISE D5.8 i,+,($&%'')-, '/$6/*$)'0:'I$&8'W8Q@':06')-,':07702$%&'/"(,D08(('=' −8))' ='Q8W'S1'8#'='@'S1'µ!<$%'='NZ µAcSQ1'' ' ⁄ & = @QZ'µ3 ⁄ C 'µ31 ?('='Z8C'3A1'"%+'8('='+Z8b'S8 Ans. F('='f'PΩ; F)0= C8C'PΩ

Example 5.4 I$&*6,'W8QQ'(-02('"%'`FGH')6"%($()06'2$)-'$)('+6"$%'"%+'&"),'),63$%"7('/0%%,/),+')0&,)-,68'I$%+')-,' + ' v 6,7")$0%(-$<' 0:' )-,' 6,(*7)$%&' )205),63$%"7' +,#$/,' $%' ),63(' 0:' )-,' FGHIJ9' <"6"3,),6(' > ! & >′! ( ' ⁄ & ) "%+'8 #! 8'`,&7,/)'/-"%%,757,%&)-'30+*7")$0%'E$8,81'λ ' & ZK 8'`0),')-")')-$(')205),63$%"7'+,#$/,'$('P%02%'"('" ')"'&3%"**&%-&'+-$(*!)!-"$8 i

!

v

#

Figure 5.22

Solution H$%/,'v ( & v *'$3<7$,('0<,6")$0%'$%')-,'(")*6")$0%'30+,1' @ ' Q + ( & 555 >′! 55555 ( v *) ' 8 #! ) Q &

`021'+ & + ( '"%+' v & v *) 1')-*(' @ ' Q + & 555 >′! 55555 ( v ' 8 #! ) & Q ' i,<7"/$%&' >′! 55555 '4;'> ! '6,(*7)('$%' & @ Q + & 555 > ! ( v ' 8 #! ) Q

5.3 MOSFET Circuits at DC

EXERCISES D5.9 I06')-,'/$6/*$)'$%'I$&8'JW8[1':$%+')-,'#"7*,'0:'F')-")'6,(*7)('$%' 8 ( & Z8d'S8''9-,'FGHIJ9'-"( Z8fQ'µ3 8 #! & Z8W'S1' µ ! < $% & Z8b '3AcSQ1'' ⁄ & & 555555555555555555555 1'"%+'λ & Z8 Z8@d'µ3 Ans. @C8['PΩ !1.8 V

R VD Q1 Figure E5.9

D5.10 I$&*6,'JW8@Z1'(-02('"'/$6/*$)'04)"$%,+'4;'"*&3,%)$%&')-,'/$6/*$)'0:'I$&8'JW8['/0%($+,6,+'$%'JB,65 /$(,'W8['2$)-'"')6"%($()06'; Q'$+,%)$/"7')0'; @'"%+'"'6,($()"%/,' F Q8'I$%+')-,'#"7*,'0:' F Q')-")'6,(*7)('$% ; Q'0<,6")$%&'")')-,',+&,'0:')-,'(")*6")$0%'6,&$0%8'n(,';0*6'(07*)$0%')0'JB,6/$(,'W8[8 Ans. QZ8d'PΩ VDD!1.8 V R2

R

Q2

Q1 Figure E5.10

Example 5.5 ^,($&%')-,'/$6/*$)'$%'I$&8'W8QC')0',()"47$(-'"'+6"$%'#07)"&,'0:'Z8@'S8'U-")'$(')-,',::,/)$#,'6,($()"%/,'4,)2,,% Q +6"$%'"%+'(0*6/,'")')-$('0<,6")$%&'<0$%)g'T,)'8 #! = @'S'"%+' > !′ ( ' ⁄ & ) = @'3AcS 8 VDD " !5 V ID

RD VD " !0.1 V

Figure 5.23 ?$6/*$)':06'JB"3<7,'W8W8

261

262 Chapter 5 MOS Field-Effect Transistors (MOSFETs) Example 5.5 continued

Solution H$%/,')-,'+6"$%'#07)"&,'$('702,6')-"%')-,'&"),'#07)"&,'4;'b8['S'"%+'8 #! = @'S1')-,'FGHIJ9'$('0<,6")$%& $%')-,')6$0+,'6,&$0%8'9-*(')-,'/*66,%)'?('$('&$#,%'4; @ Q ' ? ( = > !′ 55555 ( 8 *) ' 8 #! )8 () ' 555 8 () Q & @ ? ( = @ × ( W ' @ ) × Z8@ ' 555 × Z8Z@ Q = Z8C[W'3A 9-,'6,O*$6,+'#"7*,':06'F('/"%'4,':0*%+'"(':07702(D 8 (( ' 8 ( 5 F ( = 5555555555555555555555 ?( W ' Z8@ = 5555555555555555 = @Q8b'PΩ Z8C[W =%'"'<6"/)$/"7'+$(/6,),5/$6/*$)'+,($&%'<6047,31'0%,'(,7,/)(')-,'/70(,()'()"%+"6+'#"7*,'"#"$7"47,':061'(";1'Wo 6,($()06(p$%')-$('/"(,1'@Q'PΩa'(,,'A<<,%+$B']8'H$%/,')-,')6"%($()06'$('0<,6")$%&'$%')-,')6$0+,'6,&$0%'2$)-'" (3"77'8()1')-,',::,/)$#,'+6"$%5)05(0*6/,'6,($()"%/,'/"%'4,'+,),63$%,+'"(':07702(D 8 () 5 6 () = 55555555 ?( Z8@ = 5555555555555 = QWC'Ω Z8C[W

EXERCISE 5.11' =:'$%')-,'/$6/*$)'0:'JB"3<7,'W8W')-,'#"7*,'0:'F('$('+0*47,+1':$%+'"<<60B$3"),'#"7*,(':06'?('"%+'8(8 Ans. Z8Q'3Aa'Z8ZW'S

5.3 MOSFET Circuits at DC

Example 5.6 A%"7;>,')-,'/$6/*$)'(-02%'$%'I$&8'W8QbE"K')0'+,),63$%,')-,'#07)"&,('")'"77'%0+,('"%+')-,'/*66,%)(')-60*&"77' 46"%/-,(8' T,)'8 #! = @'S' "%+' > !′ ( ' ⁄ & ) = @'3AcS Q 8' `,&7,/)' )-,' /-"%%,757,%&)-' 30+*7")$0%' ,::,/) E$8,81'"((*3,' λ = ZK8 VDD " !10 V

!10 V 0.5 µA

ID

RD " 6 k( 10 M(

RG1 " 10 M(

6 k( 0

10 # 6 ID

!5 V 6 ID RG2 " 10 M(

RS " 6 k(

10 M(

6 k( ID

(a)

(b)

Figure 5.24 1(2'?$6/*$)':06'JB"3<7,'W8N8'1/2'9-,'/$6/*$)'2$)-'(03,'0:')-,'"%"7;($('+,)"$7('(-02%8

Solution H$%/,')-,'&"),'/*66,%)'$('>,601')-,'#07)"&,'")')-,'&"),'$('($3<7;'+,),63$%,+'4;')-,'#07)"&,'+$#$+,6':063,+ 4;')-,')20'@Z5FΩ'6,($()06(1 F *Q @Z 5 = @Z × 555555555555555555 = +W'S 8 * = 8 (( 55555555555555555555555 @Z + @Z F *Q + F *@ U$)-')-$('<0($)$#,'#07)"&,'")')-,'&"),1')-,'`FGH')6"%($()06'2$77'4,')*6%,+'0%8'U,'+0'%0)'P%021'-02,#,61 2-,)-,6')-,')6"%($()06'2$77'4,'0<,6")$%&'$%')-,'(")*6")$0%'6,&$0%'06'$%')-,')6$0+,'6,&$0%8'U,'(-"77'"((*3, (")*6")$0%56,&$0%'0<,6")$0%1'(07#,')-,'<6047,31'"%+')-,%'/-,/P')-,'#"7$+$);'0:'0*6'"((*3<)$0%8'G4#$0*(7;1 $:' 0*6' "((*3<)$0%' )*6%(' 0*)' %0)' )0' 4,' #"7$+1' 2,' 2$77' -"#,' )0' (07#,' )-,' <6047,3' "&"$%' :06' )6$0+,56,&$0% 0<,6")$0%8 i,:,6' )0' I$&8' W8QbE4K8' H$%/,' )-,' #07)"&,' ")' )-,' &"),' $(' W' S' "%+' )-,' #07)"&,' ")' )-,' (0*6/,' $( ? ( ' ( 3A ) × N' ( PΩ ) = N? ( 1 '2,'-"#, 8 *) = W ' N? ( 9-*(1'?('$('&$#,%'4; @ ' Q ? ( = 555 > !′ 55555 ( 8 *) ' 8 #! ) Q & @ Q = 555 × @ × ( W ' N? ( ' @ ) Q 2-$/-'6,(*7)('$%')-,':07702$%&'O*"+6")$/',O*")$0%'$%'?(D Q

@d? ( ' QW? ( + d = Z

263

264 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

Example 5.6 continued

9-$(',O*")$0%';$,7+(')20'#"7*,(':06'?(D'Z8d['3A'"%+'Z8W'3A8'9-,':$6()'#"7*,'6,(*7)('$%'"'(0*6/,'#07)"&,'0: N × Z8d[ = W8Cb S1 '2-$/-'$('&6,"),6')-"%')-,'&"),'#07)"&,'"%+'+0,('%0)'3"P,'<-;($/"7'(,%(,'"('$)'20*7+ $3<7;')-")')-,'`FGH')6"%($()06'$('/*)'0::8'9-*(1 ? ( = Z8W'3A 8 ) = Z8W × N = +C'S 8 *) = W ' C = Q'S 8 ( = @Z ' N × Z8W = +f'S

H$%/,' 8 ( > 8 * ' 8 #! 1 ')-,')6"%($()06'$('0<,6")$%&'$%'(")*6")$0%1'"('$%$)$"77;'"((*3,+8

EXERCISES 5.12' I06')-,'/$6/*$)'0:'I$&8'W8Qb1'2-")'$(')-,'7"6&,()'#"7*,')-")'F('/"%'-"#,'2-$7,')-,')6"%($()06'6,3"$%( $%')-,'(")*6")$0%'30+,g Ans. @Q'PΩ D5.13' i,+,($&%')-,'/$6/*$)'0:'I$&8'W8Qb':06')-,':07702$%&'6,O*$6,3,%)(D' 8 (( = +W'S1 ? ( = Z8CQ'3A1 8) = @8N S1'8('='C8b'S1'2$)-'"'@5µA'/*66,%)')-60*&-')-,'#07)"&,'+$#$+,6'F*@1'F*Q8'A((*3,')-,'("3, FGHIJ9'"('$%'JB"3<7,'W8N8 Ans. F*@'='@8N'FΩa'F*Q'='C8b'FΩ1'F)'='F('='W'PΩ

Example 5.7 ^,($&%' )-,' /$6/*$)' 0:' I$&8' W8QW' (0' )-")' )-,' )6"%($()06' 0<,6"),(' $%' (")*6")$0%' 2$)-' ? ( = Z8W'3A ' "%+ 8 ( = +C'S8 T,)' )-,' ,%-"%/,3,%)5);<,' _FGH' )6"%($()06' -"#,' 8 #" = ' @'S ' "%+' > "′ ( ' ⁄ & ) = ' @ 3AcSQ8 A((*3,'λ'='Z8'U-")'$(')-,'7"6&,()'#"7*,')-")'F('/"%'-"#,'2-$7,'3"$%)"$%$%&'(")*6")$0%56,&$0%'0<,6")$0%g VDD " !5 V

RG1

VD " !3 V RG2

RD ID " 0.5 mA

Figure 5.25 ?$6/*$)':06'JB"3<7,'W8f8

5.3 MOSFET Circuits at DC

Solution H$%/,')-,'FGHIJ9'$(')0'4,'$%'(")*6")$0%1'2,'/"%'26$), @ ' ? ( & 555 > "′ 55555 8:8 Q &

Q

Q

H*4()$)*)$%&'?('='Z8W'3A'"%+' > "′' ⁄ & = @'3AcS 1'2,'04)"$% 8 :8 = @'S "%+ 8 )* & 8 #" ( 8 :8 & @ ( @ & Q'S H$%/,')-,'(0*6/,'$('")'+W'S1')-,'&"),'#07)"&,'3*()'4,'(,)')0'+C'S8'9-$('/"%'4,'"/-$,#,+'4;')-, "<<60<6$"), (,7,/)$0%'0:')-,'#"7*,('0:'F*@'"%+'F*Q8'A'<0(($47,'(,7,/)$0%'$('F*@'='Q'FΩ'"%+'F*Q'='C'FΩ8 9-,'#"7*,'0:'F('/"%'4,':0*%+':603 8 C F ( = 555555( = 5555555 = N'PΩ ?( Z8W H")*6")$0%530+,'0<,6")$0%'2$77'4,'3"$%)"$%,+'*<')0')-,'<0$%)')-")'8(',B/,,+('8*'4;' 8 #" a )-")'$(1'*%)$7 8 ( 3"B = C + @ = b'S 9-$('#"7*,'0:'+6"$%'#07)"&,'$('04)"$%,+'2$)-'F('&$#,%'4; b F ( = 5555555 = d'PΩ Z8W

EXERCISE D5.14 'I06')-,'/$6/*$)'$%'I$&8'JW8@b1':$%+')-,'#"7*,'0:'F')-")'6,(*7)('$%')-,'_FGH')6"%($()06'0<,6")$%&'2$)"%'0#,6+6$#,'#07)"&,' 8 :8 & Z8N'S8'9-,')-6,(-07+'#07)"&,'$(' 8 #" & ' Z8b'S1')-,'<60/,((')6"%(/0%5 +*/)"%/,'<"6"3,),6'> " ′ & Z8@'3AcSQ1'"%+''c&'e'@Z'µ3cZ8@d'µ38 Ans. dZZ'Ω "1.8 V R

Figure E5.14

265

266 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

Example 5.8 9-,' `FGH' "%+' _FGH' )6"%($()06(' $%' )-,' /$6/*$)' 0:' I$&8' W8QNE"K' "6,' 3")/-,+1' 2$)- > !′ ( ' ! ⁄ & ! ) = Q > "′( ' " ⁄ & " ) = @'3AcS '"%+' 8 #! = ' 8 #" = @'S8 'A((*3$%&' λ = Z ':06'40)-'+,#$/,(1':$%+')-,'+6"$%'/*65 6,%)('+(I'"%+'+(J1'"('2,77'"(')-,'#07)"&,'v: 1':06' v ? = Z'S1 +Q8W'S1'"%+' ' Q8W'S8 !2.5 V

!2.5 V

QP

QP

iDP vI

vO

iDN QN

IDP vO

0V IDN QN

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55@5 Q

Q

× @ × ( Q8W ' @ ) = @8@QW'3A

5.3 MOSFET Circuits at DC

267

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v : = ' Q8bb'S

`0),')-")' 8 () = −Q8bb ' ( ' Q8W ) = Z8ZN'S1 2-$/-'$('(3"77'"('"((*3,+8 I$%"77;1')-,'($)*")$0%':06')-,'/"(,'v ? = ' Q8W'S'qI$&8'W8QNE+Kr'2$77'4,')-,',B"/)'/03<7,3,%)'0:')-,'/"(, v ? = +Q8W'SD' 96"%($()06' ;I' 2$77' 4,' 0::8' 9-*(' ? (I = Z1' ;J' 2$77' 4,' 0<,6")$%&' $%' )-,' )6$0+,' 6,&$0%' 2$)? (J = Q8bb'3A'"%+' v : = +Q8bb'S8

EXERCISE 5.15' 9-,' `FGH' "%+' _FGH' )6"%($()06(' $%' )-,' /$6/*$)' 0:' I$&8' JW8@W' "6,' 3")/-,+' 2$)-' > !′ ( ' ! ⁄ & ! ) = Q > "′ ( ' " ⁄ & " ) = @'3AcS '"%+'8 #! = ' 8 #" = @'S8'A((*3$%&' λ = Z':06'40)-'+,#$/,(1':$%+')-,'+6"$% /*66,%)('+(I'"%+'+(J'"%+')-,'#07)"&,'v:':06'v ? = Z'S1'+Q8W'S1'"%+'−Q8W'S8 Ans. v? '='Z'SD'Z'3A1'Z'3A1'Z'Sa'v? '='+Q8W'SD'Z8@Zb'3A1'Z'3A1'@8Zb'Sa'v? '='−Q8W'SD'Z'3A1'Z8@Zb'3A1 −@8Zb'S !2.5 V

QN vI

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iDP QP

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268 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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A

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(a)

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EXERCISE 5.16

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269

270 Chapter 5 MOS Field-Effect Transistors (MOSFETs) vDS VDD

A

VDD ID

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Q

VDS

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B C

(a)

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Vt

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vGS

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VDD

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! #

! vGS # (a)

vDS

VDD

A Slope at Q 5 voltage gain vds

VDS

Q

Time

B C Vt

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271

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Example 5.9 ?0%($+,6' )-,' "3<7$:$,6' /$6/*$)' (-02%' $%' I$&8' W8Q[E"K8' 9-,' )6"%($()06' $(' (<,/$:$,+' )0' -"#,' 8 # & Z8b' S1 > !′ & Z8b '3AcSQ1''c&'e'@Z1'"%+' λ & Z 8'A7(01'7,)' 8 (( & @8d 'S1' F ( & @f8W 'P Ω 1'"%+'8 *) & Z8N'S8 E"K'I06' v 71 & Z 'E"%+'-,%/,' v ,1 & Z K1':$%+'8 :8 1' ? (1'8 () 1'"%+' G v8 E4K' U-")' $(' )-,' 3"B$3*3' (;33,)6$/"7' ($&%"7' (2$%&' "7702,+' ")' )-,' +6"$%g' !,%/,' :$%+' )-,' 3"B$3*3 "7702"47,'"3<7$)*+,'0:'"'($%*(0$+"7' v 718

Solution E"K'U$)-'8 *) & Z8N 'S1' 8 :8 & Z8N ' Z8b & Z8Q'S8' 9-*(1' @ Q ? ( & 555 × Z8b × @Z × Z8Q & Z8Zd '3A Q 8 () & 8 (( ' F ( ? ( & @8d ' @f8W × Z8Zd & Z8b 'S

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274 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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280 Chapter 5 MOS Field-Effect Transistors (MOSFETs) vGS V VGS

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281

282 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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283

284 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

Example 5.10 continued

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285

286 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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EXERCISES D5.30 =)' $(' 6,O*$6,+' )0' +,($&%' "' (0*6/,' :07702,6' )-")' $3<7,3,%)(' )-,' 4*::,6' "3<7$:$,6' (-02%' $%' I$&8 W8b[E/K8'=:')-,'FGHIJ9'$('0<,6"),+'2$)-'"%'0#,6+6$#,'#07)"&,' 8 :8 & Z8QW'S1'")'2-")'+6"$%'/*65 6,%)'(-0*7+'$)'4,'4$"(,+g'I$%+')-,'0*)<*)'($&%"7'"3<7$)*+,'"%+')-,'($&%"7'"3<7$)*+,'4,)2,,%'&"), "%+'(0*6/,8 Ans. @8QW'3Aa'Z8[@'Sa'[@'3S D5.31 A'FGHIJ9'$('/0%%,/),+'$%')-,'(0*6/,5:07702,6'/0%:$&*6")$0%'"%+',3<70;,+'"(')-,'0*)<*)'()"&, 0:'"'/"(/"+,'"3<7$:$,68'=)'$('6,O*$6,+')0'<60#$+,'"%'0*)<*)'6,($()"%/,'0:'QZZ' Ω 8'=:')-,'FGHIJ9 -"(' >′! & Z8b '3AcSQ'"%+'$('0<,6"),+'")' 8 :8 ' & Z8QW 'S1':$%+')-,'6,O*$6,+''c&'6")$08'A7(0'(<,/$:; )-,'+/'4$"('/*66,%)' ? ( 8 '=:')-,'"3<7$:$,6'70"+'6,($()"%/,'#"6$,('0#,6')-,'6"%&,'@'P Ω ')0'@Z'P Ω1 2-")'$(')-,'6"%&,'0:' * v '0:')-,'(0*6/,':07702,6g Ans. WZa'Z8NQW'3Aa'Z8dC'ScS')0'Z8[d'ScS 5.32 i,:,6')0'I$&8'W8WZE4K8'H-02')-")')"P$%&' 6 $ '$%)0'"//0*%)'6,(*7)('$% 6$ G v$ ' & 55555555555555555555555 5 6$ ( @ ⁄ 7@ `021'6,/"77$%&')-")' 6 $ & 8 G ⁄ ? ( '"%+' 7 @ & Q? ( ⁄ 8 :8 1':$%+' G v$ '$%'),63('0:' 8 G '"%+' 8 :8 8'I06'" ),/-%070&;':06'2-$/-'8 G & QZ 'S1'2-")'$(')-,'3"B$3*3' 8 :8 '")'2-$/-')-,')6"%($()06'/"%'4,'0<,65 "),+'2-$7,'04)"$%$%&' G v$ ≥ Z8[[ 'ScSg Ans.' G v$ & @ ⁄ [ @ ( 8 :8 ⁄ Q8 G ]a'Z8b'S

5.6.7 Summary and Comparisons I06',"(;'6,:,6,%/,'"%+')0',%"47,'/03<"6$(0%(1'2,'<6,(,%)'$%'9"47,'W8b')-,':063*7"(':06'+,),65 3$%$%&' )-,' /-"6"/),6$()$/' <"6"3,),6(' 0:' +$(/6,),' FGH' "3<7$:$,6(8' `0),' )-")' 6 $' -"(' 4,,% %,&7,/),+')-60*&-0*)8'9-$('$('4,/"*(,'0*6'$%),6,()'$%')-$('/-"<),6'$('<6$3"6$7;'$%'+$(/6,),5/$6/*$) "3<7$:$,6(8'A('"76,"+;'3,%)$0%,+1' 6 $'-"('"'6,7")$#,7;'(3"77',::,/)'0%')-,'<,6:063"%/,'0:'+$(5 /6,),5/$6/*$)'"3<7$:$,6('"%+'/"%'*(*"77;'4,'%,&7,/),+8'=%'(03,'/"(,(1'-02,#,61'$)'$('#,6;',"(;')0 )"P,' 6 $'$%)0'"//0*%)1'(*/-'"('$%')-,'/"(,'0:')-,'?H'"%+'?^'"3<7$:$,6(1'"%+'0%,'$(',%/0*6"&,+')0 +0'(08'I06'$%),&6"),+5/$6/*$)'"3<7$:$,6(1'6 $'@-1#0"72";('4,')"P,%'$%)0'"//0*%)8

305

306 Chapter 5 MOS Field-Effect Transistors (MOSFETs) '

Table 5.4 Characteristics of MOSFET Amplifiers 38$+$4-,+'.-'4."1)4 9#:%';',+)-<:, ?0330%'(0*6/, EI$&8'W8bWK

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7 @ ( F ( || F & ) ' 55555555555555555555555555555 @ ( 7@ F1

F ( || F & ' 555555555555555555555555 5 @ ⁄ 7@ ( F1

F ( || F & 5 ' 555555555555555555555555 @ ⁄ 7@ ( F1

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5.7 Biasing in MOS Amplifier Circuits A('+$(/*((,+'$%'H,/)$0%'W8b1'"%',((,%)$"7'(),<'$%')-,'+,($&%'0:'"'FGHIJ9'"3<7$:$,6'/$6/*$)'$( )-,' ,()"47$(-3,%)' 0:' "%' "<<60<6$"),' +/' 0<,6")$%&' <0$%)' :06' )-,' )6"%($()068' 9-$(' $(' )-,' (),< P%02%'"('4$"($%&'06'4$"('+,($&%8'A%'"<<60<6$"),'+/'0<,6")$%&'<0$%)'06'4$"('<0$%)'$('/-"6"/5 ),6$>,+'4;'"'()"47,'"%+'<6,+$/)"47,'+/'+6"$%'/*66,%)'?('"%+'4;'"'+/'+6"$%5)05(0*6/,'#07)"&,'8() )-")',%(*6,('0<,6")$0%'$%')-,'(")*6")$0%'6,&$0%':06'"77',B<,/),+'$%<*)5($&%"7'7,#,7(8'

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307

308 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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5.7 Biasing in MOS Amplifier Circuits

309

0<<0($),')0')-")'$%$)$"77;'"((*3,+8'9-*(')-,'"/)$0%'0:'F)'206P(')0'P,,<'?('"('/0%()"%)'"('<0(5 ($47,8' 9-$(' %,&")$#,' :,,+4"/P' "/)$0%' 0:' F)' &$#,(' $)' )-,' %"3,' '&,&*&$(-)"*+ $&!)!-(*%&1' " %"3,')-")'2,'2$77'"<<6,/$"),'3*/-'4,)),6'")'"'7"),6'<0$%)'$%')-$('),B)8@Z I$&*6,' W8WQE4K' <60#$+,(' "' &6"<-$/"7' $77*()6")$0%' 0:' )-,' ,::,/)$#,%,((' 0:' )-$(' 4$"($%& (/-,3,8' !,6,' )00' 2,' (-02' )-,' +(Vv*)' /-"6"/),6$()$/(' :06' )20' +,#$/,(' )-")' 6,<6,(,%)' )-, ,B)6,3,('0:'"'4")/-'0:'FGHIJ9(8'H*<,6$3<0(,+'0%')-,'+,#$/,'/-"6"/),6$()$/('$('"'()6"$&-) 7$%,')-")'6,<6,(,%)(')-,'/0%()6"$%)'$3<0(,+'4;')-,'4$"('/$6/*$)p%"3,7;1'JO8'EW8[CK8'9-,'$%),65 (,/)$0%'0:')-$('()6"$&-)'7$%,'2$)-')-,'+(Vv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v($&')0')-, "3<7$:$,6'$%<*)'2$)-0*)'+$()*64$%&')-,'FGHIJ9'+/'4$"('<0$%)8'9-,'#"7*, 0:' <<@' (-0*7+' 4,' (,7,/),+' 7"6&,' ,%0*&-' )0' "<<60B$3"),' "' (-06)' /$6/*$)' ")' "77' ($&%"7' :6,5 O*,%/$,('0:'$%),6,()8'U,'(-"77'()*+;'/"<"/$)$#,7;'/0*<7,+'FGHIJ9'"3<7$:$,6(1'2-$/-'"6, (*$)"47,'0%7;'$%'+$(/6,),'/$6/*$)'+,($&%1'$%'H,/)$0%'W8d8'I$%"77;1'%0),')-")'$%')-,'/$6/*$)'0: I$&8'W8WQE/K1'6,($()06'F('$('(,7,/),+')0'4,'"('7"6&,'"('<0(($47,')0'04)"$%'-$&-'&"$%'4*)'(3"77 ,%0*&-')0'"7702':06')-,'+,($6,+'($&%"7'(2$%&'")')-,'+6"$%'2-$7,'P,,<$%&')-,'FGHIJ9'$% (")*6")$0%'")'"77')$3,(8' U-,%')20'<02,6'(*<<7$,('"6,'"#"$7"47,1'"('$('0:),%')-,'/"(,1')-,'(03,2-")'($3<7,6'4$"( "66"%&,3,%)'0:'I$&8'W8WQE,K'/"%'4,'*)$7$>,+8'9-$('/$6/*$)'$('"%'$3<7,3,%)")$0%'0:'JO8'EW8[CK1 2$)-'8*'6,<7"/,+'4;'8))8'i,($()06'F*',()"47$(-,('"'+/'&60*%+'")')-,'&"),'"%+'<6,(,%)('"'-$&$%<*)' 6,($()"%/,' )0' "' ($&%"7' (0*6/,' )-")' 3";' 4,' /0%%,/),+' )0' )-,' &"),' )-60*&-' "' /0*<7$%& /"<"/$)068

Example 5.12 =)'$('6,O*$6,+')0'+,($&%')-,'/$6/*$)'0:'I$&8'W8WQE/K')0',()"47$(-'"'+/'+6"$%'/*66,%)'?('='Z8W'3A8'9-,'FGHIJ9'$( Q (<,/$:$,+')0'-"#,'8#'='@'S'"%+ > !′' ⁄ & = @'3AcS 8'I06'($3<7$/$);1'%,&7,/)')-,'/-"%%,757,%&)-'30+*7")$0% ,::,/)'E$8,81'"((*3,'λ = 0K8'n(,'"'<02,65(*<<7;'8(('='@W'S8'?"7/*7"),')-,'<,6/,%)"&,'/-"%&,'$%')-,'#"7*,'0: ?('04)"$%,+'2-,%')-,'FGHIJ9'$('6,<7"/,+'2$)-'"%0)-,6'*%$)'-"#$%&')-,'("3, > !′' ⁄ &'4*)'8#'='@8W'S8

Solution A('"'6*7,'0:')-*34':06'+,($&%$%&')-$('/7"(($/"7'4$"($%&'/$6/*$)1'2,'/-00(,'F('"%+'F)')0'<60#$+,'0%,5)-$6+'0: )-,'<02,65(*<<7;'#07)"&,'8(('"('"'+60<'"/60((',"/-'0:'F(1')-,')6"%($()06'E$8,81'8()K'"%+'F)8'I06'8(('='@W'S1

9-,'"/)$0%'0:' F ) '$%'()"4$7$>$%&')-,'#"7*,'0:')-,'4$"('/*66,%)' ? ('$('%0)'*%7$P,')-")'0:')-,'6,($()"%/,' F 11 2-$/-'2,'$%/7*+,+'$%')-,'(0*6/,'7,"+'0:'"'?H'"3<7$:$,6'$%'H,/)$0%'W8N8b8'=%')-,'7")),6'/"(,'"7(01' F 1'206P( )0'6,+*/,')-,'/-"%&,'$%' + ('2$)-')-,'6,(*7)')-")')-,'"3<7$:$,6'&"$%'$('6,+*/,+8 @Z

310 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

Example 5.12 continued

)-$('/-0$/,'3"P,('8('='+@Z'S'"%+'8)'='+W'S8'`021'($%/,'?('$('6,O*$6,+')0'4,'Z8W'3A1'2,'/"%':$%+')-,'#"75 *,('0:'F('"%+'F)'"(':07702(D 8 (( ' 8 ( @W ' @Z 5 = 555555555555555555 = @Z'PΩ F ( = 5555555555555555555555 ?( Z8W 8 W F ) = 55555) = 5555555 = @Z'PΩ Z8W F) 9-,'6,O*$6,+'#"7*,'0:'8*)'/"%'4,'+,),63$%,+'4;':$6()'/"7/*7")$%&')-,'0#,6+6$#,'#07)"&,'8:8':603 Q

? ( = @55Q5 > !′ ( ' ⁄ & )8 :8 Z8W =

@ 555 Q

Q

× @ × 8 :8

2-$/-';$,7+('8:8'e'@'S1'"%+')-*(1' 8 *) = 8 # + 8 :8 = @ + @ = Q'S `021'($%/,'8)'='+W'S1'8*'3*()'4, 8 * = 8 ) + 8 *) = W + Q = f'S 90',()"47$(-')-$('#07)"&,'")')-,'&"),'2,'3";'(,7,/)'F*@'='d'FΩ'"%+'F*Q'='f'FΩ8'9-,':$%"7'/$6/*$)'$('(-02% $%'I$&8'W8WC8'G4(,6#,')-")')-,'+/'#07)"&,'")')-,'+6"$%'E+@Z'SK'"7702(':06'"'<0($)$#,'($&%"7'(2$%&'0:'+W'S E$8,81'*<')0'8((K'"%+'"'%,&")$#,'($&%"7'(2$%&'0:'Vb'S'q$8,81'+02%')0'E8*'V'8#Kr8' VDD " !15 V ID " 0.5 mA 8 M(

RD " 10 k( VD " !10 V

VG " !7 V VS " !5 V ID " 0.5 mA 7 M(

RS " 10 k(

Figure 5.53 ?$6/*$)':06'JB"3<7,'W8@Q8

5.7 Biasing in MOS Amplifier Circuits

=:')-,'`FGH')6"%($()06'$('6,<7"/,+'2$)-'"%0)-,6'-"#$%&'8#'='@8W'S1')-,'%,2'#"7*,'0:'?('/"%'4,':0*%+ "(':07702(D ?( =

@ 555 Q

× @ × ( 8 *) ' @8W )

Q

EW8[bK

8 * = 8 *) + ? ( F ) f = 8 *) + @Z? (

EW8[WK

H07#$%&'JO(8'EW8[bK'"%+'EW8[WK')0&,)-,6';$,7+( ? ( = Z8bWW'3A 9-*(')-,'/-"%&,'$%'?('$( ∆? ( = Z8bWW ' Z8W = ' Z8ZbW'3A ' Z8ZbW 2-$/-'$(' 55555555555555555 × @ZZ = ' [o'/-"%&,8 Z8W

EXERCISES 5.33' ?0%($+,6')-,'FGHIJ9'$%'JB"3<7,'W8@Q'2-,%':$B,+58*)'4$"('$('*(,+8'I$%+')-,'6,O*$6,+'#"7*,'0:'8*) )0 ,()"47$(-'"'+/'4$"('/*66,%)'?('='Z8W'3A8'i,/"77')-")')-,'+,#$/,'<"6"3,),6('"6,'8#'='@'S1 > !′' ⁄ & = Q @'3AcS 1 "%+'λ'='Z8'U-")'$(')-,'<,6/,%)"&,'/-"%&,'$%'?('04)"$%,+'2-,%')-,')6"%($()06'$('6,<7"/,+ 2$)-'"%0)-,6'-"#$%&'8#'='@8W'Sg Ans. 8*)'='Q'Sa'−fWo D5.34' ^,($&%')-,'/$6/*$)'0:'I$&8'W8WQE,K')0'0<,6"),'")'"'+/'+6"$%'/*66,%)'0:'Z8W'3A'"%+'8('='+Q'S8'T,)'8# Q ='@ S1''> !′' ⁄ & = @'3AcS 1 λ'='Z1'8(('='8))'='W'S8'n(,'()"%+"6+'Wo'6,($()06'#"7*,('E(,,'A<<,%+$B ]K1'"%+'&$#,')-,'6,(*7)$%&'#"7*,('0:''?(1'8(1'"%+'8)8 Ans. F('='F)'='N8Q'PΩa'?('='Z8b['3A1'8)'='−@8[N'S1'"%+'8('='+@8[N'S8'F*'/"%'4,'(,7,/),+'$%')-, 6"%&,'0:'@'FΩ')0'@Z'FΩ.

5.7.3 Biasing Using a Drain-to-Gate Feedback Resistor A'($3<7,'"%+',::,/)$#,'+$(/6,),5/$6/*$)'4$"($%&'"66"%&,3,%)'*)$7$>$%&'"':,,+4"/P'6,($()06'/0%5 %,/),+'4,)2,,%')-,'+6"$%'"%+')-,'&"),'$('(-02%'$%'I$&8'W8Wb8'!,6,')-,'7"6&,':,,+4"/P'6,($(5 )"%/,'F*'E*(*"77;'$%')-,'3,&0-3'6"%&,K':06/,(')-,'+/'#07)"&,'")')-,'&"),')0'4,',O*"7')0')-")'") )-,'+6"$%'E4,/"*(,'?*'='ZK8'9-*('2,'/"%'26$),

8 *) = 8 () = 8 (( ' F ( ? ( 2-$/-'/"%'4,'6,26$)),%'$%')-,':063

8 (( = 8 *) + F ( ? (

EW8[NK

311

312 Chapter 5 MOS Field-Effect Transistors (MOSFETs) 2-$/-'$('$+,%)$/"7'$%':063')0'JO8'EW8[CK1'2-$/-'+,(/6$4,(')-,'0<,6")$0%'0:')-,'4$"('(/-,3, +$(/*((,+' "40#,' q)-")' $%' I$&8' W8WQE"Kr8' 9-*(1' -,6,' )001' $:' ?(' :06' (03,' 6,"(0%' /-"%&,(1' ("; $%/6,"(,(1' )-,%' JO8' EW8[NK' $%+$/"),(' )-")' 8*)' 3*()' +,/6,"(,8' 9-,' +,/6,"(,' $%' 8*)' $%' )*6% /"*(,('"'+,/6,"(,'$%'?( 1'"'/-"%&,')-")'$('0<<0($),'$%'+$6,/)$0%')0')-,'0%,'06$&$%"77;'"((*3,+8 9-*(')-,'%,&")$#,':,,+4"/P'06'+,&,%,6")$0%'<60#$+,+'4;'F*'206P(')0'P,,<')-,'#"7*,'0:'?('"( /0%()"%)'"('<0(($47,8 9-,'/$6/*$)'0:'I$&8'W8Wb'/"%'4,'*)$7$>,+'"('"%'"3<7$:$,6'4;'"<<7;$%&')-,'$%<*)'#07)"&,'($&%"7 )0')-,'&"),'#$"'"'/0*<7$%&'/"<"/$)06'(0'"('%0)')0'+$()*64')-,'+/'4$"('/0%+$)$0%('"76,"+;',()"45 7$(-,+8'9-,'"3<7$:$,+'0*)<*)'($&%"7'")')-,'+6"$%'/"%'4,'/0*<7,+')0'"%0)-,6'<"6)'0:')-,'/$6/*$)1 "&"$%'#$"'"'/"<"/$)068'U,'-"#,'/0%($+,6,+'(*/-'"%'"3<7$:$,6'/$6/*$)'$%'H,/)$0%'W8W'EJB"3<7, W8@ZK8 VDD

RD 0

ID

RG

ID ! VDS

! VGS #

#

Figure 5.54 L$"($%&')-,'FGHIJ9'*($%&'"'7"6&,'+6"$%5)05&"),':,,+4"/P'6,($()"%/,1'F* 8

EXERCISE D5.35' ^,($&%' )-,' /$6/*$)' $%' I$&8' W8Wb' )0' 0<,6"),' ")' "' +/' +6"$%' /*66,%)' 0:' Z8W' 3A8' A((*3,'8((' =' +W Q S1 >′! ' ⁄ & = @'3AcS 1 '8#'='@'S1'"%+'λ'='Z8'n(,'"'()"%+"6+'Wo'6,($()"%/,'#"7*,':06'F(1'"%+'&$#, )-,'"/)*"7'#"7*,('04)"$%,+':06'?('"%+'8(8 Ans. F('='N8Q'PΩa' ? ( " Z8b['3Aa 8 ( " @8[N'S

5.7.4 Biasing Using a Constant-Current Source 9-,'30()',::,/)$#,'(/-,3,':06'4$"($%&'"'FGHIJ9'"3<7$:$,6'$(')-")'*($%&'"'/0%()"%)5/*66,%) (0*6/,8'I$&*6,'W8WWE"K'(-02('(*/-'"%'"66"%&,3,%)'"<<7$,+')0'"'+$(/6,),'FGHIJ98'!,6,'F* E*(*"77;'$%')-,'3,&0-3'6"%&,K',()"47$(-,('"'+/'&60*%+'")')-,'&"),'"%+'<6,(,%)('"'7"6&,'6,($(5 )"%/,' )0' "%' $%<*)' ($&%"7' (0*6/,' )-")' /"%' 4,' /"<"/$)$#,7;' /0*<7,+' )0' )-,' &"),8' i,($()06' F( ,()"47$(-,(' "%' "<<60<6$"),' +/' #07)"&,' ")' )-,' +6"$%' )0' "7702' :06' )-,' 6,O*$6,+' 0*)<*)' ($&%"7 (2$%&'2-$7,',%(*6$%&')-")')-,')6"%($()06'"72";('6,3"$%('$%')-,'(")*6")$0%'6,&$0%8

5.7 Biasing in MOS Amplifier Circuits

VDD

VDD

RD ID " I Q

To source of transistor Q in Fig. 5.55 (a)

R IREF

0

ID2

ID1

RG

Q1 I

#VSS

! VGS #

Q2

#VSS

(a)

(b)

Figure 5.55 1(2' L$"($%&' )-,' FGHIJ9' *($%&' "' /0%()"%)5/*66,%)' (0*6/,' ?8' 1/2' =3<7,3,%)")$0%' 0:' )-, /0%()"%)5/*66,%)'(0*6/,'?'*($%&'"'/*66,%)'3$66068

A'/$6/*$)':06'$3<7,3,%)$%&')-,'/0%()"%)5/*66,%)'(0*6/,'?'$('(-02%'$%'I$&8'W8WWE4K8'9-, -,"6)'0:')-,'/$6/*$)'$(')6"%($()06';@1'2-0(,'+6"$%'$('(-06),+')0'$)('&"),1'"%+')-*('$('0<,6")$%&'$% )-,'(")*6")$0%'6,&$0%1'(*/-')-")'

@ ' Q ? (@ = 555 > !′ 55555 ( 8 *) ' 8 # ) ' Q &@

EW8[fK

2-,6,'2,'-"#,'%,&7,/),+'/-"%%,757,%&)-'30+*7")$0%'E$8,81'"((*3,+'λ'='ZK8'9-,'+6"$%'/*66,%) 0:';@'$('(*<<7$,+'4;'8((')-60*&-'6,($()06'F8'H$%/,')-,'&"),'/*66,%)('"6,'>,601

8 (( + 8 )) ' 8 *) 5 ? (@ = ? iJI = 5555555555555555555555555555555555555 F

EW8[dK

2-,6,')-,'/*66,%)')-60*&-'F'$('/0%($+,6,+')0'4,')-,'6/M/6/!./0.-66/!#'0:')-,'/*66,%)'(0*6/, "%+'$('+,%0),+'?iJI8']$#,%')-,'<"6"3,),6'#"7*,('0:';@'"%+'"'+,($6,+'#"7*,':06'?iJI1'JO(8'EW8[fK "%+'EW8[dK'/"%'4,'*(,+')0'+,),63$%,')-,'#"7*,'0:'F8'`02'/0%($+,6')6"%($()06';QD'=)'-"(')-, ("3,'8*)'"(';@a')-*('$:'2,'"((*3,')-")'$)'$('0<,6")$%&'$%'(")*6")$0%1'$)('+6"$%'/*66,%)1'2-$/-'$( )-,'+,($6,+'/*66,%)'?'0:')-,'/*66,%)'(0*6/,1'2$77'4,

@ ' Q ? = ? (Q = 555 > !′ 55555 ( 8 *) ' 8 # ) Q & Q

EW8[[K

2-,6,'2,'-"#,'%,&7,/),+'/-"%%,757,%&)-'30+*7")$0%8'JO*")$0%('EW8[dK'"%+'EW8[[K',%"47,'*( )0'6,7"),')-,'/*66,%)'?')0')-,'6,:,6,%/,'/*66,%)'?iJI1

(' ⁄ &) ? = ? iJI 5555555555555555555Q ( ' ⁄ & )@

EW8@ZZK

9-*('?'$('6,7"),+')0'?iJI'4;')-,'6")$0'0:')-,'"(<,/)'6")$0('0:';@'"%+';Q8'9-$('/$6/*$)1'P%02%'"('" %#$$&*-+B)$$"$1'$('#,6;'<0<*7"6'$%')-,'+,($&%'0:'=?'FGH'"3<7$:$,6('"%+'2$77'4,'()*+$,+'$% &6,")'+,)"$7'$%'?-"<),6'f8

313

314 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

EXERCISE D5.36 n($%&')20')6"%($()06(';@'"%+';Q'-"#$%&',O*"7'7,%&)-('4*)'2$+)-('6,7"),+'4;'' Q ⁄ ' @ = W1'+,($&%')-, Q /$6/*$)'0:'I$&8'W8WWE4K')0'04)"$%'?'='Z8W'3A8'T,)'8(('=' −8))' =' W'S1 > !′ ( ' ⁄ & ) @ = Z8d'3AcS 108#'= @ S1'"%+'λ'='Z8'I$%+')-,'6,O*$6,+'#"7*,':06'F8'U-")'$(')-,'#07)"&,'")')-,'&"),('0:';@'"%+';Qg'U-") $(')-,'702,()'#07)"&,'"7702,+'")')-,'+6"$%'0:';Q'2-$7,';Q'6,3"$%('$%')-,'(")*6")$0%'6,&$0%g Ans. dW'PΩa'−C8W'Sa'−b8W'S

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318 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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322 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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Vo (dB) Vsig

Low-frequency band

High-frequency band

Midband • All capacitances can be neglected

• Gain falls off due to the effect of CC1, CS, and CC2

• Gain falls off due to the internal capacitive effects of the MOSFET

3 dB

20 log |AM| (dB)

fH

fL

f (Hz)

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CHAPTER 5

Section 5.2: Current–Voltage Characteristics

332 Chapter 5 MOS Field-Effect Transistors (MOSFETs)

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Section 5.3: MOSFET Circuits at DC

CHAPTER 5

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CHAPTER 6

Bipolar Junction Transistors (BJTs) Introduction 6.1

351

Device Structure and Physical Operation 352

6.2 Current–Voltage Characteristics 365 6.3 BJT Circuits at DC

378

6.4 Applying the BJT in Amplifier Design 396 6.5 Small-Signal Operation and Models 403

6.6 Basic BJT Amplifier Configurations 422 6.7 Biasing in BJT Amplifier Circuits 446 6.8 Discrete-Circuit BJT Amplifiers

453

6.9 Transistor Breakdown and Temperature Effects 463 Summary

465

Problems

466

IN THIS CHAPTER YOU WILL LEARN 1. The physical structure of the bipolar transistor and how it works. 2. How the voltage between two terminals of the transistor controls the current that flows through the third terminal, and the equations that describe these current–voltage characteristics. 3. How to analyze and design circuits that contain bipolar transistors, resistors, and dc sources. 4. How the transistor can be used to make an amplifier. 5. How to obtain linear amplification from the fundamentally nonlinear BJT. 6. The three basic ways for connecting a BJT to be able to construct amplifiers with different properties. 7. Practical circuits for bipolar-transistor amplifiers that can be constructed by using discrete components.

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351

352 Chapter 6 Bipolar Junction Transistors (BJTs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6.1 Device Structure and Physical Operation

Emitter (E)

n-type

p-type

n-type

Emitter region

Base region

Collector region

Emitter–base junction (EBJ)

Base (B)

Metal contact Collector (C)

Collector–base junction (CBJ)

Figure 6.1 I#'&3*6&@&+0#'$,/($/,+#2@#$%+#!"!#$,)"'&'$2,?

Metal contact E

p

n

p

Emitter region

Base region

Collector region

C

B Figure 6.2 I#'&3*6&@&+0#'$,/($/,+#2@#$%+#"!"#$,)"'&'$2,?

Table 6.1 BJT Modes of Operation A20+

E;<

F;<

F/$2@@ I($&7+ C)$/,)$&2"

J+7+,'+ D2,.),0 D2,.),0

J+7+,'+ J+7+,'+ D2,.),0

@0,4$,4(++,0$$,0"2#&+:5,/"*#;$,/*##($#0,21,92&",72+*#(&($0[&"*&,(05,$+$/)0,*)-,"2+$0[ 7*#&(/(7*&$,(),&"$,/3##$)&%/2)-3/&(2),7#2/$00,(),*,9(72+*#,&#*)0(0&2#5,4"(/",(0,&"$,#$*02),12# &"$,)*'$,#$"%&'(
6.1.2 Operation of the npn Transistor in the Active Mode J1,&"$,&"#$$,'2-$0,21,27$#*&(2),21,&"$,BC!5,&"$,*/&(.$,'2-$,(0,&"$,'20&,('72#&*)&<,!"$#$12#$5 4$,9$;(),23#,0&3-:,21,&"$,BC!,9:,/2)0(-$#();,(&0,7":0(/*+,27$#*&(2),(),&"$,*/&(.$,'2-$
=%&'#'%2/60#9+#(2"$,)'$+0#.&$%#$%+#'&$/)$&2"#&"#$%+#ABCDE=-#.%+,+#(/,,+"$#&'#(2"0/($+0#91#(%),L+ (),,&+,'#2@#2"+#$1*+#2"61H#+6+($,2"'#&"#!5(%)""+6#0+7&(+'#2,#%26+'#&"#"5(%)""+6#0+7&(+'?#!"#+),6&+,#0)1''23+#,+@+,,+0#$2#DE='#)'#/"&*26),#0+7&(+'? M =%+#3)$+,&)6#&"#$%&'#'+($&2"#)''/3+'#$%)$#$%+#,+)0+,#&'#@)3&6&),#.&$%#$%+#2*+,)$&2"#2@#$%+#"!#4/"($&2" /"0+,#@2,.),059&)'#(2"0&$&2"'#:C+($&2"#N?G>?

353

354 Chapter 6 Bipolar Junction Transistors (BJTs) Reverse-biased

Forward-biased n

Diffusing electrons

Injected electrons

E

Collected electrons

iC

C

iB2

iE

iE

n

p

Injected holes (iB1)

iC

Recombined electrons (iB2)

iB –

v BE

iB

+

iE

iE VBE

B

–

v CB

+ iC

iC VCB

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6.1 Device Structure and Physical Operation

Carrier concentration

Emitter (n)

EBJ depletion region

Base (p)

CBJ depletion region

Collector (n)

Electron concentration np (ideal) Hole concentration

pn0

np (0)

pn (0)

np (with recombination)

Distance (x)

Effective base width W Figure 6.4 O,2@&6+'#2@#3&"2,&$15(),,&+,#(2"(+"$,)$&2"'#&"#$%+#9)'+#)"0#&"#$%+#+3&$$+,#2@#)"#!"!#$,)"'&'$2, 2*+,)$&"L#&"#$%+#)($&7+#320+8# v )* > P #)"0# v -) ≥ P ?

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6.1 Device Structure and Physical Operation

6.5

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6.6

D2,#$%+#(&,(/&$#&"#D&L?#W?W:)>#)")61h+0#&"#ET)3*6+#W?K-#@&"0#$%+#3)T&3/3#7)6/+#2@# > - #$%)$#.&66#'$&66 ,+'/6$#&"#)($&7+5320+#2*+,)$&2"? Ans. e?NK#U Ω

6.1.3 Structure of Actual Transistors L(;3#$,X
E

p

B

C

n n

Figure 6.7 F,2''5'+($&2"#2@#)"#!"!#;<=?

!"$,0/&3#$,(),L(;<,X
EXERCISE 6.7

e

] KG

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!@#$%+#+3&$$+,#)"0#(266+($2,#),+#,+7+,'+0g$%)$#&'-#$%+#F;<#&'#@2,.),0#9&)'+0#)"0#$%+#E;<#&'#,+7+,'+ 9&)'+0g$%+#0+7&(+#2*+,)$+'#&"#)#320+#()66+0#$%+#R,+7+,'+5)($&7+#320+?S#=%+#,+'/6$&"L#7)6/+'#2@#α )"0 β-#0+"2$+0#α> )"0#β>#:.&$%#>#0+"2$&"L#,+7+,'+>-#),+#3/(%#62.+,#$%)"#$%+#7)6/+'#2@#α )"0#β-#,+'*+($&7+6129$)&"+0#&"#$%+#R@2,.),0S#)($&7+#320+#0&'(/''+0#)927+?#\+"(+-#$%+#,+7+,'+5)($&7+#320+#%)'#"2#*,)($&()6 )**6&()$&2"?#=%+#ABCDE=-#2"#$%+#2$%+,#%)"0-#9+&"L#)#*+,@+($61#'133+$,&()6#0+7&(+-#()"#2*+,)$+#+V/)661 .+66#.&$%#&$'#0,)&"#)"0#'2/,(+#$+,3&")6'#&"$+,(%)"L+0?#

361

362 Chapter 6 Bipolar Junction Transistors (BJTs)

6.1.4 Operation in the Saturation Mode5 I'#3+"$&2"+0#)927+-#@2,#$%+#;<=#$2#2*+,)$+#&"#$%+#)($&7+#320+-#$%+#F;<#3/'$#9+#,+7+,'+ 9&)'+0?#=%/'#@),-#.+#%)7+#'$)$+0#$%&'#(2"0&$&2"#@2,#$%+#!"!#$,)"'&'$2,#)'# v -) ≥ P?#\2.+7+,.+#U"2.#$%)$#)#"!#4/"($&2"#02+'#"2$#+@@+($&7+61#9+(23+#@2,.),0#9&)'+0#/"$&6#$%+#@2,.),0 726$)L+#)(,2''#&$#+T(++0'#)**,2T&3)$+61#P?e#]?#!$#@2662.'#$%)$#2"+#()"#3)&"$)&"#)($&7+5320+ 2*+,)$&2"#2@#)"#!"!#$,)"'&'$2,#@2,#"+L)$&7+# v -) #02."#$2#)**,2T&3)$+61# ] P?e ]?#=%&'#&'#&66/'5 $,)$+0#&"#D&L?#W?f-#.%&(%#&'#)#'U+$(%#2@# $ - #7+,'/'# v -) #@2,#)"#!"!#$,)"'&'$2,#2*+,)$+0#.&$%#) (2"'$)"$#+3&$$+,#(/,,+"$# . * ?#I'#+T*+($+0-# $ - #&'#&"0+*+"0+"$#2@# v -) #&"#$%+#)($&7+#320+-#)#'&$5 /)$&2"# $%)$# +T$+"0'# @2,# v -) # L2&"L# "+L)$&7+# $2# )**,2T&3)$+61# ] P?e ]?# ;+62.# $%&'# 7)6/+# 2@ v -)-#$%+# F;<#9+L&"'#$2# (2"0/($#'/@@&(&+"$61#$%)$#$%+#$,)"'&'$2,#6+)7+'# $%+#)($&7+#320+# )"0 +"$+,'#$%+#')$/,)$&2"#320+#2@#2*+,)$&2"-#.%+,+# $ - #0+(,+)'+'? =2#'++#.%1# $ - #0+(,+)'+'#&"#')$/,)$&2"-#.+#()"#(2"'$,/($#)#320+6#@2,#$%+#')$/,)$+0#!"! $,)"'&'$2,#)'#@2662.'?#Y+#)/L3+"$#$%+#320+6#2@#D&L?#W?G:(>#.&$%#$%+#@2,.),05(2"0/($&"L#F;< 0&20+# 1 - -#)'#'%2."#&"#D&L?#W?a?#B9'+,7+#$%)$#$%+#(/,,+"$# $ )- #.&66#'/9$,)($#@,23#$%+#(2"5 $,266+05'2/,(+#(/,,+"$-#,+'/6$&"L#&"#$%+#,+0/(+0#(266+($2,#(/,,+"$# $ - #L&7+"#91 $- d .6 4

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0

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6.1 Device Structure and Physical Operation

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β @2,(+0 d 555-5

,≤ β

TX
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@0,4(++,9$,0"24),+*&$#5,(),*)*+:>();,*,/(#/3(&,4$,/*),-$&$#'()$,4"$&"$#,&"$,BC!,(0,(),&"$ 0*&3#*&(2),'2-$,9:,$(&"$#,21,&"$,12++24();,&42,&$0&0Y 1. =0,&"$,6BC,12#4*#-,9(*0$-,9:,'2#$,&"*),O<8,_f, 2. !'#$%+#,)$&2# $ - ⁄ $ ) #62.+,#$%)"# β _ !"$,/2++$/&2#%&2%$'(&&$#,.2+&*;$, v -* ,21,*,0*&3#*&$-,&#*)0(0&2#,/*),9$,123)-,1#2',L(;<,X
TX
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EXERCISES 6.8

^'+#EV?#:W?Ke>#$2#'%2.#$%)$# $ - #,+)(%+'#h+,2#)$# + -* d + , 6" ( . 6- ⁄ . 6 ) F)6(/6)$+# + -* #@2,#)#$,)"'&'$2,#.%2'+#F;<#%)'#KPP#$&3+'#$%+#),+)#2@#$%+#E;
6.9

^'+#EV'?#:W?Ke>-#:W?KG>-#)"0#:W?KW>#$2#'%2.#$%)$#)#;<=#2*+,)$&"L#&"#')$/,)$&2"#.&$%# +-* d +-*')$ %)'#)#@2,(+0# β #L&7+"#91 + -*')$ ⁄ + , 4 ] . 6- ⁄ . 6 5 β @2,(+0 d β 555555555555555555555555555555555555555555555 + -*')$ ⁄ + , 4 e β . 6- ⁄ . 6 D&"0#β@2,(+0#@2,# β d KPP-# . 6- ⁄ . 6 d KPP-#)"0# + -*')$ d P?M #]? Ans. MM?M

363

364 Chapter 6 Bipolar Junction Transistors (BJTs)

6.1.5 The pnp Transistor !"#$!"!$%&'()*)%+&$+,#&'%#)$*($'$-'((#&$)*-*.'&$%+$%"'%$+/$%"#$"!"$0#1*2#$0#)2&*3#0$'3+1#4 5*67&#$849:$)"+;)$'$!"!$%&'()*)%+&$3*')#0$%+$+,#&'%#$*($%"#$'2%*1#$-+0#4$<#&#$%"#$1+.%'6#$#$% 2'7)#)$%"#$!=%>,#$#-*%%#&$%+$3#$"*6"#&$*($,+%#(%*'.$%"'($%"#$"=%>,#$3')#?$%"7)$/+&;'&0=3*')*(6 %"#$#-*%%#&@3')#$A7(2%*+(4$!"#$2+..#2%+&@3')#$A7(2%*+($*)$
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v%$$"')$%+$3# &#,.'2#0$3>$ v$%4$E.)+?$%"#$.'&6#=)*6('.?$'2%*1#=-+0#$+,#&'%*+($+/$%"#$!"!$%&'()*)%+&$2'($3# -+0#.#0$3>$'(>$+/$/+7&$#K7*1'.#(%$2*&27*%)$)*-*.'&$%+$%"+)#$/+&$%"#$"!"$%&'()*)%+&$*($5*64 84L4$!;+$+/$%"#)#$/+7&$2*&27*%)$'&#$)"+;($*($5*64$84994$5*('..>?$;#$(+%#$%"'%$%"#$!"!$%&'(= )*)%+&$2'($+,#&'%#$*($%"#$)'%7&'%*+($-+0#$*($'$-'((#&$'('.+6+7)$%+$%"'%$0#)2&*3#0$/+&$%"# "!"$0#1*2#4 Reverse-biased

Forward-biased p

E

Diffusing holes

Injected holes

iE iE

p

n

iC

Collected holes

iB2

Injected electrons

iC C

Recombined holes

iB1 iB +

v EB

iB

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iE

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B

+

v BC

–

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Figure 6.10 !"##$%&'()*+',%'-'!"!'&#-%.,.&*#'/,-.$0'&*'*1$#-&$',%'&2$'-3&,4$'5*0$6

iC

6.2 Current–Voltage Characteristics

iE iE

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$ vEB %

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Figure 6.11 =.2#6),L+5'&L")6#320+6'#@2,#$%+#"!"#$,)"'&'$2,#2*+,)$&"L#&"#$%+#)($&7+#320+?

,, EXERCISES 6.10 F2"'&0+,#$%+#320+6#&"#D&L?#W?KK:)>#)**6&+0#&"#$%+#()'+#2@#)#"!"#$,)"'&'$2,#.%2'+#9)'+#&'#L,2/"0+0$%+#+3&$$+,#&'#@+0#91#)#(2"'$)"$5(/,,+"$#'2/,(+#$%)$#'/**6&+'#)#M53I#(/,,+"$#&"$2#$%+#+3&$$+,#$+,3&")6)"0#$%+#(266+($2,#&'#(2""+($+0#$2#)#Q KP5]#0(#'/**61?#D&"0#$%+#+3&$$+,#726$)L+-#$%+#9)'+#(/,,+"$-#)"0 $%+#(266+($2,#(/,,+"$#&@#@2,#$%&'#$,)"'&'$2,#β#=#GP#)"0#.6#=#KPQKe#I? Ans. P?WGP#]H#Na?M#µIH#K?aW#3I 6.11

D2,#)#"!"#$,)"'&'$2,#%)7&"L#.6#=#KPQKK#I#)"0#β#=#KPP-#()6(/6)$+#v*)#@2,#$-#=#K?G#I? Ans. O
6.2 Current–Voltage Characteristics 6.2.1 Circuit Symbols and Conventions !"$,7":0(/*+,0/&3#$,30$-,&"30,1*#,&2,$A7+*(),&#*)0(0&2#,27$#*&(2),(0,#*&"$#,/3'9$#02'$,&2 $'7+2:,(),-#*4();,&"$,0/"$'*&(/,21,*,'3+&(&#*)0(0&2#,/(#/3(&<,L2#&3)*&$+:5,*,.$#:,-$0/#(7&(.$ *)-,/2).$)($)&,/(#/3(&,0:'92+,$A(0&0,12#,&"$,BC!<,L(;3#$,X();,&42,-/,.2+&*;$,023#/$05

365

366 Chapter 6 Bipolar Junction Transistors (BJTs)

npn

pnp

(a)

(b)

(a)

Figure 6.12 F&,(/&$#'13926'#@2,#;<='?

(b)

Figure 6.13 ]26$)L+#*26),&$&+'#)"0#(/,,+"$#@62.#&"#$,)"'&'$2,'#9&)'+0#&"#$%+#)($&7+#320+?

(0,)2&,*,303*+,2)$,*)-,(0,30$-,"$#$,'$#$+:,&2,(++30&#*&$,27$#*&(2)<,g#*/&(/*+,9(*0();,0/"$'$0 4(++,9$,7#$0$)&$-,(),K$/&(2),X
6.2 Current–Voltage Characteristics

L#2',&"$,-(0/300(2),21,K$/&(2),X
Table 6.2 Summary of the BJT Current–Voltage Relationships in the Active Mode v )* ⁄ + ,

$- = .6 4 $ . v)* ⁄ +, $ ) = 555-5 = 55565 4

β

β

α

α

$ . v)* ⁄ +, $ * = 555-5 = 55565 4 7%?4O#D2,#$%+#"!"#$,)"'&'$2,-#,+*6)(+#v)*#.&$%#v*)?

$* 5 $ ) = ( K ] α )$ * = 55555555555 β+K $- = β $) $ * = ( β + K )$ ) α β β = 555555555555 α = 555555555555 K]α β+K P, +,# =#$%+,3)6#726$)L+# = 555555 ! MG#3] #)$#,223#$+3*+,)$/,+ 0 $- = α $*

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367

368 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.2 =%+#$,)"'&'$2,#&"#$%+#(&,(/&$#2@#D&L?#W?Ke:)>#%)'#β#=#KPP#)"0#+T%&9&$'#)#v)*#2@#P?d#]#)$#$-#=#K#3I?#X+'&L"#$%+ (&,(/&$#'2#$%)$#)#(/,,+"$#2@#M#3I#@62.'#$%,2/L%#$%+#(266+($2,#)"0#)#726$)L+#2@#+G#]#)**+),'#)$#$%+#(266+($2,? $15 V

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6.2 Current–Voltage Characteristics

369

] P?dKd + KG = 555555555555555555555555555555 = d?Pd#UΩ M?PM =%&'# (23*6+$+'# $%+# 0+'&L"?# Y+# '%2/60# "2$+-# %2.+7+,-# $%)$# $%+# ()6(/6)$&2"'# )927+# .+,+# 3)0+# .&$%# ) 0+L,++#2@#*,+(&'&2"#$%)$#&'#/'/)661#"+&$%+,#"+(+''),1#"2,#4/'$&@&+0#&"#*,)($&(+#&"#7&+.-#@2,#&"'$)"(+-#2@#$%+ +T*+($+0#$26+,)"(+'#2@#(23*2"+"$#7)6/+'?#b+7+,$%+6+''-#.+#(%2'+#$2#02#$%+#0+'&L"#*,+(&'+61#&"#2,0+,#$2 &66/'$,)$+#$%+#7),&2/'#'$+*'#&"7267+0? ,

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372 Chapter 6 Bipolar Junction Transistors (BJTs)

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6.2.4 An Alternative Form of the Common-Emitter Characteristics @),*+&$#)*&(.$,4*:,21,$A7#$00();,&"$,&#*)0(0&2#,/2''2)%$'(&&$#,/"*#*/&$#(0&(/0,(0,(++30&#*&$-,() L(;<,X#.+#%)7+#&0+"$&@&+0#)#*),$&(/6),#*2&"$#l?#b2$+#$%)$#$%&'#2*+,)$&"L#*2&"$#@2,#$%+#$,)"'&'$2, &'#(%),)($+,&h+0#91#)#9)'+#(/,,+"$# . ) - #)#(266+($2,#(/,,+"$# .- - #)"0#)#(266+($2,Q+3&$$+,#726$)L+#+-* ? =%+#,)$&2# . - ⁄ . ) #&'#$%+#$,)"'&'$2,#β?#\2.+7+,-#$%+,+#&'#)"2$%+,#.)1#$2#3+)'/,+#β 8#(%)"L+#$%+#9)'+ (/,,+"$#91#)"#&"(,+3+"$# ∆$ ) #)"0#3+)'/,+#$%+#,+'/6$&"L#&"(,+3+"$# ∆$ - - #.%&6+#U++*&"L# +-* #(2"5 '$)"$?#=%&'#&'#&66/'$,)$+0#&"#D&L?#W?Ka:9>?#=%+#,)$&2# ∆$ - ⁄ ∆$ ) #'%2/60-#)((2,0&"L#$2#2/,#'$/01#$%/'#@),1&+60#)"#&0+"$&()6#7)6/+#@2,#β?#!$#$/,"'#2/$-#%2.+7+,-#$%)$#$%+#6)$$+,#7)6/+#2@#β#:()66+0#$!E(4I4!?'&2,#)(-#β >#&'#)#6&$$6+#0&@@+,+"$#@,23#$%+#0(#β :&?+?-# . - ⁄ . ) >?#C/(%#)#0&'$&"($&2"-#%2.+7+,-#&'#$22#'/9$6+ @2,#2/,#"++0'#&"#$%&'#922U?#Y+#'%)66#/'+#β $2#0+"2$+#92$%#0(#)"0#&"(,+3+"$)6#7)6/+'?KP The Saturation Voltage VCEsat and Saturation Resistance RCEsat J+@+,# "+T$# $2# $%+ +T*)"0+0#7&+.#2@#$%+#(2332"5+3&$$+,#(%),)($+,&'$&('#&"#$%+#')$/,)$&2"#,+L&2"#'%2."#&"#D&L? W?Ka:(>?#=%+#R9/"(%&"L#$2L+$%+,S#2@##$%+#(/,7+'##&"#$%+#')$/,)$&2"#,+L&2"#&3*6&+'#$%)$#$%+#&"5 (,+3+"$)6#β#&'#62.+,#$%+,+#$%)"#&"#$%+#)($&7+#,+L&2"?#I#*2''&96+#2*+,)$&"L#*2&"$#&"#$%+#')$/5 ,)$&2"#,+L&2"#&'#$%)$#6)9+6+0#m?#!$#&'#(%),)($+,&h+0#91#)#9)'+#(/,,+"$#.)-#)#(266+($2,#(/,,+"$ .-')$-#)"0#)#(266+($2,Q+3&$$+,#726$)L+#+-*')$?##D,23#2/,#*,+7&2/'#0&'(/''&2"#2@#')$/,)$&2"-#,+()66 $%)$#.-')$#`#β @2,(+0#.)-#.%+,+#β @2,(+0#i#β? !"$,$-− v-*,/3#.$0,(),0*&3#*&(2),*#$,#*&"$#,0&$$75,()-(/*&();,&"*&,&"$,0*&3#*&$-,&#*)0(0&2# $A"(9(&0,*,+24,/2++$/&2#%&2%$'(&&$#,#$0(0&*)/$,>-*0*&5

∂v

-* > -*')$ ≡ 5555555555 ∂$-

$) = .) $ - = . -')$

TX
=1*&()661-#>-*')$#,)"L+'#@,23#)#@+.#2%3'#$2#)#@+.#$+"'#2@#2%3'? A)"/@)($/,+,'#2@#9&*26),#$,)"'&'$2,'#/'+#DS*#$2#0+"2$+#$%+#0(#7)6/+#2@#β )"0#DG4#$2#0+"2$+#$%+#&"(,+3+"5 $)6# β?#=%+'+#'13926'#(23+#@,23#$%+#D5*),)3+$+,#0+'(,&*$&2"#2@#$.25*2,$#"+$.2,U'#:'++#I**+"0&T#F>.&$%#$%+#'/9'(,&*$#S:GT#0+"2$&"L#@2,.),0#)"0#*:4>#0+"2$&"L#(2332"#+3&$$+,? KP

6.2 Current–Voltage Characteristics

iC Saturation region

iC

Active region iB = IB1 .

..

iB = IB2 .

..

∆iC

iB = IB + ∆iB

IB vCE

IC

iB = IB

Q

iB

iB = . . . 0

VCE iB = 0

(a)

vCE

(b)

iB " IB bIB Slope " ICsat

1 RCEsat

X

VCEsat (c) Figure 6.19 F2332"5+3&$$+,#(%),)($+,&'$&('?#:'>#;)'&(#FE#(&,(/&$H#"2$+#$%)$#&"#:&>##$%+#%2,&h2"$)6#'()6+#&' +T*)"0+0#),2/"0#$%+#2,&L&"#$2#'%2.#$%+#')$/,)$&2"#,+L&2"#&"#'23+#0+$)&6?#I#3/(%#L,+)$+,#+T*)"'&2"#2@#$%+ ')$/,)$&2"#,+L&2"#&'#'%2."#&"#:)>?

!"*&, &"$, /2++$/&2#%&2%$'(&&$#, #$0(0&*)/$, 21, *, 0*&3#*&$-, BC!, (0, 0'*++, 0"23+-, "*.$, 9$$) *)&(/(7*&$-,1#2',&"$,1*/&,&"*&,9$&4$$),6,*)-,M,4$,)24,"*.$,&42,12#4*#-%/2)-3/&();,-(2-$0 (),0$#($0??,T0$$,*+02,L(;<,X
KK

!"#$%+#(2,,+'*2"0&"L#320+#2@#2*+,)$&2"#@2,#$%+#ABCDE=-#$%+#$,&20+#,+L&2"-#$%+#,+'&'$)"(+#9+$.++" 0,)&"#)"0#'2/,(+#&'#'3)66#9+()/'+#&$#&'#$%+#,+'&'$)"(+#2@#$%+#(2"$&"/2/'#:"2"5*&"(%+052@@>#(%)""+6?

375

376 Chapter 6 Bipolar Junction Transistors (BJTs) I#'&3*6+#320+6#@2,#$%+#')$/,)$+0#;<=#&'#'%2."#&"#D&L?#W?MP?#\+,+# + )* #&'#)''/3+0#(2"5 '$)"$#:)**,2T&3)$+61#P?d#]>#)"0# + -* #)6'2#&'#)''/3+0#(2"'$)"$-# + -*')$ ! P?M #]?#=%)$#&'-#.+ %)7+#"+L6+($+0#$%+#'3)66#')$/,)$&2"#,+'&'$)"(+# > -*')$ #@2,#$%+#')U+#2@#3)U&"L#$%+#320+6#'&35 *6+#@2,#%)"0#()6(/6)$&2"'?######### ICsat

IB B

$

$

VBE

0.7 V

%

0.2 V

VCEsat % Figure 6.20 I#'&3*6&@&+0#+V/&7)6+"$5(&,(/&$# 320+6#2@#$%+#')$/,)$+0#$,)"'&'$2,?

E

Example 6.3 D2,#$%+#(&,(/&$#&"#D&L?#W?MK-#&$#&'#,+V/&,+0#$2#0+$+,3&"+#$%+#7)6/+#2@#$%+#726$)L+# +)) #$%)$#,+'/6$'#&"#$%+#$,)"5 '&'$2,#2*+,)$&"L :)>#&"#$%+#)($&7+#320+#.&$%# + -* d G #]# :9>#)$#$%+#+0L+#2@#')$/,)$&2" :(>#0++*#&"#')$/,)$&2"#.&$%# β @2,(+0 d KP # D2,#'&3*6&(&$1-#)''/3+#$%)$# + )* #,+3)&"'#(2"'$)"$#)$#P?d#]?#=%+#$,)"'&'$2,#β#&'#'*+(&@&+0#$2#9+#GP? VCC " 10V VBB IC RB " 10 k&

RC " 1 k&

IB $ $

VCE

VBE %

%

Figure 6.21 F&,(/&$#@2,#ET)3*6+#W?N?

Solution :)>#=2#2*+,)$+#&"#$%+#)($&7+#320+#.&$%# + -* d G #]+ -- ] + -* 5 . - d 5555555555555555555555555 >KP ] G d 555555555555555 d G #3I K#UΩ

6.2 Current–Voltage Characteristics

. G . ) d 5555- d 555555 d P?K #3I β GP b2.#$%+#,+V/&,+0#7)6/+#2@# + )) #()"#9+#@2/"0#)'#@2662.'8 + )) d . ) > ) e + )* d P?K × KP e P?d d K?d#]

:9>#B*+,)$&2"#)$#$%+#+0L+#2@#')$/,)$&2"#&'#29$)&"+0#.&$%# + -* d P?N #]?#=%/' KP ] P?N . - d 5555555555555555555 d a?d ,'@ K C&"(+-#)$#$%+#+0L+#2@#')$/,)$&2"-# . - #)"0# . ) #),+#'$&66#,+6)$+0#91#βa?d . ) d 5555555 d P?Kae ,'@ GP =%+#,+V/&,+0#7)6/+#2@# +)) #()"#9+#0+$+,3&"+0#)' +)) d P?Kae × KP e P?d d M?We,_ :(>#=2#2*+,)$+#0++*#&"#')$/,)$&2"-# + -* d + -*')$ ! P?M ,_ =%/'KP ] P?M , . - d 5555555555555555555 d a?f ,'@ K Y+#$%+"#/'+#$%+#7)6/+#2@#@2,(+0 β#$2#0+$+,3&"+#$%+#,+V/&,+0#7)6/+#2@# . ) #)' .5 d a?f 5555555 d P?af ,'@ . ) d 5555555555555 β @2,(+0 KP )"0#$%+#,+V/&,+0# +)) #()"#"2.#9+#@2/"0#)' +)) d P?af × KP e P?d d KP?G ,_ B9'+,7+#$%)$#2"(+#$%+#$,)"'&'$2,#&'#&"#')$/,)$&2"-#&"(,+)'&"L#+)) #)"0#$%/'# . ) #,+'/6$'#&"#"+L6&L&96+#(%)"L+#&" . - #'&"(+# + -*')$ #.&66#(%)"L+#2"61#'6&L%$61?#=%/'# . - #&'#')&0#$28B'?U('?4-#.%&(%#&'#$%+#2,&L&"#2@#$%+#")3+ R')$/,)$&2"#320+#2@#2*+,)$&2"?S

EXERCISES 6.19 J+*+)$#ET)3*6+#W?N#@2,# > - d KP#U Ω? Ans. P?f#]H#P?fae#]H#K?Wf#] 6.20 D2,#$%+#(&,(/&$#&"#D&L?#W?MK-#@&"0# + -* #@2,# +)) d P ]? Ans. c#KP#] 6.21 D2,#$%+#(&,(/&$#&"#D&L?#W?MK-#6+$# +)) #9+#'+$#$2#$%+#7)6/+#29$)&"+0#&"#ET)3*6+#W?N-#*),$#:)>-#")3+61+)) d K?d #]?#]+,&@1#$%)$#$%+#$,)"'&'$2,#&'#&"0++0#2*+,)$&"L#&"#$%+#)($&7+#320+?#b2.-#.%&6+#U++*&"L +)) #(2"'$)"$-#@&"0#$%)$#7)6/+#$2#.%&(%# > - #'%2/60#9+#&"(,+)'+0#&"#2,0+,#$2#29$)&"#:)>#2*+,)$&2"#)$ $%+#+0L+#2@#')$/,)$&2"-#)"0#:9>#2*+,)$&2"#0++*#&"#')$/,)$&2"#.&$%# β @2,(+0 d KP? Ans. :)>#K?ae#U ΩH #:9>#a?f#U Ω

377

378 Chapter 6 Bipolar Junction Transistors (BJTs)

6.3 BJT Circuits at DC W$, *#$, )24, #$*-:, &2, /2)0(-$#, &"$, *)*+:0(0, 21, BC!, /(#/3(&0, &2, 4"(/", 2)+:, -/, .2+&*;$0, *#$ *77+($-<,=),&"$,12++24();,$A*'7+$0,4$,4(++,30$,&"$,0('7+$,'2-$+,(),4"(/", + )* 21,*,/2)% -3/&();,&#*)0(0&2#,(0,O();, *, /(#/3(&, &"$, 1(#0&, S3$0&(2), &"*&, 2)$, '30&, *)04$#, (0Y, .! AD$ED8 I%548 $B8 ?D48 ?('!B$B?%(8 %"4('?$!Cf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`, &"*&, (05, (0, v-), 21, *), !"!, &#*)0(0&2#, ;#$*&$#, &"*) −O<8 _,T2#,v-),21,*,"!",&#*)0(0&2#,+24$#,&"*),O<8,_Vf,=1,&"$,*)04$#,(0,:$05,&"$),23#,&*0G,(0 /2'7+$&$<,=1,&"$,*)04$#,(0,)25,*003'$,0*&3#*&(2)%'2-$,27$#*&(2)5,*)-,7#2/$$-,&2,-$&$#'()$ /3##$)&0,*)-,.2+&*;$0,*)-,&"$),&2,/"$/G,12#,/2)0(0&$)/:,21,&"$,#$03+&0,4(&",&"$,*003'7&(2),21 0*&3#*&(2)%'2-$,27$#*&(2)<,R$#$,&"$,&$0&,(0,303*++:,&2,/2'73&$,&"$,#*&(2, . - ⁄ . ) ,*)-,&2,.$#(1: &"*&,(&,(0,+24$#,&"*),&"$,&#*)0(0&2#,β,T(<$<5,β12#/$-,i,β V<,K()/$,β,12#,*,;(.$),&#*)0(0&2#,&:7$,.*#($0 2.$#,*,4(-$,#*);$5?P,2)$,'30&,30$,&"$,+24$0&,07$/(1($-, β,12#,&"(0,&$0&<,L()*++:5,)2&$,&"*&,&"$ 2#-$#,21,&"$0$,&42,*003'7&(2)0,/*),9$,#$.$#0$-<,@0,*,13#&"$#,*(-,&2,&"$,#$*-$#5,4$,7#2.(-$,() !*9+$,X<\,*,03''*#:,21,&"$,/2)-(&(2)0,*)-,'2-$+0,12#,&"$,27$#*&(2),21,&"$,BC!,(),(&0,&"#$$ 7200(9+$,'2-$0<

KM

=%)$#&'-#&@#2"+#9/1'#;<='#2@#)#(+,$)&"#*),$#"/39+,-#$%+#3)"/@)($/,+,#L/),)"$++'#2"61#$%)$#$%+&,#7)6/+' 2@#β @)66#.&$%&"#)#(+,$)&"#,)"L+-#')1#GP#$2#KGP?

+,#"-,#($. !#"$%/0)1,)-%#+,*'.#"$%/0)1,)-%#+,*'-

&'#()* !#"$%/0)1,)-%#+,*'.#"$%&'(')*'%#+,*'-

!"#$%% !"#$%&'(')*'%#+,*'.#"$%&'(')*'%#+,*'-

!

!

"

VBE ! 0.7 V

B

IB > 0

"

!

IB > 0 !

VBE ! 0.7 V

B

"

VBE < 0.5 V

B !

IB # O !

IB

E

VBC ! 0.5 V

E

bIB

VBC < 0.4 V

E

IC # O

C

C

C

"

VCEsat ! 0.2 V

!

" I #b C forced IB

"

VCE > 0.3 V

!

" I # bI C B

"

"

VCE

IC !

VBC < 0.4 V

"

! ! VBE

" VBC

!"!

Table 6.3 Conditions and Models for the Operation of the BJT in Various Modes

IB # O

"

"

E

bIB

C

"

B

IB > 0 "

! IC = bforcedIB

C

"

!

C

VEC > 0.3 V

!

IC # O

! IC # bIB

!

"

"

VCB ! 0.5 V

E

VCB < 0.4 V

E

VCB < 0.4 V

!

IC

VEC

!

VECsat ! 0.2 V

IB > 0 "

"

" " VCB

!

VEB ! 0.7 V

!

B

VEB ! 0.7 V

!

B

VEB < 0.5 V

!

IB

VEB

"!"

6.3 BJT Circuits at DC

379

380 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.4 62)0(-$#,&"$,/(#/3(&,0"24),(),L(;<,X$ &"(0, /(#/3(&, &2, -$&$#'()$, *++, )2-$, .2+&*;$0, *)-, 9#*)/", /3##$)&0<, W$, 4(++, *003'$, &"*&, β, (0, 07$/(1($-, &2 9$ ?OO< $10 V

IC

RC " 4.7 k&

RC " 4.7 k&

$4 V VC IB

10 V

VE 4V

IE

RE " 3.3 k&

RE " 3.3 k&

(b)

(a) $10 V

3

0.99 ) 1 " 0.99 mA 4.7 k& 10 % 0.99 ) 4.7

$4 V

5

5.3 V

4

1.00 % 0.99 " 0.01 mA 4 % 0.7 " 3.3 V 3.3 k&

3.3 " 1 mA 3.3

1

2

(c) Figure 6.22 I")61'&'#2@#$%+#(&,(/&$#@2,#ET)3*6+#W?e8#;'<#(&,(/&$H#;&<#(&,(/&$#,+0,)."#$2#,+3&"0#$%+#,+)0+,#2@#$%+#(2"5 7+"$&2"#/'+0#&"#$%&'#922U#$2#'%2.#(2""+($&2"'#$2#$%+#*2.+,#'/**61H#;)<#)")61'&'#.&$%#$%+#'$+*'#"/39+,+0?

Solution n6)"(&"L#)$#$%+#(&,(/&$#&"#D&L?#W?MM:)>-#.+#"2$+#$%)$#$%+#9)'+#&'#(2""+($+0#$2#+e#]#)"0#$%+#+3&$$+,#&'#(2"5 "+($+0#$2#L,2/"0#$%,2/L%#)#,+'&'$)"(+#>*?#=%+,+@2,+-#&$#&'#')@+#$2#(2"(6/0+#$%)$#$%+#9)'+Q+3&$$+,#4/"($&2"

6.3 BJT Circuits at DC

.&66#9+#@2,.),0#9&)'+0?#I''/3&"L#$%)$#$%&'#&'#$%+#()'+#)"0#)''/3&"L#$%)$#+)*#&'#)**,2T&3)$+61#P?d#]-#&$#@265 62.'#$%)$#$%+#+3&$$+,#726$)L+#.&66#9+# + * = e ] + )* #! e ] P?d = N?N#] Y+#),+#"2.#&"#)"#2**2,$/"+#*2'&$&2"H#.+#U"2.#$%+#726$)L+'#)$#$%+#$.2#+"0'#2@#>*#)"0#$%/'#()"#0+$+,3&"+ $%+#(/,,+"$#.*#$%,2/L%#&$+* ] P N?N 5 = 5555555 = K#3I . * = 55555555555555 >* N?N C&"(+#$%+#(266+($2,#&'#(2""+($+0#$%,2/L%#>-#$2#$%+#+KP5]#*2.+,#'/**61-#&$#)**+),'#*2''&96+#$%)$#$%+#(266+(5 $2,#726$)L+#.&66#9+#%&L%+,#$%)"#$%+#9)'+#726$)L+-#.%&(%#&3*6&+'#)($&7+5320+#2*+,)$&2"?#I''/3&"L#$%)$#$%&' &'#$%+#()'+-#.+#()"#+7)6/)$+#$%+#(266+($2,#(/,,+"$#@,23 .- = α .* =%+#7)6/+#2@#α#&'#29$)&"+0#@,23

β KPP α = 555555555555 = 555555555 #!#P?aa β+K KPK =%/'#.-#.&66#9+#L&7+"#91 . - = P?aa × K = P?aa#3I Y+#),+#"2.#&"#)#*2'&$&2"#$2#/'+#B%3k'#6).#$2#0+$+,3&"+#$%+#(266+($2,#726$)L+#+- -# + - = KP ] . - > - = KP ] P?aa × e?d#! +G?N#] C&"(+# $%+# 9)'+# &'# )$# +e# ]-# $%+# (266+($2,Q9)'+# 4/"($&2"# &'# ,+7+,'+# 9&)'+0# 91# K?N# ]-# )"0# $%+# $,)"'&'$2,# &' &"0++0#&"#$%+#)($&7+#320+#)'#)''/3+0? !$#,+3)&"'#2"61#$2#0+$+,3&"+#$%+#9)'+#(/,,+"$#.)-#)'#@2662.'8 .* K5 5 = 55555555 . ) = 55555555555 #!#P?PK#3I β+K KPK ;+@2,+#6+)7&"L#$%&'#+T)3*6+#.+#.&'%#$2#+3*%)'&h+#'$,2"L61#$%+#7)6/+#2@#(),,1&"L#2/$#$%+#)")61'&' 0&,+($61#2"#$%+#(&,(/&$#0&)L,)3?#B"61#&"#$%&'#.)1#.&66#2"+#9+#)96+#$2#)")61h+#(23*6+T#(&,(/&$'#&"#)#,+)'2"5 )96+#6+"L$%#2@#$&3+?#D&L/,+#W?MM:(>#&66/'$,)$+'#$%+#)927+#)")61'&'#2"#$%+#(&,(/&$#0&)L,)3-#.&$%#$%+#2,0+,#2@ $%+#)")61'&'#'$+*'#&"0&()$+0#91#$%+#(&,(6+0#"/39+,'?#

381

382 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.5 Y+#.&'%#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?MN:)>#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$' $%,2/L%#)66#9,)"(%+'?#b2$+#$%)$#$%&'#(&,(/&$#&'#&0+"$&()6#$2#$%)$#2@#D&L?#W?MM#+T(+*$#$%)$#$%+#726$)L+#)$ $%+#9)'+#&'#"2.#+W#]?#I''/3+#$%)$#$%+#$,)"'&'$2,# β#&'#'*+(&@&+0#$2#9+#'?8&4'B?#GP? $10 V

$10 V 3

1.6 mA 4.7 k&

4.7 k&

10 % 1.6 ) 4.7 " 2.48 Impossible, not in active mode

$6 V

$6 V

6 % 0.7 " $5.3 V 3.3 k&

3.3 k&

5.3 " 1.6 mA 3.3

4

1

2

(b)

(a)

(c) Figure 6.23 I")61'&'#2@#$%+#(&,(/&$#@2,#ET)3*6+#W?G?#b2$+#$%)$#$%+#(&,(6+0#"/39+,'#&"0&()$+#$%+#2,0+,#2@ $%+#)")615 '&'#'$+*'?

6.3 BJT Circuits at DC

Solution Y&$%#cW#]#)$#$%+#9)'+-#$%+#9)'+Q+3&$$+,#4/"($&2"#.&66#9+#@2,.),0#9&)'+0H#$%/'+ * = + W ] + )* #!#W ] P?d = G?N#] )"0 G?N . * = 5555555 = K?W#3I N?N b2.-#)''/3&"L#)($&7+5320+#2*+,)$&2"-#.-#`#α.*8!#.*H#$%/'+ - = +KP ] e?d × . - #!#KP ] d?GM = M?ef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aW#3I e?d *)-,.),/*),)24,9$,123)-,*0 . ) = . * ] . - = K?W ] P?aW = P?We#3I !"30,&"$,&#*)0(0&2#,(0,27$#*&();,*&,*,12#/$-,β,21 . P?aW β @2,(+0 = 5555- = 5555555555 = K?G .)

P?We

K()/$,β12#/$-,(0,+$00,&"*),&"$,I$!$IUI,07$/(1($-,.*+3$,21,β5,&"$,&#*)0(0&2#,(0,()-$$-,0*&3#*&$-<,W$,0"23+$'7"*0(>$, "$#$, &"*&, (), &$0&();, 12#, 0*&3#*&(2), &"$, '()('3', .*+3$, 21, β, 0"23+-, 9$, 30$-<, B:, &"$, 0*'$ &2G$)5,(1,4$,*#$,-$0(;)();,*,/(#/3(&,(),4"(/",*,&#*)0(0&2#,(0,&2,9$,0*&3#*&$-5,&"$,-$0(;),0"23+-,9$,9*0$2),&"$,'()('3',07$/(1($-,β<,J9.(230+:5,(1,*,&#*)0(0&2#,4(&",&"(0,'()('3',β,(0,0*&3#*&$-5,&"$),&#*)0(0&2#0 4(&","(;"$#,.*+3$0,21,β,4(++,*+02,9$,0*&3#*&$-<,!"$,-$&*(+0,21,&"$,*)*+:0(0,*#$,0"24),(),L(;<,X
383

384 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.6 Y+# .&'%# $2# )")61h+# $%+# (&,(/&$# &"# D&L?# W?Me:)># $2# 0+$+,3&"+# $%+# 726$)L+'# )$# )66# "20+'# )"0# $%+# (/,,+"$' $%,2/L%#)66#9,)"(%+'?#b2$+#$%)$#$%&'#(&,(/&$#&'#&0+"$&()6#$2#$%)$#(2"'&0+,+0#&"#ET)3*6+'#W?e#)"0#W?G#+T(+*$ $%)$#"2.#$%+#9)'+#726$)L+#&'#h+,2?

2 1

(a)

(b)

Figure 6.24 ET)3*6+#W?W8#;'<#(&,(/&$H#;&<#)")61'&'-#.&$%#$%+#2,0+,#2@#$%+#)")61'&'#'$+*'#&"0&()$+0#91#(&,(6+0#"/39+,'?

Solution C&"(+#$%+#9)'+#&'#)$#h+,2#726$'#)"0#$%+#+3&$$+,#&'#(2""+($+0#$2#L,2/"0#$%,2/L%#>*-#$%+#9)'+Q+3&$$+,#4/"($&2"#()"5 "2$#(2"0/($#)"0#$%+#+3&$$+,#(/,,+"$#&'#h+,2?#b2$+#$%)$#$%&'#'&$/)$&2"#.&66#29$)&"#)'#62"L#)'#$%+#726$)L+#)$#$%+#9)'+#&' 6+''#$%)"#P?G#]#2,#'2?#I6'2-#$%+#(266+($2,Q9)'+#4/"($&2"#()""2$#(2"0/($-#'&"(+#$%+#!5$1*+#(266+($2,#&'#(2""+($+0 $%,2/L%#>-#$2#$%+#*2'&$&7+#*2.+,#'/**61#.%&6+#$%+#"5$1*+#9)'+#&'#)$#L,2/"0?#!$#@2662.'#$%)$#$%+#(266+($2,#(/,,+"$ .&66#9+#h+,2?#=%+#9)'+#(/,,+"$#.&66#)6'2#%)7+#$2#9+#h+,2-#)"0#$%+#$,)"'&'$2,#&'#&"#$%+#EU?%GG#320+#2@#2*+,)$&2"? =%+#+3&$$+,#726$)L+#.&66#9+#h+,2-#.%&6+#$%+#(266+($2,#726$)L+#.&66#9+#+V/)6#$2#+KP ]-#'&"(+#$%+#726$)L+ 0,2*'#)(,2''#>*#)"0#>-#),+#h+,2?#D&L/,+#W?Me:9>#'%2.'#$%+#)")61'&'#0+$)&6'? ,,,,,,,,,,

EXERCISES D6.22 D2,#$%+#(&,(/&$#&"#D&L?#W?MM:)>-#@&"0#$%+#%&L%+'$#726$)L+#$2#.%&(%#$%+#9)'+#()"#9+#,)&'+0#.%&6+#$%+ $,)"'&'$2,#,+3)&"'#&"#$%+#)($&7+#320+?#I''/3+#α#!#K? Ans. +e?d#] D6.23 J+0+'&L"#$%+#(&,(/&$#2@#D&L?#W?MM:)>#:&?+?-#@&"0#"+.#7)6/+'#@2,#>*#)"0#>->#$2#+'$)96&'%#)#(266+($2, (/,,+"$#2@#P?G#3I#)"0#)#,+7+,'+59&)'#726$)L+#2"#$%+#(266+($2,Q9)'+#4/"($&2"#2@#M#]?#I''/3+#α#!#K? Ans. >*#=#W?W#UΩH#>-#=#f#UΩ 6.24 D2,#$%+#(&,(/&$#&"#D&L?#W?MN:)>-#@&"0#$%+#7)6/+#$2#.%&(%#$%+#9)'+#726$)L+#'%2/60#9+#(%)"L+0#'2#$%)$ $%+#$,)"'&'$2,#2*+,)$+'#&"#')$/,)$&2"#.&$%#)#@2,(+0#β#2@#G? Ans. +^
6.3 BJT Circuits at DC

385

Example 6.7 Y+# .)"$# $2# )")61h+# $%+# (&,(/&$# 2@# D&L?# W?MG:)># $2# 0+$+,3&"+# $%+# 726$)L+'# )$# )66# "20+'# )"0# $%+# (/,,+"$' $%,2/L%#)66#9,)"(%+'? V $ " $10 V

$10 V 10 % 0.7 " 4.65 mA 2

2 k&

RE " 2 k&

$0.7 V 5

2

1

0.05 mA

%10 $ 4.6 ) 1 " %5.4 V RC " 1 k&

4

1 k& 3

0.99 ) 4.65

V % " %10 V

4.6 mA %10 V

(a)

(b)

Figure 6.25 ET)3*6+#W?d8#;'<#(&,(/&$H#;&<#)")61'&'-#.&$%#$%+#'$+*'#&"0&()$+0#91#(&,(6+0#"/39+,'?

Solution =%+#9)'+#2@#$%&'#"!"#$,)"'&'$2,#&'#L,2/"0+0-#.%&6+#$%+#+3&$$+,#&'#(2""+($+0#$2#)#*2'&$&7+#'/**61#:+ +#=#+KP#]> $%,2/L%#>*?#!$#@2662.'#$%)$#$%+#+3&$$+,Q9)'+#4/"($&2"#.&66#9+#@2,.),0#9&)'+0#.&$% + * = + *) #!#P?d#] =%/'#$%+#+3&$$+,#(/,,+"$#.&66#9+#L&7+"#91# +

+ ]+ KP ] P?d . * = 55555555555555555*5 = 5555555555555555555 = e?WG#3I M >* K()/$,&"$,/2++$/&2#,(0,/2))$/&$-,&2,*,)$;*&(.$,0377+:,T'2#$,)$;*&(.$,&"*),&"$,9*0$,.2+&*;$V,&"#23;",>-5,(& (0,"%BB$#&4,&"*&,&"(0,&#*)0(0&2#,(0,27$#*&();,(),&"$,*/&(.$,'2-$<,@003'();,&"(0,&2,9$,&"$,/*0$5,4$,29&*() .- = α .* K()/$,)2,.*+3$,12#,β "*0,9$$),;(.$)5,4$,0"*++,*003'$,β,=,?OO5,4"(/",#$03+&0,(),α,=,O
+- = + + .- >= # −KP + e?W × K = ] G?e#]

386 Chapter 6 Bipolar Junction Transistors (BJTs) ,,,

=%/'# $%+# (266+($2,Q9)'+# 4/"($&2"# &'# ,+7+,'+# 9&)'+0# 91# G?e# ]-# )"0# $%+# $,)"'&'$2,# &'# &"0++0# &"# $%+# )($&7+ 320+-#.%&(%#'/**2,$'#2/,#2,&L&")6#)''/3*$&2"? !$#,+3)&"'#2"61#$2#()6(/6)$+#$%+#9)'+#(/,,+"$.* 5 = e?WG 5555555555 #!#P?PG#3I . ) = 55555555555 β+K KPK B97&2/'61-#$%+#7)6/+#2@#β#(,&$&()661#)@@+($'#$%+#9)'+#(/,,+"$?#b2$+-#%2.+7+,-#$%)$#&"#$%&'#(&,(/&$#$%+#7)6/+#2@#β .&66#%)7+#"2#+@@+($#2"#$%+#320+#2@#2*+,)$&2"#2@#$%+#$,)"'&'$2,?#C&"(+#β#&'#L+"+,)661#)"#&665'*+(&@&+0#*),)3+$+,$%&'#(&,(/&$#,+*,+'+"$'#)#L220#0+'&L"?#I'#)#,/6+-#2"+#'%2/60#'$,&7+#$2#54B$C!8?D48E$(EU$?8BUED8?D'?8$?B8"4(G%(M I'!E48$B8'B8$!B4!B$?$F48?%8?D48F'&U48%G8β8'B8"%BB$#&4@#=%+#)")61'&'#0+$)&6'#),+#&66/'$,)$+0#&"#D&L?#W?MG:9>?

EmIAO[E#G?d EXERCISES D6.25#D2,#$%+#(&,(/&$#&"#D&L?#W?MG:)>-#@&"0#$%+#6),L+'$#7)6/+#$2#.%&(%#>-#()"#9+#,)&'+0#.%&6+#$%+#$,)"'&'$2, ,+3)&"'#&"#$%+#)($&7+#320+? Ans. M?MW#UΩ D6.26 J+0+'&L"#$%+#(&,(/&$#2@#D&L?#W?MG:)>#:&?+?-#@&"0#"+.#7)6/+'#@2,#>*#)"0#>->#$2#+'$)96&'%#)#(266+($2, (/,,+"$#2@#K#3I#)"0#)#,+7+,'+#9&)'#2"#$%+#(266+($2,Q9)'+#4/"($&2"#2@#e#]?#I''/3+#α#!#K? Ans. >*#=#a?N#UΩH#>-#=#W#UΩ

Example 6.8 Y+#.)"$#$2#)")61h+#$%+#(&,(/&$#&"#D&L?#W?MW:)>#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#&"#)66 9,)"(%+'?#I''/3+#β# =#KPP?

(a)

(b)

Figure 6.26 ET)3*6+#W?f8#;'<#(&,(/&$H#;&<#)")61'&'-#.&$%#$%+#'$+*'#&"0&()$+0#91#$%+#(&,(6+0#"/39+,'?

6.3 BJT Circuits at DC

387

Solution =%+#9)'+Q+3&$$+,#4/"($&2"#&'#(6+),61#@2,.),0#9&)'+0?#=%/'+G ] + )* G ] P?d #!# 5555555555555555 = P?PeN#3I . ) = 555555555555555555555 >) KPP I''/3+#$%)$#$%+#$,)"'&'$2,#&'#2*+,)$&"L#&"#$%+#)($&7+#320+?#Y+#"2.#()"#.,&$+ . - = β . ) = KPP × P?PeN = e?N#3I =%+#(266+($2,#726$)L+#()"#"2.#9+#0+$+,3&"+0#)' + - = +KP ] . - > - = KP ] e?N × M = +K?e#] C&"(+#$%+#9)'+#726$)L+#+)#&'# + ) = + )* #!#+ P?d#] &$#@2662.'#$%)$#$%+#(266+($2,Q9)'+#4/"($&2"#&'#,+7+,'+59&)'+0#91#P?d#]#)"0#$%+#$,)"'&'$2,#&'#&"0++0#&"#$%+#)($&7+ 320+?#=%+#+3&$$+,#(/,,+"$#.&66#9+#L&7+"#91 . * = ( β + K ). ) = KPK × P?PeN#!#e?N#3I Y+#"2$+#@,23#$%&'#+T)3*6+#$%)$#$%+#(266+($2,#)"0#+3&$$+,#(/,,+"$'#0+*+"0#(,&$&()661#2"#$%+ 7)6/+#2@# β?#!" @)($-#&@#β#.+,+#KPo#%&L%+,-#$%+#$,)"'&'$2,#.2/60#6+)7+#$%+#)($&7+#320+#)"0#+"$+,#')$/,)$&2"?#=%+,+@2,+#$%&' (6+),61#&'#)##'5#0+'&L"?#=%+#)")61'&'#0+$)&6'#),+#&66/'$,)$+0#&"#D&L?#W?MW:9>?

EXERCISE D6.27 =%+#(&,(/&$#2@#D&L?#W?MW:)>#&'#$2#9+#@)9,&()$+0#/'&"L#)#$,)"'&'$2,#$1*+#.%2'+#β#&'#'*+(&@&+0#$2#9+ &"#$%+#,)"L+#2@#GP#$2#KGP?#=%)$#&'-#&"0&7&0/)6#/"&$'#2@#$%&'#')3+#$,)"'&'$2,#$1*+#()"#%)7+#β#7)6/+' )"1.%+,+# &"# $%&'# ,)"L+?# J+0+'&L"# $%+# (&,(/&$# 91# '+6+($&"L# )# "+.# 7)6/+# @2,# >-# '2# $%)$# )66 @)9,&()$+0# (&,(/&$'# ),+# L/),)"$++0# $2# 9+# &"# $%+# )($&7+# 320+?# Y%)$# &'# $%+# ,)"L+# 2@# (266+($2, 726$)L+'#$%)$#$%+#@)9,&()$+0#(&,(/&$'#3)1#+T%&9&$_ Ans. >-,=,?<^,GΩ`,+-,=,O<\,_,&2,X
388 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.9 Y+#.)"$#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?Md#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#$%,2/L% )66#9,)"(%+'?#=%+#3&"&3/3#7)6/+#2@#β#&'#'*+(&@&+0#$2#9+#NP? $5 V $5 V 4 1 k&

IE "

5 % ( VB $ 0.7) 1

2 IB " VB /10

10 k&

7 IC "

$

10 k& 1

10 k&

1 k&

VEC sat " 0.2 V %

VB

VB $ 0.5 % (%5) 10

%5 V (a)

VE " VB $ 0.7

3

5

VC " VB $ 0.5

6

10 k& %5 V

(b)

Figure 6.27 ET)3*6+#W?a8#;'<#(&,(/&$H#;&<#)")61'&'#.&$%#'$+*'#"/39+,+0?

Solution I#V/&(U#L6)"(+#)$#$%&'#(&,(/&$#,+7+)6'#$%)$#$%+#$,)"'&'$2,#.&66#9+#+&$%+,#)($&7+#2,#')$/,)$+0?#I''/3&"L#)($&7+5 320+#2*+,)$&2"#)"0#"+L6+($&"L#$%+#9)'+#(/,,+"$-#.+#'++#$%)$#$%+#9)'+#726$)L+#.&66#9+#)**,2T&3)$+61#h+,2 726$'-#$%+#+3&$$+,#726$)L+#.&66#9+#)**,2T&3)$+61#+P?d#]-#)"0#$%+#+3&$$+,#(/,,+"$#.&66#9+#)**,2T&3)$+61#e?N 3I?#C&"(+#$%+#3)T&3/3#(/,,+"$#$%)$#$%+#(266+($2,#()"#'/**2,$#.%&6+#$%+#$,)"'&'$2,#,+3)&"'#&"#$%+#)($&7+ 320+#&'#)**,2T&3)$+61#P?G#3I-#&$#@2662.'#$%)$#$%+#$,)"'&'$2,#&'#0+@&"&$+61#')$/,)$+0? I''/3&"L# $%)$# $%+# $,)"'&'$2,# &'# ')$/,)$+0# )"0# 0+"2$&"L# $%+# 726$)L+# )$# $%+# 9)'+# 91# +)# :,+@+,# $2# D&L? W?Md9>-#&$#@2662.'#$%)$ + * = + ) + + *) #!#+ ) + P?d + - = + * ] + *-')$ #!#+ ) + P?d ] P?M = + ) + P?G +G ] + G ] + ) ] P?d . * = 555555555555555555*5 = 5555555555555555555555555555 = e?N ] + ) # 3I K K + . ) = 55555)5 = P?K+ ) # 3I KP +- Q ( ]G ) + ) + P?G + G 5 = 5555555555555555555555555555 5 = P?K+ ) + P?GG# 3I . - = 5555555555555555555555 KP KP

6.3 BJT Circuits at DC

c0();,&"$,#$+*&(2)0"(7,.*, =, .),+,.- 5,4$,29&*() e?N ] + ) = P?K+ ) + P?K+ ) + P?GG 4"(/",#$03+&0,() N?dG + ) = 5555555555 #!#N?KN#] K?M K390&(&3&();,(),&"$,$S3*&(2)0,*92.$5,4$,29&*() + * = N?fN#] + - = N?WN#] . * = K?Kd#3I . - = P?fW#3I . ) = P?NK#3I 1#2',4"(/",4$,0$$,&"*&,&"$,&#*)0(0&2#,(0,0*&3#*&$-5,0()/$,&"$,.*+3$,21,12#/$-,β,(0 P?fW β @2,(+0 = 5555555555 #!#M?f P?NK

.%&(%#&'#3/(%#'3)66+,#$%)"#$%+#'*+(&@&+0#3&"&3/3#β?

,,,,,,,,,,,

389

390 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.10 Y+#.)"$#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?Mf:)>#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#$%,2/L% )66#9,)"(%+'?#I''/3+#β #=#KPP? $15 V

$15 V

RC " 5 k&

RB 1 " 100 k&

RC " 5 k&

VBB " $5 V RBB " 33.3 k&

IE

IB

RB 2 " 50 k&

RE " 3 k&

RE " 3 k&

L

(b)

(a) $15 V

$15 V

1.28 mA 0.103 mA

5 k& $8.6 V

$5 V

100 k& 0.013 mA

33.3 k&

$4.57 V 0.013 mA

$3.87 V

$4.57 V 1.29 mA

50 k&

3 k&

(c)

0.09 mA

(d)

Figure 6.28 F&,(/&$'#@2,#ET)3*6+#W?KP?

Solution =%+#@&,'$#'$+*#&"#$%+#)")61'&'#(2"'&'$'#2@#'&3*6&@1&"L#$%+#9)'+#(&,(/&$#/'&"L#=%p7+"&"k'#$%+2,+3?#=%+#,+'/6$ &'#'%2."#&"#D&L?#W?Mf:9>-#.%+,+ > )M GP = KG 555555555555555555555 = +G#] + )) = +KG 55555555555555555555555 > )K + > )M KPP + GP

6.3 BJT Circuits at DC

> )) = > )K #qq#> )M = KPP#qq#GP = NN?N#UΩ =2#+7)6/)$+#$%+#9)'+#2,#$%+#+3&$$+,#(/,,+"$-#.+#%)7+#$2#.,&$+#)#622*#+V/)$&2"#),2/"0#$%+#622*#6)9+6+0#[#&" D&L?#W?Mf:9>?#b2$+-#%2.+7+,-#$%)$#$%+#(/,,+"$#$%,2/L%# >))#&'#0&@@+,+"$#@,23#$%+#(/,,+"$#$%,2/L%#>*?#=%+ 622*#+V/)$&2"#.&66#9+ + )) = . ) > )) + + )* + . * > * b2.-#)''/3&"L#)($&7+5320+#2*+,)$&2"-#.+#,+*6)(+#.)#.&$%# .* 5 . ) = 55555555555 β+K )"0#,+),,)"L+#$%+#+V/)$&2"#$2#29$)&" + )) ] + )* 5 . * = 55555555555555555555555555555555555555555555555 > * + [ > )) ⁄ ( β + K ) ] D2,#$%+#"/3+,&()6#7)6/+'#L&7+"#.+#%)7+ G ] P?d . * = 5555555555555555555555555555555555555 = K?Ma#3I N + ( NN?N ⁄ KPK ) =%+#9)'+#(/,,+"$#.&66#9+ K?Ma . ) = 5555555555 = P?PKMf#3I KPK =%+#9)'+#726$)L+#&'#L&7+"#91 + ) = + )* + . * > * = P?d + K?Ma × N = e?Gd#] W$,/*),$.*+3*&$,&"$,/2++$/&2#,/3##$)&,*0, . - = α . * = P?aa × K?Ma = K?Mf#3I =%+#(266+($2,#726$)L+#()"#"2.#9+#+7)6/)$+0#)'# + - = +KG ] . - > - = KG ] K?Mf × G = f?W#] !$#@2662.'#$%)$#$%+#(266+($2,#&'#%&L%+,#&"#*2$+"$&)6#$%)"#$%+#9)'+#91#e?PN#]-#.%&(%#3+)"'#$%)$#$%+ $,)"'&'$2, &'#&"#$%+#)($&7+#320+-#)'#%)0#9++"#)''/3+0?#=%+#,+'/6$'#2@#$%+#)")61'&'#),+#L&7+"#&"#D&L?#W?Mf:(-#0>?

EXERCISE 6.28 !@#$%+#$,)"'&'$2,#&"#$%+#(&,(/&$#2@#D&L?#W?Mf:)>#&'#,+*6)(+0#.&$%#)"2$%+,#%)7&"L#%)6@#$%+#7)6/+#2@#β :&?+?- β =#GP>-#@&"0#$%+#"+.#7)6/+#2@#.--#)"0#+T*,+''#$%+#(%)"L+#&"#.-#)'#)#*+,(+"$)L+? Ans. .-,=,?
391

392 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.11 Y+# .)"$# $2# )")61h+# $%+# (&,(/&$# &"# D&L?# W?Ma:)># $2# 0+$+,3&"+# $%+# 726$)L+'# )$# )66# "20+'# )"0# $%+# (/,,+"$' $%,2/L%#)66#9,)"(%+'? $15 V

RE2 " 2 k&

RC1 " 5 k&

RB 1 " 100 k&

IE2

Q2 IC1

IB2

Q1

IC2 RC2 " 2.7 k&

RB 2 " 50 k&

RE " 3 k&

(a) $15 V 2.78 mA

1.252 mA

0.103 mA

100 k&

$9.44 V $8.74 V Q1

$4.57 V

2 k&

5 k& Q2 0.0275 mA 1.28 mA

$7.43 V

0.013 mA $3.87 V 50 k& 0.09 mA

2.7 k&

3 k& 1.29 mA

2.75 mA

(b) Figure 6.29 F&,(/&$'#@2,#ET)3*6+#W?KK?

Solution Y+#@&,'$#,+(2L"&h+#$%)$#*),$#2@#$%&'#(&,(/&$#&'#&0+"$&()6#$2#$%+#(&,(/&$#.+#)")61h+0#&"#ET)3*6+#W?KP g")3+61$%+# (&,(/&$# 2@# D&L?# W?Mf:)>?# =%+# 0&@@+,+"(+-# 2@# (2/,'+-# &'# $%)$# &"# $%+# "+.# (&,(/&$# .+# %)7+# )" )00&$&2")6

6.3 BJT Circuits at DC

$,)"'&'$2,#VM#$2L+$%+,#.&$%#&$'#)''2(&)$+0#,+'&'$2,'#>*M#)"0#>-M?#I''/3+#$%)$#VK#&'#'$&66#&"#$%+#)($&7+#320+? =%+#@2662.&"L#7)6/+'#.&66#9+#&0+"$&()6#$2#$%2'+#29$)&"+0#&"#$%+#*,+7&2/'#+T)3*6+8 +)?,=,+8<^N,_

,.*?,=,?
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\2.+7+,-#$%+#(266+($2,#726$)L+#.&66#9+#0&@@+,+"$#$%)"#*,+7&2/'61#()6(/6)$+0-#'&"(+#*),$#2@#$%+#(266+($2,#(/,5 ,+"$#.-K#.&66#@62.#&"#$%+#9)'+#6+)0#2@#VM#:.)M>?#I'#)#@&,'$#)**,2T&3)$&2"#.+#3)1#)''/3+#$%)$#.)M#&'#3/(% '3)66+,# $%)"# .-KH# $%)$# &'-# .+# 3)1# )''/3+# $%)$# $%+# (/,,+"$# $%,2/L%# >-K# &'# )632'$# +V/)6# $2# .-K?# =%&'# .&66 +")96+#/'#$2#()6(/6)$+#+-K8 + -K #!#+KG ] . -K > -K = KG ] K?Mf × G = +f?W#] =%/'#VK#&'#&"#$%+#)($&7+#320+-#)'#%)0#9++"#)''/3+0? I'#@),#)'#VM#&'#(2"(+,"+0-#.+#"2$+#$%)$#&$'#+3&$$+,#&'#(2""+($+0#$2#+KG#]#$%,2/L%#>*M?#!$#&'#$%+,+@2,+ ')@+#$2#)''/3+#$%)$#$%+#+3&$$+,Q9)'+#4/"($&2"#2@#VM#.&66#9+#@2,.),0#9&)'+0?#=%/'#$%+#+3&$$+,#2@#VM#.&66#9+ )$#)#726$)L+#+*M#L&7+"#91# + *M = + -K + + *)

VM

#!#f?W + P?d = +a?N#]

=%+#+3&$$+,#(/,,+"$#2@#VM#3)1#"2.#9+#()6(/6)$+0#)'# +KG ] + *M KG ] a?N 5 = 5555555555555555555 = M?fG#3I . *M = 55555555555555555555555 M > *M K()/$, &"$, /2++$/&2#, 21, VP, (0, #$&3#)$-, &2, ;#23)-, .(*, >-P5,(&, (0, 7200(9+$, &"*&,VP, (0, 27$#*&();,(),&"$, */&(.$ '2-$<,@003'$,&"(0,&2,9$,&"$,/*0$<,W$,)24,1()-,.-P,*0, . -M = α M . *M = P?aa × M?fG = M?fM#3I

( )''/3&"L# β M = KPP )

=%+#(266+($2,#726$)L+#2@#VM#.&66#9+# + -M = . -M > -M = M?fM × M?d = d?WM#] .%&(%#&'#62.+,#$%)"#+)M#91#P?af#]?#=%/'#VM#&'#&"#$%+#)($&7+#320+-#)'#)''/3+0? !$# &'# &3*2,$)"$# )$# $%&'# '$)L+# $2# @&"0# $%+# 3)L"&$/0+# 2@# $%+# +,,2,# &"(/,,+0# &"# 2/,# ()6(/6)$&2"'# 91# $%+ )''/3*$&2"#$%)$#.)M#&'#"+L6&L&96+?#=%+#7)6/+#2@#.)M#&'#L&7+"#91 . *M M?fG = 5555555555 = P?PMf#3I . )M = 55555555555555 βM + K KPK 4"(/",(0,()-$$-,'3/",0'*++$#,&"*),.-?,T? -K = . -K ] . )M = K?Mf ] P?PMf = K?MGM#3I + -K = KG ] G × K?MGM = f?de#] + *M = f?de + P?d = a?ee#] KG ] a?ee . *M = 5555555555555555555555 = M?df#3I M

393

394 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.11 continued

. -M = P?aa × M?df = M?dG#3I + -M = M?dG × M?d = d?eN#] M?df . )M = 5555555555 = P?PMdG#3I KPK b2$+#$%)$#$%+#"+.#7)6/+#2@#.)M#&'#7+,1#(62'+#$2#$%+#7)6/+#/'+0#&"#2/,#&$+,)$&2"-#)"0#"2#@/,$%+,#&$+,)$&2"' ),+#.),,)"$+0?#=%+#@&")6#,+'/6$'#),+#&"0&()$+0#&"#D&L?#W?Ma:9>? =%+#,+)0+,#4/'$&@&)961#3&L%$#9+#.2"0+,&"L#)92/$#$%+#"+(+''&$1#@2,#/'&"L#)"#&$+,)$&7+#'(%+3+#&"#'2675 &"L#)#6&"+),#:2,#6&"+),&h+0>#*,296+3?#!"0++0-#.+#()"#29$)&"#$%+#+T)($#'26/$&2"#:&@#.+#()"#()66#)"1$%&"L#.+ ),+#02&"L#.&$%#)#@&,'$52,0+,#320+6#+T)($j>#91#.,&$&"L#)**,2*,&)$+#+V/)$&2"'?#=%+#,+)0+,#&'#+"(2/,)L+0#$2 @&"0#$%&'#'26/$&2"#)"0#$%+"#(23*),+#$%+#,+'/6$'#.&$%#$%2'+#29$)&"+0#)927+?#!$#&'#&3*2,$)"$#$2#+3*%)'&h+%2.+7+,-#$%)$#&"#32'$#'/(%#*,296+3'#&$#&'#V/&$+#'/@@&(&+"$#$2#29$)&"#)"#)**,2T&3)$+#'26/$&2"-#*,27&0+0#.+ ()"#29$)&"#&$#V/&(U61#)"0-#2@#(2/,'+-#(2,,+($61?

!"#$%+#)927+#+T)3*6+'-#.+#@,+V/+"$61#/'+0#)#*,+(&'+#7)6/+#2@# α $2#()6(/6)$+#$%+#(266+($2, (/,,+"$?#C&"(+# α#!#K-#$%+#+,,2,#&"#'/(%#()6(/6)$&2"'#.&66#9+#7+,1#'3)66#&@#2"+#)''/3+'# α#=#K#)"0 .- = .*?#=%+,+@2,+-#+T(+*$#&"#()6(/6)$&2"'#$%)$#0+*+"0#(,&$&()661#2"#$%+#7)6/+#2@#α#:+?L?-#$%+#()6(/6)5 $&2"#2@#9)'+#(/,,+"$>-#2"+#/'/)661#)''/3+'#α ! K?

EXERCISES 6.29 D2,#$%+#(&,(/&$#&"#D&L?#W?Ma-#@&"0#$%+#$2$)6#(/,,+"$#0,)."#@,23#$%+#*2.+,#'/**61?#\+"(+#@&"0#$%+ *2.+,#0&''&*)$+0#&"#$%+#(&,(/&$? Ans. 8
6.29

Figure E6.30

Ans. +N
6.3 BJT Circuits at DC

395

,

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On

0 3.9 mA 5 – 0.7 = 10 + 101 × 1 0.039 mA

Off 0

–5V (a)

(b)

Figure 6.30 ET)3*6+#W?KM8#;'<#(&,(/&$H#;&<#)")61'&'#.&$%#$%+#'$+*'#"/39+,+0?

Solution ;1#+T)3&"&"L#$%+#(&,(/&$-#.+#(2"(6/0+#$%)$#$%+#$.2#$,)"'&'$2,'#VK#)"0#VM#()""2$#9+#'&3/6$)"+2/'61#(2"0/($&"L? =%/'#&@#VK#&'#2"-#VM#.&66#9+#2@@-#)"0#7&(+#7+,')?#I''/3+#$%)$#VM#&'#2"?#!$#@2662.'#$%)$#(/,,+"$#.&66#@62.#@,23 L,2/"0#$%,2/L%#$%+#K5UΩ#,+'&'$2,#&"$2#$%+#+3&$$+,#2@#VM?#=%/'#$%+#9)'+#2@#VM#.&66#9+#)$#)#"+L)$&7+#726$)L+-#)"0 9)'+#(/,,+"$#.&66#9+#@62.&"L#2/$#2@#$%+#9)'+#$%,2/L%#$%+#KP5UΩ#,+'&'$2,#)"0#&"$2#$%+#+G5]#'/**61?#=%&'#&'#&3*2'5 '&96+-#'&"(+#&@#$%+#9)'+#&'#"+L)$&7+-#(/,,+"$#&"#$%+#KP5UΩ#,+'&'$2,#.&66#%)7+#$2#@62.#&"$2#$%+#9)'+?#=%/'#.+#(2"5 (6/0+#$%)$#2/,#2,&L&")6#)''/3*$&2"g$%)$#VM#&'#2"g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

##########

EXERCISES 6.31 K2+.$,&"$,7#29+$',(),MA*'7+$,X
396 Chapter 6 Bipolar Junction Transistors (BJTs)

6.4 Applying the BJT in Amplifier Design W$,)24,9$;(),23#,0&3-:,21,&"$,3&(+(>*&(2),21,&"$,BC!,(),&"$,-$0(;),21,*'7+(1($#0
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RC

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vO " vCE

Edge of Saturation Z

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6.5 Small-Signal Operation and Models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v#4,&"*&,(0,037$#('% 720$-,2),+)*< Y+# (2"'&0+,# @&,'$# $%+# 0(# 9&)'# (2"0&$&2"'# 91# '+$$&"L# $%+# '&L")6# v#4# $2# h+,2?# =%+# (&,(/&$ ,+0/(+'#$2#$%)$#&"#D&L?#W?NW:9>-#)"0#.+#()"#.,&$+#$%+#@2662.&"L#,+6)$&2"'%&*'#@2,#$%+#0(#(/,5 ,+"$'#)"0#726$)L+'8

.- = .6 4

+ )* ⁄ + ,

.* = .- ⁄ α

TX<\XV TX<\NV

403

404 Chapter 6 Bipolar Junction Transistors (BJTs) iC

IC RC

RC iB

$

vbe

$ $ % vBE

VBE

%

vCE

IB

VCC

$ VCE

%

VCC

%

VBE

iE

IE

(b)

(a)

Figure 6.36 ;'<#F2"(+*$/)6#(&,(/&$#$2#&66/'$,)$+#$%+#2*+,)$&2"#2@#$%+#$,)"'&'$2,#)'#)"#)3*6&@&+,?#;&<#=%+#(&,5 (/&$#2@#;'<#.&$%#$%+#'&L")6#'2/,(+#v#4#+6&3&")$+0#@2,#0(#:9&)'>#)")61'&'?

.) = .- ⁄ β

TX<\EV

+ -* = + -- ] . - > -

TX<\DV

B97&2/'61-#@2,#)($&7+5320+#2*+,)$&2"-#+-#'%2/60#9+#L,+)$+,#$%)"#:+)#−#P?e>#91#)"#)32/"$ $%)$#)662.'#@2,#$%+#,+V/&,+0#'&L")6#'.&"L#)$#$%+#(266+($2,?

6.5.1 The Collector Current and the Transconductance =1,*,0(;)*+, v#4,(0,*77+($-,*0,0"24),(),L(;<,X<\XT*V5,&"$,&2&*+,()0&*)&*)$230,9*0$]$'(&&$#,.2+&% *;$,v)*,9$/2'$0 v )*

= + )* + v #4

62##$072)-();+:5,&"$,/2++$/&2#,/3##$)&,9$/2'$0

$- = .6 4 = .6 4

v )* ⁄ + ,

= .6 4

( + )* + v #4 ) ⁄ + ,

+ )* ⁄ + , v #4 ⁄ + ,

4

c0$,21,MS<,TX<\XV,:($+-0

$- = .- 4

v#4 ⁄ + ,

TX<8OV

Q245,(1,v#4 *,+, 5,4$,'*:,*77#2A('*&$,MS<,TX<8OV,*0 v

#4 5 $ - #! . - K + 55555 +,

TX<8?V

R$#$,4$,"*.$,$A7*)-$-,&"$,$A72)$)&(*+,(),MS<,TX<8OV,(),*,0$#($0,*)-,#$&*()$-,2)+:,&"$,1(#0& &42,&$#'0<,!"(0,*77#2A('*&(2)5,4"(/",(0,.*+(-,2)+:,12#,v#4,+$00,&"*),*77#2A('*&$+:,?O,'_5,(0 #$1$##$-,&2,*0,&"$,("'++5(#60'+-'44%*?#"'$#*0<,c)-$#,&"(0,*77#2A('*&(2)5,&"$,&2&*+,/2++$/&2# /3##$)&,(0,;(.$),9:,MS<,TX<8?V,*)-,/*),9$,#$4#(&&$)

.v $ - = . - + 55555 + , #4

TX<8PV

6.5 Small-Signal Operation and Models

!"30,&"$,/2++$/&2#,/3##$)&,(0,/2'720$-,21,&"$,-/,9(*0,.*+3$,.-,*)-,*,0(;)*+,/2'72)$)&,$E 5

.$ E = 55555 v + , #4

TX<8\V

!"(0, $S3*&(2), #$+*&$0,&"$,0(;)*+, /3##$)&, (), &"$,/2++$/&2#,&2, &"$, /2##$072)-();,9*0$]$'(&&$# 0(;)*+,.2+&*;$<,=&,/*),9$,#$4#(&&$),*0

$ E = C I v #4

TX<88V

4"$#$,CI,(0,/*++$-,&"$,$%'0()*02/)$'0)!5,*)-,1#2',MS<,TX<8\V5,(&,(0,;(.$),9:

.C I = 55555 +,

TX<8^V

W$,290$#.$,&"*&,&"$,&#*)0/2)-3/&*)/$,21,&"$,BC!,(0,-(#$/&+:,7#272#&(2)*+,&2,&"$,/2++$/&2#,9(*0 /3##$)&,.-<,!"30,&2,29&*(),*,/2)0&*)&,7#$-(/&*9+$,.*+3$,12#,CI5,4$,)$$-,*,/2)0&*)&,7#$-(/&*9+$ .-<,L()*++:5,4$,)2&$,&"*&,BC!0,"*.$,#$+*&(.$+:,"(;",&#*)0/2)-3/&*)/$,T*0,/2'7*#$-,&2,IJK% LM!05,4"(/",4$,0&3-($-,(),6"*7&$#,^V`,12#,()0&*)/$5,*&,.-,=,?,'@5, C I ! eP#3IZ]? @,;#*7"(/*+,()&$#7#$&*&(2),12#,CI,(0,;(.$),(),L(;<,X<\N5,4"$#$,(&,(0,0"24),&"*&,CI,(0,$S3*+ &2,&"$,0+27$,21,&"$,$- ]v)*,/"*#*/&$#(0&(/,/3#.$,*&,$-,=,.-,T(<$<5,*&,&"$,9(*0,72()&,kV<,!"305

∂ $C I = 55555555555

∂ v )*

TX<8XV $ - =. -

Q

Figure 6.37 [&"+),#2*+,)$&2"#2@#$%+#$,)"'&'$2,#/"0+,#$%+#'3)665'&L")6#(2"0&$&2"8#I#'3)66#'&L")6#v#4#.&$%#) $,&)"L/6),#.)7+@2,3#&'#'/*+,&3*2'+0#2"#$%+#0(#726$)L+#+)*?#!$#L&7+'#,&'+#$2#)#(266+($2,#'&L")6#(/,,+"$#$E-#)6'2 2@ $,&)"L/6),#.)7+@2,3-#'/*+,&3*2'+0#2"#$%+#0(#(/,,+"$#.-?#\+,+-#$E#=#CIv#4-#.%+,+#CI#&'#$%+#'62*+#2@#$%+#$- Qv)* (/,7+#)$#$%+#9&)'#*2&"$#l?

405

406 Chapter 6 Bipolar Junction Transistors (BJTs) !"$,0'*++%0(;)*+,*77#2A('*&(2),('7+($0,G$$7();,&"$,0(;)*+,*'7+(&3-$,0311(/($)&+:,0'*++,&"*& %"4('?$%!8$B8(4B?($E?458?%8'!8'&I%B?M&$!4'(8B4CI4!?8%G8?D48$- Rv)*843"%!4!?$'&8EU(F4@,=)/#$*0% ();,&"$,0(;)*+,*'7+(&3-$,4(++,#$03+&,(),&"$,/2++$/&2#,/3##$)&,"*.();,/2'72)$)&0,)2)+()$*#+: #$+*&$-,&2,v#4<,!"(05,21,/23#0$5,(0,&"$,0*'$,*77#2A('*&(2),&"*&,4$,-(0/300$-,(),&"$,/2)&$A&,21 &"$,*'7+(1($#,&#*)01$#,/3#.$,(),K$/&(2),X<8< !"$,*)*+:0(0,*92.$,03;;$0&0,&"*&,12#,0'*++,0(;)*+0,Tv#4,*,+,V5,&"$,&#*)0(0&2#,9$"*.$0,*0,* .2+&*;$%/2)++$-,/3##$)&,023#/$<,!"$,()73&,72#&,21,&"(0,/2)++$-,023#/$,(0,9$&4$$),9*0$ *)-,$'(&&$#5,*)-,&"$,23&73&,72#&,(0,9$&4$$),/2++$/&2#,*)-,$'(&&$#<,!"$,&#*)0/2)-3/&*)/$,21 &"$,/2)++$-,023#/$,(0,CI5,*)-,&"$,23&73&,#$0(0&*)/$,(0,()1()(&$<,!"$,+*&&$#,(-$*+,7#27$#&:,(0,* #$03+&,21,23#,1(#0&%2#-$#,'2-$+,21,&#*)0(0&2#,27$#*&(2),(),4"(/",&"$,/2++$/&2#,.2+&*;$,"*0,)2 $11$/&,2),&"$,/2++$/&2#,/3##$)&,(),&"$,*/&(.$,'2-$<,@0,4$,"*.$,0$$),(),K$/&(2),X
EXERCISES 6.34 ^'+#EV?#:W?eW>#$2#0+,&7+#$%+#+T*,+''&2"#@2,#CI#&"#EV?#:W?eG>? 6.35 6*+/3+*&$,&"$,.*+3$,21,CI,12#,*,BC!,9(*0$-,*&,.-,d,O<^,'@< Ans. MP#3IZ]

6.5.2 The Base Current and the Input Resistance at the Base !2, -$&$#'()$, &"$, #$0(0&*)/$, 0$$), 9:, v#45, 4$, 1(#0&, $.*+3*&$, &"$, &2&*+, 9*0$, /3##$)&, $), 30(); MS< TX<8PV5,*0,12++240Y

$ . K .$ ) = 555-5 = 555-5 + 555 55555 v β β β + , #4 !"305

$) = .) + $#

TX<8NV

4"$#$,.),(0,$S3*+,&2, . - ⁄ β *)-,&"$,0(;)*+,/2'72)$)&,$#,(0,;(.$),9:

K .$ # = 555 55555 v β + , #4

TX<8EV

C $ # = 55555I v #4

TX<8DV

K390&(&3&();,12#, . - ⁄ + , ,9:,CI,;(.$0

β

!"$,0'*++%0(;)*+,()73&,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#5,&%%P$!C8$!?%8?D48#'B4W,(0,-$)2&$9:,(π,*)-,(0,-$1()$-,*0 v

#4 5 ( π ≡ 55555 $#

TX<^OV

6.5 Small-Signal Operation and Models

c0();,MS<,TX<8DV,;(.$0

β

( π = 55555 CI

TX<^?V

!"30,(π,(0,-(#$/&+:,-$7$)-$)&,2),β,*)-,(0,().$#0$+:,7#272#&(2)*+,&2,&"$,9(*0,/3##$)&,.- <,K390&(% &3&();, 12#, CI, (), MS<, TX<^?V, 1#2', MS<, TX<8^V, *)-, #$7+*/();, .- oβ, 9:, .), ;(.$0, *), *+&$#)*&(.$ $A7#$00(2),12#,(π 5

+ ( π = 55555, .)

TX<^PV

EXERCISE 6.36 I#;<=#)3*6&@&+,#&'#9&)'+0#$2#2*+,)$+#)$#)#(2"'$)"$#(266+($2,#(/,,+"$# . - d P?G #3I#&,,+'*+($&7+#2@ $%+#7)6/+# β ?#!@#$%+#$,)"'&'$2,#3)"/@)($/,+,#'*+(&@&+'# β #$2#,)"L+#@,23#GP#$2#MPP-#L&7+#$%+#+T*+($+0 ,)"L+#2@# C I-# . ) - #)"0# ( π ? Ans. C I ,(0,/2)0&*)&,*&,PO,'@o_`, . ) d KP ,µ@,&2,P<^,µ@`, ( π d M?G,G Ω ,&2,?O,G Ω

6.5.3 The Emitter Current and the Input Resistance at the Emitter !"$,&2&*+,$'(&&$#,/3##$)&,$*,/*),9$,-$&$#'()$-,1#2'

$ . $ $ * = 555-5 = 555-5 + 555E

α

α

α

!"305,

$* = .* + $4

TX<^\V

4"$#$,.*,(0,$S3*+,&2,.- oα,*)-,&"$,0(;)*+,/3##$)&,$4,(0,;(.$),9:

$ . .5 v #4 = 55555* v #4 $ 4 = 555E = 555555555 α α +, +,

TX<^8V

=1,4$,-$)2&$,&"$,0'*++%0(;)*+,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#,&%%P$!C8$!?%8?D484I$??4(,9: (45,(&,/*),9$,-$1()$-,*0, v

#4 5 ( 4 ≡ 55555 $4

TX<^^V

c0();,MS<,TX<^8V,4$,1()-,&"*&,(45,/*++$-,&"$,!"#$$!%-%!(#($'0)!5,(0,;(.$),9:

+ ( 4 = 55555, .*

TX<^XV

α K ( 4 = 55555 !# 55555 CI CI

TX<^NV

62'7*#(02),4(&",MS<,TX<8^V,#$.$*+0,&"*&

407

408 Chapter 6 Bipolar Junction Transistors (BJTs) !"$,#$+*&(2)0"(7,9$&4$$),(π,*)-,(4,/*),9$,123)-,9:,/2'9()();,&"$(#,#$07$/&(.$,-$1()(&(2)0,() MS0<,TX<^OV,*)-,TX<^^V,*0, v #4

= $# (π = $4 (4

!"305

( π = ( $ 4 ⁄ $ # )( 4 4"(/",:($+-0

( π = ( β + K )( 4

TX<^EV

L(;3#$,X<\E,(++30&#*&$0,&"$,-$1()(&(2),21,(π,*)-,(4<

ib $

$ vbe

vbe

r+ #

% vbe ib

% re #

ie

vbe ie

Figure 6.38 !66/'$,)$&"L#$%+#0+@&"&$&2"#2@#(π#)"0#(4?

EXERCISE 6.37 I#;<=#%)7&"L#β# =#KPP#&'#9&)'+0#)$#)#0(#(266+($2,#(/,,+"$#2@#K#3I?#D&"0#$%+#7)6/+#2@#CI-#(4-#)"0#(π#)$ $%+#9&)'#*2&"$? Ans. eP#3IZ]H#25 ΩH#M?G#UΩ

6.5.4 Voltage Gain W$,"*.$,$0&*9+(0"$-,*92.$,&"*&,&"$,&#*)0(0&2#,0$)0$0,&"$,9*0$]$'(&&$#,0(;)*+, v#4,*)-,/*30$0,* 7#272#&(2)*+,/3##$)&,CIv#4,&2,1+24,(),&"$,/2++$/&2#,+$*-,*&,*,"(;",T(-$*++:,()1()(&$V,('7$-*)/$ +$.$+<,=),&"(0,4*:,&"$,&#*)0(0&2#,(0,*/&();,*0,*,.2+&*;$%/2)++$-,/3##$)&,023#/$<,!2,29&*(),*) 23&73&,.2+&*;$,0(;)*+5,4$,'*:,12#/$,&"(0,/3##$)&,&2,1+24,&"#23;",*,#$0(0&2#5,*0,(0,-2)$,(),L(;< X<\XT*V<,!"$),&"$,&2&*+,/2++$/&2#,.2+&*;$,v-*,4(++,9$ v -*

= + -- ] $ - > = + -- ] ( . - + $ E )> = ( + -- ] . - > - ) ] $ E > = + -* ] $ E > -

TX<^DV

6.5 Small-Signal Operation and Models

R$#$,&"$,S3*)&(&:,+-*,(0,&"$,-/,9(*0,.2+&*;$,*&,&"$,/2++$/&2#5,*)-,&"$,0(;)*+,.2+&*;$,(0,;(.$),9: v E4

= ] $ E > - = ] C I v #4 > -

TX
= ( ] C I > - ) v #4 !"30,&"$,.2+&*;$,;*(),21,&"(0,*'7+(1($#,/v,(0 v

E4 5 = ]CI >/ v ≡ 55555

v #4

TX
R$#$, *;*(), 4$, )2&$, &"*&, 9$/*30$, CI, (0, -(#$/&+:, 7#272#&(2)*+, &2, &"$, /2++$/&2#, 9(*0, /3##$)&5 &"$ ;*(),4(++,9$,*0,0&*9+$,*0,&"$,/2++$/&2#,9(*0,/3##$)&,(0,'*-$<,K390&(&3&();,12#,CI,1#2' MS<,TX<8^V,$)*9+$0,30,&2,$A7#$00,&"$,;*(),(),&"$,12#'

.- >5 / v = ] 5555555555 +,

TX
4"(/",(0,(-$)&(/*+,&2,&"$,$A7#$00(2),4$,-$#(.$-,(),K$/&(2),X<8,TMS<,X<\?V<,,,,,

EXERCISE 6.38 !"#$%+#(&,(/&$#2@#D&L?#W?NW:)>-#+)*#&'#)04/'$+0#$2#1&+60#)#0(#(266+($2,#(/,,+"$#2@#K#3I?#[+$#+--#=#KG#]>- =#KP#UΩ-#)"0#β# =#KPP?#D&"0#$%+#726$)L+#L)&"# v E4 ⁄ v #4 ? !@#v#4#=#P?PPG#'&" ω ?#726$-#@&"0#v-:?>#)"0#$):?>? Ans. ] ePP#]Z]H #G#Q#M#'&" ω ?#726$'H#KP#+#M#'&" ω ?#µI

6.5.5 Separating the Signal and the DC Quantities !"$, *)*+:0(0, *92.$, ()-(/*&$0, &"*&, $.$#:, /3##$)&, *)-, .2+&*;$, (), &"$, *'7+(1($#, /(#/3(&, 21 L(;< X<\XT*V,(0,/2'720$-,21,&42,/2'72)$)&0Y,*,-/,/2'72)$)&,*)-,*,0(;)*+,/2'72)$)&<,L2# ()0&*)/$5, v)*,=,+)*,+,v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

RC C ib " vbe /r+ B vbe

$ %

$ vce

$ vbe %

ic " gm vbe

%

E

vbe ie " r e

Figure 6.39 =%+# )3*6&@&+,# (&,(/&$# 2@# D&L?# W?NW:)># .&$%# $%+ 0(# '2/,(+'# :+)*# )"0# +--># +6&3&")$+0# :'%2,$5(&,(/&$+0>?# =%/' 2"61#$%+#'&L")6#(23*2"+"$'#),+#*,+'+"$?#b2$+#$%)$#$%&'#&'#)#,+*5 ,+'+"$)$&2"#2@#$%+#'&L")6#2*+,)$&2"#2@#$%+#;<=#)"0#"2$#)"#)($/)6 )3*6&@&+,#(&,(/&$?

409

410 Chapter 6 Bipolar Junction Transistors (BJTs) /3##$)&,023#/$05,&"$0$,423+-,"*.$,9$$),#$7+*/$-,9:,27$),/(#/3(&0<,Q2&$5,"24$.$#5,&"*&,&"$ /(#/3(&,21,L(;<,X<\D,(0,30$13+,2)+:,(),02,1*#,*0,(&,0"240,&"$,.*#(230,0(;)*+,/3##$)&0,*)-,.2+&% *;$0`,(&,(0,!%?,*),*/&3*+,*'7+(1($#,/(#/3(&5,0()/$,&"$,-/,9(*0,/(#/3(&,(0,)2&,0"24)< L(;3#$,X<\D,*+02,0"240,&"$,$A7#$00(2)0,12#,&"$,/3##$)&,()/#$'$)&0,T$E5,$#5,*)-,$4V,29&*()$4"$),*,0'*++,0(;)*+,v#4,(0,*77+($-<,!"$0$,#$+*&(2)0"(70,/*),9$,#$7#$0$)&$-,9:,*,/(#/3(&<,K3/",*,/(#% /3(&,0"23+-,"*.$,&"#$$,&$#'()*+0[65,B5,*)-,M[*)-,0"23+-,:($+-,&"$,0*'$,&$#'()*+,/3##$)&0,()-(% /*&$-,(),L(;<,X<\D<,!"$,#$03+&();,/(#/3(&,(0,&"$),40U$F'&4!?8?%8?D48?('!B$B?%(8'B8G'(8'B8BI'&&MB$C!'& %"4('?$%!8$B8E%!E4(!45W,*)-,&"30,(&,/*),9$,/2)0(-$#$-,*),$S3(.*+$)&,0'*++%0(;)*+,/(#/3(&,'2-$+<

6.5.6 The Hybrid-π Model @),$S3(.*+$)&,/(#/3(&,'2-$+,12#,&"$,BC!,(0,0"24),(),L(;<,X<8OT*V<,!"(0,'2-$+,#$7#$0$)&0,&"$,BC! *0,*,.2+&*;$%/2)++$-,/3##$)&,023#/$,*)-,$A7+(/(&+:,()/+3-$0,&"$,()73&,#$0(0&*)/$,+22G();,()&2 &"$,9*0$5,(π <,!"$,'2-$+,29.(230+:,:($+-0,$E,=,CIv#4,*)-, $ # = v#4 ⁄ ( π ? ,Q2&,02,29.(2305,"24$.$#5,(0 &"$,1*/&,&"*&,&"$,'2-$+,*+02,:($+-0,&"$,/2##$/&,$A7#$00(2),12#,$4<,!"(0,/*),9$,0"24),*0,12++240Y @&,&"$,$'(&&$#,)2-$,4$,"*.$ v

v

#4 #4 5 + C I v #4 = 55555 5 ( K + CI (π ) $ 4 = 55555 (π (π

v #4 (π 5 ( K + β ) = v #4 ## 55555555555 5 = 55555 (π K+β = v #4 ⁄ ( 4

@,0+(;"&+:,-(11$#$)&,$S3(.*+$)&%/(#/3(&,'2-$+,/*),9$,29&*()$-,9:,$A7#$00();,&"$,/3##$)& 21,&"$,/2)++$-,023#/$,TCIv#4V,(),&$#'0,21,&"$,9*0$,/3##$)&,$#,*0,12++240Y

C I v #4 = C I ( $ # ( π ) = ( C I ( π )$ # = β $ # !"(0,#$03+&0,(),&"$,*+&$#)*&(.$,$S3(.*+$)&%/(#/3(&,'2-$+,0"24),(),L(;<,X<8OT9V<,R$#$,&"$,&#*)% 0(0&2#,(0,#$7#$0$)&$-,*0,*,/3##$)&%/2)++$-,/3##$)&,023#/$5,4(&",&"$,/2)+,/3##$)&,9$();,$#<

ic

ib B

C + vbe –

ic

ib

C

B

rp

+ vbe –

gmvbe

ie

rp

bib

gm = IC /VT rp = b/gm

E

ie (a)

E

Figure 6.40 =.2#'6&L%$61#0&@@+,+"$#7+,'&2"'#2@#$%+#%19,&05π#320+6#@2,#$%+#'3)665'&L")6#2*+,)$&2"#2@#$%+ ;<=?#=%+#+V/&7)6+"$#(&,(/&$#&"#;'<#,+*,+'+"$'#$%+#;<=#)'#)#726$)L+5(2"$,266+0#(/,,+"$#'2/,(+#:)#$,)"'(2"5 0/($)"(+#)3*6&@&+,>-#)"0#$%)$#&"#;&<#,+*,+'+"$'#$%+#;<=#)'#)#(/,,+"$5(2"$,266+0#(/,,+"$#'2/,(+#:)#(/,,+"$ )3*6&@&+,>?

6.5 Small-Signal Operation and Models

!"$,&42,'2-$+0,21,L(;<,X<8O,*#$,0('7+(1($-,.$#0(2)0,21,4"*&,(0,G)24),*0,&"$,":9#(-%π '2-$+<,!"(0,(0,&"$,'20&,4(-$+:,30$-,'2-$+,12#,&"$,BC!< =&, (0, ('72#&*)&, &2, )2&$, &"*&, &"$, 0'*++%0(;)*+, $S3(.*+$)&, /(#/3(&0, 21, L(;<, X<8O, '2-$+, &"$ 27$#*&(2), 21, &"$, BC!, '?8 '8 C$F4!8 #$'B8 "%$!?<, !"(0, 0"23+-, 9$, 29.(230, 1#2', &"$, 1*/&, &"*& &"$ '2-$+,7*#*'$&$#0,CI,*)-,(π,-$7$)-,2),&"$,.*+3$,21,&"$,-/,9(*0,/3##$)&,.- 5,*0,()-(/*&$-,() L(;<,X<8O<,=&,(0,()&$#$0&();,*)-,30$13+,&2,)2&$,&"*&,&"$,'2-$+0,21,L(;<,X<8O,T*V,*)-,T9V,*#$,&"$ 0'*++%0(;)*+,.$#0(2)0,21,&"$,'2-$+0,21,L(;<,X<^T/V,*)-,T-V5,#$07$/&(.$+:<,K7$/(1(/*++:5,290$#.$ &"*&,(π ,(0,&"$,()/#$'$)&*+,#$0(0&*)/$,21,1)<

EXERCISE 6.39 L2#,&"$,'2-$+,(),L(;<,X<8OT9V,0"24,&"*&,$E,=,CIv#488*)-, $ 4 = v #4 ⁄ ( 4 ?

6.5.7 The T Model @+&"23;", &"$,":9#(-%π, '2-$+, T(),2)$,21,(&0, &42,.*#(*)&0,0"24),(),L(;<,X<8OV, /*),9$,30$&2 /*##:,23&,0'*++%0(;)*+,*)*+:0(0,21,*):,&#*)0(0&2#,/(#/3(&5,&"$#$,*#$,0(&3*&(2)0,(),4"(/",*) *+&$#)*&(.$, '2-$+5, 0"24), (), L(;<, X<8?5, (0, '3/", '2#$, /2).$)($)&<, !"(0, '2-$+5, /*++$-, &"$ @ "*2!+5,(0,0"24),(),&42,.$#0(2)0,(),L(;<,X<8?<, !"$,'2-$+,21,L(;<,X<8?T*V,#$7#$0$)&0,&"$ BC!,*0,*,.2+&*;$%/2)++$-,/3##$)&,023#/$,4(&",&"$,/2)+,.2+&*;$,9$();,v#4<,R$#$5,"24$.$#5 &"$,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#5,+22G();,()&2,&"$,$'(&&$#5,(0,$A7+(/(&+:,0"24)<,L#2' L(;<,X<8?T*V,4$,0$$,/+$*#+:,&"*&,&"$,'2-$+,:($+-0,&"$,/2##$/&,$A7#$00(2)0,12#,$E,*)-,$4<,L2#,$# 4$,)2&$,&"*&,*&,&"$,9*0$,)2-$,4$,"*.$,,

C ic

,i e ib B $ vbe

ie

re

%

E (a)

(b)

Figure 6.41 =.2#'6&L%$61#0&@@+,+"$#7+,'&2"'#2@#.%)$#&'#U"2."#)'#$%+#,8I%54@#$%+#;<=?#=%+#(&,(/&$#&" ;'< &'#)#726$)L+5(2"$,266+0#(/,,+"$#'2/,(+#,+*,+'+"$)$&2"#)"0#$%)$#&"#;&<#&'#)#(/,,+"$5(2"$,266+0#(/,,+"$#'2/,(+ ,+*,+'+"$)$&2"?# =%+'+# 320+6'# +T*6&(&$61# '%2.# $%+# +3&$$+,# ,+'&'$)"(+# (4# ,)$%+,# $%)"# $%+# 9)'+# ,+'&'$)"(+# (π @+)$/,+0#&"#$%+#%19,&05π#320+6?

411

412 Chapter 6 Bipolar Junction Transistors (BJTs) v

v

#4 #4 5 ( K ] CI (4 ) $ # = 55555 5 ] C I v #4 = 55555 (4 (4

β 5 #4 #4 5 ( K ] α ) = 55555 5 K ] 55555555555 = 55555 (4 (4 β+K v

v

v

v

#4 #4 5 = 55555 5 = 555555555555555555555 ( β + K )( 4 (π

)'#'%2/60#9+#$%+#()'+? =1,(),&"$,'2-$+,21,L(;<,X<8?T*V,&"$,/3##$)&,21,&"$,/2)++$-,023#/$,(0,$A7#$00$-,(),&$#'0 21,&"$,$'(&&$#,/3##$)&,*0

C I v #4 = C I ( $ 4 ( 4 ) = ( C I ( 4 )$ 4 = α $ 4 4$,29&*(),&"$,*+&$#)*&(.$,!,'2-$+,0"24),(),L(;<,X<8?T9V<,R$#$,&"$,BC!,(0,#$7#$0$)&$-,*0,* /3##$)&%/2)++$-,/3##$)&,023#/$,93&,4(&",&"$,/2)+,0(;)*+,9$();,$4< !$#&'#&"$+,+'$&"L#)"0#/'+@/6#$2#"2$+#$%)$#$%+#320+6'#2@#D&L?#W?eK:)>#)"0#:9>#),+#$%+#'3)665 '&L")6#7+,'&2"'#2@#$%+#320+6'#&"#D&L?#W?G:)>#)"0#:9>-#,+'*+($&7+61?#C*+(&@&()661#29'+,7+#$%)$#(4 &'#$%+#&"(,+3+"$)6#,+'&'$)"(+#2@#1*?

6.5.8 Small-Signal Models of the pnp Transistor @+&"23;",&"$,0'*++%0(;)*+,'2-$+0,(),L(;0<,X<8O,*)-,X<8?,4$#$,-$.$+27$-,12#,&"$,/*0$,21,&"$ !"!,&#*)0(0&2#5,&"$:,*77+:,$S3*++:,4$++,&2,&"$,"!",&#*)0(0&2#,A$?D8!%8ED'!C48$!8"%&'($?$4B<

6.5.9 Application of the Small-Signal Equivalent Circuits =%+# )7)&6)9&6&$1# 2@# $%+# '3)665'&L")6# ;<=# (&,(/&$# 320+6'# 3)U+'# $%+# )")61'&'# 2@# $,)"'&'$2, )3*6&@&+,#(&,(/&$'#)#'1'$+3)$&(#*,2(+''?#=%+#*,2(+''#(2"'&'$'#2@#$%+#@2662.&"L#'$+*'8 1. M+('()*&$,&"$,0(;)*+,023#/$,*)-,-$&$#'()$,&"$,-/,27$#*&();,72()&,21,&"$,BC!,*)-,(),7*#% &(/3+*#,&"$,-/,/2++$/&2#,/3##$)&,.-< 2. 6*+/3+*&$, &"$, .*+3$0, 21, &"$, 0'*++%0(;)*+, '2-$+, 7*#*'$&$#0Y, C I = . - ⁄ + , - , ( π = β ⁄ C I *)-, ( 4 = + , ⁄ . * = α ⁄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

6.5 Small-Signal Operation and Models

Example 6.14 Y+#.&'%#$2#)")61h+#$%+#$,)"'&'$2,#)3*6&@&+,#'%2."#&"#D&L?#W?eM:)>#$2#0+$+,3&"+#&$'#726$)L+#L)&"# v % ⁄ v $ ? I''/3+#β# =#KPP? VCC

10 V

$10 V 2.3 mA

VC

100 k

RBB

3 k&

3k

RC

vo

0.023 mA

vi VBB

$3.1 V

$3 V 100 k&

$0.7 V 2.323 mA

3V

(a )

(b)

Re

RBB

vi

RBB " 100 k& B

$ vi

$ %

vo

$ %

r+

$ vbe

C gm vbe

%

vo RC " 3 k&

E (d)

% (c) Figure 6.42 ET)3*6+#W?Ke8#;'<#)3*6&@&+,#(&,(/&$H#;&<#(&,(/&$#@2,#0(#)")61'&'H#;)<#)3*6&@&+,#(&,(/&$#.&$%#0(#'2/,(+' ,+*6)(+0#91#'%2,$#(&,(/&$'H#;2<-)3*6&@&+,#(&,(/&$#.&$%#$,)"'&'$2,#,+*6)(+0#91#&$'#%19,&05π, '3)665'&L")6#320+6'?

Solution Y+#'%)66#@2662.#$%+#@&7+5'$+*#*,2(+''#2/$6&"+0#)927+8

1. !"$,1(#0&,0&$7,(),&"$,*)*+:0(0,/2)0(0&0,21,-$&$#'()();,&"$,S3($0/$)&,27$#*&();,72()&<,L2#,&"(0,73#% 720$,4$,*003'$,&"*&,v$,=,O,*)-,&"30,29&*(),&"$,-/,/(#/3(&,0"24),(),L(;<,X<8PT9V<,!"$,-/,9*0$,/3#% #$)&,4(++,9$

413

414 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.14 continued

+ )) ] + )* 5 . ) = 55555555555555555555555 > )) N ] P?d ! 5555555555555555 = P?PMN#3I KPP =%+#0(#(266+($2,#(/,,+"$#.&66#9+ . - = β . ) #=#KPP × P?PMN = M?N#3I =%+#0(#726$)L+#)$#$%+#(266+($2,#.&66#9+ + - = + -- ] . - > = +?O,−,P<\,× 3 = +3.1 _ C&"(+#+)#)$#+P?d#]#&'#6+''#$%)"#+- -#&$#@2662.'#$%)$#&"#$%+#V/&+'(+"$#(2"0&$&2"#$%+#$,)"'&'$2,#.&66#9+ 2*+,)$&"L#&"#$%+#)($&7+#320+?#=%+#0(#)")61'&'#&'#&66/'$,)$+0#&"#D&L?#W?eM:9>?

2. R*.();,-$&$#'()$-,&"$,27$#*&();,72()&5,4$,/*),)24,7#2/$$-,&2,-$&$#'()$,&"$,0'*++%0(;)*+,'2-$+ 7*#*'$&$#0Y + MG#3] ( 4 = 55555,5 = 55555555555555555555555555555555555555 = KP?f#Ω .* ( M?N ⁄ P?aa )#3I .M?N#3I 5 = 555555555555555555 = aM#3IZ] C I = 55555 MG#3] +,

β KPP ( π = 555555 = 555555555 = K?Pa#UΩ CI aM 3. U$7+*/();,+)),*)-,+--8,4(&",0"2#&,/(#/3(&0,#$03+&0,(),&"$,/(#/3(&,(),L(;<,X<8PT/V< 4. !2,/*##:,23&,&"$,0'*++%0(;)*+,*)*+:0(05,(&,(0,$S3*++:,/2).$)($)&,&2,$'7+2:,$(&"$#,21,&"$,&42,":9#(-% π5,$S3(.*+$)&%/(#/3(&,'2-$+0,21,L(;<,X<8O,&2,#$7+*/$,&"$,&#*)0(0&2#,(),&"$,/(#/3(&,21,L(;<,X<8PT/V< c0();,&"$,1(#0&,#$03+&0,(),&"$,*'7+(1($#,$S3(.*+$)&,/(#/3(&,;(.$),(),L(;<,X<8PT-V<, 5. I")61'&'#2@#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?eM:0>#*,2(++0'#)'#@2662.'8 (π v #4 = v $ 55555555555555555555 ( π + > )) K?Pa = v $ 5555555555555555 = P?PKK v $ KPK?Pa

TX
!"$,23&73&,.2+&*;$,v%,(0,;(.$),9: v % = ] C I v #4 > -

= ] aM × P?PKK v $ × N = ] N?Pe v $ =%/'#$%+#726$)L+#L)&"#.&66#9+ v

/ v = 5555% = ] N?Pe #]Z] v$

TX
6.5 Small-Signal Operation and Models

Example 6.15 =2#L)&"#32,+#&"'&L%$#&"$2#$%+#2*+,)$&2"#2@#$,)"'&'$2,#)3*6&@&+,'-#.+#.&'%#$2#(2"'&0+,#$%+#.)7+@2,3'#)$#7),5 &2/'#*2&"$'#&"#$%+#(&,(/&$#)")61h+0#&"#$%+#*,+7&2/'#+T)3*6+?#D2,#$%&'#*/,*2'+#)''/3+#$%)$#v$#%)'#)#$,&)"L/6), .)7+@2,3?#D&,'$#0+$+,3&"+#$%+#3)T&3/3#)3*6&$/0+#$%)$#v$#&'#)662.+0#$2#%)7+?#=%+"-#.&$%#$%+#)3*6&$/0+#2@ v$#'+$#$2#$%&'#7)6/+-#L&7+#$%+#.)7+@2,3'#2@#$%+#$2$)6#V/)"$&$&+'#$):?>-#v)*:?>-#$-:?>-#)"0#v-:?>?

Solution B"+#(2"'$,)&"$#2"#'&L")6#)3*6&$/0+#&'#$%+#'3)665'&L")6#)**,2T&3)$&2"-#.%&(%#'$&*/6)$+'#$%)$#v#4#'%2/60#"2$ +T(++0#)92/$#KP#3]?#!@#.+#$)U+#$%+#$,&)"L/6),#.)7+@2,3# v#4#$2#9+#MP#3]#*+)U5$25*+)U#)"0#.2,U#9)(U5 .),0-#EV?#:W?WN>#()"#9+#/'+0#$2#0+$+,3&"+#$%+#3)T&3/3#*2''&96+#*+)U#2@#v$ v #4 KP vt % = 5555555555555 = 5555555555555 = P?aK#]

P?PKK

P?PKK

=2# (%+(U# .%+$%+,# $%+# $,)"'&'$2,# ,+3)&"'# &"# $%+# )($&7+# 320+# .&$%# v$# %)7&"L# )# *+)U# 7)6/+ vt $ = P?aK#]- .+#%)7+#$2#+7)6/)$+#$%+#(266+($2,#726$)L+?#=%+#726$)L+#)$#$%+#(266+($2,#.&66#(2"'&'$#2@#)#$,&)"5 L/6),#.)7+#v%#'/*+,&3*2'+0#2"#$%+#0(#7)6/+#+-#=#N?K#]?#=%+#*+)U#726$)L+#2@#$%+#$,&)"L/6),#.)7+@2,3#.&66 9+ vt % = vt $ × L)&" = P?aK × N?Pe = M?dd#]

!$#@2662.'#$%)$#.%+"#$%+#2/$*/$#'.&"L'#"+L)$&7+-#$%+#(266+($2,#726$)L+#,+)(%+'#)#3&"&3/3#2@#N?K#Q#M?dd = P?NN ]-#.%&(%#&'#62.+,#$%)"#$%+#9)'+#726$)L+#91#6+''#$%)"#P?e#]?#=%/'#$%+#$,)"'&'$2,#.&66#,+3)&"#&"#$%+ )($&7+#320+#.&$%# v$#%)7&"L#)#*+)U#7)6/+#2@#P?aK#]?#b+7+,$%+6+''-#$2#9+#2"#$%+#')@+#'&0+-#.+#.&66#/'+#) '23+.%)$#62.+,#7)6/+#@2,# vt $ #2@#)**,2T&3)$+61#P?f#]-#)'#'%2."#&"#D&L?#W?eN:)>-#)"0#(23*6+$+#$%+#)")61'&' 2@#$%&'#*,296+3#/$&6&h&"L#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?eM:0>?#=%+#'&L")6#(/,,+"$#&"#$%+#9)'+#.&66#9+#$,&)"5 L/6),-#.&$%#)#*+)U#7)6/+# $t# #2@ vt

P?f $ 5 = 5555555555555555555555555 = P?PPf#3I $t# = 5555555555555555555 > )) + ( π KPP + K?Pa =%&'# $,&)"L/6),5.)7+# (/,,+"$# .&66# 9+# '/*+,&3*2'+0# 2"# $%+# V/&+'(+"$# 9)'+# (/,,+"$# .)-# )'# '%2."# &"# D&L? W?eN:9>?#=%+#9)'+Q+3&$$+,#726$)L+#.&66#(2"'&'$#2@#)#$,&)"L/6),5.)7+#(23*2"+"$#'/*+,&3*2'+0#2"#$%+#0( +)*#$%)$#&'#)**,2T&3)$+61#P?d#]?#=%+#*+)U#7)6/+#2@#$%+#$,&)"L/6),#.)7+@2,3#.&66#9+ ( ( π + > ))

K?Pa KPP + K?Pa

π vt #4 = vt $ 55555555555555555555 = P?f 5555555555555555555555555 = f?W#3]

=%+#$2$)6#v)*#&'#'U+$(%+0#&"#D&L?#W?eN:(>? =%+#'&L")6#(/,,+"$#&"#$%+#(266+($2,#.&66#9+#$,&)"L/6),#&"#.)7+@2,3-#.&$%#)#*+)U#7)6/+# t$E #L&7+"#91 t$ E = β t$ # = KPP × P?PPf = P?f#3I

=%&'#(/,,+"$#.&66#9+#'/*+,&3*2'+0#2"#$%+#V/&+'(+"$#(266+($2,#(/,,+"$#.-#:=M?N#3I>-#)'#'%2."#&"#D&L? W?eN:0>? =%+#'&L")6#726$)L+#)$#$%+#(266+($2,#()"#9+#29$)&"+0#91#3/6$&*61&"L#v$#91#$%+#726$)L+#L)&"H#$%)$ &'-# vt % = N?Pe × P?f = M?eN#]

D&L/,+# W?eN:+># '%2.'# )# 'U+$(%# 2@# $%+# $2$)6# (266+($2,# 726$)L+# v-# 7+,'/'# $&3+?# b2$+# $%+# *%)'+# ,+7+,')6 9+$.++"#$%+#&"*/$#'&L")6#v$#)"0#$%+#2/$*/$#'&L")6#v%? D&")661-#.+#29'+,7+#$%)$#+)(%#2@#$%+#$2$)6#V/)"$&$&+'#&'#$%+#'/3#2@#)#0(#V/)"$&$1#:@2/"0#@,23#$%+#0(#(&,5 (/&$#&"#D&L?#W?eM9>-#)"0#)#'&L")6#V/)"$&$1#:@2/"0#@,23#$%+#(&,(/&$#&"#D&L?#W?eM0>?

415

416 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.15 continued vi $0.8 V

vˆ i

0

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417

418 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.16 continued

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419

420 Chapter 6 Bipolar Junction Transistors (BJTs)

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421

422 Chapter 6 Bipolar Junction Transistors (BJTs)

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6.6 Basic BJT Amplifier Configurations

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β ( π = 555555 CI

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423

424 Chapter 6 Bipolar Junction Transistors (BJTs)

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430 Chapter 6 Bipolar Junction Transistors (BJTs) J90$#.$,&"*&,"$#$,&"$,'3+&(7+(/*&(.$,1*/&2#,(0, β - ,4"(/",(0,&"$,#*&(2,21, $ E ,&2, $ # H ,&"(0,'*G$0 0$)0$,9$/*30$,4$,*#$,30();,&"$,#*&(2,21,#$0(0&*)/$0,(),&"$,/2++$/&2#,*)-,&"$,9*0$<,!"$,#$*-$# (0,3#;$-,&2,#$1+$/&,2),&"$0$,$A7#$00(2)0,4"(+$,#$1$##();,&2,L(;<,X<^O< Performing the Analysis Directly on the Circuit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v π #.%&6+#'$&66#)((2/"$&"L#@2,#$%+#+@@+($#2@# ( % ?

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6.6 Basic BJT Amplifier Configurations

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431

432 Chapter 6 Bipolar Junction Transistors (BJTs)

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6.6 Basic BJT Amplifier Configurations

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433

434 Chapter 6 Bipolar Junction Transistors (BJTs) =1,*,+2*-,#$0(0&*)/$, > X ,(0,/2))$/&$-,*&,&"$,*'7+(1($#,23&73&5, / v ,/*),9$,123)-,*0, >X 5 / v d / v% 55555555555555555 >X e >% >>X 5 555555555555555555 5 d ] α 555555555555555 (4 e >4 >X e >> - || > X 5 d ] α 55555555555555555 (4 e >4

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6.6 Basic BJT Amplifier Configurations

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436 Chapter 6 Bipolar Junction Transistors (BJTs)

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!"(0,$S3*&(2), ()-(/*&$0, &"*&, &"$, 2.$#*++, ;*()5, &"23;", +24$#,&"*),2)$5, /*), 9$, /+20$,&2, 2)$, (1 ( β e K )> X ,(0,+*#;$#,2#,/2'7*#*9+$,(),.*+3$,&2, > '&L ? ,!"(0,*;*(),/2)1(#'0,&"$,*/&(2),21,&"$,$'(&% &$#,12++24$#,(),-$+(.$#();,*,+*#;$,7#272#&(2),21, v '&L ,&2,*,+24%.*+3$-,+2*-,#$0(0&*)/$, > X ,$.$) &"23;", > '&L ,/*),9$,'3/",+*#;$#,&"*), > X<,!"$,G$:,72()&,(0,&"*&, > X ,(0,'3+&(7+($-,9:, ( β e K ) KW !"#*,)($&(+-#$%+#7)6/+#2@# / v% #.&66#9+#62.+,#$%)"-#9/$#(62'+#$2#/"&$1?#D2,#2"+#$%&"L-# ( % - #.%&(%#.+#%)7+ "+L6+($+0-#.2/60#3)U+# / v% d ( % ⁄ ( ( % e ( 4 )?#I6'2-#)'#)6,+)01#3+"$&2"+0-#$%+,+#3)1#9+#2$%+,#,+'&'$)"(+' :+?L?-#@2,#9&)'&"L#*/,*2'+'>#)$$)(%+0#$2#$%+#+3&$$+,?

441

442 Chapter 6 Bipolar Junction Transistors (BJTs) Rsig

Rsig / (b$1)

(b$1) re

vsig

$ %

(b$1) RL

re

$

vsig

$ %

RL

vo %

(a)

$ vo %

(b)

Figure 6.56 C&3*6+#+V/&7)6+"$#(&,(/&$'#@2,#$%+#+3&$$+,#@2662.+,#29$)&"+0#91#;'<#,+@6+($&"L#(4#)"0#>X#$2#$%+ 9)'+#'&0+-#)"0#;&<#,+@6+($&"L#v'&L#)"0#>'&L#$2#$%+#+3&$$+,#'&0+?#b2$+#$%)$#$%+#(&,(/&$#&"#;&<#()"#9+#29$)&"+0#@,23 $%)$#&"#;'<#91#'&3*61#0&7&0&"L#)66#,+'&'$)"(+'#91#T β e K>?

9$12#$,(&,(0,a7#$0$)&$-,&2,&"$,023#/$ X ,&2,&"$,9*0$,0(-$<,!"$,2.$#*++,.2+&*;$,;*() Q v ≡ v % ⁄ v '&L ,/*),9$,-$&$#'()$-,-(#$/&+:,*)-,.$#:,0('7+:,1#2',&"(0,/(#/3(&,9:,30();,&"$,.2+&*;$ -(.(-$#,#3+$<,!"$,#$03+&,(0,&"$,$A7#$00(2),12#, Q v ,*+#$*-:,;(.$),(),MS<,TX '&L ,1#2',&"$,9*0$,0(-$,&2 &"$,$'(&&$#,0(-$<,=),&"(0,#$1+$/&(2)5, v '&L ,-2$0,)2&,/"*);$5,93&, > '&L ,(0,-(.(-$-,9:, β e K<,!"305 4$,$(&"$#,#$1+$/&,&2,&"$,9*0$,0(-$,*)-,29&*(),&"$,/(#/3(&,(),L(;<,X<^XT*V,2#,#$1+$/&,&2,&"$,$'(&&$# 0(-$,*)-,29&*(),&"$,/(#/3(&,(),L(;<,X<^XT9V<,L#2',&"$,+*&&$#5, Q v ,/*),9$,123)-,*0, v >X Q v ≡ 555555%5 d 5555555555555555555555555555555555555555555555555555 5 v '&L > X e ( 4 e > '&L ⁄ ( β e K )

TX
J90$#.$,&"*&,&"(0,$A7#$00(2),(0,&"$,0*'$,*0,&"*&,(),MS<,TX '&L ,9:,&"$,1*/&2#, ( β e K ) ,9$12#$,a7#$0$)&();,(&,&2,&"$,+2*-,#$0(0&*)/$, > XbY,*) ('7$-*)/$,&#*)012#'*&(2),&"*&,"*0,&"$,0*'$,9311$#();,$11$/&< @&,&"(0,72()&,(&,(0,('72#&*)&,&2,)2&$,&"*&,*+&"23;",&"$,$'(&&$#,12++24$#,-2$0,)2&,7#2.(-$ .2+&*;$,;*(),(&,"*0,*,/3##$)&,;*(),21, β e K< Thévenin Representation of the Emitter-Follower Output I# 32,+# L+"+,)6# ,+*,+5 '+"$)$&2"# 2@# $%+# +3&$$+,5@2662.+,# 2/$*/$# &'# '%2."# &"# D&L?# W?Gd:)>?# \+,+# Q v% # &'# $%+# 27+,)66 2*+"5(&,(/&$# 726$)L+# L)&"# $%)$# ()"# 9+# 29$)&"+0# 91# '+$$&"L# > X d ∞ # &"# $%+# (&,(/&$# 2@# D&L? W?GW:9>-#)'#&66/'$,)$+0#&"#D&L?#W?Gd:9>?#=%+#,+'/6$#&'# Q v% d K?#=%+#2/$*/$#,+'&'$)"(+# > 2/$ #&'#5$GM G4(4!?8@,23# > % ? #=2#0+$+,3&"+# > 2/$ #.+#'+$# v '&L #$2#h+,2#:,)$%+,#$%)"#'+$$&"L# v $ #$2#h+,2>?#IL)&" .+#()"#/'+#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?GW:9>#$2#02#$%&'-#)'#&66/'$,)$+0#&"#D&L?#W?Gd:(>?#Y+ '++#$%)$ > '&L > 2/$## d ( 4 e 55555555555 5 βeK

TX
6.6 Basic BJT Amplifier Configurations

443

Rsig / (b$1) Rout $ Gvo vsig

RL

$ %

vsig

vo

re $ %

%

Gvo " 1

$ vo " vsig %

(b)

(a)

Rsig / (b$1)

Rsig re E

Rsig Rout " re $ % b$1 (c)

Rsig Rout " re$% (b$1)

re vsig

$ %

RL

Rin " (b$1) (re$RL) (d)

Figure 6.57 ;'<#=%p7+"&"#,+*,+'+"$)$&2"#2@#$%+#2/$*/$#2@#$%+#+3&$$+,#@2662.+,?#:&>#B9$)&"&"L#Qv%#@,23#$%+ +V/&7)6+"$#(&,(/&$#&"#D&L?#W?GW:9>?#;)<#B9$)&"&"L#>2/$#@,23#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?GW:9>#.&$%#v'&L#'+$#$2 h+,2?-;2<#=%+#+3&$$+,#@2662.+,#.&$%#>&"#)"0#>2/$#0+$+,3&"+0#'&3*61#91#622U&"L#&"$2#$%+#&"*/$#)"0#2/$*/$#$+,5 3&")6'-#,+'*+($&7+61?

D&")661-# .+# '%2.# &"# D&L?# W?Gd:0># $%+# +3&$$+,5@2662.+,# (&,(/&$# $2L+$%+,# .&$%# &$'# > &" # )"0 > 2/$ ? #B9'+,7+#$%)$# > &" #&'#0+$+,3&"+0#91#,+@6+($&"L# ( 4 #)"0# > X #$2#$%+#9)'+#'&0+#:91#3/6$&*615 &"L# $%+&,# 7)6/+'# 91# β e K>?# =2# 0+$+,3&"+# > 2/$ - # L,)9# %260# 2@# $%+# +3&$$+,# )"0# .)6U# :2,# 4/'$ 622Uj>#9)(U.),0#.%&6+# v '&L d P? #s2/#.&66#'++# ( 4 #&"#'+,&+'#.&$%# > '&L - #.%&(%#9+()/'+#&$#&'#&" $%+#9)'+#3/'$#9+#0&7&0+0#91#( β e K )? W$,)2&$,&"*&,3)+(G$,&"$,6M,*)-,6B,*'7+(1($#0,4$,0&3-($-,$*#+($#5,&"$,$'(&&$#,12++24$#,(0,!%? 3)(+*&$#*+<,!"(0,(0,'*)(1$0&$-,9:,&"$,1*/&,&"*&, > &" ,-$7$)-0,2), > X ,*)-, > 2/$ ,-$7$)-0,2), > '&L ?

Example 6.19 !$#&'#,+V/&,+0#$2#0+'&L"#)"#+3&$$+,#@2662.+,#$2#&3*6+3+"$#$%+#9/@@+,#)3*6&@&+,#2@#D&L?#W?Ge:(>?#C*+(&@1#$%+ ,+V/&,+0#9&)'#(/,,+"$# . * #)"0#$%+#3&"&3/3#7)6/+#$%+#$,)"'&'$2,# β #3/'$#%)7+?#X+$+,3&"+#$%+#3)T&3/3 )662.+0#7)6/+#2@# v B$C #&@# v π #&'#$2#9+#6&3&$+0#$2#G#3]#&"#2,0+,#$2#29$)&"#,+)'2")961#6&"+),#2*+,)$&2"?#Y&$% v '&L# d MPP #3]-#0+$+,3&"+#$%+#'&L")6#726$)L+#)$#$%+#2/$*/$#&@# > X #&'#(%)"L+0#$2#M#U Ω- #)"0#$2#P?G#U Ω?

444 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.19 continued

Rsig " 100 k& Ro " 10 & vo

vsig

$ % " 200 mV

RL " 1 k&

Rin " 100 k&

Figure 6.58 F&,(/&$#@2,#ET)3*6+#W?Ka?#

Solution =%+#+3&$$+,5@2662.+,#(&,(/&$#&'#'%2."#&"#D&L?#W?Gf?#=2#29$)&"# > % d KP#Ω- #.+#9&)'#$%+#$,)"'&'$2,#$2 29$)&"# ( 4 d KP#Ω? #=%/'+ KP#Ω d 55555,5 .* . * d M?G ,'@ !"$,()73&,#$0(0&*)/$, > &" ,4(++,9$ > &" d ( β e K ) ( ( 4 e > X ) KPP d ( β e K ) ( P?PK e K )

=%/'-#$%+#;<=#'%2/60#%)7+#)# β #.&$%#)#3&"&3/3#7)6/+#2@#af?#I#%&L%+,# β #.2/60#297&2/'61#9+#9+"+@&(&)6? =%+#27+,)66#726$)L+#L)&"#()"#9+#0+$+,3&"+0#@,23 v >X Q v ≡ 555555%5 d 5555555555555555555555555555555555555555 5 v '&L > '&L > X e ( 4 e 5555555555555555 5 (β e K) I''/3&"L# β d KPP -#$%+#7)6/+#2@# Q v #29$)&"+0#&'

Q v d P?G =%/'#.%+"# v '&L d MPP #3]-#$%+#'&L")6#)$#$%+#2/$*/$#.&66#9+#KPP#3]?#C&"(+#$%+#KPP#3]#)**+),'#)(,2''#$%+ K5U Ω #62)0-#$%+#'&L")6#)(,2''#$%+#9)'+Q+3&$$+,#4/"($&2"#()"#9+#@2/"0#@,23 v% v π d 555555 × ( 4

>X

KPP d 555555555555 × KP d K #3] KPPP !@# vt π d G#3]#$%+"# v '&L #()"#9+#&"(,+)'+0#91#)#@)($2,#2@#G-#,+'/6$&"L#&"# vt '&L d K#]? =2#29$)&"# v % #)'#$%+#62)0#&'#7),&+0-#.+#/'+#$%+#=%p7+"&"#+V/&7)6+"$#2@#$%+#+3&$$+,#@2662.+,-#'%2."#&" D&L?#W?Gd:)>#.&$%# Q v% d K #)"0 > '&L KPP > 2/$## d 555555555555 e ( 4 d 555555555 e P?PK d K#UΩ KPK βeK

6.6 Basic BJT Amplifier Configurations

445

$2#29$)&" > > X e > 2/$

X v % d v '&L 555555555555555555555

D2,# > X d M#UΩM MeK

v % d MPP#3] × 555555555555 d KNN?N#3]

)"0#@2,# > X d P?G#UΩP?G P?G e K

v % d MPP#3] × 5555555555555555 d WW?d#3]

EXERCISE 6.46 I"#+3&$$+,#@2662.+,#/$&6&h+'#)#$,)"'&'$2,#.&$%# β d KPP #)"0#&'#9&)'+0#)$# . - d G#3I?#!$#2*+,)$+'#9+5 $.++"#)#'2/,(+#%)7&"L#)#,+'&'$)"(+#2@#KP#U Ω #)"0#)#62)0#2@#K#U Ω? #D&"0# > &" - # Q v% - # > 2/$ - #)"0# Q v ? Y%)$#&'#$%+#*+)U#)3*6&$/0+#2@# v '&L #$%)$#,+'/6$'#&"# v π #%)7&"L#)#*+)U#)3*6&$/0+#2@#G#3]_#D&"0#$%+ ,+'/6$&"L#*+)U#)3*6&$/0+#)$#$%+#2/$*/$? Ans. KPK?G#U Ω H#K#]Z]H#KPe# Ω H#P?aK#]Z]H#K?K#]H#K#]

6.6.7 Summary and Comparisons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

446 Chapter 6 Bipolar Junction Transistors (BJTs) ?

TABLE 6.5 Characteristics of BJT Amplifiers)-#9-#(

> &" F2332" +3&$$+, :D&L?#W?GP>

( β e K )( 4

F2332" +3&$$+,#.&$%#

( β e K )( (4 e >4 )

/ v% ]CI >-

>% >-

/v ] C I ( > - || > X ) > - || > X 5 ] α 55555555555555555 (4

>4

CI >5 ] 55555555555555555555 K e CI >4

>-

] C I ( > - || > X ) 55555555555555555555555555555555 K e CI >4

Qv > - || > X 5 ] β 555555555555555555555555555555555555 > '&L e ( β e K )( 4 > - || > X 5 ] β 55555555555555555555555555555555555555555555555555555 > '&L e ( β e K ) ( ( 4 e > 4 )

> - || > X 5 ] α 55555555555555555 (4 e >4

:D&L?#W?GM>

F2332"#9)'+ :D&L?#W?GN>

(4

CI >-

>-

E3&$$+, @2662.+, :D&L?#W?GG>

( β e K )( (4 e >X )

K

(4

> || > > '&L e ( 4

C I ( > - || > X ) > - || > X 5 α 55555555555555555 (4

X 5 α 555555555555555555

>X 5555555555555555 >X e (4

>X 5555555555555555555555555555555555555555555555555555 5 > X e ( 4 e > '&L ⁄ ( β e K ) # Q v% d K

> '&L > 2/$ d ( 4 e 55555555555 5 βeK ' #

#D2,#$%+#&"$+,*,+$)$&2"#2@#>I-#/v%-#)"0#>%#,+@+,#$2#D&L?#W?ea? #=%+#;<=#2/$*/$#,+'&'$)"(+#(%#%)'#9++"#"+L6+($+0-#.%&(%#&'#*+,3&$$+0#&"#$%+#0&'(,+$+5(&,(/&$#)3*6&@&+,'#'$/0&+0#&"#$%&'#(%)*$+,?#D2,#&"$+L,)$+05(&,(/&$#)3*6&5

@&+,'#:F%)*$+,#d>-#( %#3/'$#)6.)1'#9+#$)U+"#&"$2#)((2/"$? E #C+$$&"L#β = ∞ ##(α = 1)#)"0#,+*6)(&"L8(4#.&$%#KZCI-#>-#.&$%#>1-#)"0#>4#.&$%#>B#,+'/6$'#&"#$%+#(2,,+'*2"0&"L#@2,3/6)'#@2,#ABCDE=#)3*6&@&+,'#:=)96+#G?e>?

6.7 Biasing in BJT Amplifier Circuits R*.();,0&3-($-,&"$,.*#(230,/2)1(;3#*&(2)0,21,BC!,*'7+(1($#05,4$,)24,*--#$00,&"$,('72#&*)& S3$0&(2),21,9(*0();,*)-,(&0,#$+*&(2)0"(7,&2,0'*++%0(;)*+,9$"*.(2#<,!"$,9(*0();,7#29+$',(0,&"*& 21,$0&*9+(0"();,*,/2)0&*)&,-/,/3##$)&,(),&"$,/2++$/&2#,21,&"$,BC!<,!"(0,/3##$)&,"*0,&2,9$,/*+/3% +*9+$5,7#$-(/&*9+$5,*)-,()0$)0(&(.$,&2,.*#(*&(2)0,(),&$'7$#*&3#$,*)-,&2,&"$,+*#;$,.*#(*&(2)0,() &"$,.*+3$,21,β,$)/23)&$#$-,*'2);,&#*)0(0&2#0,21,&"$,0*'$,&:7$<,@)2&"$#,('72#&*)&,/2)0(-$#% *&(2),(),9(*0,-$0(;),(0,+2/*&();,&"$,-/,9(*0,72()&,(),&"$,$- ]v-*,7+*)$,&2,*++24,12#,'*A('3' 23&73&,0(;)*+,04();,T0$$,&"$,-(0/300(2),(),K$/&(2),X<8 ) - ,(0,*+02,)2&,*,#$/2''$)-$-,*77#2*/"<,R$#$,&"$ &:7(/*++:,+*#;$,.*#(*&(2)0,(),&"$,.*+3$,21,β,*'2);,3)(&0,21,&"$,0*'$,-$.(/$,&:7$,4(++,#$03+&,() /2##$072)-();+:,+*#;$,.*#(*&(2)0,(),.-,*)-,"$)/$,(),+-*<

6.7 Biasing in BJT Amplifier Circuits

VCC

VCC

RB1

RB

RC

RC IC

IC IB $ RB2

VCE

VCE $

IB

VBE

VBE %

%

(b)

(a)

Figure 6.59 =.2#297&2/'#'(%+3+'#@2,#9&)'&"L#$%+#;<=8#;'<#91#@&T&"L# +)*H#;&<#91#@&T&"L#.)?#;2$%#,+'/6$ &" .&0+# 7),&)$&2"'# &"# .-# )"0# %+"(+# &"# +-*# )"0# $%+,+@2,+# ),+# (2"'&0+,+0# $2# 9+# R9)0?S# b+&$%+,# '(%+3+# &' ,+(233+"0+0?

6.7.1 The Classical Discrete-Circuit Bias Arrangement L(;3#$, X?5,>P<,=),*--(&(2)5,*,#$0(0&2#,>*,(0,/2))$/&$-,&2,&"$,$'(&&$#< VCC

VBB " VCC

%

R2 R1 $ R2

& RC

RC

R1

VCC

IB RB " R1 $ R2

R2

RE

(a)

L

IC

IE RE

(b)

Figure 6.60 F6)''&()6# 9&)'&"L# @2,# ;<='# /'&"L# )# '&"L6+# *2.+,# '/**618# ;'<# (&,(/&$H# ;&<# (&,(/&$# .&$%# $%+ 726$)L+#0&7&0+,#'/**61&"L#$%+#9)'+#,+*6)(+0#.&$%#&$'#=%p7+"&"#+V/&7)6+"$?

L(;3#$,X
>M 5+ + )) = 5555555555555555 > K + > M --

TX
447

448 Chapter 6 Bipolar Junction Transistors (BJTs) >K >M 5 > ) = 5555555555555555 >K + >M

TX
!"$,/3##$)&,.*,/*),9$,-$&$#'()$-,9:,4#(&();,*,q(#/""211,+227,$S3*&(2),12#,&"$,9*0$]$'(&&$#] ;#23)-,+2275,+*9$+$-,F5,*)-,0390&(&3&();, . ) = . * ⁄ ( β + K ) 8

+ )) ] + )* 5 . * = 555555555555555555555555555555555555555 >* + >) ⁄ ( β + K )

TX
!2,'*G$,.*,()0$)0(&(.$,&2,&$'7$#*&3#$,*)-, β,.*#(*&(2)5?N,4$,-$0(;),&"$,/(#/3(&,&2,0*&(01:,&"$ 12++24();,&42,/2)0&#*()&0Y

+)) #!#+)* > > *# ! 55555555555 # )5 β+K

TX
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
;&)'#0+'&L"#'++U'#$2#'$)9&6&h+#+&$%+,#.*#2,#.-#'&"(+#.-#=#α.*#)"0#α#7),&+'#7+,1#6&$$6+?#=%)$#&'-#)#'$)96+#.* .&66#,+'/6$#&"#)"#+V/)661#'$)96+#.--#)"0#7&(+#7+,')? Kf !@#$%+#&"*/$#'&L")6#&'#(2/*6+0#$2#$%+#$,)"'&'$2,#9)'+-#$%+#$.2#9&)'#,+'&'$)"(+'#>?,*)-8>P#+@@+($&7+61#)**+), &"#*),)66+6#9+$.++"#$%+#9)'+#)"0#L,2/"0?#=%/'-#62.#7)6/+'#@2,#>?,*)-8>P,.&66#,+'/6$#&"#62.+,&"L#>&"? Kd

6.7 Biasing in BJT Amplifier Circuits

449

Example 6.20 Y+#.&'%#$2#0+'&L"#$%+#9&)'#"+$.2,U#2@#$%+#)3*6&@&+,#&"#D&L?#W?WP#$2#+'$)96&'%#)#(/,,+"$#.*#=#K#3I#/'&"L#) *2.+,#'/**61#+--# =# +KM#]?#=%+#$,)"'&'$2,#&'#'*+(&@&+0#$2#%)7+#)#"23&")6#β#7)6/+#2@#KPP?

Solution Y+#'%)66#@2662.#$%+#,/6+#2@#$%/39#3+"$&2"+0#)927+#)"0#)662()$+#2"+5$%&,0#2@#$%+#'/**61#726$)L+#$2#$%+ 726$)L+#0,2*#)(,2''#>M#)"0#)"2$%+,#2"+5$%&,0#$2#$%+#726$)L+#0,2*#)(,2''#>- -#6+)7&"L#2"+5$%&,0#@2,#*2''&96+ "+L)$&7+#'&L")6#'.&"L#)$#$%+#(266+($2,?#=%/'+ ) = +e#] + * = e ] + )* #!#N?N#] *)-,>*,(0,-$&$#'()$-,1#2' + N?N > * = 55555*5 = 5555555 = N?N#UΩ .* K L#2',&"$,-(0/300(2),*92.$,4$,0$+$/&,*,.2+&*;$,-(.(-$#,/3##$)&,21, P?K. * = P?K × K = P?K#3I? ,Q$;+$/&(); &"$,9*0$,/3##$)&5,4$,1()KM > K + > M = 5555555 = KMP#UΩ P?K *)>M 55555555555555555 5+ = e#] > K + > M -!"30,>P,=,8O,GΩ,*)-,>?,=,EO,GΩ<, @&,&"(0,72()&5,(&,(0,-$0(#*9+$,&2,1()-,*,'2#$,*//3#*&$,$0&('*&$,12#,.*5,&*G();,()&2,*//23)&,&"$,)2)>$#2 9*0$,/3##$)&<,c0();,MS<,TX*,1#2',\<\,GΩ,9:,&"$,'*;)(% &3-$,21,&"$,0$/2)-,&$#',(),&"$,-$)2'()*&2#,TO*,(),&"(0,/*0$ 423+-,9$,>*,=,\,GΩ5,4"(/",#$03+&0,(),.*,=,??,=,E,GΩ,*)-,>P,=,8,GΩ<,W$,0"*++,#$1$#,&2,&"$,/(#/3(&,30();,&"$0$,+*&&$#,.*+3$0,*0 -$0(;),P5,12#,4"(/",&"$,*/&3*+,.*+3$,21,.*,30();,&"$,()(&(*+,.*+3$,21,>*,21,\<\,GΩ,4(++,9$ e ] P?d . * = 555555555555555555555555555 = P?aa#!#K#3I N?N + P?PMd ?D

I6$%2/L%#,+0/(&"L# >*88 ,+'$2,+'# .*#$2#$%+#0+'&L"#7)6/+#2@# ?,'@-#&$#02+'#"2$#'267+#$%+#*,296+3#2@#$%+ 0+*+"0+"(+#2@#$%+#7)6/+#2@#.*#2"#β. C++#ET+,(&'+#W?ed? Ka

450 Chapter 6 Bipolar Junction Transistors (BJTs)

Example 6.20 continued

=),&"(0,/*0$5,-$0(;),P5,4$,)$$-,)2&,/"*);$,&"$,.*+3$,21,>*< D&")661-#$%+#7)6/+#2@#>-#()"#9+#0+$+,3&"+0#@,23# KM ] + > - = 55555555555555555-5 .C/9'$&$/$&"L# . - = α . * #= P?aa × K = P?aa#3I#!#K#3I #,+'/6$'-#@2,#92$%#0+'&L"'-#&" KM ] f > - = 555555555555555 = e#UΩ K

EXERCISE 6.47 D2,#0+'&L"#K#&"#ET)3*6+#W?MP-#()6(/6)$+#$%+#+T*+($+0#,)"L+#2@#.*#&@#$%+#$,)"'&'$2,#/'+0#%)'#β#&"#$%+ ,)"L+#2@#GP#$2#KGP?#ET*,+''#$%+#,)"L+#2@#.*#)'#)#*+,(+"$)L+#2@#$%+#"23&")6#7)6/+#:.*#!#K#3I>#295 $)&"+0#@2,#β =#KPP?#J+*+)$#@2,#0+'&L"#M? Ans. D2,#0+'&L"#K8#P?ae#3I#$2#K?Pe#3I-#)#KPo#,)"L+H#@2,#0+'&L"#M8#P?afe#3I#$2#P?aaG#3I-#)#K?Ko ,)"L+?

6.7.2 A Two-Power-Supply Version of the Classical Bias Arrangement @, 02'$4"*&, 0('7+$#, 9(*0, *##*);$'$)&, (0, 7200(9+$, (1, &42, 724$#, 0377+($0, *#$, *.*(+*9+$5, *0 0"24),(),L(;<,X
+ ** ] + )* . * = 5555555555555555555555555555555555555555 , >* + >) ⁄ ( β + K )

TX
Figure 6.61 ;&)'&"L# $%+# ;<=# /'&"L# $.2# *2.+,# '/**6&+'?# J+'&'$2,# >)# &' "++0+0#2"61#&@#$%+#'&L")6#&'#$2#9+#()*)(&$&7+61#(2/*6+0#$2#$%+#9)'+?#B$%+,5 .&'+-#$%+#9)'+#()"#9+#(2""+($+0#0&,+($61#$2#L,2/"0-#2,#$2#)#L,2/"0+0#'&L")6 '2/,(+-#,+'/6$&"L#&"#)632'$#$2$)6#β 5&"0+*+"0+"(+#2@#$%+#9&)'#(/,,+"$?

6.7 Biasing in BJT Amplifier Circuits

!"(0,$S3*&(2),(0,(-$)&(/*+,&2,MS<,TX),/*),9$,$+('()*&$-,*+&2;$&"$#< J),&"$,2&"$#,"*)-5,(1,&"$,()73&,0(;)*+,(0,&2,9$,/237+$-,&2,&"$,9*0$5,&"$),>),(0,)$$-$-<,W$,0"*++ 0&3-:,/2'7+$&$,/(#/3(&0,21,&"$,.*#(230,BC!,*'7+(1($#,/2)1(;3#*&(2)0,(),K$/&(2),X
EXERCISE D6.48 =%+#9&)'#),,)"L+3+"$#2@#D&L?#W?WK#&'#$2#9+#/'+0#@2,#)#(2332"59)'+#)3*6&@&+,?#X+'&L"#$%+#(&,(/&$ $2#+'$)96&'%#)#0(#+3&$$+,#(/,,+"$#2@#K#3I#)"0#*,27&0+#$%+#%&L%+'$#*2''&96+#726$)L+#L)&"#.%&6+#)65 62.&"L#@2,#)#3)T&3/3#'&L")6#'.&"L#)$#$%+#(266+($2,#2@#±M#]?#^'+#+KP5]#)"0#−G5]#*2.+,#'/**6&+'? Ans. >),=,O`,>*,=,8<\,GΩ`,>-,=,E<8,GΩ

6.7.3 Biasing Using a Collector-to-Base Feedback Resistor L(;3#$, X),/2))$/&$-,9$&4$$),&"$,/2++$/% &2#,*)-,&"$,9*0$<,U$0(0&2#,>),7#2.(-$0,)$;*&(.$,1$$-9*/G5,4"(/","$+70,&2,0&*9(+(>$,&"$,9(*0 72()&,21,&"$,BC!<,W$,0"*++,0&3-:,1$$-9*/G,12#'*++:,(),6"*7&$#,?O< @)*+:0(0,21,&"$,/(#/3(&,(0,0"24),(),L(;<,X
+ -- = . * > - + . ) > ) + + )* .* 5 > + + )* = . * > - + 55555555555 β+K ) !"30,&"$,$'(&&$#,9(*0,/3##$)&,(0,;(.$),9:

+ -- ] + )* 5 . * = 555555555555555555555555555555555555555 >- + >) ⁄ ( β + K )

(a)

iE is sum on top and on bottom all can do KCL

TX
(b)

Figure 6.62 ;'<#I#(2332"5+3&$$+,#$,)"'&'$2,#)3*6&@&+,#9&)'+0#91#)#@++09)(U#,+'&'$2,#>)?#;&<#I")61'&'#2@ $%+#(&,(/&$#&"#;'
451

452 Chapter 6 Bipolar Junction Transistors (BJTs) =&,(0,()&$#$0&();,&2,)2&$,&"*&,&"(0,$S3*&(2),(0,(-$)&(/*+,&2,MS<,TX-,#$7+*/$0,>*<,=&,12++240,&"*&,&2 29&*(), *, .*+3$, 21, .*, &"*&, (0,()0$)0(&(.$, &2, .*#(*&(2),21, β5,4$, 0$+$/&, > ) ⁄ ( β + K ) #*#> - ?,Q2&$5 "24$.$#5,&"*&,&"$,.*+3$, 21,>),-$&$#'()$0,&"$,*++24*9+$,)$;*&(.$,0(;)*+, 04();,*&,&"$,/2++$/&2# 0()/$

>) 5, + -) = . ) > ) = . * 55555555555 β+K

TX
EXERCISE D6.49 X+'&L"#$%+#(&,(/&$#2@#D&L?#W?WM#$2#29$)&"#)#0(#+3&$$+,#(/,,+"$#2@#K#3I-#3)T&3/3#L)&"-#)"0#)#±M5] '&L")6#'.&"L#)$#$%+#(266+($2,H#$%)$#&'-#0+'&L"#@2,#+-*#=#+M?N#]?#[+$#+--#=#KP#]#)"0#β# =#KPP? Ans. >),=,?XP,GΩ`,>-,=,N),=,?XO,GΩ,*)-,>-,=,N<^,GΩ<,!"(0,#$03+&0,(),.*,=,?
6.7.4 Biasing Using a Constant-Current Source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β,.*+3$05,4$,/*) )$;+$/&,&"$(#,9*0$,/3##$)&0<,!"30,&"$,/3##$)&,&"#23;",V?,4(++,9$,*77#2A('*&$+:,$S3*+,&2,.UML5

+ -- ] ( ] + ** ) ] + )* 5 . JED = 55555555555555555555555555555555555555555555555 >

0.7

TX
VCC IREF

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Q2

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(b)

Figure 6.63 ;'<#I#;<=#9&)'+0#/'&"L#)#(2"'$)"$5(/,,+"$#'2/,(+#.?#;&<#F&,(/&$#@2,#&3*6+3+"$&"L#$%+#(/,,+"$ '2/,(+#.?

6.8 Discrete-Circuit BJT Amplifiers

Q245,0()/$,V?,*)-,VP,"*.$,&"$,0*'$,+)*5,&"$(#,/2++$/&2#,/3##$)&0,4(++,9$,$S3*+5,#$03+&();,(),

+ -- + + ** ] + )* . = . JED = 55555555555555555555555555555555555555 >

TX
Q$;+$/&();,&"$,M*#+:,$11$/&,(),VP5,&"$,/2++$/&2#,/3##$)&,4(++,#$'*(),/2)0&*)&,*&,&"$,.*+3$ ;(.$),9:,&"(0,$S3*&(2),*0,+2);,*0,VP,#$'*()0,(),&"$,*/&(.$,#$;(2)<,!"(0,/*),9$,;3*#*)&$$-,9: G$$7();,&"$,.2+&*;$,*&,&"$,/2++$/&2#5,+5,;#$*&$#,&"*),&"*&,*&,&"$,$'(&&$#,T−+**V,9:,*&,+$*0&,O<\_< !"$,/2))$/&(2),21,V?,*)-,VP,(),L(;<,X
EXERCISE 6.50 D2,#$%+#(&,(/&$#&"#D&L?#W?WN:)>#.&$%#+--#=#KP#]-#.#=#K#3I-#β#=#KPP-#>)#=#KPP#UΩ-#)"0#>-#=#d?G#UΩ-#@&"0 $%+#0(#726$)L+#)$#$%+#9)'+-#$%+#+3&$$+,-#)"0#$%+#(266+($2,?#D2,#+**#=#KP#]-#)"0#"+L6+($&"L#9)'+#(/,,+"$'@&"0#$%+#,+V/&,+0#7)6/+#2@#>#&"#2,0+,#@2,#$%+#(&,(/&$#2@#D&L?#W?WN:9>#$2#&3*6+3+"$#$%+#(/,,+"$#'2/,(+#.? Ans. −K#]H#−K?d#]H#+M?W#]H#Ka?N#UΩ

6.8 Discrete-Circuit BJT Amplifiers Y&$%#2/,#'$/01#2@#;<=#)3*6&@&+,#9)'&('#(23*6+$+-#.+#"2.#*/$#+7+,1$%&"L#$2L+$%+,#91#*,+'+"$5 &"L#*,)($&()6#(&,(/&$'#@2,#0&'(,+$+5(&,(/&$#)3*6&@&+,'?#=%+'+#(&,(/&$'-#.%&(%#/$&6&h+#$%+#)3*6&@&+, (2"@&L/,)$&2"'#'$/0&+0#&"#C+($&2"#W?W#)"0#2"+#2@#$%+#9&)'&"L#3+$%20'#2@#C+($&2"#W?d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

6.8.1 The Basic Structure D&L/,+#W?We#'%2.'#$%+#9)'&(#(&,(/&$#$%)$#.+#'%)66#/$&6&h+#$2#&3*6+3+"$#$%+#7),&2/'#(2"@&L/,)5 $&2"'#2@#0&'(,+$+#;<=#)3*6&@&+,'?#I32"L#$%+#7),&2/'#9&)'&"L#'(%+3+'#*2''&96+#@2,#0&'(,+$+#;<= )3*6&@&+,'#:C+($&2"#W?d>-#.+#%)7+#'+6+($+0-#@2,#'&3*6&(&$1#)"0#+@@+($&7+"+''-#$%+#2"+#+3*621&"L (2"'$)"$5(/,,+"$#9&)'&"L?#D&L/,+#W?We#&"0&()$+'#$%+#0(#(/,,+"$'#&"#)66#9,)"(%+'#)"0#$%+#0(#726$5 )L+'#)$#)66#"20+'?#Y+#'%2/60#"2$+#$%)$#2"+#.2/60#.)"$#$2#'+6+($#)#6),L+#7)6/+#@2,#>)#&"#2,0+,#$2 U++*#$%+#&"*/$#,+'&'$)"(+#)$#$%+#9)'+#6),L+?#\2.+7+,-#.+#)6'2#.)"$#$2#6&3&$#$%+#0(#726$)L+#0,2* )(,2''#>)#)"0#+7+"#32,+#&3*2,$)"$61#$%+#7),&)9&6&$1#2@#$%&'#0(#726$)L+#,+'/6$&"L#@,23#$%+#7),&)5 $&2"#&"# β#7)6/+'#)32"L#$,)"'&'$2,'#2@#$%+#')3+#$1*+?#=%+#0(#726$)L+#+)#0+$+,3&"+'#$%+#)662.5 )96+#"+L)$&7+#'&L")6#'.&"L#)$#$%+#(266+($2,?##

453

454 Chapter 6 Bipolar Junction Transistors (BJTs) VCC IC " #I RC VC " VCC % #RC I VB " %

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EXERCISE 6.51 F2"'&0+,#$%+#(&,(/&$#2@#D&L?#W?We#@2,#$%+#()'+#+--#=#+**#=#KP#]-#.#=#K#3I-#>)#=#KPP#UΩ-#>-#=#f#UΩ)"0#β#=#KPP?#D&"0#)66#0(#(/,,+"$'#)"0#726$)L+'?#Y%)$#),+#$%+#)662.)96+#'&L")6#'.&"L'#)$#$%+#(266+($2, &"#92$%#0&,+($&2"'_#\2.#02#$%+'+#7)6/+'#(%)"L+#)'#β#&'#(%)"L+0#$2#GP_#=2#MPP_#D&"0#$%+#7)6/+'#2@ $%+#;<=#'3)665'&L")6#*),)3+$+,'#)$#$%+#9&)'#*2&"$#:.&$%#β# =#KPP>?#=%+#E),61#726$)L+#+/#=#KPP#]? Ans. C++#D&L?#EW?GK?#C&L")6#'.&"L8#@2,# β# =#KPP-#+f#]-#QN?e#]H#@2,# β#=#GP-#+f#]-#Qe?e#]H#@2, β = MPP-#+f ]-#QM?a#]? $10 V C

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6.8 Discrete-Circuit BJT Amplifiers

455

6.8.2 The Common-Emitter (CE) Amplifier @0, '$)&(2)$-, (), K$/&(2), X$#2,('7$-*)/$`,(<$<5,(),$11$/&5,*,0"2#&,/(#/3(&V,*&,*++,0(;)*+ 1#$S3$)/($0,21,()&$#$0&<,=),&"(0,4*:5,&"$,$'(&&$#,0(;)*+,/3##$)&,7*00$0,&"#23;",-*,&2,;#23)*)-,&"30,#H"'BB4B,&"$,23&73&,#$0(0&*)/$,21,&"$,/3##$)&,023#/$,.,T*)-,*):,2&"$#,/(#/3(&,/2'% 72)$)&, &"*&, '(;"&, 9$, /2))$/&$-, &2, &"$, $'(&&$#V`, "$)/$, -* (0, /*++$-, *, &94'((- )'4')#$*%< J9.(230+:5,&"$,+24$#,&"$,0(;)*+,1#$S3$)/:5,&"$,+$00,$11$/&(.$,&"$,9:7*00,/*7*/(&2#,9$/2'$0< !"(0,(003$,4(++,9$,0&3-($-,(),K$/&(2),D
RC

CC2

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ii

RL $ v p " vi

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vi

$ %

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0V

RB

%

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ii

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vo = –gmv+(RC || RL || ro)

$ vp

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gmvp

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ro

rp

E

Ro = RC ||ro

(b) Figure 6.65 ;'<#I#(2332"5+3&$$+,#)3*6&@&+,#/'&"L#$%+#'$,/($/,+#2@#D&L?#W?We?#;&<#EV/&7)6+"$#(&,(/&$ 29$)&"+0#91#,+*6)(&"L#$%+#$,)"'&'$2,#.&$%#&$'#%19,&05π#320+6?

456 Chapter 6 Bipolar Junction Transistors (BJTs) (0, */&();, *0, *, 7$#1$/&, 0"2#&, /(#/3(&, *)-, &"30, (0, $0&*9+(0"();, *, >$#2, 0(;)*+, .2+&*;$, *&, &"$ $'(&&$#< =), 2#-$#,)2&, &2,-(0&3#9,&"$,-/,9(*0, /3##$)&0,*)-,.2+&*;$05,&"$,0(;)*+,&2,9$,*'7+(1($-5 0"24), *0, *, .2+&*;$, 023#/$, v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vE5,(0,/237+$-,&2,&"$,+2*-,#$0(0&*)/$,>X,.(* *)2&"$#,/237+();,/*7*/(&2#,--P<,W$,0"*++,*003'$,&"*&,--P,*+02,*/&0,*0,*,7$#1$/&,0"2#&,/(#/3(& *&,*++,0(;)*+,1#$S3$)/($0,21,()&$#$0&`,&"30,&"$,23&73&,.2+&*;$, v%,=, vE<,Q2&$,&"*&,>X,/*),9$,*) */&3*+,+2*-,#$0(0&2#,&2,4"(/",&"$,*'7+(1($#,(0,#$S3(#$-,&2,7#2.(-$,(&0,23&73&,.2+&*;$,0(;)*+5,2# (&,/*),9$,&"$,()73&,#$0(0&*)/$,21,*,0390$S3$)&,*'7+(1($#,0&*;$,(),/*0$0,4"$#$,'2#$,&"*),2)$ 0&*;$,21,*'7+(1(/*&(2),(0,)$$-$-<,TW$,4(++,0&3-:,'3+&(0&*;$,*'7+(1($#0,(),6"*7&$#,E &" 5, / v 5, > %5,*)-, Q v ,(),$A*/&+:,&"$,0*'$,4*:,4$,30$-,12#,&"$,a0&#(77$-%-24)b .$#0(2), 21, &"$, 6M, *'7+(1($#, (), K$/&(2), X ) ,&"*&,*77$*#0,*/#200,&"$,*'7+(1($#,()73&,*)&"30,/"*);$0, > &" ,&2 > &"## d > ) || ( π

TX
!@# > ) ! ( π #.+#()"#"+L6+($#&$'#+@@+($-#)"0#.+#),+#9)(U#$2#$%+#'&3*6+,#(&,(/&$#2@#D&L?#W?GP:9> )"0# $%+# @2,3/6)'# 0+,&7+0# &"# C+($&2"# W?W?N?# =%2'+# @2,3/6)'-# .&$%# ( % # "+L6+($+0-# .+,+# *,+5 '+"$+0#&"#$%+#FE#+"$,1#&"#=)96+#W?e? !@# > ) #&'#"2$#3/(%#L,+)$+,#$%)"# ( π -#$%+"#&$#3/'$#9+#$)U+"#&"$2#)((2/"$#&"#$%+#)")61'&'?#=%&' &'#)#'&3*6+#$)'U-#)"0#.+#/,L+#$%+#,+)0+,'#$2#4/'$#.2,U#$%+&,#.)1#$%,2/L%#$%+#(&,(/&$#,)$%+, $%)"# ,+61&"L#2"#3+32,&h+0#@2,3/6)'?#I'# )#(%+(U-# %2.+7+,-#$%+,+# &'#)# '&3*6+# )**,2)(%#$2 )0)*$#$%+#FE#@2,3/6)'#2@#=)96+#W?e#$2#$%+#()'+#)$#%)"08#I**61#$%+#=%p7+"&"#$%+2,+3#$2#$%+ "+$.2,U# (23*2'+0# 2@# v '&L - # > '&L - # )"0# > ) - # $%/'# ,+0/(&"L# &$# $2# )# L+"+,)$2,# v′'&L d ( > ) ⁄ ( > ) e > '&L ) ) v '&L #)"0#)#,+'&'$)"(+# >′ '&L d > '&L || > ) ? #b2.#$%+#@2,3/6)'#&"#$%+#FE#+"$,1#&" =)96+#W?e#()"#9+#(%)"L+0#)'#@2662.'8#J+*6)(+#$%+#+T*,+''&2"#@2,# > &" #91#$%)$#&"#EV?#:W?KKM>H 3/6$&*61#$%+#+T*,+''&2"#@2,# Q v #91#$%+#@)($2,# > ) ⁄ ( > ) e > '&L ) H #)"0#,+*6)(+# > '&L #&"#$%)$#+T*,+'5 '&2"#91# ( > '&L || > ) )?

6.8 Discrete-Circuit BJT Amplifiers

EXERCISE 6.52 F2"'&0+,#$%+#FE#)3*6&@&+,#2@#D&L?#W?WG:)>#.%+"#9&)'+0#)'#&"#ET+,(&'+#W?GK?#!"#*),$&(/6),-#,+@+,#$2 D&L? EW?GK#@2,#$%+#9&)'#(/,,+"$'#)"0#$%+#7)6/+'#2@#$%+#+6+3+"$'#2@#$%+#;<=#320+6#)$#$%+#9&)'#*2&"$?#E7)65 /)$+#>&"#:.&$%2/$#)"0#.&$%#>)#$)U+"#&"$2#)((2/"$>-#/v%#:.&$%2/$#)"0#.&$%#(%#$)U+"#&"$2#)((2/"$>-#)"0 >2#:.&$%2/$#)"0#.&$%#(%#$)U+"#&"$2#)((2/"$>?#D2,#>X#=#G#UΩ-#@&"0#/v?#!@#>'&L#=#G#UΩ-#@&"0#$%+#27+,)66 726$)L+#L)&"#Qv?#!@#$%+#'&"+5.)7+# vπ#&'#$2#9+#6&3&$+0#$2#G#3]#*+)U-#.%)$#&'#$%+#3)T&3/3#)662.+0 *+)U#)3*6&$/0+#2@#v'&L#)"0#$%+#(2,,+'*2"0&"L#*+)U#)3*6&$/0+#2@#v%_ Ans. P<^,GΩ5,P<8,GΩ`,]\PO,_o_5,]PDX,_o_`,E,GΩ5,N<8,GΩ`,]??D,_o_`,]\D,_o_`,?^ '_`,O
6.8.3 The Common-Emitter Amplifier with an Emitter Resistance I'#0+32"'$,)$+0#&"#C+($&2"#W?W?e-#)#"/39+,#2@#9+"+@&(&)6#,+'/6$'#()"#9+#29$)&"+0#91#(2""+($5 &"L#)#,+'&'$)"(+# > 4 #&"#$%+#+3&$$+,#2@#$%+#$,)"'&'$2,?#=%&'#&'#'%2."#&"#D&L?#W?WW:)>#.%+,+# > 4 #&'2@# (2/,'+-# /"91*)''+0?# D&L/,+# W?WW:9># '%2.'# $%+# '3)665'&L")6-# +V/&7)6+"$5(&,(/&$# 320+6? B9'+,7+#$%)$#$%+#2"61#0&@@+,+"(+#9+$.++"#$%&'#(&,(/&$#)"0#$%+#'&3*6&@&+0#7+,'&2"#'$/0&+0#&" C+($&2"#W?W?e#&'#$%+#&"(6/'&2"#2@#$%+#9&)'#,+'&'$)"(+# > ) -#.%&(%#/"@2,$/")$+61#()"#6&3&$#$%+ &"(,+)'+#&"# > &" #0/+#$2# > 4 - #'&"(+ > &" d > ) || [ ( β e K ) ( ( 4 e > 4 ) ]

TX
=%+#)")61'&'#2@#$%+#(&,(/&$'#&"#D&L?#W?WW#&'#'$,)&L%$@2,.),0#)"0#&'#&66/'$,)$+0#&"#$%+#@&L/,+?#=%+ @2,3/6)'#L&7+"#&"#=)96+#W?e#()"#9+#)0)*$+0#$2#)**61#$2#$%+#(&,(/&$#%+,+#91#,+*6)(&"L#$%+#@2,5 3/6)#@2,# > &" #.&$%#$%)$#&"#EV?#:W?KKN>-#,+*6)(&"L# > '&L #91# >′'&L d > '&L || > ) - #)"0#3/6$&*61&"L#$%+ +T*,+''&2"# @2,# Q v # 91# $%+# @)($2,# > ) ⁄ ( > ) e > '&L ) ?# B"(+# )L)&"-# .+# 02# "2$# ,+(233+"0# $%&' )**,2)(%#2@#*6/LL&"L#&"$2#@2,3/6)'H#,)$%+,-#'&"(+#+)(%#(&,(/&$#$%+#,+)0+,#.&66#+"(2/"$+,#.&66 9+#0&@@+,+"$-#&$#&'#3/(%#32,+#/'+@/6#$2#.2,U#2"+k'#.)1#$%,2/L%#$%+#(&,(/&$#/'&"L#$%+#)")61'&' 3+$%20'#'$/0&+0#)'#)#L/&0+?

EXERCISE 6.53# F2"'&0+,#$%+#+3&$$+,50+L+"+,)$+0#FE#(&,(/&$#2@#D&L?#W?WW#.%+"#9&)'+0#)'#&"#ET+,(&'+#W?GK?#!"#*),5 $&(/6),-#,+@+,#$2#D&L?#EW?GK#@2,#$%+#9&)'#(/,,+"$'#)"0#@2,#$%+#7)6/+'#2@#$%+#+6+3+"$'#2@#$%+#;<=#320+6 )$#$%+#9&)'#*2&"$?#[+$#$%+#)3*6&@&+,#9+#@+0#@,23#)#'2/,(+#%)7&"L#>'&L#=#G#UΩ-#)"0#6+$#>X#=#G#UΩ?#D&"0 $%+#7)6/+#2@#>4#$%)$#,+'/6$'#&"#>&"#+V/)6#$2#@2/,#$&3+'#$%+#'2/,(+#,+'&'$)"(+#>'&L?#D2,#$%&'#7)6/+#2@#>4@&"0#/v%-#>2-#/v -#)"08Qv ?#!@#vπ#&'#$2#9+#6&3&$+0#$2#G#3]-#.%)$#&'#$%+#3)T&3/3#7)6/+#v'&L#()"#%)7+#.&$% )"0#.&$%2/$#>4#&"(6/0+0_#D&"0#$%+#(2,,+'*2"0&"L#v%? Ans. PP^,Ω`,]\P,_o_`,E,GΩ`,]?P<\,_o_`,]D
457

458 Chapter 6 Bipolar Junction Transistors (BJTs) VCC (0 V)

RC

CC2

vo CC1

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ii

ib

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6.8 Discrete-Circuit BJT Amplifiers

6.8.4 The Common-Base (CB) Amplifier L(;3#$,X$#25, 4$, "*.$, /2))$/&$-, &"$, 9*0$, -(#$/&+:, &2 ;#23)-5, &"30, $+('()*&();, #$0(0&2#, >), *+&2;$&"$#<, 6237+();, /*7*/(&2#0, --?, *)-8 --P, 7$#12#' 0('(+*#,13)/&(2)0,&2,&"20$,(),&"$,6M,/(#/3(&< !"$,0'*++%0(;)*+5,$S3(.*+$)&%/(#/3(&,'2-$+,21,&"$,*'7+(1($#,(0,0"24),(),L(;<,X$-,(),-$&*(+,(),K$/&(2),X$-,(),&"$,6B,$)&#:,(),!*9+$ X<85,*77+:,-(#$/&+:,"$#$< VCC (0 V)

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Figure 6.67 ;'<#I#(2332"59)'+#)3*6&@&+,#/'&"L#$%+ '$,/($/,+#2@#D&L?#W?We?#;&<#EV/&7)6+"$#(&,(/&$#29$)&"+0#91 ,+*6)(&"L#$%+#$,)"'&'$2,#.&$%#&$'#=#320+6?

459

460 Chapter 6 Bipolar Junction Transistors (BJTs)

EXERCISE 6.54 F2"'&0+,#$%+#F;# )3*6&@&+,# 2@#D&L?#W?WW:)>#.%+"#0+'&L"+0#/'&"L#$%+#;<=#)"0#(23*2"+"$#7)6/+' '*+(&@&+0#&"#ET+,(&'+#W?GK?#C*+(&@&()661-#,+@+,#$2#D&L?#EW?GK#@2,#$%+#9&)'#V/)"$&$&+'#)"0#$%+#7)6/+'#2@ $%+#(23*2"+"$'#2@#$%+#;<=#'3)665'&L")6#320+6?#[+$#>'&L#=#>X#=#G#UΩ?#D&"0#$%+#7)6/+'#2@#>&"-#/v%-#>%/v -# v $ ⁄ v '&L - #)"0#Qv?#=2#.%)$#7)6/+#'%2/60#>'&L#9+#,+0/(+0#:/'/)661#"2$#*2''&96+#$2#02j>#$2#29$)&"#)" 27+,)66#726$)L+#L)&"#+V/)6#$2#$%)$#@2/"0#@2,#$%+#FE#)3*6&@&+,#&"#ET+,(&'+#W?GM-#$%)$#&'-#QNa#]Z]_ Ans. P^,Ω`,+\PO,_o_`,E,GΩ`,+?P\,_o_`,O
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6.8 Discrete-Circuit BJT Amplifiers

J+*6)(&"L#$%+#;<=#.&$%#&$'#=#320+6#)"0#"+L6+($&"L# ( % - #.+#29$)&"#$%+#+V/&7)6+"$#(&,(/&$ '%2."#&"#D&L?#W?Wf:9>?#=%&'#(&,(/&$#&'#&0+"$&()6#$2#$%)$#&"#$%+#'$,&**+0502."#()'+#)")61h+0#&" C+($&2"#W?W?W#+T(+*$#%+,+#.+#%)7+#$%+#9&)'#,+'&'$)"(+# > ) ? #b2$+#$%)$#&$#&'#7+,1#&3*2,$)"$#$2 '+6+($#)'#6),L+#)#7)6/+#@2,# > ) #)'#*+,3&$$+0#91#0(#9&)'#(2"'&0+,)$&2"'-#'&"(+#)#62.# > ) #(2/60 0+@+)$# $%+# */,*2'+# 2@# $%+# +3&$$+,# @2662.+,?# =2# )**,+(&)$+# $%&'# *2&"$# ,+()66# $%)$# $%+# 32'$ &3*2,$)"$#@+)$/,+#2@#$%+#+3&$$+,#@2662.+,#&'#$%)$#&$#3/6$&*6&+'# > X #91# ( β e K )-#$%/'#*,+'+"$&"L#) %&L%#&"*/$#,+'&'$)"(+#$2#$%+#'&L")6#'2/,(+?#\+,+-#%2.+7+,-# > ) #)**+),'#&"#*),)66+6#.&$%#$%&' &"(,+)'+0#,+'&'$)"(+-#,+'/6$&"L#&" > &"## d > ) || ( β e K ) ( ( 4 e > X )

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461

462 Chapter 6 Bipolar Junction Transistors (BJTs) Vo Vsig (dB)

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6.9 Transistor Breakdown and Temperature Effects

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463

464 Chapter 6 Bipolar Junction Transistors (BJTs)

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465

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CHAPTER 6

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CHAPTER 6

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CHAPTER 6

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CHAPTER 6

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Problems 483

T(V,=)73&,#$0(0&*)/$, > &" d MP ,G Ω? T((V,W"$),1$-,1#2',*,0(;)*+,023#/$,4(&",*,7$*G,*'7+(&3-$,21 O 4 ,*)-,&"$,9(*0,/3##$)&, . - <,!"$,BC!,"*0, β d KPP? =1,&"$,&2&*+,#$0(0&*)/$,(),&"$,/2++$/&2#,(0,^,G Ω5,1()-,&"$,2.$#% *++, .2+&*;$, ;*(), Q v , *)-, &"$, 7$*G, *'7+(&3-$, 21, &"$, 23&73& 0(;)*+, v % ?

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PROBLEMS

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CHAPTER 6

D 6.118,Z$0(;),*,6M,*'7+(1($#,4(&",*,#$0(0&*)/$, > 4 ,(),&"$ $'(&&$#,&2,'$$&,&"$,12++24();,07$/(1(/*&(2)0Y,

484 Chapter 6 Bipolar Junction Transistors (BJTs)

PROBLEMS

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CHAPTER 6

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Problems 485

CHAPTER 6

Z$0(;), &"(0, /(#/3(&, 12#, β, =, DO<, c0$, *, /3##$)&, &"#23;", >)P $S3*+, &2, &"$, 9*0$, /3##$)&<, Q245, 4"*&, .*+3$0, 21, +-, *)-, .#$03+&,4(&",β,=,∞f

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CHAPTER 6

PROBLEMS

486 Chapter 6 Bipolar Junction Transistors (BJTs) D *6.140 L2#, &"$, /(#/3(&, (), L(;<, gXK = >M *)-,G$$7();,&"$,/3##$)&,(),$*/",H3)/&(2),&"$,0*'$5,&"$,/3#% #$)&,.N,4(++,9$ + -5 . N = 55555555 M> * 4"(/",(0,()-$7$)-$)&,21,+)*<,W"*&,'30&,&"$,#$+*&(2)0"(7,21 >*,&2,>?,*)-,>P,9$f,L2#,+--,=,?O,_,*)-,+)*,=,O
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Section 6.8: Discrete-Circuit BJT Amplifiers 6.142 L2#, &"$, /2''2)%$'(&&$#, *'7+(1($#, 0"24), ()

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Problems 487

PROBLEMS

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CHAPTER 6

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PART II

Integrated-Circuit Amplifiers CHAPTER 7

Building Blocks of IC Amplifiers

492

CHAPTER 8

Differential and Multistage Amplifiers

586

CHAPTER 9

Frequency Response

686

CHAPTER 10

Feedback

802

CHAPTER 11

Output Stages and Power Amplifiers 910 CHAPTER 12

Operational-Amplifier Circuits

974

H

aving studied the MOSFET and the BJT and become familiar with their basic circuit applications, we are now ready to consider their use in the design of practical amplifier circuits that can be fabricated in integrated-circuit (IC) form. Part II is devoted to this rich subject. Its six chapters constitute a coherent treatment of IC amplifier design and can thus serve as a second course in electronic circuits. Beginning with a brief introduction to the philosophy of IC design, Chapter 7 presents the basic circuit building blocks that are utilized in the design of IC amplifiers. However, the most important building block of all, the differential pair configuration, is deferred to Chapter 8, where it is the main topic. Chapter 8 also considers the design of amplifiers that require a number of cascaded stages. As mentioned at various points in Part I, amplifiers have finite bandwidths. Chapter 9 is devoted to the frequency-response analysis of amplifiers; it provides a comprehensive study of the mechanisms that limit the bandwidth and the tools and methods that are utilized to estimate it for a wide variety of amplifier circuit configurations. While the study of the first half or so of Chapter 9 is essential, some of its later sections can be postponed to a later point in the course or even to subsequent courses. An essential tool in amplifier design is the judicious use of feedback. Chapter 10 deals with this exceedingly important subject. A thorough understanding of feedback concepts, insight into feedback configurations, and proficiency in the use of the feedback analysis method are invaluable to the serious circuit designer. In Chapter 11, we switch gears from dealing with primarily small-signal amplifiers to those that are required to handle large signals and large amounts of power. Finally, Chapter 12 brings together all the topics of Part II in an important application: namely, the design of operational amplifier circuits. We will then have come full circle, from considering the op amp as a black box in Chapter 2 to understanding what is inside the box in Chapter 12. Throughout Part II, MOSFET and BJT circuits are treated side-by-side. Because over 90% of ICs today employ the MOSFET, its circuits are presented first. Nevertheless, BJT circuits are presented with equal depth, although sometimes somewhat more briefly. In this regard, we draw the reader’s attention to Appendix 7.A, which presents a valuable compilation of the properties of both types of transistors, allowing interesting comparisons to be made. As well, typical device parameter values are provided for a number of CMOS and bipolar fabrication process technologies.

491

CHAPTER 7

Building Blocks of Integrated-Circuit Amplifiers Introduction 7.1

493

IC Design Philosophy

7.2 The Basic Gain Cell

494

495

7.3 The Cascode Amplifier

506

7.4 IC Biasing—Current Sources, Current Mirrors, and Current-Steering Circuits 526

7.5 Current-Mirror Circuits with Improved Performance 537 7.6 Some Useful Transistor Pairings Summary

553

Appendix 7.A: Comparison of the MOSFET and the BJT 554 Problems

569

546

IN THIS CHAPTER YOU WILL LEARN 1. The basic integrated-circuit (IC) design philosophy and how it differs from that for discrete-circuit design. 2. The basic gain cells of IC amplifiers, namely, the CS and CE amplifiers with current-source loads. 3. How to increase the gain realized in the basic gain cells by employing the principle of cascoding. 4. Analysis and design of the cascode amplifier and the cascode current source in both their MOS and bipolar forms. 5. How current sources are used to bias IC amplifiers and how the reference current generated in one location is replicated at various other locations on the IC chip by using current mirrors. 6. Some ingenious analog circuit design techniques that result in current mirrors with vastly improved characteristics. 7. How to pair transistors to realize amplifiers with characteristics superior to those obtained from a single-transistor stage.

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501

502 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

Example 7.2 continued

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;-,'),20' ( $$ '%,?,(($)"),(')-,'(-$B)5'"%+')-,'0$%*('($&%'/B' v'&$#,('2$(,')/')-,'XBA$44$%&'"2/*%+Y'/B')-, A/"+'?*2#,G ;-,'&2"4-$?"A'?/%()2*?)$/%'/B'9$&G'LGNC?F'?"%'>,'*(,+')/'+,),20$%,' v 3 'B/2',#,23'#"A*,'/B' v ' 5'4/$%)'>3 4/$%)P';-,'#"A*,'/B' v ' '+,),20$%,(')-,'4"2)$?*A"2'?-"2"?),2$()$?'?*2#,'/B' & T '/%'.-$?-')-,'/4,2")$%&'4/$%) A$,(G';-,'/4,2")$%&'4/$%)'.$AA'>,'")')-,'$%),2(,?)$/%'/B')-$('4"2)$?*A"2'&2"4-'"%+')-,'A/"+'?*2#,G';-,'-/2$@ S/%)"A'?//2+$%"),'/B')-,'/4,2")$%&'4/$%)')-,%'&$#,(')-,'#"A*,'/B' v 3 G Z2/?,,+$%&'$%')-,'0"%%,2'1*()',K4A"$%,+5'.,'/>)"$%')-,'_;E'(-/.%'$%'9$&G'LGNC+FG'J('$%+$?"),+5'$) -"('B/*2'+$()$%?)'(,&0,%)(5'A">,A,+'D5'DD5'DDD5'"%+'D_G':"?-'(,&0,%)'$('/>)"$%,+'B/2'/%,'/B')-,'B/*2'?/0>$@ %")$/%('/B')-,'0/+,('/B'/4,2")$/%'/B' & T '"%+' & M 5 '.-$?-'"2,'"A(/'$%+$?"),+'$%')-,'+$"&2"0G'c/),')-")'., -"#,'A">,A,+')./'$04/2)"%)'>2,"H'4/$%)('/%')-,')2"%(B,2'?-"2"?),2$()$?'CJ'"%+'(,2#,' )-")' $% 2,&$/%'DDD')-,')2"%(B,2'?*2#,'$('"A0/()'A$%,"2'"%+'$('#,23'(),,45'$%+$?")$%&'A"2&,'#/A)"&,'&"$%G'D%'2,&$/% DDD'>/)-')-,'"04A$B3$%&')2"%($()/2' & T '"%+')-,'A/"+')2"%($()/2' & M '"2,'/4,2")$%&'$%'(")*2")$/%G';-,',%+ 4/$%)('/B'2,&$/%'DDD'"2,'J'"%+'3' v 3 Z ( $$ [ ( 3(M 5' & M ',%),2(')-,')2$/+,'2,&$/%5 "%+'")'<5'+,B$%,+'>3' v 3 Z v ' [ ( 85 5 ' & T ',%),2(')-,')2$/+,'2,&$/%G'I-,%')-,'"04A$B$,2'$('>$"(,+'")'" 4/$%)'$%'2,&$/%'DDD5')-,'(0"AA@($&%"A'#/A)"&,'&"$%'?"%'>,'+,),20$%,+'"('.,'-"#,'+/%,'$%'9$&G'LG[C?FG ;-,' O*,()$/%' 2,0"$%(' "(' )/' -/.' .,' "2,' &/$%&' )/' &*"2"%),,' )-")' )-,' +?' ?/04/%,%)' /B' v ' ' .$AA' -"#, (*?-' "' #"A*,' )-")' .$AA' 2,(*A)' $%' /4,2")$/%' $%' 2,&$/%' DDDG' ;-")' $(' .-3' /#,2"AA' %,&")$#,' B,,+>"?H' $( %,,+,+5'"('.$AA'>,'+,0/%()2"),+'A"),2G <,B/2,'A,"#$%&')-$(',K"04A,'$)'$('*(,B*A')/'2,$),2"),')-")')-,'*44,2'A$0$)'/B')-,'"04A$B$,2'2,&$/%'C$G,G5 4/$%)'JF'$('+,B$%,+'>3' ( 3/ Z ( $$ [ ( 3(M '"%+')-,'A/.,2'A$0$)'C$G,G5'4/$%)'3' ( 3, Z ( 3(T5 .-,2,' ( 3(T '?"%'>,'"442/K$0"),A3'+,),20$%,+'>3'"((*0$%&')-")' ' $T " ' a:9 G'J'0/2,'42,?$(,'#"A*,'B/2 ( 3, '?"%'>,'/>)"$%,+'>3')"H$%&'$%)/'"??/*%)')-,':"2A3',BB,?)'$%'>/)-' & T'"%+' & M 5 '"('.$AA'>,'+,0/%()2"),+ $%')-,'%,K)',K"04A,G

7.2 The Basic Gain Cell

Example 7.3 E/%($+,2')-,'E678'?/00/%@(/*2?,'"04A$B$,2'$%'9$&G'LGNC"F'B/2')-,'?"(,' ( $$ = ['_5'( 85 = (87 = ^GR'_5 M M µ 5 % .6 = M^^'µJ ` _ 5 ' "%+' µ 7 % .6 = RQ'µJ ` _ G ' 9/2' "AA' )2"%($()/2(5' " =' ^GN' µ0' "%+' !4 =4 N µ0G' JA(/5 ( /5 = M^'_5' (/7 = T^'_5'"%+' ' a:9 = T^^'µJG'9$%+')-,'(0"AA@($&%"A'#/A)"&,'&"$%G'JA(/5'B$%+')-,'?//2+$@ %"),('/B')-,',K)2,0$)$,('/B')-,'"04A$B$,2'2,&$/%'/B')-,')2"%(B,2'?-"2"?),2$()$?e)-")'$(5'4/$%)('J'"%+
Solution

0 1T = =

! M: 5′ @@@@@ ' a:9 " T N M × M^^ × @@@@@@@ × T^^ = ^GR['0J`_ ^GN

(/5 M^'_ @ @ = @@@@@@@@@@@@@@@@@ = M^^'HΩ - .T = @@@@@@@ ^GT'0J ' $T (/7 T^'_ @ @ = @@@@@@@@@@@@@@@@@ - .M = @@@@@@@@@@ = T^^'HΩ ^GT'0J ' $M ;-*(5

/ v = [ 0 1T ( - .T || - .M ) = [ ^GR[ ( 0J`_ ) × ( M^^ || T^^ ) ( HΩ ) = [ NM'_`_

J442/K$0"),'#"A*,('B/2')-,',K)2,0$)$,('/B')-,'"04A$B$,2'2,&$/%'/B')-,')2"%(B,2'?-"2"?),2$()$?'C2,&$/%'DDDF ?"%'>,'+,),20$%,+'"('B/AA/.(P'c,&A,?)$%&')-,':"2A3',BB,?)5'"AA')-2,,')2"%($()/2('"2,'?"223$%&',O*"A'?*22,%)( ' a:9 5 '"%+')-*('.,'?"%'+,),20$%,')-,'/#,2+2$#,'#/A)"&,('")'.-$?-')-,3'"2,'/4,2")$%&G';2"%($()/2(' & M '"%+ & [ '.$AA'-"#,',O*"A'/#,2+2$#,'#/A)"&,(5' ( 3([ 5'+,),20$%,+'B2/0 T ! ' $[ Z ' a:9 " @@@ ( µ 7 % .6 ) @@@@@ M "

[

( 3([

M

8*>()$)*)$%&5' ' a:9' Z T^^ 'µJ5' µ 7 % .6 Z RQ 'µJ`_ 5' ( ! ⁄ " ) [ Z N ⁄ ^GN Z T^ '2,(*A)('$% M

;-*(5

( 3([ Z ^GQQ '_ ( 3/ Z ( $$ [ ( 3([ Z MGNQ '_

c,K)'.,'+,),20$%,' ( 3(T 'B2/0 T ! M ' $T " ' a:9 " @@@ ( µ 5 % .6 ) @@@@@@ ( 3(T M "T 8*>()$)*)$%&5' ' a:9' Z T^^ 'µJ5' µ 5 % .6 Z M^^ 'µJ`_M5' ( ! ⁄ " ) T Z N ⁄ ^GN Z T^ '2,(*A)('$% ( 3(T Z ^G[M '_ ;-*(5' ( 3, Z ( 3(T Z ^G[M '_G 6/2,'42,?$(,'#"A*,('B/2' ( 3/'"%+'( 3, '?"%'>,'+,),20$%,+'>3')"H$%&')-,':"2A3',BB,?)'$%'"AA')2"%($()/2( $%)/'"??/*%)'"('B/AA/.(G

503

504 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

Example 7.3 continued

9$2()5'.,'+,),20$%,' ( )* '/B'&M'"%+'&['?/22,(4/%+$%&')/' ' $[ = ' a:9 = 'T^^'µJ'*($%& ()$ M @ ( ()* [ (87 ) T + @@@@@@@@@@ (/7 [

T ! ' $[ = @@@ : 7′ @@@@@ M " ;-*(5

T N T^^' = @@@ × RQ @@@@@@@ M ^GN

(3([

M

^GR + (3([ @ T + @@@@@@@@@@@@@@@@@@@@@@@@@@@ T^

CLGT]F

.-,2,' (3([ '$(')-,'0"&%$)*+,'/B')-,'/#,2+2$#,'#/A)"&,'")'.-$?-'&['"%+'&M'"2,'/4,2")$%&5'"%+'.,'-"#, *(,+')-,'B"?)')-")5'B/2'&[5' ()$ = ()* G':O*")$/%'CLGT]F'?"%'>,'0"%$4*A"),+')/')-,'B/20 M

^GM] = (3([ ( T + ^G^] (3([ ) .-$?-'>3'"')2$"A@"%+@,22/2'42/?,(('3$,A+( (3([ = ^GQ['_ ;-*(5 ()* = ^GR + ^GQ[ = TGT['_ "%+ (3/ = ($$ − (3([ = MGNL'_ ;/'B$%+')-,'?/22,(4/%+$%&'#"A*,'/B' v ' 5 ' ( '/ 5 '.,'+,2$#,'"%',K42,(($/%'B/2' v 3 '#,2(*(' v ' '$%'2,&$/%'DDDG c/)$%&')-")'$%'2,&$/%'DDD5'&T'"%+'&M'"2,'$%'(")*2")$/%'"%+'/>#$/*(A3'?/%+*?)',O*"A'?*22,%)(5'.,'?"%'.2$), 9 $T = 9 $M ( $$ [ v 3 v3 T ! ! T M @@@ : 5′ @@@@@ ( v ' − (85 ) T + @@@@@@@@@@@ = @@@ : 7′ @@@@@ ( ( )* [ ( 87 ) M T + @@@@@@@@@@@@@@@@@@@@@ M (/5 (/7 " T " M M 8*>()$)*)$%&'%*0,2$?"A'#"A*,(5'.,'/>)"$% T [ ^G^\ v 3 M @ " ( T [ ^GT[ v 3 ) \GQQ ( v ' [ ^GR ) = @@@@@@@@@@@@@@@@@@@@@@@@@ T + ^G^Q v 3 .-$?-'?"%'>,'0"%$4*A"),+')/')-,'B/20 v 3 = LGR] [ RQGLL ( v ' [ ^GR )

M

4\=ST8

M ;-$('$(')-,',O*")$/%'/B'(,&0,%)'DDD'/B')-,')2"%(B,2'?-"2"?),2$()$?G'JA)-/*&-'$)'$%?A*+,(' v ' 5

')-,'2,"+,2'(-/*A+ %/)'>,'"A"20,+P'<,?"*(,'2,&$/%'DDD'$('#,23'%"22/.5' v ' '?-"%&,('#,23'A$))A,5'"%+')-,'?-"2"?),2$()$?'$('%,"2A3 A$%,"2G'8*>()$)*)$%&' v 3 = MGNL'_ '&$#,(')-,'?/22,(4/%+$%&'#"A*,'/B' v ' U')-")'$(5' ( '/ = ^G\\'_G ';/'+,),20$%, )-,'?//2+$%"),('/B'<5'.,'%/),')-")')-,3'"2,'2,A"),+'>3' (3, = (', [ (85 G '8*>()$)*)$%&'$%':OG'CLGM^F'"%+'(/A#$%& &$#,(' ( ', = ^G]['_ '"%+'( 3, = ^G[['_G';-,'.$+)-'/B')-,'"04A$B$,2'2,&$/%'$(')-,2,B/2, ∆v ' = (', [ ('/ = ^G^Q'_ "%+')-,'?/22,(4/%+$%&'/*)4*)'2"%&,'$( ∆v 3 '= (3, [ ( 3/ = [ MGTN'_ ;-*(5')-,'XA"2&,@($&%"AY'#/A)"&,'&"$%'$( ∆v 3 MGTN @@@@@@@@@ = [ ' @@@@@@@@@@ = [ NMG\ '_`_ ∆v ' ^G^Q .-$?-'$('#,23'?A/(,')/')-,'(0"AA@($&%"A'#"A*,'/B'−NM5'$%+$?")$%&')-")'(,&0,%)'DDD'/B')-,')2"%(B,2'?-"2"?),2@ $()$?'$('O*$),'A$%,"2G

The Basic Gain Cell

EXERCISES 7.2 J'E678'?/00/%@(/*2?,'"04A$B$,2'(*?-'"(')-")'$%'9$&G'LGNC"F5'B">2$?"),+'$%'"'^GT\@µ0'),?-%/A/&35 M M -"('!B"'='LGM'µ0`^G[R'µ0'B/2'"AA')2"%($()/2(5' : 5′ = [\L'µJ`_ 5 ' : 7′ = \R'µJ`_ 5' ' 'a:9 = T^^'µJ5 (/5 ′ = Q'_`µ05'"%+' (′/7 = ' R'_`µ0G'9$%+' 0 1T5' - .T 5' - .M 5 '"%+')-,'#/A)"&,'&"$%G Ans. TGMQ'0J`_U'T\'HΩU'MTGR'HΩU''−TMG['_`_ 7.3 E/%($+,2')-,'"?)$#,@A/"+,+'E:'"04A$B$,2'.-,%')-,'?/%()"%)@?*22,%)'(/*2?,'''$('$04A,0,%),+'.$)-'" 757')2"%($()/2G'g,)' ' = ^GT'0J5 '' ( / = Q^'_ 'CB/2'>/)-')-,'575'"%+')-,'757')2"%($()/2(F5'"%+' β = T^^G 9$%+' # $% 5 ' - .'CB/2',"?-')2"%($()/2F5' 0 1 5 ' / ^ 5'"%+')-,'"04A$B$,2'#/A)"&,'&"$%G Ans. SC-HΩI-T=C-KΩI-O-95]JI-STTT-J]JI-−NTTT-J]J

7.2.4 Increasing the Gain of the Basic Cell I,'?/%?A*+,')-$('(,?)$/%'>3'?/%($+,2$%&'"'O*,()$/%P'!/.'?"%'.,'$%?2,"(,')-,'#/A)"&,'&"$% />)"$%,+'B2/0')-,'>"($?'&"$%'?,AAV';-,'"%(.,2'A$,('$%'B$%+$%&'"'."3')/'2"$(,')-,'A,#,A'/B')-, /*)4*)'2,($()"%?,'/B'>/)-')-,'"04A$B3$%&')2"%($()/2'"%+')-,'A/"+')2"%($()/2G';-")'$(5'.,'(,,H'" ?$2?*$)')-")'4"((,(')-,'?*22,%)' 0 1 v 9 '42/#$+,+'>3')-,'"04A$B3$%&')2"%($()/2'2$&-)')-2/*&-5'>*) $%?2,"(,(')-,'2,($()"%?,'B2/0' - . ')/'"'0*?-'A"2&,2'#"A*,G';-$('2,O*$2,0,%)'$('$AA*()2"),+'$% 9$&G'LGQG'9$&*2,'LGQC"F'(-/.(')-,'E8'"04A$B3$%&')2"%($()/2' & T ')/&,)-,2'.$)-'$)('/*)4*)',O*$#@ "A,%)'?$2?*$)G'c/),')-")'B/2')-,')$0,'>,$%&'.,'"2,'%/)'(-/.$%&')-,'A/"+'+,#$?,G'D%'9$&G'LGQC>F .,'-"#,'$%(,2),+'"'(-"+,+'>/K'>,).,,%')-,'+2"$%'/B' & T '"%+'"'%,.'/*)4*)'),20$%"A'A">,A,+ C M G '!,2,'"&"$%'.,'"2,'%/)'(-/.$%&')-,'A/"+')/'.-$?-' C M '.$AA'>,'?/%%,?),+G'7*2'X>A"?H'>/KY )"H,('$%')-,'/*)4*)'?*22,%)'/B' & T '"%+'4"((,('$)')/')-,'/*)4*)U')-*('")'$)('/*)4*)'.,'-"#,')-, ,O*$#"A,%)'?$2?*$)'(-/.%5'?/%($()$%&'/B')-,'("0,'?/%)2/AA,+'(/*2?,' 0 1T v 9 '>*)'.$)-')-,'/*)4*) 2,($()"%?,'$%?2,"(,+'>3'"'B"?)/2';G' c/.5'.-")'+/,(')-,'>A"?H'>/K'2,"AA3'+/V'8$%?,'$)'4"((,(')-,'?*22,%)'>*)'-<9=>=')-,'2,($(@ )"%?,'A,#,A5'$)'$('"'!"##$%&*2"55$#G'D)'$(')-,'+*"A'/B')-,'#/A)"&,'>*BB,2'C)-,'(/*2?,'"%+',0$)),2 B/AA/.,2(F5'.-$?-'4"((,(')-,'?.@8<0>'>*)'@.A>-=')-,'2,($()"%?,'A,#,AG c/.' (,"2?-$%&' /*2' 2,4,2)/$2,' /B' )2"%($()/2' "04A$B$,2' ?/%B$&*2")$/%(' ()*+$,+' $%' 8,?)$/%( QGR' "%+' RGR5' )-,' /%A3' ?"%+$+"),' B/2' $04A,0,%)$%&' )-$(' ?*22,%)@>*BB,2$%&' "?)$/%' $(' )-, ?/00/%@&"),'C/2'?/00/%@>"(,'$%'>$4/A"2F'"04A$B$,2G'D%+,,+5'2,?"AA')-")')-,'Ef'"%+'E<'?$2@ ?*$)('-"#,'"'*%$)3'?*22,%)'&"$%G'I-")'.,'-"#,'%/)'3,)'$%#,()$&"),+5'-/.,#,25'$(')-,$2'2,($(@ )"%?,')2"%(B/20")$/%'42/4,2)3G'I,'(-"AA'+/')-$('$%')-,'%,K)'(,?)$/%G ;./'$04/2)"%)'B$%"A'?/00,%)(P 1. D)'$('%/)'(*BB$?$,%)')/'2"$(,')-,'/*)4*)'2,($()"%?,'/B')-,'"04A$B3$%&')2"%($()/2'/%A3G'I, "A(/' %,,+' )/' 2"$(,' )-,' /*)4*)' 2,($()"%?,' /B' )-,' ?*22,%)@(/*2?,' A/"+G' 7>#$/*(A35' ., ?"%'*(,'"'?*22,%)'>*BB,2')/'+/')-$('"A(/G 2. ZA"?$%&' "'Ef' C/2'"' E*BB,2$%&'"?)$/%'$('?"AA,+'!,(!)-.%3G'I,'.$AA',K4A"$%')-,'/2$@ &$%'/B')-$('%"0,'(-/2)A3G

505

506 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

To Load ro1

d1

gm1vi

Q1

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d1

ro1

(a) To Load Out

d2

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In

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d1

ro1

gm1vi

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(b) Figure 7.5 ;/'$%?2,"(,')-,'#/A)"&,'&"$%'2,"A$S,+'$%')-,'>"($?'&"$%'?,AA'(-/.%'$%'0,15'"'B*%?)$/%"A'>A/?H5 (-/.%'"('"'>A"?H'>/K'$%'0215'$('?/%%,?),+'>,).,,%'CD'"%+')-,'A/"+G';-$('%,.'>A/?H'$('2,O*$2,+')/'4"((')-,'?*2@ 2,%)'01Tv9'2$&-)')-2/*&-'>*)'2"$(,')-,'2,($()"%?,'A,#,A'>3'"'B"?)/2';G';-,'B*%?)$/%"A'>A/?H'$('"'?*22,%)'>*BB,2G

7.3 The Cascode Amplifier 7.3.1 Cascoding E"(?/+$%&'2,B,2(')/')-,'*(,'/B'"')2"%($()/2'?/%%,?),+'$%')-,'?/00/%@&"),'C/2')-,'?/00/%@ >"(,F'?/%B$&*2")$/%')/'42/#$+,'!"##$%&*2"55$#.%3'B/2')-,'/*)4*)'/B'"'?/00/%@(/*2?,'C/2'" ?/00/%@,0$)),2F' "04A$B3$%&' )2"%($()/2G' 9$&*2,' LGR' $AA*()2"),(' )-,' ),?-%$O*,' B/2' )-,' 678 ?"(,G'!,2,')-,'E8')2"%($()/2' & T '$(')-,'"04A$B3$%&')2"%($()/2'"%+' & M 5 '?/%%,?),+'$%')-,'Ef ?/%B$&*2")$/%'.$)-'"'+?'>$"('#/A)"&,' (* M 'C($&%"A'&2/*%+F'")'$)('&"),5'$(')-,'?"(?/+,')2"%($(@ )/2GT'J'($0$A"2'"22"%&,0,%)'"44A$,('B/2')-,'>$4/A"2'?"(,'"%+'.$AA'>,'?/%($+,2,+'A"),2G I,' .$AA' (-/.' $%' )-,' B/AA/.$%&' )-")' )-,' ,O*$#"A,%)' ?$2?*$)' ")' )-,' /*)4*)' /B' )-,' ?"(?/+, "04A$B$,2'$(')-")'(-/.%'$%'9$&G'LGRG';-*(5')-,'?"(?/+,')2"%($()/2'4"((,(')-,'?*22,%)' 0 1T v 9 ')/ )-,'/*)4*)'%/+,'.-$A,'2"$($%&')-,'2,($()"%?,'A,#,A'>3'"'B"?)/2';G'I,'.$AA'+,2$#,'"%',K42,(($/% B/2';G T ;-,' %"0,' E<=E.C>' $(' "' ?"223/#,2' B2/0' )-,' +"3(' /B' #"?**0' )*>,(' "%+' $(' "' (-/2),%,+' #,2($/%' /B XE<=E"+,+'?")-.C>YU'$%')-,')*>,'#,2($/%5')-,'"%/+,'/B')-,'"04A$B3$%&')*>,'C?/22,(4/%+$%&')/')-,'+2"$% /B' & TF'B,,+(')-,'?")-/+,'/B')-,'?"(?/+,')*>,'C?/22,(4/%+$%&')/')-,'(/*2?,'/B' & MFG

7.3 The Cascode Amplifier

To Load

d2 VG2

Kro1 d2 To Load

Q2 ro1

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gm1vi

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515

516 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

RL

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`_5'"%+'/B'?/*2(,')-, /#,2"AA'&"$%'$('%/.'/%A3'[ ( 0 1 - . )G '!/.,#,25'"('.$AA'>,'(,,%'$%'E-"4),2']5')-$(')2"+,@/BB'/B')-, /#,2"AA'&"$%')/'/>)"$%',K),%+,+'>"%+.$+)-'$('$%'(/0,'?"(,('"'&//+'>"2&"$%l

EXERCISES 7.7

;-,'?/00/%@&"),')2"%($()/2'$%'9$&G'LGT['$('>$"(,+'")'"'+2"$%'?*22,%)'/B'^GMQ'0J'"%+'$('/4,2")$%& .$)-'"%'/#,2+2$#,'#/A)"&,' ( 3( Z ^GMQ '_G';-,')2"%($()/2'-"('"%':"2A3'#/A)"&,' (/ '/B'Q'_G C"F'9$%+' # $% 'B/2' # " Z ∞5 'T'6Ω5'T^^'HΩ5'M^'HΩ5'"%+'^G C>F'9$%+' # . 'B/2' # = Z ^ 5'T'HΩ5'T^'HΩ5'M^'HΩ,'"%+'T^^'HΩ. Ans. C"F' ∞ 5'MQGQ'HΩ5'['HΩ5'T'HΩ5'^GQ'HΩU'C>F'M^'HΩ5'RT'HΩ5'N[^'HΩ5'\N^'HΩ5'NGTM'6Ω

7.8

E/%($+,2'"'?"(?/+,'"04A$B$,2'B/2'.-$?-')-,'E8'"%+'Ef')2"%($()/2('"2,'$+,%)$?"A'"%+'"2,'>$"(,+')/ /4,2"),'")' ' $ Z ^GT '0J'.$)-' ( 3( Z ^GM '_G'JA(/'A,)' ( / Z M '_G'9$%+' / vT5' / vM 5 '"%+' / v 'B/2')./ ?"(,(P'C"F' # " Z M^ 'HΩ'"%+'C>F' # " Z N^^ 'HΩG Ans. C"F'bTG\M'_`_5'T^GQ'_`_5'bT]G^'_`_U'C>F'bT^GM'_`_5'T]GR'_`_5'bM^^'_`_

7.3.4 The Output Resistance of a Source-Degenerated CS Amplifier D%'8,?)$/%'QGRGN'.,'+$(?*((,+'(/0,'/B')-,'>,%,B$)(')-")'"2,'/>)"$%,+'.-,%'"'2,($()"%?,' # = '$( $%?A*+,+'$%')-,'(/*2?,'A,"+'/B'"'E8'"04A$B$,25'"('$%'9$&G'LGTNC"FG'8*?-'"'2,($()"%?,'$('2,B,22,+')/ "('"'(/*2?,@+,&,%,2")$/%'2,($()"%?,'>,?"*(,'/B'$)('"?)$/%'$%'2,+*?$%&')-,',BB,?)$#,')2"%(?/%+*?@ )"%?,'/B')-,'E8'()"&,')/' 0 1 ⁄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f')2"%($()/2G';-*(' # . '$('&$#,%'>3 #. Z #= ^ -. ^ 01 -. #=

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;-*(' (/*2?,' +,&,%,2")$/%' $%?2,"(,(' )-,' /*)4*)' 2,($()"%?,' /B' )-,' E8' "04A$B$,2' B2/0' - . ' )/ ( T ^ 0 1 # = )- . 5 ' "&"$%' >3' )-,' ("0,' B"?)/2' ( T ^ 0 1 # = )G ' D%' E-"4),2' T^5' .,' .$AA' B$%+' )-")' # = $%)2/+*?,('%,&")$#,'C+,&,%,2")$#,F'B,,+>"?H'/B'"%'"0/*%)' ( T ^ 0 1 # = )G

517

518 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

Ro

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EXERCISE 7.9

f$#,%')-")'(/*2?,'+,&,%,2")$/%'2,+*?,(')-,')2"%(?/%+*?)"%?,'/B'"'E8'"04A$B$,2'B2/0' 0 1 ')/'"442/K@ $0"),A3' 0 1 ⁄ ( T ^ 0 1 # = ) '"%+'$%?2,"(,('$)('/*)4*)'2,($()"%?,'>3'"442/K$0"),A3')-,'("0,'B"?)/25'.-") -"44,%(')/')-,'/4,%@?$2?*$)'#/A)"&,'&"$%' / v. V'c/.5'B$%+'"%',K42,(($/%'B/2' / v '.-,%'"'A/"+'2,($()@ "%?,' # " '$('?/%%,?),+')/')-,'/*)4*)G Ans. / v. '2,0"$%('?/%()"%)'")' 0 1 - . P #" / v Z ( 0 1 - . ) @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ # " ^ ( T ^ 0 1 # = )- .

CLGN^F

7.3.5 Double Cascoding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v $) 'C")'A,"()',O*"A')/' (3( F5 "%+'2,?"AA$%&')-")'0/+,2%'678'),?-%/A/&3'*)$A$S,('4/.,2'(*44A$,('$%')-,'2"%&,'/B'T'_')/ M _5'.,'(,,')-")')-,2,'$('"'A$0$)'/%')-,'%*0>,2'/B')2"%($()/2('$%'"'?"(?/+,'()"?HG

7.3 The Cascode Amplifier

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519

520 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers ;-,'(0"AA@($&%"A'/4,2")$/%'/B')-,'?$2?*$)'$%'9$&G'LGTR'$('($0$A"2')/')-")'/B')-,'c678'?"(@ ?/+,G';-,'+$BB,2,%?,'-,2,'$(')-")')-,'($&%"A'?*22,%)' 0 1 v 9 '$('K.@C>C4C.A5'"%+'0"+,')/'BA/. $%)/' )-,' (/*2?,' ),20$%"A' /B' & M 5 ' .-$?-' &$#,(' )-,' ?$2?*$)' )-,' %"0,' 5)+-$-* !,(!)-$G[' ;-, B/A+,+'?"(?/+,'$('"'#,23'4/4*A"2'>*$A+$%&'>A/?H'$%'E678'"04A$B$,2(G

EXERCISE 7.10

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524 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

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526 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

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Example 7.5 f$#,%' ($$ = ['_ ' "%+' *($%&' ' a:9 = T^^ ' µJ5' +,($&%' )-,' ?$2?*$)' /B' 9$&G' LGMM' )/' />)"$%' "%' /*)4*)' ?*22,%) .-/(,'%/0$%"A'#"A*,'$('T^^'µJG'9$%+'#'$B' & T '"%+' & M '"2,'0")?-,+'"%+'-"#,'?-"%%,A'A,%&)-('/B'T'µ05'?-"%@ M %,A'.$+)-('/B'T^'µ05' ( 8 = ^GL'_5 '"%+' : 5′ = M^^'µJ`_ G 'I-")'$(')-,'A/.,()'4/(($>A,'#"A*,'/B' (3 V 'J((*0@ $%&' )-")' B/2' )-$(' 42/?,((' ),?-%/A/&35' )-,' :"2A3' #/A)"&,' (/′ = M^'_`µ05' B$%+' )-,' /*)4*)' 2,($()"%?,' /B' )-, ?*22,%)'(/*2?,G'JA(/5'B$%+')-,'?-"%&,'$%'/*)4*)'?*22,%)'2,(*A)$%&'B2/0'"'+T@_'?-"%&,'$%' (3 G

Solution T ! M ' $T = ' a:9 ' = @@@ : 5′ @@@@@ ( 3( M " T T M T^^ = @@@ × M^^ × T^( 3( M ;-*(5 (3( ' = ^G[TR'_

530 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

Example 7.5 continued

"%+ ( *) ' = ( 8 + ( 3( ' = ^GL + ^G[TR "T'_ ($$ [ (*) [[T @ ' = @@@@@@@@@@@@@@@@@@ ' = M^'HΩ # = @@@@@@@@@@@@@@@@@@@@@@@@ ^GT'0J ' a:9 (30$% = (3( " ^G['_ 9/2')-,')2"%($()/2('*(,+5'"'='T'µ0G';-*(5 (/ = M^ × T' = M^'_ M^'_ - .M = @@@@@@@@@@@@@@@@@@@ ' = ^GM'6Ω T^^'µJ ;-,'/*)4*)'?*22,%)'.$AA'>,'T^^'µJ'")' (3 = (*) ' = T'_G 'DB' (3 '?-"%&,('>3'+T'_5')-,'?/22,(4/%+$%&'?-"%&, $%' ' 3 '.$AA'>, ∆( T'_ ∆' 3 ' = @@@@@@@@@3@ ' = @@@@@@@@@@@@@@@@@@@ ' = Q *µ5 ^GM'6Ω - .M

EXERCISE D7.15 D%')-,'?*22,%)'(/*2?,'/B':K"04A,'LGQ5'$)'$('2,O*$2,+')/'2,+*?,')-,'?-"%&,'$%'/*)4*)'?*22,%)5' ∆' 3 5 ?/22,(4/%+$%&')/'"'?-"%&,'$%'/*)4*)'#/A)"&,5' ∆( 3 5 '/B'T'_')/'Tm'/B' ' 3 G 'I-")'(-/*A+')-,'+$0,%@ ($/%('/B' & T '"%+' & M '>,'?-"%&,+')/V'J((*0,')-")' & T '"%+' & M '"2,')/'2,0"$%'0")?-,+G Ans. "'='Q'µ0U'!'='Q^'µ0

7.4.2 MOS Current-Steering Circuits 5:-9$"#+0"$(-$'&2+$&?-0"*$-'-*0":#'"#-*,&&$"#-1':-/$$"-%$"$&'#$(?-+#-*'"-/$-&$62+*'#$(-#0-6&0) <+($-(*-/+':-0&-20'(-*,&&$"#:-.0&-#1$-<'&+0,:-'962+.+$&-:#'%$:-+"-'"-!F=-F,&&$"#-9+&&0&:-*'" 0/<+0,:23- /$- ,:$(- #0- +962$9$"#- #1+:- *,&&$"#):#$$&+"%- .,"*#+0"=- W+%,&$- \=SC- :10@:- '- :+962$ *,&&$"#):#$$&+"%-*+&*,+#=-a$&$- & T -#0%$#1$&-@+#1-#-($#$&9+"$-#1$-&$.$&$"*$-*,&&$"#- ' a:9 G ->&'") :+:#0&:- & T 5 - & M 5 -'"(- & [ -.0&9-'-#@0)0,#6,#-*,&&$"#-9+&&0&?

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7.4 IC Biasing—Current Sources, Current Mirrors, and Current-Steering Circuits

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7.4 IC Biasing—Current Sources, Current Mirrors, and Current-Steering Circuits

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7.4 IC Biasing—Current Sources, Current Mirrors, and Current-Steering Circuits

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542 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

EXERCISE 7.21

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548 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

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!VEE (c)

550 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

EXERCISE 7.24 9/2')-,'h"2A$%&)/%'#/A)"&,'B/AA/.,2'$%'9$&G'LGN^C>F5'(-/.')-")P # $% ' = ( β T + T ) [ - >T + ( β M + T ) ( - >M + # + ) ] - >T + [ # ($& ⁄ ( β T + T ) ] @ # /*) ' = # + || - >M + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ βM + T v #+ @@@@@@.@ ' = @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ v ($& # + + - >M + [ - >T + # ($& ⁄ ( β T + T ) ] ⁄ ( β M + T )

:#"A*"),' # $% 5 ' # /*) 5 ' "%+' v . ⁄ v($& ' B/2' )-,' ?"(,' ' +M ' = Q'0J5 ' β T ' = β M ' = T^^5 ' # + ' = T'HΩ5 ' "%+ # ($& '=' T^^'HΩG Ans. T^G['6ΩU'M^'ΩU'^G]\'_`_

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VCC VCC

VDD I

Q1

vi

I

vo Rin Q1

vi

Q2

vo VBIAS

Q2

vi

Q2

Q1

vo Rin

I

2I

!VEE (a)

Rin 2I

!VSS

!VEE (b)

(c)

Figure 7.41 0,1' J' EEbE<' "04A$B$,2G' C2F' J%/)-,2' #,2($/%' /B' )-,' EEbE<' ?$2?*$)' .$)-' nM' $04A,0,%),+ *($%&'"'757')2"%($()/2G'C!F';-,'6789:;'#,2($/%'/B')-,'?$2?*$)'$%'C,FG

7.6 Some Useful Transistor Pairings

:10@+"%?-10@$<$&?-10@-#1$-(*-<02#'%$-'#-#1$-/':$-0.- & T -+:-:$#-0&-#1$-*+&*,+#-#1'#-($#$&9+"$: #1$-(*-<02#'%$-'#-#1$-*022$*#0&-0.- & M G -R0#1-+::,$:-'&$-,:,'223-200H$(-'.#$&-+"-#1$-2'&%$&-*+&) *,+#-0.-@1+*1-#1$-FF[FR-'962+.+$&-+:-'-6'&#= 5"-+"#$&$:#+"%-<$&:+0"-0.-#1$-FF[FR-*0".+%,&'#+0"-+:-:10@"-+"-W+%=-\=ON4/8=-a$&$-#1$ FR- :#'%$- +:- +962$9$"#$(- @+#1- '- 757- #&'":+:#0&=- 52#10,%1- 0"23- 0"$- *,&&$"#- :0,&*$- +:- "0@ "$$($(?-0/:$&<$-#1'#-@$-'2:0-"$$(-#0-$:#'/2+:1-'"-'66&06&+'#$-/+':-<02#'%$-'#-#1$-/':$-0.- & M G >1+:-*+&*,+#-+:-6'&#-0.-#1$-+"#$&"'2-*+&*,+#-0.-#1$-606,2'&-\ON-06-'96?-@1+*1-@+22-/$-:#,(+$(-+" F1'6#$&-NS= >1$-KLBWG>-<$&:+0"-0.-#1$-*+&*,+#-+"-W+%=-\=ON4'8-+:-#1$-Fe[Fg-'962+.+$&-:10@"-+" W+%=-\=ON4*8=-

Example 7.8 9/2')-,'EEbE<'"04A$B$,2('$%'9$&G'LGNTC"F'"%+'C>F5'B$%+' # $% 5 ' v . ⁄ v 9 5 '"%+' v . ⁄ v ($& '.-,%',"?-'"04A$B$,2'$( B,+'.$)-'"'($&%"A'(/*2?,'-"#$%&'"'2,($()"%?,' # ($& 5 '"%+'"'A/"+'2,($()"%?,' # " '$('?/%%,?),+'")')-,'/*)4*)G'9/2 ($04A$?$)35'%,&A,?)' - . G

Solution ;-,'"%"A3($('/B'>/)-'?$2?*$)('$('$AA*()2"),+'$%'9$&G'LGNMG'7>(,2#,')-")'>/)-'"04A$B$,2('-"#,')-,'("0,' # $% "%+' v . ⁄ v 9 G ';-,'/#,2"AA'#/A)"&,'&"$%' v . ⁄ v ($& '?"%'>,'B/*%+'"(' v # $% αM #" @@@@@@.@ Z @@@@@@@@@@@@@@@@@@@@@ @ @ @@@@@@@@@@@ v ($& # $% ^ # ($& M- >

RL Rsig

$2vi ! 2re

vi

$2 RL vo # ! v i 2re Q2

Q1 re

re

vsig " !

vi )2re Rin# (b1"1)(2re) (a)

Figure 7.42 'E$2?*$)('B/2':K"04A,'LG\G'CE.5895L>C4.54K.@@.A95047<0>F

551

552 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

Example 7.8 continued

Rsig

vi

Q1 re

vsig " !

re

vi)2re

Q2

Rin# (b1"1)(2re)

$2vi ! 2re

$2 RL vo # ! vi 2re RL

(b) Figure 7.42 'CE.5895L>CF

EXERCISES 7.25

9/2')-,'"04A$B$,2('$%':K"04A,'LG\'B$%+' # $% 5' v . ⁄ v 9 5 '"%+' v . ⁄ v ($& 'B/2')-,'?"(,'''d'T'0J5' β Z T^^G # " Z # ($& Z Q'HΩG Ans. QG^Q' HΩU 'T^^'_`_U'Q^'_`_

D7.26

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553

Summary D%),&2"),+@?$2?*$)'B">2$?")$/%'),?-%/A/&3'/BB,2(')-,'?$2?*$) +,($&%,2'0"%3',K?$)$%&'/44/2)*%$)$,(5')-,'0/()'$04/2)"%) /B' .-$?-' $(' )-,' A"2&,' %*0>,2' /B' $%,K4,%($#,' (0"AA@"2," 678')2"%($()/2(G'J%'/#,22$+$%&'?/%?,2%'B/2'DE'+,($&%,2(5 -/.,#,25'$(')-,'0$%$0$S")$/%'/B'?-$4'"2,"'/2'X($A$?/%'2,"A ,()"),GY'J('"'2,(*A)5'A"2&,@#"A*,+'2,($()/2('"%+'?"4"?$)/2( "2,'#$2)*"AA3'">(,%)G

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554 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

Appendix 7.A Comparison of the MOSFET and the BJT !"-#1+:-'66$"(+7-@$-6&$:$"#-'-*096'&+:0"-0.-#1$-*1'&'*#$&+:#+*:-0.-#1$-#@0-9'Q0&-$2$*#&0"+* ($<+*$:`- #1$- KLBWG>- '"(- #1$- Rb>=- >0- .'*+2+#'#$- #1+:- *096'&+:0"?- #36+*'2- <'2,$:- .0&- #1$ +960&#'"#- 6'&'9$#$&:- 0.- #1$- #@0- ($<+*$:- '&$- .+&:#- 6&$:$"#$(=- V$- '2:0- (+:*,::- #1$- ($:+%" 6'&'9$#$&:-'<'+2'/2$-@+#1-$'*1-0.-#1$-#@0-($<+*$:?-:,*1-':-'%-+"-#1$-Rb>?-'"(-'$44'"(-(3(-+" #1$-KLBWG>?-'"(-#1$-#&'($)0..:-$"*0,"#$&$(-+"-($*+(+"%-0"-:,+#'/2$-<'2,$:-.0&-#1$:$=

7.A.1 Typical Values of MOSFET Parameters ;34$?"A'#"A*,('B/2')-,'$04/2)"%)'4"2"0,),2('/B'c678'"%+'Z678')2"%($()/2('B">2$?"),+'$%'" %*0>,2'/B'E678'42/?,((,('"2,'(-/.%'$%';">A,'LGJGTG':"?-'42/?,(('$('?-"2"?),2$S,+'>3')-, 0$%$0*0'"AA/.,+'?-"%%,A'A,%&)-5' " 0$% U ')-*(5'B/2',K"04A,5'$%'"'^GT\@µ0'42/?,((5')-,'(0"AA,() )2"%($()/2'-"('"'?-"%%,A'A,%&)-'"'='^GT\'µ0G';-,'),?-%/A/&$,('42,(,%),+'$%';">A,'LGJGT'"2, $%'+,(?,%+$%&'/2+,2'/B'?-"%%,A'A,%&)-5'.$)-')-")'-"#$%&')-,'(-/2),()'?-"%%,A'A,%&)-'>,$%&')-, 0/()'0/+,2%G'JA)-/*&-')-,'^G\@µ0'42/?,(('$('%/.'/>(/A,),5'$)('+")"'"2,'$%?A*+,+')/'(-/. )2,%+('$%')-,'#"A*,('/B'#"2$/*('4"2"0,),2(G'D)'(-/*A+'"A(/'>,'0,%)$/%,+')-")'"A)-/*&-';">A, LGJGT'()/4('")')-,'^GT[@µ0'42/?,((5'>3'M^^]')-,2,'.,2,']^@5'RQ@5'"%+'NQ@%0'42/?,((,('"#"$A@ ">A,5'"%+'42/?,((,('+/.%')/'MM'%0'.,2,'$%'#"2$/*('()"&,('/B'+,#,A/40,%)G';-,'^GT\@µ0'"%+ )-,'^GT[@µ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µ9- 6&0*$::=- 4>1$- EC)"9- 6&0*$::?- "0#- :10@"- +"- >'/2$- \=5=N?- 1':- '" 07+($-#1+*H"$::-0.-N=S-"9=8-B+"*$-#1$-07+($-*'6'*+#'"*$-%.6-+:-+"<$&:$23-6&060&#+0"'2-#0-8.6?

Table 7.A.1 Typical Values of CMOS Device Parameters ^G\'µ0

^GQ'µ0

^GMQ'µ0

Z"2"0,),2

c678

Z678

c678

Z678

c678

8.6'C%0F %.6'CB9`µ0MF µ'C?0M`_⋅(F µ%.6'CµJ`_MF (8^'C_F ($$'C_F (/′ C_`µ0F %.v'CB9`µ0F

TQ MG[ QQ^ TML ^GL Q MQ ^GM

TQ MG[ MQ^ Q\ −^GL Q M^ ^GM

] [G\ Q^^ T]^ ^GL [G[ M^ ^GN

] [G\ T\^ R\ −^G\ [G[ T^ ^GN

R QG\ NR^ MRL ^GQ MGQ Q ^G[

Z678 R QG\ TR^ ][ −^GR MGQ R ^G[

^GT\'µ0

^GT['µ0

c678

Z678

c678

N \GR NQ^ [\L ^GQ TG\ Q ^G[L

N \GR T^^ \R −^GQ TG\ R ^G[[

MGL TMG\ N^^ QTT ^GN TG[ Q ^G[R

Z678 MGL TMG\ T^^ TM\ b^GN TG[ R ^G[[

Appendix 7.A Comparison of the MOSFET and the BJT

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555

556 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers

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Appendix 7.A Comparison of the MOSFET and the BJT

557

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7.A.3 Comparison of Important Characteristics >'/2$-\=5=_-6&0<+($:-'-*096+2'#+0"-0.-#1$-+960&#'"#-*1'&'*#$&+:#+*:-0.-#1$-XKLB-'"(-#1$ 575-#&'":+:#0&:=->1$-9'#$&+'2-+:-6&$:$"#$(-+"-'-9'""$&-#1'#-.'*+2+#'#$:-*096'&+:0"=-!"-#1$-.02) 20@+"%?-@$-*099$"#-0"-#1$-<'&+0,:-+#$9:-+"->'/2$-\=5=_=-5:-@$22?-'-",9/$&-0.-",9$&+*'2 $7'962$:- '"(- $7$&*+:$:- '&$- 6&0<+($(- #0- +22,:#&'#$- 10@- #1$- @$'2#1- 0.- +".0&9'#+0"- +"- >'/2$ \=5=_-*'"-/$-6,#-#0-,:$=-R$.0&$-6&0*$$(+"%?-"0#$-#1'#-#1$-YKLB-'"(-#1$-757-#&'":+:#0&:-*'" /$-*096'&$(-+"-'-:+9+2'&-@'3=Table 7.A.3 Comparison of the MOSFET and the BJT c678 E$2?*$)'830>/A

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558 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers Table 7.A.3 continued !"#$ %&'()*+,-+./01 2 "&3+4

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Appendix 7.A Comparison of the MOSFET and the BJT

Table 7.A.3 continued c678 E"4"?$)"%?,(

M % 0= = @@@ !"% .6 + !" .v % .6 [

% 0C = !" .v % .6

;2"%($)$/% 92,O*,%?34K2

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h,($&%'Z"2"0,),2( f//+'J%"A/&'8.$)?-V

575 % π '= % C> + % V>

% C> = τ U 0 1 % V> " M% V>^

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559

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Example 7.A.1 4'8 W0&-'"-XKLB-#&'":+:#0&-@+#1-!B"-=-NT-.'/&+*'#$(-+"-#1$-T=ND)µ9-6&0*$::-@10:$-('#'-'&$-%+<$"-+"->'/2$ \=5=N?-.+"(-#1$-<'2,$:-0.- (3( -'"(- (*) -&$P,+&$(-#0-06$&'#$-#1$-($<+*$-'#- ' $ ' = T^^ -µ5=- !%"0&$- *1'""$2) 2$"%#1-90(,2'#+0"= 4/8 W+"(- ( ,+ - .0&- '"- 575- #&'":+:#0&- .'/&+*'#$(- +"- #1$- 20@)<02#'%$- 6&0*$::- :6$*+.+$(- +"- >'/2$- \=5=S- '"( 06$&'#$(-'#- ' % ' = T^^ -µ5=-!%"0&$-/':$)@+(#1-90(,2'#+0"=

Solution 4'8-

T ! M ' $ ' = @@@ ( µ 5 % .6 ) @@@@@ ( 3( M "

8*>()$)*)$%&' ' $ ' = T^^ 'µJ5'!B"'='T^5'"%+5'B2/0';">A,'LGJGT5' µ 5 % .6 ' = [\L 'µJ`_M'2,(*A)('$%' T M T^^' = @@@ × [\L × T^ × ( 3( M (3( ' = ^GM['_ ;-*(5 (*) = (85 + (3( = ^GQ + ^GM[' = ^GL['_ 4/8-

'% ' = ') >

( ,+ ⁄ ( 2

8*>()$)*)$%&' ' % = T^^ 'µJ'"%+5'B2/0';">A,LGJGM5' ' ) ' = R × T^ [R

[ T\

T^^ × T^ @ = ^GLR'_ ( ,+ ' = ^G^MQ A% @@@@@@@@@@@@@@@@@@@@@@@@ [ T\ R × T^

'J '&$#,(5

Appendix 7.A Comparison of the MOSFET and the BJT

EXERCISE 7.A.1 C"F'9/2'c678')2"%($()/2('B">2$?"),+'$%')-,'^GT\@µ0'),?-%/A/&3'(4,?$B$,+'$%';">A,'LGJGT5'B$%+')-, 2"%&,'/B' '$ '/>)"$%,+'B/2' (3( '2"%&$%&'B2/0'^GM'_')/'^GN'_'"%+' !B"' Z ^GT ')/'T^^G'c,&A,?)'?-"%%,A@ A,%&)-'0/+*A")$/%G' C>F'DB'"'($0$A"2'2"%&,'/B'?*22,%)'$('2,O*$2,+'$%'"%'575')2"%($()/2'B">2$?"),+'$%')-,'A/.@#/A)"&,'42/?,(( (4,?$B$,+'$%';">A,'LGJGM5'B$%+')-,'?/22,(4/%+$%&'?-"%&,'$%'$)(' (,+ G ' Ans. C"F' ' $0$% ' = ^G\ 'µJ'"%+' Ι $0"K = 3.1 '0J'B/2'"'2"%&,'/B'">/*)'N^^^PTU'C>F'B/2' ' % '#"23$%&'/#,2 "'N^^^PT'2"%&,5' ∆(,+ = M^L'0_

Low-Frequency Small-Signal Models ' >1$-20@).&$P,$"*3-90($2:-.0&-#1$-#@0-($<+*$: '&$-<$&3-:+9+2'&-$7*$6#?-0.-*0,&:$?-.0&-#1$-.+"+#$-/':$-*,&&$"#-4.+"+#$- β 8-0.-#1$-Rb>?-@1+*1 %+<$:-&+:$-#0- - π -+"-#1$-13/&+()π-90($2-'"(-#0-#1$-,"$P,'2-$9+##$&-'"(-*022$*#0&-*,&&$"#:-+"-#1$ >-90($2:- ( α < T )G -a$&$-+#-+:-+"#$&$:#+"%-#0-"0#$-#1'#-#1$-20@).&$P,$"*3?-:9'22):+%"'2-90($2: /$*09$-+($"#+*'2-+.-0"$-#1+"H:-0.-#1$-KLBWG>-':-'-Rb>-@+#1- β ' =' ∞' ( α' ='T ) G W0&- /0#1- ($<+*$:?- #1$- 13/&+()π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v S= 5 -%+<$:-&+:$-#0-'-(&'+"-*,&&$"#-*0960"$"#- 0 1S v S= 5 -@1$&$-#1$-/0(3-#&'":*0"(,*#'"*$- 0 1S +:-6&060&#+0"'2-#0- 0 1 U -#1'#-+:?- 0 1S ' = χ 0 1 5 -@1$&$-#1$-.'*#0&- χ -+:-+"-#1$-&'"%$-0.-T=N-#0-T=S= >1$-/0(3-$..$*#-1':-"0-*0,"#$&6'&#-+"-#1$-Rb>= The Transconductance 9/2' )-,' <=;5' )-,' )2"%(?/%+*?)"%?,' 0 1 ' +,4,%+(' .5@Q' /%' )-,' +? ?/AA,?)/2'?*22,%)' ' % G 'Ca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k:- 0 1 -+:-#1$-90:#-(+&$*#23-*096') &'/2$-@+#1-#1$-.0&9,2'-.0&-#1$-Rb>=-!#-+"(+*'#$:-#1'#-.0&-#1$-:'9$-06$&'#+"%-*,&&$"#?- 0 1 -0.-#1$ KLBWG>-+:-:9'22$&-#1'"-#1'#-0.-#1$-Rb>=->1+:-+:-/$*',:$- (3( ⁄ M -+:-#1$-&'"%$-0.-T=TC-J-#0 T=NC J?-@1+*1-+:-#@0-#0-:+7-#+9$:-#1$-*0&&$:60"(+"%-#$&9-+"-#1$-Rb>k:-.0&9,2'?-"'9$23- ( 2 G >1$-:$*0"(-.0&9,2'-.0&-#1$-KLBWG>k:- 0 1 -+"(+*'#$:-#1'#-.0&-'-%+<$"-($<+*$-4+=$=?-%+<$" !B"8?- 0 1 -+:-6&060&#+0"'2-#0- (3( G ->1,:-'-1+%1$&- 0 1 -+:-0/#'+"$(-/3-06$&'#+"%-#1$-KLBWG> '#- '- 1+%1$&- 0<$&(&+<$- <02#'%$=- a0@$<$&?- @$- :10,2(- &$*'22- #1$- 2+9+#'#+0":- +960:$(- 0"- #1$ 9'%"+#,($-0.- (3( -/3-#1$-2+9+#$(-<'2,$-0.- ($$ G -Y,#-(+..$&$"#23?-#1$-"$$(-#0-0/#'+"-'-&$':0"'/23 1+%1- 0 1 -*0":#&'+":-#1$-($:+%"$&k:-+"#$&$:#-+"-&$(,*+"%- (3( G >1$-#1+&(- 0 1 -.0&9,2'-:10@:-#1'#-.0&-'-%+<$"-#&'":+:#0&-4+=$=?-%+<$"-!B"8?- 0 1 -+:-6&060&#+0"'2-#0 ' $ G ->1+:-:10,2(-/$-*0"#&':#$(-@+#1-#1$-/+602'&-*':$?-@1$&$- 0 1 -+:-(+&$*#23-6&060&#+0"'2-#0- ' % G Output Resistance ->1$-0,#6,#-&$:+:#'"*$-.0&-/0#1-($<+*$:-+:-($#$&9+"$(-/3-:+9+2'&-.0&) 9,2':?-@+#1- - . -/$+"%-#1$-&'#+0-0.- (/ -#0-#1$-/+':-*,&&$"#- C ' $ -0&- ' % FG ->1,:?-.0&-/0#1-#&'":+:#0&:?

561

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$&-+22,:#&'#$(-:10= A0 (log scale) Subthreshold region 1000

Strong inversion region

100

1 Slope # !2

10 1

10! 6

10! 5

10! 4

10! 3

10! 2

ID (A) (log scale)

Figure 7.A.1 ;-,' $%)2$%($?' &"$%' /B' )-,' 6789:;' #,2(*(' >$"(' ?*22,%)' '$G' 7*)($+,' )-,' (*>)-2,(-/A+' 2,&$/%5 )-$( $('"'4A/)'/B' / = ( ′ M µ % !" ` ' 'B/2')-,'?"(,P'µ5%.6'='M^''µJ`_M5' (/′ = M^'_`µ05 '"'='M'µ05'"%+ ^ / 5 .6 $ !'='M^'µ0G

Appendix 7.A Comparison of the MOSFET and the BJT

563

Example 7.A.2 I,'.$(-')/'?/04"2,')-,'#"A*,('/B' 0 1 5 '$%4*)'2,($()"%?,'")')-,'&"),'C>"(,F5' - . 5 '"%+' / ^ 'B/2'"%'c678')2"%@ ($()/2'B">2$?"),+'$%')-,'^GMQ@µ0'),?-%/A/&3'(4,?$B$,+'$%';">A,'LGJGT'"%+'"%'575')2"%($()/2'B">2$?"),+'$% )-,'A/.@#/A)"&,'),?-%/A/&3'(4,?$B$,+'$%';">A,'LGJGMG'J((*0,'>/)-'+,#$?,('"2,'/4,2")$%&'")'"'+2"$%'C?/AA,?@ )/2F'?*22,%)'/B'T^^'µJG'9/2')-,'6789:;5'A,)'"'='^GN'µ0'"%+'!'='N'µ05'"%+'(4,?$B3')-,'2,O*$2,+' (3( G

Solution 9/2')-,'c678')2"%($()/25 T ! M ' $ ' = @@@ ( µ 5 % .6 ) @@@@@ ( 3( M " T N M T^^' = @@@ × MRL × @@@@@@@ × ( 3( M ^GN ;-*(5 (3( ' = ^GML'_ 01 ' = =

! M ( µ 5 % .6 ) @@@@@ ' $ " M × MRL × T^ × T^^' = ^GL['0J`_

# $% ' = ∞ (/′ " Q × ^GN ' = @@@@@@@@@@@@@@@@ ' = M^'HΩ - . ' = @@@@@@@@@@@ '$ ^GT / ^ ' = 0 1 - . ' = ^GL[ × M^'= TNGR'_`_ 9/2')-,'575')2"%($()/25 '% ^GT'0J @ ' = @@@@@@@@@@@@@@@@@@@ ' = N'0J`_ 0 1 ' = @@@@@ (2 ^G^MQ'_ T^^ # $% ' = - π ' = β ^ ⁄ 0 1 ' = @@@@@@@@@@@@@@@@@@@ ' = MQ'HΩ N'0J`_ ( [Q - . ' = @@@@@/@ ' = @@@@@@@@@@@@@@@@@@ ' = [Q^'HΩ ^GT'0J '% / ^ ' = 0 1 - . ' = N × [Q^' = TN^^'_`_

EXERCISE 7.A.2 9/2' "%' c678' )2"%($()/2' B">2$?"),+' $%' )-,' ^GQ@µ0' 42/?,((' (4,?$B$,+' $%' ;">A,' LGJGT' .$)" = ^GQ µ05'B$%+')-,')2"%(?/%+*?)"%?,'"%+')-,'$%)2$%($?'&"$%'/>)"$%,+'")' ' $ '= T^ 'µJ5'T^^'µJ5'"%+'T'0JG Ans. ^GM'0J`_5'M^^'_`_U'^GR'0J`_5'RM'_`_U'M'0J`_5'M^'_`_

564 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers High-Frequency Operation >1$-:+962+.+$(-1+%1).&$P,$"*3-$P,+<'2$"#-*+&*,+#:-.0&-#1$ KLBWG>- '"(- #1$- Rb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`-#1$-*1'""$2-2$"%#1-.0&-#1$-KLBWG>-'"(-#1$ /':$-@+(#1-.0&-#1$-Rb>=->1$:$-.0&9,2':-'2:0-*2$'&23-+"(+*'#$-#1'#-:10&#$&)*1'""$2-KLBWG>:NT '"(-"'&&0@$&)/':$-Rb>:-'&$-+"1$&$"#23-*'6'/2$-0.-'-@+($&-/'"(@+(#1-0.-06$&'#+0"=-!#-+:-'2:0 +960&#'"#-#0-"0#$-#1'#-@1+2$-.0&-#1$-Rb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gaM-#0-ST-gaM-':-*096'&$(-#0-#1$-OTT-KaM-#0-ETT-KaM-0/#'+"$(-@+#1-#1$-:#'"('&(-1+%1) <02#'%$-6&0*$::=-!"-#1$- KLB- *':$?- XKLB- #&'":+:#0&:- .'/&+*'#$(-+"- '-90($&"- :,/9+*&0" #$*1"020%3?-:,*1-':-#1$-T=ND)µ9-6&0*$::?-'*1+$<$-K2-<'2,$:-+"-#1$-&'"%$-0.-C-gaM-#0-NC-gaM= R$.0&$- 2$'<+"%- #1$- :,/Q$*#- 0.- 1+%1).&$P,$"*3- 06$&'#+0"?- 2$#k:- 200H- +"#0- #1$- $..$*#- 0.- ' *'6'*+#+<$-20'(-0"-#1$-/'"(@+(#1-0.-#1$-*0990"):0,&*$-4*0990")$9+##$&8-'962+.+$&=-W0& #1+:-6,&60:$-@$-:1'22-'::,9$-#1'#-#1$-.&$P,$"*+$:-0.-+"#$&$:#-'&$-9,*1-20@$&-#1'"-K2-0.-#1$ #&'":+:#0&=-a$"*$-@$-:1'22-"0#-#'H$-#1$-#&'":+:#0&-*'6'*+#'"*$:-+"#0-'**0,"#=-W+%,&$-\=5=S4'8 :10@:-'-*0990"):0,&*$-'962+.+$&-@+#1-'-*'6'*+#+<$-20'(- % " G->1$-<02#'%$-%'+"-.&09-%'#$-#0 (&'+"-*'"-/$-.0,"(-':-.0220@:`

(. ' = [ 0 1 (0= ( - . || % " ) T - . @@@@@@@@ =% " ' = [ 0 1 (0= @@@@@@@@@@@@@@@@@@@ T - . + @@@@@@@@ =% " ( 01 -. @ / v ' = @@@@@@.@ ' = [ @@@@@@@@@@@@@@@@@@@@@@ (0= T + =% " - .

'CLGJGTF

>1,:- #1$- %'+"- 1':?- ':- $76$*#$(?- '- 20@).&$P,$"*3- <'2,$- 0.- 0 1 - . ' = / ^ - '"(- '- .&$P,$"*3 &$:60":$-0.-#1$-:+"%2$)#+9$)*0":#'"#-4B>F8-20@)6'::-#36$-@+#1-'-/&$'H-4602$8-.&$P,$"*3-'#

T ω W ' = @@@@@@@@@@@

'CLGJGMF

%" -.

L/<+0,:23-#1+:-602$-+:-.0&9$(-/3- - . -'"(- % " G-5-:H$#*1-0.-#1$-9'%"+#,($-0.-%'+"-<$&:,:-.&$) P,$"*3-+:-:10@"-+"-W+%=-\=5=S4/8=-V$-0/:$&<$-#1'#-#1$-%'+"-*&0::$:-#1$-T)(R-2+"$-'#-.&$P,$"*3

ω8 5

T %" -.

ω 8 ' = / ^ ω W ' = ( 0 1 - . ) @@@@@@@@@@@ JA)-/*&-')-,'2,"(/%'$('>,3/%+'/*2'?"4">$A$)$,('")')-$('()"&,5'K2'/B'6789:;(')-")'-"#,'#,23'(-/2)'?-"%@ %,A('#"2$,('$%#,2(,A3'.$)-'"42")-,2')-"%'.$)-'"SG

T^

Appendix 7.A Comparison of the MOSFET and the BJT

G

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Vo (dB) Vgs

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frequency (log scale)

f3dB (b) Figure 7.A.2 92,O*,%?3'2,(4/%(,'/B'"'E8'"04A$B$,2'A/"+,+'.$)-'"'?"4"?$)"%?,'%"'"%+'B,+'.$)-'"%'$+,"A #/A)"&,'(/*2?,G'D)'$('"((*0,+')-")')-,')2"%($()/2'$('/4,2")$%&'")'B2,O*,%?$,('0*?-'A/.,2')-"%'K25'"%+')-*(')-, $%),2%"A'?"4"?$)"%?,('"2,'%/)')"H,%'$%)/'"??/*%)G

>1,:?

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ω 8 ' = @@@@@1@

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>1'#- +:?- #1$- "%.&<'3,.%*5#$;"$%!<-0&?-$P,+<'2$"#23?- #1$-3,.%=2,%->.-&4*6#)-"!&NN- ω 8 -+: #1$-&'#+0-0.- 0 1 -'"(- % " G -V$-#1,:-*2$'&23-:$$-#1'#-.0&-'-%+<$"-*'6'*+#+<$-20'(- % " 5 -'-2'&%$& %'+"[/'"(@+(#1- 6&0(,*#- +:- '*1+$<$(- /3- 06$&'#+"%- #1$- KLBWG>- '#- '- 1+%1$&- 0 1 G - !($"#+*'2 '"'23:+:-'"(-*0"*2,:+0":-'6623-#0-#1$-*':$-0.-#1$-Rb>=-!"-$'*1-*':$?-/'"(@+(#1-+"*&$':$:-': /+':-*,&&$"#-+:-+"*&$':$(= Design Parameters W0&-#1$-Rb>-#1$&$-'&$-#1&$$-($:+%"-6'&'9$#$&:; ' % 5 - (,+ 5 -'"(- ' ) 40&?- $P,+<'2$"#23?- #1$- '&$'- 0.- #1$- $9+##$&[/':$- Q,"*#+0"8;'"(- #1$- ($:+%"$&- *'"- :$2$*# '"3-#@0=-a0@$<$&?-:+"*$- ' % -+:-$760"$"#+'223-&$2'#$(-#0- (,+ -'"(-+:-<$&3-:$":+#+<$-#0-#1$ TT ;-,'*%$)3@&"$%'B2,O*,%?3'"%+')-,'&"$%b>"%+.$+)-'42/+*?)'/B'"%'"04A$B$,2'"2,')-,'("0,'.-,%')-,'B2,O*,%?3 2,(4/%(,'$('/B')-,'($%&A,@4/A,')34,U'/)-,2.$(,')-,')./'4"2"0,),2('0"3'+$BB,2G

565

566 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers <'2,$-0.- (,+ - C(,+ -*1'"%$:-/3-0"23-ET-9J-.0&-'-.'*#0&-0.-NT-*1'"%$-+"- ' % F5 - ' % -+:-9,*1 90&$-,:$.,2-#1'"- (,+ -':-'-($:+%"-6'&'9$#$&=-5:-9$"#+0"$(-$'&2+$&?-#1$-,#+2+#3-0.-#1$-GRb '&$'-':-'-($:+%"-6'&'9$#$&-+:-&'#1$&-2+9+#$(-/$*',:$-0.-#1$-"'&&0@-&'"%$-0<$&-@1+*1- / + *'"- <'&3=- !#- .0220@:- #1'#- .0&-#1$- Rb>-#1$&$- +:- 0"23- 0"$- $..$*#+<$- ($:+%"- 6'&'9$#$&`- #1$ *022$*#0&-*,&&$"#- ' % G -W+"'223?-"0#$-#1'#-@$-1'<$-"0#-*0":+($&$(- (%+ -#0-/$-'-($:+%"-6'&'9$#$&? :+"*$-+#:-$..$*#-0"- ' % -+:-0"23-:$*0"('&3=-L.-*0,&:$?-':-@$-2$'&"$(-+"-F1'6#$&-E?- (%+ -'..$*#:-#1$ 0,#6,#):+%"'2-:@+"%= W0&- #1$- KLBWG>- #1$&$- '&$- .0,&- ($:+%"- 6'&'9$#$&:; ' $ 5 - (3( 5 - "?- '"(- !;'"(- #1$ ($:+%"$&- *'"- :$2$*#- '"3- #1&$$=- W0&- '"'20%- *+&*,+#- '662+*'#+0":- #1$- #&'($)0..- +"- :$2$*#+"%- ' <'2,$-.0&-"-+:-/$#@$$"-#1$-1+%1$&-:6$$(-0.-06$&'#+0"-4@+($&-'962+.+$&-/'"(@+(#18-0/#'+"$(-'# 20@$&-<'2,$:-0.-"-'"(-#1$-1+%1$&-+"#&+":+*-%'+"-0/#'+"$(-'#-2'&%$&-<'2,$:-0.-"=-f:,'223-0"$ :$2$*#:-'"-"-0.-'/0,#-SCc-#0-CTc-%&$'#$&-#1'"- " 0$% G >1$-:$*0"(-($:+%"-6'&'9$#$&-+:- (3( G-V$-1'<$-'2&$'(3-9'($-",9$&0,:-&$9'&H:-'/0,# #1$-$..$*#-0.-#1$-<'2,$-0.- (3( -0"-6$&.0&9'"*$=-f:,'223?-.0&-:,/9+*&0"-#$*1"020%+$:?- (3( -+: :$2$*#$(-+"-#1$-&'"%$-0.-T=N-J-#0-T=_-J= L"*$-<'2,$:-.0&-"-'"(- (3( -1'<$-/$$"-:$2$*#$(?-#1$-($:+%"$&-+:-2$.#-@+#1-#1$-:$2$*#+0" 0.-#1$-<'2,$-0.- ' $ -0&-!-40&?-$P,+<'2$"#23?-!B"8=-W0&-'-%+<$"-6&0*$::-'"(-.0&-#1$-:$2$*#$( <'2,$:-0.-"-'"(-(3( 5- ' $ -+:-6&060&#+0"'2-#0-!B"=-!#-+:-+960&#'"#-#0-"0#$-#1'#-#1$-*10+*$-0. ' $ -0&?-$P,+<'2$"#23?-0.-!B"-1':-"0-/$'&+"%-0"-#1$-<'2,$-0.-+"#&+":+*-%'+"- / ^ -'"(-#1$-#&'") :+#+0"- .&$P,$"*3- K2 =- a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ain! (dB) 20 log A0

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Figure 7.A.3 D%?2,"($%&''$'/2'!`"'$%?2,"(,(')-,'>"%+.$+)-'/B'"'6789:;'"04A$B$,2'/4,2"),+'")'"'?/%()"%) (3('"%+'A/"+,+'>3'"'?/%()"%)'?"4"?$)"%?,'%"G

Appendix 7.A Comparison of the MOSFET and the BJT '

Example 7.A.3 D%' )-$(' ,K"04A,' .,' $%#,()$&"),' )-,' &"$%' "%+' )-,' -$&-@B2,O*,%?3' 2,(4/%(,' /B' "%' 575' )2"%($()/2' "%+' "% c678')2"%($()/2G'9/2')-,'575')2"%($()/25'"((*0,')-")'$)'$('B">2$?"),+'$%')-,'A/.@#/A)"&,'42/?,(('(4,?$B$,+ $%';">A,'LGJGM5'"%+'"((*0,')-")' % µ "% µ ^ G '9/2' ' % = T^ 'µJ5'T^^'µJ5'"%+'T'0J5'B$%+' 0 1 5 ' - . 5 ' / ^ 5 ' % C> 5 % V> 5 ' % π 5 ' % µ 5 ' "%+' K 2 G ' JA(/5' B/2' ,"?-' #"A*,' /B' ' % 5 ' B$%+' )-,' &"$%b>"%+.$+)-' 42/+*?)' K8' /B' "' ?/00/%@ ,0$)),2'"04A$B$,2'A/"+,+'>3'"'TX49'?"4"?$)"%?,5'%,&A,?)$%&')-,'$%),2%"A'?"4"?$)"%?,('/B')-,')2"%($()/2G'9/2 )-,'c678')2"%($()/25'"((*0,')-")'$)'$('B">2$?"),+'$%')-,'^GMQ@µ0'E678'42/?,(('.$)-'" ='^GN'µ0G'g,)')-, )2"%($()/2'>,'/4,2"),+'")' (3( = ^GMQ'_G '9$%+ !B"')-")'$('2,O*$2,+')/'/>)"$%' ' $ ' = T^ 'µJ5'T^^'µJ5'"%+ T 0JG'J)',"?-'#"A*,'/B' ' $ 5 'B$%+ 0 1 5 ' - . 5 ' / ^ 5 ' % 0= 5 ' % 0C 5 '"%+' K 2 G'JA(/5'B/2',"?-'#"A*,'/B' ' $ 5 '+,),20$%, )-,'&"$%b>"%+.$+)-'42/+*?)'K8'/B'"'?/00/%@(/*2?,'"04A$B$,2'A/"+,+'>3'"'T@49'?"4"?$)"%?,5'%,&A,?)$%&')-, $%),2%"A'?"4"?$)"%?,('/B')-,')2"%($()/2G

Solution 9/2')-,'575')2"%($()/25 '% '% @ ' = @@@@@@@@@@@@ @ ' = N^' % -5]J 0 1 ' = @@@@@ (2 ^G^MQ ( [Q - . ' = @@@@@/@ ' = @@@@@@ 'Ω '% '% ( [Q / ^ ' = @@@@@/@ ' = @@@@@@@@@@@@@ ' = TN^^ -J]J (2 ^G^MQ % C> ' = τ U 0 1 ' = T^ × T^

[ TM

[]

× N^' % ' = ^GN × T^ ' % 9 '

%V> " M% V>^ = T^ -.W %π ' = % C> + % V> %µ " % µ ^ ' = Q -.W 01 @ K 2 ' = @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ M π ( %π + %µ ) 01 01 @ ' = @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @ K 8 ' = @@@@@@@@@@@@ M π % " M π × T × T^ [TM I,')-*('/>)"$%')-,'B/AA/.$%&'2,(*A)(P '% --NT-µ5 NTT-µ5 ----N 95

0 1 'C0J`_F

-.'CH+F

T=O O OT

_CTT _CT _C

/ ^ 'C_`_F % C> 'CB 9F % V> 'CB 9F % π 'CB 9F % µ 'CB 9F NOTT NOTT NOTT

O OT OTT

NT NT NT

9/2')-,'c678')2"%($()/25 ! M T ' $ ' = @@@ µ 5 % .6 @@@@@ ( 3( " M T ! T = @@@ × MRL × @@@@@ × @@@@@@ M " TR

NO CT ONT

C C C

K 2 'Cf!SF _=O NN=E NC=_

K 8 'C6!SF EO EOT EOTT

567

568 Chapter 7 Building Blocks of Integrated-Circuit Amplifiers Example 7.A.3 continued

>1,:? ! @@@@@ ' = ^GTM' $ " '$ '$ @ ' = @@@@@@@@@@@@@@@@ @ ' = \' $ -5]J 0 1 ' = @@@@@@@@@@@@@@@ (3( ⁄ M ^GMQ ⁄ M (′/ " × ^GN@ @@@@ M @ ' = Q@@@@@@@@@@@@@@@ '= @ Ω - . ' = @@@@@@@@@@ '$ '$ '$

-

/ ^ ' = 0 1 - . = TR -J]J % 0= ' = @@M[@ !"% .6 + % .v ' = @@M[@ ! × ^GN × QG\ + ^GR! % 0C = % .v = ^GR! 01 K2 = @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ M π ( % 0= + % 0C ) 01 @ K8 = @@@@@@@@@@@@ M π %" I,')-*('/>)"$%')-,'B/AA/.$%&'2,(*A)(P '$

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N=S NS NST

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-.'CH+F STT ST S

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N=T_ NT=_ NT_

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NS=\ NS\ NS\T

EXERCISE 7.A.3

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Appendix 7.A Comparison of the MOSFET and the BJT

569

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CHAPTER 7 P R O B L E M S

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CHAPTER 7 P R O B L E M S

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CHAPTER 7 P R O B L E M S

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CHAPTER 8

Differential and Multistage Amplifiers Introduction 8.1

587

The MOS Differential Pair

588

8.2 Small-Signal Operation of the MOS Differential Pair 599 8.3 The BJT Differential Pair

612

8.4 Other Nonideal Characteristics of the Differential Amplifier 629

8.5 The Differential Amplifier with Active Load 635 8.6 Multistage Amplifiers Summary

666

Problems

667

651

IN THIS CHAPTER YOU WILL LEARN 1. The essence of the operation of the MOS and the bipolar differential amplifiers: how they reject common-mode noise or interference and amplify differential signals. 2. The analysis and design of MOS and BJT differential amplifiers. 3. Differential-amplifier circuits of varying complexity; utilizing passive resistive loads, current-source loads, and cascodes—the building blocks we studied in Chapter 7. 4. An ingenious and highly popular differential-amplifier circuit that utilizes a current-mirror load. 5. The structure, analysis, and design of amplifiers composed of two or more stages in cascade. Two practical examples are studied in detail: a two-stage CMOS op amp and a four-stage bipolar op amp.

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8.3 The BJT Differential Pair F,;@)#$ G7HC$ /"(9/$ *"#$ 3&/,-$ gk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l*"&*$,/:$,1$/(%#$&++2,-&*,(1/$*"#$*9( -(22#-*()/$ %&<$ 3#$ -(11#-*#0$ *($ -@))#1*$ /(@)-#/$ )&*"#)$ *"&1$ )#/,/*,?#$ 2(&0/7$ I* ,/$ #//#1*,&2: *"(@;":$*"&*$*"#$-(22#-*()$-,)-@,*/$3#$/@-"$*"&*$!H$&10$!J$1#?#)$#1*#)$/&*@)&*,(17

8.3 The BJT Differential Pair

+ –

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Figure 8.15 !"#$3&/,-$gk!$ 0,..#)#1*,&2A+&,)$-(1.,;@)&*,(17

8.3.1 Basic Operation !/$ 4##$ "/5$ *"#$ >?!$ %&''#(#)*&+,$ .+&($ 5/(84;$ 1/)4&%#($ '&(4*$ *"#$ 1+4#$ /'$ *"#$ *5/$ 7+4#4$ [/&)#% */2#*"#($+)%$1/))#1*#%$*/$+$1/00/)-0/%#$
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0

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Figure 8.16 e,..#)#1*$ %(0#/$ (.$ (+#)&*,(1$ (.$ *"#$ gk!$ 0,..#)#1*,&2$ +&,)]$ 4,5$ *"#$ 0,..#)#1*,&2$ +&,)$ 9,*"$ & -(%%(1A%(0#$,1+@*$?(2*&;#$%&' \$465$*"#$0,..#)#1*,&2$+&,)$9,*"$&$`2&);#a$0,..#)#1*,&2$,1+@*$/,;1&2\$4!5$*"#$0,.A .#)#1*,&2$+&,)$9,*"$&$2&);#$0,..#)#1*,&2$,1+@*$/,;1&2$(.$+(2&),*<$(++(/,*#$*($*"&*$,1$465\$4&5$*"#$0,..#)#1*,&2$+&,) 9,*"$&$/%&22$0,..#)#1*,&2$,1+@*$/,;1&2$v) 7$P(*#$*"&*$9#$"&?#$&//@%#0$*"#$3,&/$-@))#1*$/(@)-#$"$*($3#$,0#&2$M,7#7: ,*$"&/$&1$,1.,1,*#$(@*+@*$)#/,/*&1-#N$&10$*"@/$"$)#%&,1/$-(1/*&1*$9,*"$*"#$-"&1;#$,1$%&'7

613

614 Chapter 8 Differential and Multistage Amplifiers

!VEE (c)

!VEd (d)

Figure 8.16 1,+-)+?/8I

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615

EXERCISE 8.9 F,10$vH:$v&H:$&10$v&J$,1$*"#$-,)-@,*$(.$F,;7$KG7_7$8//@%#$*"&*$ v GH (.$&$-(10@-*,1;$*)&1/,/*()$,/$&+A +)(>,%&*#2<$U7D$T$&10$*"&*$α$%$H7 "5 V

1 k% vE "0.5 V

Q1

Q2

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vC2 1 k%

1 k%

!5 V

Ans. +U7D$T\$−C$T\$−U7D$T

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$MG7RDN

e x EXERCISE 8.10 e#*#)%,1#$*"#$,1+@*$-(%%(1A%(0#$)&1;#$.()$&$3,+(2&)$0,..#)#1*,&2$&%+2,.,#)$(+#)&*,1;$.)(%$ ± J7C AT +(9#)$/@++2,#/$&10$3,&/#0$9,*"$&$/,%+2#$-@))#1*$/(@)-#$*"&*$0#2,?#)/$&$-(1/*&1*$-@))#1*$(.$U7L$%8$&10 )#S@,)#/$&$%,1,%@%$(.$U7Q$T$.()$,*/$+)(+#)$(+#)&*,(17$!"#$-(22#-*()$)#/,/*&1-#/$ # & ] C $= Ω7 Ans. \ H7C $T$*($ZH7_$T

616 Chapter 8 Differential and Multistage Amplifiers

8.3.3 Large-Signal Operation S#$)/5$.(#4#)*$+$2#)#(+,$+)+,64&4$/'$*"#$>?!$%&''#(#)*&+,$.+&($/'$:&29$Y9AX9$G'$5#$%#)/*#$*"#
" ( vGH− vH ) ⁄ %J ) HH = AAAA* /

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$MG7R_N

α α

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) HH H AAAAAAAAAAAAAAAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ( v GJ − v GH ) ⁄ % J ) HH + ) HJ H+/

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) HH + ) HJ = "

$MG7DJN

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EXERCISE 8.11

F()$*"#$gk!$0,..#)#1*,&2$+&,)$(.$F,;7$G7HC:$.,10$*"#$?&2@#$(.$,1+@*$0,..#)#1*,&2$/,;1&2$*"&*$,/$/@..,-,#1* *($-&@/#$)HH =$U7__"7 Ans. HHC$%T

617

618 Chapter 8 Differential and Multistage Amplifiers VCC

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$MG7DCN $MG7DRN

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vid 2(b " 1) (re " Re)

Figure 8.21 8$0,..#)#1*,&2$&%+2,.,#)$9,*"$#%,**#)$)#/,/*&1-#/7$512<$/,;1&2$S@&1*,*,#/$&)#$/"(91$M,1$-(2()N7

!"34$ *"#$ 1/,,#1*/($ /'$ !A$ 5&,,$ #L"&7&*$ +$ 13((#)*$ &)1(#0#)*$ )1$ +)%$ *"#$ 1/,,#1*/($ /'$ !T$ 5&,, #L"&7&*$+$13((#)*$%#1(#0#)*$)1P

αv

v

)8 ) 1 = α ) / = AAAAAAAAA = 9 : AAAA)8A J./ J

$MG7GQN

U/*#$*"+*$&)$:&29$Y9TI$5#$"+<#$4"/5)$4&2)+,$J3+)*&*$/),69$G*$&4$&0.,&#%;$/'$1/3(4#;$*"+* #+1"$*(+)4&4*/($&4$7&+4#%$+*$+)$#0&**#($13((#)*$/'$ " ⁄ J 9 !"&4$0#*"/%$/'$+)+,64&4$&4$.+(*&13,+(,6$34#'3,$5"#)$(#4&4*+)1#4$+(#$&)1,3%#%$&)$*"#$#0&**#(4;$+4$4"/5)$&)$:&29$Y9TA9$:/($*"&4$1&(13&*$5#$"+<# v

)8 A ) / Y AAAAAAAAAAAAAAAAAAAAA J./ + J# /

$MG7GLN

Input Differential Resistance m12,=#$*"#$456$0,..#)#1*,&2$&%+2,.,#):$9",-"$"&/$&1$,1.,1,*# ,1+@*$)#/,/*&1-#:$*"#$3,+(2&)$0,..#)#1*,&2$+&,)$#>",3,*/$&$.,1,*#$,1+@*$)#/,/*&1-#:$&$)#/@2*$(.$*"# .,1,*#$β$(.$*"#$gk!7 !"#$&).3*$%&''#(#)*&+,$(#4&4*+)1#$&4$*"#$(#4&4*+)1#$4##)$7#*5##)$*"#$*5/$7+4#4`$*"+*$&4;$&*$&4 *"#$(#4&4*+)1#$4##)$76$*"#$%&''#(#)*&+,$&).3*$4&2)+,$v)8 9$:/($*"#$%&''#(#)*&+,$+0.,&'&#($&)$:&249$Y9AH +)%$Y9TI$&*$1+)$7#$4##)$*"+*$*"#$7+4#$13((#)*$/'$!A$4"/54$+)$&)1(#0#)*$)C$+)%$*"#$7+4#$13((#)* /'$!T$4"/54$+)$#J3+,$%#1(#0#)*; v )8 ⁄ J./ )/ A = AAAAAAAAAAAAAAAA A ) C = AAAAAAAAAAA β +H β +H

$MG7GCN

!"34$*"#$%&''#(#)*&+,$&).3*$(#4&4*+)1#$#)8$&4$2&<#)$76$ v

#)8 ≡ AAAA)8A = ( β $ +$H )J./ = J.π )C

$MG7GRN

621

622 Chapter 8 Differential and Multistage Amplifiers !"&4$(#43,*$&4$[34*$+$(#4*+*#0#)*$/'$*"#$'+0&,&+($(#4&4*+)1#-(#',#1*&/)$(3,#`$)+0#,6;$->/7./2)2-A+1/ 2//+7C/-=//+7->/7-=,7CA2/27)27/K?AB7-,7->/7-,-AB7./2)2-A+1/7)+7->/7/:)--/.71).1?)-7:?B-)EB)/87CD Lβ$+$MN9 S#$1+)$#0.,/6$*"&4$(3,#$*/$'&)%$*"#$&).3*$%&''#(#)*&+,$(#4&4*+)1#$'/($*"#$1&(13&*$&)$:&29$Y9TA$+4$

# )8 = ( β $ + H ) ( J./ + J# / )

$MG7GDN

Differential Voltage Gain E#$"&?#$#/*&32,/"#0$*"&*$.()$/%&22$0,..#)#1-#$,1+@*$?(2*&;#/ Mv)8$&$J%J \$,7#7:$v)8$/%&22#)$*"&1$&3(@*$JU$%TN:$*"#$-(22#-*()$-@))#1*/$&)#$;,?#1$3< v

) &H = "& + 9 : AAAA)8A J

$MG7GGN

v

) &J = "& $− 9 : AAAA)8A J

$MG7G_N

α" "& = AAAAAA J

$MG7_UN

5"#(#

!"34$*"#$*/*+,$
v &H

= ( %&& \ "& # & ) \ 9 : # & AAAA)8A J

v &J

= ( %&& \ "& # & ) + 9 : # & AAAA)8A J

v

$MG7_HN $MG7_JN

!"#$J3+)*&*$&)$.+(#)*"#4#4$+(#$4&0.,6$*"#$%1$
,8 A = 9: #& F 8 = AAAAA

v )8

$MG7_QN

:/($*"#$%&''#(#)*&+,$+0.,&'&#($5&*"$(#4&4*+)1#4$&)$*"#$#0&**#($,#+%4$C:&29$Y9TAF;$*"#$%&''#(#)*&+,$2+&)$&4$2&<#)$76

α ( J# & ) #& A % AAAAAAAAAAAAAAA A F 8 = AAAAAAAAAAAAAAAAAAAAA J./ + J# / ./ + # /

$MG7_LN

!"&4$#J3+*&/)$&4$+$'+0&,&+($/)#P$G*$4*+*#4$*"+*$->/7O,B-A9/79A)+7)27/K?AB7-,7->/7.A-),7,@7->/7-,-AB ./2)2-A+1/7)+7->/71,BB/1-,.71).1?)-$LP#& N$-,7->/7-,-AB7./2)2-A+1/7)+7->/7/:)--/.71).1?)-$LP./$+$P#/ N9 The Differential Half-Circuit 8/$,1$*"#$456$-&/#:$*"#$0,..#)#1*,&2$;&,1$(.$*"#$gk!$0,.A .#)#1*,&2$&%+2,.,#)$-&1$3#$(3*&,1#0$3<$-(1/,0#),1;$,*/$0,..#)#1*,&2$"&2.A-,)-@,*7$F,;@)#$G7JJM&N /"(9/$&$0,..#)#1*,&2$&%+2,.,#)$.#0$3<$&$0,..#)#1*,&2$/,;1&2$v)8$*"&*$,/$&++2,#0$,1$&$!"#/*'#'$+,17 M/038=/0**$()$6,*,$!'&N$%&11#)7$!"&*$,/:$9",2#$*"#$3&/#$(.$!H$,/$)&,/#0$3<$ v )8 ⁄ J :$*"#$3&/#$(. !J$,/$2(9#)#0$3< v )8 ⁄ J7$E#$"&?#$&2/($,1-2@0#0$*"#$(@*+@*$)#/,/*&1-#$#HH$(.$*"#$3,&/$-@))#1* /(@)-#7$F)(%$/<%%#*)<:$,*$.(22(9/$*"&*$*"#$/,;1&2$?(2*&;#$&*$*"#$#%,**#)/$9,22$3#$O#)(7$!"@/$*"# -,)-@,*$,/$#S@,?&2#1*$*($*"#$*9($-(%%(1A#%,**#)$&%+2,.,#)/$/"(91$,1$F,;7 G7JJM3N:$9"#)#$#&-" (.$*"#$*9($*)&1/,/*()/$,/$3,&/#0$&*$&1$#%,**#)$-@))#1*$(.$ " ⁄ J7$P(*#$*"&*$*"#$.,1,*#$(@*+@*$)#/,/*&1-# #HH7(.$*"#$-@))#1*$/(@)-#$9,22$"&?#$1($#..#-*$(1$*"#$(+#)&*,(17$!"#$#S@,?&2#1*$-,)-@,*$,1$F,;7 G7JJM3N$,/$?&2,0$.()$0,..#)#1*,&2$(+#)&*,(1$(12<7 G)$ 0+)6$+..,&1+*&/)4$ *"#$%&''#(#)*&+,$ +0.,&'&#($ &4$)/*$ '#%$&)$+$ 1/0.,#0#)*+(6$'+4"&/)` (+*"#(;$*"#$&).3*$4&2)+,$0+6$7#$+..,&#%$*/$/)#$/'$*"#$&).3*$*#(0&)+,4$5"&,#$*"#$/*"#($*#(0&)+,

8.3 The BJT Differential Pair

RC

RC !

vo1 v " id 2

vod

"

Q1

RC

vo2 v ! id 2

Q2 0V

RC

v vo1 = ! od 2 v " id 2

vo2 = Q1

Q2

vod 2

v ! id 2

REE Biased at I 2 (a)

(b)

Figure 8.22 KS@,?&2#1-#$(.$*"#$gk!$0,..#)#1*,&2$&%+2,.,#)$,1$4,5$*($*"#$*9($-(%%(1A#%,**#)$&%+2,.,#)/$,1 465>$!",/$#S@,?&2#1-#$&++2,#/$(12<$.()$0,..#)#1*,&2$,1+@*$/,;1&2/7$K,*"#)$(.$*"#$*9($-(%%(1A#%,**#)$&%+2,.,#)/ ,1$465$-&1$3#$@/#0$*($.,10$*"#$0,..#)#1*,&2$;&,1:$0,..#)#1*,&2$,1+@*$)#/,/*&1-#:$.)#S@#1-<$)#/+(1/#:$&10$/($(1:$(. *"#$0,..#)#1*,&2$&%+2,.,#)7

RC !

vo1

" vid " !

RC vod

"

Q1

v % id 2!

Q2 ve % vid "2

v i# Re %0 EE

vo2

REE

! vid % " 2 REE ' re Figure 8.23 !"#$ 0,..#)#1*,&2$ &%+2,.,#)$ .#0$ ,1$ & /,1;2#A#10#0$.&/",(17

&4$2(/3)%#%;$+4$4"/5)$&)$:&29$Y9Tc9$G)$*"&4$1+4#$*"#$4&2)+,$
P(*#$*"&*$#HH$&++#&)/$,1$+&)&22#2$9,*"$*"#$%@-"$/%&22#)$./$(.$!J7$

623

624 Chapter 8 Differential and Multistage Amplifiers v vo1 = ! od 2

Figure 8.24 KS@,?&2#1*A-,)-@,*$%(0#2$(.$*"#$0,..#)#1*,&2$"&2.A-,)-@,*$.()%#0$3<$!H$,1$F,;7$G7JJM3N7

&4$8)/5)$+4$*"#$&.22'1'$+.,*(8,*2%!.1!0.+9$G'$5#$*+8#$*"#$1/00/)-#0&**#($*(+)4&4*/($'#%$5&*" +v)8 /T$ +4$ *"#$ %&''#(#)*&+,$ "+,'-1&(13&*$ +)%$ (#.,+1#$ *"#$ *(+)4&4*/($ 5&*"$ &*4$ ,/5-'(#J3#)16; #J3&<+,#)*-1&(13&*$0/%#,;$*"#$1&(13&*$&)$:&29$Y9TB$(#43,*49$G)$#<+,3+*&)2$*"#$0/%#,$.+(+0#*#(4 .π ;$9:;$+)%$.,;$5#$034*$(#1+,,$*"+*$*"#$"+,'-1&(13&*$&4$7&+4#%$+*$"/T9$!"#$
F 8 = 9: ( # & || ., ) $

$MG7_CN

!"#$&).3*$%&''#(#)*&+,$(#4&4*+)1#$/'$*"#$%&''#(#)*&+,$+0.,&'&#($&4$*5&1#$*"+*$/'$*"#$"+,'-1&(13&*e *"+*$&4;$T.π 9$:&)+,,6;$5#$)/*#$*"+*$*"#$%&''#(#)*&+,$"+,'-1&(13&*$/'$*"#$+0.,&'&#($/'$:&29$Y9TA$&4$+ 1/00/)-#0&**#($*(+)4&4*/($5&*"$+$(#4&4*+)1#$#/$&)$*"#$#0&**#($,#+%9

8.3.5 Common-Mode Gain and CMRR :&23(#$ Y9TX$ 4"/54$ +$ 7&./,+($ %&''#(#)*&+,$ +0.,&'&#($ 5&*"$ +)$ &).3*$ 1/00/)-0/%#$ 4&2)+, v )1: 7 $K#(#$ # HH $&4$*"#$/3*.3*$(#4&4*+)1#$/'$*"#$7&+4$13((#)*$4/3(1#$"9$S#$5&4"$*/$'&)%$*"#
α #& . / ^ J# HH

$MG7_RN

α #& . / ^ J# HH

$MG7_DN

v ,H ] \ AAAAAAAAAAAAAAAAAAAAAAA v )1:

6,%,2&)2<:$ v ,J $9,22$3# v ,J ] \ AAAAAAAAAAAAAAAAAAAAAAA v )1:

9"#)#$9#$"&?#$1#;2#-*#0$*"#$*)&1/,/*()$ . , : $.()$/,%+2,-,*<7$!"#$0,..#)#1*,&2$(@*+@*$/,;1&2$ v ,8 -&1$3#$(3*&,1#0$&/ v ,8 ] v ,J \ v ,H ] U

!"@/:$9",2#$*"#$?(2*&;#/$&*$*"#$*9($-(22#-*()/$9,22$-(1*&,1$-(%%(1A%(0#$1(,/#$()$,1*#).#)A #1-#$-(%+(1#1*/:$*"#$(@*+@*$0,..#)#1*,&2$?(2*&;#$9,22$3#$.)##$.)(%$/@-"$,1*#).#)#1-#7$!",/ -(10,*,(1:$"(9#?#):$,/$3&/#0$(1$*"#$&//@%+*,(1$(.$+#).#-*$%&*-",1;$3#*9##1$*"#$*9($/,0#/$(. *"#$0,..#)#1*,&2$&%+2,.,#)7$81<$%,/%&*-"$9,22$)#/@2*$,1$ v ,8 $&-S@,),1;$&$-(%+(1#1*$+)(+()A *,(1&2$*($ v )1: 7 $F()$#>&%+2#:$-(1/,0#)$*"#$-&/#$(.$&$%,/%&*-"$ ∆# & $3#*9##1$*"#$*9($-(22#-*() )#/,/*&1-#/]$I.$*"#$-(22#-*()$(.$ ! H $"&/$&$-(22#-*()$)#/,/*&1-#$ # & :

8.3 The BJT Differential Pair

RC

RC

RC

vo1 vicm

Q1

vicm

vicm

Q2

!

vo1

vo2

RC vod

Q1

2REE

"

vo2 Q2

Biased at I"2

vicm

2REE

REE

(a)

(b)

Figure 8.25 4,5$ !"#$ 0,..#)#1*,&2$ &%+2,.,#)$ .#0$ 3<$ &$ -(%%(1A%(0#$ ,1+@*$ /,;1&2$ v)1:7$ 465$ KS@,?&2#1* `"&2.A-,)-@,*/a$.()$-(%%(1A%(0#$-&2-@2&*,(1/7

α #& J# HH ^ . /

v ,H ] \ AAAAAAAAAAAAAAAAAAAAAAA v )1:

&10$*"#$-(22#-*()$(.$ ! J $"&/$&$-(22#-*()$)#/,/*&1-#$ ( # & ^ ∆# & ):

α ( # & ^ ∆# & )

v ,J ] \ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA v )1:

J# HH ^ . /

*"#1$*"#$0,..#)#1*,&2$(@*+@*$?(2*&;#$ v ,8 $9,22$3#$ v ,8 ≡ v ,J \ v ,H

α ∆# & Av ] \ AAAAAAAAAAAAAAAAAAAAAA J# HH ^ . / )1: &10$*"#$-(%%(1A%(0#$;&,1$9,22$3#$ v ,8 α ∆# & A ] \ AAAAAAAAAAAAAAAAAAAAAA F 1: ≡ AAAAAAAA A v )1: J# HH ^ . /

$MG7_GN

6,1-#$ α % H:$ . / & J# HH : $KS7$MG7_GN$-&1$3#$&++)(>,%&*#0$&10$9),**#1$,1$*"#$.()% #& A F 1: % \ AAAAAAAAAAA J# HH

∆# & AAAAAAAAAA #&

$MG7__N

!"#$-(%%(1A%(0#$)#'#-*,(1$)&*,($-&1$1(9$3#$.(@10$.)(% F8 B4VV$ ] AAAAAAAAAAA F 1:

*(;#*"#)$9,*"$@/,1;$KS/7$MG7_QN$&10$MG7__N:$9,*"$*"#$)#/@2*$*"&* ∆# B4VV$ ] ( J9 : # HH )$$$ AAAAAAAAA&A #&

$MG7HUUN

625

626 Chapter 8 Differential and Multistage Amplifiers

Q2

Q1 vicm

vicm

+ –

2REE

REE 2Ricm

Ricm

(b) Figure 8.26 4,5$e#.,1,*,(1$(.$*"#$,1+@*$-(%%(1A%(0#$)#/,/*&1-#$#)1:7$465$!"#$#S@,?&2#1*$-(%%(1A%(0# "&2.A-,)-@,*7

9",-"$,/$/,%,2&)$,1$.()%$*($*"#$#>+)#//,(1$.()$*"#$456$+&,)$nKS7$MG7CUNo7$!"@/:$*($(3*&,1$& ",;"$B4VV:$9#$0#/,;1$*"#$-@))#1*$/(@)-#$*($"&?#$&$2&);#$(@*+@*$)#/,/*&1-#$ # HH $&10$/*),?# .()$-2(/#$%&*-",1;$(.$*"#$-(22#-*()$)#/,/*&1-#/7 Common-Mode Input Resistance !"#$0#.,1,*,(1$(.$*"#$-(%%(1A%(0#$,1+@*$)#/,/*&1-# # )1: $,/$,22@/*)&*#0$,1$F,;7$G7JRM&N7$F,;@)#$G7JRM3N$/"(9/$*"#$#S@,?&2#1*$-(%%(1A%(0#$"&2.A -,)-@,*\$,*/$,1+@*$)#/,/*&1-#$,/$ J# )1: 7 $!"#$?&2@#$(.$ J# )1: $-&1$3#$0#*#)%,1#0$3<$&1&2
Example 8.4 !"#$0,..#)#1*,&2$&%+2,.,#)$,1$F,;7$G7JD$@/#/$*)&1/,/*()/$9,*"$β$ =$HUU7$K?&2@&*#$*"#$.(22(9,1;] M&N M3N M-N M0N M#N

!"#$,1+@*$0,..#)#1*,&2$)#/,/*&1-#$#)8 7 !"#$(?#)&22$0,..#)#1*,&2$?(2*&;#$;&,1$v,8 / v/,;$M1#;2#-*$*"#$#..#-*$(.$.,N7 !"#$9()/*A-&/#$-(%%(1A%(0#$;&,1$,.$*"#$*9($-(22#-*()$)#/,/*&1-#/$&)#$&--@)&*#$*($9,*",1$±Hh7 !"#$B4VV:$,1$0g7 !"#$,1+@*$-(%%(1A%(0#$)#/,/*&1-#$M&//@%,1;$*"&*$*"#$K&)2<$?(2*&;#$%F$=$HUU$TN7

$MG7HUHN

8.3 The BJT Differential Pair

! vod "

"

+ –

vid

+ –

Rid

!

Figure 8.27 B,)-@,*$.()$K>&%+2#$G7L7

Solution M&N K&-"$*)&1/,/*()$,/$3,&/#0$&*$&1$#%,**#)$-@))#1*$(.$U7C$%87$!"@/ % JC$%T . /H = . /J = AAAAAJA = AAAAAAAAAAAAAAAAAA = CU$Ω U7C$%8 "H !"#$,1+@*$0,..#)#1*,&2$)#/,/*&1-#$-&1$1(9$3#$.(@10$&/ # )8 = J ( β + H ) ( ./ + # H ) = J × HUH × ( CU + HCU ) % LU$=Ω M3N !"#$?(2*&;#$;&,1$.)(%$*"#$/,;1&2$/(@)-#$*($*"#$3&/#/$(.$!H$&10$!J$,/$ v )8 # )8 AAAAAA A = AAAAAAAAAAAAAAAAAAAAA A v /,; # /,; + # )8

LU = AAAAAAAAAAAAAAAAAAAAAAAA = U7G$TXT C + C + LU !"#$?(2*&;#$;&,1$.)(%$*"#$3&/#/$*($*"#$(@*+@*$,/$ v ,8

!(*&2$)#/,/*&1-#$,1$*"#$-(22#-*()/ AAAAAAA % AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA v )8 !(*&2$)#/,/*&1-#$,1$*"#$#%,**#)/

627

628 Chapter 8 Differential and Multistage Amplifiers

Example 8.4 continued

J# & J × HU A $ = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA $= CU$TXT = AAAAAAAAAAAAAAAAAAAAAAAA J ( ./ Z # H ) J ( CU Z HCU ) × HU [Q !"#$(?#)&22$0,..#)#1*,&2$?(2*&;#$;&,1$-&1$1(9$3#$.(@10$&/ v

v v

v /,;

v /,; v )8

,8 )8 ,8 A $ = AAAAAA A AAAAAAA $= U7G × CU $= LU $TXT F 8 = AAAAAA

M-N m/,1;$KS7$MG7__N: # & ∆# & A $ AAAAAAAAAA F 1: $= AAAAAAAAAAA J# HH # & 9"#)#$∆#&$=$U7UJ#&$,1$*"#$9()/*$-&/#7$!"@/:

F8 M0N B4VV = JU$2(; AAAAAAAAAAA F 1:

C#F$m/,1;$KS7$MG7HUHN:

HU [L F 1: = AAAAAAAAAAAAAAAAAA × U7UJ = C × HU $TXT J × JUU LU A = _G$0g = JU $2(; AAAAAAAAAAAAAAAAAA [L C × HU %F HUU A = AAAAAAAAA = JUU$=Ω . , = AAAAAAAA "⁄J U7C # )1: = R7R 4Ω

EXERCISES 8.12 F()$*"#$-,)-@,*$,1$F,;7$G7H_:$2#*$"$=$H$%8:$%&&$=$HC$T:$#&$=$HU$=Ω:$9,*"$α$=$H:$&10$2#*$*"#$,1+@*$?(2*&;#/ 3#]$vGH$=$C$+$U7UUC$/,1$Jπ ×$HUUU-:$?(2*/:$&10$vGJ$=$C$−$U7UUC$/,1$Jπ$ ×$HUUU-:$?(2*/7$M&N$I.$*"#$gk!/ &)#$/+#-,.,#0$*($"&?#$vGH$(.$U7D$T$&*$&$-(22#-*()$-@))#1*$(.$H$%8:$.,10$*"#$?(2*&;#$&*$*"#$#%,**#)/7$M3N F,10$9:$.()$#&-"$(.$*"#$*9($*)&1/,/*()/7$M-N$F,10$)&$.()$#&-"$(.$*"#$*9($*)&1/,/*()/7$M0N$F,10$v&$.()$#&-" (.$*"#$*9($*)&1/,/*()/7$M#N$F,10$*"#$?(2*&;#$3#*9##1$*"#$*9($-(22#-*()/7$M.N$F,10$*"#$;&,1$#>+#),#1-#0 3<$*"#$HUUUAbO$/,;1&27 Ans. M&N$L7QHD$T\$M3N$JU$%8XT\$M-N$)&H$=$U7C$+$U7H$/,1$Jπ$×$HUUU-:$%8$&10$)&J$=$U7C$[$U7H$/,1$Jπ$×$HUUU-: %8\$M0N$v&H$=$HU$[$H$/,1$Jπ$ ×$HUUU-:$T$&10$v&J$=$HU$+$H$/,1$Jπ $×$HUUU-:$T\$M#N$v&J$[$v&H$=$J$/,1$Jπ$ × HUUU-:$T\$M.N$JUU$TXT 8.13 8$3,+(2&)$0,..#)#1*,&2$&%+2,.,#)$@*,2,O#/$&$/,%+2#$M,7#7:$&$/,1;2#$BK$*)&1/,/*()N$-@))#1*$/(@)-#$*($/@++2< &$3,&/$-@))#1*$"7(.$JUU$µ8:$&10$/,%+2#$-@))#1*A/(@)-#$2(&0/$.()%#0$3<$E+E$*)&1/,/*()/7$ F()$ &22$ *)&1A /,/*()/:$ β ] HUU$&10$ % F ] HU $T7$F,10$9 : : $ # & : $ F 8 :$ # )8 : $ # HH : $B4VV$M,.$*"#$*9($2(&0$*)&1/,/*()/ #>",3,*$&$Hh$%,/%&*-"$,1$*"#,)$ .,c/N:$&10$ # )1: 7 Ans. L$%8XT\$HUU$= Ω \$LUU$TXT\$CU$= Ω: $CU$= Ω\ $GR$0g\$H7RD$4 Ω

8.4 Other Nonideal Characteristics of the Differential Amplifier

8.4 Other Nonideal Characteristics of the Differential Amplifier 8.4.1 Input Offset Voltage of the MOS Differential Pair B(1/,0#)$ *"#$ 3&/,-$ 456$ 0,..#)#1*,&2$ &%+2,.,#)$ 9,*"$ 3(*"$ ,1+@*/$ ;)(@10#0:$ &/$ /"(91$ ,1 F,;7 G7JGM&N7$I.$*"#$*9($/,0#/$(.$*"#$0,..#)#1*,&2$+&,)$9#)#$+#).#-*2<$%&*-"#0$M,7#7:$!H$&10$!J ,0#1*,-&2$&10$#$H$=$#$J$=$#$N:$*"#1$-@))#1*$"$9(@20$/+2,*$#S@&22<$3#*9##1$!H$&10$!J:$&10$%6 9(@20$3#$O#)(7$g@*$+)&-*,-&2$-,)-@,*/$#>",3,*$%,/%&*-"#/$*"&*$)#/@2*$,1$&$0-$(@*+@*$?(2*&;#$%6 #?#1$9,*"$3(*"$,1+@*/$;)(@10#07$E#$-&22$%6$*"#$"0+/0+(&!("223'+()"*+,-'7$4()#$-(%%(12<: 9#$0,?,0#$%6$3<$*"#$0,..#)#1*,&2$;&,1$(.$*"#$&%+2,.,#):$F8 :$*($(3*&,1$&$S@&1*,*<$=1(91$&/$*"# .$/0+("223'+()"*+,-':$%6* : %6*$ =$%6 /F8

$MG7HUJN

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∆#$`$*"+*$&4;

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Figure 8.28 4,5$ !"#$ 456$ 0,..#)#1*,&2$ +&,)$ 9,*"$ 3(*"$ ,1+@*/$ ;)(@10#07$ 59,1;$ *($ 0#?,-#$ &10$ )#/,/*() %,/%&*-"#/:$&$.,1,*#$0-$(@*+@*$?(2*&;#$%6$)#/@2*/7$465$8++2,-&*,(1$(.$&$?(2*&;#$#S@&2$*($*"#$,1+@*$(../#*$?(2*&;# %6*$*($*"#$,1+@*$*#)%,1&2/$9,*"$(++(/,*#$+(2&),*<$)#0@-#/$%6$*($O#)(7

629

630 Chapter 8 Differential and Multistage Amplifiers ∆# # $J = # $ \ AAAAAAAAA$A J

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g#-&@/#$!H$&10$!J$&)#$%&*-"#0:$*"#$-@))#1*$"$9,22$/+2,*$#S@&22<$3#*9##1$*"#%7$P#?#)*"#2#//: 3#-&@/#$(.$*"#$%,/%&*-"$,1$2(&0$)#/,/*&1-#/:$*"#$(@*+@*$?(2*&;#/$%$H$&10$%$J$9,22$3#

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H

4 H 4 = AAAAA + AAA ∆ AAAAA 5 J 5

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H 4 = 4 AAAAA \ AAA ∆ AAAAA 5 J 5

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" ∆M4 ⁄ 5NA " J = AAA H \ AAAAAAAAAAAAAAAAAAAA J JM4 ⁄ 5N

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" ∆M4 ⁄ 5N AAA AAAAAAAAAAAAAAAAAAAAA J M4 ⁄ 5N

8.4 Other Nonideal Characteristics of the Differential Amplifier

76$9:$2&<#4$*"#$&).3*$/''4#*$
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631

632 Chapter 8 Differential and Multistage Amplifiers

EXERCISE 8.14 F()$*"#$456$0,..#)#1*,&2$+&,)$/+#-,.,#0$,1$K>#)-,/#$G7L:$.,10$*"#$*")##$-(%+(1#1*/$(.$*"#$,1+@*$(../#* ?(2*&;#7$i#*$∆#$X#$$=$Jh:$∆M4<5NXM4<5N$=$Jh:$&10$∆%-$=$J$%T7$m/#$KS7$MG7HHCN$*($(3*&,1$&1$#/*,A %&*#$(.$*"#$*(*&2$%6*7 Ans. J$%T\$J$%T\$J$%T\$Q7C$%T

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∆# # &H = # & + AAAAAAAAA&A J ∆# # &J = # & \ AAAAAAAAA&A J

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8.4 Other Nonideal Characteristics of the Differential Amplifier

α" %&H = %&& \ AAAAAA J α " %&J = %&& \ AAAAAA J

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∆# # & + AAAAAAAAA&A J ∆# & # & \ AAAAAAAAAA J

" %6 = %&J \ %&H = α AAA ( ∆# & ) J +)%$*"#$&).3*$/''4#*$
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" %6 = α AAA J

∆" * AAAAAAAA # & "*

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634 Chapter 8 Differential and Multistage Amplifiers +)%$*"#$1/((#4./)%&)2$&).3*$/''4#*$
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EXERCISE 8.15 F()$&$gk!$0,..#)#1*,&2$&%+2,.,#)$@*,2,O,1;$*)&1/,/*()/$"&?,1;$β$=$HUU:$%&*-"#0$*($HUh$()$3#**#):$&10 &)#&/$*"&*$&)#$%&*-"#0$*($HUh$()$3#**#):$&2(1;$9,*"$-(22#-*()$)#/,/*()/$*"&*$&)#$%&*-"#0$*($Jh$() 3#**#):$.,10$%6* :$"G :$&10$"6* 7$!"#$0-$3,&/$-@))#1*$"$,/$HUU$µ87 Ans. J7CC$%T\$U7C$µ8\$CU$18

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S#$/74#(<#$*"+*$*/$/7*+&)$+$,+(2#$@Mbb;$5#$4#,#1*$+)$&0.,#0#)*+*&/)$/'$*"#$7&+4&)2$13((#)* 4/3(1#$ "$ *"+*$ '#+*3(#4$ +$ "&2"$ /3*.3*$ (#4&4*+)1#9$ O31"$ 1&(13&*4$ &)1,3%#$ *"#$ 1+41/%#$ 13((#)* 4/3(1#$+)%$*"#$S&,4/)$13((#)*$4/3(1#$4*3%&#%$&)$O#1*&/)$R9X9$$$$$$

EXERCISE 8.16 81$&-*,?#A2(&0#0$456$0,..#)#1*,&2$&%+2,.,#)$(.$*"#$*<+#$/"(91$,1$F,;7$G7QJM&N$,/$/+#-,.,#0$&/$.(22(9/] M4/ 5N+$=$HUU:$M4/ 5NE$=$JUU:$µ+&,;$=$JµE&,;$=$U7J$%8XTJ:$%F+ = %FE = JU$T: $"$=$U7G$%8:$#**$=$JC =Ω7 B&2-@2&*#$(::$#,:$F8:$ F 1: : $&10$B4VV7 Ans. B$0=h_`$TX$8Ω`$AII$_h_`$I9IIX$_h_`$TI;III$/($YZ$%>

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v

= \ 9 :H AAAA)8A ( . /Q || . ,Q || . ,H || . π L ) J

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) , = 9 :J AAAA)8A \ 9 :L v CL J

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(: = 9:

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648 Chapter 8 Differential and Multistage Amplifiers

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Systematic Input Offset Voltage G)$+%%&*&/)$*/$*"#$(+)%/0$/''4#*$
" H AAAAL = AAAAAAAAAAAAAAA J "Q H + AAAAA

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8.6 Multistage Amplifiers

EXERCISE 8.18

F,10$(:$&10$#,L:$#,C:$#,:$&10$F8$.()$*"#$0,..#)#1*,&2$&%+2,.,#)$,1$F,;7$G7LU$@10#)$*"#$.(22(9,1;$-(1A 0,*,(1/]$"$=$H$%8:$$βR$=$CU:$βS$=$HUU:$&10$%F$=$HUU$T7 Ans. TI$0=h_`$AI$MΩ`$AI$MΩ`$X$MΩ`$105$_h_$/($AII$%>

8.6 Multistage Amplifiers f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
8.6.1 A Two-Stage CMOS Op Amp :&23(#$Y9BA$4"/54$+$./.3,+($4*(31*3(#$'/($@MNO$/.$+0.4$8)/5)$+4$*"#$+?"%3+,-'(!"$2.-0% 1,+."$9$!"#$1&(13&*$3*&,&Q#4$*5/$./5#($43..,$5"&1"$1+)$(+)2#$'(/0$±T9X$_$'/($*"#$I9X-µ0 *#1")/,/26$%/5)$*/$±I9H$_$'/($*"#$I9AY-µ0$*#1")/,/269$=$(#'#(#)1#$7&+4$13((#)*$"bD:$&4$2#)#(+*#%$#&*"#($#L*#()+,,6$/($34&)2$/)-1"&.$1&(13&*49$N)#$431"$1&(13&*$5&,,$7#$%&41344#%$4"/(*,69 !"#$13((#)*$0&((/($'/(0#%$76$!Y$+)%$!X$43..,$*"#$%&''#(#)*&+,$.+&($!A$−$!T$5&*"$7&+4$13((#)*9$!"#$4/ 5$(+*&/$/'$!X$&4$4#,#1*#%$*/$6&#,%$*"#$%#4&(#%$<+,3#$'/($*"#$&).3*-4*+2#$7&+4$13((#)* "$C/($"/ T$'/($#+1"$/'$!A$+)%$!TF9$!"#$&).3*$%&''#(#)*&+,$.+&($&4$+1*&<#,6$,/+%#%$5&*"$*"#$13((#)* 0&((/($'/(0#%$76$!c$+)%$!B9$!"34$*"#$&).3*$4*+2#$&4$&%#)*&1+,$*/$*"+*$4*3%&#%$&)$O#1*&/)$Y9X

651

652 Chapter 8 Differential and Multistage Amplifiers

I

CC D2

D6

Figure 8.41 !5/-4*+2#$@MNO$/.-+0.$1/)'&23(+*&/)9

C#L1#.*$*"+*$"#(#$*"#$%&''#(#)*&+,$.+&($&4$&0.,#0#)*#%$5&*"$m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||$.,RF$+)%$&4$*"34 (+*"#($"&2"9$!"&4$1&(13&*;$*"#(#'/(#;$&4$)/*$43&*+7,#$'/($%(&<&)2$,/5-&0.#%+)1#$,/+%49$U#<#(*"#,#44;$*"#$1&(13&*$&4$<#(6$./.3,+($+)%$&4$34#%$'(#J3#)*,6$'/($&0.,#0#)*&)2$/.$+0.4$&)$_EOG 1&(13&*4;$ 5"#(#$ *"#$ /.$ +0.$ )##%4$ */$ %(&<#$ /),6$ +$ 40+,,$ 1+.+1&*&<#$ ,/+%;$ '/($ #L+0.,#;$ &) 45&*1"#%-1+.+1&*/($1&(13&*4$C@"+.*#($ARF9$!"#$4&0.,&1&*6$/'$*"#$1&(13&*$(#43,*4$&)$+)$/.$+0.$/' (#+4/)+7,6$2//%$J3+,&*6$(#+,&Q#%$&)$+$<#(6$40+,,$1"&.$+(#+9 Voltage Gain

!"#$
F H = \ 9 :H ( . ,J || . ,L )

$MG7HDLN

5"#(#$9:A$&4$*"#$*(+)41/)%31*+)1#$/'$#+1"$/'$*"#$*(+)4&4*/(4$/'$*"#$'&(4*$4*+2#;$*"+*$&4;$!A$+)%$!T9 !"#$ 4#1/)%$ 4*+2#$ &4$ 13((#)*-4/3(1#-,/+%#%;$ 1/00/)-4/3(1#$ +0.,&'&#($ 5"/4#$
F J = \ 9 :R ( . ,R || . ,D ) !"#$%1$/.#)-,//.$2+&)$/'$*"#$/.$+0.$&4$*"#$.(/%31*$/'$FA$+)%$FT9

$MG7HDCN

8.6 Multistage Amplifiers

Example 8.5 @/)4&%#($*"#$1&(13&*$&)$:&29$Y9BA$5&*"$*"#$'/,,/5&)2$%#<&1#$2#/0#*($C&)$µ0F9 Transistor 4/ 5$$

Q1 $$$$$$TI/ I9Y

Q2 $$$TI/ I9Y

Q3

Q4

Q5

Q6

Q7

$$$$X/ I9Y

$$X/ I9Y

$$BI/ I9Y

$$AI/ I9Y

$$BI/ I9Y

Q8 $$BI/ I9Y$

E#*$"bD:$=$HI$µ=;$%-+$=$I9R$_;$%-E$=$\I9Y$_;$µ+&,;7=7AZI7µ=h_T;7µE&,;7=7BI7µ=h_T;$ % F $C'/($+,,$%#<&1#4F$= AI$_;$%$$$=$%**$= T9X$_9$:/($+,,$%#<&1#4;$#<+,3+*#$"$;$ %6% ;$ %(* ;$9:;$+)%$.,9$=,4/$'&)%$FA;$FT;$*"#$%1$/.#),//.$
Solution b#'#($*/$:&29$Y9BA9$O&)1#$!Y$+)%$!X$+(#$0+*1"#%;$"$=$"bD:9$!"34$!A;$!T;$!c;$+)%$!B$#+1"$1/)%31*4$+$13((#)* #J3+,$*/$"/T$]$BX$µ=9$O&)1#$!R$&4$0+*1"#%$*/$!X$+)%$!Y;$*"#$13((#)*$&)$!R$&4$#J3+,$*/$"bD:$=$HI$µ=9$:&)+,,6;$!Z 1/)%31*4$+)$#J3+,$13((#)*$/'$HI$µ=9 S&*"$"$$/'$#+1"$%#<&1#$8)/5);$5#$34# "$ =

J H AAA M µ & NM4 / 5N%6% ,; J

*/$%#*#(0&)#$ %6% $'/($#+1"$*(+)4&4*/(9$!"#)$5#$'&)%$ %(* $'(/0$ %(* $=$ %- $+$ %6% 9$!"#$(#43,*4$+(# 2&<#)$&)$!+7,#$Y9A9 !"#$*(+)41/)%31*+)1#$/'$#+1"$%#<&1#$&4$%#*#(0&)#%$'(/0 9 : ] J" $ ⁄ %6% !"#$<+,3#$/'$.,$&4$%#*#(0&)#%$'(/0 ., = %F ⁄ "$ !"#$(#43,*&)2$<+,3#4$/'$9:$+)%7.,$+(#$2&<#)$&)$!+7,#$Y9A9 !"#$
"$$Cµ=F %6% C_F %(* C_F 9:$C0=h_F .,$C8ΩF

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$$$$$BX $$$$I9c $$$$A9A $$$$I9c $$$TTT

$$$$$$$BX $$$$$$I9c $$$$$$$$$A $$$$$$I9c $$$$$TTT

$$$$$$$BX $$$$$$I9c $$$$$$$$$A $$$$$$I9c $$$$$TTT

$$$$$$$HI $$$$$$I9c $$$$$$A9A $$$$$$I9Z $$$$$AAA

$$$$$$$HI $$$$$$I9c $$$$$$$$$A $$$$$$I9Z $$$$$AAA

$$$$$$$HI $$$$$$I9c $$$$$$A9A $$$$$$I9Z $$$$$AAA

$$$$$$$HI $$$$$$I9c $$$$$$A9A $$$$$$I9Z $$$$$AAA

653

654 Chapter 8 Differential and Multistage Amplifiers

Example 8.5 continued

!"34$*"#$/<#(+,,$%1$/.#)-,//.$2+&)$&4 F U = F H F J = ( \ QQ7Q ) × ( \ QQ7Q )$ = HHU_$ TX T /( TI$,/2AAIH$]$ZA$%> !"#$,/5#($,&0&*$/'$*"#$&).3*$1/00/)-0/%#$(+)2#$&4$*"#$<+,3#$/'$&).3*$ = J7J \ H7H = H7H$T

!"#$"&2"#4*$+,,/5+7,#$/3*.3*$
Input Offset Voltage !"#$%#<&1#$0&40+*1"#4$&)#<&*+7,6$.(#4#)*$&)$*"#$&).3*$4*+2#$2&<# (&4#$*/$+)$&).3*$/''4#*$#1+34#$%#<&1#$0&40+*1"#4$+(#$(+)%/0; *"#$(#43,*&)2$/''4#*$?!$/.$+0.4;$+)%$5#$"+<#$#)1/3)*#(#%$&*$&)$O#1*&/)$Y9X9X; &* &4$ 343+,,6$ 031"$ 0/(#$ .(/)/3)1#%$ &)$ @MNO$ /.$ +0.4$ 7#1+34#$ *"#&($ 2+&)-.#(-4*+2#$ &4 (+*"#($,/59 !/$4##$"/5$464*#0+*&1$/''4#*$1+)$/113($&)$*"#$1&(13&*$/'$:&29$Y9BA;$,#*$*"#$*5/$&).3*$*#(0&)+,4$7#$2(/3)%#%9$G'$*"#$&).3*$4*+2#$&4$.#('#1*,6$7+,+)1#%;$*"#)$*"#$
M4 / 5N " R = AAAAAAAAAAAAAAAAAR M" / JN M4 / 5N L

$MG7HDRN

G)$/(%#($'/($)/$/''4#*$
M4 / 5N " D = AAAAAAAAAAAAAAAAAD " M4 / 5N C

$MG7HDDN

U/5;$*"#$1/)%&*&/)$'/($0+8&)2$"Z$]$"R$1+)$7#$'/3)%$'(/0$DJ49$CY9ARZF$+)%$CY9ARRF$+4

M4 / 5N M4 / 5N AAAAAAAAAAAAAAAAAR = J AAAAAAAAAAAAAAAAAD M4 / 5N L M4 / 5N C

$MG7HDGN

8.6 Multistage Amplifiers

G'$*"&4$1/)%&*&/)$&4$)/*$0#*;$+$464*#0+*&1$/''4#*$5&,,$(#43,*9$:(/0$*"#$4.#1&'&1+*&/)$/'$*"#$%#<&1# 2#/0#*($&)$DL+0.,#$Y9X;$5#$1+)$<#(&'6$*"+*$1/)%&*&/)$CY9ARYF$&4$4+*&4'&#%;$+)%;$*"#(#'/(#;$*"# /.$+0.$+)+,6Q#%$&)$*"+*$#L+0.,#$4"/3,%$)/*$#L"&7&*$+$464*#0+*&1$&).3*$/''4#*$
EXERCISE 8.19

B(1/,0#)$*"#$B456$(+$&%+$(.$F,;7$G7LH$9"#1$.&3),-&*#0$,1$&$U7GAµ%$B456$*#-"1(2(;<$.()$9",-"

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M4/5NH$=$M4/5NJ$=$M4/5NC$=$JUU:$&10$M4/5NQ$=$M4/5NL$=$HUU7 M&N F,10$*"#$M4/5N$)&*,(/$(.$!R$&10$!D$/($*"&*$"R$Y$HUU$µ87 M3N F,10$*"#$(?#)0),?#$?(2*&;#:$p%6%p:$&*$9",-"$#&-"$(.$!H:$!J:$&10$!R$,/$(+#)&*,1;7 M-N F,10$9:$.()$!H:$!J:$&10$!R7 M0N I.$p%Fp$=$HU$T:$.,10$.,J:$.,L:$.,R:$&10$.,D7 M#N F,10$*"#$?(2*&;#$;&,1/$FH$&10$FJ:$&10$*"#$(?#)&22$;&,1$F7 Ans. C+F$C4/5FZ$=$C4/5FR$=$TII`$C7F$I9ATH$_;$I9ATH$_;$I9AIX$_`$C1F$I9RRX$0=h_;$I9RRX$0=h_; A9HI 0=h_`$C%F$TII$8Ω;$TII$8Ω;$AII$8Ω;$AII$8Ω`$C#F$\RR9X$_h_;$\HX$_h_;$RcZc$_h_

A Bias Circuit That Stabilizes gm S#$1/)1,3%#$*"&4$4#1*&/)$76$.(#4#)*&)2$+$7&+4$1&(13&* '/($*"#$*5/-4*+2#$@MNO$/.$+0.9$!"#$1&(13&*$.(#4#)*#%$"+4$*"#$&)*#(#4*&)2$+)%$34#'3,$.(/.#(*6 /'$ .(/<&%&)2$ +$ 7&+4$ 13((#)*$ 5"/4#$ <+,3#$ &4$ &)%#.#)%#)*$ /'$ 7/*"$ *"#$ 43..,6$
H 4 " G = AAA µ + & ,; AAAAA J 5

J

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J

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( %(*HJ \ %- ) HJ

+)%;

H 4 " G = AAA µ + & ,; AAAAA J 5

( %(*HQ \ %- ) HQ

:(/0$*"#$1&(13&*;$5#$4##$*"+*$*"#$2+*#-4/3(1#$
%(*HQ = %(*HJ + "G # G C E#$0#1(*#$*"#$3,&/$-@))#1*$(.$*",/$-,)-@,*$3<$"G7$I.$*",/$-,)-@,*$,/$@*,2,O#0$*($3,&/$*"#$B456$(+$&%+$(.$ F,;7$G7LH:$*"#1$"G$3#-(%#/$*"#$)#.#)#1-#$-@))#1*$"VKF7

655

656 Chapter 8 Differential and Multistage Amplifiers VDD

Q9

Q8

IB

IB

Q11

Q10

Q13

Q12 RB !VSS

Figure 8.42 g,&/$-,)-@,*$.()$*"#$B456$(+$&%+7

O37*(+1*&)2$%-$'(/0$7/*"$4&%#4$/'$*"&4$#J3+*&/)$+)%$34&)2$DJ49$CY9ARHF$+)%$CY9AYIF$*/$(#.,+1# C%(*AT$\$%-F$+)%$C%(*Ac$\$%-F$(#43,*4$&)

J"G AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A= µ + & ,; M4 / 5N HQ

J"G AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A+" # µ + & ,; M4 / 5N HJ G G

$MG7HGHN

!"&4$#J3+*&/)$1+)$7#$(#+((+)2#%$*/$6&#,%

J " G = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAJA µ + & ,; M4 / 5N HJ # G

M4 / 5N HJ AAAAAAAAAAAAAAAAAA A\H M4 / 5N HQ

J

$MG7HGJN

'(/0$5"&1"$5#$/74#(<#$*"+*$"G$&4$%#*#(0&)#%$76$*"#$%&0#)4&/)4$/'$!AT$+)%$*"#$<+,3#$/'$#G$+)%$76 *"#$(+*&/$/'$*"#$%&0#)4&/)4$/'$!AT$+)%$!Ac9$:3(*"#(0/(#;$DJ9$CY9AYTF$1+)$7#$(#+((+)2#%$*/$*"#$'/(0

J # G = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA J µ + & ,; M4 / 5N HJ " G

M4 / 5N HJ AAAAAAAAAAAAAAAAAAA \ H M4 / 5N HQ

&)$5"&1"$5#$(#1/2)&Q#$*"#$'+1*/($ J µ + & ,; M4 / 5N HJ " G $+4$9:AT`$*"34;

J 9 :HJ = AAAAAA #G

M4 / 5N HJ AAAAAAAAAAAAAAAAAA A\H M4 / 5N HQ

$MG7HGQN

!"&4$&4$+$<#(6$&)*#(#4*&)2$(#43,*P$9:AT$&4$%#*#(0&)#%$4/,#,6$76$*"#$<+,3#$/'$#G$+)%$*"#$(+*&/$/'$*"# %&0#)4&/)4$/'$!AT$+)%$!Ac9$:3(*"#(0/(#;$4&)1#$9:$/'$+$MNO:D!$&4$.(/./(*&/)+,$*/$ "$ M4 / 5N: #+1"$*(+)4&4*/($7&+4#%$76$*"#$1&(13&*$/'$:&29$Y9BT`$*"+*$&4;$#+1"$*(+)4&4*/($5"/4#$7&+4$13((#)*$&4 %#(&<#%$'(/0$"G$5&,,$"+<#$+$9:$<+,3#$*"+*$&4$+$03,*&.,#$/'$9:AT9$O.#1&'&1+,,6;$*"#$)*"$+-1"+))#, MNO:D!$5&,,$"+<#$

"$) M4 / 5N ) 9 :) = 9 :HJ AAAAAAAAAAAAAAAAAAAAAAA A " G M4 / 5N HJ

8.6 Multistage Amplifiers

+)%$*"#$)*"$E-1"+))#,$%#<&1#$5&,,$"+<#

µ E "$) M4 / 5N ) 9 :) = 9 :HJ AAAAAAAAAAAAAAAAAAAAAAAAAAAAA A µ + " G M4 / 5N HJ :&)+,,6;$&*$4"/3,%$7#$)/*#%$*"+*$*"#$7&+4$1&(13&*$/'$:&29$Y9BT$#0.,/64$/"3.+.)'(2''&6,!@; +)%$*"34$1+(#$4"/3,%$7#$#L#(1&4#%$&)$&*4$%#4&2)$*/$+
EXERCISES 8.20 B(1/,0#)$*"#$3,&/$-,)-@,*$(.$F,;7$G7LJ$.()$*"#$-&/#$(.$M4/5NG$=$M4/5N_$=$M4/5NHU$=$M4/5NHH =$M4/5NHQ$= JU$&10$M4/5NHJ$=$GU7$!"#$-,)-@,*$,/$.&3),-&*#0$,1$&$+)(-#//$*#-"1(2(;<$.()$9",-"$µ+&,;$=$_U$µ8XTJ7 F,10$*"#$?&2@#$(.$#G$*"&*$)#/@2*/$,1$&$3,&/$-@))#1*$"G$=$HU$µ87$82/(:$.,10$*"#$*)&1/-(10@-*&1-#$9:HJ7 Ans. C7JD$=Ω\$U7QD_$%8XT D8.21 e#/,;1$*"#$3,&/$-,)-@,*$(.$F,;7$G7LJ$*($(+#)&*#$9,*"$*"#$B456$(+$&%+$(.$K>&%+2#$G7C7$m/#$!G$&10 !_$&/$,0#1*,-&2$0#?,-#/$9,*"$!G$"&?,1;$*"#$0,%#1/,(1/$;,?#1$,1$K>&%+2#$G7C7$!)&1/,/*()/$!HU:$!HH: &10$!HQ$&)#$*($3#$,0#1*,-&2:$9,*"$*"#$/&%#$9:$&/$!G$&10$!_7$!)&1/,/*()$!HJ$,/$*($3#$.(@)$*,%#/$&/ 9,0#$&/$!HQ7$F,10$*"#$)#S@,)#0$?&2@#$(.$#G7$E"&*$,/$*"#$?(2*&;#$0)(+$&-)(//$#GW$82/($;,?#$*"#$?&2A @#/$(.$*"#$0-$?(2*&;#/$&*$*"#$;&*#/$(.$!HJ:$!HU:$&10$!G7 Ans. A9ZR$8Ω`$AXI$0_`$−A9X$_`$−I9X$_`$+A9B$_

8.6.2 A Bipolar Op Amp N3($4#1/)%$#L+0.,#$/'$03,*&4*+2#$+0.,&'&#(4$ &4$*"#$'/3(-4*+2#$7&./,+($/.$+0.$4"/5)$&) :&29$ Y9Bc9$ !"#$ 1&(13&*$ 1/)4&4*4$ /'$ '/3($ 4*+2#49$ !"#$ &.22'1'$+.,*%.$;( &.22'1'$+.,*%"0+$ &).3* 4*+2#$1/)4&4*4$/'$*(+)4&4*/(4$!A$+)%$!T;$5"&1"$+(#$7&+4#%$76$13((#)*$4/3(1#$!c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
657

658 Chapter 8 Differential and Multistage Amplifiers

to amplif y

make input re= 10 k shift (there is stil gain but..)

make sure out resis small as current source

Figure 8.43 8$.(@)A/*&;#$3,+(2&)$(+$&%+7

+11/0.,&4"#%$&)$*"#$@MNO$/.$+0.$5#$"+<#$7##)$4*3%6&)2$76$34&)2$1/0.,#0#)*+(6$%#<&1#4 '/($*"#$*5/$4*+2#4P$*"+*$&4;$E-1"+))#,$'/($*"#$'&(4*$4*+2#$+)%$+-1"+))#,$'/($*"#$4#1/)%$4*+2#9 !"#$/3*.3*$4*+2#$/'$*"#$/.$+0.$1/)4&4*4$/'$#0&**#($'/,,/5#($!Y9$=4$5#$8)/5$'(/0$/3( 4*3%6$/'$/.$+0.4$&)$@"+.*#($T;$&%#+,,6$*"#$/3*.3*$/.#(+*#4$+(/3)%$Q#(/$?!$/.$+0.$5&,,$7#$&,,34*(+*#%$&)$DL+0.,#$Y9Z9

Example 8.6 G)$*"&4$#L+0.,#;$5#$+)+,6Q#$*"#$%1$7&+4$/'$*"#$7&./,+($/.-+0.$1&(13&*$/'$:&29$Y9Bc9$!/5+(%$*"+*$#)%;$:&29 Y9BB$4"/54$*"#$1&(13&*$5&*"$*"#$*5/$&).3*$*#(0&)+,4$1/))#1*#%$*/$2(/3)%9 M&N f#).()%$&1$&++)(>,%&*#$0-$&1&2
8.6 Multistage Amplifiers

Figure 8.44 B,)-@,*$.()$K>&%+2#$G7R7

C1F G'$*(+)4&4*/(4$!A$+)%$!T$"+<#$β$ =$AII;$1+,13,+*#$*"#$&).3*$7&+4$13((#)*$/'$*"#$/.$+0.9 C%F S"+*$&4$*"#$&).3*$1/00/)-0/%#$(+)2#$/'$*"&4$/.$+0.V

Solution C+F !"#$<+,3#4$/'$+,,$%1$13((#)*4$+)%$
659

660 Chapter 8 Differential and Multistage Amplifiers

Example 8.6 continued

C7F !/$1+,13,+*#$*"#$./5#($%&44&.+*#%$&)$*"#$1&(13&*$&)$*"#$J3)#)*$4*+*#$C&9#9;$5&*"$Q#(/$&).3*$4&2)+,F$5# 4&0.,6$#<+,3+*#$*"#$%1$13((#)*$*"+*$*"#$1&(13&*$%(+54$'(/0$#+1"$/'$*"#$*5/$./5#($43..,1$:(/0$*"#$+AX _ 43..,6$*"#$%1$13((#)*$&4$" +$=$I9TX$+$I9TX$+$A$+$A$+$A$+$X$=$Y9X$0=9$!"34$*"#$./5#($43..,&#%$76$*"#$./4&*&<# ./5#($43..,6$&4$R +$=$AX$×$Y9X$=$ATR9X$0S9$!"#$\AX-_$43..,6$.(/<&%#4$+$13((#)*$"7\$2&<#)$76$"7\$=$I9X$+ I9X +$T$+$A$+$X$=$H$0=9$!"34$*"#$./5#($.(/<&%#%$76$*"#$)#2+*&<#$43..,6$&4$R \$=$AX$×$H$=$AcX$0S9$=%%&)2 R +$+)%$R \$.(/<&%#4$*"#$*/*+,$./5#($%&44&.+*#%$&)$*"#$1&(13&*$R$P$R$$=$R +$+$R \$=$TZT9X$0S9 C1F$!"#$&).3*$7&+4$13((#)*$/'$*"#$/.$+0.$&4$*"#$+<#(+2#$/'$*"#$%1$13((#)*4$*"+*$',/5$&)$*"#$*5/$&).3*$*#(0&)+,4$C&9#9;$&)$*"#$7+4#4$/'$!A$+)%$!TF9$!"#4#$*5/$13((#)*4$+(#$#J3+,$C7#1+34#$5#$"+<#$+4430#%$0+*1"#% %#<&1#4F`$*"34$*"#$7&+4$13((#)*$&4$2&<#)$76 " HH A $ %$J7C$µ8 " G = AAAAAAAAAAA β+H C%F !"#$3..#($,&0&*$/)$*"#$&).3*$1/00/)-0/%#$
Example 8.7 a4#$*"#$%1$7&+4$J3+)*&*$#<+,3+*#%$&)$DL+0.,#$Y9Z$*/$+)+,6Q#$*"#$1&(13&*$&)$:&29$Y9Bc;$*/$%#*#(0&)#$*"# &).3*$(#4&4*+)1#;$*"#$
Solution !"#$&).3*$%&''#(#)*&+,$(#4&4*+)1#$#)8$&4$2&<#)$76 # )8 = . π H + . π J O&)1#$!A$+)%$!T$+(#$#+1"$/.#(+*&)2$+*$+)$#0&**#($13((#)*$/'$I9TX$0=;$&*$'/,,/54$*"+* JC . /H = . /J = AAAAAAAAAA = HUU$Ω U7JC =4430#$β$ =$AII`$*"#) . π H = . π J = HUH × HUU = HU7H$=Ω !"34; #)8 = TI9T$8Ω !/$#<+,3+*#$*"#$2+&)$/'$*"#$'&(4*$4*+2#;$5#$'&(4*$'&)%$*"#$&).3*$(#4&4*+)1#$/'$*"#$4#1/)%$4*+2#;$#)T; # )J = . π L + . π C !B$+)%$!X$+(#$#+1"$/.#(+*&)2$+*$+)$#0&**#($13((#)*$/'$A$0=`$*"34 . /L = . /C = JC$Ω

8.6 Multistage Amplifiers

Figure 8.45 KS@,?&2#1*$-,)-@,*$.()$-&2-@2&*,1;$*"#$;&,1 (.$*"#$,1+@*$/*&;#$(.$*"#$&%+2,.,#)$,1$F,;7$G7LQ7

. π L = . π C = HUH × JC = J7CJC $=Ω !"34$#)T$=$X9IX$8Ω9$!"&4$(#4&4*+)1#$+..#+(4$7#*5##)$*"#$1/,,#1*/(4$/'$!A$+)%$!T;$+4$4"/5)$&)$:&29$Y9BX9 !"34$*"#$2+&)$/'$*"#$'&(4*$4*+2#$5&,,$7#$ v ,H A $% !(*&2$)#/,/*&1-#$,1$-(22#-*()$-,)-@,* AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA F H ≡ AAAAAA v )8 !(*&2$)#/,/*&1-#$,1$#%,**#)$-,)-@,*

# )J || ( # H + # J ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA . /H + . /J C7UC$=Ω || LU$=Ω = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA = JJ7L$TXT $$$$$ JUU$Ω :&23(#$Y9BZ$4"/54$+)$#J3&<+,#)*$1&(13&*$'/($1+,13,+*&)2$*"#$2+&)$/'$*"#$4#1/)%$4*+2#9$=4$&)%&1+*#%; *"#$&).3*$
R3 vo2

!

Q4

Q5

Ri3

vo1 " Figure 8.46 KS@,?&2#1*$-,)-@,*$.()$-&2-@2&*,1;$*"#$;&,1$(.$*"#$/#-(10$/*&;#$(.$*"#$&%+2,.,#)$,1$F,;7$G7LQ7

661

662 Chapter 8 Differential and Multistage Amplifiers

Example 8.7 continued

03,*&.,6&)2$*"#$*/*+,$(#4&4*+)1#$&)$*"#$#0&**#($/'$!R$76$Cβ$+$AFP # )Q = ( β + H ) ( # L + . /D ) O&)1#$!R$&4$/.#(+*&)2$+*$+)$#0&**#($13((#)*$/'$A$0=; JC . /D = AAAAAA = JC$Ω H # )Q = HUH × J7QJC = JQL7G$=Ω

k

S#$1+)$)/5$'&)%$*"#$2+&)$FT$/'$*"#$4#1/)%$4*+2#$+4$*"#$(+*&/$/'$*"#$*/*+,$(#4&4*+)1#$&)$*"#$1/,,#1*/($1&(13&* */$*"#$*/*+,$(#4&4*+)1#$&)$*"#$#0&**#($1&(13&*P v ,J # Q || # )Q A $%$ \ AAAAAAAAAAAAAAAAAAA F J ≡ AAAAAA v ,H . /L + . /C

Q$=Ω || JQL7G$=Ω = \ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA = \ C_7J$TXT CU$Ω !/$/7*+&)$*"#$2+&)$/'$*"#$*"&(%$4*+2#$5#$(#'#($*/$*"#$#J3&<+,#)*$1&(13&*$4"/5)$&)$:&29$Y9BR;$5"#(#$#)B$&4 *"#$&).3*$(#4&4*+)1#$/'$*"#$/3*.3*$4*+2#$'/(0#%$76$!Y9$a4&)2$*"#$(#4&4*+)1#-(#',#1*&/)$(3,#;$5#$1+,13,+*#$*"# <+,3#$/'$#)B$+4 # )L = ( β + H ) ( . /G + # R ) 5"#(# JC . /G = AAAAAA = C$Ω C # )L = HUH ( C + QUUU ) = QUQ7C$=Ω $$$$$$$$$$

Figure 8.47 KS@,?&2#1*$-,)-@,*$.()$#?&2@&*,1;$*"#$;&,1$(.$*"# *",)0$/*&;#$,1$*"#$&%+2,.,#)$-,)-@,*$(.$F,;7$G7LQ7

8.6 Multistage Amplifiers

Figure 8.48 KS@,?&2#1*$-,)-@,*$(.$*"#$(@*+@*$/*&;#$(.$*"#$&%+2,.,#)$-,)A -@,*$(.$F,;7$G7LQ7

!"#$2+&)$/'$*"#$*"&(%$4*+2#$&4$2&<#)$76 v ,Q # C || # )L A $%$ \ AAAAAAAAAAAAAAAAAA F Q ≡ AAAAAA A v ,J . /D + # L

HC7D$=Ω || QUQ7C$=Ω = \ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA = \ R7LJ$TXT J7QJC$=Ω :&)+,,6;$*/$/7*+&)$*"#$2+&)$FB$/'$*"#$/3*.3*$4*+2#$5#$(#'#($*/$*"#$#J3&<+,#)*$1&(13&*$&)$:&29$Y9BY$+)%$5(&*# v #R A F L ≡ AAAAAA,A = AAAAAAAAAAAAAAAAAA v ,Q # R + . /G

QUUU = AAAAAAAAAAAAAAAAAAAAA = U7__G$%$H QUUU + C !"#$/<#(+,,$
AAAAA,A = F H F J F Q F L = GCHQ$TXT v )8

/($RY9Z$%>9 !/$/7*+&)$*"#$/3*.3*$(#4&4*+)1#$#,$5#$f2(+7$"/,%g$/'$*"#$/3*.3*$*#(0&)+,$&)$:&29$Y9Bc$+)%$,//8$7+18 &)*/$*"#$1&(13&*9$>6$&)4.#1*&/)$5#$'&)% # , = # R || [ . /G + # C ⁄ ( β + H ) ] 5"&1"$2&<#4

#, $=$ HCJ$Ω

663

664 Chapter 8 Differential and Multistage Amplifiers

EXERCISE 8.22 m/#$*"#$)#/@2*/$(.$K>&%+2#$G7D$*($-&2-@2&*#$*"#$(?#)&22$?(2*&;#$;&,1$(.$*"#$&%+2,.,#)$,1$F,;7$G7LQ 9"#1$,*$,/$-(11#-*#0$*($&$/(@)-#$"&?,1;$&$)#/,/*&1-#$(.$HU$=Ω$&10$&$2(&0$(.$H$=Ω7 Ans. BHBc$_h_

Analysis Using Current Gains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
= # R ) /G

v )8

= # )H ) )

!"34;$*"#$
R1

Ri3

R2

R4

R3

ib5

Q7

ic2 ic1 = ic2

ii Q1

ib7

ic5 Q4

Q2

"

ic7 ib8 Q8

Q5

ib4 # ib5

vid

ie8 R5

R6

! ii

Ri2

vo

Ri4

Ri1 Figure 8.49 !"#$-,)-@,*$(.$*"#$%@2*,/*&;#$&%+2,.,#)$(.$F,;7$G7LQ$+)#+&)#0$.()$/%&22A/,;1&2$&1&2
8.6 Multistage Amplifiers

U#L*;$5#$#L.+)%$*"#$13((#)*$2+&)$C)/Yh))F$&)$*#(04$/'$*"#$4&2)+,$13((#)*4$*"(/32"/3*$*"#$1&(13&* +4$'/,,/54P

) /G ) CG ) 1D ) CD ) 1C ) CC ) 1J ) /G AAAAA ] AAAAA × AAAAA × AAAAA × AAAAA × AAAAA × AAAAA × AAAAA ) CG ) 1D ) CD ) 1C ) CC ) 1J ) ) )) D+1"$/'$*"#$13((#)*-*(+)40&44&/)$'+1*/(4$/)$*"#$(&2"*-"+)%$4&%#$&4$#&*"#($*"#$13((#)*$2+&)$/'$+ *(+)4&4*/($ /($*"#$ (+*&/$ /'$ +$ 13((#)*$%&<&%#(9$ !"34;$ (#'#(#)1#$ */$ :&29$ Y9BH$ #)+7,#4$34$*/$ '&)% *"#4#$'+1*/(4$76$&)4.#1*&/)P

) /G AAAAA = βG + H ) CG ) CG #C AAAAA = AAAAAAAAAAAAAAAAAA A ) 1D # C + # )L ) 1D AAAAA = βD ) CD

) CD #Q AAAAA ] AAAAAAAAAAAAAAAAAA A ) 1C # Q + # )Q ) 1C AAAAA = βC ) CC ( #H + #J ) ) CC AAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A ) 1J ( # H + # J ) + # )J ) 1J AAAAA = β J ))

because same voltage vet vo1

!"#4#$(+*&/4$1+)$7#$#+4&,6$#<+,3+*#%$+)%$*"#&($<+,3#4$34#%$*/$%#*#(0&)#$*"#$
EXERCISE 8.23 m/#$*"#$?&2@#/$(.$,1+@*$)#/,/*&1-#$.(@10$,1$K>&%+2#$G7D$*($#?&2@&*#$*"#$/#?#1$-@))#1*A*)&1/%,//,(1 .&-*()/$&10$"#1-#$*"#$(?#)&22$-@))#1*$;&,1$&10$?(2*&;#$;&,17 Ans. !"#$13((#)*-*(+)40&44&/)$'+1*/(4$&)$*"#$/(%#($/'$*"#&($,&4*&)2$+(#$AIA;$I9IBHT;$AII;$I9IATZ; AII;$I9YYRH;$AII$=h=`$*"#$/<#(+,,$13((#)*$2+&)$&4$XXHHc$=h=`$*"#$
665

666 Chapter 8 Differential and Multistage Amplifiers

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PROBLEMS

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PROBLEMS

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CHAPTER 8

Section 8.4: Other Nonideal Characteristics of the Differential Amplifier

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CHAPTER 9

Frequency Response Introduction 9.1

687

Low-Frequency Response of the CS and CE Amplifiers 689

9.2 Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT 701

9.6 High-Frequency Response of the CG and Cascode Amplifiers 746 9.7 High-Frequency Response of the Source and Emitter Followers 756 9.8 High-Frequency Response of Differential Amplifiers 760

9.3 High-Frequency Response of the CS and CE Amplifiers 711

9.9 Other Wideband Amplifier Configurations 770

9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers 721

9.10 Multistage Amplifier Examples

9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 731

Summary

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IN THIS CHAPTER YOU WILL LEARN 1. How coupling and bypass capacitors cause the gain of discrete-circuit amplifiers to fall off at low frequencies, and how to obtain an estimate of the frequency !" at which the gain decreases by 3 dB below its value at midband. 2. The internal capacitive effects present in the MOSFET and the BJT and how to model these effects by adding capacitances to the hybrid- π model of each of the two transistor types. 3. The high-frequency limitation on the gain of the CS and CE amplifiers and how the gain falloff and the upper 3-dB frequency !# are mostly determined by the small capacitance between the drain and gate (collector and base). 4. Powerful methods for the analysis of the high-frequency response of amplifier circuits of varying complexity. 5. How the cascode amplifier studied in Chapter 7 can be designed to obtain wider bandwidth than is possible with the CS and CE amplifiers. 6. The high-frequency performance of the source and emitter followers. 7. The high-frequency performance of differential amplifiers. 8. Circuit configurations for obtaining wideband amplification.

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@<,#<',/'&<$'F5:8$'@$'@)8:6'<5F$')+&5,.$67'<56'@$'5//8-$6'&<5&' % %I 8 ' % %< 8 '5.6' % & '@$*$'5#&,.= 5/'%$*($#&'/<)*&'#,*#8,&/2'L.'&<,/'*$=5*67'.)&$'&<5&'5&'-,6+5.6'(*$>8$.#,$/^&<5&',/7'5&'(*$>8$.#,$/ / \ $ ω ' -8#<' <,=<$*' &<5.' ω 2I 8 ' ω 2< 8 ' 5.6' ω 2M ^!>2' RC24S' /<)@/' &<5&' ) , ⁄ ) 6)4 ' 5%%*)5#<$/ [ 4 5 7'5/'/<)8:6'+$'&<$'#5/$2 Determining the Lower 3-dB Frequency, fL !+%# (54*)&1$%# "/# &+%# 5(7,)/)%'# 45)*8 ) , ⁄ ) 6)4 #5&#/'%01%*23# ω #25*#>%#">&5)*%$#>3#61>6&)&1&)*4# / \ $ ω #)*#H0:#=;:N?#5*$#%@5,15&)*4 &+%#(54*)&1$%#"/#&+%#&'5*6/%'#/1*2&)"*:#F*#&+)6#-538#&+%#/'%01%*23#'%67"*6%#"/#&+%#5(7,)/)%' 25*#>%#7,"&&%$#@%'616#/'%01%*238#5*$#&+%#,"-%'#M.$O#/'%01%*23#!"#25*#>%#$%&%'()*%$#56#&+% /'%01%*23#5&#-+)2+# ) , ⁄ ) 6)4 #$'"76#&"# 4 5 ⁄ < :#P#6)(7,%'#577'"52+8#+"-%@%'8#)6#7"66)>,%#)/ &+%#>'%5C#/'%01%*2)%6# ω 2I8 # ω 2< 8 #5*$# ω 2M #5'%#61//)2)%*&,3#6%75'5&%$:#F*#&+)6#256%8#-%#25* %(7,"3#&+%#O"$%#7,"&#'1,%6#=6%%#P77%*$)Q#9?#&"#6C%&2+#5#O"$%#7,"&#/"'#&+%#45)*#(54*)&1$%: D12+#5#7,"&#)6#6+"-*#)*#9)4:#;:M:#R>6%'@%#&+5)*2%#&+%#>'%5C#/'%01%*2)%6#5'%#61//)2)%*&,3 6%75'5&%$8#&+%)'#%//%2&6#577%5'#$)6&)*2&:#P&#%52+#>'%5C#/'%01%*238#&+%#6,"7%#"/#&+%#563(7&"&% &"#&+%#45)*#/1*2&)"*#)*2'%56%6#>3#')%/#'%@)%-#"/#7",%6#5*$#U%'"68#'%/%'#&"#P77%*$)Q#9:?

Vo Vsig (dB) #3 dB 20 dB"decade

40 dB"decade 20 log !AM !

60 dB"decade

# fL 0

fP1

fP3

fP2

f (Hz) (log scale)

Figure 9.3 0E$&#<')('&<$':)@G(*$>8$.#9'-5=.,&86$'*$/%)./$')('5';0'5-%:,(,$*'()*'@<,#<'&<$'&<*$$'%):$'(*$G >8$.#,$/'5*$'/8((,#,$.&:9'/$%5*5&$6'()*'&<$,*'$(($#&/'&)'5%%$5*'6,/&,.#&2

9.1 Low-Frequency Response of the Common-Source and Common-Emitter Amplifiers 693

N'>8,#E'@59'()*'$/&,-5&,.='&<$'PG6H'(*$>8$.#9'!"',/'%)//,+:$',('&<$'<,=<$/&G(*$>8$.#9'%):$ R<$*$7'!285:'&)'&<$'<,=<$/&')('&<$'%):$'(*$>8$.#,$/7' ! " # # '! 2<

_/85::97'&<$'<,=<$/&G(*$>8$.#9'%):$',/'&<$').$'#58/$6'+9' % & : '?<,/',/'+$#58/$' % & ',.&$*5#&/ @,&<' I ⁄ - 3 8 '@<,#<',/'*$:5&,F$:9':)@'R/$$'!>2'C2YS2 Determining the Pole Frequencies by Inspection O%/"'%# ,%5@)*4# &+)6# 6%2&)"*8# -% 7'%6%*#6)(7,%#(%&+"$#/"'#/)*$)*4#&+%#&)(%#2"*6&5**$#+%*2%#&+%#7",%#/'%01%*23#566"2). 5&%$#-)&+#%52+#"/#&+%#&+'%%#25752)&"'6:#!+%#7'"2%$1'%#)6#6)(7,%V 1. T%$12%#)6)4#&"#U%'": 2. G"*6)$%'#%52+#25752)&"'#6%75'5&%,3W#&+5&#)68#5661(%#&+5&#&+%#"&+%'#&-"#25752)&"'6#5'% 52&)*4#56#7%'/%2+"')'21)&6: 3. 9"'#%52+#25752)&"'8#/)*$#&+%#&"&5,#'%6)6&5*2%#6%%*#>%&-%%*#)&6#&%'()*5,6:#!+)6#)6#&+% '%6)6&5*2%#&+5&#$%&%'()*%6#&+%#&)(%#2"*6&5*ȶ"2)5&%$#-)&+#&+)6#25752)&"': ?<$' *$56$*' ,/' $.#)8*5=$6' &)' 5%%:9' &<,/' %*)#$68*$' &)' %%D7' %&7' 5.6' %%U' 5.6' &<8/' /$$' &<5& !>/2 RC2US7'RC2YS7'5.6'RC23S'#5.'+$'@*,&&$.'+9',./%$#&,).2 Selecting Values for the Coupling and Bypass Capacitors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

Example 9.1 A%#-)6+#&"#6%,%2Ɂ'"7')5&%#@5,1%6#/"'#&+%#2"17,)*4#25752)&"'6#%%I#5*$#%%<#5*$#&+%#>37566#25752). &"'#%&#/"'#5#GD#5(7,)/)%'#/"'#-+)2+##01#=#Z:[#\Ω, 0*#=#0"#=#IY#CΩ, 06)4#=#ILL#CΩ8#5*$#-3#=#I#(PS]: F&#)6#'%01)'%$#&"#+5@%#!"#5&#ILL#BU#5*$#&+5&#&+%#*%5'%6&#>'%5C#/'%01%*23#>%#5&#,%56#$%25$%#,"-%': Solution A%#6%,%2&#%"#&+5& I ! 2< = ............................ = ! " < π ( %& ⁄ -3 )

!+168 [M -3 I × IL . = ......................... . = I:^#µ9 % & = .......... < π × ILL < π !"

9"'#!2I#=#!2M#=#IL#BU8#-%#">&5)* I IL = ........................................................^. < π % %I ( L:I + Z:[ ) × IL

694 Chapter 9 Frequency Response

Example 9.1 continued

-+)2+#3)%,$6 % %I = M:M#*9

5*$ -+)2+#'%61,&6#)*

I IL = .....................................................M. < π % %< ( IY + IY ) × IL % %< = L:YM#µ9

EXERCISE 9.1# P#GD#5(7,)/)%'#+56#%%I#=#%&#=#%%<#=#I#µ98#01#=#IL#\Ω8#06)4#=#ILL#CΩ8#-3#=#<#(PS]8#0*#=#0"#=#IL CΩ. 9)*$#45 8#!2I8#!2<8#!2M8#5*$#!": Ans. `;:;#]S]W#L:LI^#BUW#MIN:M#BUW#N#BUW#MIN:M#BU

9.1.2 The CE Amplifier B,=8*$'C2Y'/<)@/'5'#)--).G$-,&&$*'5-%:,(,$*'&<5&'8&,:,Q$/'#)8%:,.='#5%5#,&)*/' % %I '5.6' % %< 5.6'$-,&&$*'+9%5//'#5%5#,&)*' % 6 2'N/',.'&<$'#5/$')('&<$'JK0'5-%:,(,$*7'&<$'$(($#&')('&<$/$ #5%5#,&)*/',/'($:&').:9'5&':)@'(*$>8$.#,$/2'K8*')+W$#&,F$',/'&)'6$&$*-,.$'&<$'5-%:,(,$*'=5,.')* &*5./($*'(8.#&,).' ) , ⁄ ) 6)4 '@,&<'&<$/$'&<*$$'#5%5#,&5.#$/'&5E$.',.&)'5##)8.&2'?)@5*6'&<5&'$.67 @$' /<)@' ,.' B,=2' C2YR+S' &<$' #,*#8,&' @,&<' &<$' 6#' /)8*#$/' $:,-,.5&$62' T$' /<5::' %$*()*-' &<$ /-5::G/,=.5:'5.5:9/,/'6,*$#&:9').'&<$'#,*#8,&2'?)'E$$%'&<$'5.5:9/,/'/,-%:$7'@$'/<5::'.$=:$#& &<$'$(($#&')(' + , 7'5/'@$'<5F$'6).$',.'&<$'JK0'#5/$2 ?<$'5.5:9/,/')('&<$'#,*#8,&',.'B,=2'C2YR+S',/'/)-$@<5&'-)*$'#)-%:,#5&$6'&<5.'&<5&'()* &<$';0'#5/$2'?<,/',/'5'*$/8:&')('&<$'(,.,&$'β')('&<$'HI?7'@<,#<'#58/$/'&<$',.%8&',-%$65.#$'5& &<$'+5/$'&)'+$'5'(8.#&,).')(' % 6 2'?<8/'&<$'$(($#&/')(' % %I '5.6' % 6 '5*$'.)':).=$*'/$%5*5+:$2 N:&<)8=<').$'#5.'#$*&5,.:9'/&,::'6$*,F$'5.'$"%*$//,).'()*'&<$')F$*5::'&*5./($*'(8.#&,).7'&<$ *$/8:&'@,::'+$'>8,&$'#)-%:,#5&$67'-5E,.=',&'6,((,#8:&'&)')+&5,.'6$/,=.',./,=<&2'?<$*$()*$'@$ /<5::'%8*/8$'5.'5%%*)",-5&$'5:&$*.5&,F$'5%%*)5#<2 Considering the Effect of Each of the Three Capacitors Separately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π'5&'&<$'+5/$')('&<$'&*5./,/&)*'#5.'+$'@*,&&$.'5/

0 = || + π . )π = )6)4 .................................................... I ( 0 = || + π ) + 0 6)4 + ........... /% %I

9.1 Low-Frequency Response of the Common-Source and Common-Emitter Amplifiers

VCC

RC

Rsig

CC2 Vo

CC1 RL

CE Vsig " !

RB I

!VEE (a)

RC

Rsig

CC2 Vo

CC1 CE

" Vsig " !

Vo

RL

RB

! (b) Figure 9.4 ''%('N'#5%5#,&,F$:9'#)8%:$6'#)--).G$-,&&$*'5-%:,(,$*2''$('?<$'#,*#8,&'%*$%5*$6'()*'/-5::G/,=.5:' 5.5:9/,/2

5.6'&<$')8&%8&'F):&5=$',/')+&5,.$6'5/

), = [ - 3 ) π ( 0 % || 0 " ) ?<$/$'&@)'$>85&,)./'#5.'+$'#)-+,.$6'&)')+&5,.'&<$'F):&5=$'=5,.' ) , ⁄ ) 6)4 ',.#:86,.='&<$'$(($#& )('%%D'5/

) ( 0 = || + π ) / . - 3 ( 0 % || 0 " ) ......................................................... .......,. = [ .................................. . ) 6)4 I ( 0 = || + π ) + 0 6)4 / + ................................................. % %I [ ( 0 = || + π ) + 0 6)4 ]

RC2DVS

695

696 Chapter 9 Frequency Response (*)-'@<,#<'@$')+/$*F$'&<5&'&<$'$(($#&')('%%D',/'&)',.&*)68#$'&<$'(*$>8$.#9G6$%$.6$.&'(5#G &)*'+$&@$$.'&<$'/>85*$'+*5#E$&/' ).'&<$'*,=<&G<5.6'/,6$')(' !>2' RC2DVS2'T$'*$#)=.,Q$' &<,/ (5#&)*'5/'&<$'&*5./($*'(*5#&,).')('5'/,.=:$G&,-$G#)./&5.&'R0?;S'#,*#8,&')('&<$'<,=8$.#9'ω2D7

I ω 2I = ................................................. % %I [ ( 0 = || + π ) + 0 6)4 ]

RC2DDS

`)&$'&<5&' [ ( 0 = || + π ) + 0 6)4 ] ,/'&<$'+8/;/:97>8'/887'?8:@887':A8':8+3;79B/',!'%%D'@A87')/,=';/'/8:':, C8+,2'?<$'0?;'<,=8$.#,$/'5&'&<$'*5&$')('3'6HO)#&5F$'RUV'6HO6$#56$S'@,&<'5'PG6H'(*$>8$.#9'5&' ! 2I = ω 2I ⁄ < π 7 5/',.6,#5&$6',.'B,=2'C21R5S2'N:/)'.)&$'&<5&'@$'<5F$'6$.)&$6'&<$'-,6+5.6'=5,.'457

( 0 = || + π ) . - 3 ( 0 % || 0 " ) 4 5 = [ .................................. ( 0 = || + π ) + 0 6)4

RC2DUS

`$"&7'@$'#)./,6$*'&<$'$(($#&')('%62'B)*'&<,/'%8*%)/$'@$'5//8-$'&<5&'%%D'5.6'%% U'5*$ 5#&,.='5/'%$*($#&'/<)*&'#,*#8,&/'5.6'&<8/')+&5,.'&<$'#,*#8,&',.'B,=2'C21R+S2'M$(:$#&,.='+8'5.6 %6',.&)'&<$'+5/$'#,*#8,&'5.6'8&,:,Q,.='&<$'?
0= I . ......................................................................... . ( ? = ) 6)4 ................... 0 = + 0 6)4 I || ( 0 = 0 6)4 ) + ( β + I ) + 8 + ......... /% 6

?<$'#)::$#&)*'#8**$.&'#5.'&<$.'+$'()8.6'5/'β (?'5.6'&<$')8&%8&'F):&5=$'5/

) , = [ β ( ? ( 0 % || 0 " ) 0= 0 = + 0 6)4

β ( 0 % || 0 " )

'' = [ .................... .......................................................................... ) 6)4

I ( 0 = || 0 6)4 ) + ( β ] I ) + 8 + ......... /% 6

?<8/'&<$'F):&5=$'=5,.',.#:86,.='&<$'$(($#&')('%6'#5.'+$'$"%*$//$6'5/U

) 0= β ( 0 % || 0 " ) / .......,. = [ ................... . .................................................... ............................................................... ) 6)4 0 = + 0 6)4 ( 0 = || 0 6)4 ) + ( β + I )+ 8 0 = || 0 6)4 / + I ⁄ % 6 + 8 + ................... β+I

RC2DPS

T$' )+/$*F$' &<5&' %6' ,.&*)68#$/' &<$' 0?;' <,=8$.#9'5&'&<$'*5&$')('3'6HO)#&5F$'@,&<'5'PG6H (*$>8$.#9'$>85:'&)'&<$'#)*.$*'R)*'%):$S'(*$>8$.#9')('&<$'<,=
I ω 2< = .......................................... 0 = || 0 6)4 % 6 + 8 + ................... β+I

RC2DYS

K+/$*F$'&<5&' [ + 8 + ==0 = || 0 6)4 ?S ( β ] I )? ] ';/':A8'+8/;/:97>8'/887'?8:@887':A8':@,':8+3;79B/ ,!'%6'@A87')/,=';/'/8:':,'C8+,2'?<$'$(($#&')('%6').'&<$'5-%:,(,$*'(*$>8$.#9'*$/%)./$',/',::8/G &*5&$6'+9'&<$'/E$&#<',.'B,=2'C21R+S2 <

#F*#>%#6+"-*#&+5&#&+%#/52&"'#(1,&)7,3)*4#&+%#+)4+.7566#&'5*6/%'#/1*2&)"*#)*#H0:#=;:IM?#)6#%015,#&"#45' "/#H0:#=;:I
9.1 Low-Frequency Response of the Common-Source and Common-Emitter Amplifiers 697

Vo (dB) Vsig

3 dB

RC Vo

gmVp Rsig

CC1

20 log !AM!

RL "

Vsig

" !

Vp

6 dB$octave 20 dB$decade

RB

fP1

! rp

f (Hz, log scale)

fP1 # 1$2p CC1 [(RB %rp) " Rsig] (a) Vo (dB) Vsig

3 dB

RC Vo

bIb

Vsig " !

20 log !AM!

RL

Ib

Rsig

RB

6 dB$octave 20 dB$decade

CE

&

(b " 1) re "

1 sCE

fP2 fP2 # 1$2pCE re "

'

f (Hz, log scale) RB %Rsig b"1

(b) Figure 9.5 N.5:9/,/')('&<$':)@G(*$>8$.#9'*$/%)./$')('&<$';!'5-%:,(,$*')('B,=2'C2YX'''%('&<$'$(($#&')('%%D',/' 6$&$*-,.$6'@,&<'%6'5.6'%%U'5//8-$6'&)'+$'5#&,.='5/'%$*($#&'/<)*&'#,*#8,&/b''$('&<$'$(($#&')('%6',/'6$&$*-,.$6' @,&<'%%D'5.6'%%U'5//8-$6'&)'+$'5#&,.='5/'%$*($#&'/<)*&'#,*#8,&/b'

B,.5::97'@$'#)./,6$*'&<$'$(($#&')('%%U2'?<$'#,*#8,&'@,&<'%%D'5.6'%6'5//8-$6'&)'+$'5#&,.= 5/'%$*($#&'/<)*&'#,*#8,&/',/'/<)@.',.'B,=2'C21R#S7'()*'@<,#<'@$'#5.'@*,&$

5.6

0 = || + π . ) π = ) 6)4 .................................. ( 0 = || + π ) + 0 6)4 0% . 0" ) , = [ - 3 ) π ................................... I .......... . 0% + + 0" /%%<

698 Chapter 9 Frequency Response Vo (dB) Vsig RC

3 dB

CC2 Vo gmVp

Rsig

20 log !AM!

RL

" Vsig

" !

Vp

6 dB$octave 20 dB$decade

RB

fP3

! rp

f (Hz, log scale)

fP3 # 1$2p CC2 (RC " RL) (c) Vo (dB) Vsig #3 dB, fL # fP2

6 dB/octave 12 dB/octave

20 log !AM!

18 dB/octave

fP3

fP1

fP2

f (Hz, log scale)

(d) Figure 9.5 R>,7:;7D8. S'')('&<$'$(($#&')('%%U',/'6$&$*-,.$6'@,&<'%%D'5.6'%6'5//8-$6'&)'+$'5#&,.='5/'%$*($#& /<)*&'#,*#8,&/b''#('/E$&#<')('&<$':)@G(*$>8$.#9'=5,.'8.6$*'&<$'5//8-%&,)./'&<5&'%%D7'%67'5.6'%%U'6)'.)&',.&$*G 5#&'5.6'&<5&'&<$,*'+*$5E'R)*'%):$S'(*$>8$.#,$/'5*$'@,6$:9'/$%5*5&$62

?<$/$'&@)'$>85&,)./'#5.'+$'#)-+,.$6'&)')+&5,.'&<$':)@G(*$>8$.#9'=5,.',.#:86,.='&<$'$(($#& )('%%U'5/

) 0 = || + π / . - 3 ( 0 % || 0 " ) ......................................... .......,. = [ .................................. I ) 6)4 ( 0 = || + π ) + 0 6)4 / + ................................ %%< ( 0 % + 0 " )

RC2D1S

T$')+/$*F$'&<5&'%% U',.&*)68#$/'&<$'(*$>8$.#9G6$%$.6$.&'(5#&)*'+$&@$$.'&<$'/>85*$'+*5#EG $&/7'@<,#<'@$'*$#)=.,Q$'5/'&<$'&*5./($*'(8.#&,).')('5'<,=8$.#9'ω2P7

I ω 2M = ................................ %%< ( 0 % + 0 " )

RC2D3S

9.1 Low-Frequency Response of the Common-Source and Common-Emitter Amplifiers 699

c$*$'@$'.)&$'&<5&'5/'$"%$#&$67'R0%'+'0"S';/':A8'+8/;/:97>8'/887'?8:@887':A8':8+3;79B/',!'%%U @A87')/,=';/'/8:':,'C8+,2'?<8/'#5%5#,&)*'%%U'#58/$/'&<$':)@G(*$>8$.#9'=5,.')('&<$'5-%:,(,$*'&) 6$#*$5/$'5&'&<$'*5&$')('3'6HO)#&5F$'@,&<'5'PG6H'(*$>8$.#9'5&' !2M = ω 2M ⁄ <π 8 '5/',::8/&*5&$6'+9 &<$'/E$&#<',.'B,=2'C21R#S2 Determining the Lower 3-dB Frequency, fL#J"-#&+5&#-%#+5@%#$%&%'()*%$#&+%#%//%2&6 "/#%52+#"/#%%I8#%68#5*$#%%<#52&)*4#5,"*%8#&+%#01%6&)"*#>%2"(%6#-+5&#-),,#+577%*#-+%*#5,, &+'%%#5'%#7'%6%*&#&+%#65(%#&)(%:#!+)6#01%6&)"*#+56#&-"#75'&6V#9)'6&8#-+5&#+577%*6#-+%*#5,, &+'%%# 25752)&"'6#5'%#7'%6%*&#>1&# $"# *"&# )*&%'52&a#!+%# 5*6-%'#)6# &+5&#&+%#5(7,)/)%'# ,"-. /'%01%*23#45)*#25*#>%#%Q7'%66%$#56 ) / .......,. = [ 4 5 ................. / + ω 2I )6)4

/ ................. / + ω 2<

/ ................. / + ω 2M

RC2DZS

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⁄ ) 6)4 ' ,.' !>2' RC2DZS' 5.6' #5:#8:5&$' &<$' (*$>8$.#9' 5&' @<,#<' ,&' 6*)%/' &) 4 5 ⁄ < : '?<$'@)*E',.F):F$6',.'6),.='&<,/7'<)@$F$*7',/'8/85::9'&))'=*$5&'5.6',/'*5*$:9'W8/&,G (,$6',.'%*5#&,#$7'%5*&,#8:5*:9'+$#58/$',.'5.9'#5/$7'!>2'RC2DZS',/'5.'5%%*)",-5&,).'+5/$6').'&<$ 5//8-%&,).' &<5&' &<$' &<*$$' #5%5#,&)*/' 6)' .)&' ,.&$*5#&2' ?<,/' :$56/' &)' &<$' /$#).6' %5*&' )(' &<$ >8$/&,).X'T<5&'<5%%$./'@<$.'5::'&<*$$'#5%5#,&)*/'5*$'%*$/$.&'5.6',.&$*5#&d'T$'6)'E.)@'&<5& %%D'5.6'%6'8/85::9',.&$*5#&'5.6'&<5&'&<$,*'#)-+,.$6'$(($#&',/'&@)'%):$/'5&'(*$>8$.#,$/'&<5& @,::'6,(($*'/)-$@<5&'(*)-' ω2D'5.6' ω2U2'K('#)8*/$7').$'#5.'6$*,F$'&<$')F$*5::'&*5./($*'(8.#G &,).'&5E,.='&<,/',.&$*5#&,).',.&)'5##)8.&'5.6'(,.6'-)*$'%*$#,/$:9'&<$':)@G(*$>8$.#9'*$/%)./$2 ?<,/7'<)@$F$*7'@,::'+$'&))'#)-%:,#5&$6'&)'9,$:6'566,&,).5:',./,=<&2'N/'5.'5:&$*.5&,F$7'()*'<5.6 #5:#8:5&,)./7' @$' #5.' )+&5,.' 5' *$5/).5+:9' =))6' $/&,-5&$' ()*' !"' 8/,.=' &<$' ()::)@,.=' ()*-8:5 R@<,#<'@$'@,::'.)&'6$*,F$'<$*$SPX

I I I I !"# # # ...... ................. + ............. + ................. < π % %I 0 %I % 6 0 6 % %< 0 %<

RC2D4S

!" = !2I + !2< + !2M

RC2DCS

)*'$>8,F5:$.&:97 @<$*$'0%D7'06 7'5.6'0%U'5*$'&<$'*$/,/&5.#$/'/$$.'+9'%%D7'%6 7'5.6'%%U7'*$/%$#&,F$:97'@<$.')/,=',/ /$&'&)'Q$*)'5.6'&<$')&<$*'&@)'#5%5#,&5.#$/'5*$'*$%:5#$6'@,&<'/<)*&'#,*#8,&/2'!>85&,)./'RC2D4S'5.6 RC2DCS'%*)F,6$',./,=<&'*$=5*6,.='&<$'*$:5&,F$'#).&*,+8&,)./')('&<$'&<*$$'#5%5#,&)*/'&)'!"2'B,.5::97 @$' .)&$' &<5&' 5' (5*' -)*$' %*$#,/$' 6$&$*-,.5&,).' )(' &<$' :)@G(*$>8$.#9' =5,.' 5.6' &<$' PG6H' (*$G >8$.#9'!"'#5.'+$')+&5,.$6'8/,.='0eL;!2 Selecting Values for CC1, CE, and CC2# A%# *"-# 5$$'%66# &+%# $%6)4*# )661%# "/# 6%,%2&)*4 577'"7')5&%#@5,1%6#/"'#%%I8#%6 8#5*$#%%<:#!+%#$%6)4*#">X%2&)@%#)6#&"#7,52%#&+%#,"-%'#M.$O#/'%. 01%*23#!"#5#67%2)/)%$#,"25&)"*#-+),%#()*)()U)*4#&+%#25752)&"'#@5,1%6:#D)*2%8#56#(%*&)"*%$ 5>"@%8#%6#1615,,3#6%%6#&+%#,"-%6&#"/#&+%#&+'%%#'%6)6&5*2%68#&+%#&"&5,#25752)&5*2%#)6#()*)()U%$ M

#!+%#)*&%'%6&%$#'%5$%'#25*#'%/%'#&"#P77%*$)Q#9:

700 Chapter 9 Frequency Response >3#6%,%2&)*4#%6#6"#&+5&#)&6#2"*&')>1&)"*#&"#!"#)6#$"()*5*&:#!+5&#)68#>3#'%/%'%*2%#&"#H0:#=;:IN?8 -%#(53#6%,%2&#%6#612+#&+5&# I ⁄ ( % 6 0 6 ) #)68#6538#NLb#"/# ω"#=#<π !"8#,%5@)*4#%52+#"/#&+%#"&+%' 25752)&"'6#&"#2"*&')>1&%#ILb#&"#&+%#@5,1%#"/# ω":#HQ5(7,%#;:<#6+"1,$#+%,7#&"#),,16&'5&%#&+)6 7'"2%66:

HcP\EKH#;:<

Example 9.2 A%#-)6+#&"#6%,%2Ɂ'"7')5&%#@5,1%6#/"'#%%I8#%%<8#5*$#%6#/"'#&+%#2"(("*.%()&&%'#5(7,)/)%'8#-+)2+ +56#0=#=#ILL#CΩ8#0%#=#N#CΩ8#0"#=#Y#CΩ8#06)4#=#Y#CΩ8# β #=#ILL8#-3#=#ZL#(PS]8#5*$#+π#=#<:Y#CΩ:#F&#)6 '%01)'%$#&"#+5@% #!"#=#ILL#BU: Solution A%#/)'6&#$%&%'()*%#&+%#'%6)6&5*2%6#6%%*#>3#&+%#&+'%%#25752)&"'6#%%I8#%68#5*$#%%<#56#/",,"-6V 0 %I = ( 0 = || + π ) + 0 6)4 = ( ILL || <:Y ) + Y = [:ZZ#CΩ 0 = || 0 6)4 . 0 6 = + 8 + ................... β+I ILL || Y = L:L
J"-8#6%,%2&)*4#%6#6"#&+5&#)"*&')>1&%6#NLb#"/#&+%#@5,1%#"/#ω"#4)@%6 I ................... = L:N × < π × ILL % 6 × [< % 6 = <[:^#µ9

J%Q&8#)/#%%I#)6#&"#2"*&')>1&%#ILb#"/#!"8 I .......................................M. = L:I × < π × ILL % %I × [:ZZ × IL % %I = <:I#µ9

D)(),5',38#)/#%%<#)6#&"#2"*&')>1&%#ILb#"/#!"8#)&6#@5,1%#6+"1,$#>%#6%,%2&%$#56#/",,"-6V I ...................................M. = L:I × < π × ILL % %< × IM × IL ''''''' % %< = I:<#µ9

F*#7'52&)2%8#-%#-"1,$#6%,%2&#&+%#*%5'%6&5*$5'$#@5,1%6#/"'#&+%#&+'%%#25752)&"'6#-+),%#%*61')*4#&+5& !" #≤#ILL#BU:

9.2 Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT 701

EXERCISE 9.2# P#2"(("*.%()&&%'#5(7,)/)%'#+56#%%I#=#%6#=#%%<#=#I#µ98#0=#=#ILL#CΩ8#06)4#=#Y#CΩ8#-3#=#ZL#(PS]8 +π =#<:Y#CΩ8#0%#=#N#CΩ8#5*$#0"#=#Y#CΩ:#P661()*4#&+5&#&+%#&+'%%#25752)&"'6#$"#*"&#)*&%'52&8#/)*$#!2I8 !2<8#5*$#!2M8#5*$#+%*2%#%6&)(5&%#!": Ans. %&&%'#%6&)(5&%#/"'#!"#)6#">&5)*%$V##<:
9.2 Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT T<,:$'#)8%:,.='5.6'+9%5//'#5%5#,&)*/'#58/$'&<$'=5,.')('&*5./,/&)*'5-%:,(,$*/'&)'(5::')(('5&'&<$':)@G (*$>8$.#9'$.67'&<$'=5,.'(5::)(('5&'<,=<'(*$>8$.#,$/',/'#58/$6'+9'&<$'#5%5#,&,F$'$(($#&/',.&$*.5:'&) &<$'&*5./,/&)*/2'L.'&<,/'/$#&,).'@$'/<5::'+*,$(:9'#)./,6$*'&<$/$'$(($#&/'5.67'-)*$',-%)*&5.&:97'/<)@ <)@'&<$'6$F,#$'/-5::G/,=.5:'-)6$:'#5.'+$'58=-$.&$6'&)'&5E$'&<$/$'$(($#&/',.&)'5##)8.&2

9.2.1 The MOSFET B*)-')8*'/&869')('&<$'%<9/,#5:')%$*5&,).')('&<$'JK0B!?',.'0$#&,).'12D7'@$'E.)@'&<5&'&<$ 6$F,#$'<5/',.&$*.5:'#5%5#,&5.#$/2'L.'(5#&7'@$'8/$6').$')('&<$/$7'&<$'=5&$G&)G#<5..$:'#5%5#,&5.#$7 ,.')8*'6$*,F5&,).')('&<$'JK0B!?' ; [ v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b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f7'g7'07'5.6'H2'?<$*$'@,::'+$'(,F$'#5%5#,&5.#$/',.'&)&5:X

702 Chapter 9 Frequency Response %-/7'%-.7'%-?7'%/?7'5.6'%.?7'@<$*$'&<$'/8+/#*,%&/',.6,#5&$'&<$':)#5&,).')('&<$'#5%5#,&5.#$/',. &<$'-)6$:2'L.'&<$'()::)@,.=7'@$'/<)@'<)@'&<$'F5:8$/')('&<$'(,F$'-)6$:'#5%5#,&5.#$/'#5. +$'6$&$*-,.$62'T$'@,::'6)'/)'+9'#)./,6$*,.='$5#<')('&<$'&@)'#5%5#,&,F$'$(($#&/'/$%5*5&$:92 The Gate Capacitive Effect ?<$'=5&$'#5%5#,&,F$'$(($#&'#5.'+$'-)6$:$6'+9'&<$'&<*$$'#5%5#,&5.#$/'%-/7'%-.7'5.6'%-?2'?<$ F5:8$/')('&<$/$'#5%5#,&5.#$/'#5.'+$'6$&$*-,.$6'5/'()::)@/X 1. A+%*#&+%#\RD9H!#)6#"7%'5&)*4#)*#&+%#&')"$%#'%4)"*#5(5,,#v*&8#&+%#2+5**%,#-),,#>% "/#1*)/"'(#$%7&+:#!+%#45&%.2+5**%,#25752)&5*2%#-),,#>%#M" %,L#5*$#25*#>%#("$%,%$ >3#$)@)$)*4#)&#%015,,3#>%&-%%*#&+%#6"1'2%#5*$#$'5)*#%*$6W#&+168

% -/ = % -. = I..<. M" % ,L

( &')"$%#'%4)"* )

RC2UVS

!+)6#)6#">@)"16,3#5*#577'"Q)(5&)"*#=56#5,,#("$%,)*4#)6?8#>1&#)&#-"'C6#-%,,#/"'#&')"$%. '%4)"*#"7%'5&)"*#%@%*#-+%*#v*&#)6#*"(5,,: 2. A+%*#&+%#\RD9H!#"7%'5&%6#)*#65&1'5&)"*8#&+%#2+5**%,#+56#5#&57%'%$#6+57%#5*$#)6 7)*2+%$#"//#5&#"'#*%5'#&+%#$'5)*#%*$:#F*#>%#6+"-*#&+5&#&+%#45&%.&".2+5**%,#25752. )&5*2%#)*#&+)6#256%#)6#577'"Q)(5&%,3# <..M. M" % ,L #5*$#25*#>%#("$%,%$#>3#566)4*)*4#&+)6 %*&)'%#5("1*&#&"#%-/8#5*$#5#U%'"#5("1*&#&"#%-.#=>%2516%#&+%#2+5**%,#)6#7)*2+%$#"//#5& &+%#$'5)*?W#&+168

% -/ = <..M. M" % ,L % -. = L

=65&1'5&)"*#'%4)"*?

RC2UDS RC2UUS

3. A+%*#&+%#\RD9H!#)6#21&#"//8#&+%#2+5**%,#$)6577%5'68#5*$#&+16#%-/#=#%-.#=#L:#B"-. %@%'8#-%#25*#=5/&%'#6"(%#'5&+%'#2"(7,%Q#'%56"*)*4?#("$%,#&+%#45&%#25752)&)@%#%//%2& >3#566)4*)*4#5#25752)&5*2%#M" %,L#&"#&+%#45&%.>"$3#("$%,#25752)&5*2%W#&+168

% -/ = % -. = L % -? = M" % ,L

=21&"// )

RC2UPS RC2UYS

4. !+%'%#)6#5*#5$$)&)"*5,#6(5,,#25752)&)@%#2"(7"*%*&#&+5+"1,$#>%#5$$%$#&"#%-/#5*$ %-.#)*#5,,#&+%#7'%2%$)*4#/"'(1,56:#!+)6#)6#&+%#25752)&5*2%#&+5&#'%61,&6#/'"(#&+%#/52& &+5&# &+%# 6"1'2%# 5*$# $'5)*# $)//16)"*6# %Q&%*$# 6,)4+&,3# 1*$%'# &+%#45&%# "Q)$%# ='%/%'#&" 9)4: Y:I?:#F/#&+%#,I8+B9F#,%*4&+#)6#$%*"&%$#",v8#-%#6%%#&+5&#&+%#+1.-2%3/)%3%)"4%&). 2"(7"*%*&#)6

% ,v = M" ,v % ,L

RC2U1S

!37)25,,38#",v#=#L:LY#&"#L:I#": The Junction Capacitances #!+%#$%7,%&)"*.,53%'#25752)&5*2%6#"/#&+%#&-"#'%@%'6%.>)56%$ F7#X1*2&)"*6#/"'(%$#>%&-%%*#%52+#"/#&+%#6"1'2%#5*$#&+%#$'5)*#$)//16)"*6#5*$#&+%#>"$3#25*#>% $%&%'()*%$#16)*4#&+%#/"'(1,5#$%@%,"7%$#)*#D%2&)"*#M:^#=H0:#M:Z[?:#!+168#/"'#&+%#6"1'2%#$)//1. 6)"*8#-%#+5@%#&+%#6"1'2%.>"$3#25752)&5*2%8#%/?8

% /?L . % /? = ..................... ) &= I + ........ )L

RC2U3S

9.2 Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT 703

@<$*$'%/?V',/'&<$'F5:8$')('%/?'5&'Q$*)'+)69G/)8*#$'+,5/7')&=',/'&<$'-5=.,&86$')('&<$'*$F$*/$G +,5/'F):&5=$7'5.6')V',/'&<$'W8.#&,).'+8,:&G,.'F):&5=$'RV23'h'&)'V24'hS2'0,-,:5*:97'()*'&<$'6*5,. 6,((8/,).7'@$'<5F$'&<$'6*5,.G+)69'#5%5#,&5.#$'%.?7

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RC2UZS

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( - 3 [ /% µ . A !8 ≡ ...>. = ......................................... I/+ π + / ( % π + % µ ) (? Z

#!+%6%#@5,1%6#577,3#/"'#$)62'%&%#$%@)2%6#5*$#$%@)2%6#/5>')25&%$#-)&+#5#'%,5&)@%,3#",$#FG#7'"2%66#&%2+. *","43#=&+%#6".25,,%$#+)4+.@",&54%#7'"2%668#6%%#P77%*$)Q#[:P?:#9"'#("$%'*#FG#/5>')25&)"*#7'"2%66%68 %π#5*$#%µ#5'%#)*#&+%#'5*4%#"/#&%*6#"/#/%(&"/5'5$6#=/ 9#?:

9.2 Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT 709

Figure 9.9 ;,*#8,&'()*'6$*,F,.='5.'$"%*$//,).'()*' A !8 ( / ) ≡ ( > ⁄ ( ? :

N&'&<$'(*$>8$.#,$/'()*'@<,#<'&<,/'-)6$:',/'F5:,67'ω %µ'%'-3 b'&<8/'@$'#5.'.$=:$#&'&<$'/%µ'&$*,.'&<$'.8-$*5&)*'5.6'@*,&$

-3 +π . A !8 # ....................................... I + / ( % π + % µ )+ π ?<8/7

β

L . A !8 = ....................................... I + / ( % π + % µ )+ π

RC2PCS

@<$*$'βV',/'&<$':)@G(*$>8$.#9'F5:8$')('β2'?<8/'A!8'<5/'5'/,.=:$G%):$'R)*'0?;S'*$/%)./$'@,&< 5'PG6H'(*$>8$.#9'5&'ω'='ωβ 7'@<$*$

I ω β = ............................

( % π + % µ )+ π

RC2YVS

B,=8*$'C2DV'/<)@/'5'H)6$'%:)&'()*' A !8 : B*)-'&<$'[3G6HO)#&5F$'/:)%$7',&'()::)@/'&<5&'&<$'(*$G >8$.#9'5&'@<,#<' A !8 '6*)%/'&)'8.,&97'@<,#<',/'#5::$6'&<$',&"475;%"&/$%&#:"#4<'ωH7',/'=,F$.'+9

ωH = β L ω β

RC2YDS

?<8/7

%π + %µ

3 ω H = ..................

Figure 9.10 H)6$'%:)&'()*' A !8 :

RC2YUS

710 Chapter 9 Frequency Response

Figure 9.11 h5*,5&,).')(''!H'@,&<'(%2

5.6

-3 ! H = .............................. < π ( %π + %µ )

RC2YPS

!+)6#%Q7'%66)"*#)6#@%'3#6)(),5'#&"#&+5&#"/#!H'' /"'#&+%#\RD9H!#=H0:#;:MI?#-)&+#%π #'%7,52)*4 %-/'5*$#%µ '%7,52)*4#%-. < ?<$'8.,&9G=5,.'+5.6@,6&<'!H 7'5:/)'E.)@.'5/'&<$'4-%&*"4"+&/0-.6,.&)77'@<,#<'=,F$/'*,/$'&) &<$'/8+/#*,%&'H7',/'8/85::9'/%$#,(,$6').'&<$'65&5'/<$$&/')('5'&*5./,/&)*2'L.'/)-$'#5/$/'!H',/'=,F$. 5/'5'(8.#&,).')('(%'5.6')%62'?)'/$$'<)@'!H'#<5.=$/'@,&<'(%7'*$#5::'&<5&'-3',/'6,*$#&:9'%*)%)*&,).5: &)'(%7'+8&').:9'%5*&')('%π'R&<$'6,((8/,).'#5%5#,&5.#$'%.8S',/'6,*$#&:9'%*)%)*&,).5:'&)'(%2'L&'()::)@/ &<5&''!H'6$#*$5/$/'5&':)@'#8**$.&/7'5/'/<)@.',.'B,=2'C2DD2'c)@$F$*7'&<$'6$#*$5/$',.'!H'5&'<,=<'#8*G *$.&/7'5:/)'/<)@.',.'B,=2'C2DD7'#5..)&'+$'$"%:5,.$6'+9'&<,/'5*=8-$.&b'*5&<$*7',&',/'68$'&)'&<$ /5-$' %<$.)-$.).' &<5&' #58/$/' βV' &)' 6$#*$5/$' 5&' <,=<' #8**$.&/' R0$#&,).' 32C2US2' L.' &<$'*$=,). @<$*$'!H',/'5:-)/&'#)./&5.&7'%π',/'6)-,.5&$6'+9'&<$'6,((8/,).'%5*&2 ?9%,#5::97'!H',/',.'&<$'*5.=$')('DVV'JcQ'&)'&$./')('=,=5<$*&Q2'?<$'F5:8$')('!H'#5.'+$ 8/$6',.'!>2'RC2YPS'&)'6$&$*-,.$'%π'+'%µ2'?<$'#5%5#,&5.#$'%µ',/'8/85::9'6$&$*-,.$6'/$%5G *5&$:9'+9'-$5/8*,.='&<$'#5%5#,&5.#$'+$&@$$.'+5/$'5.6'#)::$#&)*'5&'&<$'6$/,*$6'*$F$*/$G+,5/ F):&5=$')%=2 H$()*$' :$5F,.=' &<,/' /$#&,).7' @$' /<)8:6' -$.&,).' &<5&' &<$' <9+*,6Gπ' -)6$:' )(' B,=2' C24 #<5*5#&$*,Q$/'&*5./,/&)*' )%$*5&,).' (5,*:9' 5##8*5&$:9' 8%' &)' 5'(*$>8$.#9' )(' 5+)8&' V2U' !H <' N& <,=<$*'(*$>8$.#,$/').$'<5/'&)'566')&<$*'%5*5/,&,#'$:$-$.&/'&)'&<$'-)6$:'5/'@$::'5/'*$(,.$ &<$'-)6$:'&)'5##)8.&'()*'&<$'(5#&'&<5&'&<$'&*5./,/&)*',/',.'(5#&'5'6,/&*,+8&$6G%5*5-$&$*'.$&G @)*E'&<5&'@$'5*$'&*9,.='&)'-)6$:'@,&<'5':8-%$6G#)-%).$.&'#,*#8,&2'K.$'/8#<'*$(,.$-$.& #)./,/&/')('/%:,&&,.='+L',.&)'5'.8-+$*')('%5*&/'5.6'*$%:5#,.='%µ'+9'5'.8-+$*')('#5%5#,&)*/7 $5#<'#)..$#&$6'+$&@$$.'&<$'#)::$#&)*'5.6').$')('&<$'&5%/')('+L2'?<,/'&)%,#',/'+$9).6'&<$ /#)%$')('&<,/'+))E2 N.',-%)*&5.&')+/$*F5&,).'&)'-5E$'(*)-'&<$'<,=8$.#9'-)6$:')('B,=2'C24',/'&<5&'5& (*$>8$.#,$/'5+)F$'1'&)' DV''!β 7').$'-59',=.)*$'&<$'*$/,/&5.#$'+π 2'L&'#5.'+$'/$$.'&<$.'&<5&'+L +$#)-$/'&<$').:9'*$/,/&,F$'%5*&')('&<$',.%8&',-%$65.#$'5&'<,=<'(*$>8$.#,$/2'?<8/'+L'%:59/'5. ,-%)*&5.&'*):$',.'6$&$*-,.,.='&<$'(*$>8$.#9'*$/%)./$')('&*5./,/&)*'#,*#8,&/'5&'<,=<'(*$>8$.G #,$/2'L&'()::)@/'&<5&'5.'5##8*5&$'6$&$*-,.5&,).')('+L'#5.'+$'-56$').:9'(*)-'5'<,=8$.#9 -$5/8*$-$.&2

9.3 High-Frequency Response of the CS and CE Amplifiers 711

EXERCISES 9.5# 9)*$#%.88#%$88#%π 8#%µ 8#5*$#!H#/"'#5#Oe!#"7%'5&)*4#5#$2#2",,%2&"'#21''%*&#(%#=#I#(P#5*$#5#GOe#'%@%'6% >)56#"/#<#]:#!+%#$%@)2%#+56#τQ#=##=#L:Y#]8#5*$#3%=R#=#L:MM: Ans./L:N#79W#ZL#/9W#L:NZ#79W#I<#/9W#[:Z[#dBU 9.6# 9"'#5#Oe!#"7%'5&%$#5&#(%#=#I#(P8#$%&%'()*%#!H#5*$#%π#)/#%µ#=#<#79#5*$# A !8 =#IL#5&#YL#\BU:# Ans./YLL#\BUW#IL:[#79 9.7# F/#%π#"/#&+%#Oe!#)*#HQ%'2)6%#;:^#)*2,1$%6#5#'%,5&)@%,3#2"*6&5*&#$%7,%&)"*.,53%'#25752)&5*2%#"/#<#798 /)*$#!H#"/#&+%#Oe!#-+%*#"7%'5&%$#5&#(%##=#L:I#(P: Ans. IML:[#\BU

Summary B)*'#).F$.,$.&'*$($*$.#$7'?5+:$'C2U'%*)F,6$/'5'/8--5*9')('&<$'*$:5&,)./<,%/'8/$6'&)'6$&$*G -,.$'&<$'F5:8$/')('&<$'%5*5-$&$*/')('&<$'HI?'<,=8$.#9'-)6$:2

Table 9.2 The BJT High-Frequency Model

B

rx

B&

C" C

" V!

r!

C!

gmV!

!

ro

E

''' - 3 = ( % ⁄ ) H

''''' + , = ) 4 ⁄ ( %

-3 . ''' % π + % µ = .......... < π !H

''' % µ = % $>L

) %= . I + ........... ) L>

''''' % π = % .8 + % $8 3

+π = βL ⁄ -3 % .8 = τ Q - 3

% $8 # # #<% $8L

8 #3 = L:M`L:Y

9.3 High-Frequency Response of the CS and CE Amplifiers !>8,%%$6' @,&<' $>8,F5:$.&G#,*#8,&' -)6$:/' &<5&' *$%*$/$.&' &<$' <,=8$.#9' )%$*5&,).' )(' &<$ JK0B!?'5.6'&<$'HI?7'@$'.)@'566*$//'&<$'>8$/&,).')('&<$'<,=8$.#9'%$*()*-5.#$')('&<$ ;0'5.6';!'5-%:,(,$*/2'K8*')+W$#&,F$',/'&)',6$.&,(9'&<$'-$#<5.,/-'&<5&':,-,&/'&<$'<,=8$.#9 %$*()*-5.#$' )(' &<$/$' ,-%)*&5.&' 5-%:,(,$*' #).(,=8*5&,)./2' N/' @$::7' @$' .$$6' &)' (,.6' 5' /,-%:$ 5%%*)5#<'&)'$/&,-5&$'&<$'(*$>8$.#9' ! # '5&'@<,#<'&<$'=5,.'(5::/'+9'P'6H'+$:)@',&/'F5:8$'5&'-,6+5.6 (*$>8$.#,$/7' 4 5 2

712 Chapter 9 Frequency Response !A! (dB)

20 log !AM !

3 dB

0

fH (or f3dB)

f

Figure 9.12 9'%01%*23#'%67"*6%#"/#5#$)'%2&.2"17,%$#=$2?#5(7,)/)%':#R>6%'@%#&+5&#&+%#45)*#$"%6#7,:#/5,,#"//# 5&#,"-#/'%01%*2)%68#5*$#&+%#()$>5*$#45)*#45#%Q&%*$6#$"-*#&"#U%'"#/'%01%*23:

?<$'5.5:9/,/'%*$/$.&$6'<$*$'5%%:,$/'$>85::9'@$::'&)'6,/#*$&$G#,*#8,&7'#5%5#,&,F$:9'#)8%:$6 5-%:,(,$*/'5.6'&)'L;'5-%:,(,$*/2'?<$'(*$>8$.#9'*$/%)./$')('&<$'(,*/&'@5/'/<)@.',.'B,=/2'123D 5.6'323C'5.6'&<5&')('&<$':5&&$*',/'/<)@.',.'B,=2'C2DU2'N&'&<$'(*$>8$.#,$/')(',.&$*$/&'&)'8/'<$*$ R&<$'<,=8$.#9'+5.6S7'5::'#)8%:,.='5.6'+9%5//'#5%5#,&)*/'+$<5F$'5/'%$*($#&'/<)*&'#,*G #8,&/'5.6'5-%:,(,$*/')('+)&<'&9%$/'<5F$',6$.&,#5:'<,=8$.#9'$>8,F5:$.&'#,*#8,&/2

9.3.1 The Common-Source Amplifier B,=8*$' C2DPR5S' /<)@/' &<$' <,=8$.#97' $>8,F5:$.&G#,*#8,&' -)6$:' )(' 5' ;0' 5-%:,(,$*2' L&' ,/ )+&5,.$6'+9'*$%:5#,.='&<$'JK0B!?',.'5.'5-%:,(,$*'#,*#8,&'/8#<'5/'&<5&',.'B,=2'C2U'+9',&/'<,=8$.#97' $>8,F5:$.&G#,*#8,&' -)6$:' )(' B,=2' C23R#S7' @<,:$' 5/' 5:@59/' $:,-,.5&,.=' 6#' /)8*#$/2 K+/$*F$'&<5&'&<$'#,*#8,&',.'B,=2'C2DPR5S',/'=$.$*5:b'()*',./&5.#$7',&',.#:86$/'5'*$/,/&5.#$' 0 1 7'@<,#< 5*,/$/').:9',.'&<$'#5/$')('5'6,/#*$&$G#,*#8,&'5-%:,(,$*2'N:/)7' 0 * '#5.'+$'$,&<$*'5'%5//,F$'*$/,/&5.#$ )*'&<$')8&%8&'*$/,/&5.#$')('5'#8**$.&G/)8*#$':)567'5.6'/,-,:5*:9'()*' 0 " 2 ?<$'$>8,F5:$.&'#,*#8,&')('B,=2'C2DPR5S'#5.'+$'/,-%:,(,$6'+9'8&,:,Q,.='?
RC2YYS

?<$'$>8,F5:$.&'#,*#8,&',.'B,=2'C2DPR+S'#5.'+$'(8*&<$*'/,-%:,(,$6',('@$'#5.'(,.6'5'@59'&)'6$5: @,&<'&<$'+*,6=,.='#5%5#,&)*'%-.'&<5&'#)..$#&/'&<$')8&%8&'.)6$'&)'&<$',.%8&'/,6$2'?)@5*6'&<5& $.67'#)./,6$*'(,*/&'&<$')8&%8&'.)6$2'L&'#5.'+$'/$$.'&<5&'&<$':)56'#8**$.&',/'R-3)-/'−'(-.S7'@<$*$ R-3)-/S',/'&<$')8&%8&'#8**$.&')('&<$'&*5./,/&)*'5.6'(-.',/'&<$'#8**$.&'/8%%:,$6'&<*)8=<'&<$'F$*9 /-5::'#5%5#,&5.#$'%-.2'N&'(*$>8$.#,$/',.'&<$'F,#,.,&9')('!#7'@<,#<'6$(,.$/'&<$'$6=$')('&<$'-,6G +5.67',&',/'*$5/).5+:$'&)'5//8-$'&<5&'(-.',/'/&,::'-8#<'/-5::$*'&<5.'R-3)-/S7'@,&<'&<$'*$/8:&'&<5& ),'#5.'+$'=,F$.'5%%*)",-5&$:9'+9

) , # # [ ( - 3 ) -/ )0 "′ = [ - 3 0 "′ ) -/

RC2Y1S

9.3 High-Frequency Response of the CS and CE Amplifiers 713

Rsig

Cgd

G

D

" Vsig

" !

RG

Vgs

" gmVgs

Cgs

ro

RD

RL

!

Vo !

S

R&L

(a) X

R&sig # Rsig % RG

Igd

G

Vo Igd

" RG V V&sig = RG " Rsig sig

" !

Vgs

Cgd

X&

gmVgs

Cgs

!

R&L R&L # ro % RD % RL

(b) Figure 9.13 f%&%'()*)*4#&+%#+)4+./'%01%*23#'%67"*6%#"/#&+%#GD#5(7,)/)%'V#'%(#%01)@5,%*)'21)&W#'$(#&+%# 2)'21)&#"/#'%(#6)(7,)/)%$#5&#&+%#)*71*$#&+%#"1&71&W#=%,7:;7D8.?

@<$*$

0′" = + , || 0 * || 0 " 0,.#$'),'=')./7'!>2'RC2Y1S',.6,#5&$/'&<5&'&<$'=5,.'(*)-'=5&$'&)'6*5,.',/'−-30′" 7 &<$'/5-$'F5:8$ 5/',.'&<$'-,6+5.62'?<$'#8**$.&'(-.'#5.'.)@'+$'()8.6'5/

( -. = /% -. ( ) -/ [ ) , ) = /% -. [ ) -/ [ ( [ - 3 0′" ) -/ ) ] = /% -. ( I + - 3 0′" )) -/ `)@7'&<$':$(&G<5.6'/,6$')('&<$'#,*#8,&',.'B,=2'C2DPR+S7'5&'SS′7'E.)@/')('&<$'$",/&$.#$')('%-. ).:9'&<*)8=<'&<$'#8**$.&'(-.2'?<$*$()*$7'@$'#5.'*$%:5#$'%-.'+9'5.'$>8,F5:$.&'#5%5#,&5.#$'%8G +$&@$$.'&<$'=5&$'5.6'=*)8.6'5/':).='5/'%8G'6*5@/'5'#8**$.&'$>85:'&)'(-.2'?<5&',/7

/% 8G ) -/ = /% -. ( I + - 3 0′" )) -/

714 Chapter 9 Frequency Response X R&sig

Igd

G

Vo # !gm R&L Vgs

" RG V RG " Rsig sig

" !

Vgs

X& Cgs

gmVgs

Ceq

R&L

! Ceq # Cgd (1 " gm R&L) Cin (c)

Vo Vsig (dB)

3 dB !20 dB"decade 20 log !AM !

fH

f (Hz) (log scale)

(d) Figure 9.13 =%,7:;7D8.S/')(#&+%#%01)@5,%*)'21)&#-)&+#%-.#'%7,52%$#5&#&+%#)*71)$%#-)&+#&+%#%01)@5,%*&# 25752)&5*2%#%8GW#'#(#&+%#/'%01%*23#'%67"*6%#7,"&8#-+)2+#)6#&+5&#"/#5#,"-.75668#6)*4,%.&)(%.2"*6&5*)'21)&:

@<,#<'*$/8:&/',.

% 8G = % -. ( I + - 3 0′" )

RC2Y3S

!+16#%-.#4)@%6#')6%#&"#5#(12+#,5'4%'#25752)&5*2%#%8G8#-+)2+#577%5'6#5&#&+%#5(7,)/)%'#)*71&: !+%#(1,&)7,)25&)"*#%//%2&#&+5&#%-.#1*$%'4"%6#2"(%6#5>"1&#>%2516%#)&#)6#2"**%2&%$#>%&-%%* 2)'21)&#*"$%6# -#5*$#.8#-+"6%#@",&54%6# 5'%#'%,5&%$#>3# 5#,5'4%#*%45&)@%#45)*#=− -30′" ?:#!+)6 %//%2&#)6#C*"-*#56#&+%#8"22.-/.00.)48#5*$#=I#+#-3#0′" ?#)6#C*"-*#56#&+%#8"22.-/!,24"32".-:#A% -),,#6&1$3#\),,%'g6#&+%"'%(#("'%#/"'(5,,3#)*#D%2&)"*#;:Z: _/,.='%8G'$.5+:$/'8/'&)'/,-%:,(9'&<$'$>8,F5:$.&'#,*#8,&'5&'&<$',.%8&'/,6$'&)'&<5&'/<)@.',. B,=2'C2DPR#S2'T$'*$#)=.,Q$'&<$'#,*#8,&')('B,=2'C2DPR#S'5/'5'/,.=:$G&,-$G#)./&5.&'R0?;S'#,*#8,&

9.3 High-Frequency Response of the CS and CE Amplifiers

)('&<$' :)@G%5//' &9%$' R0$#&,).' D23' 5.6' N%%$.6,"' !S2' M$($*$.#$' &)' ?5+:$' D2U'$.5+:$/' 8/' &) $"%*$//'&<$')8&%8&'F):&5=$')-/')('&<$'0?;'#,*#8,&',.'&<$'()*-

01 I . ) ............... ) -/ = .................... 0 1 + 0 6)4 6)4 / I + ......

RC2YZS

ωL

@<$*$' ω V',/'&<$'#)*.$*'(*$>8$.#97'&<$'+*$5E'(*$>8$.#97')*'&<$'%):$'(*$>8$.#9')('&<$'0?; #,*#8,&7

ω L = I ⁄ % )* 0′6)4

RC2Y4S

% )* = % -/ + % 8G = % -/ + % -. ( I + - 3 0′" )

RC2YCS

0 6)4 ′ = 0 6)4 || 0 1

RC21VS

@,&< 5.6 ;)-+,.,.='!>/2'RC2Y1S'5.6'RC2YZS'*$/8:&/',.'&<$'()::)@,.='$"%*$//,).'()*'&<$'<,=8$.#9 =5,.')('&<$';0'5-%:,(,$*7

01 ) I . .......,. = [ .................... . ( - 3 0′") .............. ) 6)4 0 1 + 0 6)4 / I + ......

RC21DS

ωL

@<,#<'#5.'+$'$"%*$//$6',.'&<$'()*-

) 45 .......,. = ............... . ) 6)4 / I + .......

RC21US

ω#

@<$*$'&<$'-,6+5.6'=5,.'45',/'=,F$.'+9'!>2'RC2YYS'5.6'ω#',/'&<$'8%%$*'PG6H'(*$>8$.#97

I ω # = ω L = ................. % )* 0′6)4

RC21PS

ω I ! # = ......#. = ........................ <π < π % )* 0′6)4

RC21YS

5.6

T$'&<8/'/$$'&<5&'&<$'<,=8$.#9'*$/%)./$'@,::'+$'&<5&')('5':)@G%5//'0?;'.$&@)*E'@,&<'5 PG6H'(*$>8$.#9'!#'6$&$*-,.$6'+9'&<$'&,-$'#)./&5.&' % )* 0′6)4 2'B,=8*$'C2DPR6S'/<)@/'5'/E$&#< )('&<$'-5=.,&86$')('&<$'<,=8$.#9'=5,.2 H$()*$':$5F,.='&<,/'/$#&,).'@$'@,/<'&)'-5E$'5'.8-+$*')(')+/$*F5&,)./X 1. !+%#177%'#M.$O#/'%01%*23#)6#$%&%'()*%$#>3#&+%#)*&%'52&)"*#"/# 0′6)4 = 0 6)4 || 0 1 #5*$ % )* = % -/ + % -. ( I + - 3 0′") :#D)*2%#&+%#>)56#'%6)6&5*2%#01#)6#1615,,3#@%'3#,5'4%8#)& 25*#>%#*%4,%2&%$8#'%61,&)*4#)*# 0′6)4 # 0 6)4 8 &+%#'%6)6&5*2%#"/#&+%#6)4*5,#6"1'2%:#F&#/",. ,"-6#&+5#,5'4%#@5,1%#"/#06)4#-),,#2516%##!##&"#>%#,"-%'%$: 2. !+%#&"&5,#)*71撘)&5*2%#%)*#)6#1615,,3#$"()*5&%$#>3#%8G8#-+)2+#)*#&1'*#)6#(5$%#,5'4% >3# &+%# (1,&)7,)25&)"*# %//%2&# &+5&# %-.# 1*$%'4"%6:# !+168# 5,&+"14+# %-.# )6# 1615,,3# 5 @%'3 6(5,,#25752)&5*2%8#)&6#%//%2&#"*#&+%#5(7,)/)%'#/'%01%*23#'%67"*6%#25*#>%#@%'3#6)4*)/)25*& 56#5#'%61,&#"/#)&6#(1,&)7,)25&)"*#>3#&+%#/52&"'#= I + - 3 0′" ?8#-+)2+#)6 577'"Q)(5&%,3#%015,

715

716 Chapter 9 Frequency Response &"#&+%#()$>5*$#45)*#"/#&+%#5(7,)/)%':#!+)6#)6#&+%#\),,%'#%//%2&8#-+)2+#2516%6#&+%#GD 5(7,)/)%'#&"#+5@%#5#,5'4%#&"&5,#)*71撘)&5*2%#%)*#5*$#+%*2%#5#,"-#!#: 3. !"# %Q&%*$# &+%# +)4+./'%01%*23# '%67"*6%# "/# 5# \RD9H!# 5(7,)/)%'8# -%# +5@%# &"# /)*$ 2"*/)41'5&)"*6# )*# -+)2+# &+%# \),,%'# %//%2&# )6# 5>6%*&# "'# 5&# ,%56&# '%$12%$:# A%# 6+5,, '%&1'*#&"#&+)6#61>X%2'%5&#,%*4&+#)*#D%2&)"*#;:^#5*$#>%3"*$: 4. !+%#5>"@%#5*5,36)68#'%61,&)*4#)*#5*#D!G#"'#5#6)*4,%.7",%#'%67"*6%8#)6#577'"Q)(5&%: D7%2)/)25,,38#)&#)6#>56%$#"*#*%4,%2&)*4#(-.#'%,5&)@%#&"#-3)-/8#5*#5661(7&)"*#&+5Ɂ,)%6 -%,,#5&#/'%01%*2)%6#*"&#&""#(12+#+)4+%'#&+5*#!#:#P*#%Q52*5,36)6#"/#&+%#2)'21)&#)* 9)4:#;:IM=5?#-),,#>%#25'')%$#"1&#)*#D%2&)"*#;:Y:#!+%#'%61,&6#5>"@%8#+"-%@%'8#5'%#("'% &+5*#61//)2)%*&#/"'#5#01)2C#%6&)(5&%#"/#!#:#P6#-%,,8#&+%#577'"Q)(5&%#577'"52+#+%,76#&" '%@%5,#&+%#7')(5'3#,)()&5&)"*#"*#&+%#+)4+./'%01%*23#'%67"*6%V#&+%#\),,%'#%//%2&:

Example 9.3 9)*$#&+%#()$>5*$#45)*#45#5*$#&+%#177%'#M.$O#/'%01%*23#!##"/#5#GD#5(7,)/)%'#/%$#-)&+#5#6)4*5,#6"1'2% +5@)*4#5*#)*&%'*5,#'%6)6&5*2%#06)4#=#ILL#CΩ:#!+%#5(7,)/)%'#+56# 0 1 = Z:[#\Ω 8#0*#=##0"#=#IY#CΩ8 - 3 = #I#(PS] 8# + , = #IYL#CΩ 8# % -/ = #I#79 8#5*$# % -. =#L:Z#79 : Solution 01 4 5 = [ ..................... - 0′ 0 1 + 0 6)4 3 "

-+%'%

0′" = + , || 0 * || 0 " = IYL || IY || IY = [:IZ#CΩ : - 3 0′" = I × [:IZ = [:IZ#]S]

!+168 Z:[ 4 5 = [ ..................... × [:IZ = [ [ #]S] Z:[ + L:I

!+%#%01)@5,%*撘)&5*2%8#%8G8#)6#/"1*$#56 % 8G = ( I + - 3 0′")% -.

'''''' = ( I + [:IZ ) × L:Z = M:<^#79 !+%#&"&5,#)*71撘)&5*2%#%)*#25*#>%#*"-#">&5)*%$#56 % )* = % -/ + % 8G = I + M:<^ = Z:<^#79

!+%#177%'#M.$O#/'%01%*23#!##)6#/"1*$#/'"( I ' ! # = ........................................ < π % )* ( 0 6)4 || 0 1 ) I .^ = .................................................................................. [ I< < π × Z:<^ × IL ( L:I || Z:[ ) × IL

'''''''''''''''''''''''''''''''''''''''''''

= MN<#CBU

9.3 High-Frequency Response of the CS and CE Amplifiers

EXERCISES 9.8# 9"'#&+%#GD#5(7,)/)%'#67%2)/)%$#)*#HQ5(7,%#;:M8#/)*$#&+%#@5,1%6#"/#45#5*$#!##&+5&#'%61,&#-+%*#&+%#6)4*5,. 6"1'2%#'%6)6&5*2%#)6#'%$12%$#&"#IL#CΩ: Ans./`[:I<#]S]W#M:[#\BU 9.9# F/#)&#)6#7"66)>,%#&"#'%7,52%#&+%#\RD9H!#16%$#)*#&+%#5(7,)/)%'#)*#HQ5(7,%#;:M#-)&+#5*"&+%'#+5@)*4#&+% 65(%#%-/#>1#6(5,,%'#%-.8#-+5&#)6#&+%#(5Q)(1(#@5,1%#&+5&#)&6#%-.#25*#>%#)*#"'$%'#&"#">&5)*#5*#!##"/ 5&#,%56&#I#\BUa Ans./L:LN#79

9.3.2 The Common-Emitter Amplifier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′6)4 '5.6'5'*$/,/&5.#$' 0′6)4 7'@,&<'&<$'F5:G 8$/',.6,#5&$6',.'&<$'(,=8*$2 '?<$'$>8,F5:$.&'#,*#8,&',.'B,=2'C2DYR+S'#5.'+$'8/$6'&)')+&5,.'&<$'-,6+5.6'=5,.' 4 5 '+9'/$&G &,.=' % π '5.6' % µ '&)'Q$*)2'?<$'*$/8:&',/ 0= ) +π . =- 3 0′" ? . .............................................. 4 5 # \ .......,. # \ [ .................... ) 6)4 0 = ] 0 6)4 + π ] + L ] ( 0 6)4 || 0 = )

RC211S

0′" # \ + , || 0 % || 0 "

RC213S

@<$*$

J%Q&#-%#">6%'@%#&+5&#&+%#2)'21)&#)*#9)4:#;:IZ=>?#)6#)$%*&)25,#&"#&+5&#"/#&+%#GD#5(7,)/)%'#)*#9)4: ;:IM=>?:#!+16#&+%#5*5,36)6#25*#/",,"-#&+%#65(%#7'"2%66#-%#16%$#/"'#&+%#GD#256%:#!+%#5*5,3. 6)6#)6#),,16&'5&%$#)*#9)4:#;:IM=2?#5*$#=$?:#!+%#/)*5,#'%61,&#)6#&+5&#&+%#GH#5(7,)/)%'#45)*#5&#+)4+ /'%01%*2)%6#)6#4)@%*#577'"Q)(5&%,3#>3 ) 45 .......,. # \ ................ ) 6)4 /. I ] ......

RC21ZS

ω#

@<$*$' 4 5 ',/'=,F$.'+9'!>2'RC211S'5.6'&<$'PG6H'(*$>8$.#9' ! # ',/'=,F$.'+9

ω I ! # # \ ......#. # \ ......................... <π < π % )* 0′6)4

RC214S

717

718 Chapter 9 Frequency Response

Rsig

B

rx

Cm

B&

C

" Vsig " !

Vp

rp

RB

" Cp

ro

gmVp

RC

!

RL V o !

E

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(a)

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!

V&sig # Vsig

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RB r! RB " Rsig r! " rx " (Rsig %RB)

!

R&L # ro %RC %RL

R&sig # r! %[rx " (RB %Rsig)] (b) X R&sig

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Im

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Cp

gmVp

R&L

!

Vo !

Cin Cin # Cp " Ceq

Vo # !gm R&LVp

# Cp " Cm(1 " gm R&L)

(c) Figure 9.14 f%&%'()*)*4#&+%#+)4+./'%01%*23#'%67"*6%#"/#&+%#GH#5(7,)/)%'V#'%(#%01)@5,%*)'21)&W#'$(#&+% 2)'21)&#"/##'%(#6)(7,)/)%$#5&#>"&+#&+%#)*71)$%#5*$#&+%#"1&71)$%W#')(#%01)@5,%*)'21)&#-)&+#%µ#'%7,52%$#5& &+%#)*71)$%#-)&+#&+%#%01)@5,%*撘)&5*2%#%8GW#=>,7:;7D8.?

9.3 High-Frequency Response of the CS and CE Amplifiers 719

Vo (dB) Vsig

3 dB

!6 dB$octave !20 dB$decade

20 log !AM!

fH # 0

fH

1 2pCin R&sig

f (Hz, log scale)

(d) Figure 9.14 =%,7:;7D8.?#'#(#6C%&2+#"/#&+%#/'%01%*23.'%67"*6%#7,"&8#-+)2+#)6#&+5&#"/#5#,"-.7566# D!G#2)'21)&:

@<$*$' % )*# \ % π ] % µ ( I ] - 3 0′")

RC21CS

0′6)4# \ + π || [ + L ] ( 0 = || 0 6)4 ) ]

RC23VS

5.6 K+/$*F$'&<5&' % )* ',/'/,-%:9'&<$'/8-')(' % π '5.6'&<$'J,::$*'#5%5#,&5.#$' % µ ( I ] - 3 0′") 2'?<$ *$/,/&5.#$' 0 6)4 ′ /$$.'+9' % )* '#5.'+$'$5/,:9'()8.6'(*)-'&<$'#,*#8,&',.'B,=2'C2DYR5S'5/'()::)@/X M$68#$' ) 6)4 '&)'Q$*)7'i=*5+'<):6j')('&<$'&$*-,.5:/'H′'5.6'!'5.6':))E'+5#E'R&)'&<$':$(&S2'k)8 @,::'/$$'+π',.'%5*5::$:'@,&<' + L 7'@<,#<',/',.'/$*,$/'@,&<' ( 0 = || 0 6)4 ) 2'?<,/'@59')('(,.6,.='&<$ *$/,/&5.#$'i/$$.'+9'5'#5%5#,&5.#$j',/'F$*9'8/$(8:'5.6'/%5*$/').$'(*)-'&$6,)8/'@)*EA' B,.5::97'#)--$.&/'F$*9'/,-,:5*'&)'&<)/$'-56$').'&<$'<,=8$.#9'*$/%)./$')('&<$';0 5-%:,(,$*'#5.'+$'-56$'<$*$'5/'@$::2

Example 9.4 F&#)6#'%01)'%$#&"#/)*$#&+%#()$>5*$#45)*#5*$#&+%#177%'#M.$O#/'%01%*23#"/#&+%#2"(("*.%()&&%'#5(7,). /)%'#"/#9)4:#;:Z=5?#/"'#&+%#/",,"-)*4#256%V#)%%#=#)66#=#IL#]8#(#=#I#(P8#0=#=#ILL#CΩ8#0%#=#N CΩ8#06)4#= Y#CΩ8#0"#=#Y#CΩ8#β L#=#ILL8#)4#=#ILL#]8#%µ#=#I#798#!H#=#NLL#\BU8#5*$#+L#=#YL#Ω: Solution !+%#&'5*6)6&"'#)6#>)56%$#5&#(%###I#(P:#!+16#&+%#@5,1%6#"/#)&6#+3>')$.π#("$%,#75'5(%&%'6#5'% (% I#(P . = ................ = ZL#(PS] - 3 = .....
720 Chapter 9 Frequency Response Example 9.4 continued'''''''''''''''''''''''''''''''' [M ZL × IL '' % π + % µ = .....3. = .......................................^ = N#79 ωH < π × NLL × IL

''' % µ = I#79 ''' % π = [#79 ''' + L = YL#Ω !+%#()$>5*$#@",&54%#45)*#)6 0= +π . - 3 0′" . .............................................. 4 5 = [ .................... 0 = + 0 6)4 + π + + L + ( 0 = || 0 6)4 )

-+%'%

0 "′ = + , || 0 % || 0 "

'''''''''''''''''''''''''''''''''''''''''''''''' = ( ILL || N || Y )#CΩ = M#CΩ !+168 - 3 0 "′ = ZL × M = I
5*$ ILL <:Y 4 5 = [ .................. × .................................................... × I
5*$
!"#$%&%'()*%#!##-%#/)'6&#/)*$#%)*8 ''''''' % )* = % π + % µ =I + - 3 0′"? = [ + I ( I + I
5*$#&+%#%//%2&)@%#6"1'2%#'%6)6&5*2%# 0 6)4 ′ 8 0 6)4 ′ = #+ π || [ + L + ( 0 = || 0 6)4 ) ] = <:Y || [ L:LY + ( ILL || Y ) ] '\'D231'EΩ

!+168

I I !# = ........................ = ......................................................................... = [YZ#CBU [ I< M < π % )* 0′6)4 < π × I
EXERCISE 9.10#9"'#&+%#5(7,)/)%'#)*#HQ5(7,%#;:Z8#/)*$#&+%#@5,1%#"/#0"#&+5&#'%$12%6#&+%#()$>5*$#45)*#&"#+5,/#&+%#@5,1% /"1*$:#A+5&#@5,1%#"/# !##'%61,&6a#J"&%#&+%#&'5$%."//#>%&-%%*#45)*#5*$#>5*$-)$&+: Ans. I:;#CΩW#I:Z<#\BU

9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers 721

9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers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

9.4.1 The High-Frequency Gain Function ?<$'5-%:,(,$*'=5,.7'&5E,.=',.&)'5##)8.&'&<$',.&$*.5:'&*5./,/&)*'#5%5#,&5.#$/7'#5.'+$'$"%*$//$6 5/'5'(8.#&,).')('&<$'#)-%:$"G(*$>8$.#9'F5*,5+:$'/',.'&<$'=$.$*5:'()*-

4 ( / )# = #4 5 Q # ( / )

RC23DS

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

( I + / ⁄ ω TI ) ( I + / ⁄ ω T< ) :#:#: ( I + / ⁄ ω T7 ) . Q # ( / )# = ................................................................................................ ( I + / ⁄ ω 2I ) ( I + / ⁄ ω 2< ):#:#: ( I + / ⁄ ω 27 )

RC23US

@<$*$' ω 2I 8 ' ω 2< 8 '2'2'2'7' ω 27 '5*$'%)/,&,F$'.8-+$*/'*$%*$/$.&,.='&<$'(*$>8$.#,$/')('&<$'7'*$5: %):$/'5.6' ω TI 8 ' ω T< 8 '2'2'2'7' ω T7 '5*$'%)/,&,F$7'.$=5&,F$7')*',.(,.,&$'.8-+$*/'*$%*$/$.&,.= &<$' (*$>8$.#,$/' )(' &<$' 7' *$5:' &*5./-,//,).' Q$*)/2' `)&$' (*)-' !>2' RC23US' &<5&7' 5/' /<)8:6' +$ $"%$#&$67'5/'/'5%%*)5#<$/'V7' Q # ( / ) '5%%*)5#<$/'8.,&9'5.6'&<$'=5,.'5%%*)5#<$/' 4 5 :

9.4.2 Determining the 3-dB Frequency fH ?<$' 5-%:,(,$*' 6$/,=.$*' 8/85::9' ,/' %5*&,#8:5*:9' ,.&$*$/&$6' ,.' &<$' %5*&' )(' &<$' <,=8$.#9 +5.6'&<5&',/'#:)/$'&)' &<$'-,6+5.62'?<,/' ,/'+$#58/$'&<$'6$/,=.$*'.$$6/'&)'$/&,-5&$^5.6' ,( .$$6'+$'-)6,(9^&<$'F5:8$')('&<$'8%%$*'PG6H'(*$>8$.#9' !# 'R)*' ω # W / ! # =# ω # ⁄ < π S2'?)@5*6 &<5&'$.6',&'/<)8:6'+$'-$.&,).$6'&<5&',.'-5.9'#5/$/'&<$'Q$*)/'5*$'$,&<$*'5&',.(,.,&9')*'/8#< <,=<'(*$>8$.#,$/'5/'&)'+$')(':,&&:$'/,=.,(,#5.#$'&)'&<$'6$&$*-,.5&,).')(' ω # : 'L(',.'566,&,).').$ )('&<$'%):$/7'/59' ω 2I 8 ',/')('-8#<':)@$*'(*$>8$.#9'&<5.'5.9')('&<$')&<$*'%):$/7'&<$.'&<,/'%):$ @,::'<5F$'&<$'=*$5&$/&'$(($#&').'&<$'F5:8$')('&<$'5-%:,(,$*' ω # : 'L.')&<$*'@)*6/7'&<,/'%):$'@,:: .,3;79:8'&<$'<,=8$.#9'*$/%)./$')('&<$'5-%:,(,$*7'5.6'&<$'5-%:,(,$*',/'/5,6'&)'<5F$'5 #+!"&%&453+2./-.*3+&*.2'L.'/8#<'#5/$/7'&<$'(8.#&,).' Q # ( / ) '#5.'+$'5%%*)",-5&$6'+9'

I Q # ( / ) # ........................ I + / ⁄ ω 2I

RC23PS

@<,#<',/'&<$'&*5./($*'(8.#&,).')('5'(,*/&G)*6$*'R)*'0?;S':)@G%5//'.$&@)*E'RN%%$.6,"'!S2'L& ()::)@/'&<5&',('5'6)-,.5.&'%):$'$",/&/7'&<$.'&<$'6$&$*-,.5&,).')(' ω # ',/'=*$5&:9'/,-%:,(,$6b

ω # # ω 2I

RC23YS

722 Chapter 9 Frequency Response ?<,/',/'&<$'/,&85&,).'@$'$.#)8.&$*$6',.'&<$'#5/$/')('&<$'#)--).G/)8*#$'5.6'#)--).G$-,&&$* 5-%:,(,$*/'5.5:9Q$6',.'0$#&,).'C2P2'N/'5'*8:$')('&<8-+7'9 .,3;797:'F,B8'8L;/:/';!':A8'B,@8/:K !+8GD87>E'F,B8';/'9:'B89/:':@,',>:9I8/'U9'!9>:,+',!'VW'9@9E'!+,3':A8'789+8/:'F,B8',+'C8+,2 L('5'6)-,.5.&'%):$'6)$/'.)&'$",/&7'&<$'PG6H'(*$>8$.#9' ω # '#5.'+$'6$&$*-,.$6'(*)-'5'%:)&')( Q # ( $ ω ) 2'N:&$*.5&,F$:97'5.'5%%*)",-5&$'()*-8:5'()*' ω # '#5.'+$'6$*,F$6'5/'()::)@/X';)./,6$*7 ()*'/,-%:,#,&97'&<$'#5/$')('5'#,*#8,&'<5F,.='&@)'%):$/'5.6'&@)'Q$*)/',.'&<$'<,=8$.#9 +5.6b'&<5&',/7

( I + / ⁄ ω TI ) ( I + / ⁄ ω T< ) Q # ( / )# = .......................................................... ( I + / ⁄ ω 2I ) ( I + / ⁄ ω 2< )

RC231S

08+/&,&8&,.=' /# =#$ ω '5.6'&5E,.='&<$'/>85*$6'-5=.,&86$'=,F$/ <

<

<

<

( I + ω ⁄ ω TI ) ( I + ω ⁄ ω T< ) < . Q # ( $ ω ) # = ................................................................. < < < < ( I + ω ⁄ ω 2I ) ( I + ω ⁄ ω 2< ) <

H9'6$(,.,&,).7'5&' ω #= ω # 8 ' Q # # =

I ... < <

b'&<8/7 <

<

<

I ( I + ω # ⁄ ω TI ) ( I + ω # ⁄ ω T< ) . ... # = ................................................................... < ( I + ω <# ⁄ ω <2I ) ( I + ω <# ⁄ ω <2< ) I I < . + ....... . + ω Z# ⁄ ω
ω 2I

RC233S

ω 2<

0,.#$' ω # ',/'8/85::9'/-5::$*'&<5.'&<$'(*$>8$.#,$/')('5::'&<$'%):$/'5.6'Q$*)/7'@$'-59'.$=:$#& Z &<$'&$*-/'#).&5,.,.=' ω # '5.6'/):F$'()*' ω # '&)')+&5,.'

I I < < . + ....... . [ ....... ω # # # #I# ....... . [ ....... . < < < ω 2I ω 2< ω TI ω
RC23ZS

?<,/'*$:5&,)./<,%'#5.'+$'$"&$.6$6'&)'5.9'.8-+$*')('%):$/'5.6'Q$*)/'5/'

ω # # # #I#

I I I I ....... . + ....... . + :#:#: [ < ....... . + ....... . + :#:#: < < < <

ω 2I

ω 2<

ω TI

ω T<

RC234S

J"&%#&+5&#)/#"*%#"/#&+%#7",%68#653# 2 I 8 #)6#$"()*5*&8#&+%*# ω 2I %# ω 2< 8 # ω 2M 8 #:#:#:#8# ω TI 8 # ω T< 8 #:#:#:#8 5*$#H0:#=;:^N?#'%$12%6#&"#H0:#=;:^;?:

Example 9.5 !+%#+)4+./'%01%*23#'%67"*6%#"/#5*#5(7,)/)%'#)6#2+5'52&%')U%$#>3#&+%#&'5*6/%'#/1*2&)"* Y

I [ /SIL . Q# ( / ) = .............................................................. Z Z ( I + /SIL ) ( I + /SZ × IL )

f%&%'()*%#&+%#M.$O#/'%01%*23#577'"Q)(5&%,3#5*$#%Q52&,3:

9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers

Solution J"&)*4#&+5&# &+%#,"-%6&./'%01%*23#7",%#5&#ILZ#'5$S6#)6#&-"#"2&5@%6#,"-%'#&+5*#&+%# 6%2"*$#7",%#5*$# 5 $%25$%#,"-%'#&+5*#&+%#U%'"8#-%#/)*$#&+5#$"()*5*&.7",%#6)&15&)"*#5,("6&#%Q)6&6#5*$# ω # # # ILZ#'5$S6:#P >%&&%'#%6&)(5&%#"/'ω##25*#>%#">&5)*%$#16)*4#H0:#=;:^N?8#56#/",,"-6V I I <. ω # = I## ........N #+# ....................N [ ......... IL IL

I^ × IL

IL

''''''' = ;NLL#'5$S6

!+%#%Q52&#@5,1%#"/#ω##25*#>%#$%&%'()*%$#/'"(#&+%#4)@%*#&'5*6/%'#/1*2&)"*#56#;YM[#'5$S6:#9)*5,,38 -%#6+"-#)*#9)4:#;:IY#5#O"$%#7,"*$#5*#%Q52,"&#/"'#&+%#4)@%*#&'5*6/%'#/1*2&)"*:#J"&%#&+5&#&+)6 )6# 5# 7,"&# "/# &+%# +)4+./'%01%*23# '%67"*6%# "/# &+%# 5(7,)/)%'# *"'(5,)U%$# '%,5&)@%# &"# )&6# ()$>5*$ 45)*:#!+5&#)68#)/#&+%#()$>5*$#45)*#)68#6538#ILL#$O8#&+%*#&+%#%*&)'%#7,"+"1,$#>%#6+)/&%$#17-5'$ >3#ILL#$O:

Figure 9.15 `)*-5:,Q$6'<,=8$.#9'*$/%)./$')('&<$'5-%:,(,$*',.'!"5-%:$'C212

723

724 Chapter 9 Frequency Response

9.4.3 Using Open-Circuit Time Constants for the Approximate Determination of fH L('&<$'%):$/'5.6'Q$*)/')('&<$'5-%:,(,$*'&*5./($*'(8.#&,).'#5.'+$'6$&$*-,.$6'$5/,:97'&<$.'@$ #5.'6$&$*-,.$'!#'8/,.='&<$'&$#<.,>8$/'5+)F$2'L.'-5.9'#5/$/7'<)@$F$*7',&',/'.)&'5'/,-%:$'-5&&$* &)'6$&$*-,.$'&<$'%):$/'5.6'Q$*)/'+9'>8,#E'<5.6'5.5:9/,/2'L.'/8#<'#5/$/'5.'5%%*)",-5&$'F5:8$ ()*'!#'#5.'+$')+&5,.$6'8/,.='&<$'()::)@,.='-$&<)62 ;)./,6$*'&<$'(8.#&,).' Q# ( / ) 'R!>2'C23US7'@<,#<'6$&$*-,.$/'&<$'<,=8$.#9'*$/%)./$ )('&<$'5-%:,(,$*2'?<$'.8-$*5&)*'5.6'6$.)-,.5&)*'(5#&)*/'#5.'+$'-8:&,%:,$6')8&'5.6' Q# ( / ) $"%*$//$6',.'&<$'5:&$*.5&,F$'()*-

I + 9 I / + 9 < / + :#:#: +#9 7 / .7 Q# ( / )# = ............................................................... < I + ? I / + ? < / + :#:#: #+#? 7 / <

7

RC23CS

@<$*$'&<$'#)$((,#,$.&/'9'5.6'?'5*$'*$:5&$6'&)'&<$'(*$>8$.#,$/')('&<$'Q$*)/'5.6'%):$/7'*$/%$#G &,F$:92'0%$#,(,#5::97'&<$'#)$((,#,$.&' ? I ',/'=,F$.'+9

I I I ? I # = ........ + ........ + :#:#: + ........

ω 2I

ω 2<

ω 27

RC2ZVS

L&'#5.'+$'/<)@.'l/$$'f*59'5.6'0$5*:$'RDC3CSm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

?I =

%; 0;

RC2ZDS

;=I

@<$*$'@$'<5F$'5//8-$6'&<5&'&<$*$'5*$'7'#5%5#,&)*/',.'&<$'<,=8$.#9'$>8,F5:$.&'#,*#8,&2' ?<,/' -$&<)6' ()*' 6$&$*-,.,.=' ?D' ,/' 8L9>:b' &<$' 5%%*)",-5&,).' #)-$/' 5+)8&' ,.' 8/,.=' &<$ F5:8$' )(' ?D' &)' 6$&$*-,.$' ω#2' 0%$#,(,#5::97' ,(' &<$' Q$*)/' 5*$' .)&' 6)-,.5.&' 5.6' ,(' ).$' )(' &<$ %):$/7'/59'2D7',/'6)-,.5.&7'&<$.'(*)-'!>2'RC2ZVS7

I ? I # # ........ '

ω 2I

RC2ZUS

H8&7' 5:/)7' &<$' 8%%$*' PG6H' (*$>8$.#9' @,::' +$' 5%%*)",-5&$:9' $>85:' &)' ω2D7' :$56,.=' &)' &<$ 5%%*)",-5&,).

I# ?I

I Σ %; 0;

ω # # # # ..... #=# ...............

RC2ZPS

;

c$*$',&'/<)8:6'+$'%),.&$6')8&'&<5&',.'#)-%:$"'#,*#8,&/'@$'8/85::9'6)'.)&'E.)@'@<$&<$*'5 6)-,.5.&' %):$' $",/&/2' `$F$*&<$:$//7' 8/,.=' !>2' RC2ZPS' &)' 6$&$*-,.$' ω#' .)*-5::9' 9,$:6/ *$-5*E5+:9'=))6'*$/8:&/1'$F$.',('5'6)-,.5.&'%):$'6)$/'.)&'$",/&2'?<$'-$&<)6'@,::'+$',::8/&*5&$6 +9'5.'$"5-%:$2

Y

#!+%#(%&+"$#"/#"7%*.2)'21)&#&)(%#2"*6&5*&6#3)%,$6#4""$#'%61,&6#"*,3#-+%*#5,,#&+%#7",%6#5'%#'%5,8#56#)6# &+%#256%#)*#&+)6#2+57&%':

9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers 725

Example 9.6 9)41'%#;:I^=5?#6+"-6#&+%#+)4+./'%01%*23#%01)@5,%*)'21)&#"/#5#2"(("*.6"1'2%#\RD9H!#5(7,)/)%': !+%#5(7,)/)%'#)6#/%$#-)&+#5#6)4*5,#4%*%'5&"'#)6)4#+5@)*4#5#'%6)6&5*2%#06)4:#T%6)6&5*2%#01#)6#$1%#&"#&+% >)56)*4#*%&-"'C:#T%6)6&5*2%# 0′" #)6#&+%#75'5,,%,#%01)@5,%*&#"/#&+%#,"5$#'%6)6&5*2%#0"8#&+%#$'5)*#>)56 '%6)6&5*2%#0*8#5*$#&+%#9H!#"1&71&#'%6)6&5*2%#+,:#G5752)&"'6#%-/#5*$#%-.#5'%#&+%#\RD9H!#)*&%'*5,#25752). &5*2%6:#9"'#06)4#=#ILL#CΩ8#01#=#Z5*$#@",&54%#45)*8#45 = ),S)6)4#5*$#&+%#177%'#M.$O#/'%01%*238# !# : Solution !+%#()$>5*$#@",&54%#45)*#)6#$%&%'()*%$#>3#5661()*4#&+5&#&+%#25752)&"'6#)*#&+%#\RD9H!#("$%, 5'%# 7%'/%2&# "7%*# 2)'21)&6:# !+)6# '%61,&6# )*# &+%# ()$>5*$# %01)@5,%*&# 2)'21)&# 6+"-*# )*# 9)4:# ;:I^=>?8 Rsig

RG

Vsig

(a) Rsig

Vsig

Rsig

RG

RG

(b)

(c)

Vgs Rsig sig R

sig

RG

RG

(d) Figure 9.16 ;,*#8,&/' ()*' !"5-%:$' C23X' '%(' <,=8$.#9' $>8,F5:$.&' #,*#8,&' )(' 5' JK0B!?' 5-%:,(,$*b' '$(' &<$ $>8,F5:$.&' #,*#8,&' 5&' -,6+5.6' (*$>8$.#,$/b' ')(' #,*#8,&' ()*' 6$&$*-,.,.=' &<$' *$/,/&5.#$' /$$.' +9' %-/b' '#(' #,*#8,&' ()* 6$&$*-,.,.='&<$'*$/,/&5.#$'/$$.'+9'%-.2

726 Chapter 9 Frequency Response

Example 9.6 continued

(*)-'@<,#<'@$'(,.6 01 ), . = [ ..................... . =- 0′ ? 4 5 ≡ ........ )6)4 0 1 + 0 6)4 3 " Z
A%#6+5,,#$%&%'()*%#ω##16)*4#&+%#(%&+"$#"/#"7%*.2)'21)&#&)(%#2"*6&5*&6:#!+%#'%6)6&5*2%#0-/#6%%*#>3#%-/#)6 /"1*$#>3#6%&&)*4#%-. = L#5*$#6+"'&.2)'21)&)*4#&+%#6)4*5,#4%*%'5&"'#)6)4:#!+)6#'%61,&6#)*#&+%#2)'21)&#"/#9)4: ;:I^=2?8#/'"(#-+)2+#-%#/)*$#&+5& 0 -/ = 0 1 ||0 6)4 = #Z
!+16#&+%#"7%*.2)'21)&#&)(%#2"*6&5*&#"/#%-/#)6

τ -/ ≡ % -/ 0 -/ = I × IL

[ I<

M

× NL:N × IL = NL:N#*6

!+%#'%6)6&5*2%#0-.#6%%*#>3#%-.#)6#/"1*$#>3#6%&&)*4#%-/#=#L#5*$#6+"'&.2)'21)&)*4#)6)4:#!+%#'%61,&#)6#&+% 2)'21)&#)*#9)4:#;:I^=$?8#&"#-+)2+#-%#577,3#5#&%6''%*&#(L:#A')&)*4#5#*"$%#%015&)"*#5&#d#4)@%6 )-/ )-/ [ ........ ( L = − ....... 0 1 0 6)4

!+168 )-/ = [ ( L 0′6)4

RC2ZYS

-+%'% 0′6)4 h#0 1 || 0 6)4 :#P#*"$%#%015&)"*#5&#f#7'"@)$%6 )-/ + )L ( L = - 3 )-/ + ................... 0′"

D1>6&)&1&)*4#/"'#)-/#/'"(#H0:#=;:[Z?#5*$#'%5''5*4)*4#&%'(6#3)%,$6 ) 0 -. ≡ .....L = 0′6)4 + 0′" + - 3 #0′" 0′6)4 = I:I^#\Ω (L

!+16#&+%#"7%*.2)'21)&#&)(%#2"*6&5*&#"/#%-.#)6

τ -. ≡ % -. 0 -. = I × IL

[ I<

^

× I:I^ × IL = II^L#*6

!+%#177%'#M.$O#/'%01%*23#ω##25*#*"-#>%#$%&%'()*%$#/'"( I

ω # # # # .................... τ -/ + τ -. I . = NL^#C'5$S6 = ................................................. [; ( NL:N + II^L ) × IL

!+168

ω

!# = ......#. = I
9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers

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′6)4 ')*' 0′" 2'L( 0′6)4 ,/'(,"$67'&<$.'()*'5'=,F$.'JK0B!?'&<$').:9'@59'&)',.#*$5/$'+5.6@,6&<',/'+9'*$68#,.='&<$':)56 *$/,/&5.#$2'_.()*&8.5&$:97'&<,/'5:/)'6$#*$5/$/'&<$'-,6+5.6'=5,.2'?<,/',/'5.'$"5-%:$')('&<$'8/85: &*56$G)(('+$&@$$.'=5,.'5.6'+5.6@,6&<7'5'#)--).'#,*#8-/&5.#$'@<,#<'@5/'-$.&,).$6'$5*:,$*2'

9.4.4 Miller’s Theorem L.')8*'5.5:9/,/')('&<$'<,=8$.#9'*$/%)./$')('&<$'#)--).G/)8*#$'5.6' #)--).G$-,&&$* 5-%:,(,$*/' R0$#&,).' C2PS7' @$' $-%:)9$6' 5' &$#<.,>8$' ()*' *$%:5#,.=' &<$' +*,6=,.=' #5%5#,&5.#$ =% -/ #"'#% µ ? '+9'5.'$>8,F5:$.&',.%8&'#5%5#,&5.#$2'?<,/'F$*9'8/$(8:'5.6'$(($#&,F$'&$#<.,>8$',/ +5/$6').'5'=$.$*5:'&<$)*$-'E.)@.'5/'8"22.-=*/4<.+-.!7'@<,#<'@$'.)@'%*$/$.&2 ;)./,6$*'&<$'/,&85&,).',.'B,=2'C2DZR5S2'N/'%5*&')('5':5*=$*'#,*#8,&'&<5&',/'.)&'/<)@.7'@$'<5F$ ,/):5&$6' &@)' #,*#8,&' .)6$/7' :5+$:$6' D' 5.6' U7' +$&@$$.' @<,#<' 5.' ,-%$65.#$' T' ,/' #)..$#&$62 `)6$/'D'5.6'U'5*$'5:/)'#)..$#&$6'&)')&<$*'%5*&/')('&<$'#,*#8,&7'5/'/,=.,(,$6'+9'&<$'+*)E$.':,.$/ $-5.5&,.='(*)-'&<$'&@)'.)6$/2'B8*&<$*-)*$7',&',/'5//8-$6'&<5&'/)-$<)@',&'<5/'+$$.'6$&$*-,.$6 &<5&'&<$'F):&5=$'5&'.)6$'U',/'*$:5&$6'&)'&<5&'5&'.)6$'D'+9

) < # = X) I

RC2Z1S

L.'&9%,#5:'/,&85&,)./'X',/'5'=5,.'(5#&)*'&<5&'#5.'+$'%)/,&,F$')*'.$=5&,F$'5.6'&<5&'<5/'5'-5=.,&86$ 8/85::9':5*=$*'&<5.'8.,&92'?<,/7'<)@$F$*7',/'.)&'5.'5//8-%&,).'()*'J,::$*n/'&<$)*$-2 J,::$*n/'&<$)*$-'/&5&$/'&<5&',-%$65.#$'T'#5.'+$'*$%:5#$6'+9'&@)',-%$65.#$/X' T I '#)..$#&$6 +$&@$$.'.)6$'D'5.6'=*)8.6'5.6' T < '#)..$#&$6'+$&@$$.'.)6$'U'5.6'=*)8.67'@<$*$

TI # = T ⁄ ( I [ X )

'RC2Z35S

I. T < # = T### I [ ... X

RC2Z3+S

5.6

&)')+&5,.'&<$'$>8,F5:$.&'#,*#8,&'/<)@.',.'B,=2'C2DZR+S2'

1

I

Z

I

2

1

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"

"

V1

V2 # KV1

V1

!

!

!

I2 # I

I1 # I

" Z1

Z1 # Z$(1 ! K), (a) Figure 9.17 !+%#\),,%'#%01)@5,%*)'21)&:

2

Z2

V2 # KV1 !

Z2 # Z (b)

(&1 ! K1 '

727

728 Chapter 9 Frequency Response ?<$'%*))(')('J,::$*n/'&<$)*$-',/'5#<,$F$6'+9'6$*,F,.='!>2'RC2Z3S'5/'()::)@/X'L.'&<$')*,=,.5: #,*#8,&' )(' B,=2' C2DZR5S7' &<$' ).:9' @59' &<5&' .)6$' D' i($$:/' &<$' $",/&$.#$j' )(' ,-%$65.#$' T' ,/ &<*)8=<' &<$' #8**$.&' (' &<5&' T' 6*5@/' 5@59' (*)-' .)6$' D2' ?<$*$()*$7' &)' E$$%' &<,/' #8**$.& 8.#<5.=$6' ,.' &<$' $>8,F5:$.&' #,*#8,&7' @$' -8/&' #<))/$' &<$' F5:8$' )(' T I ' /)' &<5&' ,&' 6*5@/' 5. $>85:'#8**$.&7

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Example 9.7 9)41'%#;:IN=5?#6+"-6#5*#)$%5,#@",&54%#5(7,)/)%'#+5@)*4#5#45)*#"/# [ ILL#]S] #-)&+#5*#)(7%$5*2%#T 2"**%2&%$#>%&-%%*#)&6#"1&71*$#)*71&#&%'()*5,6:#9)*$#&+%#\),,%'#%01)@5,%*)'21)&#-+%*#T#)6#=5? 5 I.\Ω#'%6)6&5*2%#5*$#=>?#5#I.79#25752)&5*2%:#F*#%52+#256%8#16%#&+%#%01)@5,%*)'21)&#&"#$%&%'()*% ) , ⁄ ) 6)4 : Solution =5? 9"'# T# =# I# \Ω8# %(7,"3)*4# \),,%'g6# &+%"'%(# '%61,&6# )*# &+%# %01)@5,%*&# 2)'21)&# )*# 9)4:# ;:IN=>?8 -+%'%# T ILLL#CΩ T I # = ............. # = ..................... = #;:;#CΩ I[X I + ILL T I#\Ω T < # = ............. # = .................. = L:;;##\Ω I I. I [ .... I + ........ X ILL

!+%#@",&54%#45)*#25*#>%#/"1*$#56#/",,"-6V ) ) ) TI .......,. # = ....., .......;. # = [ ILL# × # ................... . )6)4 ); )6)4 T I + 0 6)4 ;:; = [ ILL × ................... # = [ Z;:[#]S] ;:; + IL

^

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9.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers 729

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730 Chapter 9 Frequency Response

Example 9.7 continued

[ ILL # = ................................................................................. [ I< M I + / × ILI × I × IL × IL × IL [ ILL . # = ............................................ [^ I + / × I:LI × IL

!+)6#)6#&+%#&'5*6/%'#/1*2&)"*#"/#5#/)'6&."'$%'#,"-.7566#*%&-"'C#-)&+#5#$2#45)*#"/#−ILL#5*$#5#M.$O#/'%. 01%*23# !M$O #"/ I . = IY[:^#CBU !M$O # = ....................................... [^ < π × I:LI × IL

B*)-' !"5-%:$' C2Z7' @$' )+/$*F$' &<5&' &<$' J,::$*' *$%:5#$-$.&' )(' 5' ($$6+5#E' )*' +*,6=,.= *$/,/&5.#$'*$/8:&/7'()*'5'.$=5&,F$'X7',.'5'/-5::$*'*$/,/&5.#$'l+9'5'(5#&)*' ( I [ X )i '5&'&<$',.%8&2 L(' &<$' ($$6+5#E' $:$-$.&' ,/' 5' #5%5#,&5.#$7' ,&/' F5:8$' ,/' -8:&,%:,$6' +9' ( I [ X ) ' &)' )+&5,.' &<$ $>8,F5:$.&' #5%5#,&5.#$' 5&' &<$' ,.%8&' /,6$2' ?<$' -8:&,%:,#5&,).' )(' 5' ($$6+5#E' #5%5#,&5.#$' +9 ( I [ X ) ' ,/' *$($**$6' &)' 5/' 8"22.-/ !,24"32")%4"+&' )*' 8"22.-/ .00.)42' T$' <5F$' $.#)8.&$*$6' &<$ J,::$*'$(($#&',.'&<$'5.5:9/,/')('&<$';0'5.6';!'5-%:,(,$*/',.'0$#&,).'C2P2'

EXERCISES 9.11

P#$)'%2&.2"17,%$#5(7,)/)%'#+56#5#$2#45)*#"/#ILLL#]S]#5*$#5*#177%'#M.$O#/'%01%*23#"/#ILL#CBU:#9)*$#&+% &'5*6/%'#/1*2&)"*#5*$#&+%#45)*`>5*$-)$&+#7'"$12&#)*#+%'&U: ILLL N# Ans. .............................. b#IL BU / I + ....................Y < π × IL

9.12

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9.13

9"'#&+%#5(7,)/)%'#$%62')>%$#)*#HQ%'2)6%#;:I<8#/)*$#&+%#%Q52*$#577'"Q)(5&%#@5,1%6#=16)*4#H0:#;:^N?#"/ ω # #=56#5#/1*2&)"*#"/# ω 2I ?#/"'#&+%#256%6#O#=#I8#<8#5*$#Z: Ans. L:^Z8#L:[IW#L:NZ8#L:N;W#L:;Y8#L:;[

9.14 9"'#&+%#5(7,)/)%'#)*#HQ5(7,%#;:^8#/)*$#&+%#45)*`>5*$-)$&+#7'"$12&#)*#(%45+%'&U:#9)*$#&+%#@5,1%#"/## 0 "′ &+5&#-),,#'%61,&#)*# !# = 180 #CBU:#9)*$#&+%#*%-#@5,1%6#"/#&+%#()$>5*$#45)*#5*$#"/#&+%#45)*`>5*$-)$&+ 7'"$12&: Ans. I:M;#\BUW#<:
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9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers

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731

732 Chapter 9 Frequency Response

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9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers

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733

734 Chapter 9 Frequency Response N.'$/&,-5&$')(' ! # '#5.'&<$.'+$'()8.6'8/,.='!>2'RC234S'5/' I I ! # # \ I### .....< ] .....<. ! 2; ! 2, ! 2; '''' \ ........................... . ! 2; < I ] ...... ! 2,

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9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 735

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RC24YS

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9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers

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RC24CS

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9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 739

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RC2C1S

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740 Chapter 9 Frequency Response

Example 9.10 continued

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EXERCISES 9.16 9"'#&+%#GD#5(7,)/)%'#)*#HQ5(7,%#;:IL8#16)*4#&+%#@5,1%#"/# !# #$%&%'()*%$#>3#&+%#%Q52*5,36)68#/)*$ &+%#45)*`>5*$-)$&+#7'"$12&:#T%25,,#&+5&#-3#=#I:
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9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 741

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RC2CZS

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742 Chapter 9 Frequency Response N:&$*.5&,F$:97'8/,.='&<$'-$&<)6')(')%$.G#,*#8,&'&,-$'#)./&5.&/'9,$:6/

τ # # = % π 0 π + % µ 0 µ + % " 0 %" = % π 0′6)4+ % µ l ( I + - 3 0′")0′6)4 + 0′"i + % " 0′"

RC2DVDS

(*)-'@<,#<' !# '#5.'+$'$/&,-5&$6'5/

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RC2DVUS

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RC2DVPS

5.67'5//8-,.='&<5&'5'6)-,.5.&'%):$'$",/&/7

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RC2DVYS

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EXERCISE 9.19 G"*6)$%'#5#>)7",5'#52&)@%.,"5$%$#GH#5(7,)/)%'#+5@)*4#&+%#,"5$#21''%*"1'2%#)(7,%(%*&%$#-)&+ 5#F7F#&'5*6)6&"':#K%&#&+%#2)'21)&#>%#"7%'5&)*4#5#I.(P#>)56#21''%*&:#!+%#&'5*6)6&"'6#5'%#67%2)/)%$ 56# /",,"-6V# β ( 7F7 )# = ?# % )* #5*$# !# #16)*4#&+%#\),,%'#577'"Q)(5&)"*W#=2?# !# #16)*4#"7%*.2)'21)& &)(%#2"*6&5*&6W#=$? !T 8# !2I 8# !2< 8#5*$#+%*2%# !# #=16%#&+%#577'"Q)(5&%#%Q7'%66)"*6#)*#H06:#;:ILY#5*$ ;:ILZ?W#5*$#=%?#&+%#45)*`>5*$-)$&+#7'"$12&: Ans. =5?# [ I[Y#]S] W#=>?#ZZN#798#N<:^#CBUW#=2?#[Y:I#CBUW#=$?#
9.5.6 The Situation When Rsig Is Low ?<$*$'5*$'5%%:,#5&,)./',.'@<,#<'&<$';0'5-%:,(,$*',/'($6'@,&<'5':)@G*$/,/&5.#$'/,=.5:'/)8*#$2 K+F,)8/:97',.'/8#<'5'#5/$7'&<$'<,=8$.#9'=5,.'@,::'.)':).=$*'+$':,-,&$6'+9'&<$',.&$*5#G &,).')('&<$'/)8*#$'*$/,/&5.#$'5.6'&<$',.%8&'#5%5#,&5.#$2'M5&<$*7'&<$'<,=8$.#9':,-,&5&,). <5%%$./'5&'&<$'5-%:,(,$*')8&%8&7'5/'@$'/<5::'.)@'/<)@2' B,=8*$'C2U1R5S'/<)@/'&<$'<,=8$.#9'$>8,F5:$.&'#,*#8,&')('&<$'#)--).G/)8*#$'5-%:,(,$* ,.'&<$':,-,&,.='#5/$'@<$.' 0 6)4 ,/'Q$*)2'?<$'F):&5=$'&*5./($*'(8.#&,). ), ⁄ )6)4 = ), ⁄ )-/ #5.'+$

9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 743

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ft # !AM! f3dB fZ fH 1 1 2! (CL " Cgd)R&L

gm 2!(CL " Cgd)

gm 2!Cgd

f (log scale)

(c) Figure 9.25 '%(#B)4+./'%01%*23#%01)@5,%*&# 2)'21)&#"/#5#GD#5(7,)/)%'#/%$# -)&+# 5#6)4*5,# 6"1'2%# +5@)*4#5 @%'3#,"-#=%//%2&)@%,3#U%'"?#'%6)6&5*2%:#'$(#!+%#2)'21)&#-)&+#)6)4#'%$12%$#&"#U%'":#')(#O"$%#7,"&#/"'#&+%#45)*#"/ &+%#2)'21)&#)*#'%(:

()8.6'+9'/$&&,.=' 0 6)4 # = L ',.'!>2'RC244S2'?<$'*$/8:&',/

), = [ - 3 0 "′ ? [ I [ / ( % -. ⁄ - 3 ) ] ....... . # = ............................................................. I + / ( % " + % -. )0′" )6)4

RC2DV3S

?<8/7' @<,:$' &<$' 6#' =5,.' 5.6' &<$' (*$>8$.#9' )(' &<$' Q$*)' 6)' .)&' #<5.=$7' &<$' <,=8$.#9 *$/%)./$',/'.)@'6$&$*-,.$6'+9'5'%):$'()*-$6'+9' % " + % -. '&)=$&<$*'@,&<' 0′" 2'?<8/'&<$'PG6H

744 Chapter 9 Frequency Response (*$>8$.#9',/'.)@'=,F$.'+9

I !# # = ....................................... < π ( % " + % -. )0′"

RC2DVZS

?)'/$$'<)@'&<,/'%):$',/'()*-$67'*$($*'&)'B,=2'C2U1R+S7'@<,#<'/<)@/'&<$'$>8,F5:$.&'#,*#8,&'@,&< &<$' ,.%8&' /,=.5:' /)8*#$' *$68#$6' &)' Q$*)2' K+/$*F$' &<5&' &<$' #,*#8,&' *$68#$/' &)' 5' #5%5#,&5.#$ ( % " + % -. ) ',.'%5*5::$:'@,&<'5'*$/,/&5.#$' 0′" 2 N/'@$'<5F$'/$$.'5+)F$7'&<$'&*5./($*G(8.#&,).'Q$*)',/'8/85::9'5&'5'F$*9'<,=<'(*$>8$.#9 5.6'&<8/'6)$/'.)&'%:59'5'/,=.,(,#5.&'*):$',.'/<5%,.='&<$'<,=8$.#9'*$/%)./$2'?<$'=5,.')( &<$';0'5-%:,(,$*'@,::'&<$*$()*$'(5::')(('5&'5'*5&$')('[3'6HO)#&5F$'R[UV'6HO6$#56$S7'*$5#<,.= 8.,&9'RV'6HS'5&'5'(*$>8$.#9' !: 7'@<,#<',/'$>85:'&)'&<$';%"&>$%&#:"#4
!: # = 4 5 ! #

I < π ( % " + % -. )0′"

' = - 3 0′" ....................................... ?<8/7

-3 . !:# = ............................... < π ( % " + % -. )

RC2DV4S

B,=8*$'C2U1R#S'/<)@/'5'/E$&#<')('&<$'<,=8$.#9'=5,.')('&<$';0'5-%:,(,$*2

Example 9.11 G"*6)$%'#&+%#GD#5(7,)/)%'#67%2)/)%$#)*#HQ5(7,%#;:N#-+%*#/%$#-)&+#5#6)4*5,#6"1'2%#+5@)*4#5#*%4,)4). >,%#'%6)6&5*2%#=):%:8# 0 6)4 # = L?: #9)*$# 4 5 8# !M$O 8# !: 8#5*$# !T :#F/#&+%#5(7,)/3)*4#&'5*6)6&"'#)6#&"#>%#"7%'. 5&%$#5&#&-)2%#&+%#"')4)*5,#"@%'$')@%#@",&54%#-+),%#M#5*$#"#'%(5)*#1*2+5*4%$8#>3#-+5&#/52&"'#(16& &+%#>)56#21''%*&#>%#2+5*4%$a#A+5'%#&+%#*%-#@5,1%6#"/# 4 5 8# !M$O 8# !: 8#5*$# ! T a#P661(%#&+5&# 0 "′ )6 &+%#75'5,,%,#%01)@5,%*&#"/#+,#"/#&+%#5(7,)/3)*4#&'5*6)6&"'#5*$#&+5&#"/#&+%#21''%*&.6"1'2%#,"5$: Solution F*#HQ5(7,%#;:N#-%#/"1*$#&+5& 4 5 # = [ - 3 0′" \ [ I<:Y#]S]

!+%#M.$O#/'%01%*23#25*#>%#/"1*$#16)*4#H0:#=;:IL[?8 I !# # = ........................................ < π ( % " + % -. )0′" I . '''''''''''''''''''''''''''= ......................................................................... [ IY M < π (
5*$#&+%#1*)&3.45)*#/'%01%*238#-+)2+#)6#%015,#&"#&+%#45)*`>5*$-)$&+#7'"$12&8#25*#>%#$%&%'()*%$#56# !: # = 4 5 #!# = I<:Y × YML:Y# = ^:^M#dBU

9.5 A Closer Look at the High-Frequency Response of the CS and CE Amplifiers

!+%#/'%01%*23#"/#&+%#U%'"#)6 I - 3. !T # = ...... ....... < π % -. [M

I I:
J"-8#&"#$"1>,%# )N) 8## ( * #(16&#>%#015$'17,%$:#!+%#*%-#@5,1%6#"/# - 3 #5*$# 0 "′ #25*#>%#/"1*$ 56#/",,"-6V (* . # = <:Y#(PS]# - 3 # = ............... )N) ⁄ < I ''''' 0′" \ ... × IL \ <:YCΩ Z

!+16#&+%#*%-#@5,1%#"/# 4 5 >%2"(%6# 4 5 # = [ - 3 0′" = [ <:Y × <:Y# = [ ^:
!+5&#"/# !# >%2"(%6

I !# # = ........................................ < π ( % " + % -. )0′" I . ''''''''''''''''''''''''' = ......................................................................... [ IY M < π (
5*$#&+%#1*)&3.45)*#/'%01%*23#=):%:8#&+%#45)*`>5*$-)$&+#7'"$12&?#>%2"(%6 !: # = ^:
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EXERCISES 9.20 9"'#&+%#GD#5(7,)/)%'#2"*6)$%'%$#)*#HQ5(7,%#;:II#"7%'5&)*4#5&#&+%#"')4)*5,#@5,1%6#"/# )N) #5*$# ( * 8 /)*$#&+%#@5,1%#&"#-+)2+# % " #6+"1,$#>%#)*2'%56%$#&"#7,52%# !: #5&#< dBU: Ans. ;Z:Z#/9 9.21 D+"-#&+5&#&+%#GD#5(7,)/)%'#-+%*#/%$#-)&+# 0 6)4 # = L #+56#5#&'5*6/%'./1*2&)"*#U%'"#-+"6%#/'%01%*23 )6#'%,5&%$#&"# !: #>3 % ! ...T. # = I + .......". !: % -.

HcP\EKH#;:II

745

746 Chapter 9 Frequency Response

9.6 High-Frequency Response of the Common-Gate and Cascode Amplifiers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

9.6.1 High-Frequency Response of the CG Amplifier B,=8*$'C2U3R5S'/<)@/'&<$';f'5-%:,(,$*'@,&<'&<$'JK0B!?',.&$*.5:'#5%5#,&5.#$/ % -/ 5.6' % -. ,.6,#5&$62'B)*'=$.$*5:,&97'5'#5%5#,&5.#$' % " ',/',.#:86$6'5&'&<$')8&%8&'.)6$'&)'*$%*$/$.&'&<$ #)-+,.5&,).')('&<$')8&%8&'#5%5#,&5.#$')('5'#8**$.&G/)8*#$':)56'5.6'&<$',.%8&'#5%5#,&5.#$')('5 /8##$$6,.=' 5-%:,(,$*' /&5=$2' ;5%5#,&5.#$' % " ' 5:/)' ,.#:86$/' &<$' JK0B!?' #5%5#,&5.#$' % .? 2 `)&$'&<$' % " '5%%$5*/',.'$(($#&',.'%5*5::$:'@,&<' % -. b'&<$*$()*$7',.'&<$'()::)@,.='6,/#8//,).'@$ @,::':8-%'&<$'&@)'#5%5#,&5.#$/'&)=$&<$*2 L&',/',-%)*&5.&'&)'.)&$'5&'&<$')8&/$&'&<5&'$5#<')('&<$'&<*$$'#5%5#,&5.#$/',.'&<$'#,*#8,& )('B,=2'C2U3R5S'<5/'5'=*)8.6$6'.)6$2'?<$*$()*$'.).$')('&<$'#5%5#,&5.#$/'8.6$*=)$/'&<$ J,::$*'-8:&,%:,#5&,).'$(($#&')+/$*F$6',.'&<$';0'/&5=$2'L&'()::)@/'&<5&'&<$';f'#,*#8,&'#5. +$' 6$/,=.$6' &)' <5F$' 5' -8#<' @,6$*' +5.6@,6&<' &<5.' &<5&' )(' &<$' ;0' #,*#8,&7' $/%$#,5::9 @<$.'&<$'*$/,/&5.#$')('&<$'/,=.5:'=$.$*5&)*',/':5*=$2 P*5,36)6#"/#&+%#2)'21)&#)*#9)4:#;:<^=5?#)6#4'%5&,3#6)(7,)/)%$#)/# + , #25*#>%#*%4,%2&%$:#F*#612+ 5#256%#&+%#)*71)$%#)6#)6",5&%$#/'"(#&+%#"1&71)$%8#5*$#&+%#+)4+./'%01%*23#%01)@5,%*)'21)& &5C%6#&+%#/"'(#6+"-*#)*#9)4:#;:<^=>?:#A%#)((%$)5&%,3#">6%'@%#&+5&#&+%'%#5'%#&-"#7",%6V#"*% 5&#&+%#)*71)$%#-)&+#5#/'%01%*23# !2I8

I !2I # = ......................................... I < π % -/ 0 6)4 || ..... -3

RC2DVCS

5.6'&<$')&<$*'5&'&<$')8&%8&'/,6$'@,&<'5'(*$>8$.#9' !2< 7

I !2< # = ...................................... < π ( %-. + % " )0 "

RC2DDVS

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0 -/ # = 0 6)4 || 0 )*

RC2DDDS

0 -.# = 0 " || 0 , #

RC2DDUS

5.6

9.6 High-Frequency Response of the Common-Gate and Cascode Amplifiers

gmVi

D

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Vo RL

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ro 1 gm

Cgs Rsig

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Vi ! (a) Rsig

gmVi

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Figure 9.26 '%(#!+%#2"(("*.45&%#5(7,)/)%'#-)&+#&+%#&'5*6)6&"'#)*&%'*5,#25752)&5*2%6#6+"-*:#P#,"5$# 25752)&5*2%#%"#)6#5,6"#)*2,1$%$:#'$(#H01)@5,%*)'21)&#/"'#&+%#256%#)*#-+)2+#+,#)6#*%4,%2&%$:

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747

748 Chapter 9 Frequency Response !"#$"%$&'%()%*+),%-.%.(-&#'% !" /

> !"' = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB % A π [ # $% & $% 8 ( # $' + # ( )& $' ]

0123345

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0123365

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Figure 9.28 N+*'34'$5,%"2"*.'0".0-")'$)''5"1@$#1:

9.6 High-Frequency Response of the Common-Gate and Cascode Amplifiers

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K+/$*F$'&<5&#!#',/',.6$$6'-8#<'<,=<$*'R-)*$'&<5.'&@,#$S'&<$'#)**$/%).6,.='F5:8$'()*'&<$';0'5-%:,G (,$*'()8.6',.'!"5-%:$'C2C2'N.)&<$*',-%)*&5.&')+/$*F5&,).'#5.'+$'-56$'+9'$"5-,.,.='&<$'&@)'#)-G %).$.&/')( τ # X'?<$'#).&*,+8&,).')('&<$',.%8&'#,*#8,&',/'U323'%/7'@<,:$'&<5&')('&<$')8&%8&'#,*#8,&',/'PZY %/b'&<8/'&<$':,-,&5&,).').'&<$'<,=8$.#9'*$/%)./$',/'%)/$6'+9'&<$')8&%8&'#,*#8,&2

749

750 Chapter 9 Frequency Response

EXERCISE 9.22 F*#"'$%'#&"#'5)6%#&+%#()$>5*$#45)*#"/#&+%#Gd#5(7,)/)%'#)*#HQ5(7,%#;:I<8#&+%#2)'21)&#$%6)4*%'#$%2)$%6 &"#16%#5#2562"$%#21''%*"1'2%#/"'#&+%#,"5$#$%@)2%8#&+16#'5)6)*4 0 " >3#5#/52&"'#"/# - 3 + , # = %2"(%6#YLL#C Ω :#9)*$# 0 )* 8#&+%#()$>5*$#45)*8#5*$# ! # :#G"((%*&#"*#&+%#'%61,&6: Ans. 5*$#45)*#+56#>%%*#)*2'%56%$#61>6&5*&)5,,3#=>3#5 /52&"'#"/#;:[?8#&+%#>5*$-)$&+# ! # #+56#>%%*#61>6&5*&)5,,3#,"-%'%$#=>3#5#/52&"'#"/#5>"1&#;:M?:#!+168#&+% +)4+./'%01%*23#5$@5*&54%#"/#&+%#Gd#5(7,)/)%'#)6#2"(7,%&%,3#,"6&k

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Cgs1 Figure 9.29 !+%#2562"$%#2)'21)&#-)&+#&+%# @5')"16#&'5*6)6&"'#25752)&5*2%6#)*$)25&%$:

9.6 High-Frequency Response of the Common-Gate and Cascode Amplifiers

5-%:,(,$*' /&5=$' R,(' 5.9S2' `)&$' &<5&' % .?I ' 5.6' % -/< ' 5%%$5*' ,.' %5*5::$:7' 5.6' @$' /<5::' #)-+,.$ &<$-',.'&<$'()::)@,.='5.5:9/,/2' 0,-,:5*:97' %"' 5.6' %-.U' 5%%$5*' ,.' %5*5::$:' 5.6' @,::' +$' #)-G +,.$62 ?<$'$5/,$/&'5.67',.'(5#&7'>8,&$',./,=<&(8:'5%%*)5#<'&)'6$&$*-,.,.='&<$'PG6H'(*$>8$.#9'!# ,/'&)'$-%:)9'&<$')%$.G#,*#8,&'&,-$G#)./&5.&/'-$&<)6X G5752)&5*2%# % -/I #6%%6#5#'%6)6&5*2%# 0 6)4 : 2. G5752)&5*2%# % -.I #6%%6#5#'%6)6&5*2%# 0 -.I 8#-+)2+#25*#>%#">&5)*%$#>3#5$57&)*4#&+%#/"'. (1,5#)*#H0:#=;:NZ?#&"# 1.

0 -.I # = ( I + - 3I 0 .I )0 6)4 + 0 .I

RC2DD3S

###-+%'%# 0 .I 8#&+%#&"&5,#'%6)6&5*2%#5&# * I 8#)6#4)@%*#>3

+ ,< + 0 " 0 .I # \ + ,I || 0 )*< = + ,I || .................. - 3< + ,<

RC2DDZS

G5752)&5*2%# ( % .?I + % -/< ) #6%%6#5#'%6)6&5*2%# 0 .I : 4. G5752)&5*2%# ( % " + % -.< ) #6%%6#5#'%6)6&5*2%# ( 0 " || 0 , ) -+%'%#0,#)6#4)@%*#>3 3.

0 , \ + ,< + + ,I + ( - 3< + ,< )+ ,I T,&<'&<$'*$/,/&5.#$/'6$&$*-,.$67'&<$'$(($#&,F$'&,-$'#)./&5.&' τ # '#5.'+$'#)-%8&$6'5/

τ # # = % -/I 0 6)4 + % -.I [ ( I + - 3I 0 .I )0 6)4 + 0 .I ]# ''''''''''''''''''''''''''''''''''''''''''' # + ( % .?I + % -/< )0 .I + ( % " + % -.< ) ( 0 " || 0 , ) 5.6'&<$'PG6H'(*$>8$.#9'! #'5/

RC2DD4S

I !# # # ............ < πτ#

?)'=5,.',./,=<&'*$=5*6,.='@<5&':,-,&/'&<$'<,=8$.#9'=5,.')('&<$'JK0'#5/#)6$'5-%:,G (,$*7'@$'*$@*,&$'!>2'RC2DD4S',.'&<$'()*-

τ # # = 0 6)4 [ % -/I + % -.I ( I + - 3I 0 .I ) ]#+ 0 .I ( % -.I + % .?I + % -/< )# ''''''''''''''''''''''''''''''# + ( 0 " || 0 , ) ( % " + % -.< )

RC2DDCS

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`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

τ # # # # ( % " + % -.< ) ( 0 " || 0 , )

751

752 Chapter 9 Frequency Response 5.6'&<$'PG6H'(*$>8$.#9'+$#)-$/

I !# # = ........................................................ < π ( % " + % -.< ) ( 0 " || 0 , )

RC2DUVS

@<,#<',/')('&<$'/5-$'()*-'5/'&<$'()*-8:5'()*'&<$';0'5-%:,(,$*'@,&<' 0 6)4 # = L 'R!>2'C2DVZS2 c$*$7'<)@$F$*7' ( 0 " || 0 " ) ',/':5*=$*'&<5&' 0 "′ '+9'5'(5#&)*')('5+)8&' 4 L 2'?<8/'&<$' !# ')('&<$'#5/G #)6$'@,::'+$':)@$*'&<5.'&<5&')('&<$';0'5-%:,(,$*'+9'&<$'/5-$'(5#&)*' 4 L 2'B,=8*$'C2PV'/<)@/'5 /E$&#<')('&<$'(*$>8$.#9'*$/%)./$')('&<$'#5/#)6$'5.6')('&<$'#)**$/%).6,.='#)--).G/)8*#$ 5-%:,(,$*2'T$')+/$*F$'&<5&',.'&<,/'#5/$7'#5/#)6,.=',.#*$5/$/'&<$'6#'=5,.'+9'5'(5#&)*'4V'@<,:$ E$$%,.='&<$'8.,&9G=5,.'(*$>8$.#9'8.#<5.=$6'5&

-3 I . !: # # # ...... ..................... < π % " + % -.<

Common Source

RC2DUDS

Cascode Vo

ro

Vi

RL

Vo A0 ro

CL

A0 RL

CL

Circuit Vi

R&L # RL % ro

!gm R&L

DC Gain f3dB ft

!A0gm R&L

1 2!(CL " Cgd)R&L

1 2!(CL " Cgd)A0 R&L

gm 2!(CL " Cgd)

gm 2!(CL " Cgd)

Gain (dB) Cascode

A0 gm R&L A0

CS

gm R&L

A0 0

f3dB!

cascode

f3dB!

CS

ft

f (log scale)

Figure 9.30 H//%2&#"/#2562"$)*4#"*#45)*#5*$#>5*$-)$&+#)*#&+%#256%#06)4#=#L:#G562"$)*4#25*#)*2'%56%#&+%#$2# 45)*#>3#&+%#/52&"'#4L#-+),%#C%%7)*4#&+%#1*)&3.45)*#/'%01%*23#2"*6&5*&:#J"&%#&+5&#&"#52+)%@%#&+%#+)4+#45)*8#&+%# ,"5$#'%6)6&5*2%#(16&#>%#)*2'%56%$#>3#&+%#/52&"'#4L:

9.6 High-Frequency Response of the Common-Gate and Cascode Amplifiers 753

Example 9.13 !+)6#%Q5(7,%#),,16&'5&%6#&+%#5$@5*&54%6#"/#2562"$)*4#>3#2"(75')*4#&+%#7%'/"'(5*2%#"/#5#2562"$% 5(7,)/)%'#-)&+#&+5&#"/#5#2"(("*.6"1'2%#5(7,)/)%'#)*#&-"#256%6V R5S ?<$'*$/,/&5.#$')('&<$'/,=.5:'/)8*#$',/'/,=.,(,#5.&7' 0 6)4 # = IL#CΩ 2 R+S 0 6)4 ,/'.$=:,=,+:9'/-5::2 N//8-$'5::'JK0B!?/'<5F$' - 3 = #I:
Solution =5? 9"'#&+%#GD#5(7,)/)%'V ############################################## 4 L # = - 3 + , # = I:
τ # # = % -/ 0 6)4 + % -. [ =I + - 3 0 "′ ?0 6)4 + 0 "′ ]#+ ( % " + % .? )0 "′ @<$*$' 0′"# = + , || 0 " # = + , || + , # = IL#CΩ

τ # # =
!+168 I . # = IZN#\BU !# # = ........................................... [ I< < π × IL[Y × IL

############################################## !: # = 4 v !# = I<:Y × IZN# = I:NY#dBU B)*'&<$'#5/#)6$'5-%:,(,$*X

'''''''''''''''''''''''' 0 , # = <+ , + ( - 3 + , )+ , #h# ( < ×
''''''''''''''''''''''' 0 .I # \ + , || 0 )*< # \
754 Chapter 9 Frequency Response

Example 9.13 continued

################################## \ IL [
''''''''''''''''''''''''''''' ''''''''''''''''''''''' ''''''

] I:ZN ( Y ] Y ]
] (
################################## \ [[<:^ #76 I . # \
##################### #####

! : # \
!+16#2562"$)*4#+56#)*2'%56%$# ! : #>3#5#/52&"'#"/#<:[: =>? 9"'#&+%#GD#5(7,)/)%'V ############################################ 4 v # = [ I<:Y#]S] ############################################# τ # # = ( % -. + % " + % .? )0 "′ ################################################= ( Y + IL + Y )IL# =#
B)*'&<$'#5/#)6$'5-%:,(,$*X #################################### 0 " # \ 0 , # \ YZL #C Ω ##################################### 4 v # \ [ - 3 ( 0 , || 0 " ) ###################################### \ [ I:
''''''''''''''''''''''''''''' 0 )*< # \

+, ] 0"
''''''''''''''''''''''''''''' 0.I # \

+ ,I || 0 )*< # \
''''''''''''''''''''''''''''''' τ# # \

0 .I ( % -.I ] % .?I ] % -/< ) ] ( 0 " || 0 , ) ( % " ] % -.< ] % .?< )

\ IL:^ ( Y ] Y ]
'\

MIN ] YZLL# \ Y[IN '%/

I # \ <[:N \BU ! # # \ ........................................... [ I< < π × Y[IN × IL ! : # \ MM[:Y × <[:N# \ ;:M; dBU

?<8/'#5/#)6,.=',.#*$5/$/'&<$'6#'=5,.'(*)-'DU21'hOh'&)'PPZ21'hOh2'?<$'8.,&9G=5,.'(*$>8$.#9'R@<,#<7',. &<,/'#5/$7',/'$>85:'&)'&<$'=5,.[+5.6@,6&<'%*)68#&S7'<)@$F$*7'*$-5,./'.$5*:9'#)./&5.&2

9.6 High-Frequency Response of the Common-Gate and Cascode Amplifiers 755

EXERCISE 9.23 F*#&+)6#%Q%'2)6%#-%#-)6+#&"#2"*&'56&#&+%#45)*#"/#5#GD#5(7,)/)%'#5*$#5#2562"$%#5(7,)/)%':#P661(%#&+5& >"&+#5'%#/%$#-)&+#5#,5'4%#6"1'2%#'%6)6&5*2%#06)4#&+5&#%//%2&)@%,3#$%&%'()*%6#&+%#+)4+./'%01%*23#'%. 67"*6%:#!+168#*%4,%2"(7"*%*&6#"/#τ##&+5&#$"#*"&#)*2,1$%#06)4:#P,6"#5661(%#&+5,,#&'5*6)6&"'6#5'% "7%'5&%$#5&#&+%#65(%#2"*$)&)"*6#5*$#&+16#2"''%67"*$)*4#6(5,,.6)4*5,#75'5(%&%'6#5'%#%015,:#P,6"8 >"&+#5(7,)/)%'6#+5@%#%015,#0"#=#+,8#5*$#-3 +,'='ZL: =5?#9)*$#&+%#'5&)"#"/#&+%#,"-./'%01%*23#45)*#"/#&+%#2562"$%#5(7,)/)%'#&"#&+5&#"/#&+%#GD#5(7,)/)%': =>?#9"'#&+%#256%#"/# % -. # \ L:?#&"#/)*$#&+%#'5&)"#"/# ! : #"/#&+%#2562"$%#&"#&+5&#"/#&+%#GD: Ans. #
9.6.3 High-Frequency Response of the Bipolar Cascode Amplifier ?<$'5.5:9/,/'-$&<)6'/&86,$6',.'&<$'%*$F,)8/'/$#&,).'#5.'+$'6,*$#&:9'5%%:,$6'&)'&<$'HI?'#5/G #)6$'5-%:,(,$*2'B,=8*$'C2PD'%*$/$.&/'&<$'#,*#8,&/'5.6'&<$'()*-8:5/'()*'6$&$*-,.,.='&<$'<,=8$.#9'*$/%)./$')('&<$'+,%):5*'#5/#)6$2

C2

Vo

R!1 # R&sig

C"2 Q2

RL

C!2 C1

Vsig " !

" V!1

CL " Ccs2

R"1 # R&sig(1 " gm1Rc1) " Rc1 ro2 " RL Rc1 # ro1 re2 ro2 " RL$( $2 " 1) #H # C!1R!1 " C"1R"1 " (Ccs1 " C!2)Rc1 " (CL " Ccs2 " C"2)(RL % Ro) Ro # $ 2 ro2

%* &

fH #

C"1

Rsig

R&sig # r!1 % (rx1 " Rsig)

Q1

Ccs1

1 2!#H

AM # !

r! g ($r % R ) r! " rx" Rsig m o L

C!1

!

Figure 9.31 f%&%'()*)*4#&+%#/'%01%*23#'%67"*6%#"/#&+%#Oe!#2562"$%#5(7,)/)%':#J"&%#&+5&#)*#5$$)&)"*#&"#&+%# Oe!#25752)&5*2%6#%π#5*$#%µ 8#&+%#25752)&5*2%#>%&-%%*#&+%#2",,%2&"'#5*$#&+%#61>6&'5&%#%>/#/"'#%52+#&'5*6)6&"'#5'%## )*2,1$%$:

'+

756 Chapter 9 Frequency Response

EXERCISE 9.24 !+%#">X%2&)@%#"/#&+)6#%Q%'2)6%#)6#&"#%@5,15&%#&+%#%//%2&#"/#2562"$)*4#"*#&+%#7%'/"'(5*2%#"/#&+%#GH#5(. 7,)/)%'# "/# HQ%'2)6%# ;:I;:# !+%# 67%2)/)25&)"*6# 5'%# 56# /",,"-6V' (# =# I# (P8# β # = /I # = % >/< # = L 8# % " # = Y#79 8# 0 6)4 # = M^#CΩ 8# 0 " #= YL#CΩ :#9)*$#0 )* 8#4 L 8# 0 ,I 8# 0 )*< 8# 0 , 8# 4 5 8# !# 8#5*$# !: :#G"(75'%# 4 5 8# ! # 8#5*$# ! : #-)&+#&+%#2"''%67"*$. )*4#@5,1%6#">&5)*%$#)*#HQ%'2)6%#;:I;#/"'#&+%#GH#5(7,)/)%':#A+5+"1,$# % " #>%#'%$12%$#&"#)*#"'$%' &"#+5@%# !# # = I#\BU a Ans. #Y:<#CΩW#Y%#'%$12%$#&"#I:^#79:

9.7 High-Frequency Response of the Source and Emitter Followers L.' &<,/' /$#&,).' @$' /&869' &<$' <,=8$.#9' *$/%)./$' )(' &@)' ,-%)*&5.&' #,*#8,&' +8,:6,.= +:)#E/X'&<$'/)8*#$'()::)@$*'5.6'&<$'$-,&&$*'()::)@$*2'H)&<'<5F$'F):&5=$'=5,.'&<5&',/':$//'&<5. +8&'#:)/$'&)'8.,&92'?<$,*'56F5.&5=$':,$/',.'&<$,*'<,=<',.%8&'*$/,/&5.#$'5.6':)@')8&%8&'*$/,/G &5.#$2'?<$9'(,.6'5%%:,#5&,).'5/'&<$')8&%8&'/&5=$')('5'-8:&,/&5=$'5-%:,(,$*2'N/'@$'@,::'/$$ /<)*&:97'+)&<'$"<,+,&'@,6$'+5.6@,6&<2

9.7.1 The Source Follower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|| + , ) . RC2DUUS 4 5 = ............................................ ( 0 " || + , ) + ( I ⁄ - 3 ) I 0 , = ...... || + , -3

RC2DUPS

G"(>)*)*4#0"#5*$#+,#)*&"#5#6)*4,%#'%6)6&5*2%# 0′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ω')*' /# = ∞: 'N:/)7'),'@,::'+$'Q$*)'5&'&<$'F5:8$')('/'&<5&'#58/$/

9.7 High-Frequency Response of the Source and Emitter Followers 757

Rsig

Cgd

G

D

" Vsig

" !

Vgs

Cgs

!

ro

gmVgs S

"

RL

CL

Vo !

(a) Rsig

G

Rsig

D

G

" Vsig " !

Cgd

Ix

Vgs

Cgs

!

gmVgs

S

" R&L

R&L = RL %rO

CL

Vo

" Vgs ! Ix

Vgs Rgs ) I x

R&L

!

(c)

(b)

Figure 9.32 P*5,36)6#"/#&+%#+)4+./'%01%*23#'%67"*6%#"/#&+%#6"1'2%#/",,"-%'V#'%(#%01)@5,%*)'21)&W#'$(# 6)(7,)/)%$#%01)@5,%*)'21)&W##')(#$%&%'()*)*4#&+%#'%6)6&5*2%#0-/#6%%*#>3#%-/:

&<$'#8**$.&',.&)'&<$',-%$65.#$' 0′" || % " '&)'+$'Q$*)2'0,.#$'&<,/'#8**$.&',/' ( - 3 + /% -/ ) )-/ 7'&<$ &*5./-,//,).'Q$*)'@,::'+$'5&' /# = / T 7'@<$*$

-3 / T # = [ ....... % -/

RC2DUYS

?<5&',/7'&<$'Q$*)'@,::'+$').'&<$'.$=5&,F$'*$5:'5",/')('&<$'/G%:5.$'@,&<'5'(*$>8$.#9'

RC2DU1S ω T # = ......3. % -/ M$#5::,.='&<5&'&<$'JK0B!?n/' ω H # = - 3 ⁄ ( % -/ + % -. ) '5.6'&<5&' % -. %#% -/ 7'@$'/$$'&<5&' ω T @,::'+$'F$*9'#:)/$'&) ω H 7 !T# # #!H

RC2DU3S

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EXERCISE 9.25 G"*6)$%'#5#6"1'2%#/",,"-%'#67%2)/)%$#56#/",,"-6V# - 3 # = I:1&)"*#&"#)&#/'"(#%52+#"/#&+'%%#25752)&5*2%6:#9)*$# !# : Ans.#L:;M#]S]W#N#dBUW#IL#dBUW#IL#CΩW#I:ZN#CΩW#L:[Z#CΩW#YL#76W#ML#76W#II#76W#;I#76W#YYbW#MMbW I
9.7.2 The Emitter Follower B,=8*$' C2PPR5S' /<)@/' 5.' $-,&&$*' ()::)@$*' /8,&5+:$' ()*' L;' (5+*,#5&,).2' L&' ,/' +,5/$6' +9' 5 #)./&5.&G#8**$.&'/)8*#$'(2'c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o8-%,.=' +, '&)=$&<$*'@,&< 0 " 8 '5.6' +L '&)=$&<$*'@,&<' 0 6)4 '5.6'-5E,.='5'/:,=<&'#<5.=$',.'&<$'@59'&<$'#,*#8,&',/'6*5@. *$/8:&/',.'&<$'/,-%:,(,$6'$>8,F5:$.&'#,*#8,&'/<)@.',.'B,=2'C2PPR#S2'T$'@,::'()::)@'5'%*)#$68*$ ()*'&<$'5.5:9/,/')('&<,/'#,*#8,&'/,-,:5*'&)'&<5&'8/$6'5+)F$'()*'&<$'/)8*#$'()::)@$*2'0%$#,(,#5::97 &)')+&5,.'&<$':)#5&,).')('&<$'&*5./-,//,).'Q$*)7'.)&$'&<5&' ), '@,::'+$'Q$*)'5&'&<$'(*$>8$.#9' / T ()*'@<,#<'&<$'#8**$.&'($6'&)' 0′" ',/'Q$*)X

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&<$'6,(($*$.&,5:'5-%:,(,$*'+$=,./'&)'6$#*$5/$7'5/',.6,#5&$6',.'B,=2'C2P1R#S2'`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l)** [ ( ( / < )0 *i8 '@$'/$$'&<5&'v*D'5.6'v*U'@,::'<5F$'&<$'/5-$'<,=8$.#9'.),/$'5/')**2'?<,/'<,=8$.#9'.),/$'&<$.'#)./&,&8&$/'5'#)--).G-)6$',.%8& /,=.5:'&)'&<$'/$#).6'6,(($*$.&,5:'/&5=$7'()*-$6'+9'PP'5.6'PY2'L('&<$'/$#).6'6,(($*$.&,5:'/&5=$ ,/' %$*($#&:9' -5&#<$67' ,&/' 6,(($*$.&,5:' )8&%8&' F):&5=$' ),' /<)8:6' +$' (*$$' )(' <,=8$.#9 .),/$2'c)@$F$*7',.'%*5#&,#$'&<$*$',/'.)'/8#<'&<,.='5/'%$*($#&'-5&#<,.=7'5.6'&<$'/$#).6'/&5=$ @,::'<5F$'5'(,.,&$'#)--).G-)6$'=5,.2'B8*&<$*-)*$7'+$#58/$')('&<$'Q$*)'()*-$6'+9'0&&'5.6 %&&')('&<$'/$#).6'/&5=$7'&<$'#)--).G-)6$'=5,.'@,::',.#*$5/$'@,&<'(*$>8$.#97'#58/,.='/)-$ )('&<$'.),/$'&)'-5E$',&/'@59'&)'),2'T,&<'#5*$(8:'6$/,=.7'&<,/'8.6$/,*5+:$'#)-%).$.&')('),'#5. +$'E$%&'/-5::2

9.8 High-Frequency Response of Differential Amplifiers 765

EXERCISE 9.28 !+%#$)//%'%*&)5,#5(7,)/)%'#67%2)/)%$#)*#HQ%'2)6%#;:<[#+56#0&&#=#
9.8.2 Analysis of the Active-Loaded MOS Amplifier T$'.$"&'#)./,6$*'&<$'(*$>8$.#9'*$/%)./$')('&<$'#8**$.&G-,**)*G:)56$6'JK0'6,(($*$.&,5:G%5,* #,*#8,&' /&86,$6' ,.' 0$#&,).' 4212' ?<$' #,*#8,&' ,/' /<)@.' ,.' B,=2' C2PZR5S' @,&<' &@)' #5%5#,&5.#$/ ,.6,#5&$6X'%37'@<,#<',/'&<$'&)&5:'#5%5#,&5.#$'5&'&<$',.%8&'.)6$')('&<$'#8**$.&'-,**)*7'5.6'%"7 @<,#<',/'&<$'&)&5:'#5%5#,&5.#$'5&'&<$')8&%8&'.)6$2';5%5#,&5.#$'%3',/'-5,.:9'()*-$6'+9'%-/P 5.6'%-/Y'+8&'5:/)',.#:86$/'%-.D7'%.?D7'5.6'%.?P7

% 3 = % -.I + % .?I + % .?M + % -/M + % -/Z

'RC2DPCS

;5%5#,&5.#$'%"',.#:86$/'%-.U7'%.?U7'%.?Y7'%-.Y'5/'@$::'5/'5.'5#&85:':)56'#5%5#,&5.#$'5.6O)*'&<$ ,.%8&'#5%5#,&5.#$')('5'/8+/$>8$.&'/&5=$'R%LS7

% " = % -.< + % .?< + % -.Z + % .?Z + % L

'RC2DYVS

?<$/$'&@)'#5%5#,&5.#$/'%*,-5*,:9'6$&$*-,.$'&<$'6$%$.6$.#$')('&<$'6,(($*$.&,5:'=5,.')('&<,/ 5-%:,(,$*').'(*$>8$.#92 N/',.6,#5&$6',.'B,=2'C2PZR5S'&<$',.%8&'6,(($*$.&,5:'/,=.5:');.',/'5%%:,$6',.'5'+5:5.#$6'(5/<,). 5.6'&<$')8&%8&'.)6$',/'/<)*&G#,*#8,&$6'&)'=*)8.6',.')*6$*'&)'6$&$*-,.$'&<$'&*5./#).68#&5.#$'132

1 gm3

Q3

Vg3

Q4 Id4

Cm

"Vid$2

Id1 # gm

Vid 2

Q1

Id2 # gm

Q2 0V (a)

Ro

,Gm, Io

Vid 2 !Vid$2

CL

gm 1g m 2 0

fP2 fZ (b)

Figure 9.37 '%(#9'%01%*23`'%67"*6%#5*5,36)6#"/#&+%#52&)@%.,"5$%$#\RD#$)//%'%*&)5,#5(7,)/)%':#'$(#!+%# "@%'5,,#&'5*62"*$12&5*2%#13#56#5#/1*2&)"*#"/#/'%01%*23:

f

766 Chapter 9 Frequency Response K+F,)8/:97'+$#58/$')('&<$')8&%8&'/<)*&'#,*#8,&7'%"'@,::'<5F$'.)'$(($#&').'132'?*5./,/&)*'PD'@,:: #).68#&'5'6*5,.'#8**$.&'/,=.5:')(' - 3 );. ⁄ <8 '@<,#<'(:)@/'&<*)8=<'&<$'6,)6$G#)..$#&$6'&*5./,/G &)*' PP' 5.6' &<8/' &<*)8=<' &<$' %5*5::$:' #)-+,.5&,).' )(' ( I ⁄ - 3M ) ' 5.6' %37' @<$*$' @$' <5F$ .$=:$#&$6'&<$'*$/,/&5.#$/'+,D'5.6'+,P'@<,#<'5*$'-8#<':5*=$*'&<5.' ( I ⁄ - 3M )8 '&<8/

- 3 ) ;. ⁄ < ) -M = [ ....................... - 3M + /% 3

'RC2DYDS

L.'*$/%)./$'&)')-P7'&*5./,/&)*'PY'#).68#&/'5'6*5,.'#8**$.&'(. Y7

- 3Z - 3 ) ;. ⁄ < . ( . Z = [ - 3Z ) -M = ............................. - 3M + /% 3 0,.#$'-3P'='-3Y7'&<,/'$>85&,).'*$68#$/'&)

- 3 ) ;. ⁄ < . ( .Z = ................... %3 . I + / ....... - 3M

'RC2DYUS

`)@7'5&'&<$')8&%8&'.)6$'&<$'&)&5:')8&%8&'#8**$.&'&<5&'(:)@/'&<*)8=<'&<$'/<)*&'#,*#8,&',/

( , = ( .Z + ( .< - 3 ) ;. ⁄ < . + - 3 ( ) ;. ⁄ < ) = ................... %3 . I + / ....... - 3M T$'#5.'&<8/')+&5,.' 1 3 '5/

%3 I ] / ........... (, <- 3M . # \ - 3 ....................... . 1 3 ≡ ...... %3 ) ;. I ] / ........ - 3M

'RC2DYPS

'RC2DYYS

!+168#56#%Q7%2&%$8#&+%#,"-./'%01%*23#@5,1%#"/#13#)6#%015,#&"#-3#"/#PI#5*$#P<:#P&#+)4+#/'%. 01%*2)%68#13#5201)'%6#5#7",%#5*$#5#U%'"8#&+%#/'%01%*2)%6#"/#-+)2+#5'% - 3M ! 2< # \ ............. . < π %3

'RC2DY1S

<- 3M ! T # \ ............. . < π %3

'RC2DY3S

5.6

?<5&' ,/7' &<$' Q$*)' (*$>8$.#9' ,/' &@,#$' &<5&' )(' &<$' %):$2' 0,.#$' %3' ,/' 5%%*)",-5&$:9' $>85:' &) % -/< ] % -/Z # \ <% -/ 7'@$'5:/)'<5F$ - 3M - 3M . # # # ...................... . # # #! H ⁄ < ! 2< # \ ............. < π %3 < π ( <% -/ )

'RC2DYZS

! T # # #! H

'RC2DY4S

5.6

9.8 High-Frequency Response of Differential Amplifiers 767

@<$*$' ! H ',/'&<$'8.,&9G=5,.'(*$>8$.#9')('&<$'JK0B!?'PP2'?<8/7'&<$'!"--+-/3+2./%&#/?.-+ )##8*'5&'F$*9'<,=<'(*$>8$.#,$/2'`$F$*&<$:$//7'&<$,*'$(($#&'#5.'+$'/,=.,(,#5.&2 B,=8*$'C2PZR+S'/<)@/'5'/E$&#<')('&<$'-5=.,&86$')('13'F$*/8/'(*$>8$.#92'L&',/',.&$*$/&,.= 5.6'8/$(8:'&)')+/$*F$'&<5&'&<$'%5&<')('&<$'/,=.5:'#8**$.&'%*)68#$6'+9'PD'<5/'5'&*5./($*'(8.#&,). 6,(($*$.&'(*)-'&<5&')('&<$'/,=.5:'#8**$.&'%*)68#$6'+9'PU2'L&',/'&<$'(,*/&'/,=.5:'&<5&'$.#)8.&$*/'%3 5.6'$"%$*,$.#$/'&<$'-,**)*'%):$2'?<,/')+/$*F5&,).':$56/'&)'5.',.&$*$/&,.='F,$@')('&<$'$(($#&')( %3').'&<$')F$*5::'&*5./#).68#&5.#$'13')('&<$'6,(($*$.&,5:'5-%:,(,$*2'N/'@$':$5*.$6',.'0$#&,). 4217'5&':)@'(*$>8$.#,$/'(.D',/'*$%:,#5&$6'+9'&<$'-,**)*' P M [ P Z ',.'&<$'6*5,.')('PY'5/'(.Y7'@<,#< 566/'&)'(.U'&)'%*)F,6$'5'(5#&)*G)(GU',.#*$5/$',.'13'R&<8/'-5E,.='13'$>85:'&)'-37'@<,#<',/'6)8+:$ &<$'F5:8$'5F5,:5+:$'@,&<)8&'&<$'#8**$.&'-,**)*S2'`)@7'5&'<,=<'(*$>8$.#,$/'%3'5#&/'5/'5'/<)*&'#,*G #8,&'#58/,.=')-P'&)'+$'Q$*)7'5.6'<$.#$'(.Y'@,::'+$'Q$*)7'*$68#,.='13'&)' - 3 ⁄ < 7'5/'+)*.$')8&'+9 &<$'/E$&#<',.'B,=2'C2PZR+S2 c5F,.=' 6$&$*-,.$6' &<$' /<)*&G#,*#8,&' )8&%8&' #8**$.&' (,7' @$' .)@' -8:&,%:9' ,&' +9' &<$' &)&5: ,-%$65.#$'+$&@$$.'&<$')8&%8&'.)6$'5.6'=*)8.6'&)'6$&$*-,.$'&<$')8&%8&'F):&5=$'),7 I #################################################### ) , # \ ( , ..................... I ..... ] /% " 0, 0, \ 1 3 ) ;. ........................ I ] /% " 0 , ?<8/7 %3 I ] / ........... ) <- 3M I . ........................ ......,. # \ ( - 3 0 , ) ....................... 'RC2DYCS ) ;. % 3 I ] /% " 0 , ....... . I]/ - 3M @<$*$ 0 , # \ + ,< || + ,Z

?<8/7',.'566,&,).'&)'&<$'%):$'5.6'Q$*)')('137'&<$'=5,.')('&<$'6,(($*$.&,5:'5-%:,(,$*'@,::'<5F$'5 %):$'@,&<'(*$>8$.#9' ! 2I 7 I ! 2I # \ ................... < π %" 0,

'RC2D1VS

?<,/7')('#)8*/$7',/'$.&,*$:9'$"%$#&$67'5.6',.'(5#&'&<,/')8&%8&'%):$',/')(&$.'6)-,.5.&7'$/%$#,5::9 @<$.'5':5*=$':)56'#5%5#,&5.#$',/'%*$/$.&2

Example 9.14 G"*6)$%'#5*#52&)@%.,"5$%$#\RD#$)//%'%*&)5,#5(7,)/)%'#"/#&+%#&37%#6+"-*#)*#9)4:#;:M[=5?:#P661(%#&+5& /"'#5,,#&'5*6)6&"'68#M/"#=#[:<#µ(SL:M^#µ(8#%-/#=#)56#21''%*&#(#=#L:<#(P8#5*$ MN[#µPS]<8# µF%,L#=#N^#µPS]<8# ) 47 &+%#>)56#21''%*"1'2%#+56#5*#"1&71&#'%6)6&5*2%#0&&#=#3#&+%#&'5*6)6&"'6#5&#&+%#"1&71&#*"$%8#&+%'%#)6#5#25752)&5*2% %L#"/#38#5*$#G\TT:#F&#)6#5,6" '%01)'%$#&"#/)*$#&+%#7",%6#5*$#U%'"#"/#4.#5*$#&+%#$"()*5*",%#"/#G\TT:

768 Chapter 9 Frequency Response

Example 9.14 continued

Solution D)*2%#(#=#L:<#(P8#%52+#"/#&+%#/"1'#&'5*6)6&"'6#)6#"7%'5&)*4#5#>)56#21''%*&#"/#ILL#µP:#!+168#/"'#PI 5*$#P<8 I [:< < ILL = ... × MN[ × .......... × ) N) < L:M^

-+)2+#,%5$6#&" )N) = L:I^#]

!+168

+ ,I

< × L:I - 3 = - 3I = - 3< = ................ = I:
9"'#PM#5*$#PZ#-%#+5@% I [:< < ILL = ... × N^ × .......... × ) N)M, Z < L:M^

!+168# )N)P7Y '=' V2PY'h7'

5*$ < × L:I - 3M = - 3Z = ................ = L:^#(PS] L:MZ ^ × L:M^ + ,M = + ,Z = ................... =
!+%#,"-./'%01%*23#@5,1%#"/#&+%#$)//%'%*&)5,#45)*#25*#>%#$%&%'()*%$#/'"( 4 . = - 3 ( + ,< || + ,Z ) = I:
!+%#,"-./'%01%*23#@5,1%#"/#&+%#2"(("*.("$%#45)*#25*#>%#$%&%'()*%$#/'"(#H0:#=N:IZ^′?#56 I 4 >3 = [ .................... <- 3M 0 && I = [ ............................. = [ L:LMM#]S] < × L:^ ×
!+%#,"-./'%01%*23#@5,1%#"/#&+%#G\TT#25*#*"-#>%#$%&%'()*%$#56 4. I<:M G\TT = ........... = ............. = M^; 4 >3 L:LMM

"'8 UV':)='P3C '=' 1D2P'6H

9.8 High-Frequency Response of Differential Amplifiers 769

!"#$%&%'()*%#&+%#7",%6#5*$#U%'"#"/#4.#-%#/)'6"(71&%#&+%#@5,1%6#"/#&+%#&-"#7%'&)*%*撘)&5*2%6 %3#5*$#%":#j6)*4#H0:#=;:IM;?8 %3'='%-.D'+'%.?D'+'%.?P'+'%-/P'+'%-/Y ='1'+'1'+'1'+'UV'+'UV'='11'(B

G5752)&5*2%#%"#)6#/"1*$#16)*4#H0:#=;:IZL?#56 %"'='%-.U'+'%.?U'+'%-.Y'+'%.?Y'+'%L ='1'+'1'+'1'+'1'+'U1'='Y1'(B

J"-8#&+%#7",%6#5*$#U%'"#"/#4.#25*#>%#/"1*$#/'"(#H06:#=;:IYL?8#=;:IZY?8#5*$#=;:IZ^?#56 I !2I = ................... < π %" 0, I = ............................................ < π × % " ( + ,< || + ,Z ) I .M = ........................................................................ [ IY < π × ZY × IL ( IN ||
!T =
!+16#&+%#$"()*5*",%#)6#&+5'"$12%$#>3#%"#5&#&+%#"1&71&#*"$%:#P6#%Q7%2&%$8#&+%#7",%#5*$#U%'"#"/ &+%#()''"'#5'%#5&#(12+#+)4+%'#/'%01%*2)%6: !+%#$"()*5*",%#"/#&+%#G\TT#)6#5&#&+%#,"25&)"*#"/#&+%#2"(("*.("$%.45)*#U%'"#)*&'"$12%$#>3 %&*$#0&&8#&+5&#)68 I !T = ........................ < π % && 0 && I . = ................................................................. [ I< M < π × L:< × IL ×
!+168#&+%#G\TT#>%4)*6#&"#$%2'%56%#5&#MI:N#\BU8#-+)2+#)6#(12+#,"-%'#&+5*#!2I:

EXERCISE 9.29 P#>)7",5'#21''%*&.()''"'.,"5$%$#$)//%'%*&)5,#5(7,)/)%'#)6#>)56%$#-)&+#5#21''%*"1'2%#(#=#I#(P: !+%#&'5*6)6&"'6#5'%#67%2)/)%$#&"#+5@%#|)4|#=#ILL#]:#!+%#&"&5,#25752)&5*2%#5&#&+%#"1&71&#*"$%#)6#< 79:#9)*$#&+%#$2#@5,1%#5*$#&+%#/'%01%*23#"/#&+%#$"()*5*&#+)4+./'%01%*23#7",%#"/#&+%#$)//%'%*&)5, @",&54%#45)*: Ans.
770 Chapter 9 Frequency Response

9.9 Other Wideband Amplifier Configurations ?<8/'(5*7'@$'<5F$'/&86,$6').$'@,6$+5.6'5-%:,(,$*'#).(,=8*5&,).X'&<$'#5/#)6$'5-%:,(,$*2';5/G #)6,.='#5.7')('#)8*/$7'+$'5%%:,$6'&)'6,(($*$.&,5:'5-%:,(,$*/'&)')+&5,.'@,6$+5.6'6,(($*$.&,5: 5-%:,(,#5&,).2' L.' &<,/' /$#&,).' @$' 6,/#8//' 5' .8-+$*' )(' )&<$*' #,*#8,&' #).(,=8*5&,)./' &<5&' 5*$ #5%5+:$')('5#<,$F,.='@,6$'+5.6@,6&
9.9.1 Obtaining Wideband Amplification by Source and Emitter Degeneration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

'RC2D1DS

0 , # # #+ , ( I ] - 3 0 / )

'RC2D1US

5.6'&<$')8&%8&'*$/,/&5.#$',/'=,F$.'+9

?<8/7'/)8*#$'6$=$.$*5&,).'*$68#$/'&<$'&*5./#).68#&5.#$'5.6',.#*$5/$/'&<$')8&%8&'*$/,/&5.#$ +9'&<$'/5-$'(5#&)*7' ( I ] - 3 0 / ) 2'?<$':)@G(*$>8$.#9'F):&5=$'=5,.'#5.'+$')+&5,.$6'5/ ) 4 5 # \ .......,. # \ [ 1 3 ( 0 , || 0 " )# \ [ 1 3 0′" ) 6)4

'RC2D1PS

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0 -. # = 0 6)4 =I + 1 3 0′" ? + 0′"

RC2D1YS

0′" = 0 " || 0 ,

RC2D11S

@<$*$

9.9 Other Wideband Amplifier Configurations

771

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772 Chapter 9 Frequency Response ?<$'()*-8:5'()*' 0 %" '#5.'+$'/$$.'&)'+$'/,-%:9

0 %" # = 0 " || 0 , # = 0 "′

RC2D13S

?<$'()*-8:5'()*' 0 -/ ',/'&<$'-)/&'6,((,#8:&'&)'6$*,F$7'5.6'&<$'6$*,F5&,).'/<)8:6'+$'%$*()*-$6 @,&<'&<$'<9+*,6G π '-)6$:'$"%:,#,&:9'8&,:,Q$62'?<$'*$/8:&',/

0 6)4 + 0 / . 0 -/ # # # .......................................... +, I + - 3 0 / ................ +, + 0"

RC2D1ZS

T<$.' 0 6)4 ',/'*$:5&,F$:9':5*=$7'&<$'(*$>8$.#9'*$/%)./$'@,::'+$'6)-,.5&$6'+9'&<$'J,::$* -8:&,%:,#5&,).')(' % -. 2'N.)&<$*'@59'()*'/59,.='&<,/',/'&<5&' % -. 0 -. '@,::'+$'&<$':5*=$/&')('&<$ &<*$$')%$.G#,*#8,&'&,-$'#)./&5.&/'&<5&'-5E$'8%' τ # 7

τ # # = % -/ 0 -/ + % -. 0 -. + % " 0 %"

RC2D14S

$.5+:,.='8/'&)'5%%*)",-5&$' τ # '5/

τ # # # #% -. 0 -.

RC2D1CS

I !# # # # ........................ < π % -. 0 -.

RC2D3VS

5.6'#)**$/%).6,.=:9'&)')+&5,.' !# '5/

J"-8#56# 0 / #)6#)*2'%56%$8#&+%#45)*#(54*)&1$%8# 4 5 # = 1 3 0′" 8#-),,#$%2'%56%8#2516)*4# 0 -. #&" $%2'%56%#=H0:#;:IYZ?8#-+)2+#)*#&1'*#2516%6#!##&"#)*2'%56%#=H0:#;:I^L?:#!"#+)4+,)4+&#&+%#&'5$%. "//#>%&-%%*#45)*#5*$#>5*$-)$&+#&+5&# 0 / #5//"'$6#&+%#$%6)4*%'8#,%#6)(7,)/3#&+%#%Q7'%66)"*#/"' 0 -. #)*#H0:#=;:IYZ?#>3#5661()*4#&+5&# 1 3 0′" $#I #5*$# 1 3 0 6)4 #$#I8 #

0 -. # # #1 3 0′" 0 6)4 = # 4 5 0 6)4 @<,#<'#5.'+$'/8+/&,&8&$6',.'!>2'RC2D3VS'&)')+&5,.

I !# # = .................................. < π % -. 0 6)4 4 5

RC2D3DS

@<,#<'F$*9'#:$5*:9'/<)@/'&<$'=5,.[+5.6@,6&<'&*56$G)((2'?<$'=5,.[+5.6@,6&<'%*)68#&'*$-5,./ #)./&5.&'5&

I < π % -. 0 6)4

#d5)*`>5*$-)$&+#7'"$12&# = 4 5 #!# = ........................

RC2D3US

9.9 Other Wideband Amplifier Configurations 773

L.'%*5#&,#$7'<)@$F$*7'&<$')&<$*'#5%5#,&5.#$/'@,::'%:59'5'*):$',.'6$&$*-,.,.=' !# 7'5.6'&<$'=5,.[ +5.6@,6&<'%*)68#&''@,::'6$#*$5/$'/)-$@<5&'5/' 0 / ',/',.#*$5/$62'

EXERCISE 9.30 G"*6)$%'# 5# GD# 5(7,)/)%'# +5@)*4# - 3# = <#(PS] 8# + , # = 5*$-)$&+#7'"$12&:#=>? T%7%5&#=5?#/"'#&+%#256%#)*#-+)2+#5#'%6)6&5*2%# 0 / #)6#2"**%2&%$#)*#6%')%6#-)&+#&+%#6"1'2%#&%'()*5,#-)&+ 5#@5,1%#6%,%2&%$#6"#&+5&#-3#0/#=#<#: Ans. #=5?#−?#−IL#]S]8#IL;#\BU8#I:I#dBU

9.9.2 The CD–CS, CC–CE and CD–CE Configurations L.'0$#&,).'Z232D'@$'6,/#8//$6'&<$'%$*()*-5.#$',-%*)F$-$.&/')+&5,.$6'+9'%*$#$6,.='&<$';0 5.6';!'5-%:,(,$*/'+9'5'+8(($*',-%:$-$.&$6'+9' 5';g')*'5';;'5-%:,(,$*7'5/',.'&<$'#,*#8,&/ /<)@.',.'B,=2'C2PC2'N'-5W)*'56F5.&5=$')('$5#<')('&<$/$'#,*#8,&/',/'@,6$*'+5.6@,6&<'&<5.'&<5& )+&5,.$6',.'&<$';0')*';!'/&5=$'5:).$2'?)'/$$'<)@'&<,/'#)-$/'5+)8&7'#)./,6$*'5/'5.'$"5-%:$ &<$';g[;0'5-%:,(,$*',.'B,='C2PCR5S'5.6'.)&$'&<5&'&<$';0'&*5./,/&)*' P < '@,::'/&,::'$"<,+,&'5 J,::$*' $(($#&' &<5&' *$/8:&/' ,.' 5' :5*=$' ,.%8&' #5%5#,&5.#$7' % )*< 7' +$&@$$.' ,&/' =5&$' 5.6' =*)8.62 c)@$F$*7'&<$'*$/,/&5.#$'&<5&'&<,/'#5%5#,&5.#$',.&$*5#&/'@,&<'@,::'+$'-8#<':)@$*'&<5.' 0 6)4 b &<$'+8(($*,.='5#&,).')('&<$'/)8*#$'()::)@$*'#58/$/'5'*$:5&,F$:9':)@'*$/,/&5.#$7'5%%*)",-5&$:9 $>85:'&)'5 I ⁄ - 3I 7'&)'5%%$5*'+$&@$$.'&<$'/)8*#$')(' P I '5.6'=*)8.6'5#*)//' % )*< 2 VDD

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774 Chapter 9 Frequency Response

Example 9.15 G"*6)$%'#5#GG`GH#5(7,)/)%'#612+#56#&+5&#)*#9)4:#;:M;=>?#-)&+#&+%#/",,"-)*4#67%2)/)25&)"*6V# ( I = ( < = I#(P 5*$#)$%*&)25,#&'5*6)6&"'6#-)&+# β# =#ILL8# !H # = ZLL #\BU8#5*$# % µ = #<#79 :#K%&#&+%#5(7,)/)%'#>% /%$#-)&+#5#6"1'2%# )6)4 #+5@)*4#5#'%6)6&5*2%# 0 6)4 # = Z#CΩ 8#5*$#5661(%#5#,"5$#'%6)6&5*2%#"/#Z#CΩ:#9)*$#&+% @",&54%#45)*# 4 5 8#5*$#%6&)(5&%#&+%#M.$O#/'%01%*238# !# :#G"(75'%#&+%#'%61,&6#-)&+#&+"6%#">&5)*%$#-)&+#5 GH#5(7,)/)%'#"7%'5&)*4#1*$%'#&+%#65(%#2"*$)&)"*6:#9"'#6)(7,)2)&38#*%4,%2&# +, #5*$# +L : Solution P*#%()&&%'#>)56#21''%*&#"/#I#(P8# P I #5*$# P < #+5@% - 3 # = ZL '-NOh + 8 # =
β

+ π # = ...... # = -3 -3 % π + % µ # = ...... # =

ωH

ILL ......... # = <:Y#CΩ ZL -3 .......... . < π !H [M

ZL × IL = ......................................^. # = IY:;#79 < π # × ZLL × IL % µ # = <#79 % π # = IM:;#79

!+%#@",&54%#45)*# 4 5 #25*#>%#$%&%'()*%$#/'"(#&+%#2)'21)+"-*#)*#9)4:#;:ZL=5?#56#/",,"-6V 0 )*< # = + π < # = <:Y#CΩ # 0 )* # = ( β I + I ) ( + 8I + 0 )*< ) = ILI ( L:L
!+168# ) ' 4 5 #h# .......,. # = [ I^L × L:;; × L:;N# = [ IYY#]S] ) 6)4

!"#$%&%'()*%# !# #-%#16%#&+%#(%&+"$#"/#"7%*.2)'21)&#&)(%#2"*6&5*&6:#9)41'%#;:ZL=>?#6+"-6#&+%#2)'. 21)&# -)&+# )6)4 # 6%&# &"# U%'"# 5*$# &+%# /"1'# 25752)&5*2%6# )*$)25&%$:# G5752)&5*2%# % µ I # 6%%6# 5# '%6)6&5*2% 0µ I 8 0 µ I # = 0 6)4 || 0 )* = Z ||
9.9 Other Wideband Amplifier Configurations 775

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!"# /)*$# &+%# '%6)6&5*2%# 0 π I # 6%%*# >3# 25752)&5*2%# % π I # -%# '%/%'# &"# &+%# 5*5,36)6# "/# &+% +)4+./'%01%*23#'%67"*6%#"/#&+%#%()&&%'#/",,"-%'#)*#D%2&)"*#;:[:<:#D7%2)/)25,,38#-%#5$57&#H0: =;:IMM?#&"#&+%#6)&15&)"*#+%'%#56#/",,"-6V 0 6)4 + 0 )*< . 0 π I # = ................................. 0 6)4 0 )*< . + ......... I + ....... + π I + 8I ZLLL +
776 Chapter 9 Frequency Response Example 9.15 continued

G5752)&5*2%# % π < #6%%6#5#'%6)6&5*2%# 0 π < 8# 0 π < = #0 )*< || 0 "1&I 0 6)4 '''''' = + π < || + 8I + .............. βI + I ZLLL '''''' =
G5752)&5*2%# % µ < #6%%6#5#'%6)6&5*2%# 0 µ < :#!"#$%&%'()*%# 0 µ < #-%#'%/%'#&"#&+%#5*5,36)6#"/#&+%#/'%01%*23 '%67"*6%#"/#&+%#GH#5(7,)/)%'#)*#D%2&)"*#;:Y#&"#">&5)* 0 µ < # = ( I + - 3< 0 " ) ( 0 )*< || 0 "1&I ) + 0 " ZLLL ''''''' = ( I + ZL × Z )
+ ZLLL

A%#*"-#25*#$%&%'()*%# τ # #/'"(#

τ# # = %µ I 0µ I + %π I 0π I + %µ < 0µ < + %π < 0π < ''''''' = < × M:;Z + IM:; × L:L^MZ + < × IZ:I + IM:; × L:L^M ''''''' = [:NN + L:NN +
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9"'#2"(75')6"*8#-%#%@5,15&%# 45 #5*$# !# #"/#5#GH#5(7,)/)%'#"7%'5&)*4#1*$%'#&+%#65(%#2"*$)&)"*6: T%/%'#&"#9)4:#;:ZL=2?:#!+%#@",&54%#45)*# 4 5 #)6#4)@%*#>3 0 )* . ( [-3 0" ) 4 5 = ..................... 0 )* + 0 6)4 +π . ( [-3 0" ) ' # = .................. + π + 0 6)4 <:Y '' = ................ ( [ ZL × Z ) <:Y + Z = [ ^I:Y#]S] 0 π # = + π || 0 6)4 # = <:Y || Z# = I:YZ#CΩ 0 µ # = ( I + - 3 0 " ) ( 0 6)4 || + π ) + 0 " = ( I + ZL × Z ) ( Z || <:Y ) + Z ='U1D2Z'EΩ

9.9 Other Wideband Amplifier Configurations 777

!+168

τ# # = %π 0π + %µ 0µ = IM:; × I:YZ + < ×
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778 Chapter 9 Frequency Response B,=2 C2YDR5S2DV' ?<$' :)@G(*$>8$.#9' 5.5:9/,/' )(' &<,/' #,*#8,&' ,.' 0$#&,).' Z232U' %*)F,6$/'()*' &<$ ,.%8&'*$/,/&5.#$7

0 )* # = ( β I + I ) ( + 8I + + 8< )

RC2D3PS

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0 )* # = <+ π

RC2D3YS

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) α< 0" ....,. # = .................. . # = I... - 0 ); + 8I + + 8< < 3 "

RC2D31S

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), 0 )* I ....... . # = ... .................... . (- 0 ) )6)4 < 0 )* + 0 6)4 3 "

RC2D33S

?<$' <,=8$.#9' 5.5:9/,/' ,/' ,::8/&*5&$6' ,.' B,=2' C2YUR5S2' c$*$' @$' <5F$' 6*5@.' &<$ <9+*,6Gπ'$>8,F5:$.&'#,*#8,&'()*'$5#<')(' P I '5.6' P < 2'M$#5::,.='&<5&'&<$'&@)'&*5./,/&)*/'5*$ )%$*5&,.='5&'$>85:'+,5/'#8**$.&/7'&<$,*'#)**$/%).6,.='-)6$:'#)-%).$.&/'@,::'+$'$>85:'R,2$27 + π I # = + π < 7' % π I # = % π < 7'$S2'T,&<'&<,/',.'-,.6'&<$'*$56$*'/<)8:6'+$'5+:$'&)'/$$'&<5&' )π I = [ )π < '5.6'&<$'<)*,Q).&5:':,.$'&<*)8=<'&<$'.)6$':5+$:$6'!',.'B,=2'C2YUR5S'#5.'+$'6$:$&$62'?<8/ &<$'#,*#8,&'*$68#$/'&)'&<5&',.'B,=2'C2YUR+S2'?<,/',/'5'F$*9'5&&*5#&,F$')8&#)-$'+$#58/$'&<$ #,*#8,&'/<)@/'#:$5*:9'&<$'&@)'%):$/'&<5&'6$&$*-,.$'&<$'<,=8$.#9'*$/%)./$X'?<$'%):$'5& &<$',.%8&7'@,&<'5'(*$>8$.#9' ! 2I 7',/

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RC2D3ZS

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RC2D34S

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9.10 Multistage Amplifier Examples 779

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(b) Figure 9.42 '%(#H01)@5,%*)'21)&#/"'#&+%#5(7,)/)%'#)*#9)4:#;:ZI=5?:#=$?#D)(7,)/)%$#%01)@5,%*)'21)&:#J"&%# &+5&#&+%#%01)@5,%*)'21)&6#)*#'%(#5*$##'$(#5,6"#577,3#&"#&+%#2)'21)+"-*#)*#9)4:#;:ZI=>?:#F*#5$$)&)"*8#&+%3#25*# >%#%56),3#5$57&%$#/"'#&+%#\RD9H!#2)'21)&#)*#9)4:#;:ZI=2?8##-)&+#<+π #%,)()*5&%$8#%π#'%7,52%$#-)&+#%-/8#%µ# '%7,52%$#-)&+#%-. 8#5*$#)π#'%7,52%$#-)&+#)-/:

EXERCISE 9.31 9"'#&+%#GG`GO#5(7,)/)%'#"/#9)4:#;:ZI=5?8#,%&#(#=#L:Y#(P8# β # = ILL 8# % π # = ^#79 8# % µ ' = <#79 8## 0 6)4 = IL#CΩ8#5*$# 0 " # = IL#CΩ :#9)*$#&+%#,"-./'%01%*23#"@%'5,,#@",&54%#45)*#45 8#&+%#/'%01%*2)%6#"/#&+% 7",%68#5*$#&+%#M.$O#/'%01%*23#!#:#9)*$#!##>"&+#%Q52&,3#5*$#16)*4#&+%#577'"Q)(5&%#/"'(1,5#)*#H0: =;:I^;?: Ans. YL#]S]W#^:Z#\BU#5*$#N#\BUW#!##>3#%Q52&#%@5,15&)"*#=#Z:^#\BUW#!##16)*4#H0:#=;:I^;?#= Y#\BU:

9.10 Multistage Amplifier Examples T$'#).#:86$'&<,/'#<5%&$*'@,&<'&<$'(*$>8$.#9G*$/%)./$'5.5:9/,/')('&<$'&@)'-8:&,/&5=$'5-%:,G (,$*/'@$'/&86,$6',.'0$#&,).'4232'N/'@$'/<5::'/$$7'&<$/$'5*$'*$:5&,F$:9'#)-%:$"'#,*#8,&/X''0,-G %:9'*$%:5#,.='$5#<'&*5./,/&)*'@,&<',&/'<,=8$.#97'$>8,F5:$.&G#,*#8,&'-)6$:'@,::'-5E$',& $"#$$6,.=:9'6,((,#8:&'()*'%$.#,:G5.6G%5%$*'5.5:9/,/7'5.6'@,::'-)/&'#$*&5,.:9'.)&':$56'&)'5.9 5.5:9/,/' 5.6' 6$/,=.' ,./,=<&2' M5&<$*7' @$' @,::' 8/$' &<$' E.)@:$6=$' 5.6' $"%$*,$.#$' @$' <5F$

780 Chapter 9 Frequency Response =5,.$6'&<*)8=<)8&'&<,/'#<5%&$*'&)'6$#,6$').'@59/'&)'/,-%:,(9'&<$'5.5:9/,/2'K8*')+W$#&,F$',/ -8:&,():6X'&)'+$'5+:$'&)'%,.%),.&'&<$'%5*&')*'%5*&/')('5'#,*#8,&'&<5&':,-,&',&/'<,=8$.#9 %$*()*-5.#$7'&)'8.6$*/&5.6'<)@'&<,/':,-,&5&,).'#)-$/'5+)8&7'&)')+&5,.'5.'$/&,-5&$')('&<$ PG6H'+5.6@,6&<' ! # 7'5.6'(,.5::9'5.6'-)/&',-%)*&5.&:97'&)'(,.6'@59/'&)',-%*)F$'&<$'6$/,=.')( &<$'#,*#8,&'/)'5/'&)'$"&$.6',&/'<,=8$.#9')%$*5&,).2' L&',/'8/$(8:'5&'&<,/'W8.#&8*$'&)'%),.&')8&'&<5&'#)-%8&$*'/,-8:5&,).'8/,.='e0%,#$'5.6'J8:&,/,,/'5'F$*9'F5:85+:$'&)):'()*'&<$'#,*#8,&'6$/,=.$*7'$/%$#,5::9'@<$.'(*$>8$.#9G*$/%)./$'5.5:9/,/',/ 8.6$*'#)./,6$*5&,).2'`$F$*&<$:$//7',&',/'5'&)):'&<5&'<5/'&)'+$'8/$6'W86,#,)8/:9'5.6'#$*&5,.:9'.)&'5/ 5'*$%:5#$-$.&'()*'5'(,*/&G#8&'%$.#,:G5.6G%5%$*'5.5:9/,/2';,*#8,&'/,-8:5&,).7'+9'8&,:,Q,.='/)%<,/&,G #5&$6'6$F,#$'-)6$:/7'@,::'$.5+:$'&<$'6$/,=.$*'&)')+&5,.'5'*$5/).5+:9'5##8*5&$'%*$6,#&,).')('@<5& &)'$"%$#&'5(&$*'&<$'#,*#8,&'<5/'+$$.'(5+*,#5&$62'L('&<$'$"%$#&$6'%$*()*-5.#$',/'8./5&,/(5#&)*97'&<$ 6$/,=.$*'@,::'&<$.'<5F$'&<$')%%)*&8.,&9'&)'5:&$*'&<$'6$/,=.'&)'-$$&'/%$#,(,#5&,)./2

9.10.1 Frequency Response of the Two-Stage CMOS Op Amp 9)41'%#;:ZM#6+"-6#&+%#&-".6&54%#G\RD#5(7,)/)%'#-%#6&1$)%$#)*#D%2&)"*#N:^:I:#O%/"'%#2"*. &)*1)*4#-)&+#&+)6#6%2&)"*8#-%#1'4%#&+%#'%5$%'#&"#'%@)%-#D%2&)"*#N:^:I#5*$#HQ5(7,%#N:Y:#!" 5*5,3U%#&+%#/'%01%*23#'%67"*6%#"/#&+%#&-".6&54%#"7#5(78#2"*6)$%'#)&6#6)(7,)/)%$#6(5,,.6)4*5, %01)@5,%*&# 2)'21)&# 6+"-*#)*# 9)4:# ;:ZZ:# B%'%# 13I# )6# &+%# &'5*62"*$12&5*2%# "/# &+%# )*71&# 6&54% =13I#=#-3I#=#-3%&-%%*#&+%#/)'6*$#6%2"*$#6&54%6

% I = % -.Z + % .?Z + % -.< + % .?< + % -/^ 13U',/'&<$'&*5./#).68#&5.#$')('&<$'/$#).6'/&5=$'R13U'='-33S7'0U',/'&<$')8&%8&'*$/,/&5.#$')('&<$ /$#).6'/&5=$' ( 0 < = + ,^ || + ,[ )8 '5.6'%U',/'&<$'&)&5:'#5%5#,&5.#$'5&'&<$')8&%8&'.)6$')('&<$')% 5-%

% < = % .?^ + % .?[ + % -.[ + % "

I

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Figure 9.43 !-".6&54%#G\RD#"7.5(7#2"*/)41'5&)"*:

D6

9.10 Multistage Amplifier Examples 781

CC

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D6

D2

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" Gm 1 Vid

C1 Vi2

R1

" Gm 2 Vi2

R2

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C2 Vo !

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) ;< . + /% I);< + /% % ( );< [ ), ) = L 1 3I );. + ...... 0I

RC2DZVS

T*,&,.='5'.)6$'$>85&,).'5&'.)6$'g3'9,$:6/

) 1 3< );< + ....,. + /% < ), + /% % =), [ );< ? = L 0<

RC2DZDS

?)'$:,-,.5&$');U'5.6'&<8/'6$&$*-,.$'),',.'&$*-/')(');.7'@$'8/$'!>2'RC2DZDS'&)'$"%*$//');U',. &$*-/')('),'5.6'/8+/&,&8&$'&<$'*$/8:&',.&)'!>2'RC2DZVS2'N(&$*'/)-$'/&*5,=<&()*@5*6'-5.,%8:5G &,)./'@$')+&5,.'&<$'5-%:,(,$*'&*5./($*'(8.#&,).

), 1 3I ( 1 3< [ /% % )0 I 0 < ...... . = ............................................................................................................................................................................................ < );. I + / [ % I 0 I + % < 0 < + % % ( 1 3< 0 I 0 < + 0 I + 0 < ) ] + / [ % I % < + % % ( % I + % < ) ]0 I 0 < RC2DZUS B,*/&'@$'.)&$'&<5&'()*'/'='V'R,2$27'6#S7'!>2'RC2DZUS'=,F$/ ) , ⁄ ) ;. = ( 1 3I 0 I ) ( 1 3< 0 < )8 '@<,#< ,/'@<5&'@$'/<)8:6'<5F$'$"%$#&$62'0$#).67'&<$'&*5./($*'(8.#&,).',.'!>2'RC2DZUS',.6,#5&$/'&<5& &<$'5-%:,(,$*'<5/'5'&*5./-,//,).'Q$*)'5&'/'='/T 7'@<,#<',/'6$&$*-,.$6'(*)-

1 3< [ / T % % = L ?<8/7

1 3< . / T = ........ %%

RC2DZPS

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1 %%

3< . ω T = ........

RC2DZYS

782 Chapter 9 Frequency Response N:/)7' &<$' 5-%:,(,$*' <5/' &@)' %):$/' &<5&' 5*$' &<$' *))&/' )(' &<$' 6$.)-,.5&)*' %):9.)-,5:' )( !>2 RC2DZUS2'L('&<$'(*$>8$.#,$/')('&<$'&@)'%):$/'5*$'6$.)&$6'ω2D'5.6'ω2U7'&<$.'&<$'6$.)-,.5&)* %):9.)-,5:'#5.'+$'$"%*$//$6'5/

I / / I /< * ( / ) = I + ........ I + ........ = I + / ........ + ........ + .................

ω 2I

ω 2<

ω 2I

ω 2<

ω 2I ω 2<

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/ /< * ( / )# # #I + ........ + .................

ω 2I

ω 2I ω 2<

RC2DZ1S

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I ω 2I = .............................................................................................. % I 0 I + % < 0 < + % % (1 3< 0 < 0 I + 0 I + 0 < )

I = ................................................................................................ 0 I [ % I + % % (I + 1 3< 0 < ) ] + 0 < ( % < + % % )

RC2DZ3S

T$'*$#)=.,Q$'&<$'(,*/&'&$*-',.'&<$'6$.)-,.5&)*'5/'5*,/,.='5&'&<$',.&$*(5#$'+$&@$$.'&<$'(,*/&'5.6 /$#).6'/&5=$/2'c$*$7'0D7'&<$')8&%8&'*$/,/&5.#$')('&<$'(,*/&'/&5=$7',/',.&$*5#&,.='@,&<'&<$'&)&5:'#5%5#G ,&5.#$'5&'&<$',.&$*(5#$2'?<$':5&&$*',/'&<$'/8-')('%D'5.6'&<$'J,::$*'#5%5#,&5.#$ % % ( I + 1 3< 0 < )8 @<,#<'*$/8:&/'(*)-'#)..$#&,.='%%',.'&<$'.$=5&,F$'($$6+5#E'%5&<')('&<$'/$#).6'/&5=$'@<)/$'=5,. ,/' 1 3< 0 < 2'`)@7'/,.#$'0D'5.6'0U'5*$'8/85::9')('#)-%5*5+:$'F5:8$7'@$'/$$'&<5&'&<$'(,*/&'&$*-',.'&<$ 6$.)-,.5&)*'@,::'+$'-8#<':5*=$*'&<5.'&<$'/$#).6'5.6'@$'#5.'5%%*)",-5&$'ω2D'5/

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ω 2I # # # ............................................................

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1 % %I %< + %% ( %I + %< )

3< % . ω 2< = ................................................

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1 %%

3I . ω : = ( 1 3I 0 I 1 3< 0 < ) ω 2I #h ........

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9.10 Multistage Amplifier Examples 783

1 3<

1 3<

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EXERCISE D9.32#G"*6)$%'#&+%#/'%01%*23#'%67"*6%#"/#&+%#"7#5(7#5*5,3U%$#)*#HQ5(7,%#N:Y:#K%&#%I#=#L:I#79#5*$#%<#= <#79:#9)*$#&+%#@5,1%#"/#%%#&+5&#'%61,&6#)*##!:#=#IL#\BU#5*$#@%')/3#&+5&# !:#)6#,"-%'#&+5*#!T#5*$#!2<:#T%25,, /'"(#&+%#'%61,&6#"/#HQ5(7,%#N:Y8#&+5&##13I#= 0.3 (Α/]#5*$# 1 # 3<#= 0.6 (Α/]. Ans. %%#=#Z:N#79W##!T#=#
9.10.2 Frequency Response of the Bipolar Op Amp of Section 8.6.2 T$'8*=$'&<$'*$56$*'&)'*$F,$@'0$#&,).'4232U'5.6'!"5-%:$/'423'5.6'42Z'+$()*$'/&869,.='&<,/ /$#&,).2'?<$'+,%):5*')%G5-%'#,*#8,&'/<)@.'$5*:,$*',.'B,=2'42YP',/'*5&<$*'#)-%:$"2'`$F$*&<$G :$//7',&',/'%)//,+:$'&)')+&5,.'5.'5%%*)",-5&$'$/&,-5&$')(',&/'<,=8$.#9'*$/%)./$2'B,=G 8*$' C2Y1R5S' /<)@/' 5.' 5%%*)",-5&$' $>8,F5:$.&' #,*#8,&' ()*' &<,/' %8*%)/$2' `)&$' &<5&' @$' <5F$ 8&,:,Q$6'&<$'$>8,F5:$.&'6,(($*$.&,5:'<5:(G#,*#8,&'#).#$%&7'@,&<'PU'*$%*$/$.&,.='&<$',.%8&'/&5=$ 5.6'P1'*$%*$/$.&,.='&<$'/$#).6'/&5=$2'T$')+/$*F$7')('#)8*/$7'&<5&'&<$'/$#).6'/&5=$',/'.)& /9--$&*,#5:7'5.6'/&*,#&:9'/%$5E,.='&<$'$>8,F5:$.&'<5:(G#,*#8,&'6)$/'.)&'5%%:92'`$F$*&<$:$//7 @$'8/$',&'5/'5.'5%%*)",-5&,).'/)'5/'&)')+&5,.'5'>8,#E'%$.#,:G5.6G%5%$*'$/&,-5&$')('&<$'6)-,G .5.&'<,=8$.#9'%):$')('&<$'5-%:,(,$*2'J)*$'%*$#,/$'*$/8:&/'#5.')('#)8*/$'+$')+&5,.$6 8/,.='#)-%8&$*'/,-8:5&,).'@,&<'0eL;!2 !"5-,.5&,).')('&<$'$>8,F5:$.&'#,*#8,&',.'B,=2'C2Y1R5S'*$F$5:/'&<5&',('&<$'*$/,/&5.#$')('&<$ /)8*#$')('/,=.5:');',/'/-5::7'&<$'<,=8$.#9':,-,&5&,).'@,::'.)&')##8*'5&'&<$',.%8&'+8&'*5&<$* 5&'&<$',.&$*(5#$'+$&@$$.'&<$'(,*/&'5.6'&<$'/$#).6'/&5=$/2'?<,/',/'+$#58/$'&<$'&)&5:'#5%5#,&5.#$'5& .)6$'N'@,::'+$'<,=<'5/'5'*$/8:&')('&<$'J,::$*'-8:&,%:,#5&,).')('%µ 12'N:/)7'&<$'&<,*6'/&5=$7'()*-$6 +9'&*5./,/&)*'PZ7'/<)8:6'$"<,+,&'=))6'<,=8$.#9'*$/%)./$7'/,.#$'PZ <5/'5':5*=$'$-,&&$*G 6$=$.$*5&,).'*$/,/&5.#$7'0P2'?<$'/5-$',/'5:/)'&*8$'()*'&<$'$-,&&$*G()::)@$*'/&5=$7'P42 ?)'6$&$*-,.$'&<$'(*$>8$.#9')('&<$'6)-,.5.&'%):$'&<5&',/'()*-$6'5&'&<$',.&$*(5#$'+$&@$$. PU' 5.6' P1' @$' /<)@' ,.' B,=2' C2Y1R+S' &<$' %$*&,.$.&' $>8,F5:$.&' #,*#8,&2' ?<$' &)&5:' *$/,/&5.#$ +$&@$$.'.)6$'N'5.6'=*)8.6'#5.'.)@'+$'()8.6'5/

0 %0 = 0 < || + ,< || + π Y 5.6'&<$'&)&5:'#5%5#,&5.#$',/'

% %0 = % µ < + % π Y + % µ Y ( I + - 3Y 0 "Y ) @<$*$

0 "Y = 0 M || + ,Y || 0 ;M ?<$'(*$>8$.#9')('&<$'%):$'#5.'+$'#5:#8:5&$6'(*)-'0$>'5.6'%$>'5/

I !2 = ...................... ' < π 0 %0 % %0

784 Chapter 9 Frequency Response

R4 R3 Q7

R2 Ri3 Q5

A Vi

Q8 R5

Q2

Vo R6

(a) A

C"2

ro2

gm2Vi

R2

r!5

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EXERCISE 9.33 f%&%'()*%#0%08#%%08#5*$#!2#/"'#&+%#5(7,)/)%'#)*#9)4:#N:ZM8#1&),)U)*4#&+%#/52&6#&+5&#P<#)6#>)56%$#5&#L:
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786 Chapter 9 Frequency Response

PROBLEMS CHAPTER 9

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CHAPTER 9

Section 9.3: High-Frequency Response of the CS and CE Amplifiers

CHAPTER 9

PROBLEMS

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9.53 P# 2"(("*.6"1'2%# \RD# 5(7,)/)%'8# -+"6%# %01)@5,%*& 2)'21)&#'%6%(>,%6#&+5&#)*#9)4:#;:I^=5?8#)6#&"#>%#%@5,15&%$#/"'#)&6 +)4+./'%01%*23# '%67"*6%:# 9"'# &+)6# 75'&)21,5'# $%6)4*8# 0 6)4 = I#\Ω 8# 0 1 = Z#\Ω 8# 0 "′ = ILL#CΩ 8# % -/ = L:<#79 8#%-.'' = L:I#798#5*$#-3 = L:Y#(PS]:#H6&)(5&%#&+%#()$>5*$#45)*#5*$ &+%#M.$O#/'%01%*23:

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CHAPTER 9

9.51 P#9H!#5(7,)/)%'#'%6%(>,)*4#&+5&#)*#HQ5(7,%#;:^8#-+%* "7%'5&%$#5&#,"-%'#21''%*&6#)*#5#+)4+%'.)(7%$5*2%#577,)25&)"*8 +56# 0 6)4 = ILL#CΩ 8# 0 )* = I:L#\Ω 8# - 3 = < # (PS]8 0 "′ = IY#CΩ 8# 5*$# % -/ = #% -. = I # 79:# 9)*$# &+%# ()$>5*$ @",&54%#45)*#45#5*$#&+%#M.$O#/'%01%*23#!#:

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Section 9.5: A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 9.60 P#GD#5(7,)/)%'#&+5*#>%#'%7'%6%*&%$#>3#&+%#%01)@5. ,%*&# 2)'21)&# "/# 9)4:# ;:I;# +56# % -/ = <#798 # % -. = L:I#798 % " = <#798 # - 3 = #Z#(PS]8 #5*$# 0′6)4 = 0 "′ = 5*$#45)*#45 8#&+%#)*71撘)&5*2%#%)*#16)*4#&+%#\),,%' 577'"Q)(5&)"*8#5*$#+%*2%#5*#%6&)(5&%#"/#&+%#M.$O#/'%01%*23#!#: P,6"8#">&5)*#5#>%&&%'#%6&)(5&%#"/#!#''16)*4#\),,%'g6#&+%"'%(: 9.61 P#GD#5(7,)/)%'#&+5*#>%#'%7'%6%*&%$#>3#&+%#%01)@5. ,%*&# 2)'21)&# "/# 9)4:# ;:I;# +56# % -/ = <#798 # % -. = L:I#798 % " = <#798 - 3 = Z#(PS]8 # 5*$# 0′6)4 = 0 "′ = 5*$#45#45)*8#5*$#%6&)(5&%#&+%#M.$O#/'%01%*23#!##16)*4 &+%#(%&+"$#"/#"7%*.2)'21)&#&)(%#2"*6&5*&6:#P,6"8#4)@%#&+%#7%'. 2%*&54%#2"*&')>1&)"*#&"# τ # #>3#%52+#"/#&+'%%#25752)&5*2%6:#=J"&% &+5&#&+)6#)6#&+%#65(%#5(7,)/)%'#2"*6)$%'%$#)*#E'">,%(#;:^L W#)/ 3"1#+5@%#6",@%$#E'">,%(#;:^L8#2"(75'%#3"1'#'%61,&6:? 9.62 P#GD#5(7,)/)%'#'%7'%6%*&%$#>3#&+%#%01)@5,%*)'21)&#"/ 9)4:# ;:I;# +56# % -/ = <#798 # % -. = #L:I, #798 # % " = #<#798 - 3 = #Z (PS]8#5*$# 0′6)4 = 0 "′ = &5)*%$# 16)*4# H06:# =;:;Z?# 5*$# =;:;Y?:# =J"&%# &+5&# &+)6# )6# &+% 65(%# 5(7,)/)%'# 2"*6)$%'%$# )*# E'">,%(6# ;:^L# 5*$# ;:^IW# )/# 3"1 +5@%# 6",@%$# %)&+%'# "'# >"&+# "/# &+%6%# 7'">,%(68# 2"(75'%# 3"1' '%61,&6:? 9.63 P#GD#5(7,)/)%'#'%7'%6%*&%$#>3#&+%#%01)@5,%*)'21)& "/# 9)4:# ;:I;# +56# % -/ = <#798 # % -. = L:I#798 # % " = <#798 - 3 = # Z (PS]8# 5*$ 0′ 6)4 = 5*$-)$&+#7'"$12&#/"'#%52+#"/#&+%#/",. ,"-)*4# @5,1%6# "/# 0 "′ V# Y# CΩ8# IL# CΩ8# 5*$# 5*$-)$&+#7'"$12&:#E'%6%*& 3"1'# '%61,&6# )*# &5>1,5'# /"'(8# 5*$# 2"((%*&# "*# &+%# 45)*` >5*$-)$&+#&'5$%."//: 9.64 P#2"(("*.%()&&%'#5(7,)/)%'#&+5*#>%#'%7'%6%*&%$ >3# &+%# %01)@5,%*&# 2)'21)&# "/# 9)4:# ;:
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CHAPTER 9

+ L = ILL#Ω8 # 0 "′ = Y#CΩ8 #5*$# 0 6)4 = I#CΩ: #9)*$#&+%#()$. >5*$# 45)*# 458# 5*$ 5*# %6&)(5&%# "/# &+%# M.$O# /'%01%*23# !# 16)*4# &+%# \),,%'# 577'"Q)(5&)"*:# P,6"8# ">&5)*# 5# >%&&%'# %6&). (5&%#"/#!##16)*4#\),,%'g6#&+%"'%(:

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794 Chapter 9 Frequency Response

(a)

9.73#G"*6)$%'#5#GD#5(7,)/)%'#,"5$%$#)*#5#21''%*"1'2%#-)&+ 5*#"1&71&#'%6)6&5*2%#%015,#&"# + , #"/#&+%#5(7,)/3)*4#&'5*6)6&"': !+%#5(7,)/)%'#)6#/%$#/'"(#5#6)4*5,#6"1'2%#-)&+# 0 6)4 # \ + , ⁄ < : !+%# &'5*6)6&"'# )6# >)56%$# &"# "7%'5&%# 5&# - 3 # \ < # (PS]# 5*$ + , \ )56#21''%*&#(#)*#&+%#%*&)'%#636&%( )6# '%$12%$# >3# 5# /52&"'# "/# Z8# 5*$# =))?# &+%# >)56# 21''%*&#(# )*# &+% %*&)'%#636&%(#)6#)*2'%56%$#>3#5#/52&"'#"/#Z:#T%(%(>%'#&+5&#>"&+ 0 6)4 #5*$# 0 " #-),,#2+5*4%#56# + , #2+5*4%6: 9.74 j6%#&+%#(%&+"$#"/#"7%*.2)'21)&#&)(%#2"*6&5*&6#&"#/)*$# ! # /"'# 5# GD# 5(7,)/)%'# /"'# -+)2+# - 3 # \ I:Y # (PS]8 % -/ # \ % -. # \ L:< # 798# + , # \ ? % " # \ IL 798#5*$#=2?# % " # \ YL 79:#G"(75'%#-)&+#&+%#@5,1%#"/ ! # #">&5)*%$#16)*4#&+%#\),,%'#577'"Q)(5&)"*:

Section 9.6: High-Frequency Response of the Common-Gate and Cascode Amplifiers

(b)

Figure P9.70

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9.75 P# Gd# 5(7,)/)%'# )6# 67%2)/)%$# &"# +5@%# % -/ = <#798 % -. = #L:I#798# % " = <#798 # - 3 = #Z#(PS]8 ## 0 6)4 =#I#CΩ 8 5*$# 0 "′ = 3# ) 6)4 #5*$ 06)4#5*$#/%%$)*4#5#,"5$#'%6)6&5*2%#0"#)*#75'5,,%,#-)&+#5#25752). &5*2%#%":# =5? D+"-#&+5&#/"'# + , = ∞ #&+%#2)'21)*#>%#6%75'5&%$#)*&" &-"#75'&6V#5*#)*71K'&#&+5'"$12%6#5#7",%#5&# I ! 2I = ..................................... < π % π ( 0 6)4 || + 8 ) 5*$#5*#"1&71K'&#&+5&#/"'(6#5#7",%#5& I ! 2< = ..................................... < π ( % µ + % " )0 " J"&%# &+5&# &+%6%# 5'%# &+%# >)7",5'# 2"1*&%'75'&6# "/# &+%# \RD %Q7'%66)"*6#)*#H06:#=;:IL;?#5*$#=;:IIL?: =>? H@5,15&%# ! 2I #5*$# ! 2< #5*$#+%*2%#">&5)*#5*#%6&)(5&%#/"' !## /"'# &+%# 256%# % π = #IZ#798 # % µ # = ##<#798 # % " = #I#798 ( % = ' I#(P8 # 0 6)4 = #I#CΩ 8#5*$# 0 " =''#IL#CΩ: #P,6"8#/)*$# !H "/#&+%#&'5*6)6&"': *9.77 G"*6)$%'# 5# Gd# 5(7,)/)%'# ,"5$%$# )*# 5# '%6)6&5*2% 0 " # \ + , # 5*$# /%$# -)&+# 5# 6)4*5,# 6"1'2%# +5@)*4# 5# '%6)6&5*2% 0 6)4 # \ + , ⁄ < :#P,6"#,%&# % " # \ % -/ :#j6%#&+%#(%&+"$#"/#"7%*. 2)'21)&#&)(%#2"*6&5*&6#&"#6+"-#&+5&#/"'# - 3 + , $ I 8#&+%#177%'#M. $O#/'%01%*23#)6#'%,5&%$#&"#&+%#\RD9H!# ! H #>3#&+%#577'"Q)(5&% %Q7'%66)"*

Problems 795

9.78 9"'#&+%#Gd#5(7,)/)%'#)*#HQ5(7,%#;:I<8#+"-#(12+#5$$). &)"*5,# 25752)&5*2%# 6+"1,$# >%# 2"**%2&%$# >%&-%%*# &+%# "1&71& *"$%#5*$#4'"1*$#&"#'%$12%# ! # #&"#MLL#\BUa

R+S !F5:85&$'!2D'5.6'!2U7'5.6'8/$'&<$'/8-G)(G&<$G/>85*$/'()*G -8:5' &)' $/&,-5&$' !#' ()*' &<$' 5-%:,(,$*' @,&<' (' =' D' -N7 % π = #Y#798 ' % µ = #Y#798 ' % >/ = % " = L8 ' β # =#ILL8 ' 5.6 + L = L ',. &<$'()::)@,.='&@)'#5/$/X =)? # 0 6)4 = I#CΩ R,,S 0 6)4 = IL#CΩ

*9.80 =5? G"*6)$%'# 5# GD# 5(7,)/)%'# +5@)*4# % -. = L:<#798 0 6)4 = 0 " = 5*$-)$&+#7'"$12&: R+S'L('5';f'/&5=$',/'#5/#56$6'@,&<'&<$';0'&*5./,/&)*',.'R5S'&)'#*$G 5&$'5'#5/#)6$'5-%:,(,$*7'6$&$*-,.$'&<$'.$@'F5:8$/')('457'!#7'5.6 =5,.[+5.6@,6&<'%*)68#&2'N//8-$'0"'*$-5,./'8.#<5.=$62'

9.84 P# Oe!# 2562"$%# 5(7,)/)%'# 16%6# &'5*6)6&"'6# /"'# -+)2+ β # \ ILL 8# ) 4 # \ ILL #]8# ! H # \ I #dBU8#5*$# % µ # \ L:I #79:#F& "7%'5&%6# 5&# 5# >)56# 21''%*&# "/# L:I# (P# >%&-%%*# 5# 6"1'2%# -)&+ 0 6)4 # \ + π # 5*$# 5# ,"5$# 0 " # \ β + , :# K%&# % " # \ % >/ # \ L # 5*$ /)*$#&+%#"@%'5,,#@",&54%#45)*#5&#$28# ! # 8#5*$# ! : :

D 9.81 F&#)6#'%01)'%$#&"#$%6)4*#5#2562"$%#5(7,)/)%'#&"#7'"@)$% 5#$2#45)*#"/#[Z#$O#-+%*#$')@%*#-)&+#5#,"-.'%6)6&5*2%#4%*%'5&"' 5*$# 1&),)U)*4# J\RD# &'5*6)6&"'6# /"'# -+)2+# )4 = #IL#]8 < µ 7 % ,L = %#"7%'5&%$:#9)*$#&+%#1*)&3.45)*#/'%01%*23#5*$#&+%#M.$O /'%01%*23:#F/#&+%#2562"$%#&'5*6)6&"'#)6#'%("@%$#5*$#0"#'%(5)*6 1*2+5*4%$8#-+5&#-),,#&+%#$2#45)*#>%2"(%a#

9.85 P# 6"1'2%# /",,"-%'# +56# - 3 = Y#(PS]8 + , = #1&)"*#"/#%52+#"/#&+%#&+'%%#25752)&5*2%6#&" &+%#&)(%.2"*6&5*&#τ#:

9.82 G"*6)$%'#5#>)7",5'#2562"$%#5(7,)/)%'#>)56%$#5#21''%*&#"/ I# (P:# !+%# &'5*6)6&"'6# 16%$# +5@%# β # =#ILL8 # + , = # ILL#CΩ8 % π = #IZ#798 # % µ = #<#798 # % >/ = #L8 # 5*$# +L# h# YL#Ω: # !+% 5(7,)/)%'#)6#/%$#-)&+#5#6)4*5,#6"1'2%#+5@)*4# 0 6)4 = #Z#CΩ: #!+% ,"5$#'%6)6&5*2%# 0 " # = <:Z#CΩ: #9)*$#&+%#,"-./'%01%*23#45)*#45 8 5*$#%6&)(5&%#&+%#@5,1%#"/#&+%#M.$O#/'%01%*23#!#:#

I ! # # # # ............................................................. % -/ < π 0 6)4 % -. ] ....................... . I ] - 3 0′"

*9.83 F*#&+)6#7'">,%(#-%#2"*6)$%'#&+%#/'%01%*23#'%67"*6%#"/ &+%# >)7",5'# 2562"$%# 5(7,)/)%'# )*# &+%# 256%# &+5&# +,# 25*# >% *%4,%2&%$: =5? T%/%'#&"#&+%#2)'21)&#)*#9)4:#;:MI8#5*$#*"&%#&+5&#&+%#&"&5,#'%6)6. &5*2%#>%&-%%*#&+%#2",,%2&"'#"/#PI#5*$#4'"1*$#-),,#>%#%015,#&" +8<8#-+)2+#)6#1615,,3#@%'3#6(5,,:#F&#/",,"-6#&+5&#&+%#7",%#)*&'". $12%$#5&#&+)6#*"$%#-),,#&37)25,,3#>%#5#@%'3#+)4+#/'%01%*23#5*$ &+16#-),,#+5@%#*%4,)4)>,%#%//%2&#"*#!#:#F,6"#/",,"-6#&+5&#&+% /'%01%*2)%6#"/#)*&%'%6&#&+%#45)*#/'"(#&+%#>56%#&"#&+%#2",,%2&"'#"/ PI#-),,#>%# [ - 3I + 8< # # # [ I: #j6%#&+)6#&"#/)*$#&+%#25752)&5*2%#5& &+%#)*71&#"/#PI#5*$#+%*2%#6+"-#&+5&#&+%#7",%#)*&'"$12%$#5&#&+% )*71&#*"$%#-),,#+5@%#5#/'%01%*23 I !2I # # # ................................................. < π 0′6)4 ( % π I + <% µ I )

Section 9.7: High-Frequency Response of the Source and Emitter Followers

9.86 j6)*4#&+%#%Q7'%66)"*#/"'#&+%#6"1'2%#/",,"-%'# ! # #)*#H0: =;:I<;?#6+"-#&+5&#/"'#6)&15&)"*6#)*#-+)2+# 0 6)4 #)6#,5'4%#5*$# 0 " )6#6(5,,8

9)*$# ! # #/"'#&+%#256%# 0 6)4 \ ILL #C Ω 8# 0 " \ I #C Ω 8# + , \ ?:# F*# 6)&15&)"*6# )*# -+)2+# 0 6)4 # )6 ,5'4%8# &+%# +)4+./'%01%*23# '%67"*6%# "/# &+%# 6"1'2%# /",,"-%'# )6 $%&%'()*%$# >3# &+%# ,"-.7566# 2)'21)&# /"'(%$# >3# 0 6)4 # 5*$# &+% )*71&# 25752)&5*2%:# P*# %6&)(5&%# "/# % )* # 25*# >%# ">&5)*%$# >3 16)*4#&+%#\),,%'#577'"Q)(5&)"*#&"#'%7,52%# % -/ #-)&+#5*#)*71& 25752)&5*2%# % 8G # \ % -/ ( I [ X ) # -+%'%# X# )6# &+%# 45)*# /'"( 45&%# &"# 6"1'2%:# j6)*4# &+%# ,"-./'%01%*23# @5,1%# "/ X# \ - 3 0′" S=I ] - 3 0′" ? # /)*$# % 8G # 5*$# +%*2%# % )* # 5*$# 5* %6&)(5&%# "/# ! # :# F6# &+)6# %6&)(5&%# +)4+%'# "'# ,"-%'# &+5*# &+5& ">&5)*%$#>3#&+%#(%&+"$#"/#"7%*.2)'21)&#&)(%#2"*6&5*&6a ' #5*$#+5@)*4 9.88 9"'#5*#%()&&%'#/",,"-%'#>)56%$#5&# ( % = I (P 0 6)4 = 0 " = I#CΩ8 # 5*$# 16)*4# 5# &'5*6)6&"'# 67%2)/)%$# &"# +5@% ! H = #<#dBU8 # % µ = #L:I#798 # + L = # ILL#Ω8 # β = # ILL8 # 5*$ )4 = #
PROBLEMS

9.79 B,.6'&<$'6#'=5,.'5.6'&<$'PG6H'(*$>8$.#9')('5'JK0'#5/G #)6$'5-%:,(,$*')%$*5&$6'5&' - 3 # \ I '-NOh'5.6' + , # \ YL E Ω 2 ?<$' JK0B!?/' <5F$' % -/ # \ ML ' (B7' % -. # \ IL ' (B7' 5.6 % .? # \ IL '(B2'?<$'5-%:,(,$*',/'($6'(*)-'5'/,=.5:'/)8*#$'@,&< 0 6)4 # \ ILL ' E Ω '5.6',/'#)..$#&$6'&)' 5':)56'*$/,/&5.#$')('U J Ω 2'?<$*$',/'5:/)'5':)56'#5%5#,&5.#$' % " ')('YV'(B2'

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CHAPTER 9

!# # \ !H ⁄ ( -3 +, )

CHAPTER 9

PROBLEMS

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'%$12%$#7"-%'#6177,38#2"*6)$%'5&)"*#)6#4)@%*#&"#'%$12)*4# ) N) &"# L:<# ]# -+),%# C%%7)*4# (# 1*2+5*4%$:# P661()*4# &+%# 21''%*&. 6"1'2%# 25752)&5*2%# &"# >%# $)'%2&,3# 7'"7"'&)"*5,# &"# &+%# $%@)2% -)$&+8#-+5&#)6#&+%#)(752&#"*# ! T #"/#&+)6#7'"7"6%$#2+5*4%a 9.93 T%7%5&#HQ%'2)6%#;:<[#/"'#&+%#6)&15&)"*#)*#-+)2+#&+%#>)56 21''%*&#)6#'%$12%$#&"#NL#µP#5*$# 0 * #)6#'5)6%$#&"#%#'5)6%$#/'"(#
K%&# β = ILL8 # ! H # = ZLL#\BU8 #5*$# % µ = <#79:

9.94 P#Oe!#$)//%'%*&)5,#5(7,)/)%'#"7%'5&)*4#-)&+#5#I.(P#21'. '%*"1'2%#16%6#&'5*6)6&"'6#/"'#-+)2+# β#=#ILL8#!H#=#^LL#\BU8 %µ#=#L:Y#798#5*$#+L#=#ILL#Ω:#H52+#"/#&+%#2",,%2&"'#'%6)6&5*2%6#)6 IL#CΩ8#5*$#+,#)6#@%'3#,5'4%:#!+%#5(7,)/)%'#)6#/%$#)*#5#63((%&'). 25,#/56+)"*#-)&+#5#6"1'2%#'%6)6&5*2%#"/#IL#CΩ#)*#6%')%6#-)&+#%52+ "/#&+%#&-"#)*71&#&%'()*5,6:

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=5? DC%&2+#&+%#$)//%'%*&)5,#+5,/.2)'21)*$#)&6#+)4+./'%01%*23 %01)@5,%*)'21)&:# =>? f%&%'()*%#&+%#,"-./'%01%*23#@5,1%#"/#&+%#"@%'5,,#$)//%'. %*&)5,#45)*: =2? j6%# &+%# \),,%'# 577'"Q)(5&)"*# &"# $%&%'()*%# &+%# )*71& 25752)&5*2%#5*$#+%*2%#%6&)(5&%#&+%#M.$O#/'%01%*23#!##5*$ &+%#45)*`>5*$-)$&+#7'"$12&: 9.95 P# $)//%'%*&)5,# 5(7,)/)%'# )6# >)56%$# >3# 5# 21''%*&# 6"1'2% +5@)*4#5*#"1&71&#'%6)6&5*2%#"/#I#\Ω#5*$#5*#"1&71撘)&5*2% "/# I# 79:# !+%# $)//%'%*&)5,# 45)*# %Q+)>)&6# 5# $"()*5*&# 7",%# 5& < \BU:#A+5'%#&+%#7",%6#"/#&+%#G\TTa 9.96 P# 21''%*&.()''"'.,"5$%$# \RD# $)//%'%*&)5,# 5(7,)/)%' )6#>)56%$#-)&+#5#21''%*"1'2%#(#=#L:<#(P:#!+%#&-"#J\RD &'5*6)6&"'6#"/#&+%#$)//%'%*&)5,#75)'#5'%#"7%'5&)*4#5&#)N)#=#L:< ]8#5*$#&+%#E\RD#$%@)2%6#"/#&+%#()''"'#5'%#"7%'5&)*4#5&#s)N) s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⁄ <π% " : #9"' ) 4 # \
Section 9.9: Other Wideband Amplifier Configurations 9.98 P#GD#5(7,)/)%'#)6#67%2)/)%$#&"#+5@%#-3#h#Y#(PS]8#+,#h ZL#CΩ, %-/#h#<#798#%-.#h#L:I#798#%"#h#I#798#0/;-#h#
Problems

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PROBLEMS

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PROBLEMS

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CHAPTER 10

Feedback

Introduction 10.1

803

The General Feedback Structure

10.2 Some Properties of Negative Feedback 809

804

10.8 Summary of the Feedback Analysis Method 863 10.9 Determining the Loop Gain 10.10 The Stability Problem

863

868

10.3 The Four Basic Feedback Topologies 814

10.11 Effect of Feedback on the Amplifier Poles 870

10.4 The Feedback Voltage Amplifier (Series—Shunt) 823

10.12 Stability Study Using Bode Plots

10.5 The Feedback Transconductance Amplifier (Series—Series) 834 10.6 The Feedback Transresistance Amplifier (Shunt—Shunt) 846 10.7 The Feedback Current Amplifier (Shunt—Series) 855

10.13 Frequency Compensation Summary

890

Problems

890

884

879

IN THIS CHAPTER YOU WILL LEARN 1. The general structure of the negative-feedback amplifier and the basic principle that underlies its operation. 2. The advantages of negative feedback, how these come about, and at what cost. 3. The appropriate feedback topology to employ with each of the four amplifier types: voltage, current, transconductance, and transresistance amplifiers. 4. An intuitive and insightful approach for the analysis of practical feedbackamplifier circuits. 5. Why and how negative-feedback amplifiers can become unstable (i.e., oscillate) and how to design the circuit to ensure stable performance.

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10.1 The General Feedback Structure ?%0-2*!@A9@!&#.;&!"#*!5$&%3!&"2-3"-2*!./!$!/**65$3)!$(4,%/%*29!B$"#*2!"#$1!&#.;%10!+.,"$0*& $16!3-22*1"&'!?%09!@A9@!%&!$!/&#!$6726.8(*&$#+$0'(;#*2*!*$3#!./!"#*!C-$1"%"%*&!8!3$1!2*42*8 &*1"!*%"#*2!$!+.,"$0*!.2!$!3-22*1"!&%01$,9!D#*!16"$;2116!$(4,%/%*2!#$&!$!0$%1!?E!"#-&!%"&!.-"4-" 81!%&!2*,$"*6!".!"#*!%14-"!8%!57

8 1 = ?8 %

Source

Σ

A

%QAT5AR

Load

Figure 10.1 F*1*2$,!&"2-3"-2*!./!"#*!/**65$3)!$(4,%/%*29!D#%&!%&!$!&%01$,8/,.;!6%$02$('!$16!"#*!C-$1"%"%*&!8 2*42*&*1"!*%"#*2!+.,"$0*!.2!3-22*1"!&%01$,&9

10.1 The General Feedback Structure

M'-%"9$&9$%81%)#%1-2%$"%$'-%,"+2%+#%;-,,%+#%$"%+%1--23+*4%/-$;"048%;')*'%&0"29*-#%+%#+.&,-%"1 $'-%"9$&9$5%M')#%#+.&,-%84%)#%0-,+$-2%$"%81%3(%$'-%2""*3$45(2$4%.+%β8

84 = β 8 1

%QAT5CR

M'-%1--23+*4%#)7/+,%84%)#%#/9&3+0&".%10".%$'-%#"90*-%#)7/+,%8#8%;')*'%)#%$'-%)/&9$%$"%$'-%*".K &,-$-%1--23+*4%+.&,)1)-08A%$"%&0"29*-%$'-%#)7/+,%8%8%;')*'%)#%$'-%)/&9$%$"%$'-%3+#)*%+.&,)1)-08

8 % = 8 # X 84

%QAT5UR

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

8 ? ? 4 ≡ 88881 = 8888888888888888 8# @ + ?β

!:@A9G<

M'-%F9+/$)$(%?β%)#%*+,,-2%$'-%6..-(#$&!8%+%/+.-%$'+$%1",,";#%10".%H)75%AT5A5%H"0%$'-%1--2K 3+*4%$"%3-%/-7+$):-8%$'-%,""&%7+)/%?β%.9#$%3-%&"#)$):-V%$'+$%)#8%$'-%1--23+*4%#)7/+,%84%#'"9,2 '+:-%$'-%#+.-%#)7/%+#%8#8%$'9#%0-#9,$)/7%)/%+%#.+,,-0%2)11-0-/*-%#)7/+,%8%5%?F9+$)"/%QAT5WR%)/2)K *+$-#%$'+$%1"0%&"#)$):-%?β%$'-%#$&!(8&%9(2""*3$45%?4%;),,%3-%#.+,,-0%$'+/%$'-%.-"!76..-(#$&! ?%3(%+%1+*$"0%-F9+,%$"%A%+%?β8%;')*'%)#%*+,,-2%$'-%$0.1!%(.2(2""*3$455 618%+#%)#%$'-%*+#-%)/%.+/(%*)0*9)$#8%$'-%,""&%7+)/%?β%)#%,+07-8%?β%!%A8%$'-/%10".%?F5%QAT5WR )$%1",,";#%$'+$ @ ?4(! 888 ( !:@A9H<

β

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
?β 84 = 8888888888888888 8 # @ + ?β

@

%QAT5PR

K1!*$2,%*2!3#$4"*2&'!;*!-&*6!"#*!&-5&32%4"!O&%0P!/.2!C-$1"%"%*&!$&&.3%$"*6!;%"#!"#*!&%01$,!&.-23*!:*909'!v&%0 $16!-&%0<9!L*!6%6!"#$"!".!$+.%6!3.1/-&%.1!;%"#!"#*!&-5&32%4"!O#'P!;#%3#!%&!-&-$,,7!-&*6!;%"#!?QD&!".!6*8 1."*!C-$1"%"%*&!$&&.3%$"*6!;%"#!"#*!&.-23*!"*2(%1$,!./!"#*!"2$1&%&".29!R"!"#%&!4.%1"'!#.;*+*2'!%"!%&!*>4*3"*6 "#$"!2*$6*2&!#$+*!5*3.(*!&-//%3%*1",7!/$(%,%$2!;%"#!"#*!&-5S*3"!"#$"!"#*!4.&&%5%,%"7!./!3.1/-&%.1!%&!(%18 %($,9!D#*2*/.2*'!;*!;%,,!2*+*2"!".!-&%10!"#*!&%(4,*2!&-5&32%4"!#!/.2!&%01$,8&.-23*!C-$1"%"%*&9

805

806 Chapter 10 Feedback M'9#%1"0%?β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

@ 8 % = 8888888888888888 8 # %QAT5OR @ + ?β 10".%;')*'%;-%*+/%:-0)1(%$'+$%1"0% ?β% !%A8%8%%3-*".-#%:-0(%#.+,,5%Y3#-0:-%$'+$%/-7+$):-

1--23+*4%0-29*-#%$'-%#)7/+,%$'+$%+&&-+0#%+$%$'-%)/&9$%$-0.)/+,#%"1%$'-%3+#)*%+.&,)1)-0%3(%$'+."9/$%"1%1--23+*48%QA%+%?β R5%J#%;),,%3-%#--/%,+$-08%)$%)#%$')#%0-29*$)"/%"1%)/&9$%#)7/+,%$'+$ 0-#9,$#%)/%$'-%)/*0-+#-2%,)/-+0)$(%"1%$'-%1--23+*4%+.&,)1)-05C

Example 10.1 M'-% /"/)/:-0$)/7% "&K+.&% *"/1)790+$)"/% #'";/% )/% H)75% AT5CQ+R% &0":)2-#% +% 2)0-*$% ).&,-.-/$+$)"/% "1% $'1--23+*4%,""&%"1%H)75%AT5A5 Rs #

Vo

A Vs

"

# "

RL

R2 R1

(a)

Rs Vo

# Vi Vs

# "

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# "

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R2 # Vf

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Figure 10.2 :$$(4,*!@A9@9!:3$(4,*&!./!"#%&I!$66%10!$!2*&%&"$13*!-"!%1!"#*!*(%""*2!./!$!MQ!$(4,%/%*2 :.2!$!2*&%&"$13*!-#!%1!"#*!&.-23*!./!$!MJ!$(4,%/%*2
10.1 The General Feedback Structure

:$42*&&%.1!/.2 "#*!/**65$3)!/$3".2!β9 :5
Solution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β%10". C -@ β ≡ 888884 a 88888888888888888 8 C1 -@ b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⁄ - N %+/2%/"$%"/%$'-%+3#",9$-%:+,9-#%"1% - @ %+/2% - N 5 Q3R%M'-%*,"#-2K,""&%7+)/% ? 4 %)#%7):-/%3( ? 8 ? 4 a 888888888888888 @ b ?β M"%.+4-% ? 4 %/-+0,(%)/2-&-/2-/$%"1%?8%;-%.9#$%-/#90-%$'+$%$'-%,""&%7+)/%?β%)#%.9*'%,+07-0%$'+/%9/)$(8 ?β ! @ -@ 8 !@ ? 88888888888888888 -@ b -N E)/*-%9/2-0%#9*'%+%*"/2)$)"/8 -@ b -N @ 8 a @ b 88888N ? 4 ! 888 a 88888888888888888 -@ β -@ $'-%*"/2)$)"/%*+/%3-%#$+$-2%+# ? ! ?4 G

Q*R%H"0% ? a @A %_`_%+/2% ? 4 a @A %_`_8%;-%#--%$'+$% ? ! ? 4 8%$'9#%;-%*+/%#-,-*$% - @ %+/2% - N %$"%"3$+)/ @ β a 88888 a A9@ ?4

807

808 Chapter 10 Feedback

Example 10.1 continued

M'9#8 @ 888 a @ b 88888N a ? 4 a @A β -@ ;')*'%()-,2# -N ⁄ -@ a X J%."0-%-G+*$%:+,9-%1"0%$'-%0+$)"% - N ⁄ - @ %*+/%3-%"3$+)/-2%10". ? 8 ? 4 a 888888888888888 @ b ?β G

@A @A a 88888888888888888888 8 G @ b @A β ;')*'%0-#9,$#%)/

β a A9AXXX +/28 -N 88888 a X9A@ -@ Q2R%M'-%+."9/$%"1%1--23+*4%)#% G

? @A @ b ? β a 88888 a 88888888 a @AAA ?4 @A ;')*'%)#%PT%2=5 Q-R%H"0% C # a @ %_8 C 1 a ? 4 C # a @A × @ a @A !T C 4 a β C 1 a A9AXXX × @A a A9XXX !T C @A C % a 888881 a 8888888G8 a A9AA@T ! ? @A Z"$-% $'+$% )1% ;-% '+2% 9#-2% $'-% +&&0"G).+$-% :+,9-% "1% β a A9@8% ;-% ;"9,2% '+:-% "3$+)/-2% C 4 a @% _% +/2 C % a A %_5 Q1R%61%?%2-*0-+#-#%3(%CTc8%$'9#%3-*".)/7% G

? a A9Y × @A !TUT $'-%:+,9-%"1% ? 4 %3-*".-# G

A9Y × @A 8 a X9XXZH !TUT ? 4 a 88888888888888888888888888888888888888888888888888888 G @ b A9Y × @A × A9AXXX $'+$%)#8%)$%2-*0-+#-#%3(%T5TCdc8%;')*'%)#%,";-0%$'+/%$'-%&-0*-/$+7-%*'+/7-%)/%?%3(%+&&0"G).+$-,(%+%1+*$"0 ( @ b ? β )5

10.2 Some Properties of Negative Feedback

EXERCISES 10.1

B*4*$"!Q>$(4,*!@A9@'!:3
10.2 B*4*$"!Q>$(4,*!@A9@'!:3
10.2 Some Properties of Negative Feedback M'-%&0"&-0$)-#%"1%/-7+$):-%1--23+*4%;-0-%.-/$)"/-2%)/%$'-%6/$0"29*$)"/5%6/%$'-%1",,";)/78 ;-%#'+,,%*"/#)2-0%#".-%"1%$'-#-%&0"&-0$)-#%)/%."0-%2-$+),5

10.2.1 Gain Desensitivity M'-%-11-*$%"1%/-7+$):-%1--23+*4%"/%2-#-/#)$)L)/7%$'-%*,"#-2K,""&%7+)/%;+#%2-."/#$0+$-2%)/ ?G+.&,-%AT5A8%;'-0-%;-%#+;%$'+$%+%CTc%0-29*$)"/%)/%$'-%7+)/%"1%$'-%3+#)*%+.&,)1)-0%7+:0)#-% $"%"/,(%+% T5TCdc%0-29*$)"/% )/%$'-% 7+)/%"1% $'-% *,"#-2K,""&% +.&,)1)-05% M')#% #-/#)$):)$(K 0-29*$)"/%&0"&-0$(%*+/%3-%+/+,($)*+,,(%-#$+3,)#'-2%+#%1",,";#5 J##9.-%$'+$%β%)#%*"/#$+/$5%M+4)/7%2)11-0-/$)+,#%"1%3"$'%#)2-#%"1%%?F5%QAT5WR%0-#9,$#%)/

.? .?4 = 88888888888888888888888N (@ + ?β)

%QAT5DR

e):)2)/7%?F5%QAT5DR%3(%?F5%QAT5WR%()-,2#

.? @ .? 888888884 = 888888888888888888888 8888888 ?4 (@ + ?β) ?

%QAT5BR

;#%3#!&$7&!"#$"!"#*!4*23*1"$0*!3#$10*!%1!?4!:6-*!".!+$2%$"%.1&!%1!&.(*!3%23-%"!4$2$(*"*2
EXERCISE 10.3 R1!$(4,%/%*2!;%"#!$!1.(%1$,!0$%1! ? a @AAA !TUT!*>#%5%"&!$!0$%1!3#$10*!./!@AW!$&!"#*!.4*2$"%10 "*(4*2$"-2*!3#$10*&!/2.(! NH° M!".! ZH°M9!K/!%"!%&!2*C-%2*6!".!3.1&"2$%1!"#*!3#$10*!".!A9@W!57!$48 4,7%10!1*0$"%+*!/**65$3)'!;#$"!%&!"#*!,$20*&"!3,.&*68,..4!0$%1!4.&&%5,*V!K/!"#2**!./!"#*&*!/**65$3) $(4,%/%*2&!$2*!4,$3*6!%1!3$&3$6*'!;#$"!.+*2$,,!0$%1!$16!0$%1!&"$5%,%"7!$2*!$3#%*+*6V Ans. @A! TUTE! @AAA! TUT'! ;%"#! $! ($>%(-(! +$2%$5%,%"7! ./! A9\W! .+*2! "#*! &4*3%/%*6! "*(4*2$"-2* 2$10*9

809

810 Chapter 10 Feedback

10.2.2 Bandwidth Extension @"/#)2-0%+/%+.&,)1)-0%;'"#-%')7'K10-F9-/*(%0-#&"/#-%)#%*'+0+*$-0)L-2%3(%+%#)/7,-%&",-5%6$# 7+)/%+$%.)2%+/2%')7'%10-F9-/*)-#%*+/%3-%-G&0-##-2%+#

?E 8 ? ( # ) = 888888888888888888888 @ + # ⁄ ωF

%QAT5ATR

;'-0-%?E%2-/"$-#%$'-%.)23+/2%7+)/%+/2%ω F%)#%$'-%9&&-0%UK2=%10-F9-/*(5%J&&,)*+$)"/%"1%/-7K +$):-% 1--23+*48% ;)$'% +% 10-F9-/*(K)/2-&-/2-/$% 1+*$"0% β8% +0"9/2% $')#% +.&,)1)-0% 0-#9,$#% )/% + *,"#-2K,""&%7+)/%?4 Q#R%7):-/%3(

?(#) ?4 ( # ) = 888888888888888888888888 @ + β?(#) E93#$)$9$)/7%1"0%?Q#R%10".%?F5%QAT5ATR%0-#9,$#8%+1$-0%+%,)$$,-%.+/)&9,+$)"/8%)/

?E ⁄ ( @ + ?E β ) ? 4 ( # ) = 88888888888888888888888888888888888888888888888 @ + # ⁄ ωF ( @ + ?E β )

%QAT5AAR

M'9#%$'-%1--23+*4%+.&,)1)-0%;),,%'+:-%+%.)23+/2%7+)/%"1% ? E ⁄ ( @ + ? E β ) %+/2%+/%9&&-0%UK 2=%10-F9-/*(%ωF4% 7):-/%3(

ω F4 = ω F ( @ + ?E β )

%QAT5ACR

6$% 1",,";#% $'+$% $'-% 9&&-0% UK2=% 10-F9-/*(% )#% )/*0-+#-2% 3(% +% 1+*$"0% -F9+,% $"% $'-% +."9/$% "1 1--23+*45 E).),+0,(8%)$%*+/%3-%#'";/%$'+$%)1%$'-%"&-/K,""&%7+)/%)#%*'+0+*$-0)L-2%3(%+%2".)/+/$%,";K 10-F9-/*(%&",-%7):)/7%0)#-%$"%+%,";-0%UK2=%10-F9-/*(% ωD8%$'-/%$'-%1--23+*4%+.&,)1)-0%;),, '+:-%+%,";-0%UK2=%10-F9-/*(%ωD4 8

ωD ω D4 = 8888888888888888888 @ + ?E β

%QAT5AUR

Z"$-%$'+$%$'-%+.&,)1)-0%3+/2;)2$'%)#%)/*0-+#-2%3(%$'-%#+.-%1+*$"0%3(%;')*'%)$#%.)23+/2 7+)/%)#%2-*0-+#-28%A+%$&+%$%$*(&)"(*+%$G9+$.:%.&)(631./0&(+&(+(01$#&+$&(<+2/"5%M')#%&")/$%)# 190$'-0%),,9#$0+$-2%3(%$'-%="2-%f,"$%)/%H)75%AT5U5 H)/+,,(8%/"$-%$'+$%$'-%+*$)"/%"1%/-7+$):-%1--23+*4%)/%-G$-/2)/7%$'-%+.&,)1)-0%3+/2;)2$' #'"9,2%/"$%3-%#90&0)#)/7I%Z-7+$):-%1--23+*4%;"04#%$"%.)/).)L-%$'-%*'+/7-%)/%7+)/%.+7/)K $92-8%)/*,92)/7%)$#%*'+/7-%;)$'%10-F9-/*(5(

EXERCISE 10.4 M.1&%6*2!"#*!1.1%1+*2"%10!.48$(4!3%23-%"!./!Q>$(4,*!@A9@9!]*"!"#*!.4*18,..4!0$%1!?!#$+*!$!,.;8/2*8 C-*137!+$,-*!./!@AG!$16!$!-1%/.2(!^_86[U.3"$+*!2.,,.//!$"!#%0#!/2*C-*13%*&!;%"#!$!\86[!/2*C-*137 ./!@AA!`=9!?%16!"#*!,.;8/2*C-*137!0$%1!$16!"#*!-44*2!\86[!/2*C-*137!./!$!3,.&*68,..4!$(4,%/%*2 ;%"#!-@!=!@!)Ω!$16!-N!=!X!)Ω9 Ans. X9XX!TUTE!@AA9@!)`=

10.2 Some Properties of Negative Feedback

A Gain 20 log (AM) (dB) #20 dB/decade "20 dB/decade

20 log (1 # AM b) 20 log (AMf) Af

log (1 # AM b)

fLf

fL

fL fLf $ " 1 # AM b

log (1 # AM b)

fH AM AMf $ " 1 # AM b

fHf

f (log scale)

fHf $ fH (1 # AM b)

Figure 10.3 R44,%3$"%.1!./!1*0$"%+*!/**65$3)!2*6-3*&!"#*!(%65$16!0$%1'!%132*$&*&!4F'!$16!2*6-3*&!4D'!$,,!57 "#*!&$(*!/$3".2'!:@a?Eβ <'!;#%3#!%&!*C-$,!".!"#*!$(.-1"!./!/**65$3)9!

10.2.3 Interference Reduction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

HUI = C# UC$

%QAT5AWR

@"/#)2-0%/-G$%$'-%*)0*9)$%)/%H)75%AT5WQ3R5%<-0-%;-%+##9.-%$'+$%)$%)#%&"##)3,-%$"%39),2%+/"$'-0 +.&,)1)-0%#$+7-%;)$'%7+)/% ? N %$'+$%2"-#%/"$%#911-0%10".%$'-%)/$-01-0-/*-%&0"3,-.5%61%$')#%)#%$'*+#-8%$'-/%;-%.+(%&0-*-2-%"90%"0)7)/+,%+.&,)1)-0% ? @ %3(%$'-%02"+$%+.&,)1)-0% ? N %+/2%+&&,( /-7+$):-%1--23+*4%+0"9/2%$'-%":-0+,,%*+#*+2-%"1%#9*'%+/%+."9/$%+#%$"%4--&%$'-%":-0+,,%7+)/ *"/#$+/$5%M'-%"9$&9$%:",$+7-%"1%$'-%*)0*9)$%)/%H)75%AT5WQ3R%*+/%3-%1"9/2%3(%#9&-0&"#)$)"/I

?@ ?N ?@ 8 + C$ 888888888888888888888888 C1 = C# 88888888888888888888888 @ + ?@ ?N β @ + ?@ ?N β

%QAT5AdR

M'9#%$'-%#)7/+,K$"K)/$-01-0-/*-%0+$)"%+$%$'-%"9$&9$%3-*".-#

H C# 888 = 88888 ? N I C$

%QAT5APR

;')*'%)#% ? N %$).-#%')7'-0%$'+/%)/%$'-%"0)7)/+,%*+#-5 >-%-.&'+#)L-%"/*-%."0-%$'+$%$'-%).&0":-.-/$%)/%#)7/+,K$"K)/$-01-0-/*-%0+$)"%3(%$'+&&,)*+$)"/%"1%1--23+*4%)#%&"##)3,-%"/,(%)1%"/-%*+/%&0-*-2-%$'-%)/$-01-0-/*-K&0"/-%#$+7-

811

812 Chapter 10 Feedback

A1

(a)

A1

A2

(b) Figure 10.4 K,,-&"2$"%10!"#*!$44,%3$"%.1!./!1*0$"%+*!/**65$3)!".!%(42.+*!"#*!&%01$,8".8%1"*2/*2*13*!2$"%.!%1 $(4,%/%*2&9

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

EXERCISE 10.5 M.1&%6*2!$!4.;*28.-"4-"!&"$0*!;%"#!+.,"$0*!0$%1! ? @ = @' !$1!%14-"!&%01$,! C# = @!T' !$16!$!#-(! C$ !./ @!T9!R&&-(*!"#$"!"#%&!4.;*2!&"$0*!%&!42*3*6*6!57!$!&($,,8&%01$,!&"$0*!;%"#!0$%1! ? N = @AA!TUT !$16 "#$"!.+*2$,,!/**65$3)!;%"#!β !=!@!%&!$44,%*69!K/! C# !$16! C$ !2*($%1!-13#$10*6'!/%16!"#*!&%01$,!$16!%1"*28 /*2*13*!+.,"$0*&!$"!"#*!.-"4-"!$16!#*13*!"#*!%(42.+*(*1"!%1!HUI9 Ans. !A%_V%!%T5TA%_V%ATT%QWT%2=R

10.2 Some Properties of Negative Feedback

v I, vS (V)

Figure 10.5 K,,-&"2$"%10!"#*!$44,%3$"%.1!./!1*0$"%+*!/**65$3)!".!2*6-3*!"#*!1.1,%1*$2!6%&".2"%.1!%1!$(4,%8 /%*2&9! M-2+*! :$
10.2.4 Reduction in Nonlinear Distortion @90:-%Q+R%)/%H)75%AT5d%#'";#%$'-%$0+/#1-0%*'+0+*$-0)#$)*%vJ%:-0#9#%v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β%=%T5TA%$"%$'-%+.&,)1)-0%;'"#-%"&-/K ,""&%:",$+7-%$0+/#1-0%*'+0+*$-0)#$)*%)#%2-&)*$-2%)/%H)75%AT5d5%M'-%0-#9,$)/7%$0+/#1-0%*'+0+*$-0)#K $)*%"1%$'-%*,"#-2K,""&%+.&,)1)-08% vJ%:-0#9#% vH8%)#%#'";/%)/%H)75%AT5d%+#%*90:-%Q3R5%<-0-%$'#,"&-%"1%$'-%#$--&-#$%#-7.-/$%)#%7):-/%3(

@AAA ?4 @ = 88888888888888888888888888888888888888 = XA9X @ + @AAA × A9A@ +/2%$'-%#,"&-%"1%$'-%/-G$%#-7.-/$%)#%7):-/%3(

@AA ?4 N = 88888888888888888888888888888888888 = HA @ + @AA × A9A@ M'9#%$'-%"02-0K"1K.+7/)$92-%*'+/7-%)/%#,"&-%'+#%3--/%*"/#)2-0+3,(%0-29*-25%M'-%&0)*-%&+)28%"1 *"90#-8% )#% +% 0-29*$)"/% )/% :",$+7-% 7+)/5% M'9#% )1% $'-% ":-0+,,% 7+)/% '+#% $"% 3-% 0-#$"0-28% + &0-+.&,)1)-0%#'"9,2%3-%+22-25%M')#%&0-+.&,)1)-0%#'"9,2%/"$%&0-#-/$%+%#-:-0-%/"/,)/-+0K2)#$"0K $)"/%&0"3,-.8%#)/*-%)$%;),,%3-%2-+,)/7%;)$'%#.+,,-0%#)7/+,#5

813

814 Chapter 10 Feedback H)/+,,(8% )$% #'"9,2% 3-% /"$-2% $'+$% /-7+$):-% 1--23+*4% *+/% 2"% /"$')/7% +$% +,,% +3"9$% +.&,)1)-0 #+$90+$)"/8%#)/*-%)/%#+$90+$)"/%$'-%7+)/%)#%:-0(%#.+,,%Q+,."#$%L-0"R%+/2%'-/*-%$'-%+."9/$%"1 1--23+*4%)#%+,."#$%9/)$(5

10.3 The Four Basic Feedback Topologies =+#-2%"/%$'-%F9+/$)$(%$"%3-%+.&,)1)-2%Q:",$+7-%"0%*900-/$R%+/2%"/%$'-%2-#)0-2%1"0.%"1%"9$&9$ Q:",$+7-%"0%*900-/$R8%+.&,)1)-0#%*+/%3-%*,+##)1)-2%)/$"%1"90%*+$-7"0)-#5%M'-#-%*+$-7"0)-#%;-02)#*9##-2%)/%@'+&$-0%A5%6/%$'-%1",,";)/78%;-%#'+,,%0-:)-;%$')#%+.&,)1)-0%*,+##)1)*+$)"/%+/2 &")/$%"9$%$'-%1--23+*4%$"&","7(%+&&0"&0)+$-%)/%-+*'%*+#-5

10.3.1 Voltage Amplifiers _",$+7-%+.&,)1)-0#%+0-%)/$-/2-2%$"%+.&,)1(%+/%)/&9$%:",$+7-%#)7/+,%+/2%&0":)2-%+/%"9$&9$ :",$+7-% #)7/+,5% M'-% :",$+7-% +.&,)1)-0% )#% -##-/$)+,,(% +% :",$+7-K*"/$0",,-2% :",$+7-% #"90*-5 M'-%)/&9$%0-#)#$+/*-%)#%0-F9)0-2%$"%3-%')7'8%+/2%$'-%"9$&9$%0-#)#$+/*-%)#%0-F9)0-2%$"%3-%,";5 E)/*-%$'-%#)7/+,%#"90*-%)#%-##-/$)+,,(%+%:",$+7-%#"90*-8%)$%)#%*"/:-/)-/$%$"%0-&0-#-/$%)$%)/ $-0.#%"1%+%M'g:-/)/%-F9):+,-/$%*)0*9)$5%6/%+%:",$+7-%+.&,)1)-08%$'-%"9$&9$%F9+/$)$(%"1%)/$-0K -#$%)#%$'-%"9$&9$%:",$+7-5%6$%1",,";#%$'+$%$'-%1--23+*4%/-$;"04%#'"9,2%#+A62"%$'-%"9$&9$ <12&+*"8%h9#$%+#%+%:",$.-$-0%.-+#90-#%+%:",$+7-5%J,#"8%3-*+9#-%"1%$'-%M'g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s Vs # "

" Vf #

1

#

Basic voltage amplifier

Feedback network

RL

Vo "

2

Figure 10.6 [,.3)! 6%$02$(!./! $!/**65$3)!+.,"$0*! $(4,%/%*29!`*2*!"#*! $442.42%$"*!/**65$3)!".4.,.07! %& &*2%*&^&#-1"9

10.3 The Four Basic Feedback Topologies

815

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10.3 The Four Basic Feedback Topologies

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10.4 The Feedback Voltage Amplifier (Series–Shunt)

&+##):-8%)$#%1"0;+02%$0+/#.)##)"/%*+/%3-%/-7,-*$-2%)/%*".&+0)#"/%$"%$'-%.9*'%,+07-0%1"0;+02 $0+/#.)##)"/%"1%$'-%3+#)*%+.&,)1)-05%>-%;),,%$'-0-1"0-%+##9.-%$'+$% ) N@ /**65$3) &! ) N@ 5$&%3 1*";.2) $(4,%/%*2 +/2%$'9#%".)$%$'-%*"/$0",,-2%#"90*-%)CAIA%+,$"7-$'-05 @".&+0-%$'-%*)0*9)$%"1%H)75%AT5AWQ3R%Q+1$-0%-,).)/+$)/7%$'-%*900-/$%#"90*-%)CAIA R%;)$'%$')2-+,%*)0*9)$%"1%H)75%AT5ACQ+R5%>-%#--%$'+$%3(%)/*,92)/7%)AA%+/2%)CC%;)$'%$'-%3+#)*%+.&,)1)-08 ;-%"3$+)/%$'-%*)0*9)$%#'";/%)/%H)75%AT5AWQ*R8%;')*'%)#%:-0(%#).),+0%$"%$'-%)2-+,%*)0*9)$5%Z";8 )1%$'-%3+#)*%+.&,)1)-0%)#%9/),+$-0+,%Q"0%+,."#$%9/),+$-0+,Rk$'+$%)#%)$%2"-#%/"$%*"/$+)/%)/$-0/+, 1--23+*4k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d8%AT5P8%+/2%AT5O%)$%;),,%3-%#--/%$'+$%$')#%#).&,09,-%+&&,)-#%+,#"%$"%$'-%"$'-0%$'0--%1--23+*4%$"&","7)-#5U >-%/-G$%*"/#)2-0%$'-%2-$-0.)/+$)"/%"1%β5%H0".%H)75%AT5AWQ*R8%;-%#--%$'+$%β%)#%-F9+,%$"%)AC "1%$'-%1--23+*4%/-$;"048

β = ) @N ≡ C 88888@ CN

!:@A9N\< I @ =A

M'9#%$"%.-+#90-%β8%"/-%+&&,)-#%+%:",$+7-%$"%&"0$%C%"1%$'-%1--23+*4%/-$;"04%+/2%.-+#90-#%$':",$+7-%$'+$%+&&-+0#%+$%&"0$%A%;'),-%$'-%,+$$-0%&"0$%)#%"&-/K*)0*9)$-25%M')#%0-#9,$%)#%)/$9)$):-,( +&&-+,)/7%3-*+9#-%$'-%"3h-*$%"1%$'-%1--23+*4%/-$;"04%)#%$"%#+.&,-%$'-%"9$&9$%:",$+7-%QCC%=%C1R +/2%&0":)2-%+%:",$+7-%#)7/+,%QCA%=%C4R%$'+$%)#%.)G-2%)/%#-0)-#%;)$'%$'-%)/&9$%#"90*-5%M'-%#-0)-# *"//-*$)"/%+$%$'-%)/&9$%#977-#$#%$'+$%Q+#%)/%$'-%*+#-%"1%1)/2)/7%$'-%,"+2)/7%-11-*$#%"1%$'-%1--2K 3+*4%/-$;"04R%β%#'"9,2%3-%1"9/2%;)$'%&"0$%A%"&-/K*)0*9)$-25

10.4.3 Summary R!&-(($27!./!"#*!2-,*&!/.2!/%16%10!"#*! ?!3%23-%"!$16! β!/.2!$!0%+*1!&*2%*&^&#-1"!/**65$3) $(4,%/%*2!./!"#*!/.2(!%1!?%09!@A9@G:$
R!&%(4,*!2-,*!".!2*(*(5*2I!K/!"#*!3.11*3"%.1!%&!#)-1"'!#).2"!%"E!%/!#"2%*&'!#"+*2!%"9

827

828 Chapter 10 Feedback

(a)

The A circuit is Rs

Vi

Basic amplifier

# "

R22

RL

Vo

R11

where R11 is obtained from

and R22 is obtained from

Feedback network

2

1

Feedback network

R11

2

R22 and the gain A is defined A

(b)

" Ro

Ri

1

#

Vo Vi

' is obtained from # V " f

'

Vf Vo

I1

1

Feedback network

2

# "

Vo

I1 $ 0

Figure 10.15 J-(($27!./!"#*!2-,*&!/.2!/%16%10!"#*!?!3%23-%"!$16!β!/.2!"#*!&*2%*&^&#-1"!3$&*!./!?%09!@A9@G:$<9

3. D#*!$3"-$,!%14-"!$16!.-"4-"!2*&%&"$13*&!./!"#*!/**65$3)!$(4,%/%*2!-&-$,,7!*>3,-6*!-# $16!-D9!D#*&*!$2*!6*1."*6!-%1!$16!-.-"!%1!?%09!@A9@G:$
- %1 = - %4 X - #

!:@A9NG<

@8 X 88888 @ - .-" = @!! 888888 - 14 - D

!:@A9NH<

Example 10.3 H)790-%AT5APQ+R%#'";#%+/%"&%+.&%*"//-*$-2%)/%$'-%/"/)/:-0$)/7%*"/1)790+$)"/5%M'-%"&%+.&%'+#%+/%"&-/K ,""&%7+)/% µ8%+%2)11-0-/$)+,%)/&9$%0-#)#$+/*-%-%. 8%+/2%+/%"9$&9$%0-#)#$+/*-%315%j-*+,,%$'+$%)/%"90%+/+,(#)#%"1 "&K+.&%*)0*9)$#%)/%@'+&$-0%C8%;-%/-7,-*$-2%$'-%-11-*$#%"1%-%.%Q+##9.-2%)$%$"%3-%)/1)/)$-R%+/2%"1%31%Q+##9.-2 )$%$"%3-%L-0"R5%<-0-%;-%;)#'%$"%9#-%$'-%1--23+*4%.-$'"2%$"%+/+,(L-%$'-%*)0*9)$%$+4)/7%3"$'%-%.%+/2%31%)/$" +**"9/$5%H)/2%-G&0-##)"/#%1"0%?8%β8%$'-%*,"#-2K,""&%7+)/% C1 ⁄ C# 8%$'-%)/&9$%0-#)#$+/*-%-)/%Q#--%H)75%AT5AP+R8 +/2%$'-%"9$&9$%0-#)#$+/*-%-"9$5%J,#"%1)/2%/9.-0)*+,%:+,9-#8%7):-/% µ%=%ATW8%-%.%=%ATT%4Ω8%31%=%A%4Ω8%-D%=%C 4Ω8%-A%=%A%4Ω8%-C%=%A%!Ω8%+/2%-#%=%AT%4Ω5

10.4 The Feedback Voltage Amplifier (Series–Shunt)

Rs

Vs

# #

# "

Rid Rin

ro

V1 "

# "

"

Vo RL

(V1

Rif Rout

1

R2

R1

2

series shunt

(a) ro

Rs # Vi " Ri

Rid

# V1 "

# "

(V1

Vo RL

R22 = (R2 # R 1 )

R11 = (R 1 R2 )

Ro (b)

I$0 # Vf "

R2 R1

Vo

(c) Figure 10.16 M%23-%"&!/.2!Q>$(4,*!@A9\9

# "

Rof

829

830 Chapter 10 Feedback Example 10.3 continued

Solution >-%"3#-0:-%$'+$%$'-%1--23+*4%/-$;"04%*"/#)#$#%"1%-C%+/2%-A5%M')#%/-$;"04%#+.&,-#%$'-%"9$&9$%:",$+7-%C1 +/2%&0":)2-#%+%:",$+7-%#)7/+,%Q+*0"##%-AR%$'+$%)#%.)G-2%)/%#-0)-#%;)$'%$'-%)/&9$%#"90*-%C#5 M'-%?%*)0*9)$%*+/%3-%-+#),(%"3$+)/-2%1",,";)/7%$'-%09,-#%"1%H)75%AT5Ad8%+/2%)#%#'";/%)/%H)75 AT5APQ3R5 Y3#-0:-%$'+$%$'-%,"+2)/7%-11-*$%"1%$'-%1--23+*4%/-$;"04%+$%$'-%)/&9$%#)2-%)#%"3$+)/-2%3(%#'"0$K*)0*9)$)/7 &"0$%C%"1%$'-%1--23+*4%/-$;"04%Q3-*+9#-%)$%)#%*"//-*$-2%)/%#'9/$R%+/2%,""4)/7%)/$"%&"0$%A8%;)$'%$'-%0-#9,$ $'+$% - @@ a - @ || - N 5%M'-%,"+2)/7%-11-*$%"1%$'-%1--23+*4%/-$;"04%+$%$'-%"9$&9$%#)2-%)#%1"9/2%3(%"&-/K*)0K *9)$)/7% &"0$% A% Q3-*+9#-% )$% )#% *"//-*$-2% )/% #-0)-#R% +/2% ,""4)/7% )/$"% &"0$% C8% ;)$'% $'-% 0-#9,$% $'+$ - NN a - N b - @ 5%H"0%$'-%0-#9,$)/7%?%*)0*9)$%)/%H)75%AT5APQ3R8%;-%*+/%;0)$-%3(%)/#&-*$)"/I C - %. - D ff ( - @ + - N ) 8 8888888888888888888888888888888888888888888888 8 ? ≡ 888881 = µ 88888888888888888888888888888888888888888888888888 C% g- D ff ( - @ + - N )h + 3 1 - %. + - # + :- @ ff - N < H"0%$'-%:+,9-#%7):-/8%;-%1)/2%$'+$%?%!%PTTT%_`_5 M'-%*)0*9)$%1"0%2-$-0.)/)/7%β%)#%#'";/%)/%H)75%AT5APQ*R8%10".%;')*'%;-%"3$+)/ -@ + -N

C C1

4 @ 8 !!!@A X\ !TUT β ≡ 88888 = 88888888888888888

M'-%:",$+7-%7+)/%;)$'%1--23+*4%*+/%/";%3-%"3$+)/-2%+# C ? _AAA ?4 ≡ 888881 = 8888888888888888 = 888888888888 = YHZ!TUT C# @ + ? β Z M'-%)/&9$%0-#)#$+/*-%-%4%2-$-0.)/-2%3(%$'-%1--23+*4%-F9+$)"/#%)#%$'-%0-#)#$+/*-%#--/%3(%$'-%-G$-0/+,%#"90*Q#--%H)75%AT5AP+R8%+/2%)#%7):-/%3( - %4 = - % ( @ + ? β ) ;'-0-%-%%)#%$'-%)/&9$%0-#)#$+/*-%"1%$'-%?%*)0*9)$%)/%H)75%AT5APQ3RI - % = - # + - %. + :- @ ff - N < H"0%$'-%:+,9-#%7):-/8%-%%!%AAA%4Ω8%0-#9,$)/7%)/ - %4 = @@@ × Z = ZZZ!)Ω M')#8%'";-:-08%)#%/"$%$'-%0-#)#$+/*-%+#4-2%1"05%>'+$%)#%0-F9)0-2%)#%-)/8%)/2)*+$-2%)/%H)75%AT5APQ+R5%M"%"3$+)/ -)/%;-%#93$0+*$%-#%10".%-%4 I - %1 = - %4 X - # H"0%$'-%:+,9-#%7):-/8%-)/%=%OUB%4Ω5%M'-%0-#)#$+/*-%-14%7):-/%3(%$'-%1--23+*4%-F9+$)"/#%)#%$'-%"9$&9$%0-#)#K $+/*-%"1%$'-%1--23+*4%+.&,)1)-08%)/*,92)/7%$'-%,"+2%0-#)#$+/*-%-D8%+#%)/2)*+$-2%)/%H)75%AT5APQ+R5%-14% )# 7):-/%3( -1 8 - 14 = 888888888888888 @ + ?β ;'-0-%-1%)#%$'-%"9$&9$%0-#)#$+/*-%"1%$'-%?%*)0*9)$5%-1%*+/%3-%"3$+)/-2%3(%)/#&-*$)"/%"1%H)75AT5APQ3R%+# - 1 = 3 1 ff - D ff ( - N + - @ ) H"0%$'-%:+,9-#%7):-/8%-1%!%PPO%Ω8%+/2 __Z - 14 = 888888888 = XH9\!Ω Z

10.4 The Feedback Voltage Amplifier (Series–Shunt)

M'-%0-#)#$+/*-%+#4-2%1"08%-"9$8%)#%$'-%"9$&9$%0-#)#$+/*-%"1%$'-%1--23+*4%+.&,)1)-0%-G*,92)/7%-D5%H0".%H)75 AT5APQ+R%;-%#--%$'+$ - 14 = - .-" ff - D

M'9#

- .-" !! @AA!Ω

Example 10.4 J#%+/"$'-0%-G+.&,-%"1%+%#-0)-#X#'9/$%1--23+*4%+.&,)1)-08%*"/#)2-0%$'-%*)0*9)$%#'";/%)/%H)75%AT5OQ3R%;')*' )#%0-&-+$-2%)/%H)75%AT5AOQ+R5%6$%)#%0-F9)0-2%$"%+/+,(L-%$')#%+.&,)1)-0%$"%"3$+)/%)$#%:",$+7-%7+)/% C 1 ⁄ C #8%)/&9$ 0-#)#$+/*-% - %18% +/2% "9$&9$% 0-#)#$+/*-% - .-" 9 % H)/2% /9.-0)*+,% :+,9-#% 1"0% $'-% *+#-% * A@ a * AN a G % .J`_8 - !@ a - !N a @A %4 Ω' % - @ a @ %4 Ω' %+/2% - N a X %4 Ω9 %H"0%#).&,)*)$(8%/-7,-*$% 3 1 %"1%-+*'%"1% K @%+/2%K N 9

Solution >-% )2-/$)1(% $'-% 1--23+*4% /-$;"04% +#% $'-% :",$+7-% 2):)2-0% Q - @ 8% - N R5% 6$#% ,"+2)/7% -11-*$% +$% $'-% )/&9$% )# "3$+)/-2%3(%#'"0$%*)0*9)$)/7%)$#%&"0$%C%Q3-*+9#-%)$%)#%*"//-*$-2%)/%#'9/$%;)$'%$'-%"9$&9$R5%M'-/8%,""4)/7 )/$"%)$#%&"0$%A8%;-%#--% - @ || - N 5%M'-%,"+2)/7%-11-*$%+$%$'-%"9$&9$%)#%"3$+)/-2%3(%"&-/K*)0*9)$)/7%&"0$%A%"1%$'1--23+*4%/-$;"04%Q3-*+9#-%)$%)#%*"//-*$-2%)/%#-0)-#%;)$'%$'-%)/&9$R5%M'-/8%,""4)/7%)/$"%&"0$%C8%;-%#--% - N )/%#-0)-#%;)$'% - @ 5%M'-%?%*)0*9)$%;),,%$'-0-1"0-%3-%+#%#'";/%)/%H)75%AT5AOQ3R5%M'-%7+)/%?%)#%2-$-0.)/-2%+# $'-%&0"29*$%"1%$'-%7+)/%"1% K @ %+/2%$'-%7+)/%"1% K N %+#%1",,";#I

///- resis in drain/ source

- !@ * A@ - !@ in C .@ resistance 8 a X 888888888888888888888888888888888888888 8 ? @ a 8888888 8 a X 8888888888888888888888888888888888888888888 || || @ ⁄ * @ * b ( ) b C% A@ @ N A@ ( - @ - N ) C ? N a 888888818 a X * AN [ - !N || ( - @ b - N ) ] C .@

C * A@ - !@ * AN [ - !N || ( - @ b - N ) ] ? a 888881 a ? @ ? N a 888888888888888888888888888888888888888888888888888888888888888888888 8 C% @ b * A@ ( - @ || - N ) H"0%$'-%/9.-0)*+,%:+,9-#%7):-/8 G × @A × G [ @A || ( @ b X ) ] ? a 8888888888888888888888888888888888888888888888888888888888 a @Z\9X !TUT @ b G ( @ || X ) M'-%:+,9-%"1% β %)#%2-$-0.)/-2%10".%$'-% β %*)0*9)$%)/%H)75%AT5AOQ*R8 C C1

-@ b -N

@ β ≡ 888884 a 88888888888888888 8

H"0%$'-%/9.-0)*+,%:+,9-#%7):-/8 @ β a 888888888888 a A9@

@bX M'-%*,"#-2K,""&%7+)/% C 1 ⁄ C #%*+/%/";%3-%1"9/2%+#

C ? @Z\9X 888881 a ?4 a 8888888888888888 a 888888888888888888888888888888888888 a X9H !TUT @ b ?β @ b @Z\9X × A9@ C#

831

832 Chapter 10 Feedback

Example 10.4 continued

RD2 RD1

Vo Q2

Q1

Rout R2

Vs Rin

R1

1

2

(a)

RD2 RD1

Vo Q2

Vd1 Q1

#

R1

Ro

I$o

R2

#

Vi R1

Ri

R2

R2

Vf

# V o "

R1

" " (b)

(c)

Figure 10.17 :$$(4,*!@A9GE!:3
D#*!%14-"!2*&%&"$13*!%&!.5+%.-&,7!%1/%1%"*!5*3$-&*!./!"#*!%1/%1%"*!%14-"!2*&%&"$13*!./!"#*!ijJ?QD9!D#* .-"4-"!2*&%&"$13*! - .-" !%&!.5"$%1*6!$&!/.,,.;&' -1 - .-"! a - 14 a 888888888888888 8 @ b ?β ;'-0-% - 1 %)#%$'-%"9$&9$%0-#)#$+/*-%"1%$'-%?%*)0*9)$5%H0".%H)75%AT5AOQ3R8% - 1 a - !N || ( - @ b - N ) a @A || @A a H !) Ω

10.4 The Feedback Voltage Amplifier (Series–Shunt)

M'-%+."9/$%"1%1--23+*4%)# @ b ? β a @ b ( @Z\9X × A9@ ) a @Y9\X M'9#8 HAAA - .-" a 8888888888888 a NZN!Ω @Y9\X ;')*'%)#%0-,+$):-,(%,";%7):-/%$'+$%$'-%"&-/K,""&%+.&,)1)-0%'+#% - 1 a HAAA!Ω 5

EXERCISES 10.10 K/! "#*! .4! $(4! ./! Q>$(4,*! @A9\! #$&! $! -1%/.2(! ^_86[U.3"$+*! #%0#8/2*C-*137! 2.,,.//! ;%"# ! 4\6[! = @ )`='!/%16!"#*!\86[!/2*C-*137!./!"#*!3,.&*68,..4!0$%1! C1 ⁄ C# 9 Ans. Z!)`= 10.11 D#*!3%23-%"!&#.;1!%1!?%09!Q@A9@@!3.1&%&"&!./!$!6%//*2*1"%$,!&"$0*!/.,,.;*6!57!$1!*(%""*2!/.,,.;*2' ;%"#!&*2%*&^&#-1"!/**65$3)!&-44,%*6!57!"#*!2*&%&".2&!-@!$16!-N9!R&&-(%10!"#$"!"#*!63!3.(4.1*1"!./ C#!%&!=*2.'!$16!"#$"! β!./!"#*![kD&!%&!+*27!#%0#'!/%16!"#*!63!.4*2$"%10!3-22*1"!./!*$3#!./!"#*!"#2** "2$1&%&".2&!$16!&#.;!"#$"!"#*!63!+.,"$0*!$"!"#*!.-"4-"!%&!$442.>%($"*,7!=*2.9!D#*1!/%16!"#*!+$,-*&!./ ?'!β'! ? 4 ≡ C1 ⁄ C#'!-%1'!$16!-.-"9!R&&-(*!"#$"!"#*!"2$1&%&".2&!#$+*!β!=!@AA9! Ans. YH9Z!TUTE!A9@!TUTE!Y9X_!TUTE!@X@!)ΩE!@X9@!Ω.

Rin

Rout

Figure E10.11

10.12 ?.2!"#*!&*2%*&^&#-1"!$(4,%/%*2!%1!?%09!@A9Z:3<'!/%16!?'! β '! ? 4 '! - %1 ' !$16! - .-" 9 !b*0,*3"! 3 1 !./!K9 Ans. ? a * A [ - ! || ( - @ b - N ) ] E! β a - @ ⁄ ( - @ b - N ) E! ? 4 a ? ⁄ ( @ b ? β ) E! - %1 a ( @ ⁄ * A ) ( @ b ? β ) E! - .-" a [ - ! || ( - @ b - N ) ] ⁄ ( @ b ? β )

833

834 Chapter 10 Feedback

10.5 The Feedback Transconductance Amplifier (Series–Series) 10.5.1 The Ideal Case R&!(*1"%.1*6!%1!J*3"%.1!@A9\'!"#*!&*2%*&^&*2%*&!/**65$3)!".4.,.07!&"$5%,%=*&! I1 ⁄ C# !$16 %&!"#*2*/.2*!5*&"!&-%"*6!/.2!"2$1&3.16-3"$13*!$(4,%/%*2&9!?%0-2*!@A9@Y:$4*3"*6'!$!6%(*1&%.1,*&&!C-$1"%"79!?%1$,,7'!1."*!"#$" "#*!&.-23*!$16!"#*!,.$6!2*&%&"$13*&!#$+*!5**1!$5&.25*6!%1&%6*!"#*!?!3%23-%"!:(.2*!.1!"#%& ,$"*2<9

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837

838 Chapter 10 Feedback

(a)

The A circuit is

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Rs Vi

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R11

RL

R22 Y%

Y Ri

Ro

where R11 is obtained from

and R22 is obtained from

Feedback network

1

2

R11 and the gain A is defined (b)

A

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- %1 = - %4 X - #

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Example 10.5 J#%+%1)0#$%-G+.&,-%"1%+%1--23+*4%$0+/#*"/29*$+/*-%+.&,)1)-08%*"/#)2-0%$'-%*)0*9)$%#'";/%)/%H)75%AT5CCQ+R5 M')#%)#%$'-%#+.-%*)0*9)$%;-%&0-#-/$-2%)/%H)75%AT5ATQ3R%+/2%;+#%$'-%#93h-*$%"1%?G-0*)#-%AT5D5%<-0-8%1"0%7-/K -0+,)$(%;-%/"$%"/,(%+##9.-%$'+$% ? @ %'+#%1)/)$-%)/&9$%+/2%"9$&9$%0-#)#$+/*-#%39$%)/*,92-%+%#"90*-%0-#)#$+/*- # 5%M'-%"3h-*$):-%)#%$"%+/+,(L-%$')#%*)0*9)$%$"%2-$-0.)/-%)$#%*,"#-2K,""&%7+)/% ? 4 ≡ I 1 ⁄ C # 8%$'-%)/&9$%0-#)#K $+/*-% "1% $'-% 1--23+*4% +.&,)1)-0% - %1 ' % +/2% $'-% "9$&9$% 0-#)#$+/*-% - .-" 9 % M'-% ,+$$-0% )#% $'-% 0-#)#$+/*-% #--/ 3-$;--/%$'-%$;"%$-0.)/+,#%"1% - D %,""4)/7%3+*4%)/$"%$'-%"9$&9$%,""&5

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/// before: learn its ro /// its series: se measure current: so like add a current source in series for output resistance, nature like if use RL to find out 2 terminal

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840 Chapter 10 Feedback

Example 10.5 continued

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841

842 Chapter 10 Feedback

Example 10.5 continued

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10.5 The Feedback Transconductance Amplifier (Series–Series)

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844 Chapter 10 Feedback

Example 10.6 continued

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Q3R%?.&,"()/7%$'-%,"+2)/7%09,-#%7):-/%)/%H)75%AT5CA8%;-%"3$+)/%$'-%?%*)0*9)$%#'";/%)/%H)75%AT5CUQ*R5%M" 1)/2% ? ≡ I1 ⁄ C% %;-%1)0#$%2-$-0.)/-%$'-%7+)/%"1%$'-%1)0#$%#$+7-5%M')#%*+/%3-%;0)$$-/%3(%)/#&-*$)"/%+# −α @ ( - 5@ ff 3 π N ) C0@ /// use 8888888 8 = 8888888888888888888888888888888888888888888888888888888888 8 multistage method 3 "@ + [ - 7@ ff ( - L + - 7N ) ] C% E)/*-% KA% )#% 3)+#-2% +$% T5P% .J8% 3"A% =% WA5O% Ω5% M0+/#)#$"0% KC% )#% 3)+#-2% +#% A% .JV% $'9#% 3π C% =% )4" ⁄ * AN = @AA ⁄ GA = N9H !)Ω9 % E93#$)$9$)/7% $'-#-% :+,9-#% $"7-$'-0% ;)$'% αA% =% T5BB8% -5A% =% B% 4Ω8% -7A% =% ATT% Ω8% -L = PWT Ω8%+/2%-7C%=%ATT%Ω8%0-#9,$#%)/ C0@ 8888888 8 = X @G9XN!TUT C% Z-G$8%;-%2-$-0.)/-%$'-%7+)/%"1%$'-%#-*"/2%#$+7-8%;')*'%*+/%3-%;0)$$-/%3(%)/#&-*$)"/%Q/"$)/7%$'+$%C9C%=%C0AR%+#% C0N 8888888 8 = X * AN { - 5N ff ( ) 4" + @ ) [ 3 "\ + ( - 7N ff ( - L + - 7@ ) ) ] } C0@

10.5 The Feedback Transconductance Amplifier (Series–Series)

845

d

E93#$)$9$)/7% * AN = GA!(RUT' % - 5N = H!)Ω' %)4"%=%ATT8% 3 "\ = NH ⁄ G = _9NH!Ω' %-7C%=%ATT%Ω8%-L%=%PWT Ω8%+/2%-7A%=%ATT%Ω8%0-#9,$#%)/ C0N 8888888 8 = X @\@9N!TUT C0@ H)/+,,(8%1"0%$'-%$')02%#$+7-%;-%*+/%;0)$-%3(%)/#&-*$)"/ I1 I "\ @ 8888888 8 = 8888888 8 = 8888888888888888888888888888888888888888888888888888888888 8 C0N C9\ 3 "\ + ( - 7N ff ( - L + - 7@ ) ) @ = 888888888888888888888888888888888888888888888 = @A9_!(RUT _9NH + ( @AA ff ZGA ) @".3)/)/7%$'-%7+)/#%"1%$'-%$'0--%#$+7-#%0-#9,$#%)/ I X\ ? ≡ 888818 = X @G9XN × X @\@9N × @A9_ × @A C% = NA9Z!RUT M'-%*,"#-2K,""&%7+)/%?4%*+/%/";%3-%1"9/2%10". I ? ?4 ≡ 888818 = 8888888888888888 C# @ + ? β NA9Z = 888888888888888888888888888888888888 = Y\9Z!(RUT @ + NA9Z × @@9X ;')*'%;-%/"$-%)#%:-0(%*,"#-%$"%$'-%+&&0"G).+$-%:+,9-%1"9/2%)/%Q+R%+3":-5 D#*!+.,"$0*!0$%1!%&!/.-16!/2.( C X I 0 - 5\ X I 1 - 5\ 888881 = 8888888888888888 8 ! 88888888888888888 = X ? 4 - 5\ C# C# C# X\

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846 Chapter 10 Feedback

Example 10.6 continued

;'-0-% - 1 %*+/%3-%2-$-0.)/-2%10".%$'-%?%*)0*9)$%)/%H)75%AT5CUQ*R%3(%30-+4)/7%$'-%*)0*9)$%3-$;--/%M%+/2%M′ 9 M'-%0-#)#$+/*-%,""4)/7%3-$;--/%$'-#-%$;"%/"2-#%*+/%3-%1"9/2%$"%3-% - 5N 8 - 1 = [ - 7N ff ( - L + - 7@ ) ] + 3 "\ + 88888888888888 )4" + @ ;')*'8%1"0%$'-%:+,9-#%7):-/8%()-,2#%-1%=%AWU5B%Ω5%M'-%"9$&9$%0-#)#$+/*-%-14%"1%$'-%1--23+*4%+.&,)1)-0%*+/%/"; 3-%1"9/2%+# - 14 = - 1 ( @ + ? β ) = @G\9X ( @ + NA9Z × @@9X ) = \H9_!)Ω L*!3$1!1.;!-&*!"#*!+$,-*!./!-14!".!.5"$%1!$1!$442.>%($"*!+$,-*!/.2!-.-"9!D.!6.!"#%&'!;*!$&&-(*!"#$"!"#* *//*3"!./!"#*!/**65$3)!%&!".!4,$3*!$!2*&%&"$13*!-14!:\H9_!)Ω
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D#%&!$,&.!%&!$!;*,3.(*!2*&-,"!/.2!"#*!"2$1&2*&%&"$13*!$(4,%/%*2!$&!%"!($)*&!%"&!+.,"$0*8.-"4-" 3%23-%"!(.2*!%6*$,E!"#*!.-"4-"!+.,"$0*!;%,,!3#$10*!,*&&!$&!;*!62$;!3-22*1"!/2.(!"#*!$(4,%/%*2 .-"4-"9!?%1$,,7'!1."*!"#$"!&)"(#)/$&(4"".9+0=(01$$"0&%1$N(:)"&)"3(+&(&)"(%$6/&(13(+&(&)"(1/&; 6/&N(+2:+B#(3"./0"#(&)"(0133"#61$.%$*(3"#%#&+$0"9

10.6.2 The Practical Case ?%0-2*!@A9NH!&#.;&!$!5,.3)!6%$02$(!/.2!$!42$3"%3$,!&#-1"^&#-1"!/**65$3)!$(4,%/%*29!D.!5* $5,*!".!$44,7!"#*!/**65$3)!*C-$"%.1&!".!"#%&!$(4,%/%*2'!;*!#$+*!".!2*42*&*1"!%"!57!"#*!%6*$, &"2-3"-2*!./!?%09!@A9NG:$<9!j-2!.5S*3"%+*!"#*2*/.2*!%&!".!6*+%&*!$!&%(4,*!(*"#.6!/.2!/%16%10 "#*!?(3%23-%"!$16! β 9![-%,6%10!.1!"#*!%1&%0#"!;*!#$+*!0$%1*6!/2.(!.-2!&"-67!./!"#*!&*2%*&^ &#-1"!$16!&*2%*&^&*2%*&!".4.,.0%*&'!;*!42*&*1"!"#*!(*"#.6!/.2!"#*!&#-1"^&#-1"!3$&*'!;%"#.-"

Basic amplifier

Rif

Rin

Figure 10.25 [,.3)!6%$02$(!/.2!$!42$3"%3$,!&#-1"^&#-1"!/**65$3)!$(4,%/%*29

Rout

Rof

10.6 The Feedback Transresistance Amplifier (Shunt–Shunt)

(a)

The A circuit is

Ii

Rs

Basic amplifier

R11

R22

#

RL

"

Ro

Ri where R11 is obtained from 1

and R22 is obtained from

Feedback network

Feedback network

1

2

R11 and the gain A is defined (b)

Vo

2

R22

Vo Ii

A

' is obtained from If

'

If Vo

# V $0 " 1

1

Feedback network

2

# "

Vo

V1 $ 0

Figure 10.26 ?%16%10!"#*!?!3%23-%"!$16!β!/.2!"#*!&#-1"^&#-1"!/**65$3)!$(4,%/%*2!%1!?%09!@A9NH9

6*2%+$"%.1'!%1!?%09!@A9N_9!R&!%1!42*+%.-&!3$&*&'!"#*!(*"#.6!./!?%09!@A9N_!$&&-(*&!"#$"!"#* 5$&%3!$(4,%/%*2!%&!-1%,$"*2$,!:.2!$,(.&"!&.*6!%1!&#-1"!$"!"#*!%14-"'!%"&!4.2"!@!%&!&#.2"83%23-%"*6!$16! β !%& /.-16!$&! I 4 ⁄ C 1 '!;#*2*! I 4 !%&!"#*!3-22*1"!"#$"!/,.;&!"#2.-0#!"#*!&#.2"!3%23-%"9 D#*!.4*18,..4!2*&%&"$13*&! - % !$16! - 1 !$2*!6*"*2(%1*6!/2.(!"#*!?!3%23-%"!$16!$2*!-&*6!%1 QC&9!:@A9GG
!:@A9G_<

@ @ - .-"!!! a @!!! 888888 8 X 888888 - 14 - D

!:@A9GZ<

849

850 Chapter 10 Feedback

Example 10.7 H)790-%AT5COQ+R%#'";#%+%1--23+*4%$0+/#0-#)#$+/*-%+.&,)1)-05%6$%)#%1"0.-2%3(%*"//-*$)/7%+%0-#)#$+/*-% - L %)/ $'-% /-7+$):-K1--23+*4% &+$'% "1% +% :",$+7-% +.&,)1)-0% ;)$'% 7+)/% µ 8% +/% )/&9$% 0-#)#$+/*-% - %. 8% +/2% +/% "9$&9$ 0-#)#$+/*-% 3 1 9 %M'-%+.&,)1)-0% µ %*+/%3-%).&,-.-/$-2%;)$'%+/%"&%+.&8%+%#).&,-%2)11-0-/$)+,%+.&,)1)-08%+%#)/K 7,-K-/2-2%)/:-0$)/7%+.&,)1)-08%"08%)/%$'-%,).)$8%+%#)/7,-K$0+/#)#$"0%@?%"0%@E%+.&,)1)-05%M'-%,+$$-0%*+#-%;),, 3-%*"/#)2-0-2%)/%?G-0*)#-%AT5Ad5%Y1%*"90#-8%$'-%')7'-0%$'-%7+)/% µ 8%$'-%."0-%)2-+,%$'-%*'+0+*$-0)#$)*#%"1%$'1--23+*4%$0+/#0-#)#$+/*-%+.&,)1)-0%;),,%3-8%#).&,(%3-*+9#-%"1%$'-%*"/*".)$+/$%)/*0-+#-%)/%,""&%7+)/5 RF

" # Is

m #

Rs

RL Vo

Rif

Rin

Rout

" Rof

(a) RF

If

/// since IF add to IS, so beta is negative

# V o "

(b)

Ii

ro # // Rs

RF

Rid

Ri

orientation / of the

Vid

"mVid # "

# RF

RL

" (c)

Figure 10.27 )$,!R!/**65$3)!"2$1&2*&%&"$13*!$(4,%/%*2E!)3,!"#*!β!3%23-%"E!:4
Vo

"

Ro

10.6 The Feedback Transresistance Amplifier (Shunt–Shunt)

:$%($"*!*>42*&&%.1!/.2!"#*!3,.&*68,..4!.4*183%23-%"!"2$1&2*&%&8 "$13*!./!"#*!/**65$3)!$(4,%/%*29 :542*&&%.1&!/.2!?'! - % '!$16! - 1 9 :342*&&%.1&!/.2!"#*!,..4!0$%1'! ? 4 '! - %4 '! - %1 '! - 14 '!$16! - .-" 9 G :6
Solution Q+R%61%$'-%,""&%7+)/% ? β %)#%,+07-8%

C @ ? 4 ≡ 888881 ! 888 I# β

;'-0-% β %*+/%3-%1"9/2%10".%$'-% β %*)0*9)$%)/%H)75%AT5COQ3R%+# I @ β ≡ 888884 a X 888888 C1

M'9#8

-L

!:@A9GY<

C 888881 ! X - L I# Z"$-%$'+$%)/%$')#%*+#-%$'-%:",$+7-%+$%$'-%)/&9$%/"2-%Q$'-%)/:-0$)/7%)/&9$%$-0.)/+,%"1% µ R%;),,%3-%:-0(%*,"#-%$" 70"9/2%+/2%$'9#%:-0(%,)$$,-8%)1%+/(8%*900-/$%1,";#%)/$"%$'-%)/&9$%$-0.)/+,%"1%$'-%+.&,)1)-05%Z-+0,(%+,,%"1% I # ;),,%1,";%$'0"97'% - L 8%0-#9,$)/7%)/% C 1 ! A X I # - L a X I # - L 5%M')#%#'"9,2%3-%0-.)/)#*-/$%"1%$'-%)/:-0$)/7 "&K+.&%*"/1)790+$)"/%#$92)-2%)/%E-*$)"/%C5C5 Q3R%E)/*-%$'-%1--23+*4%/-$;"04%*"/#)#$#%"1% - L 8%$'-%,"+2)/7%-11-*$%+$%$'-%+.&,)1)-0%)/&9$%+/2%"9$&9$%;),, #).&,(%3-% - L 5%M')#%)#%)/2)*+$-2%)/%$'-%?%*)0*9)$%#'";/%)/%H)75%AT5COQ*R5%M'-%"&-/K,""&%$0+/#0-#)#$+/*-%? *+/%3-%"3$+)/-2%+#%1",,";#I C %. a I % - %

!:@A9GX<

- % a - %. || - L || - #

!:@A9HA<

( - L || - D ) C 1 a X µ C %. 888888888888888888888888888888888 3 1 b ( - L || - D )

!:@A9H@<

;'-0-

@".3)/)/7%?F#5%QAT5WBR%+/2%QAT5dAR%7):-# ( - L || - D ) C ? ≡ 888881 a X µ - % 888888888888888888888888888888888 I% 3 1 b ( - L || - D )

!:@A9HN<

M'-%"&-/K,""&%"9$&9$%0-#)#$+/*-%*+/%3-%"3$+)/-2%3(%)/#&-*$)"/%"1%$'-%?%*)0*9)$%;)$'% I % %#-$%$"%T5%>-%#--%$'+$ C %. a A 8%+/2 - 1 a 3 1 || - L || - D Q*R%M'-%,""&%7+)/% ? β *+/%3-%"3$+)/-2%3(%*".3)/)/7%?F#5%QAT5WDR%+/2%QAT5dCR8 ( - L || - D ) ? β a µ 888888% 888888888888888888888888888888888 - L 3 1 b ( - L || - D )

!:@A9H\<

851

852 Chapter 10 Feedback

Example 10.7 continued

Y3#-0:-%$'+$%+,$'"97'%3"$'%?%+/2% β %+0-%/-7+$):-8% ? β %)#%&"#)$):-8%+%*".1"0$)/7%1+*$%*"/1)0.)/7%$'+$%$'1--23+*4%)#%/-7+$):-5%J,#"%/"$-%$'+$% ? β %)#%2).-/#)"/,-##8%+#%)$%.9#$%+,;+(#%3-5 D#*!3,.&*68,..4!0$%1! ? 4 !3$1!1.;!5*!/.-16!$&! C ? ? 4 ≡ 888881 a 8888888888888888 I# @ b ?β M'9# ( - L || - D ) X µ - % 888888888888888888888888888888888 3 1 b ( - L || - D ) ? 4 a 88888888888888888888888888888888888888888888888888888888 8 !:@A9HG< -% ( - L || - D ) @ b µ 888888 888888888888888888888888888888888 - L 3 1 b ( - L || - D ) Z"$-%$'+$%$'-%*"/2)$)"/%"1% ? β ! @%;')*'%0-#9,$#%)/% ? 4 ! X - L %*"00-#&"/2#%$"% ( - || - ) - L 3 1 b ( - L || - D )

L D µ 888888% 888888888888888888888888888888888 !@

!:@A9HH<

M'-%)/&9$%0-#)#$+/*-%;)$'%1--23+*48% - %4 8%)#%"3$+)/-2%3(%2):)2)/7% - % %3(% ( @ b ? β ) %;)$'%$'-%0-#9,$ -% - %4 a 888888888888888 8 @ b ?β "0 ( - L || - D ) µ @8 @ ?β @ 88888 a 88888 b 8888888 a 88888 b 888888 888888888888888888888888888888888 - %4 - % - % - % - L 3 1 b ( - L || - D ) E93#$)$9$)/7% 1"0% - % % 10".% ?F5% QAT5dTR% +/2% 0-&,+*)/7% µ ( - L || - D )!! [ 3 1 b ( - L || - D ) ] % 3(% µ′ ' % ;'-0-% µ′ % )# ,";-0%$'+/%39$%9#9+,,(%*,"#-%$"%$'-%:+,9-%"1% µ 8%0-#9,$#%)/

-%4!e!-%.!ff!-L!ff!-#(ff!:-L!U! µ′ < M'-%$;"%$-0.#%*"/$+)/)/7% - L %*+/%3-%*".3)/-28 - %4 a - # || - %. || [ - L ⁄ ( µ′ b @ ) ]

!:@A9H_<

E)/*-% - %4 a - # || - %1 8%;-%#--%$'+$% - %1 a - %. || [ - L || ( µ′ b @ ) ] N#9+,,(% - %. %)#%,+07-%+/2%$'9# -L 8 ! 88888L8 - %1 ! 8888888888888 µ′ b @ µ′ 10".%;')*'%;-%"3#-0:-%$'+$%1"0%,+07-%+.&,)1)-0%7+)/% µ 8%$'-%)/&9$%0-#)#$+/*-%;),,%3-%,";5 !D#*!.-"4-"!2*&%&"$13*!;%"#!/**65$3)! - 14 !3$1!5*!/.-16!57!6%+%6%10! - 1 !57! ( @ b ? β )I ! -1 - 14 a 888888888888888 8 @ b ?β M'9#8 @8 @ β 888888 a 88888 b ? 8888888 - 14 - 1 - 1 ( - L || - D ) @ @ b 88888 88888 a 88888 µ 8% 888888888888888888888888888888888 - L 3 1 b ( - L || - D ) - 1 -1

!:@A9HZ<

10.6 The Feedback Transresistance Amplifier (Shunt–Shunt)

E93#$)$9$)/7%1"0% - 1 %10".%?F5%QAT5dUR8 -% @ @8 @ @ b @ b µ 88888 888888 8 8888 a 888888 b 88888 8 8888 - 14 - D - L 3 1 -L 31 @8 @ b @ b 888 a 88888 @ b µ 888888% 8 888888 3 -D -L 1 L M'9#8 31 8 - 14 a - D || - L || 8888888888888888888 @ b µ 888888% -L

E)/*-8%."0-":-08

- 14 a - D || - .-" ;-%"3$+)/%1"0% - .-" 31 8 - .-" a - L || 8888888888888888888 -% @ b µ 888888 -L N#9+,,(% - L ! 3 1 ⁄ [ ( @ b µ ( - % ⁄ -L ) ] V%$'9#8 31 ! 88888L8 - .-" ! 8888888888888888888 -% -% @ b µ 888888 -L

31 8888

µ

10".%;')*'%;-%#--%$'+$%1"0%,+07-% µ 8%$'-%"9$&9$%0-#)#$+/*-%;),,%3-%*"/#)2-0+3,(%0-29*-25 Q2R%H"0%$'-%/9.-0)*+,%:+,9-#%7):-/I - % a - %. || - L || - # a ∞ || @A || @ a A9X@!)Ω - 1 a 3 1 || - L || - # a A9@ || @A || @ a XA!Ω ( - L || - D ) ? a X µ - % 888888888888888888888888888888888 3 1 b ( - L || - D ) ( @A || @ ) G a X @A × A9X@ × 888888888888888888888888888888888 a X Y@XY!)Ω A9@ b ( @A || @ ) @ @ β a X 888888 a X 888888 a X A9@ %.J`_ -L

@A

? β a Y@X9Y @ b ? β a YNA9Y ? Y@XY ? 4 a 8888888888888888 a X 8888888888888 a X X9XX!)Ω @ b ?β YNA9Y ;')*'%)#%:-0(%*,"#-%$"%$'-%)2-+,%:+,9-%"1%X - L a X @A!)Ω9 -% X@A 8 a 8888888888888 a @9@@!Ω - %4 a 888888888888888 @ b ?β YNA9Y @ @ - %1 a 88888888888888888 8 X 88888888888888888888888888888 ! @9@@!Ω @ 8 X 88888888888 @ 8 @ @ 888888888 888888 X 88888 - %4 - % @9@@ @AAA

853

854 Chapter 10 Feedback

Example 10.7 continued

;')*'%)#%:-0(%,";8%+%')7',(%2-#)0+3,-%&0"&-0$(5%>-%+,#"%'+:-1 XA 8 8 a 888888888888 - 14 a 888888888888888 a A9@@!Ω @ b ?β YNA9Y @ @ - .-" a 88888888888888888888 a 88888888888888888888888888888 ! A9@@!Ω @ @ @ @ 8888888 X 888888 8888888888 X 888888888888 - 14 - D A9@@ @AAA ;')*'%+#%;-,,%)#%:-0(%,";8%+/"$'-0%')7',(%2-#)0+3,-%&0"&-0$(5 Q-R%61%$'-%+.&,)1)-0%)#%1-2%;)$'%+%:",$+7-%#"90*-% C # %'+:)/7%+%0-#)#$+/*-% - # a @!)Ω 8%$'-%"9$&9$%:",$+7-%*+/ 3-%1"9/2%10". C C 1 a ? 4 I # a ? 4 88888# -# M'9#8 C ? 888881 a 888884 a X X9XX!)Ω 88888888888888888888 a X X9XX !TUT C# -# @!)Ω

EXERCISE 10.15 ?.2!"#*!"2$1&2*&%&"$13*!$(4,%/%*2!%1!?%09!Q@A9@H'!2*4,$3*!"#*!ijJ?QD!;%"#!%"&!*C-%+$,*1"83%23-%" (.6*,!$16!-&*!/**65$3)!$1$,7&%&!".!&#.;!"#*!/.,,.;%10I

I (ideal) Rf

Vo

* Q

Is

Rout

Rs Rin

Figure E10.15

:$
10.7 The Feedback Current Amplifier (Shunt–Series)

-4 8 :6
10.6.3 An Important Note D#*!/**65$3)!$1$,7&%&!(*"#.6!%&!42*6%3$"*6!.1!"#*!$&&-(4"%.1!"#$"!$,,!:.2!(.&"*23%&*!@A9@H!$5.+*!%& &%(4,*!$16!3$1!5*!$1$,7=*6!6%2*3",7!:%9*9'!;%"#.-"!%1+.)%10!"#*!/**65$3)!$442.$3#
10.7 The Feedback Current Amplifier (Shunt–Series) 10.7.1 The Ideal Case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
!:@A9HX<

D#*!/**65$3)!3-22*1"!$(4,%/%*2!3$1!5*!2*42*&*1"*6!57!"#*!*C-%+$,*1"!3%23-%"!%1!?%09!@A9NY:5<9

855

856 Chapter 10 Feedback

Ii S

Ri

AIi

Ro

S%

Is

O

S

Rif

Af Is

S% (b)

Io

Rof

O%

Figure 10.28 :$
b."*!"#$"! ? 4 !%&!"#*!&#.2"83%23-%"!3-22*1"!0$%19!D#*!%14-"!2*&%&"$13*! - %4 !%&!/.-16!57!6%+%6%10 - % !57! ( @ b ? β ) '!;#%3#!%&!$!2*&-,"!./!"#*!&#-1"!3.11*3"%.1!$"!"#*!%14-"9!D#-&' -% - %4 a 888888888888888 8 @ b ?β

!:@A9_A<

D#*!.-"4-"!2*&%&"$13*! - 14 !%&!"#*!2*&%&"$13*!.5"$%1*6!57!&*""%10! I # a A' !52*$)%10!"#*!&#.2"8 3%23-%"!.-"4-"!,..4'!$"!&$7! jj′ '!$16!(*$&-2%10!"#*!2*&%&"$13*!5*";**1!"#*!";.!"*2(%1$,&!"#-& 32*$"*69!J%13*!"#*!&*2%*&!/**65$3)!3.11*3"%.1!$,;$7&!2$%&*&!2*&%&"$13*'!;*!3$1!.5"$%1! - 14 !57 (-,"%4,7%10! - 1 !57!( @ b ? β )' - 14 a ( @ b ? β )- 1

!:@A9_@<

10.7.2 The Practical Case ?%0-2*!@A9NX!&#.;&!$!5,.3)!6%$02$(!/.2!$!42$3"%3$,!&#-1"^&*2%*&!/**65$3)!$(4,%/%*29!D.!5* $5,*!".!$44,7!"#*!/**65$3)!*C-$"%.1&!".!"#%&!$(4,%/%*2'!;*!#$+*!".!2*42*&*1"!%"!57!"#*!%6*$, &"2-3"-2*!./!?%09!@A9NY:$<9!j-2!.5S*3"%+*!"#*2*/.2*!%&!".!6*+%&*!$!&%(4,*!(*"#.6!/.2!/%16%10 "#*! ?! $16! β !3%23-%"&9! [-%,6%10! .1! "#*! %1&%0#"!;*! #$+*! 0$%1*6! /2.(! "#*!&"-67! ./! "#*!"#2** ."#*2!".4.,.0%*&'!;*!42*&*1"!"#*!(*"#.6!/.2!"#*!&#-1"^&*2%*&!3$&*!;%"#.-"!6*2%+$"%.1'!%1!?%09 @A9\A9!R&!%1!42*+%.-&!3$&*&'!"#*!(*"#.6!./!?%09!@A9\A!$&&-(*&!"#$"!"#*!5$&%3!$(4,%/%*2!%&!-1%8 ,$"*2$,!:.2!$,(.&"!&.
10.7 The Feedback Current Amplifier (Shunt–Series)

Io Is

Basic amplifier

Rs Rif

Y

Rin

Rof

Io Feedback network

1

RL

Y% Rout

2

Figure 10.29 [,.3)!6%$02$(!/.2!$!42$3"%3$,!&#-1"^&*2%*&!/**65$3)!$(4,%/%*29

(a)

The A circuit is

Ii

Io Rs

Basic amplifier

R11

RL

R22 Y

Y%

Ri

Ro

where R11 is obtained from 1

Feedback network

R11 and the gain A is defined as (b)

and R22 is obtained from

A

2

Feedback network

1

2

R22

Io Ii

' is obtained from If

'

If Io

# V $0 1 " 1

Feedback network

2

Io

V1 $ 0

Figure 10.30 ?%16%10!"#*!?!3%23-%"!$16!β!/.2!"#*!3-22*1"8(%>%10!3-22*1"8&$(4,%10!:&#-1"^&*2%*&
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864 Chapter 10 Feedback

10.9 Determining the Loop Gain

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H)/+,,(8% )$% #'"9,2% 3-% /"$-2% $'+$% )/% #".-% *+#-#% )$% .+(% 3-% *"/:-/)-/$% $"% 2-$-0.)/-% ?β% 3( +&&,()/7%+%$-#$%*900-/$%I&%+/2%1)/2)/7%$'-%0-$90/-2%*900-/$%#)7/+,%I35%6/%$')#%*+#-8% ?β = X I 3 ⁄ I & 9 J/%+,$-0/+$):-%-F9):+,-/$%.-$'"2%1"0%2-$-0.)/)/7%?β%Q#--%j"#-/#$+048%ABDPR%$'+$%)#%9#9K +,,(%*"/:-/)-/$%$"%-.&,"(%-#&-*)+,,(%)/%Ef6@?%#).9,+$)"/#%)#%+#%1",,";#I%J#%3-1"0-8%$'-%,""& )#%30"4-/%+$%+%*"/:-/)-/$%&")/$5%M'-/%$'-%"&-/K*)0*9)$%:",$+7-%$0+/#1-0%19/*$)"/%@10%)#%2-$-0K .)/-2% +#% )/2)*+$-2% )/% H)75% AT5UCQ*R8% +/2% $'-% #'"0$K*)0*9)$% *900-/$% $0+/#1-0% 19/*$)"/% @#0% )# 2-$-0.)/-2%+#%#'";/%)/%H)75%AT5UCQ2R5%M'-#-%$;"%$0+/#1-0%19/*$)"/#%+0-%$'-/%*".3)/-2%$" "3$+)/%$'-%,""&%7+)/%?β8

@ @ ? β = X @!! 8888888 + 888888 @10 @#0

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

! { - D ff [ - N + - @ ff ( - %. + - ) ] } [ - @ ff ( - %. + - ) ]! - %. ! 8888888888888888888888888888888888888888888888888 8 8888888888888888 8 %QAT5DTR C3 = X µ C @ 888888888888888888888888888888888888888888888888888888888888888888888888888888 { - D ff [ - N + - @ ff ( - %. + - ) ] } + 3 1 [ - @ ff ( - %. + - ) ] + - N - %. + M')#%-F9+$)"/%*+/%3-%9#-2%2)0-*$,(%$"%1)/2%$'-%,""&%7+)/% D = ? β = X C3 ⁄ C& = X C3 ⁄ C@ 9 E)/*-%$'-%,""&%7+)/%D%)#%7-/-0+,,(%+%19/*$)"/%"1%10-F9-/*(8%)$%)#%9#9+,%$"%*+,,%)$%6..-(%+$!/7 0&//&.!%+/2%$"%2-/"$-%)$%3(%DQ#R%"0(DQ PωR5

865

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X " V t !

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10.9.2 Equivalence of Circuits from a Feedback-Loop Point of View !4+5(,-*(6,/3&(+0(7"47/",(,-*+4&()*(=#+)(,-$,(,-*(1+%*6(+0($(7"47/",($4*("#3*1*#3*#,(+0(,-* *<,*4#$%( *<7",$,"+#:( @#( 0$7,( ,-*( 1+%*6'( +4( ,-*( #$,/4$%( 5+3*6( A)-"7-( "6( $( 5+4*( $114+14"$,*

10.9 Determining the Loop Gain

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867

868 Chapter 10 Feedback

EXERCISES 10.18 )*+,!-./!0112!34*+! ! β !516!-./!5//,7489!4:20*5*/6!*+!)*3%!#$%#;!"<=4:20/!#$%>(%!?/-!( " M $I !76/49 -./!0112!4-!-./!34-/!15! % K I !4220@!4!A10-43/! ( ) !-1!-./!34-/!15! % K I !4+,!,/-/6:*+/!-./!6/-B6+/,!A10-43/ ( * !4-!-./!,64*+!15! % # % !!4+, 81:246/!-1!-./!A40B/!17-4*+/,!*+!<=4:20/!#$%>%!D/30/8-! * +# !4+,! * +K % . # . /# , -K . /K LLLLLLLLLLLLLLLLLLLL L E!#F%F;!"81:246/,!-1!#;%'G!17-4*+/,!*+!<=4:20/!#$%>( Ans. ! β M LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL # # . /K N . K N . # || LLLLLLLL . # N LLLLLLLL , -# , -K 10.19 )*+,!-./!0112!34*+! ! β !516!-./!5//,7489!4:20*5*/6!*+!)*3%!<#$%#H!"<=/68*C/!#$%#H(%!?/-! 0 " M $I!76/49 -./!0112!4-!-./!34-/!15!%I!4220@!4!A10-43/! ( ) !-1!-./!34-/!15!%&'4+,!,/-/6:*+/!-./!A10-43/! ( * !-.4422/46C!4861CC! . " %!)*+,!-./!A40B/!15! ! β !BC*+3!-./!81:21+/+-!A40B/C!3*A/+!*+!<=/68*C/!#$%#HI!4+, 81:246/!-1!-./!A40B/!3*A/+!*+!-./!4+CJ/6!-1!<=/68*C/!#$%#H% ,- *+ ." Ans. ! β M LLLLLLLLLLLLLLLLLLLLLLLLLLL E!'%KK!"81:246/,!-1!'%$'!17-4*+/,!*+!<=/68*C/!#$%#H( *+ N .# N ."

10.10 The Stability Problem 10.10.1 Transfer Function of the Feedback Amplifier !"#$#%&&'($)*#$+,-.%.&/#01)2#$0#32$3#/&,/&0&"3&'#(4#32&"&/$-#03/1)31/%#7.58#9:89;#32,&"< -66,#5$."#!#.0#5&"&/$--4#$# %1")3.6"#6%#%/&=1&")4;# $"'# .3# 0261-'#32&/&%6/&#(&#+6/&# $))1/$3&-4 )$--&'#32&#!"#$%&!!"'()*$+,#)',-$.(/!$;#!>"?8#@-06;#A$B&#(&&"#$001+."5#%6/#32&#+603#,$/3 32$3#32&#%&&'($)*#"&3A6/*#.0#/&0.03.B&#$"'#2&") $3#32&#%&&'($)*#%$)36/# β#.0#)6"03$"3;#(13#32.0 "&&'#"63#(&#$-A$40#32&#)$0&8#C$--#32&/&%6/&#$001+ $3#."#32&"&/$-#)$0 &#,##01*.2 ()*$+,#)',-$.(/!$#.0#β >"?8#!3#%6--6A0#32$3#32&#.&!+#0%&!!"'()*$+,#)',-$.(/!$#!# >"?#.0#5.B&"#(4

!(") ! # ( " ) = LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL # + !(")β(")

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E6#%6)10#$33&"3.6"#6"#32&#,6."30#)&"3/$-#36#61/#'.0)100.6"#."#32.0#0&)3.6";#A$--#$001+& 32$3#32&#$+,-.%.&/#.0#'./&)3#)61,-&'#A.32#)6"03$"3#')#5$."#!:#$"'#A.32#,6-&0#$"'#F&/60#6))1/< /."5#."#32.52<%/&=1&")4#($"'8#@-06;#%6/#32.+&#(&."5#-&3#10#$001+ $3#$3#-6A#%/&=1&"< ).&0# β >"?# /&'1)&0# 36# $# )6"03$"3# B$-1&8# E210# $3# -6A# %/&=1&").&0# 32&# -66,# 5$."# !>"?β >"? (&)6+&0#$#)6"03$"3;#A2.)2#0261-'#(&#$#,60.3.B&#"1+(&/G#632&/A.0 &#%&&'($)*#A61-'#"63 (&#"&5$3.B&8#E2&#=1&03.6"#32&"#.0H#C2$3#2$,,&"0#$3#2.52&/#%/&=1&").&0I 76/#,240.)$-#%/&=1&").&0#"#=#$ω;#J=8#>9:8D9?#(&)6+&0 !($ω) ! # ( $ ω ) = LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL # + !($ω)β($ω)

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10.10 The Stability Problem

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Q 4 = ? ( P ω @YA ) β ( P ω @YA )Q % = X Q % E)/*-%Q4%)#%190$'-0%.9,$)&,)-2%3(%XA%)/%$'-%#9..-0%3,"*4%+$%$'-%)/&9$8%;-%#--%$'+$%$'-%1--2K 3+*4%*+9#-#%$'-%#)7/+,%Q%%+$%$'-%+.&,)1)-0%)/&9$%$"%3-%#/#&+%$".5%M'+$%)#8%10".%$')#%&")/$%"/8 $'-0-%;),,%3-%#)/9#")2+,%#)7/+,#%+$%$'-%+.&,)1)-0%)/&9$%+/2%"9$&9$%"1%10-F9-/*(%ωADT5%M'9#%$'+.&,)1)-0%)#%#+)2%$"%"#*),,+$-%+$%$'-%10-F9-/*(%ωADT5 M'-%F9-#$)"/%/";%)#I%>'+$%'+&&-/#%)1%+$% ωADT%$'-%.+7/)$92-%"1%$'-%,""&%7+)/%)#%70-+$-0 $'+/% 9/)$(n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h-*$):-%'-0-%)#%h9#$ $'-%"&&"#)$-I%Z";%$'+$%;-%4/";%'";%"#*),,+$)"/#%*"9,2%"**90%)/%+%/-7+$):-K1--23+*4%+.&,)K 1)-08%;-%;)#'%$"%1)/2%.-$'"2#%$"%&0-:-/$%$'-)0%"**900-/*-5

10.10.2 The Nyquist Plot M'-%Z(F9)#$%&,"$%)#%+%1"0.+,)L-2%+&&0"+*'%1"0%$-#$)/7%1"0%#$+3),)$(%3+#-2%"/%$'-%2)#*9##)"/ +3":-5% 6$% )#% #).&,(% +% &",+0% &,"$% "1% ,""&% 7+)/% ;)$'% 10-F9-/*(% 9#-2% +#% +% &+0+.-$-05% H)790AT5UW%#'";#%#9*'%+%&,"$5%Z"$-%$'+$%$'-%0+2)+,%2)#$+/*-%)#% ? β %+/2%$'-%+/7,-%)#%$'-%&'+#+/7,-% φ5%M'-%#",)2K,)/-%&,"$%)#%1"0%&"#)$):-%10-F9-/*)-#5%E)/*-%$'-%,""&%7+)/k+/2%1"0%$'+$ .+$$-0%+/(%7+)/%19/*$)"/%"1%+%&'(#)*+,%/-$;"04k'+#%+%.+7/)$92-%$'+$%)#%+/%-:-/%19/*$)"/ "1%10-F9-/*(%+/2%+%&'+#-%$'+$%)#%+/%"22%19/*$)"/%"1%10-F9-/*(8%$'-(?β(&,"$%1"0%/-7+$):-%10-K F9-/*)-#%Q#'";/%)/%H)75%AT5UW%+#%+%30"4-/%,)/-R%*+/%3-%20+;/%+#%+%.)00"0%).+7-%$'0"97'%$'j-%+G)#5 M'-%Z(F9)#$%&,"$%)/$-0#-*$#%$'-%/-7+$):-%0-+,%+G)#%+$%$'-%10-F9-/*(% ωADT5%M'9#8%)1%$')# )/$-0#-*$)"/%"**90#%$"%$'-%,-1$%"1%$'-%&")/$%QXA8%TR8%;-%4/";%$'+$%$'-%.+7/)$92-%"1%,""&%7+)/ +$% $')#% 10-F9-/*(% )#% 70-+$-0% $'+/% 9/)$(% +/2% $'-% +.&,)1)-0% ;),,% 3-% 9/#$+3,-5% Y/% $'-% "$'-0 '+/28%)1%$'-%)/$-0#-*$)"/%"**90#%$"%$'-%0)7'$%"1%$'-%&")/$%QXA8%TR%$'-%+.&,)1)-0%;),,%3-%#$+3,-5 6$% 1",,";#% $'+$% )1% $'-% Z(F9)#$% &,"$% "$0%302"#% $'-% &")/$% QXA8% TR% $'-/% $'-% +.&,)1)-0% ;),,% 3-

869

870 Chapter 10 Feedback

Figure 10.34 !"#$%&'()*+$,-.+$./$01$(1*+02-#$03,-)/)#45

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EXERCISE 10.20 @.1*):#4$0$/##:20
Ans. ω GHI =

J

K × GI $40:L*M$ β <4 = I5IIH

10.11 Effect of Feedback on the Amplifier Poles F,(*%/5'060(4*64(=!("8;*4(#5-"#(*%".*#$%&0'0$;*%4(*.($(4/0"(.*.04(8$';*&;*0$#*5-'(#)*F,(4(9 6-4(*2(*#,%''*0"3(#$0G%$(*$,(*(66(8$*-6*6((.&%8?*-"*$,(*5-'(#*-6*$,(*%/5'060(4)H

6

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10.11 Effect of Feedback on the Amplifier Poles

10.11.1 Stability and Pole Location >-%#'+,,%3-7)/%3(%*"/#)2-0)/7%$'-%0-,+$)"/#')&%3-$;--/%#$+3),)$(%+/2%&",-%,"*+$)"/5%H"0%+/ +.&,)1)-0%"0%+/(%"$'-0%#(#$-.%$"%3-%#$+3,-8%)$#%&",-#%#'"9,2%,)-%)/%$'-%,-1$%'+,1%"1%$'-%#%&,+/-5%J &+)0%"1%*".&,-GK*"/h97+$-%&",-#%"/%$'-(Pω%+G)#%7):-#%0)#-%$"%#9#$+)/-2%#)/9#")2+,%"#*),,+$)"/#5 f",-#%)/%$'-%0)7'$%'+,1%"1%$'-%#%&,+/-%7):-%0)#-%$"%70";)/7%"#*),,+$)"/#5 M"%:-0)1(%$'-%#$+$-.-/$%+3":-8%*"/#)2-0%+/%+.&,)1)-0%;)$'%+%&",-%&+)0%+$%#(=( σT% ± Pω$5%61 $')#%+.&,)1)-0%)#%#93h-*$-2%$"%+%2)#$903+/*-8%#9*'%+#%$'+$%*+9#-2%3(%*,"#90-%"1%$'-%&";-0K #9&&,(%#;)$*'8%)$#%$0+/#)-/$%0-#&"/#-%;),,%*"/$+)/%$-0.#%"1%$'-%1"0. v(&)

σ &

= " A ["

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σA &

] = N"

3.&( ω $ & )

σA &

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M')#%)#%+%#)/9#")2+,%#)7/+,%;)$'%+/%-/:-,"&-% " 5%Z";%)1%$'-%&",-#%+0-%)/%$'-%,-1$%'+,1%"1%$'# &,+/-8%$'-/% σT%;),,%3-%/-7+$):-%+/2%$'-%"#*),,+$)"/#%;),,%2-*+(%-G&"/-/$)+,,(%$";+02%L-0"8%+# #'";/%)/%H)75%AT5UdQ+R8%)/2)*+$)/7%$'+$%$'-%#(#$-.%)#%#$+3,-5%618%"/%$'-%"$'-0%'+/28%$'-%&",-#%+0-%)/

(a)

(b)

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10.11.2 Poles of the Feedback Amplifier H0".%$'-%*,"#-2K,""&%$0+/#1-0%19/*$)"/%)/%?F5%QAT5DAR8%;-%#--%$'+$%$'-%&",-#%"1%$'-%1--23+*4 +.&,)1)-0%+0-%$'-%L-0"#%"1%A%+%?Q#Rβ Q#R5%M'+$%)#8%$'-%1--23+*4K+.&,)1)-0%&",-#%+0-%"3$+)/-2%3( #",:)/7%$'-%-F9+$)"/

@ + ?:#< β :#< = A

%QAT5DdR

;')*'% )#% *+,,-2% $'-% 49$+$4%"+&/%&4( ">1$%&.!% "1% $'-% 1--23+*4% ,""&5% 6$% #'"9,2% $'-0-1"0-% 3+&&+0-/$%$'+$%+&&,()/7%1--23+*4%$"%+/%+.&,)1)-0%*'+/7-#%)$#%&",-#5 6/% $'-% 1",,";)/78% ;-% #'+,,% *"/#)2-0% '";% 1--23+*4% +11-*$#% $'-% +.&,)1)-0% &",-#5% H"0% $')# &90&"#-%;-%#'+,,%+##9.-%$'+$%$'-%"&-/K,""&%+.&,)1)-0%'+#%0-+,%&",-#%+/2%/"%1)/)$-%L-0"#%Q)5-58 +,,%$'-%L-0"#%+0-%+$%#%=%∞R5%M')#%;),,%#).&,)1(%$'-%+/+,(#)#%+/2%-/+3,-%9#%$"%1"*9#%"90%+$$-/$)"/ "/%$'-%19/2+.-/$+,%*"/*-&$#%)/:",:-25%>-%#'+,,%+,#"%+##9.-%$'+$%$'-%1--23+*4%1+*$"0% β%)# )/2-&-/2-/$%"1%10-F9-/*(5

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?A 8 ?:#< = 888888888888888888888 @ + # ⁄ ωR

%QAT5DPR

M'-%*,"#-2K,""&%$0+/#1-0%19/*$)"/%)#%7):-/%3(

?A ⁄ ( @ + ?A β ) 8 ? 4 :#< = 888888888888888888888888888888888888888888888 @ + # ⁄ ωR ( @ + ?A β )

%QAT5DOR

M'9#%$'-%1--23+*4%.":-#%$'-%&",-%+,"/7%$'-%/-7+$):-%0-+,%+G)#%$"%+%10-F9-/*(%ωR4 8

ω R4 = ω R ( @ + ? A β )

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(b)

(a)

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EXERCISE 10.21

R1!.4!$(4!#$+%10!$!&%10,*84.,*!2.,,.//!$"!@AA!`=!$16!$!,.;8/2*C-*137!0$%1!./!@AH!%&!.4*2$"*6!%1 $!/**65$3)!,..4!;%"#!β!=!A9A@9!L#$"!%&!"#*!/$3".2!57!;#%3#!/**65$3)!&#%/"&!"#*!4.,*V!D.!;#$"!/2*8 C-*137V!K/!β!%&!3#$10*6!".!$!+$,-*!"#$"!2*&-,"&!%1!$!3,.&*68,..4!0$%1!./!+@'!".!;#$"!/2*C-*137!6.*& "#*!4.,*!&#%/"V! Ans. @AA@E!@AA9@!)`=E!@A!i`=

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?A 8 ?:#< = 888888888888888888888888888888888888888888888888888888888 :@ + # ⁄ ω R@ < ( @ + # ⁄ ω RN )

%QAT5BTR

6/%$')#%*+#-8%$'-%*,"#-2K,""&%&",-#%+0-%"3$+)/-2%10".%A%+%?Q#Rβ%=%T8%;')*'%,-+2#%$"% N

# + # ( ω R@ + ω RN ) + ( @ + ? A β ) ω R@ ω RN = A

%QAT5BAR

M'9#%$'-%*,"#-2K,""&%&",-#%+0-%7):-/%3(

@ @ N %QAT5BCR # = X 888 ( ω R@ + ω RN ) !±! 888 ( ω R@ + ω RN ) X G ( @ + ? A β ) ω R@ ω RN N N H0".% ?F5% QAT5BCR% ;-% #--% $'+$% +#% $'-% ,""&% 7+)/% ?T β% )#% )/*0-+#-2% 10".% L-0"8% $'-% &",-#% +0-

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874 Chapter 10 Feedback

Figure 10.37 B.."8,.3-&! 6%$02$(! /.2! $! /**65$3) $(4,%/%*2! ;#.&*! .4*18,..4! "2$1&/*2! /-13"%.1! #$&! ";. 2*$,!4.,*&9

H0".% $'-% 0""$K,"*9#% 2)+70+.% "1% H)75% AT5UO% ;-% #--% $'+$% $')#% 1--23+*4% +.&,)1)-0% +,#"% )# 9/*"/2)$)"/+,,(%#$+3,-5%J7+)/8%$')#%0-#9,$%#'"9,2%*".-%+#%/"%#90&0)#-V%$'-%.+G).9.%&'+##')1$%"1%?Q#R%)/%$')#%*+#-%)#%ADT°%QBT°%&-0%&",-R8%39$%$')#%:+,9-%)#%0-+*'-2%+$%ω%=%∞5%M'9#%$'-0)#%/"%1)/)$-%10-F9-/*(%+$%;')*'%$'-%&'+#-%#')1$%0-+*'-#%ADT°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

ωA ! N 8 + ω NA = A # + # 8888888 K

%QAT5BUR

;'-0-%ωT%)#%*+,,-2%$'-%-.6"(2+">1"!4;%+/2%K%)#%*+,,-2%-.6"(!(2$4%.+5%M'-%&",-#%+0-%*".&,-G )1%K%)#%70-+$-0%$'+/%T5d5%J%7-".-$0)*%)/$-0&0-$+$)"/%1"0%ωT%+/2%K%"1%+%&+)0%"1%*".&,-GK*"/h97+$&",-#%)#%7):-/%)/%H)75%AT5UD8%10".%;')*'%;-%/"$-%$'+$% ωT%)#%$'-%0+2)+,%2)#$+/*-%"1%$'-%&",-# 10".%$'-%"0)7)/%+/2%$'+$%K%)/2)*+$-#%$'-%2)#$+/*-%"1%$'-%&",-#%10".%$'-%Pω%+G)#5%f",-#%"/%$'Pω%+G)#%'+:-%K%=%∞5% =(%*".&+0)/7%?F#5%QAT5BAR%+/2%QAT5BUR%;-%"3$+)/%$'-%K%1+*$"0%1"0%$'-%&",-#%"1%$'-%1--2K 3+*4%+.&,)1)-0%+#

( @ + ? A β ) ω R@ ω RN K = 888888888888888888888888888888888888888888888 ω R@ + ω RN

%QAT5BWR

Figure 10.38 d*/%1%"%.1! ./! ωA! $16! K! ./! $! 4$%2! ./! 3.(4,*>8 3.1S-0$"*!4.,*&9

Normalized gain (dB)

10.11 Effect of Feedback on the Amplifier Poles

Q$1 Q $ 0.707 (maximally flat response)

0 Q $ 0.5

"12 dB/octave

Q $ 0.3

+ (log scale) Figure 10.39 b.2($,%=*6!0$%1!./!$!";.84.,*!/**65$3)!$(4,%/%*2!/.2!+$2%.-&!+$,-*&!./!K9!b."*!"#$"!K!%& 6*"*2(%1*6!57!"#*!,..4!0$%1!$33.26%10!".!QC9!:@A9XG<9

H0".% $'-% #$92(% "1%#-*"/2K"02-0% /-$;"04% 0-#&"/#-#% )/%@'+&$-0% AP8% )$% ;),,% 3-% #--/% $'+$% $'0-#&"/#-%"1%$'-%1--23+*4%+.&,)1)-0%9/2-0%*"/#)2-0+$)"/%#'";#%/"%&-+4)/7%1"0%K%≤%T5OTO5%M'3"9/2+0(%*+#-%*"00-#&"/2)/7%$"%K%=%T5OTO%Q&",-#%+$%Wd°%+/7,-#R%0-#9,$#%)/%$'-%0$:&0$66; 26$%%0-#&"/#-5%H)790-%AT5UB%#'";#%+%/9.3-0%"1%&"##)3,-%0-#&"/#-#%"3$+)/-2%1"0%:+0)"9#%:+,K 9-#%"1%K%Q"08%*"00-#&"/2)/7,(8%:+0)"9#%:+,9-#%"1%?Tβ R5

EXERCISE 10.22 R1!$(4,%/%*2!;%"#!$!,.;8/2*C-*137!0$%1!./!@AA!$16!4.,*&!$"!@AG!2$6U&!$16!@A_!2$6U&!%&!%13.24.2$"*6 %1!$!1*0$"%+*8/**65$3)!,..4!;%"#!/**65$3)!/$3".2!β9!?.2!;#$"!+$,-*!./!β!6.!"#*!4.,*&!./!"#*!3,.&*68 ,..4!$(4,%/%*2!3.%13%6*V!L#$"!%&!"#*!3.22*&4.16%10!K!./!"#*!2*&-,"%10!&*3.168.26*2!&7&"*(V!?.2 ;#$"!+$,-*!./! β!%&!$!($>%($,,7!/,$"!2*&4.1&*!$3#%*+*6V!L#$"!%&!"#*!,.;8/2*C-*137!3,.&*68,..4 0$%1!%1!"#*!($>%($,,7!/,$"!3$&*V Ans. A9NGHE!A9HE!A9HE!@9X_!TUT

Example 10.9 J#%+/%),,9#$0+$)"/%"1%#".-%"1%$'-%)2-+#%h9#$%2)#*9##-28%;-%*"/#)2-0%$'-%&"#)$):-K1--23+*4%*)0*9)$%#'";/%)/ H)75%AT5WTQ+R5%H)/2%$'-%,""&%$0+/#.)##)"/%DQ#R%+/2%$'-%*'+0+*$-0)#$)*%-F9+$)"/5%E4-$*'%+%0""$K,"*9#%2)+70+. 1"0%:+0()/7%S8%+/2%1)/2%$'-%:+,9-%"1%S%$'+$%0-#9,$#%)/%+%.+G).+,,(%1,+$%0-#&"/#-%+/2%$'-%:+,9-%"1%S%$'+$ .+4-#%$'-%*)0*9)$%"#*),,+$-5%J##9.-%$'+$%$'-%+.&,)1)-0%'+#%10-F9-/*(K)2-&-/2-/$%7+)/8%)/1)/)$-%)/&9$%).&-2K +/*-8%+/2%L-0"%"9$&9$%).&-2+/*-5%

Solution M"% "3$+)/% $'-% ,""&% $0+/#.)##)"/8% ;-% #'"0$K*)0*9)$% $'-% #)7/+,% #"90*-% +/2% 30-+4% $'-% ,""&% +$% $'-% +.&,)1)-0 )/&9$5%>-%$'-/%+&&,(%+%$-#$%:",$+7-%C&%+/2%1)/2%$'-%0-$90/-2%:",$+7-%C3 8%+#%)/2)*+$-2%)/%H)75%AT5WTQ3R5%M'-%

875

876 Chapter 10 Feedback Example 10.9 continued

# Vs "

R

C

R

R # Vr "

C

C

C

Vo

#K

R

#K Vt

# V1 "

# "

(b)

(a) j+

K$3 Q$*

K $ 1.586 Q $ 0.707 s plane

K$0 1 Q$ 3

450

K$1 Q $ 0.5

,

45-

K $ 1.586 Q $ 0.707 K$3 Q$* (c) Figure 10.40 M%23-%"&!$16!4,."!/.2!Q>$(4,*!@A9X9

,""&%$0+/#.)##)"/% D ( # ) ≡ ? ( # ) β ( # ) %)#%7):-/%3( C D ( # ) = X 888883 = X S@ ( # ) C&

!:@A9XH<

;'-0-%@Q#R%)#%$'-%$0+/#1-0%19/*$)"/%"1%$'-%$;"K&"0$%j@%/-$;"04%#'";/%)/#)2-%$'-%30"4-/K,)/-%3"G%)/%H)75 AT5WTQ3RI C #:@ ⁄ 5- < 8 @( # ) ≡ 888883 = 888888888888888888888888888888888888888888888888888888888888 !:@A9X_< C@ # N + # :\ ⁄ 5- < + :@ ⁄ 5-
10.11 Effect of Feedback on the Amplifier Poles

M'9#8 X # ( ST5- ) 8 D ( # ) = 88888888888888888888888888888888888888888888888888888888 N N # + # ( \T5- ) + ( @T5- )

!:@A9XZ<

@ + D(#) = A

!:@A9XY<

M'-%*'+0+*$-0)#$)*%-F9+$)"/%)#

$'+$%)#8 \! @ N # + # 88888888 + 88888888 55-

N

S X # 88888888 = A 5-

\XS @ N N # + # 8888888888888 + 88888888 = A !:@A9XX< 55=(% *".&+0)/7% $')#% -F9+$)"/% $"% $'-% #$+/2+02% 1"0.% "1% $'-% #-*"/2K"02-0% *'+0+*$-0)#$)*% -F9+$)"/% Q?F5 AT5BUR%;-%#--%$'+$%$'-%&",-%10-F9-/*(%ωT%)#%7):-/%3( @ ω A = 88888888

!:@A9@AA<

@ K = 8888888888888 \XS

!:@A9@A@<

5-

+/2%$'-%K%1+*$"0%)#

M'9#% 1"0% S% =% T8% $'-% &",-#% '+:-% K = @88\8 ( +/2% +0-% $'-0-1"0-% ,"*+$-2% "/% $'-% /-7+$):-% 0-+,% +G)#5% J#% S% )# )/*0-+#-28%$'-%&",-#%+0-%30"97'$%*,"#-0%$"7-$'-0%+/2%-:-/$9+,,(%*")/*)2-%QK%=%T5d8%S%=%AR5%H90$'-0%)/*0-+#K )/7%S%0-#9,$#%)/%$'-%&",-#%3-*".)/7%*".&,-G%+/2%*"/h97+$-5%M'-%0""$%,"*9#%)#%$'-/%+%*)0*,-%3-*+9#-%$'0+2)+,%2)#$+/*-%ωT%0-.+)/#%*"/#$+/$%Q?F5%AT5ATTR%)/2-&-/2-/$%"1%$'-%:+,9-%"1%S5 D#*!($>%($,,7!/,$"!2*&4.1&*!%&!.5"$%1*6!;#*1!K!=!A9ZAZ'!;#%3#!2*&-,"&!;#*1!S(=!@9HY_9!K1!"#%&!3$&* "#*!4.,*&!$2*!$"!GH°!$10,*&'!$&!%16%3$"*6!%1!?%09!@A9GA:3<9!D#*!4.,*&!32.&&!"#*!Pω!$>%&!%1".!"#*!2%0#"!#$,/!./ "#*!#!4,$1*!$"!"#*!+$,-*!./!S!"#$"!2*&-,"&!%1!K!=!∞'!"#$"!%&'!S!=!\9!D#-&!/.2!S ≥ \!"#%&!3%23-%"!5*3.(*&!-1&"$8 5,*9!D#%&!(%0#"!$44*$2!".!3.1"2$6%3"!.-2!*$2,%*2!3.13,-&%.1!"#$"!"#*!/**65$3)!$(4,%/%*2!;%"#!$!&*3.168.26*2 2*&4.1&*!%&!-13.16%"%.1$,,7!&"$5,*9!b."*'!#.;*+*2'!"#$"!"#*!3%23-%"!%1!"#%&!*>$(4,*!%&!C-%"*!6%//*2*1"!/2.( "#*!1*0$"%+*8/**65$3)!$(4,%/%*2!"#$"!;*!#$+*!5**1!&"-67%109!`*2*!;*!#$+*!$1!$(4,%/%*2!;%"#!$!4.&%"%+* 0$%1!S!$16!$!/**65$3)!1*";.2)!;#.&*!"2$1&/*2!/-13"%.1!@:#
?G+.&,-%AT5B%),,9#$0+$-#%$'-%9#-%"1%1--23+*4%Q&"#)$):-%1--23+*4%)/%$')#%*+#-R%$"%.":-%$'&",-#%"1%+/%j@%/-$;"04%10".%$'-)0%/-7+$):-%0-+,K+G)#%,"*+$)"/#%$"%*".&,-GK*"/h97+$-%,"*+K $)"/#5%Y/-%*+/%+**".&,)#'%$'-%#+.-%$+#4%9#)/7%/-7+$):-%1--23+*48%+#%$'-%0""$K,"*9#%2)+70+. "1%H)75%AT5UO%2-."/#$0+$-#5%M'-%&0"*-##%"1%&",-%*"/$0",%)#%$'-%-##-/*-%"1%+0&%<";4%2&"3%."#%*$N +#%;),,%3-%2)#*9##-2%)/%@'+&$-0%AP5

10.11.5 Amplifiers with Three or More Poles H)790-% AT5WA% #'";#% $'-% 0""$K,"*9#% 2)+70+.% 1"0% +% 1--23+*4% +.&,)1)-0% ;'"#-% "&-/K,""& 0-#&"/#-%)#%*'+0+*$-0)L-2%3(%$'0--%&",-#5%J#%)/2)*+$-28%)/*0-+#)/7%$'-%,""&%7+)/%10".%L-0" .":-#% $'-% ')7'-#$K10-F9-/*(% &",-% "9$;+02% ;'),-% $'-% $;"% "$'-0% &",-#% +0-% 30"97'$% *,"#-0 $"7-$'-05% J#% ?Tβ% )#% )/*0-+#-2% 190$'-08% $'-% $;"% &",-#% 3-*".-% *")/*)2-/$% +/2% $'-/% 3-*".*".&,-G%+/2%*"/h97+$-5%J%:+,9-%"1%?Tβ%-G)#$#%+$%;')*'%$')#%&+)0%"1%*".&,-GK*"/h97+$-%&",-# -/$-0#%$'-%0)7'$%'+,1%"1%$'-%#%&,+/-8%$'9#%*+9#)/7%$'-%+.&,)1)-0%$"%3-*".-%9/#$+3,-5%

877

878 Chapter 10 Feedback

Figure 10.41 B.."8,.3-&! 6%$02$(! /.2 $1!$(4,%/%*2!;%"#!"#2**!4.,*&9!D#*!$22.;& %16%3$"*! "#*! 4.,*! (.+*(*1"! $&! ?A β! %& %132*$&*69

M')#%0-#9,$% )#%/"$%-/$)0-,(% 9/-G&-*$-28%#)/*-% +/% +.&,)1)-0%;)$'%$'0--% &",-#%'+#%+% &'+##')1$% $'+$% 0-+*'-#% XCOT°% +#% ω% +&&0"+*'-#% ∞5% M'9#% $'-0-% -G)#$#% +% 1)/)$-% 10-F9-/*(8% ωADT8% +$ ;')*'%$'-%,""&%7+)/%'+#%ADT°%&'+#-%#')1$5 H0".% $'-% 0""$K,"*9#% 2)+70+.% "1% H)75% AT5WA8% ;-% "3#-0:-% $'+$% "/-% *+/% +,;+(#% .+)/$+)/ +.&,)1)-0%#$+3),)$(%3(%4--&)/7%$'-%,""&%7+)/%?T β%#.+,,-0%$'+/%$'-%:+,9-%*"00-#&"/2)/7%$"%$'&",-#%-/$-0)/7%$'-%0)7'$%'+,1K&,+/-5%6/%$-0.#%"1%$'-%Z(F9)#$%2)+70+.8%$'-%*0)$)*+,%:+,9-%"1%?T β )#% $'+$% 1"0% ;')*'% $'-% 2)+70+.% &+##-#% $'0"97'% $'-% QXA8% TR% &")/$5% j-29*)/7% ?T β% 3-,";% $')# :+,9-%*+9#-#%$'-%Z(F9)#$%&,"$%$"%#'0)/4%+/2%$'9#%)/$-0#-*$%$'-%/-7+$):-%0-+,%+G)#%$"%$'-%0)7'$%"1 $'-%QXA8%TR%&")/$8%)/2)*+$)/7%#$+3,-%+.&,)1)-0%&-01"0.+/*-5%Y/%$'-%"$'-0%'+/28%)/*0-+#)/7%?T β +3":-%$'-%*0)$)*+,%:+,9-%*+9#-#%$'-%Z(F9)#$%&,"$%$"%-G&+/28%$'9#%-/*)0*,)/7%$'-%QXA8%TR%&")/$ +/2%)/2)*+$)/7%9/#$+3,-%&-01"0.+/*-5% H"0%+%7):-/%"&-/K,""&%7+)/%?T%$'-%*"/*,9#)"/#%+3":-%*+/%3-%#$+$-2%)/%$-0.#%"1%$'-%1--2K 3+*4%1+*$"0%β5%M'+$%)#8%$'-0-%-G)#$#%+%A+8%A/A(<+2/"%1"0%β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

EXERCISE 10.23 M.1&%6*2!$!/**65$3)!$(4,%/%*2!/.2!;#%3#!"#*!.4*18,..4!"2$1&/*2!/-13"%.1!?:#
\

10.12 Stability Study Using Bode Plots

879

]*"!"#*!/**65$3)!/$3".2!β!5*!/2*C-*137!%16*4*16*1"9!?%16!"#*!3,.&*68,..4!4.,*&!$&!/-13"%.1&!./!β' $16!&#.;!"#$"!"#*!2.."!,.3-&!%&!"#$"!./!?%09!Q@A9N\9!R,&.!/%16!"#*!+$,-*!./!β!$"!;#%3#!"#*!$(4,%/%*2 5*3.(*&!-1&"$5,*9!:V1&",!D#%&!%&!"#*!&$(*!$(4,%/%*2!"#$"!;$&!3.1&%6*2*6!%1!Q>*23%&*!@A9NA9<

Figure 10.E23

Ans. E--%H)75%?AT5CUV%β*0)$)*+,%=%T5TTD

10.12 Stability Study Using Bode Plots 10.12.1 Gain and Phase Margins H0".%E-*$)"/#%AT5AT%+/2%AT5AA%;-%4/";%$'+$%;'-$'-0%+%1--23+*4%+.&,)1)-0%)#%"0%)#%/"$%#$+K 3,-%*+/%3-%2-$-0.)/-2%3(%-G+.)/)/7%)$#%,""&%7+)/% ?β%+#%+%19/*$)"/%"1%10-F9-/*(5%Y/-%"1 $'-%#).&,-#$%+/2%."#$%-11-*$):-%.-+/#%1"0%2")/7%$')#%)#%$'0"97'%$'-%9#-%"1%+%="2-%&,"$%1"0%?β8 #9*'%+#%$'-%"/-%#'";/%)/%H)75%AT5WC5%QZ"$-%$'+$%3-*+9#-%$'-%&'+#-%+&&0"+*'-#%XUPT°8%$'-%/-$K ;"04%-G+.)/-2%)#%+%1"90$'K"02-0%"/-5R%M'-%1--23+*4%+.&,)1)-0%;'"#-%,""&%7+)/%)#%&,"$$-2%)/ H)75%AT5WC%;),,%3-%#$+3,-8%#)/*-%+$%$'-%10-F9-/*(%"1%ADT°%&'+#-%#')1$8%ωADT8%$'-%.+7/)$92-%"1%$',""&%7+)/%)#%,-##%$'+/%9/)$(%Q/-7+$):-%2=R5%M'-%2)11-0-/*-%3-$;--/%$'-%:+,9-%"1% ? β %+$%ωADT +/2%9/)$(8%*+,,-2%$'-%#$&!(0$+#&!8%)#%9#9+,,(%-G&0-##-2%)/%2-*)3-,#5%M'-%7+)/%.+07)/%0-&0-K #-/$#% $'-% +."9/$% 3(% ;')*'% $'-% ,""&% 7+)/% *+/% 3-% )/*0-+#-2% ;'),-% #$+3),)$(% )#% .+)/$+)/-25 H--23+*4% +.&,)1)-0#% +0-% 9#9+,,(% 2-#)7/-2% $"% '+:-% #911)*)-/$% 7+)/% .+07)/% $"% +,,";% 1"0% $')/-:)$+3,-%*'+/7-#%)/%,""&%7+)/%;)$'%$-.&-0+$90-8%$).-8%+/2%#"%"/5% J/"$'-0%;+(%$"%)/:-#$)7+$-%$'-%#$+3),)$(%+/2%$"%-G&0-##%)$#%2-70--%)#%$"%-G+.)/-%$'-%="2&,"$%+$%$'-%10-F9-/*(%1"0%;')*'% ? β %=%A8%;')*'%)#%$'-%&")/$%+$%;')*'%$'-%.+7/)$92-%&,"$ *0"##-#%$'-%TK2=%,)/-5%61%+$%$')#%10-F9-/*(%$'-%&'+#-%+/7,-%)#%,-##%Q)/%.+7/)$92-R%$'+/%ADT°8 $'-/% $'-% +.&,)1)-0% )#% #$+3,-5% M')#% )#% $'-% #)$9+$)"/% ),,9#$0+$-2% )/% H)75% AT5WC5% M'-% 2)11-0-/*3-$;--/% $'-% &'+#-% +/7,-% +$% $')#% 10-F9-/*(% +/2% ADT°% )#% $-0.-2% $'-% -9$/"( 0$+#&!5% Y/% $'"$'-0%'+/28%)1%+$%$'-%10-F9-/*(%"1%9/)$(%,""&K7+)/%.+7/)$92-8%$'-%&'+#-%,+7%)#%)/%-G*-##%"1%ADT°8 $'-%+.&,)1)-0%;),,%3-%9/#$+3,-5

880 Chapter 10 Feedback

Figure 10.42 [.6*!4,."!/.2!"#*!,..4!0$%1!?β!%,,-&"2$"%10!"#*!6*/%1%"%.1&!./!"#*!0$%1!$16!4#$&*!($20%1&9

EXERCISE 10.24 M.1&%6*2!$1!.4!$(4!#$+%10!$!&%10,*84.,*'!.4*18,..4!2*&4.1&*!;%"#!?A!=!@AH!$16!4R!=!@A!`=9!]*" "#*!.4 $(4!5*!%6*$,!."#*2;%&*!:%1/%1%"*!%14-"!%(4*6$13*'!=*2.!.-"4-"!%(4*6$13*'!*"39<9!K/!"#%&!$(8 4,%/%*2!%&!3.11*3"*6!%1!"#*!1.1%1+*2"%10!3.1/%0-2$"%.1!;%"#!$!1.(%1$,!,.;8/2*C-*137'!3,.&*68,..4 0$%1!./!@AA'!/%16!"#*!/2*C-*137!$"!;#%3#! ? β != @9!R,&.'!/%16!"#*!4#$&*!($20%19 Ans. ATW%
10.12.2 Effect of Phase Margin on Closed-Loop Response H--23+*4%+.&,)1)-0#%+0-%/"0.+,,(%2-#)7/-2%;)$'%+%&'+#-%.+07)/%"1%+$%,-+#$%Wd°5%M'-%+."9/$ "1% &'+#-% .+07)/% '+#% +% &0"1"9/2% -11-*$% "/% $'-% #'+&-% "1% $'-% *,"#-2K,""&% 7+)/% 0-#&"/#-5% M" #-- $')#%0-,+$)"/#')&8%*"/#)2-0%+%1--23+*4%+.&,)1)-0%;)$'%+%,+07-%,";K10-F9-/*(%,""&%7+)/8 ?Tβ% ! A5%6$%1",,";#%$'+$%$'-%*,"#-2K,""&%7+)/%+$%,";%10-F9-/*)-#%)#%+&&0"G).+$-,(%A`β5%e-/"$K )/7%$'-%10-F9-/*(%+$%;')*'%$'-%.+7/)$92-%"1%,""&%7+)/%)#%9/)$(%3(%ωA8%;-%'+:-%Q0-1-0%$"%H)75 AT5WCR

? ( P ω@ ) β = @ × "

XP θ

:@A9@AN$<

;'-0-

θ = @YA° X 4#$&*!($20%1

:@A9@AN5<

10.12 Stability Study Using Bode Plots

J$%ω1 $'-%*,"#-2K,""&%7+)/%)#

? ( P ω@ ) 8 ?4 ( P ω @ ) = 88888888888888888888888888888 @ + ? ( P ω@ ) β

!:@A9@A\<

E93#$)$9$)/7%10".%?F5%QAT5ATC+R%7):-# XP θ

( @ ⁄ β )" 8 ?4 ( P ω @ ) = 8888888888888888888888 XP θ @+"

!:@A9@AG<

M'9#%$'-%.+7/)$92-%"1%$'-%7+)/%+$%ω1%)#

@⁄β 8 ?4 ( P ω @ ) = 8888888888888888888 XP θ @+"

!:@A9@AH<

H"0%+%&'+#-%.+07)/%"1%Wd°, θ = 13d°;%+/2%;-%"3$+)/

@ ?4 ( P ω @ ) = @9\ 888

β

!:@A9@A_<

M'+$%)#8%$'-%7+)/%&-+4#%3(%+%1+*$"0%"1%A5U%+3":-%$'-%,";K10-F9-/*(%:+,9-%"1%A/β5%M')#%&-+4)/7 )/*0-+#-#%+#%$'-%&'+#-%.+07)/%)#%0-29*-28%-:-/$9+,,(%0-+*')/7%∞%;'-/%$'-%&'+#-%.+07)/%)# L-0"5%o-0"%&'+#-%.+07)/8%"1%*"90#-8%).&,)-#%$'+$%$'-%+.&,)1)-0%*+/%#9#$+)/%"#*),,+$)"/#%l&",-# "/%$'-%Pω%+G)#V%Z(F9)#$%&,"$%&+##)/7%$'0"97'%Q−A8%TRm5

EXERCISE 10.25 ?%16!"#*!3,.&*68,..4!0$%1!$"!ω@!2*,$"%+*!".!"#*!,.;8/2*C-*137!0$%1!;#*1!"#*!4#$&*!($20%1!%&!\A°' _A°'!$16!XA°9 Ans. A5BUV%AV%T5OTO

10.12.3 An Alternative Approach for Investigating Stability 6/:-#$)7+$)/7%#$+3),)$(%3(% *"/#$09*$)/7% ="2-% &,"$#% 1"0% $'-% ,""&% 7+)/% ?β% *+/% 3-% +% $-2)"9#% +/2 $).-K*"/#9.)/7%&0"*-##8%-#&-*)+,,(%)1%;-%'+:-%$"%)/:-#$)7+$-%$'-%#$+3),)$(%"1%+%7):-/%+.&,)1)-0 1"0%+%:+0)-$(%"1%1--23+*4%/-$;"04#5%J/%+,$-0/+$):-%+&&0"+*'8%;')*'%)#%.9*'%#).&,-08%)#%$" *"/#$09*$%+%="2-%&,"$%1"0%$'-%"&-/K,""&%7+)/%?Q PωR%"/,(5%J##9.)/7%1"0%$'-%$).-%3-)/7%$'+$%β )#%)/2-&-/2-/$%"1%10-F9-/*(8%;-%*+/%&,"$%CT%,"7QA`βR%+#%+%'"0)L"/$+,%#$0+)7'$%,)/-%"/%$'-%#+.&,+/-%9#-2%1"0%CT ,.0 ? 9 %M'-%2)11-0-/*-%3-$;--/%$'-%$;"%*90:-#%;),,%3-

@ NA ,.0 ? ( P ω ) X NA ,.0 888 ! = NA ,.0 ? β

β

!:@A9@AZ<

;')*'%)#%$'-%,""&%7+)/%Q)/%2=R5%>-%.+(%$'-0-1"0-%#$92(%#$+3),)$(%3(%-G+.)/)/7%$'-%2)11-0-/*3-$;--/%$'-%$;"%&,"$#5%61%;-%;)#'%$"%-:+,9+$-%#$+3),)$(%1"0%+%2)11-0-/$%1--23+*4%1+*$"08%;-%#).K &,(%20+;%+/"$'-0%'"0)L"/$+,%#$0+)7'$%,)/-%+$%$'-%,-:-,%CT%,"7QA`β R5 M"%),,9#$0+$-8%*"/#)2-0%+/%+.&,)1)-0%;'"#-%"&-/K,""&%$0+/#1-0%19/*$)"/%)#%*'+0+*$-0)L-2%3( $'0--%&",-#5%H"0%#).&,)*)$(%,-$%$'-%$'0--%&",-#%3-%;)2-,(%#-&+0+$-2k#+(8%+$%T5A%!
881

882 Chapter 10 Feedback

dB $A$ 100 90

20 log $A' $

"20 dB/decade X1

20 log 1/' $ 85 dB (stable)

80

(a) 25 dB gain margin

70 20 log 1/' for zero margins

60 50

"40 dB/decade X2 (b)

20 log 1/' $ 50 dB (unstable)

40 30

"60 dB/decade

20 f180 -

10 0 10

102

103

104

105

106 f180 -

107

108

f (Hz)

105

106

107

108

f (Hz)

. 10

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104

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@A 8 ? = 88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 H _ Z :@ + P4 ⁄ @A < :@ + P4 ⁄ @A < :@ + P4 ⁄ @A <

!:@A9@AY<

10".%;')*'% ? %*+/%3-%-+#),(%2-$-0.)/-2%1"0%+/(%10-F9-/*(%4%Q)/%
φ = −g"$1 X@ ( 4 ⁄ @A H ) + "$1 X@ ( 4 ⁄ @A _ ) + "$1 X@ ( 4 ⁄ @A Z )h

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M'-% .+7/)$92-% +/2% &'+#-% 70+&'#% #'";/% )/% H)75% AT5WU% +0-% "3$+)/-2% 9#)/7% $'-% .-$'"2% 1"0 *"/#$09*$)/7% ="2-% &,"$#% QJ&&-/2)G% HR5% M'-#-% 70+&'#% &0":)2-% +&&0"G).+$-% :+,9-#% 1"0

10.12 Stability Study Using Bode Plots

).&"0$+/$%+.&,)1)-0%&+0+.-$-0#8%;)$'%."0-%-G+*$%:+,9-#%"3$+)/+3,-%10".%?F#5%QAT5ATDR%+/2 QAT5ATBR5%H"0%-G+.&,-8%$'-%10-F9-/*(%4ADT%+$%;')*'%$'-%&'+#-%+/7,-%)#%ADT°%*+/%3-%1"9/2%10". H)75%AT5WU%$"%3-%+&&0"G).+$-,(%U5C%/%ATP%

EXERCISE 10.26 @"/#)2-0%+/%"&%+.&%;'"#-%"&-/K,""&%7+)/%)#%)2-/$)*+,%$"%$'+$%"1%H)75%AT5WU5%J##9.-%$'+$%$'-%"& +.&%)#%)2-+,%"$'-0;)#-5%[-$%$'-%"&%+.&%3-%*"//-*$-2%+#%+%2)11-0-/$)+$"05%N#-%$'-%09,-%"1%$'9.3 +3":-%$"%#'";%$'+$%1"0%#$+3,-%&-01"0.+/*-%$'-%2)11-0-/$)+$"0%$).-%*"/#$+/$%#'"9,2%3-%70-+$-0%$'+/ AdB%.#5%lF%$&,%j-*+,,%$'+$%1"0%+%2)11-0-/$)+$"08%$'-%="2-%&,"$%1"0% @ ⁄ β ( P ω ) %'+#%+%#,"&-%"1%+CT 2=`2-*+2-%+/2%)/$-0#-*$#%$'-%TK2=%,)/-%+$%A`τ8%;'-0-%τ%)#%$'-%2)11-0-/$)+$"0%$).-%*"/#$+/$5m

883

884 Chapter 10 Feedback

10.13 Frequency Compensation 6/%$')#%#-*$)"/8%;-%#'+,,%2)#*9##%.-$'"2#%1"0%."2)1()/7%$'-%"&-/K,""&%$0+/#1-0%19/*$)"/%?Q#R "1%+/%+.&,)1)-0%'+:)/7%$'0--%"0%."0-%&",-#%#"%$'+$%$'-%*,"#-2K,""&%+.&,)1)-0%)#%#$+3,-%1"0%+ 7):-/%2-#)0-2%:+,9-%"1%*,"#-2K,""&%7+)/5 dB Y%

Z% "20 dB/decade

A

100 A0

80

"40 dB/decade A%

60 20 log 1/' $ 40 dB

Y

Z

40

"60 dB/decade

20

0 10

102

103

fD

fD%

104

105 fP1

106 fP2

107

108

f (Hz)

fP3

Figure 10.44 ?2*C-*137!3.(4*1&$"%.1!/.2! β!=!@A−N9!D#*!2*&4.1&*!,$5*,*6! ?′ !%&!.5"$%1*6!57!%1"2.6-3%10 $1!$66%"%.1$,!4.,*!$"!4!9!D#*! ?″ !2*&4.1&*!%&!.5"$%1*6!57!(.+%10!"#*!.2%0%1$,!,.;8/2*C-*137!4.,*!".! 4!′ 9

10.13.1 Theory M'-%#).&,-#$%.-$'"2%"1%10-F9-/*(%*".&-/#+$)"/%*"/#)#$#%"1%)/$0"29*)/7%+%/-;%&",-%)/%$'19/*$)"/% ?Q#R% +$% +% #911)*)-/$,(% ,";% 10-F9-/*(8% 4!8% #9*'% $'+$% $'-% ."2)1)-2% "&-/K,""&% 7+)/8 ?′ ( # )' %)/$-0#-*$#%$'-%CT%,"7 ( @ ⁄ β ) %*90:-%;)$'%+%#,"&-%2)11-0-/*-%"1%CT%2=`2-*+2-5%J#%+/ -G+.&,-8%,-$%)$%3-%0-F9)0-2%$"%*".&-/#+$-%$'-%+.&,)1)-0%;'"#-% ?Q#R%)#%#'";/%)/%H)75%AT5WW #9*'% $'+$% *,"#-2K,""&% +.&,)1)-0#% ;)$'% β% +#% ')7'% +#% AT−C% Q)5-58% *,"#-2K,""&% 7+)/#% +#% ,";% +# +&&0"G).+$-,(%WT%2=R%;),,%3-%#$+3,-5%H)0#$8%;-%20+;%+%'"0)L"/$+,%#$0+)7'$%,)/-%+$%$'-%WTK2= ,-:-,%$"%0-&0-#-/$%CT%,"7QA`β R8%+#%#'";/%)/%H)75%AT5WW5%>-%$'-/%,"*+$-%&")/$%M%"/%$')#%,)/-%+$ $'-% 10-F9-/*(% "1% $'-% 1)0#$% &",-8% 4RA5% H0".% M% ;-% 20+;% +% ,)/-% ;)$'% −CTK2=`2-*+2-% #,"&-% +/2 2-$-0.)/-%$'-%&")/$%+$%;')*'%$')#%,)/-%)/$-0#-*$#%$'-%2*%7+)/%,)/-8%&")/$% M′9 %M')#%,+$$-0%&")/$ 7):-#% $'-% 10-F9-/*(% 4!% "1% $'-% /-;% &",-% $'+$% '+#% $"% 3-% )/$0"29*-2% )/% $'-% "&-/K,""&% $0+/#1-0 19/*$)"/5

10.13 Frequency Compensation

M'-% *".&-/#+$-2% "&-/K,""&% 0-#&"/#-% ?′ ( # ) % )#% )/2)*+$-2% )/% H)75% AT5WW5% 6$% '+#% 1"90 &",-#I%+$%4!8%4RA8%4RC8%+/2%4RU5%M'9#% ?′ %3-7)/#%$"%0",,%"11%;)$'%+%#,"&-%"1%−CT%2=`2-*+2-%+$%4!5 J$%4RA%$'-%#,"&-%*'+/7-#%$"%X WT%2=`2-*+2-8%+$%4RC%)$%*'+/7-#%$"%XPT%2=`2-*+2-8%+/2%#"%"/5 E)/*-%$'-%CT%,"7QA`β R%,)/-%)/$-0#-*$#%$'-% NA! ,.0 ?′ %*90:-%+$%&")/$%M%"/%$'-%−CTK2=`2-*+2#-7.-/$8%$'-%*,"#-2K,""&%+.&,)1)-0%;)$'%$')#%β%:+,9-%Q"0%,";-0%:+,9-#R%;),,%3-%#$+3,-5 J%#-0)"9#%2)#+2:+/$+7-%"1%$')#%*".&-/#+$)"/%.-$'"2%)#%$'+$%+$%."#$%10-F9-/*)-#%$'-%"&-/K ,""&%7+)/%'+#%3--/%20+#$)*+,,(%0-29*-25%M')#%.-+/#%$'+$%+$%."#$%10-F9-/*)-#%$'-%+."9/$%"1 1--23+*4%+:+),+3,-%;),,%3-%#.+,,5%E)/*-%+,,%$'-%+2:+/$+7-#%"1%/-7+$):-%1--23+*4%+0-%2)0-*$,( &0"&"0$)"/+,%$"%$'-%+."9/$%"1%1--23+*48%$'-%&-01"0.+/*-%"1%$'-%*".&-/#+$-2%+.&,)1)-0%;),, 3-%).&+)0-25 @+0-19,%-G+.)/+$)"/%"1%H)75%AT5WW%#'";#%$'+$%$'-%7+)/% ?′ ( # ) %)#%,";%3-*+9#-%"1%$'-%&",-%+$ 4RA5%61%;-%*+/%#".-'";%-,).)/+$-%$')#%&",-8%$'-/k0+$'-0%$'+/%,"*+$)/7%&")/$%M8%20+;)/7%MM′ ' +/2%#"%"/k;-%*+/%#$+0$%10".%&")/$%O%Q+$%$'-%10-F9-/*(%"1%$'-%#-*"/2%&",-R%+/2%20+;%$'-%,)/OO′5%M')#%;"9,2%0-#9,$%)/%$'-%"&-/K,""&%*90:-% ?″ ( # )' %;')*'%#'";#%*"/#)2-0+3,(%')7'-0%7+)/ $'+/% ?′ ( # )5 J,$'"97'%)$%)#%/"$%&"##)3,-%$"%-,).)/+$-%$'-%&",-%+$%4RA8%)$%)#%9#9+,,(%&"##)3,-%$"%#')1$%$'+$ &",-%10".%4%=%4RA%$"% 4 = 4 !′ 9 %M')#%.+4-#%$'-%&",-%2".)/+/$%+/2%-,).)/+$-#%$'-%/--2%1"0%)/$0"K 29*)/7%+/%+22)$)"/+,%,";-0K10-F9-/*(%&",-8%+#%;),,%3-%-G&,+)/-2%/-G$5

10.13.2 Implementation >-% #'+,,% /";% +220-##% $'-% F9-#$)"/% "1% ).&,-.-/$)/7% $'-% 10-F9-/*(K*".&-/#+$)"/% #*'-.2)#*9##-2% +3":-5% M'-% +.&,)1)-0% *)0*9)$% /"0.+,,(% *"/#)#$#% "1% +% /9.3-0% "1% *+#*+2-2% 7+)/ #$+7-#8%;)$'%-+*'%#$+7-%0-#&"/#)3,-%1"0%"/-%"0%."0-%"1%$'-%$0+/#1-0K19/*$)"/%&",-#5%M'0"97' .+/9+,%+/2`"0%*".&9$-0%+/+,(#)#%"1%$'-%*)0*9)$8%"/-%)2-/$)1)-#%;')*'%#$+7-%)/$0"29*-#%-+*'%"1 $'-%).&"0$+/$%&",-#%4RA8%4RC8%+/2%#"%"/5%H"0%$'-%&90&"#-%"1%"90%2)#*9##)"/8%+##9.-%$'+$%$'-%1)0#$ &",-%4RA%)#%)/$0"29*-2%+$%$'-%)/$-01+*-%3-$;--/%$'-%$;"%*+#*+2-2%2)11-0-/$)+,%#$+7-#%#'";/%)/ H)75% AT5WdQ+R5%6/% H)75%AT5WdQ3R% ;-% #'";%+% #).&,-% #.+,,K#)7/+,%."2-,% "1% $'-%*)0*9)$% +$% $')# )/$-01+*-5%@900-/$%#"90*-%I8%0-&0-#-/$#%$'-%"9$&9$K#)7/+,%*900-/$%"1%$'-%KA−KC%#$+7-5%j-#)#K $+/*-%-8%+/2%*+&+*)$+/*-%58%0-&0-#-/$%$'-%$"$+,%0-#)#$+/*-%+/2%*+&+*)$+/*-%3-$;--/%$'-%$;" /"2-#%=%+/2% [′ 5%6$%1",,";#%$'+$%$'-%&",-%4RA%)#%7):-/%3(

@ 4R@ = 888888888888888888 N π 58 -8

!:@A9@@A<

[-$% 9#% /";% *"//-*$% $'-% *".&-/#+$)/7% *+&+*)$"0% 55% 3-$;--/% /"2-#% =% +/2% [′5% M')#% ;),, 0-#9,$% )/% $'-% ."2)1)-2% -F9):+,-/$% *)0*9)$% #'";/% )/% H)75% AT5WdQ*R% 10".% ;')*'% ;-% #--% $'+$ $'- &",-% )/$0"29*-2% ;),,% /"% ,"/7-0% 3-% +$% 4RAV% 0+$'-08% $'-% &",-% *+/% 3-% +$% +/(% 2-#)0-2% ,";-0 10-F9-/*(% 4!′ I

@ 4 !′ = 888888888888888888888888888888888888 N π ( 5 8 + 5 5 )- 8

!:@A9@@@<

>-%$'9#%*"/*,92-%$'+$%"/-%*+/%#-,-*$%+/%+&&0"&0)+$-%:+,9-%1"0%55%$"%#')1$%$'-%&",-%10-F9-/*( 10".%4RA%$"%$'-%:+,9-% 4!′ %2-$-0.)/-2%3(%&")/$% O′ %)/%H)75%AT5WW5 J$%$')#%h9/*$90-%)$%#'"9,2%3-%&")/$-2%"9$%$'+$%+22)/7%$'-%*+&+*)$"0%55%;),,%9#9+,,(%0-#9,$ )/%*'+/7-#%)/%$'-%,"*+$)"/%"1%$'-%"$'-0%&",-#%Q$'"#-%+$%4RC%+/2%4RUR5%Y/-%.)7'$%$'-0-1"0-%/--2%$" *+,*9,+$-%$'-%/-;%,"*+$)"/%"1%4RC%+/2%&-01"0.%+%1-;%)$-0+$)"/#%$"%+00):-%+$%$'-%0-F9)0-2%:+,91"0%555

885

886 Chapter 10 Feedback

B% B

Q1

(a)

B%

B%

B

B

(b)

(c)

Figure 10.45 )$,!D;.!3$&3$6*6!0$%1!&"$0*&!./!$!(-,"%&"$0*!$(4,%/%*29!)3,!QC-%+$,*1"!3%23-%"!/.2!"#*!%1"*28 /$3*!5*";**1!"#*!";.!&"$0*&!%1!:$<9!)4,!J$(*!3%23-%"!$&!%1!:3<'!5-"!;%"#!$!3.(4*1&$"%10!3$4$3%".2!55!$66*69 b."*!"#$"!"#*!$1$,7&%&!#*2*!$44,%*&!*C-$,,7!;*,,!".!ijJ!$(4,%/%*2&9

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

10.13.3 Miller Compensation and Pole Splitting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µ8% +/2% 5C% )/*,92-#% $'-% )/&9$% *+&+*)$+/*-% "1% $'-% #9**--2)/7% +.&,)1)-0% #$+7-5 H)/+,,(8%I%%0-&0-#-/$#%$'-%"9$&9$%#)7/+,%*900-/$%"1%$'-%&0-*-2)/7%#$+7-5

10.13 Frequency Compensation

(a)

(b)

Figure 10.46 )$,!R!0$%1!&"$0*!%1!$!(-,"%&"$0*!$(4,%/%*2!;%"#!$!3.(4*1&$"%10!3$4$3%".2!3.11*3"*6!%1!"#* /**65$3)!4$"#'!$16!)3,!$1!*C-%+$,*1"!3%23-%"9!b."*!"#$"!$,"#.-0#!$![kD!%&!&#.;1'!"#*!$1$,7&%&!$44,%*&!*C-$,,7 ;*,,!".!"#*!ijJ?QD!3$&*9

6/% $'-% +3#-/*-% "1% $'-% *".&-/#+$)/7% *+&+*)$"0% 54 8% ;-% *+/% #--% 10".% H)75% AT5WPQ3R% $'+$ $'-0-%+0-%$;"%&",-#k"/-%+$%$'-%)/&9$%+/2%"/-%+$%$'-%"9$&9$5%[-$%9#%+##9.-%$'+$%$'-#-%$;" &",-#%+0-%4RA%+/2%4RC%"1%H)75%AT5WWV%$'9#8

@ 4RN = 8888888888888888888 N π 5N -N

@ 4R@ = 8888888888888888888 N π 5@ -@

!:@A9@@N<

>)$'%54% &0-#-/$8%+/+,(#)#%"1%$'-%*)0*9)$%()-,2#%$'-%$0+/#1-0%19/*$)"/ C ( #54 − * A )- @ - N 888881 = 88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 N I% @ + # [ 5 @ - @ + 5 N - N + 5 4 ( * A - @ - N + - @ + - N ) ] + # [ 5 @ 5 N + 5 4 ( 5 @ + 5 N ) ]- @ - N

!:@A9@@\<

M'-%L-0"%)#%9#9+,,(%+$%+%.9*'%')7'-0%10-F9-/*(%$'+/%$'-%2".)/+/$%&",-8%+/2%;-%#'+,,%/-7,-*$ )$#%-11-*$5%M'-%2-/".)/+$"0%&",(/".)+,%!Q#R%*+/%3-%;0)$$-/%)/%$'-%1"0. N

@ # # @ # ! ( # ) = @ + 8888888888 @ + 8888888888 = @ + # 8888888888 + 8888888888 + 888888888888888888888 ω R@ ′ ω RN ′ ω R@ ′ ω RN ′ ω R@ ′ ωRN ′

!:@A9@@G<

;'-0-% ω R@ ′ %+/2% ω RN ′ %+0-%$'-%/-;%10-F9-/*)-#%"1%$'-%$;"%&",-#5%Z"0.+,,(%"/-%"1%$'-%&",-#%;),, 3-%2".)/+/$V% ω R@ ′ & ω RN ′ 5%M'9#8

#N # ! ( # ) ! @ + 8888888888 + 888888888888888888888

ω R@ ′

ω R@ ′ ω RN ′

!:@A9@@H<

?F9+$)/7%$'-%*"-11)*)-/$#%"1%#%)/%$'-%2-/".)/+$"0%"1%?F5%QAT5AAUR%+/2%)/%?F5%QAT5AAdR%0-#9,$# )/

@ ω R@ ′ = 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 5@ -@ + 5N -N + 54 ( *A -@ -N + -@ + -N )

;')*'%*+/%3-%+&&0"G).+$-2%3(

@ *A -N 54 -@

ω R@ ′ ! 8888888888888888888888888

!:@A9@@_<

887

888 Chapter 10 Feedback ′ % ;-% -F9+$-% $'-% *"-11)*)-/$#% "1% #C% )/% $'-% 2-/".)/+$"0% "1% ?F5% QAT5AAUR% +/2% )/ M"% "3$+)/% ωRN ?F5 QAT5AAdR%+/2%9#-%?F5%QAT5AAPRI

* 5 5@ 5N + 54 ( 5@ + 5N )

A 4 8 ω′RN ! 888888888888888888888888888888888888888888888888

!:@A9@@Z<

′ %)#%0-29*-2%+/2% ω′RN %)# H0".%?F#5%QAT5AAPR%+/2%QAT5AAOR8%;-%#--%$'+$%+#%54%)#%)/*0-+#-28%ωR@ )/*0-+#-25%M')#%+*$)"/%)#%0-1-00-2%$"%+#%-.6"(/-6&%%&!#5%Z"$-%$'+$%$'-%)/*0-+#-%)/%ω′RN %)#%')7',( 3-/-1)*)+,V%)$%+,,";#%9#%$"%.":-%&")/$%O%Q#--%H)75%AT5WWR%190$'-0%$"%$'-%0)7'$8%$'9#%0-#9,$)/7%)/ ')7'-0%*".&-/#+$-2%"&-/K,""&%7+)/5%H)/+,,(8%/"$-%10".%?F5%QAT5AAPR%$'+$%54%)#%.9,$)&,)-2%3( $'-%!),,-0K-11-*$%1+*$"0%*A-C8%$'9#%0-#9,$)/7%)/%+%.9*'%,+07-0%-11-*$):-%*+&+*)$+/*-8%*A-C54 5 6/%"$'-0%;"02#8%$'-%0-F9)0-2%:+,9-%"1%54%;),,%3-%.9*'%#.+,,-0%$'+/%$'+$%"1%55%)/%H)75%AT5Wd5

Example 10.10 M.1&%6*2!$1!.4!$(4!;#.&*!.4*18,..4!"2$1&/*2!/-13"%.1!%&!%6*1"%3$,!".!"#$"!&#.;1!%1!?%09!@A9G\9!L*!;%&#!". 3.(4*1&$"*!"#%&!.4!$(4!&.!"#$"!"#*!3,.&*68,..4!$(4,%/%*2!;%"#!2*&%&"%+*!/**65$3)!%&!&"$5,*!/.2!$17!0$%1 :%9*9'!/.2!β!-4!".!-1%"7<9!R&&-(*!"#$"!"#*!.48$(4!3%23-%"!%13,-6*&!$!&"$0*!&-3#!$&!"#$"!./!?%09!@A9G_!;%"#!5@ =!@AA!4?'!5N!=!H!4?'!$16!*A!=!GA!(RUT'!"#$"!"#*!4.,*!$"!4R@!%&!3$-&*6!57!"#*!%14-"!3%23-%"!./!"#$"!&"$0*'!$16 "#$"!"#*!4.,*!$"!4RN!%&!%1"2.6-3*6!57!"#*!.-"4-"!3%23-%"9!?%16!"#*!+$,-*!./!"#*!3.(4*1&$"%10!3$4$3%".2!/.2!";. 3$&*&I!*%"#*2!%/!%"!%&!3.11*3"*6!5*";**1!"#*!%14-"!1.6*![!$16!02.-16'!.2!%1!"#*!/**65$3)!4$"#!./!"#*!"2$1&%&8 ".29

Solution ?%2&"!;*!6*"*2(%1*!-@!$16!-N!/2.( @ 4R@ = A9@!i`= = 8888888888888888888 N π 5@ -@ D#-&' H

@A - @ = 88888888 !Ω Nπ @ 4RN = @!i`= = 8888888888888888888 N π 5N -N D#-&' H

@A - N = 88888888 !Ω

π

61%+%*".&-/#+$)/7%*+&+*)$"0%55%)#%*"//-*$-2%+*0"##%$'-%)/&9$%$-0.)/+,#%"1%$'-%$0+/#)#$"0%#$+7-8%$'-/%$'10-F9-/*(%"1%$'-%1)0#$%&",-%*'+/7-#%10".%4RA%$"% 4′! I @ 4 !′ = 8888888888888888888888888888888888888 N π ( 5 @ + 5 5 )- @ D#*!&*3.16!4.,*!2*($%1&!-13#$10*6!$"!@8i`=9!D#*!2*C-%2*6!+$,-*!/.2! 4!′ %&!6*"*2(%1*6!57!62$;%10!$!−NA8 6[U6*3$6*!,%1*!/2.(!"#*!@8i`=!/2*C-*137!4.%1"!.1!"#*!NA!,.0:@Uβ
//z' case: draw -20 from second pole

10.13 Frequency Compensation

889

;#%3#!2*&-,"&!%1!55 ! @!µ?'!;#%3#!%&!C-%"*!,$20*!$16!3*2"$%1,7!3$11."!5*!%13,-6*6!.1!"#*!KM!3#%49 b*>"'! %/! $! 3.(4*1&$"%10! 3$4$3%".2! 54! %&! 3.11*3"*6! %1! "#*! /**65$3)! 4$"#! ./! "#*! "2$1&%&".2'! "#*1! 5."# 4.,*&!3#$10*!,.3$"%.1!".!"#*!+$,-*&!0%+*1!57!QC&9!:@A9@@_
* A 54 8 ! ! 4′RN!! 88888888888888888888888888888888888888888888888888888888888 N π [ 5 @ 5 N + 54 ( 5 @ + 5 N ) ]

QAT5AADR

D.!6*"*2(%1*!;#*2*!;*!&#.-,6!,.3$"*!"#*!/%2&"!4.,*'!;*!1**6!".!)1.;!"#*!+$,-*!./! 4RN ′ 9 !R&!$1!$442.>%($8 "%.1'!,*"!-&!$&&-(*!"#$"! 5 4 !!5 N ' !;#%3#!*1$5,*&!-&!".!.5"$%1 *A 8 = _A9_!i`= ′ ! 88888888888888888888888888888 4RN N π ( 5@ + 5N ) D#-&!%"!$44*$2&!"#$"!"#%&!4.,*!;%,,!(.+*!".!$!/2*C-*137!#%0#*2!"#$1!4R\!:;#%3#!%&!@A!i`=<9!]*"!-&!"#*2*/.2* $&&-(*!"#$"!"#*!&*3.16!4.,*!;%,,!5*!$"!4R\9!D#%&!2*C-%2*&!"#$"!"#*!/%2&"!4.,*!5*!,.3$"*6!$" Z 4R\ @A !`= 8 = 8888888888888888 8 = @AA!`= ′ = 88888 4R@ H ?A @A

D#-&' @ 4R@ ′ = @AA!`= = 8888888888888888888888888888888 N π * A - N 54 - @ ;#%3#!2*&-,"&!%1!54 !=!ZY9H!4?9!R,"#.-0#!"#%&!+$,-*!%&!%16**6!(-3#!02*$"*2!"#$1!5N'!;*!3$1!6*"*2(%1*!"#* ,.3$"%.1!./!"#*!4.,*! 4RN ′ !/2.(!QC9!:@A9@@Y<'!;#%3#!7%*,6&! 4RN ′ != HZ9N!i`=' !3.1/%2(%10!"#$"!"#%&!4.,*!#$& %16**6!5**1!(.+*6!4$&"!4R\9 L*!3.13,-6*!"#$"!-&%10!i%,,*2!3.(4*1&$"%.1!1."!.1,7!2*&-,"&!%1!$!(-3#!&($,,*2!3.(4*1&$"%10!3$4$38 %".2!5-"'!.;%10!".!4.,*!&4,%""%10'!$,&.!*1$5,*&!-&!".!4,$3*!"#*!6.(%1$1"!4.,*!$!6*3$6*!#%0#*2!%1!/2*C-*1379 D#%&!2*&-,"&!%1!$!;%6*2!5$16;%6"#!/.2!"#*!3.(4*1&$"*6!.4!$(49

EXERCISE 10.27 R!(-,"%4.,*!$(4,%/%*2!#$+%10!$!/%2&"!4.,*!$"!@!i`=!$16!$1!.4*18,..4!0$%1!./!@AA!6[!%&!".!5*!3.(8 4*1&$"*6!/.2!3,.&*68,..4!0$%1&!$&!,.;!$&!NA!6[!57!"#*!%1"2.6-3"%.1!./!$!1*;!6.(%1$1"!4.,*9!R" ;#$"!/2*C-*137!(-&"!"#*!1*;!4.,*!5*!4,$3*6V Ans. @AA!`= 10.28 ?.2!"#*!$(4,%/%*2!6*&32%5*6!%1!Q>*23%&*!@A9NZ'!2$"#*2!"#$1!%1"2.6-3%10!$!1*;!6.(%1$1"!4.,*'!;* 3$1!-&*!$66%"%.1$,!3$4$3%"$13*!$"!"#*!3%23-%"!1.6*!$"!;#%3#!"#*!/%2&"!4.,*!%&!/.2(*6!".!2*6-3*!"#* /2*C-*137!./!"#*!/%2&"!4.,*9!K/!"#*!/2*C-*137!./!"#*!&*3.16!4.,*!%&!@A!i`=!$16!%/!%"!2*($%1&!-18 3#$10*6!;#%,*!$66%"%.1$,!3$4$3%"$13*!%&!%1"2.6-3*6!$&!(*1"%.1*6'!/%16!"#*!/2*C-*137!".!;#%3#!"#* /%2&"!4.,*!(-&"!5*!,.;*2*6!&.!"#$"!"#*!2*&-,"%10!$(4,%/%*2!%&!&"$5,*!/.2!3,.&*68,..4!0$%1&!$&!,.;!$& NA!6[9![7!;#$"!/$3".2!(-&"!"#*!3$4$3%"$13*!$"!"#*!3.1"2.,,%10!1.6*!5*!%132*$&*6V Ans. @AAA!`=E!@AAA

890 Chapter 10 Feedback

Summary b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β <' ;#%3#!/.2!1*0$"%+*!/**65$3)!(-&"!5*!$!4.&%"%+*!6%(*18 &%.1,*&&!1-(5*2'!$16!"#*!$(.-1"!./!/**65$3)!:@!+!?β <9 D#*!,$""*2!6%2*3",7!6*"*2(%1*&!0$%1!2*6-3"%.1'!0$%1!6*8 &*1&%"%+%"7'! 5$16;%6"#! *>"*1&%.1'! $16! 3#$10*&! %1! -% $16!-19 J%13*! ?! $16! β! $2*! %1! 0*1*2$,! /2*C-*137! 6*4*16*1"'! "#* 4.,*&!./!"#*!/**65$3)!$(4,%/%*2!$2*!.5"$%1*6!57!&.,+%10 "#*!3#$2$3"*2%&"%3!*C-$"%.1!@!+!?:#<β :#
?.2!"#*!/**65$3)!$(4,%/%*2!".!5*!&"$5,*'!%"&!4.,*&!(-&"!$,, 5*!%1!"#*!,*/"!#$,/!./!"#*!#!4,$1*9 J"$5%,%"7! %&! 0-$2$1"**6! %/! $"! "#*! /2*C-*137! /.2! ;#%3#! "#* 4#$&*!$10,*!./!?β!%&!@YA°!:%9*9'!ω@YA<'! ? β !%&!,*&&!"#$1!-1%8 "7E!"#*!$(.-1"!57!;#%3#!%"!%&!,*&&!"#$1!-1%"7'!*>42*&&*6!%1 6*3%5*,&'!%&!"#*!0$%1!($20%19!R,"*21$"%+*,7'!"#*!$(4,%/%*2!%& &"$5,*!%/'!$"!"#*!/2*C-*137!$"!;#%3#! ? β = @' !"#*!4#$&* $10,*!%&!,*&&!"#$1!@YA°E!"#*!6%//*2*13*!%&!"#*!4#$&*!($20%19 D#*! &"$5%,%"7! ./! $! /**65$3)! $(4,%/%*2! 3$1! 5*! $1$,7=*6! 57 3.1&"2-3"%10!$![.6*!4,."!/.2! ? !$16!&-4*2%(4.&%10! .1!%"!$ 4,."!/.2! @ ⁄ β 9!J"$5%,%"7!%&!0-$2$1"**6!%/!"#*!";.!4,."&!%1"*28 &*3"!;%"#!$!6%//*2*13*!%1!&,.4*!1.!02*$"*2!"#$1!_ 6[U.3"$+*9 D.!($)*!$!0%+*1!$(4,%/%*2!&"$5,*!/.2!$!0%+*1!/**65$3)!/$38 ".2!β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

PROBLEMS

Computer Simulation Problems l2.5,*(&! %6*1"%/%*6! 57! "#%&! %3.1! $2*! %1"*16*6! ". 6*(.1&"2$"*!"#*!+$,-*!./!-&%10!JlKMQ!&%(-,$"%.1!".!+*28 %/7!#$16!$1$,7&%&!$16!6*&%01'!$16!".!%1+*&"%0$"*!%(4.2"$1" %&&-*&!&-3#!$&!$,,.;$5,*!&%01$,!&;%10!$16!$(4,%/%*2!1.18 ,%1*$2! 6%&".2"%.19! K1&"2-3"%.1&! ".! $&&%&"! %1! &*""%10! -4 lJ4%3*! $16! i-,"%&%(! &%(-,$"%.1&! /.2! $,,! "#*! %16%3$"*6 42.5,*(&! 3$1!5*!/.-16! %1! "#*! 3.22*&4.16%10! /%,*&!.1! "#* 6%&39!b."*!"#$"!%/!$!4$2"%3-,$2!4$2$(*"*2!+$,-*!%&!1."!&4*38 %/%*6!%1!"#*!42.5,*(!&"$"*(*1"'!7.-!$2*!".!($)*!$!2*$&.18 $5,*! $&&-(4"%.19! p! 6%//%3-,"! 42.5,*(E! pp! (.2*! 6%//%3-,"E ppp! +*27! 3#$,,*10%10! $16U.2! "%(*83.1&-(%10E! dI! 6*&%01 42.5,*(9

Section 10.1: The General Feedback Structure 10.1 R!1*0$"%+*8/**65$3)!$(4,%/%*2!#$&!$!3,.&*68,..4!0$%1 ?4!=!@AA!$16!$1!.4*18,..4!0$%1!?!=!@AG9!L#$"!%&!"#*!/**68 5$3)!/$3".2!β V!K/!$!($1-/$3"-2%10!*22.2!2*&-,"&!%1!$!2*6-3"%.1 ./!?!".!@A\'!;#$"!3,.&*68,..4!0$%1!2*&-,"&V!L#$"!%&!"#*!4*28 3*1"$0*!3#$10*!%1!?4!3.22*&4.16%10!".!"#%&!/$3".2!./!@A!2*6-38 "%.1!%1!?V 10.2 M.1&%6*2! "#*! .48$(4! 3%23-%"! &#.;1! %1! ?%09! l@A9N' ;#*2*!"#*!.4!$(4!#$&!%1/%1%"*!%14-"!2*&%&"$13*!$16!=*2.!.-"8 4-"!2*&%&"$13*!5-"!/%1%"*!.4*18,..4!0$%1!?9 :$
Problems 891

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PROBLEMS

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CHAPTER 10

:3
CHAPTER 10

PROBLEMS

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CHAPTER 11

Output Stages and Power Amplifiers Introduction

11.7 Power BJTs

911

11.1 Classification of Output Stages 11.2 Class A Output Stage

913

11.3 Class B Output Stage

918

11.4 Class AB Output Stage

912

11.8 Variations on the Class AB Configuration 950 11.9 IC Power Amplifiers

955

11.10 MOS Power Transistors

924

11.5 Biasing the Class AB Circuit

943

929

11.6 CMOS Class AB Output Stages

933

Summary

967

Problems

968

962

IN THIS CHAPTER YOU WILL LEARN 1. The classification of amplifier output stages on the basis of the fraction of the cycle of an input sine wave during which the transistor conducts. 2. Analysis and design of a variety of output-stage types ranging from the simple but power-inefficient emitter follower (class A) to the popular push–pull class AB circuit in both bipolar and CMOS technologies. 3. Thermal considerations in the design and fabrication of high-outputpower circuits. 4. Useful and interesting circuit techniques employed in the design of power amplifiers. 5. Special types of MOS transistors optimized for high-power applications.

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911

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11.1 Classification of Output Stages Q,)&,)#0)*1/0#*(/#-4*00$+$/3#*--'(3$"1#)'#)./#-'44/-)'(#-,((/")#5*2/+'(%#).*)#(/0,4)0#5./"#*" $"&,)#0$1"*4#$0#*&&4$/37#R$1,(/#EE7E#$44,0)(*)/0#)./#-4*00$+$-*)$'"#+'(#)./#-*0/#'+#*#0$",0'$3*4 $"&,)# 0$1"*47# ;./# -4*00# !# 0)*1/9# 5.'0/# *00'-$*)/3# 5*2/+'(%# $0# 0.'5"# $"# R$17# EE7EA*D9# $0 =$*0/3#*)#*#-,((/")#,-#1(/*)/(#).*"#)./#*%&4$),3/#'+#)./#0$1"*4#-,((/")9# . $ 7#;.,0#)./#)(*"0$0)'(#$" *#-4*00#!#0)*1/#-'"3,-)0#+'(#)./#/")$(/#-:-4/#'+#)./#$"&,)#0$1"*4S#).*)#$09#)./#-'"3,-)$'"#*"14/ $0 TUG°7#@"#-'")(*0)9#)./#-4*00#M#0)*1/9#5.'0/#*00'-$*)/3#5*2/+'(%#$0#0.'5"#$"#R$17#EE7EA=D9 $0 =$*0/3#*)#V/('#3-#-,((/")7#;.,0#*#)(*"0$0)'(#$"#*#-4*00#M#0)*1/#-'"3,-)0#+'(#'"4:#.*4+#)./ -:-4/#'+#)./#$"&,)#0$"/#5*2/9#(/0,4)$"1#$"#*#-'"3,-)$'"#*"14/#'+#EWG°7#!0#5$44#=/#0//"#4*)/(9

Figure 11.1 H'44/-)'(#-,((/")#5*2/+'(%0#+'(#)(*"0$0)'(0#'&/(*)$"1#$"#4#5#-4*00#!9#465#-4*00#M9#4+5#-4*00#!M9 *"3#4,5#-4*00#H#*%&4$+$/(#0)*1/07

11.2 Class A Output Stage

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11.2 Class A Output Stage M/-*,0/#'+#$)0#4'5#',)&,)#(/0$0)*"-/9#)./#/%$))/(#+'44'5/(#$0#)./#%'0)#&'&,4*(#-4*00#!#',)&,) 0)*1/7#J/#.*2/#*4(/*3:#0),3$/3#)./#/%$))/(#+'44'5/(#$"#H.*&)/(#US#$"#)./#+'44'5$"1#5/#-'"6 0$3/(#$)0#4*(1/60$1"*4#'&/(*)$'"7

11.2.1 Transfer Characteristic R$1,(/#EE7I#0.'50#*"#/%$))/(#+'44'5/(#0E#=$*0/3#5$).#*#-'"0)*")#-,((/")#,#0,&&4$/3#=:#)(*"0$0)'( 0I7#8$"-/#)./#/%$))/(#-,((/")##1E#=#,#+##/9#)./#=$*0#-,((/")#,#%,0)#=/#1(/*)/(#).*"#)./#4*(1/0)#"/1*)$2/ 4'*3#-,((/")S#')./(5$0/9#0E#-,)0#'++#*"3#-4*00#!#'&/(*)$'"#5$44#"'#4'"1/(#=/#%*$")*$"/37 !"#$%&'()*#&$+"'&'+%#&,)%,+$-*$%"#$#.,%%#&$*-//-0#&$-*$1,23$4435$,)$6#)+&,7#6$78 v3

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913

914 Chapter 11 Output Stages and Power Amplifiers

Figure 11.2 !"# /%$))/(# +'44'5/(# A0ED =$*0/3# 5$).# *# -'"0)*")# -,((/")# ,# 0,&&4$/3# =: )(*"0$0)'(#0I7

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11.2 Class A Output Stage

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9443K:

EXERCISES D11.1 R'(#)./#/%$))/(#+'44'5/(#$"#R$17#EE7I9#6--#=#EF#Z9#6-10*)#=#G7I#Z9#621#=#G7[#Z#*"3#-'"0)*")9#*"3#β #$0 2/(:#.$1.7#R$"3#)./#2*4,/#'+#4#).*)#5$44#/0)*=4$0.#*#=$*0#-,((/")#0,++$-$/")4:#4*(1/#)'#*44'5#)./#4*(1/0) &'00$=4/#',)&,)#0$1"*4#05$"1#+'(#4/#=#E#XΩ7#C/)/(%$"/#)./#(/0,4)$"1#',)&,)#0$1"*4#05$"1#*"3#)./ %$"$%,%#*"3#%*<$%,%#/%$))/(#-,((/")0#+'(#0E7 Ans. G7\[#XΩS#−E]7W#Z#)'#+E]7W#ZS#G#)'#I\7U#%! 11.2 R'(#)./#/%$))/(#+'44'5/(#'+#O')/#).*)#)./#$"-(/%/")*4#2'4)*1/#1*$"#1$2/0#)./#04'&/#'+#)./#v36 2/(0,06v,#-.*(*-)/($0)$-7 Ans. −\7TU#Z9#G7U[#Z9#EG7UW#ZS#G7\\F#Z_Z9#G7\\W#Z_Z9#G7\\\#Z_Z

11.2.2 Signal Waveforms L-(),6#&$ %"#$ -;#&'%,-($ -*$ %"#$ #.,%%#&B*-//-0#&$ +,&+<,%$ -*$ 1,23$ 4435$ *-&$ ),(#B0'>#$ ,(;<%3 M#2/#+%,(2$6-1)'%C$0#$)##$%"'%$,*$%"#$7,')$+<&&#(%$,$,)$;&-;#&/8$)#/#+%#6C$%"#$-<%;<%$>-/%'2#$+'( )0,(2$*&-.$−6--$%-$+6--$0,%"$%"#$J<,#)+#(%$>'/<#$7#,(2$N#&-C$')$)"-0($,($1,23$443H9':3$1,2<&# 443H97:$)"-0)$%"#$+-&&#);-(6,(2$0'>#*-&.$-*$ v-14$=$6--$− v33$M-0C$'))<.,(2$%"'%$%"#$7,') +<&&#(%$,$,)$)#/#+%#6$%-$'//-0$'$.'O,.<.$(#2'%,>#$/-'6$+<&&#(%$-*$ 6-- ⁄ 4 / C$%"'%$,)C

, Q 6 -- ⁄ 4 / %"#$ +-//#+%-&$ +<&&#(%$ -*$ 04$ 0,//$ "'>#$ %"#$ 0'>#*-&.$ )"-0($ ,($ 1,23$ 443H9+:3$ 1,('//8C$ 1,23 443H96:$)"-0)$%"#$0'>#*-&.$-*$%"#$*)-!#)!#)0"/-%2"30'%,*--*2#!*")$,($04C$

*8E ≡ v -1E # -E

9443?:

11.2.3 Power Dissipation 1,2<&#$443H96:$,(6,+'%#)$%"'%$%"#$.'O,.<.$,()%'(%'(#-<)$;-0#&$6,)),;'%,-($,($04$,)$6-- ,3$!",) ,)$ #J<'/$ %-$ %"#$ ;-0#&$ 6,)),;'%,-($ ,($ 04$ 0,%"$ $ (-$ ,(;<%$ ),2('/$ ';;/,#6C$ %"'%$ ,)C$ %"#$ J<,#)+#(% ;-0#&$6,)),;'%,-(3$!"<)$%"#$#.,%%#&B*-//-0#&$%&'(),)%-&$6,)),;'%#)$%"#$/'&2#)%$'.-<(%$-*$;-0#& 0"#($v3$=$@3$P,(+#$%",)$+-(6,%,-($9(-$,(;<%$),2('/:$+'($#'),/8$;&#>',/$*-&$;&-/-(2#6$;#&,-6)$-* %,.#C$%&'(),)%-&$04$.<)%$7#$'7/#$%-$0,%")%'(6$'$+-(%,(<-<)$;-0#&$6,)),;'%,-($-*$6-- ,3

915

916 Chapter 11 Output Stages and Power Amplifiers

(d) Figure 11.4 P*<$%,%# 0$1"*4# 5*2/+'(%0# $"# )./# -4*00# !# ',)&,)# 0)*1/# '+# R$17# EE7I# ,"3/(# )./# -'"3$)$'" , = 6-- ⁄ 4 / # '(9# /?,$2*4/")4:95 4 / = 6-- ⁄ ,7 5 >')/# ).*)# )./# )(*"0$0)'(# 0*),(*)$'"# 2'4)*1/0# .*2/# =//" "/14/-)/37

!"#$;-0#&$6,)),;'%,-($,($04$6#;#(6)$-($%"#$>'/<#$-*$4/3$L-(),6#&$%"#$#O%&#.#$+')#$-* '($-<%;<%$-;#($+,&+<,%C$%"'%$,)C$4/$=$∞3$=($%",)$+')#C$#-4$=5,$,)$+-()%'(%$'(6$%"#$,()%'(%'(#-<) ;-0#&$ 6,)),;'%,-($ ,($ 04$ 0,//$ 6#;#(6$ -($ %"#$ ,()%'(%'(#-<)$ >'/<#$ -*$ v33$ !"#$ .'O,.<. ;-0#&$6,)),;'%,-($0,//$-++<&$0"#($ v3$=$−6--C$*-&$,($%",)$+')#$ v-14$,)$'$.'O,.<.$-*$56-'(6$ *84$ =$ 56-- ,3$ !",)$ +-(6,%,-(C$ "-0#>#&C$ 0-'/C$ )-$ %"#$ 6#),2($ (##6$ (-%$ 7#$ %"'%$ +-()#&>'%,>#3$ R7)#&>#$ %"'%$ 0,%"$ '($ -;#(B+,&+<,% /-'6C$%"#$'>#&'2#$;-0#&$6,)),;'%,-($,($04$,)$6-- ,3$F$*'&$.-&#$6'(2#&-<)$),%<'%,-($-++<&)$'% %"#$-%"#&$#O%&#.#$-*$4/S);#+,*,+'//8C$4/$=$@3$=($%"#$#>#(%$-*$'($-<%;<%$)"-&%$+,&+<,%C$'$;-)B ,%,>#$,(;<%$>-/%'2#$0-#&8 /'&2#$+<&&#(%$.'8$*/-0$%"&-<2"$04C$'(6$,*$%"#$)"-&%B+,&+<,%$+-(6,%,-($;#&),)%)C$%"#$&#)'/<#$-* v-15$,)$56--C$%"#$.'O,.<.$,()%'(%'(#-<)$;-0#&$6,)),;'%,-($,($05$,)$56-- ,3$!",)$.'O,.<.C "-0#>#&C$-++<&)$0"#($v3$=$6--C$'$+-(6,%,-($%"'%$0-',/$*-&$'$;&-/-(2#6 ;#&,-6$-*$%,.#3$F$.-&#$),2(,*,+'(%$J<'(%,%8$*-&$6#),2($;<&;-)#)$,)$%"#$'>#&'2#$;-0#&$6,)),;'B %,-($,($05C$0",+"$,)$6-- ,3

11.2 Class A Output Stage

Example 11.1 H'"0$3/(#)./#/%$))/(#+'44'5/(#$"#R$17#EE7I#5$).# 6 -- Q EG #Z9#,#`#EGG#%!9#*"3# 4 / Q EGG#Ω7 A*D#R$"3#)./#&'5/(#3$00$&*)/3#$"# 0 E #*"3# 0 I #,"3/(#?,$/0-/")#-'"3$)$'"0# ( v 3 Q G )7 A=D#R'(#*#0$",0'$3*4#',)&,)#2'4)*1/#'+#%*<$%,%#&'00$=4/#*%&4$),3/#A"/14/-)$"1#6 -10*) D9#+$"3#)./#*26 /(*1/#&'5/(#3$00$&*)$'"#$"# 0 E #*"3# 0 I 7 #!40'#+$"3#)./#4'*3#&'5/(7

Solution A*D a"3/(#?,$/0-/")#-'"3$)$'"0# v 3 Q G 9#*"3#/*-.#'+# 0 E #*"3# 0 I #-'"3,-)0#*#-,((/")#,#`#EGG#%! ` G7E ! *"3#.*0#*#2'4)*1/# 6 -1 Q 6 -- Q EG #Z9#).,0 < 8E Q < 8I Q 6 -- , Q EG × G7E Q E J A=D R'(#*#0$",0'$3*4#',)&,)#2'4)*1/#'+#%*<$%,%#&'00$=4/#*%&4$),3/#A$7/79# EG6Z #&/*XD9#)./#$"0)*")*"/',0 &'5/(#3$00$&*)$'"#$"# 0 E #5$44#=/#*0#0.'5"#$"#R$17#EE7]A3D7#;.,0#)./#*2/(*1/#&'5/(#3$00$&*)$'"#$"# 0 E 5$44#=/# E E < 8E Q 666 6 -- , Q 666 × EG × G7E Q G7F J # I I R'(# 0 I 9#)./#-,((/")#$0#-'"0)*")#*)#,##`#G7E#!#*"3#)./#2'4)*1/#*)#)./#-'44/-)'(#5$44#.*2/#*"#*2/(*1/#2*4,/#'+ G#Z7#;.,0#)./#*2/(*1/#2'4)*1/#*-('00# 0 I #5$44#=/# 6 -- #*"3#)./#*2/(*1/#3$00$&*)$'"#5$44#=/ < 8I Q , × v -1

*2/(*1/

Q , × 6 -- Q G7E × EG Q E J # R$"*44:9#)./#&'5/(#3/4$2/(/3#)'#)./#4'*3#-*"#=/#+',"3#+('% I

6 7(%0 6 < / Q 66666666666 4/ I

( EG ⁄ I ) Q 666666666666666666666666 Q G7FJ # EGG

11.2.4 Power-Conversion Efficiency ;./#&'5/(6-'"2/(0$'"#/++$-$/"-:#'+#*"#',)&,)#0)*1/#$0#3/+$"/3#*0 ^'*3#&'5/(# ( < / ) 6 η ≡ 6666666666666666666666666666666666666666666 8,&&4:#&'5/(# ( <= )

9443V:

1-&$%"#$#.,%%#&$*-//-0#&$-*$1,23$4435C$'))<.,(2$%"'%$%"#$-<%;<%$>-/%'2#$,)$'$),(<)-,6$0,%"$%"# ;#'U$>'/<#$ 6b 7 C$%"#$'>#&'2#$/-'6$;-0#&$0,//$7# I I A6b7 ⁄ ID E 6b 7 6# < / = 66666666666666666666666 = 666 666666 4/ I 4/

9443W:

P,(+#$%"#$+<&&#(%$,($05$,)$+-()%'(%$9,:C$%"#$;-0#&$6&'0($*&-.$%"#$(#2'%,>#$)<;;/84$,)$6-- ,3 !"#$+9!:+;!$+<&&#(%$,($04$,)$#J<'/$%-$,C$'(6$%"<)$%"#$'>#&'2#$;-0#&$6&'0($*&-.$%"#$;-),%,># E

;.$0#3'/0#%7&#$"-4,3/#)./#&'5/(#3(*5"#=:#)./#=$*0$"1#(/0$0)'(#4#*"3#)./#3$'3/6-'""/-)/3#)(*"0$0)'(#0T7

917

918 Chapter 11 Output Stages and Power Amplifiers )<;;/8$,)$6-- ,3$!"<)$%"#$%-%'/$'>#&'2#$)<;;/8$;-0#&$,)

<= = I6-- , $

9443X:

IJ<'%,-()$9443W:$'(6$9443X:$+'($7#$+-.7,(#6$%-$8,#/6 I 6b # ] ,4 / 6--

E 7 6 η = 666 6666666666666666 E = 666 ]

6b7 6666666 6 ,4 /

6b7 66666666 6 6--

94434@:

P,(+#$ 6b7 ≤ 6-- $'(6$ 6b7 ≤ ,4 /C$.'O,.<.$#**,+,#(+8$,)$-7%',(#6$0"#(

6b7 = 6-- = ,4 /

944344:

!"#$.'O,.<.$#**,+,#(+8$'%%',('7/#$,)$5KY3$Z#+'<)#$%",)$,)$'$&'%"#&$/-0$*,2<&#C$%"#$+/')) F$-<%;<%$)%'2#$,)$&'&#/8$<)#6$,($",2"B;-0#&$';;/,+'%,-()$9[4$\:3$M-%#$'/)-$%"'%$,($;&'+B %,+#$%"#$-<%;<%$>-/%'2#$)0,(2$,)$/,.,%#6$%-$/-0#&$>'/<#)$%-$'>-,6$%&'(),)%-&$)'%<&'%,-($'(6$'))-B +,'%#6$ (-(/,(#'&$ 6,)%-&%,-(3$ !"<)$ %"#$ #**,+,#(+8$ '+",#>#6$ ,($ ;&'+%,+#$ ,)$ <)<'//8$ ,($ %"# 4@Y$%-$5@Y$&'(2#3

EXERCISE 11.3 R'(#)./#/%$))/(#+'44'5/(#'+#R$17#EE7I9#4/)#6--#=#EG#Z9#,#=#EGG#%!9#*"3#4/#=#EGG#Ω7#@+#)./#',)&,) 2'4)*1/#$0#*"#W6Z6&/*X#0$",0'$39#+$"3#)./#+'44'5$"1c#A*D#)./#&'5/(#3/4$2/(/3#)'#)./#4'*3S#A=D#)./ *2/(*1/#&'5/(#3(*5"#+('%#)./#0,&&4$/0S#A-D#)./#&'5/(6-'"2/(0$'"#/++$-$/"-:7#@1"'(/#)./#4'00#$" 0T#*"3#47 Ans. @3E5$\G$5$\G$4?Y

11.3 Class B Output Stage R$1,(/#EE7F#0.'50#*#-4*00#M#',)&,)#0)*1/7#@)#-'"0$0)0#'+#*#-'%&4/%/")*(:#&*$(#'+#)(*"0$0)'(0 A*"#%*%#*"3#*#*%*D#-'""/-)/3#$"#0,-.#*#5*:#).*)#=').#-*""')#-'"3,-)#0$%,4)*"/',04:7

11.3.1 Circuit Operation \"#($%"#$,(;<%$>-/%'2#$ v,$,)$N#&-C$7-%"$%&'(),)%-&)$'&#$+<%$-**$'(6$%"#$-<%;<%$>-/%'2#$ v3$,) N#&-3$F)$ v,$2-#)$;-),%,>#$'(6$#O+##6)$'7-<%$@3K$AC$0>$+-(6<+%)$'(6$-;#&'%#)$')$'($#.,%%#& *-//-0#&3$ =($ %",)$ +')#$ v3$ *-//-0)$ v,$ 9,3#3C$ v3$ =$ v,$ −5 v21>:$ '(6$ 0>$ )<;;/,#)$ %"#$ /-'6$ +<&&#(%3 ]#'(0",/#C$%"#$#.,%%#&D7')#$T<(+%,-($-*$0<$0,//$7#$&#>#&)#B7,')#6$78$%"#$621$-*$0>C$0",+"$,) ';;&-O,.'%#/8$@3V$A3$!"<)$0<$0,//$7#$+<%$-**3

11.3 Class B Output Stage

Figure 11.5 !#-4*00#M#',)&,)#0)*1/7

=*$%"#$,(;<%$2-#)$(#2'%,>#$78$.-&#$%"'($'7-<%$@3K$AC$0<$%<&()$-($'(6$'+%)$')$'($#.,%%#& *-//-0#&3$F2',($v3$*-//-0)$v,$9,3#3C$v3$=$v,$+$v12<:C$7<%$,($%",)$+')#$0<$)<;;/,#)$%"#$/-'6$+<&&#(% '(6$0>$0,//$7#$+<%$-**3 \#$+-(+/<6#$%"'%$%"#$%&'(),)%-&)$,($%"#$+/'))$Z$)%'2#$-*$1,23$443K$'&#$7,')#6$'%$N#&-$+<&B &#(%$'(6$+-(6<+%$-(/8$0"#($%"#$,(;<%$),2('/$,)$;&#)#(%3$!"#$+,&+<,%$-;#&'%#)$,($'$2/-&72/$$ *')",-(^$0>$*?(@!($9)-<&+#):$+<&&#(%$,(%-$%"#$/-'6$0"#($ v,$,)$;-),%,>#C$'(6$0<$*?AA($9),(U): +<&&#(%$*&-.$%"#$/-'6$0"#($v,$,)$(#2'%,>#3

11.3.2 Transfer Characteristic F$)U#%+"$-*$%"#$%&'()*#&$+"'&'+%#&,)%,+$-*$%"#$+/'))$Z$)%'2#$,)$)"-0($,($1,23$443?3$M-%#$%"'% %"#&#$#O,)%)$'$&'(2#$-*$ v,$+#(%#$'&-<(6$N#&-$0"#&#$7-%"$%&'(),)%-&)$'&#$+<%$-**$'(6$ v3$,) N#&-3$!",)$,0#,%6#),$&#)#3$!"#$#**#+%$-*$+&-))->#&$6,)%-&%,-($0,//$7#$.-)%$;&-(-<(+#6$0"#($%"#

Figure 11.6 ;(*"0+/(#-.*(*-)/($0)$-#+'(#)./#-4*00#M#',)&,)#0)*1/#$"#R$17#EE7F7

919

920 Chapter 11 Output Stages and Power Amplifiers

Figure 11.7 @44,0)(*)$"1#.'5#)./#3/*3#=*"3#$"#)./#-4*00#M#)(*"0+/(#-.*(*-)/($0)$-#(/0,4)0#$"#-('00'2/(#3$0)'()$'"7

'.;/,%<6#$-*$%"#$,(;<%$),2('/$,)$).'//3$L&-))->#&$6,)%-&%,-($,($'<6,-$;-0#&$'.;/,*,#&)$2,>#) &,)#$%-$<(;/#')'(%$)-<(6)3

11.3.3 Power-Conversion Efficiency !-$+'/+#&),-($#**,+,#(+8C$ ηC$-*$%"#$+/'))$Z$)%'2#C$0#$(#2/#+%$%"#$+&-))B ->#&$6,)%-&%,-($'(6$+-(),6#&$%"#$+')#$-*$'($-<%;<%$),(<)-,6$-*$;#'U$'.;/,%<6#$ 6b77 $ !"#$'>#&B '2#$/-'6$;-0#&$0,//$7# I E6b 7 # 6 < / = 666 66666 I 4/

944345:

!"#$+<&&#(%$6&'0($*&-.$#'+"$)<;;/8$0,//$+-(),)%$-*$"'/*B),(#$0'>#)$-*$;#'U$'.;/,%<6#$ A6b7 ⁄ 4 / D 3 !"<)$%"#$'>#&'2#$+<&&#(%$6&'0($*&-.$#'+"$-*$%"#$%0-$;-0#&$)<;;/,#)$0,//$7#$6b7 ⁄ π 4 /3$=%$*-//-0) %"'%$%"#$'>#&'2#$;-0#&$6&'0($*&-.$#'+"$-*$%"#$%0-$;-0#&$)<;;/,#)$0,//$7#$%"#$)'.#C$

E #6b <=+ = <=− = 666 6666676 6-π 4/

94434E:

'(6$%"#$%-%'/$)<;;/8$;-0#&$0,//$7#$

I6b7 6# 6 <= = 666 66666 π 4 / --

94434H:

I E 6b π #6b7 I 6b η = 666 666667 # 666 666667 6-- = 666 66666666 π 4/ ] 6-I 4/

94434K:

!"<)$%"#$#**,+,#(+8$0,//$7#$2,>#($78

11.3 Class B Output Stage

=%$*-//-0)$%"'%$%"#$.'O,.<.$#**,+,#(+8$,)$-7%',(#6$0"#($ 6b7 $,)$'%$,%)$.'O,.<.3$!",)$.'O,B .<.$,)$/,.,%#6$78$%"#$)'%<&'%,-($-*$0>$'(6$0<$%-$6--$−$6-1)'%$!$6--3$F%$%",)$>'/<#$-*$;#'U -<%;<%$>-/%'2#C$%"#$;-0#&B+-(>#&),-($#**,+,#(+8$,)

π η %*< = 666 = [W7Fd $ ]

94434?:

!",)$>'/<#$,)$.<+"$/'&2#&$%"'($%"'%$-7%',(#6$,($%"#$+/'))$F$)%'2#$95KY:3$1,('//8C$0#$(-%#$%"'% %"#$.'O,.<.$'>#&'2#$;-0#&$'>',/'7/#$*&-.$'$+/'))$Z$-<%;<%$)%'2#$,)$-7%',(#6$78$)<7)%,%<%B ,(2$ 6b7 = 6-- $,($IJ3$944345:C I

E 6-6 < /%*< = 666 6666666666 I 4/

94434V:

11.3.4 Power Dissipation _(/,U#$%"#$+/'))$F$)%'2#C$0",+"$6,)),;'%#)$.'O,.<.$;-0#&$<(6#&$J<,#)+#(%$+-(6,%,-()$9v3$=$@:C %"#$J<,#)+#(%$;-0#&$6,)),;'%,-($-*$%"#$+/'))$Z$)%'2#$,)$N#&-3$\"#($'($,(;<%$),2('/$,)$';;/,#6C$%"# +9!:+;!$;-0#&$6,)),;'%#6$,($%"#$+/'))$Z$)%'2#$,)$2,>#($78

<8 = <= D
94434W:

P<7)%,%<%,(2$*-&$<=$*&-.$IJ3$94434H:$'(6$*-&$
94434X:

1&-.$)8..#%&8$0#$)##$%"'%$"'/*$-*$<8$,)$6,)),;'%#6$,($0>$'(6$%"#$-%"#&$"'/*$,($0<3$!"<)$0> '(6 0<$.<)%$7#$+';'7/#$-*$)'*#/8$6,)),;'%,(2$ E66I6 <8 $0'%%)3$P,(+#$<8$6#;#(6)$-($ 6b7 C$0#$.<)%$*,(6$%"# 0-&)%B+')#$;-0#&$6,)),;'%,-(C$<8.'O3$`,**#&#(%,'%,(2$IJ3$94434X:$0,%"$&#);#+%$%-$ 6b7 $'(6$#J<'%B ,(2$%"#$6#&,>'%,>#$%-$N#&-$2,>#)$%"#$>'/<#$-*$ 6b7 $%"'%$&#)#&'2#$;-0#&$6,)),B ;'%,-($')

6b7

<8%*<

I = 666 6--

94435@:

π

P<7)%,%<%,(2$%",)$>'/<#$,($IJ3$94434X:$2,>#) I

I6 -6 <8%*< = 66666666666666 π I 4/

944354:

!"<)C I

6-- 6 <8>%*< = <8<%*< = 6666666666 πI 4/

944355:

F%$%"#$;-,(%$-*$.'O,.<.$;-0#&$6,)),;'%,-(C$%"#$#**,+,#(+8$+'($7#$#>'/<'%#6$78$)<7)%,%<%,(2 *-&$ 6b7 $*&-.$IJ3$94435@:$,(%-$IJ3$94434K:G$"#(+#C$ η = FGd 3 1,2<&#$443W$$)"-0)$'$)U#%+"$-*$<8$9IJ3$4434X:$>#&)<)$%"#$;#'U$-<%;<%$>-/%'2#$ 6b7 3$L<&>#) )<+"$')$%",)$'&#$<)<'//8$2,>#($-($%"#$6'%'$)"##%)$-*$=L$;-0#&$'.;/,*,#&)3$a_)<'//8C$"-0#>#&C I <8$,)$;/-%%#6$>#&)<)$'%,-($*-/B /-0)$*&-.$1,23$443W^$=(+&#'),(2$ 6b7 $7#8-(6$ I6-- ⁄ π $'!$:!+(!($%"#$;-0#&$6,)),;'%#6$,($%"#

921

922 Chapter 11 Output Stages and Power Amplifiers

Figure 11.8 e'5/(#3$00$&*)$'"#'+#)./#-4*00#M#',)&,)#0)*1/#2/(0,0#*%&4$),3/#'+#)./#',)&,)#0$",0'$37

+/'))$Z$)%'2#$0",/#$,(+&#'),(2$%"#$/-'6$;-0#&3$!"#$;&,+#$;',6$,)$'($,(+&#')#$,($(-(/,(#'&$6,)B %-&%,-($')$'$&#)$'(6$0<3$!&'(),)%-& )'%<&'%,-($*/'%%#()$%"#$;#'U)$-*$%"#$-<%;<%$),(#$0'>#*-&.3$_(*-&%<('%#/8C$%",)$%8;#$-*$6,)%-&B %,-($ +'((-%$ 7#$ ),2(,*,+'(%/8$ <+#6$ 78$ %"#$ ';;/,+'%,-($ -*$ (#2'%,>#$ *##67'+U$ 9)##$ P#+%,-( 4@35:C$'(6$%"<)$%&'(),)%-&$)'%<&'%,-($)"--,6#6$,($';;/,+'%,-()$&#J<,&,(2$/-0$!c`3

Example 11.2 @)#$0#(/?,$(/3#)'#3/0$1"#*#-4*00#M#',)&,)#0)*1/#)'#3/4$2/(#*"#*2/(*1/#&'5/(#'+#IG#J#)'#*"#W6Ω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

Solution 8$"-/ E 6b < / = 666 6666676 I 4/ I

)./" 6b7 = =

I< / 4/ I × IG × W = E[7\#Z

;./(/+'(/#5/#0/4/-)#6--#=#IT#Z7 ;./#&/*X#-,((/")#3(*5"#+('%#/*-.#0,&&4:#$0 6b7 6 = E[7\ 6666666666 = I7I]#! ,b7 = 66666 W 4/

11.3 Class B Output Stage

8$"-/#/*-.#0,&&4:#&('2$3/0#*#-,((/")#5*2/+'(%#'+#.*4+60$",0'$309#)./#*2/(*1/#-,((/")#3(*5"#+('%#/*-.#0,&6 f &4:#5$44#=/# ,b7 ⁄ π 7 #;.,0#)./#*2/(*1/#&'5/(#3(*5"#+('%#/*-.#0,&&4:#$0 E < =+ = < =− = π666 × I7I] × IT = EU7]#J *-&$'$%-%'/$)<;;/8$;-0#&$-*$E53W$\3$!"#$;-0#&B+-(>#&),-($#**,+,#(+8$,) < IG η = 66666/6 = 6666666666 × EGG = UEd TI7W

<=

!"#$.'O,.<.$;-0#&$6,)),;'%#6$,($#'+"$%&'(),)%-&$,)$2,>#($78$IJ3$944355:G$%"<)C I

6 -6 <8>%*< = <8<%*< = 66666666666 I π 4/ I

( IT ) = 66666666666666 = U7[#J I π ×W

11.3.5 Reducing Crossover Distortion !"#$+&-))->#&$6,)%-&%,-($-*$'$+/'))$Z$-<%;<%$)%'2#$+'($7#$<+#6$)<7)%'(%,'//8$78$#.;/-8,(2 '$",2"B2',($-;$'.;$'(6$->#&'//$(#2'%,>#$*##67'+UC$')$)"-0($,($1,23$443X3$!"#$±@3VBA$6#'6 7'(6$,)$<+#6$%-$ ± G7[ ⁄ B G $>-/%C$0"#&#$B@$,)$%"#$6+$2',($-*$%"#$-;$'.;3$M#>#&%"#/#))C$%"# )/#0B&'%#$/,.,%'%,-($-*$%"#$-;$'.;$0,//$+'<)#$%"#$'/%#&('%#$%<&(,(2$-($'(6$-**$-*$%"#$-<%;<% %&'(),)%-&)$ %-$ 7#$ (-%,+#'7/#C$ #);#+,'//8$ '%$ ",2"$ *&#J<#(+,#)3$ F$ .-&#$ ;&'+%,+'/$ .#%"-6$ *-& <+,(2$'(6$'/.-)%$#/,.,('%,(2$+&-))->#&$6,)%-&%,-($,)$*-<(6$,($%"#$+/'))$FZ$)%'2#C$0",+" 0,//$7#$)%<6,#6$,($%"#$(#O%$)#+%,-(3

Figure 11.9 H4*00# M# -$(-,$)# 5$).# *"# '&# *%&# -'""/-)/3# $"# *# "/1*)$2/6+//3=*-X# 4''&# )'# (/3,-/# -('00'2/( 3$0)'()$'"7

923

924 Chapter 11 Output Stages and Power Amplifiers

11.3.6 Single-Supply Operation ;./# -4*00# M# 0)*1/# -*"# =/# '&/(*)/3# +('%# *# 0$"14/# &'5/(# 0,&&4:9# $"# 5.$-.# -*0/# )./# 4'*3# $0 -*&*-$)$2/4:# -',&4/39# *0# 0.'5"# $"# R$17# EE7EG7# >')/# ).*)# )'# %*X/# )./# +'(%,4*0# 3/($2/3# $" 8/-)$'"#EE7T7]#3$(/-)4:#*&&4$-*=4/9#)./#0$"14/#&'5/(#0,&&4:#$0#3/"')/3#I6--7

Figure 11.10 H4*00#M#',)&,)#0)*1/#'&/(*)/3#5$). *#0$"14/#&'5/(#0,&&4:7

EXERCISE 11.4 R'(#)./#-4*00#M#',)&,)#0)*1/#'+#R$17#EE7F9#4/)#6--#=#U#Z#*"3#4/#=#]#Ω7#@+#)./#',)&,)#$0#*#0$",0'$3#5$). ]7F6Z#&/*X#*%&4$),3/9#+$"3#A*D#)./#',)&,)#&'5/(S#A=D#)./#*2/(*1/#&'5/(#3(*5"#+('%#/*-.#0,&&4:S#A-D )./#&'5/(#/++$-$/"-:#'=)*$"/3#*)#).$0#',)&,)#2'4)*1/S#A3D#)./#&/*X#-,((/")0#0,&&4$/3#=:# v,9#*00,%$"1 ).*)#β>#=#β<#=#FGS#A/D#)./#%*<$%,%#&'5/(#).*)#/*-.#)(*"0$0)'(#%,0)#=/#-*&*=4/#'+#3$00$&*)$"1#0*+/4:7 Ans.%9':$53KE$\G$97:$534K$\G$9+:$KXYG$96:$5534$.FG$9#:$@3X4$\

11.4 Class AB Output Stage L&-))->#&$6,)%-&%,-($+'($7#$>,&%<'//8$#/,.,('%#6$78$7,'),(2$%"#$+-.;/#.#(%'&8$-<%;<%$%&'(),)%-&) '%$'$).'//$(-(N#&-$+<&&#(%3$!"#$&#)-/%'2#$622$,)$';;/,#6$7#%0##($%"#$7')#)$-*$0>$'(6$0<3$1-&$v,$=$@C$v3$=$@C$'(6$'$>-/%'2#$ 622 ⁄ I ';;#'&)$'+&-))$%"#$7')#D#.,%%#&$T<(+%,-($-*$#'+"$-*$0>$'(6$0<3$F))<.,(2$.'%+"#6$6#>,+#)C

# > = # < = ,0 = , = !

622 ⁄ I6C

94435E:

!"#$>'/<#$-*$622$,)$)#/#+%#6$%-$8,#/6$%"#$&#J<,$J<,#)+#(%$+<&&#(%$,03

11.4.1 Circuit Operation \"#($ v,$2-#)$;-),%,>#$78$'$+#&%',($'.-<(%C$%"#$>-/%'2#$'%$%"#$7')#$-*$0>$,(+&#')#)$78$%"# )'.#$'.-<(%$'(6$%"#$-<%;<%$7#+-.#)$;-),%,>#$'%$'($'/.-)%$#J<'/$>'/<#C v3

622 6 D v 21> = v , + 6666666 I

94435H:

11.4 Class AB Output Stage

Figure 11.11 H4*00#!M#',)&,)#0)*1/7#!#=$*0#2'4)*1/#622#$0#*&&4$/3#=/)5//"#)./#=*0/0#'+#0>#*"3#0<9#1$2$"1 ($0/#)'#*#=$*0#-,((/")#,0#1$2/"#=:#O?7#AEE7ITD7#;.,09#+'(#0%*44#v,9#=').#)(*"0$0)'(0#-'"3,-)#*"3#-('00'2/(#3$06 )'()$'"#$0#*4%'0)#-'%&4/)/4:#/4$%$"*)/37

!"#$;-),%,>#$v3$+'<)#)$'$+<&&#(%$#/$%-$*/-0$%"&-<2"$4/C$'(6$%"<)$#>$.<)%$,(+&#')#G$%"'%$,)C

#> = #< + #/

94435K:

!"#$,(+&#')#$,($#>$0,//$7#$'++-.;'(,#6$78$'$+-&&#);-(6,(2$,(+&#')#$,($v21>$9'7->#$%"#$J<,#)B +#(%$>'/<#$-*$622d5:3$c-0#>#&C$),(+#$%"#$>-/%'2#$7#%0##($%"#$%0-$7')#)$&#.',()$+-()%'(%$'% 622C$%"#$,(+&#')#$,($v21>$0,//$&#)$'(6$#<$+'($7#$6#&,>#6$')$*-//-0)^ v 21>

+ v 12< = 622

,0 # # 6C 4" 666>6 + 6C 4" 666<6 = I6C 4" 6666 ,= ,= ,= I

#> #< = ,0

94435?:

!"<)C$ ')$ #>$ ,(+&#')#)C$ #<$ 6#+&#')#)$ 78$ %"#$ )'.#$ &'%,-$ 0",/#$ %"#$ ;&-6<+%$ &#.',()$ +-()%'(%3 IJ<'%,-()$94435K:$'(6$94435?:$+'($7#$+-.7,(#6$%-$8,#/6$#>$*-&$'$2,>#($#/$')$%"#$)-/<%,-($%-$%"# J<'6&'%,+$#J<'%,-( I

I

#> D #/ #> D ,0 = G

94435V:

1&-.$ %"#$ #J<'%,-()$ '7->#C$ 0#$ +'($ )##$ %"'%$ *-&$ ;-),%,>#$ -<%;<%$ >-/%'2#)C$ %"#$ /-'6$ +<&&#(%$ ,) )<;;/,#6$78$0>C$0",+"$'+%)$')$%"#$-<%;<%$#.,%%#&$*-//-0#&3$]#'(0",/#C$0<$0,//$7#$+-(6<+%,(2$' +<&&#(%$%"'%$6#+&#')#)$')$v3$,(+&#')#)G$*-&$/'&2#$v3$%"#$+<&&#(%$,($0<$+'($7#$,2(-$'/%-2#%"#&3 1-&$(#2'%,>#$,(;<%$>-/%'2#)$%"#$-;;-),%#$-++<&)^$!"#$/-'6$+<&&#(%$0,//$7#$)<;;/,#6$78$0$+-(6<+%)$'$+<&&#(%$%"'%$2#%)$).'//#&$')$v, 7#+-.#)$.-&#$(#2'%,>#3$IJ<'%,-($94435?:C$&#/'%,(2$#>$'(6$##$,(;<%)$')$0#//3 \#$+-(+/<6#$%"'%$%"#$+/'))$FZ$)%'2#$-;#&'%#)$,($.<+"$%"#$)'.#$.'((#&$')$%"#$+/'))$Z +,&+<,%C$ 0,%"$ -(#$ ,.;-&%'(%$ #O+#;%,-(^$ 1-&$ ).'//$ v,C$ 7-%"$ %&'(),)%-&)$ +-(6<+%C$ '(6$ ')$ v,$ ,) ,(+&#')#6$ -&$ 6#+&#')#6C$ -(#$ -*$ %"#$ %0-$ %&'(),)%-&)$ %'U#)$ ->#&$ %"#$ -;#&'%,-(3$ P,(+#$ %"#

925

926 Chapter 11 Output Stages and Power Amplifiers

Figure 11.12 ;(*"0+/(#-.*(*-)/($0)$-#'+#)./#-4*00#!M#0)*1/#$"#R$17#EE7EE7

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

11.4.2 Output Resistance =*$0#$'))<.#$%"'%$%"#$)-<&+#$)<;;/8,(2$v,$,)$,6#'/C$%"#($%"#$-<%;<%$&#),)%'(+#$-*$%"#$+/'))$FZ )%'2#$+'($7#$6#%#&.,(#6$*&-.$%"#$+,&+<,%$,($1,23$4434E$')

4 ',) = : !> || : !<

94435W:

0"#&#$:!>$'(6$:!<$'&#$%"#$).'//B),2('/$#.,%%#&$&#),)%'(+#)$-*$0>$'(6$0#/83$F%$' 2,>#($,(;<%$>-/%'2#C$%"#$+<&&#(%)$#>$'(6$#<$+'($7#$6#%#&.,(#6C$'(6$:!>$'(6$:!<$'&#$2,>#($78

!"<)C

6 : !> = 66666C #> 6C : !< = 66666 #<

6 6 6C 4 ',) = 66666C ## 66666C = 66666666666666 #> #< #< + #>

94435X: 9443E@:

9443E4:

P,(+#$ ')$ #>$ ,(+&#')#)C$ #<$ 6#+&#')#)C$ '(6$ >,+#$ >#&)'C$ %"#$ -<%;<%$ &#),)%'(+#$ &#.',()$ ';;&-O,B .'%#/8$ +-()%'(%$ ,($ %"#$ ,-($ '&-<(6$ v,$ =$ @3$ !",)C$ ,($ #**#+%C$ ,)$ %"#$ &#')-($ *-&$ %"#$ >,&%<'/

11.4 Class AB Output Stage

Figure 11.13 C/)/(%$"$"1# )./# 0%*4460$1"*4# ',)&,)# (/0$0)*"-/# '+ )./#-4*00#!M#-$(-,$)#'+#R$17#EE7EE7

'7)#(+#$-*$+&-))->#&$6,)%-&%,-(3$F%$/'&2#&$/-'6$+<&&#(%)C$#,%"#&$#>$-&$#<$0,//$7#$),2(,*,+'(%C$'(6 4-<%$6#+&#')#)$')$%"#$/-'6$+<&&#(%$,(+&#')#)3

Example 11.3 @"#).$0#/<*%&4/#5/#/<&4'(/#)./#3/)*$40#'+#)./#)(*"0+/(#-.*(*-)/($0)$-9# v 3 #2/(0,0# v , 9#'+#)./#-4*00#!M#-$(-,$) $"#R$17#EE7EE7#R'(#).$0#&,(&'0/#4/)# 6 -- Q EF#Z9# , 0 Q I #%!9#*"3# 4 / Q EGG#Ω 7#!00,%/#).*)# 0 > #*"3# 0 < D ET *(/#%*)-./3#*"3#.*2/# , = Q EG !7#R$(0)9#3/)/(%$"/#)./#(/?,$(/3#2*4,/#'+#)./#=$*0#2'4)*1/# 6 22 7#;./"9 +$"3#)./#)(*"0+/(#-.*(*-)/($0)$-#+'(# v 3 #$"#)./#(*"1/# D EG #Z#)'# gEG #Z7

Solution ;'#3/)/(%$"/#)./#(/?,$(/3#2*4,/#'+# 6 22 #5/#,0/#O?7#AEE7ITD#5$).# , 0 Q I #%!#*"3# , = Q EG

D ET

!7#;.,09

6 22 Q I6 C 4" ( , 0 ⁄ , = ) DT

Q I × G7GIF 4" ( I × EG ⁄ EG

D ET

) Q E7EWU #Z

;./#/*0$/0)#5*:#)'#3/)/(%$"/#)./#)(*"0+/(#-.*(*-)/($0)$-#$0#)'#5'(X#=*-X5*(3S#).*)#$09#+'(#*#1$2/"# v 3 #5/ 3/)/(%$"/#)./#-'((/0&'"3$"1#2*4,/#'+# v , 7#J/#0.*44#',)4$"/#)./#&('-/00#+'(#&'0$)$2/# v 3 c

1. F))<.#$'$>'/<#$*-&$ v 3 3 2. `#%#&.,(#$%"#$/-'6$+<&&#(%$ # / C #/ Q v3 ⁄ 4/

3. _)#$IJ3$94435V:$%-$6#%#&.,(#$%"#$+<&&#(%$+-(6<+%#6$78$ 0 > 9 $ # > 7 4. `#%#&.,(#$ v 21> $*&-. v 21> Q 6 C 4" ( # > ⁄ , = )

5. C/)/(%$"/# v , #+('% v , Q v 3 e v 21> D 6 22 ⁄ I

927

928 Chapter 11 Output Stages and Power Amplifiers

Example 11.3 continued

@)#$0#*40'#,0/+,4#)'#+$"3# # < #*"3# v 12< #*0#+'44'50c# #< Q #> D #/ v 12< Q 6 C 4" ( # < ⁄ , = )

!#0$%$4*(#&('-/00#-*"#=/#/%&4':/3#+'(#"/1*)$2/# v 3 7#B'5/2/(9#0:%%/)(:#-*"#=/#,)$4$V/39#'=2$*)$"1 )./#"//3#)'#(/&/*)#)./#-*4-,4*)$'"07#;./#(/0,4)0#'=)*$"/3#*(/#3$0&4*:/3#$"#)./#+'44'5$"1#)*=4/c vO (V) iL (mA)

+4@3@ +K3@ +43@ +@3K +@35 +@34 $$$$@ −@34 −@35 −@3K −43@ −K3@ −4@3@

4@@ K@ 4@ K 5 4 @ −4 −5 −K −4@ −K@ −4@@

iN (mA)

iP (mA)

vBEN (V)

vEBP (V)

4@@3@H K@3@W 4@3EX K3V@ E35H 53K? 5 43K? 435H @3V@ @3EX @3@W @3@H

@3@H @3@W @3EX @3V@ 435H 43K? 5 53K? E35H K3V@ 4@3EX K@3@W 4@@3@H

@3?X4 @3?VE @3?EH @3?4X @3?@K @3KXX @3KXE @3KWV @3KW4 @3K?V @3KK5 @3K4E @3HXK

@3HXK @3K4E @3KK5 @3K?V @3KW4 @3KWV @3KXE @3KXX @3?@K @3?4X @3?EH @3?VE @3?X4

vI (V)

4@34 K3@W 43@H4 @3K5? @3545 @34@? @ −@34@? −@3545 −@3K5? −43@H4 −K3@W −4@34

vO / v I

R out (W)

vo / vi

@3XX @3XW @3X? @3XK @3XH @3XH S @3XH @3XH @3XK @3X? @3XW @3XX

@35K @3K@ 53E5 H3@E K3KW ?3@V ?35K ?3@V K3KW H3@E 53E5 @3K@ @35K

43@@ 43@@ @3XW @3X? @3XK @3XH @3XH @3XH @3XK @3X? @3XW 43@@ 43@@

;./#)*=4/#*40'#&('2$3/0#2*4,/0#+'(#)./#3-#1*$"# v 3 ⁄ v , #*0#5/44#*0#)./#$"-(/%/")*4#1*$"# v 7 ⁄ v # #*)#)./#2*($',0 2*4,/0#'+# v 3 7#;./#$"-(/%/")*4#1*$"#$0#-'%&,)/3#*0#+'44'50 v7 4/ 6666 Q 66666666666666666666 6 v# 4 / e 4 ',) 5./(/# 4 ',) #$0#)./#0%*4460$1"*4#',)&,)#(/0$0)*"-/#'+#)./#*%&4$+$/(9#1$2/"#=:#O?7#AEE7TED7#;./#$"-(/%/")*4 1*$"#$0#)./#04'&/#'+#)./#2'4)*1/#)(*"0+/(#-.*(*-)/($0)$-9#*"3#)./#%*1"$),3/#'+#$)0#2*($*)$'"#'2/(#)./#(*"1/#'+ v 3 #$0#*"#$"3$-*)$'"#'+#)./#4$"/*($):#'+#)./#',)&,)#0)*1/7#Q=0/(2/#).*)#+'(# G ≤ v 3 ≤ EG#Z 9#)./#$"-(/%/")*4 1*$"#-.*"1/0#+('%#G7\]#)'#E7GG9#*=',)#Ud7#!40'#'=0/(2/#*0# v 3 #=/-'%/0#&'0$)$2/9# 0 > #0,&&4$/0#%'(/#*"3 f %'(/#'+# # / #*"3# 0 < #$0#-'((/0&'"3$"14:#(/3,-/37#;./#'&&'0$)/#.*&&/"0#+'(#"/1*)$2/# v 3 7

EXERCISE 11.5 ;'#$"-(/*0/#)./#4$"/*($):#'+#)./#-4*00#!M#',)&,)#0)*1/9#)./#?,$/0-/")#-,((/")# , 0 #$0#$"-(/*0/37#;./#&($-/ &*$3#$0#*"#$"-(/*0/#$"#?,$/0-/")#&'5/(#3$00$&*)$'"7#R'(#)./#',)&,)#0)*1/#-'"0$3/(/3#$"#O<*%&4/#EE7Tc A*D#R$"3#)./#?,$/0-/")#&'5/(#3$00$&*)$'"7 A=D#@+# , 0 #$0#$"-(/*0/3#)'#EG#%!9#+$"3# v7 ⁄ v # #*)# v 3 Q G #*"3#*)# v 3 Q EG #Z9#*"3#./"-/#)./#&/(-/")*1/ -.*"1/7#H'%&*(/#)'#)./#-*0/#$"#O<*%&4/#EE7T7 A-D#R$"3#)./#?,$/0-/")#&'5/(#3$00$&*)$'"#+'(#)./#-*0/#$"#A=D7 Ans. A*D#UG#%JS#A=D#G7\WW#)'#E7GGS#+'(#*#-.*"1/#'+#E7Id#-'%&*(/3#)'#)./#Ud#-.*"1/#$"#O<*%&4/ EE7TS#A-D#TGG#%J

11.5 Biasing the Class AB Circuit

11.5 Biasing the Class AB Circuit =($%",)$)#+%,-($0#$6,)+<))$%0-$';;&-'+"#)$*-&$2#(#&'%,(2$%"#$>-/%'2#$622$&#J<,$*-&$7,'),(2 %"#$+/'))$FZ$-<%;<%$)%'2#3

11.5.1 Biasing Using Diodes 1,2<&#$4434H$)"-0)$'$+/'))$FZ$+,&+<,%$,($0",+"$%"#$7,')$>-/%'2#$622$,)$2#(#&'%#6$78$;')),(2$' +-()%'(%$+<&&#(%$,Z=FP$%"&-<2"$'$;',&$-*$6,-6#)C$-&$6,-6#B+-((#+%#6$%&'(),)%-&)C$84$'(6$853$=($+,&B +<,%)$%"'%$)<;;/8$/'&2#$'.-<(%)$-*$;-0#&C$%"#$-<%;<%$%&'(),)%-&)$'&#$/'&2#B2#-.#%&8$6#>,+#)3 !"#$ 7,'),(2$ 6,-6#)C$ "-0#>#&C$ (##6$ (-%$ 7#$ /'&2#$ 6#>,+#)C$ '(6$ %"<)$ %"#$ J<,#)+#(%$ +<&&#(%$ ,0 #)%'7/,)"#6$,($0>$'(6$0<$0,//$7#$,0$=$%,Z=FPC$0"#&#$%$,)$%"#$&'%,-$-*$%"#$#.,%%#&DT<(+%,-($'&#'$-* %"#$-<%;<%$6#>,+#)$%-$%"#$T<(+%,-($'&#'$-*$%"#$7,'),(2$6,-6#)3$=($-%"#&$0-&6)C$%"#$)'%<&'%,-($9-& )+'/#:$+<&&#(%$,=$-*$%"#$-<%;<%$%&'(),)%-&)$,)$%$%,.#)$%"'%$-*$%"#$7,'),(2$6,-6#)3$F&#'$&'%,-,(2$,) ),.;/#$%-$,.;/#.#(%$,($,(%#2&'%#6$+,&+<,%)$7<%$6,**,+
IBIAS

D1 D2 Figure 11.14 !#-4*00#!M#',)&,)#0)*1/#,)$4$V$"1 3$'3/0#+'(#=$*0$"17#@+#)./#h,"-)$'"#*(/*#'+#)./#',)6 &,)#3/2$-/09#0>#*"3#0< 9#$0#%#)$%/0#).*)#'+#)./#=$*06 $"1# 3/2$-/0# 8E# *"3# 8I 9# *# ?,$/0-/")# -,((/") ,0 ` %,M@!8#+4'50#$"#)./#',)&,)#3/2$-/07

\"#($%"#$-<%;<%$)%'2#$-*$1,23$4434H$,)$)-<&+,(2$+<&&#(%$%-$%"#$/-'6C$%"#$7')#$+<&&#(%$-*$0> ,(+&#')#)$*&-.$ ,0 ⁄ β > $90",+"$,)$<)<'//8$).'//:$%-$';;&-O,.'%#/8$ #/ ⁄ β > 3$!",)$7')#$+<&&#(% 6&,>#$.<)%$7#$)<;;/,#6$78$%"#$+<&&#(%$)-<&+#$,Z=FP3$=%$*-//-0)$%"'%$,Z=FP$.<)%$7#$2&#'%#&$%"'($%"# .'O,.<.$'(%,+,;'%#6$7')#$6&,>#$*-&$0>3$!",)$)#%)$'$/-0#&$/,.,%$-($%"#$>'/<#$-*$,Z=FP3$M-0C ),(+#$% =5,05D5,2,B=C$'(6$),(+#$,0$,)$<)<'//8$.<+"$).'//#&$%"'($%"#$;#'U$/-'6$+<&&#(%$9<4@Y:C$0# )##$%"'%$0#$+'((-%$.'U#$%$'$/'&2#$(<.7#&3$=($-%"#&$0-&6)C$0#$+'((-%$.'U#$%"#$6,-6#)$.<+" ).'//#&$%"'($%"#$-<%;<%$6#>,+#)3$!",)$,)$'$6,)'6>'(%'2#$-*$%"#$6,-6#$7,'),(2$)+"#.#3 1&-.$%"#$6,)+<)),-($'7->#$0#$)##$%"'%$%"#$+<&&#(%$%"&-<2"$%"#$7,'),(2$6,-6#)$0,//$6#+&#')# 0"#($ %"#$ -<%;<%$ )%'2#$ ,)$ )-<&+,(2$ +<&&#(%$ %-$ %"#$ /-'63$ !"<)$ %"#$ 7,')$ >-/%'2#$ 622$ 0,//$ '/)6#+&#')#C$'(6$%"#$'('/8),)$-*$P#+%,-($443H$.<)%$7#$.-6,*,#6$%-$%'U#$%",)$#**#+%$,(%-$'++-<(%3 !"#$6,-6#$7,'),(2$'&&'(2#.#(%$"')$'($,.;-&%'(%$'6>'(%'2#^$=%$+'($;&->,6#$%"#&.'/$)%'7,/,N'B %,-($-*$%"#$J<,#)+#(%$+<&&#(%$,($%"#$-<%;<%$)%'2#3$!-$';;&#+,'%#$%",)$;-,(%C$&#+'//$%"'%$%"#$+/'))$FZ -<%;<%$)%'2#$6,)),;'%#)$;-0#&$<(6#&$J<,#)+#(%$+-(6,%,-()3$f-0#&$6,)),;'%,-($&',)#)$%"#$,(%#&('/ %#.;#&'%<&#$-*$%"#$Zg!)3$1&-.$L"';%#&$?$0#$U(-0$%"'%$'$&,)#$,($%&'(),)%-&$%#.;#&'%<&#$&#)#/8C$,*$621$,)$"#/6$+-()%'(%$'(6$%"#$%#.;#&'%<&#$,(+&#')#)C$%"#$+-//#+%-&$+<&&#(%$,(+&#')#)3$!"# ,(+&#')#$,($+-//#+%-&$+<&&#(%$,(+&#')#)$%"#$;-0#&$6,)),;'%,-(C$0",+"$,($%<&($,(+&#')#)$%"#$T<(+%,-(

929

930 Chapter 11 Output Stages and Power Amplifiers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

Example 11.4 H'"0$3/(#)./#-4*00#!M#',)&,)#0)*1/#,"3/(#)./#-'"3$)$'"0#).*)# 6-- = EF#Z9#4 / = EGG#Ω9 #*"3#)./#',)&,)#$0#0$",6 D ET 0'$3*4#5$).#*#%*<$%,%#*%&4$),3/#'+#EG#Z7#^/)#0>#*"3#0<#=/#%*)-./3#5$).# , = = EG #! #*"3# β = FG7 #!00,%/ ).*)#)./#=$*0$"1#3$'3/0#.*2/#'"/6).$(3#)./#h,"-)$'"#*(/*#'+#)./#',)&,)#3/2$-/07#R$"3#)./#2*4,/#'+# , M@!8 #).*)#1,*(6 *")//0#*#%$"$%,%#'+#E#%!#).(',1.#)./#3$'3/0#*)#*44#)$%/07#C/)/(%$"/#)./#?,$/0-/")#-,((/")#*"3#)./#?,$/0-/") &'5/(#3$00$&*)$'"#$"#)./#',)&,)#)(*"0$0)'(0#A$7/79#*)# v 3 = G D7#!40'#+$"3#622#+'(# v 3 = G9 #+EG#Z9#*"3#−EG#Z7

Solution ;./# %*<$%,%# -,((/")# ).(',1.#0>#$0# *&&('<$%*)/4:# /?,*4#)'# # /%*< = EG#Z_G7E#XΩ = EGG#%!7 # ;.,0# )./ %*<$%,%# =*0/# -,((/")# $"# 0># $0# *&&('<$%*)/4:# I# %!7# ;'# %*$")*$"# *# %$"$%,%# '+# E %!# ).(',1.# )./ 3$'3/09#5/#0/4/-)# ,M@!8 = T#%!7 #;./#*(/*#(*)$'#'+#T#:$/430#*#?,$/0-/")#-,((/")#'+#\#%!#).(',1.#0>#*"3 0<7#;./#?,$/0-/")#&'5/(#3$00$&*)$'"#$0 <80 = I × EF × \ = I[G#%J R'(# v 3 = G9 #)./#=*0/#-,((/")#'+#0>#$0# \ ⁄ FE!#G7EW#%!9 4/*2$"1#*#-,((/")#'+#T#−#G7EW#=#I7WI#%!#)' +4'5 ).(',1.#)./#3$'3/07#8$"-/#)./#3$'3/0#.*2/# , = = E66T6 × EG DET !9 #)./#2'4)*1/#622#5$44#=/ I7WI#%! 622 = I6C 4" 666666666666666666666 = E7IU#Z ,= !)# v 3 = +EG#Z9#)./#-,((/")#).(',1.#)./#3$'3/0#5$44#3/-(/*0/#)'#E#%!9#(/0,4)$"1#$"# 622 ! E7IE#Z7 #!)#)./ ')./(#/<)(/%/#'+# v 3 = D E G#Z9 #0>#5$44#=/#-'"3,-)$"1#*#2/(:#0%*44#-,((/")S#).,0#$)0#=*0/#-,((/")#5$44#=/ "/14$1$=4:#0%*44#*"3#*44#'+# , M@!8 #AT#%!D#+4'50#).(',1.#)./#3$'3/09#(/0,4)$"1#$"# 622 ! E7IU#Z7

EXERCISES 11.6 R'(#)./#-$(-,$)#'+#O<*%&4/#EE7]9#+$"3##>#*"3##<#+'(# v 3 = +EG#Z #*"3# v 3 = −EG#Z7 #AE#%&c#a0/#)./ 622 #2*4,/0#+',"3#$"#O<*%&4/#EE7]7D Ans. EGG7E#%!9#G7E#%!S#G7W#%!9#EGG7W#%! 11.7# @+#)./#-'44/-)'(#-,((/")#'+#*#)(*"0$0)'(#$0#./43#-'"0)*")9#$)0#v21#3/-(/*0/0#=:#I#%Z#+'(#/2/(:#E°H#($0/#$" )/%&/(*),(/7#!4)/("*)$2/4:9#$+#v21#$0#./43#-'"0)*")9#)./"##-#$"-(/*0/0#=:#*&&('<$%*)/4:#;F#×#I#%Z#+'( /2/(:#E°H#($0/#$"#)/%&/(*),(/7#R'(#*#3/2$-/#'&/(*)$"1#*)#,-#=#EG#%!9#+$"3#)./#-.*"1/#$"#-'44/-)'(#-,(6 (/")#(/0,4)$"1#+('%#*"#$"-(/*0/#$"#)/%&/(*),(/#'+#F°H7 Ans. H$.F

11.5 Biasing the Class AB Circuit

11.5.2 Biasing Using the VBE Multiplier F($'/%#&('%,>#$7,'),(2$'&&'(2#.#(%$%"'%$;&->,6#)$%"#$6#),2(#&$0,%"$+-(),6#&'7/8$.-&#$*/#O,B 7,/,%8$,($7-%"$6,)+&#%#$'(6$,(%#2&'%#6$6#),2()$,)$)"-0($,($1,23$4434K3$!"#$7,')$+,&+<,%$+-(),)%) -*$%&'(),)%-&$04$0,%"$'$&#),)%-&$44$+-((#+%#6$7#%0##($7')#$'(6$#.,%%#&$'(6$'$*##67'+U$&#),)B %-&$45$+-((#+%#6$7#%0##($+-//#+%-&$'(6$7')#3$!"#$&#)#($78

621E , 4 = 6666666666 4E

9443E5:

'(6$%"#$>-/%'2#$622$'+&-))$%"#$7,')$(#%0-&U$0,//$7#

622 = , 4 ( 4 E + 4 I )

9443EE:

4 = 621E E + 66666I 4E !"<)$%"#$+,&+<,%$),.;/8$.,-<)/8$<(6#&$%"#$6#),2(#&j)$+-(%&-/$'(6$+'($7# <)#6$ %-$ #)%'7/,)"$ %"#$ >'/<#$ -*$ 622$ &#J<,$ %-$ 8,#/6$ '$ 6#),$ J<,#)+#(%$ +<&&#(%$ ,03$ =($ =L 6#),2($ ,%$ ,)$ &#/'%,>#/8$ #')8$ %-$ +-(%&-/$ '++<&'%#/8$ %"#$ &'%,-$ -*$ %0-$ &#),)%'(+#)3$ =($ 6,)+&#%#B +,&+<,%$6#),2(C$'$;-%#(%,-.#%#&$+'($7#$<)#6C$')$)"-0($,($1,23$4434?C$'(6$,)$.'(<'//8$)#%$%;&-6<+#$%"#$6#),$>'/<#$-*$,03 !"#$>'/<#$-*$6214$,($IJ3$9443EE:$,)$6#%#&.,(#6$78$%"#$;-&%,-($-*$,Z=FP$%"'%$*/-0)$%"&-<2" %"#$+-//#+%-&$-*$04G$%"'%$,)C

, -E = , M@!8 D , 4

IBIAS

Figure 11.15 !#-4*00#!M#',)&,)#0)*1/#,)$4$V$"1#*#621#%,4)$&4$/(#+'(#=$*0$"17

9443EH:

931

932 Chapter 11 Output Stages and Power Amplifiers

IBIAS

Figure 11.16 !#3$0-(/)/6-$(-,$)#-4*00#!M#',)&,)#0)*1/#5$).#*#&')/")$'%/)/(#,0/3#$"#)./#621#%,4)$&4$/(7#;./ &')/")$'%/)/(#$0#*3h,0)/3#)'#:$/43#)./#3/0$(/3#2*4,/#'+#?,$/0-/")#-,((/")#$"#0>#*"3#0< 7

, -E 621E = 6C 4" 666666 , =E

9443EK:

0"#&#$0#$"'>#$(#2/#+%#6$%"#$7')#$+<&&#(%$-*$0>C$0",+"$,)$(-&.'//8$).'//$7-%"$<(6#&$J<,#)B +#(%$+-(6,%,-()$'(6$0"#($%"#$-<%;<%$>-/%'2#$,)$)0,(2,(2$(#2'%,>#3$c-0#>#&C$*-&$;-),%,>#$v3C #);#+,'//8$'%$'(6$(#'&$ ,%)$ ;#'U$ >'/<#C$%"#$7')#$ +<&&#(%$ -*$ 0>$ +'($ 7#+-.#$),N'7/#$ '(6$ 0,// <+#$%"#$+<&&#(%$'>',/'7/#$*-&$%"#$621$.#&%"#/#))C$),(+#$/'&2#$+"'(2#)$,($,-4 +-&&#);-(6$%-$-(/8$).'//$+"'(2#)$,($6214C$%"#$6#+&#')#$,($+<&&#(%$0,//$7#$.-)%/8$'7)-&7#6$78 04C$/#'>,(2$,4C$'(6$"#(+#$622C$'/.-)%$+-()%'(%3

EXERCISE 11.8 H'"0$3/(#*#621#%,4)$&4$/(#5$).#4E#=#4I#=#E7I#XΩ9#,)$4$V$"1#*#)(*"0$0)'(#).*)#.*0#621#=#G7U#Z#*)#,-#=#E#%!9 *"3#*#2/(:#.$1.#β7#A*D#R$"3#)./#2*4,/#'+#)./#-,((/")#,#).*)#0.',43#=/#0,&&4$/3#)'#)./#%,4)$&4$/(#)'#'=)*$" *#)/(%$"*4#2'4)*1/#'+#E7I#Z7#A=D#R$"3#)./#2*4,/#'+#,#).*)#5$44#(/0,4)#$"#)./#)/(%$"*4#2'4)*1/#-.*"1$"1#A+('% )./#E7I6Z#2*4,/D#=:#+FG#%Z9#+EGG#%Z9#+IGG#%Z9#iFG#%Z9#iEGG#%Z9#iIGG#%Z7 Ans. 9':$43K$.FG$97:$E35H$.FC$V3XE$.FC$KK34W$.FC$@3WK$.FC$@3KX$.FC$@3HE$.F

k,U#$%"#$6,-6#$7,'),(2$(#%0-&UC$%"#$621 D.,6#$%"#&.'/$)%'7,/,N'B %,-($-*$,03$!",)$,)$#);#+,'//8$%&<#$,*$44$=$45 C$'(6$04$,)$,($+/-)#$%"#&.'/$+-(%'+%$0,%"$%"#$-<%;<% %&'(),)%-&)3

11.6 CMOS Class AB Output Stages

Example 11.5 @)#$0#(/?,$(/3#)'#(/3/0$1"#)./#',)&,)#0)*1/#'+#O<*%&4/#EE7]#,)$4$V$"1#*# 621#%,4)$&4$/(#+'(#=$*0$"17#a0/#* 0%*4461/'%/)(:#)(*"0$0)'(#+'(#0E#5$).#,=#=#EGiE]#!#*"3#3/0$1"#+'(#*#?,$/0-/")#-,((/")#,0#=#I#%!7

Solution 8$"-/#)./#&/*X#&'0$)$2/#-,((/")#$0#EGG#%!9#)./#=*0/#-,((/")#'+#0>#-*"#=/#*0#.$1.#*0#I#%!7#J/#0.*44#)./(/6 +'(/#0/4/-)#,M@!8#=#T#%!9#).,0#&('2$3$"1#)./#%,4)$&4$/(#5$).#*#%$"$%,%#-,((/")#'+#E#%!7 a"3/(#?,$/0-/")#-'"3$)$'"0#Av3#=#G#*"3##/#=#GD#)./#=*0/#-,((/")#'+#0>#-*"#=/#"/14/-)/3#*"3#*44#'+#,M@!8 +4'50#).(',1.#)./#%,4)$&4$/(7#J/#"'5#%,0)#3/-$3/#'"#.'5#).$0#-,((/")#AT#%!D#$0#)'#=/#3$2$3/3#=/)5//" ,-E#*"3#,47#@+#5/#0/4/-)#,4#1(/*)/(#).*"#E#%!9#)./#)(*"0$0)'(#5$44#=/#*4%'0)#-,)#'++#*)#)./#&'0$)$2/#&/*X#'+#v37 ;./(/+'(/9#5/#0.*44#0/4/-)#,45=#G7F#%!9#4/*2$"1#I7F#%!#+'(#,-E7 ;'#'=)*$"#*#?,$/0-/")#-,((/")#'+#I#%!#$"#)./#',)&,)#)(*"0$0)'(09#622#0.',43#=/ DT

I × EG 6 = E7E\#Z 622 = I6C 4" 666666666666666666 D ET EG J/#-*"#"'5#3/)/(%$"/#4E#+#4I#*0#+'44'50c 622 E7E\ 6 = 6666666666 = I7TW#XΩ 4 E + 4 I = 66666666 G7F ,4 !)#*#-'44/-)'(#-,((/")#'+#I7F#%!9#0E#.*0 DT

I7F × EG 6 = G7UU#Z 621E = 6C 4" 66666666666666666666666 D E] EG ;./#2*4,/#'+#4E#-*"#"'5#=/#3/)/(%$"/3#*0 G7UU 4 E = 6666666666 = E7TI#XΩ G7F *"3#4I#*0 4 I = I7TW D E7TI = E7GU#XΩ

11.6 CMOS Class AB Output Stages @"#).$0#0/-)$'"#5/#0),3:#HPQ8#-4*00#!M#',)&,)#0)*1/07#J/#=/1$"#5$).#)./#HPQ8#-',")/(&*() '+#)./#MN;#-4*00#!M#',)&,)#0)*1/#0),3$/3#$"#)./#&(/2$',0#0/-)$'"7#!0#5/#0.*44#0//9#).$0#-$(-,$) 0,++/(0#+('%#*#(/4*)$2/4:#4'5#',)&,)#0$1"*4605$"19#*#0/($',0#4$%$)*)$'"#/0&/-$*44:#$"#2$/5#'+#)./ 0.($"X$"1#&'5/(60,&&4:#2'4)*1/0#-.*(*-)/($0)$-#'+#%'3/("#3//&60,=%$-('"#HPQ8#)/-."'4'6 1$/07#J/#5$44#)./"#4''X#*)#*"#*))(*-)$2/#*4)/("*)$2/#-$(-,$)#).*)#'2/(-'%/0#).$0#&('=4/%7

11.6.1 The Classical Configuration R$1,(/#EE7E[#0.'50#)./#-4*00$-*4#HPQ8#-4*00#!M#',)&,)#0)*1/7#;./#-$(-,$)#$0#)./#/<*-)#-',"6 )/(&*()#'+#)./#=$&'4*(#-$(-,$)#0.'5"#$"#R$17#EE7E]#5$).#)./#=$*0$"1#3$'3/0#$%&4/%/")/3#5$). 3$'3/6-'""/-)/3#)(*"0$0)'(0# 0 E #*"3# 0 I 7 #;./#-'"0)*")#-,((/")# , M@!8 #+4'5$"1#).(',1.# 0 E #*"3 0 I #/0)*=4$0./0#*#3-#=$*0#2'4)*1/#6 GG #=/)5//"#)./#1*)/0#'+# 0 > #*"3# 0 < 7 #;.$0#2'4)*1/#$"#),("

933

934 Chapter 11 Output Stages and Power Amplifiers !VDD

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/0)*=4$0./0#)./#?,$/0-/")# ( v 3 Q G ) #-,((/")# , 0 #$"# 0 > #*"3# 0 < 7 #a"4$X/#)./#MN;#-$(-,$)#$"#R$17 EE7E]9#./(/#)./#V/('#3-#1*)/#-,((/")#'+# 0 > #(/0,4)0#$"#)./#-,((/")#).(',1.# 0 E #*"3# 0 I #(/%*$"$"1 -'"0)*")#*)# , M@!8 #$((/0&/-)$2/#'+#)./#2*4,/#'+# v 3 #*"3#)./#4'*3#-,((/")# # / 7 #;.,0# 6 GG #(/%*$"0 -'"0)*")#*"3#)./#-$(-,$)#$0#%'(/#4$X/#)./#$3/*4$V/3#=$&'4*(#-*0/#0.'5"#$"#R$17#EE7EE7 ;./#2*4,/#'+# , 0 #-*"#=/#3/)/(%$"/3#=:#,)$4$V$"1#)./# # 8 D v G= #/?,*)$'"0#+'(#)./#+',(#PQ8 )(*"0$0)'(0#+'(#)./#-*0/# v 3 Q G 7#>/14/-)$"1#-.*""/464/"1).#%'3,4*)$'"9#5/#-*"#5($)/#+'(# 0 E9 E I , 8E Q , M@!8 Q 666 H%′ ( I ⁄ / ) E ( 6 G=E D 6 &% ) I

9443E?:

E I , 8I Q , M@!8 Q 666H *′ ( I ⁄ / ) I ( 6 =GI D 6 &* ) I

9443EV:

*"3#+'(# 0 I 9

O?,*)$'"0# AEE7TUD# *"3# AEE7T[D# -*"# =/# ,0/3# )'# +$"3# 6 G=E# *"3# 6 =GI 9# 5.$-.# 5./"# 0,%%/3 :$/43# 6 GG S#).,09 6 GG Q 6 G=E e 6 =GI Q 6 &% e 6 &* e I, M@!8

E E 66666666666666666666666666666 e 66666666666666666666666666666 H%′ ( I ⁄ / ) E H *′ ( I ⁄ / ) I

9443EW:

J/#-*"#+'44'5#*#0$%$4*(#&('-/00#+'(# 0 > #*"3# 0 < #5.$-.9#+'(# v 3 Q G 9#*(/#-'"3,-)$"1#)./#?,$6 /0-/")#-,((/")# , 0 S#).,09 6 GG Q 6 G=> e 6 =G< Q 6 &% e 6 &* e I, 0

E E 666666666666666666666666666 6 e 6666666666666666666666666666 H′%( I ⁄ / ) % H′* ( I ⁄ / ) *

9443EX:

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I

9443H@:

11.6 CMOS Class AB Output Stages

5.$-.#$"3$-*)/0#).*)# , 0 #$0#3/)/(%$"/3#=:# , M@!8 #)'1/)./(#5$).#)./# ( I ⁄ / ) #(*)$'0#'+#)./#+',( )(*"0$0)'(07#R'(#)./#-*0/# 0 E #*"3# 0 I #*(/#%*)-./39#).*)#$09 H′* ( I ⁄ / ) I Q H′%( I ⁄ / ) E

9443H4:

*"3# 0 > #*"3# 0 < #*(/#%*)-./39#).*)#$09 H*′ ( I ⁄ / ) * Q H′%( I ⁄ / ) %

9443H5:

(I ⁄ /) , 0 Q , M@!8 666666666666666666%6 ( I ⁄ / )E

9443HE:

O?,*)$'"#AEE7]GD#0$%&4$+$/0#)'

5.$-.#$0#*"#$"),$)$2/4:#*&&/*4$"1#(/0,4)7

EXERCISE 11.9 R'(#)./#HPQ8#-4*00#!M#',)&,)#0)*1/#'+#R$17#EE7E[9#-'"0$3/(#)./#-*0/#'+#%*)-./3# 0 E #*"3# 0 I 9#*"3 %*)-./3# 0 > #*"3# 0 < 7#@+# , 0 Q E #%!#*"3# , M@!8### Q G7I #%!9#+$"3# ( I ⁄ / ) #+'(#/*-.#'+# 0 E 9# 0 I 9# 0 > 9 *"3# 0 < #0'#).*)#$"#)./#?,$/0-/")#0)*)/#/*-.#)(*"0$0)'(#'&/(*)/0#*)#*"#'2/(3($2/#2'4)*1/#'+#G7I#Z7#^/) I I 6 88 Q 6 == Q I7F#Z9# H′% Q IFG#µ! ⁄ Z 9# H′* Q EGG#µ! ⁄ Z 9#*"3# 6 &% Q D 6 &* Q G7F #Z7#!40'#+$"3 6 GG 7 Ans. ]GS#EGGS#IGGS#FGGS#E7]#Z

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9443HH:

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935

936 Chapter 11 Output Stages and Power Amplifiers

EXERCISE 11.10 R'(#)./#-$(-,$)#0&/-$+$/3#$"#O #$0 0,&&4:$"1#*44#'+# # /%*< #*"3#).*)# 6 36 Q G7I #Z7 M@!8## Ans. E7E[#Z

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11.6.2 An Alternative Circuit Utilizing Common-Source Transistors ;./#*44'5*=4/#(*"1/#'+# v 3 #-*"#=/#$"-(/*0/3#=:#(/&4*-$"1#)./#0',(-/#+'44'5/(0#5$).#*#&*$(#'+ -'%&4/%/")*(:#)(*"0$0)'(0#-'""/-)/3#$"#)./#-'%%'"60',(-/#-'"+$1,(*)$'"9#*0#0.'5"#$"#R$17 EE7EW7#B/(/# 0 < #0,&&4$/0#)./#4'*3#-,((/")#5./"# v 3 #$0#&'0$)$2/#*"3#*44'50# v 3 #)'#1'#*0#.$1.#*0 ( 6 88 D v 36< ) 9#*#%,-.#.$1./(#2*4,/#).*"#).*)#1$2/"#=:#O?7#AEE7]UD7#R'(#"/1*)$2/# v 3 9# 0 > 0$"X0#)./#4'*3#-,((/")#*"3#*44'50# v 3 #)'#1'#*0#4'5#*0# D 6 == e v 36> 7#;.$0#*40'#$0#4*(1/(#$"#%*16 "$),3/#).*"#)./#2*4,/#1$2/"#=:#O?7#AEE7][D7#;.,09#)./#-$(-,$)#'+#R$17#EE7EW#&('2$3/0#*"#',)&,) 2'4)*1/#(*"1/#).*)#$0#5$).$"#*"#'2/(3($2/#2'4)*1/#'+#/*-.#'+#)./#0,&&4$/07#;./#3$0*32*")*1/ '+#)./#-$(-,$)9#.'5/2/(9#$0#$)0#.$1.#',)&,)#(/0$0)*"-/9 4 ',) Q : 7% || : 7*

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9443HX:

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937

938 Chapter 11 Output Stages and Power Amplifiers VDD vI

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9443KE:

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11.6 CMOS Class AB Output Stages

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9443KK:

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9443KV:

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939

940 Chapter 11 Output Stages and Power Amplifiers a0,*44:#)./#)5'#)(*"0$0)'(0#*(/#%*)-./39 I I H *′ 66666 Q H %′ 66666 Q H / * / % ;.,09 E I , 0 Q 666 H6 36 I

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941

942 Chapter 11 Output Stages and Power Amplifiers

Example 11.6 continued

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At the edge of triode region iLmax RL

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Figure 11.22 A#D# H$(-,$)# $"# )./# ?,$/0-/")# 0)*)/S A6D -$(-,$)# *)# )./# &'$")# *)# 5.$-.# 0># ),("0# '++S A+D -'"3$)$'"0#*)#v3 ` v3%*<7

11.7 Power BJTs

5./(/ I, I×E ; F* Q ; F% Q 6666666606 Q 666666666666 Q IG #%!_Z 6 36 G7E ;.,0 E 4 ',) Q 66666666666666666666666666666666666666 Q I7F#Ω EG ( G7GI e G7GI ) >/<)#5/#5$0.#)'#3/)/(%$"/#)./#%*<$%,%#*"3#%$"$%,%#*44'5/3#2*4,/0#'+# v 3 7 #8$"-/#)./#-$(-,$)#$0 0:%%/)($-*49#5/#"//3#)'#-'"0$3/(#'"4:#/$)./(#)./#&'0$)$2/6',)&,)#'(#"/1*)$2/6',)&,)#-*0/7#R'(# v 3 #&'0$)$2/9 0 < #-'"3,-)0#%'(/#'+#)./#',)&,)#-,((/")# # / 7 #O2/"),*44:9# 0 > #),("0#'++#*"3# 0 < #-'"3,-)0#*44#'+# # / 7 #;'#+$"3 )./#2*4,/#'+# v 3 #*)#5.$-.#).$0#'--,(09#"')/#).*)# 0 > #),("0#'++#5./"#)./#2'4)*1/#*)#$)0#1*)/#3('&0#+('%#)./ ?,$/0-/")#2*4,/#'+# D E7\ #Z#A0//#R$17#EE7II*D#)'# D I #Z9#*)#5.$-.#&'$")# v G=> Q 6 &% 7 #!"#/?,*4#-.*"1/#'+ D G7E #Z#*&&/*(0#*)#)./#',)&,)#'+#)./#)'&#*%&4$+$/(9#*0#0.'5"#$"#R$17#EE7IIA=D7#!"*4:0$0#'+#)./#-$(-,$)#$"#R$17 EE7IIA=D#0.'50#).*)# # / Q # 8< Q ] #%! v 3 Q # / 4 / Q ] × EG

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× EGG Q G7] #Z

R'(# v 3 > G7] #Z9# 0 < #%,0)#-'"3,-)#*44#)./#-,((/")# # / 7#;./#0$),*)$'"#*)# v 3 Q v 3 %*< #$0#$44,0)(*)/3#$"#R$17 EE7IIA-D7#!"*4:0$0#'+#).$0#-$(-,$)#(/0,4)09#*+)/(#0'%/#0)(*$1.)+'(5*(3#=,)#)/3$',0#%*"$&,4*)$'"09#$" v 3%*< ! I7GF #Z

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EXERCISES 11.11

8,&&'0/#$)#$0#(/?,$(/3#)'#(/3,-/#)./#0$V/#'+# 0 > #*"3# 0 < #$"#)./#-$(-,$)#-'"0$3/(/3#$"#)./#*='2/#/<6 *%&4/#=:#*#+*-)'(#'+#I#5.$4/#X//&$"1# , 0 #*)#E#%!7#J.*)#2*4,/#0.',43#=/#,0/3#+'(# 6 36 l#J.*)#$0 )./#"/5#2*4,/#+'(#)./#1*$"#/(('(#*"3#+'(# 4 ',) #*)#)./#?,$/0-/")#&'$")l Ans. G7E]#ZS# D T7F dS#T7F# Ω

11.12

8.'5#).*)#$"#)./#HPQ8#-4*00#!M#-'%%'"60',(-/#',)&,)#0)*1/9# 0 > #),("0#'++#5./"# v 3 Q ], 0 4 / *"3#).*)# 0 < #),("0#'++#5./"# v 3 Q D ], 0 4 /7#;.$0#$0#/?,$2*4/")#)'#0*:$"1#).*)#'"/#'+#)./#)(*"0$0)'(0 ),("0#'++#5./"# # / #(/*-./0# ], 0 7

11.7 Power BJTs ;(*"0$0)'(0#).*)#*(/#(/?,$(/3#)'#-'"3,-)#-,((/")0#$"#)./#*%&/(/#(*"1/#*"3#)'#5$).0)*"3#&'5/( 3$00$&*)$'"#$"#)./#5*))0#*"3#)/"06'+65*))0#(*"1/0#3$++/(#$"#)./$(#&.:0$-*4#0)(,-),(/9#&*-X*1$"19 *"3#0&/-$+$-*)$'"#+('%#)./#0%*4460$1"*4#)(*"0$0)'(0#-'"0$3/(/3#$"#/*(4$/(#-.*&)/(07#@"#).$0#0/-6 )$'"# 5/# -'"0$3/(# 0'%/# '+# )./# $%&'()*")# &('&/()$/0# '+# &'5/(# )(*"0$0)'(09# /0&/-$*44:# ).'0/

943

944 Chapter 11 Output Stages and Power Amplifiers *0&/-)0# ).*)# &/()*$"# )'# )./# 3/0$1"# '+# -$(-,$)0# '+# )./# ):&/# 3$0-,00/3# /*(4$/(7# ;./(/# *(/9# '+ -',(0/9#')./(#$%&'()*")#*&&4$-*)$'"0#'+#&'5/(#)(*"0$0)'(09#0,-.#*0#)./$(#,0/#*0#05$)-.$"1#/4/6 %/")0#$"#&'5/(#$"2/()/(0#*"3#%')'(6-'")('4#-$(-,$)07#8,-.#*&&4$-*)$'"0#*(/#"')#0),3$/3#$"#).$0 =''X7

11.7.1 Junction Temperature e'5/(# )(*"0$0)'(0# 3$00$&*)/# 4*(1/# *%',")0# '+# &'5/(# $"# )./$(# -'44/-)'(i=*0/# h,"-)$'"07# ;./ 3$00$&*)/3#&'5/(#$0#-'"2/()/3#$")'#./*)9#5.$-.#(*$0/0#)./#h,"-)$'"#)/%&/(*),(/7#B'5/2/(9#)./ h,"-)$'"#)/%&/(*),(/#CJ#%,0)#"')#=/#*44'5/3#)'#/<-//3#*#0&/-$+$/3#%*<$%,%9#CJ%*
11.7.2 Thermal Resistance L-(),6#&$ *,&)%$ %"#$ ),%<'%,-($ -*$ '$ %&'(),)%-&$ -;#&'%,(2$ ,($ *&##$ ',&S%"'%$ ,)C$ 0,%"$ (-$ );#+,'/ '&&'(2#.#(%)$*-&$+--/,(23$!"#$"#'%$6,)),;'%#6$,($%"#$%&'(),)%-&$ T<(+%,-($0,//$7#$+-(6<+%#6 '0'8$*&-.$%"#$T<(+%,-($%-$%"#$%&'(),)%-&$+')#C$'(6$*&-.$%"#$+')#$%-$%"#$)<&&-<(6,(2$#(>,&-(B .#(%3$=($'$)%#'68$)%'%#$,($0",+"$%"#$%&'(),)%-&$,)$6,)),;'%,(2$<8$0'%%)C$%"#$%#.;#&'%<&#$&,)#$-* %"#$T<(+%,-($&#/'%,>#$%-$%"#$)<&&-<(6,(2$'.7,#(+#$+'($7#$#O;&#))#6$')

CJ D CB = θ JB <8

9443?X:

0"#&#$ θJB$ ,)$ %"#$ !&0'(#$% '0-*-!#)+0$ 7#%0##($ T<(+%,-($ '(6$ '.7,#(+#C$ "'>,(2$ %"#$ <(,%)$ -* 6#2&##)$L#/),<)$;#&$0'%%3$M-%#$%"'%$θJB$),.;/8$2,>#)$%"#$&,)#$,($T<(+%,-($%#.;#&'%<&#$->#&$%"# '.7,#(%$%#.;#&'%<&#$*-&$#'+"$0'%%$-*$6,)),;'%#6$;-0#&3$P,(+#$0#$0,)"$%-$7#$'7/#$%-$6,)),;'%# /'&2#$'.-<(%)$-*$;-0#&$0,%"-<%$&',),(2$%"#$T<(+%,-($%#.;#&'%<&#$'7->#$CJ.'OC$,%$,)$6#),&'7/# %-$"'>#C$*-&$%"#$%"#&.'/$&#),)%'(+#$θJBC$')$).'//$'$>'/<#$')$;-)),7/#3$1-&$-;#&'%,-($,($*&##$',&C θJB$6#;#(6)$;&,.'&,/8$-($%"#$%8;#$-*$+')#$,($0",+"$%"#$%&'(),)%-&$,)$;'+U'2#63$!"#$>'/<#$-* θJB$,)$<)<'//8$);#+,*,#6$-($%"#$%&'(),)%-&$6'%'$)"##%3

Figure 11.23 O4/-)($-*4#/?,$2*4/")#-$(-,$)#'+#)./#)./(%*46 -'"3,-)$'"#&('-/00S#CJ −#CB#=#<8θJΑ.

O?,*)$'"# AEE7U\D9# 5.$-.# 3/0-($=/0# )./# )./(%*46-'"3,-)$'"# &('-/009# $0# *"*4'1',0# )' Q.%m0#4*59#5.$-.#3/0-($=/0#)./#/4/-)($-*46-'"3,-)$'"#&('-/007#@"#).$0#*"*4'1:9#&'5/(#3$00$6 &*)$'"#-'((/0&'"30#)'#-,((/")9#)/%&/(*),(/#3$++/(/"-/#-'((/0&'"30#)'#2'4)*1/#3$++/(/"-/9#*"3 )./(%*4#(/0$0)*"-/#-'((/0&'"30#)'#/4/-)($-*4#(/0$0)*"-/7#;.,09#5/#%*:#(/&(/0/")#)./#)./(%*46 -'"3,-)$'"#&('-/00#=:#)./#/4/-)($-#-$(-,$)#0.'5"#$"#R$17#EE7IT7

11.7.3 Power Dissipation Versus Temperature !"#$%&'(),)%-&$.'(<*'+%<&#&$<)<'//8$);#+,*,#)$%"#$.'O,.<.$T<(+%,-($%#.;#&'%<&#$CJ.'OC$%"# .'O,.<.$;-0#&$6,)),;'%,-($'%$'$;'&%,+
11.7 Power BJTs

945

Figure 11.24 P*<$%,%#*44'5*=4/#&'5/(#3$00$&*)$'"#2/(0,0#*%=$/")#)/%&/(*),(/#+'(#*#MN;#'&/(*)/3#$" +(//#*$(7#;.$0#$0#X"'5"#*0#*#K&'5/(63/(*)$"1L#-,(2/7

%"#&.'/$&#),)%'(+#$ θJB3$=($'66,%,-(C$'$2&';"$)<+"$')$%"'%$)"-0($,($1,23$4435H$,)$<)<'//8$;&-B >,6#63$ !"#$ 2&';"$ ),.;/8$ )%'%#)$ %"'%$ *-&$ -;#&'%,-($ '%$ '.7,#(%$ %#.;#&'%<&#)$ 7#/-0$ CB@C$ %"# 6#>,+#$+'($)'*#/8$6,)),;'%#$%"#$&'%#6$>'/<#$-*$<8@$0'%%)3$c-0#>#&C$,*$%"#$6#>,+#$,)$%-$7#$-;#&B '%#6$ '%$ ",2"#&$ '.7,#(%$ %#.;#&'%<&#)C$ %"#$ .'O,.<.$ '//-0'7/#$ ;-0#&$ 6,)),;'%,-($ .<)%$ 7# ,0'#!0,$'++-&6,(2$%-$%"#$)%&',2"%$/,(#$)"-0($,($1,23$4435H3$!"#$2"30'1,0'#!*);%+/'80$,)$' 2&';",+'/$&#;&#)#(%'%,-($-*$IJ3$9443?X:3$P;#+,*,+'//8C$(-%#$%"'%$,*$%"#$'.7,#(%$%#.;#&'%<&#$,) CB@$'(6$%"#$;-0#&$6,)),;'%,-($,)$'%$%"#$.'O,.<.$'//-0#6$9<8@:C$%"#($%"#$T<(+%,-($%#.;#&'%<&# 0,//$7#$CJ.'O3$P<7)%,%<%,(2$%"#)#$J<'(%,%,#)$,($IJ3$9443?X:$&#)
CJ%*< D CBG θ JB = 6666666666666666666666666 <8G

9443V@:

0",+"$,)$%"#$,(>#&)#$-*$%"#$)/-;#$-*$%"#$;-0#&B6#&'%,(2$)%&',2"%$/,(#3$F%$'($'.7,#(%$%#.;#&'B %<&#$ CBC$",2"#&$%"'($CB@C$%"#$.'O,.<.$'//-0'7/#$ ;-0#&$6,)),;'%,-($ <8.'O$+'($7#$ -7%',(#6 *&-.$IJ3$9443?X:$78$)<7)%,%<%,(2$CJ$=$CJ.'OG$%"<)C$

CJ%*< D CB 6 <8%*< = 6666666666666666666666

θ JB

9443V4:

R7)#&>#$%"'%$')$CB$';;&-'+"#)$CJ.'OC$%"#$'//-0'7/#$;-0#&$6,)),;'%,-($6#+&#')#)G$%"#$/-0#& %"#&.'/$ 2&'6,#(%$ /,.,%)$ %"#$ '.-<(%$ -*$ "#'%$ %"'%$ +'($ 7#$ &#.->#6$ *&-.$ %"#$ T<(+%,-(3$ =($ %"# #O%&#.#$),%<'%,-($-*$CB$=$CJ.'OC$(-$;-0#&$+'($7#$6,)),;'%#6$7#+'<)#$(-$"#'%$+'($7#$&#.->#6 *&-.$%"#$T<(+%,-(3

Example 11.7 !#MN;#$0#0&/-$+$/3#)'#.*2/#*#%*<$%,%#&'5/(#3$00$&*)$'"#<8G#'+#I#J#*)#*"#*%=$/")#)/%&/(*),(/#CBG#'+ IF°H9#*"3#*#%*<$%,%#h,"-)$'"#)/%&/(*),(/#CJ%*<#'+#EFG°H7#R$"3#)./#+'44'5$"1c A*D ;./#)./(%*4#(/0$0)*"-/#θJB7 A=D ;./#%*<$%,%#&'5/(#).*)#-*"#=/#0*+/4:#3$00$&*)/3#*)#*"#*%=$/")#)/%&/(*),(/#'+#FG°H7 A-D ;./#h,"-)$'"#)/%&/(*),(/#$+#)./#3/2$-/#$0#'&/(*)$"1#*)#CB#=#IF°H#*"3#$0#3$00$&*)$"1#E#J7

946 Chapter 11 Output Stages and Power Amplifiers Example 11.7 continued

Solution

CJ%*< D CBG EFG D IF 6 = 666666666666666666666 = UI7F°H_J A*D θ JB = 66666666666666666666666666 <8G I CJ%*< D CB EFG D FG A=D <8%*< = 666666666666666666666666 = 666666666666666666666 = E7U#J UI7F θ JB A-D CJ = CB + θ JB < 8 = IF + UI7F × E = W[7F°H

11.7.4 Transistor Case and Heat Sink !"#$%"#&.'/$&#),)%'(+#$7#%0##($T<(+%,-($'(6$'.7,#(+#C$θJBC$+'($7#$#O;&#))#6$')

θ JB = θ J- + θ -B

9443V5:

0"#&#$θJ-$,)$%"#$%"#&.'/$&#),)%'(+#$7#%0##($T<(+%,-($'(6$%&'(),)%-&$+')#$9;'+U'2#:$'(6$θ-B$,) %"#$%"#&.'/$&#),)%'(+#$7#%0##($+')#$'(6$'.7,#(+#3$1-&$'$2,>#($%&'(),)%-&C$θJ-$,)$*,O#6$78$%"# 6#>,+#$6#),2($'(6$;'+U'2,(23$!"#$6#>,+#$.'(<*'+%<&#&$+'($<+#$ θJ-$78$#(+';),+#$,($'$&#/'%,>#/8$/'&2#$.#%'/$+')#$'(6$;/'+,(2$%"#$+-//#+%-&$90"#&#$.-)%$-*$%"#$"#'%$,) 6,)),;'%#6:$,($6,&#+%$+-(%'+%$0,%"$%"#$+')#3$]-)%$",2"B;-0#&$%&'(),)%-&)$'&#$;'+U'2#6$,($%",) *')",-(3$1,2<&#$4435K$)"-0)$'$)U#%+"$-*$'$%8;,+'/$;'+U'2#3 Figure 11.25 ;./#&'&,4*(#;QT#&*-X*1/#+'(#&'5/(#)(*"0$0)'(07#;./#-*0/#$0 %/)*4#5$).#*#3$*%/)/(#'+#*=',)#I7I#-%S#)./#',)0$3/#3$%/"0$'"#'+#)./#K0/*)$"1 &4*"/L#$0#*=',)#]#-%7#;./#0/*)$"1#&4*"/#.*0#)5'#.'4/0#+'(#0-(/50#)'#='4)#$)#)'#* ./*)# 0$"X7# ;./# -'44/-)'(# $0# /4/-)($-*44:# -'""/-)/3# )'# )./# -*0/7# ;./(/+'(/# *" /4/-)($-*44:# $"0,4*)$"1# =,)# )./(%*44:# -'"3,-)$"1# 0&*-/(# $0# ,0/3# =/)5//"# )./ )(*"0$0)'(#-*0/#*"3#)./#K./*)#0$"X7L

F/%"-<2"$ %"#$ +,&+<,%$ 6#),2(#&$ "')$ (-$ +-(%&-/$ ->#&$ θJ-$ 9-(+#$ '$ ;'&%,+'/<#$9);#+,*,#6 78$%"#$.'(<*'+%<&#&$')$;'&%$-*$ θJB:3$l#6<+%,-($-*$ θ-B$+'($7#$#**#+%#6$78$;&->,6,(2$.#'()$%*'+,/,%'%#$"#'%$%&'()*#&$*&-.$+')#$%-$'.7,#(+#3$F$;-;#&8$).'//3$F/)-C$"#'%$,)$#**,+,#(%/8$%&'()*#&$978$+-(>#+%,-($'(6 &'6,'%,-(:$*&-.$%"#$"#'%$),(U$%-$%"#$'.7,#(+#C$&#)#($78

θ -B = θ -= + θ =B

9443VE:

+'($7#$).'//$7#+'<)#$,%)$%0-$+-.;-(#(%)$+'($7#$.'6#$).'//$78$%"#$+"-,+#$-*$'($';;&-;&,'%# "#'%$),(U35$1-&$#O'.;/#C$,($>#&8$",2"B;-0#&$';;/,+'%,-()$%"#$"#'%$),(U$,)$<)<'//8$#J<,;;#6 0,%"$*,()$%"'%$*<&%"#&$*'+,/,%'%#$+--/,(2$78$&'6,'%,-($'(6$+-(>#+%,-(3 I

!0#"')/3#/*(4$/(9#)./#%/)*4#-*0/#'+#*#&'5/(#)(*"0$0)'(#$0#/4/-)($-*44:#-'""/-)/3#)'#)./#-'44/-)'(7#;.,0#*" /4/-)($-*44:#$"0,4*)$"1#%*)/($*4#0,-.#*0#%$-*#$0#,0,*44:#&4*-/3#=/)5//"#)./#%/)*4#-*0/#*"3#)./#%/)*4#./*) 0$"X7#!40'9#$"0,4*)$"1#=,0.$"10#*"3#5*0./(0#*(/#1/"/(*44:#,0/3#$"#='4)$"1#)./#)(*"0$0)'(#)'#)./#./*)#0$"X7

11.7 Power BJTs

Figure 11.26 O4/-)($-*4#*"*4'1#'+#)./#)./(%*4#-'"3,-)$'"#&('-/00#5./"#*#./*)#0$"X#$0#,)$4$V/37

Figure 11.27 P*<$%,%#*44'5*=4/#&'5/(#3$00$&*)$'"#2/(0,0#)(*"0$0)'(6-*0/#)/%&/(*),(/7

!"#$#/#+%&,+'/$'('/-2$-*$%"#$%"#&.'/B+-(6<+%,-($;&-+#))$0"#($'$"#'%$),(U$,)$#.;/-8#6$,) )"-0($,($1,23$4435?C$*&-.$0",+"$0#$+'($0&,%#

CJ D CB = <8 ( θ J- + θ -= + θ =B )

9443VH:

F)$0#//$')$);#+,*8,(2$ θJ-C$%"#$6#>,+#$.'(<*'+%<&#&$<)<'//8$)<;;/,#)$'$6#&'%,(2$+<&>#$*-& <8.'O$>#&)<)$%"#$+')#$%#.;#&'%<&#C$C-3$P<+"$'$+<&>#$,)$)"-0($,($1,23$4435V3$M-%#$%"'%$%"# )/-;#$-*$%"#$;-0#&B6#&'%,(2$)%&',2"%$/,(#$,)$−4/θJ-3$1-&$'$2,>#($%&'(),)%-&C$%"#$.'O,.<. ;-0#&$6,)),;'%,-($'%$'$$+(!5&!F*!:+&?:!5C-@$9<)<'//8$5K°L:$,)$.<+"$2&#'%#&$%"'($%"'%$'%$'( +FK#!%&5&!F*!:+&?:!5CB@$9<)<'//8$5K°L:3$=*$%"#$6#>,+#$+'($7#$.',(%',(#6$'%$'$+')#$%#.;#&B '%<&#$ C- C5 C-@5 ≤ C-5 ≤5 CJ.'OC %"#($ %"#$ .'O,.<.$ )'*#$ ;-0#&$ 6,)),;'%,-($ ,)$ -7%',(#6$ 0"#( CJ = CJ.'OC

CJ%*< D C<8%*< = 66666666666666666666666

θ J-

9443VK:

947

948 Chapter 11 Output Stages and Power Amplifiers

Example 11.8 !#MN;#$0#0&/-$+$/3#)'#.*2/#CJ%*<#=#EFG°H#*"3#)'#=/#-*&*=4/#'+#3$00$&*)$"1#%*<$%,%#&'5/(#*0#+'44'50c ]G#J#*)# C- = IF°H I#J#*)# CB = IF°H !='2/#IF°H9#)./#%*<$%,%#&'5/(#3$00$&*)$'"#$0#)'#=/#3/(*)/3#4$"/*(4:#5$).#θJ-#=#T7EI°H/J#*"3#θJB#=#UI7F°H/J7 R$"3#)./#+'44'5$"1c A*D ;./#%*<$%,%#&'5/(#).*)#-*"#=/#3$00$&*)/3#0*+/4:#=:#).$0#)(*"0$0)'(#5./"#'&/(*)/3#$"#+(//#*$(#*)#CB#=#FG°H7 A=D ;./#%*<$%,%#&'5/(#).*)#-*"#=/#3$00$&*)/3#0*+/4:#=:#).$0#)(*"0$0)'(#5./"#'&/(*)/3#*)#*"#*%=$/")#)/%6 &/(*),(/#'+#FG°H9#=,)#5$).#*#./*)#0$"X#+'(#5.$-.#θ-=#=#G7F°H/J#*"3#θ=B#=#]°H/J7#R$"3#)./#)/%&/(*),(/ '+#)./#-*0/#*"3#'+#)./#./*)#0$"X7 A-D ;./#%*<$%,%#&'5/(#).*)#-*"#=/#3$00$&*)/3#0*+/4:#$+#*"##%"#%#&!5@!+&5(#%H#$0#,0/3#*"3#CB#=#FG°H7

Solution A*D

CJ%*< D CB EFG D FG = 666666666666666666666 = E7U#J <8%*< = 666666666666666666666666 UI7F θ JB

A=D J$).#*#./*)#0$"X9#θJB#=/-'%/0

θ JB = θ J- + θ -= + θ =B = T7EI + G7F + ] = [7UI°H_J !"<)C EFG D FG < 8%*< = 666666666666666666666 = ET7E#J [7UI R$1,(/#EE7IW#0.'50#)./#)./(%*4#/?,$2*4/")#-$(-,$)#5$).#)./#2*($',0#)/%&/(*),(/0#$"3$-*)/37

Figure 11.28 ;./(%*4#/?,$2*4/")#-$(-,$)#+'(#O<*%&4/#EE7W7

11.7 Power BJTs

A-D !"#$"+$"$)/#./*)#0$"X9#$+#$)#/<$0)/39#5',43#-*,0/#)./#-*0/#)/%&/(*),(/#C-#)'#/?,*4#)./#*%=$/")#)/%&/(*6 ),(/#CB7#;./#$"+$"$)/#./*)#0$"X#.*0#θ-B#=#G7#Q=2$',04:9#'"/#-*""')#=,:#*"#$"+$"$)/#./*)#0$"XS#"/2/()./6 4/009#).$0#)/(%$"'4'1:#$0#,0/3#=:#0'%/#%*",+*-),(/(0#)'#3/0-($=/#)./#&'5/(63/(*)$"1#-,(2/#'+#R$17#EE7I[7 ;./#*=0-$00*#$0#)./"#4*=/4/3#CB#*"3#)./#-,(2/#$0#-*44/3#K&'5/(#3$00$&*)$'"#2/(0,0#*%=$/")#)/%&/(*),(/ 5$).#*"#$"+$"$)/#./*)#0$"X7L#R'(#',(#/<*%&4/9#5$).#$"+$"$)/#./*)#0$"X9 CJ%*< D CB EFG D FG = 666666666666666666666 = TI#J < 8%*< = 666666666666666666666666 T7EI θ J-

;./#*32*")*1/#'+#,0$"1#*#./*)#0$"X#$0#-4/*(4:#/2$3/")#+('%#O<*%&4/#EE7Wc#J$).#*#./*)#0$"X9#)./ %*<$%,%#*44'5*=4/#&'5/(#3$00$&*)$'"#$"-(/*0/0#+('%#E7U#J#)'#ET7E#J7#!40'#"')/#).*)#*4).',1.#)./ )(*"0$0)'(#-'"0$3/(/3#-*"#=/#-*44/3#*#K]G6J#)(*"0$0)'(9L#).$0#4/2/4#'+#&'5/(#3$00$&*)$'"#-*""')#=/ *-.$/2/3#$"#&(*-)$-/S#$)#5',43#(/?,$(/#*"#$"+$"$)/#./*)#0$"X#*"3#*"#*%=$/")#)/%&/(*),(/#CB5≤ IF°H7

EXERCISE 11.13

;./#I>UTGU#&'5/(#)(*"0$0)'(#$0#0&/-$+$/3#)'#.*2/#CJ%*<#=#IGG°H#*"3#<8%*<#=#EIF#J#+'(#C-5 ≤ IF°H7 R'(#C-5 ≥ IF°H9#θJ-5=5E7]°H_J7#@+#$"#*#&*()$-,4*(#*&&4$-*)$'"#).$0#3/2$-/#$0#)'#3$00$&*)/#FG#J#*"3 '&/(*)/#*)#*"#*%=$/")#)/%&/(*),(/#'+#IF°H9#+$"3#)./#%*<$%,%#)./(%*4#(/0$0)*"-/#'+#)./#./*)#0$"X ).*)#%,0)#=/#,0/3#A$7/79#θ=BD7#!00,%/#θ-=5=5G7U°H_J7#J.*)#$0#)./#-*0/#)/%&/(*),(/9#C-l Ans. 43K°L/\; 130°L

11.7.5 The BJT Safe Operating Area @"#*33$)$'"#)'#0&/-$+:$"1#)./#%*<$%,%#&'5/(#3$00$&*)$'"#*)#3$++/(/")#-*0/#)/%&/(*),(/09#&'5/(6 )(*"0$0)'(#%*",+*-),(/(0#,0,*44:#&('2$3/#*#&4')#'+#)./#=',"3*(:#'+#)./#0*+/#'&/(*)$"1#*(/*#A8Q!D $"#)./##- i v-1#&4*"/7#;./#8Q!#0&/-$+$-*)$'"#)*X/0#)./#+'(%#$44,0)(*)/3#=:#)./#0X/)-.#$"#R$17#EE7I\S )./#+'44'5$"1#&*(*1(*&.#",%=/(0#-'((/0&'"3#)'#)./#=',"3*($/0#'"#)./#0X/)-.7 1. !"#$.'O,.<.$'//-0'7/#$+<&&#(%$,-.'O3$IO+##6,(2$%",)$+<&&#(%$-($'$+-(%,(<-<)$7'),)$+'( &#),+#$%-$%"#$;'+U'2#$%#&.,('/)3 2. ;./# %*<$%,%# &'5/(# 3$00$&*)$'"# .:&/(='4*7# ;.$0# $0# )./# 4'-,0# '+# )./# &'$")0# +'(# 5.$-. v-1 #-#=#<8%*<#A*)#C-GD7#R'(#)/%&/(*),(/0 C-# n#C-G 9 )./#&'5/(63/(*)$"1#-,(2/0#3/0-($=/3#$" 8/-)$'"#EE7[7]#0.',43#=/#,0/3#)'#'=)*$"#)./#*&&4$-*=4/#<8%*<#*"3#).,0#*#-'((/0&'"3$"14: 4'5/(#.:&/(='4*7#!4).',1.#)./#'&/(*)$"1#&'$")#-*"#=/#*44'5/3#)'#%'2/#)/%&'(*($4:#*='2/ )./#.:&/(='4*9#)./#+9!:+;!#&'5/(#3$00$&*)$'"#0.',43#"')#=/#*44'5/3#)'#/<-//3#<8%*<7 3. ;./# -0+"),16'0#<,"3)# 4$%$)7# 8/-'"3# =(/*X3'5"# $0# *# &./"'%/"'"# ).*)# (/0,4)0 =/-*,0/# -,((/")# +4'5# *-('00# )./# /%$))/(i=*0/# h,"-)$'"# $0# "')# ,"$+'(%7# Y*)./(9# )./ -,((/")#3/"0$):#$0#1(/*)/0)#"/*(#)./#&/($&./(:#'+#)./#h,"-)$'"7#;.$0#K+/''0)!%+'"3,*);L 1$2/0#($0/#)'#$"-(/*0/3#4'-*4$V/3#&'5/(#3$00$&*)$'"#*"3#./"-/#)/%&/(*),(/#($0/#A*)#4'-*6 )$'"0#-*44/3#&"!%-2"!-D7#8$"-/#*#)/%&/(*),(/#($0/#-*,0/0#*"#$"-(/*0/#$"#-,((/")9#*#4'-*46 $V/3#+'(%#'+%!&0'(#$%'/)#3#9#-*"#'--,(9#4/*3$"1#)'#h,"-)$'"#3/0)(,-)$'"7

949

950 Chapter 11 Output Stages and Power Amplifiers

BVCEO Figure 11.29 8*+/#'&/(*)$"1#*(/*#A8Q!D#'+#*#MN;7

4. ;./#-'44/-)'(6)'6/%$))/(#=(/*X3'5"#2'4)*1/9#26-137#;./#$"0)*")*"/',0#2*4,/#'+# v-1 0.',43# "/2/(# =/# *44'5/3# )'# /<-//3# 26-13S# ')./(5$0/9# *2*4*"-./# =(/*X3'5"# '+# )./ -'44/-)'(i=*0/#h,"-)$'"#%*:#'--,(#A0//#8/-)$'"#U7\D7 R$"*44:9# $)# 0.',43# =/# %/")$'"/3# ).*)# 4'1*($).%$-# 0-*4/0# *(/# ,0,*44:# ,0/3# +'(# #-# *"3# v-19 4/*3$"1#)'#*"#8Q!#=',"3*(:#).*)#-'"0$0)0#'+#0)(*$1.)#4$"/07

11.7.6 Parameter Values of Power Transistors Q5$"1#)'#)./$(#4*(1/#1/'%/)(:#*"3#.$1.#'&/(*)$"1#-,((/")09#&'5/(#)(*"0$0)'(0#3$0&4*:#):&$-*4 &*(*%/)/(# 2*4,/0# ).*)# -*"# =/# ?,$)/# 3$++/(/")# +('%# ).'0/# '+# 0%*4460$1"*4# )(*"0$0)'(07# ;./ $%&'()*")#3$++/(/"-/0#*(/#*0#+'44'50c 1. F%$",2"$+<&&#(%)C$%"#$#O;-(#(%,'/$#- D v21$&#/'%,-()",;$#O",7,%)$'$*'+%-&$-*$5$<+%,-($,( %"#$#O;-(#(%G$%"'%$,)C$ # - = , = ! v21 ⁄ I6C 3 2. β#$0#4'59#):&$-*44:#TG#)'#WG9#=,)#-*"#=/#*0#4'5#*0#F7#B/(/9#$)#$0#$%&'()*")#)'#"')/#).*)#β .*0#*#&'0$)$2/#)/%&/(*),(/#-'/++$-$/")7 3. !)#.$1.#-,((/")09#:π#=/-'%/0#2/(:#0%*44#A*#+/5#'.%0D#*"3#:L#=/-'%/0#$%&'()*")#A:L#$0 3/+$"/3#*"3#/<&4*$"/3#$"#8/-)$'"#\7I7ID7 4. "C# $0# 4'5# A*# +/5# %/1*./()VD9# -µ# $0# 4*(1/# A.,"3(/30# '+# &$-'+*(*30D9# *"3# -π# $0# /2/" 4*(1/(7#A;./0/#&*(*%/)/(0#*(/#3/+$"/3#*"3#/<&4*$"/3#$"#8/-)$'"#\7I7ID7 5. ,-23#$0#4*(1/#A*#+/5#)/"0#'+#%$-('*%&0D#*"39#*0#,0,*49#3',=4/0#+'(#/2/(:#EG°H#($0/#$" )/%&/(*),(/7 6. 26-13#$0#):&$-*44:#FG#)'#EGG#Z#=,)#-*"#=/#*0#.$1.#*0#FGG#Z7 7. ,-%*<#$0#):&$-*44:#$"#)./#*%&/(/#(*"1/#=,)#-*"#=/#*0#.$1.#*0#EGG#!7

11.8 Variations on the Class AB Configuration =($%",)$)#+%,-(C$0#$6,)+<))$'$(<.7#&$-*$+,&+<,%$,.;&->#.#(%)$'(6$;&-%#+%,-($%#+"(,J<#)$*-& %"#$Zg!$+/'))$FZ$-<%;<%$)%'2#3

11.8 Variations on the Class AB Configuration

11.8.1 Use of Input Emitter Followers 1,2<&#$443E@$)"-0)$'$+/'))$FZ$+,&+<,%$7,')#6$<),(2$%&'(),)%-&)$04$'(6$05C$0",+"$'/)-$*<(+B %,-($')$#.,%%#&$*-//-0#&)C$%"<)$;&->,6,(2$%"#$+,&+<,%$0,%"$'$",2"$,(;<%$&#),)%'(+#3$=($#**#+%C$%"# +,&+<,%$ *<(+%,-()$ ')$ '$ <(,%8B2',($ 7<**#&$ '.;/,*,#&3$ P,(+#$ '//$ *-<&$ %&'(),)%-&)$ '&#$ <)<'//8 .'%+"#6C$%"#$J<,#)+#(%$+<&&#(%$9v,$=$@C$4/$=$∞:$,($0E$'(6$0H$,)$#J<'/$%-$%"'%$,($04$'(6$053 l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c-0#>#&C$ #O+#//#(%$ &#)#$ 7##($ -7%',(#6$ 0,%"$ %",)$ +,&+<,%$ ,.;/#.#(%#6$ ,($ "87&,6$ %",+UB*,/.$ %#+"(-/-28$ 9\-(2 '(6$ P"#&0,(C$ 4XVX:3$ !",)$ %#+"(-/-28$ ;#&.,%)$ +-.;-(#(%$ %&,..,(2C$ *-&$ ,()%'(+#C$ %-$ .,(,B .,N#$%"#$-<%;<%$-**)#%$>-/%'2#3$!"#$+,&+<,%$+'($7#$<)#6$'/-(#$-&$%-2#%"#&$0,%"$'($-;$'.;$%;&->,6#$,(+&#')#6$-<%;<%$6&,>,(2$+';'7,/,%83$!"#$/'%%#&$';;/,+'%,-($0,//$7#$6,)+<))#6$,($%"# (#O%$)#+%,-(3

Figure 11.30 !#-4*00#!M#',)&,)#0)*1/#5$).#*"#$"&,)#=,++/(7#@"#*33$)$'"#)'#&('2$3$"1#*#.$1.#$"&,)#(/0$06 )*"-/9#)./#=,++/(#)(*"0$0)'(0#0E#*"3#0I#=$*0#)./#',)&,)#)(*"0$0)'(0#0T#*"3#0]7

951

952 Chapter 11 Output Stages and Power Amplifiers

EXERCISE 11.14

A>7&!M#!4).',1.#2/(:#$"0)(,-)$2/9#).$0#/*)$'"*4#8/%$-'"3,-)'(9 /<-/&)#).*)#4T#=#4]#=#I Ω#)./(/7D#A*D#R'(#v,#=#G#*"3# 4 / = ∞ 9#+$"3#)./#?,$/0-/")#-,((/")#$"#/*-.#'+#)./ +',(#)(*"0$0)'(0#*"3#v37#A=D#R'(# 4 / = ∞9#+$"3##-E9##-I9##-T9##-]9#*"3#v3#+'(#v,#=#+EG#Z#*"3#−EG#Z7#A-D Y/&/*)#A=D#+'(#4/#=#EGG#Ω7 Ans. 9':$53WV$.FG$@$AG$97:$*-&$v,$=$+4@$A^$@3WW$.FC$H3WV$.FC$43XK$.FC$43XK$.FC$+X3XW$AG$*-&$v, =$−4@$A^$H3WV$.FC$@3WW$.FC$43XK$.FC$43XK$.FC$−X3XW$AG$9+:$*-&$v,$=$+4@$A^$@3EW$.FC$H3WV$.FC 4@@$.FC$@3@5$.FC$+$X3W?$AG $*-&$v,$=$−4@$A^$H3WV$.FC$@3EW$.FC$@3@5$.FC$4@@$.FC$−X3W?$A

11.8.2 Use of Compound Devices !-$,(+&#')#$%"#$+<&&#(%$2',($-*$%"#$-<%;<%B)%'2#$%&'(),)%-&)C$'(6$%"<)$<+#$%"#$&#J<,$7')# +<&&#(%$6&,>#C$%"#$`'&/,(2%-($+-(*,2<&'%,-($)"-0($,($1,23$443E4$,)$*&#J<#(%/8$<)#6$%-$&#;/'+# %"#$%*%$%&'(),)%-&$-*$%"#$+/'))$FZ$)%'2#3$!"#$`'&/,(2%-($+-(*,2<&'%,-($,)$#J<,>'/#(%$%-$'$),(B 2/#$%*%$%&'(),)%-&$"'>,(2$β$!$β4β 5C$7<%$'/.-)%$%0,+#$%"#$>'/<#$-*$6213 !"#$ `'&/,(2%-($ +-(*,2<&'%,-($ +'($ 7#$ '/)-$ <)#6$ *-&$ *%*$ %&'(),)%-&)C$ '(6$ %",)$ ,)$ ,(6##6 6-(#$,($6,)+&#%#B+,&+<,%$6#),2(3$=($=L$6#),2(C$"-0#>#&C$%"#$/'+U$-*$2--6BJ<'/,%8$*%*$%&'(),)B %-&)$;&-.;%#6$%"#$<)#$-*$%"#$'/%#&('%,>#$+-.;-<(6$+-(*,2<&'%,-($)"-0($,($1,23$443E53$!",) +-.;-<(6$6#>,+#$,)$#J<,>'/#(%$%-$'$),(2/#$*%*$%&'(),)%-&$"'>,(2$β$! β4β 53$\"#($*'7&,+'%#6 0,%"$)%'(6'&6$=L$%#+"(-/-28C$04$,)$<)<'//8$'$/'%#&'/$*%*$"'>,(2$'$/-0$β$9β$=$K$−$4@:$'(6$;--& ",2"B*&#J<#(+8$&#);-()#$9 "C ! K$]cN:G$)##$F;;#(6,O$F$'(6$F;;#(6,O$V3F3$!"#$+-.;-<(6 6#>,+#C$ '/%"-<2"$ ,%$ "')$ '$ &#/'%,>#/8$ ",2"$ #J<,>'/#(%$ βC$ )%,//$ )<**#&)$ *&-.$ '$ ;--&$ ",2"B *&#J<#(+8$&#);-()#3$=%$'/)-$)<**#&)$*&-.$'(-%"#&$;&-7/#.^$!"#$*##67'+U$/--;$*-&.#6$78$04 '(6$05$,)$;&-(#$%-$",2"B*&#J<#(+8$-)+,//'%,-()$90,%"$*&#J<#(+8$(#'&$"C$-*$%"#$*%*$6#>,+#C$,3#3C '7-<%$ K$ ]cN:3$ ]#%"-6)$ #O,)%$ *-&$ ;&#>#(%,(2$ )<+"$ -)+,//'%,-()3$ !"#$ )<7T#+%$ -*$ *##67'+UB '.;/,*,#&$)%'7,/,%8$0')$)%<6,#6$,($L"';%#&$4@3

Figure 11.31 ;./#C*(4$"1)'"#-'"+$1,(*)$'"7

11.8 Variations on the Class AB Configuration

Figure 11.32 ;./#-'%&',"36*%*#-'"+$1,(*)$'"7

!-$,//<)%&'%#$%"#$';;/,+'%,-($-*$%"#$`'&/,(2%-($+-(*,2<&'%,-($'(6$-*$%"#$+-.;-<(6$*%*N$0# )"-0$,($1,23$443EE$ '($-<%;<%$)%'2#$<%,/,N,(2$7-%"3$L/'))$FZ$7,'),(2$,)$'+",#>#6$<),(2$'$621 .,6#$'$7,')$>-/%'2#$-*$'7-<%$5$A3$!"#$6#),2($-*$%",)$+/'))$FZ$)%'2#$,)$,(>#)B %,2'%#6$,($f&-7/#.$443HE3$$

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Figure 11.33 !#-4*00#!M#',)&,)#0)*1/#,)$4$V$"1#*#C*(4$"1)'"#%*%#*"3#*#-'%&',"3#*%*7#M$*0$"1#$0#'=)*$"/3 ,0$"1#*#621#%,4)$&4$/(7

953

954 Chapter 11 Output Stages and Power Amplifiers

EXERCISE 11.15

A*D Y/+/(#)'#R$17#EE7TI7#8.'5#).*)9#+'(#)./#-'%&'0$)/#*%*#)(*"0$0)'(9 #6 # 2 #! 66666666666

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#1 ! #B/"-/#0.'5#).*) # - ! β > , =< ! v12 / 6C *"3#).,0#)./#)(*"0$0)'(#.*0#*"#/++/-)$2/#0-*4/#-,((/") ,= = β > ,=< 5./(/#,=<#$0#)./#0*),(*)$'"#-,((/")#'+#)./#*%*#)(*"0$0)'(#0E7 A=D R'(#β<#=#IG9#β>#=#FG9#Ι=<#=#EG−E]#!9#+$"3#)./#/++/-)$2/#-,((/")#1*$"#'+#)./#-'%&',"3#3/2$-/#*"3 $)0#v12#5./"##-#=#EGG#%!7 Ans. A=D#EGGGS#G7UFE#Z

11.8.3 Short-Circuit Protection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

EXERCISE D11.16 @"#)./#-$(-,$)#'+#R$17#EE7T]#4/)#,M@!8 = I#%!. R$"3#)./#2*4,/#'+#41E#).*)#-*,0/0#0F#)'#),("#'"#*"3 *=0'(=#*44#I#%!#5./"#)./#',)&,)#-,((/")#=/$"1#0',(-/3#(/*-./0#EFG#%!7#R'(#0F9#,=#=#EG−E]#!7 @+#)./#"'(%*4#&/*X#',)&,)#-,((/")#$0#EGG#%!9#+$"3#)./#2'4)*1/#3('&#*-('00#41E#*"3#)./#-'44/-)'( -,((/")#'+#0F7 Ans. H3E$ΩG$HE@$.AG$@3E$µF

11.9 IC Power Amplifiers

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EXERCISE 11.20 B*"'&,(-#$%(#)&-).&$#*3#8&<>#EE>?F#+&$%#+E#=#+G#=#EF#HΩ/#+C#=#I#HΩ/#+?#=#EI#HΩ/#0",#+##=#J#Ω>#8&", $%(#K*2$0<(#<0&"#0",#$%(#&"1.$#-('&'$0")(>#:%(#1*+(-#'.1124#.'(,#&'#±EJ#L>#!3#v,#&'#0#CF=L#1(0H=$*=1(0H '&"(#+0K(/#+%0$#&'#$%(#1(0H=$*=1(0H#*.$1.$#K*2$0<(M#N%0$#&'#$%(#1(0H#2*0,#).--("$M#N%0$#&'#$%(#2*0, 1*+(-M Ans. G#LOLP#EF#HΩP#QF#LP#G>RI#@P#IQ>CI#N

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11.10.2 Characteristics of Power MOSFETs =($ );,%#$ -*$ %"#,&$ &'6,+'//8$ 6,**#&#(%$ )%&<+%<&#C$ ;-0#&$ ]RP1I!)$ #O",7,%$ +"'&'+%#&,)%,+)$ %"'% '&#$J<,%#$),.,/'&$%-$%"-)#$-*$%"#$).'//B),2('/$]RP1I!)$)%<6,#6$,($L"';%#&$K3$=.;-&%'(%$6,*B *#&#(+#)$#O,)%C$"-0#>#&C$'(6$%"#)#$'&#$6,)+<))#6$(#O%3 f-0#&$]RP1I!)$"'>#$%"&#)"-/6$>-/%'2#)$,($%"#$&'(2#$-*$5$A$%-$H$A3$=($)'%<&'%,-(C$%"# 6&',($+<&&#(%$,)$&#/'%#6$%-$ vG=$78$%"#$)J<'&#B/'0$+"'&'+%#&,)%,+$-*$IJ3$9443W@:3$c-0#>#&C$') )"-0($,($1,23$443H5C$%"#$#8DvG=$+"'&'+%#&,)%,+$7#+-.#)$/,(#'&$*-&$/'&2#&$>'/<#)$-*$vG=3$!"#$/,(B #'&$;-&%,-($-*$%"#$+"'&'+%#&,)%,+$-++<&)$')$'$&#)#/-+,%8$ -*$ +"'&2#$ +'&&,#&)$ %-$ &#'+"$ '($ <;;#&$ /,.,%C$ '$ ;"#(-.#(-( U(-0($ ')$ 80$"+*!9% -#!/'#!*")K3$ !"#$ /,(#'&$ #8DvG=$ &#/'%,-()",;$ ,.;/,#)$ '$ +-()%'(%$ ;F$ ,($ %"# >#/-+,%8B)'%<&'%,-($,-(3 !"#$#8−vG=$+"'&'+%#&,)%,+$)"-0($,($1,23$443H5$,(+/<6#)$'$)#2.#(%$/'7#/#6$h)<7%"&#)"-/63i !"-<2"$ -*$ /,%%/#$ ),2(,*,+'(+#$ *-&$ ;-0#&$ 6#>,+#)C$ %"#$ )<7%"&#)"-/6$ ,-($ -*$ -;#&'%,-($ ,)$ -* ,(%#&#)%$,($>#&8B/-0B;-0#&$';;/,+'%,-()$9)##$P#+%,-($K343X:3$$

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964 Chapter 11 Output Stages and Power Amplifiers

Figure 11.42 ;:&$-*4##8ivG=#-.*(*-)/($0)$-#+'(#*#&'5/(#PQ8RO;7

11.10.3 Temperature Effects R*$+-(),6#&'7/#$,(%#&#)%$,($%"#$6#),2($-*$]RP$;-0#&$+,&+<,%)$,)$%"#$>'&,'%,-($-*$%"#$]RP1I! +"'&'+%#&,)%,+)$0,%"$%#.;#&'%<&#C$,//<)%&'%#6$,($1,23$443HE3$R7)#&>#$%"'%$%"#&#$,)$'$>'/<#$-*$vG=$9,(

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11.10 MOS Power Transistors

%"#$&'(2#$-*$H$A$%-$?$A$*-&$.-)%$;-0#&$]RP1I!):$'%$0",+"$%"#$%#.;#&'%<&#$+-#**,+,#(%$-*$#8$,) N#&-3$F%$",2"#&$>'/<#)$-*$v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v36$Q 9vG= − 6& :$,)$&#/'%,>#/8$/-0C$'(6$%"#$%#.;#&'%<&#$6#;#(6#(+#$,)$6-.,('%#6$78$%"#$(#2'%,># %#.;#&'%<&#$+-#**,+,#(%$-*$6&$9,($%"#$&'(2#$-*$DE$.Ad°L$%-$D?$.Ad°L:$0",+"$+'<)#)$ v36$%&,)#$0,%"$%#.;#&'%<

11.10.4 Comparison with BJTs !"#$;-0#&$]RP1I!$6-#)$(-%$)<**#&$*&-.$)#+-(6$7&#'U6-0(C$0",+"$/,.,%)$%"#$)'*#$-;#&'%,(2 '&#'$ -*$ Zg!)3$ F/)-C$ ;-0#&$ ]RP1I!)$ 6-$ (-%$ &#J<,&#$ %"#$ /'&2#$ 6+$ 7')#B6&,>#$ +<&&#(%)$ -* ;-0#&$Zg!)3$M-%#C$"-0#>#&C$%"'%$%"#$6&,>#&$)%'2#$,($'$]RP$;-0#&$'.;/,*,#&$)"-
11.10.5 A Class AB Output Stage Utilizing Power MOSFETs F)$'($';;/,+'%,-($-*$;-0#&$]RP1I!)C$0#$)"-0$,($1,23$443HH$'$+/'))$FZ$-<%;<%$)%'2#$<%,/,N,(2 '$;',&$-*$+-.;/#.#(%'&8$]RP1I!)$'(6$#.;/-8,(2$Zg!)$*-&$7,'),(2$'(6$,($%"#$6&,>#&$)%'2#3 !"#$/'%%#&$+-(),)%)$-*$+-.;/#.#(%'&8$`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965

966 Chapter 11 Output Stages and Power Amplifiers

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Figure 11.44 !#-4*00#!M#*%&4$+$/(#5$).#PQ8#',)&,)#)(*"0$0)'(0#*"3#MN;#3($2/(07#Y/0$0)'(#4T#$0#*3h,0)/3#)' &('2$3/#)/%&/(*),(/#-'%&/"0*)$'"#5.$4/#4E#$0#*3h,0)/3#)'#:$/43#)./#3/0$(/3#2*4,/#'+#?,$/0-/")#-,((/")#$"#)./#',)&,) )(*"0$0)'(07#Y/0$0)'(0#4G#*(/#,0/3#)'#0,&&(/00#&*(*0$)$-#'0-$44*)$'"0#*)#.$1.#+(/?,/"-$/07#;:&$-*44:9#4G#=#EGG#Ω7

EXERCISES 11.21 R'(#)./#-$(-,$)#$"#R$17#EE7]]9#+$"3#)./#(*)$'#4T / 4]#).*)#&('2$3/0#)/%&/(*),(/#0)*=$4$V*)$'"#'+#)./#?,$6 /0-/")#-,((/")#$"#0>#*"3#0<7#!00,%/#).*)# 6 & #-.*"1/0#*)#−T#%Z_°H#*"3#).*)# ∂621 ⁄ ∂C = D I#%Z_°H7 Ans. I 11.22 R'(#)./#-$(-,$)#$"#R$17#EE7]]#*00,%/#).*)#)./#MN;0#.*2/#*#"'%$"*4#621#'+#G7[#Z#*"3#).*)#)./#PQ86 I RO;0#.*2/# 6 & = T Z#*"3# µ % - 7L ( I ⁄ / ) = I !_Z 7 @)#$0#(/?,$(/3#)'#/0)*=4$0.#*#?,$/0-/")#-,((/")#'+ EGG#%!#$"#)./#',)&,)#0)*1/#*"3#IG#%!#$"#)./#3($2/(#0)*1/7#R$"3# 6G= 956GG9#49#*"3# 4 E ⁄ 4 I7# a0/ )./#2*4,/#'+#4T / 4]#+',"3#$"#O
11.10 MOS Power Transistors

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PROBLEMS

Computer Simulation Problems e('=4/%0#$3/")$+$/3#=:#).$0#$-'"#*(/#$")/"3/3#)'#3/%6 '"0)(*)/#)./#2*4,/#'+#,0$"1#8e@HO#0$%,4*)$'"#)'#2/($+:#.*"3 *"*4:0$0#*"3#3/0$1"9#*"3#)'#$"2/0)$1*)/#$%&'()*")#$00,/0#0,-. *0#*44'5*=4/#0$1"*4#05$"1#*"3#*%&4$+$/(#"'"4$"/*(#3$0)'()$'"7 @"0)(,-)$'"0#)'#*00$0)#$"#0/))$"1#,&#e8&$-/#*"3#P,4)$0%#0$%,6 4*)$'"0# +'(# *44# )./# $"3$-*)/3# &('=4/%0# -*"# =/# +',"3# $"# )./ -'((/0&'"3$"1# +$4/0# '"# )./# 3$0-7# >')/# ).*)# $+# *# &*()$-,4*( &*(*%/)/(# 2*4,/# $0# "')# 0&/-$+$/3# $"# )./# &('=4/%# 0)*)/%/")9 :',#*(/#)'#%*X/#*#(/*0'"*=4/#*00,%&)$'"7 o#3$++$-,4)#&('=4/%S#oo#%'(/#3$++$-,4)S#ooo#2/(:#-.*44/"1$"1 *"3_'(#)$%/6-'"0,%$"1S#Cc#3/0$1"#&('=4/%7

Section 11.2: Class A Output Stage 11.1 F$ +/'))$ F$ #.,%%#&$ *-//-0#&C$ 7,')#6$ <),(2$ %"#$ +,&+<,% )"-0($,($1,23$4435C$<)#)$6--$=$K$AC$4$=$4/$=$4$UΩC$0,%"$'// %&'(),)%-&)$ 9,(+/<6,(2$ 0E:$ ,6#(%,+'/3$ F))<.#$ 621$ =$ @3V$ AC 6-1)'%$=$@3E$AC$'(6$ β$%-$7#$>#&8$/'&2#3$1-&$/,(#'&$-;#&'%,-(C 0"'%$ '&#$ %"#$ <;;#&$ '(6$ /-0#&$ /,.,%)$ -*$ -<%;<%$ >-/%'2#C$ '(6 %"# +-&&#);-(6,(2$,(;<%)n$c-0$6-$%"#)#$>'/<#)$+"'(2#$,*$%"# #.,%%#&D7')#$T<(+%,-($'&#'$-*$0E$,)$.'6#$%0,+#$')$7,2$')$%"'% -* 05n$c'/*$')$7,2n 11.2 F$ )-<&+#B*-//-0#&$ +,&+<,%$ <),(2$ M]RP$ %&'(),)%-&)$ ,) +-()%&<+%#6$ *-//-0,(2$ %"#$ ;'%%#&($ )"-0($ ,($ 1,23$ 44353$ F// %"&##$ %&'(),)%-&)$ <)#6$ '&#$ ,6#(%,+'/C$ 0,%"$ 6&$ =$ 4$ A$ '(6 µ%-7L I⁄/ $=$5@ .FdA5G$6--$=$K$AC$4$=$4/$=$4$UΩ3$1-&$/,(#'& -;#&'%,-(C$0"'%$'&#$%"#$<;;#&$'(6$/-0#&$/,.,%)$-*$%"#$-<%;<% >-/%'2#C$'(6$%"#$+-&&#);-(6,(2$,(;<%)n D 11.3 _),(2$%"#$*-//-0#&$+-(*,2<&'%,-($)"-0($,($1,23$4435 0,%"$±XBA$)<;;/,#)C$;&->,6#$'$6#),2($+';'7/#$-*$±VBA$-<%B ;<%)$0,%"$'$4BUΩ$/-'6C$<),(2$%"#$).'//#)%$;-)),7/#$%-%'/$)<;B ;/8$ +<&&#(%3$ o-<$ '&#$ ;&->,6#6$ 0,%"$ *-<&$ ,6#(%,+'/C$ ",2"Bβ Zg!)$'(6$'$&#),)%-&$-*$8-<&$+"-,+#3 D 11.4 F($#.,%%#&$*-//-0#&$<),(2$%"#$+,&+<,%$-*$1,23$ 4435C *-&$0",+"$%"#$-<%;<%$>-/%'2#$&'(2#$,)$±K$AC$,)$&#J<,$<),(2 6--$=$4@$A3$!"#$+,&+<,%$,)$%-$7#$6#),2(#6$)<+"$%"'%$%"#$+<&B &#(%$>'&,'%,-($,($%"#$#.,%%#&B*-//-0#&$%&'(),)%-&$,)$(-$2&#'%#& %"'($ '$ *'+%-&$ -*$ 4@C$ *-&$ /-'6$ &#),)%'(+#)$ ')$ /-0$ ')$ 4@@$ Ω3 \"'%$,)$%"#$>'/<#$-*$4$&#J<,n$1,(6$%"#$,(+&#.#(%'/$>-/%B '2#$2',($-*$%"#$&#)#&$%",)$&'(2#$-*$v3n *11.5 L-(),6#&$ %"#$ -;#&'%,-($ -*$ %"#$ *-//-0#&$ +,&+<,%$ -* 1,23 4435$*-&$0",+"$ 4 / = 6-- ⁄ ,9 $0"#($6&,>#($78$'$)J<'&# 0'>#$)<+"$%"'%$%"#$-<%;<%$&'(2#)$*&-.$+6--$%-$−6--$9,2(-&,(2 6-1)'%:3$1-&$%",)$),%<'%,-(C$)U#%+"$%"#$#J<,>'/#(%$-*$1,23$443H$*-& v3C$#-4C$'(6$*843$l#;#'%$*-&$'$)J<'&#B0'>#$-<%;<%$%"'%$"')$;#'U /#>#/)$-*$ ±6-- ⁄ I7 $\"'%$,)$%"#$'>#&'2#$;-0#&$6,)),;'%,-($,( 04$ ,($ #'+"$ +')#n$ L-.;'&#$ %"#)#$ &#)#)$-*$;#'U$'.;/,%<6#$6--$'(6$ 6-- ⁄ I 9 $&#);#+%,>#/83

11.6 L-(),6#&$ %"#$ ),%<'%,-($ 6#)+&,7#6$ ,($ f&-7/#.$ 443K3$ 1-& )J<'&#B0'>#$ -<%;<%)$ "'>,(2$ ;#'UB%-B;#'U$ >'/<#)$-*$ 56--$ '(6 6--C$'(6$*-&$),(#$0'>#)$-*$%"#$)'.#$;#'UB%-B;#'U$>'/<#)C$*,(6 %"#$'>#&'2#$;-0#&$/-))$,($%"#$+<&&#(%B)-<&+#$%&'(),)%-&$053 11.7 l#+-(),6#&$%"#$),%<'%,-($6#)+&,7#6$,($IO#&+,)#$443E$*-& >'&,'%,-($,($6-- S);#+,*,+'//8$*-&$6--$=$4?$AC$45$AC$4@$AC '(6$W$A3$F))<.#$6-1)'%$,)$(#'&/8$N#&-3$\"'%$,)$%"#$;-0#&B +-(>#&),-($#**,+,#(+8$,($#'+"$+')#n

Section 11.3: Class B Output Stage 11.8 L-(),6#&$%"#$+,&+<,%$-*$'$+-.;/#.#(%'&8BZg!$+/'))$Z -<%;<%$ )%'2#3$ 1-&$ 0"'%$ '.;/,%<6#$ -*$ ,(;<%$ ),2('/$ 6-#)$ %"# +&-))->#&$6,)%-&%,-($&#;&#)#(%$'$4@Y$/-))$,($;#'U$'.;/,%<6#n 11.9 L-(),6#&$ %"#$ *##67'+U$ +-(*,2<&'%,-($ 0,%"$ '$ +/'))$ Z -<%;<%$)%'2#$)"-0($,($1,23$443X3$k#%$%"#$'.;/,*,#&$2',($B@$= 4@@$ AdA3$ `#&,>#$ '($ #O;&#)),-($ *-&$ v3$ >#&)<)$ v, C$ '))<.,(2 %"'%$ 621 = G7[#Z7 $PU#%+"$%"#$%&'()*#&$+"'&'+%#&,)%,+$v3$>#&B )<)$v, C$'(6$+-.;'&#$,%$0,%"$%"'%$0,%"-<%$*##67'+U3 11.10 L-(),6#&$ %"#$ +/'))$ Z$ -<%;<%$ )%'2#C$ <),(2 #("'(+#.#(%$ ]RP1I!)C$ )"-0($ ,($ 1,23$ f4434@3$ k#%$ %"# 6#>,+#)$"'>#$ 6 & = G7F#Z $'(6$ µ -7LI ⁄ /$=$5$.FdA53$\,%" '$4@BUcN$),(#B0'>#$,(;<%$-*$KBA$;#'U$'(6$'$",2"$>'/<#$-* /-'6$&#),)%'(+#C$0"'%$;#'U$-<%;<%$0-#$;#&,-6$6-#)$%"#$+&-))->#&$,(%#&>'/ &#;&#)#(%n$1-&$0"'%$>'/<#$-*$/-'6$&#),)%-&$,)$%"#$;#'U$-<%;<% >-/%'2#$<+#6$%-$"'/*$%"#$,(;<%n

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11.11 L-(),6#&$%"#$+-.;/#.#(%'&8BZg!$+/'))$Z$-<%;<%$)%'2# '(6$ (#2/#+%$ %"#$ #**#+%)$ -*$ *,(,%#$ 621$ '(6$ 6-1)'%3$ 1-&$ ±10BA ;-0#&$)<;;/,#)$'(6$'$4@@BΩ$/-'6$&#),)%'(+#C$0"'%$,)$%"#$.'O,B .<.$),(#B0'>#$-<%;<%$;-0#&$'>',/'7/#n$\"'%$)<;;/8$;-0#& +-&&#);-(6)n$ \"'%$ ,)$ %"#$ ;-0#&B+-(>#&),-($ #**,+,#(+8n$ 1-& -<%;<%$),2('/)$-*$"'/*$%",)$'.;/,%<6#C$*,(6$%"#$-<%;<%$;-0#&C %"#$)<;;/8$;-0#&C$'(6$%"#$;-0#&B+-(>#&),-($#**,+,#(+83 D 11.12 F$+/'))$Z$-<%;<%$)%'2#$-;#&'%#)$*&-.$±KBA$)<;;/,#)3 F))<.,(2$&#/'%,>#/8$,6#'/$%&'(),)%-&)C$0"'%$,)$%"#$-<%;<%$>-/%'2#

Problems 969

11.14 L-(),6#&$%"#$+/'))$Z$Zg!$-<%;<%$)%'2#$0,%"$'$)J<'&#B 0'>#$-<%;<%$>-/%'2#$-*$'.;/,%<6#$ 6b7 $'+&-))$'$/-'6$4/$'(6 #.;/-8,(2$ ;-0#&$ )<;;/,#)$ ±6==3$ M#2/#+%,(2$ %"#$ #**#+%)$ -* *,(,%#$ 621$ '(6$ 6-1)'%C$ 6#%#&.,(#$ %"#$ /-'6$ ;-0#&C$ %"#$ )<;;/8 ;-0#&C$ %"#$ ;-0#&B+-(>#&),-($ #**,+,#(+8C$ %"#$ .'O,.<. '%%',('7/#$;-0#&B+-(>#&),-($#**,+,#(+8$'(6$%"#$+-&&#);-(6B ,(2$ >'/<#$ -*$ 6b7 9 $ '(6$ %"#$ .'O,.<.$ '>',/'7/#$ /-'6$ ;-0#&3 F/)-$*,(6$%"#$>'/<#$-*$ 6b 7 $'%$0",+"$%"#$;-0#&$6,)),;'%,-($,( %"#$ %&'(),)%-&)$ &#'+"#)$ ,%)$ ;#'UC$ '(6$ %"#$ +-&&#);-(6,(2 >'/<#$-*$;-0#&B+-(>#&),-($#**,+,#(+83

Section 11.4: Class AB Output Stage D 11.15 `#),2($ %"#$ J<,#)+#(%$ +<&&#(%$ -*$ '$ +/'))$ FZ$ Zg! -<%;<%$)%'2#$)-$%"'%$%"#$,(+&#.#(%'/$>-/%'2#$2',($*-&$v,$,($%"# >,+,(,%8$ -*$ %"#$ -&,2,($ ,)$ ,($ #O+#))$ -*$ @3XW$ AdA$ *-&$ /-'6) /'&2#&$%"'($4@@$Ω3$F))<.#$%"'%$%"#$Zg!)$"'>#$621$-*$@3V$A$'%$' +<&&#(%$-*$4@@$.F$'(6$6#%#&.,(#$%"#$>'/<#$-*$622$&#J<,? 11.16 R'(# )./# -4*00# !M# ',)&,)# 0)*1/# -'"0$3/(/3# $"# O<*%&4/ EE7T9# *33# )5'# -'4,%"0# )'# )./# )*=4/# '+# (/0,4)0# *0# +'44'50c# )./ )')*4#$"&,)#-,((/")#3(*5"#+('%# v , #A # , 9#%!DS#*"3#)./#4*(1/60$16 "*4# $"&,)# (/0$0)*"-/# 4 $" ≡ v , ⁄ # , 7# !00,%/# β > Q β < Q β Q ]\ 7#H'%&*(/#)./#2*4,/0#'+# 4 $" #)'#)./#*&&('<$%*)/#2*4,/ '=)*$"/3#,0$"1#)./#(/0$0)*"-/#(/+4/-)$'"#(,4/9# 4 $" ! β 4 / 7 11.17 @"#).$0#&('=4/%#5/#$"2/0)$1*)/#*"#$%&'()*")#)(*3/6'++ $"# )./# 3/0$1"# '+# )./# -4*00# !M# ',)&,)# 0)*1/# '+# R$17# EE7EEc @"-(/*0$"1#)./#?,$/0-/")#-,((/")# , 0 #(/3,-/0#)./#"'"4$"/*($): '+#)./#)(*"0+/(#-.*(*-)/($0)$-#*)#)./#/<&/"0/#'+#$"-(/*0/3#?,$6 /0-/")#&'5/(#3$00$&*)$'"7#!0#*#%/*0,(/#'+#"'"4$"/*($):9#5/ ,0/# )./# %*<$%,%# 3/2$*)$'"# '+# )./# 0)*1/# $"-(/%/")*4# 1*$"9 5.$-.#'--,(0#*)# v3 Q G 9#"*%/4:

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A3D#R'(# 6 -- Q EF #Z#*"3# 4 / Q EGG#Ω 9#+$"3#)./#(/?,$(/3 2*4,/0#'+# < 8 #*"3# , 0 #$+# ε #$0#)'#=/#Fd9#Id9#*"3#Ed7 *11.18 F$+/'))$FZ$-<%;<%$)%'2#C$&#)#.7/,(2$%"'%$,($1,23$44344 7<%$<%,/,N,(2$'$),(2/#$)<;;/8$-*$+4@$A$'(6$7,')#6$'%$6,$=$?$AC ,)$+';'+,%,>#/8$+-<;/#6$%-$'$4@@BΩ$/-'63$1-&$%&'(),)%-&)$*-& 0",+"$ 621 = G7[#Z $'%$4$.F$'(6$*-&$'$7,')$>-/%'2#$622$= 43H$AC$0"'%$J<,#)+#(%$+<&&#(%$&#)-/%'2#)$ -*$ N#&-C$ *,(6$ %"#$ /'&2#)% ;-)),7/#$ ;-),%,>#B2-,(2$ '(6$ (#2'%,>#B2-,(2$ )%#;)$ '%$ %"# -<%;<%3

Section 11.5: Biasing the Class AB Circuit D 11.19 L-(),6#&$ %"#$ 6,-6#B7,')#6$ +/'))$ FZ$ +,&+<,%$ -* 1,23$4434H3$1-&$,Z=FP$=$4@@$µFC$*,(6$%"#$&#/'%,>#$),N#$9%:$%"'% )"-,+#)$9,($+-.;'&,)-($%-$%"# 7,'),(2$6#>,+#):$%-$#()<&#$%"'%$'($-<%;<%$&#),)%'(+#$-*$4@$Ω$-& /#))$,)$-7%',(#6$,($%"#$J<,#)+#(%$)%'%#3$M#2/#+%$%"#$&#),)%'(+# -*$%"#$7,'),(2$6,-6#)3 D *11.20 F$+/'))$FZ$-<%;<%$)%'2#$<),(2$'$%0-B6,-6#$7,') (#%0-&U$ ')$ )"-0($ ,($ 1,23$ 4434H$ <%,/,N#)$ 6,-6#)$ "'>,(2$ %"# )'.#$T<(+%,-($'&#'$')$%"#$-<%;<%$%&'(),)%-&)3$1-&$6--$=$4@$AC ,Z=FP$ =$ @3K$ .FC$ 4/$ =$ 4@@$ ΩC$ β>$=$ K@C$ '(6$ 6-10*) = G#Z9 0"'%$,)$%"#$J<,#)+#(%$+<&&#(%n$\"'%$'&#$%"#$/'&2#)%$;-)),7/# ;-),%,>#$'(6$(#2'%,>#$-<%;<%$),2('/$/#>#/)n$!-$'+",#>#$'$;-)B ,%,>#$;#'U$-<%;<%$/#>#/$#J<'/$%-$%"#$(#2'%,>#$;#'U$/#>#/C$0"'% >'/<#$-*$ β>$,)$(##6#6$,*$,Z=FP$,)$(-%$+"'(2#6n$\"'%$>'/<#$-* ,Z=FP$,)$(##6#6$,*$ β>$,)$"#/6$'%$K@n$1-&$%",)$>'/<#C$0"'%$6-#) ,0$7#+-.#n **11.21 F$ +/'))$ FZ$ -<%;<%$ )%'2#$ <),(2$ '$ %0-B6,-6#$ 7,') (#%0-&U$ ')$ )"-0($ ,($ 1,23$ 4434H$ <%,/,N#)$ 6,-6#)$ "'>,(2$ %"# )'.#$T<(+%,-($'&#'$')$%"#$-<%;<%$%&'(),)%-&)3$F%$'$&--.$%#.B ;#&'%<&#$ -*$ '7-<%$ 5@°L$ %"#$ J<,#)+#(%$ +<&&#(%$ ,)$ 4$ .F$ '(6 621 = G7U#Z7$ !"&-<2"$'$ .'(<*'+%<&,(2$ #&&-&C$ %"#$ %"#&.'/ +-<;/,(2$ 7#%0##($ %"#$ -<%;<%$ %&'(),)%-&)$ '(6$ %"#$ 7,'),(2 6,-6#B+-((#+%#6$ %&'(),)%-&)$ ,)$ -.,%%#63$ F*%#&$ )-.#$ -<%;<% '+%,>,%8C$%"#$-<%;<%$6#>,+#)$"#'%$<;$%-$V@°L$0",/#$%"#$7,')B ,(2$ 6#>,+#)$ &#.',($ '%$ 5@°LR5 !"<)C$ 0",/#$ %"#$ 621$ -*$ #'+" 6#>,+#$&#.',()$<(+"'(2#6C$%"#$J<,#)+#(%$+<&&#(%$,($%"#$-<%B ;<%$ 6#>,+#)$ ,(+&#')#)3$ !-$ +'/+'/<#C &#+'//$ %"'%$ %"#&#$ '&#$ %0-$ #**#+%)^$ ,=$ ,(+&#')#)$ 78$ '7-<% E]d_°H $ '(6 6 C = HC/ S$ +"'(2#)C$ 0"#&#$ C$ =$ 95VE°$ +

PROBLEMS

D 11.13 F$+/'))$Z$-<%;<%$)%'2#$,)$&#J<,$%-$6#/,>#&$'($'>#&'2# ;-0#&$-*$4@@$\$,(%-$'$4?BΩ$/-'63$!"#$;-0#&$)<;;/8$)"-#$-<%;<%$>-/%'2#3 `#%#&.,(#$ %"#$ ;-0#&B)<;;/8$ >-/%'2#$ &#J<,$ 9%-$ %"#$ (#'&#)% >-/%$ ,($ %"#$ ';;&-;&,'%#$ 6,&#+%,-(:C$ %"#$ ;#'U$ +<&&#(%$ *&-. #'+"$)<;;/8C$%"#$%-%'/$)<;;/8$;-0#&C$'(6$%"#$;-0#&B+-(>#&B ),-($ #**,+,#(+83$ F/)-C$ 6#%#&.,(#$ %"#$ .'O,.<.$ ;-)),7/# ;-0#&$6,)),;'%,-($,($#'+"$%&'(),)%-&$*-&$'$),(#B0'>#$,(;<%3

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CHAPTER 11

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CH A PT ER 1 1

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PROBLEMS

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CHAPTER 11

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CH A PT ER 1 1

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CHAPTER 11

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PROBLEMS

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CHAPTER 12

OperationalAmplifier Circuits Introduction 12.1

975

The Two-Stage CMOS Op Amp

976

12.2 The Folded-Cascode CMOS Op Amp 991 12.3 The 741 Op-Amp Circuit 12.4 DC Analysis of the 741

1002 1006

12.5 Small-Signal Analysis of the 741

1013

12.6 Gain, Frequency Response, and Slew Rate of the 741 1026 12.7 Modern Techniques for the Design of BJT Op Amps 1031 Summary

1050

Problems

1051

IN THIS CHAPTER YOU WILL LEARN 1. The design and analysis of the two basic CMOS op-amp architectures: the two-stage circuit and the single-stage, folded-cascode circuit. 2. The complete circuit of an analog IC classic: the 741 op amp. Though 40 years old, the 741 circuit includes so many interesting and useful design techniques that its study is still a must. 3. Interesting and useful applications of negative feedback within op-amp circuits to achieve bias stability and increased CMRR. 4. How to break a large analog circuit into its recognizable blocks, to be able to make the analysis amenable to a pencil-and-paper approach, which is the best way to learn design. 5. Some of the modern techniques employed in the design of low-voltage, single-supply BJT op amps. 6. Most importantly, how the different topics we learned about in the preceding chapters come together in the design of the most important analog IC, the op amp.

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v-#)"1#$%+#)//3.)=/+#,)"6+#34#$#&) 8#9%&'#&'#0'0)//2#$%+#()'+#&"#$%+#7EFG#)5*/&4&+, (&,(0&$#0"1+,#'$0128

EXERCISE 12.1

K3,#)#*),$&(0/),#1+'&6"#34#$%+#$.3A'$)6+#7EFG#3*#)5*#34#K&68#Q;8Q-#±Q8ZUAH#'0**/&+'#),+#0$&/&C+1 )"1#)//#$,)"'&'$3,'#+?(+*$#43,#!Z#)"1#!O#),+#3*+,)$+1#.&$%#3:+,1,&:+#:3/$)6+'#34#R8TAH#5)6"&$01+^ !Z#)"1#!O#0'+#3:+,1,&:+#:3/$)6+'#34#R8UAH#5)6"&$01+8#9%+#4)=,&()$&3"#*,3(+''#+5*/32+1#*,3:&1+'#$+ , =# $+1 #=#R8U#H8#K&"1#$%+#&"*0$#(3553"A531+#,)"6+#)"1#$%+#,)"6+#)//3.+1#43,#v-8# Ans. −=
12.1.3 Voltage Gain !*$3#)#'.&:#$)"#$@*2)-5#$5-&:$-:3$)"#$%'#Y0#:/4$'#(+*:(#I$/*:(&3#'$-$(&.+2&%$#Y0&@-2#:) /&'/0&)$.*3#2$%*'$)"#$(.-22,(&5:-2$*+#'-)&*:$*%$)"#$6789$-.+2&%&#'$S;&5<$=><>UI$1"#'#$#-/" *%$)"#$)1*$()-5#($&($.*3#2#3$-($-$)'-:(/*:30/)-:/#$-.+2&%&#'<$Z($#G+#/)#3I$)"#$&:+0)$'#(&(, )-:/#$&($+'-/)&/-224$&:%&:&)#I

3 &" = ∞ !"#$%&'(),()-5#$)'-:(/*:30/)-:/#$*2=$&($#Y0-2$)*$)"#$)'-:(/*:30/)-:/#$*%$#-/"$*%$!=$-:3$!> S(##$9#/)&*:$E
* 2Q # = ' 2Q = ' 2;

$S=>
12.1 The Two-Stage CMOS Op Amp

CC ! ! Vid "

! Gm 1 Vid

C1 Vi2

R1

! Gm 2 Vi2

"

R2

C2 Vo "

" Figure 12.2 G5)//A'&6")/#+@0&:)/+"$#(&,(0&$#43,#$%+#3*#)5*#&"#K&68#Q;8Q8

9&:/#$ !=$ -:3$ !>$ -'#$ *+#'-)#3$ -)$ #Y0-2$ ?&-($ /0''#:)($ S # ⁄ ; U$ -:3$ #Y0-2$ *@#'3'&@#$ @*2)-5#(I $-$= =$$-$>I$

;(# ⁄ ;) # * 2Q # = AAAAAAAAAAAAAAAAA = AAAAAAAAAAA $-$Q $-$Q

$S=><[U

T#(&()-:/#$3=$'#+'#(#:)($)"#$*0)+0)$'#(&()-:/#$*%$)"#$%&'()$()-5#I$)"0(

3 Q # = 5 6; || 5 6P

$S=>
$4; A 5 6; # = AAAAAAAAAA #⁄;

$S=><\U

$4P A 5 6P # = AAAAAAAA #⁄;

$S=><=PU

1"#'#

-:3

!"#$3/$5-&:$*%$)"#$%&'()$()-5#$&($)"0(

4 Q # = L * 2Q 3 Q

$S=><==U

= L ' 2Q ( 5 6; || 5 6P )

$S=><=>U

Q ; Q = L AAAAAAAAAAA ## AAAAAAAAAAA + AAAAAAAA $4P $-$Q $4;

$S=><=MU

8?(#'@#$)"-)$)"#$.-5:&)03#$*%$4=$&($&:/'#-(#3$?4$*+#'-)&:5$)"#$3&%%#'#:)&-2,+-&'$)'-:(&()*'(I !=$-:3$ !>I$-)$-$2*1$*@#'3'&@#$@*2)-5#I$-:3$?4$/"**(&:5$-$2*:5#'$/"-::#2$2#:5)"$)*$*?)-&: 2-'5#'$X-'24$@*2)-5#(I$ $4 <$ T#)0':&:5$)*$)"#$#Y0&@-2#:)$/&'/0&)$&:$;&5<$=><>$-:3$2#-@&:5$)"#$3&(/0((&*:$*%$)"#$@-'&*0( .*3#2$/-+-/&)-:/#($0:)&2$9#/)&*:$=><= &($5&@#:$?4 $

;# .Z A * 2; = ' 2Z = AAAAAAAAAA $-$Z

$S=><=NU

979

980 Chapter 12 Operational-Amplifier Circuits T#(&()-:/#$3>$'#+'#(#:)($)"#$*0)+0)$'#(&()-:/#$*%$)"#$(#/*:3$()-5#I$)"0(

3 ; = 5 6Z || 5 6O

$S=><=OU

$4Z A 56Z = AAAAAAA #.Z

$S=><=FU

$4O $4O A = AAAAAAAAAA A 5 6O = AAAAAAAAAA # .O # .Z

$S=><=[U

1"#'#

-:3

!"#$@*2)-5#$5-&:$*%$)"#$(#/*:3$()-5#$/-:$:*1$?#$%*0:3$-(

4 ; = L * 2; 3 ;

$S=><=EU

= L ' 2Z ( 5 6Z || 5 6O )

$S=><=\U

; Q Q = L AAAAAAAAAAA ## AAAAAAAA + AAAAAAAAAAA $-$Z $4Z $4O

$S=><>PU

H#'#$-5-&:$1#$*?(#'@#$)"-)$)*$&:/'#-(#$)"#$.-5:&)03#$*%$4>I$!F$"-($)*$?#$*+#'-)#3$-)$-$2*1 *@#'3'&@#$@*2)-5#I$-:3$)"#$/"-::#2$2#:5)"($*%$!F$-:3$![$("*023$?#$.-3#$2*:5#'<$ !"#$*@#'-22$3/$@*2)-5#$5-&:$/-:$?#$%*0:3$-($)"#$+'*30/)$4=4>I

4v = 4Q 4; = * 2Q 3 Q * 2; 3 ;

$S=><>=U

= ' 2Q ( 5 6; || 5 6P )' 2Z ( 5 6Z || 5 6O )

$S=><>>U

]*)#$)"-)$4v$&($*%$)"#$*'3#'$*%$S'256U><$!"0($)"#$@-20#$*%$4v$1&22$?#$&:$)"#$'-:5#$*%$OPP$AQA$)* OPPP$AQA< ;&:-224I$1#$:*)#$)"-)$)"#$*0)+0)$'#(&()-:/#$*%$)"#$*+$-.+$&($#Y0-2$)*$)"#$*0)+0)$'#(&()-:/# *%$)"#$(#/*:3$()-5#I

3 6 = 5 6Z || 5 6O

$S=><>MU

H#:/#$36$/-:$?#$2-'5#$S&<#
12.1 The Two-Stage CMOS Op Amp

EXERCISES 12.2 9%+#7EFG#3*#)5*#34#K&68#Q;8Q#&'#4)=,&()$+1#&"#)#*,3(+''#43,#.%&(%# $ 4, ′ #=# $ 41 ′ #=#;R#H[µ58#K&"1 4Q-#4;-#)"1#4v#&4#)//#1+:&(+'#),+#Q#µ5#/3"6-#$-$Q#=#R8;#H-#)"1#$-$Z#=#R8U#H8#L/'3-#4&"1#$%+#3*A)5*#30$*0$ ,+'&'$)"(+#3=$)&"+1#.%+"#$%+#'+(3"1#'$)6+#&'#=&)'+1#)$#R8U#5L8 Ans. −QRR#H[H^#−PR#H[H^#PRRR#H[H^#;R#BΩ 12.3

!4#$%+#7EFG#3*#)5*#&"#K&68#Q;8Q#&'#(3""+($+1#)'#)#0"&$2A6)&"#=044+,-#'%3.#$%)$#$%+#(/3'+1A/33*#30$A *0$#,+'&'$)"(+#&'#6&:+"#=2 3 30$ ! Q ⁄ ' 2Z [ ' 2Q ( 5 6; || 5 6P ) ]

12.1.4 Common-Mode Rejection Ratio (CMRR) 9%+#7EWW#34#$%+#$.3A'$)6+#3*#)5*#34#K&68#Q;8Q#&'#1+$+,5&"+1#=2#$%+#4&,'$#'$)6+8#9%&'#.)' )")/2C+1#&"#G+($&3"#V8U8P#)"1#$%+#,+'0/$#&'#6&:+"#&"#M@8#XV8QPOY-#")5+/27EWW ` [ ' 2Q ( 5 6; || 5 6P ) ] [ ;' 2T 3 %% ]

$S=><>NU

.%+,+# 3 %% #&'#$%+#30$*0$#,+'&'$)"(+#34#$%+#=&)'#(0,,+"$#'30,(+# ! U 8 #F='+,:+#$%)$#7EWW#&'#34 ; $%+#3,1+,#34# ( ' 2 5 6 ) #)"1#$%0'#()"#=+#,+)'3")=/2#%&6%8#L/'3-#'&"(+# ' 2 5 6 #&'#*,3*3,$&3")/#$3 $ 4 ⁄ $ -$ ` $′4 0 ⁄ $ -$ - #$%+#7EWW#&'#&"(,+)'+1#&4#/3"6#(%)""+/'#),+#0'+1-#+'*+(&)//2#43,# ! U)"1#$%+#$,)"'&'$3,'#),+#3*+,)$+1#)$#/3.#3:+,1,&:+#:3/$)6+'8

12.1.5 Frequency Response T#%#'$)*$)"#$#Y0&@-2#:)$/&'/0&)$&:$;&5<$=><><$6-+-/&)-:/#$&=$&($)"#$)*)-2$/-+-/&)-:/#$?#)1##: )"#$*0)+0)$:*3#$*%$)"#$%&'()$()-5#$-:3$5'*0:3I$)"0(

& Q = & '(; + & (7; + & '(P + & (7P + & '8Z

$S=><>OU

6-+-/&)-:/#$&>$'#+'#(#:)($)"#$)*)-2$/-+-/&)-:/#$?#)1##:$)"#$*0)+0)$:*3#$*%$)"#$*+$-.+$-:3 5'*0:3$-:3$&:/203#($1"-)#@#'$2*-3$/-+-/&)-:/#$&0$)"-)$)"#$-.+2&%&#'$&($'#Y0&'#3$)*$3'&@#I$)"0(

& ; = & (7Z + & (7O + & '(O + & 0

$S=><>FU

_(0-224I$&0$&($2-'5#'$)"-:$)"#$)'-:(&()*'$/-+-/&)-:/#(I$1&)"$)"#$'#(02)$)"-)$&>$?#/*.#($.0/" 2-'5#'$ )"-:$ &=<$ ;&:-224I$ :*)#$ )"-)$ &'(F$ ("*023$ ?#$ ("*1:$ &:$ +-'-22#2$ 1&)"$ &&$ ?0)$ "-($ ?##: &5:*'#3$?#/-0(#$&&$&($0(0-224$.0/"$2-'5#'< !"#$#Y0&@-2#:)$/&'/0&)$*%$;&5<$=><>$1-($-:-24J#3$&:$3#)-&2$&:$9#/)&*:$\I$1"#'#$&)$1-($%*0:3 )"-)$&)$"-($)1*$+*2#($-:3$-$+*(&)&@#$'#-2,-G&($J#'*$1&)"$)"#$%*22*1&:5$-++'*G&.-)#$%'#Y0#:/&#(K

Q 9:Q ! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ; π 3 Q * 2; 3 ; & &

$S=><>[U

981

982 Chapter 12 Operational-Amplifier Circuits * 2; A 9:; ! AAAAAAAAAAAA ; π &; * 2; A 9; ! AAAAAAAAAAAA ; π &&

$S=><>EU $S=><>\U

H#'#I$ 9:=$ &($ )"#$ 3*.&:-:)$ +*2#$ %*'.#3$ ?4$ )"#$ &:)#'-/)&*:$ *%$ 7&22#',.02)&+2$ &&$ a&<#3>U&&$ !$ *2>3>&&b$ -:3$ 3=<$ !*$ -/"&#@#$ )"#$ 5*-2$ *%$ -$ 0:&%*'.$ L>P,3cQ3#/-3#$ 5-&: '*22*%%$3*1:$)*$P$3cI$)"#$0:&)4,5-&:$%'#Y0#:/4$9+I

9+ = 4v 9:Q

$S=>
* 2Q A = AAAAAAAAAAAA ; π &&

$S=>
.0()$?#$2*1#'$)"-:$9:>$-:3$9;I$)"0($)"#$3#(&5:$.0()$(-)&(%4$)"#$%*22*1&:5$)1*$/*:3&)&*:(

-:3

* 2Q * 2; AAAAAAAA A < AAAAAAAAA && &;

$S=>U

* 2Q < * 2;

$S=>
Simplified Equivalent Circuit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hase Margin 9%+#4,+@0+"(2#(35*+"')$&3"#'(%+5+#0$&/&C+1#&"#$%+#$.3A'$)6+#7EFG#)5A */&4&+,#&'#34#$%+#*3/+A'*/&$$&"6#$2*+-#'$01&+1#&"#G+($&3"#QR8QT8T]#!$#*,3:&1+'")#135&")"$#/3.A 4,+@0+"(2#*3/+#.&$%#4,+@0+"(2#9:Q#)"1#'%&4$'#$%+#'+(3"1#*3/+#=+23"1#9+8#K&60,+#Q;8P#'%3.'#)

CC

!

0V

! Vid " "

Gm1Vid

"$

! Vo "

Figure 12.3 L"# )**,3?&5)$+# %&6%A 4,+@0+"(2# +@0&:)/+"$# (&,(0&$# 34# $%+# $.3A '$)6+# 3*# )5*8# 9%&'# (&,(0&$# )**/&+'# 43, 4,+@0+"(&+'#9# # #9:Q8

12.1 The Two-Stage CMOS Op Amp

20 log "A" (dB) 20 log "Av "

0

fP2 fZ fP1

f (log scale)

ft

! 0

f (log scale)

"90º "180º

Phase margin

Figure 12.4 92*&()/#4,+@0+"(2#,+'*3"'+#34#$%+#$.3A'$)6+#3*#)5*8

,+*,+'+"$)$&:+#J31+#*/3$#43,#$%+#6)&"#5)6"&$01+#)"1#*%)'+8#S3$+#$%)$#)$#$%+#0"&$2A6)&"#4,+@0+"(2 9+-#$%+#*%)'+#/)6#+?(++1'#$%+#`R°#()0'+1#=2#$%+#135&")"$#*3/+#)$#9:Q8#9%&'#'3A()//+1#+?(+''#*%)'+ '%&4$#&'#10+#$3#$%+#'+(3"1#*3/+-

9 9:;

+ A φ :; = L $)" LQ AAAAAA

$S=>
-:3$)"#$'&5"),"-2%,+2-:#$J#'*I

$S=>
9 9;

φ ; = L $)"LQ AAAA+

$S=>
!"0($)"#$+"-(#$2-5$-)$9$=$9+$1&22$?#$

φ $3$)/ = `R° + $)" LQX 9+ ⁄ 9:; Y + $)" LQ X 9+ ⁄ 9; Y

$S=>
-:3$)"0($)"#$+"-(#$.-'5&:$1&22$?#$

a%)'+#5),6&" = QVR° L φ $3$)/ LQ

LQ

# = `R° L # $)" X 9+ ⁄ 9:; Y L # $)" X 9+ ⁄ 9; Y

$S=>
;'*.$*0'$()034$*%$)"#$()-?&2&)4$*%$%##3?-/V$-.+2&%&#'($&:$9#/)&*:$=P<=><>I$1#$V:*1$)"-)$)"# .-5:&)03#$*%$)"#$+"-(#$.-'5&:$(&5:&%&/-:)24$-%%#/)($)"#$/2*(#3,2**+$5-&:<$!"#'#%*'#I$*?)-&:, &:5$-$3#(&'#3$.&:&.0.$@-20#$*%$+"-(#$.-'5&:$&($0(0-224$-$3#(&5:$'#Y0&'#.#:)<

983

984 Chapter 12 Operational-Amplifier Circuits CC

R

! ! Vid "

! Gm 1 Vid

R1

C1 Vi2 "

! Gm 2 Vi2

R2

C2 Vo "

" Figure 12.5 G5)//A'&6")/#+@0&:)/+"$#(&,(0&$#34#$%+#3*#)5*#&"#K&68#Q;8Q#.&$%#)#,+'&'$)"(+#3#&"(/01+1#&"#'+,&+' .&$%#&&8

!"#$ +'*?2#.$ *%$ )"#$ -33&)&*:-2$ +"-(#$ 2-5$ +'*@&3#3$ ?4$ )"#$ '&5"),"-2%,+2-:#$ J#'*$ "-($ '-)"#'$(&.+2#$-:3$#2#5-:)$(*20)&*:K$c4$&:/203&:5$-$'#(&()-:/#$3$&:$(#'&#($1&)"$&&I$-($("*1:$&: ;&5<$=>
$<; AAAAAAAAAAAAAAAAAA A = *2; $<; Q 3 + AAAAAAAAA 8&& !"0($)"#$J#'*$&($:*1$-)

Q 8 = Q#& & AAAAAAAAA L 3 * 2;

$S=>
D#$*?(#'@#$)"-)$?4$(#2#/)&:5$ 3 = Q ⁄ * 2; - $1#$/-:$+2-/#$)"#$J#'*$-)$&:%&:&)#$%'#Y0#:/4<$Z: #@#:$?#))#'$/"*&/#$1*023$?#$)*$(#2#/)$3$5'#-)#'$)"-:$Q ⁄ * 2; I$)"0($+2-/&:5$)"#$J#'*$-)$-$:#5-, )&@#$'#-2,-G&($2*/-)&*:$1"#'#$)"#$+"-(#$&)$&:)'*30/#($=((8$)*$)"#$+"-(#$.-'5&:< $

EXERCISE 12.4 L#*),$&(0/),#&5*/+5+"$)$&3"#34#$%+#7EFG#)5*/&4&+,#34#K&6'8#Q;8Q#)"1#Q;8;#*,3:&1+'#*2Q#=#Q#5L[H*2;#=#;#5L[H-#56;#=#56P#=#QRR#BΩ-#56Z#=#56O#=#PR#BΩ-#)"1#&;#=#Q#*K8 X)Y K&"1#$%+#:)/0+#34#&&#$%)$#,+'0/$'#&" #9 + #=#QRR#E
12.1.6 Slew Rate !"#$(2#1,'-)#$2&.&)-)&*:$*%$*+$-.+($&($3&(/0((#3$&:$6"-+)#'$><$H#'#I$1#$("-22$&220()'-)#$)"#$*'&, 5&:$*%$)"#$(2#1&:5$+"#:*.#:*:$&:$)"#$/*:)#G)$*%$)"#$)1*,()-5#$6789$-.+2&%&#'$0:3#'$()034<

12.1 The Two-Stage CMOS Op Amp

1V

Figure 12.6 L#0"&$2A6)&"#43//3.+,#.&$%#)#/),6+#'$+*#&"*0$8#G&"(+#$%+#30$*0$#:3/$)6+#()""3$#(%)"6+#&55+A 1&)$+/2-#)#/),6+#1&44+,+"$&)/#:3/$)6+#)**+),'#=+$.++"#$%+#3*A)5*#&"*0$#$+,5&")/'8

73"'&1+,#$%+#0"&$2A6)&"#43//3.+,#34#K&68#Q;8Z#.&$%#)#'$+*#34-#')2-#Q#H#)**/&+1#)$#$%+#&"*0$8 J+()0'+#34#$%+#)5*/&4&+,#12")5&('-#&$'#30$*0$#.&//#"3$#(%)"6+#&"#C+,3#$&5+8#9%0'-#&55+1&A )$+/2#)4$+,#$%+#&"*0$#&'#)**/&+1-#$%+#+"$&,+#:)/0+#34#$%+#'$+*#.&//#)**+),#)'#)#1&44+,+"$&)/#'&6")/ =+$.++"#$%+#$.3#&"*0$#$+,5&")/'8#!"#)//#/&B+/&%331-#'0(%#)#/),6+#'&6")/#.&//#+?(++1#$%+#:3/$)6+ ,+@0&,+1#$3#$0,"#344#3"+#'&1+#34#$%+#&"*0$#1&44+,+"$&)/#*)&,#X ;$-$Q]#'++#+),/&+,#&//0'$,)$&3"K&68#V8ZY#)"1"'.&$(%#$%+#+"$&,+#=&)'#(0,,+"$###$3#$%+#3$%+,#'&1+8#W+4+,+"(+#$3#K&68#Q;8Q#'%3.' $%)$#43,#30,#+?)5*/+-#!;#.&//#$0,"#344-#)"1#!Q#.&//#(3"10($#$%+#+"$&,+#(0,,+"$##8#9%0'#!P#.&// '&"B# )# (0,,+"$# ## $%)$# .&//# =+# *0//+1# 4,35# &&-# )'# '%3."# &"# K&68# Q;8O8# # <+,+-# )'# .+# 1&1# &" K&68 Q;8T-#.+#),+#531+/&"6#$%+#'+(3"1#'$)6+#)'#)"#&1+)/#&"$+6,)$3,8#D+#'++#$%)$#$%+#30$*0$ :3/$)6+#.&//#=+#)#,)5*#.&$%#)#'/3*+#34# # ⁄ & & ] v6 ( + )

# = AAAAAA"+ &&

!"0($)"#$(2#1$'-)#I$%3I$&($5&@#:$?4

# %3 = AAAAAA &&

$S=>
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985

986 Chapter 12 Operational-Amplifier Circuits )"1#XQ;8PRY#)"1#"3$&"6#$%)$#*2Q#=#'2Q#=# # ⁄ $-$Q -#$3#3=$)&"

%3 = ; π 9+ $-$

$S=>
%3 = $-$ ω +

$S=>U

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EXERCISE 12.5 K&"1# %3# 43,# $%+# 7EFG# 3*# )5*# 34# K&68# Q;8Q# 43,# $%+# ()'+ #9 +# =# QRR# EF$AQµ(W$>PP µZ

12.1.7 Power-Supply Rejection Ratio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aGWWY8# 9%+#aGWW#&'#1+4&"+1#)'#$%+#,)$&3#34#$%+#)5*/&4&+,#1&44+,+"$&)/#6)&"#$3#$%+#6)&"#+?*+,&+"(+1 =2#)#(%)"6+#&"#$%+#*3.+,A'0**/2#:3/$)6+#X v (( #)"1# v 88Y8#K3,#(&,(0&$'#0$&/&C&"6#$.3#*3.+,#'0*A */&+'-#.+#1+4&"+

)"1

.%+,+

4 c aGWW ≡ AAAAAc(A 4

$S=>U

4( L aGWW ` AAAAAAA A L 4

$S=>
v

c 4 ≡ AAAAAA6A

v ((

$S=>
12.1 The Two-Stage CMOS Op Amp L

v v 88

4 ` AAAAAA6

$S=>
F=:&30'/2-#$3#5&"&5&C+#$%+#+44+($#34#$%+#*3.+,A'0**/2#,&**/+-#.+#,+@0&,+#$%+#3*#)5*#$3#%):+ )#/),6+#aGWW8# L#1+$)&/+1#)")/2'&'#34#$%+#aGWW#34#$%+#$.3A'$)6+#7EFG#3*#)5*#&'#=+23"1#$%+#'(3*+#34 $%&'#=33B#X'++#d,)2#+$#)/8-#;RR`Y8#S+:+,$%+/+''-#.+#5)B+#$%+#43//3.&"6#=,&+4#,+5),B'8#!$#()" c =+#'%3."#$%)$#$%+#(&,(0&$#&'#,+5),B)=/2#&"'+"'&$&:+#$3#:),&)$&3"'#&"#$ .. -#)"1#$%0'# aGWW #&' :+,2#%&6%8#9%&'#&'#"3$#$%+#()'+-#%3.+:+,-#43,#$%+#"+6)$&:+A'0**/2#,&**/+# v 88 -#.%&(%#&'#(30*/+1 $3#$%+#30$*0$#*,&5),&/2#$%,306%#$%+#'+(3"1A'$)6+#$,)"'&'$3,'#! Z#)"1#! O8#!"#*),$&(0/),-#$%+#*3,A $&3"#34# v 88#$%)$#)**+),'#)$#$%+#3*A)5*#30$*0$#&'#1+$+,5&"+1#=2#$%+#:3/$)6+#1&:&1+,#43,5+1#=2 $%+#30$*0$#,+'&'$)"(+'#34# ! Z#)"1#! O-

9%0'-

5 6O A v 6 ` v 88 AAAAAAAAAAAAAAAAAAA 5 6Z ^ 5 6O

$S=>
v 5 6O L 4 ≡ AAAAAA6 ` AAAAAAAAAAAAAAAAAAA A v 88 5 6Z ^ 5 6O

$S=>
S3.#0$&/&C&"6# 4 ( #4,35#M@8#XQ;8;;Y#6&:+' 4( L A ` ' 2Q ( 5 6; || 5 6P )' 2Z 5 6Z aGWW ≡ AAAAAAA L 4 L

$S=>
;

9%0'-#aGWW &'#34#$%+#43,5#( ' 2 5 6 ) #)"1#$%+,+43,+#&'#5)?&5&C+1#=2#'+/+($&"6#/3"6#(%)""+/'#0 X$3#&"(,+)'+# $ 4 Y-#)"1#3*+,)$&"6#)$#/3.# $ -$ 8

12.1.8 Design Trade-offs 9%+#*+,43,5)"(+#*),)5+$+,'#34#$%+#$.3A'$)6+#7EFG#)5*/&4&+,#),+#*,&5),&/2#1+$+,5&"+1#=2 $.3#1+'&6"#*),)5+$+,'] 1. !"#$2#:5)"$0$0(#3$%*'$)"#$/"-::#2$*%$#-/"$789;X!< 2. 9%+#3:+,1,&:+#:3/$)6+# $ -$ #)$#.%&(%#+)(%#$,)"'&'$3,#&'#3*+,)$+18# 9%,306%30$# $%&'# '+($&3"-# .+# %):+# 430"1# $%)$# )# /),6+,# 0# )"1# (3,,+'*3"1&"6/2# /),6+,# $ 4 &"(,+)'+'# $%+# )5*/&4&+,# 6)&"-# 7EWW# )"1# a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` AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A ;π ( & '8 ^ & '( )

$S=>
987

988 Chapter 12 Operational-Amplifier Circuits K3,#)"#,A(%)""+/#EFGKM9-#.+#()"#'%3.#$%)$#X'++#L**+"1&?#O8LY Q8U µ , $ -$ A 9 > ! AAAAAAAAAAAAAAAAAAAAAA ; ;π 0

$S=>
L#'&5&/),#,+/)$&3"'%&*#)**/&+'#43,#$%+#aEFG#$,)"'&'$3,-#.&$%# µ 1 #)"1# $ -$ #,+*/)(&"6# µ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

Example 12.1 D+# (3"(/01+# 30,# '$012# 34# $%+# $.3A'$)6+# 7EFG# 3*# )5*# .&$%# )# 1+'&6"# +?)5*/+8# I+$# &$# =+# ,+@0&,+1# $3 1+'&6"#$%+#(&,(0&$#$3#3=$)&"#)#1(#6)&"#34#PRRR#H[H8#L''05+#$%)$#$%+#):)&/)=/+#4)=,&()$&3"#$+(%"3/362#&'#34 $%+#R8UAµ5#$2*+#43,#.%&(%#$+ , #=# $+1 #=#R8U#H-# ?,′#=#;RR#µL[H;-# ?1′#=#VR#µL[H;-# $4, ′ =# $41 ′ #=#;R#H[µ5)"1#$..#=#$%%#=#Q8ZU#H8#93#)(%&+:+#)#,+)'3")=/+#1(#6)&"#*+,#'$)6+-#0'+#0#=#Q#µ5#43,#)//#1+:&(+'8#L/'3-#43, '&5*/&(&$2-#3*+,)$+#)//#1+:&(+'#)$#$%+#')5+# $-$ -#&"#$%+#,)"6+#34#R8;#H#$3#R8P#H8#\'+###=#;RR#µL-#)"1#$3 3=$)&"#)#%&6%+,#*2;-#)"1#%+"(+#)#%&6%+,#9:;-#0'+##.Z =#R8U 5L8#G*+(&42#$%+# / ⁄ 0 #,)$&3'#43,#)//#$,)"'&'$3,'8 L/'3#6&:+#$%+#:)/0+'#,+)/&C+1#43,#$%+#&"*0$#(3553"A531+#,)"6+-#$%+#5)?&505#*3''&=/+#30$*0$#'.&"6-#3&" )"1#368#L/'3#1+$+,5&"+#$%+#7EWW#)"1#aGWW#,+)/&C+18#!4#&Q#=#R8;#*K#)"1#&;#=#R8V#*K-#4&"1#$%+#,+@0&,+1 :)/0+'#34#&&#)"1#$%+#'+,&+'#,+'&'$)"(+#3#$3#*/)(+#$%+#$,)"'5&''&3"#C+,3#)$#8#=#∞#)"1#$3#3=$)&"#$%+#%&6%+'$ *3''&=/+#9+#(3"'&'$+"$#.&$%#)#*%)'+#5),6&"#34#OU°8#M:)/0)$+#$%+#:)/0+'#3=$)&"+1#43, #9 +#)"1#%38

Solution \'&"6#$%+#:3/$)6+A6)&"#+?*,+''&3"#&"#M@8#XQ;8;;YA v = ' 2Q ( 5 6; || 5 6P )' 2Z ( 5 6Z || 5 6O )

$4 ;# .Z Q $4 ;(# ⁄ ;) Q = AAAAAAAAAAAAAAAAA × AAA × AAAAAAAAAAAAA × AAAAAAAAAA × AAA × AAAAAAA ; ( # ⁄ ; ) $-$ ; # .Z $-$ $4 A = AAAAAAAA $-$

;

93#3=$)&"#4v#=#PRRR-#6&:+"#$4#=#;R#HPRR A PRRR = AAAAAAAA ; $-$

12.1 The Two-Stage CMOS Op Amp

$-$ = R8TQZ#H !*$*?)-&:$)"#$'#Y0&'#3$S/ ⁄ 0 U$'-)&*($*%$!=$-:3$!>I Q / ; #.Q = AAA ? 1′ AAAAA $ -$ ; 0 Q Q / QRR = AAA × VR AAAAA ; 0

× R8TQZ

;

Q

!"0(I / AAAAA 0

Q

;U#µ5 = AAAAAAAAAAAAAAAA Q#µ5

/ AAAAA 0

;

;U#µ5 = AAAAAAAAAAAAAAAA Q#µ5

-:3

;*'$!M$-:3$!N$1#$1'&)# Q / QRR = AAA × ;RR AAAAA ; 0

× R8TQZ

;

T

)*$*?)-&: / AAAAA 0

T

/ = AAAAA 0

QR#µ5 = AAAAAAAAAAAAAAAA Q#µ5

P

;*'$!OI Q / ;RR = AAA × VR AAAAA ; 0

× R8TQZ

;

U

!"0(I / AAAAA 0

U

UR#µ5 = AAAAAAAAAAAAAAAA Q#µ5

9&:/#$![$&($'#Y0&'#3$)*$/*:30/)$OPP$µZI$&)($S/ ⁄ 0U$'-)&*$("*023$?#$>
O

/ = ;8U AAAAA 0

U

Q;U#µ5 = AAAAAAAAAAAAAAAAAAA Q#µ5

;*'$!F$1#$1'&)# Q / URR = AAA × ;RR × AAAAA ; 0

× R8TQZ Z

!"0(I / AAAAA 0

Z

UR#µ5 = AAAAAAAAAAAAAAAA Q#µ5

;

989

990 Chapter 12 Operational-Amplifier Circuits

Example 12.1 continued

;&:-224I$2#)d($(#2#/)$ # WMK = ;R#µL-$)"0( / AAAAA 0

V

/ = R8Q AAAAA 0

U

U#µ5 = AAAAAAAAAAAAA Q#µ5

!"#$&:+0)$/*..*:,.*3#$'-:5#$/-:$?#$%*0:3$0(&:5$)"#$#G+'#((&*:$&:$XY<$S=>
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.%+,+# 3 %% ` 5 6U ` $ 4 ⁄ # 8#9%0'$4 ;(# ⁄ ; ) Q ;(# ⁄ ;) $ 7EWW ` AAAAAAAAAAAAAAAAA × AAA × AAAAAAAAAAAAA × ; × AAAAAAAAAAAAAAAAA × AAAAA4A $ -$ $ -$ # ; (# ⁄ ;) $4 A ` ; AAAAAAAA $ -$

;

;R ` ; AAAAAAAAAAAAA R8TQZ

;

` VRRR

M?*,+''+1#&"#1+(&=+/'-#.+#%):+ 7EWW ` ;R#/36#VRRR# ` OV #1J

9%+#aGWW#&'#1+$+,5&"+1#0'&"6#M@8#XQ;8PVY] aGWW## ` ' 2Q ( 5 6; || 5 6P )' 2Z 5 6Z $4 ;# .Z $ 4 ;(# ⁄ ;) Q ` AAAAAAAAAAAAAAAAA × AAA × AAAAAAAAAAAAA × AAAAAAAAAA × AAAAAAA ; ( # ⁄ ; ) $ -$ # .Z $ -$ $4 A ` ; AAAAAAAA $ -$

;

;R ` ; AAAAAAAAAAAAA R8TQZ

;

` VRRR

3,-#+?*,+''+1#&"#1+(&=+/'aGWW ` ;R#/36#VRRR# ` OV #1J !*$3#)#'.&:#$9:>$1#$0(#$XY<$S=><>EU$-:3$(0?()&)0)#$%*'$*2>I ;# .Z ; × R8U * 2; = ' 2Z = AAAAAAAAAA = AAAAAAAAAAAAAAAA = T8;#5L[H R8TQZ $-$ !"0(I LT

T8; × QR A = ZTO#E
12.2 The Folded-Cascode CMOS Op Amp

!*$.*@#$)"#$)'-:(.&((&*:$J#'*$)*$ 8 = ∞- $1#$(#2#/)$)"#$@-20#$*%$3$-( Q Q A = TQZ#Ω 3 = AAAAAAAAA = AAAAAAAAAAAAAAAAAAAAAAA LT * 2; T8; × QR ;*'$-$+"-(#$.-'5&:$*%$[O°I$)"#$+"-(#$("&%)$30#$)*$)"#$(#/*:3$+*2#$-)$ 9 = 9+ $.0()$?#$=O°I$)"-)$&(I LQ 9 $)" AAAAA+A = QU° 9:;

!"0(I 9+ = ZTO × $)" QU° = QOQ#E
12.2 The Folded-Cascode CMOS Op Amp C:$)"&($(#/)&*:$1#$()034$-:*)"#'$)4+#$*%$6789$*+,-.+$/&'/0&)K$)"#$%*23#3$/-(/*3#<$!"#$/&', /0&)$&($?-(#3$*:$)"#$%*23#3,/-(/*3#$-.+2&%&#'$()03$&:$9#/)&*:$[
12.2.1 The Circuit ;&50'#$=>$%*'. )"#$ &:+0)$ 3&%%#'#:)&-2$ +-&'I$ -:3$ !M$ -:3$ !N$ -'#$ )"#$ /-(/*3#$ )'-:(&()*'(<$ T#/-22$ )"-)$ %*'

991

992 Chapter 12 Operational-Amplifier Circuits VDD

IB

!

Cascode transistors

IB

Q1

Q2

"

Q3

Q4 VBIAS1 vo

Input differential pair

I

Q5

Q6

Q7

Q8

CL

Cascode current mirror

"VSS Figure 12.8 G$,0($0,+#34#$%+#43/1+1A()'(31+#7EFG#3*#)5*8

3&%%#'#:)&-2$&:+0)$(&5:-2(I$#-/"$*%$!=$-:3$!>$-/)($-($-$/*..*:,(*0'/#$-.+2&%&#'<$Z2(*$:*)# )"-)$)"#$5-)#$)#'.&:-2($*%$!M$-:3$!N$-'#$/*::#/)#3$)*$-$/*:()-:)$3/$@*2)-5#$S$cCZ9=U$-:3$"#:/# -'#$-) (&5:-2$5'*0:3<$!"0(I$%*'$3&%%#'#:)&-2$&:+0)$(&5:-2(I$#-/"$*%$)"#$)'-:(&()*'$+-&'($!=L!M -:3$ !>L!N$ -/)($ -($ -$ %*23#3,/-(/*3#$ -.+2&%&#'I$ (0/"$ -($ )"#$ *:#$ &:$ ;&5<$ [<=F<$ ]*)#$ )"-)$ )"# &:+0)$3&%%#'#:)&-2$ +-&'$&($ ?&-(#3$ ?4$ -$/*:()-:),/0''#:)$ (*0'/#$ #<$!"0($#-/"$ *%$!=$ -:3$ !>$&( *+#'-)&:5$-)$-$?&-($/0''#:)$ # ⁄ ; <$Z$:*3#$#Y0-)&*:$-)$#-/"$*%$)"#&'$3'-&:($("*1($)"-)$)"#$?&-( /0''#:)$*%$#-/"$*%$!M$-:3$!N$&($ ( # @ L # ⁄ ; )8 $9#2#/)&:5$ # @ = # $%*'/#($-22$)'-:(&()*'($)*$*+#'-)# -)$)"#$(-.#$?&-($/0''#:)$*%$ # ⁄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cCZ9=I$$cCZ9>I$-:3$$cCZ9M$-'#$:*)

12.2 The Folded-Cascode CMOS Op Amp VDD

Q9

Q10

VBIAS2

!

Q1

Q2

"

Q3

Q4 Ro4

VBIAS1

vO VBIAS3

Ro6 Q11

Q5

Q6

Q7

Q8

CL

"VSS Figure 12.9 L#53,+#(35*/+$+#(&,(0&$#43,#$%+#43/1+1A()'(31+#7EFG#)5*/&4&+,#34#K&68#Q;8V8

("*1:<$]#@#')"#2#((I$1#$-'#$&:)#'#()#3$&:$"*1$)"#$@-20#($*%$)"#(#$@*2)-5#($-'#$)*$?#$(#2#/)#3< !*1-'3$)"-)$#:3I$1#$#@-20-)#$)"#$&:+0)$/*..*:,.*3#$'-:5#$-:3$)"#$-22*1-?2#$*0)+0)$(1&:5<

12.2.2 Input Common-Mode Range and Output Swing !*$%&:3$)"#$&:+0)$/*..*:,.*3#$'-:5#I$2#)$)"#$)1*$&:+0)$)#'.&:-2($?#$)$)*5#)"#'$-:3$/*:, :#/)#3$)*$-$@*2)-5#$$#&) <$!"#$.-G&.0.$@-20#$*%$$#&)$&($2&.&)#3$?4$)"#$'#Y0&'#.#:)$)"-)$!=$-:3 !>$*+#'-)#$&:$(-)0'-)&*:$-)$-22$)&.#(<$!"0($$#&).-G$("*023$?#$-)$.*()$$+,$@*2)($-?*@#$)"# @*2)-5# -)$)"#$3'-&:($*%$!=$-:3$!><$!"#$2-))#'$@*2)-5#$&($3#)#'.&:#3$?4$$cCZ9=$-:3$.0()$-22*1$%*'$-$@*2), -5#$3'*+$-/'*(($!\$-:3$!=P$-)$2#-()$#Y0-2$)*$)"#&'$*@#'3'&@#$@*2)-5#I$ $-$` $=$ $-$QR 8$Z((0.&:5 )"-)$!\$-:3$!=P$-'#$&:3##3$*+#'-)#3$-)$)"#$#35#$*%$(-)0'-)&*:I$$#&).-G$1&22$?#

$#&)5)? = $.. L $-$` + $+,

$S=>
1"&/"$/-:$?#$2-'5#'$)"-:$$..I$-$(&5:&%&/-:)$&.+'*@#.#:)$*@#'$)"#$/-(#$*%$)"#$)1*,()-5#$/&', /0&)<$!"#$@-20#$*%$$cCZ9>$("*023$?#$(#2#/)#3$)*$4$)"#$'#Y0&'#3$@-20#$*%$#@"1"&2#$*+#'-)&:5 !\$-:3$!=P$-)$-$(.-22$@-20#$*%$ $-$ $S#<5$A$*'$(*U<$!"#$.&:&.0.$@-20#$*%$$#&)$/-:$?# *?)-&:#3$-(

$#&)5&" = L $%% + $-$QQ + $-$Q + $+,

$S=>U

!"#$+'#(#:/#$*%$)"#$)"'#("*23$@*2)-5#$$+ ,$&:$)"&($#G+'#((&*:$&:3&/-)#($)"-)$$#&).&:$&($:*)$(0%%&, /&#:)24$2*1<$B-)#'$&:$)"&($(#/)&*:$1#$("-22$3#(/'&?#$-:$&:5#:&*0($)#/":&Y0#$%*'$(*2@&:5$)"&( +'*?2#.<$;*'$)"#$)&.#$?#&:5I$:*)#$)"-)$)"#$@-20#$*%$$cCZ9M$("*023$?#$(#2#/)#3$)*$+'*@&3#$)"#

993

994 Chapter 12 Operational-Amplifier Circuits '#Y0&'#3$@-20#$*%$#$1"&2#$*+#'-)&:5$!==$-)$-$2*1$*@#'3'&@#$@*2)-5#<$6*.?&:&:5$XY(<$S=>U$+'*@&3#(

L $%% + $-$QQ + $-$Q + $+, ≤ $#&) ≤ $.. L $-$` + $+,

$S=>
!"#$0++#'$#:3$*%$)"#$-22*1-?2#$'-:5#$*%$v-$&($3#)#'.&:#3$?4$)"#$:##3$)*$.-&:)-&:$!=P$-:3$!N &:$(-)0'-)&*:<$]*)#$)"-)$!=P$1&22$*+#'-)#$&:$(-)0'-)&*:$-($2*:5$-($-:$*@#'3'&@#$@*2)-5#I$ $-$QR -++#-'($-/'*(($&)<$C)$%*22*1($)"-)$)*$.-G&.&J#$)"#$-22*1-?2#$+*(&)&@#$(1&:5$*%$v-$S-:3$$#&).-GUI 1#$("*023$(#2#/)$)"#$@-20#$*%$$cCZ9=$(*$)"-)$!=P$*+#'-)#($-)$)"#$#35#$*%$(-)0'-)&*:I$)"-)$&(I

$J!LGQ = $.. L $-$QR L $%* P

$S=>
!"#$0++#'$2&.&)$*%$v-$1&22$)"#:$?# v -5)?

= $.. L $-$QR L $-$P

$S=>
1"&/"$ &($ )1*$ *@#'3'&@#$ @*2)-5#( ?#2*1$ $..<$ !"#$ (&)0-)&*:$ &($ :*)$ -($ 5**3I$ "*1#@#'I$ -)$ )"# *)"#'$#:3K$9&:/#$)"#$@*2)-5#$-)$)"#$5-)#$*%$!F$&($−$%%$+$$*%[$+$$*%O$*'$#Y0&@-2#:)24$−$%%$+$$-$[ +$ $-$O$ +$ >$+,I$ )"#$ 2*1#()$ +*((&?2#$ v-$ &($ *?)-&:#3$ 1"#:$ !F$ '#-/"#($ )"#$ #35#$ *%$ (-)0'-)&*:I :-.#24I$1"#:$v-$3#/'#-(#($?#2*1$)"#$@*2)-5#$-)$)"#$5-)#$*%$!F$?4$$+,I$)"-)$&(I v -5&"

= −$%% + $-$O + $-$U + $+ ,

$S=>
]*)#$)"-)$)"&($@-20#$&($)1*$*@#'3'&@#$@*2)-5#($1AB8$-$)"'#("*23$@*2)-5#$-?*@#$ L $%% <$!"&($&($3'-1?-/V$*%$0)&2&J&:5$)"#$/-(/*3#$.&''*'<$!"#$+'*?2#.$/-:$?#$-22#@&-)#3$?4$0(&:5$-$.*3&% .&''*'$/&'/0&)I$-($1#$("-22$("*')24$(##<

EXERCISE 12.6 K3,#)#*),$&(0/),#1+'&6"#34#$%+#43/1+1A()'(31+#3*#)5*#34#K&68#Q;8`-#±Q8ZUAH#'0**/&+'#),+#0$&/&C+1#)"1 )// $,)"'&'$3,'#),+#3*+,)$+1#)$#3:+,1,&:+#:3/$)6+'#34#R8TAH#5)6"&$01+8#9%+#4)=,&()$&3"#*,3(+'' +5*/32+1 *,3:&1+'# $+, = $+1 = R8U#H8 # K&"1# $%+# &"*0$# (3553"A531+# ,)"6+# )"1# $%+# ,)"6+# )/A /3.+1#43, v-8 Ans. −R8UU#H#$3#+Q8VU#H^#−R8UU#H#$3#+Q8RU#H8

12.2.3 Voltage Gain 9%+# 43/1+1A()'(31+# 3*# )5*# &'# '&5*/2# )# $,)"'(3"10($)"(+# )5*/&4&+,# .&$%# )"# &"4&"&$+# &"*0$ ,+'&'$)"(+-#)#$,)"'(3"10($)"(+#*2#)"1#)"#30$*0$#,+'&'$)"(+#368#*2#&'#+@0)/#$3#'2#34#+)(%#34 $%+#$.3#$,)"'&'$3,'#34#$%+#1&44+,+"$&)/#*)&,-

* 2 = ' 2Q = ' 2;

$S=>
;(# ⁄ ;) # * 2 = AAAAAAAAAAAAAAAAA = AAAAAAAAAAA $-$Q $-$Q

$S=>
!"0(I

12.2 The Folded-Cascode CMOS Op Amp

!"#$ *0)+0)$ '#(&()-:/#$ 36$ &($ )"#$ +-'-22#2$ #Y0&@-2#:)$ *%$ )"#$ *0)+0)$ '#(&()-:/#$ *%$ )"#$ /-(/*3# -.+2&%&#'$-:3$)"#$*0)+0)$'#(&()-:/#$*%$)"#$/-(/*3#$.&''*'I$)"0(

3 6 = 3 6P || 3 6Z

$S=>
T#%#'#:/#$)*$;&5<$=><\$("*1($)"-)$)"#$'#(&()-:/#$36N$&($)"#$*0)+0)$'#(&()-:/#$*%$)"#$6e$)'-:, (&()*'$!N<$!"#$2-))#'$"-($-$'#(&()-:/#$ ( 5 6; || 5 6QR ) $&:$&)($(*0'/#$2#-3I$)"0(

3 6P ! ( ' 2P 5 6P ) ( 5 6; || 5 6QR )

$S=>
!"#$ '#(&()-:/#$ 36F$ &($ )"#$ *0)+0)$ '#(&()-:/#$ *%$ )"#$ /-(/*3#$ .&''*'$ -:3$ &($ )"0($ 5&@#:$ ?4 XY< S[<>OUI$)"0(

3 6Z ! ' 2Z 5 6Z 5 6V

$S=>
6*.?&:&:5$XY(<$S=>
3 6 = [ ' 2P 5 6P ( 5 6; || 5 6QR ) ] || ( ' 2Z 5 6Z 5 6V )

$S=>U

!"#$3/$*+#:,2**+$5-&:$/-:$:*1$?#$%*0:3$0(&:5$*2$-:3$36I$-(

4v = *2 36

$S=>
!"0(I

4 v = ' 2Q { [ ' 2P 5 6P ( 5 6; || 5 6QR ) ] || ( ' 2Z 5 6Z 5 6V ) }

$S=>
;&50'#$=><=P$("*1($)"#$#Y0&@-2#:),/&'/0&)$.*3#2$&:/203&:5$)"#$2*-3$/-+-/&)-:/#$&0I$1"&/" 1#$("-22$)-V#$&:)*$-//*0:)$("*')24< c#/-0(#$)"#$%*23#3,/-(/*3#$*+$-.+$&($-$)'-:(/*:30/)-:/#$-.+2&%&#'I$&)$"-($?##:$5&@#: )"#$:-.#$)+$4&#')2&3,#4&2!()2-*(#&2($,&%+3'.'$4,S678U<$C)($@#'4$"&5"$*0)+0)$'#(&()-:/#I ; 1"&/"$&($*%$)"#$*'3#'$*%$ ' 2 5 6 $S(##$XY<$=>U$&($1"-)$.-V#($&)$+*((&?2#$)*$'#-2&J#$-$'#2-)&@#24 "&5"$@*2)-5#$5-&:$&:$-$(&:52#$-.+2&%&#'$()-5#<$H*1#@#'I$(0/"$-$"&5"$*0)+0)$'#(&()-:/#$.-4$?# -$/-0(#$*%$/*:/#':$)*$)"#$'#-3#'W$-%)#'$-22I$&:$6"-+)#'$>I$1#$()-)#3$)"-)$-:$&3#-2$*+$-.+$"-($J#'*$*0)+0)$'#(&()-:/#f$!*$-22#@&-)#$)"&($/*:/#':$(*.#1"-)I$2#)$0($%&:3$)"#$/2*(#3,2**+$*0), +0)$'#(&()-:/#$*%$-$0:&)4,5-&:$%*22*1#'$%*'.#3$?4$/*::#/)&:5$)"#$*0)+0)$)#'.&:-2$*%$)"#$/&', /0&)$*%$;&5<$=><\$?-/V$)*$)"#$:#5-)&@#$&:+0)$)#'.&:-2<$9&:/#$)"&($%##3?-/V$&($*%$)"#$@*2)-5# (-.+2&:5$)4+#I$&)$'#30/#($)"#$*0)+0)$'#(&()-:/#$?4$)"#$%-/)*'$ ( Q + 4 β ) I$1"#'#$ 4 = 4 v -:3 β = Q- $)"-)$&(I

36 3 A ! AAAAA6 3 69 = AAAAAAAAAAAAAA Q + 4v 4v !

Vo

! Vid

GmVid

" "

$S=>
Ro

CL

Figure 12.10 G5)//A'&6")/# +@0&:)/+"$# (&,A (0&$# 34# $%+# 43/1+1A()'(31+# 7EFG# )5*/&4&+,8 S3$+# $%)$# $%&'# (&,(0&$# &'# &"# +44+($# )"# 3*+,)A $&3")/#$,)"'(3"10($)"(+#)5*/&4&+,#XF9LY8

995

996 Chapter 12 Operational-Amplifier Circuits 90?()&)0)&:5$%*'$4v$%'*.$XY<$S=>
Q 3 69 ! AAAAAAA *2

$S=>
1"&/"$ &($ -$ 5#:#'-2$ '#(02)$ )"-)$ -++2&#($ )*$ -:4$ 8!Z$ )*$ 1"&/"$ =PPg$ @*2)-5#$ %##3?-/V$ &( -++2<$;*'$*0'$+-')&/02-'$/&'/0&)I$ * 2 = ' 2QI$)"0(

3 69 = Q ⁄ ' 2Q

$S=>
9&:/#$'2=$&($*%$)"#$*'3#'$*%$=$.ZQAI$369$1&22$?#$*%$)"#$*'3#'$*%$=$VΩ<$Z2)"*05"$)"&($&($:*) @#'4$(.-22I$&)$&($'#-(*:-?2#$&:$@
$*%$)"#$(&.+2&/&)4$*%$)"#$*+,-.+$/&'/0&)$-($1#22$-($)"#$%-/) )"-)$)"&($)4+#$*%$*+$-.+$&($:*)$0(0-224$&:)#:3#3$)*$3'&@#$2*1,@-20#3$'#(&()&@#$2*-3(<

EXERCISE 12.7

9%+#7EFG#3*#)5*#34#K&6'8#Q;8V#)"1#Q;8`#&'#4)=,&()$+1#&"#)#*,3(+''#43,#.%&(%# $4, ′ #=# $41 ′ #=#;R H[µ58 !4#)//#1+:&(+'# %):+#QAµ5#(%)""+/# /+"6$%# )"1# ),+#3*+,)$+1#)$#+@0)/#3:+,1,&:+# :3/$)6+'#34 R8;AH#5)6"&$01+-#4&"1#$%+#:3/$)6+#6)&"#3=$)&"+18#!4#+)(%#34#!Q#$3#!V#&'#=&)'+1#)$#QRR#µL-#.%)$#:)/0+ 34#36#&'#3=$)&"+1b Ans. QT-TTT#H[H^#QT8T#EΩ

12.2.4 Frequency Response ;'*.$9#/)&*:$\<=P$1#$/-:$1'&)#

$ *2 36 AAAAAA6A = AAAAAAAAAAAAAAAAAAAAAAA A $ <( Q + 8& 0 3 6

$S=>
!"0(I$)"#$3*.&:-:)$+*2#$"-($-$%'#Y0#:/4$9 :I

Q 9: = AAAAAAAAAAAAAAAAAAA ; π &0 36

$S=>
-:3$)"#$0:&)4,5-&:$%'#Y0#:/4$9 +$1&22$?#

*2 A 9+ = * 2 3 6 9: = AAAAAAAAAAAA ; π &0

$S=><[PU

;'*.$-$3#(&5:$+*&:)$*%$@
I$)"#$@-20#$*%$&0$("*023$?#$(0/"$)"-)$-)$9$ =$9 +$)"#$#G/#(($+"-(# '#(02)&:5$%'*.$)"#$:*:3*.&:-:)$+*2#($&($(.-22$#:*05"$)*$+#'.&)$)"#$'#Y0&'#3$+"-(#$.-'5&:$)* ?#$-/"&#@#3<$C%$&0$&($:*)$2-'5#$#:*05"$)*$-/"&#@#$)"&($+0'+*(#I$&)$/-:$?#$-05.#:)#3<

12.2 The Folded-Cascode CMOS Op Amp

C)$&($&.+*')-:)$)*$:*)#$)"#$3&%%#'#:)$#%%#/)($*%$&:/'#-(&:5$)"#$2*-3$/-+-/&)-:/#$*:$)"#$*+#', -)&*:$*%$)"#$)1*$*+,-.+$/&'/0&)($1#$"-@#$()03<$C:$)"#$)1*,()-5#$/&'/0&)I$&%$&0$&($&:/'#-(#3I )"#$%'#Y0#:/4$*%$)"#$(#/*:3$+*2#$3#/'#-(#(I$)"#$#G/#(($+"-(#$("&%)$-)$9$=$9 +$&:/'#-(#(I$-:3$)"# +"-(#$ .-'5&:$ &($ '#30/#3<$ H#'#I$ *:$ )"#$ *)"#'$ "-:3I$ 1"#:$ &0$ &($ &:/'#-(#3I$ 9 +$ 3#/'#-(#(I$ ?0) )"# +"-(#$.-'5&:$&:/'#-(#(<$C:$*)"#'$1*'3(I$-$"#-@&#'$/-+-/&)&@#$2*-3$3#/'#-(#($)"#$?-:31&3)" *%$)"#$%*23#3,/-(/*3#$-.+2&%&#'$?0)$3*#($:*)$&.+-&'$&)($'#(+*:(#$S1"&/"$"-++#:($1"#:$)"# +"-(#$ .-'5&:$ 3#/'#-(#(U<$ 8%$ /*0'(#I$ &%$ -:$ &:/'#-(#$ &:$ &0$ &($ -:)&/&+-)#3$ &:$ )"#$ )1*,()-5# 3*A)5* $/-(#I$)"#$3#(&5:#'$/-:$&:/'#-(#$&&I$)"0($3#/'#-(&:5$9 +$ -:3$'#()*'&:5$)"#$+"-(#$.-'5&: )*$&)($'#Y0&'#3$@-20#<

12.2.5 Slew Rate Z($ 3&(/0((#3$ &:$ 9#/)&*:$ =><=$/0)( *%%$ -:3$ !=$ /*:30/)($ )"#$ #:)&'#$ ?&-($ /0''#:)$ #<$ D#$ (##$ )"-)$ !M$ 1&22$ :*1$ /-''4$ -$ /0''#:) ( # @ L # )I$ -:3$ !N$ 1&22$ /*:30/)$ -$ /0''#:)$ #@<$ !"#$ /0''#:)$ .&''*'$ 1&22$ (##$ -:$ &:+0)$ /0''#:) *% ( # @ L # )$)"'*05"$!O$-:3$![$-:3$)"0($&)($*0)+0)$/0''#:)$&:$)"#$3'-&:$*%$!F$1&22$?#$( # @ L # )8 C) %*22*1($ )"-)$ -)$ )"#$ *0)+0)$ :*3#$ )"#$ /0''#:)$ )"-)$ 1&22$ %2*1$ &:)*$ &0$ 1&22$ ?#$ #N$ −$ #F$ =$ #@$− ( # @ L # ) = #8$!"0($)"#$*0)+0)$v-$1&22$?#$-$'-.+$1&)"$-$(2*+#$*%$ # ⁄ & 0 $1"&/"$&($)"#$(2#1$'-)#I

# %3 = AAAAAA &0

$S=><[=U

]*)#$ )"-)$ )"#$ '#-(*:$ %*'$ (#2#/)&:5$ # @ > # $ &($ )*$ -@*&3$ )0':&:5$ *%%$ )"#$ /0''#:)$ .&''*'$ /*., +2#)#24W$ &%$ )"#$ /0''#:)$ .&''*'$ )0':($ *%%I$ )"#$ *0)+0)$ 3&()*')&*:$ &:/'#-(#(<$ !4+&/-224I$ #@$ &($ (#) =Pg$)*$>Pg$2-'5#'$)"-:$#<$;&:-224I$XY(<$S=><[PUI$S=><[=UI$ -:3$S=>
%3 = ; π 9+ #$-$Q

$S=><[>U

1"&/"$ &($ &3#:)&/-2$ )*$ )"#$ /*''#(+*:3&:5$ '#2-)&*:("&+$ &:$ )"#$ /-(#$ *%$ )"#$ )1*,()-5#$ 3#(&5:< ]*)#I$"*1#@#'I$)"-)$)"&($'#2-)&*:("&+$-++2&#($*:24$1"#:$ # @ > #8

Example 12.2 6*:(&3#'$-$3#(&5:$*%$)"#$%*23#3,/-(/*3#$*+$-.+$*%$;&5<$=><\$%*'$1"&/"$#$=$>PP$µZI$#@$=$>OP$µZI$$-:3 ; $ -$ $%*'$-22$)'-:(&()*'($&($P<>O$A<$Z((0.#$)"-)$)"#$%-?'&/-)&*:$+'*/#(($+'*@&3#($ ? ,′$=$=PP µL[H - $ ? 1′ $=$NP ; µL[H I$ $ 4′ = ;R#H[µ58 $ $.. = $%% = ;8U#H- $-:3$ $ + = R8OU#H8$B#)$-22$)'-:(&()*'($"-@#$ 0 = Q#µ5 -:3$-((0.#$)"-)$ & 0 = U#*K8 $;&:3$#.I$'2I$56I$-:3$// 0$%*'$-22$)'-:(&()*'(<$;&:3$)"#$-22*1-?2#$'-:5#$*%$ $#&) -:3$*%$)"#$*0)+0)$@*2)-5#$(1&:5<$h#)#'.&:#$)"#$@-20#($*%$4v I$9 +I$ 9:I$ -:3$%3<$D"-)$&($)"#$+*1#'$3&((&+-)&*: *%$)"#$*+$-.+i

Solution ;'*.$)"#$5&@#:$@-20#($*%$#$-:3$#@$1#$/-:$3#)#'.&:#$)"#$3'-&:$/0''#:)$#.$%*'$#-/"$)'-:(&()*'<$!"#$)'-:(/*:, 30/)-:/#$*%$#-/"$3#@&/#$&($%*0:3$0(&:5 ;# . ;# A ' 2 = AAAAAAAA.A = AAAAAAAAA $ -$ R8;U

997

998 Chapter 12 Operational-Amplifier Circuits

Example 12.2 continued

-:3$)"#$*0)+0)$'#(&()-:/#$56$%'*.

$4 ;R A = AAAAAA 5 6 = AAAAAAAA #. #.

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1004 Chapter 12 Operational-Amplifier Circuits !1*$.*'#$)'-:(&()*'(I$!=E$-:3$!=\I$)-V#$+-')$&:$)"#$3/$?&-($+'*/#((<$!"#$+0'+*(#$*%$!=E -:3$!=\$&($)*$#()-?2&("$)1*$$@D$3'*+($?#)1##:$)"#$?-(#($*%$)"#$*0)+0)$)'-:(&()*'($!=N$-:3$!>P<

12.3.2 Short-Circuit Protection Circuitry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
12.3.3 The Input Stage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

12.3.4 The Second Stage !"#$(#/*:3$*'$&:)#'.#3&-)#$()-5#$&($/*.+*(#3$*%$!=FI$!=[I$!=M@I$-:3$)"#$)1*$'#(&()*'($3E$-:3 3\< !'-:(&()*'$ !=F$ -/)($ -($ -:$ #.&))#'$ %*22*1#'I$ )"0($ 5&@&:5$ )"#$ (#/*:3$ ()-5#$ -$ "&5"$ &:+0)

12.3 The 741 Op-Amp Circuit

'#(&()-:/#<$!"&($.&:&.&J#($)"#$2*-3&:5$*:$)"#$&:+0)$()-5#$-:3$-@*&3($2*(($*%$5-&:<$Z2(*I -33&:5$!=F$1&)"$&)($OP,VΩ$#.&))#'$'#(&()-:/#$S1"&/"$&($(&.&2-'$)*$![$-:3$3MU$&:/'#-(#($)"# (4..#)'4$ *%$)"#$%&'()$ ()-5#$ -:3$)"0($&.+'*@#($&)($67TT<$ !'-:(&()*'$ !=[$-/)($-($ -$/*., .*:,#.&))#'$ -.+2&%&#'$ 1&)"$ -$ =PP,Ω$ '#(&()*'$ &:$ )"#$ #.&))#'<$ C)($ 2*-3$ &($ /*.+*(#3$ *%$ )"# "&5"$*0)+0)$'#(&()-:/#$*%$)"#$1,1$/0''#:)$(*0'/#$!=M@$&:$+-'-22#2$1&)"$)"#$&:+0)$'#(&()-:/# *%$)"#$*0)+0)$()-5#$S(##:$2**V&:5$&:)*$)"#$?-(#$*%$!>MU<$_(&:5$-$)'-:(&()*'$/0''#:)$(*0'/#$-( -$2*-3$'#(&()-:/#$S=H+P,3cQ3#/-3#$5-&:$'*22*%%$1&)"$-$0:&)4,5-&:$?-:31&3)"$*%$-?*0)$=$7HJ<$C)$("*023 ?#$ +*&:)#3$ *0)$ )"-)$ -2)"*05"$ &&$ &($ (.-22$ &:$ @-20#I$ )"#$ /"&+$ -'#-$ )"-)$ &)$ *//0+&#($ &($ -?*0) =M )&.#($)"-)$*%$-$()-:3-'3$,1,$)'-:(&()*'f

12.3.5 The Output Stage !"#$+0'+*(#$*%$)"#$*0)+0)$()-5#$S6"-+)#'$==U$&($)*$+'*@&3#$)"#$-.+2&%&#'$1&)"$-$2*1$*0)+0) '#(&()-:/#<$C:$-33&)&*:I$)"#$*0)+0)$()-5#$("*023$?#$-?2#$)*$(0++24$'#2-)&@#24$2-'5#$2*-3$/0', '#:)($1&)"*0)$3&((&+-)&:5$-:$0:3024$2-'5#$-.*0:)$*%$+*1#'$&:$)"#$C6<$!"#$[N=$0(#($-:$#%%&, /&#:)$/2-(($Zc$*0)+0)$()-5#I$1"&/"$1#$("-22$()034$&:$3#)-&2$&:$9#/)&*:$=>PI$1"#'#$!>P$&( -$8B78+5=+E"1,1$S(##$Z++#:3&G$ZU<$!'-:(&()*'($!=E$-:3$!=\$-'#$%#3$?4$/0''#:)$(*0'/#$!=M4$-:3 ?&-($)"#$*0)+0)$)'-:(&()*'($!=N$-:3$!>P<$!'-:(&()*'$!>M$S1"&/"$&($-:*)"#'$(0?()'-)#$1,1U$-/)($-( -:$ #.&))#'$ %*22*1#'I$ )"0($ .&:&.&J&:5$ )"#$ 2*-3&:5$ #%%#/)$ *%$ )"#$ *0)+0)$ ()-5#$ *:$ )"#$ (#/*:3 ()-5#<

12.3.6 Device Parameters C:$)"#$%*22*1&:5$(#/)&*:($1#$("-22$/-''4$*0)$-$3#)-&2#3$-:-24(&($*%$)"#$[N=$/&'/0&)<$;*'$)"# ()-:3-'3$,1,$-:3$1,1$)'-:(&()*'(I$)"#$%*22*1&:5$+-'-.#)#'($1&22$?#$0(#3K L QP

,1,]

# % = QR

1,1]

# % = QR

L-# β = ;RR-# $4 = Q;U#H

L QP

L-# β = UR-# $4 = UR#H

C:$ )"#$ [N=$ /&'/0&)$ )"#$ :*:()-:3-'3$ 3#@&/#($ -'#$ !=MI$ !=NI$ -:3$ !>P<$ !'-:(&()*'$ !=M$ 1&22$ ?# -((0.#3$)*$?#$#Y0&@-2#:)$)*$)1*$)'-:(&()*'(I$!=M4$-:3$!=M@I$1&)"$+-'-22#2$?-(#L#.&))#'$R0:/, )&*:($-:3$"-@&:5$)"#$%*22*1&:5$(-)0'-)&*:$/0''#:)(K

# %4 = R8;U × QR

L QP

L

# %@ = R8OU × QR

L QP

L

!'-:(&()*'($!=N$-:3$!>P$1&22$?#$-((0.#3$)*$#-/"$"-@#$-:$-'#-$)"'##$)&.#($)"-)$*%$-$()-:3-'3 3#@&/#<$80)+0)$)'-:(&()*'($0(0-224$"-@#$'#2-)&@#24$2-'5#$-'#-(I$)*$?#$-?2#$)*$(0++24$2-'5#$2*-3 /0''#:)($-:3$3&((&+-)#$'#2-)&@#24$2-'5#$-.*0:)($*%$+*1#'$1&)"$*:24$-$.*3#'-)#$&:/'#-(#$&: 3#@&/#$)#.+#'-)0'#<

1005

1006 Chapter 12 Operational-Amplifier Circuits

EXERCISES 12.10

K3,#$%+#'$)"1),1#,1,#$,)"'&'$3,#.%3'+#*),)5+$+,'#),+#6&:+"#&"#G+($&3"#Q;8T8Z-#4&"1#)**,3?&5)$+ :)/0+'#43,#$%+#43//3.&"6#*),)5+$+,'#)$##&#=#Q#5L]#$@D-#'2-#5E-#5π -#)"1#568 Ans. ZTT#5H^#PR#5L[H^#;U#Ω^#U#BΩ^#Q;U#BΩ

12.11

K3,#$%+#(&,(0&$#&"#K&68#MQ;8QQ-#"+6/+($#=)'+#(0,,+"$'#)"1#0'+#$%+#+?*3"+"$&)/#<& _v@D#,+/)$&3"'%&*#$3 '%3.#$%)$ # %T # %P # T = # Q AAAAAAAAAAAA A # %Q # %;

!15 V I1 Q3 Q1 I3

Q2

Q4

"15 V

Figure E12.11

12.4 DC Analysis of the 741 C:$ )"&($ (#/)&*:I$ 1#$ ("-22$ /-''4$ *0)$ -$ 3/$ -:-24(&($ *%$ )"#$ [N=$/&'/0&)$ )*$ 3#)#'.&:#$ )"#$ ?&-( +*&:)$ *%$ #-/"$ 3#@&/#<$ ;*'$ )"#$ 3/$ -:-24(&($ *%$ -:$ *+,-.+$ /&'/0&)I$ )"#$ &:+0)$ )#'.&:-2($ -'# 5'*0:3#3<$!"#*'#)&/-224$(+#-V&:5I$)"&($("*023$'#(02)$&:$J#'*$3/$@*2)-5#$-)$)"#$*0)+0)<$H*1, #@#'I$?#/-0(#$)"#$*+$-.+$"-($@#'4$2-'5#$5-&:I$-:4$(2&5")$-++'*G&.-)&*:$&:$)"#$-:-24(&($1&22 ("*1$)"-)$)"#$*0)+0)$@*2)-5#$&($%-'$%'*.$?#&:5$J#'*$-:3$&($/2*(#$)*$#&)"#'$+$&&$*'$L$DD<$C: -/)0-2$ +'-/)&/#I$ -:$*+$ -.+$ 2#%)$*+#:,2**+$1&22$"-@#$ -:$*0)+0)$@*2)-5#$(-)0'-)#3$/2*(#$)* *:#$*%$)"#$)1*$(0++2&#(<$!*$*@#'/*.#$)"&($+'*?2#.$&:$)"#$3/$-:-24(&(I$&)$1&22$?#$-((0.#3 )"-)$)"#$*+$-.+$&($/*::#/)#3$&:$-$:#5-)&@#$%##3?-/V$2**+$)"-)$()-?&2&J#($)"#$*0)+0)$3/$@*2), -5#$)*$J#'*$@*2)(<

12.4 DC Analysis of the 741

1007

12.4.1 Reference Bias Current !"#$ '#%#'#:/#$ ?&-($ /0''#:)$ #TX;$ &($ 5#:#'-)#3$ &:$ )"#$ ?'-:/"$ /*.+*(#3$ *%$ )"#$ )1*$ 3&*3#, /*::#/)#3$)'-:(&()*'($!==$-:3$!=>$-:3$'#(&()*'$3O<$D&)"$'#%#'#:/#$)*$;&5<$=><=MI$1#$/-:$1'&)#

$&& L $D@Q; L $@DQQ L ( L $DD ) A # WMK = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 3U ;*'$$&& =$$DD =$=O$A$-:3$$@D== =$$D@=> !$P<[$AI$1#$"-@#$#TX; =$P<[M$.Z<

12.4.2 Input-Stage Bias !'-:(&()*'$!==$&($?&-(#3$?4$#TX;I$-:3$)"#$@*2)-5#$3#@#2*+#3$-/'*(($&)$&($0(#3$)*$?&-($!=PI$1"&/" "-($-$(#'&#($#.&))#'$'#(&()-:/#$3N<$!"&($+-')$*%$)"#$/&'/0&)$&($'#3'-1:$&:$;&5<$=><=N$-:3$/-:$?# '#/*5:&J#3$ -($ )"#$ D&32-'$ /0''#:)$ (*0'/#$ ()03$ &:$ 9#/)&*:$ [
$@DQQ L $@DQR = # &QR 3 P !"0(

# WMK A = #&QR 3 P $ > /" AAAAAAAA #&QR

$S=><[OU

1"#'#$&)$"-($?##:$-((0.#3$)"-)$#%=P$=$#%==<$90?()&)0)&:5$)"#$V:*1:$@-20#($%*'$#TX;$-:3$3NI$)"&($#Y0-, )&*:$/-:$?#$(*2@#3$?4$)'&-2$-:3$#''*'$)*$3#)#'.&:#$#&=P<$;*'$*0'$/-(#I$)"#$'#(02)$&($#&=P =$=\$µZ<

Figure 12.14 9%+# D&1/),# (0,,+"$# '30,(+# $%)$ =&)'+'#$%+#&"*0$#'$)6+8

EXERCISE D12.12 g+'&6"#$%+#D&1/),#(0,,+"$#'30,(+#34#K&68#Q;8QP#$3#6+"+,)$+#)#(0,,+"$##&QR =#QR#µL#6&:+"#$%)$##WMK = Q#5L8#!4#)$#)#(3//+($3,#(0,,+"$#34#Q#5L-#$@D = #R8O#H-#4&"1#$@DQQ#)"1#$@DQR8 Ans. 3P#=#QQ8U#BΩ^#$@DQQ#=#R8O#H^#$@DQR#=#R8UVU#H

1008 Chapter 12 Operational-Amplifier Circuits

!I

!I

Figure 12.15 9%+#1(#)")/2'&'#34#$%+#OPQ#&"*0$#'$)6+8

H-@&:5$3#)#'.&:#3$#&=PI$1#$+'*/##3$)*$3#)#'.&:#$)"#$3/$/0''#:)$&:$#-/"$*%$)"#$&:+0),()-5# )'-:(&()*'(<$j-')$*%$)"#$&:+0)$()-5#$&($'#3'-1:$&:$;&5<$=><=O<$;'*.$(4..#)'4I$1#$(##$)"-)

# &Q = # &; h#:*)#$)"&($/0''#:)$?4$#<$D#$(##$)"-)$&%$)"#$,1,$β$&($"&5"I$)"#:

# DT = # DP ! ## -:3$)"#$?-(#$/0''#:)($*%$!M$-:3$!N$-'#$#Y0-2I$1&)"$-$@-20#$*%$ # ⁄ ( β : + Q ) ! # ⁄ β : I$1"#'#$β: 3#:*)#($β$*%$)"#$1,1$3#@&/#(< !"#$/0''#:)$.&''*'$%*'.#3$?4$!E$-:3$!\$&($%#3$?4$-:$&:+0)$/0''#:)$*%$>#<$_(&:5$)"#$'#(02) &:$XY<$S[
;# # &` = AAAAAAAAAAAAAAAAAAAAAA Q + ; ⁄ β: D#$/-:$:*1$1'&)#$-$:*3#$#Y0-)&*:$%*'$:*3#$I$&:$;&5<$=><=O$-:3$)"0($3#)#'.&:#$)"#$@-20# *% #<$C%$ β : ###Q- $)"#:$)"&($:*3#$#Y0-)&*:$5&@#(

;# ! # &QR ;*'$)"#$[N=I$#&=P =$=\$µZW$)"0($#"!$\
# &Q = # &; ! # &T = # &P = `8U#µL Z)$)"&($+*&:)I$1#$("*023$:*)#$)"-)$)'-:(&()*'($!=$)"'*05"$!NI$!EI$-:3$!\$%*'.$-$2$1&#'=$0 .$$-<&(>,3))+I$1"&/"$1*'V($)*$()-?&2&J#$)"#$@-20#$*%$#$-)$-++'*G&.-)#24$ # &QR ⁄ ;<$!*$-++'#/&, -)#$ )"&($ %-/)I$ -((0.#$ )"-)$ %*'$ (*.#$ '#-(*:$ )"#$ /0''#:)$ #$ &:$ !=$ -:3$ !>$ &:/'#-(#(<$ !"&($ 1&22

12.4 DC Analysis of the 741

IC3 ! I

IC4 ! I Q7

Q16

!0

!I

IB 16 ! 0 !I

Q5

Q6 I/& N

I/& N !I

R1

R3

!I

R2

"VEE Figure 12.16 9%+#1(#)")/2'&'#34#$%+#OPQ#&"*0$#'$)6+-#(3"$&"0+18

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` # &P ! #8 #9,)"'&'$3,'# ! U#)"1# ! Z#),+#&1+"$&()/#)"1#%):+#+@0)/#,+'&'$)"(+'# 3 Q#)"1# 3 ;#&" $%+&,#+5&$$+,'^#$%0'# &U ` # &Z

$S=><[FU

S3.#&4#$%+#=)'+#(0,,+"$'#34#! O#)"1# ! QZ#()"#=+#"+6/+($+1-#$%+" # &U ! # &T ! #

$S=><[[U

# &Z ! # &P ! #

$S=><[EU

)"1

9%0'#=3$%#$%+#'255+$,2#34# ! U#)"1# ! Z#)"1#$%+#"31+#+@0)$&3"'#)$#$%+&,#(3//+($3,'#43,(+#$%+&, (0,,+"$'#$3#=+#+@0)/#)"1#$3#+@0)/##8#L'#.&//#=+#'%3."#'%3,$/2-#"3$#3"/2#),+#$%+#=)'+#(0,,+"$' 34# ! O #)"1# ! QZ #"+6/&6&=/+-#=0$#$%+&,#:)/0+'#),+#)/'3#,+)'3")=/2#(/3'+-#.%&(%#&'#)"#)11+1#%+/*8 9%+#=&)'#(0,,+"$#34#!O#()"#=+#1+$+,5&"+1#4,35

;# $@DZ + #3 ; A # &O ! # DO = AAAAAA + AAAAAAAAAAAAAAAAAAAAAAAA βJ 3T

$S=><[\U

1009

1010 Chapter 12 Operational-Amplifier Circuits 1"#'#$βJ$3#:*)#($β$*%$)"#$,1,$)'-:(&()*'(<$!*$3#)#'.&:#$$@DF$1#$0(#$)"#$)'-:(&()*'$#G+*:#:, )&-2$'#2-)&*:("&+$-:3$1'&)#

# $@DZ = $ > #/"# AAAA #%

90?()&)0)&:5$ #% =$ =P−=N$ Z$ -:3$ # =$ \<[\U$4($#&[ =$=P
12.4.3 Input Bias and Offset Currents !"#$'2+*#,<'&!,(*44$2#$*%$-:$*+$-.+$&($3#%&:#3$S6"-+)#'($>$-:3$EU$-(

# @Q ^ # @; A # @ = AAAAAAAAAAAAAAAAAA ; ;*'$)"#$[N=$1#$*?)-&:

# # @ = AAAAAA

βJ

_(&:5$βJ =$>PPI$4($#@ =$N[I$)"#$&:+0)$?-(#$/0''#:)($1&22 :*)$?#$#Y0-2<$e&@#:$)"#$@-20#$*%$)"#$ β$.&(.-)/"I$*:#$/-:$0(#$XY<$SE<=M=U$)*$/-2/02-)#$)"# '2+*#,)..!$#,(*44$2#I$3#%&:#3$-(

# -% = # @Q L # @;

12.4.4 Input Offset Voltage ;'*.$6"-+)#'$E$1#$V:*1$)"-)$)"#$&:+0)$*%%(#)$@*2)-5#$&($3#)#'.&:#3$+'&.-'&24$?4$.&(.-)/"#( ?#)1##:$)"#$)1*$(&3#($*%$)"#$&:+0)$()-5#<$C:$)"#$[N=$*+$-.+I$)"#$&:+0)$*%%(#)$@*2)-5#$&($30#$)* .&(.-)/"#($?#)1##:$!=$-:3$!>I$?#)1##:$!M$-:3$!NI$?#)1##:$!O$-:3$!FI$-:3$?#)1##:$3=$-:3 3><$X@-20-)&*:$*%$)"#$/*.+*:#:)($*%$$-%$/*''#(+*:3&:5$)*$)"#$@-'&*0($.&(.-)/"#($%*22*1($)"# .#)"*3$*0)2&:#3$&:$9#/)&*:$E
12.4.5 Input Common-Mode Range !"#$'2+*#,()%%)20%)-$,4&21$$&($)"#$'-:5#$*%$&:+0)$/*..*:,.*3#$@*2)-5#($*@#'$1"&/" )"#$&:+0)$()-5#$'#.-&:($&:$)"#$2&:#-'$-/)&@#$.*3#<$T#%#'$)*$;&5<$=><=M<$D#$(##$)"-)$&:$)"#$[N= /&'/0&)$)"#$&:+0)$/*..*:,.*3#$'-:5#$&($3#)#'.&:#3$-)$)"#$0++#'$#:3$?4$(-)0'-)&*:$*%$!=$-:3 !>I$-:3$-)$)"#$2*1#'$#:3$?4$(-)0'-)&*:$*%$!M$-:3$!N<

EXERCISE 12.13

S+6/+($#$%+#:3/$)6+#1,3*'#)(,3''#3Q#)"1#3;#)"1#)''05+#$%)$#$&& =#$DD =#QU#H8#G%3.#$%)$#$%+#&"*0$ (3553"A531+#,)"6+#34#$%+#OPQ#&'#)**,3?&5)$+/2#_Q;8` H#$3#+QP8O H8#XL''05+#$%)$#$@D#!#R8Z#H#)"1 $%)$#$3#):3&1#')$0,)$&3"#$&@#'#−R8T#H#43,#)"#,1,#$,)"'&'$3,-#)"1#$@&#'#−R8T#H#43,#)#1,1#$,)"'&'$3,8Y

12.4 DC Analysis of the 741

12.4.6 Second-Stage Bias C%$1#$:#52#/)$)"#$?-(#$/0''#:)$*%$!>M$)"#:$1#$(##$%'*.$;&5<$=><=M$)"-)$)"#$/*22#/)*'$/0''#:)$*% !=[$&($-++'*G&.-)#24$#Y0-2$)*$)"#$/0''#:)$(0++2$?4$/0''#:)$(*0'/#$!=M@<$c#/-0(#$!=M@$"-($(/-2#$/0''#:)$P<[O$)&.#($)"-)$*%$!=>I$&)($/*22#/)*'$/0''#:)$1&22$?#$#&=M@$ !$P<[O#TX;I$1"#'#$1# "-@#$-((0.#3$)"-)$ β : ###Q<$!"0($#&=M@ =$OOP$µZ$-:3$#&=[$!$OOP$µZ<$Z)$)"&($/0''#:)$2#@#2$)"# ?-(#L#.&))#'$@*2)-5#$*%$!=[$&(

# &QO A = ZQV#5H $@DQO = $> /" AAAAAAA #% !"#$/*22#/)*'$/0''#:)$*%$!=F$/-:$?#$3#)#'.&:#3$%'*.

# DQO 3 V + $@DQO A # &QZ ! # DQZ = # @QO + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 3` !"&($ /-2/02-)&*:$ 4($ #&=F =$ =F<>$ µZ<$ ]*)#$ )"-)$ )"#$ ?-(#$ /0''#:)$ *%$ !=F$ -)$ P
12.4.7 Output-Stage Bias ;&50'#$=><=[$("*1($)"#$*0)+0)$()-5#$*%$)"#$[N=$1&)"$)"#$("*'),/&'/0&),+'*)#/)&*:$/&'/0&)'4 *.&))#3<$ 60''#:)$ (*0'/#$ !=M4$ 3#2&@#'($ -$ /0''#:)$ *%$ P<>O#TX;$ S?#/-0(#$ #%$ *%$ !=M 4$ &($ P<>O

! 0.25IREF

Figure 12.17 9%+#OPQ#30$*0$#'$)6+#.&$%30$#$%+#'%3,$A(&,(0&$#*,3$+($&3"#1+:&(+'8

1011

1012 Chapter 12 Operational-Amplifier Circuits )&.#($)"#$#%$*%$!=>U$)*$)"#$:#)1*'V$/*.+*(#3$*%$!=EI$!=\I$-:3$3=P<$C%$1#$:#52#/)$)"#$?-(# /0''#:)($*%$!=N$-:3$!>PI$)"#:$)"#$#.&))#'$/0''#:)$*%$!>M$1&22$-2(*$?#$#Y0-2$)*$P<>O#TX;<$!"0(

# &;T ! # D;T ! R8;U# WMK = QVR#µL !"0($1#$(##$)"-)$)"#$?-(#$/0''#:)$*%$!>M$&($*:24$ QVR ⁄ UR $=$M
# DQV = QVR L QU = QZU#µL Z2(*I

# &QV ! # DQV = QZU#µL Z)$ )"&($ @-20#$ *%$ /0''#:)$ 1#$ %&:3$ )"-)$ $@D=E$ =$ OEE$ .AI$ 1"&/"$ &($ Y0&)#$ /2*(#$ )*$ )"#$ @-20# -((0.#3<$!"#$?-(#$/0''#:)$*%$!=E$&($=FO/ >PP$=$P
# &Q` ! # DQ` = QU8V#µL !"#$@*2)-5#$3'*+$-/'*(($)"#$?-(#L#.&))#'$R0:/)&*:$*%$!=\$/-:$:*1$?#$3#)#'.&:#3$-(

# &Q` A = UTR#5H $@DQ` = $ > #/"# AAAAAAA #% Z($.#:)&*:#3$&:$9#/)&*:$=>P<$!"&($@*2)-5#$3'*+I$$@@I$/-:$?# :*1$/-2/02-)#3$-(

$@@ = $@DQV + $@DQ` = UVV + UTR = Q8QQV#H 9&:/#$$@@$-++#-'($-/'*(($)"#$(#'&#($/*.?&:-)&*:$*%$)"#$?-(#L#.&))#'$R0:/)&*:($*%$!=N$-:3$!>PI 1#$/-:$1'&)#

# &QP # &;R A + $ >#/" AAAAAAA A $@@ = $ > #/" AAAAAAA #%QP #%;R _(&:5$)"#$/-2/02-)#3$@-20#$*%$$@@$-:3$(0?()&)0)&:5$#%=N$`$#%>P$=$M$×$=P−=N$ZI$1#$3#)#'.&:#$)"# /*22#/)*'$/0''#:)($-(

# &QP = # &;R = QUP#µL !"&($&($)"#$(.-22$/0''#:)$-)$1"&/"$)"#$/2-(($Zc$*0)+0)$()-5#$&($?&-(#3<

12.4.8 Summary ;*'$%0)0'#$'#%#'#:/#I$!-?2#$=><=$+'*@&3#($-$2&()&:5$*%$)"#$@-20#($*%$)"#$/*22#/)*'$?&-($/0''#:)( *%$)"#$[N=$)'-:(&()*'(<$

12.5 Small-Signal Analysis of the 741

Table 12.1 DC Collector Currents of the 741 Circuit (µA) !Q

`8U

!V

Q`

!QT@

UUR

!Q`

QU8V

!;

`8U

!`

Q`

!QP

QUP

!;R

QUP

!T

`8U

!QR

Q`

!QU

R

!;Q

R

!P

`8U

!QQ

OTR

!QZ

QZ8;

!;;

R

!U

`8U

!Q;

OTR

!QO

UUR

!;T

QVR

!Z

`8U

!QT4

QVR

!QV

QZU

!;P

R

!O

QR8U

EXERCISE 12.14

!4#&"#$%+#(&,(0&$#34#K&68#Q;8QO#$%+#!QV_!Q`#"+$.3,B#&'#,+*/)(+1#=2#$.3#1&31+A(3""+($+1#$,)"'&'$3,'4&"1#$%+#(0,,+"$#&"#!QP#)"1#!;R8#XK<,+L#\'+#$%+#,+'0/$#34#M?+,(&'+#Q;8QQ8Y Ans. UPR#µL

12.5 Small-Signal Analysis of the 741 12.5.1 The Input Stage ;&50'#$=><=E$("*1($+-')$*%$)"#$[N=$&:+0)$()-5#$%*'$)"#$+0'+*(#$*%$+#'%*'.&:5$(.-22,(&5:-2 -:-24(&(<$]*)#$)"-)$(&:/#$)"#$/*22#/)*'($*%$!=$-:3$!>$-'#$/*::#/)#3$)*$-$/*:()-:)$3/$@*2)-5#I )"#4$ -'#$ ("*1:$ 5'*0:3#3<$ Z2(*I$ )"#$ /*:()-:),/0''#:)$ ?&-(&:5$ *%$ )"#$ ?-(#($ *%$ !M$ -:3$ !N$ &( #Y0&@-2#:)$)*$"-@&:5$)"#$/*..*:$?-(#$)#'.&:-2$*+#:,/&'/0&)#3< !"#$3&%%#'#:)&-2$(&5:-2$v<$-++2$?#)1##:$)"#$&:+0)$)#'.&:-2($#%%#/)&@#24$-++#-'($-/'*(( %*0'$#Y0-2$#.&))#'$'#(&()-:/#($/*::#/)#3$&:$(#'&#(l)"*(#$*%$!=I$!>I$!MI$-:3$!N<$Z($-$'#(02)I #.&))#'$(&5:-2$/0''#:)($%2*1$-($&:3&/-)#3$&:$;&5<$=><=E$1&)" v

< E = AAAAAA
$S=>
Rid

Figure 12.18 G5)//A'&6")/#)")/2'&'#34#$%+ OPQ#&"*0$#'$)6+8

1013

1014 Chapter 12 Operational-Amplifier Circuits 1"#'#$5E$3#:*)#($)"#$#.&))#'$'#(&()-:/#$*%$#-/"$*%$!=$)"'*05"$!N<$!"0(

$ ;U#5H 5 E = AAAAA> = AAAAAAAAAAAAAAAAA = ;8ZT#BΩ # `8U#µL !"0($)"#$%*0'$)'-:(&()*'($!=$)"'*05"$!N$(0++24$)"#$2*-3$/&'/0&)$1&)"$-$+-&'$*%$/*.+2#.#:)-'4 /0''#:)$(&5:-2($α<=E< !"#$&:+0)$3&%%#'#:)&-2$'#(&()-:/#$*%$)"#$*+$-.+$/-:$?#$*?)-&:#3$%'*.$;&5<$=><=E$-(

3 <( = P ( β J + Q )5 E

$S=>
;*'$βJ$=$>PPI$1#$*?)-&:$3<($=$><=$7Ω< j'*/##3&:5$1&)"$)"#$&:+0),()-5#$-:-24(&(I$1#$("*1$&:$;&5<$=><=\$)"#$2*-3$/&'/0&)$%#3$1&)" )"#$/*.+2#.#:)-'4$+-&'$*%$/0''#:)$(&5:-2($%*0:3$#-'2&#'<$]#52#/)&:5$)"#$(&5:-2$/0''#:)$&:$)"# ?-(#$*%$![I$1#$(##$)"-)$)"#$/*22#/)*'$(&5:-2$/0''#:)$*%$!O$&($-++'*G&.-)#24$#Y0-2$)*$)"#$&:+0) /0''#:)$ α
<6 = ; α
$S=>U

!"#$%-/)*'$*%$>$&:$)"&($#Y0-)&*:$&:3&/-)#($)"-)$/*:@#'(&*:$%'*.$3&%%#'#:)&-2$)*$(&:52#,#:3#3$&( +#'%*'.#3$1&)"*0)$2*(&:5$"-2%$)"#$(&5:-2<$!"#$)'&/VI$*%$/*0'(#I$&($)"#$0(#$*%$)"#$/0''#:)$.&''*' )*$&:@#')$*:#$*%$)"#$/0''#:)$(&5:-2($-:3$)"#:$-33$)"#$'#(02)$)*$)"#$*)"#'$/0''#:)$(&5:-2$S(## 9#/)&*:$EU$ /-:$ ?#$ /*.?&:#3$ )*$ *?)-&:$ )"#$ )'-:(/*:30/)-:/#$ *%$ )"# &:+0)$()-5#I$*2=K

< α * 2Q ≡ AAA6 = AAAAAAA $ v< ;5 E

)ie

$S=>
)ie

io % 2)ie 4

Q7 2 )ie

1

)ie 3

!0

Q5

Q6

R1 % 1 k(

R3 % 50 k(

R2 % 1 k(

Figure 12.19 9%+#/3)1#(&,(0&$#34#$%+#&"*0$#'$)6+#4+1#=2#$%+#$.3#(35*/+5+"$),2#(0,,+"$#'&6")/'#6+"+,)$+1#=2 !Q#$%,306%#!P#&"#K&68#Q;8QV8#7&,(/+1#"05=+,'#&"1&()$+#$%+#3,1+,#34#$%+#)")/2'&'#'$+*'8#

12.5 Small-Signal Analysis of the 741

90?()&)0)&:5$5E$=$>F$.ZQA<$$$!"#$#G+'#((&*:$%*'"*2=$/-: ?#$1'&))#:$&:$)"#$-2)#':-)#$%*'.

* 2Q ` QAAA ' 2Q ;

XQ;8VT′Y

.%+,+#'2Q#&'#$%+#$,)"'(3"10($)"(+#34#+)(%#34#!Q#$3#!P8

EXERCISE 12.15

K3,#$%+#(&,(0&$#&"#K&68#Q;8Q`-#4&"1#&"#$+,5'#34#
!*$/*.+2#)#$*0'$.*3#2&:5$*%$)"#$[N=$&:+0)$()-5#I$1#$.0()$%&:3$&)($*0)+0)$'#(&()-:/#$36=< !"&($ &($)"#$ '#(&()-:/#$ (##:$ m2**V&:5$ ?-/Vn$ &:)*$ )"#$ /*22#/)*'$)#'.&:-2$*%$ !F$ &:$;&5<$ =><=\< !"0($36=$&($)"#$+-'-22#2$#Y0&@-2#:)$*%$)"#$*0)+0)$'#(&()-:/#$*%$)"#$/0''#:)$(*0'/#$(0++24&:5 )"#$(&5:-2$/0''#:)$α<=E<$;&:3&:5$)"&($'#(&()-:/#$&($/*:(&3#'-?24$(&.+2&, %$&%$1#$-((0.#$)"-)$)"#$/*..*:$?-(#($*%$!M$-:3$!N$-'#$-)$-$F<5+B=A"'56B,(<$!"&($*%$/*0'(# "-++#:($*:24$1"#:$)"#$&:+0)$(&5:-2$v<$&($-++2$&:$-$/*.+2#.#:)-'4$%-("&*:<$]#@#')"#2#((I )"&($-((0.+)&*:$3*#($:*)$'#(02)$&:$-$2-'5#$#''*'< Z((0.&:5$)"-)$)"#$?-(#$*%$!N$&($-)$@&')0-2$5'*0:3I$)"#$'#(&()-:/#$1#$-'#$-%)#'$&($36NI$&:3&, /-)#3$ &:$ ;&5<$ =><>PS-U<$ !"&($ &($ )"#$ *0)+0)$ '#(&()-:/#$ *%$ -$ /*..*:,?-(#$ )'-:(&()*'$ )"-)$ "-( - '#(&()-:/#$ S5E$ *%$ !>U$ &:$ &)($ #.&))#'<$ !*$ %&:3$ 36N$ 1#$ .-4$ 0(#$ )"#$ %*22*1&:5$ #G+'#((&*: SXY< [
3 6 = 5 6 [ Q + ' 2 ( 3 E hh5 π ) ]

$S=>
90?()&)0)&:5$ 3 E = 5 E ≡ ;8ZT#BΩ $-:3$ 5 6 = $4 [# I$1"#'#$$4$=$OP$A$-:3$#$=$\F$7ΩUI$-:3$:#52#/)&:5$5π$(&:/#$&)$&($Sβ $+$=U$)&.#($2-'5#'$)"-:$3DI$'#(02)($&:"36N$=$=P
Figure 12.20 G&5*/&4&+1# (&,(0&$'# 43,# 4&"1&"6# $%+ $.3# (35*3"+"$'# 34# $%+# 30$*0$# ,+'&'$)"(+# 36Q# 34# $%+ 4&,'$#'$)6+8

1015

1016 Chapter 12 Operational-Amplifier Circuits !"#$(#/*:3$/*.+*:#:)$*%$)"#$*0)+0)$'#(&()-:/#$&($)"-)$(##:$2**V&:5$&:)*$)"#$/*22#/)*'$*% !F$&:$;&5<$=><=\$1&)"$)"#$α < E $5#:#'-)*'$(#)$)*$P<$Z2)"*05"$)"#$?-(#$*%$!F$&($:*)$-)$(&5:-2$5'*0:3I 1#$("-22$-((0.#$)"-)$)"#$(&5:-2$@*2)-5#$-)$)"#$?-(#$&($(.-22$#:*05"$)*$.-V#$)"&($-++'*G&.-, )&*:$@-2&3<$!"#$/&'/0&)$)"#:$)-V#($)"#$%*'.$("*1:$&:$;&5<$=><>PS?UI$-:3$36F$/-:$?#$3#)#'.&:#3 0(&:5$XY<$S=><$!"0($ 3 6Z ! QV8;#EΩ< ;&:-224I$1#$/*.?&:#$36N$-:3$36F$&:$+-'-22#2$)*$*?)-&:$)"#$*0)+0)$'#(&()-:/#$*%$)"#$&:+0) ()-5#I$36=I$-($36=$=$F<[$7Ω< ;&50'#$=><>=$("*1($)"#$#Y0&@-2#:)$/&'/0&)$)"-)$1#$"-@#$3#'&@#3$%*'$)"#$&:+0)$()-5#<

Figure 12.21#G5)//A'&6")/#+@0&:)/+"$#(&,(0&$#43,#$%+#&"*0$#'$)6+#34#$%+#OPQ#3*#)5*8

Example 12.3 D+#.&'%#$3#4&"1#$%+#&"*0$#344'+$#:3/$)6+#,+'0/$&"6#4,35#)#;i#5&'5)$(%#=+$.++"#$%+#,+'&'$)"(+'#3Q#)"1#3; &"#K&68#Q;8QT8

Solution 73"'&1+,#4&,'$#$%+#'&$0)$&3"#.%+"#=3$%#&"*0$#$+,5&")/'#),+#6,30"1+1-#)"1#)''05+#$%)$#3Q#=#3#)"1#3;#=#3#+ ∆3-#.%+,+#∆3/ 3#=#R8R;8#K,35#K&68#Q;8;;#.+#'++#$%)$#.%&/+#!U#'$&//#(3"10($'#)#(0,,+"$#+@0)/#$3##-#$%+#(0,A ,+"$#&"#!Z#.&//#=+#'5)//+,#=2#∆#8#9%+#:)/0+#34#∆##()"#=+#430"1#4,35 $@DU + #3 = $@DZ + ( # L ∆# ) ( 3 + ∆3 ) 9%0' $@DU L $@DZ = #∆3 L ∆# ( 3 + ∆3 )

S=>
9%+#@0)"$&$2#3"#$%+#/+4$A%)"1#'&1+#&'#&"#+44+($#$%+#(%)"6+#&"#$@D#10+#$3#)#(%)"6+#&"##D#34#∆#8#D+#5)2#$%+,+A 43,+#.,&$+ $@DU L $@DZ #!#∆#5 E

S=>
M@0)$&3"'#XQ;8VUY#)"1#XQ;8VZY#()"#=+#(35=&"+1#$3#3=$)&" ∆# ∆3 AAAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAAA A # 3 + ∆3 + 5 E

S=>
G0='$&$0$&"6#3#=#Q#BΩ#)"1#5E#=#;8ZT#BΩ#'%3.'#$%)$#)#;i#5&'5)$(%#=+$.++"#3Q#)"1#3;#6&:+'#,&'+#$3#)" LT 30$*0$#(0,,+"$# ∆# = U8U × QR #8 #93#,+10(+#$%&'#30$*0$#(0,,+"$#$3#C+,3#.+#%):+#$3#)**/2#)"#&"*0$#:3/$)6+ $-%#6&:+"#=2

12.5 Small-Signal Analysis of the 741

1017

LT

∆# U8U × QR # $-% = AAAAAAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAA * 2Q * 2Q

S=>
90?()&)0)&:5$#$=$\
!

Figure 12.22 !"*0$#'$)6+#.&$%#=3$%#&"*0$'#6,30"1+1#)"1#)#5&'5)$(%#∆3#=+$.++"#3Q#)"1#3;8

Example 12.4 !$#&'#,+@0&,+1#$3#4&"1#$%+#7EWW#34#$%+#OPQ#&"*0$#'$)6+8#L''05+#$%)$#$%+#(&,(0&$#&'#=)/)"(+1#+?(+*$#43,#5&'A 5)$(%+'#&"#$%+#(0,,+"$A5&,,3,#/3)1#$%)$#,+'0/$#&"#)"#+,,3,# ε 2 #&"#$%+#5&,,3,j'#(0,,+"$A$,)"'4+,#,)$&3^#$%)$#&'$%+#,)$&3#=+(35+'# ( Q L ε 2 ) 8

Solution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v

1018 Chapter 12 Operational-Amplifier Circuits

Example 12.4 continued

Q9

Q8 2i

!2i i vicm

Q1

Q2

i 2i

Y

i

2i/bP

Q3

vicm

i !vicm

Q4

i/bP i/bP

i

io ! !mi

vicm /Ro

0

Q10 R4

Ro

i (1 " !m)

i In

Out

Gmcm !

Current Mirror

!mi vicm

Figure 12.23 SM41:3($ AB5TU$ Q-43N/+/$ %8$ *2( )%11%-91%0($ ;4+-$ %8$ *2($ VTA$ +-:"*$ /*4;(5$ =%*($ *24* ( ) ( ( )D $XX$( )AW 7$ 24/$ &((-$ I:"33(0$ %"*J$ 4-0$ /2%./(:(#4*(3N7$ 3(4,+-;$&(2+-0$+0(43$)"##(-*$/%"#)(/$ 'D$4-0 'AW5

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v !*$ B! B! * 999999 ( 99999999 9 β+ ()

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Q//"1+-;$ β + # A7$*2+/$(<"4*+%-$/+1:3+8+(/$*% v

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62"/$*2($)%11%-91%0($*#4-/)%-0")*4-)($%8$*2($+-:"*$/*4;($+/$;+,(-$&N !) ε$ ! , $*$ ≡ 999999999 ( 999999999

v !*$

v !*$

12.5 Small-Signal Analysis of the 741

1019

G0='$&$0$&"6#43,#<#4,35#M@8#XQ;8`QY#6&:+'#

ε

2 * 2H2 ` AAAAAAAA A ;3 6

S=><\MU

K&")//2-# $%+# 7EWW# ()"# =+# 430"1# )'# $%+# ,)$&3# 34# $%+# 1&44+,+"$&)/# $,)"'(3"10($)"(+# * 2Q# 430"1# &"# M@8 XQ;8VT′Y#)"1#$%+#(3553"A531+#$,)"'(3"10($)"(+# * 2H2 * 2Q 7EWW ≡ AAAAAAAAAAAA ` ;' 2Q 3 6 ⁄ ε 2 * 2H2

S=><\NU

.%+,+# ' 2Q#&'#$%+#$,)"'(3"10($)"(+#34# ! Q8#S3.#'0='$&$0$&"6#43,# 3 6 #4,35#M@8#XQ;8V`Y-#.+#3=$)&" 7EWW# ` ;' 2Q ( 3 6` || 3 6QR ) ⁄ ε 2

S=><\OU

J+43,+#/+):&"6#$%&'#+?)5*/+-#.+#3='+,:+#$%)$#&4#$%+#4++1=)(B#.+,+#"3$#*,+'+"$-#$%+#;<#$+,5#&"#M@8#XQ;8`RY .30/1#=+#)='+"$#)"1#$%+#(0,,+"$#<#.30/1#=+(35+# β : ( v

EXERCISES 12.16 G%3.# $%)$# &4# $%+# '30,(+# 34# $%+# &5=)/)"(+# &"# $%+# (0,,+"$A5&,,3,# /3)1# &'# $%)$# .%&/+ 3 Q ` 3-#3 ; ` 3 ^ ∆3 -#$%+#+,,3,# ε 2 #&'#6&:+"#=2 ∆3 ε 2 ` AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 3 ^ 5 EU ^ ∆3

M:)/0)$+# ε 2 #43,# ∆3 ⁄ 3 ` R8R;8 LT Ans. ε 2 ` U8U × QR 12.17 W+4+,#$3#K&68#Q;8;T#)"1#)''05+#$%)$#$%+#=)'+'#34#! ` #)"1#! QR#),+#)$#)**,3?&5)$+/2#(3"'$)"$#:3/$)6+' X'&6")/#6,30"1Y8#K&"1# 3 6` -# 3 6QR-#)"1#%+"(+# 3 6 8#\'+# $ 4 ` Q;U#H #43,#,1,")"1#UR#H#43,#1,1#$,)"A '&'$3,'8#\'+#$%+#=&)'#(0,,+"$#:)/0+'#&"#9)=/+#Q;8Q8 Ans. 3 6` ` ;8ZT#EΩ ^# 3 6QR ` TQ8Q#EΩ ^# 3 6 ` ;8PT#EΩ 12.18 \'+#$%+#,+'0/$'#34#M?+,(&'+'#Q;8QZ#)"1#Q;8QO#$3#1+$+,5&"+# * 2H2 #)"1#7EWW#34#$%+#OPQ#&"*0$#'$)6+8 D%)$#.30/1#$%+#7EWW#=+#&4#$%+#(3553"A531+#4++1=)(B#.+,+#"3$#*,+'+"$b#L''05+# β : ` UR8 LZ U Ans. * 2H2 ` Q8QT × QR # 5L[H^# 7EWW# ` Q8ZV × QR # 3,# QRP8U# 1J^# .&$%30$# (3553"A531+ 4++1=)(B-#7EWW#k#OR8U#1J

12.5.2 The Second Stage ;&50'#$=><>N$("*1($)"#$[N=$(#/*:3$()-5#$+'#+-'#3$%*'$(.-22,(&5:-2$-:-24(&(<$C:$)"&($(#/)&*: 1#$("-22$-:-24J#$)"#$(#/*:3$()-5#$)*$3#)#'.&:#$)"#$@-20#($*%$)"#$+-'-.#)#'($*%$)"#$#Y0&@-2#:) /&'/0&)$("*1:$&:$;&5<$=><>O< Input Resistance

!"#$&:+0)$'#(&()-:/#$3<>$/-:$?#$%*0:3$?4$&:(+#/)&*:$)*$?#

3 <; = ( β QZ + Q ) { 5 EQZ + [ 3 ` hh ( β QO + Q ) ( 5 EQO + 3 V ) ] }

$S=><\FU

1020 Chapter 12 Operational-Amplifier Circuits

Figure 12.24 9%+# OPQ# '+(3"1# '$)6+# *,+*),+1# 43, '5)//A'&6")/#)")/2'&'8

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Figure 12.25 G5)//A'&6")/#+@0&:)/+"$A(&,(0&$#531+/#34#$%+#'+(3"1#'$)6+8

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αv

7QO A < HQO = AAAAAAAAAAAAAAAAAAA 5 EQO + 3 V ( 3 ` hh 3
$S=><\[U

3
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$S=><\EU

1"#'#$1#$"-@#$:#52#/)#3$56=F$?#/-0(#$56=F$ # $3\<$!"#(#$#Y0-)&*:($/-:$?#$/*.?&:#3$)*$*?)-&:

< HQO A * 2; ≡ AAAAAA v <;

$S=><=PPU

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12.5 Small-Signal Analysis of the 741

Figure 12.26 g+4&"&$&3"#34#36QO8

C)$%*22*1($)"-)$36>$&($5&@#:$?4$

3 6; = ( 3 6QT@ hh 3 6QO )

$S=><=P=U

1"#'#$36=M@$&($)"#$'#(&()-:/#$2**V&:5$&:)*$)"#$/*22#/)*'$*%$!=M@$1"&2#$&)($?-(#$-:3$#.&))#'$-'# /*::#/)#3$)*$5'*0:3<$C)$/-:$?#$#-(&24$(##:$)"-)

3 6QT@ = 5 6QT@

$S=><=P>U

;*'$)"#$[N=$/*.+*:#:)$@-20#($1#$*?)-&:$36=M@$=$\P<\$VΩ< !"#$(#/*:3$/*.+*:#:)$&:$XY<$S=><=P=UI$36=[I$&($)"#$'#(&()-:/#$(##:$2**V&:5$&:)*$)"#$/*22#/, )*'$*%$!=[I$-($&:3&/-)#3$&:$;&5<$=><>F<$9&:/#$)"#$'#(&()-:/#$?#)1##:$)"#$?-(#$*%$!=[$-:3$5'*0:3 &( '#2-)&@#24$ (.-22I$ *:#$ /-:$ /*:(&3#'-?24$ (&.+2&%4$ .-))#'($ ?4$ -((0.&:5$ )"-)$ )"#$ ?-(#$ &( 5'*0:3#3<$ h*&:5$ )"&(I$ 1#$ /-:$ 0(#$ XY<$ S=>$=$E=$VΩ< Thévenin Equivalent Circuit !"#$(#/*:3,()-5#$#Y0&@-2#:)$/&'/0&)$/-:$?#$/*:@#')#3$)* )"#$!"o@#:&:$%*'.I$-($("*1:$&:$;&5<$=><>[<$]*)#$)"-)$)"#$()-5#$*+#:,/&'/0&)$@*2)-5#$5-&:$&( −*2>36><$

Figure 12.27 9%l:+"&"#43,5#34#$%+#'5)//A'&6")/#531+/#34#$%+#'+(3"1#'$)6+8

EXERCISES 12.19

\'+#M@8#XQ;8`ZY#$3#'%3.#$%)$#3<;#!#P#EΩ8

12.20 \'+#M@'8#XQ;8`OY#$3#XQ;8QRRY#$3#:+,&42#$%)$#*2;#&'#Z8U#5L[H8 12.21

H+,&42#$%)$#36;#!#VQ#BΩ8

12.22

K&"1#$%+#3*+"A(&,(0&$#:3/$)6+#6)&"#34#$%+#'+(3"1#'$)6+#34#$%+#OPQ8 Ans. −U;Z8U#H[H

1021

1022 Chapter 12 Operational-Amplifier Circuits

12.5.3 The Output Stage !"#$[N=$*0)+0)$()-5#$&($("*1:$&:$;&5<$=><>E$1&)"*0)$)"#$("*'),/&'/0&),+'*)#/)&*:$/&'/0&)'4< !"#$()-5#$&($("*1:$3'&@#:$?4$)"#$(#/*:3,()-5#$)'-:(&()*'$!=[$-:3$2*-3#3$1&)"$-$>,VΩ$'#(&(, )-:/#<$!"#$/&'/0&)$&($*%$)"#$Zc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utput Voltage Limits !"#$ .-G&.0.$+*(&)&@#$*0)+0)$@*2)-5#$&($2&.&)#3$?4$)"#$(-)0'-, )&*: $*%$/0''#:),(*0'/#$)'-:(&()*'$!=M4<$!"0(I v -5)?

= $&& L $&D')$ L $@DQP $

$S=><=PMU

1"&/"$&($-?*0)$=$A$?#2*1$$&&<$!"#$.&:&.0.$*0)+0)$@*2)-5#$S&<#
Figure 12.28 9%+#OPQ#30$*0$#'$)6+#.&$%30$#$%+#'%3,$A(&,(0&$A*,3$+($&3"#(&,(0&$,28#

12.5 Small-Signal Analysis of the 741

Rout

Gvo3vo2

Rin3

Figure 12.29 E31+/#43,#$%+#OPQ#30$*0$#'$)6+8

v -5&" = L $DD + $&D')$ + $D@;T + $D@;R $

$S=><=PNU

1"&/"$&($-?*0)$=<>\<$!"#$.*3#2$&($("*1:$%#3$?4$v6>I$1"&/"$&($)"#$*+#:,/&'/0&)$*0)+0)$@*2)-5# *%$)"#$(#/*:3$()-5#<$;'*.$;&5<$=><>[I$v6>$&($5&@#:$?4 v 6; = L * 2; 3 6; v <;

$S=><=POU

1"#'#$*2>$-:3$36>$1#'#$+'#@&*0(24$3#)#'.&:#3$-($*2>$=$F$=$E=$VΩ<$T#(&(, )-:/#$ 3&:M$ &($ )"#$ &:+0)$ '#(&()-:/#$ *%$ )"#$ *0)+0)$ ()-5#$ 3#)#'.&:#3$ 1&)"$ )"#$ -.+2&%&#'$ 2*-3#3 1&)"$30<$Z2)"*05"$)"#$#%%#/)$*%$2*-3&:5$-:$-.+2&%&#'$()-5#$*:$&)($&:+0)$'#(&()-:/#$&($:#52&5&?2# &:$)"#$&:+0)$-:3$(#/*:3$()-5#(I$)"&($&($:*)$)"#$/-(#$&:$5#:#'-2$&:$-:$*0)+0)$()-5#<$h#%&:&:5$3&:M &:$)"&($.-::#'$#:-?2#($/*''#/)$#@-20-)&*:$*%$)"#$@*2)-5#$5-&:$*%$)"#$(#/*:3$()-5#I$4>I$-( v 3 &"T 4 ; ≡ AAAAA
$S=><=PFU

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3 &"T #!# β ;T × OP#BΩ 1"&/"$%*'$ β>M$=$OP$&($3&:M$!$M<[$7Ω<$9&:/#$36>$=$E=$VΩI$1#$(##$)"-)$3&:M$#$36>I$-:3$)"# @-20#$*%$3&:M$1&22$"-@#$2&))2#$#%%#/)$*:$)"#$+#'%*'.-:/#$*%$)"#$*+$-.+<$9)&22$1#$/-:$0(#$)"#$@-20# *?)-&:#3$%*'$3&:M$)*$3#)#'.&:#$)"#$5-&:$*%$)"#$(#/*:3$()-5#$0(&:5$XY<$S=><=PFU$-($4> = −O=O$AQA< !"#$ @-20#$ *%$ 4>$ 1&22$ ?#$ :##3#3$ &:$ 9#/)&*:$ =><>\$)"-)$*v 6M$&($)"#$)+$20('4(*'#,)=$4&33,=)3#&1$,1&'2$*%$)"#$*0)+0)$()-5#I v v 6;

* v6T = AAAAAA6A

$S=><=P[U 30 = ∞

1023

1024 Chapter 12 Operational-Amplifier Circuits

Rout !

Figure 12.30 7&,(0&$#43,#4&"1&"6#$%+#30$*0$#,+'&'$)"(+#330$8

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3 6; A+5 3 6;T = AAAAAAAAAAAAAAA β ;T + Q E;T

$S=><=PEU

90?()&)0)&:5$36>$=$E=$VΩI$ β>M$=$OPI$-:3$5E>M$=$>O/ P<=E$=$=M\$Ω$4($36>M$=$=<[M$VΩ<$!"&( '#(&()-:/#$-++#-'($&:$+-'-22#2$1&)"$)"#$(#'&#($/*.?&:-)&*:$*%$56=M4$-:3$)"#$'#(&()-:/#$*%$)"# !=EL!=\$:#)1*'V<$9&:/#$56=M4$-2*:#$SP<>E$7ΩU$&($.0/"$2-'5#'$)"-:$36>MI$)"#$#%%#/)&@#$'#(&(, )-:/#$?#)1##:$)"#$?-(#$*%$!>P$-:3$5'*0:3$&($-++'*G&.-)#24$#Y0-2$)*$36>M<$]*1$1#$/-:$%&:3 )"#$*0)+0)$'#(&()-:/#$3*0)$-(

3 6;T A+5 3 30$ = AAAAAAAAAAAAAAA β ;R + Q E;R

$S=><=P\U

;*'$ β>P$=$OPI$)"#$%&'()$/*.+*:#:)$*%$3*0)$&($MN$Ω<$!"#$(#/*:3$/*.+*:#:)$3#+#:3($/'&)&/-224 *:$)"#$@-20#$*%$*0)+0)$/0''#:)<$;*'$-:$*0)+0)$/0''#:)$*%$O$.ZI$5E>P$&($O$Ω$-:3$3*0)$&($M\$Ω<$!* )"&($@-20#$1#$.0()$-33$)"#$'#(&()-:/#$3[$S>[$ΩU$S(##$;&5<$=><=MUI$1"&/"$&($&:/203#3$%*'$("*'), /&'/0&)$+'*)#/)&*:<$!"#$*0)+0)$'#(&()-:/#$*%$)"#$[N=$&($(+#/&%$)*$?#$)4+&/-224$[O$Ω<

12.5 Small-Signal Analysis of the 741

1025

EXERCISES 12.23 \'&"6#)#'&5*/+#X5π-#'2Y#531+/#43,#+)(%#34#$%+#$.3#$,)"'&'$3,'#!QV#)"1#!Q`#&"#K&68#MQ;8;T-#4&"1#$%+ '5)//A'&6")/# ,+'&'$)"(+# =+$.++"# 4# )"1# 4′8# XJ6+EL# K,35# 9)=/+# Q;8Q-# #&QV# =# QZU# µL# )"1# #&Q` ! QZ µL8# Ans. QZT#Ω#

Figure E12.23#

12.24 K&60,+#MQ;8;P#'%3.'#$%+#(&,(0&$#43,#1+$+,5&"&"6#$%+#3*A)5*#30$*0$#,+'&'$)"(+#.%+"#v-#&'#*3'&$&:+ )"1#!QP#&'#(3"10($&"6#53'$#34#$%+#(0,,+"$8#\'&"6#$%+#,+'&'$)"(+#34#$%+#!QV_!Q`#"+$.3,B#()/(0/)$+1 &"#M?+,(&'+#Q;8;T#)"1#"+6/+($&"6#$%+#/),6+#30$*0$#,+'&'$)"(+#34#!QT4-#4&"1#330$#.%+"#!QP#&'#'30,(&"6 )"#30$*0$#(0,,+"$#34#U#5L8 Ans. QP8P#Ω

Rout

Figure E12.24

1026 Chapter 12 Operational-Amplifier Circuits Output Short-Circuit Protection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

12.6 Gain, Frequency Response, and Slew Rate of the 741 C:$)"&($(#/)&*:$1#$("-22$#@-20-)#$)"#$*@#'-22$(.-22,(&5:-2$@*2)-5#$5-&:$*%$)"#$[N=$*+$-.+<$D# ("-22$)"#:$/*:(&3#'$)"#$*+$-.+d($%'#Y0#:/4$'#(+*:(#$-:3$&)($(2#1,'-)#$2&.&)-)&*:<

12.6.1 Small-Signal Gain !"#$ *@#'-22$ (.-22,(&5:-2$ 5-&:$ /-:$ ?#$ %*0:3$ %'*.$ )"#$ /-(/-3#$ *%$ )"#$ #Y0&@-2#:)$ /&'/0&)( 3#'&@#3$&:$)"#$+'#/#3&:5$(#/)&*:($%*'$)"#$)"'##$*+,-.+$()-5#(<$!"&($/-(/-3#$&($("*1:$&: ;&5<$=>$VΩI$1"&/"$&($)"#$)4+&/-2$@-20#$0(#3$&:$.#-(0'&:5$-:3$(+#/&%4, &:5$)"#$[N=$3-)-<$!"#$*@#'-22$5-&:$/-:$?#$#G+'#((#3$-($ v6

v v

v<

v < v <; v 6;

v

6; 6 AAAA = AAAA<;A AAAAA A AAAAAA

$S=><==PU

30 = L * 2Q ( 3 6Q hh 3 <; ) ( L * 2; 3 6; )* v6T AAAAAAAAAAAAAAAAAAAA 3 0 + 3 30$

$S=><===U

Rout Rin3 Gvo3vo2

Figure 12.31 7)'()1&"6#$%+#'5)//A'&6")/#+@0&:)/+"$#(&,(0&$'#34#$%+#&"1&:&10)/#'$)6+'#43,#$%+#+:)/0)$&3"#34 $%+#3:+,)//#:3/$)6+#6)&"8

12.6 Gain, Frequency Response, and Slew Rate of the 741

_(&:5$)"#$@-20#($%*0:3$#-'2&#'$4($%*'$)"#$*@#'-22$*+#:,/&'/0&)$@*2)-5#$5-&:I v

4 R ≡ AAAA6 = L POZ8Q × ( L U;Z8U ) × R8`O = ;PT-QPO#H[H v<

$S=><==>U

≡ QRO8O#1J

12.6.2 Frequency Response !"#$ [N=$ &($ -:$ &:)#':-224$ /*.+#:(-)#3$ *+$ -.+<$ C)$ #.+2*4($ )"#$ 7&22#'$ /*.+#:(-)&*:$ )#/", :&Y0#I$()03$&:$9#/)&*:$=P<=M<=MU

& &" = & & ( Q + 4 ; )

$S=><==MU

1"#'#$4>$&($)"#$(#/*:3,()-5#$5-&:<$_(#$*%$)"#$@-20#$/-2/02-)#3$%*'$4>$&:$9#/)&*:$=>$= −O=OI$'#(02)($&:$&&:$=$=OINEP$+;<$9&:/#$)"&($/-+-/&)-:/#$&($Y0&)#$2-'5#I$1#$("-22$:#52#/)$-22 *)"#'$/-+-/&)-:/#($?#)1##:$)"#$?-(#$*%$!=F$-:3$(&5:-2$5'*0:3<$!"#$)*)-2$'#(&()-:/#$?#)1##: )"&($:*3#$-:3$5'*0:3$&(

3 + = 3 6Q hh 3 <; = Z8O#EΩ hh P#EΩ = ;8U#EΩ

$S=><==NU

!"0($)"#$3*.&:-:)$+*2#$"-($-$%'#Y0#:/4$9:$5&@#:$?4

Q 9: = AAAAAAAAAAAAAAAAAAA = P8Q#
$S=><==OU

C)$("*023$?#$:*)#3$)"-)$)"&($-++'*-/"$&($#Y0&@-2#:)$)*$0(&:5$)"#$-++'*G&.-)#$%*'.02-$&: XY<$S=P<==FU< Z($3&(/0((#3$&:$9#/)&*:$=P<=MPPPUb< Z((0.&:5$)"-)$-22$:*:3*.&:-:)$+*2#($-'#$-)$@#'4$"&5"$%'#Y0#:/&#(I$)"#$/-2/02-)#3$@-20#( 5&@#$'&(#$)*$)"#$c*3#$+2*)$("*1:$&:$;&5<$=>I$1"#'#$9M3c$=$9:<$!"#$0:&)4,5-&:$?-:31&3)"$ 9 $$/-: + ?#$/-2/02-)#3$%'*.

9+ = 4 R 9 T1J $

$S=><==FU

9+ = ;PT-QPO × P8Q #!#Q#E
$S=><==[U

!"0(I

Z2)"*05"$ )"&($ c*3#$ +2*)$ &.+2&#($ )"-)$ )"#$ +"-(#$ ("&%)$ -)$9 +$ &($ −\P°$ -:3$ )"0($ )"-)$ )"#$ +"-(# .-'5&:$&($\P°I$&:$+'-/)&/#$-$+"-(#$.-'5&:$*%$-?*0)$EP°$&($*?)-&:#3<$!"#$#G/#(($+"-(#$("&%) S-?*0)$=P°U$&($30#$)*$)"#$:*:3*.&:-:)$+*2#(<$!"&($+"-(#$.-'5&:$&($(0%%&/&#:)$)*$+'*@&3#$()-?2# *+#'-)&*:$*%$/2*(#3,2**+$-.+2&%&#'($1&)"$-:4$@-20#$*%$%##3?-/V$%-/)*'$β<$!"&($/*:@#:&#:/#$*%

1027

1028 Chapter 12 Operational-Amplifier Circuits

! Figure 12.32 J31+#*/3$#43,#$%+#OPQ#6)&"-#"+6/+($&"6#"3"135&")"$#*3/+'8

0(#$ *%$ )"#$ &:)#':-224$ /*.+#:(-)#3$ [N=$ &($ -/"&#@#3$ -)$ )"#$ #G+#:(#$ *%$ -$ 5'#-)$ '#30/)&*:$ &: *+#:,2**+$5-&:$-:3$"#:/#$&:$)"#$-.*0:)$*%$:#5-)&@#$%##3?-/V<$C:$*)"#'$1*'3(I$&%$*:#$'#Y0&'#( -$/2*(#3,2**+$-.+2&%&#'$1&)"$-$5-&:$*%$=PPPI$)"#:$)"#$[N=$&($6FE5H621E,8=+E($%*'$(0/"$-: -++2&/-)&*:I$-:3$*:#$1*023$?#$.0/"$?#))#'$*%%$3#(&5:&:5$*:#d($*1:$/*.+#:(-)&*:$S-((0.&:5I *%$/*0'(#I$)"#$-@-&2-?&2&)4$*%$-:$*+$-.+$)"-)$&($:*)$-2'#-34$&:)#':-224$/*.+#:(-)#3U<

12.6.3 A Simplified Model ;&50'#$=><=
$6 ( 8 ) * 2Q A = AAAAAAAA A 4 ( 8 ) ≡ AAAAAAAAAAAA 8& & $< ( 8 )

Figure 12.33 L#'&5*/+#531+/#43,#$%+#OPQ#=)'+1#3"#531+/&"6#$%+#'+(3"1#'$)6+#)'#)"#&"$+6,)$3,8

$S=><==EU

12.6 Gain, Frequency Response, and Slew Rate of the 741

!"#

%$" #< ( ( ( ) ω ) = (((((((((((( ) ω $$

&'()*((+,

-./&0"1&2-3.40#/1&56&3-4.&718521$&#.409&-0&ω&=&ω!%&:"1;1

" $$

#< (& ω ! = ((((((((

&'()*()<,

=#7$040#04.3&"#(&=&(>?*)@&2A>B&-./&$$&=&C<&DE&941F/$

ω

% ! = ((((((! "!"<">?@ =π

&'()*()(,

:"48"&4$&1G#-F&05&0"1&H-F#1&8-F8#F-01/&7165;1*&I0&$"5#F/&71&D54.01/&5#0%&"5:1H1;%&0"-0&0"4$ 25/1F& 4$& H-F4/& 5.F9& -0& 6;1G#1.841$& %& !& %C/J*& A0& $#8"& 6;1G#1.841$& 0"1& 3-4.& 6-FF$& 566& :40"& $F5D1&56&−)<&/J>/18-/1%&K#$0&F4L1&0"-0&56&-.&4.013;-05;*

12.6.4 Slew Rate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v* ( ! )

=' = (((((( ! $$

&'()*()),

Figure 12.34 !"#$%&'()*%$"+,--,./0".%&1"*"-*0)/"2&/3"%$3#&4"5%$6/"&1/",#&3#&"7,-&*)/"6*$$,&"61*$)/"%$2&*$( &*$/,#2-'8"*"-*0)/"9%++/0/$&%*-"7,-&*)/"*33/*02":/&.//$"&1/",3(*;3"%$3#&"&/0;%$*-24

1029

1030 Chapter 12 Operational-Amplifier Circuits

Figure 12.35 E31+/#43,#$%+#OPQ#3*#)5*#.%+"#)#/),6+#*3'&$&:+#1&44+,+"$&)/#'&6")/#&'#)**/&+18

!"0($)"#$(2#1$'-)#$%3$&($5&@#:$?4

;# %3 = AAAAAA &&

$S=><=>MU

;*'$)"#$[N=I$#$=$\PPPU<

EXERCISE 12.25# \'+#$%+#:)/0+#34#$%+#'/+.#,)$+#()/(0/)$+1#)=3:+#$3#4&"1#$%+#40//A*3.+,#=)"1.&1$%#9)#34#$%+#OPQ#3* )5*8#L''05+#$%)$#$%+#5)?&505#30$*0$#&'#±QR#H8 Ans. QR#B
12.6.5 Relationship Between ft and SR Z$(&.+2#$'#2-)&*:("&+$#G&()($?#)1##:$)"#$0:&)4,5-&:$?-:31&3)"$ 9 $+ -:3$)"#$(2#1$'-)#$%3<$!"&( '#2-)&*:("&+$&($*?)-&:#3$?4$/*.?&:&:5$XY(<$S=><=>PUI$S=><=>MUI$-:3

;# %3 = AAAAAAAAA ω + $ * 2Q

$S=><=>NU

)"1#$%+"#0'&"6#M@8#XQ;8VT′Y#$3#3=$)&"

P# %3 = AAAAAAAA ω + $ ' 2Q

$S=><=>OU

S3.-#'&"(+#'2Q#&'#$%+#$,)"'(3"10($)"(+#34#+)(%#34#!Q#$%,306%#!P-

!"0(I

# ' 2Q = AAAAA $>

$S=><=>FU

%3 = P$> ω +

$S=><=>[U

Z($-$/"#/VI$%*'$)"#$[N=$1#$"-@# LT

Z

%3 = P × ;U × QR × ; π × QR = R8ZT#H[µ'

12.7 Modern Techniques for the Design of BJT Op Amps

1"&/"$ &($ )"#$ '#(02)$ *?)-&:#3$ +'#@&*0(24<$ 8?(#'@#$ )"-)$ XY<$ S=><=>[U$ &($ *%$ )"#$ (-.#$ %*'.$ -( XY< S=>UI$1"&/"$-++2&#($)*$)"#$)1*,()-5#$6789$*+$-.+<$H#'#I$N$>$'#+2-/#($$-$<$9&:/#I$)4+&, /-224I$$-$$1&22$?#$)1*$)*$)"'##$)&.#($)"#$@-20#$*%$N$> I$-$)1*,()-5#$6789$*+$-.+$1&)"$-: $9 + #Y0-2$)*$)"-)$*%$)"#$[N=$#G"&?&)($-$(2#1$'-)#$)"-)$&($)1*$)*$)"'##$)&.#($-($2-'5#$-($)"-)$*%$)"#$[N=< Z$5#:#'-2$%*'.$%*'$)"#$'#2-)&*:("&+$?#)1##:$%3$-:3$ ω+$%*'$-:$*+$-.+$1&)"$-$()'0/)0'# (&.&2-'$)*$)"-)$*%$)"#$[N=$S&:/203&:5$)"#$)1*,()-5#$6789$/&'/0&)U$&(

%3 = ω + ⁄ =

$S=><=>EU

1"#'#$=$&($)"#$/*:()-:)$*%$+'*+*')&*:-2&)4$'#2-)&:5$)"#$)'-:(/*:30/)-:/#$*%$)"#$%&'()$()-5# *2=I$)*$)"#$+6+=A$?&-($/0''#:)$*%$)"#$&:+0)$3&%%#'#:)&-2$()-5#<$!"-)$&(I$%*'$)"#$[N=$/&'/0&) *2=$=$=S># UI$1"&2#$%*'$)"#$6789$/&'/0&)$*%$;&5<$=><=I$*2=$=$=#NM$ ;*'$-$5&@#:$ω+I$-$"&5"#' @-20#$*%$%3$&($*?)-&:#3$?4$.-V&:5$=$(.-22#'W$)"-)$&(I$)"#$)*)-2$?&-($/0''#:)$&($V#+)$/*:, ()-:)$-:3$*2=$&($'#30/#3<$!"&($&($-$@&-?2#$)#/":&Y0#$%*'$&:/'#-(&:5$(2#1$'-)#<$C)$&($'#%#''#3$)*$-( )"#$!"04$-*(#')2,%$#?)-$S(##$XG#'/&(#$=><>[U<

EXERCISES 12.26# 73"'&1+,#$%+#&"$+6,)$3,#531+/#34#$%+#3*#)5*#&"#K&68#Q;8TT8#K&"1#$%+#:)/0+#34#$%+#,+'&'$3,#$%)$-#.%+" (3""+($+1#)(,3''#&&-#*,3:&1+'#$%+#(3,,+($#:)/0+#34#$%+#1(#6)&"8 Ans. Q;O`#EΩ D12.27#!4#)#,+'&'$)"(+#3D#&'#&"(/01+1#&"#+)(%#34#$%+#+5&$$+,#/+)1'#34#!T#)"1#!P#'%3.#$%)$#%3#=#PX$>#+##3D / ;Yω+8 <+"(+#4&"1#$%+#:)/0+#34#3D#$%)$#.30/1#130=/+#$%+#OPQ#'/+.#,)$+#.%&/+#B++*&"6#ω+#)"1###0"(%)"6+18 D%)$#),+#$%+#"+.#:)/0+'#34#&&-#$%+#1(#6)&"-#)"1#$%+#TA1J#4,+@0+"(2b Ans. U8;Z#BΩ^#QU#*K^#QRQ8O#1J#X)#ZA1J#1+(,+)'+Y^#V8;#
12.7 Modern Techniques for the Design of BJT Op Amps L/$%306%#$%+#&"6+"&30'#$+(%"&@0+'#+5*/32+1#&"#$%+#1+'&6"#34#$%+#OPQ#3*#)5*#%):+#'$331#$%+ $+'$# 34# $&5+-# $%+2# ),+# "3.# 53,+# $%)"# PR# 2+),'# 3/1m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d8

12.7.1 Special Performance Requirements E)"2#34#$%+#'*+(&)/#*+,43,5)"(+#,+@0&,+5+"$'#'$+5#4,35#$%+#"++1#$3#3*+,)$+#531+,"#3*#)5*' 4,35#*3.+,#'0**/&+'#34#50(%#/3.+,#:3/$)6+'8#9%0'#.%&/+#$%+#OPQA$2*+#3*#)5*#3*+,)$+1#4,35 T 9%+#1&44+,+"(+#&'#>0'$#)#5)$$+,#34#"3$)$&3"^#D+#0'+1###$3#1+"3$+#$%+#$3$)/#=&)'#(0,,+"$#34#$%+#&"*0$# 1&44+,+"$&)/#'$)6+#34#$%+#7EFG#(&,(0&$-#)"1#.+#0'+1#;##43,#$%+#OPQ#()'+m

1031

1032 Chapter 12 Operational-Amplifier Circuits VCC % !15 V

VCC % 3 V

" 741 !

" Modern !

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9%)$#&'-#$%+#0**+,#+"1#34#$%+#&"*0$#(3553"A531+#,)"6+#&'#)$#/+)'$#R8V#H#=+/3.#$ && -#)#'+:+,+ /&5&$)$&3"8 93#,+()*-#.%&/+#$%+#(&,(0&$#&"#K&68#Q;8PRX=Y#%)'# $ #&)5&" #34#)#4+.#$+"$%'#34#)#:3/$#=+/3.#$%+ "+6)$&:+# *3.+,A'0**/2# ,)&/# X)$# 6,30"1# :3/$)6+Y-# $%+# 0**+,# +"1# 34# $ #&) # &'# ,)$%+,# 4),# 4,35 $ && L R8T# ≤ $ #&) ≤ $ && L R8V

12.7 Modern Techniques for the Design of BJT Op Amps

VCC RC

RC vo

Q3

VBIAS

Q4

Q6

Figure 12.41 9%+#(35*/+5+"$#34#$%+#(&,(0&$#&"#K&68#Q;8PRX=Y8#D%&/+ $%+#&"*0$#(3553"A531+#,)"6+#34#$%+#(&,(0&$#&"#K&60,+#Q;8PRX=Y#+?$+"1' =+/3.#6,30"1-#%+,+#&$#+?$+"1'#)=3:+#$&& 8#73""+($&"6#$%+#$.3#(&,(0&$'#&" *),)//+/-#)'#.&//#=+#'%3."-#,+'0/$'#&"#)#,)&/A$3A,)&/#$#&)#,)"6+8

.%+,+#.+#%):+#)''05+1# $ 3& ` R8T#H 8#93#+?$+"1#$%+#0**+,#+"1#34# $ #&) -#.+#)13*$#)#'3/0$&3" '&5&/),#$3#$%)$#0'+1#&"#$%+#7EFG#()'+#XG+($&3"#Q;8;8Z-#K&68#Q;8QQY-#")5+/2-#.+#0$&/&C+#)#*),A )//+/#(35*/+5+"$),2#&"*0$#'$)6+8#93.),1#$%)$#+"1-#"3$+#$%)$#$%+#,1,#:+,'&3"#34#$%+#(&,(0&$#34 K&68#Q;8PRX=Y-#'%3."#&"#K&68#Q;8PQ-#%)'#)#(3553"A&"*0$#,)"6+#34 R8V ≤ $ #&) ≤ $ && ^ R8T

.%+,+#.+#%):+#)''05+1#$%)$# $ 3& ` R8T#H8#9%0'-#)'#+?*+($+1-#$%+#%&6%#+"1#5++$'#30,#'*+(&4&A ()$&3"'#)"1#&"#4)($#&'#)=3:+#$%+#*3'&$&:+#'0**/2#,)&/#=2#R8T#H8#9%+#/3.+,#+"1-#%3.+:+,-#13+' "3$^#=0$#$%&'#'%30/1#()0'+#0'#"3#(3"(+,"#=+()0'+#$%+#/3.+,#+"1#.&//#=+#/33B+1#)4$+,#=2#$%+ 1,1#*)&,8#K&")//2-#"3$+#$%)$#$%+,+#&'#)#,)"6+#34# $ #&) #&"#.%&(%#=3$%#$%+#1,1#)"1#$%+#,1,#(&,A (0&$'#.&//#=+#)($&:+#)"1#*,3*+,/2#3*+,)$&"6R8V ≤ $ #&) ≤ $ && L R8V

K&60,+# Q;8P;# '%3.'# )"# &"*0$# '$)6+# $%)$# )(%&+:+'# 53,+# $%)"# ,)&/A$3A,)&/# &"*0$# (3553"A 531+#,)"6+#=2#0$&/&C&"6#)#1,1#1&44+,+"$&)/#*)&,#X! Q-#! ; Y#)"1#)"",1,#1&44+,+"$&)/#*)&,#X! T-#! P Y(3""+($+1#&"#*),)//+/8#93#B++*#$%+#1&)6,)5#'&5*/+-#.+#),+#"3$#'%3.&"6#$%+#*),)//+/#(3""+(A $&3"#34#$%+#&"*0$#$+,5&")/'^#$%+#c#&"*0$#$+,5&")/'#),+#)''05+1#$3#=+#(3""+($+1#$36+$%+,-#)"1 '&5&/),/2#43,#$%+#_#&"*0$#$+,5&")/'8#!"#3,1+,#$3#&"(,+)'+#$%+#6)&"#3=$)&"+1#4,35#$%+#,+'&'$&:+/2 /3)1+1#1&44+,+"$&)/#*)&,'-#)#43/1+1#()'(31+#'$)6+#&'#)11+18#<+,+# 3 O #)"1# 3 V#),+#$%+#,+'&'$&:+ /3)1'#34#$%+#1,1#*)&,# ! QL ! ; -#)"1# ! O L ! V #),+#&$'#()'(31+#$,)"'&'$3,'8#G&5&/),/2-# 3 ` #)"1# 3 QR ),+# $%+# ,+'&'$&:+# /3)1'# 34# $%+# ,1,# *)&,# ! T L ! P - # )"1# ! ` L ! QR# ),+# &$'# ()'(31+# $,)"'&'$3,'8 F='+,:+#$%)$#$%+#()'(31+#$,)"'&'$3,'#13#e130=/+#10$28f#K3,#&"'$)"(+-# ! O L ! V #3*+,)$+#)'#$%+ ()'(31+# 1+:&(+'# 43,# ! Q L ! ; # )"1# )$# $%+# ')5+# $&5+# )'# (0,,+"$A'30,(+# /3)1'# 43,# ! ` L ! QR8# L '&5&/),#'$)$+5+"$#()"#=+#5)1+#)=30$# ! ` L ! QR8#9%+#30$*0$#:3/$)6+#34#$%+#4&,'$#'$)6+-# v 6( -#&' $)B+"#=+$.++"#$%+#(3//+($3,'#34#$%+#()'(31+#1+:&(+'8 K3,# $ #&) * R8V#H -# $%+# ,1,# '$)6+# .&//# =+# &")($&:+# )"1# $%+# 6)&"# &'# 1+$+,5&"+1# =2# $%+ $,)"'(3"10($)"(+# * 2 #34#$%+# ! Q L ! ; #*)&,#$36+$%+,#.&$%#$%+#30$*0$#,+'&'$)"(+#'++"#=+$.++" $%+#(3//+($3,'#34#$%+#()'(31+#$,)"'&'$3,'8#L$#$%+#3$%+,#+"1#34# $ #&) -#$%)$#&'-# $ #&) # $ && L R8V$%+# ! Q L ! ; #'$)6+#.&//#=+#&")($&:+-#)"1#$%+#6)&"#.&//#=+#1+$+,5&"+1#=2#$%+#$,)"'(3"10($)"(+ * 2 # 34# $%+# ! T L ! P # *)&,# )"1# $%+# 30$*0$# ,+'&'$)"(+# =+$.++"# $%+# (3//+($3,'# 34# $%+# ()'(31+ 1+:&(+'8#!"#$%+#3:+,/)*#,+6&3"# R8V ≤ $ #&) ≤ $ && L R8V- #=3$%#$%+#1,1#)"1# ,1,#'$)6+'#.&//#=+ )($&:+#)"1#$%+&,#+44+($&:+#$,)"'(3"10($)"(+'# * 2 #)11#0*-#$%0'#,+'0/$&"6#&"#)#%&6%+,#6)&"8#9%+ 1+*+"1+"(+#34#$%+#1&44+,+"$&)/#6)&"#3"#$%+#&"*0$#(3553"A531+# $ #&) #&'#0'0)//2#0"1+'&,)=/+

1037

1038 Chapter 12 Operational-Amplifier Circuits )"1#()"#=+#,+10(+1#(3"'&1+,)=/2#=2#),,)"6&"6#$%)$#3"+#34#$%+#$.3#1&44+,+"$&)/#*)&,'#&'#$0,"+1 344#.%+"#$%+#3$%+,#3"+#&'#)($&:+8P VCC R9

VBIAS 1

R10

Q5

Q10 Q9

Q1

Q2

" vO1

"v

od

!

!

Q4

Q3

!

"

VBIAS 3 vO2 Q8

Q7

VB VB

VBIAS2

Q6

npn pair

R7 pnp pair

R8

Cascode

Figure 12.42 !"*0$#'$)6+#.&$%#,)&/A$3A,)&/#&"*0$#(3553"A531+#,)"6+#)"1#)#43/1+1A()'(31+#'$)6+#$3 &"(,+)'+#$%+#6)&"8#S3$+#$%)$#)//#$%+#=&)'#:3/$)6+'#&"(/01&"6#$J!LGT#)"1#$@#),+#6+"+,)$+1#+/'+.%+,+#3"#$%+ (%&*8

Example 12.5 !$#&'#,+@0&,+1#$3#4&"1#$%+#&"*0$#,+'&'$)"(+#)"1#$%+#:3/$)6+#6)&"#34#$%+#&"*0$#'$)6+#'%3."#&"#K&68#Q;8P;8#I+$ $ #&) * R8V#H #'3#$%)$#$%+# ! T L ! P #*)&,#&'#3448#L''05+#$%)$# ! U #'0**/&+'#QR#µL-#$%)$#+)(%#34# ! O #$3# ! QR #&' =&)'+1#)$#QR#µL-#)"1#$%)$#)//#430,#()'(31+#$,)"'&'$3,'#),+#3*+,)$&"6#&"#$%+#)($&:+#531+8#9%+#&"*0$#,+'&'A $)"(+#34#$%+#'+(3"1#'$)6+#34#$%+#3*#)5*#X"3$#'%3."Y#&'# 3 0 ` ;#EΩ 8#9%+#+5&$$+,A1+6+"+,)$&3"#,+'&'$)"(+' ),+# 3 O ` 3 V ` ;R#BΩ-# )"1# 3 ` ` 3 QR ` TR#BΩ8 # W+()//# $%)$# $%+# 1+:&(+# *),)5+$+,'# ),+# β J ` PRβ : ` QR- #$ 4, ` TR #H-# $ 41 ` ;R #H8

Solution G&"(+#$%+#'$)6+#&'#40//2#=)/)"(+1-#.+#()"#0'+#$%+#1&44+,+"$&)/#%)/4A(&,(0&$#'%3."#&"#K&68#Q;8PTX)Y8#9%+#&"*0$ ,+'&'$)"(+# 3 <( #&'#$.&(+#$%+#:)/0+#34# 5 π Q 3 <( ` ;5 π Q ` ; β : ⁄ ' 2Q .%+,+ LZ # &Q U × QR A A ` AAAAAAAAAAAAAAAAAAAAA ` R8;#5L[H ' 2Q ` AAAAAA LT $> ;U × QR

P

9%&'#&'#13"+#&"#$%+#SMU;TP#3*#)5*-#.%3'+#(&,(0&$#&'#1+'(,&=+1#)"1#)")/2C+1#&"#6,+)$#1+$)&/#&"#d,)2# +$ )/8-#X;RR`Y8

12.7 Modern Techniques for the Design of BJT Op Amps

1039

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!"#$% 8 × 7E + (* ! /////////////// ! 7EE'HΩ E68 !&'()*+',"-'$"&.,/0).0#),',.1*$0&*+#0,1*0-%'2-'$"&.,',"-'&#,3#,',&'4.&#*+'1$'$"&2*')*'5)46'7869:;<='1*+ ()*+' & '7'1$ ( ,I & '7 ! //////////// / v (* ⁄ 8 >,'*&+-'!'2-'"1?-'(&#.'31.1@@-@'.-$)$,1*0-$',&'4.&#*+% " ./ 8E'G/ / ! //////////// ! 9'KΩ - )7 ! ////////// J'µ> # $7 + I ! 8E'HΩ " .0 :E'G / ! //////////////// ! :'KΩ - )I ! /////// 7E'µ> # $I " 8J'CG 7 - 1I $ //////// ! //////3/ ! //////////////// ! 86J'HΩ 7E'µ> 2 'I # $I A
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1040 Chapter 12 Operational-Amplifier Circuits

Example 12.5 continued

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β: QR A A ` AAAAAAAAAAAAAAAAAAAAAAA ` ;U#BΩ 5 π ` ` AAAAAAA ' 2` R8P#5L[H 9%0' LT

T

3 6` ` ; ^ ( TR || ;U ) × QR ( Q ^ R8P × ; × QR ) ` Q;8`#EΩ 9%+# ,+'&'$)"(+# 3 6O # &'# $%+# 30$*0$# ,+'&'$)"(+# 34# ! O - # .%&(%# %)'# )"# +5&$$+,A1+6+"+,)$&3"# ,+'&'$)"(+ ( 3 O || 5 6Q ) ! 3 O 8 #9%0'3 6O ` 5 6O ^ ( 3 O || 5 π O ) ( Q ^ ' 2O 5 6O ) .%+,+ $ 4, TR#H A ` AAAAAAAAAAAAAAA ` T#EΩ 5 6O ` AAAAAAA QR µL # &O # &O QR#µL A ` AAAAAAAAAAAAAAAA ' 2O ` AAAAAA ` R8P#5L[H ;U#5H $>

βJ PR A ` AAAAAAA ` QRR#BΩ 5 π O ` AAAAAAA ' 2O R8P 9%0'LT

T

3 6O ` T ^ ( ;R || QRR ) × QR ( Q ^ R8P × T × QR ) ` ;T#EΩ 30 ;#EΩ AAAAAA ` AAAAAAAAAAAAAAA ` Q#EΩ ; ;

12.7 Modern Techniques for the Design of BJT Op Amps

9%+#$3$)/#,+'&'$)"(+#3#()"#"3.#=+#430"1#)'# 3 ` Q;8` || ;T || Q ` R8V`#EΩ

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` R8QV × R8V` × QR ` QZR#H[H

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1041

1042 Chapter 12 Operational-Amplifier Circuits VCC R9

R10

I3

I4

VBIAS3

(determined by the op amp bias network)

Q10

Q9

vO2

In

vO1 Q8

Q7

Common-Mode Feedback Circuit

Out

VB

I2

I1

R8

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Figure 12.44 9%+#()'(31+#30$*0$#(&,(0&$#34#$%+#&"*0$#'$)6+#)"1#$%+#7EK#(&,(0&$#$%)$#,+'*3"1'#$3#$%+#(35A 53"A531+#(35*3"+"$#$ &) ` QAA;A ( v -Q ^ v -; ) #=2#)1>0'$&"6#$@#'3#$%)$#!O_!V#(3"10($#+@0)/#(0,,+"$'#$3#!`_!QR )"1#!O_!QR#3*+,)$+#&"#$%+#)($&:+#531+8

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Figure 12.45 L"# 3*# )5*# '+(3"1# '$)6+# &"(3,*3,)$&"6# $%+# (3553"A531+# 4++1=)(B# (&,(0&$# 43,# $%+# &"*0$ '$)6+8# S3$+# $%)$# $%+# (&,(0&$# 6+"+,)$+'# $%+# :3/$)6+# $J# "++1+1# $3# =&)'# $%+# ()'(31+# (&,(0&$# &"# $%+# 4&,'$# '$)6+8 g&31+#.#&'#)#G(%3$$B2A=),,&+,#1&31+#.%&(%#+?%&=&$'#)#43,.),1#:3/$)6+#1,3*#34#)=30$#R8PH8

12.7 Modern Techniques for the Design of BJT Op Amps

1043

v -Q ` $ &) ^ v ( ⁄ ; v -; ` $ &) L v ( ⁄ ;

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Example 12.6 73"'&1+,#$%+#3*+,)$&3"#34#$%+#(&,(0&$#&"#K&68#Q;8PP8#L''05+#$%)$# $ #&) * R8V#H #)"1#$%0'#$%+#,1,#&"*0$ *)&,# XK&68# Q;8P;Y# &'# 3448# <+"(+# # T ` # P ` R8 # L/'3# )''05+# $%)$# 3"/2# 1(# :3/$)6+'# ),+# *,+'+"$# )"1# $%0' # Q ` # ; ` U#µL8 # M)(%# 34# ! O # $3# ! QR # &'# =&)'+1# )$# QR# µL-# $ && ` T#H- # $ J!LGT# ` $ && L Q3 O ` 3 V ` ;R#BΩ- #)"1# 3 ` ` 3 QR ` TR#BΩ8 #S+6/+($#=)'+#(0,,+"$'#)"1#"+6/+($#$%+#/3)1&"6#+44+($#34#$%+ 7EK#(&,(0&$#3"#$%+#30$*0$#"31+'#34#$%+#()'(31+#(&,(0&$8#9%+#7EK#(&,(0&$#*,3:&1+'#$ @ ` $ &) ^ R8P 8# X)Y g+$+,5&"+#$%+#"35&")/#:)/0+'#34#$ @ #)"1# $ &) 8#g3+'#$%+#:)/0+#34# $ &) #+"'0,+#3*+,)$&3"#&"#$%+#)($&:+ 531+#43,#!O#$%,306%#!QRb# X=Y !4#$%+#7EK#(&,(0&$#.+,+#"3$#*,+'+"$-#.%)$#.30/1#=+#$%+#(%)"6+#&"# v -Q #)"1# v -; #X&8+8-#&"# $ &) Y#)'#) ,+'0/$#34#)#(0,,+"$#5&'5)$(%# ∆# ` R8T#µL #=+$.++"# ! O L ! V #)"1# ! ` L ! QR b#\'+#$%+#30$*0$#,+'&'$)"(+ :)/0+'#430"1#&"#M?)5*/+#Q;8U8 X(Y S3.-#&4#$%+#7EK#(&,(0&$#&'#(3""+($+1-#.%)$#(%)"6+#.&//#&$#()0'+#&"#$ @ #$3#+/&5&")$+#$%+#(0,,+"$#5&'A 5)$(%# ∆# b#D%)$#&'#$%+#(3,,+'*3"1&"6#(%)"6+#&"#$ &) #4,35#&$'#"35&")/#:)/0+b

Solution X)Y#9%+#"35&")/#:)/0+#34# $ @ #&'#430"1#)'#43//3.'] $ @ ` $ @DO ^ ( # DO ^ # Q )3 O LT

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1044 Chapter 12 Operational-Amplifier Circuits

Example 12.6 continued

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12.7 Modern Techniques for the Design of BJT Op Amps

1045

X(Y D&$%#$%+#7KJ#(&,(0&$#&"#*/)(+-#$%+#4++1=)(B#.&//#)1>0'$#$ @ #=2# ∆$ @ #'3#$%)$#$%+#(0,,+"$'#&"# ! O #)"1# ! V .&//#(%)"6+#=2#)#&"(,+5+"$#+@0)/#$3# ∆# -#$%0'#,+'$3,&"6#(0,,+"$#+@0)/&$28#G&"(+#)#(%)"6+# ∆$ @ #,+'0/$'#&" ∆$ @ ∆# &O ` ∆# &V ` AAAAAAAAAAAAAAAAAA A 5 EO ^ 3 O $%+" ∆$ @ ∆# ` AAAAAAAAAAAAAAAAAA A 5 EO ^ 3 O ∆$ @ ` ∆# ( 5 EO ^ 3 O ) ` R8T#µL ;U#5H AAAAAAAAAAAAAAAA ^ ;R#BΩ QR#µL ` R8T × ;;8U ` Z8OU#5H 73,,+'*3"1&"6/2 ∆$ &) ` ∆$ @ ` Z8OU#5H 9%0'-#$3#,+'$3,+#$%+#(0,,+"$#+@0)/&$2-#$%+#(%)"6+#,+@0&,+1#&"# $ @ #)"1# $ &) #&'#3"/2#Z8OU#5H8

12.7.5 Output-Stage Design for Near Rail-to-Rail Output Swing L'#5+"$&3"+1#+),/&+,-#531+,"#/3.A:3/$)6+#=&*3/),#3*#)5*'#()""3$#)443,1#$3#0'+#$%+#(/)''&()/ +5&$$+,A43//3.+,A=)'+1#(/)''#LJ#30$*0$#'$)6+^#&$#.30/1#(3"'05+#$33#50(%#34#$%+#*3.+,#'0*A */2# :3/$)6+8# !"'$+)1-# )# (35*/+5+"$),2# *)&,# 34# (3553"A+5&$$+,# $,)"'&'$3,'# ),+# 0$&/&C+1-# )' '%3."#&"#K&68#Q;8PZ8#9%+#30$*0$#$,)"'&'$3,'# ! : #)"1# ! J #),+#3*+,)$+1#&"#)#(/)''#LJ#4)'%&3"8 92*&()//2-# < 0 # ()"# =+# )'# %&6%# )'# QR# 5L# $3# QU# 5L# )"1# &'# 1+$+,5&"+1# =2# v - # )"1# 3 0 8 # K3, < 0 ` R- # < : ` < J ` # ! - #.%+,+#$%+#@0&+'(+"$#(0,,+"$# # ! #&'#"3,5)//2#)#4,)($&3"#34#)#5&//&)5*8# 9%+#30$*0$#'$)6+#&"#K&68#Q;8PZ#&'#1,&:+"#=2#$.3#8E1=5=+E"7B+"ESB=A"8<',=A8-# v @: #)"1# v @J 8 D%+"# v @: #)"1# v @J #),+#%&6%-# ! J #'0**/&+'#$%+#/3)1#(0,,+"$#&"#$%+#1&,+($&3"#3**3'&$+#$3#$%)$ '%3."U#)"1#$%+#30$*0$#:3/$)6+# v - #()"#'.&"6#$3#.&$%&"#R8Q#H#3,#'3#34#6,30"18#!"#$%+#5+)"A $&5+-# ! : # &'# &")($&:+8# S+:+,$%+/+''-# &"# 3,1+,# $3# 5&"&5&C+# (,3''3:+,# 1&'$3,$&3"-# ! : # &' VCC

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1046 Chapter 12 Operational-Amplifier Circuits *,+:+"$+1#4,35#$0,"&"6#344#)"1#&'#43,(+1#X)'#.&//#=+#'%3."#'%3,$/2Y#$3#(3"10($#)#5&"&505 (0,,+"$#34#)=30$# # ! ⁄ ; 8 9%+#3**3'&$+#%)**+"'#.%+"# v @: #)"1# v @J #),+#/3.]# ! : #'0**/&+'#$%+#/3)1#(0,,+"$# < 0 #&"#$%+ 1&,+($&3"#&"1&()$+1-#)"1# v - #()"#63#0*#)'#%&6%#)'# $ && L R8Q#H 8#!"#$%+#5+)"$&5+-# ! J #&'#&")(A $&:+# =0$#&'# *,+:+"$+1#4,35# $0,"&"6#344#)"1#43,(+1#$3#(3"10($#)# 5&"&505#(0,,+"$# 34# )=30$ # ! ⁄ ;8 K,35#$%+#1+'(,&*$&3"#)=3:+-#.+#'++#$%)$# v - #()"#'.&"6#$3#.&$%&"#R8Q#H#34#+)(%#34#$%+#'0*A */2#,)&/'8#9%&'#"+),#,)&/A$3A,)&/#3*+,)$&3"#&'#$%+#5)>3,#)1:)"$)6+#34#$%&'#7M#30$*0$#'$)6+8#!$' 1&')1:)"$)6+#&'#$%+#,+/)$&:+/2#%&6%#30$*0$#,+'&'$)"(+8#<3.+:+,-#6&:+"#$%)$#$%+#3*#)5*#.&// )/53'$#)/.)2'#=+#0'+1#.&$%#)#"+6)$&:+A4++1=)(B#/33*-#$%+#(/3'+1A/33*#30$*0$#,+'&'$)"(+#()" '$&//#=+#:+,2#/3.8 A Buffer/Driver Stage 9%+#30$*0$#$,)"'&'$3,'#()"#=+#()//+1#3"#$3#'0**/2#(0,,+"$'#&"#$%+ QR#5L#$3#QU#5L#,)"6+8#D%+"#$%&'#%)**+"'-#$%+#=)'+#(0,,+"$'#34# ! : #)"1# ! J #()"#=+#'0='$)"A $&)/#X,+()//#$%)$# β : ! QR #)"1# β J ! PRY8#G0(%#/),6+#(0,,+"$'#()""3$#0'0)//2#=+#'0**/&+1#1&,+($A /2#=2#$%+#)5*/&4&+,#'$)6+#*,+(+1&"6#$%+#30$*0$#'$)6+8#W)$%+,#)#=044+,[1,&:+,#'$)6+#&'#0'0)//2 "++1+1-#)'#'%3."#&"#K&68#Q;8PO8#<+,+#)"#+5&$$+,#43//3.+,# ! T #&'#0'+1#$3#1,&:+#! J 8 #<3.+:+,=+()0'+#34#$%+#/3.# β : - #)#130=/+#=044+,#(3"'&'$&"6#34#(35*/+5+"$),2#+5&$$+,#43//3.+,'#! Q#)"1 ! ; #&'#0'+1#$3#1,&:+#! : 8 #9%+#1,&:+,#'$)6+#&'#4+1#=2#$.3#'+*),)$+#=0$#&1+"$&()/#'&6")/'# v #: #)"1 v #J #$%)$#(35+#4,35#$%+#*,+(+1&"6#)5*/&4&+,#'$)6+#X.%&(%#&'#0'0)//2#$%+#'+(3"1#'$)6+Y#&"#$%+ 3*#)5*#(&,(0&$8Z

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12.7 Modern Techniques for the Design of BJT Op Amps

1047

EXERCISE 12.30 X)Y#K3,#$%+#(&,(0&$#&"#K&68#Q;8PO-#4&"1#$%+#(0,,+"$#6)&"#4,35#+)(%#34#$%+# v #: #)"1# v #J #$+,5&")/'#$3 $%+#30$*0$#&"#$+,5'#34# β : #)"1# β J 8 X=Y#K3,# < 0 ` ± QR #5L-#%3.#50(%#'&6")/#(0,,+"$#&'#"++1+1#)$#$%+# v #: #)"1# v #J #&"*0$'b ; ; Ans. X)Y#β J β : -# β J ^#X=Y#;8U#µL-#Z8;U#µL

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1048 Chapter 12 Operational-Amplifier Circuits

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12.7 Modern Techniques for the Design of BJT Op Amps

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1050 Chapter 12 Operational-Amplifier Circuits

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CHAPTER 12

PROBLEMS

1052 Chapter 12 Operational-Amplifier Circuits 12.10 Z$)1*,()-5#$6789$*+$-.+$'#(#.?2&:5$)"-)$&:$;&5< =><=$&($%*0:3$)*$"-@#$-$(2#1$'-)#$*%$FP$ H[µ'$-:3$-$0:&)4,5-&: ?-:31&3)"$9+$*%$OP$7HJ<

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Problems 1053

CHAPTER 12

%&'()$ -:3$ (#/*:3$ ()-5#($ "-($ -$ %'#Y0#:/4$ 9: ! ' 2T ⁄ ; π & : < ]*1I$ &%$ )"&($ &($ )"#$ *:24$ :*:3*.&:-:)$ +*2#I$ 1"-)$ &($ )"# 2-'5#()$@-20#$)"-)$&:$/-:$?#$S#G+'#((#3$-($-$%'-/)&*:$*%$&0 U 1"&2#$ -$ +"-(#$ .-'5&:$ *%$ [O°$ &($ -/"&#@#3i$ Z((0.#$ )"-)$ -22 )'-:(&()*'($ -'#$ *+#'-)#3$ -)$ )"#$ (-.#$ ?&-($ /0''#:)$ -:3$ *@#', 3'&@#$@*2)-5#<

PROBLEMS

Section 12.3: The 741 Op-Amp Circuit 12.23 C:$)"#$[N=$*+,-.+$/&'/0&)$*%$;&5<$=><=MI$!=I$!>I$!OI

-:3$ !F$ -'#$ ?&-(#3$ -)$ /*22#/)*'$ /0''#:)($ *%$ \$µZW$-:3$!=[$&($?&-(#3$-) -$/*22#/)*'$/0''#:)$*%$OOP$µZ<$Z22$)"#(#$3#@&/#($-'#$*%$)"# m()-:3-'3$,1,n$)4+#I$"-@&:5$#%$=$=PL=N$ZI$β$=$>PPI$-:3$$4$= =>O$A<$;*'$#-/"$*%$)"#(#$)'-:(&()*'(I$%&:3$$@DI$'2I$5EI$5π I$-:3 56<$ j'*@&3#$ 4*0'$ '#(02)($ &:$ )-?2#$ %*'.<$ S]*)#$ )"-)$ )"#(# +-'-.#)#'$@-20#($-'#$0)&2&J#3$&:$)"#$)#G)$&:$)"#$-:-24(&($*% )"#$[N=$/&'/0&)
D 12.24 ;*'$ )"#$ S.&''*'U$ ?&-($ /&'/0&)$ ("*1:$ &:$ ;&5<

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12.25 !'-:(&()*'$!=M$&:$)"#$/&'/0&)$*%$;&5<$=><=M$/*:(&()(I

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12.26 C:$ )"#$ /&'/0&)$ *%$ ;&5<$ =><=MI$ !=$ -:3$ !>$ #G"&?&)

#.&))#'L?-(#$?'#-V3*1:$-)$[$AI$1"&2#$%*'$!M$-:3$!N$(0/"$?'#-V3*1:$ *//0'($ -)$ -?*0)$ OP$ A<$ D"-)$ 3&%%#'#:)&-2$ &:+0) @*2)-5#$ 1*023$ '#(02)$ &:$ )"#$ ?'#-V3*1:$ *%$ )"#$ &:+0),()-5# )'-:(&()*'(i

D *12.27 ;&50'#$j=><>[$("*1($)"#$6789$@#'(&*:$*%$)"#

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Section 12.4: DC Analysis of the 741 D 12.28 ;*'$)"#$[N=$/&'/0&)I$#()&.-)#$)"#$&:+0)$'#%#'#:/#

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CHAPTER 12

PROBLEMS

1054 Chapter 12 Operational-Amplifier Circuits -(+#/)($*%$)"#$(#2#/)#3$0:&)($)*$?#$:*'.-2I$1"-)$.&:&.0.$βJ -:3$1"-)$βJ$@-'&-)&*:$-'#$&.+2i

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Problems 1055

12.54 6*:(&3#'$ )"#$ +*(&)&@#$ /0''#:),2&.&)&:5$ /&'/0&)

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CHAPTER 12

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PART III

Digital Integrated Circuits CHAPTER 13

CMOS Digital Logic Circuits

1060

CHAPTER 14

Advanced MOS and Bipolar Logic Circuits

1142

CHAPTER 15

Memory Circuits

T

1202

here are two indisputable facts about digital systems. They have dramatically changed our lives; and the digital revolution is driven by microelectronics. Evidence of the pervasiveness and influence of digital systems can be found by thinking of what we do in our daily lives. Digital circuits exist in almost every electrical appliance we use in our homes; in the vehicles and transportation systems we use to travel; in the telephones and, most obviously, the cell phones we use to communicate; in the medical equipment needed to care for our health; in the computers we use to do our work; and in the audio and video systems and the radio and TV sets we use to entertain ourselves. Indeed, it is very difficult to conceive of modern life without digital systems, none of which would have been possible without microelectronics. Although the idea of a digital computing machine was conceived as early as the 1830s, early implementations were very cumbersome and expensive mechanical devices. The first serious digital computers using vacuum tubes appeared in the 1930s and 1940s. These early computers used thousands of tubes and were housed literally in many rooms. Their fundamental limitation was low

reliability: vacuum tubes had a finite life and needed large amounts of power. Had it not been for the invention of the transistor in 1947 ushering in the era of solid-state electronics, digital computers would have remained specialized machines used primarily in military and scientific applications. By the mid 1950s, the first digital logic gates made of discrete bipolar transistors became commercially available. The invention of the integrated circuit in the late 1950s was also key, leading to the first digital IC in the early 1960s. Early digital ICs were made of bipolar transistors, with the most successful logic-circuit family of this type being transistortransistor logic (or TTL), which dominated digital circuit design, until the early 1980s. Bipolar was replaced by NMOS, and NMOS by CMOS, again predominantly because of power dissipation and the need to pack more and more transistors on each IC chip. Bearing out Moore’s law, which predicted in 1968 that IC chips would double the number of their transistors every two to three years (see Section 13.5), digital ICs have grown from a few transistors to 2.3 billion devices and to memory chips with 4 Gbit capacity. Part III aims to provide a brief but nonetheless comprehensive and sufficiently detailed exposure to digital IC design. Our treatment is almost self-contained, requiring for the most part only a thorough understanding of the MOSFET material presented in Chapter 5. Thus Part III can be studied right after Chapter 5. The only exceptions to this are the last two sections in Chapter 14, which require knowledge of the BJT (Chapter 6). Also, knowledge of the MOSFET internal capacitances (Section 9.2.2) will be needed. Chapter 13 is the cornerstone of Part III. It provides an introduction to digital circuits and then concentrates on the bread-and-butter topic of digital IC design: the CMOS inverter and logic gates. Today, CMOS represents 98% of newly designed digital systems. The material in Chapter 13 is the minimum needed to learn something meaningful about digital circuits; it is a must study! Chapter 14 builds on the foundation established in Chapter 13 and introduces three important types of MOS logic circuits and a significant family of bipolar logic circuits. The chapter concludes with an interesting digital circuit technology that attempts to combine the best of bipolar and CMOS: BiCMOS. Digital circuits can be broadly divided into logic and memory circuits. The latter is the subject of Chapter 15.

1059

CHAPTER 13

CMOS Digital Logic Circuits Introduction 13.1

13.4 CMOS Logic-Gate Circuits

1061

Digital Logic Inverters

13.2 The CMOS Inverter

1062

1089

13.3 Dynamic Operation of the CMOS Inverter 1098

1110

13.5 Implications of Technology Scaling: Issues in Deep-Submicron Design 1122 Summary

1132

Problems

1134

IN THIS CHAPTER YOU WILL LEARN 1. How the operation of the basic element in digital circuits, the logic inverter, is characterized by such parameters as noise margins, propagation delay, and power dissipation, and how it is implemented by using one of three possible arrangements of voltage-controlled switches (transistors). 2. That the three most significant metrics in digital IC design are speed of operation, power dissipation, and silicon area, and that each design is in effect a trade-off among the three metrics. 3. How and why CMOS has become the dominant technology for digital IC design. 4. The structure, circuit operation, static and dynamic performance analysis, and the design of the CMOS inverter. 5. The synthesis and design optimization of CMOS logic circuits. 6. The implications of technology scaling (Moore’s law) over 40 years and continuing, and some of the current challenges in the design of deepsubmicron ( < 0.25 µm) circuits.

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1061

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13.1 Digital Logic Inverters

A VDD

vO

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Q in triode

Saturation

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1063

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13.1 Digital Logic Inverters

Table 13.1 Important Parameters of the VTC of the Logic Inverter (Refer to Fig. 13.3) "'!0 "')0 "&!0 "&)0 +,!0 +,)0

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Slope $ 1 VM

VIL

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1065

1066 Chapter 13 CMOS Digital Logic Circuits

13.1.4 The Ideal VTC <2,*A3,/1#-6*6&13'&%%(*&'#/,/*&/*1-*+2&1*8-6/1#131,/*&6*#5,&%*=<>*9-'*&6*#60,'1,';*<2,*&6/+,' 9-%%-+/*5#',81%(*9'-$*12,*4',8,5#6:*5#/83//#-6?*J6*#5,&%*=<>*#/*-6,*12&1*$&7#$#K,/*12,*-31L 431*/#:6&%*/+#6:*&65*12,*6-#/,*$&':#6/;*D-'*&6*#60,'1,'*-4,'&1,5*9'-$*&*4-+,'*/344%(*" %% 7 $&7#$3$*/#:6&%*/+#6:*#/*-.1,5*+2,6 " ') ! " %%

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1068 Chapter 13 CMOS Digital Logic Circuits H : %G ! E%%% ( µ $ - ?0 ) ????? ( " BG I " # ) ! Ans. N9%Pc%J Ω 9%M9%ENO% µH

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1069

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Example 13.1

Resistively Loaded MOS Inverter

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1070 Chapter 13 CMOS Digital Logic Circuits

Example 13.1 continued

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13.1 Digital Logic Inverters

1071

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1072 Chapter 13 CMOS Digital Logic Circuits

Example 13.1 continued

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13.1 Digital Logic Inverters

1073

% !"2$7 EEDNP EEDNP ? ! NO%JΩ E % ! ?????????????????????? ! ?????????????????????????????????????? I] J′$ ( H ⁄ ! ) FMM × EM × EDO !"*%#.8*+)*+%,#$$#(')*$%(-B*+%-.4:%B"*.%)"*%-2)(2)%#$%4-B7%#.%B"#&"%&'$*%)"*%&2++*.)%,+'B.%6+-5%)"*%$2(? (4:%#$ " %% I " '! I MDEN? ? ! EDc ??????????????????????? ! ]^%µI & %% ! ???????????????????????? NO%JΩ E% '.,%)"*%(-B*+%,+'B.%6+-5%)"*%$2((4:%,2+#./%)"*%4-B?-2)(2)%#.)*+8'4%#$ K % ! " %% & %% ! EDc × ]^ ! ENE%µH >#.&*%)"*%#.8*+)*+%$(*.,$%"'46%-6%)"*%)#5*%#.%)"#$%$)')*7 E K %'8*+'/* ! ??? K % ! ]MDO%µH N @*C H*%.-B%&'.%5'J*%'%6*B%&-55*.)$%-.%)"*%&"'+'&)*+#$)#&$%-6%)"#$%#.8*+)*+%&#+&2#)%#.%&-5('+#$-.%)-%)"* #,*'4%&"'+'&)*+#$)#&$0 1.

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EXERCISES D13.3 1.%'.%'))*5()%)-%+*,2&*%)"*%+*T2#+*,%8'42*%-6% E % 7 %)-%EM% JΩ7 %)"*%,*$#/.*+%-6%)"*%#.8*+)*+%#.%SG? '5(4*%EFDE%,*&#,*$%)-%J**(%)"*%('+'5*)*+% " 0 %2.&"'./*,%32)%#.&+*'$*$%H[!D%H"')%#$%)"*%.*B%8'42* +*T2#+*,%6-+%H[!b%U-%)"*%.-#$*%5'+/#.$%&"'./*b%H"')%,-*$%)"*%(-B*+%,#$$#(')#-.%3*&-5*b Ans. FD^O9%.-9%EOE% µH D13.4 1.%'.%'))*5()%)-%+*,2&*%)"*%+*T2#+*,%8'42*%-6% E % %)-%EM% JΩ7 %)"*%,*$#/.*+%-6%)"*%#.8*+)*+%#.%SG'5? (4*$%EFDE%,*&#,*$%)-%&"'./*% " 0 %B"#4*%J**(#./%H[!%2.&"'./*,D%H"')%.*B%8'42*%-6% " 0 %#$%.**,*,b H"')%,-%)"*%.-#$*%5'+/#.$%3*&-5*b%H"')%,-*$%)"*%(-B*+%,#$$#(')#-.%3*&-5*b Ans. " 0 ! MDNN%K9 % +, ! ! MDP]%K7 % +, ) ! MDP`%K9 %EF`% µH

1074 Chapter 13 CMOS Digital Logic Circuits !

Example 13.2

The Saturated NMOS-Load Inverter

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λ : ! λ ! ! ?$/42 + , ≡ + -: ⁄ + -! 9 : =-> 8#'$$ "" ! :9Q$P? $ $ * ! <9R$P?$( . ⁄ ' ) : ! R? $/42$( . ⁄ ' ) ! ! HHH ? $5142$47)&'1(/.$%/.7&0$5#'$/..$,/'/)H R &*&'0$/42$5#'$*+&$4#10&$)/'61409 ! =(> I5$ +′- ! ;<<$µG ⁄ P ? $5142$*+&$/%&'/6&$,#3&'$21001,/*&2$14$*+&$14%&'*&'?$/007)146$*+/*$1*$0,&420$+/.5 *+&$*1)&$14$&/(+$#5$1*0$*3#$0*/*&09 =2> J7/.1*/*1%&.B$2&0('1-&$+#3$*+&$-#2B$&55&(*$14$ # ! $/55&(*0$*+&$4#10&$)/'61409 =&> K#))&4*$ #4$ *+&$ (+/'/(*&'10*1(0$ #5$ *+10$ 14%&'*&'$ 1),.&)&4*/*1#4$ %10HLH%10$ *+&$ 12&/.$ (+/'/(*&'10*1(09 M#3$071*/-.&$10$*+10$(1'(71*$5#'$1),.&)&4*/*1#4$14$IK$5#')N

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13.1 Digital Logic Inverters

1075

Solution @'C%!"*%#.8*+)*+%K!;%&'.%3*%,*)*+5#.*,%/+'("#&'44:%3:%$2(*+#5(-$#./%)"*%4-',%&2+8*7%B"#&"%#$%)"*% ( I v &"'+'&)*+#$)#&%-6%)"*%,#-,*?&-..*&)*,%)+'.$#$)-+% L N 7 %$"-B.%#.%R#/D%EFDEE@3C7%-.%)"*% ( I v %&"'+'&)*+#$)#&$%-6 L ED%I$%B*%"'8*%,-.*%#.%)"*%/+'("#&'4%'.'4:$#$%-6%<=>RS!%&#+&2#)$%#.%>*&)#-.%ODP7%B*%$"#6)%)"*%4-',%&2+8* "-+#Q-.)'44:%3:% " %% %'.,%64#(%#)%'+-2.,%)"*%8*+)#&'4%'G#$7%'$%$"-B.%#.%R#/D%EFDEE@&CD%!"*%+*$24)#./%K!;%#$ $"-B.%#.%R#/D%EFDEE@,CD R-+% v & < " #E7% L E %B#44%3*%-667%B"#&"%6-+&*$%)"*%&2++*.)%#.% L N %)-%3*%Q*+-D%!+'.$#$)-+% L N 7 %'4)"-2/"%#) B#44%3*%&-.,2&)#./%'%Q*+-%&2++*.)7%B#44%"'8*%'%8-4)'/*%,+-(%-6%" #N D%!"#$%#$%'%+*$24)%-6%#)$% ( I v %&"'+'&)*+#$)#& $"-B.%#.%R#/D%EFDEE@3CD%!"2$%)"*%-2)(2)%8-4)'/*% v ' %B#44%.-)%+*'&"% " %% %32)%B#44%3*%')%" %% I " #N 7 %)"')%#$7N " ') ! " %% I " #

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1076 Chapter 13 CMOS Digital Logic Circuits

Example 13.2 continued

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13.1 Digital Logic Inverters

1077

!"2$7 +, ! ! " &! I " '! ! MDO I MDMP ! MDP]%K +, ) ! " ') I " &) ! EDF I MD^O ! MDOO%K @&C%!"*%#.8*+)*+%,#$$#(')*$%(-B*+%-.4:%B"*.% v ' ! " '! D %1.%)"#$%&'$*7%)"*%&2++*.)%,+'B.%6+-5%)"*%$2((4:%#$ E N & %% ! ( %N ! ??? J $N ( " %% I " '! I " # ) N !"2$7 E E N & %% ! ??? × FMM × ??? × ( EDc I MDMP I MDO ) N O ! P^D]%µI '.,7 K % ! " %% & %% ! EDc × P^D] ! cOD^%µH >#.&*%)"*%#.8*+)*+%#$%#.%)"*%4-B?-2)(2)%$)')*%6-+%"'46%)"*%)#5*7 E K %'8*+'/*%% ! ??? × cOD^ ! PND` %µH N @,C%>#.&*%)"*%3-,:%-6% L N %#$%&-..*&)*,%)-%/+-2.,7%#)$%$-2+&*?)-?3-,:%8-4)'/*% " GM %#$ "GM ! v ' W-B7%$#.&*%)"*%)"+*$"-4,%8-4)'/*%#$%/#8*.%3: " #N ! " #M H γ [ " GM H Nφ D I Nφ D ]

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1078 Chapter 13 CMOS Digital Logic Circuits

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1083

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1084 Chapter 13 CMOS Digital Logic Circuits

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1085

1086 Chapter 13 CMOS Digital Logic Circuits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GaAs

13.1 Digital Logic Inverters

$&5,*4-//#.%,*%,0,%/*-9*#61,:'&1#-6*B-'*8#'83#1L4&8R#6:*5,6/#1#,/C*&65*&*'&6:,*-9*&44%#8&1#-6/) 6,#12,'*-9*+2#82*+-3%5*2&0,*.,,6*4-//#.%,*+#12*.#4-%&'*1,826-%-:(;*D3'12,'$-',)*>b^" 8-61#63,/*1-*&50&68,)*+2,',&/*12,',*&44,&'*1-*.,*9,+*#66-0&1#-6/*&1*12,*4',/,61*1#$,*#6*.#4-L %&'*5#:#1&%*8#'83#1/;*"-$,*-9*12,*',&/-6/*9-'*>b^"*5#/4%&8#6:*.#4-%&'*1,826-%-:(*#6*5#:#1&% &44%#8&1#-6/*&',*&/*9-%%-+/; 1. >b^"*%-:#8*8#'83#1/*5#//#4&1,*$382*%,//*4-+,'*12&6*.#4-%&'*%-:#8*8#'83#1/*&65*123/*-6, 8&6*4&8R*$-',*>b^"*8#'83#1/*-6*&*82#4*12&6*#/*4-//#.%,*+#12*.#4-%&'*8#'83#1/; 2. <2,*2#:2*#6431*#$4,5&68,*-9*12,*b^"*1'&6/#/1-'*&%%-+/*12,*5,/#:6,'*1-*3/,*82&':,*/1-'L &:,*&/*&*$,&6/*9-'*12,*1,$4-'&'(*/1-'&:,*-9*#69-'$&1#-6*#6*.-12*%-:#8*&65*$,$-'(*8#'L 83#1/;*<2#/*1,826#A3,*8&66-1*.,*3/,5*#6*.#4-%&'*8#'83#1/; 3. <2,*9,&13',*/#K,*B#;,;)*$#6#$3$*82&66,%*%,6:12C*-9*12,*b^"*1'&6/#/1-'*2&/*5,8',&/,5*5'&L $&1#8&%%(*-0,'*12,*(,&'/)*+#12*/-$,*',8,61%(*',4-'1,5*5,/#:6/*31#%#K#6:*82&66,%*%,6:12/*&/ /2-'1*&/*FW*6$;*<2#/*4,'$#1/*0,'(*1#:21*8#'83#1*4&8R#6:*&65)*8-'',/4-65#6:%()*0,'(*2#:2 %,0,%/*-9*#61,:'&1#-6;*J*$#8'-4'-8,//-'*82#4*',4-'1,5*#6*WQQ`*2&5*W;F*.#%%#-6*1'&6/#/1-'/; ^9*12,*0&'#-3/*9-'$/*-9*>b^")*8-$4%,$,61&'(*>b^"*8#'83#1/*.&/,5*-6*12,*#60,'1,'*/135#,5 #6*",81#-6*EF;W*&',*12,*$-/1*+#5,%(*3/,5;*<2,(*&',*&0&#%&.%,*.-12*&/*%+#--2%4#-)(&$!)*"#!)5 BAABC* 8#'83#1* 4&8R&:,/* B8-61#6:* EIEQ* %-:#8* :&1,/C* &65* +)5&0+2%4#-)( &$!)*"#!)5* BFABC 8#'83#1* 4&8R&:,/* BEQIEQQ* :&1,/* 4,'* 82#4C* 9-'* &//,$.%#6:* 5#:#1&%* /(/1,$/* -6* 4'#61,5L8#'83#1 .-&'5/;* b-',* /#:6#9#8&61%()* 8-$4%,$,61&'(* >b^"* #/* 3/,5* #6* 3)";2-#"*)2%4#-)2&$!)*"#!)5 8?@AB9*%-:#8*B+#12*$#%%#-6/*-9*:&1,/*4,'*82#4C*&65*$,$-'(L8#'83#1*5,/#:6;*@6*/-$,*&44%#8&L 1#-6/)*8-$4%,$,61&'(*>b^"*#/*/344%,$,61,5*.(*-6,*B-'*.-12C*-9*1+-*-12,'*b^"*%-:#8*8#'83#1 9-'$/;*<2,/,*&',*4/,35-LZb^")*/-L6&$,5*.,8&3/,*-9*12,*/#$#%&'#1(*-9*#1/*/1'3813',*1-*Zb^" %-:#8)*&65*4&//L1'&6/#/1-'*%-:#8)*.-12*-9*+2#82*+#%%*.,*/135#,5*#6*>2&41,'*EG; J*9-3'12*1(4,*-9*>b^"*%-:#8*8#'83#1*31#%#K,/*5(6&$#8*1,826#A3,/*1-*-.1*9&/1,'*8#'83#1 -4,'&1#-6)*+2#%,*R,,4#6:*12,*4-+,'*5#//#4&1#-6*0,'(*%-+;*U(6&$#8*>b^"*%-:#8)*/135#,5*#6 >2&41,'*EG)*',4',/,61/*&6*&',&*-9*:'-+#6:*#$4-'1&68,;*a&/1%()*>b^"*1,826-%-:(*#/*3/,5*#6 12,*5,/#:6*-9*$,$-'(*82#4/)*&/*+#%%*.,*5,1&#%,5*#6*>2&41,'*EM; Bipolar <+-*%-:#8L8#'83#1*9&$#%#,/*.&/,5*-6*12,*.#4-%&'*]3681#-6*1'&6/#/1-'*&',*#6*/-$, 3/,*&1*4',/,61?*<a;*<'&6/#/1-'I1'&6/#/1-'*%-:#8*B<U*&88-$4&6(#6:*12#/*.--R*&65*-6*12,*.--Rf/*+,./#1,; <2,*-12,'*.#4-%&'*%-:#8L8#'83#1*9&$#%(*#6*4',/,61*3/,*#/*,$#11,'L8-34%,5*%-:#8*BV>aC;*@1*#/ .&/,5*-6*12,*83'',61L/+#182*#$4%,$,61&1#-6*-9*12,*#60,'1,'*/2-+6*#6*D#:;*EF;`;*<2,*.&/#8 ,%,$,61*-9*V>a*#/*12,*5#99,',61#&%*cd<*4&#'*/135#,5*#6*>2&41,'*X;*c,8&3/,*V>a*#/*.&/#8&%%(*& 83'',61L/1,,'#6:* %-:#8)* &65)* 8-'',/4-65#6:%()* &%/-* 8&%%,5* 40"")$!2+'5)( -'*&4* B>baC)* #6 +2#82*/&13'&1#-6*#/*&0-#5,5)*0,'(*2#:2*/4,,5/*-9*-4,'&1#-6*&',*4-//#.%,;*@65,,5)*-9*&%%*12, 8-$$,'8#&%%(*&0&#%&.%,*%-:#8L8#'83#1*9&$#%#,/)*V>a*#/*12,*9&/1,/1;*V>a*#/*&%/-*3/,5*#6*=a"@ 8#'83#1* 5,/#:6* +2,6* 0,'(* 2#:2* -4,'&1#6:* /4,,5/* &',* ',A3#',5* &65* 12,* 5,/#:6,'* #/* +#%%#6:* 1&88,41*2#:2,'*4-+,'*5#//#4&1#-6*&65*#68',&/,5*/#%#8-6*&',&;*J/*/382)*V>a*#/*8-6/#5,',5*&6 #$4-'1&61*/4,8#&%1(*1,826-%-:(*&65*+#%%*.,*5#/83//,5*#6*>2&41,'*EG;

1087

1088 Chapter 13 CMOS Digital Logic Circuits Bi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a2$? )#6#*$%)"*%5-+*%&-5(4*G% (+-&*$$% )*&".-4-/:% #)% +*T2#+*$D% I% 3+#*6% ,#$&2$$#-.% -6% V#;<=>% #$ (+-8#,*,%#.%;"'()*+%EPD Gallium Arsenide (GaAs) <2,*2#:2*8&''#,'*$-.#%#1(*#6*g&J/*',/3%1/*#6*0,'(*2#:2*/4,,5/ -9* -4,'&1#-6;* <2#/* 2&/* .,,6* 5,$-6/1'&1,5* #6* &* 63$.,'* -9* 5#:#1&%* @>* 82#4/* 31#%#K#6:* g&J/ 1,826-%-:(;*@1*/2-3%5*.,*4-#61,5*-31)*2-+,0,')*12&1*g&J/*',$/*&6*S,$,':#6:*1,826-%-:()T -6,* 12&1* &44,&'/* 1-* 2&0,* :',&1* 4-1,61#&%* .31* 2&/* 6-1* (,1* &82#,0,5* /382* 4-1,61#&%* 8-$$,'L 8#&%%(;*J/*/382)*#1*+#%%*6-1*.,*/135#,5*#6*12#/*.--R;*Z,0,'12,%,//)*8-6/#5,'&.%,*$&1,'#&%*-6 g&J/*5,0#8,/*&65*8#'83#1/)*#68%35#6:*5#:#1&%*8#'83#1/)*8&6*.,*9-365*-6*12,*>U*&88-$4&6(#6: 12#/*.--R*&65*-6*12,*.--Rf/*+,./#1,;

13.1.11 Styles for Digital-System Design <2,*8-60,61#-6&%*&44'-&82*1-*5,/#:6#6:*5#:#1&%*/(/1,$/*8-6/#/1/*-9*&//,$.%#6:*12,*/(/1,$ 3/#6:*/1&65&'5*@>*4&8R&:,/*-9*0&'#-3/*%,0,%/*-9*8-$4%,7#1(*B&65*2,68,*#61,:'&1#-6C;*b&6( /(/1,$/* 2&0,* .,,6* .3#%1* 12#/* +&(* 3/#6:)* 9-'* ,7&$4%,)* <#?.*"!G&*82#4/;*e-+,0,')*83/1-$*@>*5,/#:6*#/*3/3&%%(*,8-6-$#8&%%(*]3/1#L 9#,5*-6%(*+2,6*12,*4'-5381#-6*0-%3$,*#/*%&':,*B:',&1,'*12&6*&.-31*EQQ)QQQ*4&'1/C; J6*#61,'$,5#&1,*&44'-&82)*R6-+6*&/*>4.(61>#?.*<4>(9$R*31#%#K,/*9/#4I/::/=*82#4/;*<2,/, &',*#61,:'&1,5*8#'83#1/*8-61#6:*EQQ)QQQ*-'*$-',*368-66,81,5*%-:#8*:&1,/;*<2,#'*#61,'8-6L 6,81#-6*8&6*.,*&82#,0,5*.(*&*9#6&%*$,1&%%#K&1#-6*/1,4*B4,'9-'$,5*&1*12,*@>*9&.'#8&1#-6*9&8#%#1(C &88-'5#6:*1-*&*4&11,'6*/4,8#9#,5*.(*12,*3/,'*1-*#$4%,$,61*12,*3/,'f/*4&'1#83%&'*93681#-6&%*6,,5; J*$-',*',8,61%(*&0&#%&.%,*1(4,*-9*:&1,*&''&()*R6-+6*&/*&*,&)-52/"'*"#++#:-)(*#!)(#""#; BG*5,/#:6;*

13.1.12 Design Abstraction and Computer Aids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

13.2 The CMOS Inverter

82&'&81,'#K,5)*&65*/1-',5*#6*&*%#.'&'(*&/*%!#$5#"5(4)--%;*<2,/,*8,%%/*8&6*12,6*.,*3/,5*.( 12,*@>*5,/#:6,'*1-*&//,$.%,*&*%&':,'*/3./(/1,$*B,;:;)*&6*&55,'*-'*&*$3%1#4%#,'C)*+2#82*#6 13'6*#/*82&'&81,'#K,5*&65*/1-',5*&/*&*93681#-6&%*.%-8R*1-*.,*3/,5*#6*12,*5,/#:6*-9*&6*,0,6 %&':,'*/(/1,$*B,;:;)*&6*,61#',*4'-8,//-'C; J1*,0,'(*%,0,%*-9*5,/#:6*&./1'&81#-6)*12,*6,,5*&'#/,/*9-'*/#$3%&1#-6*&65*-12,'*8-$431,' 4'-:'&$/* 12&1* 2,%4* $&R,* 12,*5,/#:6* 4'-8,//* &/*&31-$&1,5* &/*4-//#.%,;* P2,',&/* "h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

13.2 The CMOS Inverter 1.%)"#$%$*&)#-.%B*%$)2,:%)"*%#.8*+)*+%&#+&2#)%-6%)"*%5-$)%B#,*4:%2$*,%,#/#)'4%1;%)*&".-4-/:0 ;<=>D%!"*%3'$#&%;<=>%#.8*+)*+%#$%$"-B.%#.%R#/D%EFDE^D%1)%2)#4#Q*$%)B-%<=>RS!$0%-.*7%L+7 B#)"%'.%$%&"'..*4%'.,%)"*%-)"*+7%LK7%B#)"%'%;%&"'..*4D%!"*%3-,:%-6%*'&"%,*8#&*%#$%&-..*&)*, )-%#)$%$-2+&*7%'.,%)"2$%.-%3-,:%*66*&)%'+#$*$D%I$%B#44%3*%$**.%$"-+)4:7%)"*%;<=>%&#+&2#)%+*'4? #Q*$% )"*% &-.&*()2'4% #.8*+)*+% #5(4*5*.)')#-.% $)2,#*,% #.% )"*% (+*8#-2$% $*&)#-.% @R#/D% EFDcC7 B"*+*%'%('#+%-6%$B#)&"*$%'+*%-(*+')*,%#.%'%&-5(4*5*.)'+:%6'$"#-.%3:%)"*%#.(2)%8-4)'/*%v& D

13.2.1 Circuit Operation P,*9#'/1*8-6/#5,'*12,*1+-*,71',$,*8&/,/?*+2,6*v&*#/*&1*%-:#8LQ*%,0,%)*+2#82*#/*Q*=\*&65*+2,6 v&*#/*&1*%-:#8LE*%,0,%)*+2#82*#/*"%%*0-%1/;*@6*.-12*8&/,/)*9-'*,&/,*-9*,74-/#1#-6*+,*/2&%%*8-6L /#5,'*12,*$L82&66,%*5,0#8,*L+*1-*.,*12,*5'#0#6:*1'&6/#/1-'*&65*12,*;L82&66,%*5,0#8,*LK*1-*.,

Figure 13.17 !"*%;<=>%#.8*+)*+D

1089

1090 Chapter 13 CMOS Digital Logic Circuits

VDD

vO $ 0 rDSN

(a)

(b)

(c)

Figure 13.18 =(*+')#-.%-6%)"*%;<=>%#.8*+)*+%B"*.%v&%#$%"#/"0%8#9%&#+&2#)%B#)"%v&%=%"%%%@4-/#&?E%4*8*47%-+% "')C9(8:9(/+'("#&'4%&-.$)+2&)#-.%)-%,*)*+5#.*%)"*%-(*+')#./%(-#.)9%849%*T2#8'4*.)%&#+&2#)D

12,*%-&5;*e-+,0,')*/#68,*12,*8#'83#1*#/*/($$,1'#8)*12#/*&//3$41#-6*#/*-.0#-3/%(*&'.#1'&'()*&65 12,*',0,'/,*+-3%5*%,&5*1-*#5,61#8&%*',/3%1/; D#:3',*EF;EX*#%%3/1'&1,/*12,*8&/,*+2,6* v&*=*"%%)*/2-+#6:*12,*(%−v%G*82&'&81,'#/1#8*83'0, 9-'*L+*+#12*vBG+*=*"%%;*BZ-1,*12&1*(%*=*(*&65*v%G+*=*v';C*"34,'#$4-/,5*-6*12,*L+*82&'&81,'#/1#8 83'0,* #/* 12,* %-&5* 83'0,)* +2#82* #/* 12,* (%−vG%* 83'0,* -9* LK* 9-'* 12,* 8&/,* vGBK* =* Q* =;* "#68, v GBK < " # )*12,*%-&5*83'0,*+#%%*.,*&*2-'#K-61&%*/1'&#:21*%#6,*&1*K,'-*83'',61*%,0,%;*<2,*-4,'&1L #6:*4-#61*+#%%*.,*&1*12,*#61,'/,81#-6*-9*12,*1+-*83'0,/)*+2,',*+,*6-1,*12&1*12,*-31431*0-%1&:, #/*K,'-*&65*12,*83'',61*12'-3:2*12,*1+-*5,0#8,/*#/*&%/-*K,'-;*<2#/*$,&6/*12&1*12,*4-+,'*5#//#L 4&1#-6*#6*12,*8#'83#1*#/*K,'-;*Z-1,)*2-+,0,')*12&1*&%12-3:2*L+*#/*-4,'&1#6:*&1*K,'-*83'',61*&65 K,'-*5'L/-3'8,*0-%1&:,*B#;,;)*&1*12,*-'#:#6*-9*12,*(%−v%G*4%&6,C)*12,*-4,'&1#6:*4-#61*#/*-6*& /1,,4* /,:$,61* -9* 12,* (%−v%G* 82&'&81,'#/1#8* 83'0,;* <23/* L+* 4'-0#5,/* &* %-+L',/#/1&68,* 4&12 .,1+,,6*12,*-31431*1,'$#6&%*&65*:'-365)*+#12*12,*',/#/1&68,*-.1,5*3/#6:*VA;*BM;EF.C*&/

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D#:3',*EF;EXB8C*/2-+/*12,*,A3#0&%,61*8#'83#1*-9*12,*#60,'1,'*+2,6*12,*#6431*#/*2#:2;*<2#/*8#'L 83#1*8-69#'$/*12&1* v ' ≡ " '! = M%K *&65*12&1*12,*4-+,'*5#//#4&1#-6*#6*12,*#60,'1,'*#/*K,'-; <2,*-12,'*,71',$,*8&/,)*+2,6*v&*=*Q*=)*#/*#%%3/1'&1,5*#6*D#:;*EF;E`;*@6*12#/*8&/,*L+*#/*-4,'L &1#6:*&1* vBG+*=*Q\*2,68,*#1/*(%−v%G*82&'&81,'#/1#8*#/*&*2-'#K-61&%*/1'&#:21*%#6,*&1*K,'-*83'',61 %,0,%;*<2,*%-&5*83'0,*#/*12,*(%−vG%*82&'&81,'#/1#8*-9*12,*;L82&66,%*5,0#8,*+#12*vGBK*=*"%%;*J/ /2-+6)*&1*12,*-4,'&1#6:*4-#61*12,*-31431*0-%1&:,*#/*,A3&%*1-*"%%)*&65*12,*83'',61*#6*12,*1+5,0#8,/*#/*/1#%%*K,'-;*<23/*12,*4-+,'*5#//#4&1#-6*#6*12,*8#'83#1*#/*K,'-*#6*.-12*,71',$,*/1&1,/; D#:3',*EF;E`B8C*/2-+/*12,*,A3#0&%,61*8#'83#1*-9*12,*#60,'1,'*+2,6*12,*#6431*#/*%-+;*e,', +,*/,,*12&1*LK*4'-0#5,/*&*%-+L',/#/1&68,*4&12*.,1+,,6*12,*-31431*1,'$#6&%*&65*12,*58*/344%( "%%)*+#12*12,*',/#/1&68,*:#0,6*.(

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13.2 The CMOS Inverter

1091

VDD rDSP vO $ VDD

(a)

(b)

(c)

Figure 13.19 =(*+')#-.%-6%)"*%;<=>%#.8*+)*+%B"*.%v&%#$%4-B0%8#9%&#+&2#)%B#)"%v&%=%M%K%@4-/#&?M%4*8*47%-+% "'!C9%8:9%/+'("#&'4%&-.$)+2&)#-.%)-%,*)*+5#.*%)"*%-(*+')#./%(-#.)9%849%*T2#8'4*.)%&#+&2#)D

<2,*,A3#0&%,61*8#'83#1*8-69#'$/*12&1*#6*12#/*8&/,* v ' ≡ " ') = " %% *&65*12&1*12,*4-+,'*5#//#4&L 1#-6*#6*12,*#60,'1,'*#/*K,'-; @1*/2-3%5*.,*6-1,5)*2-+,0,')*12&1*#6*/4#1,*-9*12,*9&81*12&1*12,*A3#,/8,61*83'',61*#/*K,'-)*12, %-&5L5'#0#6:*8&4&.#%#1(*-9*12,*>b^"*#60,'1,'*#/*2#:2;*D-'*#6/1&68,)*+#12*12,*#6431*2#:2)*&/*#6 12,*8#'83#1*-9*D#:;*EF;EX)*1'&6/#/1-'*L+*8&6*/#6R*&*',%&1#0,%(*%&':,*%-&5*83'',61;*<2#/*83'',61 8&6* A3#8R%(*5#/82&':,*12,*%-&5*8&4&8#1&68,)*&/*+#%%*.,*/,,6*/2-'1%(;*c,8&3/,*-9*#1/*&81#-6*#6 /#6R#6:*%-&5*83'',61*&65*123/*43%%#6:*12,*-31431*0-%1&:,*5-+6*1-+&'5*:'-365)*1'&6/#/1-'*L+ #/* R6-+6* &/* 12,* /0--25'.$* 5)3&4);* "#$#%&'%()* +#12* 12,* #6431* %-+)* &/* #6* 12,* 8#'83#1* -9 D#:; EF;E`)*1'&6/#/1-'*LK*8&6*/-3'8,*&*',%&1#0,%(*%&':,*%-&5*83'',61;*<2#/*83'',61*8&6*A3#8R%( 82&':,* 34* &* %-&5 8&4&8#1&68,)* 123/* 43%%#6:* 12,* -31431* 0-%1&:,* 34* 1-+&'5* "%%;* e,68,)* LK #/ R6-+6*&/*12,*/0--20/*5)3&4);*<2,*',&5,'*+#%%*',8&%%*12&1*+,*3/,5*12#/*1,'$#6-%-:(*#6*8-6L 6,81#-6*+#12 12,*8-68,413&%*#60,'1,'*8#'83#1*-9*D#:;*EF;X; D'-$*12,*&.-0,)*+,*8-68%35,*12&1*12,*.&/#8*>b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i!*'&1#-/*-'*-12,' 5,0#8,*4&'&$,1,'/;*D3'12,'$-',)*12,*%-+*-31431*',/#/1&68,*$&R,/*12,*#60,'1,'*%,//*/,6/#L 1#0,*1-*12,*,99,81/*-9*6-#/,*&65*-12,'*5#/13'.&68,/; 4. <2,*&81#0,*43%%L34*&65*43%%L5-+6*5,0#8,/*4'-0#5,*12,*#60,'1,'*+#12*2#:2*-31431L5'#0L #6:* 8&4&.#%#1(* #6* .-12* 5#',81#-6/;* J/* +#%%* .,* /,,6)* 12#/* /4,,5/* 34* 12,* -4,'&1#-6 8-6/#5,'&.%(;

1092 Chapter 13 CMOS Digital Logic Circuits 5. <2,*#6431*',/#/1&68,*-9*12,*#60,'1,'*#/*#69#6#1,*B.,8&3/,*&B*=*QC;*<23/*12,*#60,'1,'*8&6*5'#0, &6*&'.#1'&'#%(*%&':,*63$.,'*-9*/#$#%&'*#60,'1,'/*+#12*6-*%-//*#6*/#:6&%*%,0,%;*^9*8-3'/,) ,&82* &55#1#-6&%* #60,'1,'* #68',&/,/* 12,* %-&5* 8&4&8#1&68,* -6* 12,* 5'#0#6:* #60,'1,'* &65 /%-+/*5-+6*12,*-4,'&1#-6;*"2-'1%()*+,*+#%%*8-6/#5,'*12,*#60,'1,'*/+#182#6:*1#$,/;

13.2.2 The Voltage-Transfer Characteristic <2,*8-$4%,1,*0-%1&:,L1'&6/9,'*82&'&81,'#/1#8*B=<>C*-9*12,*>b^"*#60,'1,'*8&6*.,*-.1,5 .(* ',4,&1#6:* 12,* :'&42#8&%* 4'-8,53',)* 3/,5* &.-0,* #6* 12,* 1+-* ,71',$,* 8&/,/)* 9-'* &%%* #61,'L $,5#&1,*0&%3,/*-9* v&;*@6*12,*9-%%-+#6:)*+,*/2&%%*8&%83%&1,*12,*8'#1#8&%*4-#61/*-9*12,*',/3%1#6: 0-%1&:,L1'&6/9,'*83'0,;*D-'*12#/*+,*6,,5*12,*(−v*',%&1#-6/2#4/*-9*L+*&65*LK;*D-'*L+)

E H ( %+ = J $′ ????? ( v & I " #$ ) v ' I ??? v N' N !$

6-+% v ' ≤ v & I " #$

%@EFDP^C

%%%%%%%%%%%6-+% v ' ≥ v & I " #$

%@EFDPcC

&65

E H N ( %+ = ??? J $′ ????? ( v & I " #$ ) N ! $ D-'*LK)

H ( %K = J ;′ ????? !

;

E N

( " %% I v & I " #; ) ( " %% I v ' ) I ??? ( " %% I v ' )

N

%6-+% v ' ≥ v & + " #;

%@EFDP`C

6-+% v ' ≤ v & + " #;

%@EFDOMC

&65

H E N ( %K = ??? J ;′ ????? ( " %% I v & I " #; ) N ! ;

%%

<2,*>b^"*#60,'1,'*#/*3/3&%%(*5,/#:6,5*1-*2&0,* "#$ = " #; % = " # ;*J%/-)*&%12-3:2*12#/*#/*6-1 &%+&(/* 12,* 8&/,)* +,* /2&%%* &//3$,* 12&1* L+* &65* LK* &',* $&182,5\* 12&1* #/)* J $′( H ⁄ ! ) $ = J ;′ ( H ⁄ ! ) ; ;*@1*/2-3%5*.,*6-1,5*12&1*/#68,* µ;*#/*Q;WM*1-*Q;M*1#$,/*12,*0&%3,*-9*µ$)*1-*$&R, J′ ( H ⁄ ! ) *-9*12,*1+-* 5,0#8,/*,A3&%)*12,*+#512* -9* 12,* ;L82&66,%*5,0#8,* #/* $&5,* 1+-*19-3'*1#$,/*12&1*-9*12,*$L82&66,%*5,0#8,;*b-',*/4,8#9#8&%%()*12,*1+-*5,0#8,/*&',*5,/#:6,5 1-*2&0,*,A3&%*%,6:12/)*+#12*+#512/*',%&1,5*.(

H µ ???????; = ?????$ H$ µ;

%@EFDOEC

<2#/*+#%%*',/3%1*#6* J $′( H ⁄ ! ) $ = J ;′( H ⁄ ! ) ; )*&65*12,*#60,'1,'*+#%%*2&0,*&*/($$,1'#8*1'&6/9,' 82&'&81,'#/1#8*&65*,A3&%*83'',61L5'#0#6:*8&4&.#%#1(*#6*.-12*5#',81#-6/*B43%%L34*&65*43%%L5-+6C; P#12* L+* &65* LK* $&182,5)* 12,* >b^"* #60,'1,'* 2&/* 12,* 0-%1&:,* 1'&6/9,'* 82&'&81,'#/1#8 /2-+6*#6*D#:;*EF;WQ;*J/*#65#8&1,5)*12,*1'&6/9,'*82&'&81,'#/1#8*2&/*9#0,*5#/1#681*/,:$,61/*8-'L ',/4-65#6:*1-*5#99,',61*8-$.#6&1#-6/*-9*$-5,/*-9*-4,'&1#-6*-9*L+*&65*LK;*<2,*0,'1#8&% /,:$,61* c>* #/* -.1,5* +2,6* .-12* L+* &65* LK* &',* -4,'&1#6:* #6* 12,* /&13'&1#-6* ',:#-6; c,8&3/,* +,* &',* 6,:%,81#6:* 12,* 9#6#1,* -31431* ',/#/1&68,* #6* /&13'&1#-6)* 12&1* #/)* &//3$#6: λ + ! λ K ! M )*12,*#60,'1,'*:*#6*12#/*',:#-6*#/*#69#6#1,;*D'-$*/($$,1'()*12#/*0,'1#8&%*/,:$,61 -883'/*&1* v & = " %% ⁄ N *&65*#/*.-365,5*.(* v ' ( V ) = " %% ⁄ N + " # %)*&1*+2#82*0&%3,*LK*,61,'/ 12,*1'#-5,*',:#-6*&65** v ' ( ; ) = " %% ⁄ N I " # )*&1*+2#82*0&%3,*L+**,61,'/*12,*1'#-5,*',:#-6;

13.2 The CMOS Inverter

M

Figure 13.20 !"*%8-4)'/*?)+'.$6*+%&"'+'&)*+#$)#&%-6%)"*%;<=>%#.8*+)*+%B"*.%L+%'.,%LK%'+*%5')&"*,D

<2,* ',&5,'* +#%%* ',8&%%* 9'-$* ",81#-6* EF;E;F* 12&1* #6* &55#1#-6* 1-* "'!* &65* "'))* 1+-* -12,' 4-#61/*-6*12,*1'&6/9,'*83'0,*5,1,'$#6,*12,*6-#/,*$&':#6/*-9*12,*#60,'1,';*<2,/,*&',*12,*$&7#L $3$*4,'$#11,5*%-:#8LQ*-'*S%-+T*%,0,%*&1*12,*#6431)*"&!)*&65*12,*$#6#$3$*4,'$#11,5*%-:#8LE -'*S2#:2T*%,0,%*&1*12,*#6431)*"&);*<2,/,*&',*9-'$&%%(*5,9#6,5*&/*12,*1+-*4-#61/*-6*12,*1'&6/9,' 83'0,*&1*+2#82*12,*#68',$,61&%*:*#/*36#1(*B#;,;)*12,*/%-4,*#/*−E*=i=C; <-*5,1,'$#6,*"&))*+,*6-1,*12&1*L+*#/*#6*12,*1'#-5,*',:#-6)*&65*123/*#1/*83'',61*#/*:#0,6*.( VA;*BEF;GOC)*+2#%,*LK*#/*#6*/&13'&1#-6*&65*#1/*83'',61*#/*:#0,6*.(*VA;*BEF;MQC;*VA3&1#6:*(%+ &65*(%K)*&65*&//3$#6:*$&182,5*5,0#8,/)*:#0,/ E E N ( v & I " # ) v ' I ??? v N' = ??? ( " %% I v & I " # ) N

N

%@EFDONC

U#99,',61#&1#6:*.-12*/#5,/*',%&1#0,*1-*v&*',/3%1/*#6


" %% ? = " &) I ???????? N

%@EFDOFC

1093

1094 Chapter 13 CMOS Digital Logic Circuits "3./1#131#6:*v&*=*"&)*&65*9-'*v'*9'-$*VA;*BEF;MFC*#6*VA;*BEF;MWC*:#0,/ E " &) = ??? ( O" %% I N" # ) c

%@EFDOPC

"&!%&'.%3*%,*)*+5#.*,%#.%'%5'..*+%$#5#4'+%)-%)"')%2$*,%)-%6#.,%"&)D%I4)*+.')#8*4:7%B*%&'. 2$*%)"*%$:55*)+:%+*4')#-.$"#(%

" %% " %% ? = ????????? I " &! " &) I ???????? N N 1-:,12,'*+#12*"&)*9'-$*VA;*BEF;MGC*1-*-.1 E " &! = ??? ( F" %% + N" # ) c

%@EFDOOC

<2,*6-#/,*$&':#6/*8&6*6-+*.,*5,1,'$#6,5*&/*9-%%-+/?

+, ) = " ') I " &) E * = " %% I ??? ( O" %% I N" # ) c

E = ??? ( F" %% + N" # ) c

%@EFDO]C

+, ! = " &! I " '! E = ??? ( F" %% + N" # ) I M c

E = ??? ( F" %% + N" # ) c

%@EFDO^C

J/*,74,81,5)*12,*/($$,1'(*-9*12,*0-%1&:,L1'&6/9,'*82&'&81,'#/1#8*',/3%1/*#6*,A3&%*6-#/,*$&'L :#6/;* ^9* 8-3'/,)* #9* L+* &65* LK* &',* 6-1* $&182,5)* 12,* 0-%1&:,L1'&6/9,'* 82&'&81,'#/1#8* +#%%* 6%-6:,'*.,*/($$,1'#8)*&65*12,*6-#/,*$&':#6/*+#%%*6-1*.,*,A3&%;

13.2.3 The Situation When QN and QP Are Not Matched 1.%)"*%'3-8*%B*%'$$25*,%)"')% L + %'.,% L K %'+*%5')&"*,9%)"')%#$7%#.%',,#)#-.%)-% " #$ ! " #; 7%)"* )+'.$&-.,2&)'.&*%('+'5*)*+$% J $ %'.,% J ; %'+*%5',*%*T2'4%3:%$*4*&)#./% H ; ⁄ H $ %'&&-+,#./%)STD%@EFDOECD%!"*%+*$24)%#$%'%$:55*)+#&'4%K!;%)"')%$B#)&"*$%')%)"*%5#,(-#.)%-6%)"*%$2((4:9 )"')%#$7% " , ! " %% ⁄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cC%'.,%@EFDOMCD%>23$)#)2)#./% v & ! v ' ! " , 7 %'.,%*T2')#./%)"*%)B-%&2++*.)$%+*$24)$%#.% : ( " %% I " #; ) H " #$ " , ! ??????????????????????????????????????????????? :HE

%@EFDOcC

13.2 The CMOS Inverter

VM (V) 1.2 !

1095

VDD $ 1.8 V Vtn $ %Vtp% $ 0.5 V

1.0 ! 0.8 ! 0.6 ! 0.4 ! 0.2 ! 1.5

!

1.0

!

!

0.5

2.0

r

Figure 13.21 K'+#')#-.%-6%)"*%#.8*+)*+%$B#)&"#./%8-4)'/*7%", 7%B#)"%)"*%('+'5*)*+% : !

J; ⁄ J$ D

B"*+* : !

J; ???? ! J$

µ ;H ; ????????????? µ $H $

%@EFDO`C

B"*+*%B*%"'8*%'$$25*,%)"')% L + %'.,% L K %"'8*%)"*%$'5*%&"'..*4%4*./)"%!7%B"#&"%#$%2$2'44: )"*%&'$*%B#)"%!%*T2'4%)-%)"*%5#.#525%'8'#4'34*%6-+%)"*%/#8*.%(+-&*$$%)*&".-4-/:D%W-)*%)"') )"*% 5')&"*,% &'$*% &-++*$(-.,$% )-% :% e% ED% R-+% " #; ! " #$ 7% '.,% :% e% E7% STD% @EFDOcC% :#*4,$ " , ! " %% ⁄ N7%'$%*G(*&)*,D%R-+%'%/#8*.%(+-&*$$7%)"')%#$7%/#8*.%8'42*$%6-+% " %% 7% " #$ 7%'.,% " #; 7 -.*%&'.% (4-)% " , % 8*+$2$%)"*%5')&"#./% ('+'5*)*+%:D%>2&"%'% (4-)7%6-+% '% MDEc?µ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

Example 13.4 ;-.$#,*+% '% ;<=>% #.8*+)*+% 6'3+#&')*,% #.% '% MDEc?µ5% (+-&*$$% 6-+% B"#&"% " %% ! EDc%K7 " #$ ! " #; ! MDO%K7 % µ $ ! P µ ; 7 %'.,% µ $- ?0 ! FMM%µI ⁄ K ND %1.%',,#)#-.7% L + %'.,% L K %"'8*%!%e%MDEc%µ5 '.,% ( H ⁄ ! ) $ ! EDOD @'C R#.,% H ; %)"')%+*$24)$%#.% " , ! " %% ⁄ N ! MD`%K D %H"')%#$%)"*%$#4#&-.%'+*'%2)#4#Q*,%3:%)"*%#.8*+)*+%#. )"#$%&'$*b @3C R-+%)"*%5')&"*,%&'$*%#.%@'C7%6#.,%)"*%8'42*$%-6% " ') 7 % " '! 7 % " &) 7 % " &!7 %'.,%)"*%.-#$*%5'+/#.$% +, ! %'., +, ) D %R-+% v & ! " &) 7 %B"')%8'42*%-6% v ' %+*$24)$b%!"#$%&'.%3*%&-.$#,*+*,%)"*%B-+$)?&'$*%8'42*%-6% " '!D >#5#4'+4:7%6-+% v & ! " &! 7 %6#.,% v ' %)"')%#$%)"*%B-+$)?&'$*%8'42*%-6% " ') D%W-B7%2$*%)"*$*%B-+$)?&'$*%8'4? 2*$%)-%,*)*+5#.*%5-+*%&-.$*+8')#8*%8'42*$%6-+%)"*%.-#$*%5'+/#.$D @&C R-+%)"*%5')&"*,%&'$*%#.%@'C7%6#.,%)"*%-2)(2)%+*$#$)'.&*%-6%)"*%#.8*+)*+%#.%*'&"%-6%#)$%)B-%$)')*$D%

1096 Chapter 13 CMOS Digital Logic Circuits Example 13.4 continued IE

@,C 16% λ $ ! λ ; ! MDN K 7%B"')%#$%)"*%#.8*+)*+%/'#.%')% v & ! " , D %16%'%$)+'#/")%4#.*%#$%,+'B.%)"+-2/"%)"* (-#.)% v & ! v ' ! " , %B#)"%'%$4-(*%*T2'4%)-%)"*%/'#.7%')%B"')%8'42*$%-6% v & %,-*$%#)%#.)*+&*()%)"*%"-+#? Q-.)'4%4#.*$% v ' ! M %'.,% v ' ! " %% b%d$*%)"*$*%#.)*+&*()$%)-%*$)#5')*%)"*%B#,)"%-6%)"*%)+'.$#)#-.%+*? /#-.%-6%)"*%K!;D @*C 16% H ; ! H $ 7%B"')%8'42*%-6% " , %+*$24)$b%H"')%,-%:-2%*$)#5')*%)"*%+*,2&)#-.%-6% +, ! %@+*4')#8*%)-%)"* 5')&"*,%&'$*C%)-%3*b%H"')%#$%)"*%(*+&*.)'/*%$'8#./$%#.%$#4#&-.%'+*'%@+*4')#8*%)-%)"*%5')&"*,%&'$*Cb @6C Y*(*')%@*C%6-+%)"*%&'$*%H ; ! NH $ D %!"#$%&'$*7%B"#&"%#$%6+*T2*.)4:%2$*,%#.%#.,2$)+:7%&'.%3*%&-.$#,*+*, )-%3*%'%&-5(+-5#$*%3*)B**.%)"*%5#.#525?'+*'%&'$*%#.%@*C%'.,%)"*%5')&"*,%&'$*D%

Solution @'C%!-%-3)'#.% " , ! " %% ⁄ N ! MD`%K 7%B*%$*4*&)% H ; %'&&-+,#./%)-%STD%@EFDOEC7 H; µ ??????? ! ?????$ ! P H$ µ; >#.&*% H $ ⁄ ! ! EDO7 % H $ ! EDO × MDEc ! MDN^%µ5D%!"2$7 H ; ! P × MDN^ ! EDMc%µ5 R-+%)"#$%,*$#/.7%)"*%$#4#&-.%'+*'%#$ S ! H$ ! H H; ! ! ! ( H$ H H; ) ! MDEc ( MDN^ H EDMc ) ! MDNPF%µ5 @3C

N

" ') ! " %% ! EDc%K " '! ! M%K

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13.2 The CMOS Inverter

1097

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1098 Chapter 13 CMOS Digital Logic Circuits Example 13.4 continued

!"2$% " , %$"#6)$%3:%-.4:%I MDEF%KD %H#)"-2)%+*&'4&24')#./% " &! %B*%&'.%*$)#5')*%)"*%+*,2&)#-.%#.% +, ! %)-%3* '((+-G#5')*4:%*T2'4%)-%)"*%$"#6)%#.% " , 7 %)"')%#$7% +, ! %3*&-5*$% MDc I MDEF ! MD]^%KD %!"*%$#4#&-.%'+*'%6-+ )"#$%,*$#/.%&'.%3*%&-5(2)*,%'$%6-44-B$0 S ! ! ( H $ H H ; ) ! MDEc ( MDN^ H MDN^ ) ! MDM`^N%µ5

N

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N

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EXERCISES 13.12 ;-.$#,*+% '% ;<=>% #.8*+)*+% 6'3+#&')*,% #.% '% MDEF?µ5% (+-&*$$% 6-+% B"#&"% " %% ! EDN%K7 N " #$ ! I " #; ! MDP%K7% µ $ ⁄ µ ; ! P7 %'.,% µ $- ?0 ! PFM%µI ⁄ K D %1.%',,#)#-.7% L + %'.,% L K %"'8*%! e%MDEF%µ5%'.,% ( H ⁄ ! ) $ ! EDM D @'C%R#.,% H ; %)"')%+*$24)$%#.% " , ! MD]%KD @3C%R-+%)"*%5')&"*,%&'$*%#.%@'C7%6#.,%)"*%8'42*$%-6%" ') 7 %" '! 7 %" &) 7 %" &! 7 % +, ) 7 %'.,% +, ! D @&C%R-+%)"*%#.8*+)*+%#.%@'C7%6#.,%)"*%-2)(2)%+*$#$)'.&*%#.%*'&"%-6%#)$%)B-%$)')*$D @,C%R-+%'%5#.#525?$#Q*%#.8*+)*+%6-+%B"#&"% ( H ⁄ ! ) ; ! ( H ⁄ ! ) $ ! EDM 7%6#.,% " , D Ans. @'C%MDON%µ59%@3C%EDN%K7%M%K7%MD]O%K7%MDOO%K7%MDOO%K7%MDOO%K7%@&C%ND`%J Ω 7%ND`%J Ω 9%@,C%MDOF%K N

D13.13 I%;<=>%#.8*+)*+%2)#4#Q*$% " %% ! O%K7 % " #$ ! " #; ! E%K7 %'.,% µ $- ?0 ! %N µ ;- ?0 !%OM%µI ⁄ K D R#.,% ( H ⁄ ! ) $ %'.,% ( H ⁄ ! ) ; %$-%)"')% " , ! NDO%K %'.,%$-%)"')%6-+% v & ! " %% 7 %)"*%#.8*+)*+%&'.%$#.J%' &2++*.)%-6%MDN%5I%B#)"%)"*%-2)(2)%8-4)'/*%.-)%*G&**,#./%MDN%KD Ans. ( H ⁄ ! ) $ ! O9 % ( H ⁄ ! ) ; ! EM

13.3 Dynamic Operation of the CMOS Inverter J/*,74%,5*#6*",81#-6*EF;E;O)*12,*/4,,5*-9*-4,'&1#-6*-9*&*5#:#1&%*/(/1,$*B,;:;)*&*8-$431,'C #/*5,1,'$#6,5*.(*12,*4'-4&:&1#-6*5,%&(*-9*12,*%-:#8*:&1,/*3/,5*1-*8-6/1'381*12,*/(/1,$;*"#68, 12,*#60,'1,'*#/*12,*.&/#8*%-:#8*:&1,*-9*&6(*5#:#1&%*@>*1,826-%-:()*12,*4'-4&:&1#-6*5,%&(*-9*12,

13.3 Dynamic Operation of the CMOS Inverter

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1099

1100 Chapter 13 CMOS Digital Logic Circuits

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1101

1102 Chapter 13 CMOS Digital Logic Circuits

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FM E K ! ??????????????????? JΩ ( H ⁄ ! );

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R2+)"*+5-+*7%#)%"'$%3**.%6-2.,%)"')%)"*$*%8'42*$%'((4:%6-+%'%.253*+%-6%;<=>%6'3+#&')#-. (+-&*$$*$%#.&42,#./%MDNO%µ57%MDEc%µ57%'.,%MDEF%µ5%@$**%X-,/*$%*)%'4D7%NMMPCD

13.3 Dynamic Operation of the CMOS Inverter

1103

Example 13.5 N

R-+%)"*%MDNO?µ5%(+-&*$$%&"'+'&)*+#Q*,%3:% " %% ! NDO%K7 %" #$ ! I " #; ! MDO%K7%% J′$ ! FDOJ′; ! EEO%µI ⁄ K 7 6#.,% # K!) 7 % # K)! 7 %'.,% # K %6-+%'.%#.8*+)*+%6-+%B"#&"% ( H ⁄ ! ) $ ! EDO %'.,% ( H ⁄ ! ) ; ! F7%'.,%6-+%-*e%EM%6RD%d$* 3-)"%)"*%'((+-'&"%3'$*,%-.%'8*+'/*%&2++*.)$%'.,%)"')%3'$*,%-.%*T2#8'4*.)%+*$#$)'.&*$7%'.,%&-5('+*%)"*%+*$24)$ -3)'#.*,D%16%)-%$'8*%-.%(-B*+%,#$$#(')#-.%)"*%#.8*+)*+%#$%-(*+')*,%')%" %% ! NDM%K7%3:%B"')%6'&)-+%,-*$% # K %&"'./*b

Solution @'C%d$#./%)"*%'8*+'/*%&2++*.)%'((+-'&"7%B*%,*)*+5#.*%6+-5%STD%@EFD]OC7 N α $ ! ???????????????????????????????????????????????N? ! ED^ MDO ^ × MDO ??? I F ???????????????? H ??????? NDO P NDO

'.,%2$#./%STD%@EFD]PC7

I EO

>#.&*% " #; ! " #$7

ED^ × EM × EM ? ! PEDN%($ # K)! ! ???????????????????????????????????????????????????? I] EEM × EM × EDO × NDO

α ; ! α $ ! ED^ '.,%B*%&'.%,*)*+5#.*% # K!) %6+-5%STD%@EFD]]C%'$% I EO

ED^ × EM × EM ? ! ^NDE%($ # K!) ! ???????????????????????????????????????????????????????????????? I] ( EEM ⁄ FDO ) × EM × F × NDO !"*%(+-('/')#-.%,*4':%&'.%.-B%3*%6-2.,%'$% E # K ! ??? ( # K)! H # K!) ) N E ! ??? ( PEDN H ^NDE ) ! O]D^%($ N @3C%d$#./%)"*%*T2#8'4*.)%+*$#$)'.&*%'((+-'&"7%B*%6#+$)%6#.,% E + %6+-5%STD%@EFD^MC%'$ ENDO E + ! ?????????? ! cDFF%JΩ EDO '.,%)"*.%2$*%STD%@EFD]cC%)-%,*)*+5#.*% # K)! 7 % F

# K)! ! MD]` × cDFF × EM × EM × EM

I EO

! O^DO%($

I EO

! ]`%($

>#5#4'+4:%B*%2$*%STD%@EFD^EC%)-%,*)*+5#.*% E K 7 %

'.,%STD%@EFD]`C%)-%,*)*+5#.*% # K!) 7

FM E K ! ?????? ! EM%JΩ F F

# K!) ! MD]` × EM × EM × EM × EM

!"2$7%B"#4*%)"*%8'42*%-3)'#.*,%6-+% # K)! %#$%"#/"*+%)"'.%)"')%6-2.,%2$#./%'8*+'/*%&2++*.)$7%)"*%8'42*%6-+ # K!) %#$%'3-2)%)"*%$'5*D%R#.'44:7% # K %&'.%3*%6-2.,%'$ E # K ! ??? ( O^DO H ]` ) ! ]FDN%($ N B"#&"%'%4#))4*%"#/"*+%)"'.%)"*%8'42*%6-2.,%2$#./%'8*+'/*%&2++*.)$D

1104 Chapter 13 CMOS Digital Logic Circuits

Example 13.5 continued

!-%6#.,%)"*%&"'./*%#.%(+-('/')#-.%,*4':$%-3)'#.*,%B"*.%)"*%#.8*+)*+%#$%-(*+')*,%')% " %% ! NDM%K7 B*%"'8*%)-%2$*%)"*%5*)"-,%-6%'8*+'/*%&2++*.)$D%@!"*%,*(*.,*.&*%-.%)"*%(-B*+?$2((4:%8-4)'/*%#$%'3$-+3*, #.%)"*%*5(#+#&'4%8'42*$%-6% E + %'.,%EK DC%d$#./%STD%@EFD]OC7%B*%B+#)* N α $ ! ???????????????????????????????????????????????N? ! NDE MDO ^ × MDO ??? I F ???????????????? H ??????? N P N

!"*%8'42*%-6% # K)! %&'.%.-B%3*%6-2.,%3:%2$#./%STD%@EFD]PC0 I EO

NDE × EM × EM # K)! ! ???????????????????????????????????????????????? ! ]FD]%($ I] EEM × EM × EDO × N >#5#4'+4:7%)"*%8'42*%-6% α ; ! α $ ! NDE%&'.%3*%$23$)#)2)*,%#.%STD%@EFD]]C%)-%-3)'#. I EO

NDE × EM × EM ? ! EEEDP%($ # K!) ! ??????????????????????????????????????????????????????????? I] ( EEM ⁄ FDO ) × EM × F × N '.,% # K %&'.%3*%&'4&24')*,%'$ E # K ! ??? ( ]FD] H EEEDP ) ! c^DO%($ N !"2$7%'$%*G(*&)*,7%+*,2&#./% " %% %"'$%+*$24)*,%#.%#.&+*'$*,%(+-('/')#-.%,*4':D

V*6-+*%4*'8#./%)"*%$23a*&)%-6%(+-('/')#-.%,*4':7%B*%$"-24,%*5("'$#Q*%)"')%"'.,%'.'4:$#$ 2$#./%)"*%$#5(4*%6-+524'$%'3-8*%$"-24,%$?#%3*%*G(*&)*,%)-%:#*4,%(+*&#$*%+*$24)$D%Y')"*+7%#)$ 8'42*%#$%#.%-3)'#.#./%,*$#/.%#.$#/")D%\+*&#$*%+*$24)$%&'.%'4B':$%3*%-3)'#.*,%2$#./%>\1;S%'., <24)#$#5%$#524')#-.$%@$**%*G'5(4*$%#.%I((*.,#G%V%'.,%)"*%*G)*.$#8*%5')*+#'4%-.%)"*%;U '.,%)"*%B*3$#)*CD%X-B*8*+7%#)%#$%.*8*+%'%/--,%#,*'%)-%2$*%$#524')#-.%#6%-.*%,-*$%.-)%J.-B 3*6-+*"'.,%'((+-G#5')*%8'42*$%-6%)"*%*G(*&)*,%+*$24)$D

EXERCISES 13.14 R-+%'%;<=>%#.8*+)*+%6'3+#&')*,%#.%'%MDEc?µ5%(+-&*$$%B#)"% " %% ! EDc%K7 % " #$ ! I " #; ! MDO%K7 N J′$ ! PJ′; ! FMM%µI ⁄ K %'.,%"'8#./% ( H ⁄ ! ) $ ! EDO %'.,%( H ⁄ ! ) ; ! F7 %6#.,% # K)! 7 % # K!) 7 %'.,% # K B"*.%)"*%*T2#8'4*.)%4-',%&'('&#)'.&*%-%e%EM%6RD%d$*%)"*%5*)"-,%-6%'8*+'/*%&2++*.)$D% Ans. NPD^%($9%P`DP%($9%F^%($ D13.15 R-+%'%;<=>%#.8*+)*+%6'3+#&')*,%#.%'%MDEF?µ5%(+-&*$$7%2$*%)"*%*T2#8'4*.)?+*$#$)'.&*$%'((+-'&"%),*)*+5#.*% ( H ⁄ ! ) $ %'.,% ( H ⁄ ! ) ; %$-%)"')% # K!) ! # K)! ! OM%($ %B"*.%)"*%*66*&)#8*%4-',%&'('&#? )'.&*%-%e%NM%6RD Ans. FDO9%cDF

13.3.2 Determining the Equivalent Load Capacitance C X'8#./%,*)*+5#.*,%)"*%(+-('/')#-.%,*4':%-6%)"*%;<=>%#.8*+)*+%#.%)*+5$%-6%)"*%*T2#8'4*.) 4-',%&'('&#)'.&*%-7%#)%.-B%+*5'#.$%)-%,*)*+5#.*%)"*%8'42*%-6%-D%R-+%)"#$%(2+(-$*7%'%)"-+-2/" 2.,*+$)'.,#./%-6%)"*%8'+#-2$%&'('&#)'.&*$%#.%'%<=>%)+'.$#$)-+%#$%*$$*.)#'47%'.,%B*%2+/*%)"* +*',*+%)-%+*8#*B%)"*%5')*+#'4%#.%>*&)#-.%`DNDED%

13.3 Dynamic Operation of the CMOS Inverter

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

VDD

VDD Cg4

Q2 Q4 Cdb2

Cgd2 VDD 0

t

vI

" !

Cgd1

Cdb1

vO

Cw

Q3

Q1 Cg3 Figure 13.24 ;#+&2#)%6-+%'.'4:Q#./%)"*%(+-('/')#-.%,*4':%-6%)"*%#.8*+)*+%6-+5*,%3:%LE%'.,%LN7%B"#&"%#$% ,+#8#./%'%$#5#4'+%#.8*+)*+%6-+5*,%3:%LF%'.,%LPD

I% /4'.&*% ')% )"*% &#+&2#)% #.% R#/D% EFDNP% $"-24,% 3*% $266#&#*.)% )-% #.,#&')*% )"')% '% (*.?'.,? ('(*+%'.'4:$#$%#$%8#+)2'44:%#5(-$$#34*D%!"')7%-6%&-2+$*7%#$%)"*%+*'$-.%B*%-()*,%6-+%)"*%$#5(4#? 6#&')#-.%-6%+*(4'&#./%'44%)"*$*%&'('&#)'.&*$%B#)"%'.%*T2#8'4*.)%&'('&#)'.&*%-D%V*6-+*%B*%&-.? $#,*+%)"*%,*)*+5#.')#-.%-6%-7%#)%#$%2$*624%)-%-3$*+8*%)"')%,2+#./%#K!)%-+%#K)!7%)"*%-2)(2)%-6%)"* 6#+$)%#.8*+)*+%&"'./*$%6+-5%M%)-% "%% ⁄ N %-+%6+-5%"%%%)-% "%% ⁄ N7%+*$(*&)#8*4:D%1)%6-44-B$%)"')%)"* $*&-.,%#.8*+)*+%+*5'#.$%#.%)"*%$'5*%$)')*%,2+#./%*'&"%-6%-2+%'.'4:$#$%#.)*+8'4$D%!"#$%-3$*+? 8')#-.%B#44%"'8*%'.%#5(-+)'.)%3*'+#./%-.%-2+%*$)#5')#-.%-6%)"*%*T2#8'4*.)%#.(2)%&'('&#)'.&* -6%)"*%$*&-.,%#.8*+)*+D%L*)A$%.-B%&-.$#,*+%)"*%&-.)+#32)#-.%-6%*'&"%-6%)"*%&'('&#)'.&*$%#. R#/D%EFDNP%)-%)"*%8'42*%-6%)"*%*T2#8'4*.)%4-',%&'('&#)'.&*%-0 1. <2,*:&1,I5'*-0,'%&4*8&4&8#1&68,*-9*LE)*-9
1105

1106 Chapter 13 CMOS Digital Logic Circuits 2. V&82*-9*12,*5'I.-5(*8&4&8#1&68,/*-<8E*&65*-<8W*2&/*&*1,'$#6&%*&1*&*8-6/1&61*0-%1&:,; <23/*9-'*12,*43'4-/,*-9*-3'*&6&%(/#/*2,',)*-<8E*&65*-<8W*8&6*.,*',4%&8,5*+#12*,A3&% 8&4&8#1&68,/*.,1+,,6*12,*-31431*6-5,*&65*:'-365;*Z-1,)*2-+,0,')*12&1*12,*9-'$3%&/ :#0,6* #6* ",81#-6* `;W;E* 9-'* 8&%83%&1#6:* -<8E* &65* -<8W* &',* /$&%%L/#:6&%* ',%&1#-6/2#4/) +2,',&/* 12,* &6&%(/#/* 2,',* #/* -.0#-3/%(* &* %&':,L/#:6&%* -6,;* J* 1,826#A3,* 2&/* .,,6 5,0,%-4,5* 9-'* 9#65#6:* ,A3#0&%,61* %&':,L/#:6&%* 0&%3,/* 9-'* -<8E* &65* -<8W* B/,,* e-5:,/ ,1 &%;)*BWQQGC*&65*[&.&,(*,1 &%;)*BWQQFCC; 3. "#68,*12,*/,8-65*#60,'1,'*5-,/*6-1*/+#182*/1&1,/)*+,*+#%%*&//3$,*12&1*12,*#6431*8&4&8#L 1&68,/*-9*LF*&65*LG*',$*&44'-7#$&1,%(*8-6/1&61*&65*,A3&%*1-*12,*1-1&%*:&1,*8&4&8#L 1&68,* ( H!- ?0 H - 9>?v H - 9
- 9F + - 9P = ( H! ) F - ?0 + ( H! ) P - ?0 + - 9>?v F + - 9?v P + - 9
- = N- 9
%@EFD^FC

Cgd1 &V

&V

&V

"

2 Cgd1

&V 2 Cgd1

Figure 13.25 !"*%<#44*+%524)#(4#&')#-.%-6%)"*%6**,3'&J%&'('&#)'.&*%-9
Example 13.6 N

N

;-.$#,*+%'%;<=>%#.8*+)*+%6'3+#&')*,%#.%'%MDNO?µ5%(+-&*$$%6-+%B"#&"%-?0%=%]% 6R[µ5 7 µ$-?0%=%EEO µI[K 7 N µ;-?0%=%FM%µI[K 7*"#$%=%−"#;%=%MDO%K7%'.,%"%%%=%NDO%KD%!"*% H ⁄ ! %+')#-%-6%L+%#$%MDF^O µ5 ⁄ MDNO %µ57%'.,%)"') 6-+%LK%#$%EDENO% µ5 ⁄ MDNO µ5D%!"*%/')*Z$-2+&*%'.,%/')*Z,+'#.%-8*+4'(%&'('&#)'.&*$%'+*%$(*#*,%)-%3*%MDF 6R[µ5 %-6%/')*%B#,)"D%R2+)"*+7%)"*%*66*&)#8*%@4'+/*?$#/.'4C%8'42*$%-6%,+'#.Z3-,:%&'('&#)'.&*$%'+*% - <8$ %= E%6R%'.,% - <8; %=%E%6RD%!"*%B#+#./%&'('&#)'.&*%-7%=%MDN%6RD%R#.,%#K)!7%#K!)7%'.,%#K%B"*.%)"*%#.8*+)*+%#$%,+#8? #./%'.%#,*.)#&'4%#.8*+)*+D

Solution R#+$)7%B*%,*)*+5#.*%)"*%8'42*%-6%)"*%*T2#8'4*.)%&'('&#)'.&*%-%2$#./%ST$D%@EFD^NC%'.,%@EFD^FC7 - = N- 9
13.3 Dynamic Operation of the CMOS Inverter

- <8E = E%6R - <8N = E%6R - 9F = MDF^O × MDNO × ] + N × MDF × MDF^O = MD^c^O%6R - 9P = EDENO × MDNO × ] + N × MDF × EDENO = NDF]NO %6R - 7 = MDN%6R <23/) - = N × MDEENO + N × MDFF^O + E + E + MD^c^O + NDF]NO + MDN = ]DNO%6R

W*G)%B*%2$*%ST$D%@EFD]PC%'.,%@EFD]OC%)-%,*)*+5#.*% # K)! 7 N α $ ! ???????????????????????????????????????????????N? ! ED^ ^ F × MDO H MDO ??????? ??? I ???????????????? NDO P NDO I EO

ED^ × ]DNO × EM ? ! NPD]%($% # K)! ! ????????????????????????????????????????????????????????????????????????????? I] EEO × EM × ( MDF^O ⁄ MDNO ) × NDO

>#5#4'+4:7%B*%2$*%ST$D%@EFD]]C%'.,%@EFD]^C%)-%,*)*+5#.*% # K!) 7

α ; ! ED^ I EO

ED^ × ]DNO × EM ? ! FEDO%($ # K!) ! ?????????????????????????????????????????????????????????????????????????? I] FM × EM × ( EDENO ⁄ MDNO ) × NDO

R#.'44:7%B*%,*)*+5#.*% # K %'$

E # K ! ??? ( NPD] H FEDO ) ! Nc%($ N

EXERCISES 13.16

;-.$#,*+%)"*%#.8*+)*+%$(*#*,%#.%SG'5(4*%EFD]%B"*.%4-',*,%B#)"%'.%',,#)#-.'4%MDE?(R%&'('&#)'.&*D H"')%B#44%)"*%(+-('/')#-.%,*4':%3*&-5*b Ans. PF^%($

13.17

1.%'.%'))*5()%)-%,*&+*'$*%)"*%'+*'%-6%)"*%#.8*+)*+%#.%SG'5(4*%EFD]7%@H[!C;%#$%5',*%*T2'4%)-%@H[!C$D H"')%#$%)"*%(*+&*.)'/*%+*,2&)#-.%#.%'+*'%'&"#*8*,b%R#.,%)"*%.*B%8'42*$%-6%-7%#K)!7%#K!)7%'.,%#KD%I$? $25*%)"')% - <8; %,-*$%.-)%&"'./*%$#/.#6#&'.)4:D Ans. (OMk9%PDNNO%6R9%E]D]%($9%NEDF%($9%E`%($

13.18

R-+%)"*%#.8*+)*+%-6%SG'5(4*%EFD]7%6#.,%)"*%5'G#525%6+*T2*.&:%')%B"#&"%#)%&'.%3*%-(*+')*,D Ans. E^D`%iXQ

13.3.3 Inverter Sizing 1.%)"#$%$*&)#-.%B*%',,+*$$%)"*%T2*$)#-.%-6%$*4*&)#./%'((+-(+#')*%@H[!C%+')#-$%6-+%)"*%)B-%)+'.? $#$)-+$% L + %'.,% L K %#.%'.%#.8*+)*+D%=2+%+*'$-.#./%&'.%3*%$255'+#Q*,%'$%6-44-B$D 1. <-* $#6#$#K,* &',&)* 12,* %,6:12* -9* &%%* 82&66,%/* #/* 3/3&%%(* $&5,* ,A3&%* 1-* 12,* $#6#$3$ %,6:12*4,'$#11,5*.(*12,*:#0,6*1,826-%-:(;

1107

1108 Chapter 13 CMOS Digital Logic Circuits 2. @6*&*:#0,6*#60,'1,')*#9*-3'*#61,',/1*#/*/1'#81%(*1-*$#6#$#K,*&',&)* ( H ⁄ ! ) $ *#/*3/3&%%(*/,%,81,5 #6*12,*'&6:,*E*1-*E;M;*<2,*/,%,81#-6*-9* ( H ⁄ ! ) ; *',%&1#0,*1-* ( H ⁄ ! ) $ *2&/*#69%3,68,*-6*12, 6-#/,*$&':#6/*&65* # K!) D *c-12*&',*-41#$#K,5*.(*$&182#6:* L K *&65* L + D *<2#/)*2-+,0,')*#/ 3/3&%%(*+&/1,93%*-9*&',&*&65*,A3&%%(*#$4-'1&61*8&6*#68',&/,*12,*,99,81#0,*8&4&8#1&68,*-) /-*12&1*&%12-3:2* # K!) *#/*$&5,*,A3&%*1-* # K)! 7 *12,*0&%3,*-9*.-12*8&6*.,*2#:2,'*12&6*#6*12, 8&/,* +#12-31* $&182#6:* B/,,* h'-.%,$* EF;GQC;* <23/)* /,%,81#6:* ( H ⁄ ! ) ; ! ( H ⁄ ! ) $ * #/* & 4-//#.#%#1()*&65* ( H ⁄ ! ) ; ! N ( H ⁄ ! ) $ *#/*&*9',A3,61%(*3/,5*8-$4'-$#/,; 3. e&0#6:*/,11%,5*-6* &6*&44'-4'#&1,*'&1#-*-9* ( H ⁄ ! ) ; *1-* ( H ⁄ ! ) $ 7 *+,*/1#%%*2&0,* 1-*/,%,81 ( H ⁄ ! ) $ * 1-* ',538,* # K * &65* 123/* &%%-+* 2#:2,'* /4,,5/* -9* -4,'&1#-6;* J6(* #68',&/,* #6 ( H ⁄ ! ) $ * &65* 4'-4-'1#-6&%%(* #6* ( H ⁄ ! ) ; * +#%%* -9* 8-3'/,* #68',&/,* &',&)* &65* 2,68,* 12, #60,'1,'*8-61'#.31#-6*1-*12,*0&%3,*-9*12,*,A3#0&%,61*8&4&8#1&68,*-;*<-*.,*$-',*4',8#/,*+, ,74',//*-*&/*12,*/3$*-9*&6*#61'#6/#8*8-$4-6,61* - #.) *8-61'#.31,5*.(* L + *&65* L K *-9*12, #60,'1,')*&65*&6*,71'#6/#8*8-$4-6,61* - *G) *',/3%1#6:*9'-$*12,*+#'#6:*&65*12,*#6431*8&4&8L #1&68,*-9*12,*5'#0,6*:&1,/) - ! - #.) H - *G)

%@EFD^PC

1.&+*'$#./% ( H ⁄ ! ) $ %'.,% ( H ⁄ ! ) ; %-6%)"*%#.8*+)*+%3:%'%6'&)-+%G%+*4')#8*%)-%)"')%-6%'%5#.? #525%$#Q*%#.8*+)*+%6-+%B"#&"% - #.) ! - #.)M %+*$24)$%#.% - ! G- #.)M H - *G)

%@EFD^OC

W-B7%#6%B*%2$*%)"*%*T2#8'4*.)?+*$#$)'.&*$%'((+-'&"%)-%&-5(2)*% # K %'.,%,*6#.*%'.%*T2#8? '4*.)%#.8*+)*+%+*$#$)'.&*% E *T %'$ E E *T ! ??? ( E + H E K ) N

%@EFD^]C

# K ! MD]`E *T -

%@EFD^^C

)"*.7

R2+)"*+7% #6% 6-+% )"*% 5#.#525?$#Q*% #.8*+)*+% E *T % #$% E *TM 7 % #.&+*'$#./% ( H ⁄ ! ) $ % '., ( H ⁄ ! ) ; %3:%)"*%6'&)-+%G%+*,2&*$% E *T %3:%)"*%$'5*%6'&)-+0 E *T ! E *TM ⁄ G

%@EFD^cC

;-53#.#./%ST$D%@EFD^^C7%@EFD^cC7%'.,%@EFD^OC7%B*%-3)'#. E *TM ? ( G- #.)M H - *G) ) # K ! MD]` ????????? G E # K ! MD]` E *TM - #.)M H ??? E *TM - *G) G

%@EFD^`C

H*%)"2$%$**%)"')%$&'4#./%)"*%H[!%+')#-$%,-*$%$?#%&"'./*%)"*%&-5(-.*.)%-6% # K %&'2$*,%3: )"*%&'('&#)'.&*$%-6% L + %'.,% L K D %1)%,-*$7%"-B*8*+7%+*,2&*%)"*%&-5(-.*.)%-6% # K %)"')%+*? $24)$% 6+-5% &'('&#)'.&*$% *G)*+.'4% )-% )"*% #.8*+)*+% #)$*46D% 1)% 6-44-B$% )"')% -.*% &'.% 2$*

13.3 Dynamic Operation of the CMOS Inverter

STD @EFD^`C%)-%,*&#,*%-.%'%$2#)'34*%$&'4#./%6'&)-+%G%)"')%J**($% # K %3*4-B%'%$(*#*,%5'G? #525%8'42*7%J**(#./%#.%5#.,%-6%&-2+$*%)"*%*66*&)%-6%#.&+*'$#./%G%-.%$#4#&-.%'+*'D

EXERCISE 13.19

R-+%)"*%#.8*+)*+%'.'4:Q*,%#.%SG'5(4*%EFD]0 @'C%R#.,%)"*%#.)+#.$#&%'.,%*G)+#.$#&%&-5(-.*.)$%-6*-D @3C%V:%B"')%6'&)-+%52$)% ( H ⁄ ! ) $ %'.,% ( H ⁄ ! ) ; %3*%#.&+*'$*,%)-%+*,2&*%)"*%*G)+#.$#&%('+)%-6% # K %3: '%6'&)-+%-6%Nb% @&C%S$)#5')*%)"*%+*$24)#./% # K D @,C%V:%B"')%6'&)-+%#$%)"*%#.8*+)*+%'+*'%#.&+*'$*,b Ans. @'C%ND`%6R7%FDFO%6R9%@3C%N9%@&C%NMDO%($9%@,C%N

13.3.4 Dynamic Power Dissipation <2,*6,:%#:#.%,*/1&1#8*4-+,'*5#//#4&1#-6*-9*>b^"*2&/*.,,6*&*/#:6#9#8&61*9&81-'*#6*#1/*5-$#L 6&68,*&/*12,*1,826-%-:(*-9*82-#8,*#6*#$4%,$,61#6:*2#:2L5,6/#1(*=a"@*8#'83#1/;*e-+,0,')*&/ 12,*63$.,'*-9*:&1,/*4,'*82#4*/1,&5#%(*#68',&/,/)*12,*5(6&$#8*4-+,'*5#//#4&1#-6*2&/*.,8-$,*& /,'#-3/*#//3,;*<2,*5(6&$#8*4-+,'*5#//#4&1,5*#6*12,*>b^"*#60,'1,'*#/*:#0,6*.(*VA;*BEF;FMC) +2#82*+,*',4,&1*2,',*&/ N

K ,:. = D -" %%

%@EFDcMC

+2,',*D*#/*12,*9',A3,68(*&1*+2#82*12,*:&1,*#/*/+#182,5;*@1*9-%%-+/*12&1*$#6#$#K#6:*-*#/*&6 ,99,81#0,*$,&6/*9-'*',538#6:*5(6&$#8L4-+,'*5#//#4&1#-6;*J6*,0,6*$-',*,99,81#0,*/1'&1,:(*#/ 12,*3/,*-9*&*%-+,'*4-+,'L/344%(*0-%1&:,;*J/*+,*2&0,*$,61#-6,5)*>b^"*4'-8,//*1,826-%-:#,/ 6-+*31#%#K,*"%%*0&%3,/*-9*E*=*-'*%,//;*<2,/,*6,+,'*82#4/)*2-+,0,')*4&8R*$382*$-',*8#'83#1'( -6* 12,* 82#4* B&/* $&6(* &/* W;F* .#%%#-6* 1'&6/#/1-'/C* &65* -4,'&1,* &1* 2#:2,'* 9',A3,68#,/* B$#8'-L 4'-8,//-'*8%-8R*9',A3,68#,/*&.-0,*F*geK*&',*6-+*&0&#%&.%,C;*<2,*5(6&$#8*4-+,'*5#//#4&1#-6 -9*/382*2#:2L5,6/#1(*82#4/*8&6*.,*-0,'*EQQ*P; 1.%',,#)#-.%)-%)"*%,:.'5#&%(-B*+%,#$$#(')#-.%)"')%+*$24)$%6+-5%)"*%(*+#-,#&%&"'+/#./%'., ,#$&"'+/#./%-6%)"*%#.8*+)*+%4-',%&'('&#)'.&*7%)"*+*%#$%'.-)"*+%&-5(-.*.)%-6%(-B*+%,#$$#('? )#-.% )"')% +*$24)$% 6+-5% )"*% &2++*.)% )"')% 64-B$% )"+-2/"% L K % '.,% L + % ,2+#./% *8*+:% $B#)&"#./ *8*.)D%R#/2+*%EFDN]%$"-B$%)"#$%#.8*+)*+%&2++*.)%'$%'%62.&)#-.%-6%)"*%#.(2)%8-4)'/*% v & %6-+%' 5')&"*,%#.8*+)*+D%H*%.-)*%)"')%)"*%&2++*.)%(*'J$%')% " , ! " %% ⁄ ND%>#.&*%')%)"#$%8-4)'/*%3-)" L + %'.,% L K %-(*+')*%#.%$')2+')#-.7%)"*%(*'J%&2++*.)%#$%/#8*.%3: E H " %% & (*'J ! ??? µ $- ?0 ????? ????????? ? I " #$ N !$ N

N

%@EFDcEC

!"*%B#,)"%-6%)"*%&2++*.)%(24$*%B#44%,*(*.,%-.%)"*%+')*%-6%&"'./*%-6% v & %B#)"%)#5*9%)"*%$4-B*+ )"*%+#$#./%*,/*%-6%)"*%#.(2)%B'8*6-+57%)"*%B#,*+%)"*%&2++*.)%(24$*%'.,%)"*%/+*')*+%)"*%*.*+/: ,+'B.%6+-5%)"*%$2((4:D%1.%/*.*+'47%"-B*8*+7%)"#$%(-B*+%&-5(-.*.)%#$%2$2'44:%52&"%$5'44*+ )"'.% K <=$ D

1109

1110 Chapter 13 CMOS Digital Logic Circuits

Figure 13.26 !"*%&2++*.)%#.%)"*%;<=>%#.8*+)*+%8*+$2$%)"*%#.(2)%8-4)'/*D

EXERCISE 13.20 R#.,%)"*%,:.'5#&%(-B*+%,#$$#(')#-.%-6%)"*%#.8*+)*+%'.'4:Q*,%#.%SG'5(4*%EFD]%B"*.%-(*+')*,%')%' E?iXQ%6+*T2*.&:D%16%)"#$%#.8*+)*+%#$%$B#)&"*,%')%#)$%5'G#525%(-$$#34*%-(*+')#./%6+*T2*.&:7%B"') #$%)"*%8'42*%-6%)"*%(-B*+Z,*4':%(+-,2&)b Ans. F`% µH 9%E`DO%6_

13.4 CMOS Logic-Gate Circuits @6* 12#/* /,81#-6)* +,* .3#%5* -6* -3'* R6-+%,5:,* -9* #60,'1,'* 5,/#:6* &65* 8-6/#5,'* 12,* 5,/#:6* -9 >b^"*8#'83#1/*12&1*',&%#K,*8-$.#6&1#-6&%L%-:#8*93681#-6/;*@6*8-$.#6&1#-6&%*8#'83#1/)*12,*-31L 431*&1*&6(*1#$,*#/*&*93681#-6*-6%(*-9*12,*0&%3,/*-9*#6431*/#:6&%/*&1*12&1*1#$,;*<23/)*12,/,*8#'L 83#1/* 5-* 6-1* 2&0,* $,$-'(* &65* 5-* 6-1* ,$4%-(* 9,,5.&8R;* >-$.#6&1#-6&%L%-:#8* 8#'83#1/* &', 3/,5*#6*%&':,*A3&61#1#,/*#6*&*$3%1#135,*-9*&44%#8&1#-6/\*#65,,5)*,0,'(*5#:#1&%*/(/1,$*8-61/ %&':,*63$.,'/*-9*8-$.#6&1#-6&%L%-:#8*8#'83#1/;

13.4.1 Basic Structure J*>b^"*%-:#8*8#'83#1*#/*#6*,99,81*&6*,71,6/#-6)*-'*&*:,6,'&%#K&1#-6)*-9*12,*>b^"*#60,'1,'? <2,*#60,'1,'*8-6/#/1/*-9*&6*Zb^"*43%%L5-+6*1'&6/#/1-')*&65*&*hb^"*43%%L34*1'&6/#/1-') -4,'&1,5*.(*12,*#6431*0-%1&:,*#6*&*8-$4%,$,61&'(*9&/2#-6;*<2,*>b^"*%-:#8*:&1,*8-6/#/1/ -9*1+-*6,1+-'R/?*12,*/0--25'.$($)!.'"J*B<>KC*8-6/1'381,5*-9*Zb^"*1'&6/#/1-'/)*&65*12, /0--20/($)!.'"J*B<=KC*8-6/1'381,5*-9*hb^"*1'&6/#/1-'/*B/,,*D#:;*EF;WOC;*<2,*1+-*6,1L +-'R/* &',* -4,'&1,5* .(* 12,* #6431* 0&'#&.%,/)* #6* &* 8-$4%,$,61&'(* 9&/2#-6;* <23/)* 9-'* 12, 12',,L#6431* :&1,* ',4',/,61,5* #6* D#:;* EF;WO)* 12,* hUZ* +#%%* 8-65381* 9-'* &%%* #6431* 8-$.#6&L 1#-6/*12&1*',A3#',*&*%-+*-31431*BP*=*QC*&65*+#%%*12,6*43%%*12,*-31431*6-5,*5-+6*1-*:'-365)

13.4 CMOS Logic-Gate Circuits

VDD

A B C

Pull-up network (PUN)

Y A B C

Pull-down network (PDN) Figure 13.27 Y*(+*$*.)')#-.% -6% '% )"+**?#.(2)% ;<=>% 4-/#& /')*D% !"*% \dW% &-5(+#$*$% \<=>% )+'.$#$)-+$7% '.,% )"*% \UW &-5(+#$*$%W<=>%)+'.$#$)-+$D

8&3/#6:*&*K,'-*0-%1&:,*1-*&44,&'*&1*12,*-31431) vP*=*Q;*"#$3%1&6,-3/%()*12,*hYZ*+#%%*.,*-99) &65*6-*5#',81*58*4&12*+#%%*,7#/1*.,1+,,6*"%%*&65*:'-365;*^6*12,*-12,'*2&65)*&%%*#6431*8-$L .#6&1#-6/*12&1*8&%%*9-'*&*2#:2*-31431*BP*=*EC*+#%%*8&3/,*12,*hYZ*1-*8-65381)*&65*12,*hYZ +#%%*12,6*43%%*12,*-31431*6-5,*34*1-*"%%)*,/1&.%#/2#6:*&6*-31431*0-%1&:,* vP* =*"%%;*"#$3%1&L 6,-3/%()*12,*hUZ*+#%%*.,*831*-99)*&65*&:)*6-*58*83'',61*4&12*.,1+,,6*"%%*&65*:'-365*+#%% ,7#/1*#6*12,*8#'83#1; Z-+)*/#68,*12,*hUZ*8-$4'#/,/*Zb^"*1'&6/#/1-'/)*&65*/#68,*&6*Zb^"*1'&6/#/1-'*8-65381/ +2,6*12,*/#:6&%*&1*#1/*:&1,*#/*2#:2)*12,*hUZ*#/*&81#0&1,5*B#;,;)*8-65381/C*+2,6*12,*#6431/*&', 2#:2;*@6*&*53&%*$&66,')*12,*hYZ*8-$4'#/,/*hb^"*1'&6/#/1-'/)*&65*&*hb^"*1'&6/#/1-'*8-65381/ +2,6*12,*#6431*/#:6&%*&1*#1/*:&1,*#/*%-+\*123/*12,*hYZ*#/*&81#0&1,5*+2,6*12,*#6431/*&',*%-+; <2,* hUZ* &65* 12,* hYZ* ,&82* 31#%#K,/* 5,0#8,/* #6* 4&'&%%,%* 1-* 9-'$* &6* ^[* 93681#-6)* &65 5,0#8,/*#6*/,'#,/*1-*9-'$*&6*JZU*93681#-6;*e,',)*12,*^[*&65*JZU*6-1&1#-6*',9,'*1-*83'',61 9%-+*-'*8-65381#-6;*D#:3',*EF;WX*/2-+/*,7&$4%,/*-9*hUZ/;*D-'*12,*8#'83#1*#6*D#:;*EF;WXB&C)*+, -./,'0,*12&1*LS*+#%%*8-65381*+2,6*S*#/*2#:2*BvS*=*"%%C*&65*+#%%*12,6*43%%*12,*-31431*6-5,*5-+6 1-*:'-365*BvP*=*Q*=)*P*=*QC;*"#$#%&'%()*LM*8-65381/*&65*43%%/*P*5-+6*+2,6*M*#/*2#:2;*<23/*P +#%%*.,*%-+*+2,6*S*#/*2#:2*?:*M*#/*2#:2)*+2#82*8&6*.,*,74',//,5*&/

P = S +M -'*,A3#0&%,61%(

P = S+M <2,*hUZ*#6*D#:;*EF;WXB.C*+#%%*8-65381*-6%(*+2,6*S*&65*M*&',*.-12*2#:2*/#$3%1&6,-3/%(; <23/*P*+#%%*.,*%-+*+2,6*S*#/*2#:2*/$<*M*#/*2#:2)

P = SM -'*,A3#0&%,61%(

P = SM

1111

1112 Chapter 13 CMOS Digital Logic Circuits

Y

Y A

A

QA B

QB

Y

QA

B

A

QB

B

QB

C

QC

QA

Y$A"B

Y $ AB

Y $ A " BC

(a)

(b)

(c)

Figure 13.28 SG'5(4*$%-6%(244?,-B.%.*)B-+J$D

VDD

VDD

A

QA

B

VDD QB

A

QA

A

B

QB

C

QC

QA

QB

B

Y

Y

Y

Y$A"B

Y$AB

Y $ A " BC

(a)

(b)

(c)

Figure 13.29 SG'5(4*$%-6%(244?2(%.*)B-+J$D

J/*&*9#6&%*,7&$4%,)*12,*hUZ*#6*D#:;*EF;WXB8C*+#%%*8-65381*&65*8&3/,*P*1-*.,*Q*+2,6*S*#/ 2#:2*?:*+2,6*M*/$<*-*&',*.-12*2#:2)*123/

P = S + M-'*,A3#0&%,61%(

P = S + MZ,71*8-6/#5,'*12,*hYZ*,7&$4%,/*/2-+6*#6*D#:;*EF;W`;*<2,*hYZ*#6*D#:;*EF;W`B&C*+#%% 8-65381*&65*43%%*P*34*1-*"%%BP*=*EC*+2,6*S*#/*%-+*?:*M*#/*%-+)*123/

P = S+M <2,*hYZ*#6*D#:;*EF;W`B.C*+#%%*8-65381*&65*4'-538,*&*2#:2* -31431*BvP*=*"%%)*P*=*EC*-6%( +2,6*S*/$<*M*&',*.-12*%-+)*123/

P = SM

13.4 CMOS Logic-Gate Circuits

NMOS

PMOS

(a)

(b)

Figure 13.30 d$2'4%'.,%'4)*+.')#8*%&#+&2#)%$:53-4$%6-+%<=>RS!$D

D#6&%%()*12,*hYZ*#6*D#:;*EF;W`B8C*+#%%*8-65381*&65*8&3/,*P*1-*.,*2#:2*B%-:#8*EC*#9*S*#/*%-+*?: #9*M*/$<*-*&',*.-12*%-+\*123/)

P = S + Me&0#6:*5,0,%-4,5*&6*365,'/1&65#6:*&65*&6*&44',8#&1#-6*-9*12,*/1'3813',*&65*-4,'&1#-6*-9 hUZ/*&65*hYZ/)*+,*6-+*8-6/#5,'*8-$4%,1,*>b^"*:&1,/;*c,9-',*5-#6:*/-)*2-+,0,')*+,*+#/2 1-*#61'-538,*&%1,'6&1#0,*8#'83#1*/($.-%/)*12&1*&',*&%$-/1*36#0,'/&%%(*3/,5*9-'*b^"*1'&6/#/1-'/*.( 5#:#1&%L8#'83#1*5,/#:6,'/;*D#:3',*EF;FQ*/2-+/*-3'*3/3&%*/($.-%/*B%,91C*&65*12,*8-'',/4-65#6: S5#:#1&%T*/($.-%/*B'#:21C;*^./,'0,*12&1*12,*/($.-%*9-'*12,*hb^"*1'&6/#/1-'*+#12*&*8#'8%,*&1*12, :&1,*1,'$#6&%*#/*#61,65,5*1-*#65#8&1,*12&1*12,*/#:6&%*&1*12,*:&1,*2&/*1-*.,*%-+*9-'*12,*5,0#8,*1.,*&81#0&1,5*B#;,;)*1-*8-65381C;*<23/)*#6*1,'$/*-9*%-:#8L8#'83#1*1,'$#6-%-:()*12,*:&1,*1,'$#6&%*-9 12,* hb^"* 1'&6/#/1-'* #/* &6* /6#(24* 3?7* #6431;* c,/#5,/* #65#8&1#6:* 12#/* 4'-4,'1(* -9* hb^" 5,0#8,/)*12,*5#:#1&%*/($.-%/*-$#1*&6(*#65#8&1#-6*-9*+2#82*-9*12,*5,0#8,*1,'$#6&%/*#/*12,*/-3'8, &65* +2#82* #/* 12,* 5'* <2#/* /2-3%5* 8&3/,* 6-* 5#99#83%1(* &1* 12#/* /1&:,* -9* -3'* /135(\* /#$4%( ',$,$.,'*12&1*9-'*&6*Zb^"*1'&6/#/1-')*12,*5'*#/*12,*1,'$#6&%*12&1*#/*&1*12,*2#:2,'*0-%1&:, B83'',61*9%-+/*9'-$*5'*1-*/-3'8,C)*&65*9-'*&*hb^"*1'&6/#/1-'*12,*/-3'8,*#/*12,*1,'$#6&%*12&1 #/*&1*12,*2#:2,'*0-%1&:,*B83'',61*9%-+/*9'-$*/-3'8,*1-*5'C;*<-*.,*8-6/#/1,61*+#12*12,*%#1,'&L 13',)*+,*/2&%%*2,68,9-'12*3/,*12,/,*$-5#9#,5*/($.-%/*9-'*b^"*1'&6/#/1-'/*#6*%-:#8*&44%#8&L 1#-6/)*,78,41*#6*%-8&1#-6/*+2,',*-3'*3/3&%*/($.-%/*2,%4*#6*365,'/1&65#6:*8#'83#1*-4,'&1#-6;

13.4.2 The Two-Input NOR Gate P,*9#'/1*8-6/#5,'*12,*>b^"*:&1,*12&1*',&%#K,/*12,*1+-L#6431*Z^[*93681#-6

P = S + M = SM

%@EFDcNC

P,*/,,*12&1*P*#/*1-*.,*%-+*BhUZ*8-65381#6:C*+2,6*S*#/*2#:2*-'*M*#/*2#:2;*<23/*12,*hUZ*8-6L /#/1/*-9*1+-*4&'&%%,%*Zb^"*5,0#8,/*+#12*S*&65*M*&/*#6431/*B#;,;)*12,*8#'83#1*#6*D#:;*EF;WX&C; D-'*12,*hYZ)*+,*6-1,*9'-$*12,*/,8-65*,74',//#-6*#6*VA;*BEF;XWC*12&1*P*#/*1-*.,*2#:2*+2,6*S &65*M*&',*.-12*%-+;*<23/*12,*hYZ*8-6/#/1/*-9*1+-*/,'#,/*hb^"*5,0#8,/*+#12*S*&65*M*&/*12, #6431/* B#;,;)* 12,* 8#'83#1* #6* D#:;* EF;W`.C;* h311#6:* 12,* hUZ* &65* 12,* hYZ* 1-:,12,'* :#0,/* 12, >b^"*Z^[*:&1,*/2-+6*#6*D#:;*EF;FE;*Z-1,*12&1*,71,6/#-6*1-*&*2#:2,'*63$.,'*-9*#6431/*#/ /1'&#:219-'+&'5?*D-'*,&82*&55#1#-6&%*#6431)*&6*Zb^"*1'&6/#/1-'*#/*&55,5*#6*4&'&%%,%*+#12*L+S &65*L+M)*&65*&*hb^"*1'&6/#/1-'*#/*&55,5*#6*/,'#,/*+#12*LKS*&65*LKM;

1113

1114 Chapter 13 CMOS Digital Logic Circuits VDD

A

QPA

B

QPB Y

QNB

QNA B

A

Figure 13.31 I%)B-?#.(2)%;<=>%W=Y%/')*D

Y$A"B

13.4.3 The Two-Input NAND Gate <2,*1+-L#6431*ZJZU*93681#-6*#/*5,/8'#.,5*.(*12,*c--%,&6*,74',//#-6

P = SM = S + M

%@EFDcFC

<-*/(612,/#K,*12,*hUZ)*+,*8-6/#5,'*12,*#6431*8-$.#6&1#-6/*12&1*',A3#',*P*1-*.,*%-+?*<2,', #/*-6%(*-6,*/382*8-$.#6&1#-6)*6&$,%()*S*&65*M*.-12*2#:2;*<23/)*12,*hUZ*/#$4%(*8-$4'#/,/ 1+-*Zb^"*1'&6/#/1-'/*#6*/,'#,/*B/382*&/*12,*8#'83#1*#6*D#:;*EF;WX.C;*<-*/(612,/#K,*12,*hYZ) +,*8-6/#5,'*12,*#6431*8-$.#6&1#-6/*12&1*',/3%1*#6*P*.,#6:*2#:2;*<2,/,*&',*9-365*9'-$*12, /,8-65*,74',//#-6*#6*VA;*BEF;XFC*&/*S*%-+*-'*M*%-+;*<23/)*12,*hYZ*8-6/#/1/*-9*1+-*4&'&%%,% hb^"*1'&6/#/1-'/*+#12*S*&65*M*&44%#,5*1-*12,#'*:&1,/*B/382*&/*12,*8#'83#1*#6*D#:;*EF;W`&C;*h31L 1#6:*12,*hUZ*&65*hYZ*1-:,12,'*',/3%1/*#6*12,*>b^"*ZJZU*:&1,*#$4%,$,61&1#-6*/2-+6*#6 D#:;* EF;FW;* Z-1,* 12&1* ,71,6/#-6* 1-* &* 2#:2,'* 63$.,'* -9* #6431/* #/* /1'&#:219-'+&'5?* D-'* ,&82 VDD

A

QPA B

QPB

Y A

QNA

B

QNB

Y $ AB

Figure 13.32 I%)B-?#.(2)%;<=>%WIWU%/')*D

13.4 CMOS Logic-Gate Circuits

&55#1#-6&%*#6431)*+,*&55*&6*Zb^"*1'&6/#/1-'*#6*/,'#,/*+#12*L+S*&65*L+M)*&65*&*hb^"*1'&6L /#/1-'*#6*4&'&%%,%*+#12*LKS*&65*LKM;

13.4.4 A Complex Gate >-6/#5,'*6,71*12,*$-',*8-$4%,7*%-:#8*93681#-6

P = S ( M + -% )

%@EFDcPC

"#68,* P = S ( M + -% ) )*+,*/,,*12&1*P*/2-3%5*.,*%-+*9-'*S*2#:2*&65*/#$3%1&6,-3/%(*,#12,'*M 2#:2*-'*-*&65*%*.-12*2#:2)*9'-$*+2#82*12,*hUZ*#/*5#',81%(*-.1,5;*<-*-.1*12,*hYZ)*+, 6,,5* 1-* ,74',//* P* #6* 1,'$/* -9* 12,* 8-$4%,$,61,5* 0&'#&.%,/;* P,* 5-* 12#/* 12'-3:2* ',4,&1,5 &44%#8&1#-6*-9*U,b-':&6f/*%&+)*&/*9-%%-+/?

P = S ( M + -% ) = S + M + -% = S + M%-% = S + M(- + %)

%@EFDcOC

<23/)*P*#/*2#:2*9-'*S*%-+*-'*M*%-+*&65*,#12,'*-*-'*%*%-+;*<2,*8-'',/4-65#6:*8-$4%,1,*>b^" 8#'83#1*+#%%*.,*&/*/2-+6*#6*D#:;*EF;FF;

13.4.5 Obtaining the PUN from the PDN and Vice Versa D'-$*12,*>b^"*:&1,*8#'83#1/*8-6/#5,',5*123/*9&'*B,;:;)*12&1*#6*D#:;*EF;FFC)*+,*-./,'0,*12&1 12,* hUZ* &65* 12,* hYZ* &',* 53&%* 6,1+-'R/?* P2,',*&* /,'#,/* .'&682* ,7#/1/* #6* -6,)* &* 4&'&%%,% .'&682*,7#/1/*#6*12,*-12,';*<23/)*+,*8&6*-.1*-6,*9'-$*12,*-12,')*&*4'-8,//*12&1*8&6*.,*/#$L 4%,'*12&6*2&0#6:*1-*/(612,/#K,*,&82*/,4&'&1,%(*9'-$*12,*c--%,&6*,74',//#-6*-9*12,*93681#-6; D-'*#6/1&68,)*#6*12,*8#'83#1*-9*D#:;*EF;FF)*+,*9-365*#1*',%&1#0,%(*,&/(*1-*-.1*12,*hUZ)*/#$L 4%(*.,8&3/,*+,*&%',&5(*2&5* P *#6*1,'$/*-9*12,*368-$4%,$,61,5*#6431/;*^6*12,*-12,'*2&65)*1-.1*12,*hYZ)*+,*2&5*1-*$&6#43%&1,*12,*:#0,6*c--%,&6*,74',//#-6*1-*,74',//*P*&/*&*9368L 1#-6*-9*12,*8-$4%,$,61,5*0&'#&.%,/)*12,*9-'$*8-60,6#,61*9-'*/(612,/#K#6:*hYZ/;*J%1,'6&L 1#0,%()*+,*8-3%5*2&0,*3/,5*12#/*53&%#1(*4'-4,'1(*1-*-.1*12,*hYZ*9'-$*12,*hUZ;*<2,*',&5,' #/*3':,5*1-*',9,'*1-*D#:;*EF;FF*1-*8-60#68,*2,'/,%9*12&1*12#/*#/*#65,,5*4-//#.%,;************** @1*/2-3%5)*2-+,0,')*.,*$,61#-6,5*12&1*&1*1#$,/*#1*#/*6-1*,&/(*1-*-.1*-6,*-9*12,*1+-*6,1L +-'R/*9'-$*12,*-12,'*3/#6:*12,*53&%#1(*4'-4,'1(;*D-'*/382*8&/,/)*-6,*2&/*1-*',/-'1*1-*&*$-', '#:-'-3/*4'-8,//)*+2#82*#/*.,(-65*12,*/8-4,*-9*12#/*.--R*B/,,*j&6:*&65*a,.%,.#8#)*E```C;

13.4.6 The Exclusive-OR Function J6*#$4-'1&61*93681#-6*12&1*-91,6*&'#/,/*#6*%-:#8*5,/#:6*#/*12,*,78%3/#0,L^[*Bk^[C*93681#-6)

P = SM + SM

%@EFDc]C

P,*-./,'0,*12&1*/#68,*P*B'&12,'*12&6* P C*#/*:#0,6)*#1*#/*,&/#,'*1-*/(612,/#K,*12,*hYZ;*P,*6-1,) 2-+,0,')*12&1*369-'136&1,%(*P*#/*6-1*&*93681#-6*-9*12,*8-$4%,$,61,5*0&'#&.%,/*-6%(*B&/*+,

1115

1116 Chapter 13 CMOS Digital Logic Circuits VDD

A

QPA

B

C

QPB

QPC D

QPD

Y A

B

QNA

C

QNC

D

QND

QNB

Y $ A(B " CD)

Figure 13.33 ;<=>% +*'4#Q')#-.% -6% '% &-5? (4*G%/')*D

+-3%5* %#R,* #1* 1-* .,C;* <23/)* +,* +#%%* 6,,5* &55#1#-6&%* #60,'1,'/;* <2,* hYZ* -.1,5* 5#',81%( 9'-$*VA;*BEF;XNC*#/*/2-+6*#6*D#:;*EF;FGB&C;*Z-1,*12&1*12,*LE)*LW*.'&682*',&%#K,/*12,*9#'/1*1,'$ B SM C)*+2,',&/*12,*LF)*LG*.'&682*',&%#K,/*12,*/,8-65*1,'$*B S M C;*Z-1,*&%/-*12,*6,,5*9-'*1+&55#1#-6&%*#60,'1,'/*1-*:,6,'&1,* S *&65* M ; J/* 9-'* /(612,/#K#6:* 12,* hUZ)* +,* 8&6* -.1* #1* &/* 12,* 53&%* 6,1+-'R* -9* 12,* hYZ* #6 D#:; EF;FGB&C;*J%1,'6&1#0,%()*+,*8&6*5,0,%-4*&6*,74',//#-6*9-'* P *&65*3/,*#1*1-*/(612,/#K,*12, hUZ;* a,&0#6:* 12,* 9#'/1* &44'-&82* 9-'* 12,* ',&5,'* 1-* 5-* &/* &6* ,7,'8#/,)* +,* /2&%%* 31#%#K,* 12, 5#',81*/(612,/#/*&44'-&82;*U,b-':&6f/*%&+*8&6*.,*&44%#,5*1-*12,*,74',//#-6*#6*VA;*BEF;XNC 1-*-.1* P *&/

P = SM + SM

%@EFDc^C

<2,*8-'',/4-65#6:*hUZ*+#%%*.,*&/*#6*D#:;*EF;FGB.C)*+2#82*/2-+/*12,*>b^"*',&%#K&1#-6*-9 12,*,78%3/#0,L^[*93681#-6*,78,41*9-'*12,*1+-*&55#1#-6&%*#60,'1,'/;*Z-1,*12&1*12,*,78%3/#0,L ^[*',A3#',/*EW*1'&6/#/1-'/*9-'*#1/*',&%#K&1#-6)*&*'&12,'*8-$4%,7*6,1+-'R;*a&1,')*#6*",81#-6*EG;W) +,* /2&%%* /2-+* &* /#$4%,'* ',&%#K&1#-6* -9* 12,* k^[* ,$4%-(#6:* &* 5#99,',61* 9-'$* -9* >b^" %-:#8; J6-12,'*#61,',/1#6:*-./,'0&1#-6*9-%%-+/*9'-$*12,*8#'83#1*#6*D#:;*EF;FGB.C;*<2,*hUZ*&65 12,*hYZ*2,',*&',*$?#*53&%*6,1+-'R/;*@65,,5)*53&%#1(*-9*12,*hUZ*&65*12,*hYZ*#/*6-1*&*6,8,/L /&'(* 8-65#1#-6;*<23/)*&%12-3:2*&* 53&%*-9*hUZ* B-'*hYZC*8&6* &%+&(/* .,*3/,5*9-'* hYZ*B-' hUZC)*12,*1+-*6,1+-'R/*&',*6-1*6,8,//&'#%(*53&%/;

13.4 CMOS Logic-Gate Circuits

VDD

VDD

A

Q1 A

Q3

A

A

B

Q2 B

Q4

B

B

Y

Y

(a)

A

A

B

B

(b)

Figure 13.34 Y*'4#Q')#-.%-6%)"*%*G&42$#8*?=Y%@m=YC%62.&)#-.0%8#9%!"*%\dW%$:.)"*$#Q*,%,#+*&)4:%6+-5 )"*%*G(+*$$#-.%#.%STD%@EFDc]CD%8:9%!"*%&-5(4*)*%m=Y%+*'4#Q')#-.%2)#4#Q#./%)"*%\dW%#.%@'C%'.,%'%\UW%)"')%#$ $:.)"*$#Q*,%,#+*&)4:%6+-5%)"*%*G(+*$$#-.%#.%STD%@EFDc^CD%W-)*%)"')%)B-%#.8*+)*+$%@.-)%$"-B.C%'+*%.**,*,%)/*.*+')*%)"*%&-5(4*5*.)*,%8'+#'34*$D%I4$-%.-)*%)"')%#.%)"#$%m=Y%+*'4#Q')#-.7%)"*%\UW%'.,%)"*%\dW%'+*%.-) ,2'4%.*)B-+J$9%"-B*8*+7%'%+*'4#Q')#-.%3'$*,%-.%,2'4%.*)B-+J$%#$%(-$$#34*%@$**%\+-34*5%EFDP^CD

13.4.7 Summary of the Synthesis Method 1. <2,*hUZ*8&6*.,*$-/1*5#',81%(*/(612,/#K,5*.(*,74',//#6: P &/*&*93681#-6*-9*12,*1$6?.I ;34.4$#4<* 0&'#&.%,/;* @9* 8-$4%,$,61,5* 0&'#&.%,/* &44,&'* #6* 12#/* ,74',//#-6)* &55#1#-6&% #60,'1,'/*+#%%*.,*',A3#',5*1-*:,6,'&1,*12,$; 2. <2,*hYZ*8&6*.,*$-/1*5#',81%(*/(612,/#K,5*.(*,74',//#6:*P*&/*&*93681#-6*-9*12,*6?.;34I .4$#4<*0&'#&.%,/*&65*12,6*&44%(#6:* 12,*368-$4%,$,61,5*0&'#&.%,/*1-*12,*:&1,/*-9*12, hb^"* 1'&6/#/1-'/;* @9* 368-$4%,$,61,5* 0&'#&.%,/* &44,&'* #6* 12,* ,74',//#-6)* &55#1#-6&% #60,'1,'/*+#%%*.,*6,,5,5; 3. <2,* hUZ* 8&6* .,* -.1,5* 9'-$* 12,* hYZ* B&65* 0#8,* 0,'/&C* 3/#6:* 12,* 53&%#1( 4'-4,'1(;

13.4.8 Transistor Sizing ^68,*&*>b^"*:&1,*8#'83#1*2&/*.,,6*:,6,'&1,5)*12,*-6%(*/#:6#9#8&61*/1,4*',$#6:*#6*12, 5,/#:6* #/* 1-* 5,8#5,* -6* H ⁄ ! *'&1#-/* 9-'* &%%* 5,0#8,/;* <2,/,* '&1#-/* 3/3&%%(* &',* /,%,81,5* 14'-0#5,* 12,* :&1,* +#12* 83'',61L5'#0#6:* 8&4&.#%#1(* #6* .-12* 5#',81#-6/* ,A3&%* 1-* 12&1* -9* 12, .&/#8*#60,'1,';*D-'*12,*.&/#8*#60,'1,'*5,/#:6)*5,6-1,* @H ⁄ ! C $ *= $*&65* @H ⁄ ! C; *=*;)*+2,', $*#/*3/3&%%(*E*1-*E;M**&65)*9-'*&*$&182,5*5,/#:6)*;*=* ( µ $ ⁄ µ ; ) $\*&%12-3:2*-91,6*;*!*W$*&65 9-'*$#6#$3$*&',&*;*!*$;*<23/)*+,*+#/2*1-*/,%,81*#65#0#53&%* H ⁄ ! *'&1#-/*9-'*&%%*1'&6/#/1-'/ #6*&*%-:#8*:&1,*/-*12&1*12,*hUZ*/2-3%5*.,*&.%,*1-*4'-0#5,*&*8&4&8#1-'*5#/82&':,*83'',61*/# 34/>#*,A3&%*1-*12&1*-9*&6*Zb^"*1'&6/#/1-'*+#12* H ⁄ ! *=*$)*&65*12,*hYZ*/2-3%5*.,*&.%,*1-

1117

1118 Chapter 13 CMOS Digital Logic Circuits 4'-0#5,* &* 82&':#6:* 83'',61* /#* 34/>#* ,A3&%* 1-* 12&1* -9* &* hb^"* 1'&6/#/1-'* +#12* H ⁄ ! * = ;; <2#/*+#%%*:3&'&61,,*&*7?:>#I6/>4*:&1,*5,%&(*,A3&%*1-*12&1*-9*12,*.&/#8*#60,'1,';G @6*12,*4',8,5#6:*5,/8'#41#-6)*12,*#5,&*-9*S+-'/1*8&/,T*/2-3%5*.,*,$42&/#K,5;*@1*$,&6/*12&1 #6*5,8#5#6:*-6*5,0#8,*/#K#6:)*+,*/2-3%5*9#65*12,*#6431*8-$.#6&1#-6/*12&1*',/3%1*#6*12,*%-+,/1 -31431* 83'',61* &65* 12,6* 82--/,* /#K,/* 12&1* +#%%* $&R,* 12#/* 83'',61* ,A3&%* 1-* 12&1* -9* 12,* .&/#8 #60,'1,';* c,9-',* +,* 8-6/#5,'* ,7&$4%,/)* +,* 6,,5* 1-* &55',//* 12,* #//3,* -9* 5,1,'$#6#6:* 12, 83'',61L5'#0#6:*8&4&.#%#1(*-9*&*8#'83#1*8-6/#/1#6:*-9*&*63$.,'*-9*b^"*5,0#8,/;*@6*-12,'*+-'5/) +,*6,,5*1-*9#65*12,*4U1(2/34$#* H ⁄ ! *:/#(?*-9*&*6,1+-'R*-9*b^"*1'&6/#/1-'/;*<-+&'5*12&1*,65) +,* 8-6/#5,'* 12,* 4&'&%%,%* &65* /,'#,/* 8-66,81#-6* -9* b^"DV
E $*+#*$ = E +E + E +N + D%D%D &-.$)'.) &-.$)'.) = ???????????????????? + ???????????????????? + D%D%D @H ⁄ ! C N @H ⁄ ! C E E E = &-.$)'.) ??????????????????? + ??????????????????? + D%D%D @H ⁄ ! C E @H ⁄ ! C N &-.$)'.) = ????????????????????? @H ⁄ ! C *T ',/3%1#6:*#6*12,*9-%%-+#6:*,74',//#-6*9-'* @H ⁄ ! C *T*9-'*1'&6/#/1-'/*8-66,81,5*#6*/,'#,/?

E @H ⁄ ! C *T = ?????????????????????????????????????????????????????????? E E ? D%D%D ??????????????????? + ?????????????????? + @H ⁄ ! C E @H ⁄ ! C N

%@EFDccC

"#$#%&'%()*+,*8&6*/2-+*12&1*12,*4&'&%%,%*8-66,81#-6*-9*1'&6/#/1-'/*+#12*H ⁄ !*'&1#-/*-9*@H ⁄ ! C E) @H ⁄ ! C N )*;*;*;*)*',/3%1/*#6*&6*,A3#0&%,61*H ⁄ !*-9

@H ⁄ ! C *T = @H ⁄ ! C E + @H ⁄ ! C N + D%D%D

%@EFDc`C

J/*&6*,7&$4%,)*1+-*#5,61#8&%*b^"*1'&6/#/1-'/*+#12*#65#0#53&%*H ⁄ !*'&1#-/*-9*G*',/3%1*#6 &6*,A3#0&%,61*H ⁄ !*-9*W*+2,6*8-66,81,5*#6*/,'#,/*&65*-9*X*+2,6*8-66,81,5*#6*4&'&%%,%;M J/*&6*,7&$4%,*-9*4'-4,'*/#K#6:)*8-6/#5,'*12,*9-3'L#6431*Z^[*#6*D#:;*EF;FM;*e,',)*12, +-'/1*8&/,*B12,*%-+,/1*83'',61C*9-'*12,*hUZ*#/*-.1,5*+2,6*-6%(*-6,*-9*12,*Zb^"*1'&6/#/L 1-'/*#/*8-65381#6:;*P,*12,',9-',*/,%,81*12,*H ⁄ !*-9*,&82*Zb^"*1'&6/#/1-'*1-*.,*,A3&%*1-*12&1 -9*12,*Zb^"*1'&6/#/1-'*-9*12,*.&/#8*#60,'1,')*6&$,%()*$;*D-'*12,*hYZ)*2-+,0,')*12,*+-'/1L 8&/,*/#13&1#-6*B&65*#65,,5*12,*-6%(*8&/,C*-883'/*+2,6*&%%*#6431/*&',*%-+*&65*12,*9-3'*/,'#,/ hb^"*1'&6/#/1-'/*&',*8-65381#6:;*"#68,*12,*,A3#0&%,61*H ⁄ !*+#%%*.,*-6,LA3&'1,'*-9*12&1*-9 P

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

13.4 CMOS Logic-Gate Circuits

VDD A

4p

B

4p

C

4p

D

4p Y$A"B"C"D

A

n

n

B

n

C

D

n

Figure 13.35 \+-(*+%)+'.$#$)-+%$#Q#./%6-+%'%6-2+?#.(2)%W=Y%/')*D%W-)*%)"')%$%'.,%;%,*.-)*%)"*% H⁄ ! %+')#-$ -6%L+%'.,%LK 7%+*$(*&)#8*4:7%-6%)"*%3'$#&%#.8*+)*+D

VDD

A

p

p

B

p

C

D

p

Y $ ABCD A

4n

B

4n

C

4n

D

4n

Figure 13.36 \+-(*+%)+'.$#$)-+%$#Q#./%6-+%'%6-2+?#.(2)%WIWU%/')*D%W-)*%)"')% $%'.,%;%,*.-)*%)"*% H⁄ ! +')#-$%-6%L+%'.,%LK 7%+*$(*&)#8*4:7%-6%)"*%3'$#&%#.8*+)*+D

,&82* hb^"* 5,0#8,)* +,* /2-3%5* /,%,81* 12,* H ⁄ ! *'&1#-*-9* ,&82* hb^"* 1'&6/#/1-'* 1-* .,* 9-3' 1#$,/*12&1*-9*LK*-9*12,*.&/#8*#60,'1,')*12&1*#/)*G;V J/*&6-12,'*,7&$4%,)* +,* /2-+* #6* D#:;*EF;FN*12,* 4'-4,'* /#K#6:*9-'* &*9-3'L#6431*ZJZU :&1,;* >-$4&'#/-6* -9* 12,* ZJZU* &65* Z^[* :&1,/* #6* D#:/;* EF;FM* &65* EF;FN* #65#8&1,/* 12&1

1119

1120 Chapter 13 CMOS Digital Logic Circuits .,8&3/,*;*#/*3/3&%%(*1+-*1-*12',,*1#$,/*$)*12,*Z^[*:&1,*+#%%*',A3#',*$382*:',&1,'*&',&*12&6 12,* ZJZU* :&1,;* D-'* 12#/* ',&/-6)* ZJZU* :&1,/* &',* :,6,'&%%(* 4',9,'',5* 9-'* #$4%,$,61#6: 8-$.#6&1#-6&%*%-:#8*93681#-6/*#6*>b^";

Example 13.7 \+-8#,*%)+'.$#$)-+% H ⁄ ! %+')#-$%6-+%)"*%4-/#&%&#+&2#)%$"-B.%#.%R#/D%EFDF^D%I$$25*%)"')%6-+%)"*%3'$#&%#.8*+)*+ $%=%EDO%'.,%;%=%O%'.,%)"')%)"*%&"'..*4%4*./)"%#$%MDNO%µ5D VDD

QPB

B

D

QPD (3.75/0.25)

(1.875/0.25)

QPC (3.75/0.25)

C

QPA (3.75/0.25)

A

Y

B A

QNB (0.75/0.25)

QNA (0.375/0.25) C

QNC (0.75/0.25)

QND (0.75/0.25)

Figure 13.37 ;#+&2#)%6-+%SG'5(4*%EFD^D

Solution Y*6*+%)-%R#/D%EFDF^7%'.,%&-.$#,*+%)"*%\UW%6#+$)D%H*%.-)*%)"')%)"*%B-+$)%&'$*%-&&2+$%B"*.%L+M%#$%-.%'., *#)"*+% L +- %-+% L +% %#$%-.D%!"')%#$7%#.%)"*%B-+$)%&'$*7%B*%"'8*%)B-%)+'.$#$)-+$%#.%$*+#*$D%!"*+*6-+*7%B*%$*4*&) *'&"%-6% L +M 7 % L +- 7 %'.,% L +% %)-%"'8*%)B#&*%)"*%B#,)"%-6%)"*%$?&"'..*4%,*8#&*%#.%)"*%3'$#&%#.8*+)*+7%)"2$ L +M 0% H ⁄ ! = N$ = F = MD^O ⁄ MDNO L +- 0% H ⁄ ! = N$ = F = MD^O ⁄ MDNO L +% 0% H ⁄ ! = N$ = F = MD^O ⁄ MDNO D-'*1'&6/#/1-'* L +S 7 */,%,81* H ⁄ ! *1-*.,*,A3&%*1-*12&1*-9*12,*$L82&66,%*5,0#8,*#6*12,*.&/#8*#60,'1,'?

L +S 0% H ⁄ ! = $ = EDO = MDF^O ⁄ MDNO

13.4 CMOS Logic-Gate Circuits ;

W*G)7%&-.$#,*+%)"*%\dWD%X*+*7%B*%$**%)"')%#.%)"*%B-+$)%&'$*7%B*%"'8*%)"+**%)+'.$#$)-+$%#.%$*+#*$0%LKS7 LK-7%'.,%LK%D%!"*+*6-+*7%B*%$*4*&)%)"*% H ⁄ ! %+')#-%-6%*'&"%-6%)"*$*%)-%3*%)"+**%)#5*$%)"')%-6%LK%#.%)"*%3'$#& #.8*+)*+7%)"')%#$7%F;7%)"2$ L KS 0% H ⁄ ! = F; = EO = FD^O ⁄ MDNO L K- 0% H ⁄ ! = F; = EO = FD^O ⁄ MDNO L K% 0% H ⁄ ! = F; = EO = FD^O ⁄ MDNO R#.'44:7%)"*% H ⁄ ! %+')#-%6-+%LKM%$"-24,%3*%$*4*&)*,%$-%)"')%)"*%*T2#8'4*.)% H ⁄ ! %-6%)"*%$*+#*$%&-..*&)#-.%-6 LKM%'.,%LKS%$"-24,%3*%*T2'4%)-%;D%1)%6-44-B$%)"')%6-+%LKM%)"*%+')#-%$"-24,%3*%EDO;7 L KM 0% H ⁄ ! = EDO; = ^DO = EDc^O ⁄ MDNO R#/2+*%EFDF^%$"-B$%)"*%&#+&2#)%B#)"%)"*%)+'.$#$)-+%$#Q*$%#.,#&')*,D

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EXERCISES 13.21 R-+%'%(+-&*$$%)*&".-4-/:%B#)"%!%=%MDEc%µ57%$%=%EDO7%;%=%F7%/#8*%)"*%$#Q*$%-6%'44%)+'.$#$)-+$%#.%@'C%' 6-2+?#.(2)%W=Y%'.,%@3C%'%6-2+?#.(2)%WIWUD%I4$-7%/#8*%)"*%+*4')#8*%'+*'$%-6%)"*%)B-%/')*$D Ans. @'C%W<=>%,*8#&*$0% H ⁄ ! %=%MDN^[MDEc7%\<=>%,*8#&*$0%NDE][MDEc9 @3C%W<=>%,*8#&*$0% H ⁄ ! %=%EDMc[MDEc7%\<=>%,*8#&*$0%MDOP[MDEc9% W=Y% '+*' ⁄ WIWU %'+*'%=%EDO

1121

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EXERCISES 13.23

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1125

1126 Chapter 13 CMOS Digital Logic Circuits

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)"*.%8*4-&#):%$')2+')#-.%J#&J$%#.%')% v %G ! " %G$') %'.,% ( % %$')2+')*$%')%'%8'42*% & %$') 7 %'$%$"-B. #.%R#/D%EFDPMD%!"*%8'42*%-6% & %$') %&'.%3*%-3)'#.*,%3:%$23$)#)2)#./% v %G ! " %G$') %#.%STD%@EFD`OC7% H E & %$') ! µ $ - ?0 ????? " %G$') " BG I " # I ??? " %G$') ! N

%@EFD`cC

!"#$%*G(+*$$#-.%&'.%3*%$#5(4#6#*,%3:%2)#4#Q#./%STD%@EFD`PC%)-%-3)'#. E & %$') ! H- ?0 2 $') " BG I " # I ??? " %G$') N

%@EFD``C

Y*(4'&#./% " BG %#.%STD%@EFD`cC%B#)"% v BG 7%'.,%#.&-+(-+')#./%)"*%&"'..*4?4*./)"%5-,24')#-. 6'&)-+% ( E H λ v %G )7 %B*%-3)'#.%'%/*.*+'4%*G(+*$$#-.%6-+%)"*%,+'#.%&2++*.)%-6%'.%W<=>%)+'.$#$? )-+%-(*+')#./%#.%8*4-&#):%$')2+')#-.7% H E ( % ! µ $ - ?0 ????? " %G$') v BG I " # I ??? " %G$') ( E H λ v %G ) ! N

%@EFDEMMC

B"#&"%'((4#*$%6-+ v BG I " # ≥ " %G$')

'.,

v %G ≥ " %G$')

%@EFDEMEC

R#/2+*%EFDPE%$"-B$%'%$*)%-6% ( % I v %G %&"'+'&)*+#$)#&%&2+8*$%'.,%&4*'+4:%,*4#.*')*$%)"*%)"+** +*/#-.$%-6%-(*+')#-.0%)+#-,*7%$')2+')#-.7%'.,%8*4-&#):%$')2+')#-.D ST2')#-.%@EFDEMMC%#.,#&')*$%)"')%#.%)"*%8*4-&#):?$')2+')#-.%+*/#-.7% ( % %#$%4#.*'+4:%+*4')*,%)v BG D %!"#$%#$%'%5'a-+%&"'./*%6+-5%)"*%T2',+')#&%+*4')#-.$"#(%)"')%&"'+'&)*+#Q*$%-(*+')#-.%#. )"*%$')2+')#-.%+*/#-.D%R#/2+*%EFDPN%5'J*$%)"#$%(-#.)%&4*'+*+%3:%(+*$*.)#./%'%/+'("%6-+% ( % %8*+? $2$% v BG % -6% '% $"-+)?&"'..*4% ,*8#&*% -(*+')#./% ')% v %G > " %G$') D % =3$*+8*% )"')% 6-+ M < v BG I " # ≤ " %G$') 7 %)"*%<=>RS!%-(*+')*$%#.%)"*%$')2+')#-.%+*/#-.%'.,% ( % %#$%+*4')*,%)-% v BG 3:%)"*%6'5#4#'+%T2',+')#&%*T2')#-.%@STD%EFD`^CD%R-+% v BG I " # ≥ " %G$') 7 %)"*%)+'.$#$)-+%*.)*+$%)"* 8*4-&#):?$')2+')#-.%+*/#-.%'.,% ( % %8'+#*$%4#.*'+4:%B#)"% v BG %@STD%EFDEMMCD% >"-+)?&"'..*4% \<=>% )+'.$#$)-+$% 2.,*+/-% 8*4-&#):% $')2+')#-.% ')% )"*% $'5*% 8'42*% -6% 2 $') ^ @'((+-G#5')*4:% EM &5 ⁄ $ C7%32)%)"*%*66*&)$%-.%)"*%,*8#&*%&"'+'&)*+#$)#&$%'+*%4*$$%(+-.-2.&*, )"'.% #.% )"*% W<=>% &'$*D% !"#$% #$% ,2*% )-% )"*% 4-B*+% 8'42*$% -6% µ ; % '.,% )"*% &-++*$(-.,#./4: "#/"*+%8'42*$%-6% F 6: %'.,%" %G$')D

13.5 Implications of Technology Scaling: Issues in Deep-Submicron Design

iD vGS ! Vt (VDSsat

Velocity saturation Triode

vGS ! Vt (VDSsat

vGS ! Vt $VDSsat Saturation 0

vGS ! Vt )VDSsat

VDSsat

vDS

Figure 13.41 !"*%(%Zv%G%&"'+'&)*+#$)#&$%-6%'%$"-+)?&"'..*4%<=>RS!D%W-)*%)"*%)"+**%,#66*+*.)%+*/#-.$%-6% -(*+')#-.0%)+#-,*9%$')2+')#-.9%'.,%8*4-&#):%$')2+')#-.D

iD

Linear Quadratic 0

Vt

(Vt "VDSsat)

vGS

Figure 13.42 !"*% (%ZvBG% &"'+'&)*+#$)#&% -6% '% $"-+)?&"'..*4% W<=>% )+'.$#$)-+% -(*+')#./% ')% v%G n "%G$')D =3$*+8*%)"*%T2',+')#&%'.,%)"*%4#.*'+%(-+)#-.$%-6%)"*%&"'+'&)*+#$)#&D%I4$-%.-)*%)"')%#.%)"*%'3$*.$*%-6%8*4-&#): $')2+')#-.7%)"*%T2',+')#&%&2+8*%B-24,%&-.)#.2*%'$%$"-B.%B#)"%)"*%3+-J*.%4#.*D

Example 13.8 ;-.$#,*+% <=>% )+'.$#$)-+$% 6'3+#&')*,% #.% '% MDNO?µ5% ;<=>% (+-&*$$% 6-+% B"#&"% " %% ! NDO%K7 N N IE IE " #$ ! I " #; ! MDO%K 7% µ $ - ?0 ! EEO%µI ⁄ K 7 % µ ; - ?0 ! FM%µI ⁄ K 7 % λ $ ! MD]%K 7 %'.,% λ ; ! MDE%K D L*)*!%e%MDNO%µ5%'.,% ( H ⁄ ! ) $ ! ( H ⁄ ! ) ; ! EDOD%<*'$2+*5*.)$%#.,#&')*%)"')%6-+%)"*%W<=>%)+'.$#$)-+7 " %G$') ! MD]F%K7 %'.,%6-+%)"*%\<=>%,*8#&*7% " %G$') ! E%KD%;'4&24')*%)"*%,+'#.%&2++*.)%-3)'#.*,%#.%*'&" -6%)"*%W<=>%'.,%\<=>%)+'.$#$)-+$%6-+% " BG ! " %G ! " %% D%;-5('+*%B#)"%)"*%8'42*$%)"')%B-24,%"'8* 3**.%-3)'#.*,%#.%)"*%'3$*.&*%-6%8*4-&#):%$')2+')#-.D%I4$-%/#8*%)"*%+'./*%-6% v %G %6-+%B"#&"% ( % %#$%$')2+')*,7 B#)"%'.,%B#)"-2)%8*4-&#):%$')2+')#-.D

Solution R-+% )"*% W<=>% )+'.$#$)-+7% " BG ! NDO%K % +*$24)$% #.% " BG I " #$ ! NDO I MDO ! N%K 7% B"#&"% #$% /+*')*+% )"'. " %G$')D%I4$-7% " %G ! NDO%K %#$%/+*')*+%)"'.%" %G$') 9%)"2$%3-)"%&-.,#)#-.$%#.%STD%@EFDEMEC%'+*%$')#$6#*,7%'.,

1127

1128 Chapter 13 CMOS Digital Logic Circuits

Example 13.8 continued

)"*% W<=>% )+'.$#$)-+% B#44% 3*% -(*+')#./% #.% )"*% 8*4-&#):?$')2+')#-.% +*/#-.7% '.,% )"2$% ( % % #$% /#8*.% 3: STD @EFDEMMC0 E I] ( % ! EEO × EM × EDO × MD]F × NDO I MDO I ??? × MD]F × ( E H MDM] × NDO ) ! NEMD]%µI N 16%8*4-&#):%$')2+')#-.%B*+*%'3$*.)7%)"*%&2++*.)%B-24,%3* E H N ( % ! ??? (µ $ - ?0 ) ????? ( v BG I " #$ ) ( E H λ v %G ) N ! $ N E I] ! ??? × EEO × EM × EDO × ( NDO I MDO ) × ( E H MDM] × NDO ) N

! F`]Dc%µI !"2$7% 8*4-&#):% $')2+')#-.% +*,2&*$% )"*% &2++*.)% 4*8*4% 3:% .*'+4:% OMkl% !"*% $')2+')#-.% &2++*.)7% "-B*8*+7% #$ -3)'#.*,%-8*+%'%4'+/*+%+'./*%-6% v %G 9%$(*#&'44:7%6-+% v %G ! MD]F%K %)-%NDO%KD%@=6%&-2+$*7%)"*%&2++*.)%,-*$ .-)%+*5'#.%&-.$)'.)%-8*+%)"#$%+'./*%3*&'2$*%-6%&"'..*4?4*./)"%5-,24')#-.DC%1.%)"*%'3$*.&*%-6%8*4-&#):%$')? 2+')#-.7%)"*%&2++*.)%$')2+')*$%')% " '" ! " BG I " # ! N%K7 %'.,%)"2$%)"*%$')2+')#-.%&2++*.)%#$%-3)'#.*,%-8*+ )"*%+'./*% v %G ! N %K%)-%NDO%KD% R-+%)"*%\<=>%)+'.$#$)-+7%B*%$**%)"')%$#.&*% " BG I " # ! N%K %'.,% " %G ! NDO%K %'+*%3-)"%4'+/*+ )"')% " %G$') ! E%K %)"*%,*8#&*%B#44%3*%-(*+')#./%#.%8*4-&#):%$')2+')#-.7%'.,% ( % %&'.%3*%-3)'#.*,%3:%','()? #./%STD%@EFDEMMC%'$%6-44-B$0 H ( % ! (µ ; - ?0 ) ????? ! ! FM × EM

I]

;

" %G$')

E " BG I " #; I ??? " %G$') ( E H λ ; " %G ) N

E × EDO × E × NDO I MDO I ??? × E ( E H MDE × NDO ) N

! cPDP%µI H#)"-2)%8*4-&#):%$')2+')#-.7%B*%"'8* E H N ( % ! ??? (µ ; - ?0 ) ????? ( " BG I " #; ) ( E H λ ; " %G ) N ! ; E I] N ! ??? × FM × EM × EDO × ( NDO I MDO ) ( E H MDE × NDO ) N ! EENDO%µI !"2$%8*4-&#):%$')2+')#-.%+*,2&*$%)"*%&2++*.)%3:%NOk%@B"#&"%#$%4*$$%)"'.%#.%)"*%&'$*%-6%)"*%W<=>%)+'.$#$? )-+C7%'.,%)"*%$')2+')*,%&2++*.)%#$%-3)'#.*,%-8*+%)"*%+'./*% " %G ! E%K %)-%NDO%KD%1.%)"*%'3$*.&*%-6%8*4-&#): $')2+')#-.7%)"*%$')2+')*,% ( % %B-24,%"'8*%3**.%-3)'#.*,%6-+% " %G ! N %K%)-%NDO%KD

EXERCISE 13.26 Y*(*')%)"*%(+-34*5%#.%SG'5(4*%EFDc%6-+%)+'.$#$)-+$%6'3+#&')*,%#.%'%MDEF?µ5%;<=>%(+-&*$$%6-+ N N B"#&"% " %% ! EDN%K7 % " #$ ! I " #; ! MDP%K7 % µ $ - ?0 ! PFM%µI ⁄ K 7% µ ; - ?0 ! EEM%µI ⁄ K 7 IE λ $ ! λ ; ! MDE%K D%L*)%!%e%MDEF%µ57% ( H ⁄ ! ) $ ! ( H ⁄ ! ) ; ! EDO7% " %G$') %@W<=>C%e%MDFP%K7 '.,% " %G$') %@\<=>C%e%MD]%KD

13.5 Implications of Technology Scaling: Issues in Deep-Submicron Design

Ans. W<=>0% & % ! EOPDP%µI7 %&-5('+*,%)-%NFEDN% %µI %B#)"-2)%8*4-&#):%$')2+')#-.9%$')2+')#-. #$%-3)'#.*,%-8*+%)"*%+'./*% v %G ! MDFP%K %)-%EDN%K7%&-5('+*,%)-% v %G ! MDc%K %)-%EDN%K%#.%)"*%'3? $*.&*%-6%8*4-&#):%$')2+')#-.D%\<=>0% & % ! OODP%µI %&-5('+*,%)-% O`D`%µI7%'.,% v %G ! MD]%K )-%EDN%K%&-5('+*,%)-%MDc%K%)-%EDN%KD

Effect on the Inverter Characteristics !"*%K!;%-6%)"*%;<=>%#.8*+)*+%&'.%3*%,*+#8*, 2$#./%)"*%5-,#6#*,% ( %I v %G %&"'+'&)*+#$)#&$%-6%)"*%<=>RS!$D%!"*%+*$24)$7%"-B*8*+7%#.,#&')* +*4')#8*4:%$5'44%&"'./*$%6+-5%)"*%K!;%,*+#8*,%#.%>*&)#-.%EFDN%2$#./%)"*%4-./?&"'..*4%*T2'? )#-.$%@$**%Y'3'*:%*)%'4D7%NMMF%'.,%X-,/*$%*)%'4D7%NMMPC7%'.,%B*%$"'44%.-)%(2+$2*%)"#$%$23a*&) "*+*D% !"*% ,:.'5#&% &"'+'&)*+#$)#&$% -6% )"*% #.8*+)*+7% "-B*8*+7% '+*% $#/.#6#&'.)4:% #5('&)*,% 3: 8*4-&#):%$')2+')#-.D%!"#$%#$%3*&'2$*%)"*%&2++*.)%'8'#4'34*%)-%&"'+/*%'.,%,#$&"'+/*%)"*%*T2#8'? 4*.)%4-',%&'('&#)'.&*%;%#$%$23$)'.)#'44:%+*,2&*,D A Remark on the MOSFET Model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

13.5.3 Subthreshold Conduction 1.% -2+% $)2,:% -6% )"*% W<=>% )+'.$#$)-+% #.% >*&)#-.% ODE7% B*% '$$25*,% )"')% &2++*.)% &-.,2&)#-. 3*)B**.%,+'#.%'.,%$-2+&*%-&&2+$%-.4:%B"*.% v BG %*G&**,$% " # D%!"')%#$7%B*%'$$25*,%)"')%6-+ v BG < " # %.-%&2++*.)%64-B$%3*)B**.%,+'#.%'.,%$-2+&*D%!"#$7%"-B*8*+7%)2+.$%-2)%.-)%)-%3*%)"* &'$*7% *$(*&#'44:% 6-+% ,**(?$235#&+-.% ,*8#&*$D% >(*#&'44:7% 6-+% v BG < " # % '% $5'44% &2++*.)% ( % 64-B$D%!-%3*%'34*%)-%$**%)"#$%%0:!1")%1'-5(4'$504!&'$7%B*%"'8*%+*,+'B.%)"*% ( % I v BG %/+'(" -6%R#/D%EFDPN7%2)#4#Q#./%'%4-/'+#)"5#&%$&'4*%6-+% ( % 7%'$%$"-B.%#.%R#/D%EFDPFD%=3$*+8*%)"')%') 4-B%8'42*$%-6% v BG 7%)"*%+*4')#-.$"#(%3*)B**.%4-/% ( % %'.,% v BG %#$%4#.*'+7%#.,#&')#./%)"')% ( % %8'+? #*$%*G(-.*.)#'44:%B#)"% v BG 7% (% ! &G 4

v BG ⁄ $" O

%@EFDEMNC

B"*+*% & G %#$%'%&-.$)'.)7% " O ! JO ⁄ U %#$%)"*%)"*+5'4%8-4)'/*% ! NO%5K %')%+--5%)*5(*+')2+*7 '.,%$%#$%'%&-.$)'.)%B"-$*%8'42*%6'44$%#.%)"*%+'./*%E%)-%N7%,*(*.,#./%-.%)"*%5')*+#'4%'.,%$)+2&? )2+*%-6%)"*%,*8#&*D^ >23)"+*$"-4,%&-.,2&)#-.%"'$%3**.%(2)%)-%/--,%2$*%#.%)"*%,*$#/.%-6%8*+:?4-B?(-B*+%&#+? &2#)$%$2&"%'$%)"-$*%.**,*,%6-+%*4*&)+-.#&%B')&"*$D%i*.*+'44:%$(*'J#./7%"-B*8*+7%$23)"+*$"? -4,%&-.,2&)#-.%#$%'%(+-34*5%#.%,#/#)'4%1;%,*$#/.D%!"#$%#$%$-%6-+%)B-%+*'$-.$D

!"#$%+*4')#-.$"#(%#$%+*5#.#$&*.)%-6%)"*% ( - I v MF %+*4')#-.$"#(%-6%'%V_!%@;"'()*+%]CD%!"#$%#$%.-%&-#.&#? ,*.&*7%6-+%)"*%$23)"+*$"-4,%&-.,2&)#-.%#.%'%<=>RS!%#$%,2*%)-%)"*%4')*+'4%3#(-4'+%)+'.$#$)-+%6-+5*,%3: )"*%$-2+&*%'.,%,+'#.%,#662$#-.$%B#)"%)"*%$23$)+')*%'&)#./%'$%)"*%3'$*%+*/#-.%@$**%R#/D%ODECD

^

1129

1130 Chapter 13 CMOS Digital Logic Circuits

iD

(log scale)

* 10

2.3 nVT 0

Vt

vGS

Figure 13.43 !"*%(% Z vBG%&"'+'&)*+#$)#&%-6%'%$"-+)%&"'..*4%<=>RS!D%!-%$"-B%)"*%,*)'#4$%-6%$23)"+*$"-4,% &-.,2&)#-.%'%4-/'+#)"5#&%$&'4*%#$%.**,*,%6-+%(%D

1. <2,*6-6K,'-*83'',61*12&1*9%-+/*9-'* v BG ! M *B/,,*D#:;*EF;GFC*8&3/,/*12,*>b^"*#60,'1,' 1-*5#//#4&1,*/1&1#8*4-+,';*<-*R,,4*12#/*',,(40"")$!*&/*%-+*&/*4-//#.%,)* " # *-9*12,*b^"L DV<*#/*R,41*',%&1#0,%(*2#:2;*<2#/*#65,,5*#/*12,*',&/-6*+2(* " # *2&/*6-1*.,,6*/8&%,5*.(*12, /&$,*9&81-'*&/*12&1*3/,5*9-'*12,*82&66,%*%,6:12;*J%12-3:2*12,*-99*83'',61*#/*%-+*BEQ*4J 1-*EQQ*4JC*&65*12,*4-+,'*5#//#4&1#-6*4,'*#60,'1,'*#/*/$&%%)*12,*4'-.%,$*.,8-$,/*/,'#-3/ #6*82#4/*+#12*&*.#%%#-6*1'&6/#/1-'/l 2. <2,*6-6K,'-*83'',61*-9*&*6-'$&%%(*-99*1'&6/#/1-'*8&6*8&3/,*12,*5#/82&':,*-9*8&4&8#1-'/*#6 5(6&$#8* b^"* 8#'83#1/;* J/* +,* /2&%%* /,,* #6* 12,* 6,71* 1+-* 82&41,'/)* 5(6&$#8* %-:#8* &65 $,$-'(*8#'83#1/*',%(*-6*82&':,*/1-'&:,*-6*8&4&8#1-'/*9-'*12,#'*4'-4,'*-4,'&1#-6;*<23/) /3.12',/2-%5*8-65381#-6*8&6*5#/'341*12,*-4,'&1#-6*-9*/382*8#'83#1/;

EXERCISE 13.27

@'C%Y*6*+%)-%R#/D%EFDPF%'.,%)-%STD%@EFDEMNCD%>"-B%)"')%)"*%#.8*+$*%-6%)"*%$4-(*%-6%)"*%$)+'#/")%4#.* +*(+*$*.)#./%$23)"+*$"-4,%&-.,2&)#-.%#$%/#8*.%3:% NDF$" O %K%(*+%,*&',*%-6%&2++*.)%&"'./*D @3C%16%5*'$2+*5*.)$%#.,#&')*%$%e%EDNN%'.,% ( % ! EMM%.I %')% v BG ! MDNE%K7%6#.,% ( % %')% v BG ! MD @&C%R-+%'%&"#(%"'8#./%OMM%5#44#-.%)+'.$#$)-+$7%6#.,%)"*%&2++*.)%,+'B.%6+-5%)"*%EDN?K%$2((4:% " %% '$%'%+*$24)%-6%$23)"+*$"-4,%&-.,2&)#-.D%X*.&*%*$)#5')*%)"*%+*$24)#./%(-B*+%,#$$#(')#-.D Ans. @3C%MDE%.I9%@&C%OM%5I7%]M%5H

13.5.4 Wiring—The Interconnect !"*%4-/#&%/')*$%-.%'%,#/#)'4%1;%&"#(%'+*%&-..*&)*,%)-/*)"*+%3:%5*)'4%B#+*$c%@$**%I((*.,#G ICD%I$%B*447%)"*%(-B*+%$2((4:% " %% %'.,%/+-2.,%'+*%,#$)+#32)*,%)"+-2/"-2)%)"*%&"#(%3:%5*)'4 B#+*$D%!*&".-4-/:%$&'4#./%#.)-%)"*%,**(?$235#&+-.%+'./*%"'8*%&'2$*,%)"*$*%B#+*$%)-%3*"'8* c

!"*$*%'+*%$)+#($%-6%5*)'4%,*(-$#)*,%-.%'.%#.$24')#./%$2+6'&*%-.%)-(%-6%)"*%&"#(D%1.%5-,*+.%,#/#)'4%1;$7% '$%5'.:%'$%*#/")%4':*+$%-6%$2&"%B#+#./%'+*%2)#4#Q*,D

13.5 Implications of Technology Scaling: Issues in Deep-Submicron Design

Figure 13.44 !"*%(-B*+?$2((4:%4#.*%#.%'%,**(%$235#&+-.%1;%"'$%.-.?Q*+-%+*$#$)'.&*D%!"*%&E%,+-($%'4-./% )"*%"%%%4#.*%&'2$*%)"*%8-4)'/*$%,*4#8*+*,%)-%8'+#-2$%&#+&2#)$%)-%,#66*+D

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1131

1132 Chapter 13 CMOS Digital Logic Circuits

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13.5 Implications of Technology Scaling: Issues in Deep-Submicron Design

1133

Table 13.3 Summary of Important Characteristics of the CMOS Logic Inverter B$3)"!)"(M0!/0!(N)%&%!#$4) %H"*.%v'%#$%4-B%@&2++*.)%$#.J#./C0

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Problems 1135

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PROBLEMS

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CHAPTER 13

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PROBLEMS

CHAPTER 13

PROBLEMS

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I# ⁄ τN

+2,',* τ N ! - ( E || E -. ) ! -E -. %6-+% ( E -. + E ) ;* e,68, /2-+*12&1*12,*1#$,*9-'*v'B#C*1-*',&82*12,*MQ_*4-#61*#/ #K)!*=*Q;N`-E-6 B8C Y/,*12,*',/3%1/*-9*B&C*&65*B.C*1-*-.1*12,*#60,'1,'*4'-4L &:&1#-6*5,%&()*5,9#6,5*&/*12,*&0,'&:,*-9*#K!)*&65*#K)!*&/ p # K ! MDFO-E%%%%6-+%E -. + E B5C "2-+*12&1*9-'*&6*#60,'1,'*12&1*/4,65/*2&%9*12,*1#$,*#6*12, QL/1&1,* &65* 2&%9* 12,* 1#$,* #6* 12,* EL/1&1,)* 12,* &0,'&:,* /1&1#8 4-+,'*5#//#4&1#-6*#/ N

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m*P2&1*9'&81#-6&%*82&6:,*#6*5,%&(I 4-+,'*4'-5381*5-*(-3*,74,81*#6*,&82*8&/,m

Section 13.2: The CMOS Inverter 13.26 ;-.$#,*+% '% ;<=>% #.8*+)*+% 6'3+#&')*,% #.% '% MDNO?µ5 ;<=>% (+-&*$$% 6-+% B"#&"% " %% ! NDO%K7% " #$ ! I " #; ! MDO%K7 %'.,% µ $ - ?0 ! FDOµ ; - ?0 ! EEO µI ⁄ K ND%1. ',,#)#-.7% L + %'.,% L K %"'8*%!%e%MDNO%µ5%'.,% ( H ⁄ ! ) $ ! EDOD% @'C%R#.,% H ; %)"')%+*$24)$%#.% " , ! " %% ⁄ ND%H"')%#$%)"*%$#4#? &-.%'+*'%2)#4#Q*,%3:%)"*%#.8*+)*+%#.%)"#$%&'$*b

Problems 1137

@&C%R-+%)"*%5')&"*,%&'$*%#.%@'C7%6#.,%)"*%-2)(2)%+*$#$)'.&*%-6 )"*%#.8*+)*+%#.%*'&"%-6%#)$%)B-%$)')*$D

13.28 R-+%'% )*&".-4-/:% #.% B"#&"% " #$ ! MDN" %% 7 % $"-B )"')% )"*% 5'G#525% &2++*.)% )"')% )"*% #.8*+)*+% &'.% $#.J B"#4*% #)$% 4-B?-2)(2)% 4*8*4% ,-*$% .-)% *G&**,% MDE " %% % #$ N MDM^O J $′ ( H ⁄ ! ) $ " %% D % R-+% " %% ! NDO%K7 % J $ ′ ! N EEO%µI ⁄ K % 7%6#.,% ( H ⁄ ! ) $ %)"')%(*+5#)$%)"#$%5'G#525 &2++*.)%)-%3*%MDO%5ID N

13.29 J*>b^"*#60,'1,'*9-'*+2#82* J $ = EMJ ; = EMM µI[K &65* "#* =* Q;M* =* #/* 8-66,81,5* &/* /2-+6* #6* D#:;* hEF;W`* 1-* & /#63/-#5&%*/#:6&%*/-3'8,*2&0#6:*&*<2r0,6#6*,A3#0&%,61*0-%1L &:,*-9*Q;EL=*4,&R*&$4%#135,*&65*',/#/1&68,*-9*EQQ*RΩ;*P2&1 /#:6&%* 0-%1&:,* &44,&'/* &1* 6-5,* S* +#12* v&* =* +E;M* =m* P#12 v& = −E;M*=m

QP

100 k,

vI QN

A

" 100-mV ! signal

Figure P13.29

D 13.30 !"*+*%'+*%$#)2')#-.$%#.%B"#&"% L + %'.,% L K %-6%)"* ;<=>%#.8*+)*+%'+*%,*4#3*+')*4:%5#$5')&"*,%)-%+*'4#Q*%'%&*+? )'#.%,*$#+*,%8'42*%6-+% " , D%>"-B%)"')%)"*%8'42*%+*T2#+*,%-6 )"*%('+'5*)*+%:*-6%STD%@EFDO`C%#$%/#8*.%3:

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'%

MDEc?µ5%

(+-&*$

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3:

" #$ ! I " #; ! MDO%K7% " %% ! EDc%K 7% '.,% µ $ ! P µ ; 7% 6#., )"*%+')#-%H ; ⁄ H $ %+*T2#+*,%)-%-3)'#.%" , ! MD]" %% D

13.31 ;-.$#,*+%)"*%;<=>%#.8*+)*+%-6%R#/D%EFDE^%B#)"% L + '.,% L K %5')&"*,%'.,%B#)"%)"*%#.(2)% v & %+#$#./%$4-B4:%6+-5%M )-% " %%D% I)% B"')% 8'42*% -6% v & % ,-*$% )"*% &2++*.)% 64-B#./ )"+-2/"% L + %'.,% L K %+*'&"%#)$%(*'Jb%i#8*%'.%*G(+*$$#-.%6-+

13.32 R-+%'%;<=>%#.8*+)*+%6'3+#&')*,%#.%'%MDEF?µ5 (+-&*$$% B#)"% " %% ! EDN%K 7% " #$ ! I " #; ! MDP%K 7 N J $′ ! PJ ;′ ! PFM%µ I ⁄ K 7%'.,%"'8#./% ( H ⁄ ! ) $ ! EDO%'., ( H ⁄ ! ) ; ! F7% 6#.,% # K)! 7% # K!) 7% '.,% # K % B"*.% )"*% *T2#8'? 4*.)%4-',%&'('&#)'.&*%-%e%EM%6RD%d$*%)"*%5*)"-,%-6%'8*+'/* &2++*.)$D D 13.33 ;-.$#,*+%'%5')&"*,%;<=>%#.8*+)*+%6'3+#&')*,%#. )"*%MDEF?µ5%(+-&*$$%$(*#*,%#.%\+-34*5%EFDFND%16%-%e%NM 6R7% 2$*% )"*% 5*)"-,% -6% '8*+'/*% &2++*.)$% )-% ,*)*+5#.*% )"* +*T2#+*,%@H[!C%+')#-$%$-%)"')% # K ≤ NM%($ D% 13.34 R-+% )"*% ;<=>% #.8*+)*+% #.% SG*+&#$*% EFDEP% 2$*% )"* 5*)"-,%-6% *T2#8'4*.)% +*$#$)'.&*%)-% ,*)*+5#.*% # K)! 7 % # K!) 7 '.,% # K D 13.35 d$*% )"*% 5*)"-,% -6% *T2#8'4*.)% +*$#$)'.&*% )-% ,*)*+? 5#.*%)"*%(+-('/')#-.%,*4':%-6%'%5#.#525?$#Q*%#.8*+)*+7%)"') #$7% -.*% 6-+% B"#&"% ( H ⁄ ! ) $ ! ( H ⁄ ! ) ; ! E7% ,*$#/.*,% #.% ' MDEc?µ5% )*&".-4-/:D% !"*% *T2#8'4*.)% 4-',% &'('&#)'.&*% -% e EM%6RD% D 13.36 d$*%)"*%5*)"-,%-6%*T2#8'4*.)%+*$#$)'.&*%)-%,*$#/. '.% #.8*+)*+% )-% 3*% 6'3+#&')*,% #.% '% MDEc?µ5% )*&".-4-/:D% 1)% #$ +*T2#+*,%)"')%6-+%-%e%EM%6R7% # K!) ! # K)! 7 %'.,% # K ≤ PM%($ D 13.37 !"*% 5*)"-,% -6% '8*+'/*% &2++*.)$%:#*4,$% $5'44*+% 8'4? 2*$%6-+% # K)! %'.,% # K!) %)"'.%)"-$*%-3)'#.*,%3:%)"*%5*)"-,%-6 *T2#8'4*.)%+*$#$)'.&*$D%<-$)%-6%)"#$%,#$&+*('.&:%#$%,2*%)-%)"* 6'&)%)"')%)"*%6-+524'%B*%,*+#8*,%6-+% & '8 %,-*$%.-)%)'J*%#.)'&&-2.)% 8*4-&#):% $')2+')#-.D% I$% B#44% 3*% $**.% #.% >*&)#-. EFDODN7%8*4-&#):%$')2+')#-.%+*,2&*$%)"*%&2++*.)%$#/.#6#&'.)4:D d$#./% )"*% +*$24)$% #.% SG'5(4*% EFDO7% 3:% B"')% 6'&)-+% ,-% :-2 *$)#5')*%)"*%&2++*.)%+*,2&)#-.%)-%3*%#.%)"*%W<=>%)+'.$#$)-+b >#.&*% # K!) % ,-*$% .-)% &"'./*7% B"')% ,-% :-2% &-.&42,*% '3-2) )"*% *66*&)% -6% 8*4-&#):% $')2+')#-.% -.% )"*% \<=>% )+'.$#$)-+% #. )"#$%)*&".-4-/:b 13.38 D#65* 12,* 4'-4&:&1#-6* 5,%&(* 9-'* &* $#6#$3$L/#K, N #60,'1,'* 9-'* +2#82* J $′ = FJ ;′ = EcM%µI[K * &65* BH ⁄ !C$* = @H ⁄ !C ; = MD^O%µ5 ⁄ MDO %µ57 * "%%* =* F;F* =)* "#$* !* I"#;* ! Q;O =)* &65* 12,* 8&4&8#1&68,* #/* '-3:2%(* W 9Diµ$* -9* 5,0#8, +#512*4%3/*E*9Di5,0#8,;*P2&1*5-,/*#K*.,8-$,*#9*12,*5,/#:6*#/ 82&6:,5* 1-* &* $&182,5* -6,m* Y/,* 12,* $,12-5* -9* &0,'&:, 83'',61; 13.39 J*$&182,5*>b^"*#60,'1,'*9&.'#8&1,5*#6*&*4'-8,//*9-' +2#82*-?0*=*F;O*9 Diµ$W)*µ$-?0*=*EXQ*µJi=W)*µ;-?0*=*GM*µJi=W) "#$ *=*− "#; *=*Q;O*=)*&65*"%%*=*F;F*=)*3/,/*H$*=*Q;OM*µ$*&65 !$*=*!;*=*Q;M*µ$;*<2,**-0,'%&4*8&4&8#1&68,*&65*12,*,99,81#0, 5'I.-5(* 8&4&8#1&68,* 4,'* $#8'-$,1,'* -9* :&1,* +#512* &', Q;G* 9D* &65* E;Q* 9D)* ',/4,81#0,%(;* <2,* +#'#6:* 8&4&8#1&68,* #/

PROBLEMS

13.27 R-+%)"*%)*&".-4-/:%$(*#*,%#.%\+-34*5%EFDN]7 #.8*$)#/')*%)"*%8'+#')#-.%-6% " , %B#)"%)"*%+')#-% H ; ⁄ H $ D%>(*? #&'44:7% &'4&24')*% " , % 6-+% @'C% H ; ! FDOH $ % @)"*% 5')&"*, &'$*C9% @3C% H ; ! H $ % @)"*% 5#.#525?$#Q*% &'$*C9% '.,% @&C H ; ! NH $ %@'%&-5(+-5#$*%&'$*CD%R-+%&'$*$%@3C%'.,%@&C7%*$)#? 5')*% )"*% '((+-G#5')*% +*,2&)#-.% #.% +, ! % '.,% $#4#&-.% '+*' +*4')#8*%)-%)"*%5')&"*,%&'$*%@'CD

)"*% (*'J% &2++*.)7% .*/4*&)#./% λ $ % '.,% λ ; D % R-+ N J $ ′ ! FMM%µI ⁄ K %7% ( H ⁄ ! ) $ ! EDO7% " %% ! EDc%K7 % '., " #$ ! MDO%K7%6#.,%)"*%8'42*%-6%)"*%(*'J%&2++*.)D

CHAPTER 13

@3C% R-+% )"*% 5')&"*,% &'$*% #.% @'C7% 6#.,% )"*% 8'42*$% -6% " ') 7

" '!7% " &) 7 % " &! 7 % +, ! 7 %'.,% +, ) D

CHAPTER 13

PROBLEMS

1138 Chapter 13 CMOS Digital Logic Circuits -7 = W* 9D;* @9* 12,* #60,'1,'* #/* 5'#0#6:* &6-12,'* #5,61#8&% #60,'1,')* 9#65* #K!))* #K)!)* &65* #K;* D-'* 2-+* $382* &55#1#-6&% 8&4&8#1&68,* %-&5* 5-,/* 12,* 4'-4&:&1#-6* 5,%&(* #68',&/,* .( MQ_m

13.43 [,4,&1* h'-.%,$* EF;F`* 9-'* &6* #60,'1,'* 9-'* +2#82 @H ⁄ !C $ = @H ⁄ !C ; = MD^O %µ5 ⁄ MDO %µ5D* D#65* #K* &65* 12, 5(6&$#8*4-+,'*5#//#4&1#-6*+2,6*12,*8#'83#1*#/*-4,'&1,5*&1*& WMQLbeK*'&1,;

D *13.40 %1.%)"#$%(+-34*5%B*%#.8*$)#/')*%)"*%*66*&)%-6%)"* $*4*&)#-.%-6%)"*%+')#-% H ; ⁄ H $ %-.%)"*%(+-('/')#-.%,*4':%-6 '.%#.8*+)*+%,+#8#./%'.%#,*.)#&'4%#.8*+)*+7%'$%#.%R#/D%EFDNPD

13.44 1.%)"#$%(+-34*5%B*%*$)#5')*%)"*%#.8*+)*+%(-B*+%,#$$#? (')#-.%+*$24)#./%6+-5%)"*%&2++*.)%(24$*%)"')%64-B$%#.% L + %'., L K %B"*.%)"*%#.(2)%(24$*%"'$%6#.#)*%+#$*%'.,%6'44%)#5*$D%Y*6*+ )-%R#/D%EFDN]%'.,%4*)% " #$ ! I " #; ! MDO%K7% " %% ! EDc%K7 N '.,% J $ ! J ; ! POM%µ I ⁄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
@'C% W-)#./% )"')% *G&*()% 6-+% - 7 % *'&"% -6% )"*% &'('&#)'.&*$% #. ST$D%@EFD^NC%'.,%@EFD^FC%#$%(+-(-+)#-.'4%)-%)"*%B#,)"%-6%)"* +*4*8'.)%)+'.$#$)-+7%$"-B%)"')%-%&'.%3*%*G(+*$$*,%'

%$H - ! - $ E H ??????;? H - 7 H$ B"*+*% - $ %#$%,*)*+5#.*,%3:%)"*%W<=>%)+'.$#$)-+$D @3C%d$#./%)"*%*T2#8'4*.)%+*$#$)'.&*$% E + %'.,% E K 7%$"-B%)"') 6-+%( H ⁄ ! ) $ ! E7 F

# K)! ! cD]NO × EM F

# K!)

NMD^ × EM ! ????????????????????????? H; ⁄ H$

@&C%d$*%)"*%+*$24)$%-6%@'C%'.,%@3C%)-%,*)*+5#.*% # K %#.%)"*%&'$* H ; ! H $ 7%#.%)*+5$%-6% - $ %'.,% - 7 D @,C% d$*% )"*% +*$24)$% -6% @'C% '.,% @3C% )-% ,*)*+5#.*% # K % #.% )"* 5')&"*,% &'$*0% )"')% #$7% B"*.% H ; ⁄ H $ % #$% $*4*&)*,% )-% :#*4, # K)! ! # K!) D @*C%;-5('+*%)"*% # K %8'42*$%#.%@&C%'.,%@,C%6-+%)"*%)B-%*G)+*5* &'$*$0 @#C% - 7 ! M @##C% - 7 - - $ H"')%,-%:-2%&-.&42,*%'3-2)%)"*%$*4*&)#-.%-6% H ; ⁄ H $ b 13.41 I.% #.8*+)*+%B"-$*%*T2#8'4*.)%4-',%&'('&#)'.&*%-%#$ &-5(-$*,% -6% EM% 6R% &-.)+#32)*,% 3:% )"*% #.8*+)*+% )+'.$#$)-+$7 '.,%NM%6R%&-.)+#32)*,%3:%)"*%B#+#./%'.,%-)"*+%*G)*+.'4%&#+? &2#)+:7%"'$%3**.%6-2.,%)-%"'8*%'%(+-('/')#-.%,*4':%-6%]M%($D V:%B"')%6'&)-+%52$)% ( H ⁄ ! ) $ %'.,% ( H ⁄ ! ) ; %3*%#.&+*'$*,%$'$%)-%+*,2&*% # K %)-%FM%($b 13.42 J*>b^"*$#8'-4'-8,//-'*82#4*8-61#6:*12,*,A3#0L &%,61* -9* E* $#%%#-6* :&1,/* -4,'&1,/* 9'-$* &* ML=* /344%(;* <2, 4-+,'*5#//#4&1#-6*#/*9-365*1-*.,*`*P*+2,6*12,*82#4*#/*-4,'L &1#6:* &1* EWQ* beK)* &65* G;O* P* +2,6* -4,'&1#6:* &1* MQ* beK; P2&1*#/*12,*4-+,'*%-/1*#6*12,*82#4*.(*/-$,*8%-8RL#65,4,6L 5,61*$,82&6#/$)*/382*&/*%,&R&:,*&65*-12,'*/1&1#8*83'',61/m @9* OQ_* -9* 12,* :&1,/* &',* &//3$,5* 1-* .,* &81#0,* &1* &6(* 1#$,) +2&1*#/*12,*&0,'&:,*:&1,*8&4&8#1&68,*#6*/382*&*5,/#:6m

Section 13.4: CMOS Logic-Gate Circuits D 13.45 "R,182* &* >b^"* ',&%#K&1#-6* 9-'* 12,* 93681#-6 P = S + M ( - + % ); D 13.46 J*>b^"*%-:#8*:&1,*#/*',A3#',5*1-*4'-0#5,*&6*-31L 431* P = SM- + SM- + SM- ;*e-+*$&6(*1'&6/#/1-'/*5-,/*#1 6,,5m*"R,182*&*/3#1&.%,*hYZ*&65*hUZ)*-.1#6:*,&82*9#'/1 #65,4,65,61%()* 12,6* -6,* 9'-$* 12,* -12,'* 3/#6:* 12,* 53&%L 6,1+-'R/*#5,&; D 13.47 g#0,* 1+-* 5#99,',61* ',&%#K&1#-6/* -9* 12,* ,78%3/#0, ^[*93681#-6*P = SM + SM*#6*+2#82*12,*hUZ*&65*12,*hYZ &',*53&%*6,1+-'R/; D 13.48 "R,182* &* >b^"* %-:#8* 8#'83#1* 12&1* ',&%#K,/* 12, 93681#-6* P = SM + SM ;* <2#/* #/* 8&%%,5* 12,* )D0&3#-)$4)* -' 4'&$4&5)$4)(,0$4!&'$; D 13.49 "R,182* &* >b^"* %-:#8* 8#'83#1* 12&1* ',&%#K,/* 12, 93681#-6*P = SM- + SM- ; D 13.50 @1*#/*',A3#',5*1-*5,/#:6*&*>b^"*%-:#8*8#'83#1*12&1 ',&%#K,/*&*12',,L#6431)*,0,6L4&'#1(*82,8R,';*"4,8#9#8&%%()*12, -31431*P*#/*1-*.,*%-+*+2,6*&6*,0,6*63$.,'*BQ*-'*WC*-9*12, #6431/*S)*M)*&65*-*&',*2#:2; B&C g#0,*12,*c--%,&6*93681#-6* PD B.C "R,182*&*hUZ*5#',81%(*9'-$*12,*,74',//#-6*9-'* PD *Z-1, 12&1*#1*',A3#',/*EW*1'&6/#/1-'/*#6*&55#1#-6*1-*12-/,*#6*12,*#60,'1L ,'/; B8C D'-$*#6/4,81#-6*-9*12,*hUZ*8#'83#1)*',538,*12,*63$.,' -9*1'&6/#/1-'/*1-*EQ; B5C D#65*12,*hYZ*&/*&*53&%*-9*12,*hUZ*#6*B8C)*&65*2,68,*12, 8-$4%,1,*',&%#K&1#-6; D 13.51 g#0,* &* >b^"* %-:#8* 8#'83#1* 12&1* ',&%#K,/* 12, 93681#-6* -9* 12',,L#6431)* -55L4&'#1(* 82,8R,';* "4,8#9#8&%%()

Problems 1139

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Y $ A 1 " A2 " … " A 6

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A4 A5 A6 (b) Figure P13.56

PROBLEMS

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CHAPTER 13

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CHAPTER 13

PROBLEMS

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CHAPTER 13

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CHAPTER 14

Advanced MOS and Bipolar Logic Circuits Introduction 14.1

1143

14.4 Emitter-Coupled Logic (ECL)

Pseudo-NMOS Logic Circuits

1144

14.2 Pass-Transistor Logic Circuits

1152

14.3 Dynamic MOS Logic Circuits

1166

14.5 BiCMOS Digital Circuits Summary

1195

Problems

1196

1189

1175

IN THIS CHAPTER YOU WILL LEARN 1. That by replacing the pull-up network (PUN) of a CMOS logic gate by a single, permanently-on PMOS transistor, considerable savings in transistor count and silicon area can be achieved in gates with high fan-in. The resulting circuits are known as pseudo-NMOS. 2. That a useful and conceptually simple form of MOS logic circuits, known as pass-transistor logic (PTL), utilizes MOS transistors as series switches in the signal path from input to output. 3. That a very effective switch for both analog and digital applications, known as transmission gate, is formed by connecting an NMOS and a PMOS transistor in parallel. 4. That eliminating the pull-up network and placing two complementary switches, operated by a clock signal, in series with the pull-down network of a CMOS gate, results in an interesting and useful class of circuits known as dynamic logic. 5. How the BJT differential-pair configuration is used as a current switch to realize the fastest commercially available logic-circuit family: emittercoupled logic (ECL). 6. How the MOSFET and the BJT are combined in BiCMOS circuits in ways that take advantage of the best attributes of each device.

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1143

1144 Chapter 14 Advanced MOS and Bipolar Logic Circuits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

14.1 Pseudo-NMOS Logic Circuits 14.1.1 The Pseudo-NMOS Inverter E.-5&3'7IC7'42,14'#':,%.=.3%'=,&:',='"23'()*!'.$;3&"3&C'V3&30',$+<'%&'.4'%&.;3$'@<'"23 .$65"';,+"#-3'12.+3'"23'-#"3',='%''.4'-&,5$%3%0'#$%'%''#/"4'#4'#$'#/".;3'+,#%'=,&'%&C'X;3$ @3=,&3'13'39#:.$3'"23',63&#".,$',='"2.4'/.&/5."'.$'%3"#.+0'#$'#%;#$"#-3',;3&'4"#$%#&%'()*! .4',@;.,54>'X#/2'.$65"'$33%4'",'@3'/,$$3/"3%'",'"23'-#"3',=',$+<',$3'"&#$4.4",&',&0'#+"3&$#A ".;3+<0' ,$+<' ,$3' #%%.".,$#+' "&#$4.4",&' J#$' H)*!L' 1.++' @3' $33%3%' =,&' 3#/2' #%%.".,$#+' -#"3 .$65"C'F254'"23'#&3#'#$%'%3+#<'63$#+".34'#&.4.$-'=&,:'.$/&3#43%'=#$A.$'.$'#'4"#$%#&%'()*! 1.++'@3'&3%5/3%C'F2.4'.4'.$%33%'"23':,".;#".,$'=,&'396+,&.$-'"2.4':,%.=.3%'.$;3&"3&'/.&/5."C F23'.$;3&"3&'/.&/5."',='E.-C'7IC7J#L'&343:@+34',"23&'=,&:4',='H)*!'+,-./'"2#"'/,$4.4"',='# %&.;3&'"&#$4.4",&'J%&L'#$%'#'+,#%'"&#$4.4",&'J.$'"2.4'/#430'%'L\'23$/3'"23'$#:3'6435%,AH)*!C VDD

VDD

Q2

QP iDP

Q2 vO

QN

(a)

vO

iD2 ! iD1

iDN vI

VDD

Q1

" vI # (b)

iD " vI #

vO

Q1

(c)

Figure 14.1 !"#'F23'6435%,AH)*!'+,-./'.$;3&"3&C'!$#'F23'3$2#$/3:3$"A+,#%'J,&'4#"5&#"3%A+,#%L'H)*!' .$;3&"3&C'!%#'F23'%36+3".,$A+,#%'H)*!'.$;3&"3&C

14.1 Pseudo-NMOS Logic Circuits 1145

E,&'/,:6#&.4,$'65&6,4340'13' 42#++'@&.3=+<':3$".,$'"1,',+%3&'=,&:4',='H)*!'+,-./C'F23 3#&+.34"' =,&:0' 6,65+#&' .$' "23' :.%A7]^_40' 5".+.T3%' #$' 3$2#$/3:3$"' )*!EXF' =,&' "23' +,#% 3+3:3$"0'.$'#'",6,+,-<'12,43'@#4./'.$;3&"3&'.4'42,1$'.$'E.-C'7IC7J@LC'`3'4"5%.3%'"2.4'.$;3&"3& /.&/5."'.$'X9#:6+3'78CS0'123&3'13'=,5$%'"2#"'."'45==3&4'=&,:'#'&3+#".;3+<'4:#++'+,-./'41.$-0 4:#++'$,.43':#&-.$40'#$%'2.-2'4"#"./'6,13&'%.44.6#".,$C'E,&'"2343'&3#4,$40'"2.4'+,-./A/.&/5." "3/2$,+,-<' .4' ;.&"5#++<' ,@4,+3"3C' ?"' 1#4' &36+#/3%' .$' "23' +#"3' 7]^_4' #$%' 3#&+<' 7]a_4' 1."2 %36+3".,$A+,#%' H)*!' /.&/5."40' .$' 12./2' #' %36+3".,$' H)*!' "&#$4.4",&' J433' !3/".,$' YC]CbL 1."2'."4'-#"3'/,$$3/"3%'",'."4'4,5&/3'.4'543%'#4'"23'+,#%'3+3:3$"C'F23'",6,+,-<',='"23'@#4./ %36+3".,$A+,#%'.$;3&"3&'.4'42,1$'.$'E.-C'7IC7J/LC ?"'1#4'.$.".#++<'3963/"3%'"2#"'"23'%36+3".,$'H)*!'1."2'!()'='_'1,5+%',63&#"3'#4'#'/,$4"#$"A /5&&3$"'4,5&/3'#$%'1,5+%'"254'6&,;.%3'#$'39/3++3$"'+,#%'3+3:3$"C7'V,13;3&0'."'1#4'B5./D+<'&3#+A .T3%'"2#"'"23'@,%<'3==3/"'.$'"23'%36+3".,$'"&#$4.4",&'/#5434'."4'*cv'/2#&#/"3&.4"./'",'%3;.#"3'/,$A 4.%3&#@+<'=&,:'"2#"',='#'/,$4"#$"A/5&&3$"'4,5&/3C'H3;3&"23+3440'%36+3".,$A+,#%'H)*!'/.&/5."4 =3#"5&3'4.-$.=./#$"'.:6&,;3:3$"4',;3&'"23.&'3$2#$/3:3$"A+,#%'/,5$"3&6#&"40'3$,5-2'",'W54".=< "23'39"&#'6&,/344.$-'4"36'&3B5.&3%'",'=#@&./#"3'"23'%36+3".,$'%3;./34'J$#:3+<0'.,$A.:6+#$".$-'"23 /2#$$3+LC'O+"2,5-2'%36+3".,$A+,#%'H)*!'2#4'@33$';.&"5#++<'&36+#/3%'@<'()*!0',$3'/#$'4".++ 433'4,:3'%36+3".,$A+,#%'/.&/5."4'.$'463/.#+.T3%'#66+./#".,$4C'`3'1.++'$,"'4"5%<'%36+3".,$A+,#% H)*!'+,-./'23&3'J"23'.$"3&34"3%'&3#%3&'/#$'&3=3&'",'"23'(U',&'"23'13@4."3',='"2.4'@,,DLC F23' 6435%,AH)*!' .$;3&"3&' "2#"' 13' #&3' #@,5"' ",' 4"5%<' .4' 4.:.+#&' ",' %36+3".,$A+,#% H)*!0'@5"'1."2'&#"23&'.:6&,;3%'/2#&#/"3&.4"./4C'?"'#+4,'2#4'"23'#%;#$"#-3',='@3.$-'%.&3/"+< /,:6#".@+3'1."2'4"#$%#&%'()*!'/.&/5."4C

14.1.2 Static Characteristics F23'4"#"./'/2#&#/"3&.4"./4',='"23'6435%,AH)*!'.$;3&"3&'/#$'@3'%3&.;3%'.$'#':#$$3&'4.:.+#& ",'"2#"'543%'=,&'4"#$%#&%'()*!C'F,1#&%'"2#"'3$%0'13'$,"3'"2#"'"23'%&#.$'/5&&3$"4',='%&'#$% %''#&3'-.;3$'@< S

* +& = 7AASA / 0 ( v , ! ! - ) ,

=,&' v " ≥ v , − ! - ''''J4#"5&#".,$L S

* +& = / 0 [ ( v , ! ! - ) v " ! 7AASA v " ] " S

* +' = 7AASA / 1 ( ! ++ ! ! - ) ,

=,&' v " ≤ v , − ! - ''''J"&.,%3L

=,&' v " ≤ ! - ''''J4#"5&#".,$L S

* +' = / 1 [ ( ! ++ ! ! - ) ( ! ++ ! v " ) − 7AASA ( ! ++ ! v " ) ] "

J7IC7L J7ICSL J7IC8L

=,&' v " ≥ ! - ''''J"&.,%3L

J7ICIL

123&3'13'2#;3'#445:3%'"2#"' !-0 '= − !-1 '=' !- 0'#$%'2#;3'543%' / 0 '=' /′0J$⁄ # L0 '#$%' / 1 'd /′1 J$⁄ # L1 '",'4.:6+.=<':#""3&4C F,' ,@"#.$' "23' ;,+"#-3A"&#$4=3&' /2#&#/"3&.4"./' ,=' "23' .$;3&"3&0' 13' 4563&.:6,43' "23' +,#% /5&;3'&36&343$"3%'@<'XB4C J7IC8L'#$%'J7ICIL',$'"23'*+cv+)'/2#&#/"3&.4"./4',='%&0'12./2'/#$'@3 &3+#@3+3%'#4'*+&cv"'#$%'%
$'=,&';#&.,54';#+534',=' v()'=' v,C'!5/2'#'->./#+'/,$4"&5/".,$'.4 42,1$'.$'E.-C'7ICS0'123&30'",'D336'"23'%.#-&#:'4.:6+30'13'42,1'"23'%&'/5&;34'=,&',$+<'"23 "1,'39"&3:3';#+534',='v,0'$#:3+<0'_'#$%'!++C'F1,',@43&;#".,$4'=,++,1> 7

O'/,$4"#$"A/5&&3$"'+,#%'6&,;.%34'#'/#6#/.",&A/2#&-.$-'/5&&3$"'"2#"'%,34'$,"'%.:.$.42'#4'v"'&.434'",1#&% !++0'#4'.4'"23'/#43'1."2'#'&34.4".;3'+,#%C'F254'"23';#+53',='-'#.',@"#.$3%'1."2'#'/5&&3$"A4,5&/3'+,#%'.4 4.-$.=./#$"+<'+,13&'"2#$'"2#"',@"#.$3%'1."2'#'&34.4".;3'+,#%'J433'G&,@+3:'7IC7LC'*='/,5&430'#'&34.4".;3 +,#%0'45/2'#4'.$'"23'/.&/5."'4"5%.3%'.$'X9#:6+3'78C70'.4'4.:6+<',5"',='"23'B534".,$'@3/#543',='"23';3&< +#&-3'4.+./,$'#&3#'."'1,5+%',//56<'J3B5.;#+3$"'",'"2#"',='"2,54#$%4',='"&#$4.4",&4eLC

1146 Chapter 14 Advanced MOS and Bipolar Logic Circuits

vI !VDD

iDN , iDP

Load curve Istat

E

0 VOL V t

vI ! 0 VDD#Vt

A VDD

vO

Figure 14.2 g>./#+'/,$4"&5/".,$'",'%3"3&:.$3'"23'fF(',='"23'.$;3&"3&'.$'E.-C'7IC7J#LC

1. F23' +,#%' /5&;3' &36&343$"4' #' :5/2' +,13&' 4#"5&#".,$' /5&&3$"' JXBC' 7IC8L' "2#$' .4' &36&3A 43$"3%'@<'"23'/,&&346,$%.$-'/5&;3'=,&'%&0'$#:3+<0'"2#"'=,&'v,'='!++C'F2.4'.4'#'&345+"',= "23'=#/"'"2#"'"23'6435%,AH)*!'.$;3&"3&'.4'545#++<'%34.-$3%'4,'"2#"'/0'.4'-&3#"3&'"2#$'/1 @<'#'=#/",&',='I'",'7_C'O4'13'1.++'42,1'42,&"+<0'"2.4'.$;3&"3&'.4',='"23'4,A/#++3%'&#".,3% "<630S'#$%'"23'&#".,' 2 ≡ / 0 ⁄ / 1 '%3"3&:.$34'#++'"23'@&3#D6,.$"4',='"23'fF(0'"2#"'.40'!"#0 !,#0'!,.0'#$%'4,',$0'#$%'"254'%3"3&:.$34'"23'$,.43':#&-.$4C'!3+3/".,$',='#'&3+#".;3+< 2.-2';#+53'=,&'2'&3%5/34'!"#'#$%'1.%3$4'"23'$,.43':#&-.$4C 2. O+"2,5-2',$3'"3$%4'",'"2.$D',='%''#4'#/".$-'#4'#'/,$4"#$"A/5&&3$"'4,5&/30'."'#/"5#++< ,63&#"34'.$'4#"5&#".,$'=,&',$+<'#'4:#++'&#$-3',='v"0'$#:3+<0' v " ≤ ! - C 'E,&'"23'&3:#.$A %3&',='"23'v"'&#$-30'%'',63&#"34'.$'"23'"&.,%3'&3-.,$C (,$4.%3&'=.&4"'"23'"1,'39"&3:3'/#434',='v,>'`23$'v,'='_0'%&3.4'/5"',=='#$%'%''.4',63&#".$-'.$ "23'"&.,%3'&3-.,$0'"2,5-2'1."2'T3&,'/5&&3$"'#$%'T3&,'%&#.$c4,5&/3';,+"#-3C'F254'"23',63&#".$6,.$"'.4'"2#"'+#@3+3%'O'.$'E.-C'7ICS0'123&3'v"'='!".'='!++0'"23'4"#"./'/5&&3$"'.4'T3&,0'#$%'"23 4"#"./'6,13&'%.44.6#".,$'.4'T3&,C'`23$'v,'='!++0'"23'.$;3&"3&'1.++',63&#"3'#"'"23'6,.$"'+#@3+3%'X .$'E.-C'7ICSC'*@43&;3'"2#"'5$+.D3'4"#$%#&%'()*!0'23&3'!"#'.4'$,"'T3&,0'#$',@;.,54'%.4#%A ;#$"#-3C' O$,"23&' %.4#%;#$"#-3' .4' "2#"' "23' -#"3' /,$%5/"4' /5&&3$"' J,4"#"L' .$' "23' +,1A,5"65" hhh 4"#"30'#$%'"254'"23&3'1.++'@3'4"#"./'6,13&'%.44.6#".,$' ( ' + = ,'4"#" × ! ++ )C

14.1.3 Derivation of the VTC E.-5&3'7IC8'42,14'"23'fF(',='"23'6435%,AH)*!'.$;3&"3&C'O4'.$%./#"3%0'."'2#4'=,5&'%.4".$/" &3-.,$40'+#@3+3%'?'"2&,5-2'?f0'/,&&346,$%.$-'",'"23'%.==3&3$"'/,:@.$#".,$4',='6,44.@+3':,%34 ,=',63&#".,$',='%&3 #$%'%'C'F23'=,5&'&3-.,$40'"23'/,&&346,$%.$-'"&#$4.4",&':,%34',=',63&#A ".,$0'#$%'"23'/,$%.".,$4'"2#"'%3=.$3'"23'&3-.,$4'#&3'+.4"3%'.$'F#@+3'7IC7C'`3'42#++'5".+.T3'"23 .$=,&:#".,$' .$' "2.4' "#@+3' ",-3"23&' 1."2' "23' %3;./3' 3B5#".,$4' -.;3$' .$' XB4C' J7IC7L' "2&,5-2 J7ICIL'",'%3&.;3'396&344.,$4'=,&'"23';#&.,54'43-:3$"4',='"23'fF('#$%'.$'6#&"./5+#&'=,&'"23 .:6,&"#$"'6#&#:3"3&4'"2#"'/2#&#/"3&.T3'"23'4"#"./',63&#".,$',='"23'.$;3&"3&C S

E,&'"23'H)*!'.$;3&"3&4'45/2'#4'"2#"'4"5%.3%'.$'X9#:6+3'78CS0'!"#'%363$%4',$'"23'&#".,',='"23'"&#$4/,$A %5/"#$/3'6#&#:3"3&4',='"23'%3;./340'"2#"'.40',$'"23'&#".,' J/′ J$⁄ # LL %&.;3& ⁄ (J/′ J$⁄ # LL+,#% C'!5/2'/.&/5."4'#&3 "23&3=,&3'D$,1$'#4'24-*567'+,-./'/.&/5."4C'!"#$%#&%'()*!'+,-./'/.&/5."4'%,'$,"'2#;3'45/2'#'%363$%3$/< #$%'/#$'"23&3=,&3'@3'/#++3%'24-*58699C

14.1 Pseudo-NMOS Logic Circuits

1147

vO(V) Region I VOH

5

Region II B

A

Slope ! #1

4

Slope ! "1

3

Region III

2

C Vt

(vO ! vI)

Region IV D

1

VOL

E

Slope ! #1 0

2

1 VOL

Vt

VIL

3 VM

4

VIH

VOH !VDD

Figure 14.3 fF('=,&'"23'6435%,AH)*!'.$;3&"3&C'F2.4'/5&;3'.4'6+,""3%'=,&'!++'='Y'f0'!-0'='−!-1'='7'f0'#$% 2 = ]C

Table 14.1 Regions of Operation of the Pseudo-NMOS Inverter i3-.,$

!3-:3$"',='fF(

%&

%'

(,$%.".,$

v, < !v" ≥ v, ! !!- ≤ v" ≤ v, ! !v" ≤ !-

?

OZ

(5",==

F&.,%3

??

Z(

!#"5&#".,$

F&.,%3

???

(U

F&.,%3

?f

UX

'F&.,%3

F&.,%3 !#"5&#".,$

5

vI (V)

1148 Chapter 14 Advanced MOS and Bipolar Logic Circuits &'()*+,-,!.'(/'+0,12#3 v " = ! ". = ! ++

#$%&'(

&'()*+,--,!.'(/'+0,24#3 XB5#".$-' *+&' =&,:' XBC' J7IC7L' #$%' *+'' =&,:' XBC' J7ICIL' ",-3"23&' 1."2' 45@4"."5".$/ 0 = 2/ 1 0'#$%'1."2'4,:3':#$.65+#".,$40'13',@"#.$ v" = !- +

S

J!++ ! !- L ! 2 ( v , ! !- L

S

#$%&)(

F23' ;#+53' ,=' !,#' /#$' @3' ,@"#.$3%' @<' %.==3&3$".#".$-' "2.4' 3B5#".,$' #$%' 45@4"."5".$∂ v " ⁄ ∂ v , 0 ! 7 '#$%'v,'='!,#>

!++ ! ! A !,# = ! - + AAAAAAAAAAAAAAAAAAAAAA 2(2 + 7)

#$%&*(

F23'"2&342,+%';,+"#-3'!:'.4'@<'%3=.$.".,$'"23';#+53',='v,'=,&'12./2'v"'='v, 0

!++ ! ! A !: = ! - + AAAAAAAAAAAAAAAAAAA 2+7

#$%&+(

E.$#++<0'"23'3$%',='"23'&3-.,$'??'43-:3$"'J6,.$"'(L'/#$'@3'=,5$%'@<'45@4"."5".$-'v"'='v, −!!.$'XBC'J7ICbL0'"23'/,$%.".,$'=,&'%&3+3#;.$-'4#"5&#".,$'#$%'3$"3&.$-'"23'"&.,%3'&3-.,$C &'()*+,---,!.'(/'+0,45# F2.4'.4'#'42,&"'43-:3$"'"2#"'.4'$,"',='-&3#"'.$"3&34"C'G,.$"'U'.4'/2#&#/"3&.T3%'@<'v"'='!-C &'()*+,-6,!.'(/'+0,57# XB5#".$-'*+&'=&,:'XBC'J7ICSL'",'*+''=&,:'XBC'J7IC8L'#$%'45@4"."5".$-'/0'='2/1'&345+"4'.$

7 S S v " = (v , ! ! - ) ! (v , ! ! - ) ! AAA (! ++ ! ! - ) 2

#$%&,(

F23' ;#+53' ,=' !,.' /#$' @3' %3"3&:.$3%' @<' %.==3&3$".#".$-' "2.4' 3B5#".,$' #$%' 43"".$∂ v " ⁄ ∂ v , = ! 7 '#$%' v , '= ! ,. 0

S !,. = !- + AAAAAAAAA (!++ ! ! - ) 82

#$%&$-(

F23';#+53',='!"#'/#$'@3'=,5$%'@<'45@4"."5".$-'v,'='!++'.$",'XBC'J7IC]L0

7 !"# = (!++ ! ! - ) 7 ! 7 ! AAA 2

#$%&$$(

F23'4"#"./'/5&&3$"'/,$%5/"3%'@<'"23'.$;3&"3&'.$'"23'+,1A,5"65"'4"#"3'.4'=,5$%'=&,:'XBC'J7IC8L'#4 S 7 , 4"#" = AAA / 1 (!++ ! ! - )

S

#$%&$.(

E.$#++<0'13'/#$'543'XB4C'J7IC^L'#$%'J7IC77L'",'%3"3&:.$3'&:#'#$%'XB4C'J7ICYL'#$%'J7IC7_L'", %3"3&:.$3'&:. >

7 7 &:# = !- ! ( !++ ! !- ) 7 ! 7 ! AAA ! AAAAAAAAAAAAAAAAAAAAAAA 2 2(2 + 7) S &:. = ( !++ ! !- ) 7 ! AAAAAAAAA 82

#$%&$/( #$%&$%(

14.1 Pseudo-NMOS Logic Circuits

O4'#'=.$#+',@43&;#".,$0'13'$,"3'"2#"'4.$/3'!++'#$%'!-'#&3'%3"3&:.$3%'@<'"23'6&,/344'"3/2$,+,-<0 "23',$+<'%34.-$'6#&#:3"3&'=,&'/,$"&,++.$-'"23';#+534',='!"#'#$%'"23'$,.43':#&-.$4'.4'"23'&#".,'2C

14.1.4 Dynamic Operation O$#+<4.4' ,=' "23' .$;3&"3&' "&#$4.3$"' &346,$43' ",' %3"3&:.$3' -'#.' 1."2' "23' .$;3&"3&' +,#%3%' @<' # /#6#/."#$/3';'.4'.%3$"./#+'",'"2#"',='"23'/,:6+3:3$"#&<'()*!'.$;3&"3&C'F23'/#6#/."#$/3'1.++ @3'/2#&-3%'@<'"23'/5&&3$"'*+'\'13'/#$'%3"3&:.$3'#$'34".:#"3'=,&'-'#.'@<'54.$-'"23'#;3&#-3';#+53 ,='*+'',;3&'"23'&#$-3'v"'='_'",'v"'='!++ ⁄ SC'F23'&345+"'.41

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α0 !α1

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14.1.5 Design F23'%34.-$'.$;,+;34'43+3/".$-'"23'&#".,'2'#$%'"23'$Q#'=,&',$3',='"23'"&#$4.4",&4C'F23';#+53',= $ ⁄ # '=,&'"23',"23&'%3;./3'/#$'"23$'@3',@"#.$3%'54.$-'2C'F23'%34.-$'6#&#:3"3&4',='.$"3&34" #&3'!"#0'&:#0'&:.0',23430''+0'-'#.0'#$%'-'.#C'?:6,&"#$"'%34.-$'/,$4.%3&#".,$4'#&3'#4'=,++,14> 1. F23'&#".,'2'%3"3&:.$34'#++'"23'@&3#D6,.$"4',='"23'fF(\'"23'+#&-3&'"23';#+53',='20'"23 +,13&'!"#'.4'JXBC'7IC77L'#$%'"23'1.%3&'"23'$,.43':#&-.$4'#&3'JXB4C'7IC78'#$%'7IC7ILC V,13;3&0'#'+#&-3&'2'.$/&3#434'"23'#4<::3"&<'.$'"23'%<$#:./'&346,$43'#$%0'=,&'#'-.;3$ J$Q#L1 0 :#D34'"23'4.+./,$'#&3#'+#&-3&C'F2540'43+3/".$-'#';#+53'=,&'2'&36&343$"4'#'/,:A 6&,:.43'@3"133$'$,.43':#&-.$4',$'"23',$3'2#$%'#$%'4.+./,$'#&3#'#$%'-'',$'"23',"23&C K45#++<0'2'.4'43+3/"3%'.$'"23'&#$-3'I'",'7_C

1149

1150 Chapter 14 Advanced MOS and Bipolar Logic Circuits 2. *$/3'2'2#4'@33$'%3"3&:.$3%0'#';#+53'=,&'J$Q#L1',&'J$Q#L0'/#$'@3'43+3/"3%'#$%'"23 ,"23&'%3"3&:.$3%C'V3&30',$3'1,5+%'43+3/"'#'4:#++'J$Q#L0'",'D336'"23'-#"3'#&3#'4:#++ #$%'"254',@"#.$'#'4:#++';#+53'=,&';C'!.:.+#&+<0'#'4:#++'J$Q#L1'D3364',4"#"'#$%''+ '+,1C *$'"23',"23&'2#$%0',$3'1,5+%'1#$"'",'43+3/"'+#&-3&'$Q#'&#".,4'",',@"#.$'+,1' -' '#$% "254'=#4"'&346,$43C'E,&'545#+'J2.-2A4633%L'#66+./#".,$40'J$Q#L1'.4'43+3/"3%'4,'"2#"',4"#" .4'.$'"23'&#$-3',='Y_ jO'",'7__'jO0'12./2'=,&'!++'='7Ca'f'&345+"4'.$''+'.$'"23'&#$-3 ,=']_ j`'",'7a_ j`C

14.1.6 Gate Circuits X9/36"'=,&'"23'+,#%'%3;./30'"23'6435%,AH)*!'-#"3'/.&/5."'.4'.%3$"./#+'",'"23'GUH',='"23'/,:A 6+3:3$"#&<' ()*!' -#"3C' E,5&A.$65"0' 6435%,AH)*!' H*i'#$%' HOHU' -#"34' #&3' 42,1$'.$ E.-C' 7ICIC' H,"3' "2#"' 3#/2' &3B5.&34' =.;3' "&#$4.4",&4' /,:6#&3%' ",' "23' 3.-2"' 543%' .$' 4"#$%#&% ()*!C'?$'6435%,AH)*!0'H*i'-#"34'#&3'6&3=3&&3%',;3&'HOHU'-#"34'@3/#543'"23'=,&:3&'%, $,"'5".+.T3'"&#$4.4",&4'.$'43&.34'#$%'"254'/#$'@3'%34.-$3%'1."2':.$.:5:A4.T3'H)*!'%3;./34C VDD

QP

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Y A

QNA

B

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C

QNC

D

QND

QP Y

A

B QNA

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Y!A"B"C"D (a)

Y ! ABCD (b)

Figure 14.4 H*i'#$%'HOHU'-#"34',='"23'6435%,AH)*!'"<63C

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14.1 Pseudo-NMOS Logic Circuits

Example 14.1 (,$4.%3&' #' 6435%,AH)*!' .$;3&"3&' =#@&./#"3%' .$' #' _CSYAj:' ()*!' "3/2$,+,-<' =,&' 12./2' µ0;5< = S S 77Y' µOQf 0 ' µ1;5<' ='8_ µOQf 0 ' !-0 '='− !-1 '='_CY'f0'#$%'!++'='SCY'fC'R3"'"23' $ ⁄ # '&#".,',='%&'@3 J_C8^Y'µ: ⁄ _CSY'µ:L'#$%'2'=']C'E.$%> J#L !".0'!"#0'!,#0'!,.0'!:0'&:.0'#$%'&:# J@L J$Q#L1 J/L ,4"#"'#$%''+ J%L -'#.0'-'.#0'#$%'-'0'#445:.$-'#'","#+'/#6#/."#$/3'#"'"23'.$;3&"3&',5"65"',='^'=E

Solution J#L !".'='!++'='SCY'f !"#'.4'%3"3&:.$3%'=&,:'XBC'J7IC77L'#4 !"# = ( SCY ! _CY ) 7 ! 7 ! 7AAA = _C77'f ]

!,#'.4'%3"3&:.$3%'=&,:'XBC'J7IC^L'#4 SCY ! _CY !,# = _CY + AAAAAAAAAAAAAAAAAAAAAAAA = _C^7'f ](] + 7) !,.'.4'%3"3&:.$3%'=&,:'XBC'J7IC7_L'#4 S !,. = _CY + AAAAAAAAAAAAAAAA × ( SCY ! _CY ) = 7CS^'f 8×] !:'.4'%3"3&:.$3%'=&,:'XBC'J7ICaL'#4 SCY ! _CY !: = _CY + AAAAAAAAAAAAAAAAAAAAA = 7C78'f ]+7 F23'$,.43':#&-.$4'/#$'$,1'@3'%3"3&:.$3%'#4 &:. = !". ! !,. = SCY ! 7CS^ = 7CS8'f &:# = !,# ! !"# = _C^7 ! _C77 = _Cb_ f *@43&;3'"2#"'"23'$,.43':#&-.$4'#&3'$,"'3B5#+'#$%'"2#"'&:#'.4'&#"23&'+,1C J@L F23' $ ⁄ # '&#".,',='%''/#$'@3'=,5$%'=&,:

µ 0 ; 5< ( $ ⁄ # ) 0 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA = ] µ 1 ; 5< ( $ ⁄ # ) 1 _C8^Y 77Y × AAAAAAAAAAAAA _CSY AAAAAAAAAAAAAAAAAAAAAAAAAAAAA = ] 8_ ( $ ⁄ # ) 1 F2540' #$Q#(16=6-&)%

1151

1152 Chapter 14 Advanced MOS and Bipolar Logic Circuits

Example 14.1 continued

J/L F23'%/'/5&&3$"'.$'"23'+,1A,5"65"'4"#"3'/#$'@3'%3"3&:.$3%'=&,:'XBC'J7IC7SL'#4 7 , 4"#" = AAA × 8_ × _CbI ( SCY ! _CY ) = 8aCI'µO S

S

F23'4"#"./'6,13&'%.44.6#".,$'/#$'$,1'@3'=,5$%'=&,: ' + = , 4"#" !++ = 8aCI × SCY = ]b'µ` J%L F23'+,1A",A2.-2'6&,6#-#".,$'%3+#<'/#$'@3'=,5$%'@<'54.$-'XB4C'J7IC7YL'#$%'J7IC7bL>

α 1 = 7Cba ! 7Y

7Cba × ^ × 7_ A 0 _CSY $4 - '#. 0 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA !b 8_ × 7_ × _CbI × SCY F23'2.-2A",A+,1'6&,6#-#".,$'%3+#<'/#$'@3'=,5$%'@<'54.$-'XB4C'J7IC7^L'#$%'J7IC7aL>

α 0 = 7CYI ! 7Y

7CYI × ^ × 7_ - '.# = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA = _C_8 $4 _C8^Y !b 77Y × 7_ × AAAAAAAAAAAAA × SCY _CSY H,10'"23'6&,6#-#".,$'%3+#<'/#$'@3'%3"3&:.$3%'#4 7 - ' = AAA ( _CSY + _C_8 ) = _C7I $4 S

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EXERCISES 14.1 `2.+3'D336.$-'2'5$/2#$-3%0'&3%34.-$'"23'.$;3&"3&'/.&/5."',='X9#:6+3'7IC7'",'+,13&'."4'4"#"./'6,13& %.44.6#".,$'",'2#+='"23';#+53'=,5$%C'E.$%'"23' $ ⁄ # 3&#".,4'=,&'"23'$31'%34.-$C'O+4,'=.$%'-'#.0'-'.#0'#$% -'0'#445:.$-'"2#"';'&3:#.$4'5$/2#$-3%C'`,5+%'"23'$,.43':#&-.$4'/2#$-3k Ans.'J $ ⁄ # L0'='7CY\'J $ ⁄ # L1'='_C8S\'_CY'$4\'_C_8'$4\'_CS^'$4\'$, 14.2 i3%34.-$'"23'.$;3&"3&',='X9#:6+3'7IC7'54.$-'2'='IC'E.$%'!"#'#$%'"23'$,.43':#&-.$4C'?='J $ ⁄ # L0'= _C8^Y'µ: ⁄ _CSY'µ:0 '=.$%'J $ ⁄ # L10' , 4"#" 0 ' ' + 0 ' - '#. 0 ' - '.# 0 '#$%'-'C'O445:3';'='^'=EC Ans.'!"#'='_CS^'f\'&:#'='_Cba'f\'&:.'='_CaY'f\'J $ ⁄ # L1'='7CII\',4"#"'='abC8'µO\''+'='_CSS':`\ -'#. = _C77'$4\'-'.#'='_C_8'$4\'-''='_C_^'$4

14.2 Pass-Transistor Logic Circuits O'/,$/36"5#++<'4.:6+3'#66&,#/2'=,&'.:6+3:3$".$-'+,-./'=5$/".,$4'5".+.T34'43&.34'#$%'6#&#++3+ /,:@.$#".,$4',=' 41."/234'"2#"' #&3' /,$"&,++3%' @<'.$65"' +,-./';#&.#@+34' ",' /,$$3/"' "23' .$65"

14.2 Pass-Transistor Logic Circuits 1153

B B

C

A

Y

A

Y C

(b)

(a)

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C

A

C

A

Y (a)

Y

C (b)

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14.2.1 An Essential Design Requirement O$'3443$".#+'&3B5.&3:3$"'.$'"23'%34.-$',='GFR'/.&/5."4'.4'3$45&.$-'"2#"'6B62C3?*2?D*-305763E49 4-3 4883 -*@693 43 85F=269*9-40?63 14-E3 6*-E623 -53 !++3 523 -53 >25D07A' F,' #66&3/.#"3' "2.4' 6,.$"0

1154 Chapter 14 Advanced MOS and Bipolar Logic Circuits

VDD

VDD

Q2 B

Q2 A Q1

B S1 C

Y

Q4

A

Y

S1

Q3

Q1

B

C

S2

(a)

(b)

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14.2.2 Operation with NMOS Transistors as Switches ?:6+3:3$".$-'"23'41."/234'.$'#'GFR'/.&/5."'1."2'4.$-+3'H)*!'"&#$4.4",&4'&345+"4'.$'#'4.:6+3 /.&/5."' 1."2' 4:#++' #&3#' #$%' 4:#++' $,%3' /#6#/."#$/34C' F2343' #%;#$"#-340' 2,13;3&0' #&3 ,@"#.$3%' #"' "23' 3963$43' ,=' 43&.,54' 42,&"/,:.$-4' .$' @,"2' "23' 4"#"./' /2#&#/"3&.4"./4' #$%' "23 %<$#:./'63&=,&:#$/3',='"23'&345+".$-'/.&/5."4C'F,'.++54"&#"30'/,$4.%3&'"23'/.&/5."'42,1$'.$ E.-C'7ICa0'123&3'#$'H)*!'"&#$4.4",&'%'.4'543%'",'.:6+3:3$"'#'41."/2'/,$$3/".$-'#$'.$65" $,%3'1."2';,+"#-3'v,'#$%'#$',5"65"'$,%3C'F23'","#+'/#6#/."#$/3'@3"133$'"23',5"65"'$,%3'#$% -&,5$%' .4' &36&343$"3%' @<' /#6#/.",&' ;C' F23' 41."/2' .4' 42,1$' .$' "23' /+,43%' 4"#"3' 1."2' "23 /,$"&,+' 4.-$#+' #66+.3%' ",' ."4' -#"3' @3.$-' 2.-2' #"' !++C' `3' 1.42' ",' #$#+
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`23$'v,'-,34'2.-20'"23'"&#$4.4",&',63&#"34'.$'"23'4#"5&#".,$':,%3'#$%'%3+.;3&4'#'/5&&3$" *+'",'/2#&-3'"23'/#6#/.",&0 S 7 * + = AAA / 0 J!++ ! v " ! !- L

S

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123&3' / 0 = /′0 J$ ⁄ # L0 '#$%'!-'.4'%3"3&:.$3%'@<'"23'@,%<'3==3/"'4.$/3'"23'4,5&/3'.4'#"'#';,+"#-3 v"' &3+#".;3' ",' "23' @,%<' J12./20' "2,5-2' $,"' 42,1$0' .4' /,$$3/"3%' ",' -&,5$%L\' "254' J433' XBC YC 7_^L0

!- = !-_ + γ ( v " + S φ J ! S φ J )

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1156 Chapter 14 Advanced MOS and Bipolar Logic Circuits vC ! VDD vI

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Example 14.2 (,$4.%3&'"23'H)*!'"&#$4.4",&'41."/2'.$'"23'/.&/5."4',='E.-4C'7ICa'#$%'7IC]'",'@3'=#@&./#"3%'.$'#'"3/2$,+A S S ,-<' =,&' 12./2' µ0;5<' =' Y_' µOQf 0 ' µ1;5<' =' S_' µOQf 0 ' ! -_ = 7'f0 ' γ' =' _CY' f$7.0' SφJ' =' _Cb f0' #$% !++ = Y f0'123&3' φJ'.4'#'62<4./#+'6#&#:3"3&C'R3"'"23'"&#$4.4",&'@3',='"23':.$.:5:'4.T3'=,&'"2.4'"3/2$,+,-<0 $#:3+<0' ' I' µ:QS' µ:0' #$%' #445:3' "2#"' "23' ","#+' /#6#/."#$/3' @3"133$' "23' ,5"65"' $,%3' #$%' -&,5$%' .4 ; = Y_ =EC J#L E,&'"23'/#43'1."2'v,'2.-2'JE.-C'7ICaL0'=.$%'!".C J@L ?='"23',5"65"'=33%4'#'()*!'.$;3&"3&'12,43' J$ ⁄ # L 1 = SCY J$ ⁄ # L 0 = 7_'µ: ⁄ S 'µ:0'=.$%'"23'4"#"./ /5&&3$"',='"23'.$;3&"3&'#$%'."4'6,13&'%.44.6#".,$'123$'."4'.$65"'.4'#"'"23';#+53'=,5$%'.$'J#LC'O+4,'=.$%'"23 .$;3&"3&',5"65"';,+"#-3C J/L E.$%'-'#.C J%L E,&'"23'/#43'1."2'v,'-,.$-'+,1'JE.-C'7IC]L0'=.$%'-'.#C J3L E.$%'-'C

Solution J#L i3=3&'",'E.-C'7ICaC'?='!".'.4'"23';#+53',='v"'#"'12./2'%'4",64'/,$%5/".$-0 "23$0

! ++ ! !". ! ! - = _ !". = !++ ! ! -

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14.2 Pass-Transistor Logic Circuits 1157

H,"3'"2#"'"2.4'&36&343$"4'#'4.-$.=./#$"'+,44'.$'4.-$#+'#:6+."5%3C J@L F23'+,#%'.$;3&"3&'1.++'2#;3'#$'.$65"'4.-$#+',='8CI'fC'F2540'."4'%''1.++'/,$%5/"'#'/5&&3$"',= 7 7_ S * +' = AAA × S_ × AAAAAA ( Y ! 8CI ! 7 ) = 7a'µO S

S

123&3'13'2#;3'#445:3%'%'33",'@3',63&#".$-'.$'4#"5&#".,$0'#4'13'4".++'3963/"'vO ,='"23'.$;3&"3&'",'@3 /+,43'",'_C'F2540'"23'4"#"./'6,13&'%.44.6#".,$',='"23'.$;3&"3&'1.++'@3 ' + = !++ * +' = Y × 7a = ]_'µ` F23',5"65"';,+"#-3',='"23'.$;3&"3&'/#$'@3'=,5$%'@<'$,".$-'"2#"'%&'1.++'@3',63&#".$-'.$'"23'"&.,%3'&3-.,$C XB5#".$-'."4'/5&&3$"'",'"2#"',='%''J.C3C0'7a'µOL'3$#@+34'54'",'%3"3&:.$3'"23',5"65"';,+"#-3'",'@3'_C_a'fC J/L F,'%3"3&:.$3'-'#.0'&3=3&'",'E.-'7ICaC'`3'$33%'",'=.$%'"23'/5&&3$"'*+'#"'-' ='_'J123&3' v"' ='_0'!-' ='!--' = 7 fL'#$%'#"'-'='-'#.'J123&3'v"'='SCY'f0'!-'",'@3'%3"3&:.$3%L0'#4'=,++,14> 7 I * + ( _ ) = AAA × Y_ × AAA × ( Y ! 7 ) = a__'µO S

S

S

!- ( #" ' v " = SCY'f ) = 7 + _CY ( SCY + _Cb ! _Cb ) = 7CI]'f 7 I * + ( - '#. ) = AAA × Y_ × AAA ( Y ! SCY ! 7CI] ) = Y_'µO S

S

S

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a__ + Y_ = AAAAAAAAAAAAAAAAAAAAA = ISY'µO S

#$%'-'#.'/#$'@3'=,5$%'#4 ; ( !++ ⁄ S ) A - '#. = AAAAAAAAAAAAAAAAAAAAAAAAA * + #; ! 7Y

Y_ × 7_ × SCY A = _CS]'$4 = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA !b ISY × 7_ J%L i3=3&'",'"23'/.&/5."'.$'E.-C'7IC]C'*@43&;3'"2#"0'23&30'!-'&3:#.$4'/,$4"#$"'#"'!--'='7'fC'O"'- d _0'%'1.++ @3',63&#".$-'.$'4#"5&#".,$0'#$%'"23'%&#.$'/5&&3$"'1.++'@3 7 I * + ( _ ) = AAA × Y_ × AAA ( Y ! 7 ) = a__'µO S

S

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= b]_'µO F2540'"23'#;3&#-3'%.4/2#&-3'/5&&3$"'.4'-.;3$'@< *+ #$%'-'.#'/#$'@3'%3"3&:.$3%'#4

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Y_ × 7_ × SCY A = _C7^'$4 - '.# = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA !b ^I_ × 7_

7 7 J3L - ' = AAA ( - '#. + - '.# ) = AAA ( _CS] + _C7^ ) = _CS8'$4 S

S

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1158 Chapter 14 Advanced MOS and Bipolar Logic Circuits

EXERCISE 14.3 R3"'"23'H)*!'"&#$4.4",&'41."/2'.$'E.-C'7ICa'@3'=#@&./#"3%'.$'#'_C7aAµ:'()*!'6&,/344'=,&'12./2 7⁄ S ! -_ 0 _CY'f0 ' γ 0 _C8'f 0 ' S φ J 0 _CaY'f0 '#$%' ! ++ 0 7Ca'fC 'E.$%' ! ". C Ans.'7C7Y'f

14.2.3 Restoring the Value of VOH to VDD X9#:6+3'7ICS'.++54"&#"34'/+3#&+<'"23'6&,@+3:',='4.-$#+A+3;3+'+,44'#$%'."4'%3+3"3&.,54'3==3/"',$ "23' ,63&#".,$' ,=' "23' 45//33%.$-' ()*!' .$;3&"3&C' !,:3' &#"23&' .$-3$.,54' "3/2$.B534' 2#;3 @33$'%3;3+,63%'",'&34",&3'"23',5"65"'+3;3+'",'!++C'`3'42#++'@&.3=+<'%.4/544'"1,'45/2'"3/2A $.B534C'*$3'.4'/.&/5."A@#43%'#$%'"23',"23&'.4'@#43%',$'6&,/344'"3/2$,+,-*?@ @'A)%'.'/#$'@3'=#@&./#"3%'@<'54.$-'.,$'.:6+#$"#".,$'",'/,$"&,+'"23';#+53',=' !-0 '#$%'#&3'D$,1$'#4 VDD

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14.2 Pass-Transistor Logic Circuits 1159

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14.2.4 The Use of CMOS Transmission Gates as Switches g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bLC Z3=,&3'13'#$#+
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E.-5&3'7IC7SJ#L'42,14'"23'"&#$4:.44.,$A-#"3'41."/2'.$'"23'M,$N'6,4.".,$'1."2'"23'.$65"0 v, 0'&.4.$-'",'!++'#"'-3='_C'O445:.$-0'#4'@3=,&30'"2#"'.$.".#++<'"23',5"65"';,+"#-3'.4'T3&,0'13'433 "2#"'%&'1.++'@3',63&#".$-'.$'4#"5&#".,$'#$%'6&,;.%.$-'#'/2#&-.$-'/5&&3$"',= 7 S * +& = AAA / 0 ( !++ ! v " ! ! -0 )

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1160 Chapter 14 Advanced MOS and Bipolar Logic Circuits vC ! VDD vI

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(b) Figure 14.12 *63&#".,$',='"23'"&#$4:.44.,$'-#"3'#4'#'41."/2'.$'GFR'/.&/5."4'1."2'!"#'v,'2.-2'#$%'!$#'v,'+,1C

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!-0 = ! -_ + γ ( v " + S φ J ! S φ J )

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F&#$4.4",&' %&' 1.++' /,$%5/"' #' %.:.$.42.$-' /5&&3$"' "2#"' &3%5/34' ",' T3&,' #"' v"' =' !++3 N3 !-0 C *@43&;30'2,13;3&0'"2#"'%'',63&#"34'1."2'!)('='!++'#$%'.4'.$.".#++<'.$'4#"5&#".,$0 S 7 * +' = AAA / 1 ( !++ ! ! -1 )

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EXERCISE 14.4'F23'"&#$4:.44.,$'-#"3',='E.-4C'7IC7SJ#L'#$%'7IC7SJ@L'.4'=#@&./#"3%'.$'#'()*!'6&,/344'"3/2$,+,-<'=,& S S 12./2' /′0 = Y_'µOQf 0 ' /′1 = S_'µOQf 0 ' !-0 = ! -1 0' !- _' =' 7' f0' γ' =' _CY' f7QS0' SφJ' =' _Cb' f0' #$% !++ = Y fC'R3"'%&'#$%'%''@3',='"23':.$.:5:'4.T3'6,44.@+3'1."2'"2.4'6&,/344'"3/2$,+,-<0'J $ ⁄ # L0 = J $ ⁄ # L1 = I µ:QS'µ:C'F23'","#+'/#6#/."#$/3'#"'"23',5"65"'$,%3'.4'^_'=EC'K".+.T3'#4':#$<',='"23'&345+"4 ,='X9#:6+3'7ICS'#4'<,5'$33%C J#L `2#"'#&3'"23';#+534',='!".'#$%'!"#k J@L E,&'"23'4."5#".,$'.$'E.-C'7IC7SJ#L0'=.$%'*+&J_L0'*+'J_L0'*+&J-'#.L0'*+'J-'#.L0'#$%'-'#.C J/L E,&'"23'4."5#".,$'%36./"3%'.$'E.-C'7IC7SJ@L0'=.$%'*+&J_L0'*+'J_L0'*+&J-'.#L0'*+'J-'.#L0'#$%'-'.#C'O"'12#" ;#+53',='v"'1.++'%''"5&$',==k J%L E.$%'-'A Ans.,J#L'Y f0'_ f\'J@L'a__'µO0'8S_'µO0'Y_'µO0'S^Y'µO0'_CSI'$4\'J/L'a__'µO0'8S_'µO0'baa'µO0'S_ µO0 _C7]'$40'7Cb'f\'J%L'_CSS'$4

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14.2 Pass-Transistor Logic Circuits 1163

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EXERCISE 14.6 K43'XBC'J7IC8bL'",'34".:#"3'"23';#+53',=' K O( '=,&'#'"&#$4:.44.,$'-#"3'=#@&./#"3%'.$'#'_C7aAµ:'()*! "3/2$,+,-<'1."2'( $ ⁄ # ) 0 0 ( $ ⁄ # ) 1 0 7CYC Ans.'aC8' DΩ

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1166 Chapter 14 Advanced MOS and Bipolar Logic Circuits

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14.3 Dynamic MOS Logic Circuits 1167

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14.3 Dynamic MOS Logic Circuits 1169

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14.3 Dynamic MOS Logic Circuits 1173

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1178 Chapter 14 Advanced MOS and Bipolar Logic Circuits

14.4 Emitter-Coupled Logic (ECL) 1179

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EXERCISE 14.13' `."2'.$65"'"3&:.$#+4'H'#$%'G'.$'E.-C'7ICSb'+3="',63$0'=.$%'"23'/5&&3$"',R'"2&,5-2'KRC'O+4,'=.$%'"23 ;,+"#-34'#"'"23'/,++3/",&',='%K'#$%'#"'"23'/,::,$'/,++3/",&',='"23'.$65"'"&#$4.4",&4'%H'#$%'%GC K43'!K'='−7C8S'f0'!GR',='%K'!'_C^Y'f0'#$%'#445:3'"2#"'β',='%K'.4';3&<'2.-2C Ans.,I':O\'c7'f\'_'f

F23'"2.&%'6#&"',='"23'X(R'-#"3'/.&/5."'.4'/,:6,43%',='"23'"1,'3:.""3&'=,++,13&40'%.'#$% %/C' F23' 3:.""3&' =,++,13&4' %,' $,"' 2#;3' ,$A/2.6' +,#%40' 4.$/3' .$' :#$<' #66+./#".,$4' ,=' 2.-2A 4633%'+,-./'/.&/5."4'"23'-#"3',5"65"'%&.;34'#'"&#$4:.44.,$'+.$3'"3&:.$#"3%'#"'"23',"23&'3$%0'#4 .$%./#"3%'.$'E.-C'7ICS^C'J),&3',$'"2.4'+#"3&'.$'!3/".,$'7ICICbCL F23'3:.""3&'=,++,13&4'2#;3'"1,'65&6,434>'E.&4"0'"23<'42.="'"23'+3;3+',='"23',5"65"'4.-$#+4 @<' ,$3' !GR' %&,6C' F2540' 54.$-' "23' &345+"4' ,=' X93&/.43' 7IC780' 13' 433' "2#"' "23' ,5"65"' +3;3+4 @3/,:3' #66&,9.:#"3+<' −7C^Y' f' #$%' −_C^Y' fC' F2343' 42.="3%' +3;3+4' #&3' /3$"3&3%' #66&,9.A :#"3+<'#&,5$%'"23'&3=3&3$/3';,+"#-3'J!K'='−7C8S'fL0'12./2':3#$4'"2#"',$3'-#"3'/#$'%&.;3 #$,"23&C'F2.4'/,:6#".@.+."<',='+,-./'+3;3+4'#"'.$65"'#$%',5"65"'.4'#$'3443$".#+'&3B5.&3:3$"'.$ "23'%34.-$',='-#"3'/.&/5."4C F23'43/,$%'=5$/".,$',='"23',5"65"'3:.""3&'=,++,13&4'.4'",'6&,;.%3'"23'-#"3'1."2'+,1',5"A 65"'&34.4"#$/34'#$%'1."2'"23'+#&-3',5"65"'/5&&3$"4'&3B5.&3%'=,&'/2#&-.$-'+,#%'/#6#/."#$/34C

1180 Chapter 14 Advanced MOS and Bipolar Logic Circuits

R

Figure 14.27 F23'6&,63&'1#<'",'/,$$3/"'2.-2A4633%'+,-./'-#"34'45/2'#4'X(RC'G&,63&+<'"3&:.$#".$-'"23 "&#$4:.44.,$'+.$3'/,$$3/".$-'"23'"1,'-#"34'3+.:.$#"34'"23'M&.$-.$-N'"2#"'1,5+%',"23&1.43'/,&&56"'"23'+,-./ 4.-$#+4C'J!33'!3/".,$'7ICICbCL

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14.4.4 Voltage-Transfer Characteristics V#;.$-'6&,;.%3%'#'B5#+."#".;3'%34/&.6".,$',='"23',63&#".,$',='"23'X(R'-#"30'13'42#++'$,1 %3&.;3' ."4' ;,+"#-3A"&#$4=3&' /2#&#/"3&.4"./4C' F2.4' 1.++' @3' %,$3' 5$%3&' "23' /,$%.".,$4' "2#"' "23 ,5"65"4'#&3'"3&:.$#"3%'.$'"23':#$$3&'.$%./#"3%'.$'E.-C'7ICS^C'O445:.$-'"2#"'"23'G'.$65"'.4 +,1'#$%'"254'%G'.4',==0'"23'/.&/5."'4.:6+.=.34'",'"2#"'42,1$'.$'E.-C'7ICSaC'`3'1.42'",'#$#+?';3&454'v,'#$%'v@>?';3&454'v,'J123&3'v,'≡'vHLC

Figure 14.28 !.:6+.=.3%';3&4.,$',='"23'X(R'-#"3'=,&'"23'65&6,43',='=.$%.$-'"&#$4=3&'/2#&#/"3&.4"./4C

14.4 Emitter-Coupled Logic (ECL)

?$'"23'#$#+<4.4'",'=,++,1'13'42#++':#D3'543',='"23'396,$3$".#+'*; cvGR'/2#&#/"3&.4"./',='"23 Z[FC'!.$/3'"23'Z[F4'543%'.$'X(R'/.&/5."4'2#;3'4:#++'#&3#4'J.$',&%3&'",'2#;3'4:#++'/#6#/.A "#$/34'#$%'23$/3'2.-2'JOL0'"23.&'4/#+3'/5&&3$"4',)'#&3'4:#++C'`3'1.++'"23&3=,&3'#445:3'"2#"'#" #$'3:.""3&'/5&&3$"',='7':O0'#$'X(R'"&#$4.4",&'2#4'#'!GR'%&,6',='_C^Y'fC The OR Transfer Curve E.-5&3' 7ICS]' .4' #' 4D3"/2' ,=' "23' *i' "&#$4=3&' /2#&#/"3&.4"./0' v>? ;3&454'v,0'1."2'"23'6#&#:3"3&4'!"#0'!".0'!,#0'#$%'!,.'.$%./#"3%C'V,13;3&0'",'4.:6+.=<'"23'/#+A /5+#".,$',='!,#'#$%'!,.0'13'42#++'543'#$'#+"3&$#".;3'",'"23'5$."
,R % AAAAAAAAAAAK = ]] ,R % H

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!GR

%K

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= !O +$ ]] = 77Y':f

12./2'-.;34

!,# =' ! 7C8S ! _C77Y = ! 7CI8Y'f O445:.$-'%H3#$%'%K'",'@3':#"/23%0'13'/#$'1&."3

!,. − !K '= !K ' − !,# 12./2'/#$'@3'543%'",'=.$%'!,.'#4

!,. 0 ! 7CS_Y'f F,',@"#.$'!"#0'13'$,"3'"2#"'%H'.4',=='#$%'%K'/#&&.34'"23'3$".&3'/5&&3$"',R0'-.;3$'@<

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Figure 14.29 F23'*i'"&#$4=3&'/2#&#/"3&.4"./'v*i';3&454'v,0'=,&'"23'/.&/5."'.$'E.-C'7ICSaC

1181

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! %6AB

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EXERCISE 14.14 E,&'"23'/.&/5."'.$'E.-C'7ICSa0'%3"3&:.$3'"23';#+534',=',R',@"#.$3%'123$'v,'='!,#0'!K0'#$%'!,.C'O+4,0 =.$%'"23';#+53',='v*i'/,&&346,$%.$-'",'v,'='!KC'O445:3'"2#"'vGR '='_C^Y'f'#"'#'/5&&3$"',='7':OC Ans.,8C]^':O\'IC__':O\'IC7S':O\'−7C87'f

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Noise Margins F23' &345+"4' ,=' X93&/.43' 7IC7I' .$%./#"3' "2#"' "23' @.#4' /5&&3$"' ,R' &3:#.$4 #66&,9.:#"3+<'/,$4"#$"C'O+4,0'"23',5"65"';,+"#-3'/,&&346,$%.$-'",'v,'='!K'.4'#66&,9.:#"3+< 3B5#+'",'!KC'H,"./3'=5&"23&'"2#"'"2.4'.4'#+4,'#66&,9.:#"3+<'"23':.%6,.$"',='"23'+,-./'41.$-\ 463/.=./#++<0

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1183

1184 Chapter 14 Advanced MOS and Bipolar Logic Circuits

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EXERCISE 14.15 (,$4.%3&' "23' /.&/5."' .$' E.-C' 7IC8SC' J#L' E,&' v,' =' !,.' =' −7CS_Y' f0' =.$%' vH*iC' J@L' E,&' v,' = !".' = −_Caa'f0'=.$%'vH*iC'J/L'E.$%'"23'4+,63',='"23'"&#$4=3&'/2#&#/"3&.4"./'#"'"23'6,.$"'v, '= !". '='−_Caa'fC J%L E.$%'"23';#+53',=' v,'#"'12./2'%H'4#"5&#"34'J.C3C0'!)LC'O445:3'"2#"'!GR'='_C^Y'f'#"'#'/5&&3$"',= 7':O0'!;R4#"'!'_C8'f0'#$%'β'='7__C Ans.,J#L'−7C^_'f\'J@L'−7C^]'f\'J/L'−_CSI'fQf\'J%L'−_CYa'f

Manufacturers’ Specifications X(R' :#$5=#/"5&3&4' 4566+<' -#"3' "&#$4=3&' /2#&#/"3&.4A "./4',='"23' =,&:' 42,1$' .$' E.-4C' 7ICS]' #$%'7IC87C' O':#$5=#/"5&3&'545#++<' 6&,;.%34' 45/2 /5&;34':3#45&3%'#"'#'$5:@3&',='"3:63&#"5&34C'?$'#%%.".,$0'#"'3#/2'&3+3;#$"'"3:63&#"5&30 1,&4"A/#43' ;#+534' =,&' "23' 6#&#:3"3&4' !,#0' !,.0' !"#0' #$%' !".' #&3' -.;3$C' F2343' 1,&4"A/#43 ;#+534'#&3'463/.=.3%'1."2'"23'.$3;."#@+3'/,:6,$3$"'",+3&#$/34'"#D3$'.$",'#//,5$"C'O4'#$ 39#:6+30' ),",&,+#' 463/.=.34' "2#"' =,&' )X(R' 7_0___' #"' SY°(0' "23' =,++,1.$-' 1,&4"A/#43

14.4 Emitter-Coupled Logic (ECL) 1185

;#+534'#66+<)

!,#:#9 = !7CI^Y'f

!,.:.$ = !7C7_Y'f

!"#:#9 = !7Cb8_'f

!".:.$ = ! _C]a_'f

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&:# = _C7YY'f

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12./2'#&3'#@,5"'2#+='"23'-C1*?48';#+534'6&3;.,54+<'/#+/5+#"3%C E,&'#%%.".,$#+'.$=,&:#".,$',$')X(R'463/.=./#".,$4'"23'.$"3&34"3%'&3#%3&'.4'&3=3&&3%'", "23'),",&,+#'J7]aa0'7]a]L'65@+./#".,$4'+.4"3%'.$'"23'@.@+.,-><'.$'O663$%.9'gC

14.4.5 Fan-Out `23$'"23'.$65"'4.-$#+'",'#$'X(R'-#"3'.4'+,1'J!"#L0'"23'.$65"'/5&&3$"'.4'3B5#+'",'"23'/5&&3$" "2#"'=+,14'.$'"23'Y_ADΩ'65++A%,1$'&34.4",&C'F2540

−7C^^ + YCS ,,# = AAAAAAAAAAAAAAAAAAAAAAAAAAA ! b]'µO Y_ `23$'"23'.$65"'.4'2.-2'J!".L0'"23'.$65"'/5&&3$"'.4'-&3#"3&'@3/#543',='"23'@#43'/5&&3$"',= "23'.$65"'"&#$4.4",&C'F2540'#445:.$-'#'"&#$4.4",&'β',='7__0'13',@"#.$

−_Caa + YCS I , ,. = AAAAAAAAAAAAAAAAAAAAAAAAAAA + AAAAAAAAA ! 7Sb' µ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

14.4.6 Speed of Operation and Signal Transmission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o.C3C0'7Y'/:Q$4LC'K$+344'463/.#+'/#&3'.4'"#D3$0'3$3&-<'"2#"'&3#/234'"23'3$% b

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1186 Chapter 14 Advanced MOS and Bipolar Logic Circuits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
14.4.7 Power Dissipation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
14.4 Emitter-Coupled Logic (ECL) 1187

O"'"2.4'W5$/"5&3'13'42,5+%'&3."3&#"3'#'6,.$"'13':#%3'3#&+.3&0'$#:3+<0'"2#"'#+"2,5-2'#$ X(R'-#"3'1,5+%',63&#"3'1."2' !RR = _ '#$%' !;; = +YCS'f0 '"23'43+3/".,$',=' !RR = ! YCS'f #$%' !;; = _'f '.4'&3/,::3$%3%0'@3/#543'.$'"23'/.&/5."0'#++'4.-$#+'+3;3+4'#&3'&3=3&3$/3%'", !;;0'#$%'-&,5$%'.4'/3&"#.$+<'#$'39/3++3$"'&3=3&3$/3C+

EXERCISE 14.16 E,&'"23'X(R'-#"3'.$'E.-C'7ICSb0'/#+/5+#"3'#$'#66&,9.:#"3';#+53'=,&'"23'6,13&'%.44.6#"3%'.$'"23'/.&A /5."'5$%3&'"23'/,$%.".,$'"2#"'#++'.$65"4'#&3'+,1'#$%'"2#"'"23'3:.""3&4',='"23',5"65"'=,++,13&4'#&3'+3=" ,63$C'O445:3'"2#"'"23'&3=3&3$/3'/.&/5."'4566+.34'=,5&'.%3$"./#+'-#"340'#$%'23$/3',$+<'#'B5#&"3&',= "23'6,13&'%.44.6#"3%'.$'"23'&3=3&3$/3'/.&/5."'42,5+%'@3'#""&.@5"3%'",'#'4.$-+3'-#"3C Ans.,SSCI':`

14.4.8 Thermal Effects ?$',5&'#$#+<4.4',='"23'X(R'-#"3',='E.-C'7ICSb0'13'=,5$%'"2#"'#"'&,,:'"3:63&#"5&3'"23'&3=A 3&3$/3' ;,+"#-3' !K' .4' −7C8S' fC' `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

Example 14.4 `3'1.42'",'%3"3&:.$3'"23'"3:63&#"5&3'/,3==./.3$"',='"23'&3=3&3$/3';,+"#-3'!K'#$%',='"23':.%6,.$"'@3"133$ !"#'#$%'!".C

Solution F,'%3"3&:.$3'"23'"3:63&#"5&3'/,3==./.3$"',='!K0'/,$4.%3&'"23'/.&/5."'.$'E.-C'X7IC7S'#$%'#445:3'"2#"'"23 "3:63&#"5&3'/2#$-34'@<'+7°(C'U3$,".$-'"23'"3:63&#"5&3'/,3==./.3$"',='"23'%.,%3'#$%'"&#$4.4",&';,+"#-3 %&,64'@<'δ0'123&3'δ'!'−S':fQ°(0'13',@"#.$'"23'3B5.;#+3$"'/.&/5."'42,1$'.$'E.-C'7IC88C'?$'"23'+#""3&'/.&A /5."0'"23'/2#$-34'.$'%3;./3';,+"#-3'%&,64'#&3'/,$4.%3&3%'#4'4.-$#+40'#$%'23$/3'"23'6,13&'4566+<'.4'42,1$ #4'#'4.-$#+'-&,5$%C ?$'"23'/.&/5."',='E.-C'7IC88'13'2#;3'"1,'4.-$#+'-3$3&#",&40'#$%'13'1.42'",'#$#+
1188 Chapter 14 Advanced MOS and Bipolar Logic Circuits Example 14.4 continued

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Figure 14.33 XB5.;#+3$"'/.&/5."'=,&'%3"3&:.$.$-' "23'"3:63&#"5&3'/,3==./.3$"',='"23'&3=3&3$/3';,+"#-3' !KC

S δ × K7 A v T7 = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA K 7 + 2 77 + 2 7S + K S 123&3'277'#$%'27S'%3$,"3'"23'.$/&3:3$"#+'&34.4"#$/34',='%.,%34'+7'#$%'+S0'&3463/".;3+

δ × K8 ∆! KS = ! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A [ K G ⁄ ( β + 7 ) ] + 2 67 + K 8 V3&3' KG' %3$,"34' "23' ","#+' &34.4"#$/3' .$' "23' @#43' /.&/5."0' #$%' 26$' %3$,"34' "23' 3:.""3&' &34.4"#$/3' ,= % 7 ' ( ! I_'Ω )C 'F2.4'/#+/5+#".,$'<.3+%4' ∆! KS ' ! ' ! δ C 'O%%.$-'"2.4';#+53'",'"2#"'%53'",'"23'-3$3&#",&'Sδ -.;34' ∆! i ' ! ! _C^ δ C 'F254'=,&'δ'= −S':fQ°(0'"23'"3:63&#"5&3'/,3==./.3$"',='!K'.4'+7CI':fQ°(C `3'$39"'/,$4.%3&'"23'%3"3&:.$#".,$',='"23'"3:63&#"5&3'/,3==./.3$"',='!"#C'F23'/.&/5."',$'12./2'",'63&A =,&:'"2.4'#$#+<4.4'.4'42,1$'.$'E.-C'7IC8IC'V3&3'13'2#;3'"2&33'-3$3&#",&4'12,43'/,$"&.@5".,$4'/#$'@3'/,$A 4.%3&3%'436#&#"3+<'#$%'"23'&345+".$-'/,:6,$3$"4',='∆!"#'45::3%C'F23'&345+"'.4 ! K ;S KO A ∆!"# ! ∆! K ' AAAAAAAAAAAAAAAAAAA ' AAAAAAAAAAAAAAAAAA 2 6K + K R K O + 2 6S ! K ;S KO A ! δ ' AAAAAAAAAAAAAAAAAAA ' AAAAAAAAAAAAAAAAAA 2 6K + K R K O + 2 6S KO ! δ ' AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA K O + 2 6S + K ;S ⁄ ( β + 7 ) !5@4"."5".$-'"23';#+534'-.;3$'#$%'"2,43',@"#.$3%'"2&,5-2,5"'"23'#$#+<4.4',='"2.4'43/".,$0'13'=.$% ∆! "# ' ! ' ! _CI8δ

14.4 Emitter-Coupled Logic (ECL)

F23'/.&/5."'=,&'%3"3&:.$.$-'"23'"3:63&#"5&3'/,3==./.3$"',='!".'.4'42,1$'.$'E.-C'7IC8Y0'=&,:'12./2'13 ,@"#.$ KO ∆! ". = ! δ ' AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 'd' ! _C]8δ K O + 2 6S + K ;S ⁄ ( β + 7 ) `3'$,1'/#$',@"#.$'"23';#&.#".,$',='"23':.%6,.$"',='"23'+,-./'41.$-'#4 ∆! "# + ∆! ". AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA '= ! _Cba δ S 12./2'.4'#66&,9.:#"3+<'3B5#+'",'"2#"',='"23'&3=3&3$/3';,+"#-3' !K ( ! _C^ δ )C ''

Figure 14.34 XB5.;#+3$"'/.&/5."'=,&'%3"3&:.$.$-'"23'"3:63&#"5&3'/,3==./.3$"',='!"#C

Figure 14.35 XB5.;#+3$"'/.&/5."'=,&'%3"3&:.$A .$-'"23'"3:63&#"5&3'/,3==./.3$"',='!".C

1189

1190 Chapter 14 Advanced MOS and Bipolar Logic Circuits

14.4.9 The Wired-OR Capability F23'3:.""3&c=,++,13&',5"65"'4"#-3',='"23'X(R'=#:.+<'#++,14'#$'#%%.".,$#+'+3;3+',='+,-./'", @3'63&=,&:3%'#"';3&<'+,1'/,4"'@<'4.:6+<'1.&.$-'"23',5"65"4',='43;3&#+'-#"34'.$'6#&#++3+C'F2.4 .4'.++54"&#"3%'.$'E.-C'7IC8b0'123&3'"23',5"65"4',='"1,'-#"34'#&3'1.&3%'",-3"23&C'H,"3'"2#"'"23 @#43c3:.""3&'%.,%34',='"23',5"65"'=,++,13&4'&3#+.T3'#$'*i'=5$/".,$>'F2.4'H);'@<9&'/,$$3/A ".,$'/#$'@3'543%'",'6&,;.%3'-#"34'1."2'2.-2'=#$A.$'#4'13++'#4'",'.$/&3#43'"23'=+39.@.+."<',= X(R'.$'+,-./'%34.-$C

Figure 14.36 F23'1.&3%A*i'/#6#@.+."<',=' X(RC

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14.5 BiCMOS Digital Circuits ?$'"2.4'43/".,$0'13'6&,;.%3'#$'.$"&,%5/".,$'",'#'f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1192 Chapter 14 Advanced MOS and Bipolar Logic Circuits VDD

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Figure 14.38 ?50-*0D67

F23'/.&/5."',='E.-C'7IC8^J#L',63&#"34'#4'=,++,14>'`23$'v,'.4'+,10'@,"2'%&'#$%'%.'#&3',== 12.+3'%''/,$%5/"4'#$%'4566+.34' %$'1."2'@#43'/5&&3$"0'"254'"5&$.$-'."',$C'F&#$4.4",&' %$'"23$ 6&,;.%34'#'+#&-3',5"65"'/5&&3$"'",'/2#&-3'"23'+,#%'/#6#/."#$/3C'F23'&345+"'.4'#';3&<'=#4"'/2#&-A .$-',='"23'+,#%'/#6#/."#$/3'#$%'/,&&346,$%.$-+<'#'42,&"'+,1A",A2.-2'6&,6#-#".,$'%3+#<0'-'#.C F&#$4.4",&'%$'"5&$4',=='123$'v"'&3#/234'#';#+53',='#@,5"'!++'−'!GR$0'#$%'"254'"23',5"65"'2.-2 +3;3+'.4'+,13&'"2#$'!++0'#'%.4#%;#$"#-3C'`23$'v ,'-,34'2.-20'%''#$%'%$'"5&$',==0'#$%'%&'"5&$4 ,$0'6&,;.%.$-'."4'%&#.$'/5&&3$"'.$",'"23'@#43',='%.C'F&#$4.4",&'%.'"23$'"5&$4',$'#$%'6&,;.%34'# +#&-3',5"65"'/5&&3$"'"2#"'B5./D+<'%.4/2#&-34'"23'+,#%'/#6#/."#$/3C'V3&3'#-#.$'"23'&345+"'.4'# 42,&"'2.-2A",A+,1'6&,6#-#".,$'%3+#<0'-'.#C'*$'"23'$3-#".;3'4.%30'%.'"5&$4',=='123$'v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`."2'v,'2.-20'#$%'#="3&'%S'/5"4',==0 v"'/,$".$534'",'=#++'@3+,1'!GRS0'#$%'"23',5"65"'$,%3'.4'65++3%'",'-&,5$%'"2&,5-2'"23'43&.34 6#"2',='%&'#$%'KSC'F254'KS'=5$/".,$4'#4'#'65++A%,1$'&34.4",&C'F23'%&cKS'6#"20'2,13;3&0'.4'# 2.-2A.:63%#$/3',$3'1."2'"23'&345+"'"2#"'65++.$-'v"'",'-&,5$%'.4'#'&#"23&'4+,1'6&,/344C'?$/,&A 6,&#".$-'"23'&34.4",&'K70'2,13;3&0'.4'%.4#%;#$"#-3,54'=&,:'#'4"#"./'6,13&A%.44.6#".,$'4"#$%A 6,.$">'`23$'v,'.4'+,10'#'%/'6#"2'39.4"4'@3"133$'!++'#$%'-&,5$%'"2&,5-2'"23'/,$%5/".$-'%' #$%'K7C'E.$#++<0'."'42,5+%'@3'$,"3%'"2#"'K7'#$%'KS'"#D3'4,:3',='"23'%&#.$'/5&&3$"4',='%''#$% %&'#1#<'=&,:'"23'@#434',='%7'#$%'%S'#$%'"254'4+.-2"+<'&3%5/3'"23'-#"3',5"65"'/5&&3$"'#;#.+A #@+3'",'/2#&-3'#$%'%.4/2#&-3'"23'+,#%'/#6#/."#$/3C

14.5 BiCMOS Digital Circuits 1193

E.-5&3'7IC8^J%L'42,14'"23'1#<'.$'12./2' K$'#$%'K.'#&3'545#++<'.:6+3:3$"3%C'O4'.$%.A /#"3%0'H)*!'%3;./34'%K$'#$%'%K.'#&3'543%'",'&3#+.T3'K$'#$%'K.C'O4'#$'#%%3%'.$$,;#".,$0 "2343'"1,'"&#$4.4",&4'#&3':#%3'",'/,$%5/"',$+<'123$'$33%3%C'F2540'%K$'1.++'/,$%5/"',$+< 123$'v,'&.4340'#"'12./2'".:3'."4'%&#.$'/5&&3$"'/,$4"."5"34'#'&3;3&43'@#43'/5&&3$"'=,&'%$0'4633%A .$-'56'."4'"5&$A,==C'!.:.+#&+<0'%K.'1.++'/,$%5/"',$+<'123$'v,'=#++4'#$%'%''/,$%5/"40'65++.$"23'-#"3',='%K.'2.-2C'F23'%&#.$'/5&&3$"',='%K.'"23$'/,$4"."5"34'#'&3;3&43'@#43'/5&&3$"'=,&'%.0 4633%.$-'56'."4'"5&$A,==C O4'#'=.$#+'/.&/5."'=,&'"23'Z.()*!'.$;3&"3&0'13'42,1'"23'4,A/#++3%'KA/.&/5."'.$'E.-C'7IC8^J3LC F2.4'/.&/5."'%.==3&4'=&,:'"2#"'.$'E.-C'7IC8^J/L'.$',$+<',$3'&3463/">'i#"23&'"2#$'&3"5&$.$-'K$'", -&,5$%0'13'2#;3'/,$$3/"3%'K$'",'"23',5"65"'$,%3',='"23'.$;3&"3&C'F2.4'4.:6+3'/2#$-3'2#4'"1, @3$3=."4C'E.&4"0'"23'6&,@+3:',='4"#"./'6,13&'%.44.6#".,$'.4'$,1'4,+;3%C'!3/,$%0'K$'$,1'=5$/A ".,$4'#4'#'65++A56'&34.4",&0'65++.$-'"23',5"65"'$,%3';,+"#-3'56'",'!++'J"2&,5-2'"23'/,$%5/".$%'L' #="3&' %$' 2#4' "5&$3%' ,==C' F2540' "23' K' /.&/5."' .$' E.-C' 7IC8^J3L' %,34' .$' =#/"' 2#;3' ,5"65" +3;3+4';3&<'/+,43'",'!++'#$%'-&,5$%C O4'#'=.$#+'&3:#&D',$'"23'Z.()*!'.$;3&"3&0'13'$,"3'"2#"'"23'/.&/5."'.4'%34.-$3%'4,'"2#" "&#$4.4",&4'%$'#$%'%.'#&3'$3;3&'4.:5+"#$3,54+<'/,$%5/".$-'#$%'$3."23&'.4'#++,13%'",'4#"5&#"3C K$=,&"5$#"3+<0'4,:3".:34'"23' &34.4"#$/3',='"23'/,++3/",&'&3-.,$',=' "23'Z[F'.$'/,$W5$/".,$ 1."2'+#&-3'/#6#/.".;3A/2#&-.$-'/5&&3$"4'/#5434'4#"5&#".,$'",',//5&C'!63/.=./#++<0'#"'+#&-3',5"A 65"'/5&&3$"40'"23';,+"#-3'%3;3+,63%'#/&,44'2;'J12./2'/#$'@3',='"23',&%3&',='7__'ΩL'/#$'+,13& "23';,+"#-3'#"'"23'.$"&.$4./'/,++3/",&'"3&:.$#+'#$%'/#543'"23'(Z['",'@3/,:3'=,&1#&%'@.#43%C O4'"23'&3#%3&'1.++'&3/#++0'4#"5&#".,$'.4'#'2#&:=5+'3==3/"'=,&'"1,'&3#4,$4>'?"'+.:."4'"23'/,++3/",& /5&&3$"'",'#';#+53'+344'"2#$'β,G0'#$%'."'4+,14'%,1$'"23'"&#$4.4",&'"5&$A,==C

14.5.2 Dynamic Operation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a0' 13' 42,1' 4.:6+.=.3%' 3B5.;#+3$"' /.&/5."4' "2#"' /#$' @3' 3:6+,<3%' .$ ,@"#.$.$-'&,5-2'34".:#"34',='-'#.'#$%'-'.#',='"23'KA"<63'Z.()*!'.$;3&"3&'J433'G&,@+3:'7ICI]LC

14.5.3 BiCMOS Logic Gates ?$'Z.()*!0'"23'+,-./'.4'63&=,&:3%'@<'"23'()*!'6#&"',='"23'-#"30'1."2'"23'@.6,+#&'6,&".,$ 4.:6+<' =5$/".,$.$-' #4' #$' ,5"65"' 4"#-3C' ?"' =,++,14' "2#"' Z.()*!' +,-./A-#"3' /.&/5."4' /#$' @3 -3$3&#"3%'=,++,1.$-'"23'4#:3'#66&,#/2'543%'.$'()*!C'O4'#$'39#:6+30'13'42,1'.$'E.-C'7IC8] #'Z.()*!'"1,A.$65"'HOHU'-#"3C O4'#'=.$#+'&3:#&D0'13'$,"3'"2#"'Z.()*!'"3/2$,+,-<'.4'#66+.3%'.$'#';#&.3"<',='6&,%5/"4 .$/+5%.$-':./&,6&,/344,&40'4"#"./'iO)40'#$%'-#"3'#&&#<4'J433'O+;#&3T0'7]]8LC

1194 Chapter 14 Advanced MOS and Bipolar Logic Circuits VDD

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Figure 14.39 XB5.;#+3$"'/.&/5."4'=,&'/2#&-.$-'#$%'%.4/2#&-.$-'#'+,#%'/#6#/."#$/3';C'H,"3'"2#"';'.$/+5%34' #++'"23'/#6#/."#$/34'6&343$"'#"'"23',5"65"'$,%3C

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EXERCISE D14.17

F23'"2&342,+%';,+"#-3',='"23'Z.()*!'.$;3&"3&',='E.-C'7IC8^J3L'.4'"23';#+53',='v,'#"'12./2'@,"2 %&'#$%'%''#&3'/,$%5/".$-'3B5#+'/5&&3$"4'#$%',63&#".$-'.$'"23'4#"5&#".,$'&3-.,$C'O"'"2.4';#+53',= v,0'%S'1.++'@3',$0'/#54.$-'"23';,+"#-3'#"'"23'4,5&/3',='%&'",'@3'#66&,9.:#"3+<'_C^'fC'?"'.4'&3B5.&3% ",'%34.-$'"23'/.&/5."'4,'"2#"'"23'"2&342,+%';,+"#-3'.4'3B5#+'",' !++ ⁄ S C'E,&'!++'='Y'f0' !- '= _Cb'f0'#$%'#445:.$-'3B5#+'/2#$$3+'+3$-"24'=,&'%&'#$%'%''#$%'"2#"'µ0'! SCY'µ10'=.$%'"23'&3B5.&3% &#".,',='1.%"240' $1 ⁄ $0 C Ans.,7

14.5 BiCMOS Digital Circuits

1195

Summary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−'!-C F23'()*!'"&#$4:.44.,$'-#"30'/,:6,43%',='"23'6#&#++3+ /,$$3/".,$' ,=' #$' H)*!' #$%' #' G)*!' "&#$4.4",&0' .4' # ;3&<'3==3/".;3'41."/2'.$'@,"2'#$#+,-'#$%'%.-."#+'#66+./#A ".,$4C'?"'6#4434'"23'3$".&33.$65"'4.-$#+'41.$-0'_'",'!++C'O4 13++0'."'2#4'#$'#+:,4"'/,$4"#$"'M,$N'&34.4"#$/3',;3&'"23 =5++',5"65"'&#$-3C

O'6#&"./5+#&'=,&:',='%<$#:./'+,-./'/.&/5."40'D$,1$'#4 U,:.$,' +,-./0' #++,14' "23' /#4/#%.$-' ,=' %<$#:./' +,-./ -#"34C X:.""3&A/,56+3%'+,-./'JX(RL'.4'"23'=#4"34"'/,::3&/.#++< #;#.+#@+3'+,-./A/.&/5."'=#:.+'X(R'7_l0'2#;.$-'-''='S'$40''+'='SY':`0'#$%''+' ='Y_'6[\'#$%'X(R'7__l0'2#;.$-'-''='_C^Y'$40''+'='I_':`0 #$%''+''='8_'6[C'X(R'7_l'.4'3#4.3&'",'543'@3/#543'"23 &.43'#$%'=#++'".:34',='."4'4.-$#+4'#&3'%3+.@3&#"3+<':#%3'+,$J#@,5"'8CY'$4LC Z3/#543',='"23';3&<'2.-2',63&#".$-'4633%4',='X(R0'/#&3 42,5+%'@3'"#D3$'.$'/,$$3/".$-'"23',5"65"',=',$3'-#"3'", "23' .$65"' ,=' #$,"23&C' F&#$4:.44.,$A+.$3' "3/2$.B534' #&3 545#++<'3:6+,<3%C F23'%34.-$',='"23'X(R'-#"3'.4',6".:.T3%'4,'"2#"'"23'$,.43 :#&-.$4' #&3' 3B5#+' #$%' &3:#.$' 3B5#+' #4' "3:63&#"5&3 /2#$-34C F23' X(R' -#"3' 6&,;.%34' "1,' /,:6+3:3$"#&<' ,5"65"40 &3#+.T.$-'"23'*i'#$%'H*i'=5$/".,$4C F23',5"65"4',='X(R'-#"34'/#$'@3'1.&3%'",-3"23&'",'&3#+A .T3'"23'*i'=5$/".,$',='"23'.$%.;.%5#+',5"65"';#&.#@+34C Z.()*!'/,:@.$34'"23'+,1A6,13&'#$%'1.%3'$,.43':#&A -.$4',='()*!'1."2'"23'2.-2'/5&&3$"A%&.;.$-'/#6#@.+."< J#$%'"254'"23'42,&"'-#"3'%3+#<4L',='Z[F4'",',@"#.$'#'"3/2A $,+,-<'"2#"'.4'/#6#@+3',='.:6+3:3$".$-';3&<'%3$430'+,1A 6,13&0' 2.-2A4633%' fR!?' /.&/5."4' "2#"' /#$' #+4,' .$/+5%3 #$#+,-'=5$/".,$4C

PROBLEMS

!"#$%&'() *+,#%,*+-) .&(*-+) /"&) '/"0&.) 1*23) 4) 23"#5-3#52 23&) 2&627) 8() 1&%%9) :"#$%&'() /"&) '/"0&.) 1*23) /(2&"*(0() 2# .&(;"*$&) 23&*") .&-"&&) #<) .*<<*;5%2=7) 4*<<*;5%2) :"#$%&'() /"& '/"0&.) 1*23) /+) /(2&"*(0) >?@A) '#"&) .*<<*;5%2) :"#$%&'() 1*23 21#) /(2&"*(0() >??@A) /+.) ,&"=) ;3/%%&+-*+-) /+.B#") 2*'&C;#+C (5'*+-):"#$%&'()1*23)23"&&)/(2&"*(0()>???@7

Section 14.1: Pseudo-NMOS Logic Circuits 14.1 D3&) :5":#(&)#<) 23*() :"#$%&') *()2#) ;#':/"&) 23&) ,/%5&

#<)!"#$)#$2/*+&.)1*23)/)"&(*(2*,&)%#/.)>(&&)E*-7)!FG7F/@)2#)23/2 #$2/*+&.)1*23)/);5""&+2H(#5";&)%#/.)>(&&)E*-7)!FG7F$@7)E#")/ ()#*+ N F7P7 S3/2)/"&)23&),/%5&()#<)> ( ⁄ # @, 9)&-# 9)&-$ 9)&. 9)&%$ 9)&%# 9)/.$ 9 /+. /.#T

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1201

CHAPTER 15

Memory Circuits

Introduction 15.1

1203

Latches and Flip-Flops

1204

15.2 Semiconductor Memories: Types and Architectures 1214 15.3 Random-Access Memory (RAM) Cells 1217

15.4 Sense Amplifiers and Address Decoders 1227 15.5 Read-Only Memory (ROM) Summary

1246

Problems

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1240

IN THIS CHAPTER YOU WILL LEARN: 1. How the basic bistable circuit, the latch, is realized by connecting two inverters in a positive-feedback loop. 2. How to augment the latch to obtain different types of flip-flops that are useful building blocks for digital systems. 3. How CMOS is particularly suited for the efficient implementation of a particular type of flip-flop, the D flip-flop. 4. How memory chips that contain as many as 4 gigabits are organized, as well as their various types and the terminology used to describe them. 5. The analysis and design of the six-transistor circuit that is almost universally used to implement the storage cell in static random access memory (SRAM) and the one-transistor circuit that is equally universal in the implementation of the storage cell in dynamic random access memory (DRAM). 6. Interesting circuit techniques for accessing a particular storage cell in a memory chip and for amplifying the signal readout from the cell. 7. How various types of read-only memory (ROM) are designed, programmed, erased, and reprogrammed.

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1206 Chapter 15 Memory Circuits @%(#0&')/''&*"#-2*C(#.(-0'#/'#$*#)*")./0(#$%-$#$%(#.-$)%#%-'#$,*#'$-2.(#*5(4-$&"6#5*&"$'+ :#-"0#D8#:$#5*&"$#D+#v6#&'#%&6%+#v9#&'#.*,+#v<#&'#.*,+#-"0#v7#&'#%&6%8#@%(#4(C(4'(#&'#$4/(#-$#5*&"$ :8#!7#,(#)*"'&0(4#9#-"0#7#-'#$%(#.-$)%#*/$5/$'+#,(#'((#$%-$#&"#*"(#*7#$%(#'$-2.(#'$-$('#>'-1#$%-$ )*44('5*"0&"6#$*#*5(4-$&"6#5*&"$#:?+# v9#&'#%&6%#>-$#=>??#-"0# v7#&'#.*,#>-$#=>@ ?8#!"#$%(#*$%(4 '$-$(#>)*44('5*"0&"6#$*#*5(4-$&"6#5*&"$#D?+#v9#&'#.*,#>-$#=>@ ?#-"0#v7#&'#%&6%#>-$#=>??8#@%/'#$%( .-$)%#&'#-#$%*('$)+#)&4)/&$#%-C&"6#$,*#)*35.(3("$-41#*/$5/$'8#@%(#'$-2.(#'$-$(# &"#,%&)%#$%( .-$)%#*5(4-$('#0(5("0'#*"#$%(#(N$(4"-.#(N)&$-$&*"#$%-$#7*4)('#&$#$*#$%(#5-4$&)/.-4#'$-$(8#@%(#.-$)% $%("#&%&"'-;%.#$%&'#(N$(4"-.#-)$&*"#21#'$-1&"6#&"0(7&"&$(.1#&"#$%(#-)I/&4(0#'$-$(8#:'#-#3(3G *41#(.(3("$#$%(#.-$)%#&'#)-5-2.(#*7#'$*4&"6#*"(#2&$#*7#&"7*43-$&*"8#;*4#&"'$-")(+#,(#)-"#-42&G $4-4&.1#0('&6"-$(#$%(#'$-$(#&"#,%&)%#v9#&'#%&6%#-"0#v7#&'#.*,#-'#)*44('5*"0&"6#$*#-#'$*4(0#.*6&) <8#@%(#*$%(4#)*35.(3("$-41#'$-$(#$%("#&'#0('&6"-$(0#21#-#'$*4(0#.*6&)#O8#;&"-..1+#,(#"*$(#$%-$ $%(#.-$)%#)&4)/&$#0(')4&2(0#&'#*7#$%(#'$-$&)#C-4&($18 !$#"*,#4(3-&"'#$*#0(C&'(#-#3()%-"&'3#21#,%&)%#$%(#.-$)%#)-"#2(# #'-AA%'%5#$*#)%-"6( '$-$(8#@%(#.-$)%#$*6($%(4#,&$%#$%(#$4&66(4&"6#)&4)/&$41#7*43'#-#3*-BC3*"B8#@%&'#,&..#2(#0&')/''(0 "(N$8#:"-.*6#2&'$-2.(#)&4)/&$'#/$&.&A&"6#*5#-35'#,&..#2(#54('("$(0#&"#D%-5$(4#
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1207

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1209

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1210 Chapter 15 Memory Circuits Example 15.1 continued

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_#Z,$=#$)&/-(.#*$,"#$,(:#$ # K?@ $9&*$,"#$&+,2+,$&9$,"#$ F 4\F 5 $(/8#*,#*?$ v F ?$,&$*(-#$9*&:$J$,&$= GG ⁄ P 6 !"#$81%+#$&9$ # K@? $)1/$<#$)1%)+%1,#.$+-(/'$,"#$2*&21'1,(&/$.#%17$9&*:+%1$.#*(8#.$(/$0"12,#*$34$EYD6 346\\F?$="()"$(-$1%-&$%(-,#.$(/$!1<%#$3464?$/1:#%7? α BH # K@? V NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN N +′B( 6 ⁄ @ ) B = GG ="#*# = #B P 4 = #B α B V P$$$ ^NNN \ NNNNNNNNNNNN N _ NNNNNNNNNN = GG 5 = GG C+<-,(,+,(/'$/+:#*()1%$81%+#-$=#$&<,1(/?$ P α B V NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNPN V P6J3 × J6O _ J6O NNNNNNN 36^O \ 4 NNNNNNNNNNNNNNNN 36] 36]

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EXERCISE 15.1

>&*$,"#$CQ$9%(2N9%&2$-2#)(9(#.$(/$YZ1:2%#$3O63?$9(/.$,"#$:(/(:+:06X@$9&*$<&,"$ F O $1/.$ F \ $-&$,"1, -=(,)"(/'$(-$1)"(#8#.$="#/$(/2+,-$D01/.$ φ $1*#$1,$ ( = GG ⁄ P )6 Ans. 3564

15.1.4 A Simpler CMOS Implementation of the Clocked SR Flip-Flop :#'&35.(4#&35.(3("$-$&*"#*7#-#).*)B(0#LR#7.&5G7.*5#&'#'%*,"#&"#;&68#<=8P8#M(4(+#5-''G$4-"'&'$*4 .*6&)#&'#(35.*1(0#$*#&35.(3("$#$%(#).*)B(0#'($\4('($#7/")$&*"'8#@%&'#)&4)/&$#&'#C(41#5*5/.-4 &"#$%(#0('&6"#*7#'$-$&)#4-"0*3G-))(''#3(3*41#>LR:Z?#)%&5'+#,%(4(#&$#&'#/'(0#-'#$%(#2-'&) 3(3*41#)(..#>L()$&*"#<=8[8
1211

1212 Chapter 15 Memory Circuits VDD

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1213

1214 Chapter 15 Memory Circuits

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15.2 Semiconductor Memories: Types and Architectures

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eHL!?# $15(8# !"0((0+# -$# -"1# 3*3("$+ 3(3*41#)%&5'#4(54('("$#$%(#'$-$(#*7#$%(#-4$#&"#5-)B&"6#0("'&$1#-"0#%(")(#&"$(64-$&*"#.(C(.8 9(6&""&"6#,&$%#$%(#&"$4*0/)$&*"#*7#$%(#KOOa?+#)%&5'#)*"$-&"&"6#[#J2&$<# -4(#-C-&.G -2.(8#!"#$%&'#-"0#$%(#"(N$#$,*#'()$&*"'+#,(#'%-..#'$/01#'*3(#*7#$%(#2-'&)#)&4)/&$'#(35.*1(0#&" eHL!#R:Z#)%&5'8#R(-0G*".1#3(3*41#)&4)/&$'#-4(#'$/0&(0#&"#L()$&*"#<=8=8

15.2.1 Memory-Chip Organization @%(#2&$'#*"#-#3(3*41#)%&5#-4(#-004(''-2.(#(&$%(4#&"0&C&0/-..1#*4#&"#64*/5'#*7#[#$*#<]8#:'#-" (N-35.(+#-#][GZ2&$#)%&5#&"#,%&)%#-..#2&$'#-4(#&"0&C&0/-..1#-004(''-2.(#&'#'-&0#$*#2(#*46-"&A(0 -'# ][Z# ,*40'# ×# <# 2&$# >*4# '&35.1# ][Z# ×# KK]# = ]P+<]Z ×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…? P $−3 6 #E%("#$%(#O$%#,*40#.&"( &'#-)$&C-$(0#7*4+#'-1+#-#/+'2."7+/'(%"&+#-..#KJ#)(..'#&"#4*,#O#,&..#54*C&0(#$%(&4#)*"$("$'#$*#$%(&4 4('5()$&C(#2&$#.&"('8#@%/'+#&7#$%(#)(..#&"#)*./3"#@#>;&68#<=8<
!"#$)121)(,7$&9$1$:#:&*7$)"(2$,&$"&%.$<(/1*7$(/9&*:1,(&/$1-$<(/1*7$.('(,-$E&*$<(,-F$(-$:#1-+*#.$(/ G(%&<(,$Ed<(,F?$:#'1<(,$ER<(,F?$1/.$'('1<(,$EU<(,F$+/(,-?$="#*#$3$d<(,$=$3JP5$<(,-?$3$R<(,$=$3JP5$×$3JP5 =$3?J5]?O^\$<(,-?$1/.?$3$U<(,$a$3JP54$<(,-6$!"+-$1$\5NR<(,$)"(2$)&/,1(/-$\^?3J]?]\5$<(,-$&9$:#:&*76

1215

1216 Chapter 15 Memory Circuits Bit line

Storage cell array

0 1

A1

Row decoder

Row address (M bits)

A0

K Word line

AM#1

Storage cell

2M#1 0

1

L

2N#1

Sense amplifiers / drivers

Column address (N bits)

AM AM$1

Column decoder

AM$N#1

I/O data Figure 15.11 K$P$QJN<(,$:#:&*7$)"(2$&*'1/(L#.$1-$1/$1**17$&9$P$$*&=-$×$PJ$)&%+:/-6

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…?$P $+J−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

15.3 Random-Access Memory (RAM) Cells

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b#4*,'+#)*./3"'+#-"0#2.*)B'8

15.2.2 Memory-Chip Timing @%(# #+#"/:. '!!+**. (%#+# &'# $%(# $&3(# 2($,(("# $%(# &"&$&-$&*"# *7# -# 4(-0# *5(4-$&*"# -"0# $%( -55(-4-")(# *7# $%(# */$5/$# 0-$-8# @%(# #+#"/:. !:!)+. (%#+# &'# $%(# 3&"&3/3# $&3(# -..*,(0 2($,(("# $,*# )*"'()/$&C(# 3(3*41# *5(4-$&*"'8# @*# 2(# *"# $%(# )*"'(4C-$&C(# '&0(+# -# 3(3*41 *5(4-$&*"#&'#/'/-..1#$-B("#$*#&")./0(#2*$%#4(-0#-"0#,4&$(#>&"#$%(#'-3(#.*)-$&*"?8#ZUL#3(3G *4&('#%-C(#-))(''#-"0#)1).(#$&3('#&"#$%(#4-"6(#*7#-#7(,#$*#-#7(,#%/"04(0#"-"*'()*"0'8

EXERCISES 15.2 K$5NR<(,$:#:&*7$)"(2$(-$21*,(,(&/#.$(/,&$4P$<%&)G-?$=(,"$#1)"$<%&)G$"18(/'$3JP5$*&=-$1/.$3P] )&%+:/-6$U(8#$,"#$/+:<#*$&9$<(,-$*#D+(*#.$9&*$,"#$*&=$1..*#--?$)&%+:/$1..*#--?$1/.$<%&)G$1..*#--6 Ans. 3JA$^A$O 15.3 !"#$=&*.$%(/#-$(/$1$21*,()+%1*$RIC$:#:&*7$)"(2$1*#$91<*()1,#.$+-(/'$2&%7-(%()&/$E-##$K22#/.(Z$KF6 !"#$*#-(-,1/)#$&9$#1)"$=&*.$%(/#$(-$#-,(:1,#.$,&$<#$O$GΩ?$1/.$,"#$,&,1%$)121)(,1/)#$<#,=##/$,"#$%(/# 1/.$'*&+/.$(-$P$2>6$>(/.$,"#$,(:#$9&*$,"#$8&%,1'#$&/$,"#$=&*.$%(/#$,&$*#1)"$ =GG ⁄ P ?$1--+:(/'$,"1,$,"# %(/#$(-$.*(8#/$<7$1$8&%,1'#$=GG$2*&8(.#.$<7$1$%&=N(:2#.1/)#$(/8#*,#*6$EJ"#%R$!"#$%(/#$(-$1),+1%%7$1 .(-,*(<+,#.$/#,=&*G$,"1,$=#$1*#$122*&Z(:1,(/'$<7$1$%+:2#.$)(*)+(,$)&/-(-,(/'$&9$1$-(/'%#$*#-(-,&*$1/. 1$-(/'%#$)121)(,&*6F Ans. ]8a#"'

15.3 Random-Access Memory (RAM) Cells :'#3("$&*"(0#&"#L()$&*"#<=8K+#$%(#3-W*4#5-4$#*7#$%(#3(3*41#)%&5#&'#$-B("#/5#21#$%(#'$*4-6( )(..'8#!$#7*..*,'#$%-$#$*#2(#-2.(#$*#5-)B#-#.-46(#"/32(4#*7#2&$'#*"#-#)%&5+#&$#&'#&35(4-$&C(#$%-$ $%(#)(..#'&A(#2(#4(0/)(0#$*#$%(#'3-..('$#5*''&2.(8#@%(#5*,(4#0&''&5-$&*"#5(4#)(..#'%*/.0#2( 3&"&3&A(0#-.'*8#@%/'+#3-"1#*7#$%(#7.&5G7.*5#)&4)/&$'#'$/0&(0#&"#L()$&*"#<=8<#-4(#$**#)*35.(N $*#2(#'/&$-2.(#7*4#&35.(3("$&"6#$%(#'$*4-6(#)(..'#&"#-#R:Z#)%&58 @%(4(# -4(# 2-'&)-..1# $,*# $15('# *7# ZUL# R:Zb# '$-$&)# -"0# 01"-3&)8# A('(%!. =B?*# >)-..(0 A=B?*#7*4#'%*4$?#/$&.&A(#'$-$&)#.-$)%('#-'#$%(#'$*4-6(#)(..'8#X1"-3&)#R:Z'#>)-..(0#C=B?*?+ *"#$%(#*$%(4#%-"0+#'$*4(#$%(#2&"-41#0-$-#*"#)-5-)&$*4'+#4('/.$&"6#&"#7/4$%(4#4(0/)$&*"#&"#)(..#-4(-+ 2/$#-$#$%(#(N5("'(#*7#3*4(#)*35.(N#4(-0#-"0#,4&$(#)&4)/&$418#!"#5-4$&)/.-4+#,%&.(#'$-$&)#R:Z' )-"#%*.0#$%(&4#'$*4(0#0-$-#&"0(7&"&$(.1+#54*C&0(0#$%(#5*,(4#'/55.1#4(3-&"'#*"+#01"-3&)#R:Z'

1217

1218 Chapter 15 Memory Circuits 4(I/&4(#B%'-"5-)0'%3'%.4-!A#$*#4(6("(4-$(#$%(#0-$-#'$*4(0#*"#)-5-)&$*4'8#@%&'#&'#2()-/'(#$%(#'$*4G -6(#)-5-)&$*4'#,&..#0&')%-46(+#$%*/6%#'.*,.1+#-'#-#4('/.$#*7#$%(#.(-B-6(#)/44("$'#&"(C&$-2.1 54('("$8#91#C&4$/(#*7#$%(&4#'3-..(4#)(..#'&A(+#01"-3&)#3(3*41#)%&5'#-4(#/'/-..1#7*/4#$&3('#-' 0("'(#-'#$%(&4#)*"$(35*4-41#'$-$&)#)%&5'8#@%/'#,%&.(#$%(#'$-$(#*7#$%(#-4$#&"#KOOa#&'#-#[GJ2&$ XR:Z#)%&5+#$%(#%&6%('$G0("'&$1#LR:Z#)%&5#%-'#<#J2&$#)-5-)&$18#9*$%#'$-$&)#-"0#01"-3&) R:Z'#-4(#N"*/#-*%S#$%-$#&'+#$%(1#4(I/&4(#$%(#)*"$&"/*/'#54('(")(#*7#-#5*,(4#'/55.18#91#)*"G $4-'$+#3*'$#RUZ'#-4(#*7#$%(#"*"C*.-$&.(#$15(+#-'#,(#'%-..#'((#&"#L()$&*"#<=8=8#!"#$%(#7*..*,G &"6#'/2'()$&*"'+#,(#'%-..#'$/01#2-'&)#LR:Z#-"0#XR:Z#'$*4-6(#)(..'8

15.3.1 Static Memory (SRAM) Cell ;&6/4(#<=82&$#*4#T? .&"(#-"0# )&%+:/ #> <(, #*4# T ?#.&"(8#T*$(#$%-$#-.$%*/6%#&"#54&")&5.(#*".1#$%(#T#*4#$%(# T #.&"( '/77&)('+#3*'$#*7$("#2*$%#-4(#/$&.&A(0+#-'#'%*,"#&"#;&68#<=8('6 3O6346$_&,(/'$,"1,$,"#$(/(,(1%$81%+#$&9$ v F $(-$J$[?$=#$)1/$-##$,"1,$)+**#/,$=(%%$9%&=$9*&:$,"#$ T Word line (W) VDD Q2 Q Q5 Q1

Bit line B Figure 15.12 K$0RIC$CQKR$:#:&*7$)#%%6

Q4 Q

Q6

Q3

Bit line B

15.3 Random-Access Memory (RAM) Cells

B line

vW " VDD vB I5 CB

Q5 CQ

vQ I1 Q1

vQ " VDD

Figure 15.13 Q#%#81/,$21*,-$&9$,"#$CQKR$)#%%$)(*)+(,$.+*(/'$1$*#1.$&2#*1,(&/$="#/$,"#$)#%%$(-$-,&*(/'$1 %&'()$ 36$ _&,#$ ,"1,$ (/(,(1%%7$ v F = = GG $ 1/.$ v F = J6 $ K%-&$ /&,#$ ,"1,$ ,"#$ T$ 1/.$ T $ %(/#-$ 1*#$ 2*#)"1*'#. ,& 1 8&%,1'#$ =GG 6

%(/#$E1),+1%%7?$9*&:$,"#$ T N%(/#$)121)(,1/)#$ H T F$,"*&+'"$ F O $1/.$(/,&$)121)(,&*$ H F ?$="()"$(,"#$-:1%%$#D+(81%#/,$)121)(,1/)#$<#,=##/$,"#$ F $/&.#$1/.$'*&+/.6$!"(-$)+**#/,$)"1*'#-$ H F 1/.$,"+-$ v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⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 $-&$,"1,$ = F ≤ = #! 6 _&,(/'$,"1,$ F O $=(%%$<#$&2#*1,(/'$(/$-1,+*1,(&/$1/.$/#'%#),(/'?$9&*$-(:2%()(,7?$,"#$<&.7 #99#),?$=#$)1/$=*(,# 3 6 P L O V NNN ( µ ! H ": ) NNNNN ( = GG \ = #! \ = F ) P @ O

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!*1/-(-,&*$ F 3 $=(%%$<#$&2#*1,(/'$(/$,"#$,*(&.#$*#'(&/?$1/.$(,-$)+**#/,$ L 3 $)1/$<#$=*(,,#/$1-$ 6 L 3 V ( µ ! H ": ) NNNNN @

3

3 P ( = GG \ = #! )= F \ NNN = F P

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YD+1,(/'$ L O $1/.$ L 3 $'(8#-$1$D+1.*1,()$#D+1,(&/$(/$ = F ? $="()"$)1/$<#$-&%8#.$,&$&<,1(/ =F (6 ⁄ @) NNNNNNNNNNNNNNNNNNNNNNN V 3 \ 3 ⁄ 3 _ NNNNNNNNNNNNNNNNNNON = GG \ = #! ( 6 ⁄ @ )3

$E3O64F

!"(-$(-$1/$1,,*1),(8#$*#%1,(&/-"(2?$-(/)#$(,$2*&8(.#-$ = F $(/$/&*:1%(L#.$9&*:$1/.$,"+-$1%=17122%(#-?$(/.#2#/.#/,$&9$,"#$2*&)#--$,#)"/&%&'7$+,(%(L#.6$>('+*#$3O635$-"&=-$1$+/(8#*-1%$2%&, c &9$ [ = F ⁄ ( = GG \ = #! ) ] $ 8#*-+-$ ( 6 ⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 6 $ >&*$ 1$ '(8#/$ 2*&)#--$ ,#)"/&%&'7?$ = GG $ 1/. = #! $1*#$.#,#*:(/#.?$1/.$,"#$2%&,$(/$>('6$3O635$)1/$<#$+-#.$,&$.#,#*:(/#$,"#$:1Z(:+:$81%+# 2#*:(,,#.$9&*$ ( 6 ⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 $="(%#$G##2(/'$ = F $<#%&=$1$.#-(*#.$81%+#6$K%,#*/1,(8#%7?$=#

1219

1220 Chapter 15 Memory Circuits

(

VQ– VDD – Vtn

( 0.5 0.4 0.3 0.2 0.1

0

1

2

3

4 (W/L) 5 (W/L)1

Figure 15.14 !"#$/&*:1%(L#.$81%+#$&9$ = F $8#*-+-$,"#$*1,(&$E6X@FOXE6X@F3$9&*$,"#$)(*)+(,$(/$>('6$3O6346$!"('*12"$)1/$<#$+-#.$,&$.#,#*:(/#$,"#$:1Z(:+:$81%+#$2#*:(,,#.$9&*$E6X@FOXE6X@F3$-&$,"1,$ = F $(-$G#2,$<#%&=$1 .#-(*#.$%#8#%6

)1/$.#*(8#$1$9&*:+%1$9&*$,"(-$2+*2&-#6$>&*$(/-,1/)#?$(9$ = F $(-$,&$<#$G#2,$<#%&=$ = #! ? $,"#$*1,(& &9$ ( 6 ⁄ @ ) O $,&$ ( 6 ⁄ @ ) 3 $:+-,$<#$G#2,$<#%&=$,"#$81%+#$&<,1(/#.$9*&:$YD6$E3O64F?$,"1,$(-? (6 ⁄ @) 3 NNNNNNNNNNNNNNNNNNON ≤ NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN N\3 P ( 6 ⁄ @ )3 = #! 3 \ NNNNNNNNNNNNNNNNNNNNNNN = GG \ = #!

$E3O65F

!"(-$(-$1/$(:2&*,1/,$.#-('/$)&/-,*1(/,$,"1,$)1/$<#$#Z2*#--#.$(/$1$-%('",%7$:&*#$'#/#*1%$9&*: <7$*#2%1)(/'$ ( 6 ⁄ @ ) O $=(,"$ ( 6 ⁄ @ ) / ? $="#*#$,"#$-+<-)*(2,$/$.#/&,#-$1))#--$,*1/-(-,&*-$ F O $1/. F \ ?$1/.$ ( 6 ⁄ @ ) 3 $=(,"$ ( 6 ⁄ @ ) ! ? $="()"$(-$,"#$6I@$*1,(&$&9$ F J $(/$#1)"$&9$,"#$,=&$(/8#*,#*-A ,"+-? (6 ⁄ @) 3 NNNNNNNNNNNNNNNNNN/N ≤ NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN N \3 P ( 6 ⁄ @ )! = #! 3 \ NNNNNNNNNNNNNNNNNNNNNN N = GG \ = #!

$E3O6OF

EXERCISE 15.4 >(/.$,"#$:1Z(:+:$1%%&=1<%#$6X@$9&*$,"#$1))#--$,*1/-(-,&*-$&9$,"#$CQKR$)#%%$(/$>('6$3O63P$-&$,"1, (/$1$*#1.$&2#*1,(&/?$,"#$8&%,1'#-$1,$F$1/.$ F $.&$/&,$)"1/'#$<7$:&*#$,"1/$ = # 6 $K--+:#$,"1,$,"# CQKR$(-$91<*()1,#.$(/$1$J63]Nµ:$,#)"/&%&'7$9&*$="()"$ = GG V 36]$[? $ = #! V = #B V J6O$[ $1/. ,"1,$ ( 6 ⁄ @ ) ! V 36O6 Ans. ( 6 ⁄ @ ) / ≤ P6O

15.3 Random-Access Memory (RAM) Cells

vW

VDD

0

v Q–

0

vQ

VDD

vB

VDD

v B–

VDD

&Vtn

%V %t

Figure 15.15 [&%,1'#$=18#9&*:-$1,$81*(&+-$/&.#-$(/$,"#$CQKR$)#%%$.+*(/'$1$*#1.N3$&2#*1,(&/6

W18(/'$ .#,#*:(/#.$ ,"#$)&/-,*1(/,$ (:2&-#.$<7$ ,"#$ *#1.$&2#*1,(&/$&/$ ,"#$ 6X@$*1,(&-$&9$ ,"# 1))#--$,*1/-(-,&*-?$=#$/&=$*#,+*/$,&$,"#$)(*)+(,$(/$>('6$3O634?$1/.$-"&=$(/$>('6$3O63O$,"#$8&%,N 1'#$=18#9&*:-$1,$81*(&+-$/&.#-$.+*(/'$1$*#1.N3$&2#*1,(&/6$I<-#*8#$,"1,$1-$=#$"18#$1%*#1.7? .(-)+--#.?$ v F $*(-#-$9*&:$L#*&$,&$1$8&%,1'#$ = F ≤ = #! 6 $0&**#-2&/.(/'%7?$,"#$)"1/'#$(/$ v F $=(%% <#$8#*7$-:1%%?$e+-,(97(/'$,"#$1--+:2,(&/$(:2%()(,$(/$,"#$1/1%7-(-$1<&8#$,"1,$ v F $*#:1(/-$)&/N -,1/,$1,$ = GG 6 $R&-,$(:2&*,1/,?$/&,#$,"1,$,"#$8&%,1'#$&9$,"#$ T $%(/#?$ v T ? $.#)*#1-#-$<7$1$-:1%% 1:&+/,$ ∆=6 $!"(-$(-$1$*#-+%,$&9$,"#$.(-)"1*'#$&9$,"#$)121)(,1/)#$&9$,"#$ T $%(/#?$ H T ? $<7$,"# )+**#/,$ L O 6 $K--+:(/'$,"1,$ L O $*#1)"#-$(,-$#D+(%(<*(+:$81%+#$(/$YD6$E3O63F$*#%1,(8#%7$D+()G%7? )121)(,&*$ H T $(-$(/$#99#),$.(-)"1*'#.$<7$1$)&/-,1/,$)+**#/,$ L O $1/.$,"#$)"1/'#$(/$(,-$8&%,1'#? ∆=? $&<,1(/#.$(/$1$,(:#$(/,#*81%$ ∆#? $)1/$<#$9&+/.$<7$=*(,(/'$1$)"1*'#N<1%1/)#$#D+1,(&/? L O ∆# V H T ∆=

!"+-? L O ∆# ∆= V NNNNNNNNN HT

$E3O6\F

W#*#$=#$/&,#$,"1,$ H T $(-$+-+1%%7$*#%1,(8#%7$%1*'#$E3`P$2>F$<#)1+-#$1$%1*'#$/+:<#*$&9$)#%%-$1*# )&//#),#.$,&$,"#$ T $%(/#6$!"#$(/)*#:#/,1%$)"1/'#$ ∆= $(-$,"#*#9&*#$*1,"#*$-:1%%$EJ63`J6P$[F? /#)#--(,1,(/'$,"#$+-#$&9$1$-#/-#$1:2%(9(#*6$;9$,"#$-#/-#$1:2%(9(#*$*#D+(*#-$1$:(/(:+:$.#)*#N :#/,$ ∆= $(/$ v T $,&$.#,#),$,"#$2*#-#/)#$&9$1$f3g?$,"#/$,"#$*#1.$.#%17$,(:#$)1/$<#$9&+/.$9*&: YD6$E3O6\F$1H T ∆= ∆# V NNNNNNNNNNNNNNNN N LO

$E3O6^F

1221

1222 Chapter 15 Memory Circuits !"(-$ #D+1,(&/$ (/.()1,#-$ ,"#$ /##.$ 9&*$ 1$ *#%1,(8#%7$ %1*'#$ L O $ ,&$ *#.+)#$ ,"#$ .#%17$ ,(:#$ ∆#6 $ K %1*'#$ L O ? $ "&=#8#*?$ (:2%(#-$ -#%#),(/'$ ( 6 ⁄ @ ) / $ /#1*$ ,"#$ +22#*$ <&+/.$ '(8#/$ <7$ YD6$ E3O6OF? ="()"$(/$,+*/$:#1/-$1/$(/)*#1-#$(/$,"#$-(%()&/$1*#1$&))+2(#.$<7$,"#$1))#--$,*1/-(-,&*-$1/. "#/)#$,"#$)#%%$1*#1?$1/$(/,#*#-,(/'$.#-('/$,*1.#N&996$

EXERCISE 15.5 >&*$,"#$CQKR$)#%%$)&/-(.#*#.$(/$YZ#*)(-#$3O65$="&-#$ ( 6 ⁄ @ ) ! V 36O $1/.$ ( 6 ⁄ @ ) / ≤ P6O? $+-# YD6$E3O6^F$,&$.#,#*:(/#$,"#$*#1.$.#%17$ ∆# $(/$,=&$)1-#-H$E1F$ ( 6 ⁄ @ ) / V P6O $1/.$E $1/.$,"1,$,"#$-#/-#$1:2%(9(#*$*#N D+(*#-$1$ ∆= $&9$:(/(:+:$:1'/(,+.#$&9$J6P$[6$h?-!#H$i-#$YD6$E3O63F$,&$.#,#*:(/#$ L O ? $1/.$*#)1%%$,"1, = F V = #!6j Ans. 36^$/-A$P6]$/-

M#$)&/)%+.#$&+*$.(-)+--(&/$&9$,"#$*#1.$&2#*1,(&/$=(,"$,=&$*#:1*G-H 1. :.$%*/6%#,(#)*"'&0(4(0#*".1#$%(#4(-0G<#*5(4-$&*"+#$%(#4(-0GO#*5(4-$&*"#&'#&0("$&)-.F#&$ &"C*.C('# F P #-"0# F \ #,&$%#$%(#-"-.1'&'#4('/.$&"6#&"#-"#/55(4#2*/"0#*"# ( 6 ⁄ @ ) \ ⁄ ( 6 ⁄ @ ) P (I/-.#$*#$%-$#,(#%-C(#7*/"0#7*4# ( 6 ⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 6 #@%&'+#*7#)*/4'(+#&'#("$&4(.1#(N5()$(0+ '&")(#$%(#)&4)/&$#&'#'133($4&)-.8#@%(#4(-0GO#*5(4-$&*"#4('/.$'#&"#-#0()4(3("$# ∆= #&"#$%( C*.$-6(#*7#$%(#T#.&"(+#,%&)%#&'#&"$(454($(0#21#$%(#'("'(#-35.&7&(4#-'#-#'$*4(0#O8# 2. !"#$)&:2&/#/,$ ∆# $&9$,"#$*#1.$.#%17$(-$*#%1,(8#%7$%1*'#$<#)1+-#$ H T $1/.$ H T $1*#$*#%1N ,(8#%7$%1*'#$E(/$,"#$2()&91*1.$*1/'#F6$K%-&?$ ∆# $(-$/&,$,"#$&/%7$)&:2&/#/,$&9$,"#$*#1. .#%17A$1/&,"#*$-('/(9()1/,$)&:2&/#/,$(-$.+#$,&$,"#$9(/(,#$*(-#$,(:#$&9$,"#$8&%,1'#$&/ ,"#$=&*.$%(/#6$ ;/.##.?$#8#/$ ,"#$)1%)+%1,(&/$ &9$ ∆# $ (-$&2,(:(-,()?$-(/)#$,"#$ =&*.$%(/# =(%%$"18#$*#1)"#.$1$8&%,1'#$%&=#*$,"1/$ = GG $&/%7?$="#/$,"#$2*&)#--$&9$.(-)"1*'(/' H T $,1G#-$2%1)#6$K-$=(%%$<#$-##/$-"&*,%7?$,"#$=*(,#$&2#*1,(&/$(-$91-,#*6 The Write Operation M#$/#Z,$)&/-(.#*$,"#$=*(,#$&2#*1,(&/6$@#,$,"#$CQKR$)#%%$&9$>('6 3O63P$<#$-,&*(/'$1$%&'()$3?$,"+-$ = F V = GG $1/.$ = F V J$[? $1/.$1--+:#$,"1,$=#$=(-"$,&$=*(,# 1$JA$,"1,$(-?$=#$=(-"$,&$"18#$,"#$9%(2N9%&2$-=(,)"$-,1,#-6$!&$=*(,#$1$L#*&?$,"#$T$%(/#$(-$%&=#*#. ,&$J$[?$1/.$,"#$ T $%(/#$(-$*1(-#.$,&$ = GG $1/.?$&9$)&+*-#?$,"#$)#%%$(-$-#%#),#.$<7$*1(-(/'$,"#$=&*. %(/#$,&$ = GG 6 $!"#$&('+*#$3O63\$-"&=-$,"#$*#%#81/,$21*,-$&9$,"#$CQKR$)(*)+(,$.+*(/'$,"#$(/,#*81%$="#/$ v F $(<#(/'$2+%%#.$+2$E>('6$3O63\1F$1/.$ v F $(-$<#(/'$2+%%#.$.&=/$E>('6$3O63\
15.3 Random-Access Memory (RAM) Cells

VDD v W = VDD I5

VDD

Q4 v W = VDD

0V

Q5

I1

C Q–

vQ

v Q–

Q1

I4

0V

Q6 I6 CQ

VDD

B – B

(a)

(b)

Figure 15.16 Q#%#81/,$21*,-$&9$,"#$\!$CQKR$)(*)+(,$&9$>('6$3O63P$.+*(/'$,"#$2*&)#--$&9$=*(,(/'$1$J6$;,$(-$ 1--+:#.$,"1,$,"#$)#%%$(-$&*('(/1%%7$-,&*(/'$1$3$1/.$,"+-$(/(,(1%%7$vF a =GG$1/.$ v F V J [6

0&/-(.#*$9(*-,$,"#$)(*)+(,$(/$>('6$3O63\E1F6$!"(-$(-$,"#$-1:#$)(*)+(,$=#$1/1%7L#.$(/$.#,1(%$(/ ,"#$-,+.7$&9$,"#$*#1.$&2#*1,(&/$1<&8#6$Q#)1%%$,"1,$,&$:1G#$,"#$*#1.$2*&)#--$/&/.#-,*+),(8#? =#$(:2&-#.$1/$+22#*$<&+/.$&/$ ( 6 ⁄ @ ) O 6 $!"1,$+22#*$<&+/.$#/-+*#.$,"1,$ v F $=(%%$/&,$*(-# 1<&8#$ = #! 6 $!"+-?$,"(-$)(*)+(,$(-$/&,$)121<%#$&9$*1(-(/'$ v F $,&$,"#$2&(/,$,"1,$(,$)1/$-,1*,$,"# *#'#/#*1,(8#$1),(&/6$M#$:+-,$,"#*#9&*#$*#%7$-&%#%7$&/$,"#$)(*)+(,$&9$>('6$3O63\E('6$3O63\E
$E3O6]F

1/. 6 L \ V ( µ ! H ": ) NNNNN @

\

3 P ( = GG \ = #! )= F \ NNN = F P

$E3O6bF

C+<-,(,+,(/'$ = #B V = #! ? $="()"$(-$+-+1%%7$,"#$)1-#?$1/.$#D+1,(/'$ L 5 $1/.$ L \ $*#-+%,-$(/$1$D+1N .*1,()$#D+1,(&/$(/$ = F $="&-#$-&%+,(&/$(-

µB ( 6 ⁄ @ ) =F NNNNNNNNNNNNNNNNNNNNNN N V 3 \ 3 \ NNNNN NNNNNNNNNNNNNNNNNN5N = GG \ = #! µ! ( 6 ⁄ @ )\

$E3O63JF

!"(-$ *#%1,(&/-"(2$ (-$ /&,$ 1-$ )&/8#/(#/,$ 1-$ ,"1,$ (/$ YD6$ E3O64F$ <#)1+-#$ ,"#$ *('",N"1/.$ -(.# (/)%+.#-$1$2*&)#--N.#2#/.#/,$D+1/,(,7?$/1:#%7?$ µ B ⁄ µ ! 6 $!"+-$=#$.&$/&,$"18#$1$+/(8#*-1%%7

1223

1224 Chapter 15 Memory Circuits

(

VQ VDD – Vtn

(

0.5 0.4 0.3 0.2 0.1

0

1

2

3

4

(W/L)4 (W/L)6

Figure 15.17 !"#$/&*:1%(L#.$81%+#$&9$=F$8#*-+-$,"#$*1,(&$E6X@F5XE6X@F\$9&*$,"#$)(*)+(,$(/$>('6$3O63\E
122%()1<%#$*#%1,(&/-"(26$_#8#*,"#%#--?$9&*$1$/+:<#*$&9$0RIC$2*&)#--$,#)"/&%&'(#-?$(/)%+.N (/'$,"#$J6PONµ:?$,"#$J63]Nµ:?$1/.$,"#$J634Nµ:$2*&)#--#-?$ µ ! ⁄ µ B " 5 6 $!"+-?$+2&/$-+<-,(,+,N (/'$ µ B ⁄ µ ! V J6PO $(/$YD6$E3O63JF?$=#$&<,1(/$,"#$-#:(+/(8#*-1%$'*12"$-"&=/$(/$>('6$3O63^6 M#$ )1/$ +-#$ ,"(-$ '*12"$ ,&$ .#,#*:(/#$ ,"#$ :1Z(:+:$ 1%%&=1<%#$ 81%+#$ &9$ ,"#$ *1,(& ( 6 ⁄ @ ) 5 ⁄ ( 6 ⁄ @ ) \ $,"1,$=(%%$#/-+*#$1$81%+#$&9$ = F ≤ = #! $9&*$'(8#/$2*&)#--$21*1:#,#*-$ = GG $1/. = #! 6 $K%,#*/1,(8#%7?$-+<-,(,+,(/'$ = F V = #! ? $ ( 6 ⁄ @ ) 5 V ( 6 ⁄ @ ) B ? $1/.$( 6 ⁄ @ ) \ V ( 6 ⁄ @ ) / ? $=# )1/$&<,1(/$,"#$+22#*$<&+/.$1/1%7,()1%%7$1-

µ (6 ⁄ @) NNNNNNNNNNNNNNNNNNBN ≤ NNNN!N ( 6 ⁄ @ )/ µB

= #! 3 \ 3 \ NNNNNNNNNNNNNNNNNNNNNN N = GG \ = #!

P

$E3O633F

I<-#*8#$,"1,$,"(-$*#%1,(&/-"(2$2*&8(.#-$1/$+22#*$<&+/.$&/$ ( 6 ⁄ @ ) B $(/$,#*:-$&9$ ( 6 ⁄ @ ) / $1/. ,"1,$,"#$*#%1,(&/-"(2$(/$YD6$E3O6OF$2*&8(.#-$1/$+22#*$<&+/.$&/$ ( 6 ⁄ @ ) / $(/$,#*:-$&9$ ( 6 ⁄ @ ) ! 6 !"+-?$,"#$,=&$*#%1,(&/-"(2-$)1/$<#$+-#.$,&'#,"#*$,&$.#-('/$,"#$CQKR$)#%%6

EXERCISE 15.6 >&*$,"#$CQKR$)#%%$)&/-(.#*#.$(/$YZ#*)(-#$3O65?$="#*#$ ( 6 ⁄ @ ) ! V 36O $1/.$ ( 6 ⁄ @ ) / ≤ P6O ? $+-# YD6$E3O633F$,&$9(/.$,"#$:1Z(:+:$1%%&=1<%#$81%+#$&9$ ( 6 ⁄ @ ) B 6 $Q#)1%%$,"1,$9&*$,"(-$J63]Nµ:$2*&)#--? µ B " 5 µ ! 6 $>&*$1%%$,*1/-(-,&*-$"18(/'$@$a$J63]$µ:?$9(/.$6 ! ? $6 B ?$1/.$ 6 / $,"1,$*#-+%,$(/$1$:(/(:+:N 1*#1$)#%%6$K--+:#$,"1,$,"#$:(/(:+:$1%%&=1<%#$=(.,"$(-$J63]$µ:6 Ans. ( 6 ⁄ @ ) B ≤ P6O ( 6 ⁄ @ ) / ? $ ,"+-$ ( 6 ⁄ @ ) B ≤ \6POA $ 9&*$ :(/(:+:$ 1*#1$ -#%#),$ 6 ! V 6 B V 6 / V J63]$µ:6

15.3 Random-Access Memory (RAM) Cells

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

15.3.2 Dynamic Memory Cell :.$%*/6%#-#C-4&($1#*7#XR:Z#'$*4-6(#)(..'#%-C(#2(("#54*5*'(0#*C(4#$%(#1(-4'+#-#5-4$&)/.-4 )(..+#'%*,"#&"#;&68#<=8<`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

Word line

Q CS Bit line Cell

Figure 15.18 !"#$&/#N,*1/-(-,&*$.7/1:()$QKR$ESQKRF$)#%%6 P

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1225

1226 Chapter 15 Memory Circuits

CS

CB

Figure 15.19 M"#/$ ,"#$ 8&%,1'#$ &9$ ,"#$ -#%#),#.$ =&*.$ %(/#$ (*1(-#.?$,"#$,*1/-(-,&*$)&/.+),-?$,"+-$)&//#),(/'$,"#$-,&*1'#$)121)(,&* HD$,&$,"#$<(,N%(/#$)121)(,1/)#$HTV

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=GG =GG N = ( H T + H D ) NNNNNNNN N + ∆= H D =HD + H T NNNNNNNN P P 74*3#,%&)%#,(#)-"#*2$-&"#7*4#∆=

HD =GG N =HD \ NNNNNNNN ∆= = NNNNNNNNNNNNNNNNNN HT + HD P

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15.4 Sense Amplifiers and Address Decoders

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
EXERCISES 15.7$ ;/$1$21*,()+%1*$.7/1:()$:#:&*7$)"(2?$HD$=$4J$9>?$HT$=$J64$2>?$1/.$=GG$=$36P$[6$>(/.$,"#$&+,2+, *#1.&+,$8&%,1'#$9&*$1$-,&*#.$3$1/.$1$-,&*#.$J6$Q#)1%%$,"1,$(/$1$*#1.$&2#*1,(&/?$,"#$<(,$%(/#-$1*#$2*#N )"1*'#.$,&$ =GG ⁄ P 6 Ans. \J$:[A$`\J$:[ 15.8 K$\5NR<(,$SQKR$)"(2$91<*()1,#.$(/$1$J65Nµ:$0RIC$,#)"/&%&'7$*#D+(*#-$P$µ:P$2#*$)#%%6$;9$,"# -,&*1'#$1**17$(-$-D+1*#?$#-,(:1,#$(,-$.(:#/-(&/-6$>+*,"#*?$(9$,"#$2#*(2"#*1%$)(*)+(,*7$E#6'6?$-#/-#$1:N 2%(9(#*-?$.#)&.#*-F$1..-$1<&+,$4Jk$,&$,"#$)"(2$1*#1?$#-,(:1,#$,"#$.(:#/-(&/-$&9$,"#$*#-+%,(/'$)"(26 Ans. <<8]#33#×#<<8]#33F#
15.4 Sense Amplifiers and Address Decoders M-C&"6#'$/0&(0#$%(#)&4)/&$'#)*33*".1#/'(0#$*#&35.(3("$#$%(#'$*4-6(#)(..'#&"#LR:Z'#-"0 XR:Z'+#,(#"*,#)*"'&0(4#'*3(#*7#$%(#*$%(4#&35*4$-"$#)&4)/&$#2.*)B'#&"#-#3(3*41#)%&58#@%( 0('&6"#*7#$%('(#)&4)/&$'+#)*33*".1#4(7(44(0#$*#-'#$%(##+#"/:.7+/%7G+/').!%/!-%(*+#54('("$' (N)&$&"6#)%-..("6('#-"0#*55*4$/"&$&('#$*#&"$(64-$(0G)&4)/&$#0('&6"(4'b#!354*C&"6#$%(#5(47*4G 3-")(#*7#5(4&5%(4-.#)&4)/&$'#)-"#4('/.$#&"#0("'(4#-"0#7-'$(4#3(3*41#)%&5'#$%-$#0&''&5-$(#.('' 5*,(48

15.4.1 The Sense Amplifier T(N$#$*# $%(#'$*4-6(#)(..'+#$%(# '("'(# -35.&7&(4# &'#$%(# 3*'$#)4&$&)-.# )*35*"("$#&"#-#3(3*41 )%&58#L("'(#-35.&7&(4'#-4(#(''("$&-.#$*#$%(#54*5(4#*5(4-$&*"#*7#XR:Z'+#-"0#$%(&4#/'(#&"#LR:Z' 4('/.$'#&"#'5((0#-"0#-4(-#&354*C(3("$'8 :# C-4&($1# *7# '("'(G-35.&7&(4# 0('&6"'# -4(# &"# /'(+# '*3(# *7# ,%&)%# ).*'(.1# 4('(32.(# $%( -)$&C(G.*-0#ZUL#0&77(4("$&-.#-35.&7&(4#'$/0&(0#&"#D%-5$(4#`8#M(4(+#,(#7&4'$#0(')4&2(#-#0&77(4G ("$&-.#'("'(#-35.&7&(4#$%-$#(35.*1'#5*'&$&C(#7((02-)B8#9()-/'(#$%(#)&4)/&$#&'#0&77(4("$&-.+#&$ )-"#2(#(35.*1(0#0&4()$.1#&"#LR:Z'+#,%(4(#$%(#LR:Z#)(..#/$&.&A('#2*$%#$%(#T#-"0#T#.&"('8 U"#$%(#*$%(4#%-"0+#$%(#*"(G$4-"'&'$*4#XR:Z#)&4)/&$#,(#'$/0&(0#&"#L()$&*"#<=8S8K#&'#-#'&"6.(G ("0(0#)&4)/&$+#/$&.&A&"6#*"(#2&$#.&"(#*".18#@%(#XR:Z#)&4)/&$+#%*,(C(4+#)-"#2(#3-0(#$*#4('(3G 2.(# -# 0&77(4("$&-.# '&6"-.# '*/4)(# $%4*/6%# $%(# /'(# *7# $%(# c0/331G)(..d# $()%"&I/(+# ,%&)%# ,(

1227

1228 Chapter 15 Memory Circuits '%-..#0&')/''#'%*4$.18#@%(4(7*4(+#,(#'%-..#-''/3(#$%-$#$%(#3(3*41#)(..#,%*'(#*/$5/$#&'#$*#2( -35.&7&(0#0(C(.*5'#-#0&77(4(")(#*/$5/$#C*.$-6(#2($,(("#$%(#T#-"0#T#.&"('8#@%&'#'&6"-.+#,%&)% )-"#4-"6(#74*3#SO#3e#$*#=OO#3e#0(5("0&"6#*"#$%(#3(3*41#$15(#-"0#)(..#0('&6"+#,&..#2( -55.&(0#$*#$%(#&"5/$#$(43&"-.'#*7#$%(#'("'(#-35.&7&(48#@%(#'("'(#-35.&7&(4#&"#$/4"#4('5*"0'#21 54*C&0&"6#-#7/..G',&"6#>O#$*#=GG?#'&6"-.#-$#&$'#*/$5/$#$(43&"-.'8#@%(#5-4$&)/.-4#-35.&7&(4#)&4)/&$ ,(#'%-..#0&')/''#%(4(#%-'#-#4-$%(4#/"/'/-.#54*5(4$1b# L#.0"2#B2#0/!50-!B2#0#%'&-!/*.0/'%0#4% ./&%W A Sense Amplifier with Positive Feedback >('+*#$ 3O6PJ$ -"&=-$ ,"#$ -#/-#$ 1:2%(9(#* ,&'#,"#*$=(,"$-&:#$&9$,"#$&,"#*$)&%+:/$)(*)+(,*7$&9$1$QKR$)"(26$_&,#$,"1,$,"#$-#/-#$1:2%(9(#* (-$/&,"(/'$<+,$,"#$91:(%(1*$%1,)"$9&*:#.$<7$)*&--N)&+2%(/'$,=&$0RIC$(/8#*,#*-H$I/#$(/8#*,#*

Word line Selected cell Cell

VDD Q6

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vB Differential sense amplifier

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Figure 15.20 K$ .(99#*#/,(1%$ -#/-#$ 1:2%(9(#*$ )&//#),#.$ ,&$ ,"#$ <(,$ %(/#-$ &9$ 1$ 21*,()+%1*$ )&%+:/6$ !"(1**1/'#:#/,$)1/$<#$+-#.$.(*#),%7$9&*$CQKR-$E="()"$+,(%(L#$<&,"$,"#$T$1/.$T$%(/#-F6$SQKR-$)1/$<#$,+*/#. (/,&$.(99#*#/,(1%$)(*)+(,-$<7$+-(/'$,"#$f.+::7N)#%%g$1**1/'#:#/,$-"&=/$%1,#*$E>('6$3O6PPF6

15.4 Sense Amplifiers and Address Decoders

(-$(:2%#:#/,#.$<7$,*1/-(-,&*-$F3$1/.$FP?$1/.$,"#$&,"#*$<7$,*1/-(-,&*-$F4$1/.$F56$!*1/-(-,&*FO$1/.$F\$1),$1-$-=(,)"#-$,"1,$)&//#),$,"#$-#/-#$1:2%(9(#*$,&$'*&+/.$1/.$=GG$&/%7$="#/$.1,1N -#/-(/'$1),(&/$(-$*#D+(*#.6$I,"#*=(-#?$ φ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vT$"('"#*$,"1/$ v T 6 $!"#$1:2%(9(#*$=(%%$,"#/$)1+-#$vT$,&$*(-#$,&$=GG$1/.$ v T ,&$91%%$,&$J$[6$!"(-$3$&+,2+,$(-$,"#/$.(*#),#.$,&$,"#$)"(2$;XI$2(/$<7$,"#$)&%+:/$.#)&.#*$E/&, -"&=/F$1/.$1,$,"#$-1:#$,(:#$(-$+-#.$,&$*#=*(,#$1$3$(/$,"#$SQKR$)#%%?$,"+-$2#*9&*:(/'$,"# *#-,&*#$&2#*1,(&/$,"1,$(-$*#D+(*#.$<#)1+-#$,"#$SQKR$*#1.&+,$2*&)#--$(-$.#-,*+),(8#6 ;&6/4(#<=8KO#-.'*#'%*,'#$%(#54()%-46(#-"0#(I/-.&A-$&*"#)&4)/&$8#U5(4-$&*"#*7#$%&'#)&4)/&$ &'#'$4-&6%$7*4,-40b#E%("#φB#6*('#%&6%#>$*#=GG?#54&*4#$*#-#4(-0#*5(4-$&*"+#-..#$%4((#$4-"'&'$*4' )*"0/)$8#E%&.(#F`#-"0#Fa#54()%-46(#$%(#T#-"0#T#.&"('#$*# =GG ⁄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φB8#@%&' ,&..#)-/'(#$%(#T#-"0#T#.&"('#$*#2(#-$#(I/-.#C*.$-6('+#(I/-.#$*# =GG ⁄ P6#@%(#).*)B#φB $%(" 6*('#.*,+#-"0#$%(#T#-"0#T#.&"('#-4(#.(7$#$*#7.*-$#7*4#-#24&(7#&"$(4C-.8 2. !"#$=&*.$%(/#$'&#-$+2?$)&//#),(/'$,"#$)#%%$,&$,"#$T$1/.$T$%(/#-6$K$8&%,1'#$,"#/$.#8#%N &2-$<#,=##/$T$1/.$T?$=(,"$ vT$"('"#*$,"1/$ v T$(9$,"#$1))#--#.$)#%%$(-$-,&*(/'$1$3?$&*$ vT %&=#*$,"1/$ v T$(9$,"#$)#%%$(-$-,&*(/'$1$J6$!&$G##2$,"#$)#%%$1*#1$-:1%%?$1/.$,&$91)(%(,1,# &2#*1,(&/$1,$"('"#*$-2##.-?$,"#$*#1.&+,$-('/1%?$="()"$,"#$)#%%$(-$*#D+(*#.$,&$2*&8(.# <#,=##/$T 1/.$T?$(-$G#2,$-:1%%$E,72()1%%7?$4J`OJJ$:[F6 3. I/)#$ 1/$ 1.#D+1,#$ .(99#*#/)#$ 8&%,1'#$ -('/1%$ "1-$ <##/$ .#8#%&2#.$ <#,=##/$ T$ 1/.$ T <7 ,"#$-,&*1'#$)#%%?$,"#$-#/-#$1:2%(9(#*$(-$,+*/#.$&/$<7$)&//#),(/'$(,$,&$'*&+/.$1/. =GG$,"*&+'"$FO$1/.$F\?$1),(81,#.$<7$*1(-(/'$,"#$-#/-#N)&/,*&%$-('/1%$ φ.6$T#)1+-#$(/(N ,(1%%7$,"#$(/2+,$,#*:(/1%-$&9$,"#$(/8#*,#*-$1*#$1,$ =GG ⁄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∆=E3F$&*$∆=EJF?$2*&8(.#.$<7$,"#$)#%%?$,& '*&=$#Z2&/#/,(1%%7$,&$#(,"#*$=GG$E9&*$1$*#1.N3$&2#*1,(&/F$&*$J$E9&*$1$*#1.NJ$&2#*1,(&/F6 !"# =18#9&*:-$&9$,"#$-('/1%$&/$,"#$T$%(/#$=(%%$<#$)&:2%#:#/,1*7$,&$,"&-#$-"&=/$(/ >('6$ 3O6P3$ 9&*$ ,"#$ T$ %(/#6$ ;/$ ,"#$ 9&%%&=(/'?$ =#$ D+1/,(97$ ,"#$ 2*&)#--$ &9$ #Z2&/#/,(1% '*&=,"$&9$vT$1/.$v T6

1229

1230 Chapter 15 Memory Circuits vB V(1) " VDD Read 1 %V(1) VDD /2

%V(0) Read 0

V(0) " 0

t Word line activated

Sense amplifier activated

Figure 15.21 M18#9&*:-$&9$vT$<#9&*#$1/.$19,#*$,"#$1),(81,(&/$&9$,"#$-#/-#$1:2%(9(#*6$;/$1$*#1.N3$&2#*1,(&/? ,"#$-#/-#$1:2%(9(#*$)1+-#-$,"#$(/(,(1%$-:1%%$(/)*#:#/,$∆=E3F$,&$'*&=$#Z2&/#/,(1%%7$,&$=GG6$;/$1$*#1.NJ$&2#*1,(&/? ,"#$/#'1,(8#$∆=EJF$'*&=-$,&$J6$0&:2%#:#/,1*7$-('/1%$=18#9&*:-$.#8#%&2$&/$,"#$T$%(/#6

A Closer Look at the Operation of the Sense Amplifier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⁄ P6 $!"+-?$9&*$-:1%%N-('/1%$&2#*1,(&/?$#1)"$(/8#*,#*$)1/ <#$:&.#%#.$+-(/'$A&!$1/.$A&B?$,"#$,*1/-)&/.+),1/)#-$&9$FJ$1/.$FK?$*#-2#),(8#%7?$#81%+1,#.$1, 1/$(/2+,$<(1-$&9$ =GG ⁄ P6 $C2#)(9()1%%7?$1$-:1%%N-('/1%$v-$-+2#*(:2&-#.$&/$ =GG ⁄ P $1,$,"#$(/2+, &9$&/#$&9$,"#$(/8#*,#*-$'(8#-$*(-#$,&$1/$(/8#*,#*$&+,2+,$)+**#/,$-('/1%$&9$EA&!$+$A&BF$ v-$≡$X&v-6 !"(-$&+,2+,$)+**#/,$(-$.#%(8#*#.$,&$&/#$&9$,"#$)121)(,&*-?$HT$&*$HT6$!"#$8&%,1'#$,"+-$.#8#%N &2#.$1)*&--$,"#$)121)(,&*$(-$,"#/$9#.$<1)G$,&$,"#$&,"#*$(/8#*,#*$1/.$(-$:+%,(2%(#.$<7$(,-$X&? ="()"$'(8#-$*(-#$,&$1/$&+,2+,$)+**#/,$9##.(/'$,"#$&,"#*$)121)(,&*?$1/.$-&$&/?$(/$1$*#'#/#*1,(8# 2*&)#--6$!"#$2&-(,(8#$9##.<1)G$(/$,"(-$%&&2$=(%%$:#1/$,"1,$,"#$-('/1%$1*&+/.$,"#$%&&2?$1/. ,"+-$ vT$ 1/.$ v T?$ =(%%$ '-.%0 "'$ 5%)/(0 %:B"!%!#-/**($ E-##$ >('6$ 3O6P3F$ =(,"$ 1$ ,(:#$ )&/-,1/,$ &9 EHT ⁄ X& F $h&*$ EHT ⁄ X& F?$-(/)#$=#$"18#$<##/$1--+:(/'$HT$=$HTj6$!"+-?$9&*$#Z1:2%#?$(/$1 *#1.N3$&2#*1,(&/$=#$&<,1(/ vT

X ⁄H # =GG N + ∆= ( 3 )% & T , = NNNNNNNN P

vT

≤ = GG

$E3O63\F

,%(4(-'#&"#-#4(-0GO#*5(4-$&*"+ vT

( X ⁄ H )# =GG N $ \ $∆ = ( J )% & T $ = NNNNNNNN P

$E3O63^F

9()-/'(#$%('(#(N54(''&*"'#%-C(#2(("#0(4&C(0#-''/3&"6#'3-..G'&6"-.#*5(4-$&*"+#$%(1#0(')4&2( $%(#(N5*"("$&-.#64*,$%#>0()-1?#*7# vT#4(-'*"-2.1#-))/4-$(.1#*".1#7*4#C-./('#).*'(#$*# =GG ⁄ P6 T(C(4$%(.(''+# $%(1# )-"# 2(# /'(0# $*# *2$-&"# -# 4(-'*"-2.(# ('$&3-$(# *7# $%(# $&3(# 4(I/&4(0# $* 0(C(.*5#-#5-4$&)/.-4#'&6"-.#.(C(.#*"#$%(#2&$#.&"(8

15.4 Sense Amplifiers and Address Decoders

1231

Example 15.2 0&/-(.#*$,"#$-#/-#N1:2%(9(#*$)(*)+(,$&9$>('6$3O6PJ$.+*(/'$,"#$*#1.(/'$&9$1$36$K--+:#$,"1,$,"#$-,&*1'#$)#%% 2*&8(.#-$1$8&%,1'#$(/)*#:#/,$&/$,"#$T$%(/#$&9$∆=E3F$=$J63$[6$;9$,"#$_RIC$.#8()#-$(/$,"#$1:2%(9(#*-$"18# E6 ⁄ @ F! $=$J6O5$µ: / J63]$µ:$1/.$,"#$VRIC$.#8()#-$"18#$ E6 ⁄ @ FB $=$P63\$µ:/J63]$µ:?$1/.$1--+:(/' ,"1,$=GG$a$36]$[?$ = #! V = #B $a$J6O [?$1/.$ µ!H":$a$5$ µBH":$a$4JJ$µKX[P?$9(/.$,"#$,(:#$*#D+(*#.$9&*$ vT$,& *#1)"$J6b$=GG6$K--+:#$HT$=$3$2>6

Solution ;&4'$+#,(#0($(43&"(#$%(#$4-"')*"0/)$-")('#A&!#-"0#A&B 6 A &! = µ ! H ": NNNNN ( =XD \ = # ) @ ! J6O5 = 4JJ$ × $ NNNNNNNNNNNNNNN ( J6b \ J6O ) J63] = J64\$:KX[ 6 A &B = µ B H ": NNNNN ( =XD \ = # ) @ B P63\ = ^O$ × $ NNNNNNNNNNNNNNN ( J6b \ J6O ) V J64\ :K ⁄ [ J63] @%/'+#$%(#&"C(4$(4#X&#&'# X & = A &! + A &B = J6^P$:KX[ -"0#$%(#$&3(#)*"'$-"$#τ#7*4#$%(#(N5*"("$&-.#64*,$%#*7#vT#,&..#2(# H X&

\ 3P

3 × 3J N = 365$/τ $ ≡ NNNNNNTN = NNNNNNNNNNNNNNNNNNNNNNNNNN \4 J6^P × 3J

T*,+#$%(#$&3(+#∆#+#7*4#vT#$*#4(-)%#O8a#=GG#)-"#2(#0($(43&"(0#74*3 J6b × 36] = J6b + J63% 4('/.$&"6#&"

∆# ⁄ 365

∆ ##=#K8`#"'

Obtaining Differential Operation in Dynamic RAMs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φ G ?#&'#-.'*#'(.()$(0+#-"0#C&)(#C(4'-F#$%-$#&'+#,%("#-#,*40#.&"(#*"

1232 Chapter 15 Memory Circuits

Equalization and precharge Left dummy cell

1 2

BK line

1 2

Sense amplifier

BK line

Right dummy cell

!D

!D

CD

CS

Word lines

CS

CS

Equalization and precharge

CS

CD

Word lines

Figure 15.22 K/$1**1/'#:#/,$9&*$&<,1(/(/'$.(99#*#/,(1%$&2#*1,(&/$9*&:$,"#$-(/'%#N#/.#.$SQKR$)#%%6$ _&,#$,"#$.+::7$)#%%-$1,$,"#$91*$*('",$1/.$91*$%#9,6

$%(#4&6%$#'&0(#&'#'(.()$(0+#$%(#0/331#)(..#*"#$%(#.(7$#>)*"$4*..(0#21# φ G ?#&'#-.'*#'(.()$(08#!" (77()$+#$%("+#$%(#0/331#)(..#'(4C('#-'#$%(#*$%(4#%-.7#*7#-#0&77(4("$&-.#XR:Z#)(..8#E%("#$%( .(7$G%-.7#2&$#.&"(#&'#&"#*5(4-$&*"+#$%(#4&6%$G%-.7#2&$#.&"(#-)$'#-'#&$'#)*35.(3("$#>*4# T #.&"(?#-"0 C&)(#C(4'-8 U5(4-$&*"#*7#$%(#)&4)/&$#&"#;&68#<=8KK#&'#-'#7*..*,'b#@%(#$,*#%-.C('#*7#$%(#.&"(#-4(#54(G )%-46(0#$*# =GG ⁄ P 0-"0#$%(&4#C*.$-6('#-4(#(I/-.&A(08#:$#$%(#'-3(#$&3(+#$%(#)-5-)&$*4'#*7#$%( $,*#0/331#)(..'#-4(#54()%-46(0#$*# =GG ⁄ P6 #@%("#-#,*40#.&"(#&'#'(.()$(0+#-"0#$%(#0/331 )(..#*"#$%(#*$%(4#'&0(#&'#("-2.(0#>,&$%# φ G #*4# φ G #4-&'(0#$*#=GG?8#@%/'#$%(#%-.7G.&"(#)*""()$(0 $*# $%(# '(.()$(0# )(..# ,&..# 0(C(.*5# -# C*.$-6(# &")4(3("$# >-4*/"0# =GG ⁄ P F # *7# ∆=>O? 0(5("0&"6#*"#,%($%(4#-#<#*4#-#O#&'#'$*4(0#&"#$%(#)(..8#Z(-",%&.(+#$%(#*$%(4#%-.7#*7#$%(#.&"( ,&..#%-C(#&$'#C*.$-6(#%(.0#(I/-.#$*#$%-$#*7#HG#>&8(8+# =GG ⁄ P F6 #@%(#4('/.$#&'#-#0&77(4("$&-.#'&6"-. *7#∆=>O?#$%-$#$%(#'("'(#-35.&7&(4#0($()$'#-"0#-35.&7&('#,%("#&$#&'#("-2.(08#:'#/'/-.+ 21#$%(#("0#*7#$%(#4(6("(4-$&C(#54*)(''+#$%(#-35.&7&(4#,&..#)-/'(#$%(#C*.$-6(#*"#*"(#%-.7#*7#$%( .&"(#$*#2()*3(#=GG#-"0#$%-$#*"#$%(#*$%(4#%-.7#$*#2()*3(#O8

EXERCISES 15.9 ;,$(-$*#D+(*#.$,&$*#.+)#$,"#$,(:#$∆#$&9$,"#$-#/-#N1:2%(9(#*$)(*)+(,$(/$YZ1:2%#$3O6P$<7$1$91),&*$&9$P <7$(/)*#1-(/'$A&$&9$,"#$,*1/-(-,&*-$E="(%#$*#,1(/(/'$,"#$:1,)"#.$.#-('/$&9$#1)"$(/8#*,#*F6$M"1,$:+-, ,"#$6I@$*1,(&-$&9$,"#$!C$1/.$BC)"1//#%$.#8()#-$<#)&:#l Ans. E6 ⁄ @ F ! $=$\A$ E6 ⁄ @ F B $=$P5 15.10 ;9$(/$,"#$-#/-#$1:2%(9(#*$&9$YZ1:2%#$3O6P?$,"#$-('/1%$181(%1<%#$9*&:$,"#$)#%%$(-$&/%7$"1%9$1-$%1*'#$E(6#6? &/%7$OJ$:[F?$="1,$=(%%$∆# $<#)&:#l Ans. 46^$/-?$1/$(/)*#1-#$&9$4Pk

15.4 Sense Amplifiers and Address Decoders

Q8

VDD – fp

VDD Q9

Q8

Q7

Word Line

Word Line Cell

(a)

Q7

Cell – B line

B line

Q9

– fp

– B line

B line (b)

Figure 15.23 BA*#.1%()0.%$E(#.)).0/(2(0%&#"*)#+)(,-.)/$0/#%-(#;$%#1$0(N#9!:#B-(#!#.0'# ! #1$0(&#.)(#+)(@ ,-.)/('#%*#$%%O#9":#%-(#!#.0'# ! #1$0(&#.)(#,-.)/('#%*#9$%% P $&:4

Alternative Precharging Arrangements !"# $%# $&# '(&$)('# %*# +)(,-.)/(# %-(# !" .0'# ! 1$0(&#%*# $ %% C #%-(#.)).0/(2(0%#$0#3$/4#564789.:#,.0#;(#<%$1$=('4#>()(#+)(,-.)/$0/#.0'#(?<.1@ $=.%$*0#*,,<)#A-(0# φ ' #$
*A4#B-(0C#D<&%#+)$*)#%*#%-(#.,%$E.%$*0#*"#%-(#A*)'#1$0(C# φ ' #/*(& -$/-4#F0*%-()#+)(,-.)/$0/#.)).0/(2(0%#<&$0/#'$*'(@,*00(,%('#GHIJ#%).0&$&%*)&#$&#&-*A0 $0#3$/4#564789;:4#!0#%-$&#,.&(C#%-(#!".0'# ! #1$0(&#.)(#,-.)/('#%*# ( $ %% ! $ & )C #.0'# ( Q #(?<.1$=(& %-($)#E*1%./(&4 An Alternative Sense Amplifier F0*%-()#+*+<1.)#$2+1(2(0%.%$*0#*"#%-(#&(0&(#.2+1$@ "$()#$&#%-(#'$""()(0%$.1#HIJ#.2+1$"$()#A$%-#.#,<))(0%@2$))*)#1*.'C#&%<'$('#$0#'(%.$1#$0#J(,%$*0 K464#>()(C#A(#+)(&(0%#.#;)$("#*E()E$(A#*"#%-(# *+().%$*0#*"#%-$&#E()&.%$1(#,$),<$%#.&#.#&(0&( .2+1$"$()4 B-(#.2+1$"$()#,$),<$%#$&#&-*A0#$0#3$/4#5647L#"('#")*2#%-(#;$%#.0'# ;$% #1$0( E*1%./(&# v ! .0'# v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v ! " v ! " $ %% ! $ & 4 #G*%(#%-.%#A(#-.E(#.&&<2('#%-.%#%-(#!".0'# ! #1$0(&#.)(#+)(,-.)/('#%* ( $ %% ! $ & ) #<&$0/#%-(#,$),<$%#$0#3$/4#564789;:4#!%#%<)0&#*<%#%-.%#%-$&#E*1%./(#$&#+.)%$,<1.)1M#,*0@ E(0$(0%# "*)# %-(# *+().%$*0# *"# %-$&# .2+1$"$()# %M+(# .&# .# &(0&(# .2+1$"$()4# F&# $0'$,.%('# $0# 3$/4 5647L9;:C#%-(#;$.&#,<))(0%##"'$E$'(&#(?<.11M#;(%A((0# ( 5 #.0'# ( 7 O #%-<&#(.,-#,*0'<,%&#.#,<)@ )(0%# # ⁄ 7 4 #B-(#,<))(0%#*"# ( 5 #$&#"('#%*#%-(#$0+<%#&$'(#*"#%-(#,<))(0%#2$))*)C#%).0&$&%*)# ( 8 O #%-<& %-(#2$))*)#+)*E$'(&#.0#(?<.1#*<%+<%#,<))(0%# # ⁄ 7 #$0#%-(#').$0#*"# ( L 4 #F%#%-(#*<%+<%#0*'(C#A( &((#%-.%#A(#-.E(#%A*#(?<.1#.0'#*++*&$%(#,<))(0%&C#1(.E$0/#.#=()*#,<))(0%#%*#"1*A#$0%*#%-(#1*.' ,.+.,$%*)4#B-<&C#$0#.0#$'(.1#&$%<.%$*0#*"#+()"(,%#2.%,-$0/C# v ) #A$11#;(#(?<.1#%*#%-(#E*1%./(#.% %-(#').$0#*"# ( 5 4

1233

1234 Chapter 15 Memory Circuits VDD

VDD Q4

Q3

Q3 vO

I 2

C vB

Q1

v B–

Q2

I 2 I 2 Q2

VB

Q1

(VDD – Vt)

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I VR

Q5

VR

Q4 0

Q5

(a)

(b)

VDD Q3

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Q4 I

I

vO I

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Q1 (VDD – Vt) + !V

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Figure 15.24 B-"%/&$*3"E1'/+"+%HIJ%+*66","($*/1%/2C1*6*",%/)%/%)"()"%/2C1*6*",7

!"#$%&'()*+",%$-"%)*$./$*'(%0-"(%$-"%!%1*("%)-'0)%/(%*(&,"2"($/1%3'1$/4"% ∆& %/5'3"%$-" 3'1$/4"%'6%$-"% ! %1*("7%8)%)-'0(%*(%9*47%:;7<=>&?@%*6% ∆& %*)%).66*&*"($1A%1/,4"@% ' < %0*11%$.,(%'66 /(+%/11%$-"%5*/)%&.,,"($%"#0*11%61'0%$-,'.4-% ' : %/(+%'(%$'% ' K 7 %B-.)%$-"%2*,,',%'.$C.$%&.,,"($ 5"&'2")%"%/(+%61'0)%$-,'.4-%$-"%/2C1*6*",%'.$C.$%$",2*(/1%$'%$-"%"D.*3/1"($%'.$C.$%&/C/&*E $/(&"%$7%B-.)#$%0*11%&-/,4"%$'% & (( %*(%$*2"% ∆)@ $& (( ∆) ! EEEEEEEEEEEEE E "

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15.4 Sense Amplifiers and Address Decoders

1235

K/$(:2&*,1/,$D+#-,(&/$,&$1/-=#*$<#9&*#$%#18(/'$,"(-$1:2%(9(#*$)(*)+(,$(-$"&=$%1*'#$(-$ ∆= ,"1,$)1+-#-$,"#$)+**#/,$L$,&$-=(,)"$9*&:$&/#$-(.#$&9$,"#$.(99#*#/,(1%$21(*$,&$,"#$&,"#*l$!"# 1/-=#*$(-$'(8#/$(/$C#),(&/$]6O$E-##$>('6$]64PF?$/1:#%7? ∆= V

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="#*#$ = >= $(-$,"#$&8#*.*(8#$8&%,1'#$1,$="()"$ F 3 $1/.$ F P $1*#$&2#*1,(/'$(/$#D+(%(<*(+:?$,"1, (-? NNLN V 3 NNN ( µ ! H ": ) 6 NNNNN P P @

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>(/1%%7?$=#$/&,#$,"1,$,"(-$-#/-#$1:2%(9(#*$.(--(21,#-$-,1,()$2&=#*$'(8#/$<7$ K V = GG L

I<-#*8#$ ,"1,$ (/)*#1-(/'$ L$ *#.+)#-$ ,"#$ ,(:#$ ∆# $ (/$ YD6$ E3O63]F$ 1,$ ,"#$ #Z2#/-#$ &9$ (/)*#1-#. 2&=#*$.(--(21,(&/6

EXERCISE D15.11 ;,$(-$*#D+(*#.$,&$.#-('/$,"#$-#/-#$1:2%(9(#*$(/$>('6$3O6P5$,&$.#,#),$1/$(/2+,$-('/1%$ ∆= V 3JJ$:[ 1/.$,&$2*&8(.#$1$9+%%$&+,2+,$(/$J6O$/-6$;9$H$a$OJ$9>$1/.$ = GG V 36]$[ ?$9(/.$,"#$*#D+(*#.$)+**#/,$L 1/.$,"#$2&=#*$.(--(21,(&/6 Ans. 3]J$ µK A$4P5$ µM

15.4.2 The Row-Address Decoder :'# 0(')4&2(0# &"# L()$&*"#<=8K+#$%(# 4*,G-004(''#0()*0(4#&'# 4(I/&4(0# $*# '(.()$# *"(#*7# $%(# K$ ,*40#.&"('#&"#4('5*"'(#$*#-"#$G2&$#-004(''#&"5/$8#:'#-"#(N-35.(+#)*"'&0(4#$%(#)-'(#$#=#S -"0#0("*$(#$%(#$%4((#-004(''#2&$'#PO+#P<+#-"0#PK+#-"0#$%(#(&6%$#,*40#.&"('# 6 J ?6 3 ? …? 6 ^ 6 D*"C("$&*"-..1+#,*40#.&"(# 6O#,&..#2(#%&6%#,%("# PO#=#O+# P<#=#O+#-"0#PK#=#OF#$%/'#,(#)-" (N54(''#6O#-'#-#9**.(-"#7/")$&*"#*7#PO+#P<+#-"0#PK+

6J = PJ P3 PP = PJ + P3 + PP @%/'#$%(#'(.()$&*"#*7#6O#)-"#2(#-))*35.&'%(0#21#-#$%4((G&"5/$#TUR#6-$(#,%*'(#$%4((#&"5/$' -4(#)*""()$(0#$*#PO+#P<+#-"0#PK#-"0#,%*'(#*/$5/$#&'#)*""()$(0#$*#,*40#.&"(#O8#E*40#.&"(#6S ,&..#2(#%&6%#,%("#PO#=#<+#P<#=#<+#-"0#PK#=#OF#$%/'+

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

1236 Chapter 15 Memory Circuits VDD

!P Row 0

!P Row 1

!P Row 2

!P

. . . . .

Row 3

!P Row 7

A2

A2

A1

A1

A0

A0

Row address Figure 15.25 K$_IQ$1..*#--$.#)&.#*$(/$1**17$9&*:6$I/#$&+,$&9$#('",$%(/#-$E*&=$%(/#-F$(-$-#%#),#.$+-(/'$1$ 4N<(,$1..*#--6

4*,#.&"(#&'#-#BG)%-""(.#0(C&)(#$%-$#&'#-)$&C-$(0+#54&*4#$*#$%(#0()*0&"6#54*)(''+#/'&"6#$%(#54(G )%-46(# )*"$4*.#'&6"-.# φK8# X/4&"6#54()%-46(# >φ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

15.4 Sense Amplifiers and Address Decoders

)*""()$(0#$*#4*,#O#2(&"6#)/$#*778#L&3&.-4.1+#4*,#S#%-'#$4-"'&'$*4'#)*""()$(0#$*# P J, P 3 ? #-"0#PK+ -"0#$%/'#&$#,&..#2(#%&6%#,%("#PO#=#<+#P<#=#<+#PK#=#O+#-"0#'*#*"8#:7$(4#$%(#0()*0(4#*/$5/$'#%-C( '$-2&.&A(0+#$%(#*/$5/$#.&"('#-4(#)*""()$(0#$*#$%(#,*40#.&"('#*7#$%(#-44-1+#/'/-..1#C&-#).*)BG)*"G $4*..(0#$4-"'3&''&*"#6-$('8#@%&'#0()*0(4#&'#B"*,"#-'#-#TUR#0()*0(48#U2'(4C(#$%-$#2()-/'(#*7 $%(#54()%-46(#*5(4-$&*"+#$%(#0()*0(4#)&4)/&$#0*('#"*$#0&''&5-$(#'$-$&)#5*,(48#

EXERCISE 15.12 W&=$:1/7$,*1/-(-,&*-$1*#$/##.#.$9&*$1$_IQ$*&=$.#)&.#*$=(,"$1/$$N<(,$1..*#--l Ans. $P$$_RIC$+$P$$VRIC$=$P$E$$+$3F

15.4.3 The Column-Address Decoder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g"7*4$/"-$(.1+#'&")(#4(.-$&C(.1#.-46(#"/32(4#*7#$4-"'&'$*4'#)-"#(N&'$#&"#$%(#'&6"-.#5-$%+#$%(#4('&'$-")(#*7#$%(#2&$ .&"('#&")4(-'('+#-"0#$%(#'5((0#0()4(-'('#)*44('5*"0&"6.18 Bit lines B0

B1

B2N#1

0

AM AM$1 N-bit column address

NOR decoder

AM$N#1

1

Pass-transistor multiplexer

2N#1

I/O data Figure 15.26 K$)&%+:/$.#)&.#*$*#1%(L#.$<7$1$)&:<(/1,(&/$&9$1$_IQ$.#)&.#*$1/.$1$21--N,*1/-(-,&*$ :+%,(2%#Z#*6

1237

1238 Chapter 15 Memory Circuits Bit lines B0

B1 A0

A0

B2 A0

A0

A1

B3

B4 A0

A0

A1

B5

B6

A2

A0

A0

A1

B7

A1

A2

I/O data Figure 15.27 K$,*##$)&%+:/$.#)&.#*6$_&,#$,"1,$,"#$)&%&*#.$21,"$-"&=-$,"#$,*1/-(-,&*-$,"1,$1*#$)&/.+),(/'$ ="#/$PJ$=$3?$P3$=$J?$1/.$PP$=$3?$,"#$1..*#--$,"1,$*#-+%,-$(/$)&//#),(/'$TO$,&$,"#$.1,1$%(/#6

EXERCISE 15.13 W&=$:1/7$,*1/-(-,&*-$1*#$/##.#.$9&*$1$,*##$.#)&.#*$="#/$,"#*#$1*#$PJ$<(,$%(/#-l Ans. PEPJ$−$3F

15.4.4 Pulse-Generation Circuits R#:&*7$)"(2-$*#D+(*#$1$%1*'#$/+:<#*$&9$2+%-#$-('/1%-?$-&:#,(:#-$=(,"$(/,*()1,#$,(:(/'$*#%1N ,(&/-"(2-$1:&/'$,"#:6$;,$(-$/&,$&+*$2+*2&-#$"#*#$,&$-,+.7$,"(-$(:2&*,1/,$-+('6$3O6P]E1F6$>('+*#$3O6P]E4&'&"6?#5*.-4&$1#-7$(4#-"*$%(4#S#K#&"$(4C-.8#!$#7*..*,'#$%-$#$%(#)&4)/&$#*')&..-$('#,&$%#-#5(4&*0

15.4 Sense Amplifiers and Address Decoders

v1 1

G1

v2 2

v3

G2

3

G3

1239

v1 1

(a) v1

v2

v3

All delays

tP

Time

(b) Figure 15.28 0'1$K$*(/'$&-)(%%1,&*$9&*:#.$<7$)&//#),(/'$,"*##$(/8#*,#*-$(/$)1-)1.#6$E_&*:1%%7$1,$%#1-,$9(8#$ (/8#*,#*-$1*#$+-#.6F$0$1$!"#$*#-+%,(/'$=18#9&*:6$I<-#*8#$,"1,$,"#$)(*)+(,$&-)(%%1,#-$=(,"$9*#D+#/)7$ 3 ⁄ \# K 6

*7#]#K#*4#)*44('5*"0&"6.1#,&$%#74(I/(")1# 3 ⁄ \# K 6 #!"#6("(4-.+#-#4&"6#,&$%#J#&"C(4$(4'#>,%(4( J#3/'$#2(#*00?#,&..#*')&..-$(#,&$%#-#5(4&*0#*7#KJ#K#-"0#74(I/(")1# 3 ⁄ PJ# K 6 :'#-#7&"-.#4(3-4B+#,(#"*$(#$%-$#$%(#4&"6#*')&..-$*4#54*C&0('#-#4(.-$&C(.1#'&35.(#3(-"'#7*4 3(-'/4&"6#$%(#&"C(4$(4#54*5-6-$&*"#0(.-18

EXERCISE 15.14$ >(/.$,"#$9*#D+#/)7$&9$&-)(%%1,(&/$&9$1$*(/'$&9$9(8#$(/8#*,#*-$(9$,"#$(/8#*,#*$2*&21'1,(&/$.#%17$(-$-2#)N (9(#.$,&$<#$3$/-6 Ans. 3JJ$RWL

A One-Shot or Monostable Multivibrator Circuit !"#$&/#N-"&,$&*$:&/&-,1<%#$:+%N ,(8(<*1,&*$ )(*)+(,$ 2*&8(.#-?$ ="#/$ ,*(''#*#.?$ 1$ -(/'%#$ &+,2+,$ 2+%-#$ =(,"$ 1$ 2*#.#,#*:(/#. =(.,"64$K$81*(#,7$&9$)(*)+(,-$#Z(-,$9&*$(:2%#:#/,(/'$,"#$&/#N-"&,$9+/),(&/?$1/.$-&:#$+-(/' &2$1:2-$=(%%$<#$-,+.(#.$(/$C#),(&/$3^6\6$W#*#?$(/$>('6$3O6PbE1F?$=#$-"&=$1$)(*)+(,$)&::&/%7 +-#.$(/$.('(,1%$;0$.#-('/6$!"#$)(*)+(,$+,(%(L#-$1/$#Z)%+-(8#NIQ$EmIQF$'1,#$,&'#,"#*$=(,"$1 .#%17$)(*)+(,6$Q#)1%%(/'$,"1,$,"#$mIQ$'1,#$2*&8(.#-$1$"('"$&+,2+,$&/%7$="#/$(,-$,=&$(/2+,1*#$.(--(:(%1*?$=#$-##$,"1,$2*(&*$,&$,"#$1**(81%$&9$,"#$(/2+,$2&-(,(8#$-,#2?$,"#$&+,2+,$=(%%$<# 4

!"#$/1:#$f:&/&-,1<%#g$1*(-#-$<#)1+-#$,"(-$)%1--$&9$)(*)+(,-$"1-$&/#$-,1<%#$-,1,#?$="()"$(-$,"#$D+(#-)#/, -,1,#6$M"#/$1$,*(''#*$(-$122%(#.?$,"#$)(*)+(,$:&8#-$,&$(,-$D+1-(N-,1<%#$-,1,#$1/.$-,17-$(/$(,$9&*$1$2*#.#,#*N :(/#.$%#/',"$&9$,(:#$E,"#$=(.,"$&9$,"#$&+,2+,$2+%-#F6$;,$,"#/$-=(,)"#-$<1)G$1+,&:1,()1%%7$,&$,"#$-,1<%# -,1,#6

1240 Chapter 15 Memory Circuits

T Delay 0

T A

t B

t

0

Y (a)

T Delay

1

2

N

(b) Figure 15.29 E'F$K$&/#N-"&,$&*$:&/&-,1<%#$)(*)+(,6$i,(%(L(/'$1$.#%17$)(*)+(,$=(,"$1$.#%17$M$1/.$1/$mIQ$'1,#? ,"(-$)(*)+(,$2*&8(.#-$1/$&+,2+,$2+%-#$&9$=(.,"$M6$E$F$!"#$.#%17$)(*)+(,$)1/$<#$(:2%#:#/,#.$1-$,"#$)1-)1.#$&9$J (/8#*,#*-$="#*#$J$(-$#8#/?$(/$="()"$)1-#$M a J#K 6

%&=6$M"#/$,"#$(/2+,$'&#-$"('"?$&/%7$,"#$T$(/2+,$&9$,"#$mIQ$=(%%$<#$"('"$1/.$,"+-$(,-$&+,2+, =(%%$'&$"('"6$!"#$"('"$(/2+,$=(%%$*#1)"$(/2+,$P$&9$,"#$mIQ$M$-#)&/.-$%1,#*?$1,$="()"$,(:# <&,"$(/2+,-$&9$,"#$mIQ$=(%%$<#$"('"$1/.$,"+-$(,-$&+,2+,$=(%%$'&$%&=6$M#$,"+-$-##$,"1,$,"#$)(*N )+(,$2*&.+)#-$1/$&+,2+,$2+%-#$=(,"$1$.+*1,(&/$M$#D+1%$,&$,"#$.#%17$&9$,"#$.#%17$<%&)G$9&*$#1)" ,*1/-(,(&/$&9$,"#$(/2+,$-('/1%6$!"#$%1,,#*$)1/$<#$(:2%#:#/,#.$<7$)&//#),(/'$1/$#8#/$/+:<#* &9$(/8#*,#*-$(/$)1-)1.#$1-$-"&=/$(/$>('6$3O6PbE
15.5 Read-only Memory (ROM) :'#3("$&*"(0#&"#L()$&*"#<=8K+#4(-0G*".1#3(3*41#>RUZ?#&'#3(3*41#$%-$#)*"$-&"'#7&N(0#0-$5-$$(4"'8#!$#&'#/'(0#&"#-#C-4&($1#*7#0&6&$-.G'1'$(3#-55.&)-$&*"'8#D/44("$.1+#-#C(41#5*5/.-4#-55.&G )-$&*"#&'#$%(#/'(#*7#RUZ#&"#3&)4*54*)(''*4#'1'$(3'#$*#'$*4(#$%(#&"'$4/)$&*"'#*7#$%(#'1'$(3i' 2-'&)# *5(4-$&"6# 54*64-38# RUZ# &'# 5-4$&)/.-4.1# '/&$(0# 7*4# '/)%# -"# -55.&)-$&*"# 2()-/'(# &$# &' "*"C*.-$&.(F#$%-$#&'+#&$#4($-&"'#&$'#)*"$("$'#,%("#$%(#5*,(4#'/55.1#&'#',&$)%(0#*778 :#RUZ#)-"#2(#C&(,(0#-'#-#)*32&"-$&*"-.#.*6&)#)&4)/&$#7*4#,%&)%#$%(#&"5/$#&'#$%(#)*..()G $&*"# *7# -004(''# 2&$'# *7# $%(# RUZ# -"0# $%(# */$5/$# &'# $%(# '($# *7# 0-$-# 2&$'# 4($4&(C(0# 74*3# $%( -004(''(0#.*)-$&*"8#@%&'#C&(,5*&"$#.(-0'#$*#$%(#-55.&)-$&*"#*7#RUZ'#&"#)*0(#)*"C(4'&*"j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

15.5.1 A MOS ROM ;&6/4(#<=8SO#'%*,'#-#'&35.&7&(0#SKG2&$#>*4#`G,*40#×#[G2&$?#ZUL#RUZ8#:'#&"0&)-$(0+#$%(#3(3G *41#)*"'&'$'#*7#-"#-44-1#*7#!G)%-""(.#ZUL;^@'#,%*'(#6-$('#-4(#)*""()$(0#$*#$%(#,*40#.&"('+ ,%*'(#'*/4)('#-4(#64*/"0(0+#-"0#,%*'(#04-&"'#-4(#)*""()$(0#$*#$%(#2&$#.&"('8#^-)%#2&$#.&"(#&'#)*"G "()$(0#$*#$%(#5*,(4#'/55.1#C&-#-#YZUL#.*-0#$4-"'&'$*4+#&"#$%(#3-""(4#*7#5'(/0*GTZUL#.*6&)

Row decoder

# W6

W7

W8

B3

B2

B1

To sense amplifiers

B0

Figure 15.30 K$-(:2%#$RIC$QIR$&*'1/(L#.$1-$]$=&*.-$×$5$<(,-6

Word address

15.5 Read-only Memory (ROM)

VDD

W1

W2

W3

W4

W5

1241

1242 Chapter 15 Memory Circuits >L()$&*"#<[8$*# ,%&)%# $4-"'&'$*4'# &"# $%(#'(.()$(0# 4*,# -4(#)*""()$(0?# 0*,"# 74*3#=GG# $*#-# C*.$-6(# ).*'(#$* 64*/"0#C*.$-6(#>$%(#.*6&)GO#.(C(.?8#@%(#2&$#.&"('#$%-$#-4(#)*""()$(0#$*#)(..'#>*7#$%(#'(.()$(0#,*40? ,&$%*/$#$4-"'&'$*4'#>&8(8+#$%(#)(..'#$%-$#-4(#'$*4&"6#-#.*6&)#.*6&)#
EXERCISE 15.15 !"#$2+*2&-#$&9$,"(-$#Z#*)(-#$(-$,&$#-,(:1,#$,"#$81*(&+-$.#%17$,(:#-$(/8&%8#.$(/$,"#$&2#*1,(&/$&9$1 QIR6$0&/-(.#*$,"#$QIR$(/$>('6$3O64J$=(,"$,"#$'1,#-$&9$,"#$VRIC$.#8()#-$.(-)&//#),#.$9*&: '*&+/.$1/.$)&//#),#.$,&$1$2*#)"1*'#$)&/,*&%$-('/1%$ φ6$@#,$1%%$,"#$_RIC$.#8()#-$"18#$ 6 ⁄ @ $= \ µ:XP$µ:$1/.$1%%$,"#$VRIC$.#8()#-$"18#$ 6 ⁄ @ $=$P5$µ:XP$µ:6$K--+:#$,"1,$µ!H":$=$OJ$µK/[P? µBH":$=$PJ$µK/[P?$=#!$=$−=#B$=$3$[?$1/.$=GG$=$O$[6 E1F S+*(/'$,"#$2*#)"1*'#$(/,#*81%?$φ$(-$%&=#*#.$,&$J$[6$Y-,(:1,#$,"#$,(:#$*#D+(*#.$,&$)"1*'#$1$<(,$%(/# 9*&:$J$[$,&$O$[6$i-#?$1-$1/$18#*1'#$)"1*'(/'$)+**#/,?$,"#$)+**#/,$-+22%(#.$<7$1$VRIC$,*1/-(-,&* 1,$1$<(,N%(/#$8&%,1'#$"1%9=17$,"*&+'"$,"#$JN[$,&$ON[$#Z)+*-(&/$E(6#6?$P6O$[F6$!"#$<(,N%(/#$)121)(N ,1/)#$(-$P$2>6$_&,#$,"1,$1%%$_RIC$,*1/-(-,&*-$1*#$)+,$&99$1,$,"(-$,(:#6 E?$="1,$(-$,"#$E3Jk$,&$bJkF *(-#$,(:#$&9$,"#$=&*.N%(/#$8&%,1'#l$M"1,$(-$,"#$8&%,1'#$*#1)"#.$1,$,"#$#/.$&9$&/#$,(:#$)&/-,1/,l E)F M#$1))&+/,$9&*$,"#$#Z2&/#/,(1%$*(-#$&9$,"#$=&*.N%(/#$8&%,1'#$<7$122*&Z(:1,(/'$,"#$=&*.N%(/#$8&%,N 1'#$<7$1$-,#2$#D+1%$,&$,"#$8&%,1'#$*#1)"#.$(/$&/#$,(:#$)&/-,1/,6$>(/.$,"#$(/,#*81%$∆#$*#D+(*#.$9&* 1/$_RIC$,*1/-(-,&*$,&$.(-)"1*'#$,"#$<(,$%(/#$1/.$%&=#*$(,-$8&%,1'#$<7$J6O$[6$E;,$(-$1--+:#.$,"1, ,"#$-#/-#$1:2%(9(#*$/##.-$1$J6ON[$)"1/'#$1,$(,-$(/2+,$,&$.#,#),$1$%&=$<(,$81%+#6F Ans. E1F$\63$/-A$E
15.5.2 Mask-Programmable ROMs @%(# 0-$-# '$*4(0# &"# $%(# RUZ'# 0&')/''(0# $%/'# 7-4# &'# 0($(43&"(0# -$# $%(# $&3(# *7# 7-24&)-$&*"+ -))*40&"6# $*# $%(# /'(4i'# '5()&7&)-$&*"'8# M*,(C(4+# $*# -C*&0# %-C&"6# $*# )/'$*3G0('&6"# (-)% RUZ# 74*3# ')4-$)%# >,%&)%# ,*/.0# 2(# (N$4(3(.1# )*'$.1?+# RUZ'# -4(# 3-"/7-)$/4(0# /'&"6# -

15.5 Read-only Memory (ROM)

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i'#'5()&7&)-$&*"'8 @%(# ()*"*3&)# -0C-"$-6('# *7# $%(# 3-'B# 54*64-33&"6# 54*)(''# '%*/.0# 2(# *2C&*/'b# :.. RUZ'#-4(#7-24&)-$(0#'&3&.-4.1F#)/'$*3&A-$&*"#*))/4'#*".1#0/4&"6#*"(#*7#$%(#7&"-.#'$(5'#&" 7-24&)-$&*"8

15.5.3 Programmable ROMs (PROMs and EPROMs) YRUZ'#-4(#RUZ'#$%-$#)-"#2(#54*64-33(0#21#$%(#/'(4+#2/$#*".1#*")(8#:#$15&)-.#-44-"6(G 3("$#(35.*1(0#&"#9k@#YRUZ'#&"C*.C('#/'&"6#5*.1'&.&)*"#7/'('#$*#)*""()$#$%(#(3&$$(4#*7 (-)%#9k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elect gate

Si

Floating gate

Oxide Si

D

Select gate $

Drain n

Source n

$

p-type silicon substrate S

(a)

(b)

Figure 15.31 0'1$0*&--$-#),(&/$1/.$0$1$)(*)+(,$-7:<&%$&9$,"#$9%&1,(/'N'1,#$,*1/-(-,&*$+-#.$1-$1/$YVQIR$ )#%%6 5

C##$K22#/.(Z$K$9&*$1$.#-)*(2,(&/$&9$-(%()&/N'1,#$,#)"/&%&'76

1243

1244 Chapter 15 Memory Circuits *$%(4#5-4$#*7#$%(#)&4)/&$F#4-$%(4+#&$#&'#.(7$#7.*-$&"6#-"0#&'#-554*54&-$(.1#)-..(0#-#@)"'(%&3.3'(+8 @%(#*$%(4#6-$(+#)-..(0#-#*+)+!(.3'(++.7/")$&*"'#&"#$%(#'-3(#3-""(4#-'#$%(#6-$(#*7#-#4(6/.-4 ("%-")(3("$#ZUL;^@8 @%(#ZUL#$4-"'&'$*4#*7#;&68#<=8S<>-?#&'#B"*,"#-'#-#@)"'(%&363'(+.(/'&*%*("/#-"0#&'#6&C(" $%(#)&4)/&$#'132*.#'%*,"#&"#;&68#<=8S<>2?8#!"#$%&'#'132*.#$%(#24*B("#.&"(#0("*$('#$%(#7.*-$G &"6#6-$(8#@%(#3(3*41#)(..#&'#B"*,"#-'#$%(#*('!8+263'(+.!+))8 H($#/'#"*,#(N-3&"(#$%(#*5(4-$&*"#*7#$%(#7.*-$&"6G6-$(#$4-"'&'$*48#9(7*4(#$%(#)(..#&'#54*G 64-33(0#>,(#,&..#'%*4$.1#(N5.-&"#,%-$#$%&'#3(-"'?+#"*#)%-46(#(N&'$'#*"#$%(#7.*-$&"6#6-$( -"0#$%(#0(C&)(#*5(4-$('#-'#-#4(6/.-4#!G)%-""(.#("%-")(3("$#ZUL;^@8#!$#$%/'#(N%&2&$'#$%( -G\vXD#)%-4-)$(4&'$&)#'%*,"#-'#)/4C(#>/?#&"#;&68#<=8SK8#T*$(#$%-$#&"#$%&'#)-'(#$%(#$%4('%*.0 C*.$-6(#>=# ?#&'#4-$%(4#.*,8#@%&'#'$-$(#*7#$%(#$4-"'&'$*4#&'#B"*,"#-'#$%(#&"(67/"3/'##+2 *('(+8# !$# &'# *"(# *7#$,*# '$-$('#&"# ,%&)%# $%(# 7.*-$&"6G6-$(#$4-"'&'$*4#)-"#(N&'$8#H($# /'# -42&G $4-4&.1#$-B(#$%(#"*$G54*64-33(0#'$-$(#$*#4(54('("$#-#'$*4(0#<8#@%-$#&'+#-#7.*-$&"6G6-$(#$4-"G '&'$*4#,%*'(#-G\vXD#)%-4-)$(4&'$&)#&'#$%-$#'%*,"#-'#)/4C(#>/?#&"#;&68#<=8SK#,&..#2(#'-&0#$*#2( '$*4&"6#-#<8 @*#54*64-3#$%(#7.*-$&"6G6-$(#$4-"'&'$*4+#-#.-46(#C*.$-6(#><]\KO#e?#&'#-55.&(0#2($,(("#&$' 04-&"#-"0#'*/4)(8#L&3/.$-"(*/'.1+#-#.-46(#C*.$-6(#>-2*/$#K=#e?#&'#-55.&(0#$*#&$'#'(.()$#6-$(8 ;&6/4(# <=8SS# '%*,'# $%(# 7.*-$&"6G6-$(# ZUL;^@# 0/4&"6# 54*64-33&"68# !"# $%(# -2'(")(# *7 -"1 )%-46(# *"# $%(# 7.*-$&"6# 6-$(+# $%(# 0(C&)(# 2(%-C('# -'# -# 4(6/.-4# !C)%-""(.# ("%-")(3("$ ZUL;^@b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iD Not programmed (1)

(a)

Programmed (0)

(b)

0 Sense voltage

vGS

Figure 15.32 ;%%+-,*1,(/'$,"#$-"(9,$(/$,"#$-G`vXD$)"1*1),#*(-,()$&9$1$9%&1,(/'N'1,#$,*1/-(-,&*$1-$1$*#-+%,$&9$2*&N '*1::(/'6

15.5 Read-only Memory (ROM)

$25 V Select gate $16 V

Oxide n channel

Drain n$

Source n$

Depletion layer p substrate

Figure 15.33 !"#$9%&1,(/'N'1,#$,*1/-(-,&*$.+*(/'$2*&'*1::(/'6

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1245

1246 Chapter 15 Memory Circuits

Summary >%(2N9%&2-$#:2%&7$&/#$&*$ :&*#$ %1,)"#-6$ !"#$<1-()$ -,1,() %1,)"$(-$1$<(-,1<%#$)(*)+(,$(:2%#:#/,#.$+-(/'$,=&$(/8#*,#*)&//#),#.$(/$1$2&-(,(8#N9##.<1)G$%&&26$!"#$%1,)"$)1/$*#:1(/ (/$#(,"#*$-,1<%#$-,1,#$(/.#9(/(,#%76 K-$ 1/$ 1%,#*/1,(8#$ ,&$ ,"#$ 2&-(,(8#N9##.<1)G$ 122*&1)"? :#:&*7$)1/$<#$2*&8(.#.$,"*&+'"$,"#$+-#$&9$)"1*'#$-,&*N 1'#6$K$/+:<#*$&9$0RIC$9%(2N9%&2-$1*#$*#1%(L#.$,"(-$=17? (/)%+.(/'$-&:#$:1-,#*`-%18#$S$9%(2N9%&2-6 K$ *1/.&:N1))#--$ :#:&*7$ EQKRF$ (-$ &/#$ (/$ ="()"$ ,"# ,(:#$ *#D+(*#.$ 9&*$ -,&*(/'$ E=*(,(/'F$ (/9&*:1,(&/$ 1/.$ 9&* *#,*(#8(/'$ E*#1.(/'F$ (/9&*:1,(&/$ (-$ (/.#2#/.#/,$ &9$ ,"# 2"7-()1%$%&)1,(&/$E=(,"(/$,"#$:#:&*7F$(/$="()"$,"#$(/9&*N :1,(&/$(-$-,&*#.6 !"#$:1e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

PROBLEMS

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PROBLEMS

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µ#()*$=$Pµ$()*$=$PT$ µ8BX 9 $!$$= P!#$=$PB$µ)K$"$$=$"#$=$L$µ)K$ 1 ' = J)X9 $"+1$122$=$A$U9 !"# H/3'$',&$'("+42&($8,"("8'&(*4'*8$32$&"8,$*+.&('&(V',"'$*4K v3$.&(4-4$v ! K$"+1$v 4$.&(4-4$v5 9$%&'&()*+&$',&$3-'5-'$32$&"8,

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CHAPTER 15

PROBLEMS

1248 Chapter 15 Memory Circuits >)?#R(5(-$#>2?#7*4#G#.*,#,&$%#$%(#).*)B# φ #6*&"6#.*,8# E.F$S&#-$,"#$&2#*1,(&/$&9$,"(-$)(*)+(,$*#%7$&/$)"1*'#$-,&*1'#l VDD Q1 Q2

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Section 15.2: Semiconductor Memories: Types and Architectures 15.12 :#5-4$&)/.-4#<#ZG2&$#'I/-4(#3(3*41#-44-1#%-'#&$'#5(4&5%G (4-.# )&4)/&$'# 4(*46-"&A(0# $*# -..*,# 7*4# $%(# 4(-0*/$# *7# -# <]G2&$ ,*408#M*,#3-"1#-004(''#2&$'#,&..#$%(#"(,#0('&6"#"((0n 15.13 ;*4# $%(# 3(3*41# )%&5# 0(')4&2(0# &"# Y4*2.(3# <=8R()-..# 74*3# 54*2.(3# <=8)-..(0 XR:Z?#21#M&$-)%&#/'('#-#O8<]Gµ3#54*)(''#,&$%#-#)(..#'&A( *7#O8S`#×#O8P]#µ3K#&"#-#
Section 15.3: Random-Access Memory (RAM) Cells 15.15 0&/-(.#*$ ,"#$ *#1.$ &2#*1,(&/$ &9$ ,"#$ \!$ CQKR$ )#%%$ &9 >('6$ 3O63P$ ="#/$ (,$ (-$ -,&*(/'$ 1$ J?$ ,"1,$ (-?$ = F V J$[? $ 1/. = F V = GG 6 $K--+:#$,"1,$,"#$<(,$%(/#-$1*#$2*#)"1*'#.$,&$ = GG

<#9&*#$,"#$=&*.N%(/#$8&%,1'#$(-$*1(-#.$,&$= GG 6 $CG#,)"$,"#$*#%#N 81/,$21*,$&9$,"#$)(*)+(,$1/.$.#-)*(<#$,"#$&2#*1,(&/6$C"&=$,"1, ,"#$1/1%7-(-$21*1%%#%-$,"1,$2*#-#/,#.$(/$,"#$,#Z,$9&*$,"#$*#1.N3 &2#*1,(&/6 D 15.16 0&/-(.#*$1$\!$CQKR$)#%%$91<*()1,#.$(/$1$J63]Nµ: 0RIC$ 2*&)#--$ 9&*$ ="()"$ = #! V = #B V J6O$[ $ 1/. = GG V 36]$[6 $ ;9$ .+*(/'$ 1$ *#1.N3$ &2#*1,(&/$ (,$ (-$ *#D+(*#. ,"1,$ = F $.&#-$/&,$#Z)##.$J6P$[?$+-#$,"#$'*12"$(/$>('6$3O635 ,&$ .#,#*:(/#$ ,"#$ :1Z(:+:$ 1%%&=1<%#$ 81%+#$ &9$ ,"#$ *1,(& ( 6 ⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 6 $>&*$ @ 3 V @ O V J63]$µ:? $-#%#),$81%N +#-$ 9&*$ 6 3 $ 1/.$ 6 O $ ,"1,$ :(/(:(L#$ ,"#$ )&:<(/#.$ 1*#1-$ &9 F 3 $ 1/.$ F O 6 $ K--+:#$ ,"1,$ ,"#$ :(/(:+:$ =(.,"$ 1%%&=#.$ (J63]$µ:6 15.17 Q#2#1,$ YZ#*)(-#$ 3O65$ 9&*$ 1/$ CQKR$ 91<*()1,#.$ (/$ 1 J6PONµ:$ 0RIC$ 2*&)#--$ 9&*$ ="()"$ = GG V P6O$[ $ 1/.

= # V J6O$[6

15.18 Q#2#1,$ YZ#*)(-#$ 3O65$ 9&*$ 1/$ CQKR$ 91<*()1,#.$ (/$ 1 J634Nµ:$ 0RIC$ 2*&)#--$ 9&*$ ="()"$ = GG V 36P$[ $ 1/.

= # V J65$[6

15.19 @&)1,#$&/$,"#$'*12"$&9$>('6$3O635$,"#$2&(/,-$K?$T?$1/. 0$,"1,$)&**#-2&/.$,&$,"#$9&%%&=(/'$,"*##$2*&)#--$,#)"/&%&'(#-H E1F$J6PONµ:H$ = GG V P6O$[ $1/.$ = # V J6O$[ E
=F $ V =# 6 *15.20 Q#9#*$,&$,"#$)(*)+(,$(/$>('6$3O634$1/.$9(/.$,"#$:1ZN (:+:$*1,(&$ ( 6 ⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 $9&*$= F ≤ = # ?$,"(-$,(:#$,1G(/' (/,&$ 1))&+/,$ ,"#$ 8#%&)(,7N-1,+*1,(&/$ #99#),$ EC#),(&/$ 346O? YD6$3463JJF6$!"#$CQKR$(-$91<*()1,#.$(/$1$J63]Nµ:$0RIC 2*&)#--$9&*$="()"$ = GG V 36]$[?$ = # V J6O$[? $1/.$9&*$,"# !N)"1//#%$ .#8()#-$ = GD-1, V J6\$[6 $ 0&:21*#$ ,&$ ,"#$ 81%+# &<,1(/#.$=(,"&+,$1))&+/,(/'$9&*$8#%&)(,7$-1,+*1,(&/6$E?-!#H 0&/8(/)#$ 7&+*-#%9$ ,"1,$ 9&*$ ,"(-$ -(,+1,(&/$ &/%7$ F O $ =(%%$ <# &2#*1,(/'$(/$8#%&)(,7$-1,+*1,(&/6F D *15.21 >&*$ ,"#$ \!$ CQKR$ &9$ >('6$ 3O63P?$ 91<*()1,#.$ (/$ 1 J63]Nµ:$ 0RIC$ 2*&)#--$ 9&*$ ="()"$ = GG V 36]$[? $ = #J V J6O$[? $ P φ 3 V J6]$[? $1/.$ γ a J64 [3XP?$9(/.$,"#$:1Z(:+: *1,(&$ ( 6 ⁄ @ ) O ⁄ ( 6 ⁄ @ ) 3 $ 9&*$ ="()"$ = F ≤ = #J $ .+*(/'$ 1 *#1.N3$ &2#*1,(&/$ E>('6$ 3O634F6$ !1G#$ (/,&$ 1))&+/,$ ,"#$ <&.7 #99#),$ (/$ F O 6 $ 0&:21*#$ ,&$ ,"#$ 81%+#$ &<,1(/#.$ =(,"&+, 1))&+/,(/'$9&*$,"#$<&.7$#99#),6 D 15.22 K$ \!$ CQKR$ )#%%$ (-$ 91<*()1,#.$ (/$ 1$ J634Nµ: 0RIC$2*&)#--$9&*$="()"$ = GG V 36P$[? $ = # V J65$[? $1/. P µ ! H ": V 54J$µK ⁄ [ 6 $ !"#$ (/8#*,#*-$ +,(%(L#$ E6I@F!$ a$ 36 Y1)"$&9$,"#$<(,$%(/#-$"1-$1$PN2>$)121)(,1/)#$,&$'*&+/.6$!"# -#/-#$1:2%(9(#*$*#D+(*#-$1$:(/(:+:$&9$J6PN[$(/2+,$9&*$*#%(N 1<%#$1/.$91-,$&2#*1,(&/6

Problems 1249

D 15.24 >&*$1$\!$CQKR$)#%%$91<*()1,#.$(/$1$J634Nµ:$0RIC 2*&)#--?$ 9(/.$ ,"#$ :1Z(:+:$ 2#*:(,,#.$ 81%+#$ &9$ ( 6 ⁄ @ ) B $ (/ ,#*:-$ &9$ ( 6 ⁄ @ ) / $ &9$ ,"#$ 1))#--$ ,*1/-(-,&*-6$ K--+:# = GG V 36P$[ ?$= #! V = #B V J65$[?$1/.$ µ ! V 5 µ B6 D 15.25 >&*$1$\!$CQKR$)#%%$91<*()1,#.$(/$1$J6PONµ:$0RIC 2*&)#--?$ 9(/.$ ,"#$ :1Z(:+:$ 2#*:(,,#.$ 81%+#$ &9$ ( 6 ⁄ @ ) B $ (/ ,#*:-$ &9$ ( 6 ⁄ @ ) / $ &9$ ,"#$ 1))#--$ ,*1/-(-,&*-6$ K--+:# = GG V P6O$[? $ = #! V = #B V J6O$[? $1/.$ µ ! " 5 µ B 6 15.26 @&)1,#$ &/$ ,"#$ '*12"$ (/$ >('6$ 3O63^$ ,"#$ 2&(/,-$ K?$ T? 1/.$0$)&**#-2&/.(/'$,&$,"#$9&%%&=(/'$,"*##$0RIC$91<*()1N ,(&/$2*&)#--#-H E1F$J6PONµ:H$ = GG V P6O$[? $ = #! V = #B V J6O$[ E&*$1%%$,"*##?$ µ ! " 5 µ B 6 $;/$#1)"$)1-#?$ = F $(-$,&$<#$%(:(,#. ,&$1$:1Z(:+:$81%+#$&9$ = #! 6 D 15.27 #X('&6"#-#3&"&3/3G'&A(#]@#LR:Z#)(..#&"#-#O8<=8=?#-"0#><=8<
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PROBLEMS

15.23 0&/-(.#*$ ,"#$ &2#*1,(&/$ &9$ =*(,(/'$ 1$ 3$ (/,&$ 1$ \! CQKR$)#%%$,"1,$(-$&*('(/1%%7$-,&*(/'$1$J6$CG#,)"$,"#$*#%#81/, 21*,$&9$,"#$)(*)+(,$1/.$#Z2%1(/$,"#$&2#*1,(&/6$M(,"&+,$.&(/' .#,1(%#.$ 1/1%7-(-?$ -"&=$ ,"1,$ ,"#$ 1/1%7-(-$ =&+%.$ %#1.$ ,& *#-+%,-$(.#/,()1%$,&$,"&-#$&<,1(/#.$(/$,"#$,#Z,$9&*$,"#$=*(,#NJ &2#*1,(&/6

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CHAPTER 15

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CHAPTER 15

PROBLEMS

1250 Chapter 15 Memory Circuits ∆= &'#$%(#&"&$&-.#0&77(4(")(GC*.$-6(#2($,(("#$%(#$,*#2&$#.&"('8 >R(7(4#$*#;&68#<=8K<8? >2? !7# $%(# 4('5*"'(# $&3(# *7# $%(# '("'(# -35.&7&(4# &'# $*# 2( 4(0/)(0#$*#*"(G%-.7#$%(#C-./(#*7#-"#*4&6&"-.#0('&6"+#21#,%-$ 7-)$*4#3/'$#$%(#,&0$%#*7#-..#$4-"'&'$*4'#2(#&")4(-'(0n >)? !7#7*4#-#5-4$&)/.-4#0('&6"+#=GG#=#<8`#e#-"0#∆=#=#O8K#e+ 7&"0#$%(#7-)$*4#21#,%&)%#$%(#,&0$%#*7#-..#$4-"'&'$*4'#3/'$#2( &")4(-'(0#'*#$%-$#∆=#&'#4(0/)(0#21#-#7-)$*4#*7#[#,%&.(#B((5G &"6##5#/")%-"6(0n D 15.35 !$# &'# 4(I/&4(0# $*# 0('&6"# -# '("'(# -35.&7&(4# *7# $%( $15(#'%*,"#&"#;&68#<=8KO#$*#*5(4-$(#,&$%#-#XR:Z#/'&"6#$%( 0/331G)(..#$()%"&I/(#&../'$4-$(0#&"#;&68#<=8KK8#@%(#XR:Z )(..# 54*C&0('# 4(-0*/$# C*.$-6('# *7# −('6 3O6P5$,&$.#,#),$1/$(/2+,$-('/1%$&9$3JJ$:[$1/.$2*&8(.#$1$9+%% &+,2+,$ (/$ J64$ /-6$ ;9$ H$ a$ \J$ 9>$ 1/.$ = GG V 36P$[? $ 9(/.$ ,"# *#D+(*#.$)+**#/,$L$1/.$,"#$2&=#*$.(--(21,(&/6 D 15.37 0&/-(.#*$ ,"#$ -#/-#$ 1:2%(9(#*$ (/$ >('6$ 3O6P5$ (/$ ,"# #D+(%(<*(+:$ )&/.(,(&/$ -"&=/$ (/$ 21*,$ E
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Problems 1251

15.42 K$*(/'N&9N#%#8#/$&-)(%%1,&*$(-$9&+/.$,&$&2#*1,#$1,$PJ RWL6$>(/.$,"#$2*&21'1,(&/$.#%17$&9$,"#$(/8#*,#*6

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PROBLEMS

D 15.43 S#-('/$ ,"#$ &/#N-"&,$ )(*)+(,$ &9$ >('6$ 3O6Pb$ ,&$ 2*&N 8(.#$ 1/$ &+,2+,$ 2+%-#$ &9$ 3JN/-$ =(.,"6$ ;9$ ,"#$ (/8#*,#*-$ 181(%N 1<%#$ "18#$ # K V P6O $ /-$ .#%17?$ "&=$ :1/7$ (/8#*,#*-$ .&$ 7&+ /##.$9&*$,"#$.#%17$)(*)+(,l

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CHAPTER 15

15.41 0&/-(.#*$1$*(/'$&-)(%%1,&*$)&/-(-,(/'$&9$9(8#$(/8#*,#*-? #1)"$"18(/'$ # K@? V \ $/-$1/.$ # K?@ V 5 $/-6$CG#,)"$&/#$&9 ,"#$&+,2+,$=18#9&*:-?$1/.$-2#)(97$(,-$9*#D+#/)7$1/.$,"#$2#*N )#/,1'#$&9$,"#$)7)%#$.+*(/'$="()"$,"#$&+,2+,$(-$"('"6

PART IV

Filters and Oscillators CHAPTER 16

Filters and Tuned Amplifiers

1254

CHAPTER 17

Signal Generators and Waveform-Shaping Circuits

1334

I

n Part IV we study an important class of analog circuits: filters and oscillators. Both topics have in common an application or system orientation. They provide dramatic and powerful illustration of the application of both negative and positive feedback. While the filters studied here are linear circuits, the design of oscillators makes use of both linear and nonlinear techniques. Chapter 16 deals with the design of filters, which are important building blocks of communication and instrumentation systems. Filter design is one of the rare areas of engineering for which a complete design theory exists, starting from specification and culminating in an actual working circuit. The material presented should allow the reader to perform such a complete design process. In the design of electronic systems, the need usually arises for signals of various waveforms—sinusoidal, pulse, square-wave, and so on. The generation of such signals is the subject of Chapter 17. It will be seen that some of the circuits utilized in waveform generation employ an op-amp version of the basic memory element studied in Chapter 15, the bistable multivibrator or latch. The study of filters and oscillators relies on a thorough familiarity with basic feedback concepts including the effect of feedback on the amplifier poles (Chapter 10), and with op-amp circuit applications (Chapter 2). As well, we assume knowledge of basic splane concepts including transfer functions, poles, zeros, and Bode plots.

1253

CHAPTER 16

Filters and Tuned Amplifiers Introduction

1255

16.1 Filter Transmission, Types, and Specification 1256 16.2 The Filter Transfer Function

1260

16.7 Second-Order Active Filters Based on the Two-Integrator-Loop Topology 1293 16.8 Single-Amplifier Biquadratic Active Filters 1299

16.3 Butterworth and Chebyshev Filters 1263

16.9 Sensitivity

16.4 First-Order and Second-Order Filter Functions 1270

16.11 Tuned Amplifiers

16.5 The Second-Order LCR Resonator 1279 16.6 Second-Order Active Filters Based on Inductor Replacement 1285

1307

16.10 Switched-Capacitor Filters

Summary

1327

Problems

1328

1315

1310

IN THIS CHAPTER YOU WILL LEARN 1. How filters are characterized by their signal-transmission properties and how they are classified into different types based on the relative location of their passband(s) and stopband(s). 2. How filters are specified and how to obtain a filter transfer function that meets the given specifications, including the use of popular special functions such as the Butterworth and the Chebyshev. 3. The various first-order and second-order filter functions and their realization using op amps and RC circuits. 4. The basic second-order LCR resonator and how it can be used to realize the various second-order filter functions. 5. The best op amp–RC circuit for realizing an inductance and how it can be used as the basis for realizing the various second-order filter functions. 6. That connecting two op-amp integrators, one inverting and one noninverting, in a feedback loop realizes a second-order resonance circuit and can be used to obtain circuit realizations of the various secondorder filter functions. 7. How second-order filter functions can be realized using a single op amp and an RC circuit, and the performance limitations of these minimal realizations. 8. How the powerful concept of circuit sensitivity can be applied to assess the performance of filter circuits in the face of finite component tolerances. 9. The basis for the most popular approach to the realization of filter functions in IC form; the switched-capacitor technique. 10. The design of tuned transistor amplifiers for radio-frequency (RF) applications.

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1255

1256 Chapter 16 Filters and Tuned Amplifiers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16.1 Filter Transmission, Types, and Specification 1257

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1258 Chapter 16 Filters and Tuned Amplifiers

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16.1 Filter Transmission, Types, and Specification 1259

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1260 Chapter 16 Filters and Tuned Amplifiers "T $, dB

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16.2 The Filter Transfer Function B%+#4&7$+,#$,)"'4+,#4/"($&3"#!E"I#()"#6+#.,&$$+"#)'#$%+#,)$&3#34#$.3#*371"35&)7'#)' 1 1bF + 9#9#9# + 2 G 2 1 " + 2 1bF " A ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 0 0bF " + 3 0bF " + 9#9#9# + 3 G

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B%+#0+2,++#34#$%+#0+"35&")$3,-#0-#&'#$%+#*$+,&-'2-/&-9#:3,#$%+#4&7$+,#(&,(/&$#$3#6+#'$)67+-#$%+ 0+2,++#34#$%+#"/5+,)$3,#5/'$#6+#7+''#$%)"#3,#+?/)7#$3#$%)$#34#$%+#0+"35&")$3,D#1#≤#09#B%+ "/5+,)$3,#)"0#0+"35&")$3,#(3+44&(&+"$'-#2G-#2F-#9#9#9#-#21#)"0#3G-#3F-#9#9#9#-#30−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`)(%#$,)"'5&''&3"#=+,3#3,#*37+#()"#6+#+&$%+,#)#,+)7#3,#)#(35*7+<#"/56+,9#L35*7+< =+,3'#)"0#*37+'-#%3.+;+,-#5/'$#3((/,#&"#(3"@/2)$+#*)&,'9#B%/'-#&4# −F#+#&N#%)**+"'#$3#6+#) =+,3-#$%+"#−F#−#&N#)7'3#5/'$#6+#)#=+,39 C&"(+#&"#$%+#4&7$+,#'$3*6)"0#$%+#$,)"'5&''&3"#&'#,+?/&,+0#$3#6+#=+,3#3,#'5)77-#$%+#4&7$+, $,)"'5&''&3"#=+,3'#),+#/'/)771#*7)(+0#3"#$%+#&ω#)<&'#)$#'$3*6)"0#4,+?/+"(&+'9#B%&'#&"0++0#&' $%+#()'+#43,#$%+#4&7$+,#.%3'+#$,)"'5&''&3"#4/"($&3"#&'#'8+$(%+0#&"#:&29#FO9P9#B%&'#*),$&(/7),#4&7A $+,#()"#6+#'++"#$3#%);+#&"4&"&$+#)$$+"/)$&3"#E=+,3#$,)"'5&''&3"I#)$#$.3#'$3*6)"0#4,+?/+"(&+'U ω/F# )"0# ω/N9# B%+# 4&7$+,# $%+"# 5/'$# %);+# $,)"'5&''&3"# =+,3'# )$# "# =# +&ω/F# )"0# " = +&ω/N9 F#B%,3/2%3/$#$%&'#(%)*$+,-#.+#/'+#$%+#")5+'#+$/'"#)"0#52-,.2/#6$7'"#&"$+,(%)"2+)6719

16.2 The Filter Transfer Function 1261

j# O x poles O zeros

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H3.+;+,-# '&"(+# (35*7+<# =+,3'# 3((/,# &"# (3"@/2)$+# *)&,'-# $%+,+# 5/'$# )7'3# 6+# $,)"'5&''&3" =+,3'#)$#"#=#−&ω/F#)"0#"#=#−&ω/N9#B%/'#$%+#"/5+,)$3,#*371"35&)7#34#$%&'#4&7$+,#.&77#%);+#$%+ 4)($3,'#E"#+#&ω/FIE"#−# &ω/FIE"#+# &ω/NIE"#−#&ω/NI-#.%&(%#()"#6+#.,&$$+"#)'# ( " N + ω N/F ) ( " N + ω N/N ) 9 :3,#"#=#&ω# E*%1'&()7# 4,+?/+"(&+'I#$%+#"/5+,)$3,#6+(35+'# ( − ω N + ω N/F ) ( − ω N + ω N/N ) -#.%&(% &"0++0#&'#=+,3#)$#ω#=#ω/F#)"0#ω#=#ω/N9 L3"$&"/&"2#.&$%#$%+#+<)5*7+#&"#:&29#FO9P-#.+#36'+,;+#$%)$#$%+#$,)"'5&''&3"#0+(,+)'+' $3.),0#−∞#)'#ω#)**,3)(%+'#∞9#B%/'#$%+#4&7$+,#5/'$#%);+#3"+#3,#53,+#$,)"'5&''&3"#=+,3'#)$ "#=#∞9#!"#2+"+,)7-#$%+#"/56+,#34#$,)"'5&''&3"#=+,3'#)$#"#= ∞#&'#$%+#0&44+,+"(+#6+$.++"#$%+ 0+2,++#34#$%+#"/5+,)$3,#*371"35&)7-#1-#)"0#$%+#0+2,++#34#$%+#0+"35&")$3,#*371"35&)7-#0-#34 $%+# $,)"'4+,# 4/"($&3"# &"# `?9# EFO9OI9# B%&'# &'# 6+()/'+# )'# "# )**,3)(%+'# ∞-# !E"I# )**,3)(%+' 0!1 *)"0#$%/'#&'#')&0#$3#%);+#0#−#1#=+,3'#)$#"*=#∞9 21 ⁄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±&ω/F-#"#=#±&ω/N-#)"0#"#= ∞9#B%/'-#$%+#$,)"'4+,#4/"($&3"#43,#$%&'#4&7$+,#&'#34#$%+#43,5 2 Q ( " N + ω N/F ) ( " N + ω N/N ) A ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA "S + 3Q "Q + 3P "P + 3N "N + 3F " + 3G

EFO9\I

>'#)"3$%+,#+<)5*7+-#(3"'&0+,#$%+#6)"0*)''#4&7$+,#.%3'+#5)2"&$/0+#,+'*3"'+#&'#'%3."#&" :&29#FO9Q9#B%&'#4&7$+,#%)'#$,)"'5&''&3"#=+,3'#)$#"#=#± &ω/F#)"0#"#=#± &ω/N9#!$#)7'3#%)'#3"+#3,#53,+ =+,3'#)$#"#=#G#)"0#3"+#3,#53,+#=+,3'#)$#"#= ∞#E6+()/'+#$%+#$,)"'5&''&3"#0+(,+)'+'#$3.),0#G##)' ω#)**,3)(%+'#G#)"0#∞I9#>''/5&"2#$%)$#3"71#3"+#=+,3#+<&'$'#)$#+)(%#34#"#=#G#)"0#"*=#∞-#$%+#4&7A $+,#5/'$#6+#34#'&<$%#3,0+,-#)"0#&$'#$,)"'4+,#4/"($&3"#$)8+'#$%+#43,5 2 S " ( " N + ω N/F ) ( " N + ω N/N ) A !( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA " O + 3 S " S + 9#9#9# + 3 G

EFO9[I

>#$1*&()7#*37+b=+,3#*73$#43,#'/(%#)#4&7$+,#&'#'%3."#&"#:&29#FO9O9 >'#)#$%&,0#)"0#4&")7#+<)5*7+-#(3"'&0+,#$%+#73.A*)''#4&7$+,#.%3'+#$,)"'5&''&3"#4/"($&3"#&' 0+*&($+0#&"#:&29#FO9^E)I9#T+#36'+,;+#$%)$#&"#$%&'#()'+#$%+,+#),+#"3#4&"&$+#;)7/+'#34#ω#)$#.%&(%

1262 Chapter 16 Filters and Tuned Amplifiers

Figure 16.6 W37+b=+,3# *)$$+,"# 43,#$%+# 6)"0A *)''#4&7$+,#.%3'+#$,)"'5&''&3"#4/"($&3"#&'#'%3." &"#:&29#FO9Q9#B%&'#&'#)#'&<$%A3,0+,#4&7$+,#E0#=#OI9

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EFO9FGI

16.3 Butterworth and Chebyshev Filters

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EXERCISES 16.3 >#'+(3"0A3,0+,#4&7$+,#%)'#&$'#*37+'#)$# " = − ( F ⁄ N ) ± & ( P ⁄ N )9 *B%+#$,)"'5&''&3"#&'#=+,3#)$# ω =#N ,)0Z'#)"0#&'#/"&$1#)$#0(#Eω#=#GI9#:&"0#$%+#$,)"'4+,#4/"($&3"9

F "N + Q Q " +"+F 16.4 >#43/,$%A3,0+,#4&7$+,#%)'#=+,3#$,)"'5&''&3"#)$#ω#=#G-#ω#=#N#,)0Z'-#)"0#ω#=#∞9#B%+#")$/,)7#530+' ),+#−G9F#±#&G9\#)"0#−G9F#±# &F9N9#:&"0#!E"I9 2P " ( "N + Q ) Ans.' ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ( " N + G9N" + G9OS ) ( " N + G9N" + F9QS ) A Ans.' ! ( " )#= AAA # AAAAAAAAAAAAAAAAAAAAA N

16.5 :&"0#$%+#$,)"'4+,#4/"($&3"#!E"I#34#)#$%&,0A3,0+,#)77A*37+#73.A*)''#4&7$+,#.%3'+#*37+'#),+#)$#)#,)0&)7 0&'$)"(+#34#F#,)0Z'#4,35#$%+#3,&2&"#)"0#.%3'+#(35*7+<#*37+'#),+#)$#PG°#)"27+'#4,35#$%+#&ω#)<&'9#B%+ 0(#2)&"#&'#/"&$19#C%3.#$%)$# !( & ω ) = F ⁄ F + ω O 9#:&"0#ω P0R#)"0#$%+#)$$+"/)$&3"#)$#ω#=#P#,)0Z'9 Ans.'!E"I#=# F ⁄ ( " + F ) E"N#+#"#+#FID#F#,)0Z'D#N\9O#0R

16.3 Butterworth and Chebyshev Filters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1263

1264 Chapter 16 Filters and Tuned Amplifiers !T ! 1 1 #1 " ' 2

0

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F !( & ω ) #= AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ω N0 F + ' N AAAAAA

EFO9FFI

ω+

F EFO9FNI !( & ω + ) = AAAAAAAAAAAAAAAAAA N F+' B%/'-#$%+#*),)5+$+,# '# 0+$+,5&"+'#$%+#5)<&5/5#;),&)$&3"# &"# *)''6)"0# $,)"'5&''&3"-#)5)<)((3,0&"2#$3 ) 5)< = NG 732 F " ' N

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N0

) ( ω " ) = ! NG 732 [ F ⁄ F + ' ( ω " ⁄ ω + ) ] N

N0

# = FG 732 [ F + ' ( ω " ⁄ ω + ) ]

EFO9FSI

16.3 Butterworth and Chebyshev Filters 1265

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8 ωG !( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ( " ! + F ) ( " ! + N ) #9#9#9# ( " ! + 0 )

EFO9FOI

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1266 Chapter 16 Filters and Tuned Amplifiers

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p1

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0

%

45*

#p

$% 1 '

1 2

0

%

p2

N)2

(a)

(b) j#

j#

p1

p2

60*

#p 60*

p1

s plane

0

$% 1 '

22.5*

p2

1 3

s plane

45*

#p

45*

$% 1 '

0

% p3

1 4

%

45* 22.5*

p3

p4 N)3 (c)

N)4 (d)

Figure 16.10 g,)*%&()7#(3"'$,/($&3"#43,#0+$+,5&"&"2#$%+#*37+'#34#)#R/$$+,.3,$%#4&7$+,#34#3,0+,#09#>77#$%+#*37+'#7&+#&"#$%+#7+4$#%)74#34 $%+#"#*7)"+#3"#)#(&,(7+#34#,)0&/'#ω G#=#ω+EFZ'IFZ0-#.%+,+#'#&'#$%+#*)''6)"0#0+;&)$&3"#*),)5+$+,#E ' = FG )5)< ⁄ FG ! F IU#>"?#$%+#2+"+,)7 ()'+D#>;?#0#=#ND#>1?#0#=#PD#>/?#0#=#Q9

Example 16.1 :&"0#$%+#R/$$+,.3,$%#$,)"'4+,#4/"($&3"#$%)$#5++$'#$%+#43773.&"2#73.A*)''#4&7$+,#'*+(&4&()$&3"'U#9+# =#FG 8H=-#)5)<#=#F#0R-#9"#=#FS#8H=-#)5&"#=#NS#0R-#0(#2)&"#=#F9

Solution C/6'$&$/$&"2#)5)<# =#F#0R#&"$3#`?9#EFO9FQI#1&+70'# '# =#G9SG\\9#`?/)$&3"#EFO9FSI#&'#$%+"#/'+0#$3#0+$+,5&"+ $%+#4&7$+,#3,0+,#61#$,1&"2#;),&3/'#;)7/+'#43,#09#T+#4&"0#$%)$#0# =#\#1&+70'#)Eω"I# =#NN9P#0R#)"0#0# =#[ 2&;+'#NS9\#0R9#T+#$%/'#'+7+($#0#=#[9

16.3 Butterworth and Chebyshev Filters 1267

Figure 16.11 W37+'#34#$%+#"&"$%A3,0+,#R/$$+,.3,$%#4&7$+,#34#`<)5*7+#FO9F9

:&2/,+# FO9FF# '%3.'# $%+# 2,)*%&()7# (3"'$,/($&3"# 43,# 0+$+,5&"&"2# $%+# *37+'9# B%+# *37+'# )77# %);+# $%+ F⁄0 F⁄[ ')5+#4,+?/+"(1#ω G = ω+ EF ⁄ ' I #=#Nπ# ×#FG #×#FGP( F ⁄ G9SG\\ ) #=#O9^^P#×#FGQ#,)0Z'9#B%+#4&,'$#*37+ +F#&'#2&;+"#61

+F = ω G ( − (3' \G° + & '&" \G° ) = ω G ( −G9F^PO + &G9[\Q\ ) N

N

L356&"&"2#+F#.&$%#&$'#(35*7+<#(3"@/2)$+#+[#1&+70'#$%+#4)($3,# ( " + "G9PQ^N ω G + ω G ) #&"#$%+#0+"35&")$3, 34# $%+# $,)"'4+,# 4/"($&3"9# B%+# ')5+# ()"# 6+# 03"+# 43,# $%+# 3$%+,# (35*7+<# *37+'-# )"0# $%+# (35*7+$+# $,)"'4+, 4/"($&3"#&'#36$)&"+0#/'&"2#`?9#EFO9FOI-

ω

[

G ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N N N ( " + ω G ) ( " + "F9\^[Q ω G + ω G ) ( " + "F9SPNF ω G + ω G )

F A # ## × AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N N N ( " + " ω G + ω G ) ( " + "G9PQ^N ω G + ω G )

16.3.2 The Chebyshev Filter :&2/,+# FO9FN# '%3.'# ,+*,+'+"$)$&;+# $,)"'5&''&3"# 4/"($&3"'# 43,# L%+61'%+;Q# 4&7$+,'# 34# +;+" )"0 300#3,0+,'9#B%+#L%+61'%+;#4&7$+,#+<%&6&$'#)"#+?/&,&**7+#,+'*3"'+#&"#$%+#*)''6)"0#)"0#) 53"3$3"&()771# 0+(,+)'&"2# $,)"'5&''&3"# &"# $%+# '$3*6)"09# T%&7+# $%+# 300A3,0+,# 4&7$+,# %)' ! ( G ) = F-#$%+#+;+"A3,0+,#4&7$+,#+<%&6&$'#&$'#5)<&5/5#5)2"&$/0+#0+;&)$&3"#)$# ω#=#G9#!"#63$% Q#

a)5+0# )4$+,# $%+# K/''&)"# 5)$%+5)$&(&)"# W9# V9# L%+61'%+;-# .%3# &"# F\[[# /'+0# $%+'+# 4/"($&3"'# &" '$/01&"2#$%+#(3"'$,/($&3"#34#'$+)5#+"2&"+'9

EFO9F^I

1268 Chapter 16 Filters and Tuned Amplifiers T

T

1

1

1 #&&&&&& 1 " '2

1 #&&&&&& 1 " '2

N)4

0

N)5

#p

0

#

#p

(a)

#

(b)

Figure 16.12 C8+$(%+'#34#$%+#$,)"'5&''&3"#(%),)($+,&'$&('#34#,+*,+'+"$)$&;+#>"?#+;+"A3,0+,#)"0#>;?#300A3,0+,#L%+61'%+;#4&7$+,'9

()'+'#$%+ $3$)7#"/56+,#34#*)''6)"0#5)<&5)#)"0#5&"&5)#+?/)7'#$%+#3,0+,#34#$%+#4&7$+,-#09#>77 $%+#$,)"'5&''&3"#=+,3'#34#$%+#L%+61'%+;#4&7$+,#),+#)$#ω#=#∞-#5)8&"2#&$#)"#)77A*37+#4&7$+,9 B%+#5)2"&$/0+#34#$%+#$,)"'4+,#4/"($&3"#34#)"#0$%A3,0+,#L%+61'%+;#4&7$+,#.&$%#)#*)''6)"0 +02+#E,&**7+#6)"0.&0$%I#ω+#&'#2&;+"#61

)"0

F !( & ω ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N !F F + ' (3' [ 0(3' ( ω ⁄ ω + ) ] F !( & ω ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N !F F + ' (3'% [ 0(3'% ( ω ⁄ ω + ) ]

43,# ω ≤ ω +

43,# ω ≥ ω +

EFO9F\I

EFO9F[I

>$#$%+#*)''6)"0#+02+-#ω#=#ω+-#$%+#5)2"&$/0+#4/"($&3"#&'#2&;+"#61 F !( & ω + ) = AAAAAAAAAAAAAAAAAA N F+' B%/'-#$%+#*),)5+$+,# #0+$+,5&"+'#$%+#*)''6)"0#,&**7+#)((3,0&"2#$3 N

) 5)< #= FG 732 ( F + ' )

EFO9NGI

L3";+,'+71-#2&;+"#)5)<-#$%+#;)7/+#34#'#&'#0+$+,5&"+0#4,35

' =

FG

) 5)< ⁄ FG

EFO9NFI

#− F

B%+#)$$+"/)$&3"#)(%&+;+0#61#$%+#L%+61'%+;#4&7$+,#)$#$%+#'$3*6)"0#+02+#Eω#=#ω"I#&'#43/"0 /'&"2#`?9#EFO9F[I#)' N

N

!F

) ( ω " ) = FG 732 [ F + ' (3'% ( 0(3'% ( ω " ⁄ ω + ) ) ]

EFO9NNI

16.3 Butterworth and Chebyshev Filters 1269

T&$%#$%+#)&0#34#)#()7(/7)$3,-#$%&'#+?/)$&3"#()"#6+#/'+0#$3#0+$+,5&"+#$%+#3,0+,#0#,+?/&,+0#$3 36$)&"#)#'*+(&4&+0#)5&"#61#4&"0&"2#$%+#73.+'$#&"$+2+,#;)7/+#34#0#$%)$#1&+70'#)Eω"I#≥#)5&"9#>' &"#$%+#()'+#34#$%+#R/$$+,.3,$%#4&7$+,-#&"(,+)'&"2#$%+#3,0+,#0#34#$%+#L%+61'%+;#4&7$+,#()/'+'#&$' 5)2"&$/0+#4/"($&3"#$3#)**,3)(%#$%+#&0+)7#6,&(8A.)77#73.A*)''#,+'*3"'+9 B%+#*37+'#34#$%+#L%+61'%+;#4&7$+,#),+#2&;+"#61 N: ! F π F ! FF + : = ! ω + '&" AAAAAAAAAAAAAAA AAA '&"% AAAA '&"% AAA 0 N 0 ' F N: ! F π !F F + & ω + (3' AAAAAAAAAAAAAAA AAA (3'% AAAA '&"% AAA 0 0 N '

EFO9NPI

:#=#F, N, 9#9#9#-#0

:&")771-#$%+#$,)"'4+,#4/"($&3"#34#$%+#L%+61'%+;#4&7$+,#()"#6+#.,&$$+"#)' 0

8 ω+ A ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 0−F ' #N ( " ! + F ) ( " ! + N ) #9#9#9# ( " ! + 0 )

EFO9NQI

.%+,+#8#&'#$%+#0(#2)&"#$%)$#$%+#4&7$+,#&'#,+?/&,+0#$3#%);+9 B3#'/55),&=+-#2&;+"#73.A*)''#$,)"'5&''&3"#'*+(&4&()$&3"'#34#$%+#$1*+#'%3."#&"#:&29#FO9P$%+#$,)"'4+,#4/"($&3"#34#)#L%+61'%+;#4&7$+,#$%)$#5++$'#$%+'+#'*+(&4&()$&3"'#()"#6+#43/"0#)'#437A 73.'U 1. X+$+,5&"+#'#4,35#`?9#EFO9NFI9 2. e'+#`?9#EFO9NNI#$3#0+$+,5&"+#$%+#3,0+,#,+?/&,+09 3. X+$+,5&"+#$%+#*37+'#/'&"2#`?9#EFO9NPI9 4. X+$+,5&"+#$%+#$,)"'4+,#4/"($&3"#/'&"2#`?9#EFO9NQI9 B%+#L%+61'%+;#4&7$+,#*,3;&0+'#)#53,+#+44&(&+"$#)**,3<&5)$&3"#$%)"#$%+#R/$$+,.3,$%#4&7A $+,9#B%/'-#43,#$%+#')5+#3,0+,#)"0#$%+#')5+#)5)<-#$%+#L%+61'%+;#4&7$+,#*,3;&0+'#2,+)$+,#'$3*A 6)"0#)$$+"/)$&3"#$%)"#$%+#R/$$+,.3,$%#4&7$+,9#>7$+,")$&;+71-#$3#5++$#&0+"$&()7#'*+(&4&()$&3"'3"+#,+?/&,+'#)#73.+,#3,0+,#43,#$%+#L%+61'%+;#$%)"#43,#$%+#R/$$+,.3,$%#4&7$+,9#B%&'#*3&"$#.&77 6+#&77/'$,)$+0##61#$%+#43773.&"2#+<)5*7+9

Example 16.2 :&"0# $%+# L%+61'%+;# $,)"'4+,# 4/"($&3"# $%)$# 5++$'# $%+# ')5+# 73.A*)''# 4&7$+,# '*+(&4&()$&3"'# 2&;+"# &" `<)5*7+ FO9FU#")5+71-##9+#=#FG#8H=-#)5)<#=#F#0R-##9"#=#FS#8H=-#)5&"#=#NS#0R-#0(#2)&"#=#F9

Solution C/6'$&$/$&"2#)5)<#=#F#0R#&"$3#`?9#EFO9NFI#1&+70'#'#=#G9SG\\9#R1#$,1&"2#;),&3/'#;)7/+'#43,#0#&"#`?9#EFO9NNI .+#4&"0#$%)$#0#=#Q#1&+70'#)Eω"I#=#NF9O#0R#)"0#0#=#S#*,3;&0+'#N[9[#0R9#T+#$%/'#'+7+($#0#=#S9#K+()77#$%)$#.+ ,+?/&,+0#)#"&"$%A3,0+,#R/$$+,.3,$%#4&7$+,#$3#5++$#$%+#')5+#'*+(&4&()$&3"'#&"#`<)5*7+#FO9F9 B%+#*37+'#),+#36$)&"+0#61#'/6'$&$/$&"2#&"#`?9#EFO9NPI#)'

+ F, + S = ω + ( −G9G\[S ± &G9[[GF ) + N, + Q = ω + ( −G9NPQN ± &G9OFF[ )

1270 Chapter 16 Filters and Tuned Amplifiers

Example 16.2 continued

+ S = ω + ( ! G9N\[S ) B%+#$,)"'4+,#4/"($&3"#&'#36$)&"+0#61#'/6'$&$/$&"2#$%+'+#;)7/+'#&"#`?9#EFO9NQI#)'

ω

S

+ A ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N \9FQG\ ( " + G9N\[S ω + ) ( " + "G9QO\Q ω + + G9QN[P ω + )

EFO9NSI

F A × AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N

" + "G9F^\[ ω + + G9[\\P ω +

.%+,+#ω+#=#$π# ×#%&'#()*+,-

EXERCISES D16.6 X+$+,5&"+#$%+#3,0+,#0#34#)#R/$$+,.3,$%#4&7$+,#43,#.%&(%#)5)<# =#F#0R-#ω " ⁄ ω + = F9S -#)"0#)5&"# = PG# 0R9# T%)$# &'# $%+# )($/)7# ;)7/+# 34# 5&"&5/5# '$3*6)"0# )$$+"/)$&3"# ,+)7&=+0h# !4# )5&"# &'# $3# 6+ +<)($71#PG#0R-#$3#.%)$#;)7/+#()"#)5)<#6+#,+0/(+0h Ans.'0#=#%%.#)/01#=#2$-34#*5.#&-6'#*5 16.7 :&"0#$%+#")$/,)7#530+'#)"0#$%+#$,)"'4+,#4/"($&3"#34#)#R/$$+,.3,$%#4&7$+,#.&$%#ω+#=#F#,)0Z'-#)5)< =#P#0R#E'#'#FI-#)"0#0#=#P9 N Ans.'−&-6# ± #& P ⁄ N #)1*#−%.#!7"8#=# F ⁄ ( " + F ) ( " + " + F ) 16.8 J6'+,;+#$%)$#`?9#EFO9F\I#()"#6+#/'+0#$3#4&"0#$%+#4,+?/+"(&+'#&"#$%+#*)''6)"0#)$#.%&(%# ! #&'#)$#&$' *+)8'#)"0#)$#&$'#;)77+1'9#EB%+#*+)8'#),+#,+)(%+0#.%+"#$%+#(3'Nc##d#$+,5#&'#=+,3-#)"0#$%+#;)77+1' (3,,+'*3"0#$3#$%+#(3'Nc##d#$+,5#+?/)7#$3#/"&$19I#:&"0#$%+'+#4,+?/+"(&+'#43,#)#4&4$%A3,0+,#4&7$+,9 Ans.'9:);,#)<#ω#=#&=#&-6>ω+=#)1*#&->6ω+.##*5.#2-2#*5 D16.10 !$#&'#,+?/&,+0#$3#0+'&2"#)#73.A*)''#4&7$+,#%);&"2#9+#=#F#8H=-#)5)<#=#F#0R-#9"#=#F9S#8H=-#)5&"#= SG#0R9#E)I#:&"0#$%+#,+?/&,+0#3,0+,#34#)#L%+61'%+;#4&7$+,9#T%)$#&'#$%+#+<(+''#'$3*6)"0#)$$+"/)A $&3"#36$)&"+0h#E6I#K+*+)$#43,#)#R/$$+,.3,$%#4&7$+,9 Ans.'7)8#0#=#3=#6#*5.#7D8#0#=#%C=#&-6#*5

16.4 First-Order and Second-Order Filter Functions !"#$%&'#'+($&3"-#.+#'%)77#'$/01#$%+#'&5*7+'$#4&7$+,#$,)"'4+,#4/"($&3"'-#$%3'+#34#4&,'$#)"0#'+(3"0 3,0+,9#B%+'+#4/"($&3"'#),+#/'+4/7#&"#$%+&,#3."#,&2%$#&"#$%+#0+'&2"#34#'&5*7+#4&7$+,'9#:&,'$A#)"0 '+(3"0A3,0+,#4&7$+,'#()"#)7'3#6+#()'()0+0#$3#,+)7&=+#)#%&2%A3,0+,#4&7$+,9#L)'()0+#0+'&2"#&'#&" 4)($#3"+#34#$%+#53'$#*3*/7),#5+$%30'#43,#$%+#0+'&2"#34#)($&;+#4&7$+,'#E$%3'+#/$&7&=&"2#3*#)5*' )"0# KL# (&,(/&$'I9# R+()/'+# $%+# 4&7$+,# *37+'# 3((/,# &"# (35*7+
16.4 First-Order and Second-Order Filter Functions 1271

$%+,+#.&77#)7'3#6+#)#4&,'$A3,0+,#4/"($&3"#&"#$%+#4)($3,&=)$&3"9#`)(%#34#$%+#'+(3"0A3,0+,#4/"(A $&3"'#c)"0#$%+#4&,'$A3,0+,#4/"($&3"#.%+"#!E"I#&'#300d#&'#$%+"#,+)7&=+0#/'&"2#3"+#34#$%+#3* )5*b KL#(&,(/&$'#$%)$#.&77#6+#'$/0&+0#&"#$%&'#(%)*$+,-#)"0#$%+#,+'/7$&"2#673(8'#),+#*7)(+0#&"#()'()0+9 !4#$%+#3/$*/$#34#+)(%#673(8#&'#$)8+"#)$#$%+#3/$*/$#$+,5&")7#34#)"#3*#)5*#.%+,+#$%+#&5*+0)"(+ 7+;+7#&'#73.#E&0+)771#=+,3I-#()'()0&"2#03+'#"3$#(%)"2+#$%+#$,)"'4+,#4/"($&3"'#34#$%+#&"0&;&0/)7 673(8'9#B%/'#$%+#3;+,)77#$,)"'4+,#4/"($&3"#34#$%+#()'()0+#&'#'&5*71#$%+#*,30/($#34#$%+#$,)"'4+, 4/"($&3"'#34#$%+#&"0&;&0/)7#673(8'-#.%&(%#&'#$%+#3,&2&")7#!E"I9

16.4.1 First-Order Filters B%+#2+"+,)7#4&,'$A3,0+,#$,)"'4+,#4/"($&3"#&'#2&;+"#61 2F " + 2G A ! ( " ) = AAAAAAAAAAAAAAAAAA " + ωG

EFO9NOI

B%&'#;$+$.&"-',-".#*&-'*0.1,$2.#(%),)($+,&=+'#)#4&,'$A3,0+,#4&7$+,#.&$%#)#")$/,)7#530+#)$#" = −ω G)#$,)"'5&''&3"#=+,3#)$# " = ! 2 G ⁄ 2 F -#)"0#)#%&2%A4,+?/+"(1#2)&"#$%)$#)**,3)(%+'#2F9#B%+#"/5+,A )$3,#(3+44&(&+"$'-#2G#)"0#2F-#0+$+,5&"+#$%+#$1*+#34#4&7$+,#E+929-#73.#*)''-#%&2%#*)''-#+$(9I9#C35+ '*+(&)7#()'+'#$32+$%+,# .&$%# *)''&;+#EKLI#)"0# )($&;+# E3*# )5*bKLI# ,+)7&=)$&3"'#),+#'%3."# &" :&29 FO9FP9# a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ω# )<&'9# EB%+1# ),+# ')&0# $3# 0&'*7)1# 5&,,3,A&5)2+# '155+$,1# .&$%# ,+'*+($# $3# $%+ &ω )<&'9I#J6'+,;+#$%)$#)7$%3/2%#$%+#$,)"'5&''&3"#34#$%+#)77A*)''#4&7$+,#&'#E&0+)771I#(3"'$)"$#)$ )77# 4,+?/+"(&+'-# &$'# *%)'+# '%3.'# 4,+?/+"(1# '+7+($&;&$19# >77A*)''# 4&7$+,'# ),+# /'+0# )'# *%)'+ '%&4$+,'#)"0#&"#'1'$+5'#$%)$#,+?/&,+#*%)'+#'%)*&"2#E+929-#&"#$%+#0+'&2"#34#(&,(/&$'#()77+0#7'/2; '<,2/%4'."=#.%&(%#()/'+#$%+#3;+,)77#$&5+#0+7)1#34#)#$,)"'5&''&3"#'1'$+5#$3#6+#(3"'$)"$#.&$% 4,+?/+"(1I9

EXERCISES D16.11 e'&"2#>F# =#FG#8Ω-#0+'&2"#$%+#3*#)5*bKL#(&,(/&$#34#:&29#FO9FPE6I#$3#,+)7&=+#)#%&2%A*)''#4&7$+, .&$%#)#(3,"+,#4,+?/+"(1#34#FGQ#,)0Z'#)"0#)#%&2%A4,+?/+"(1#2)&"#34#FG9 Ans.'>$#=#%&&#;Ω.#?#=#&-&%#µE D16.12 #X+'&2"#$%+#3*#)5*bKL#(&,(/&$#34#:&29#FO9FQ#$3#,+)7&=+#)"#)77A*)''#4&7$+,#.&$%#)#[G*#*%)'+#'%&4$#)$ FGP#,)0Z'9#C+7+($#'/&$)67+#(35*3"+"$#;)7/+'9 Ans.'9F,,0DA:#G?F0G:,H#>#=#>%#=#>$#=#%&#;Ω.#?#=#&-%#µE

16.4.2 Second-Order Filter Functions B%+#2+"+,)7#'+(3"0A3,0+,#E3,#;$90"/-",$1I#4&7$+,#$,)"'4+,#4/"($&3"#&'#/'/)771#+<*,+''+0#&"#$%+ '$)"0),0#43,5

1272 O

a0 a1

#0

#0

j#

#0

O 0

0

0

%

%

%

j#

O at &

j#

s-Plane Singularities

Figure 16.13 :&,'$A3,0+,#4&7$+,'9

2F " + 2G !E"I = AAAAAAAAAAAAAAAAAAAA " + ωG

7G8 N:1:()A

2F " !E"I = AAAAAAAAAAAAAAA " + ωG

7D8 L0M?#K),,#7L98

2G !E"I = AAAAAAAAAAAAAAA " + ωG

7)8 IFJ#K),,#7I98

Filter Type and T(s)

0

20 log ! a1 !

#0

!T !, dB a0 20 log ! ! #0

0

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a0 20 log ! ! #0

!T !, dB

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dB decade

a0 # ! ! (log) a1

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dB !20 decade

Bode Plot for |T|

C

R

CR ) 1 #0 DC gain ) 1

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R2

a1 a0

R2 R1 " R2 C1 HF gain ) C1 " C2 DC gain )

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C1

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R2

Op Amp–RC Realization

1273

#0

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#0

j#

Singularities

Figure 16.14 :&,'$A3,0+,#)77A*)''#4&7$+,9

2F > G

" ! ωG !E"I = −2 F AAAAAAAAAAAAAAA " + ωG

OAA#K),,#7O98

T(s)

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%

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|T| and φ

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R

R1

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Op Amp–RC Realization

1274 Chapter 16 Filters and Tuned Amplifiers

Figure 16.15 X+4&"&$&3"#34#$%+#*),)5+$+,'# ωG#)"0#@#34#)#*)&, 34#(35*7+
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ω

N

+ F, + N #= ! AAAAAAGA ± & ω G F ! ( F ⁄ Q@ ) N@

EFO9N^I

EFO9N\I

T+#),+#/'/)771#&"$+,+'$+0#&"#$%+#()'+#34#(35*7+#G9S9 :&2/,+#FO9FS#'%3.'#$%+#73()$&3"#34#$%+#*)&,#34#(35*7+"#&"4&"&$+#;)7/+#43,#@#73()$+'#$%+#*37+'#3"#$%+#&ω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⁄ N 9#B%+#,+'*3"'+#36$)&"+0#43,# @ = F ⁄ N #&'#$%+ R/$$+,.3,$%-#3,#5)<&5)771#47)$-#,+'*3"'+9 B%+#%&2%A*)''#EHWI#4/"($&3"#'%3."#&"#:&29#FO9FOE6I#%)'#63$%#$,)"'5&''&3"#=+,3'#)$#"#=#G E0(I9#B%+#5)2"&$/0+#,+'*3"'+#'%3.'#)#*+)8#43,#@ > F ⁄ N-#.&$%#$%+#0+$)&7'#34#$%+#,+'*3"'+#)' &"0&()$+09#J6'+,;+#$%+#0/)7&$1#6+$.++"#$%+#VW#)"0#HW#,+'*3"'+'9 a+<$#(3"'&0+,#$%+#6)"0*)''#ERWI#4&7$+,#4/"($&3"#'%3."#&"#:&29#FO9FOE(I9#H+,+-#3"+#$,)"'A 5&''&3"#=+,3#&'#)$#"#=#G#E0(I-#)"0#$%+#3$%+,#&'#)$#"#=#∞9#B%+#5)2"&$/0+#,+'*3"'+#*+)8'#)$#ω#= ωG9#B%/'#$%+#1&.,&-'*-&90&.1:#34#$%+#6)"0*)''#4&7$+,#&'#+?/)7#$3#$%+#*37+#4,+?/+"(1#ωG9#B%+ '+7+($&;&$1#34#$%+#'+(3"0A3,0+,#6)"0*)''#4&7$+,#&'#/'/)771#5+)'/,+0#61#&$'#AB7C*3257D%7-E9#B%&'

16.4 First-Order and Second-Order Filter Functions

&'#$%+#0&44+,+"(+#6+$.++"#$%+#$.3#4,+?/+"(&+'#ωF#)"0#ωN#)$#.%&(%#$%+#5)2"&$/0+#,+'*3"'+#&' P#0R#6+73.#&$'#5)<&5/5#;)7/+#E)$#ωGI9#!$#()"#6+#'%3."#$%)$

ω N ω F, ω N = ω G F + ( F ⁄ Q@ ) ± AAAAAAGA

EFO9N[I

CF ≡ ω N ! ω F = ω G ⁄ @

EFO9PGI

N@

B%/'-

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EXERCISES 16.13 :3,#)#5)<&5)771#47)$#'+(3"0A3,0+,#73.A*)''#4&7$+,# E@ = F ⁄ N I-#'%3.#$%)$#)$# ω#=# ωG#$%+#5)2"&A $/0+#,+'*3"'+#&'#P#0R#6+73.#$%+#;)7/+#)$#0(9 16.14 g&;+#$%+#$,)"'4+,#4/"($&3"#34#)#'+(3"0A3,0+,#6)"0*)''#4&7$+,#.&$%#)#(+"$+,#4,+?/+"(1#34#FG S#,)0Z'-#) (+"$+,A4,+?/+"(1#2)&"#34#FG-#)"0#)#PA0R#6)"0.&0$%#34#FGP#,)0Z'9 Q

FG "

A Ans.'! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N P FG " + FG " + FG

16.15 E)I#:3,#$%+#'+(3"0A3,0+,#"3$(%#4/"($&3"#.&$%# ω5#=# ωG-#'%3.#$%)$#43,#$%+#)$$+"/)$&3"#$3#6+#2,+)$+, $%)"#) 0R#3;+,#)#4,+?/+"(1#6)"0#CF2-#$%+#;)7/+#34#@#&'#2&;+"#61

ω

G A @ ≤ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ) ⁄ FG CF2 FG !F

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1275

1276 2 @

Figure 16.16 C+(3"0A3,0+,#4&7$+,&"2#4/"($&3"'9

ωG

F A Q:1<:(RS(:TU:1GB#M)01# = AAAAAAAAA

2F " !E"I = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ωG N N " + " AAAAAA + ω G @

7G8 5)1*K),,#7598

L0M?RS(:TU:1GB#M)01#=#2$

2N " !E"I = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ωG N N " + " AAAAAA + ω G @

N

7D8 L0M?#K),,#7L98

ωG

N

2G !E"I = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ωG N N " + " AAAAAA + ω G @ 2 PQ#M)01# = AAAAAGA

7)8 IFJ#K),,#7I98

Filter Type and T(s)

2Q

#0

#0

2Q

#0

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0

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Figure 16.16 EI$5-%5,'7I

L0M?RS(:TU:1GB#M)01#=#2$

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ω

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N

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ω

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N

7:8 IFJRK),,#1F
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" + ωG !E"I = 2 N AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ωG N N " + " AAAAAA + ω G @

7*8 VF
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s-Plane Singularities

#1

#2

|T|

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a

1278 ωG

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Figure 16.16 EI$5-%5,'7I

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" ! " AAAAAA + ω G @ !E"I = 2 N AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ωG N N " + " AAAAAA + ω G @

N

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16.5 The Second-Order LCR Resonator 1279

16.5 The Second-Order LCR Resonator !"#$%&'#'+($&3"#.+#'%)77#'$/01#$%+#'+(3"0A3,0+,#VLK#,+'3")$3,#'%3."#&"#:&29#FO9F^E)I9#B%+ /'+#34#$%&'#,+'3")$3,#$3#0+,&;+#(&,(/&$#,+)7&=)$&3"'#43,#$%+#;),&3/'#'+(3"0A3,0+,#4&7$+,#4/"($&3"' .&77#6+#0+53"'$,)$+09#!$#.&77#6+#'%3."#&"#$%+#"+<$#'+($&3"#$%)$#,+*7)(&"2#$%+#&"0/($3,#J#61#) '&5/7)$+0#&"0/($)"(+#36$)&"+0#/'&"2#)"#3*#)5*bKL#(&,(/&$#,+'/7$'#&"#)"#3*#)5*bKL#,+'3")$3,9 B%+#7)$$+,#43,5'#$%+#6)'&'#34#)"#&5*3,$)"$#(7)''#34#)($&;+AKL#4&7$+,'#$3#6+#'$/0&+0#&"#C+($&3"#FO9O9

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EFO9PFI

"⁄? A = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N " + " ( F ⁄ ?> ) + ( F ⁄ J? ) N

N

`?/)$&"2#$%+#0+"35&")$3,#$3#$%+#'$)"0),0#43,5# c" + " ( ω G ⁄ @ ) + ω G d#7+)0'#$3## N

ω G #= F ⁄ J?

EFO9PNI

ω G ⁄ @ #= F ⁄ ?>

EFO9PPI

)"0

x

L

" R z

C

L y

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I

C L

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1280 Chapter 16 Filters and Tuned Amplifiers B%/'-

ω G #= F ⁄ J?

EFO9PQI

@#= ω G ?>

EFO9PSI

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EFO9POI

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16.5 The Second-Order LCR Resonator 1281

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( i ) HPN (# n . # 0 ) Figure 16.18 K+)7&=)$&3"' 34# ;),&3/'# '+(3"0A3,0+,# 4&7$+,# 4/"($&3"'# /'&"2# $%+# VLK# ,+'3")$3,# 34# :&29# FO9F^E6IU' >"?# 2+"+,)7 '$,/($/,+-#>;?#VW-#>1?#HWB#>/?#RW-#>&?#"3$(%#)$#ωG-#>*?#2+"+,)7#"3$(%-#>8?#VWa# Eω 5 ≥ ω G I -'>6?'VWa#)'# " → ∞ -#>$?'HWa# Eω 5 < ω G I 9

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EFO9P^I

F ⁄ J? A = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N " + " ( F ⁄ ?> ) + ( F ⁄ J? )

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#$ 2N " A EFO9P\I ! ( " ) ≡ AAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N #% " + " ( ωG ⁄ @ ) + ωG .%+,+#ωG#)"0#@#),+#$%+#")$/,)7#530+#*),)5+$+,'#2&;+"#61#`?'9#EFO9PQI#)"0#EFO9PSI#)"0#2N#&' $%+# %&2%A4,+?/+"(1# $,)"'5&''&3"9# B%+# ;)7/+# 34# 2N# ()"# 6+# 0+$+,5&"+0# 4,35# $%+# (&,(/&$# 61 36'+,;&"2#$%)$#)'#"#)**,3)(%+'#∞-#$%+#()*)(&$3,#)**,3)(%+'#)#'%3,$#(&,(/&$#)"0##$#)**,3)(%+' #%-#,+'/7$&"2#&"#2N#=#F9

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EFO9P[I

" ( F ⁄ ?> ) A = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N " + " ( F ⁄ ?> ) + ( F ⁄ J? )

16.5.6 Realization of the Notch Functions B3# 36$)&"# )# *)&,# 34# $,)"'5&''&3"# =+,3'# 3"# $%+# &ω# )<&'-# .+# /'+# )# *),)77+7# ,+'3")"(+# (&,(/&$ &" $%+#'+,&+'#),5-#)'#'%3."#&"#:&29#FO9F\E+I9#J6'+,;+#$%)$#$%&'#(&,(/&$#&'#36$)&"+0#61#0&'(3"A "+($&"2#63$%#"30+'#K#)"0#;#4,35#2,3/"0#)"0#(3""+($&"2#$%+5#$32+$%+,#$3##%9#B%+#&5*+0)"(+ 34#$%+#VL#(&,(/&$#6+(35+'#&"4&"&$+#)$#ω = ω G = F ⁄ J?-#$%/'#()/'&"2#=+,3#$,)"'5&''&3"#)$#$%&' 4,+?/+"(19#B%+#'%/"$#&5*+0)"(+#&'#,+'&'$&;+#)"0#$%/'#03+'#"3$#&"$,30/(+#$,)"'5&''&3"#=+,3'9 !$#43773.'#$%)$#$%+#(&,(/&$#&"#:&29#FO9F\E+I#.&77#,+)7&=+#$%+#"3$(%#$,)"'4+,#4/"($&3" N

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EFO9QGI

16.5 The Second-Order LCR Resonator 1283

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EFO9QOI

16.5.7 Realization of the All-Pass Function B%+#)77A*)''#$,)"'4+,#4/"($&3" N

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EXERCISES 16.17 e'+#$%+#(&,(/&$#34#:&29#FO9F\E6I#$3#,+)7&=+#)#'+(3"0A3,0+,#73.A*)''#4/"($&3"#34#$%+#5)<&5)771#47)$ $1*+#.&$%#)#PA0R#4,+?/+"(1#34#FGG#8H=9# Ans.'W:A:G<01M#>#=#%#;Ω=#J:#FD<)01#?#=#%%$6#KE#)1*#J#=#$-$6#/L16.18 e'+# $%+# (&,(/&$# 34# :&29# FO9F\E+I# $3# 0+'&2"# )# "3$(%# 4&7$+,# $3# +7&5&")$+#)# 63$%+,'35+# *3.+,A'/**71 %/5#)$#)#OGAH=#4,+?/+"(19#B%+#4&7$+,#&'#$3#%);+#)#PA0R#6)"0.&0$%#34#FG#H=#E&9+9-#$%+#)$$+"/)$&3"#&' 2,+)$+,#$%)"#P#0R#3;+,#)#FGAH=#6)"0#),3/"0#$%+#OGAH=#(+"$+,#4,+?/+"(1D#'++#`<+,(&'+#FO9FS#)"0 :&29#FO9FO0I9#e'+#> =#FG#8Ω9 Ans.'?#=#%-C#µE#)1*#J#=#'-'$#L#7VF<:#
16.6 Second-Order Active Filters Based on Inductor Replacement

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1285

1286 Chapter 16 Filters and Tuned Amplifiers

(a)

(b) Figure 16.20 #>"?#B%+#>"$3"&3/#&"0/($)"(+A'&5/7)$&3"#(&,(/&$9#>;?#>")71'&'#34#$%+#(&,(/&$#)''/5&"2#&0+)7#3*#)5*'9#B%+#3,0+,#34 $%+#)")71'&'#'$+*'#&'#&"0&()$+0#61#$%+#(&,(7+0#"/56+,'9

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16.6 Second-Order Active Filters Based on Inductor Replacement

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ω G = F ⁄ J? O = F ⁄ ? Q ? O > F > P > S ⁄ > N

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16.6 Second-Order Active Filters Based on Inductor Replacement 1289

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16.6.4 The All-Pass Circuit :,35#`?9#EFO9Q\I#.+#'++#$%)$#)"#)77A*)''#4/"($&3"#.&$%#)#47)$#2)&"#34#/"&$1#()"#6+#.,&$$+"#)' >W#= F − ERW#.&$%#)#(+"$+,A4,+?/+"(1#2)&"#34#NI

EFO9SSI

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EXERCISES D16.19 e'+#$%+#(&,(/&$#34#:&29#FO9NNE(I#$3#0+'&2"#)#'+(3"0A3,0+,#6)"0*)''#4&7$+,#.&$%#)#(+"$+,#4,+?/+"(1#34 FG#8H=-#)#PA0R#6)"0.&0$%#34#SGG#H=-#)"0#)#(+"$+,A4,+?/+"(1#2)&"#34#FG9#e'+#?#=#F9N#":9 Ans.#>%#=#>$#=#>2#=#>6#=#%2-$C#;Ω.#>C#=#$C6#;Ω.#?'#=#?C#=#%-$#1E.#8#=#%&=#.%#=#%& ;Ω=#.$#= >& ;Ω D16.20 K+)7&=+#$%+#L%+61'%+;#4&7$+,#34#`<)5*7+#FO9N-#.%3'+#$,)"'4+,#4/"($&3"#&'#2&;+"#&"#`?9#EFO9NSI-#)' $%+#()'()0+#(3""+($&3"#34#$%,++#(&,(/&$'U#$.3#34#$%+#$1*+#'%3."#&"#:&29#FO9NNE)I#)"0#3"+#4&,'$A3,0+, 3*#)5*bKL#(&,(/&$#34#$%+#$1*+#'%3."#&"#:&29#FO9FPE)I9#a3$+#$%)$#13/#()"#5)8+#$%+#0(#2)&"#34#)77 '+($&3"'#+?/)7#$3#/"&$19#X3#'39#e'+#)'#5)"1#FGA8Ω#,+'&'$3,'#)'#*3''&67+9 Ans.#E0(,%#=#>$#= %&#;Ω=#?#=#6-6#1E.#,:GF1*RF(*:(#,:G<0F1#J0%#=#>$#=#>2#=#>6#=#%&#;Ω=#>C#=#%'#;Ω=#?'#=#?C#=#$-'2#1E=#.%#=#∞=#.$#=#&. ,:GF1*RF(*:(#,:G<0F1#J0%#=#>$#=#>2#=#>6#=#%&#;Ω=#>C#= 66-C#;Ω=#?'#=#?C#=#%-C 1E=#.%#=#∞=#.$#=#&

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1290 Chapter 16 Filters and Tuned Amplifiers

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(c) BP Figure 16.22 #K+)7&=)$&3"'#43,#$%+#;),&3/'#'+(3"0A3,0+,#4&7$+,#4/"($&3"'#/'&"2#$%+#3*#)5*bKL#,+'3")$3,#34 :&29#FO9NFE6IU#>"?#VW-#>;?#HW-#>1?#RW9#B%+#(&,(/&$'#),+#6)'+0#3"#$%+#VLK#(&,(/&$#&"#:&29#FO9F\9#X+'&2"#(3"'&0A +,)$&3"'#),+#2&;+"#&"#B)67+#FO9F9

16.6 Second-Order Active Filters Based on Inductor Replacement 1291

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(f) HPN, # n 0 # 0 Figure 16.22 *EI$5-%5,'7I*>/?#a3$(%#)$#ωG-#>&?#VWa-# ω 5 ≥ ω G -#>* ?#HWa-# ω 5 ≤ ω G 9#

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Table 16.1 Design Data for the Circuits of Fig. 16.22 L&,(/&$

B,)"'4+,#:/"($&3"#)"0#J$%+,#W),)5+$+,'

# X+'&2"#`?/)$&3"'

K+'3")$3, :&29#FO9NFE6I

ωG = F ⁄ ?Q ?O >F >P >S ⁄ >N

##### ? Q = ? O = ?#E*,)($&()7#;)7/+I

?O >N @ = > O AAAAAA AAAAAAAAAAAAAAAAAAA ?Q >F >P >S

##### > F = > N = > P = > S = F ⁄ ω G ? ##### > O = @ ⁄ ω G ?

V3.A*)''#EVWI :&29#FO9NNE)I

8> N ⁄ ? Q ? O > F > P > S ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F N " + " AAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?O >O ?Q ?O >F >P >S

H&2%A*)''#EHWI :&29#FO9NNE6I

8" ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F N " + " AAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?O >O ?Q ?O >F >P >S

R)"0*)''#ERWI :&29#FO9NNE(I

8" ⁄ ? O > O ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F N " + " AAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?O >O ?Q ?O >F >P >S

*****8#=#XL#2)&"

N

*****8#=#H&2%A4,+?/+"(1#2)&"#

*****8#=#L+"$+,A4,+?/+"(1#2)&"

N

K+2/7),#"3$(%#EaI# :&29#FO9NNE0I

8 [ " + ( >N ⁄ ?Q ?O >F >P >S ) ] ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F N " + " AAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?O >O ?Q ?O >F >P > S

*****8#=#V3.A#)"0#%&2%A4,+?/+"(1#2)&"

16.7 Second-Order Active Filters Based on the Two-Integrator-Loop Topology

V3.A*)''#"3$(%#EVWaI# :&29#FO9NNE+I

? OF !( " ) = 8 AAAAAAAAAAAAAAAAAAAAAAA ? OF + ? ON N

" + ( > N ⁄ ? Q ? OF > F > P > S ) # × AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F N " + " AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ( ? OF + ? ON )> O ? Q ( ? OF + ? ON )> F > P > S

ω 5 = F ⁄ ? Q ? OF > F > P > S ⁄ > N ω G = F ⁄ ? Q ( ? OF + ? ON )> F > P > S ⁄ > N ? OF + ? ON > N @ = > O AAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAA >F >P >S ?Q

8#=#XL#2)&"

?OF#+#?ON#=#?O#=#? ? OF = ? ( ω G ⁄ ω 5 )

N

?ON#=#?#−#?OF

N

H&2%A*)''#"3$(%#EHWaI# :&29#FO9NNE4I

" + ( > N ⁄ ? Q ? O > F > P > SF ) ! ( " ) = 8 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F F F N " + " AAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAA + AAAAAAAA ? O > O ? Q ? O > F > P > SF > SN

8#=#H&2%A4,+?/+"(1#2)&"

ω 5 = F ⁄ ? Q ? O > F > P > SF ⁄ > N

F F F AAAAAAAA + AAAAAAAA = AAAAAA = ω G ? > SF > SN > S

>N F F A AAAAAAAA + AAAAAAAA ω G = AAAAAAAAAAAAAAAAAAAAAAAAA

> SF = > S ( ω G ⁄ ω 5 )

? Q ? O > F > P > SF

> SN

N

N

> SN = > S ⁄ [ F ! ( ω 5 ⁄ ω G ) ]

?O >N F F @ = > O AAAAAA AAAAAAAAAAAA AAAAAAAA + AAAAAAAA ? Q > F > P > SF > SN

>77A*)''#E>WI :&29#FO9NNE2I

>N F .N N " ! " AAAAAAAAAAAAA AAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?O > O .F ?Q ?O >F > P > S ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA >N F N " + " AAAAAAAAAAAAA + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?O >O ?Q ?O >F > P > S

ω4 = ωG

@4 = @ ( .F ⁄ .N )

:7)$#2)&" = F

.F#=#.N#=#.#E),6&$,),1I >0@/'$#.N#$3#5)8+#@4#=#@

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16.7.1 Derivation of the Two-Integrator-Loop Biquad B3#0+,&;+#$%+#$.3A&"$+2,)$3,A733*#6&?/)0,)$&(#(&,(/&$-#3,#;$90"/#)'#&$#&'#(3553"71#8"3."-\ (3"'&0+,#$%+#'+(3"0A3,0+,#%&2%A*)''#$,)"'4+,#4/"($&3" N # %* 8" A AAAAAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N #% " + " ( ωG ⁄ @ ) + ωG

EFO9SOI

\#B%+#")5+#6&?/)0#'$+5'#4,35#$%+#4)($#$%)$#$%&'#(&,(/&$#&"#&$'#53'$#2+"+,)7#43,5#&'#()*)67+#34#,+)7&=&"2#)

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1293

1294 Chapter 16 Filters and Tuned Amplifiers .%+,+#8#&'#$%+#%&2%A4,+?/+"(1#2)&"9#L,3''A5/7$&*71&"2#`?9#EFO9SOI#)"0#0&;&0&"2#63$%#'&0+'#34 $%+#,+'/7$&"2#+?/)$&3"#61#"N#E$3#2+$#)77#$%+#$+,5'#&";37;&"2#"#&"#$%+#43,5# F ⁄ "- #.%&(%#&'#$%+ $,)"'4+,#4/"($&3"#34#)"#&"$+2,)$3,I#2&;+' N

ωG F ωG EFO9S^I # %* + AAAA AAAAAA # %* + AAAAANA # %* = 8# % @ " " !"# $%&'# +?/)$&3"# .+# 36'+,;+# $%)$# $%+# '&2")7# ( ω G ⁄ " )#%*# ()"# 6+# 36$)&"+0# 61# *)''&"2# #%* $%,3/2%#)"#&"$+2,)$3,#.&$%#)#$&5+#(3"'$)"$#+?/)7#$3#F ⁄ ω G9#:/,$%+,53,+-#*)''&"2#$%+#,+'/7$&"2 '&2")7# $%,3/2%# )"3$%+,# &0+"$&()7# &"$+2,)$3,# ,+'/7$'# &"# $%+# $%&,0# '&2")7# &";37;&"2# #%*# &" N N `?9 EFO9S^IY")5+71-# ( ω G ⁄ " )#%*9#:&2/,+#FO9NPE)I#'%3.'#)#673(8#0&)2,)5#43,#'/(%#)#$.3A &"$+2,)$3,#),,)"2+5+"$9#a3$+#$%)$#&"#)"$&(&*)$&3"#34#$%+#/'+#34#$%+#&";+,$&"2#3*A)5*#f&77+, &"$+2,)$3,#(&,(/&$#EC+($&3" N9S9NI#$3#&5*7+5+"$#+)(%#&"$+2,)$3,-#$%+#&"$+2,)$3,#673(8'#&"#:&29 FO9NPE)I#%);+#6++"#)''&2"+0#"+2)$&;+#'&2"'9 B%+#*,367+5#'$&77#,+5)&"'-#%3.+;+,-#34#%3.#$3#43,5# #%*-#$%+#&"*/$#'&2")7#4++0&"2#$%+ $.3#()'()0+0#&"$+2,)$3,'9#B3.),0#$%)$#+"0-#.+#,+),,)"2+#`?9#EFO9S^I-#+<*,+''&"2##%*#&"#$+,5' 34#&$'#'&"27+A#)"0#03/67+A&"$+2,)$+0#;+,'&3"'#)"0#34##%#)' N

# %*

ω Fω = 8#% ! AAAA AAAAAGA # %* ! AAAAANGA # %* @ " "

EFO9S\I

.%&(%# '/22+'$'# $%)$# #%*# ()"# 6+# 36$)&"+0# 61# /'&"2# $%+# .+&2%$+0# '/55+,# 34# :&29# FO9NPE6I9 a3.#&$#'%3/70#6+#+)'1#$3#'++#$%)$#)#(35*7+$+#673(8#0&)2,)5#,+)7&=)$&3"#()"#6+#36$)&"+0#61 (356&"&"2#$%+#&"$+2,)$3,#673(8'#34#:&29#FO9NPE)I#.&$%#$%+#'/55+,#673(8#34#:&29#FO9NPE6I-#)' '%3."#&"#:&29#FO9NPE(I9

(a)

(b)

(c) Figure 16.23 X+,&;)$&3"#34#)#673(8#0&)2,)5#,+)7&=)$&3"#34#$%+#$.3A&"$+2,)$3,A733*#6&?/)09

16.7 Second-Order Active Filters Based on the Two-Integrator-Loop Topology 1295

!"#$%+#,+)7&=)$&3"#34#:&29#FO9NPE(I-##%*-#36$)&"+0#)$#$%+#3/$*/$#34#$%+#'/55+,-#,+)7&=+'#$%+ %&2%A*)''#$,)"'4+,#4/"($&3"# ! %* ≡ # %* ⁄ #% #34#`?9#EFO9SOI9#B%+#'&2")7#)$#$%+#3/$*/$#34#$%+#4&,'$ &"$+2,)$3,#&'#− ( ω G ⁄ " )#%*-#.%&(%#&'#)#6)"0*)''#4/"($&3"( ! ω G ⁄ " )# %* 8ω G " AAAAAAAAAAAAAAAAAAAAAAAAAAAAA = ! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A = ! 6* ( " ) N #% " + " ( ω G ⁄ @ ) + ω NG

EFO9S[I

B%+,+43,+#$%+#'&2")7#)$#$%+#3/$*/$#34#$%+#4&,'$#&"$+2,)$3,#&'#7)6+7+0##6*9#a3$+#$%)$#$%+#(+"$+,A 4,+?/+"(1#2)&"#34#$%+#6)"0*)''#4&7$+,#,+)7&=+0#&'#+?/)7#$3#−8@Q !"#)#'&5&7),#4)'%&3"-#.+#()"#'%3.#$%)$#$%+#$,)"'4+,#4/"($&3"#,+)7&=+0#)$#$%+#3/$*/$#34#$%+ '+(3"0#&"$+2,)$3,#&'#$%+#73.A*)''#4/"($&3"N

N

( ω G ⁄ " )# %* 8ω NG AAAAAAAAAAAAAAAAAAAAAAAAAAA A = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A = ! 7* ( " ) N #% " + " ( ω G ⁄ @ ) + ω NG

EFO9OGI

B%/'#$%+#3/$*/$#34#$%+#'+(3"0#&"$+2,)$3,#&'#7)6+7+0##7*9#a3$+#$%)$#$%+#0(#2)&"#34#$%+#73.A*)'' 4&7$+,#,+)7&=+0#&'#+?/)7#$3#89 T+# (3"(7/0+# $%)$# $%+# $.3A&"$+2,)$3,A733*# 6&?/)0# '%3."# &"# 673(8# 0&)2,)5# 43,5# &" :&29#FO9NPE(I#,+)7&=+'#$%+#$%,++#6)'&(#'+(3"0A3,0+,#4&7$+,&"2#4/"($&3"'-#VW-#RW-#)"0#HW-#"%6,/B -25'$,"/;9#B%&'#;+,')$&7&$1#%)'#5)0+#$%+#(&,(/&$#;+,1#*3*/7),#)"0#%)'#2&;+"#&$#$%+#")5+#,5%B P'."2/*2I-%P'*9%/-'.9

16.7.2 Circuit Implementation B3#36$)&"#)"#3*A)5*#(&,(/&$#&5*7+5+"$)$&3"#34#$%+#$.3A&"$+2,)$3,A733*#6&?/)0#34#:&29#FO9NPE(I.+# ,+*7)(+# +)(%# &"$+2,)$3,# .&$%# )# f&77+,# &"$+2,)$3,# (&,(/&$# %);&"2# ?> = F ⁄ ω G -# )"0# .+ ,+*7)(+#$%+#'/55+,#673(8#.&$%#)"#3*A)5*#'/55&"2#(&,(/&$#$%)$#&'#()*)67+#34#)''&2"&"2#63$% *3'&$&;+# )"0# "+2)$&;+# .+&2%$'# $3# &$'# &"*/$'9# B%+# ,+'/7$&"2# (&,(/&$-# 8"3."# )'# $%+# m+,.&"b H/+7'5)"ba+.(356#3,#CDE';$90"/-#)4$+,#&$'#&";+"$3,'-#&'#'%3."#&"#:&29#FO9NQE)I9#g&;+" ;)7/+'# 43,# ωG-# @-# )"0# 8-# $%+# 0+'&2"# 34# $%+# (&,(/&$# &'# '$,)&2%$43,.),0U# T+# '+7+($# '/&$)671 *,)($&()7# ;)7/+'# 43,# $%+# (35*3"+"$'# 34# $%+# &"$+2,)$3,'# ?# )"0# ># '3# $%)$# ?> = F ⁄ ω G 9 # B3 0+$+,5&"+#$%+#;)7/+'#34#$%+#,+'&'$3,'#)''3(&)$+0#.&$%#$%+#'/55+,-#.+#4&,'$#/'+#",+'.+$"%B -%$5#$3#+<*,+''#$%+#3/$*/$#34#$%+#'/55+,##%*#&"#$+,5'#34#&$'#&"*/$'-##%-##6*#)"0##7*#)'# >P >N > > > A F " AAAAA9 " # 6* AAAAAAAAAAAAAAAAA A F " AAAAA9 ! # 7* AAAAA9 # %* Y # % AAAAAAAAAAAAAAAAA >N " >P > " > > >F >F N P F N

N

C/6'$&$/$&"2# # 6* Y ! ( ω G ⁄ " )# %* #)"0# # 7* Y ( ω G ⁄ " )# %* #2&;+' N

>P >N ωG >9 ωG >9 >9 # %* = AAAAAAAAAAAAAAAAAA F + AAAAA # % + AAAAAAAAAAAAAAAAAA F + AAAAA ! AAAAAA # %* ! AAAAA AAAAANA # %* >N + >P >F >N + >P >F " >F "

EFO9OFI

`?/)$&"2#$%+#7)'$#,&2%$A%)"0A'&0+#$+,5'#34#`?'9#EFO9OFI#)"0#EFO9S\I#2&;+' >9 ⁄ >F = F

EFO9ONI

.%&(%#&5*7&+'#$%)$#.+#()"#'+7+($#),6&$,),1#6/$#*,)($&()771#(3";+"&+"$#+?/)7#;)7/+'#43,#>F#)"0 >99#B%+"-#+?/)$&"2#$%+#'+(3"0A$3A7)'$#$+,5'#3"#$%+#,&2%$A%)"0#'&0+#34#`?'9#EFO9OFI#)"0#EFO9S\I )"0#'+$$&"2#>F#=#>9#1&+70'#$%+#,)$&3# > P ⁄ > N #,+?/&,+0#$3#,+)7&=+#)#2&;+"#@#)'

1296 Chapter 16 Filters and Tuned Amplifiers R1 Rf

Vi

R2

C

R

! "

C

R

! "

! "

Vhp

Vlp

Vbp

R3 (a)

Vhp Vbp Vlp

RH

RF

RB ! "

RL

Vo

(b) Figure 16.24 >"?#B%+#mHa#6&?/)0#(&,(/&$-#36$)&"+0#)'#)#0&,+($#&5*7+5+"$)$&3"#34#$%+#673(8#0&)2,)5#34 :&29#FO9NPE(I9#B%+#$%,++#6)'&(#4&7$+,&"2#4/"($&3"'-#HW-#RW-#)"0#VW-#),+#'&5/7$)"+3/'71#,+)7&=+09#>;?#B3#36$)&" "3$(%# )"0# )77A*)''# 4/"($&3"'-# $%+# $%,++# 3/$*/$'# ),+# '/55+0# .&$%# )**,3*,&)$+# .+&2%$'# /'&"2# $%&'# 3*A)5* '/55+,9

> P ⁄ > N = N@ ! F

EFO9OPI

B%/'#)"#),6&$,),1#6/$#(3";+"&+"$#;)7/+#()"#6+#'+7+($+0#43,#+&$%+,#>N#3,#>P-#)"0#$%+#;)7/+#34#$%+ 3$%+,#,+'&'$)"(+#()"#6+#0+$+,5&"+0#/'&"2#`?9#EFO9OPI9#:&")771-#+?/)$&"2#$%+#(3+44&(&+"$'#34##%#&" `?'9#EFO9OFI#)"0#EFO9S\I#)"0#'/6'$&$/$&"2#>9#=#>F#)"0#43,#> P ⁄ > N#4,35#`?9#EFO9OPI#,+'/7$'#&" 8 = N ! EF ⁄ @I

EFO9OQI

B%/'#$%+#2)&"#*),)5+$+,#8#&'#4&<+0#$3#$%&'#;)7/+9 B%+# mHa# 6&?/)0# ()"# 6+# /'+0# $3# ,+)7&=+# "3$(%# )"0# )77A*)''# 4/"($&3"'# 61# '/55&"2 .+&2%$+0#;+,'&3"'#34#$%+#$%,++#3/$*/$'-#VW-#RW-#)"0#HW9#C/(%#)"#3*A)5*#'/55+,#&'#'%3."#&" :&29#FO9NQE6ID#43,#$%&'#'/55+,#.+#()"#.,&$+ > > > #$ = ! # AAAAAAR # %* + AAAAARA # 6* + AAAAARA # 7* >G >C >J >R >R >R = ! # % # AAAAAA ! %* + AAAAAA ! 6* + AAAAAA ! 7* >G >C >J

EFO9OSI

C/6'$&$/$&"2#43,#!%*-#!6*-#)"0#!7*#4,35#`?'9#EFO9SOI-#EFO9S[I-#)"0#EFO9OGI-#,+'*+($&;+71-#2&;+' $%+#3;+,)77#$,)"'4+,#4/"($&3" N

N

# E> R ⁄ > G I" ! " ( > R ⁄ > C ) ω G + ( > R ⁄ > J ) ω G A AAAAA$ = ! 8 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N #% " + "(ω ⁄ @) + ω G

G

EFO9OOI

16.7 Second-Order Active Filters Based on the Two-Integrator-Loop Topology 1297

4,35#.%&(%#.+#()"#'++#$%)$#0&44+,+"$#$,)"'5&''&3"#=+,3'#()"#6+#36$)&"+0#61#$%+#)**,3*,&)$+ '+7+($&3"#34#$%+#;)7/+'#34#$%+#'/55&"2#,+'&'$3,'9#:3,#&"'$)"(+-#)#"3$(%#&'#36$)&"+0#61#'+7+($A &"2#>C#=#∞#)"0 >G ω AAAAAA = AAAAAA5A >J ωG

N

EFO9O^I

16.7.3 An Alternative Two-Integrator-Loop Biquad Circuit >"#)7$+,")$&;+#$.3A&"$+2,)$3,A733*#6&?/)0#(&,(/&$#&"#.%&(%#)77#$%,++#3*#)5*'#),+#/'+0#&"#)#'&"27+A +"0+0#530+#()"#6+#0+;+73*+0#)'#43773.'U#K)$%+,#$%)"#/'&"2#$%+#&"*/$#'/55+,#$3#)00#'&2")7' .&$%# *3'&$&;+# )"0# "+2)$&;+# (3+44&(&+"$'-# .+# ()"# &"$,30/(+# )"# )00&$&3")7# &";+,$+,-# )'# '%3."# &" :&29 FO9NSE)I9#a3.#)77#$%+#(3+44&(&+"$'#34#$%+#'/55+,#%);+#$%+#')5+#'&2"-#)"0#.+#()"#0&'*+"'+ .&$%#$%+#'/55&"2#)5*7&4&+,#)7$32+$%+,#)"0#*+,43,5#$%+#'/55)$&3"#)$#$%+#;&,$/)7A2,3/"0#&"*/$#34 $%+#4&,'$#&"$+2,)$3,9#J6'+,;+#$%)$#$%+#'/55&"2#.+&2%$'#34#F-#FZ@-#)"0#8#),+#,+)7&=+0#61#/'&"2 ,+'&'$)"(+'#34#>-#@>-#)"0#>Z8-#,+'*+($&;+719#B%+#,+'/7$&"2#(&,(/&$#&'#'%3."#&"#:&29#FO9NSE6I-#4,35 .%&(%#.+#36'+,;+#$%)$#$%+#%&2%A*)''#4/"($&3"#&'#"3#73"2+,#);)&7)67+i#B%&'#&'#$%+#*,&(+#*)&0#43, 36$)&"&"2#)#(&,(/&$#$%)$#/$&7&=+'#)77#3*#)5*'#&"#)#'&"27+A+"0+0#530+9#B%+#(&,(/&$#34#:&29#FO9NSE6I &'#8"3."#)'#$%+#F25GF627"#';$90"/-#)4$+,#&$'#3,&2&")$3,'9 K)$%+,#$%)"#/'&"2#)#43/,$%#3*#)5*#$3#,+)7&=+#$%+#4&"&$+#$,)"'5&''&3"#=+,3'#,+?/&,+0#43, $%+#"3$(%#)"0#)77A*)''#4/"($&3"'-#)'#.)'#03"+#.&$%#$%+#mHa#6&?/)0-#)"#+(3"35&()7#9''79$.B D2.7#'(%+5+#()"#6+#+5*731+0#.&$%#$%+#B3.bB%35)'#(&,(/&$9#C*+(&4&()771-#$%+#;&,$/)7#2,3/"0 );)&7)67+#)$#$%+#&"*/$#34#+)(%#34#$%+#$%,++#3*#)5*'#&"#$%+#B3.bB%35)'#(&,(/&$#*+,5&$'#$%+ &"*/$#'&2")7#$3#6+#4+0#$3#)77#$%,++#3*#)5*'-#)'#'%3."#&"#:&29#FO9NO9#!4##$#&'#$)8+"#)$#$%+#3/$*/$ 34#$%+#0)5*+0#&"$+2,)$3,-#'$,)&2%$43,.),0#)")71'&'#1&+70'#$%+#4&7$+,#$,)"'4+,#4/"($&3"#

"1 Vi

K

1

1 Q Vhp

# ! 0 s

# ! 0 s

Vbp

!1

Vlp

!Vlp

(a)

R Rd ) QR C Rg ) Vi

R K

C r R

! "

r

! " Vbp

! "

!Vlp

Vlp (b)

Figure 16.25 >"?#X+,&;)$&3"#34#)"#)7$+,")$&;+#$.3A&"$+2,)$3,A733*#6&?/)0#&"#.%&(%#)77#3*#)5*'#),+#/'+0#&" )#'&"27+A+"0+0#4)'%&3"9#>;?#B%+#,+'/7$&"2#(&,(/&$-#8"3."#)'#$%+#B3.bB%35)'#6&?/)09

1298 Chapter 16 Filters and Tuned Amplifiers

Figure 16.26 B%+#B3.bB%35)'#6&?/)0#.&$%#4++043,.),09#B%+#$,)"'4+,#4/"($&3"#34#`?9#EFO9O\I'&'#,+)7&=+0 61#4++0&"2#$%+#&"*/$#'&2")7#$%,3/2%#)**,3*,&)$+#(35*3"+"$'#$3#$%+#&"*/$'#34#$%+#$%,++#3*#)5*'9#B%&'#(&,(/&$ ()"#,+)7&=+#)77#'*+(&)7#'+(3"0A3,0+,#4/"($&3"'9#B%+#0+'&2"#+?/)$&3"'#),+#2&;+"#&"#B)67+#FO9N9

Table 16.2 >77#()'+' VW W3'&$&;+#RW a+2)$&;+#RW HW a3$(% E)77#$1*+'I >W

Design Data for the Circuit in Fig. 16.26 ?#=#),6&$,),1-# > = F ⁄ ω G ?- #.#=#),6&$,),1 ?F#=#G-#>F#=#∞-#>N#=#>Z0(#2)&"-#>P#=#∞ ?F#=#G-#>F#=#∞-#>N#=#∞- > P = @. ⁄ (+"$+,A4,+?/+"(1#2)&" ?F#=#G-# > F = @> ⁄ (+"$+,A4,+?/+"(1#2)&" -#>N#=#∞- >P#=#∞ ?F#=#?#×#%&2%A4,+?/+"(1#2)&"-#>F#=#∞- >N#=#∞-#>P#=#∞ ?F#=#?#×#%&2%A4,+?/+"(1#2)&"-#>F#=#∞> N = > ( ω G ⁄ ω 5 )N ⁄ %&2%A4,+?/+"(1#2)&"- >P#=#∞ ?F#=#?#×#47)$#2)&"-#>F#=#∞-# > N = > ⁄ 2)&" -# > P = @. ⁄ 2)&"

F F F N ? . A " AAAAAFA + " AAAA AAAAA ! AAAAAAAAA A + AAAAAAAAAAAAAAA N ? ? >> > #$ ? >> N F P AAAAA = ! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA F F #% N A " + " AAAAAAAAAAAA + AAAAAAAAAAA @?> ? N > N

EFO9O\I

J?0G?#G)1#D:#U,:*#
16.7.4 Final Remarks B.3A&"$+2,)$3,A733*#6&?/)0'#),+#+<$,+5+71#;+,')$&7+#)"0#+)'1#$3#0+'&2"9#H3.+;+,-#$%+&,#*+,A 43,5)"(+#&'#)0;+,'+71#)44+($+0#61#$%+#4&"&$+#6)"0.&0$%#34#$%+#3*#)5*'9#C*+(&)7#$+(%"&?/+' +<&'$#43,#(35*+"')$&"2#$%+#(&,(/&$#43,#'/(%#+44+($'#c'++#$%+#CW!L`#'&5/7)$&3"#+<)5*7+#3"#$%+ LX#)"0#$%+#.+6'&$+-#)"0#C+0,)#)"0#R,)(8+$$#EF[^\Id9

16.8 Single-Amplifier Biquadratic Active Filters 1299

EXERCISES D16.21 X+'&2"#$%+#mHa#(&,(/&$#$3#,+)7&=+#)#%&2%A*)''#4/"($&3"#.&$%#9G#=#FG#8H=#)"0#@#=#N9#L%33'+#?#=#F ":9#T%)$#&'#$%+#;)7/+#34#%&2%A4,+?/+"(1#2)&"#36$)&"+0h#T%)$#&'#$%+#(+"$+,A4,+?/+"(1#2)&"#34#$%+ 6)"0*)''#4/"($&3"#$%)$#&'#'&5/7$)"+3/'71#);)&7)67+#)$#$%+#3/$*/$#34#$%+#4&,'$#&"$+2,)$3,h Ans.#>#=#%6->#;Ω.#>%#=#>9#=#>$#=#%&#;Ω#7)(D0<()(B8.#>2#=#2&#;Ω.#%-6.#2 D16.22 e'+#$%+#mHa#(&,(/&$#$32+$%+,#.&$%#)"#3/$*/$#'/55&"2#)5*7&4&+,#$3#0+'&2"#)#73.A*)''#"3$(%#4&7$+, .&$%#9G =#S#8H=-#95#=#\#8H=-#@#=#S-#)"0#)#0(#2)&"#34#P9#C+7+($#?#=#F#":#)"0#>J#=#FG#8Ω9 Ans.#>#=#2%-32#;Ω.#>%#=#>9 #=#>$#=#%&#;Ω#7)(D0<()(B8.#>2#=#>&#;Ω.#>G#=#$6-C#;Ω.#>R#=#%C-4#;Ω.# >C#=#∞ D16.23 e'+#$%+#B3.bB%35)'#6&?/)0#E:&29#FO9NS6I#$3#0+'&2"#)#'+(3"0A3,0+,#6)"0*)''#4&7$+,#.&$%#9G#=#FG 8H=-#@ =#NG-#)"0#/"&$1#(+"$+,A4,+?/+"(1#2)&"9#!4#>#=#FG#8Ω-#2&;+#$%+#;)7/+'#34#?-#>7-#)"0#>L9 Ans.#%-6>#1E.#$&&#;Ω.#$&&#;Ω D16.24 e'+#$%+#0)$)#34#B)67+#FO9N#$3#0+'&2"#$%+#6&?/)0#(&,(/&$#34#:&29#FO9NO#$3#,+)7&=+#)"#)77A*)''#4&7$+, .&$% ωG#=#FGQ#,)0Z'-#@#=#S-#)"0#47)$#2)&"#=#F9#e'+#?#=#FG#":#)"0#.#=#FG#8Ω9 Ans.#>#=#%&#;Ω.#@R*:<:(/0101M#(:,0,%#=#∞.#>$#=#%&#;Ω.#>2#=#6&#;Ω

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1300 Chapter 16 Filters and Tuned Amplifiers

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1304 Chapter 16 Filters and Tuned Amplifiers

EXERCISE 16.27 e'+# $%+# (35*3"+"$# ;)7/+'# 36$)&"+0# &"# `<+,(&'+# FO9NS# $3# 0+'&2"# $%+# 6)"0*)''# (&,(/&$# 34 :&29 FO9PGE)I9# X+$+,5&"+# $%+# ;)7/+'# 34# E> Q ⁄ α I# )"0# > Q ⁄ EF ! α I # $3# 36$)&"# )# (+"$+,A4,+?/+"(1 2)&"#34#/"&$19 Ans.#%&&#;Ω.#%&&#;Ω

16.8.3 Generation of Equivalent Feedback Loops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b#-9#EK+()77#$%)$#.+#/'+0#$%&'#*,3*+,$1#&"#2+"+,)$&"2#)#(&,(/&$ ,+)7&=)$&3"#43,#$%+#)77A*)''#4/"($&3"#&"#C+($&3"#FO9O9I >**7&()$&3"# 34# $%+# (35*7+5+"$),1# $,)"'43,5)$&3"# $3# )# 4++06)(8# 733*# $3# 2+"+,)$+# )" +?/&;)7+"$#4++06)(8#733*#&'#)#$.3A'$+*#*,3(+''U 1. a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a3$+# $%)$# &"# $%+ 7)$$+,#733*#$%+#3*#)5*#&'#/'+0#&"#$%+#/"&$1A2)&"#43773.+,#(3"4&2/,)$&3"9#T+#'%)77#"3.#'%3. $%)$#$%+#$.3#733*'#34#:&29#FO9PN#),+#+?/&;)7+"$9 !4#$%+#3*#)5*#%)'#)"#3*+"A733*#2)&"#)-#$%+#43773.+,#&"#$%+#(&,(/&$#34#:&29#FO9PNE6I#.&77 %);+#)#2)&"#34# ) ⁄ ( ) + F ) 9 #B%&'-#$32+$%+,#.&$%#$%+#4)($#$%)$#$%+#$,)"'4+,#4/"($&3"#34#"+$.3,8#5 4,35#I#$3#2#&'#F#−#-#E'++#:&29#FO9PFI-#+")67+'#/'#$3#.,&$+#43,#$%+#(&,(/&$#&"#:&29#FO9PNE6I#$%+ (%),)($+,&'$&(#+?/)$&3" ) F ! AAAAAAAAAAAA ( F ! - ) = G )+F B%&'#+?/)$&3"#()"#6+#5)"&*/7)$+0#$3#$%+#43,5 F + )- = G

#

16.8 Single-Amplifier Biquadratic Active Filters 1305

c

(b)

(a)

Figure 16.31 !"$+,(%)"2&"2#&"*/$#)"0#2,3/"0#,+'/7$'#&"#$%+#(35*7+5+"$#34#$%+#$,)"'4+,#4/"($&3"9

1 ! t(s)

t(s)

Network n

Network n

! "

A

" !

A

Figure 16.32 >**7&()$&3"#34#$%+#(35*7+5+"$),1#$,)"'43,5)$&3"#$3#$%+#4++06)(8#733*#&"#>"?#,+'/7$'#&"#$%+ +?/&;)7+"$#733*#E')5+#*37+'I#'%3."#&"#>;?9

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`?'9# EFO9^PI N $%,3/2%#EFO9^OIU#")5+71-#>P#=#>-# > Q = > ⁄ Q@ -#?F#=#?N#=#?-# ?> = N@ ⁄ ω G -#)"0#$%+#;)7/+ 34 ?#&'#),6&$,),&71#(%3'+"#$3#6+#*,)($&()771#(3";+"&+"$9 >'#)"3$%+,#+<)5*7+-# :&29# FO9PQE)I#'%3.'# $%+# 4++06)(8#733*# 2+"+,)$+0# 61# *7)(&"2#$%+ $.3A*3,$#KL#"+$.3,8#34#:&29#FO9N\E6I#&"#$%+#"+2)$&;+A4++06)(8#*)$%#34#)"#3*#)5*9#:3,#)" &0+)7#3*#)5*-#$%&'#4++06)(8#733*#,+)7&=+'#)#*)&,#34#(35*7+
ωG = F ⁄ ?P ?Q >F >N

EFO9^^I

1306 Chapter 16 Filters and Tuned Amplifiers

!

!

"

" V

(a)

(b)

Figure 16.33 !"#!"##$%&'(!)**+!*%,&-.#$!%/!&++)/-.0!,1#!'*2+)#2#.,&3/!,3&.45*32&,-*.!,*!,1#!)**+!-. "-06!7869:6!;$#%<.=#',-.0!,1#!-.+>,!4-0.&)!,13*>01!!7!3#&)-?#4!,1#!1-01@+&44!5>.',-*.6!A1-4!-4!*.#!*5!,1#!B&))#.@ &.$@C#/!5&2-)/!*5!'-3'>-,46

C3

!

R2

R1

"

C4

C4

R2

! R1

C3

"

(b)

(a)

! " C4

R2

" Vo !

R1

C3 " Vi !

(c) Figure 16.34 !"#!"##$%&'(!)**+!*%,&-.#$!%/!+)&'-.0!,1#!%3-$0#$@A!.#,D*3(!*5!"-06!7869E;%F!-.!,1#!.#0&,-G#@ 5##$%&'(!+&,1!*5!&.!*+!&2+6!!$#!HI>-G&)#.,!5##$%&'(!)**+!0#.#3&,#$!%/!&++)/-.0!,1#!'*2+)#2#.,&3/!,3&.45*3@ 2&,-*.!,*!,1#!)**+!-.!!"#6!!&#!J!)*D@+&44!5-),#3!*%,&-.#$!%/!-.=#',-.0!"#!,13*>01!$7!-.,*!,1#!)**+!-.!!$#6

16.9 Sensitivity 1307

?P ?Q >F >N F F AAAAA + AAAAA @ = AAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?Q >F >N

!F

EFO9^\I

a3,5)771#$%+#0+'&2"#34#$%&'#(&,(/&$#&'#6)'+0#3"#'+7+($&"2#>F#=#>N#=#>-#?Q#=#?-#)"0#?P#=#?Z69 T%+"#'/6'$&$/$+0#&"#`?'9#EFO9^^I#)"0#EFO9^\I-#$%+'+#1&+70 6 = Q@

N

?> = N@ ⁄ ω G

EFO9^[I EFO9\GI

.&$%#$%+#,+5)&"&"2#0+2,++#34#4,++035#E$%+#;)7/+#34#?#3,#>I#7+4$#$3#$%+#0+'&2"+,#$3#(%33'+9 !"@+($&"2#$%+#&"*/$#'&2")7#$3#$%+#?Q#$+,5&")7#$%)$#&'#(3""+($+0#$3#2,3/"0#()"#6+#'%3."#$3 ,+'/7$#&"#)#6)"0*)''#,+)7&=)$&3"9#!4-#%3.+;+,-#.+#)**71#$%+#(35*7+5+"$),1#$,)"'43,5)$&3"#$3 $%+#4++06)(8#733*#&"#:&29#FO9PQE)I-#.+#36$)&"#$%+#+?/&;)7+"$#733*#&"#:&29#FO9PQE6I9#B%+#733* +?/&;)7+"(+#5+)"'#$%)$#$%+#(&,(/&$#34#:&29#FO9PQE6I#%)'#$%+#')5+#*37+'#)"0#$%/'#$%+#')5+#ωG )"0# @# )"0# $%+# ')5+# 0+'&2"# +?/)$&3"'# E`?'9# FO9^^# $%,3/2%# FO9\GI9# B%+# "+.# 733*# &" :&29 FO9PQE6I# ()"# 6+# /'+0# $3# ,+)7&=+# )# 73.A*)''# 4/"($&3"# 61# &"@+($&"2# $%+# &"*/$# '&2")7# )' '%3."#&"#:&29#FO9PQE(I9

EXERCISES 16.28 >")71=+#$%+#(&,(/&$#&"#:&29#FO9PQE(I#$3#0+$+,5&"+#&$'#$,)"'4+,#4/"($&3"##$ ( " ) ⁄ #% ( " )#)"0#$%/'#'%3. $%)$#ωG#)"0#@#),+#&"0++0#$%3'+#&"#`?'9#EFO9^^I#)"0#EFO9^\I9#>7'3#'%3.#$%)$#$%+#0(#2)&"#&'#/"&$19 D16.29 X+'&2"#$%+#(&,(/&$#&"#:&29#FO9PQE(I#$3#,+)7&=+#)#73.A*)''#4&7$+,#.&$%#9G#=#Q#8H=#)"0#@ = F ⁄ N9 e'+#FGA8Ω#,+'&'$3,'9 Ans.#>%#=#>$#=#%&#;Ω.#?2#=#$-3%#1E.#?'#=#6-C2#1E

16.9 Sensitivity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⁄; ; V&5 ∆; AAAAAAAAAAAAA U K ≡ ∆K→0 ∆K ⁄ K

EFO9\FI

∂; K U ;K = AAAAA AA ∂K ;

EFO9\NI

B%/'-

1308 Chapter 16 Filters and Tuned Amplifiers H+,+-#K#0+"3$+'#$%+#;)7/+#34#)#(35*3"+"$#E)#,+'&'$3,-#)#()*)(&$3,-#3,#)"#)5*7&4&+,#2)&"I#)"0#; 0+"3$+'#)#(&,(/&$#*),)5+$+,#34#&"$+,+'$#E')1-#ωG#3,#@I9#:3,#'5)77#(%)"2+' ∆; ⁄ ; U ;K ' AAAAAAAAAAAAA ∆K ⁄ K

EFO9\PI

B%/'#.+#()"#/'+#$%+#;)7/+#34# U ;K #$3#0+$+,5&"+#$%+#*+,A/"&$#(%)"2+#&"#;#0/+#$3#)#2&;+"#*+,A/"&$ (%)"2+#&"#K9#:3,#&"'$)"(+-#&4#$%+#'+"'&$&;&$1#34#@#,+7)$&;+#$3#)#*),$&(/7),#,+'&'$)"(+#>F#&'#S-#$%+" )#F_#&"(,+)'+#&"#>F#,+'/7$'#&"#)#S_#&"(,+)'+#&"#$%+#;)7/+#34#@9#

Example 16.3 :3,#$%+#4++06)(8#733*#34#:&29#FO9N[-#4&"0#$%+#'+"'&$&;&$&+'#34# ωG#)"0#@#,+7)$&;+#$3#)77#$%+#*)''&;+#(35*3A "+"$'#)"0#$%+#3*A)5*#2)&"9#`;)7/)$+#$%+'+#'+"'&$&;&$&+'#43,#$%+#0+'&2"#(3"'&0+,+0#&"#$%+#*,+(+0&"2#'+($&3" 43,#.%&(%#?F#=#?N9

Solution B3#4&"0#$%+#'+"'&$&;&$&+'#.&$%#,+'*+($#$3#$%+#*)''&;+#(35*3"+"$'-#()77+0#!"##$%&'#&.#$,$%$,$&#-#.+#)''/5+ $%)$#$%+#3*A)5*#2)&"#&'#&"4&"&$+9#!"#$%&'#()'+-#ωG#)"0#@#),+#2&;+"#61#`?'9#EFO9^PI#)"0#EFO9^QI9#B%/'#43,#ωG .+#%);+

F ω G = AAAAAAAAAAAAAAAAAAAAAAAAAAAAA ?F ?N >P >Q

.%&(%#()"#6+#/'+0#$32+$%+,#.&$%#$%+#'+"'&$&;&$1#0+4&"&$&3"#34#`?9#EFO9\NI#$3#36$)&"

U?ωFG = U?ωNG = U>ωPG = U>ωQG = ! FAANA :3,#@#.+#%);+

@ =

F F F ? F ? N > P > Q AAAAAA + AAAAAA AAAAA ?F ?N >P

!F

$3#.%&(%#.+#)**71#$%+#'+"'&$&;&$1#0+4&"&$&3"#$3#36$)&"

? ? AAAAANA ! AAAAAFA ?F ?N

F @ U ?F = AAA N

?N ? AAAAAA + AAAAAFA ?F ?N

!F

@

:3,#$%+#0+'&2"#.&$%#?F#= ?N#.+#'++#$%)$# U ?F = G9#C&5&7),71-#.+#()"#'%3.#$%)$ @

U ?N = G-

@

U >P = FAANA -

@

U > Q = ! FAANA

!$#&'#&5*3,$)"$#$3#,+5+56+,#$%)$#$%+#'+"'&$&;&$1#+<*,+''&3"#'%3/70#6+#0+,&;+0#3'9$.'#;)7/+'#(3,,+'*3"0&"2 $3#)#*),$&(/7),#0+'&2"#),+#'/6'$&$/$+09 a+<$#.+#(3"'&0+,#$%+#'+"'&$&;&$&+'#,+7)$&;+#$3#$%+#)5*7&4&+,#2)&"9#!4#.+#)''/5+#$%+#3*#)5*#$3#%);+#) 4&"&$+#2)&"#)-#$%+#(%),)($+,&'$&(#+?/)$&3"#43,#$%+#733*#6+(35+'

F + )- ( " ) = G

EFO9\QI

.%+,+#-E"I#&'#2&;+"#&"#:&29#FO9N\E)I9#B3#'&5*7&41#5)$$+,'#.+#()"#'/6'$&$/$+#43,#$%+#*)''&;+#(35*3"+"$'#61 $%+&,#0+'&2"#;)7/+'9#B%&'#()/'+'#"3#+,,3,'#&"#+;)7/)$&"2#'+"'&$&;&$&+'-#'&"(+#.+#),+#"3.#4&"0&"2#$%+

16.9 Sensitivity 1309

'+"'&$&;&$1#.&$%#,+'*+($#$3#$%+#)5*7&4&+,#2)&"9#e'&"2#$%+#0+'&2"#;)7/+'#36$)&"+0#+),7&+,Y")5+71-#?F#=#?N#= N ?-#>P#=#>-#> Q = > ⁄ Q@ -#)"0# ?> = N@ ⁄ ω G Y.+#2+$ N

" + " ( ω G ⁄ @ ) + ω NG A EFO9\SI - ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N " + " ( ω G ⁄ @ ) ( N@ + F ) + ω NG J?:(:#ω&#)1*#@#*:1F<:#
ω

ω

N N N " + " AAAAAGA ( N@ + F ) + ω NG + ) " + " AAAAAGA + ω NG = G @ @

O,,U/01M#
ω N@ N " + " AAAAAGA F + AAAAAAAAAAAA + ω NG = G @ )+F N

EFO9\OI

E(F/#
ω G2 = ω G

EFO9\^I

@ A @ 2 = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N F + N@ ⁄ ( ) + F )

EFO9\\I

X?U,

U)ωG2 = G N

) N@ ⁄ ( ) + F ) @ A U ) 2 = AAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N ) + F F + N@ ⁄ ( ) + F ) N EF(# ) @ N@ #)1*# ) @ F #J:#FD<)01 N @ N@ U ) 2 #' AAAAAAAAAA ) [<#0,#U,U)A#
N@ @ U ) #' AAAAAAAAAA ) VF<:#

16.9.1 A Concluding Remark B%+[,+'/7$'#34#`<)5*7+#FO9P#&"0&()$+#)#'+,&3/'#0&')0;)"$)2+#34#'&"27+A)5*7&4&+,#6&?/)0'Y $%+#'+"'&$&;&$1#34#@#,+7)$&;+#$3#$%+#)5*7&4&+,#2)&"#&'#?/&$+#%&2%9#>7$%3/2%#)#$+(%"&?/+#+<&'$' @ 43,#,+0/(&"2# U ) #&"#C>R'#E'++#C+0,)#+$#)79-#F[\GI-#$%&'#&'#03"+#)$#$%+#+<*+"'+#34#&"(,+)'+0 *)''&;+#'+"'&$&;&$&+'9#a+;+,$%+7+''-#$%+#,+'/7$&"2#C>R'#),+#/'+0#+<$+"'&;+71#&"#5)"1#)**7&()A $&3"'9# H3.+;+,-# 43,# 4&7$+,'# .&$%# @# 4)($3,'# 2,+)$+,# $%)"# )63/$# FG-# 3"+# /'/)771# 3*$'# 43,# 3"+ @ 34 $%+# 5/7$&)5*7&4&+,# 6&?/)0'# '$/0&+0# &"# C+($&3"'# FO9O# )"0# FO9^9# :3,# $%+'+# (&,(/&$'# U ) # &' N *,3*3,$&3")7#$3#@-#,)$%+,#$%)"#$3#@ #)'#&"#$%+#C>R#()'+#E`?9#FO9\[I9# [#

R+()/'+#$%+#3*+"A733*#2)&"#)#34#3*#)5*'#/'/)771#%)'#.&0+#$37+,)"(+-#&$#&'#&5*3,$)"$#$3#8++*# U ω) G #)"0

U@ ) #;+,1#'5)779

EFO9\[I

1310 Chapter 16 Filters and Tuned Amplifiers

EXERCISE 16.30 !"#)#*),$&(/7),#4&7$+,#/$&7&=&"2#$%+#4++06)(8#733*#34#:&29#FO9N[-#.&$%#?F#=#?N-#/'+#$%+#,+'/7$'#34 `<)5*7+#FO9P#$3#4&"0#$%+#+<*+($+0#*+,(+"$)2+#(%)"2+#&"# ωG#)"0#@#/"0+,#$%+#(3"0&$&3"'#$%)$#E)I >P#&'#N_#%&2%-#E6I#>Q#&'#N_#%&2%-#E(I#63$%#>P#)"0#>Q#),+#N_#%&2%-#)"0#E0I#63$%#()*)(&$3,'#),+#N_ 73.#)"0#63$%#,+'&'$3,'#),+#N_#%&2%9 Ans.#7)8#−%]=#+%].#7D8#−%]=#−%].#7G8#−$]=#&].#7*8#&]=#&]

16.10 Switched-Capacitor Filters B%+#)($&;+AKL#4&7$+,#(&,(/&$'#*,+'+"$+0#)63;+#%);+#$.3#*,3*+,$&+'#$%)$#5)8+#$%+&,#*,30/($&3" &"#53"37&$%&(#!L#43,5#0&44&(/7$-#&4#"3$#*,)($&()771#&5*3''&67+D#$%+'+#),+#$%+#"++0#43,#7),2+A;)7A /+0#()*)(&$3,'#)"0#$%+#,+?/&,+5+"$#34#)((/,)$+#KL#$&5+#(3"'$)"$'9#B%+#'+),(%#$%+,+43,+#%)' (3"$&"/+0#43,#)#5+$%30#34#4&7$+,#0+'&2"#$%)$#.3/70#7+"0#&$'+74#53,+#")$/,)771#$3#!L#&5*7+5+"A $)$&3"9#!"#$%&'#'+($&3"#.+#'%)77#&"$,30/(+#3"+#'/(%#5+$%309

16.10.1 The Basic Principle B%+#'.&$(%+0A()*)(&$3,#4&7$+,#$+(%"&?/+#&'#6)'+0#3"#$%+#,+)7&=)$&3"#$%)$#)#()*)(&$3,#'.&$(%+0 6+$.++"#$.3#(&,(/&$#"30+'#)$#)# '/44&(&+"$71# %&2%#,)$+#&'#+?/&;)7+"$#$3#)#,+'&'$3,#(3""+($&"2 $%+'+#$.3#"30+'9#B3#6+#'*+(&4&(-#(3"'&0+,#$%+#)($&;+AKL#&"$+2,)$3,#34#:&29#FO9PSE)I9#B%&'#&' $%+# 4)5&7&),# f&77+,# &"$+2,)$3,-# .%&(%# .+# /'+0# &"# $%+# $.3A&"$+2,)$3,A733*# 6&?/)0# &" C+($&3" FO9^9#!"#:&29#FO9PSE6I#.+#%);+#,+*7)(+0#$%+#&"*/$#,+'&'$3,#>F#61#)#2,3/"0+0#()*)(&$3, ?F#$32+$%+,#.&$%#$.3#fJC#$,)"'&'$3,'#)($&"2#)'#'.&$(%+'9#!"#'35+#(&,(/&$'-#53,+#+7)63,)$+ '.&$(%#(3"4&2/,)$&3"'#),+#/'+0-#6/$#'/(%#0+$)&7'#),+#6+13"0#3/,#*,+'+"$#"++09 B%+# $.3# fJC# '.&$(%+'# &"# :&29# FO9PSE6I# ),+# 0,&;+"# 61# )# 5$5$P'./2++%5L# $.3A*%)'+ (73(89# :&2/,+# FO9PSE(I# '%3.'# $%+# (73(8# .);+43,5'9# T+# '%)77# )''/5+# &"# $%&'# &"$,30/($3,1 +<*3'&$&3"#$%)$#$%+#(73(8#4,+?/+"(1# 9I ( 9I = F ⁄ !I ) #&'#5/(%#%&2%+,#$%)"#$%+#4,+?/+"(1#34#$%+ &"*/$#'&2")7#v%9#B%/'#0/,&"2#(73(8#*%)'+# φ F - #.%+"#?F#&'#(3""+($+0#)(,3''#$%+#&"*/$#'&2")7 '3/,(+#v%-#$%+#;),&)$&3"'#&"#$%+#&"*/$#'&2")7#),+#"+27&2&671#'5)779#!$#43773.'#$%)$#0/,&"2# φ F ()*)(&$3,#?F#(%),2+'#/*#$3#$%+#;37$)2+#v%< ?F = ? F v% B%+"-#0/,&"2#(73(8#*%)'+# φ N -#()*)(&$3,#?F#&'#(3""+($+0#$3#$%+#;&,$/)7A2,3/"0#&"*/$#34#$%+ 3* )5*-#)'#&"0&()$+0#&"#:&29#FO9PSE0I9#L)*)(&$3,#?F#&'#$%/'#43,(+0#$3#0&'(%),2+-#)"0#&$'#*,+;&A 3/'#(%),2+#
16.10 Switched-capacitor Filters 1311

(a)

(b)

(d)

(c)

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1312 Chapter 16 Filters and Tuned Amplifiers

16.10.2 Practical Circuits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g%)/'&-#)"0#V)8+,#EF[[GI9#R1#,+;+,')7#34#$%+#(73(8 *%)'+'#3"#$.3#34#$%+#'.&$(%+'-#$%+#(&,(/&$#&"#:&29#FO9POE6I#&'#36$)&"+09#B%&'#(&,(/&$#,+)7&=+'#$%+ &";+,$&"2#&"$+2,)$3,#4/"($&3"-#7&8+#$%+#(&,(/&$#34#:&29#FO9PSE6I-#6/$#&'#&"'+"'&$&;+#$3#'$,)1#()*)(&A $)"(+'# E.%&(%# $%+# 3,&2&")7# (&,(/&$# 34# :&29# FO9PS6# &'# "3$I9# B%+# (35*7+5+"$),1# &"$+2,)$3,'# 34 :&29 FO9PO#%);+#6+(35+#$%+#'$)"0),0#6/&70&"2#673(8'#&"#$%+#0+'&2"#34#'.&$(%+0A()*)(&$3,#4&7$+,'9 V+$#/'#"3.#(3"'&0+,#$%+#,+)7&=)$&3"#34#)#(35*7+$+#6&?/)0#(&,(/&$9#:&2/,+#FO9P^E)I#'%3.' $%+# )($&;+AKL-# $.3A&"$+2,)$3,A733*# (&,(/&$# '$/0&+0# +),7&+,9# R1# (3"'&0+,&"2# $%+# ()'()0+# 34

(a)

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16.11 Tuned Amplifiers 1315

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1316 Chapter 16 Filters and Tuned Amplifiers

Figure 16.38 :,+?/+"(1#,+'*3"'+#34#)#$/"+0#)5*7&4&+,9

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"7!+$*$&-9#B%+#)5*7&4&+,#+?/&;)7+"$#(&,(/&$#&'#'%3."#&"#:&29#FO9P[E6I9#H+,+#>#0+"3$+'#$%+#*),A )77+7#+?/&;)7+"$#34#>J#)"0#$%+#3/$*/$#,+'&'$)"(+#.$#34#$%+#:`B-#)"0#?#&'#$%+#*),)77+7#+?/&;)7+"$ 34#?J#)"0#$%+#:`B#3/$*/$#()*)(&$)"(+#E/'/)771#;+,1#'5)77I9#:,35#$%+#+?/&;)7+"$#(&,(/&$#.+ ()"#.,&$+ ! L 6 #% ! L 6 #% A #$ = AAAAAAAAAAAAAA = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA OJ "? + F ⁄ > + F ⁄ "J B%/'#$%+#;37$)2+#2)&"#()"#6+#+<*,+''+0#)' L #$ " AAAAA = ! AAAAA6A AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA #% ? " N + " ( F ⁄ ?> ) + F ⁄ J?

EFO9FGFI

16.11 Tuned Amplifiers 1317

.%&(%#&'#)#'+(3"0A3,0+,#6)"0*)''#4/"($&3"9#B%/'#$%+#$/"+0#)5*7&4&+,#%)'#)#(+"$+,#4,+?/+"(1#34

ω G = F ⁄ J?

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F C = AAAAAAAA ?>

EFO9FGPI

@ ≡ ω G ⁄ C = ω G ?>

EFO9FGQI

#$ ( & ω G ) AAAAAAAAAAAAAAAAAA A = !L6 > #% ( & ω G )

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Example 16.4 !$#&'#,+?/&,+0#$3#0+'&2"#)#$/"+0#)5*7&4&+,#34#$%+#$1*+#'%3."#&"#:&29#FO9P[-#%);&"2#9G#=#F#fH=-#PA0R#6)"0A .&0$%#=#FG#8H=-#)"0#(+"$+,A4,+?/+"(1#2)&"#=#bFG#MZM9#B%+#:`B#);)&7)67+#%)'#)$#$%+#6&)'#*3&"$#L6#=#S#5>Z M#)"0#.$#=#FG#8Ω9#B%+#3/$*/$#()*)(&$)"(+#&'#"+27&2&671#'5)779#X+$+,5&"+#$%+#;)7/+'#34#>J-#?J-#)"0#J9

Solution L+"$+,A4,+?/+"(1#2)&"#=#bFG#=#bS>9#B%/'#>#=#N#8Ω9#C&"(+#>#=#>J ||.$-#$%+"#>J#=#N9S#8Ω9 F Q C = N π × FG = AAAAAAAA ?> B%/'

F A = ^[S\#*: ? = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Q P N π × FG × N × FG O

C&"(+# ω G = N π × FG = F ⁄ J? -#.+#36$)&"

F A = P9F\#µH J = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N FN ! FN Q π × FG × ^[S\ × FG

16.11.2 Inductor Losses B%+#*3.+,#73''#&"#$%+#&"0/($3,#&'#/'/)771#,+*,+'+"$+0#61#)#'+,&+'#,+'&'$)"(+#."#)'#'%3."#&" :&29 FO9QGE)I9#H3.+;+,-#,)$%+,#$%)"#'*+(&41&"2#$%+#;)7/+#34#."-#$%+#/'/)7#*,)($&(+#&'#$3#'*+(&41 $%+#&"0/($3,#@#4)($3,#)$#$%+#4,+?/+"(1#34#&"$+,+'$-

ωG J @ G ≡ AAAAAAAAAA ."

EFO9FGOI

1318 Chapter 16 Filters and Tuned Amplifiers

(a)

(b)

Figure 16.40 !"0/($3,#+?/&;)7+"$#(&,(/&$'9

B1*&()771-#@G#&'#&"#$%+#,)"2+#34#SG#$3#NGG9 B%+#)")71'&'#34#)#$/"+0#)5*7&4&+,#&'#2,+)$71#'&5*7&4&+0#61#,+*,+'+"$&"2#$%+#&"0/($3,#73'' 61#)#*),)77+7#,+'&'$)"(+#>+-#)'#'%3."#&"#:&29#FO9QGE6I9#B%+#,+7)$&3"'%&*#6+$.++"#>+#)"0#@G ()"#6+#43/"0#61#.,&$&"2-#43,#$%+#)05&$$)"(+#34#$%+#(&,(/&$#&"#:&29#FO9QGE)IF O ( & ω G ) = AAAAAAAAAAAAAAAAAAAAAA ." + & ωG J

:3,#@ G @ F-

F F + & (F ⁄ @ G ) F F = AAAAAAAAAAAA # AAAAAAAAAAAAAAAAAAAAAAAAAAAAA = AAAAAAAAAAAA # AAAAAAAAAAAAAAAAAAAAAAAAAAAAA & ω G J F ! & ( F ⁄ @ G ) & ω G J F + (F ⁄ @ N ) G

F# F O ( & ω G )#' # AAAAAAAAAAAA F + & AAAAAA & ωG J @G

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`?/)$&"2#$%&'#$3#$%+#)05&$$)"(+#34#$%+#(&,(/&$#&"#:&29#FO9QGE6I#2&;+' >+ @ G = AAAAAAAAAA ωG J

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> + = ω G J@ G

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EXERCISE 16.32 !4#$%+#&"0/($3,#&"#`<)5*7+#FO9Q#%)'#@G#=#FSG-#4&"0#>+#)"0#$%+"#4&"0#$%+#;)7/+#$3#.%&(%#>J#'%3/70 6+#(%)"2+0#$3#8++*#$%+#3;+,)77#@-#)"0#%+"(+#$%+#6)"0.&0$%-#/"(%)"2+09 Ans.'2#;Ω.#%6#;Ω

16.11 Tuned Amplifiers 1319

16.11.3 Use of Transformers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`<)5*7+#FO9Q-#$%+"#)#(3&7#.&$%#&"0/($)"(+#J4 = [#5 P9F\#=#N\9O#µH#)"0#)#()*)(&$)"(+#?4#=#^[S\ ⁄ [#=#\\Q#*:#.&77#6+#,+?/&,+09#R3$%#$%+'+#;)7/+' ),+#53,+#*,)($&()7#$%)"#$%+#3,&2&")7#3"+'9

Figure 16.41 >#$)**+0#&"0/($3,#&'#/'+0#)'#)"#&5*+0)"(+#$,)"'43,5+,#$3#)773.#/'&"2#)#%&2%+,#&"0/($)"(+J4-#)"0#)#'5)77+,#()*)(&$)"(+-#?49

Ic L I

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I

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n2 Rin

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(b) Figure 16.42 >"?#B%+#3/$*/$#34#)#$/"+0#)5*7&4&+,#&'#(3/*7+0#$3#$%+#&"*/$#34#)"3$%+,#)5*7&4&+,#;&)#)#$)**+0 (3&79#>;?#>"#+?/&;)7+"$#(&,(/&$9#a3$+#$%)$#$%+#/'+#34#)#$)**+0#(3&7#&"(,+)'+'#$%+#+44+($&;+#&"*/$#&5*+0)"(+#34 $%+#'+(3"0#)5*7&4&+,#'$)2+9

1320 Chapter 16 Filters and Tuned Amplifiers !"# )**7&()$&3"'# $%)$# &";37;+# (3/*7&"2# $%+# 3/$*/$# 34# )# $/"+0# )5*7&4&+,# $3# $%+# &"*/$# 34 )"3$%+,#)5*7&4&+,-#$%+#$)**+0#(3&7#()"#6+#/'+0#$3#,)&'+#$%+#+44+($&;+#&"*/$#,+'&'$)"(+#34#$%+#7)$A $+,#)5*7&4&+,#'$)2+9#!"#$%&'#.)1-#3"+#()"#);3&0#,+0/($&3"#34#$%+#3;+,)77#@9#B%&'#*3&"$#&'#&77/'A $,)$+0#&"#:&29#FO9QN#)"0#&"#$%+#43773.&"2#+<+,(&'+'9

EXERCISES D16.33 L3"'&0+,#$%+#(&,(/&$#&"#:&29#FO9QNE)I-#4&,'$#.&$%3/$#$)**&"2#$%+#(3&79#V+$#J#=#S#µH#)"0#)''/5+ $%)$#>F#&'#4&<+0#)$#F#8Ω9#T+#.&'%#$3#0+'&2"#)#$/"+0#)5*7&4&+,#.&$%#9G#=#QSS#8H=#)"0#)#PA0R 6)"0.&0$%#34#FG#8H=#c$%&'#&'#$%+#&"$+,5+0&)$+#4,+?/+"(1#E!:I#)5*7&4&+,#34#)"#>f#,)0&3d9#!4#$%+ RoB# %)'# >&"# =# F# 8Ω# )"0#?&"# =# NGG# *:-# 4&"0# $%+# )($/)7# 6)"0.&0$%# 36$)&"+0# )"0# $%+# ,+?/&,+0 ;)7/+#34#?F9 Ans.'%2#;L^.#$'-$4#1E D16.34 C&"(+#$%+#6)"0.&0$%#,+)7&=+0#&"#`<+,(&'+#FO9PP#&'#2,+)$+,#$%)"#0+'&,+0-#4&"0#)"#)7$+,")$&;+#0+'&2" /$&7&=&"2#)#$)**+0#(3&7#)'#&"#:&29#FO9QNE)I9#:&"0#$%+#;)7/+#34#5#$%)$#)773.'#$%+#'*+(&4&()$&3"'#$3#6+ @/'$#5+$9#>7'3#4&"0#$%+#"+.#,+?/&,+0#;)7/+#34#?F#)"0#$%+#(/,,+"$#2)&"# M I ⁄ M #)$#,+'3")"(+9#>''/5+ $%)$#)$#$%+#6&)'#*3&"$#$%+#RoB#%)'#L6#=#QG#5>ZM9 Ans.'%-2C.#$'-2C#1E.#%>-%#O+O

16.11.4 Amplifiers with Multiple Tuned Circuits B%+#'+7+($&;&$1#)(%&+;+0#.&$%#$%+#'&"27+#$/"+0#(&,(/&$#34#:&29#FO9P[#&'#"3$#'/44&(&+"$#&"#5)"1 )**7&()$&3"'Y43,#&"'$)"(+-#&"#$%+#!:#)5*7&4&+,#34#)#,)0&3#3,#)#BM#,+(+&;+,9#g,+)$+,#'+7+($&;&$1 &'#36$)&"+0#61#/'&"2#)00&$&3")7#$/"+0#'$)2+'9#:&2/,+#FO9QP#'%3.'#)#Ro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f&77+,#+44+($FN#0/+#$3#()*)(&$)"(+#?µ9#C&"(+#$%+#73)0#&'#"3$#'&5*71#,+'&'$&;+-#)'#.)'#$%+ ()'+#&"#$%+#)5*7&4&+,'#'$/0&+0#&"#C+($&3"#[9S9N-#$%+#f&77+,#&5*+0)"(+#)$#$%+#&"*/$#.&77#6+#(35A *7+<9#B%&'#,+47+($+0#&5*+0)"(+#.&77#()/'+#0+$/"&"2#34#$%+#&"*/$#(&,(/&$#)'#.+77#)'#k'8+.&"2l#34 $%+#,+'*3"'+#34#$%+#&"*/$#(&,(/&$9#a++07+''#$3#')1-#$%+#(3/*7&"2#&"$,30/(+0#61#?µ#5)8+'#$/"A &"2#E3,#)7&2"&"2I#$%+#)5*7&4&+,#?/&$+#0&44&(/7$9#T3,'+#'$&77-#$%+#()*)(&$3,#?µ#()"#()/'+#3'(&77)A $&3"'#$3#3((/,#c'++#g,)1#)"0#C+),7+#EF[O[I#)"0#W,367+5#FO9^Sd9 f+$%30'# +<&'$# 43,# .&0,-"+$A$.8# $%+# +44+($# 34# ?µ-# /'&"2# )00&$&3")7# (&,(/&$'# ),,)"2+0# $3 4++0# 6)(8# )# (/,,+"$# +?/)7# )"0# 3**3'&$+# $3# $%)$# $%,3/2%# ?µ9# >"# )7$+,")$&;+-# )"0# *,+4+,,+0)**,3)(%#&'#$3#/'+#(&,(/&$#(3"4&2/,)$&3"'#$%)$#03#"3$#'/44+,#4,35#$%+#f&77+,#+44+($9#B%+'+#),+ 0&'(/''+0#7)$+,9#R+43,+#7+);&"2#$%&'#'+($&3"-#%3.+;+,-#.+#.&'%#$3#*3&"$#3/$#$%)$#(&,(/&$'#34#$%+ $1*+#'%3."#&"#:&29#FO9QP#),+#/'/)771#0+'&2"+0#/$&7&=&"2#$%+#;A*),)5+$+,#530+7#34#$%+#RoB

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16.11 Tuned Amplifiers 1321

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16.11.5 The Cascode and the CC−CB Cascade :,35#3/,#'$/01#34#)5*7&4&+,#4,+?/+"(1#,+'*3"'+#&"#L%)*$+,#[-#.+#8"3.#$%)$#$.3#)5*7&4&+, (3"4&2/,)$&3"'#03#"3$#'/44+,#4,35#$%+#f&77+,#+44+($9#B%+'+#),+#$%+#()'(30+#(3"4&2/,)$&3"#)"0 $%+#(3553"A(377+($3,-#(3553"A6)'+#()'()0+9#:&2/,+#FO9QQ#'%3.'#$/"+0#)5*7&4&+,'#6)'+0#3" $%+'+#$.3# (3"4&2/,)$&3"'9#B%+#LL−LR# ()'()0+#&'#/'/)771#*,+4+,,+0# &"# !L#&5*7+5+"$)$&3"' 6+()/'+#&$'#0&44+,+"$&)7#'$,/($/,+#5)8+'#&$#'/&$)67+#43,#!L#6&)'&"2#$+(%"&?/+'9#Ea3$+#$%)$#$%+ 6&)'&"2#0+$)&7'#34#$%+#()'(30+#(&,(/&$#),+#"3$#'%3."#&"#:&29#FO9QQ)9#R&)'&"2#()"#6+#03"+#/'&"2 ),,)"2+5+"$'#'&5&7),#$3#$%3'+#0&'(/''+0#&"#+),7&+,#(%)*$+,'9I#

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1322 Chapter 16 Filters and Tuned Amplifiers

(a)

(b) Figure 16.44 B.3#$/"+0A)5*7&4&+,#(3"4&2/,)$&3"'#$%)$#03#"3$#'/44+,#4,35#$%+#f&77+,#+44+($U#>"?'()'(30+ )"0#>;?#(3553"A(377+($3,-#(3553"A6)'+#()'()0+9#Ea3$+#$%)$#6&)'#0+$)&7'#34#$%+#()'(30+#(&,(/&$#),+#"3$#'%3."9I

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EXERCISE D16.35 L3"'&0+,#$%+#0+'&2"#34#)"#!:#)5*7&4&+,#43,#)"#:f#,)0&3#,+(+&;+,9#e'&"2#$.3#'1"(%,3"3/'71#$/"+0 '$)2+'#.&$%#9G#=#FG9^#fH=-#4&"0#$%+#PA0R#6)"0.&0$%#34#+)(%#'$)2+#'3#$%)$#$%+#3;+,)77#6)"0.&0$% &'#NGG#8H=9#e'&"2#PAµH#&"0/($3,'#4&"0#?#)"0#>#43,#+)(%#'$)2+9 Ans.'2%&-3#;L^.#42-4#KE.#C->6#;Ω

16.11 Tuned Amplifiers 1323

!T ! (dB) 3 dB

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16.11.7 Stagger-Tuning >#5/(%#6+$$+,#3;+,)77#,+'*3"'+#&'#36$)&"+0#61#'$)22+,A$/"&"2#$%+#&"0&;&0/)7#'$)2+'-#)'#&77/'A $,)$+0#&"#:&29#FO9QO9#C$)22+,A$/"+0#)5*7&4&+,'#),+#/'/)771#0+'&2"+0#'3#$%)$#$%+#3;+,)77#,+'*3"'+ +<%&6&$'#62K%62/*9/2-5'""#),3/"0#$%+#(+"$+,#4,+?/+"(1#9G9#C/(%#)#,+'*3"'+#()"#6+#36$)&"+0#61 $,)"'43,5&"2#$%+#,+'*3"'+#34#)#5)<&5)771#47)$#ER/$$+,.3,$%I#73.A*)''#4&7$+,#/*#$%+#4,+?/+"(1 )<&'#$3#ωG9#T+#'%3.#%+,+#%3.#$%&'#()"#6+#03"+9

1324 Chapter 16 Filters and Tuned Amplifiers B%+#$,)"'4+,#4/"($&3"#34#)#'+(3"0A3,0+,#6)"0*)''#4&7$+,#()"#6+#+<*,+''+0#&"#$+,5'#34#&$' *37+'#)' 2F " A ! ( " ) = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ωG ω F F " + AAAAAAA ! & ω G F ! AAAAAAAAANA " + AAAAAAGA + & ω G F ! AAAAAAAAANA N@ N@ Q@ Q@

EFO9FFFI

:3,#)#"),,3.A6)"0#4&7$+,-#@#3#F-#)"0#43,#;)7/+'#34#"#&"#$%+#"+&2%63,%330#34#+&ωG#E'++#:&29#FO9Q^6I$%+#'+(3"0#4)($3,#&"#$%+#0+"35&")$3,#&'#)**,3<&5)$+71#E"*+#&ωG#' N"I9#H+"(+#`?9#EFO9FFFI#()" 6+#)**,3<&5)$+0#&"#$%+#"+&2%63,%330#34#&ωG#61 2F ⁄ N 2F ⁄ N A = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A ! ( " )#' AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ( " ! & ω G ) + ω G ⁄ N@ " + ω G ⁄ N@ ! & ω G

EFO9FFNI

B%&'#&'#8"3."#)'#$%+#."--253;"./'"!!-2@$7",$2.9FP#a3$+#$%)$#$%+#5)2"&$/0+#,+'*3"'+-#43, "#=#&ω-#%)'#)#*+)8#;)7/+#34#2F@ ⁄ ω G#)$#ω#=#ωG-#)'#+<*+($+09 a3.#(3"'&0+,#)#4&,'$A3,0+,#73.A*)''#"+$.3,8#.&$%#)#'&"27+#*37+#)$# + = ! ω G ⁄ N@ #E.+#/'+ +#$3#0+"3$+#$%+#(35*7+<#4,+?/+"(1#;),&)67+#43,#$%+#73.A*)''#4&7$+,I9#!$'#$,)"'4+,#4/"($&3"#&'# 8 ! ( + ) = AAAAAAAAAAAAAAAAAAAAAAAAAAA + + ω G ⁄ N@

EFO9FFPI

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EFO9FFQI

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ω GF = ω G + AAAAAAAAAA N N

C C F = AAAAAAA N

Nω @ F #' AAAAAAAAAAAAAGA C

FP# B%+#6)"0*)''#,+'*3"'+#&'#L'$6'-.%I2//;*";66'-.%I2/#),3/"0#$%+#(+"$+,#4,+?/+"(1# ω

EFO9FFSI

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16.11 Tuned Amplifiers 1325

Low-pass filter

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"

1326 Chapter 16 Filters and Tuned Amplifiers Bandpass filter j# Low-pass filter

$

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s ) p " j# 0 0.707

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Figure 16.48 J6$)&"&"2#$%+#*37+'#)"0#$%+#4,+?/+"(1#,+'*3"'+#34#)#43/,$%A3,0+,#'$)22+,A$/"+0-#"),,3.A6)"0#6)"0*)''#)5*7&4&+, 61#$,)"'43,5&"2#)#'+(3"0A3,0+,#73.A*)''-#5)<&5)771#47)$#,+'*3"'+9

16.11 Tuned Amplifiers

1327

EXERCISES D16.36 >#'$)22+,A$/"+0#0+'&2"#43,#$%+#!:#)5*7&4&+,#'*+(&4&+0#&"#`<+,(&'+#FO9PS#&'#,+?/&,+09#:&"0#9GF-#CF9GN-#)"0#CN9#>7'3#2&;+#$%+#;)7/+#34#?#)"0#>#43,#+)(%#34#$%+#$.3#'$)2+'9#EK+()77#$%)$#PAµH#&"0/($3,' ),+#$3#6+#/'+09I Ans.#%&-44#_L^.#%'%-'#;L^.#%&-C2#_L^.#%'%-'#;L^.#4$-3#KE.#%6-6#;Ω.#4'-4#KE.#%6-%#;Ω 16.37 e'&"2#$%+#4)($#$%)$#$%+#;37$)2+#2)&"#)$#,+'3")"(+#&'#*,3*3,$&3")7#$3#$%+#;)7/+#34#>-#4&"0#$%+#,)$&3#34 $%+#2)&"#)$#FG9^#fH=#34#$%+#'$)22+,A$/"+0#)5*7&4&+,#0+'&2"+0#&"#`<+,(&'+#FO9PO#)"0#$%+#'1"(%,3A "3/'71#$/"+0#)5*7&4&+,#0+'&2"+0#&"#`<+,(&'+#FO9PS9#EG%5-H#:3,#$%+#'$)22+,A$/"+0#)5*7&4&+,-#"3$+ $%)$#$%+#2)&"#)$# ωG#&'#+?/)7#$3#$%+#*,30/($#34#$%+#2)&"'#34#$%+#&"0&;&0/)7#'$)2+'#)$#$%+&,#PA0R#4,+A ?/+"(&+'9I Ans.#$-'$

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1328 Chapter 16

Filters and Trusted Amplifiers

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PROBLEMS

Computer Simulation Problems W,367+5'#&";37;&"2#0+'&2"#),+#5),8+0#.&$%#X#$%,3/2%A 3/$#$%+#$+<$9#>'#.+77-#*,367+5'#),+#5),8+0#.&$%#)'$+,&'8'#$3 0+'(,&6+# $%+&,# 0+2,++# 34# 0&44&(/7$19# X&44&(/7$# *,367+5'# ),+ 5),8+0# .&$%# )"# )'$+,&'8# EpID# 53,+# 0&44&(/7$# *,367+5'# .&$% $.3# )'$+,&'8'# EppID# )"0# ;+,1# (%)77+"2&"2# )"0Z3,# $&5+A(3"A '/5&"2#*,367+5'#.&$%#$%,++#)'$+,&'8'#EpppI9

Section 16.1: Filter Transmission, Types and Specification 16.1 B%+# $,)"'4+,# 4/"($&3"# 34# )# 4&,'$A3,0+,# 73.A*)''# 4&7$+, E'/(%#)'#$%)$#,+)7&=+0#61#)"#KL#(&,(/&$I#()"#6+#+<*,+''+0#)' ! ( " ) = ω G ⁄ ( " + ω G ) - #.%+,+# ωG#&'#$%+#PA0R#4,+?/+"(1#34#$%+ 4&7$+,9#g&;+#&"#$)67+#43,5#$%+#;)7/+'#34# ! -#φ-#(-*)"0#)#)$#ω#q G-#G9SωG-#ωG-#NωG-#SωG-#FGωG-#)"0#FGGωG9 *16.2 >#4&7$+,#%)'#$%+#$,)"'4+,#4/"($&3"# ! ( " ) = F ⁄ cE"#+#FI E"N# +#"*+#FId9#C%3.#$%)$# ! = F + ω O #)"0#4&"0#)"#+<*,+'A '&3"#43,#&$'#*%)'+#,+'*3"'+# φEωI9#L)7(/7)$+#$%+#;)7/+'#34# !

)"0# φ#43, ω =#G9F-#F-#)"0#FG#,)0Z'#)"0#$%+"#4&"0#$%+#3/$*/$ (3,,+'*3"0&"2#$3#+)(%#34#$%+#43773.&"2#&"*/$#'&2")7'U E)I N#'&"#G9F-#E;37$'I E6I N#'&"#-#E;37$'I E(I N#'&"#FG-#E;37$'I 16.3 :3,# $%+# 4&7$+,# .%3'+# 5)2"&$/0+# ,+'*3"'+# &'# '8+$(%+0 E)'#$%+#(373,+0#(/,;+I#&"#:&29#FO9P-#4&"0# ! #)$#ω#=#G-#ω#=#ω+)"0#ω#=#ω"9#)5)<#=#G9S#0R-#)"0#)5&"#=#QG#0R9# D 16.4 ># 73.A*)''# 4&7$+,# &'# ,+?/&,+0# $3# *)''# )77# '&2")7' .&$%&"#&$'#*)''6)"0-#+<$+"0&"2#4,35#G#$3#Q#8H=-#.&$%#)#$,)"'A 5&''&3"#;),&)$&3"#34#)$#53'$#FG_#E&9+9-#$%+#,)$&3#34#$%+#5)<&A 5/5# $3# 5&"&5/5# $,)"'5&''&3"# &"# $%+# *)''6)"0# '%3/70# "3$ +<(++0#F9FI9#B%+#$,)"'5&''&3"#&"#$%+#'$3*6)"0-#.%&(%#+<$+"0' 4,35#S#8H=#$3#∞-#'%3/70#"3$#+<(++0#G9F_#34#$%+#5)<&5/5 *)''6)"0# $,)"'5&''&3"9# T%)$# ),+# $%+# ;)7/+'# 34# )5)<-# )5&")"0#$%+#'+7+($&;&$1#4)($3,#43,#$%&'#4&7$+,h 16.5 ># 73.A*)''# 4&7$+,# &'# '*+(&4&+0# $3# %);+# )5)<# =# F# 0R )"0#)5&"#=#FG#0R9#!$#&'#43/"0#$%)$#$%+'+#'*+(&4&()$&3"'#()"

Problems

16.6 C8+$(%#$,)"'5&''&3"#'*+(&4&()$&3"'#43,#)#%&2%A*)''#4&7A $+,#%);&"2#)#*)''6)"0#0+4&"+0#61#9#≥ N#8H=#)"0#)#'$3*6)"0 0+4&"+0#61#9#≤ F#8H=9#)5)<#=#G9S#0R-#)"0#)5&"#=#SG#0R9

Section 16.3: Butterworth and Chebyshev Filters D 16.12 X+$+,5&"+# $%+# 3,0+,# 0# 34# $%+# R/$$+,.3,$%# 4&7$+, 43,#.%&(%#)5)<#=#F#0R-#)5&"# ≥#NG#0R-#)"0#$%+#'+7+($&;&$1 ,)$&3# ω " ⁄ ω + = F9P9 # T%)$# &'# $%+# )($/)7# ;)7/+# 34# 5&"&5/5 '$3*6)"0# )$$+"/)$&3"# ,+)7&=+0h# !4# )5&"# &'# $3# 6+# +<)($71# NG 0R-#$3#.%)$#;)7/+#()"#)5)<#6+#,+0/(+0h# 16.13 L)7(/7)$+# $%+# ;)7/+# 34# )$$+"/)$&3"# 36$)&"+0# )$# ) 4,+?/+"(1#F9O#$&5+'#$%+#PA0R#4,+?/+"(1#34#)#'+;+"$%A3,0+, R/$$+,.3,$%#4&7$+,9

Section 16.2: The Filter Transfer Function

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PROBLEMS

16.7 C8+$(%# $,)"'5&''&3"# '*+(&4&()$&3"'# 43,# )# 6)"0'$3* 4&7$+,#$%)$#&'#,+?/&,+0#$3#*)''#'&2")7'#3;+,#$%+#6)"0'#G#≤#9#≤ FG#8H=#)"0#NG#8H=#≤#9#≤#∞#.&$%#)5)<#34#F#0R9#B%+#'$3*6)"0 +<$+"0'# 4,35# 9# =# FN# 8H=# $3# 9# = FO# 8H=-# .&$%# )# 5&"&5/5 ,+?/&,+0#)$$+"/)$&3"#34#QG#0R9#

CHAPTER 16

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1329

CHAPTER 16

PROBLEMS

1330 Chapter 16 Filters and Tuned Amplifiers

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Problems 1331

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PROBLEMS

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CHAPTER 16

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CHAPTER 16

PROBLEMS

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**16.77 E)I#e'&"2#$%+#4)($#$%)$#43,# @# 3F#$%+#'+(3"0A3,0+, 6)"0*)''#,+'*3"'+#&"#$%+#"+&2%63,%330#34# ωG#&'#$%+#')5+ )'# $%+# ,+'*3"'+# 34# )# 4&,'$A3,0+,# 73.A*)''# .&$%# PA0R 4,+?/+"(1#34# E ω G ⁄ N@ I -#'%3.#$%)$#$%+#6)"0*)''#,+'*3"'+#)$ ω = # ω G + δω -#43,# δω # 7 # ω G - #&'#2&;+"#61#

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N0

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N0

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PROBLEMS

16.73 ># (3&7# %);&"2# )"# &"0/($)"(+# 34# FG# µH# &'# &"$+"0+0 43,#)**7&()$&3"'#),3/"0#FAfH=#4,+?/+"(19#!$'#@#&'#'*+(&4&+0 $3#6+#NGG9#:&"0#$%+#+?/&;)7+"$#*),)77+7#,+'&'$)"(+#>+9#T%)$ &'# $%+# ;)7/+# 34# $%+# ()*)(&$3,# ,+?/&,+0# $3# *,30/(+# ,+'3A ")"(+# )$# F fH=h# T%)$# )00&$&3")7# *),)77+7# ,+'&'$)"(+# &' ,+?/&,+0#$3#*,30/(+#)#PA0R#6)"0.&0$%#34#FG#8H=h

! ( & ωG ) ! ( & ω ) #' AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA N N F + Q@ E δω ⁄ ω G I

CHAPTER 16

J =#F#µH#)"0#?#=#NGG#*:9#B%+#$,)"'&'$3,#&'#6&)'+0#)$#F#5> )"0#%)'# β#=#NGG-#?π#=#FG#*:-#)"0#?µ#=#F#*:9#B%+#$,)"'&'$3, 73)0#&'#)#,+'&'$)"(+#34#S#8Ω99#:&"0#ωG-#@-#$%+#PA0R#6)"0.&0$%)"0#$%+#(+"$+,A4,+?/+"(1#2)&"#34#$%&'#'&"27+A$/"+0#)5*7&4&+,9

CHAPTER 17

Signal Generators and Waveform-Shaping Circuits Introduction

17.6 Generation of a Standardized Pulse—The Monostable Multivibrator

1335

17.1 Basic Principles of Sinusoidal Oscillators 1336 17.2 Op Amp–RC Oscillator Circuits 17.3 LC and Crystal Oscillators 17.4 Bistable Multivibrators

17.7 Integrated-Circuit Timers 1342

1349

1355

17.5 Generation of Square and Triangular Waveforms Using Astable Multivibrators 1363

1369

17.8 Nonlinear Waveform-Shaping Circuits 1374 17.9 Precision Rectifier Circuits Summary

1386

Problems

1387

1378

1367

IN THIS CHAPTER YOU WILL LEARN 1. That an oscillator circuit that generates sine waves can be implemented by connecting a frequency-selective network in the positive-feedback path of an amplifier. 2. The conditions under which sustained oscillations are obtained and the frequency of the oscillations. 3. How to design nonlinear circuits to control the amplitude of the sine wave obtained in a linear oscillator. 4. A variety of circuits for implementing a linear sine-wave oscillator. 5. How op amps can be combined with resistors and capacitors to implement precision multivibrator circuits. 6. How a bistable circuit can be connected in a feedback loop with an opamp integrator to implement a generator of square and triangular waveforms. 7. The application of one of the most popular IC chips of all time, the 555 timer, in the design of generators of pulse and square waveforms. 8. How a triangular waveform can be shaped by a nonlinear circuit to provide a sine waveform. 9. How op amps and diodes can be combined to implement a variety of high-precision rectifier circuits.

Introduction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

1335

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17.1 Basic Principles of Sinusoidal Oscillators !"#$%)(#(&.$)+"2#9&#($4'0#$%U().#7/)".)7-&(#+,#$%&#'&()*"#+,#-)"&5/#()"&@956&#+(.)--5$+/(;#!" (7)$&#+,#$%&#"51&#!"#$%&'()*"!!%+(&,'(+1&#,+/1#+,#"+"-)"&5/)$0#%5(#$+#8&#&17-+0&'#$+#7/+6)'& .+"$/+-#+,#$%ȅ-)$4'&#+,#$%&#+4$74$#()"μ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

17.1.1 The Oscillator Feedback Loop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β()) 9%&/ &#"+$&#$%&#"&*5$)6&#()*"#)"#$%&#'&"+1)"5$+/;

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17.1 Basic Principles of Sinusoidal Oscillators

Amplifier A

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1337

1338 Chapter 17 Signal Generators and Waveform-Shaping Circuits

Figure 17.2 Z&7&"'&".&#+,#$%&#+(.)--5$+/@,/&34&".0#($58)-)$0#+"#$%&#(-+7&#+,#$%%5(&#/&(7+"(&;#Q#($&&7 7%5(&#/&(7+"(&#J);&;2#-5/*φ/ 5ωK#/&(4-$(#)"#5#(15--#∆ω U#,+/#5#*)6&"#.%5"*&#)"#7%5(&#∆φ#[/&(4-$)"*#,/+1#5 .%5"*&#J'4&2#,+/#&:517-&2#$+#$&17&/5$4/&K#)"#5#.)/.4)$#.+17+"&"$\;

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EXERCISES 17.1

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1339

1340 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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17.1 Basic Principles of Sinusoidal Oscillators

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1341

1342 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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17.2 Op Amp–RC Oscillator Circuits 1343

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1344 Chapter 17 Signal Generators and Waveform-Shaping Circuits

EXERCISES 17.3 T+/#$%&#.)/.4)$#)"#T)*;#BC;NL#J5K#Z)(/&*5/')"*#$%&#-)1)$&/#.)/.4)$2#,)"'#$%&#-+.5$)+"#+,#$%&#.-+(&'@-++7 7+-&(;#J8K#T)"'#$%&#,/&34&".0#+,#+(.)--5$)+";#J.K#H)$%#$%&#-)1)$&/#)"#7-5.&2#,)"'#$%ȅ-)$4'&#+,#$%&#+4$@ 74$#()"μ&#J5((41&#$%5$#$%&#')+'&#'/+7#)(#U;C#bK; Ans./J5K#JBUN/ BOKJU;UBN#±# 6K>#J8K#B#=]?>#J.K#XB;DO#b#J7&5=@$+@7&5=K

A%&# .)/.4)$# +,# T)*;# BC;O# &17-+0(# 5"# )"&:7&"()6&# )17-&1&"$5$)+"# +,# $%&# 75/51&$&/@ 65/)5$)+"#1&.%5")(1#+,#517-)$4'&#.+"$/+-;#c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

EXERCISES 17.4 T+/#$%&#.)/.4)$#)"#T)*;#BC;O#,)"'#$%&#,+--+9)"*L#J5K#A%&#(&$$)"*#+,#7+$&"$)+1&$&/#E#5$#9%).%#+(.)--5$)+"( ^4($#($5/$;#J8K#A%&#,/&34&".0#+,#+(.)--5$)+"; Ans./J5K/XU#=Ω#$+#*/+4"'>#J8K#B#=]?

17.2.2 The Phase-Shift Oscillator A%U().#($/4.$4/&#+,#$%%5(&@(%),$#+(.)--5$+/#)(#(%+9"#)"#T)*;#BC;C;#!$#.+"()($(#+,#5#"&*5$)6&@ *5)"#517-),)&/#J−FK#9)$%#5#$%/&&@(&.$)+"#J$%)/'@+/'&/K#EF#-5''&/#"&$9+/=#)"#$%&#,&&'85.=;#A%& .)/.4)$#9)--#+(.)--5$$#$%&#,/&34&".0#,+/#9%).%#$%%5(&#(%),$#+,#$%&#EF#"&$9+/=#)(#BIU°;#_"-0 5$#$%)(#,/&34&".0#9)--#$%&#$+$5-#7%5(&#(%),$#5/+4"'#$%&#-++7#8&#U°#+/#DOU°;#]&/ &#(%+4-'#"+$& $%5$#$%&#/&5(+"#,+/#4()"*#5#$%/&&@(&.$)+"#EF#"&$9+/=#)(#$%5$#$%/&&#)(#$%
)")141#"418&/#+, (&.$)+"(#J);&;2#-+9&($#+/'&/K#$%5$#)(#.5758-&#+,#7/+'4.)"*#5#BIU°#7%5(&#(%),$#5$#5#,)")$&#,/&34&".0; T+/#+(.)--5$)+"(#$+#8&#(4($5)"&'2#$%A-4&#+,#F#(%+4-'#8&#&345-#$+#$%&#)"6&/(&#+,#$%*@ ")$4'&# +,# $%&# EF# "&$9+/=# $/5"(,&/# ,4".$)+"# 5$# $%&# ,/&34&".0# +,# +(.)--5$)+";# ]+9&6&/2# $+ &"(4/&#$%5$#+(.)--5$)+"(#($5/$2#$%A-4&#+,#F#%5(#$+#8&#.%+(&"#(-)*%$-0#%)*%&/#$%5"#$%A-4& $%5$#(5$)(,)&(#$%&# 4")$0@-++7@*5)"#.+"')$)+";#_(.)--5$)+"(#9)--#$%&"#*/+9#)"#15*")$4'&# 4"$)-)1)$&'#80#(+1&#"+"-)"&5/#.+"$/+-#1&.%5")(1; T)*4/&#BC;I#(%+9(#5#7/5.$).5-#7%5(&@(%),$#+(.)--5$+/#9)$%#5#,&&'85.=#-)1)$&/2#.+"()($)"*#+, ')+'&(# =B# 5"'# =X# 5"'# /&()($+/(# >B2# >X2# >D2# 5"'# >M# ,+/# 517-)$4'&# ($58)-)?5$)+";# A+# ($5/$

17.2 Op Amp–RC Oscillator Circuits 1345

D1

P D2

Rs Cs

Cp 16 nF

Rp

Figure 17.6 Q#H)&"@8/)'*&#+(.)--5$+/#9)$%#5"#5-$&/"5$)6
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Figure 17.7 Q#7%5(&@(%),$#+(.)--5$+/;

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X

ω C >> . M + 6 ( D ω C> ! B ⁄ ω C> )

Ans./ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

17.6 d(&#$%&#&:7/&(()+"#'&/)6&'#)"#Y:&/.)(&#BC;N#$+#,)"'#$%&#,/&34&".0#+,#+(.)--5$)+"#.U#5"'#$%
)")141 /&34)/&'#65-4&#+,#>.#,+/#+(.)--5$)+"(#$+#($5/$#)"#$%&#.)/.4)$#+,#T)*;#BC;I; Ans./ω0 = 1/ D#C>>#>. ≥ 12 >>#.U e NCM;D#]?>#>.# e#BXU#=Ω

1346 Chapter 17 Signal Generators and Waveform-Shaping Circuits

D1

D2

Figure 17.8 Q#7/5.$).5-#7%5(&@(%),$#+(.)--5$+/#9)$%#5#-)1)$&/#,+/#517-)$4'&#($58)-)?5$)+";

17.2.3 The Quadrature Oscillator A%,*1,%31'/"#-$00,%"1#)(#85(&'#+"#$%&#$9+@)"$&*/5$+/#-++7#($4')&'#)"#<&.$)+"#BO;C;#Q(#5" 5.$)6&#,)-$&/2#$%&#-++7#)(#'517&'#$+#-+.5$&#$%+-&(#)"#$%&#-&,$#%5-,#+,#$%&#)#7-5"&;#]&/&2#"+ (4.%#'517)"*#9)--#8(&'2#()". )(%#$+#-+.5$&#$%+-&(#+"#$%&# 6 ω #5:)(#$+#7/+6)'&#(4(@ $5)"&'#+(.)--5$)+"(;#!"#,5.$2#$+#&"(4/&#$%5$#+(.)--5$)+"(#($5/$2#$%+-&(#5/&#)")$)5--0#-+.5$&'#)" $%&#/)*%$#%5-,@7-5""'#$%&"#V74--&'#85.=W#80#$%&#"+"-)"&5/#*5)"#.+"$/+-; T)*4/&#BC;R#(%+9(#5#7/5.$).5-#345'/5$4/&#+(.)--5$+/;#Q17-),)&/#B#)(#.+""&.$&'#5(#5"#)"6&/$@ )"*#f)--&/#)"$&*/5$+/#9)$%#5#-)1)$&/#)"#$%&#,&&'85.=#,+/#517-)$4'&#.+"$/+-;#Q17-),)&/#X#)(#.+"@ "&.$&'# 5(# 5# "+")"6&/$)"*# )"$&*/5$+/# J$%4(# /&7-5.)"*# $%&# .5(.5'&# .+""&.$)+"# +,# $%&# f)--&/ )"$&*/5$+/#5"'#$%&#)"6&/$&/#)"#$%&#$9+@)"$&*/5$+/#-++7#+,#T)*;#BO;XN8K;#A+#4"'&/($5"'#$%&#+7&/5@ $)+"#+,#$%)(#"+")"6&/$)"*#)"$&*/5$+/2#.+"()'&/#$%&#&34)65-&"$#.)/.4)$#(%+9"#)"#T)*;#BC;RJ8K;#]&/&2 9&#%56&#/&7-5.&'#$%&#)"$&*/5$+/#)"74$#6+-$5*&#v#80#$%&#S+/$+" &34)65-&"$#.+17+(&'#+,#5#.4//&"$#(+4/.&# v #5"'#5#75/5--&-#/&()($5".&#X>;#S+92#()".& v .#9)--#8& (Xv ! v ) ⁄ > . = v ⁄ > . #)"#$%&#')/&.$)+"#,/+1#+4$74$#$+#)"74$;#A%4(#>.#*)6&(#/)(&#$+#5#"&*5$)6& )"74$#/&()($5".&2# −>. 2'5(#)"').5$&'#)"#$%&#&34)65-&"$#.)/.4)$#+,#T)*;#BC;RJ8K;#S+1)"5--02# >.' )( 15'&#&345-#$+#X>2#5"'#$%4(#−>.'.5".&-(#X>2#5"'#5$#$%&#)"74$#9/&#-&,$#9)$%#5#.4//&"$#(+4/.& 0 #,&&')"*#5#.575.)$+/#C;#A%&#/&(4-$#)(#$%5$# v = @@@CB@ +U @@@@@@@@ X> C> U . = X>2 #$%&#.)/.4)$#,4".$)+"(#5(#5#7&/,&.$#"+")"6&/$)"*#)"$&*/5$+/;#!,2#%+9&6&/2 >. ' )(#15'&#(15--&/#$%5"#X>2#5#"&$#"&*5$)6&#/&()($5".Ɂ&5/(#)"#75/5--&-#9)$%#C;

17.2 Op Amp–RC Oscillator Circuits 1347

v# D1

vO1 2R

2R

D2

C

vO2 2

!Rf

(b)

2

v

(a) Figure 17.9 :,;#Q#345'/5$4/&@+(.)--5$+/#.)/.4)$;#:+;#Y34)65-&"$#.)/.4)$#5$#$%&#)"74$#+,#+7#517#X;

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JBC;BMK

A%4(#$%&#-++7#9)--#+(.)--5$$#,/&34&".0# ω U 2 *)6&"#80 B ω U = @@@@@@@@ C>

JBC;BNK

T)"5--02# )$# (%+4-'# 8&# 7+)"$&'# +4$# $%5$# $%&# "51&# 23%5&%+3&$' ()*"!!%+(&# )(# 4(&'# 8&.54(& $%& .)/.4)$#7/+6)'&(#$9+#()"4(+)'(#9)$%#RU°#7%5(&#'),,&/&".&;#A%)(#)(#$%&#.5(&.54(&# v
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1348 Chapter 17 Signal Generators and Waveform-Shaping Circuits

f0

v2 "V v1 !V Figure 17.10 P-+.=#')5*/51#+,#$%.$)6&@,)-$&/@$4"&'#+(.)--5$+/;

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EXERCISES 17.7 d()"*# C = BO#"T2 # ,)"'# $%&# 65-4&# +,# ># (4.%# $%5$# $%&# .)/.4)$# +,# T)*;# BC;BB# 7/+'4.&(# B@=]?# ()"& 956&(;#!,#$%&#')+'&#'/+7#)(#U;C#b2#,)"'#$%&5=@$+@7&5=#517-)$4'&#+,#$%&#+4$74$#()"μ&;#JI"#+J#Q (345/&# 956&# 9)$%# 7&5=@$+@7&5=# 517-)$4'&# +,# ?# 6+-$(# %5(# 5# ,4"'51&"$5-# .+17+"&"$# 9)$%# M? ⁄ π 6+-$(#7&5=@$+@7&5=#517-)$4'&;K Ans./ BU#=Ω> /D;O#b

17.3 LC and Crystal Oscillators

A2

A1

D1

D2

Figure 17.11 Q#7/5.$).5-#)17-&1&"$5$)+"#+,#$%.$)6&@,)-$&/@$4"&'#+(.)--5$+/;

17.2.5 A Final Remark A%&# +7# 517gEF# +(.)--5$+/# .)/.4)$(# ($4')&'# 5/&# 4(&,4-# ,+/# +7&/5$)+"# )"# $%&# /5"*&# BU# ]?# $+ BUU =]?#J+/#7&/%57(#B#f]?#5$#1+($K;#H%&/&5(#$%&#-+9&/#,/&34&".0#-)1)$#)(#').$5$&'#80#$%& ()?&#+,#75(()6&#.+17+"&"$(#/&34)/&'2#$%ǝ&/#-)1)$#)(#*+6&/"&'#80#$%&#,/&34&".0@/&(7+"(& 5"'#(-&9@/5$&#-)1)$5$)+"(#+,#+7#517(;#T+/#%)*%&/#,/&34&".)&(2#.)/.4)$(#$%5$#&17-+0#$/5"()($+/( $+*&$%&/# 9)$%# GF@$4"&'# .)/.4)$(# +/# ./0($5-(# 5/&# ,/&34&"$-0# 4(&';D# A%&(&# 5/&# ')(.4((&'# )" <&.$)+"#BC;D;

17.3 LC and Crystal Oscillators _(.)--5$+/(#4$)-)?)"*#$/5"()($+/(#JTYA(#+/#P`A(K2#9)$%#GF@$4"&'#.)/.4)$(#+/#./0($5-(#5(#,&&'@ 85.=#&-&1&"$(2#5/(&'#)"#$%&#,/&34&".0#/5"*&#+,#BUU#=]?#$+#%4"'/&'(#+,#1&*5%&/$?;#A%&0 &:%)8)$#%)*%&/#:#$%5"#$%&#EF#$07&(;#]+9&6&/2#GF#+(.)--5$+/(#5/&#'),,).4-$#$+#$4"&#+6&/#9)'& /5"*&(2#5"'#./0($5-#+(.)--5$+/(#+7&/5$$#5#()"*-&#,/&34&".0;

17.3.1 LC-Tuned Oscillators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

1349

1350 Chapter 17 Signal Generators and Waveform-Shaping Circuits

(b) (a) Figure 17.12 A9+#.+11+"-0#4(&'#.+",)*4/5$)+"(#+,#GF@$4"&'#+(.)--5$+/(L#:,;#F+-7)$$(#5"'#:+;#]5/$-&0;

,&&'85.=#)(#5.%)&6&'#80#950#+,#5#.575.)$)6&#')6)'&/#)"#$%&#F+-7)$$(#+(.)--5$+/#5"'#80#950 +,# 5"# )"'4.$)6&# ')6)'&/# )"# $%&# ]5/$-&0# .)/.4)$;# A+# ,+.4(# 5$$&"$)+"# +"# $%&# +(.)--5$+/a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

B X @ ω U = B# @ @@@@@@@@@@@@@@@@@

JBC;BOK

5"'#,+/#$%&#]5/$-&0#+(.)--5$+/#9&#%56&

ω U = B ⁄ ( @ B + @ X )C

JBC;BCK

A%&#/5$)+# @ B ⁄ @ X #+/# C B ⁄ C X #'&$&/1)"&(#$%&#,&&'85.=#,5.$+/#5"'#$%4(#14($#8'^4($&'#)"#.+"@ ^4".$)+"#9)$%#$%&#$/5"()($+/#*5)"#$+#&"(4/&#$%5$#+(.)--5$)+"(#9)--#($5/$;#A+#'&$&/1)"&#$%&#+(.)-@ -5$)+"# .+"')$)+"# ,+/# $%&# F+-7)$$(# +(.)--5$+/2# 9&# /&7-5.&# $%&# $/5"()($+/# 9)$%# )$(# &34)65-&"$ .)/.4)$2# 5(# (%+9"# )"# T)*;# BC;BD;# A+# ()17-),0# $%&# 5"5-0()(2# 9&# %56&# "&*-&.$&'# $%&# $/5"()($+/ .575.)$5".&# C µ #J C L5 #,+/#5#TYAK;#F575.)$5".&# C π #JCL)#,+/#5#TYAK2#5-$%+4*%#"+$#(%+9"2#.5" 8&#.+"()'&/&'#$+#8#75/$#+,#CX;#A%&#)"74$#/&()($5".&# & π #J)",)")$&#,+/#5#TYAK#%5(#5-(+#8&&" "&*-&.$&'2# 5((41)"*# $%5$# 5$# $%&# ,/&34&".0# +,# +(.)--5$)+"# & π @ ( B ⁄ ω C X ) ;# T)"5--02# 5(# 1&"@ $)+"&'#&5/-)&/2#$%&#/&()($5".&#>#)".-4'&(#&(#+,#$%&#$/5"()($+/; A+#,)"'#$%&#-++7#*5)"2#9/&5=#$%&#-++7#5$#$%&#$/5"()($+/#85(&2#577-0#5"#)"74$#6+-$5*&# ? π 2 5"'# ,)"'# $%&# /&$4/"&'# 6+-$5*&# $%5$# 577&5/(# 5./+((# $%&# )"74$# $&/1)"5-(# +,# $%&# $/5"()($+/;# H& $%&"#&345$&#$%&#-++7#*5)"#$+#4")$0;#Q"#5-$&/"5$)6Ɂ/+5.%#)(#$+#5"5-0?&#$%&#.)/.4)$#5"'#&-)1@ )"5$&# 5--# .4//&"$# 5"'# 6+-$5*&# 65/)58-&(2# 5"'# $%4(# +8$5)"# +"&# &345$)+"# $%5$# *+6&/"(# .)/.4)$ +7&/5$)+";#_(.)--5$)+"(#9)--#($5/$#),#$%)(#&345$)+"#)(#(5$)(,)&';#A%4(#$%&#/&(4-$)"*#&345$)+"#9)-*)6(#$%&#.+"')$)+"(#,+/#+(.)--5$)+";

17.3 LC and Crystal Oscillators 1351

sC2 V$

Vc # V$ ( 1 " s2 LC2 )

L

C

sC2 V$

"

C2

V$ !

g m V$

C1

R

Figure 17.13 Y34)65-&"$#.)/.4)$#+,#$%&#F+-7)$$(#+(.)--5$+/#+,#T)*;#BC;BXJ5K;#A+#()17-),0#$%"5-0()(2#Cµ#5"' &π#5/&#"&*-&.$&';#H&#.5"#.+"()'&/#Cπ#$+#8K/$#+,#CX2#5"'#9&#.5"#)".-4'&#&(#)"#>;

Q#"+'&#&345$)+"#5$#$%&#$/5"()($+/#.+--&.$+/#J"+'&#FK#)"#$%&#.)/.4)$#+,#T)*;#BC;BD#0)&-'( B X )C X ?π + L 9 ?π + @@@ + ) C B ( B + ) @C X )? π = U > <)".&# ?π ≠ U #J+(.)--5$)+"(#%56&#($5/$&'K2#)$#.5"#8&#&-)1)"5$&'2#5"'#$%&#&345$)+"#.5"#8&#/&5/@ /5"*&'#)"#$%&#,+/1 B D X ) @C B C X + ) ( @C X ⁄ > ) + ) ( C B + C X ) + L 9 + @@@ >

= U

JBC;BIK

<48($)$4$)"*# ) = 6 ω #*)6&( X

B ω @C D L 9 + @@@ ! @@@@@@@@@@@@@@@@X + 6 [ ω ( C B + C X ) ! ω @C B C X ] = U > >

JBC;BRK

T+/#+(.)--5$)+"(#$+#($5/$2#8+$%#$%&#/&5-#5"'#)15*)"5/0#75/$(#14($#8&#?&/+;#Y345$)"*#$%&#)15*)@ "5/0#75/$#$+#?&/+#*)6&(#$%&#,/&34&".0#+,#+(.)--5$)+"#5( C C CB + CX

B X @ ω U = B# @ @@@@@@@@@@@@@@@@@

JBC;XUK

9%).%#)(#$%&#/&(+"5".&#,/&34&".0#+,#$%&#$5"=#.)/.4)$2#5(#5"$).)75$&';M#Y345$)"*#$%&#/&5-#75/$#$+ ?&/+#$+*&$%&/#9)$%#Y3;#JBC;XUK#*)6&( CX ⁄ CB = L9 >

JBC;XBK

9%).%#%5(#5#()17-%0().5-#)"$&/7/&$5$)+"L#T+/#(4($5)"&'#+(.)--5$)+"(2#$%*")$4'&#+,#$%& *5)"#,/+1#85(&#$+#.+--&.$+/#JL9>K#14($#8&#&345-#$+#$%&#)"6&/(&#+,#$%+-$5*&#/5$)+#7/+6)'&' 80#$%&#.575.)$)6&#')6)'&/2#9%).%#,/+1#T)*;#BC;BXJ5K#.5"#8&#(&&"#$+#8&# v $D ⁄ v *$ = C B ⁄ C X ; #_, .+4/(&2#,+/#+(.)--5$)+"(#$+#($5/$2#$%&#-++7#*5)"#14($#8'&#*/&5$&/#$%5"#4")$02#5#.+"')$)+" $%5$#.5"#8&#($5$&'#)"#$%&#&34)65-&"$#,+/1 L9 > > CX ⁄ CB

M#!,# &

JBC;XXK

π #)(#$5=&"#)"$+#5..+4"$2#$%&#,/&34&".0#+,#+(.)--5$)+"#.5"#8&#(%+9"#$+#(%),$#(-)*%$-0#,/+1#$%A-4& *)6&"#80#Y3;#JBC;XUK;

1352 Chapter 17 Signal Generators and Waveform-Shaping Circuits

Figure 17.14 F+17-&$&# .)/.4)$# ,+/# 5# F+-7)$$( +(.)--5$+/;

Q(#+(.)--5$)+"(#*/+9#)"#517-)$4'&2#$%&#$/5"()($+/a(#"+"-)"&5/#.%5/5.$&/)($).(#/&'4.&#$%&#&,,&.@ $)6A-4&#+,#L9#5"'2#.+//&(7+"')"*-02#/&'4.&#$%&#-++7#*5)"#$+#4")$02#$%4(#(4($5)")"*#$%&#+(.)-@ -5$)+"(; Q"5-0()(# ()1)-5/# $+# $%&# ,+/&*+)"*# .5"# 8&# .5//)&'# +4$# ,+/# $%&# ]5/$-&0# .)/.4)$# J(&&# -5$&/L Y:&/.)(&#BC;IK;#Q$#%)*%#,/&34&".)&(2#1+/..4/5$&#$/5"()($+/#1+'&-(#14($#8(&';#Q-$&/"5@ $)6&-02#$%#75/51&$&/(#+,#$%&#$/5"()($+/#.5"#8
&5(4/&'#5$#$%&#)"$&"'&'#,/&34&".0# ω U 2 #5"' $%&# 5"5-0()(# .5"# $%&"# 8&# .5//)&'# +4$# 4()"*# $%&# 4@75/51&$&/# 1+'&-# J(&&# Q77&"'):# FK;# A%)( )( 4(45--0# ()17-&/# 5"'# 1+/&# 5..4/5$&2# &(7&.)5--0# 5$# ,/&34&".)&(# 58+6&# 58+4$# DUh# +,# $%& $/5"()($+/#.M; Q(#5"#&:517-&#+,#5#7/5.$).5-#GF#+(.)--5$+/2#9&#(%+9#)"#T)*;#BC;BM#$%&#.)/.4)$#+,#5#F+-7)$$( +(.)--5$+/2#.+17-&$ )$%#8)5(#'&$5)-(;#]&/&#$%&#/5')+@,/&34&".0#.%+=&#JETFK#7/+6)'&(#5#%)*% /&5.$5".$# ω U #84$#5#-+9#'.#/&()($5".&; T)"5--02# 5# ,&9# 9+/'(# 5/&# )"# +/'&/# +"# $%&# 1&.%5")(1# $%5$# '&$&/1)"&(# $%&# 517-)$4'&# +, +(.)--5$)+"(#)"#$%&#GF@$4"&'#+(.)--5$+/(#')(.4((&'#58+6&;#d"-)=&#$%&#+7@517#+(.)--5$+/(#$%5$ )".+/7+/5$&#(7&.)5-#517-)$4'&@.+"$/+-#.)/.4)$/02#GF@$4"&'#+(.)--5$+/(#4$)-)?&#$%&#"+"-)"&5/#"C g vNO#.%5/5.$&/)($).(#+,#$%&#P`A#J$%&#"= gvPQ#.%5/5.$&/)($).(#+,#$%&#TYAK#,+/#517-)$4'&#.+"$/+-; A%4(# $%&(&# GF@$4"&'# +(.)--5$+/(# 5/&# ="+9"# 5(# )$!.R!"9"+"#L' ()*"!!%+(&);# <7&.),).5--02# 5(# $%& +(.)--5$)+"(#*/+9#)"#517-)$4'&2#$%&#&,,&.$)6&#*5)"#+,#$%&#$/5"()($+/#)(#/&'4.&'#8&-+9#)$(#(15--@ ()*"5-#65-4&;#Y6&"$45--02#5"#517-)$4'&#)(#/&5.%&'#5$#9%).%#$%&#&,,&.$)6&#*5)"#)(#/&'4.&'#$+#$%& 7+)"$#$%5$#$%&#P5/=%54(&"#./)$&/)+"#)(#(5$)(,)&'#&:5.$-0;#A%ȅ-)$4'&#$%&"#/&15)"(#.+"($5"$ 5$#$%)(#65-4&; E&-)5".&#+"#$%&#"+"-)"&5/#.%5/5.$&/)($).(#+,#$%&#P`A#J+/#$%&#TYAK#)17-)&(#$%5$#$%&#.+--&.$+/ J'/5)"K# .4//&"$# 956&,+/1# 9)--# 8&# "+"-)"&5/-0# ')($+/$&';# S&6&/$%&-&((2# $%&# +4$74$# 6+-$5*& ()*"5-#9)--#($)--#8#()"4(+)'#+,#%)*%#74/)$0#8&.54(&#+,#$%&#,)-$&/)"*#5.$)+"#+,#$%&#GF@$4"&' .)/.4)$;# Z&$5)-&'# 5"5-0()(# +,# 517-)$4'&# .+"$/+-2# 9%).%# 15=&(# 4(&# +,# "+"-)"&5/@.)/.4)$ $&.%")34&(2#)(#8&0+"'#$%&#(.+7&#+,#$%)(#8++=;

17.3 LC and Crystal Oscillators 1353

EXERCISES 17.8 <%+9#$%5$#,+/#$%&#]5/$-&0#+(.)--5$+/#+,#T)*;#BC;BXJ8K2#$%&#,/&34&".0#+,#+(.)--5$)+"#)(#*)6&"#80 Y3; JBC;BCK#5"'#$%5$#,+/#+(.)--5$)+"(#$+#($5/$#L9>'>' ( @ B ⁄ @ X ) ;

D17.9 d()"*#5#P`A#8)5(&'#5$#;C' =#B#1Q2#'&()*"#5#F+-7)$$(#+(.)--5$+/#$+#+7&/5$$#ωU =#BU6 /5'i(;#d(&#CB = U;UB#µT#5"'#5((41&#$%5$#$%&#.+)-#565)-58-&#%5(#5#:#+,#BUU#J$%)(#.5"#8&#/&7/&(&"$&'#80#5#/&()($5".&#)" 75/5--&-#9)$%#CB#*)6&"#80#: ⁄ωUCBK;#Q-(+#5((41&#$%5$#$%&/&#)(#5#-+5'#/&()($5".$#$%&#.+--&.$+/#+,#X =Ω#5"'#$%5$#,+/#$%&#P`A2#&(#=#BUU#=Ω;#T)"'#CX#5"'#@; Ans./U;OO#µT>#BUU#µ]#J5#(+1&9%5$#(15--&/#CX#9+4-'#8(&'#$+#5--+9#+(.)--5$)+"(#$+#*/+9#)" 517-)$4'&K

17.3.2 Crystal Oscillators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ωU @ /&# $%5$# .5"# 8&# 5(# %)*%# 5(# 5 ,&9 %4"'/&'#$%+4(5"'2#5"'#5#75/5--&-#.575.)$5".&#C/#J5#,&9#7).+,5/5'(K;#F575.)$+/#C/#/&7/&@ (&"$(#$%&#&-&.$/+($5$).#.575.)$5".&$9&&"#$%&#$9+#75/5--&-#7-5$&(#+,#$%&#./0($5-;#S+$&#$%5$ C/ @#C);

(a)

(b)

(c)

Figure 17.15 Q# 7)&?+&-&.$/).# ./0($5-;# :,;# F)/.4)$# (018+-;# :+;# Y34)65-&"$# .)/.4)$;# :-;# F/0($5-# /&5.$5".& 6&/(4(#,/&34&".0#["+$&#$%5$2#"&*-&.$)"*#$%&#(15--#/&()($5".&#&2#A./0($5-#=#6HJωK\;

1354 Chapter 17 Signal Generators and Waveform-Shaping Circuits <)".&#$%&#:#,5.$+/#)(#6&/0#%)*%2#9–#"&*-&.$#$%&#/&()($5".&#"'#&:7/&((#$%&#./0($5)17&'5".( B A ( ) ) = B # )C/ + @@@@@@@@@@@@@@@@@@@@@@@@@@@ )@ + B ⁄ )C) 9%).%#.5"#8")74-5$&'#$+#$%&#,+/1 X

) + ( B ⁄ @C) ) B @ A ( ) ) = @@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ X )C/ ) + [ ( C/ + C) ) ⁄ @C) C/ ]

JBC;XDK

T/+1#Y3;#JBC;XDK#5"'#,/+1#T)*;#BC;BNJ8K2#9&#(&&#$%5$#$%&#./0($5-#%5(#$9+#/&(+"5".&#,/&34&"@ .)&(L#5#(&/)&(#/&(+"5".$#ω)

ω ) = #B ⁄ @C )

JBC;XMK

5"'#5#75/5--&-#/&(+"5".$#ω/ CC C) + C/

) / @ ω / = B## @ @@@@@@@@@@@@@@@@@

JBC;XNK

A%4(#,+/#)#=#6ω#9&#.5"#9/)$& X

X

B ω ! ω) @ A ( 6 ω ) = ! 6 @@@@@@@@@@ @@@@@@@@@@@@@@@@@ ω C / ω X ! ω X/

JBC;XOK

T/+1#Y3(;#JBC;XMK#5"'#JBC;XNK#9&#"+$&#$%5$# ω/#># ω);#]+9&6&/2#()".&#C/ @#C)2#$%&#$9+#/&(+@ "5".&#,/&34&".)&(#5/&/0#.-+(&;#Y:7/&(()"*#AJ 6ωK#=#6HJωK2#$%&#./0($5-#/&5.$5".&#HJωK#9)-%56&# $%&# (%57&# (%+9"# )"# T)*;# BC;BNJ.K;# H&# +8(&/6&# $%5$# $%&# ./0($5-# /&5.$5".&# )(# )"'4.$)6& +6&/#$%&/0#"5//+9#,/&34&".0#85"'#8&$9&&"#ω)#5"'#ω/;#T+/#5#*)6&"#./0($5-2#$%)(#,/&34&".0 85"'# )(# 9&--# '&,)"&';# A%4(# 9&# 150# 4(&# $%&# ./0($5-# $+# /&7-5.&# $%&# )"'4.$+/# +,# $%&# F+-7)$$( +(.)--5$+/#JT)*;#BC;BX5K;#A%&#/&(4-$)"*#.)/.4)$#9)--#+(.)--5$$#$%&#/&(+"5".&#,/&34&".0#+,#$%& ./0($5-#)"'4.$5".&#@#9)$%#$%&#(&/)&(#&34)65-&"$#+,#C)#5"'# JC/ + C B C X ⁄ ( C B + C X )K ;#<)".&#C) )(#14.%#(15--&/#$%5"#$%&#$%/&&#+$%&/#.575.)$5".&(2#)$#9)--#8&#'+1)"5"$#5"'

ω U ! B ⁄ @C ) = ω )

JBC;XCK

!"#5'')$)+"#$+#$%U().#F+-7)$$(#+(.)--5$+/2#5#65/)&$0#+,#.+",)*4/5$)+"(#&:)($#,+/#./0($5-#+(.)--5@ $+/(;#T)*4/&#BC;BO#(%+9(#5#7+74-5/#.+",)*4/5$)+"#J.5--&'#$%&#>$'1-'/"#-$00,%"1K# 4$)-)?)"*# 5 Ff_<#)"6&/$&/#J(&&#<&.$)+"#BD;XK#5(#5"#517-),)&/;#E&()($+/#>.#'&$&/1)"&(#5#'.#+7&/5$)"* 7+)"$#)"#$%&#%)*%@*5)"#/&*)+"#+,#$%&#bAF#+,#$%&#Ff_<#)"6&/$&/;#E&()($+/#>B#$+*&$%&/#9)$% .575.)$+/#CB 7/+6)'&(#5#-+9@75((#,)-$&/#$%5$#')(.+4/5*&(#$%&#.)/.4)$#,/+1#+(.)--5$)"*#5$#5#%)*%&/ %5/1+").# +, $%&# ./0($5-# ,/&34&".0;# S+$&# $%5$# $%)(# .)/.4)$# 5-(+# )(# 85(&'# +"# $%&# F+-7)$$( .+",)*4/5$)+"; A%&# &:$/&1&-0# ($58-&# /&(+"5".&# .%5/5.$&/)($).(# 5"'# $%&# 6&/0# %)*%# :# ,5.$+/(# +,# 345/$? ./0($5-(#/&(4-$#)"#+(.)--5$+/(#9)$%#6&/0#5..4/5$"'#($58-&#,/&34&".)&(;#F/0($5-(#5/ȵ)-58-& 9)$%#/&(+"5".&#,/&34&".)&(#)"#$%&#/5"*&#+,#5#,&9#=)-+%&/$?#$+#%4"'/&'(#+,#1&*5%&/$?;#A&1@ 7&/5$4/&# .+&,,).)&"$(# +,# ωU# +,# B# +/# X# 75/$(# 7&/# 1)--)+"# J771K# 7&/# '&*/&&# F&-()4(# 5/& 5.%)&658-&;# d",+/$4"5$&-02# %+9&6&/2# ./0($5-# +(.)--5$+/(2# 8&)"*# 1&.%5").5-# /&(+"5$+/(2# 5/& ,):&'@,/&34&".0#.)/.4)$(;

17.4 Bistable Multivibrators

Figure 17.16 Q# c)&/.&# ./0($5-# +(.)--5$+/# 4$)-)?)"*# 5 Ff_<#)"6&/$&/#5(#5"#517-),)&/;

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1362 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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17.5 Generation of Square and Triangular Waveforms Using Astable Multivibrators

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1364 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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17.5 Generation of Square and Triangular Waveforms Using Astable Multivibrators 1365

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1366 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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1368 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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1370 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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1377

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1380 Chapter 17 Signal Generators and Waveform-Shaping Circuits

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EXERCISES 17.24#F+"()'&/#$%&#+7&/5$)+"5-#/&.$),)&/#+/#(47&/')+'&#.)/.4)$#+,#T)*;#BC;DDJ5K2#9)$%#>#=#B#=Ω;#T+/#v;#=#BU 1b2#B#b2#5"'#−B#b2#9%5$#5/&#$%+-$5*&(#$%5$#/&(4-$#5$#$%&#/&.$),)&/#+4$74$#5"'#5$#$%&#+4$74$#+,#$%&#+7 517l#Q((41&#$%5$#$%&#+7#517#)(#)'&5-#5"'#$%5$#)$(#+4$74$#(5$4/5$&(#5$#±BX#b;#A%&#')+'&#%5(#5#U;C@ b#'/+7#5$#B@1Q#.4//&"$2#5"'#$%+-$5*&#'/+7#.%5"*&(#80#U;B#b#7&/#'&.5'&#+,#.4//&"$#.%5"*&; Ans. BU#1b2#U;NB#b>#B#b2#B;C#b>#U#b2#gBX#b 17.25#!,#$%&#')+'&#)"#$%&#.)/.4)$#+,#T)*;#BC;DDJ5K#)(#/&6&/(&'2#9%5$#)(#$%&#$/5"(,&/#.%5/5.$&/)($).# v<#5(#5 ,4".$)+"#+,#v;l Ans.#v<#=#U#,+/#v; ≥ 0; vO = vI ,+/ vI ≤ 0

17.26#F+"()'&/#$%&#.)/.4)$#)"#T)*;#BC;DMJ5K#9)$%#>B#=#B#=Ω#5"'#>X#=#BU#=Ω;#T)"'#v<#5"'#$%+-$5*$#$%& 517-),)&/#+4$74$#,+/#v;#=#+B#b2#−BU#1b2#5"'#−B#b;#Q((41&#$%&#+7#517#$+#8&#)'&5-#9)$%#(5$4/5$)+" 6+-$5*&(#+,#±BX#b;#A%&#')+'&(#%56&#U;C@b#6+-$5*&#'/+7(#5$#B#1Q2#5"'#$%+-$5*&#'/+7#.%5"*&( 80#U;B#b#7&/#'&.5'&#+,#.4//&"$#.%5"*&; Ans.#U#b2#−0;61C#b>#U;B#b2#U;O#b>#BU#b2#BU;C#b

17.27#!,#$%&#')+'&(#)"#$%&#.)/.4)$#+,#T)*;#BC;DMJ5K#5/&#/&6&/(&'2#9%5$#)(#$%&#$/5"(,&/#.%5/5.$&/)($).#v<#5(#5 ,4".$)+"#+,#v;l Ans. v<#=#−( > X ⁄ > B Kv;#,+/#v; ≥ U> vO = U#,+/#vI ≤ U 17.28#T)"'#$%&#$/5"(,&/#.%5/5.$&/)($).#,+/#$%&#.)/.4)$#)"#T)*;#YBC;XI;

D2

D1

Figure E17.28

Ans.#v<#=#U#,+/#v; ≥ −N#b; vO = −vI#−#N#,+/#vI ≤ −N#b

1381

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or

17.9 Precision Rectifier Circuits 1383

! A

D2 A2

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Figure 17.37 :,;#c/&.)()+"#,4--@956&#/&.$),)&/#85(&'#+"#$%&#.+".&7$45-#.)/.4)$#+,#T)*;#BC;DO;/:+;#A/5"(,&/ .%5/5.$&/)($).#+,#$%&#.)/.4)$#)"#:,;;

EXERCISES 17.29 !"#$%&#,4--@956&#/&.$),)&/#.)/.4)$#+,#T)*;#BC;DCJ5K2#-&$#>B#=#>X#=#>@#=#BU#=Ω#5"'#5((41&#$%&#+7#517( $+#8&#)'&5-#&:.&7$#,+/#+4$74$#(5$4/5$)+"#5$#±BX#b;#H%&"#.+"'4.$)"*#5#.4//&"$#+,#B#1Q2#&5.%#')+'& &:%)8)$(#5#6+-$5*&#'/+7#+,#U;C#b2#5"'#$%)(#6+-$5*&#.%5"*&(#80#U;B#b#7&/#'&.5'&#+,#.4//&"$#.%5"*&; T)"'#v<2#vO2#5"'#vU#.+//&(7+"')"*#$+#v;#=#+U;B#b2#+B#b2#+BU#b2#gU;B#b2#5"'#−BU#b; Ans. #+ U;B#b2#+ U;O#b2#−BX#b>#+B#b2#+B;O#b2#−BX#b>#+BU#b2#+BU;C#b2#−BX#b>#+#U;B#b2#−BX#b2#+ U;OD#b> +B#b2#−BX#b2#+ B;OD#b>#+BU#b2#−BX#b2#+BU;CD#b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

( (a)

(b)

Figure E17.30

6+-$5*&2#$+#8&#&345-#$+#$%&#"&*5$)6&#+,#$%&#)"74$#6+-$5*$#Q#5"'#$%4(#7+()$)6&;#A%&#.+18)"5@ $)+"#+,#7+()$)6+-$5*$#F#5"'#"&*5$)6+-$5*$#Q#.54(&(#$%&#+4$74$#+,#QX#$+#(5$4/5$&#)" $%&#"&*5$)6&#')/&.$)+"2#$%4(#=&&7)"*#=X#+,,;

1384 Chapter 17 Signal Generators and Waveform-Shaping Circuits

D1

D4

D2

D3

Figure 17.38 d(&# +,#$%&# ')+'/)'*&# )"# $%&#'&()*"# +, 5"#5.#6+-$1&$&/;

A%&#+6&/5--#/&(4-$#)(#7&/,&.$#,4--@956&#/&.$),).5$)+"2#5(#/&7/&(&"$&'#80#$%&#$/5"(,&/#.%5/5.@ $&/)($).#)"#T)*;#BC;DCJ8K;#A%)(#7/&.)()+"#)(2#+,#.+4/(&2#5#/&(4-$#+,#7-5.)"*#$%&#')+'&(#)"#+7@517 ,&&'85.=#-++7(2#$%4(#15(=)"*#$%&)/#"+")'&5-)$)&(;#A%)(#.)/.4)$#)(#+"&#+,#15"0#7+(()8-/&.)@ ()+"#,4--@956&@/&.$),)&/#+/#,+#"03%'(&,03'/-$1-3$%#;#Q"+$%&/#/&-5$&'#)17-&1&"$5$)+"#+,#$%)( ,4".$)+"#)(#&:51)"&'#)"#Y:&/.)(&#BC;DU;

17.9.5 A Precision Bridge Rectifier for Instrumentation Applications A%/)'*&#/&.$),)&/#.)/.4)$#($4')&'#)"#F%57$&/#M#.5"#8&#.+18)"&'#9)$%#5"#+7#517#$+#7/+6)'& 4(&,4-#7/&.)()+"#.)/.4)$(;#_"&#(4.%#5//5"*&1&"$#)(#(%+9"#)"#T)*;#BC;DI;#A%)(#.)/.4)$#.54(&(#5 .4//&"$#&345-#$+# v 1 ⁄ > #$+#,-+9#$%/+4*%#$%
+6)"*@.+)-#1&$&/#f;#A%4(#$%
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EXERCISES D17.31 !"#$%&#.)/.4)$#+,#T)*;#BC;DI2#,)"'#$%A-4&#+,#>#$%5$#9+4-'#.54(&#$%
&$&/#$+#7/+6)'#,4--@(.5-& /&5')"*#9%&"#$%&#)"74$#6+-$5*&#)(#5#()"μ&#+,#N#b#/1(;#G&$#1&$&/#f#%56#B@1Q2#NU@Ω#1+6&@ 1&"$# J);&;2 )$(# /&()($5".&# )(# NU# Ω2# 5"'# )$# 7/+6)'&(# ,4--@(.5-&# '&,-&.$)+"# 9%&"# $%&# 56&/5*&# .4//&"$ $%/+4*%#)$#)(#B 1QK;#H%5$#5/&#$%Ɂ/+:)15$:)141#5"'#1)")141#6+-$5*&(#5$#$%&#+7#517a( +4$74$l#Q((41&#$%5$#$%&#')+'&(#%56&#.+"($5"$#U;C@b#'/+7(#9%&"#.+"'4.$)"*; Ans.#M;N#=Ω>#+I;NN#b>#−I;NN#b

17.9 Precision Rectifier Circuits

17.9.6 Precision Peak Rectifiers !".-4')"*#$%&#')+'&#+,#$%&5=#/&.$),)&/#($4')&'#)"#F%57$&/#M#)"()'&#$%&#"&*5$)6&@,&&'85.= -++7#+,#5"#+7#5172#5(#(%+9"#)"#T)*;#BC;DR2#/&(4-$(#)"#5#7/&.)()+"#7&5=#/&.$),)&/;#A%&#')+'&g +7@517#.+18)"5$)+"#9)--#8&#/&.+*")?&'#5(#$%&#(47&/')+'&#+,#T)*;#BC;DDJ5K;#_7&/5$)+"#+,#$%& .)/.4)$#)" T)*;#BC;DR#)(#34)$&#($/5)*%$,+/95/';#T+/#v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

17.9.7 A Buffered Precision Peak Detector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v; )"./&5(&(#58+6&#$%A-4&#($+/&'#+"#C2#9%).%#)(#&345-#$+#$%&#+4$74$#6+-$5*&#v<2#+7#517#QB#(&&(

Figure 17.39 Q#7/&.)()+"#7&5=#/&.$),)&/#+8$5)"&'#80#7-5.)"*#$%&#')+'&#)"#$%&#,&&'85.=#-++7#+,#5"#+7#517;

D2 D1

Figure 17.40 Q#84,,&/&'#7/&.)()+"#7&5=#/&.$),)&/;

1385

1386 Chapter 17 Signal Generators and Waveform-Shaping Circuits

Figure 17.41 Q#7/&.)()+"#.-517)"*#.)/.4)$;

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CHAPTER 17

PROBLEMS

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CHAPTER 17

8&#)"'&7&"'&"$#+,#$%&#')+'&a(#"+"-)"&5/)$)&(#5"'#65/)58)-)$0; !"').5$&#%+9#$%)(#150#8&#'+"&#&5()-0;

1395

Appendixes on DVD F

or your convenience, seven additional chapters on important reference topics are included on the in-text DVD. In PDF format, the Appendixes are fully searchable and can be bookmarked.

Appendix A: VLSI Fabrication Technology This article is a concise explanation of the technology that goes into fabricating integrated circuits. The different processes used are described and compared, and the characteristics of the resulting devices. Design considerations that restrict IC designers are explored.

Appendix B: SPICE Device Models and Design Simulation Examples Using PSpice® and Multisim™ This three-part appendix could stand as a book on its own. Part 1 describes the models SPICE programs use to represent op amps, diodes, MOSFETs, and BJTs in integrated circuits. A thorough understanding of these models is critical for designers trying to extract meaningful information from an analysis. Part 2 describes and discusses all the PSpice® simulations included in the Lab-on-a-Disc, while Part 3 does the same for the Multisim™ simulations. The entire Lab-on-a-Disc is a rich resource to help analyze, experiment with, and design examples that relate to the topics studied in Microelectronic Circuits.

Appendix C: Two-Port Network Parameters

Throughout the text, we use different possible ways to characterize linear two-port networks. This appendix summarizes the y, z, h, and g parameters and explains equivalent-circuit representation, a useful tool.

Appendix D: Some Useful Network Theorems

This article reviews Thévenin’s theorem, Norton’s theorem, and the source-absorption theorem, all of which are useful in simplifying the analysis of electronic circuits.

Appendix E: Single-Time-Constant Circuits STC circuits are composed of, or can be reduced to, one reactive component (inductance or capacitance) and one resistance. This is important to the design and analysis of linear and digital circuits. Analyzing an amplifier circuit can usually be reduced to the analysis of one or more STC circuits.

Appendix F: s-Domain Analysis: Poles, Zeroes, and Bode Plots Most of the work in analyzing the frequency response of an amplifier involves finding the amplifier voltage gain as a function of the complex frequency s. The tools to do this are summarized in this appendix.

Appendix G: Bibliography

An excellent resource for students beginning research projects, this bibliography outlines key reference works on electronic circuits, circuit and system analysis, devices and IC fabrication, op amps, analog and digital circuits, filters and tuned amplifiers, and SPICE.

Appendix H: Standard Resistance Values and Unit Prefixes H-1 Appendix I: Answers to Selected Problems I-1

1397

Appendix

Appendix A

VLSI Fabrication Technology

A-1

Appendix B

NEW–SPICE appendix

B-1

Appendix C

Two-Port Network Theorems

C-1

Appendix D

Some Useful Network Theorems Appendix E

Single-Time-Constant Circuits

E-1

D-1

Appendix F

Bibliography

F-1

Appendix G

Standard Resistance Values and Unit Prefixes

G-1

Appendix H

All NEW from ISM answers

H-1

Appendix CD

Domain Analysis: Poles, Zeros, and Bode Plots

CD-1

APPENDIX A

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(b)

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

A.1.6 Ion Implantation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

A.1.7 Chemical Vapor Deposition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i??eG9: ;)&+"31#%&81+&13-#%&"+&4+%,/&'(%#&1&+"3"$-#&316%*&0"33&J%&,%K-+"'%,&-#&'(%&01)%*:&;)&'(%&*%1$7 '"-#&'%@K%*1'4*%& "+&("8(& %#-48(& 51J-2%&
A-5

A-6 Appendix A VLSI Fabrication Technology

8

16 1

1

Figure A.4 D.1@K3%+&-)&1#&b7K"#&K31+'"$&,4137"#73"#%&;G&K1$N18%&1#,&1&<]7K"#&+4*)1$%7@-4#'&K1$N18%:

+"3"$-#&545:30#)9/&+"#$%&"'&$-#+"+'+&-)&@1#6&+@133&$*6+'13+&-)&+"3"$-#&13"8#%,&"#&*1#,-@&)1+(7 "-#:&^-36+"3"$-#&316%*+&1*%&#-*@1336&,-K%,&2%*6&(%12"36&'-&)-*@&("8(36&$-#,4$'"2%&*%8"-#+ '(1'&$1#&J%&4+%,&)-*&%3%$'*"$13&"#'%*$-##%$'"-#+:

A.1.8 Metallization E(%&K4*K-+%&-)&@%'133"M1'"-#&"+&'-&"#'%*$-##%$'&'(%&21*"-4+&$-@K-#%#'+&5'*1#+"+'-*+/&$1K1$"7 '-*+/&%'$:9&'-&)-*@&'(%&,%+"*%,&"#'%8*1'%,&$"*$4"':&A%'133"M1'"-#&"#2-32%+&'(%&,%K-+"'"-#&-)&1 @%'13& -2%*& '(%& %#'"*%& +4*)1$%& -)& '(%& +"3"$-#:& E(%& *%O4"*%,& "#'%*$-##%$'"-#& K1''%*#& "+& '(%# +%3%$'"2%36&%'$(%,:&E(%&@%'13&316%*&"+&#-*@1336&,%K-+"'%,&2"1&1&+K4''%*"#8&K*-$%++:&U&K4*% @%'13&,"+N&5%:8:/&==:==j&134@"#4@&'1*8%'9&"+&K31$%,&4#,%*&1#&U*&51*8-#9&"-#&84#&"#+",%&1 21$44@&$(1@J%*:&E(%&01)%*+&1*%&13+-&@-4#'%,&"#+",%&'(%&$(1@J%*&1J-2%&'(%&'1*8%':&E(%&U* "-#+&0"33&#-'&*%1$'&0"'(&'(%&@%'13/&+"#$%&1*8-#&"+&1&#-J3%&81+:&g-0%2%*/&'(%&"-#+&1*%&@1,%&'K(6+"$1336&J-@J1*,&'(%&'1*8%'&1#,&3"'%*1336&N#-$N&@%'13&1'-@+&-4'&-)&'(%&'1*8%':&E(%+%&@%'13 1'-@+&0"33&'(%#&$-1'&133&'(%&+4*)1$%&"#+",%&'(%&$(1@J%*/&"#$34,"#8&'(%&01)%*+:&E(%&'("$N#%++ -)&'(%&@%'13&)"3@&$1#&J%&$-#'*-33%,&J6&'(%&3%#8'(&-)&'(%&+K4''%*"#8&'"@%/&0("$(&"+&#-*@1336&"# '(%&*1#8%&-)&<&'-&L&@"#4'%+:&E(%&@%'13&"#'%*$-##%$'+&$1#&'(%#&J%&,%)"#%,&4+"#8&K(-'-3"'(-87 *1K(6&1#,&%'$("#8&+'%K+:

A.1.9 Packaging U&)"#"+(%,&+"3"$-#&01)%*&@16&$-#'1"#&+%2%*13&(4#,*%,+&-)&)"#"+(%,&$"*$4"'+&-*&$("K+:&U&$("K @16&$-#'1"#&)*-@&
A.2 VLSI Processes ;#'%8*1'%,7$"*$4"'& )1J*"$1'"-#& '%$(#-3-86& 01+& -*"8"#1336& ,-@"#1'%,& J6& J"K-31*& '%$(#-3-86: S6&'(%&31'%&<=>?+/&@%'13&-.",%&+%@"$-#,4$'-*&5AB!9&'%$(#-3-86&J%$1@%&@-*%&K*-@"+"#8 )-*&HI!;&"@K3%@%#'1'"-#&0"'(&("8(%*&K1$N"#8&,%#+"'6&1#,&3-0%*&K-0%*&$-#+4@K'"-#:&!"#$% '(%& %1*36& <=b?+/& $-@K3%@%#'1*6& AB!& 5GAB!9& '%$(#-3-86& (1+& 13@-+'& $-@K3%'%36 ,-@"#1'%,&'(%&HI!;&+$%#%/&3%12"#8&J"K-31*&'%$(#-3-86&'-&)"33&+K%$"13"M%,&)4#$'"-#+&+4$(&1+

A.2 VLSI Processes

("8(7+K%%,&1#13-8&1#,&YC&$"*$4"'+:&GAB!&'%$(#-3-8"%+&$-#'"#4%&'-&%2-32%/&1#,&"#&'(%&31'% <=b?+/& '(%& "#$-*K-*1'"-#& -)& J"K-31*& ,%2"$%+& 3%,& '-& '(%& %@%*8%#$%& -)& ("8(7K%*)-*@1#$% J"K-31*7GAB!&5S"GAB!9&)1J*"$1'"-#&K*-$%++%+&'(1'&K*-2",%,&'(%&J%+'&-)&J-'(&'%$(#-3-8"%+: g-0%2%*/& S"GAB!& K*-$%++%+& 1*%& -)'%#& 2%*6& $-@K3"$1'%,& 1#,& $-+'36/& +"#$%& '(%6& *%O4"*% 4K01*,+& -)&
A.2.1 Twin-Well CMOS Process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i:&U&@"#"@4@&-)&
A-7

A-8 Appendix A VLSI Fabrication Technology

Arsenic implant

Phosphorus implant Silicon nitride sidewall spacers

Photoresist

Photoresist (mask #2) n+ p-well

n+

n-well

STI

p-well

n-well

p-substrate

p-substrate (a) p-well and n-well formation (masks # 1 and #2)

(e) n+ diffusion (mask #7) Boron implant Photoresist n+

n+

STI

p-well

p+ n-well

p-substrate

p-substrate (b) Trench etch and STI refill (mask #3)

(f) p+ diffusion (mask #8) CVD oxide

Polysilicon gate

STI

p+

p-well

n-well

p-well

STI

n+

n+ n-well

SiO2 STI

p+

p+ n-well

p-well p-substrate

p-substrate (c) Gate oxidation and polysilicon patterning (mask #4)

(g) Contact holes (mask #9)

Arsenic implant n-MOSFET

Photoresist (mask #6)

p-well

n+

n+

STI n-well p-substrate

(d) n- and p-LDD (lightly doped drain) (mask #5 and 6)

p-MOSFET SiO2 STI

p+

p+ n-well

p-well p-substrate (h) Metallization (mask #10)

Figure A.5 U&@-,%*#&'0"#70%33&GAB!&K*-$%++&)3-0&0"'(&+(133-0&'*%#$(&"+-31'"-#&5!E;9:

=2:30754-707.+)8 5I__9&*%8"-#+&)-*&AB!CDE+&-)&J-'(&'6K%+&'-&+4KK*%++&'(%&8%#%*1'"-#&-)&=520-:-92.58/&'(1'

A.2 VLSI Processes

@"8('&1))%$'&'(%&*%3"1J"3"'6&-)&'(%&'*1#+"+'-*+:&U&#-#$*"'"$13&@1+N/&'-8%'(%*&0"'(&'(%&K-36+"3"7 $-#&81'%+/&"+&4+%,&'-&)-*@&'(%&+%3)713"8#%,&I__&*%8"-#+&5C"8:&U:i,9:& ^*"-*&'-&'(%&!c&1#,&"c&,*1"#&*%8"-#&"@K31#'/&1&+",%0133&+K1$%*&+'%K&"+&K%*)-*@%,:&U&'("$N 316%*&-)&+"3"$-#&#"'*",%&"+&,%K-+"'%,&4#")-*@36&-#&'(%&01)%*:&_4%&'-&'(%&$-#)-*@13
'4*%&-) '(%&,%K-+"'"-#/&'(%&'("$N#%++&-)&'(%&+"3"$-#&#"'*",%&316%*&1'&133&316%*&%,8%+&5":%:/&1'&J-'(&%#,+&-) '(%&K-36+"3"$-#&81'%&%3%$'*-,%9&0"33&J%&'("$N%*&'(1#&'(-+%&,%K-+"'%,&-2%*&1&)31'&+4*)1$%:&U)'%* 1&'"@%,&Y;D&,*6&%'$(&'-&*%@-2%&133&'(%&+"3"$-#&#"'*",%&316%*/&K-$N%'+&-)&+"3"$-#&#"'*",%&0"33 *%@1"#& 1'& '(%& %,8%& -)& '(%& K-36+"3"$-#& 81'%& %3%$'*-,%& 5C"8:& U:i%9:& !4$(& K-$N%'+& -)& +"3"$-# #"'*",%&1*%&$133%,&+",%0133&+K1$%*+:&E(%6&1*%&4+%,&'-&J3-$N&+4J+%O4%#'&!c&-*&"c&+-4*$%Z,*1"# "@K31#'+/&K*-'%$'"#8&'(%&I__&*%8"-#+: U&(%126&1*+%#"$&"@K31#'&$1#&J%&4+%,&'-&)-*@&'(%&!c&+-4*$%&1#,&,*1"#&*%8"-#+&-)&'(%&!7 AB!CDE+:&E(%&K-36+"3"$-#&81'%&13+-&1$'+&1+&1&J1**"%*&)-*&'("+&"@K31#'&'-&K*-'%$'&'(%&$(1#7 #%3&*%8"-#:&U&316%*&-)&K(-'-*%+"+'&$1#&J%&4+%,&'-&J3-$N&'(%&*%8"-#+&0(%*%&"7AB!CDE+&1*% '-&J%&)-*@%,&5C"8:&U:i%9:&E(%&'("$N&)"%3,&-.",%&+'-K+&'(%&"@K31#'&1#,&K*%2%#'+&!c&*%8"-#+ )*-@&)-*@"#8&-4'+",%&'(%&1$'"2%&*%8"-#+:&U&*%2%*+%,&K(-'-3"'(-8*1K(6&+'%K&$1#&J%&4+%,&'K*-'%$'& '(%& !7AB!CDE+& ,4*"#8& '(%& "c& J-*-#& +-4*$%& 1#,& ,*1"#& "@K31#'& )-*& '(%& "7AB!7 CDE+& 5C"8:& U:i)9:& W-'%& '(1'& "#& J-'(& $1+%+& '(%& +%K1*1'"-#& J%'0%%#& '(%& +-4*$%& 1#,& ,*1"# ,"))4+"-#+l$(1##%3& 3%#8'(l"+& ,%)"#%,& J6& '(%& K-36+"3"$-#& 81'%& @1+N& 13-#%/& (%#$%& '(% +%3)713"8#%,&K*-K%*'6: S%)-*%&$-#'1$'&(-3%+&1*%&-K%#%,/&1&'("$N&316%*&-)&GH_&-.",%&"+&,%K-+"'%,&-2%*&'(%&%#'"*% 01)%*:&U&K(-'-@1+N&"+&4+%,&'-&,%)"#%&'(%&$-#'1$'&0"#,-0&-K%#"#8&5C"8:&U:i89/&)-33-0%,&J6 1& 0%'& -*& ,*6& -.",%& %'$(:& U& '("#& 134@"#4@& 316%*& "+& '(%#& %21K-*1'%,& -*& +K4''%*%,& -#'-& '(% 01)%*:&U&)"#13&@1+N"#8&1#,&%'$("#8&+'%K&"+&4+%,&'-&K1''%*#&'(%&"#'%*$-##%$'"-#&5C"8:&U:i(9: W-'&+(-0#&"#&'(%&K*-$%++&)3-0&"+&'(%&)"#13&K1++"21'"-#&+'%K&K*"-*&'-&K1$N18"#8&1#,&0"*% J-#,"#8:&U&'("$N&GH_&-.",%&-*&K6*-.&831++&"+&4+41336&,%K-+"'%,&-#&'(%&01)%*&'-&+%*2%&1+&1 K*-'%$'"2%&316%*:

A.2.2 Integrated Devices S%+",%+&'(%&-J2"-4+&!&1#,&"7$(1##%3&AB!CDE+/&-'(%*&,%2"$%+&$1#&J%&-J'1"#%,&J6&1KK*-K*"7 1'%&@1+N"#8&K1''%*#+:&E(%+%&"#$34,%&"!&T4#$'"-#&,"-,%+/&AB!&$1K1$"'-*+/&1#,&*%+"+'-*+:

A.2.3 MOSFETs E(%&!7$(1##%3&AB!CDE&"+&'(%&K*%)%**%,&,%2"$%&"#&$-@K1*"+-#&'-&'(%&"7AB!CDE&5C"8:&U:]9: E(%&%3%$'*-#&+4*)1$%&@-J"3"'6&"+&'0-&'-&'(*%%&'"@%+&("8(%*&'(1#&'(1'&)-*&(-3%+:&E(%*%)-*%/&0"'( '(%&+1@%&,%2"$%&+"M%&5#&1#,&$9/&'(%&!7AB!CDE&-))%*+&("8(%*&$4**%#'&,*"2%&5-*&3-0%*&-#7 *%+"+'1#$%9&1#,&("8(%*&'*1#+$-#,4$'1#$%:

n-MOSFET n+

n+

p-MOSFET SiO2 STI

p+

L

p-well

p+ n-well

p-substrate

Figure A.6 G*-++7+%$'"-#13&,"18*1@&-)&!7&1#,&"7AB!CDE+:

W

A-9

A-10 Appendix A VLSI Fabrication Technology ;#&1#&"#'%8*1'%,7$"*$4"'&,%+"8#&%#2"*-#@%#'/&AB!CDE+&1*%&$(1*1$'%*"M%,&J6&'(%"*&'(*%+(7 -3,&2-3'18%&1#,&J6&'(%"*&,%2"$%&+"M%+:&f+41336&'(%&!%&1#,&"7$(1##%3&AB!CDE+&1*%&,%+"8#%, '-&(12%&'(*%+(-3,&2-3'18%+&-)&+"@"31*&@18#"'4,%&)-*&1&K1*'"$431*&K*-$%++:&E(%&'*1#+$-#,4$7 '1#$%&$1#&J%&1,T4+'%,&J6&$(1#8"#8&'(%&,%2"$%&+4*)1$%&,"@%#+"-#+&5#&1#,&$9:&E("+&)%1'4*%&"+ #-'&121"31J3%&)-*&J"K-31*&'*1#+"+'-*/&@1N"#8&'(%&,%+"8#&-)&"#'%8*1'%,&AB!CDE&$"*$4"'+&@4$( @-*%&)3%."J3%:

A.2.4 Resistors Y%+"+'-*+&"#&"#'%8*1'%,&)-*@&1*%&#-'&2%*6&K*%$"+%:&E(%6&$1#&J%&@1,%&)*-@&21*"-4+&,"))4+"-# *%8"-#+&1+&+(-0#&"#&C"8:&U:>:& _"))%*%#'&,"))4+"-#&*%8"-#+&(12%& ,"))%*%#'&*%+"+'"2"'6:&E(%& ! 0%33&"+&4+41336&4+%,&)-*&@%,"4@72134%&*%+"+'-*+/&0("3%&'(%&!c&1#,&"c&,"))4+"-#+&1*%&4+%)43 )-*&3-072134%&*%+"+'-*+:&E(%&1$'413&*%+"+'1#$%&2134%&$1#&J%&,%)"#%,&J6&$(1#8"#8&'(%&3%#8'( 1#,&0",'(&-)&,"))4+%,&*%8"-#+:&E(%&'-3%*1#$%&-)&'(%&*%+"+'-*&2134%&"+&2%*6&K--*&5L?Xi?j9/&J4' '(%&@1'$("#8&-)&'0-&+"@"31*&*%+"+'-*&2134%+&"+&O4"'%&8--,&5ij9:&E(4+&$"*$4"'&,%+"8#%*+&+(-43, ,%+"8#&$"*$4"'+&'(1'&%.K3-"'&*%+"+'-*&@1'$("#8&1#,&+(-43,&12-",&,%+"8#+&'(1'&*%O4"*%&1&+K%$")"$ *%+"+'-*&2134%: U33&,"))4+%,&*%+"+'-*+&1*%&+%3)7"+-31'%,&J6&'(%&*%2%*+%7J"1+%,&"!&T4#$'"-#+:&U&+%*"-4+&,*107 J1$N& )-*& '(%+%& *%+"+'-*+& "+& '(%& )1$'& '(1'& '(%6& 1*%& 1$$-@K1#"%,& J6& 1& +4J+'1#'"13& K1*1+"'"$ T4#$'"-#& $1K1$"'1#$%/& @1N"#8& '(%@& #-'& 2%*6& 4+%)43& )-*& ("8(7)*%O4%#$6& 1KK3"$1'"-#+:& E(% *%2%*+%7J"1+%,&"!&T4#$'"-#+&13+-&%.("J"'&1&o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

A.2.5 Capacitors E0-& '6K%+& -)& $1K1$"'-*& +'*4$'4*%& 1*%& 121"31J3%& "#& GAB!& K*-$%++%+p& AB!& 1#,& "#'%*K-36 $1K1$"'-*+:&E(%&31''%*&1*%&13+-&+"@"31*&'-&@%'13X"#+431'-*X@%'13&5A;A9&$1K1$"'-*+:&E(%&$*-++ +%$'"-#+&-)&'(%+%&+'*4$'4*%+&1*%&1+&+(-0#&"#&C"8:&U:b:&E(%&AB!&81'%&$1K1$"'1#$%/&,%K"$'%,&J6 '(%&$%#'%*&+'*4$'4*%/&"+&J1+"$1336&'(%&81'%7'-7+-4*$%&$1K1$"'1#$%&-)&1&AB!CDE:&E(%&$1K1$"7 '1#$%&2134%&"+&,%K%#,%#'&-#&'(%&81'%&1*%1:&E(%&-.",%&'("$N#%++&"+&'(%&+1@%&1+&'(%&81'%&-.",%

Polyresistor

n+ diffusion resistor

SiO2

n+ n+ polysilicon p-substrate

p+ diffusion resistor

n+ well resistor SiO2

n+

SiO2

n+

p+

n+ well Parasitic capacitance

Figure A.7 G*-++&+%$'"-#+&-)&21*"-4+&*%+"+'-*&'6K%+&121"31J3%&)*-@&1&'6K"$13&!70%33&GAB!&K*-$%++:

A.2 VLSI Processes

MOS capacitor

Interpoly capacitor

SiO2

SiO2

n+ Poly 2

Poly 1 p-substrate

MOS capacitor with implant

SiO2

n+ n-well

n+implant

Parasitic capacitance

Figure A.8 ;#'%*K-36&1#,&AB!&$1K1$"'-*+&"#&1#&!70%33&GAB!&K*-$%++:

'("$N#%++&"#&'(%&AB!CDE+:&E("+&$1K1$"'-*&%.("J"'+&1&31*8%&2-3'18%&,%K%#,%#$%:&E-&%3"@"#1'% '("+&K*-J3%@/&1#&1,,"'"-#&!c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g-0%2%*/&'("+&$1K1$"'-*&0-*N+&-#36&0"'(&*%2%*+%7J"1+&2-3'18%+:& C-*&'(%&"#'%*K-36&1#,&AB!&$1K1$"'-*+/&'(%&$1K1$"'1#$%&2134%+&$1#&J%&$-#'*-33%,&'-&0"'("#
A.2.6 pn Junction Diodes P(%#%2%*&!7'6K%&1#,&"7'6K%&,"))4+"-#&*%8"-#+&1*%&K31$%,&#%.'&'-&%1$(&-'(%*/&1&"!&T4#$'"-# ,"-,%&*%+43'+:&U&4+%)43&+'*4$'4*%&"+&'(%&!70%33&,"-,%&+(-0#&"#&C"8:&U:=:&E(%&,"-,%&)1J*"$1'%, "#& 1#& !& 0%33& $1#& K*-2",%& 1& ("8(& J*%1N,-0#& 2-3'18%:& E("+& ,"-,%& "+& %++%#'"13& )-*& '(%& "#K4' $31@K"#8&$"*$4"'+&)-*&K*-'%$'"-#&181"#+'&%3%$'*-+'1'"$&,"+$(1*8%:&E(%&,"-,%&"+&13+-&2%*6&4+%)43 1+&1#&-#7$("K&'%@K%*1'4*%&+%#+-*&J6&@-#"'-*"#8&'(%&21*"1'"-#&-)&"'+&)-*01*,&2-3'18%&,*-K:

pn junction diode

n+

SiO2

p+

n-well p-substrate

Figure A.9 U&"!&T4#$'"-#&,"-,%&"#&1#&!70%33&GAB!&K*-$%++:

A-11

A-12 Appendix A VLSI Fabrication Technology

A.2.7 BiCMOS Process U#&!"!&2%*'"$13&J"K-31*&'*1#+"+'-*&$1#&J%&"#'%8*1'%,&"#'-&'(%&!70%33&GAB!&K*-$%++&0"'(&'(% 1,,"'"-#&-)&1&"7J1+%&,"))4+"-#&*%8"-#&5C"8:&U:
n+

npn-bipolar transistor E B C

p-MOSFET

SiO2

n+

p-epitaxial layer

p+

p+

SiO2

n+

n-well p-substrate

n+

p+ p-base

n-well

n+ buried layer

Figure A.10 G*-++7+%$'"-#13&,"18*1@&-)&1&S"GAB!&K*-$%++:

A.2.8 Lateral pnp Transistor E(%&)1$'&'(1'&@-+'&S"GAB!&K*-$%++%+&,-&#-'&(12%&-K'"@"M%,&"!"&'*1#+"+'-*+&@1N%+&$"*$4"' ,%+"8#&+-@%0(1'&,"))"$43':&g-0%2%*/&"#&#-#$*"'"$13&+"'41'"-#+/&1&K1*1+"'"$&31'%*13&"!"&'*1#+"+7 '-*&$1#&J%&4+%,&5C"8:&U:<<9:& ;#&'("+&$1+%/&'(%&!&0%33&+%*2%+&1+&'(%&!7J1+%&*%8"-#/&0"'(&'(%&"c&,"))4+"-#+&1+&'(%&%@"''%* 1#,&'(%&$-33%$'-*:&E(%&J1+%&0",'(&"+&,%'%*@"#%,&J6&'(%&+%K1*1'"-#&J%'0%%#&'(%&'0-&"c&,"))47 +"-#+:&!"#$%&'(%&,-K"#8&K*-)"3%&"+&#-'&-K'"@"M%,&)-*&'(%&J1+%X$-33%$'-*&T4#$'"-#+&1#,&J%$14+% '(%&J1+%&0",'(&"+&3"@"'%,&J6&'(%&@"#"@4@&K(-'-3"'(-8*1K("$&*%+-34'"-#/&'(%&K%*)-*@1#$%&-) '("+&,%2"$%&"+&#-'&2%*6&8--,p&'6K"$1336/&β&-)&1*-4#,&
p+

n+

n-well p-substrate

Figure A.11 &I1'%*13&"!"&'*1#+"+'-*:

A.2.9 p-Base and Pinched-Base Resistors P"'(&'(%&1,,"'"-#13&"7J1+%&,"))4+"-#&"#&'(%&S"GAB!&K*-$%++/&'0-&1,,"'"-#13&*%+"+'-*&+'*4$7 '4*%+& 1*%& 121"31J3%:& E(%& "7J1+%& ,"))4+"-#& $1#& J%& 4+%,& '-& )-*@& 1& +'*1"8(')-*01*,& "7J1+%

A.2 VLSI Processes p-base resistor

SiO2

p+

Pinched-base resistor SiO2

p+ p-base

n-well

p+

n+

p+

SiO2

p-base

n+buried layer

Figure A.12 "7J1+%&1#,&K"#$(%,&"7J1+%&*%+"+'-*+:

*%+"+'-*&1+&+(-0#&"#&C"8:&U:
A.2.10 SiGe BiCMOS Process P"'(& '(%& J4*8%-#"#8& -)& 0"*%3%++& 1KK3"$1'"-#+/& '(%& ,%@1#,& )-*& ("8(7K%*)-*@1#$%/& ("8(7 )*%O4%#$6& YC& "#'%8*1'%,& $"*$4"'+& "+& '*%@%#,-4+:& B0"#8& '-& '(%& )4#,1@%#'13& 3"@"'1'"-#+& -) K(6+"$13&@1'%*"13&K*-K%*'"%+/&+"3"$-#7J1+%,&'%$(#-3-86&01+&#-'&1J3%&'-&$-@K%'%&0"'(&@-*% %.K%#+"2%&'%$(#-3-8"%+&*%36"#8&-#&$-@K-4#,+&)*-@&8*-4K+&;;;&'(*-48(&;H/&+4$(&1+&V1U+: S6&"#$-*K-*1'"#8&1&$-#'*-33%,&1@-4#'&5'6K"$1336&#-&@-*%&'(1#&
A-13

A-14 Appendix A VLSI Fabrication Technology npn SiGe heterojunction bipolar transistor

C

Polysilicon

SiO2

B

E

n+ polysilicon emitter B C n+

n+ n+ well

p+

RC1

n+ buried layer p+ substrate

RC3 RC2

p+ polysilicon

SiO2 Polysilicon

SiGe p-base

Polysilicon refill

Trench isolation

Figure A.13 G*-++7+%$'"-#13&,"18*1@&-)&1&+6@@%'*"$&+%3)713"8#%,&!"V%&(%'%*-T4#$'"-#&J"K-31*&'*1#+"+'-*/ -*&gSE:

A.3 VLSI Layout E(%&,%+"8#%,&$"*$4"'&+$(%@1'"$&@4+'&J%&'*1#+)-*@%,&"#'-&1&316-4'&'(1'&$-#+"+'+&-)&'(%&8%-7 @%'*"$& *%K*%+%#'1'"-#& -)& '(%& $"*$4"'& $-@K-#%#'+& 1#,& "#'%*$-##%$'"-#+:& E-,16/& $-@K4'%*7 1",%,&,%+"8#&'--3+&133-0&@1#6&-)&'(%&$-#2%*+"-#&+'%K+/&)*-@&+$(%@1'"$&'-&316-4'/&'-&J%&$1*7 *"%,& -4'& +%@"7& -*& )4336& 14'-@1'"$1336:& g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
A.3 VLSI Layout A

VDD Q2 X

VDD Y

W2

Gate 2

L2

Q2

Q2 X

Y

n-well

Q1

Active region (LOCOS)

L1

W1

Gate 1

Poly 1 (Poly-Si gate) GND

n+ diffusion p+ diffusion A!

Contact hole Metal 1

Figure A.14 U&GAB!&"#2%*'%*&+$(%@1'"$&1#,&"'+&316-4':

p+

n+

Q1

VDD

Y

X

n+

p-substrate

SiO2

p+

Q2

p+

n+

n-well

Figure A.15 G*-++&+%$'"-#&13-#8&'(%&K31#%&UU'&-)&1&GAB!&"#2%*'%*:&W-'%&'(1'&'("+&K1*'"$431* 316-4'&"+&8--,&)-*&"334+'*1'"-#&K4*K-+%+/&J4'&"+&#-'&#%$%++1*"36&1KK*-K*"1'%&)-*&31'$(4K&K*%2%#'"-#:

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

A-15

A-16 Appendix A VLSI Fabrication Technology

(a) n-well

(b) Active region

(c) Poly 1

(d) n+ diffusion

(e) p+ diffusion

(f) Contact hole

Photographic plate

(g) Metal 1

Figure A.16 U& +%'& -)& K(-'-@1+N+& )-*& '(%& !70%33& GAB! "#2%*'%*:& W-'%& '(1'& %1$(& 316%*& *%O4"*%+& 1& +%K1*1'%& K31'%:& ^(-'-7 K31'%+&5+9/&579/&5-9/&1#,&5,9&1*%&,1*N7)"%3,&@1+N+/&0("3%&5B9/&599/ 1#,&5>9&1*%&$3%1*7)"%3,&@1+N+:

%O4"K@%#'&1#,&@16&*%+43'&"#&3-0%*&6"%3,:&g%#$%/&%1$(&1,,"'"-#13&@1+N&0"33&J%&*%)3%$'%,&"#&1# "#$*%1+%&"#&'(%&)"#13&$-+'&-)&'(%&;G&$("K:

Summary E("+&1KK%#,".&K*%+%#'+&1#&-2%*2"%0&-)&'(%&21*"-4+&1+K%$'+&-)&HI!;&)1J*"$1'"-#&K*-$%,4*%+: E("+&"#$34,%+&$-@K-#%#'&$(1*1$'%*"+'"$+/&K*-$%++&)3-0+/&1#,&316-4'+:&E("+&"+&J6&#-&@%1#+&1

Bibliography

$-@K3%'%& 1$$-4#'& -)& +'1'%7-)7'(%71*'& HI!;& '%$(#-3-8"%+:& ;#'%*%+'%,& *%1,%*+& +(-43,& $-#+43' -'(%*&*%)%*%#$%+&-#&'("+&+4JT%$'&)-*&@-*%&,%'1"3%,&,%+$*"K'"-#+:

Bibliography o:&_:&^34@@%*/&A:_:&_%13/&1#,&^:S:&V*"))"#/&,-.-/0!&*$,1&23/4!0.056/&fKK%*&!1,,3%&Y"2%*/ Wo/&^*%#'"$%&g133/&L???: Y:&!:&A433%*/&E:;:&h1@"#+/&1#,&A:&G(1#/&+37-/3&8.3/9:0!-/;&<0:&1!935:=93>&?-:/@-9;A&[*,&%,:/ g-J-N%#/&Wo/&o-(#&P"3%6&r&!-#+/&L??[: !:&P-3)/&B-/:0/4-"&B=!@<=/9@:-!5/&I1''"$%&^*%++&5000:31''"$%K*%++:$-@9/&L??\:&

A-17

APPENDIX B

SPICE DEVICE MODELS AND DESIGN SIMULATION EXAMPLES USING PSPICE AND MULTISIM Introduction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

B.1 SPICE Device Models !-%0"(%*($#6)(.D%0"(%1&:5(%-4%$#35:&0#-)%.($5:0$%#$%&%*#.(,0%45),0#-)%-4%0"(%M5&:#02%-4%0"(%3-*< (:$%5$(*%4-.%0"(%*(1#,($;%!"(%3-.(%4�"45::2%0"(%3-*(:%.('.($()0$%0"(%1&.#-5$%,"&.&,0(.#$0#,$ -4%0"(%*(1#,(D% 0"(%3-.(%&,,5.&0(:2%0"(% $#35:&0#-)%.($5:0$% /#::%*($,.#=(% 0"(%-'(.&0#-)%-4%&) &,05&:%4&=.#,&0(*%,#.,5#0;%A)%-0"(.%/-.*$D%0-%$((%0"(%(44(,0%-)%,#.,5#0%'(.4-.3&),(%-4%1&.#-5$ #3'(.4(,0#-)$%#)%*(1#,(%-'(.&0#-)D%0"($(%#3'(.4(,0#-)$%35$0%=(%#),:5*(*%#)%0"(%*(1#,(%3-*(: 5$(*%=2%0"(%,#.,5#0%$#35:&0-.;

B.1.1 The Op-Amp Model A)%$#35:&0#)6%,#.,5#0$%0"&0%5$(%-)(%-.%3-.(%-'%&3'$D%#0%#$%5$(45:%0-%50#:#I(%&%!"#$%!%&'()0.('.($()0%(&,"%-'%&3';%N%3&,.-3-*(:%#$%=&$(*%-)%0"(%-=$(.1(*%0(.3#)&:%,"&.&,0(.#$0#,$%-4 0"(% -'%&3'%.&0"(.%0"&)%-)%0"(%3-*(:#)6%-4%(1(.2%0.&)$#$0-.% #)%0"(%-'<&3'%#)0(.)&:%,#.,5#0; 9&,.-3-*(:$% ,&)% =(% *(1(:-'(*% 4.-3% *&0&<$"((0% $'(,#4#,&0#-)$% /#0"-50% L)-/:(*6(% -4% 0"( *(0&#:$%-4%0"(%#)0(.)&:%,#.,5#0.2%-4%0"(%-'%&3'; Linear Macromodel !"(% $,"(3&0#,% ,&'05.(% -4% &% :#)(&.% 3&,.-3-*(:% 4-.% &)% #)0(.)&::2 ,-3'()$&0(*%-'%&3'%/#0"%4#)#0(%6&#)%&)*%=&)*/#*0"%#$%$"-/)%#)%F#6;%?;@;%A)%0"#$%(M5#1&:()0< ,#.,5#0%3-*(:D%0"(%6&#)%,-)$0&)0%NO!%-4%0"(%1-:0&6(<,-)0.-::(*%1-:0&6(%$-5.,(%C!%,-..($'-)*$

B-1

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B-3

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B-10 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim C iC

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B-11

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B-13

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B-14 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.2.1 continued

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B.2 PSpice Examples

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B-15

B-16 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.2.2 continued Ep d

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B.2 PSpice Examples

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B-17

B-18 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.2.2 continued

1.2 V 0.8 V 0.4 V Slope # !0.5 V'&s 0V Slope # "0.5 V/&s !0.4 V !0.8 V !1.2 V

0

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30

40

50

60

70

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Time (&s)

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Example PS.4.1 Design of a DC Power Supply =5%+#4.%$C,12*$:%;$%;4**%&$.4-5%,%&'%2);$0%./22*<%/.45-%+#$%0$'+464$0%'40'/4+%;#).$%',2+/0$%.'#$1,+4'%4. .#);5%45%@4-!%A!7H!%"#4.%'40'/4+%')5.4.+.%)6%,%6/**3;,($%&4)&$%0$'+464$0:%,%64*+$0%',2,'4+)0:%,5&%,%T$5$0%()*+3 ,-$%0$-/*,+)0!%"#$%)5*<%2$0#,2.%2/TT*45-%')12)5$5+%4.%+#$%'4.)*,+4)5:%+#$%7DD3F %0$.4.+)0%9$+;$$5%+#$%.$')5&3 ,0<%;45&45-%)6%+#$%+0,5.6)01$0%,5&%-0)/5&!%"#4.%0$.4.+)0%4.%45'*/&$&%+)%20)(4&$%&'%')5+45/4+<%,5&%+#/.%jS$$2 NQ=EK%#,2245%@4-!%A!7H?%20)(4&$%,%5)145,*%&'%()*+,-$%)6%\%I%,5&%9$ ,9*$%+)%./22*<%,%*),&%'/00$5+1%*),&%,.%*,0-$%,.%8\%1OR%+#,+%4.:%'*),&%',5%9$%,.%*);%,.%8DD% !%"#$%2);$0%./22*< 4.%6$&%60)1%,%78D3I%>01.?%MD3YT%,'%*45$!%V)+$%+#,+%45%+#$%QN24'$%.'#$1,+4'%>@4-!%A!7H?:%;$%/.$%,%.45/.)43 &,*%()*+,-$%.)/0'$%;4+#%,%7Mb3I%2$,S%,12*4+/&$%+)%0$20$.$5+%+#$%78D3I%01.%./22*<%>,.%78D3I%01.% %7Mb3I 2$,S?!%O../1$%+#$%,(,4*,94*4+<%)6%,%\!73I%T$5$0%&4)&$%#,(45-%7T% %7D% %,+%%=% %8D%1O%>,5&%+#/.%"=D% L!b I?:%,5&%+#,+%+#$%0$B/40$&%14541/1%'/00$5+%+#0)/-#%+#$%T$5$0%&4)&$%4.%%=145% %\%1O!

B.2 PSpice Examples

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B-19

B-20 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.4.1 continued 12V

Smoothing Capacitor Voltage VC

10V 8V 6V

Load Voltage VO

4V 2V 0V

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100m

150m

200m

Time (s)

Figure B.14 !"(%1-:0&6(%v0%&,.-$$%0"(%$3--0"#)6%,&'&,#0-.%0%&)*%0"(%1-:0&6(%v#%&,.-$$%0"(%:-&*%.($#$0-.%':-&*% %HOO #)%0"(%d<[%'-/(.%$5'':2%-4%C+&3':(%78;U;@;

5.25V

Rload # 500 Ω Rload # 250 Ω 5.00V Rload # 200 Ω Rload # 150 Ω

4.75V

4.50V 160

165 170 V (7, 4)

175

180

185

190

195

200

Time (ms)

Figure B.15 !"(%-50'50<1-:0&6(%/&1(4-.3%4.-3%0"(%d<[%'-/(.%$5'':2%R#)%C+&3':(%78;U;@S%4-.%1&.#-5$%:-&*%.($#$< 0&),($>%':-&*% %dOO% D%HdO% D%HOO% D%&)*%@dO% ;%!"(%1-:0&6(%.(65:&0#-)%#$%:-$0%&0%&%:-&*%.($#$0&),(%-4%@dO% ;

B.2 PSpice Examples

:-/%&$%HOO% R%:-&*%$ Hd%3NS;%F-.%':-&*% %@dO% %R/"#,"%#3':#($%%:-&*%$ JJ;J%3ND%6.(&0(.%0"&)%0"(%3&+#353 *($#6)(*%1&:5(SD%/(%$((%&%$#6)#4#,&)0%*.-'%#)%v#%R0-%&=-50%U;^%[SD%&$%/(::%&$%&%:&.6(%#),.(&$(%#)%0"(%.#'':( 1-:0&6(%&0%0"(%-50'50%R0-%&=-50%@fO%3[S;%!"#$%#$%=(,&5$(%0"(%I()(.%.(65:&0-.%#$%)-%:-)6(.%-'(.&0#-)&:j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

EXERCISE B.1 Y$(%78'#,(%0-%#)1($0#6&0(%0"(%-'(.&0#-)%-4%0"(%1-:0&6(%*-5=:(.%/"-$(%$,"(3&0#,%,&'05.(%#$%$"-/)%#) F#6;%?;@gR&S;%8'(,#4#,&::2D%':-0%0"(%0.&)$#()0%=("&1#-.%-4%0"(%1-:0&6($%vH%&)*%v-50%/"()%0"(%#)'50%#$%&%$#)5< $-#*%-4%@O<[%'(&L%&)*%@% %@OO%[D%%=>% %@OO% NS; Ans. !"(%1-:0&6(%/&1(4-.3$%&.(%$"-/)%#)%F#6;%?;@gR=S; PARAMETERS: C1 # 1u C2 # 1u VOFF # 0 VAMPL # 10V FREQ # 1K

IN

{C1}

D2

2

OUT

D1N4148 " !

0

D1 D1N4148

{C2}

0

0

(a) Figure B.16 R"S%8,"(3&0#,%,&'05.(%-4%0"(%1-:0&6(<*-5=:(.%,#.,5#0%#)%C+(.,#$(%?;@;%%4J5%[&.#-5$%1-:0&6(% /&1(4-.3$%#)%0"(%1-:0&6(<*-5=:(.%,#.,5#0;%!"(%0-'%6.&'"%*#$':&2$%0"(%#)'50%$#)(
B-21

B-22 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

10V 5V 0V !5V !10V V (IN) 20V 10V 0V !10V !20V V (2) 0V !5V !10V !15V !20V

0

1m V (OUT)

2m

3m

4m

5m Time (s) (b)

Figure B.16%)23/(3FE!

6m

7m

8m

9m

10m

B.2 PSpice Examples

Example PS.5.1 The CS Amplifier =5%+#4.%$C,12*$:%;$%;4**%/.$%QN24'$%+)%,5,*
%4 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < @ <<< D3 " H#" @ " 4$ H

PJ

O;Ud @O <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< $ dJ @ <<< @TO;@ @O Pg O;J H @ O;@ @;@ H

>A!7b?

8 ;#$0$% D 3 3 0 2A % %7`D!7% OJI %>60)1%",9*$%A!H?!%Y$0$:%?$66%0,+#$0%+#,5%?14.%/.$&%+)%1)0$%,''/0,+$*< ')12/+$%%4!%"#$%$66$'+%)6%/.45-%@$66%0,+#$0%+#,5% @%4.%1/'#%*$..%412)0+,5+%9$',/.$%+<24',**<% @%(%@2v! "#/.:%'#)).45-%?% %D!M% 1%0$./*+.%45%?$6611 %?1 %8?2v1 %D!LL% 1%,5&%@% %8H!H% 1!%V)+$%+#,+%;$%'#).$%?

VDD PARAMETERS: CCI # 10u CCO # 10u CS # 10u RD # 4.2K RG1 # 2E6 RG2 # 1.3E6 RL # 50K RS # 630 Rsig # 10K

{RG1}

VDD

IN

" DC # {VDD} !

" !

{RD}

OUT

{CCI} {RL}

W # {W} L # {L}

{RG2} 0

{CCO}

0

1Vac 0Vdc

W # 22u L # 0.6u VDD # 3.3

{Rsig}

VDD

0

{RS} 0

0

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Figure B.17 8,"(3&0#,%,&'05.(%-4%0"(%B8%&3':#4#(.%#)%C+&3':(%78;d;@;

J

!"(%.(&*(.%#$%.(3#)*(*%0"&0%0"(%$,"(3&0#,%,&'05.(%*#&6.&3$%&)*%0"(%,-..($'-)*#)6%78'#,(%$#35:&0#-)%4#:($%-4 &:: 87ABC%(+&3':($%#)%0"#$%=--L%,&)%=(%4-5)*%-)%0"(%0(+0m$%BK;%A)%0"($(%$,"(3&0#,$%R&$%$"-/)%#)%F#6;%?;@TSD%/( 5$(*%1&.#&=:(%'&.&3(0(.$%0-%()0(.%0"(%1&:5($%-4%0"(%1&.#-5$%,#.,5#0%,-3'-)()0$D%#),:5*#)6%0"(%*#3()$#-)$%-4%0"( 9E8FC!;%!"#$%/#::%&::-/%0"(%.(&*(.%0-%#)1($0#6&0(%0"(%(44(,0%-4%,"&)6#)6%,-3'-)()0%1&:5($%=2%$#3':2%,"&)6#)6 0"(%,-..($'-)*#)6%'&.&3(0(.%1&:5($;

B-23

B-24 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.5.1 continued

.*4-#+*<%*,0-$0%+#,5%?145!%"#4.%4.%,%')11)5%20,'+4'$%45%+#$%&$.4-5%)6%,5,*)-%=E.%+)%145414T$%+#$%$66$'+.%)6 6,904',+4)5%5)54&$,*4+4$.%)5%+#$%,'+/,*%(,*/$%)6%?!%O.%.#);5%45%+#$%+$C+:%+#4.%4.%2,0+4'/*,0*<%412)0+,5+%;#$5 +#$%'40'/4+%2$06)01,5'$%&$2$5&.%)5%+#$%1,+'#45-%9$+;$$5%+#$%&41$5.4)5.%)6%+;)%)0%1)0$%F[N@K".%>$!-!: 45%+#$%'/00$5+31400)0%'40'/4+.%.+/&4$&%45%E#,2+$0%M?!% V$C+:%'4%4.%',*'/*,+$&%9,.$&%)5%+#$%&$.40$&%()*+,-$%-,45e +v

9* '4 '? 72

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;#$0$%9*% %H!D%1OJI%,5&%72% %88!8%S Y$5'$:%+#$%)/+2/+%94,.%()*+,-$%4.% "#% % "44 P % 4 ' 4 %7!Hb%I!%O5 '$ " # P " 44 J % 4 gJO% %4.%5$$&$&%+)%94,.%+#$%F[N@K"%,+%,% "4$ " 44 J; %@45,**<:%0$.4.+)0. 'S7% % 8% F ,5&% 'S8% % 7!H% F ,0$% '#).$5% +)% .$+% +#$% -,+$% 94,.% ()*+,-$% ,+ % 4 ' $ " #" " /3 $ @;Hf%[ d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d% 3N;% Z(+0D% 0-% 3(&$5.(% 0"( 3#*=&)*%6&#)%+P%&)*%0"(%J<*?%4.(M5(),#($U%-?%&)*%-VD%/(%&'':2%&%@<[%&,%1-:0&6(%&0%0"(%#)'50D%'(.4-.3%&)%&,< &)&:2$#$% $#35:&0#-)D% &)*% ':-0% 0"(% -50'50<1-:0&6(% 3&6)#05*(% R#)% *?S% 1(.$5$% 4.(M5(),2% &$% $"-/)% #) F#6; ?;@^;%!"#$%,-..($'-)*$%0-%0"(%3&6)#05*(%.($'-)$(%-4%0"(%B8%&3':#4#(.%=(,&5$(%/(%,"-$(%&%@<[%#)'50 $#6)&:;d% N,,-.*#)6:2D% 0"(% 3#*=&)*% 6&#)% #$% +P% % f;dd% [a[% &)*% 0"(% J<*?% =&)*/#*0"% #$1 &@1 1 -V1 1 -?% $ @HH;@ 9VI;%F#65.(%?;@^%45.0"(.%$"-/$%0"&0%0"(%6&#)%=(6#)$%0-%4&::%-44%&0%&=-50%JOO%VI%=50%4:&00()$%-50%&6&#) &0%&=-50%@O%VI;%!"#$%4:&00()#)6%#)%0"(%6&#)%&0%:-/%4.(M5(),#($%#$%*5(%0-%&%.(&:%0.&)$3#$$#-)%I(.-g%#)0.-*5,(* #)% 0"(% 0.&)$4(.% 45),0#-)% -4% 0"(% &3':#4#(.% =2% '$% 0-6(0"(.% /#0"% 0$;% !"#$% I(.-% -,,5.$% &0% &% 4.(M5(),2 - = Z @ RH ' $0 $ S % %Hd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g;% !"#$% 4&,0-.% #$% &''.-+#3&0(:2% (M5&:% 0-% R@1 1 9*'$SD% &$ (+'(,0(*%4.-3%-5.%$05*2%-4%0"(%B8%&3':#4#(.%/#0"%&%$-5.,(<*(6()(.&0#-)%.($#$0&),(%#)%8(,0#-) d;g;U; Z-0(%0"&0%0"(%=&)*/#*0"%&@%"&$%#),.(&$(*%=2%&''.-+#3&0(:2%0"(%$&3(%4&,0-.%&$%0"(%*.-'%#)%6&#)1+P;%N$ /(%/#::%:(&.)%#)%B"&'0(.%f%/"()%/(%$05*2%)(6&0#1(%4((*=&,LD%0"(%$-5.,(<*(6()(.&0#-)%.($#$0-.%'$%'.-< 1#*($%)(6&0#1(%4((*=&,LD%/"#,"%&::-/$%5$%0-%0.&*(%-44%6&#)%4-.%/#*(.%=&)*/#*0"; ")%')5'*/&$%+#4.%$C,12*$:%;$%;4**%&$1)5.+0,+$%+#$%4120)($&%94,.%.+,94*4+<%,'#4$($&%;#$5%,%.)/0'$ 0$.4.+)0% '$% 4.% /.$&% >.$$% +#$% &4.'/..4)5% 45% N$'+4)5% \!`!8?!% N2$'464',**<:% ;$% ;4**% '#,5-$% >45% +#$% F[N@K" *$($*37%1)&$*%6)0%2,0+%VF[NDQ\?%+#$%(,*/$%)6%+#$%T$0)394,.%+#0$.#)*&%()*+,-$%2,0,1$+$0%I"D%9<% 7\h ,5&%2$06)01%,%94,.32)45+%.41/*,+4)5%45%QN24'$!%",9*$%A!\%.#);.%+#$%')00$.2)5&45-%(,04,+4)5.%45%%4%,5&%"# 6)0%+#$%',.$%45%;#4'#% ' $ gJO !%@)0%+#$%',.$%;4+#)/+%.)/0'$%&$-$5$0,+4)5:%;$%/.$%,5% ' $ O %45%+#$ U

Z-% *(0&#:(*% L)-/:(*6(% -4% 4.(M5(),2<.($'-)$(% ,&:,5:&0#-)$% #$% .(M5#.(*% 4-.% 0"#$% (+&3':(j% &::% 0"&0% #$% )((*(*% #$ 8(,0#-) d;^;g;%Z(1(.0"(:($$D%&40(.%0"(%$05*2%-4%0"(%4.(M5(),2%.($'-)$(%-4%0"(%B8%&3':#4#(.%#)%8(,0#-)$%^;@%0".-56" ^;JD%0"(%.(&*(.%/#::%=()(4#0%=2%.(05.)#)6%0-%0"#$%(+&3':(%&)*%5$#)6%78'#,(%0-%(+'(.#3()0%45.0"(.%/#0"%0"(%,#.,5#0; d !"(%.(&*(.%$"-5:*%)-0%=(%&:&.3(*%&=-50%0"(%5$(%-4%$5,"%&%:&.6(%$#6)&:%&3':#05*(;%P(,&::%0"&0%#)%&%$3&::<$#6)&: R&,S%$#35:&0#-)D%87ABC%4#.$0%4#)*$%0"(%$3&::<$#6)&:%(M5#1&:()0%,#.,5#0%&0%0"(%=#&$%'-#)0%&)*%0"()%&)&:2I($%0"#$%:#)(&. ,#.,5#0;%85,"%&,%&)&:2$#$%,&)D%-4%,-5.$(D%=(%*-)(%/#0"%&)2%&,%$#6)&:%&3':#05*(;%V-/(1(.D%&%@<[%&,%#)'50%#$%,-)1()< #()0%0-%5$(%=(,&5$(%0"(%.($5:0#)6%&,%-50'50%,-..($'-)*$%0-%0"(%1-:0&6(%6&#)%-4%0"(%,#.,5#0; g P(&*(.$%/"-%"&1(%)-0%2(0%$05*#(*%'-:($%&)*%I(.-$%,&)%$L#'%0"($(%4(/%$()0(),($;

B.2 PSpice Examples

20 CS # 10 uF

AM # 19.6 dB

fL # 54.2 Hz

fH # 122.1 MHz

15

CS # 0

10

AM # 11.3 dB

fL # 0.3 Hz

fH # 276.5 MHz

5

0 10m

100m 1.0 dB (V(OUT))

10

100

1.0K

10K

100K

1.0M

10M

100M

1.0G

Frequency (Hz)

Figure B.18 F.(M5(),2%.($'-)$(%-4%0"(%B8%&3':#4#(.%#)%C+&3':(%78;d;@%/#0"%0$% %@O% F%&)*%0$% %O%%R#;(;D%0$% .(3-1(*S;

.'#$1,+4'%)6%@4-!%A!7`!%@/0+#$01)0$:%+)%)9+,45%+#$%.,1$%%4%,5&%"#%45%9)+#%',.$.%>6)0%+#$%5)145,*%+#0$.#)*& ()*+,-$%"/D% D!`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able B.5 Variations in the Bias Point with the MOSFET Threshold Voltage RS = 630

RS = 0

Vtn0

ID (mA)

VO (V)

O;gO O;T O;^@

%%%O;dg %%%O;Ug %%%O;Jg

O;fgH @;Jf @;^@

ID (mA) %%%%%%%%%%%%%%%O;T@ %%%%%%%%%%%%%%%O;Ud %%%%%%%%%%%%%%%O;H@

VO (V) O;JJ%% @;UO H;UO

B-25

B-26 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.6.1 Dependence of the BJT

on the Bias Current

=5%+#4.% $C,12*$:% ;$% /.$%QN24'$% +)% .41/*,+$% +#$% &$2$5&$5'$%)6% &'% )5% +#$% ')**$'+)0%94,.% '/00$5+% 6)0%+#$ g8VHbDL%&4.'0$+$%Af"%>60)1%@,40'#4*&%N$14')5&/'+)0?%;#).$%1)&$*%2,0,1$+$0.%,0$%*4.+$&%45%",9*$%A!M ,5&%,0$%,(,4*,9*$%45%QN24'$!`%O.%.#);5%45%+#$%.'#$1,+4'%',2+/0$W%)6%@4-!%A!7b:%+#$%"0,%)6%+#$%Af"%4.%64C$& /.45-%,%')5.+,5+%()*+,-$%.)/0'$%>45%+#4.%$C,12*$:%"0,% %8%I?%,5&%,%&'%'/00$5+%.)/0'$%%&%4.%,22*4$&%,+%+#$ 9,.$!%")%4**/.+0,+$%+#$%&$2$5&$5'$%)6% &'%)5%+#$%')**$'+)0%'/00$5+%%0 :%;$%2$06)01%,%&'3,5,*<.4.%.41/*,+4)5 45%;#4'#%+#$%.;$$2%(,04,9*$%4.%+#$%'/00$5+%.)/0'$%%&!%"#$% &'1)6%+#$%Af":%;#4'#%')00$.2)5&.%+)%+#$%0,+4)%)6 +#$% ')**$'+)0% '/00$5+% %0% +)% +#$% 9,.$% '/00$5+% %&:% ',5% +#$5% 9$% 2*)++$&% ($0./.% %0% /.45-% Q0)9$% >+#$% -0,2#4',* 45+$06,'$%)6%QN24'$?:%,.%.#);5%45%@4-!%A!8D!%a$%.$$%+#,+%+)%)2$0,+$%,+%+#$%1,C41/1%(,*/$%)6% &'%>4!$!:% &'% 7MH?:%,+%"0,% %8%I:%+#$%Af"%1/.+%9$%94,.$&%,+%,5%%0% %7D%1O!%N45'$%45'0$,.45-%+#$%94,.%'/00$5+%)6%,%+0,5.4.3 +)0%45'0$,.$.%+#$%2);$0%&4..42,+4)5:%4+%4.%'*$,0%60)1%@4-!%A!8D%+#,+%+#$%'#)4'$%)6%'/00$5+%%0%4.%,%+0,&$3)66 9$+;$$5%+#$%'/00$5+%-,45% &'%,5&%+#$%2);$0%&4..42,+4)5!%]$5$0,**<%.2$,S45-:%+#$%)2+41/1%%0%&$2$5&.%)5 +#$% ,22*4',+4)5% ,5&% +$'#5)*)-<% 45% #,5&!% @)0% $C,12*$:% 6)0% +#$% g8VHbDL% Af"% )2$0,+45-% ,+% "0,% % 8% I: &$'0$,.45-%%0%9<%,%6,'+)0%)6%8D%>60)1%7D%1O%+)%D!\%1O?%0$./*+.%45%,%&0)2%45% &'%)6%,9)/+%8\h%>60)1%7MH +) 78H?!%% PARAMETERS: IB # 10u VCE # 2V

Q1 "

Q2N3904 ! "

{IB}

DC # {VCE} !

0

0

0

Figure B.19 !"(%78'#,(%0($0%=(),"%5$(*%0-%*(3-)$0.&0(%0"(%*('()*(),(%-4% nHZJfOU%*#$,.(0(%?G!%RC+&3':(%78;g;@S;

*,

%-)%0"(%,-::(,0-.%=#&$%,5..()0%%014-.%0"(

Table B.6 Spice Model Parameters of the Q2N3904 Discrete BJT

!"#$%&'() !8)#$$%&9: <=<#'%$'9> +;#5'7%64,,

*+!#', *+3#/%6 :=<#%'296 +)#'2/%5>,

-.#/%// 3;#%&'&/, 0=<#%&6, !+)#%(,

01)#&(%2' 4<#5, )<#%6, 0+)#(,

3)#(/$%( !"<#2, <=-#(%(7'> *+)#5,

4-#/%567, !"-#$%&'() !8;#2 ;<#/ :=-#%567', 0=-#%&6,, ;3#/2

T !"(%nHZJfOU%3-*(:%#$%#),:5*(*%#)%0"(%(1&:5&0#-)%RC[NQS%:#=.&.2%-4%78'#,(%/"#,"%#$%&1&#:&=:(%-)%0"(%BK%&,< ,-3'&)2#)6%0"#$%=--L; ^% !"(%.(&*(.%#$%.(3#)*(*%0"&0%0"(%$,"(3&0#,$%*#&6.&3$%&)*%0"(%,-..($'-)*#)6%78'#,(%$#35:&0#-)%4#:($%-4%&::%87ABC (+&3':($%#)%0"#$%=--L%,&)%=(%4-5)*%-)%0"(%0(+0m$%BK;%A)%0"($(%$,"(3&0#,$%R&$%$"-/)%#)%F#6;%?;@fSD%/(%5$(%1&.#&=:( '&.&3(0(.$%0-%()0(.%0"(%1&:5($%-4%0"(%1&.#-5$%,#.,5#0%,-3'-)()0$;%!"#$%&::-/$%-)(%0-%#)1($0#6&0(%0"(%(44(,0%-4 ,"&)6#)6%,-3'-)()0%1&:5($%=2%$#3':2%,"&)6#)6%0"(%,-..($'-)*#)6%'&.&3(0(.%1&:5($;

B.2 PSpice Examples

175 VCE # 2V 150 IC # 10 mA, bdc # 162.4 125 IC # 0.5 mA, bdc # 122.9 100 75 50 25 0 0A

5m A IC (Q1)"IB (Q1)

Figure B.20 K('()*(),(%-4%

10 mA

15 mA

20 mA

25 mA

30 mA

IC (Q1) *,

%-)%%0%R&0%"0,% %H%[S%#)%0"(%nHZJfOU%*#$,.(0(%?G!%RC+&3':(%78;g;@S;

Example PS.6.2 The CE Amplifier with Emitter Resistance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d%3N%#$%$(:(,0(*%4-.%0"( ?G!D%.($5:0#)6%#)% *,% %@HJ;%!"#$%,"-#,(%-4%%0%#$%&%.(&$-)&=:(%,-3'.-3#$(%=(0/(()%'-/(.%*#$$#'&0#-)%&)* ,5..()0%6&#);%F5.0"(.3-.(D%&%,-::(,0-.%=#&$%1-:0&6(%"0%-4%O [%R#;(;D%&0%0"(%3#*c$5'':2%.&#:S%#$%$(:(,0(*%0-

B-27

B-28 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.6.2 continued VCC

PARAMETERS: CE # 10u CCI # 10u CCO # 10u RC # 10K RB # 340K RE # 6K Rce # 130 RL # 10K Rsig # 10K

{RC}

{CCO} OUT

{Rsig}

IN VCC

VEE

" DC # {VCC}

"

Q2N3904

{RL} 0

VCC # 5 VEE # !5

!

{CCI}

1Vac 0Vdc

" !

AC Source

{RB} {RE}

! DC # {VEE}

{CE} {Rce}

0

0

0

0

VEE

0

Figure B.21 8,"(3&0#,%,&'05.(%-4%0"(%BC%&3':#4#(.%#)%C+&3':(%78;g;H;

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B.2 PSpice Examples

+#$%$14++$03&$-$5$0,+4)5%0$.4.+)0%'E%&$'0$,.$.%+#$%()*+,-$%-,45% + P %9<%,%6,'+)0%)6 ' ' $#6 < @ <<<<
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B-29

B-30 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.6.2 continued 35 AM # 31.7 dB

fL # 131.1 Hz

fH # 145.8 kHz

Rce # 0 )

30

AM # 25.6 dB 25

Rce # 130 )

20

fL # 62.9 Hz

fH # 287.1 kHz

15

10

5

0 1.0

10 dB (V(OUT))

100

1.0 K

10 K

100 K

1.0 M

10 M

Frequency (Hz)

Figure B.22 F.(M5(),2%.($'-)$(%-4%0"(%BC%&3':#4#(.%#)%C+&3':(%78;g;H%/#0"% ' )E

O %&)*% ' )E @JO%

Table B.7 Variations in the Bias Point of the CE Amplifier with the SPICE Model-Parameter BF of BJT RE BF (in SPICE) HO^ U@g;U%R)-3#)&:%1&:5(S ^JH

&,

@Og @UJ @TJ

*,

%%fU;f @HJ @UU

6k IC (mA) O;UdH O;UfU O;d@^

RE VC (V) O;U^U O;OgH O;@^J

&,

@Of @U^ @^@

*,

fg;f @HT @d@

0 IC (mA)

VC (V)

O;JTT O;UfU O;d^^

@;HHT O;OgO O;^T^

Example PS.7.1 The CMOS CS Amplifier =5%+#4.%$C,12*$:%;$%;4**%/.$%QN24'$%+)%')12/+$%+#$%&'%+0,5.6$0%'#,0,'+$04.+4'%)6%+#$%EN%,12*464$0%;#).$ ',2+/0$%.'#$1,+4'%4.%.#);5%45%@4-!%A!8H!%a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

;

B.2 PSpice Examples

PARAMETERS: Iref # 100u M#2 M1 # 10

VDD

M # {M} W # 37.5u L # 6u

VDD # 10

{Iref}

VDD

M3

M2

M # {M} W # 37.5u L # 6u

"

OUT

!

0

VDD

IN " DC # {VDD} !

M1

VIN 1.5Vdc

M # {M1} W # 12.5u L # 6u

" !

0

0

0

Figure B.23 8,"(3&0#,%,&'05.(%-4%0"(%B8%&3':#4#(.%#)%C+&3':(%78;T;@;

D

D iD

iD iD m

G

iD m Q1

Q2

Qm

S

S Aspect ratio # mW L

iD m

Aspect ratio of each MOSFET # W L

Figure B.24 !.&)$#$0-.%(M5#1&:(),2;

%4 %

@ @< H <<< 0 2A * <<<<<<< " H ? (44 #"

>A!8L?

;#$0$%?$66%0,+#$0%+#,5%?%4.%/.$&%+)%1)0$%,''/0,+$*<%$.+41,+$%+#$%&0,45%'/00$5+! "#$%EN%,12*464$0%45%@4-!%A!8H%4.%&$.4-5$&%6)0%,%94,.%'/00$5+%)6%7DD% O%,../145-%,%0$6$0$5'$%'/00$5+ %0$6 7DD% O%,5&%"44% %7D%I!%"#$%'/00$5+%1400)0%+0,5.4.+)0.%P8%,5&%PH%,0$%.4T$&%6)0%"#"8% %"#"H% %7%I:

B-31

B-32 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.7.1 continued

;#4*$%+#$%452/+%+0,5.4.+)0%P7%4.%.4T$&%6)01"#"7% %D!\%I!%V)+$%+#,+%,%.1,**$0%)($0&04($%()*+,-$%4.%.$*$'+$&%6)0 P7%+)%,'#4$($%,%*,0-$0%()*+,-$%-,45%Sv%6)0%+#$%EN%,12*464$0:%.45'$ Sv %

P 9 *@ ' ?

P 9 *@ 7 2@ 7 2H %

"+3 "+6 H P <<<<<<<<<<< <<<<<<<<<<<<<<<<<<<<<<< "#"@ "+3 "+6

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8V

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Figure B.25 4"5%[-:0&6(%0.&)$4(.%,"&.&,0(.#$0#,%-4%0"(%B8%&3':#4#(.%#)%C+&3':(%78;T;@;%4J5%C+'&)*(*%1#(/%-4%0"( 0.&)$4(.% ,"&.&,0(.#$0#,% #)% 0"(% "#6"<6&#)% .(6#-);% N:$-% $"-/)% &.(% 0"(% 0.&)$4(.% ,"&.&,0(.#$0#,$% /"(.(% '.-,($$% 1&.#&0#-)$ ,&5$(%0"(%/#*0"%-4%0.&)$#$0-.%P@10-1,"&)6(%=2% @dk%&)*% @dk%4.-3%#0$%)-3#)&:%1&:5(%-4%@@% %@H;d 3;%

B.2 PSpice Examples

10V (1.5V, 9.0V) for W1 # 12.5u ! 15% 8V

6V

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4V

2V (1.5V, 0.836V) for W1 # 12.5u " 15% 0V 1.30V

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Figure 8.25 )23/(3FE!

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Example PS.8.1 A Multistage Differential BJT Amplifier "#$%.'#$1,+4'%',2+/0$%)6%+#$%1/*+4.+,-$%)23,12%'40'/4+%,5,*60)1% @,40'#4*& @@

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B-33

B-34 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.8.1 continued

N$14')5&/'+)0?%6)0%+#$%363%,5&%636%Af".:%0$.2$'+4($*P)<71#$'.')6QF A8 g;TJU4 `!A J% AbF gg;T^3 `!? %@;d BGB J;gJ^' 9GB% ;JO^d !P HJf;d)%% !F %JO@;H'% KLMNO>R)<71#$'.')6QF A8 @;U@4 `!A% J% AbF ^O3 `!? %@;d BGB %f;TH^' 9GB% ;dTTg !P JJ;UH)%% !F @Tf;J'%

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% Table B.9 DC Collector Currents of the Op-Amp Circuit in Fig. B.26 as Computed by Hand Analysis (Example 8.6) and by PSpice Collector Currents (mA) Transistor W@ WH WJ WU Wd Wg WT W^ Wf

Hand Analysis (Example 8.6)

PSpice

Error (%)

O;Hd O;Hd O;d @;O @;O H;O @;O d;O O;d

O;H^@ O;H^@ O;dgT @;HT @;H@ H;dO @;HT g;@T O;U^

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A)%78'#,(D%0"(%,-33-)<3-*(%#)'50%1-:0&6(%"0P%-4%0"(%-'<&3'%,#.,5#0%#$%$(0%0-%O%[%R#;(;D%0-%0"(%&1(.&6( -4%0"(%*,%'-/(.<$5'':2%1-:0&6($%"00%&)*%",,S%0-%3&+#3#I(%0"(%&1&#:&=:(%#)'50%$#6)&:%$/#)6;%N%=#&$<'-#)0 $#35:&0#-)%#$%'(.4-.3(*%0-%*(0(.3#)(%0"(%*,%-'(.&0#)6%'-#)0;%!&=:(%?;f%$533&.#I($%0"(%1&:5(%-4%0"(%*, ,-::(,0-.%,5..()0$%&$%,-3'50(*%=2%78'#,(%&)*%&$%,&:,5:&0(*%=2%0"(%"&)*%&)&:2$#$%#)%C+&3':(%T;g;%P(,&:: 0"&0%-5.%"&)*%&)&:2$#$%&$$53(*%=-0"% %&)*%0"(%C&.:2%1-:0&6(%"+%-4%0"(%?G!$%0-%=(%#)4#)#0(;%V-/(1(.D%-5. 87ABC%$#35:&0#-)$%#)%C+&3':(%78;g;@%R/"(.(%/(%#)1($0#6&0(*%0"(%*('()*(),(%-4% %-)%0"(%,-::(,0-.%,5.< .()0% % 0 S%#)*#,&0(%0"&0%0"(%nHZJfOU%"&$% $ @Hd %&0% % 0 % O;Hd%3N ;%F5.0"(.3-.(D%#0$%4-./&.*%C&.:2%1-:0< &6(%R87ABC%'&.&3(0(.%[NFS%#$%TU%[D%&$%6#1()%#)%!&=:(%?;^;%Z(1(.0"(:($$D%/(%-=$(.1(%4.-3%!&=:(%?;f 0"&0%0"(%:&.6($0%(..-.%#)%0"(%,&:,5:&0#-)%-4%0"(%*,%=#&$%,5..()0$%#$%-)%0"(%-.*(.%-4%HOk;%N,,-.*#)6:2D%/(%,&) ,-),:5*(%0"&0%&%M5#,L%"&)*%&)&:2$#$%5$#)6%6.-$$%&''.-+#3&0#-)$%,&)%$0#::%2#(:*%.(&$-)&=:(%.($5:0$%4-.%&%'.(< :#3#)&.2%($0#3&0(%&)*D%-4%,-5.$(D%"&)*%&)&:2$#$%2#(:*$%35,"%#)$#6"0%#)0-%0"(%,#.,5#0%-'(.&0#-);%A)%&**#0#-) 0-%0"(%*,%=#&$%,5..()0$%:#$0(*%#)%!&=:(%?;fD%0"(%=#&$<'-#)0%$#35:&0#-)%#)%78'#,(%$"-/$%0"&0%0"(%-50'50%*, -44$(0%R#;(;D%"EY!%/"()%"!% O S%#$%J;gH%[%&)*%0"&0%0"(%#)'50%=#&$%,5..()0% % &@ %#$%H;^^% N;%%

B.2 PSpice Examples

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B-35

B-36 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.8.1 continued 20 V

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B.2 PSpice Examples

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"#$%(,*/$.%)6%+#$%.1,**3.4-5,*%2,0,1$+$0.%,.%')12/+$&%9<%QN24'$%',5%9$%6)/5&%45%+#$%)/+2/+%64*$%)6%,%94,.3 2)45+% >)0% ,5% ,'3,5,*<.4.?% .41/*,+4)5!% d.45-% +#$.$% (,*/$.% 0$./*+.% 45% 0 (M JJ^ 2@:% ' (M S :% ,5& - V @g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d %)5*A!8M?%-4($.%,%'*).$%,220)C41,+4)5%6)0%-V%45%+#$%',.$%)6%,%.<13 1$+04'%'40'/4+:%;$%45.$0+%,%0$.4.+)0% ' J %>;#).$%.4T$%4.%$B/,*%+)% ' J ?%45%+#$%')**$'+)0%)6% W U !%V)+$%+#,+%+#4. ;4**%#,($%)5*<%,%145)0%$66$'+%)5%+#$%&'%)2$0,+45-%2)45+!%"#$%)23,12%'40'/4+%;4+#% W U %#,(45-%,%')**$'+)0 0$.4.+)0% ' J 4.%+#$5%.41/*,+$&%45%QN24'$!%@4-/0$%A!8W>9?%.#);.%+#$%0$./*+45-%60$B/$5'<%0$.2)5.$%)6%+#4. .<11$+04'%)2%,12:%;#$0$% - V @dd;T SYT!%O'')0&45-*<:%45%+#$%',.$%)6%,%2$06$'+*<%.<11$+04'%)23,12%'403 '/4+:%+#$%(,*/$%)6%-V%45%KB!%>A!8M?%'*).$*<%,220)C41,+$.%+#$%(,*/$%')12/+$&%9<%QN24'$!%E)12,045-%+#$%60$3 B/$5'<%0$.2)5.$.%)6%+#$%5)5.<11$+04'%>@4-!%A!8W,?%,5&%+#$%.<11$+04'%>@4-!%A!8W9?%)23,12%'40'/4+.:%;$ 5)+$% +#,+% +#$% H3&A% 60$B/$5'<% )6% +#$% )2% ,12% &0)2.% 60)1% 8\M!b% SYT% +)% 7\\!`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b?%,5&%+#$ )/+2/+%&'%()*+,-$%4.%.+,94*4T$&%,+%T$0)!%"#/.:%+#$%.1,**3.4-5,*%2$06)01,5'$%)6%+#$%)23,12%'40'/4+%',5 9$%1)0$%,''/0,+$*<%.41/*,+$&%9<%94,.45-%+#$%'40'/4+%.)%,.%+)%6)0'$%)2$0,+4)5%,+%+#4.%*$($*%)6%)/+2/+%()*+3 ,-$!% "#4.% ',5% 9$% $,.4*<% &)5$% 9<% ,22*<45-% ,% &466$0$5+4,*% &'% 452/+% )6% "#$!% N/2$0412).$&% )5% +#4.% &'

@H

!"#$%'&.0%-4%0"(%(+&3':(%.(M5#.($%$05*2%-4%8(,0#-)$%^;^%&)*%^;@O;H;

B-37

B-38 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.8.1 continued 100 Ad # 82.8 dB

fH # 256.9 kHz

80

60

40

20

0 1.0

10 100 dB (V (OUT))

1.0 K

10 K

100 K

1.0 M

10 M

100 M

1.0 G

100 M

1.0 G

Frequency (Hz) (a)

100 Ad # 82.5 dB

fH # 155.7 kHz

80

60

40

20

0 1.0

10 100 dB (V (OUT))

1.0 K

10 K

100 K

1.0 M

10 M

Frequency (Hz) (b)

Figure B.28 F.(M5(),2%.($'-)$(%-4%4"5%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;Hg%&)*%4J5%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;Hg =50%/#0"%&%.($#$0-.% ' J 'J%#)$(.0(*%#)%0"(%,-::(,0-.%-4%WU%0-%3&L(%0"(%-'<&3'%,#.,5#0%$233(0.#,&:;

B.2 PSpice Examples

452/+:%;$%',5%,22*<%,5%,'%.4-5,*%+)%2$06)01%,5%,'3,5,*<.4.%.41/*,+4)5%6)0%+#$%2/02).$%)6:%6)0%$C,12*$: ')12/+45-%+#$%&466$0$5+4,*%-,45%,5&%+#$%H3&A%60$B/$5',.%&4.'/..$&%$,0*4$0? ,5&:%+#/.:%20$($5+%20$1,+/0$%.,+/0,+4)5%)6%+#$%Af".!%"#$%')00$.2)5&45-%)/+2/+%()*+,-$%"[d"%4.%2*)++$&%45 @4-!%A!8b>,?!%@0)1%+#4.%')11)531)&$%&'%+0,5.6$0%'#,0,'+$04.+4'%;$%645&%+#,+%+#$%,12*464$0%9$#,($.%*453 $,0*<% )($0% +#$% "0P% 0,5-$% 7L!7 I% +)% W!b I:% ;#4'#% 4.% +#$0$6)0$% +#$% 7+,-.) #%!!%+9!%&') $"+3'!% =5 KC,12*$% `!M:% ;$% 5)+$&% +#,+% +#$% /22$0% *414+% )6% +#4.% 0,5-$% 4.% &$+$0145$&% 9<% W @ % ,5&% W H % .,+/0,+45-: ;#$0$,.%+#$%*);$0%*414+%4.%&$+$0145$&%9<% W J %.,+/0,+45-!%")%($046<%+#4.%,..$0+4)5:%;$%0$B/$.+$&%QN24'$%+) 2*)+%+#$%(,*/$.%)6%+#$%')**$'+)0P9,.$%()*+,-$.%)6%+#$.$%Af".%($0./.%+#$%452/+%')11)531)&$%()*+,-$%"0P! "#$%0$./*+.%,0$%.#);5%45%@4-!%A!8b>9?:%60)1%;#4'#%;$%5)+$%+#,+%)/0%,..$0+4)5%4.%45&$$&%')00$'+%>0$',**%+#,+ ,5%363%Af"%$5+$0.%4+.%.,+/0,+4)5%0$-4)5%;#$5%4+.%9,.$P')**$'+)0%X/5'+4)5%9$')1$.%6)0;,0&%94,.$&:%4!$!: " &0 O ?! 5V

0V Input Common-Mode Range

!5 V

!10 V

!15 V !15

!10 V (OUT)

!5

0

5

10

15

V_VCM (V) (a)

Figure B.29 4"5%!"(%:&.6(<$#6)&:%,-33-)<3-*(%0.&)$4(.%,"&.&,0(.#$0#,%-4%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;Hg;%!"(%*#4< 4(.()0#&:%#)'50%1-:0&6(%"!%#$%$(0%0-%c"#$% %cHgO% [%0-%'.(1()0%'.(3&05.(%$&05.&0#-);%4J5%!"(%(44(,0%-4%0"(%,-33-)<3-*(% #)'50%1-:0&6(%[B9%-)%0"(%:#)(&.#02%-4%0"(%#)'50%$0&6(%-4%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;Hg;%!"(%=&$(c,-::(,0-.%1-:0&6(%-4% W@%&)*%WJ%#$%$"-/)%&$%&%45),0#-)%-4%[B9;%!"(%#)'50%$0&6(%-4%0"(%-'<&3'%,#.,5#0%:(&1($%0"(%&,0#1(%.(6#-)%/"()%0"(% =&$(c,-::(,0-.%X5),0#-)%-4%(#0"(.%W@%-.1WJ%=(,-3($%4-./&.*%=#&$(*%R#;(;D%/"()% [?B O S;

B-39

B-40 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.8.1 continued 10 V

!0 V

VBC of Q3

!10 V

!20 V VBC of Q1

!30 V !15

!10 V (Q3:B)–V (Q3:C)

!5 0 V (Q1:B)–V (Q1:C)

5

10

15

V_VCM (V) (b)

Figure B.29 R023/!LS;

Example PS.9.1 Frequency Response of the CMOS CS and the Folded-Cascode Amplifiers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d< 3% B9E8% 0(,")-:-62% 4-.% 0"(% 9E8FC!$% &)*% 5$(% '&.0$ Z9E8E7d%&)*%79E8E7d%/"-$(%87ABC%:(1(:<@%3-*(:%'&.&3(0(.$%&.(%:#$0(*%#)%!&=:(%?;J;%!-%$'(,#42%0"( *#3()$#-)$%-4%0"(%9E8FC!$%#)%78'#,(D%/(%/#::%5$(%0"(%35:0#':#,&0#1(%4&,0-.%*D%0-6(0"(.%/#0"%0"(%,"&))(: :()60"1?%&)*%,"&))(:%/#*0"%@%R&$%/(%*#*%#)%C+&3':(%78;T;@S;%

The CMOS CS Amplifier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

B.2 PSpice Examples

PARAMETERS: Cload # 0.5p CS # 1 Iref # 100u M#4 M1 # 18

VDD

VDD

M # {M} W # 5u L # 0.6u

M3

M # {M} W # 5u L # 0.6u

M2

Rsig # 100 VDD # 3.3

{Iref}

"

OUT

!

{Cload} 0 {Rsig}

M1

M # {M1} W # 1.25u L # 0.6u

IN

VDD

" DC # {VDD} !

0

1Vac 2.45Vdc

" !

Vsig

0

{Iref}

0

"

{CS}

!

0

0

Figure B.30 %8,"(3&0#,%,&'05.(%-4%0"(%B8%&3':#4#(.%#)%C+&3':(%78;f;@

,5,*<.4.!%=5%E#,2+$0%`:%;$%6)/5&%)/+:%45%+#$%')5+$C+%)6 .+/&<45-%+#$%&466$0$5+4,*%2,40:%#);%+#$%-),*.%)6%+#4. 94,.45-%,220),'#%6)0%+#$%EN%,12*464$0%,0$%0$,*4T$&%45%20,'+4',*%=E%412*$1$5+,+4)5.! "#$%EN%,12*464$0%45%@4-!%A!HD%4.%&$.4-5$&%,../145-%,%0$6$0$5'$%'/00$5+%%0$6% 7DD% O%,5&%"44% %H!H%I! "#$%'/00$5+31400)0%+0,5.4.+)0.:%P8%,5&%PH:%,0$%.4T$&%6)0%"#"8% %"#"H% %D!H%I:%;#4*$%+#$%452/+%+0,5.4.+)0%P7%4. .4T$&%6)0%"#"7% %D!7\%I!%d54+3.4T$%+0,5.4.+)0.%,0$%/.$&%;4+#% @ ? % %7!8\% 3 O;g %D!M% 1%6)0%+#$%VF[N &$(4'$.%,5&% @ ? % %\% 3 O;g % 1%6)0%+#$%QF[N%&$(4'$.!%"#/.:%/.45-%+#$%.B/,0$%*,;%%4%P%"#"%)6%+#$ F[N@K"%+)-$+#$0%;4+#%+#$%D!\3 1%EF[N%20)'$..%2,0,1$+$0.%45%",9*$%A!L:%;$%645&%*7% %7W%,5&%*8% %*H% %L! @/0+#$01)0$:%KB!%>A!8\?%-4($.%Sv% % P UU;U%[a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

B-41

B-42 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.9.1 continued 0 0

CS Amplifier Gv # 34.5 dB

fH # 7.49 MHz with Rsig # 100 )

0 fH # 293.2 kHz with Rsig # 1 M) 0 0 0

dB (V(OUT))

(a)

0

Cascode Amplifier

fH # 2.93 MHz with Rsig # 100 )

0 Gv # 42.4 dB

fH # 1.44 MHz with Rsig # 1 M)

0 0 0 0 1.0

10 dB (V(OUT))

100

1.0 K

10 K

100 K

1.0 M

10 M

100 M

1.0 G

Frequency (Hz) (b)

Figure B.31 F.(M5(),2%.($'-)$(%-4%4"5%0"(%B8%&3':#4#(.%&)*%4J5%0"(%4-:*(*<,&$,-*(%&3':#4#(.%#)%C+&3':(%78;f;@D% /#0"%'$#6% %@OO% &)*%'$#6% %@%9 ;

[9.$0($%+#,+%-V%&0)2.%;#$5%'.4-%4.%45'0$,.$&!%"#4.%4.%,5+4'42,+$&%60)1%)/0%.+/&<%)6%+#$%#4-#360$B/$5'< 0$.2)5.$%)6%+#$%EN%,12*464$0%45%N$'+4)5%W!H!%N2$'464',**<:%,.%'.4-%45'0$,.$.:%+#$%2)*$% -6

#)

@< <<<<<<<<<<<<<<< @ < <<<<< H ' $#6 0 #)

>A!8`?

6)01$&% ,+% +#$% ,12*464$0% 452/+% ;4**% #,($% ,5% 45'0$,.45-*<% .4-5464',5+% $66$'+% )5% +#$% )($0,**% 60$B/$5'< 0$.2)5.$% )6% +#$% ,12*464$0!% O.% ,% 0$./*+:% +#$% $66$'+4($% +41$% ')5.+,5+% V % 45% KB!% >W!W\?% 45'0$,.$.% ,5& -V &$'0$,.$.!%a#$5%'.4-%9$')1$.%($0<%*,0-$:%,.%4+%4.%;#$5%'.4-% %7%F :%, &)145,5+%2)*$%4.%6)01$&%9<%'.4,5&%045!%"#4.%0$./*+.%45 -V $ - 6

>A!8W?

#)

")%$.+41,+$%-6:45:%;$%5$$&%+)%',*'/*,+$%+#$%452/+%',2,'4+,5'$%045%)6%+#$%,12*464$0!%d.45-%F4**$0i.%+#$)0$1: ;$%#,($ 0 #)% 0 9:@

0 9!@ R@

9 *@ ' ? %S

H <<< * @ ? 0 J @ @ @ 2A

0 9:D%2v@

0 9!D%2v@ R@

9 *@ ' ? %S

>A!8b?

B.2 PSpice Examples

Table B.10 Dependence of the 3-dB Bandwidth fH on Rsig for the CS and the Folded-Cascode Amplifiers in Example PS.9.1 fH Rsig

B8%N3':#4#(.

F-:*(*
@OO% @%9

T;Uf%9VI HfJ;H%LVI

H;fJ%9VI @;UU%9VI

;#$0$ '?

>A!HD?

7 2@ 7 2H

"#/.:%045%',5%9$%',*'/*,+$&%/.45-%+#$%(,*/$.%)6%09:7%,5&%09!7:%;#4'#%,0$%')12/+$&%9<%QN24'$%,5&%',5%9$ 6)/5&%45%+#$%)/+2/+%64*$%)6%+#$%94,.32)45+%.41/*,+4)5!%O*+$05,+4($*<:%045%',5%9$%6)/5&%/.45-%KB!%>A!8b?%;4+# +#$%(,*/$.%)6%+#$%)($0*,2%',2,'4+,5'$.%09::%2v7%,5&%09!:%2v7%',*'/*,+$&%/.45-%+#$%20)'$..%2,0,1$+$0.%45%",9*$ A!L%>,.%&$.'049$&%45%KB.!%A!b%,5&%A!7D?R%+#,+%4.e 0 9:D%2v@ %

* @ @@ 0S$#

>A!H7?

0 9!D%2v@ %

* @ @@ 0S4#

>A!H8?

"#4.% 0$./*+.% 45% 045% % D!\H% 2@% ;#$5% Sv % 9 *@ ' ? dJ;H%[a[ !% O'')0&45-*<:% /.45-% KB.! >A!8`?% ,5& >A!8W?:%-V% %HDD!H%SYT%;#$5%'.4-% %7%F :%;#4'#%4.%'*).$%+)%+#$%(,*/$%')12/+$&%9<%QN24'$!

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B-43

0

DC # {VDD}

1Vac 2.45Vdc

M # {M} W # 5u L # 0.6u

!

"

!

"

M4

0

Vsig

{Rsig}

{Iref}

0

VDD

M1

0

{Iref}

IN

M3

!

"

0

{CS}

M # {M1} W # 1.25u L # 0.6u

M # {2*{M}} W # 5u L # 0.6u

VDD

D

!

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0

M5

M # {M} W # 5u L # 0.6u

{Iref}

M6

VDD

M # {M} W # 1.25u L # 0.6u

Figure B.32 8,"(3&0#,%,&'05.(%-4%0"(%-4%4-:*(*%,&$,-*(%%&3':#4#(.%#)%C+&3':(%78;f;@;

!

"

VDD

PARAMETERS: Cload # 0.5p CS # 1 Iref # 100u M#4 M1 # 18 Rsig # 100 VDD # 3.3

Example PS.9.1 continued

0

M # {M} W # 1.25u L # 0.6u

{Cload}

OUT

M2

0

M8

M7

!

"

0

{Iref}

M # {M} W # 5u L # 0.6u

M # {M} W # 5u L # 0.6u

VDD

B-44 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

B.2 PSpice Examples

4.%+#$%)/+2/+%0$.4.+,5'$%)6%+#$%,12*464$0!%Y$0$:%')/+8%4.%+#$%0$.4.+,5'$%.$$5%*))S45-%45+)%+#$%&0,45%)6%+#$%',.3 ')&$%+0,5.4.+)0%P8:%;#4*$%')/+\%4.%+#$%0$.4.+,5'$%.$$5%*))S45-%45+)%+#$%&0,45%)6%+#$%'/00$5+31400)0%+0,5.4.+)0 P\!%d.45-%KB!%>M!8\?:%;$%#,($ ' -50H $ 9 *H 7 2H ' :H

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@ @< <<<<<<<<<<<<<<<<<< <<<<< H ' -50 0 -50

>A!LD?

N45'$%+#$%)/+2/+%0$.4.+,5'$%)6%+#$%6)*&$&3',.')&$%,12*464$0%4.%*,0-$0%+#,5%+#,+%)6%+#$%EN%,12*464$0%>9<%, 6,'+)0%)6%,220)C41,+$*<%H:%,.%6)/5&%+#0)/-#%+#$%#,5&%,5,*<.4.%,9)($?%;#4*$%+#$40%)/+2/+%',2,'4+,5'$.%,0$ ,220)C41,+$*<%$B/,*:%+#$%6)*&$&3',.')&$%,12*464$0%#,.%,%*);$0%-V%45%+#4.%',.$! [5%+#$%)+#$0%#,5&:%;#$5%':(9%4.%*,0-$:%-V%)6%+#$%6)*&$&3',.')&$%,12*464$0%4.%1/'#%#4-#$0%+#,5%+#,+%)6%+#$ EN%,12*464$0!%"#4.%4.%9$',/.$:%45%+#4.%',.$:%+#$%$66$'+%)6%+#$%2)*$%,+%-6: 45%)5%+#$%)($0,**%60$B/$5'<%0$.2)5.$%)6 +#$%,12*464$0%9$')1$.%.4-5464',5+!%N45'$:%&/$%+)%+#$%F4**$0%$66$'+:%045%)6%+#$%EN%,12*464$0%4.%1/'#%*,0-$0 +#,5%+#,+%)6%+#$%6)*&$&3',.')&$%,12*464$0:%4+.%-V%4.%1/'#%*);$0%45%+#4.%',.$!%")%')56401%+#4.%2)45+:%)9.$0($ +#,+%045%)6%+#$%6)*&$&3',.')&$%,12*464$0%',5%9$%$.+41,+$&%9<%0$2*,'45-% ' ? %45%KB!%>A!8b?%;4+#%+#$%+)+,*%0$.4.3 +,5'$%'!7%9$+;$$5%+#$%&0,45%)6%P7%,5&%-0)/5&!%Y$0$: ' !@ %

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>A!LH?

B-45

B-46 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.9.1 continued

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

Example PS.10.1 Determining the Loop Gain of a Feedback Amplifier "#4.%$C,12*$%4**/.+0,+$.%+#$%/.$%)6%NQ=EK%+)%')12/+$%+#$%*))2%-,45%+ !%@)0%+#4.%2/02).$:%;$%.#,**%/.$%+#$ .#/5+P.$04$.%6$$&9'S%,12*464$0%.#);5%45%@4-!%A!HH%>.$$%,*.)%Q0)9*$1%b!7D7?! !-%,-3'50(%0"(%:--'%6&#)D%/(%$(0%0"(%#)'50%$#6)&:%"$%0-%I(.-D%&)*%/(%,"--$(%0-%=.(&L%0"(%4((*=&,L%:--' =(0/(()%0"(%,-::(,0-.%-4%W@%&)*%0"(%=&$(%-4%WH;%V-/(1(.D%#)%=.(&L#)6%0"(%4((*=&,L%:--'D%/(%35$0%()$5.( 0"&0%0"(%4-::-/#)6%0/-%,-)*#0#-)$%0"&0%(+#$0(*%'.#-.%0-%=.(&L#)6%0"(%4((*=&,L%:--'%*-%)-0%,"&)6(>%R@S%0"( *,%=#&$%$#05&0#-)%&)*%RHS%0"(%&,%$#6)&:%0(.3#)&0#-); VCC # "12 V VCC # "12 V RB1 100 k)

Rs 10 k) Vs

RC2 8 k)

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RC1 10 k) Q2

CC1

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CE1

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Figure B.33 B#.,5#0%-4%0"(%$"5)0c$(.#($%4((*=&,L%&3':#4#(.%#)%C+&3':(%78;@O;@;

Cf *

B.2 PSpice Examples

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

Method 1 X:(391/;E126E3G)(7)F(/1H3!1:;27/G)(7)F(/1/7H3:-E71-F3)/(23: O.%&$.'049$&%45%N$'+4)5%b!b:%+#$%*))2%-,45%',5%9$%$C20$..$&%,. +

@ P @ % <<<<<<< < 2)

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"2) <<<<<< < "/

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Method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f;fD +

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B-47

B-48 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim Example PS.10.1 continued

VCC VCC

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B.2 PSpice Examples

VCC VCC RC2 RB1

CC2

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Q2

CC1 Q1

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Vr

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Amplifier circuit

Cti

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! Rf VCC VCC Cto RB1

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Replica circuit

Q1

RE2 RB2

RE1

CE1

Cf

Rf

Figure B.35 B#.,5#0%4-.%$#35:&0#)6%0"(%:--'%6&#)%-4%0"(%4((*=&,L%&3':#4#(.%,#.,5#0%#)%F#6; ?;JJ%5$#)6%0"(%.(':#,&< ,#.,5#0%3(0"-*;

!-%,-3'50(%0"(%:--'%6&#)%+ %-4%0"(%4((*=&,L%&3':#4#(.%,#.,5#0%#)%F#6; ?;JJ%5$#)6%78'#,(D%/(%,"--$( 0-% $#35:&0(% 0"(% ,#.,5#0% #)% F#6; ?;Jd;% A)% 0"(% 78'#,(% $#35:&0#-)$D% /(% 5$(*% '&.0% nHZJfOU% R/"-$(% 87ABC 3-*(:%#$%6#1()%#)%!&=:(%?;gS%4-.%0"(%?G!$D%&)*%/(%$(0%?=.(&L%0-%=(%@%]V%&)*%0"(%,-5':#)6%&)*%=2'&$$%,&'&,< #0-.$%0-%=(%@ LF;%!"(%3&6)#05*(%&)*%'"&$(%-4%+ %&.(%':-00(*%#)%F#6; ?;JgD%4.-3%/"#,"%/(%$((%0"&0%0"(%4((*< =&,L%&3':#4#(.%"&$%&%6&#)%3&.6#)%-4%dJ;T%*?%&)*%&%'"&$(%3&.6#)%-4%^^;T ;%%%%

B-49

B-50 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim Example PS.10.1 continued 40 20

|AB|V # 35.5 dB

0

GM # 53.7 dB

!20 !40 !60

dB (V (returned) /V (test))

0d !30d !60d !90d !120d

PM # 88.7

!150d !180d 1.0

10 100 1.0 K P (–V (returned) /V (test))

10 K

100 K

1.0 M

10 M

100 M

1.0 G

Frequency (Hz)

Figure B.36 4"5%9&6)#05*(%&)*%4J5%'"&$(%-4%0"(%:--'%6&#)%+ %-4%0"(%4((*=&,L%&3':#4#(.%,#.,5#0%#)%F#6; ?;JJ;

Example PS.11.1 Class B BJT Output Stage a$%45($.+4-,+$%+#$%)2$0,+4)5%)6%+#$%'*,..%A%)/+2/+%.+,-$%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45%@4-!%A!H`! @)0%+#$%2);$0%+0,5.4.+)0.:%;$%/.$%+#$%&4.'0$+$%Af".%FfK8LH%,5&%FfK8\H%>60)1%[V%N$14')5&/'+)0?:7H ;#4'#%,0$%0,+$&%6)0%,%1,C41/1%')5+45/)/.%')**$'+)0%'/00$5+%%01,C% %L%O%,5&%,%1,C41/1%')**$'+)0P$14++$0 ()*+,-$%)6%"0,1,C%Z%7DD%I!%")%2$014+%')12,04.)5%;4+#%+#$%#,5&%,5,*<.4.%2$06)01$&%45%KC,12*$%7H!7:%%45%+#$ .41/*,+4)5:%;$%/.$%')12)5$5+%,5&%()*+,-$%(,*/$.%4&$5+4',*%>)0%'*).$?%+)%+#).$%)6%+#$%'40'/4+%&$.4-5$&%45 KC,12*$%7H!7!%N2$'464',**<:%;$%/.$%,%*),&%0$.4.+,5'$%)6%W :%,5%452/+%.45$3;,($%.4-5,*%)6%7`!b3I%2$,S%,5& 73SYT%60$B/$5'<:%,5&%8H3I%2);$0%./22*4$.!%=5%QN24'$:%,%+0,5.4$5+3,5,*<.4.%.41/*,+4)5%4.%2$06)01$&%)($0%+#$ 45+$0(,*%D%1.%+)%H%1.:%,5&%+#$%;,($6)01.%)6%(,04)/.%5)&$%()*+,-$.%,5&%90,5'#%'/00$5+.%,0$%2*)++$&!%=5%+#4. $C,12*$:%Q0)9$%>+#$%-0,2#4',*%45+$06,'$%)6%QN24'$?%4.%/+4*4T$&%+)%')12/+$%(,04)/.%2);$03&4..42,+4)5%(,*/$.! N)1$%)6%+#$%0$./*+45-%;,($6)01.%,0$%&4.2*,<$&%45%@4-! A!HW!%"#$%/22$0%,5&%14&&*$%-0,2#.%.#);%+#$ *),&%()*+,-$%,5&%'/00$5+:%0$.2$'+4($*
A)%78'#,(D%/(%"&1(%,.(&0(*%?G!%'&.0$%4-.%0"($(%'-/(.%0.&)$#$0-.$%=&$(*%-)%0"(%1&:5($%-4%0"(%87ABC%3-*(:%'&< .&3(0(.$%&1&#:&=:(%-)%0"(%*&0&%$"((0$%&1&#:&=:(%4.-3%EZ%8(3#,-)*5,0-.;%P(&*(.$%,&)%4#)*%0"($(%'&.0$%R:&=(:(* n9GCHUJ%&)*%n9GCHdJS%#)%0"(%8CKPN;-:=%:#=.&.2D%/"#,"%#$%&1&#:&=:(%-)%0"(%BK%&,,-3'&)2#)6%0"#$%=--L;

B.2 PSpice Examples

VCC PARAMETERS: RL # 8 VCC # 23

VCC QN QMJE243

" {VCC} ! " {VCC} !

IN

0

VOFF # 0 VAMPL # 17.9 FREQ # 1K

" !

OUT QMJE253

Vin QP

0

!VCC

{RL} 0

!VCC

Figure B.37 B&'05.(%$,"(3&0#,%-4%0"(%,:&$$%?%-50'50%$0&6(%#)%C+&3':(%78;@@;@;

20 V 0V !20 V

V (OUT)

4.0 A 0A !4.0 A

I (RL)

40 W 20 W 0W

0

0.5 I (RL) *V (OUT)

1.0 1.5 AVG (I (RL) *V (OUT))

2.0

2.5

3.0

Time (ms)

Figure B.38 8(1(.&:%/&1(4-.3$%&$$-,#&0(*%/#0"%0"(%,:&$$%?%-50'50%$0&6(%R$"-/)%#)%F#6;%?;JTS%/"()%(+,#0(*%=2%& @T;f<[D%@
-0,2#%&4.2*,<.%+#$%45.+,5+,5$)/.%,5&%+#$%,($0,-$%2);$0%&4..42,+$&%45%+#$%*),&%0$.4.+,5'$%,.%')12/+$& /.45-% Q0)9$% 9<% 1/*+42*<45-% +#$% ()*+,-$% ,5&% '/00$5+% (,*/$.% +)% )9+,45% +#$% 45.+,5+,5$)/.% 2);$0:% ,5& +,S45-%,%0/5545-%,($0,-$%6)0%+#$%,($0,-$%*),&%2);$0%O?!%"#$%+0,5.4$5+%9$#,(4)0%)6%+#$%,($0,-$%*),& 2);$0:%;#4'#%$($5+/,**<%.$++*$.%45+)%,%B/,.4')5.+,5+%.+$,&<%.+,+$%)6%,9)/+%7`!M%a:%4.%,5%,0+46,'+%)6%+#$ QN24'$%,*-)04+#1%/.$&%+)%')12/+$%+#$%0/5545-%,($0,-$%)6%,%;,($6)01! "#$%/22$0%+;)%-0,2#.%)6%@4-!%A!Hb%.#);%+#$%()*+,-$%,5&%'/00$5+%;,($6)01.:%0$.2$'+4($*<:%)6%+#$%2).3 4+4($% ./22*<:% "00L1 "#$% 9)++)1% -0,2#% .#);.% +#$% 45.+,5+,5$)/.% ,5&% ,($0,-$% 2);$0% ./22*4$&% 9<% "00 !

B-51

B-52 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.11.1 continued

40 V 20 V 0V 4.0 A

V ("VCC)

2.0 A 0A

!I ("VCC)

50 W 25 W 0W

0

0.5 1.0 !I ("VCC) *V ("VCC)

1.5 2.0 2.5 AVG (!I ("VCC) *V ("VCC))

3.0

Time (ms) Figure B.39 !"(% 1-:0&6(% R5''(.% 6.&'"SD% ,5..()0% R3#**:(% 6.&'"SD% &)*% #)$0&)0&)(-5$% &)*% &1(.&6(% '-/(.% R=-00-3 6.&'"S%$5'':#(*%=2%0"(%'-$#0#1(%1-:0&6(%$5'':2%R "00S%#)%0"(%,#.,5#0%-4%F#6;%?;JT;

N414*,0%;,($6)01.%',5%9$%2*)++$&%6)0%+#$%5$-,+4($%./22*<:% "00 L1"#$%,($0,-$%2);$0%20)(4&$&%9<%$,'# ./22*<%4.%6)/5&%+)%9$%,9)/+%7\%a:%6)0%,%+)+,*%./22*<%2);$0%O$%)6%HD%a!%"#/.:%+#$%2);$03')5($0.4)5%$6643 '4$5'<%',5%9$%')12/+$&%+)%9$ O? O$

@T;g <<<<<<<<<< JO

@OOk

d^;gk

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p*#'q%#)%0"(%'-/(.%/&1(4-.3%1&)#$"($;%!"(%&1(.&6(%'-/(.%*#$$#'&0(*%#)%(&,"%-4%WB%&)* WO%,&)%=(%,-3'50(*%=2%7.-=(%&)*%&.(%4-5)*%0-%=(%&''.-+#3&0(:2%g%_; !&=:(%?;@@%'.-1#*($%&%,-3'&.#$-)%-4%0"(%.($5:0$%4-5)*%4.-3%0"(%78'#,(%$#35:&0#-)%&)*%0"(%,-..($'-)*#)6 1&:5($%-=0&#)(*%5$#)6%"&)*%&)&:2$#$%#)%C+&3':(%@J;@;%E=$(.1(%0"&0%0"(%0/-%$(0$%-4%.($5:0$%&.(%M5#0(%,:-$(; !-%#)1($0#6&0(%0"(%,.-$$-1(.%*#$0-.0#-)%45.0"(.D%/(%'.($()0%#)%F#6; ?;U@%&%':-0%-4%0"(%1-:0&6(%0.&)$4(. ,"&.&,0(.#$0#,%R[!BS%-4%0"(%,:&$$%?%-50'50%$0&6(;%!"#$%':-0%#$%-=0&#)(*%0".-56"%&%*,<&)&:2$#$%$#35:&0#-) /#0"%vAZ%$/('0%-1(.%0"(%.&)6(% @O%[%0-% @O%[%#)%@;O<3[%#),.(3()0$;%Y$#)6%7.-=(D%/(%*(0(.3#)(%0"&0%0"( $:-'(%-4%0"(%[!B%#$%)(&.:2%5)#02%&)*%0"&0%0"(%*(&*%=&)*%(+0()*$%4.-3% O;gO [%0-% O;d^%[;%!"(%(44(,0%-4 0"(%,.-$$-1(.%*#$0-.0#-)%,&)%=(%M5&)0#4#(*%=2%'(.4-.3#)6%&%F-5.#(.%&)&:2$#$%-)%0"(%-50'50%1-:0&6(%/&1(< 4-.3%#)%78'#,(;%!"#$%&)&:2$#$%*(,-3'-$($%0"(%/&1(4-.3%6()(.&0(*%0".-56"%&%0.&)$#()0%&)&:2$#$%#)0-%#0$

B.2 PSpice Examples

0V !20 V !40 V

V (QP:C) ! V (QP:E)

0A !2.0 A !4.0 A

IC (QP)

20 W 10 W 0W

0

0.5 1.0 IC (QP) * (V (QP:C) ! V (QP:E))

1.5 2.0 2.5 3.0 AVG (IC (QP) * (V (QP:C) ! V (QP:E)))

Time (ms) Figure B.40 _&1(4-.3$%-4%0"(%1-:0&6(%&,.-$$D%0"(%,5..()0%0".-56"D%&)*%0"(%'-/(.%*#$$#'&0(*%#)%0"(%636%0.&)$#$0-. WO%-4%0"(%-50'50%$0&6(%$"-/)%#)%F#6;%?;JT;

Table B.11 Various Power Terms Associated with the Class B Output Stage Shown in Fig. B.37 as Computed by Hand and by PSpice Analysis 7-/(.aC44#,#(),2

%% CM5&0#-)

V&)*%N)&:2$#$ RC+&3':(%78;@@;@S

H "r2 '?

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%%%%%%%%%%% <<< <<<<<< " 00

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2 2 %%%%%%%%%%% <<< <<<<<< " 00 P <<< <<<<<<<<

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%%%%%%%%%%%%JO;O%_

%%%%%%%%%%%%%%%U

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%%%%%%%%%%%%%%%U;g

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P(:&0#1(%'(.,()0&6(%(..-.%=(0/(()%0"(%1&:5($%'.(*#,0(*%=2%"&)*%&)*%=2%78'#,(;

F-5.#(.<$(.#($%,-3'-)()0$;%F5.0"(.D%78'#,(%,-3'50($%0"(%0-0&:%"&.3-)#,%*#$0-.0#-)%R!VKS%-4%0"(%-50'50 /&1(4-.3;%!"(%.($5:0$%-=0&#)(*%4.-3%0"(%$#35:&0#-)%-50'50%4#:(%&.(%$"-/)%-)%0"(%)(+0%'&6(;% !"($(%F-5.#(.%,-3'-)()0$%&.(%5$(*%0-%':-0%0"(%:#)(%$'(,0.53%$"-/)%#)%F#6; ?;UH;%_(%)-0(%0"&0%0"(%-50< '50%/&1(4-.3%#$%.&0"(.%.#,"%#)%-**%"&.3-)#,$%&)*%0"&0%0"(%.($5:0#)6%!VK%#$%.&0"(.%"#6"%RH;@UkS;

B-53

B-54 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.11.1 continued

10 V

5V

0V

!5 V

!10 V !10

V (OUT)

0

!5

5

10

V_Vin (V)

Figure B.41 !.&)$4(.%,"&.&,0(.#$0#,%-4%0"(%,:&$$%?%-50'50%$0&6(%-4%F#6;%?;JT;

FOURIER COMPONENTS OF TRANSIENT RESPONSE V(OUT) DC COMPONENT = -1.525229E-02 HARMONIC NO 1 2 3 4 5 6 7 8 9 10

FREQUENCY (HZ) 1.000E+03 2.000E+03 3.000E+03 4.000E+03 5.000E+03 6.000E+03 7.000E+03 8.000E+03 9.000E+03 1.000E+04

FOURIER COMPONENT 1.674E+01 9.088E-03 2.747E-01 4.074E-03 1.739E-01 5.833E-04 1.195E-01 5.750E-04 9.090E-02 3.243E-04

NORMALIZED COMPONENT 1.000E+00 5.428E-04 1.641E-02 2.433E-04 1.039E-02 3.484E-05 7.140E-03 3.435E-05 5.429E-03 1.937E-05

PHASE (DEG)

NORMALIZED PHASE (DEG)

-2.292E-03 9.044E+01 -1.799E+02 9.035E+01 -1.799E+02 9.159E+01 -1.800E+02 9.128E+01 -1.800E+02 9.120E+01

0.000E+00 9.044E+01 -1.799E+02 9.036E+01 -1.799E+02 9.161E+01 -1.799E+02 9.129E+01 -1.799E+02 9.122E+01

TOTAL HARMONIC DISTORTION = 2.140017E+00 PERCENT

B.2 PSpice Examples

0 Normalized Magnitude [dB]

!10 !20 !30 !40 !50 !60 !70 !80 !90 1

2

3

4

5 6 7 Frequency [kHz]

8

9

10

Figure B.42 F-5.#(.<$(.#($%,-3'-)()0$%-4%0"(%-50'50%/&1(4-.3%-4%0"(%,:&$$%?%-50'50%$0&6(%#)%F#6;%?;JT;

Example PS.12.1 Frequency Compensation of the Two-Stage CMOS Op Amp =5% +#4.% $C,12*$:% ;$% ;4**% /.$% QN24'$% +)% ,4&% 45% &$.4-545-% +#$% 60$B/$5'<% ')12$5.,+4)5% )6% +#$% +;)3.+,-$ EF[N%'40'/4+%;#).$%',2+/0$%.'#$1,+4'%4.%.#);5%45%@4-!%A!LH!%QN24'$%;4**%+#$5%9$%$12*)<$&%+)%&$+$0145$ +#$%60$B/$5'<%0$.2)5.$%,5&%+#$%.*$;%0,+$%)6%+#$%)2%,12!%a$%;4**%,../1$%,%D!\3 1%33;$**%EF[N%+$'#5)*3 )-<%6)0%+#$%F[N@K".%,5&%;4**%/.$%+#$%NQ=EK%*$($*37%1)&$*%2,0,1$+$0.%*4.+$&%45%",9*$%A!L!%[9.$0($%+#,+ +)%$*4145,+$%+#$%9)&<%$66$'+%,5&%4120)($%+#$%1,+'#45-%9$+;$$5%P7%,5&%P8:%+#$%.)/0'$%+$0145,*.%)6%+#$ 452/+%QF[N%+0,5.4.+)0.%P7%,5&%P8%,0$%')55$'+$&%+)%+#$40%3%;$**! "#$%)23,12%'40'/4+%45%@4-!%A!LH%4.%&$.4-5$&%/.45-%,%0$6$0$5'$%'/00$5+%%GK@% %bD% O:%,%./22*<%()*+,-$%"44 1 H!H%I:%,5&%,%*),&%',2,'4+)0%0?% %7%2@!%d54+3.4T$%+0,5.4.+)0.%;4+#% @ ? %@;Hd% 3 %O;g% 3 %,0$%/.$&%6)0%9)+# +#$%VF[N%,5&%QF[N%&$(4'$.!%"#$%+0,5.4.+)0.%,0$%.4T$&%6)0%,5%)($0&04($%()*+,-$ "#" O;J%[;% %"#$%')03 0$.2)5&45-%1/*+42*4',+4($%6,'+)0.%,0$%-4($5%45%@4-! A!LH! =5%QN24'$:%+#$%')11)531)&$%452/+%()*+,-$%"0P%)6%+#$%)23,12%'40'/4+%4.%.$+%+)% "44 H %Z%7!M\%I!%O%94,.3 2)45+%.41/*,+4)5%4.%2$06)01$&%+)%&$+$0145$%+#$%&'%)2$0,+45-%2)45+!%d.45-%+#$%(,*/$.%6)/5&%45%+#$%.41/*,3 +4)5%)/+2/+%64*$%6)0%+#$%.1,**3.4-5,*%2,0,1$+$0.%)6%+#$%F[N@K".:%;$%)9+,457L

@U P(,&::%0"&0%S*@%&)*%S*H%&.(%0"(%0.&)$,-)*5,0&),($%-4D%.($'(,0#1(:2D%0"(%4#.$0%&)*%$(,-)*%$0&6($%-4%0"(%-'%&3'; B&'&,#0-.$%0@%&)*%0H%.('.($()0%0"(%0-0&:%,&'&,#0&),(%0-%6.-5)*%&0%0"(%-50'50%)-*($%-4D%.($'(,0#1(:2D%0"(%4#.$0%&)* $(,-)*%$0&6($%-4%0"(%-'%&3';

B-55

!

"

0

d

0

{VCM} !

" d

d " !

INP

En " " !

INN

0

! GAIN # 0.5

0

! GAIN # 0.5

"

Ep

M8

0

Iref

0

VDD

!

" {VDD} !

{Iref}

"

M # {M8} W # 1.25u L # 0.6u

VDD

M1

M # {M3} W # 1.25u L # 0.6u

INN

Figure B.43 8,"(3&0#,%,&'05.(%-4%0"(%0/-<$0&6(%B9E8%-'%&3'%#)%C+&3':(%78;@H;@

1Vac 0Vdc

Vd

VCM # 1.65 VDD # 3.3

R # 1.53K

M1 # 8 M2 # 8 M3 # 2 M4 # 2 M5 # 16 M6 # 4 M7 # 16 M8 # 16

Iref # 90u

PARAMETERS: Cc # 0.6p Cload # 1p

Example PS.12.1 continued

0

M3

M # {M1} W # 1.25u L # 0.6u

M5

M4

M # {M2} W # 1.25u L # 0.6u

M # {M5} W # 1.25u L # 0.6u

VDD

INP

0

M # {M4} W # 1.25u L # 0.6u

A

{R}

M2

M6

{Cc}

M7

0

M # {M6} W # 1.25u L # 0.6u

M # {M7} W # 1.25u L # 0.6u

VDD

0

{Cload}

OUT

B-56 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

B.2 PSpice Examples

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S *@ <<<<<<<<<<<<< H 00

%>A!L\?

d.45-%KB.!%>A!LL?%,5&%>A!L\?:%;$%&$+$0145$%+#,+%')12$5.,+4)5%',2,'4+)0.%)6%00% %D!`W%2@%,5&%00% %8%2@ ,0$%0$B/40$&%+)%,'#4$($%2#,.$%1,0-45.%)6%QF% %\\ %,5&%QF% %`\ :%0$.2$'+4($*00% %D?!%[9.$0($%+#,+%+#$%/54+<%-,45%60$B/$5'<%-/%&0)2.%60)1%`D!8%FYT%+)%8M!L FYT%,.%00%4.%45'0$,.$&%+)%4120)($%QF%>,.%,5+4'42,+$&%60)1%KB!%A!L\?! G,+#$0% +#,5% 45'0$,.45-% +#$% ')12$5.,+4)5% ',2,'4+)0% 00:% +#$% (,*/$% )6% +#$% .$04$.% 0$.4.+)0% '% ',5% 9$ 45'0$,.$&%+)%4120)($%+#$%2#,.$%1,0-45%QFe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`\ ! =5'0$,.45-%+#$%QF%4.%&$.40,9*$%9$',/.$%4+%0$&/'$.%+#$%)($0.#))+%45%+#$%.+$2%0$.2)5.$%)6%+#$%)2 ,12!%") ($046<%+#4.%2)45+:%;$%.41/*,+$%45%QN24'$%+#$%.+$2%0$.2)5.$%)6%+#$%)2%,12%6)0%QF% %\\ %,5&%QF% %`\ !%") &)%+#,+:%;$%')55$'+%+#$%)2%,12%45%,%/54+<3-,45%')564-/0,+4)5:%,22*<%,%.1,**%>7D31I?%2/*.$%.4-5,*%,+%+#$ 452/+%;4+#%($0<%.#)0+%>732.?%04.$%,5&%6,**%+41$.%+)%$1/*,+$%,%.+$2%452/+:%2$06)01%,%+0,5.4$5+3,5,*<.4.%.41/3 *,+4)5:%,5&%2*)+%+#$%)/+2/+%()*+,-$%,.%.#);5%45%@4-!%A!L`!%[9.$0($%+#,+%+#$%)($0.#))+%45%+#$%.+$2%0$.2)5.$ &0)2.%60)1%7\h%+)%7!Lh%;#$5%+#$%2#,.$%1,0-45%4.%45'0$,.$&%60)1%\\ %+)%`\ ! a$%')5'*/&$%+#4.%$C,12*$%9<%')12/+45-%$':%+#$%.*$;%0,+$%)6%+#$%)2%,12!%@0)1%KB!%>7D!LD?: $'

H -/ "#"

S *@ <<<<<<<<< "#" 00

@gg;d [a $

B-57

B-58 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.12.1 continued 75 CC # 0 50 25

CC # 0.6 pF

0 !25 dB (V (OUT)) 0d

CC # 0

!45d !90d CC # 0.6 pF !135d PM # 55 !180d 1.0

10 100 P (V (OUT))

1.0 K

10 K

100 K 1.0 M

10 M

100 M 1.0 G

Frequency (Hz)

Figure B.44 9&6)#05*(%&)*%'"&$(%.($'-)$(%-4%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;UJ>%'% %@;dJ%L D%00% %O%R)- 4.(M5(),2% ,-3'()$&0#-)SD%&)*%00% %O;g%'F%R79% %dd S; 75 CC # 0 50 25

CC # 1.8 pF

0 !25 dB (V (OUT)) 0d

CC # 0

!45d !90d CC # 1.8 pF !135d !180d 1.0

PM # 75 10 100 P (V (OUT))

1.0 K

10 K

100 K 1.0 M

10 M

100 M 1.0 G

Frequency (Hz)

Figure B.45 9&6)#05*(%&)*%'"&$(%.($'-)$(%-4%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;UJ>%'% %@;dJ%L D%00% %O%R)-%4.(M5(),2% ,-3'()$&0#-)SD%&)*%00% %@;^%'F%R79% %Td S;

B.2 PSpice Examples

75 50 25 R # 3.2 kΩ 0 R # 1.53 kΩ !25 dB (V (OUT)) 0d !45d R # 3.2 kΩ !90d !135d !180d 1.0

R # 1.53 kΩ 10 100 P (V (OUT))

1.0 K

10 K

100 K 1.0 M

10 M

100 M 1.0 G

Frequency (Hz)

Figure B.46 9&6)#05*(%&)*%'"&$(%.($'-)$(%-4%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;UJ>%00% %O;g%'FD%'% %@;dJ%L %R79% dd SD%&)*%'% %J;H%L %R79% %Td S; 1.660 V PM # 55 1.656 V PM # 75 1.652 V

1.648 V PM # 75 PM # 55

1.644 V 150

200 V (OUT)

250

300

350

Time (ns)

Figure B.47 83&::<$#6)&:%$0('%.($'-)$(%R4-.%&%@O<3[%$0('%#)'50S%-4%0"(%-'<&3'%,#.,5#0%#)%F#6;%?;UJ%,-))(,0(*%#)%& 5)#02<6&#)%,-)4#65.&0#-)>%79% %dd %R00% %O;g%'FD%'% %@;dJ%L S%&)*%79% %Td %R00% %O;g%'FD%'% %J;H%L S;

;#$5%00% %D!M%2@!%V$C+:%+)%&$+$0145$%$'%/.45-%QN24'$%>.$$%KC,12*$%QN!8!8?:%;$%,-,45%')55$'+%+#$%)2 ,12%45%,%/54+<3-,45%')564-/0,+4)5%,5&%2$06)01%,%+0,5.4$5+3,5,*<.4.%.41/*,+4)5!%Y);$($0:%;$%5);%,22*<

B-59

B-60 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.12.1 continued 4.0 V Slope # !160 V/us

Slope # 60 V/us

3.0 V

2.0 V

1.0 V

0V !0.5 V

0

50 V (IN)

100 V (OUT)

150

200

250

300

350

400

Time (ns)

Figure B.48 Q&.6(<$#6)&:% $0('% .($'-)$(% R4-.% &% J;J<[% $0('<#)'50S% -4% 0"(% -'<&3'% ,#.,5#0% #)% F#6;% ?;UJ% ,-))(,0(*% #)% & 5)#02<6&#)%,-)4#65.&0#-);%!"(%$:-'(%-4%0"(%.#$#)6%&)*%4&::#)6%(*6($%-4%0"(%-50'50%/&1(4-.3%,-..($'-)*%0-%0"(%$:(/%.&0(%-4 0"(%-'%&3';

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

Example PS.13.1 Operation of the CMOS Inverter =5%+#4.%$C,12*$:%;$%;4**%/.$%QN24'$%+)%.41/*,+$%+#$%EF[N%45($0+$0%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45 @4-:%A!Lb!%a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a$%;4**%.41/*,+$%+#$%45($0+$0%6)0%+;)%',.$.e%>,?%.$++45-% *6 * 3 @ %.)%+#,+%+#$ VF[N%,5&%QF[N%+0,5.4.+)0.%#,($%$B/,*%;4&+#.:%,5&%>9?%.$++45-% *6 *3 U %.)%+#,+%+#$%QF[N 3 6 +0,5.4.+)0%4.%6)/0%+41$.%;4&$0%+#,5%+#$%VF[N%+0,5.4.+)0%>+)%')12$5.,+$%6)0%+#$%*);$0%1)94*4+<%45%63'#,53 5$*%&$(4'$.%,.%')12,0$&%;4+#%33'#,55$*%)5$.?!%Y$0$:%*31,5&1*6%,0$%+#$%1/*+42*4',+4($%6,'+)0.%)6:%0$.2$'3 +4($*<:%+#$%VF[N%,5&%QF[N%+0,5.4.+)0.%)6%+#$%45($0+$0!

B.2 PSpice Examples

VDD

PARAMETERS: CL # 0.5p MN # 1 MP # 1

M # {MP} W # 1.25u L # 0.5u

VDD # 3.3

PMOS0P5

VDD

"

OUT

IN

Vsupply DC # {VDD}

!

V1 # 0 V2 # {VDD} TD # 2n TR # 1p TF # 1p PW # 6n PER # 12n

0

M # {MN} W # 1.25u L # 0.5u

" !

{CL}

NMOS0P5

0

0

0

Figure B.49 8,"(3&0#,%,&'05.(%-4%0"(%B9E8%#)1(.0(.%#)%C+&3':(%78;@J;@;

!-%,-3'50(%=-0"%0"(%1-:0&6(%0.&)$4(.%,"&.&,0(.#$0#,%R[!BS%-4%0"(%#)1(.0(.%&)*%#0$%$5'':2%,5..()0%&0%1&.< #-5$%1&:5($%-4%0"(%#)'50%1-:0&6(%"#)D%/(%&'':2%&%*,%1-:0&6(%$-5.,(%&0%0"(%#)'50%&)*%'(.4-.3%&%*,%&)&:2$#$ /#0"%"#)%$/('0%-1(.%0"(%.&)6(%-4%O%0-%"44;%!"(%.($5:0#)6%[!B%#$%':-00(*%#)%F#6;%?;dO;%Z-0(%0"&0%0"(%$:-'(%-4 0"(%[!B%#)%0"(%$/#0,"#)6%.(6#-)%R/"(.(%=-0"%0"(%Z9E8%&)*%79E8%*(1#,($%&.(%#)%$&05.&0#-)S%#$%)-0%#)4#< )#0(%&$%'.(*#,0(*%4.-3%0"(%$#3':(%0"(-.2%'.($()0(*%#)%B"&'0(.%@U%R8(,0#-)%@U;HD%F#6;%@U;HOS;%P&0"(.D%0"( )-)I(.-%1&:5(%-4% %,&5$($%0"(%#)1(.0(.%6&#)%0-%=(%4#)#0(;%Y$#)6%0"(%*(.#1&0#1(%4(&05.(%-4%7.-=(D%/(%,&)%4#)* 0"(%0/-%'-#)0$%-)%0"(%[!B%&0%/"#,"%0"(%#)1(.0(.%6&#)%#$%5)#02%R#;(;D%0"(%[!B%$:-'(%#$% @%[a[S%&)*D%"(),(D *(0(.3#)(%"%?%&)*%"%V;%Y$#)6%0"(%.($5:0$%6#1()%#)%F#6;%?;dOD%0"(%,-..($'-)*#)6%)-#$(%3&.6#)$%&.(%BP?% BPV% %@;JU%[%4-.%0"(%#)1(.0(.%/#0"% *6 *3 U D%/"#:(%BP?% %O;fTd%[%&)*%BPV% %@;TU%[%4-.%0"(%#)1(.0(. /#0"% *6 *3 @ ;%E=$(.1(%0"&0%0"($(%.($5:0$%,-..(:&0(%.(&$-)&=:2%/(::%/#0"%0"(%1&:5($%-=0&#)(*%5$#)6%0"( &''.-+#3&0(%4-.35:&%#)%CM;%R@U;d^S;%F5.0"(.3-.(D%)-0(%0"&0%/#0"% *6 *3 % 3 6 U D%0"(%Z9E8%&)* 79E8%*(1#,($%&.(%,:-$(:2%3&0,"(*%&)*D%"(),(D%0"(%0/-%)-#$(%3&.6#)$%&.(%(M5&:; "#$%+#0$.#)*&%()*+,-$% "P %)6%+#$%EF[N%45($0+$0%4.%&$645$&%,.%+#$%452/+%()*+,-$%v=V%+#,+%0$./*+.%45%,5 4&$5+4',*%)/+2/+%()*+,-$%v[d":%+#,+%4.: "P

v AZ

v EY!

v AZ

%

%>A!LM?

"#/.:%,.%.#);5%45%@4-!%A!\7:%"P%4.%+#$%45+$0.$'+4)5%)6%+#$%I"E:%;4+#%+#$%.+0,4-#+%*45$%')00$.2)5&45-%+)%v[d" v=V%>+#4.%*45$%',5%9$%.412*<%-$5$0,+$&%45%Q0)9$%9<%2*)++45-%v =V%($0./.%v[d":%,.%.#);5%45%%%@4-!%A!\7?!%V)+$ +#,+% "P $ "44 H %6)0%+#$%45($0+$0%;4+#% *6 * 3 U !%@/0+#$01)0$:%&$'0$,.45-% *6 *3 %&$'0$,.$.% "P ! @4-/0$%A!\7%,*.)%.#);.%+#$%45($0+$0%./22*<%'/00$5+%($0./.% v=V!%[9.$0($%+#,+%+#$%*)',+4)5%)6%+#$%./22*<3 '/00$5+%2$,S%.#46+.%;4+#%+#$%+#0$.#)*&%()*+,-$!

B-61

B-62 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.13.1 continued 3.3 V

VIL # 0.975 V

VIL # 1.34 V

2.475 V

mp"mn # 1

1.65 V

mp"mn # 4

0.825 V

VIH # 1.96 V

VIH # 1.56 V 0V 0V

0.825 V

1.65 V

V (OUT)

2.475 V

3.3 V

V (IN)

Figure B.50 A)'50c-50'50% 1-:0&6(% 0.&)$4(.% ,"&.&,0(.#$0#,% R[!BS% -4% 0"(% B9E8% #)1(.0(.% #)% C+&3':(% 78;@J;@% /#0" *6 * 3 @ %&)*% *6 * 3 U ;

3.3 V mp"mn # 1

2.475 V

mp"mn # 4 VM # 1.64 V

1.65 V

VM # 1.35 V

0.825 V 0V V (OUT)

V (IN) (a)

Figure B.51 4"5% E50'50% 1-:0&6(% &)*% 4J5% $5'':2% ,5..()0% 1(.$5$% #)'50% 1-:0&6(% 4-.% 0"(% B9E8% #)1(.0(.% #)% C+&3':( 78;@J;@%/#0"% *6 * 3 @ %&)*% *6 * 3 U ;%

B.2 PSpice Examples

400 uA

mp"mn # 4 200 uA

mp"mn # 1 0A 0V

0.825 V !I (Vsupply)

1.650 V

2.475 V

3.3 V

V (IN) (b)

Figure B.51 R023/!LS 3.3 V 2.475 V 1.65 V 0.825 V 0V V (IN) 3.3 V mp"mn # 4

mp"mn # 1

2.475 V tPHL # 0.34 ns 1.65 V tPLH # 0.29 ns

tPLH # 1.13 ns

0.825 V 0V

0

2n V (OUT)

4n

6n

8n

10 n

12 n

14 n

Time (s)

Figure B.52 !.&)$#()0%.($'-)$(%-4%0"(%B9E8%#)1(.0(.%#)%C+&3':(%78;@J;@%/#0"% *6 * 3

@ %&)*% *6 * 3

%U ;

")%45($.+4-,+$%+#$%&<5,14'%)2$0,+4)5%)6%+#$%45($0+$0%;4+#%QN24'$:%;$%,22*<%,%2/*.$%.4-5,*%,+%+#$ 452/+%>@4-!%A!Lb?:%2$06)01%,%+0,5.4$5+%,5,*<.4.:%,5&%2*)+%+#$%452/+%,5&%)/+2/+%;,($6)01.%,.%.#);5%45 @4-!%A!\8!%"#$%04.$%,5&%6,**%+41$.%)6%+#$%2/*.$%.)/0'$%,0$%'#).$5%+)%9$%($0<%.#)0+!%V)+$%+#,+%45'0$,.45*6 * 3 %60)1%7%+)%L%&$'0$,.$.%/O?V%>60)1%7!7H%5.%+)%D!8b%5.?%9$',/.$%)6%+#$%45'0$,.$&%'/00$5+%,(,4*,9*$ +)%'#,0-$%0?:%;4+#%)5*<%,%145)0%45'0$,.$%45%/OV?%>60)1%D!HH 5.%+)%D!HL%5.?!%"#$%+;)%20)2,-,+4)5%&$*,<.: /O?V%,5&%/OV?:%,0$%5)+%$C,'+*<%$B/,*%;#$5% *6 *3 U :%9$',/.$%+#$%VF[N%,5&%QF[N%+0,5.4.+)0.%,0$%.+4** 5)+%2$06$'+*<%1,+'#$&%>$!-!:% " /3 " /6 ?;

B-63

B-64 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.14.1 Static and Dynamic Operation of an ECL Gate =5%+#4.%$C,12*$:%;$%/.$%QN24'$%+)%45($.+4-,+$%+#$%.+,+4'%,5&%&<5,14'%)2$0,+4)5%)6%+#$%KE_%-,+$%>.+/&3 4$&%45%N$'+4)5%7\!L?%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45%@4-!%A!\H!%%%% Y,(45-%5)%,''$..%+)%+#$%,'+/,*%(,*/$.%6)0%+#$%NQ=EK%1)&$*%2,0,1$+$0.%)6%+#$%Af".%/+4*4T$&%45%')13 1$0'4,**<%,(,4*,9*$%KE_:%;$%#,($%.$*$'+$&%2,0,1$+$0%(,*/$.%0$20$.$5+,+4($%)6%+#$%+$'#5)*)-<%/+4*4T$&%+#,+: 60)1%)/0%$C2$04$5'$:%;)/*&%*$,&%+)%0$,.)5,9*$%,-0$$1$5+%9$+;$$5%.41/*,+4)5%0$./*+.%,5&%+#$%1$,./0$& 0

PARAMETERS: R1 # 907 R2 # 4.98K R3 # 6.1K Ra # 50K Rb # 50K Rc1 # 220 Rc2 # 245 Re # 779

{Rc1}

{R1}

{Rc2} QOR QNOR

OR

Q1

NOR A

QA

QB

Q2

QR

B

Q3

R {Ra}

{Rb}

{Re}

{R3}

{R2}

VEE Logic Circuit

Reference-Voltage Circuit

Figure B.53 8,"(3&0#,%,&'05.(%-4%0"(%0/-<#)'50%CBQ%6&0(%4-.%C+&3':(%78;@U;@

NOR

A NOR B vA " ! VOL # !1.77 V

" !

OR VEE

OR

v NOR

vOR

RT2 # 50 )

RT1 # 50 )

VEE2 # !2.0 V VEE1 # !5.2 V

Figure B.54 B#.,5#0%&..&)6(3()0%4-.%,-3'50#)6%0"(%1-:0&6(%0.&)$4(.%,"&.&,0(.#$0#,$%-4%0"(%CBQ%6&0(%#)%F#6;%?;dJ;

B.2 PSpice Examples

2$06)01,5'$% &,+,% ./22*4$&% 9<% +#$% 1,5/6,'+/0$0!% =+% .#)/*&% 9$% 5)+$&% +#,+% +#4.% 20)9*$1% ;)/*&% 5)+% 9$ $5')/5+$0$&%9<%,5%=E%&$.4-5$0%/.45-%NQ=EK%,.%,5%,4&R%20$./1,9*<:%+#$%&$.4-5$0%;)/*&%#,($%6/**%,''$..%+) +#$%20)204$+,0<%20)'$..%2,0,1$+$0.%,5&%+#$%')00$.2)5&45-%&$(4'$%1)&$*%2,0,1$+$0.!%=5%,5<%',.$:%6)0%+#$ .41/*,+4)5.%;$%')5&/'+$&:%;$%#,($%/+4*4T$&%+#$%6)**);45-%Af"%1)&$*%2,0,1$+$0%(,*/$.7\e%%$% %D!8M%6O: Q% %7DDR% '% %7:% Q% %D!7%5.:%05E% %7%2@:%05)% %0 % %7!\%2@:%,5&% "+ % %7DD%I! a$%/.$%+#$%'40'/4+%,00,5-$1$5+%)6%@4-!%A!\L%+)%')12/+$%+#$%()*+,-$%+0,5.6$0%'#,0,'+$04.+4'.%)6%+#$%KE_ -,+$:%+#,+%4.:%v[G%,5&%vV[G%($0./.%v+:%;#$0$%v+%4.%+#$%452/+%()*+,-$%,+%+$0145,*%O!%@)0%+#4.%45($.+4-,+4)5:%+#$%)+#$0 452/+%4.%&$,'+4(,+$&%9<%,22*<45-%,%()*+,-$%v&% %"#?% 7!``%I!%=5%QN24'$:%;$%2$06)01%,%&'3,5,*<.4.%.41/*,3 +4)5%;4+#%v+%.;$2+%)($0%+#$%0,5-$% 8%I%+)%D%I%45%7D31I%45'0$1$5+.%,5&%2*)+%v[G%,5&%vV[G%($0./.%v+!%"#$%.41/3 *,+4)5% 0$./*+.% ,0$% .#);5% 45% @4-!% A!\\!% a$% 411$&4,+$*<% 0$')-54T$% +#$% I"E.% ,.% +#).$% ;$% #,($% .$$5% ,5& >2,0+4,** 7!H8%I?:%;#4'#%4.%,*.)%4&$5+4',*%+)%+#$%(,*/$%;$%&$+$0145$&%9<%#,5&%,5,*<.4.%)6%+#$%0$6$03 $5'$3()*+,-$%'40'/4+! d+4*4T45-% Q0)9$% >+#$% -0,2#4',*% 45+$06,'$% )6% QN24'$?:% )5$% ',5% &$+$0145$% +#$% (,*/$.% )6% +#$% 412)0+,5+ 2,0,1$+$0.%)6%+#$%I"E:%,.%6)**);.e [G%)/+2/+e "#?% % 7!``%I:%"#V% % D!WW%I:%"%?% % 7!L7%I:%,5&%"%V% % 7!88%IR%+#/.:% BPV% %D!HL%I%,5&%BP?% %D!HM%I V[G%)/+2/+e "#?% % 7!`W%I:%"#V% % D!WW%I:%"%?% % 7!L7%I:%,5&%"%V% % 7!88%IR%+#/.:% BPV% %D!HL%I%,5&%BP?% %D!H`%I !0.8 V !1.0 V !1.2 V

Reference voltage

!1.4 V !1.6 V

OR output

NOR output

!1.8 V !2.0 V !2.0 V v(NOR)

!1.5 V v(OR)

!1.0 V v(R)

!0.5 V

0.0 V

vA

Figure B.55 [-:0&6(%0.&)$4(.%,"&.&,0(.#$0#,$%-4%0"(%EP%&)*%ZEP%-50'50$%R$((%F#6;%?;dUS%4-.%0"(%CBQ%6&0(%$"-/)%#)% F#6;%?;dJ;%N:$-%#)*#,&0(*%#$%0"(%.(4(.(),(%1-:0&6(D%"'% % @;JH%[;

@d

A)%78'#,(D%/(%"&1(%,.(&0(*%&%'&.0%,&::(*%nCBQ%=&$(*%-)%0"($(%?G!%3-*(:%'&.&3(0(.%1&:5($;%P(&*(.$%,&)%4#)* 0"#$%'&.0%#)%0"(%8CKPN;-:=%:#=.&.2D%/"#,"%#$%&1&#:&=:(%-)%0"(%BK%&,,-3'&)2#)6%0"#$%=--L;

B-65

B-66 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.14.1 continued

"#$.$%(,*/$.%,0$%0$1,0S,9*<%'*).$%+)%+#).$%6)/5&%9<%2$5'4*3,5&32,2$0%,5,*<.4.%45%N$'+4)5%7\!L! a$% 5$C+% /.$% QN24'$% +)% 45($.+4-,+$% +#$% +$12$0,+/0$% &$2$5&$5'$% )6% +#$% +0,5.6$0% '#,0,'+$04.+4'.!% "#$ 0$,&$0%;4**%0$',**%+#,+%45%N$'+4)5%7\!L:%;$%&4.'/..$&%+#4.%2)45+%,+%.)1$%*$5-+#%,5&%',004$&%)/+%,%#,5&%,5,*<3 .4.%45%KC,12*$%7\!`!%Y$0$:%;$%/.$%QN24'$%+)%645&%+#$%()*+,-$%+0,5.6$0%'#,0,'+$04.+4'.%,+%+;)%+$12$0,+/0$.: D E%,5&%`D E%>+#$%I"E.%.#);5%45%@4-!%A!\\%;$0$%')12/+$&%,+%8` E?%6)0%+;)%&466$0$5+%',.$.e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a#$5%"'%4.%5)+%+$12$0,+/0$%&$2$5&$5+:%+#$%.<13 1$+0<%)6%"#?%,5&%"#V%,0)/5& "'%4.%5) *)5-$0%1,45+,45$&:%,.%&$1)5.+0,+$&%45%@4-!%A!\M>9?!%@45,**<:%;$%.#); .)1$%)6%+#$%(,*/$.%)9+,45$&%45%",9*$%A!78!%[9.$0($%+#,+%6)0%+#$%+$12$0,+/0$3')12$5.,+$&%',.$:%+#$%,($0,-$ (,*/$%)6%"#?%,5&%"#V%0$1,45.%($0<%'*).$%+)%"'!%"#$%0$,&$0%4.%$5')/0,-$&%+)%')12,0$%+#$.$%0$./*+.%+)%+#).$ )9+,45$&%45%KC,12*$%7\!L!% !0.8 V !1.0 V 70+C !1.2 V !1.4 V 0+C !1.6 V 70+C

70+C

!1.8 V 0+C !2.0 V !2.0 V v(NOR)

0+C !1.5 V v(OR)

!1.0 V v(R)

!0.5 V

0.0 V

vA (a)

Figure B.56 B-3'&.#)6%0"(%1-:0&6(%0.&)$4(.%,"&.&,0(.#$0#,$%-4%0"(%EP%&)*%ZEP%-50'50$%R$((%F#6;%?;dUS%-4%0"(%CBQ 6&0(%$"-/)%#)%F#6;%?;dJD%/#0"%0"(%.(4(.(),(%1-:0&6(%"'% 6()(.&0(*%5$#)6>%4"5%0"(%0(3'(.&05.(<,-3'()$&0(*%=#&$%)(0< /-.L%-4%F#6;%?;dJj%4J5%&%0(3'(.&05.(<#)*('()*()0%1-:0&6(%$-5.,(;

B.2 PSpice Examples

!0.8 V !1.0 V 0+C and 70+C

!1.2 V !1.4 V !1.6 V 70+C

70+C

!1.8 V 0+C

0+C

!2.0 V !2.0 V v(NOR)

!1.5 V v(OR)

!1.0 V v(R)

!0.5 V

0.0 V

vA (b)

Figure B.56 R023/!LS;

Table B.12 PSpice-Computed Parameter Values of the ECL Gate, With and Without Temperature Compensation, at Two Different Temperatures %%%%%%%%%%%%%%!(3'(.&05.(
%%%%7&.&3(0(.

O B

"&16

EP

ZEP

@;TTf%[ O;f@UH%[

@;Tff%[ O;fOfH%[

@;T^g%[ O;f@UH%[

@;Tff%[ O;fOfH%[

"#? "#V <<<<<<<<<<<<<<<<<<<<<<<< < H

@;JUgg%[

@;JdU@%[

@;JdO@%[

@;JdU@%[

@;JUd%[

@;JUd%[

@;JH%[

@;JH%[

%%@;g%3[

%%f;@%3[

JO;@%3[

JU;@%3[

" &16 P "'

"&16

%%%%%ZEP

"#? "#V

"'

TO B

EP

%%%%%Z-0%!(3'(.&05.(
"#? "#V

@;TUH%[ O;^JJ^%[

@;Tdf%[ O;^H^d%[

@;THf%[ O;^JJ^%[

@;Tdf%[ O;^H^d%[

"#? "#V <<<<<<<<<<<<<<<<<<<<<<<< < H

@;H^^%[

@;HfU%[

@;H^@U%[

@;HfU%[

@;HT@%[ @T%3[

@;HT@%[ HJ%3[

"'

"&16 P "'

@;JH%[ J^%3[

@;JH%[ Hg;H%3[

"#$%&<5,14'%)2$0,+4)5%)6%+#$%KE_%-,+$%4.%45($.+4-,+$&%/.45-%+#$%,00,5-$1$5+%)6%@4-!%A!\`!%Y$0$:%+;) -,+$.%,0$%')55$'+$&%9<%,%7!\31%'),C4,*%',9*$%#,(45-%,%'#,0,'+$04.+4'%412$&,5'$%>=D?%)6%\D !%"#$%1,5/6,'3 +/0$0%.2$'464$.%+#,+%.4-5,*.%20)2,-,+$%,*)5-%+#4.%',9*$%>;#$5%4+%4.%6726E78J1/E7*(3H/E!?%,+%,9)/+%#,*6%+#$%.2$$& )6%*4-#+:%)0%7\%'1J5.!%"#/.%;$%;)/*&%$C2$'+%+#$%7!\31%',9*$%;$%,0$%/.45-%+)%45+0)&/'$%,%&$*,<%/!%)6%7D%5.! [9.$0($% +#,+% 45% +#4.% '40'/4+% >@4-!% A!\`?:% 0$.4.+)0% '<7% 20)(4&$.% +#$% 20)2$0% ',9*$% +$0145,+4)5!% "#$% ',9*$% 4.

B-67

B-68 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.14.1 continued Transmission line 1.5 m IN

IN2

OUT1

OUT

Z0 # 50 ) td # 10 ns

v IN " ! VEE1 # !5.2 V

RT2 # 50 )

vOUT RT3 # 50 )

RT1 # 50 )

VEE1 # !5.2 V

VEE2 # !2 V

VEE2 # !2 V

RT4 # 50 )

VEE2 # !2 V

Figure B.57 B#.,5#0%&..&)6(3()0%4-.%#)1($0#6&0#)6%0"(%*2)&3#,%-'(.&0#-)%-4%CBQ;%!/-%CBQ%6&0($%RF#6; ?;dJS%&.( ,-))(,0(*%#)%,&$,&*(%1#&%&%@;d<3%,-&+#&:%,&=:(%/"#,"%"&$%&%,"&.&,0(.#$0#,%#3'(*&),(%=O% %dO% &)*%&%'.-'&6&0#-)%*(:&2 /!% %@O%)$;%P($#$0-.%'<@%RdO% S%'.-1#*($%'.-'(.%0(.3#)&0#-)%4-.%0"(%,-&+#&:%,&=:(;

!0.8 V !1.0 V v(IN2) !1.2 V

v(IN)

v(OUT)

v(OUT1)

!1.4 V !1.6 V !1.8 V !2.0 V

0 v(IN)

5 v(OUT1)

10 v(IN2)

15 v(OUT) Time (ns)

20

25

30

Figure B.58 !.&)$#()0%.($'-)$(%-4%&%,&$,&*(%-4%0/-%CBQ%6&0($%#)0(.,-))(,0(*%=2%&%@;d<3%,-&+#&:%,&=:(%"&1#)6%&% ,"&.&,0(.#$0#,%#3'(*&),(%-4%dO% %&)*%&%*(:&2%-4%@O%)$%R$((%F#6;%?;dTS;

,../1$&%+)%9$%*)..*$..%,5&%4.%1)&$*$&%45%QN24'$%/.45-%+#$%/7H3:*(::(2318(3E%$*$1$5+%>+#$%"%2,0+%45%+#$%O5,3 *)-%*490,0
B.2 PSpice Examples

!0.5 V

!1.0 V

!1.5 V

!2.0 V

0

v(IN)

50 100 150 v(OUT1) v(IN2)

200 v(OUT) Time (ns)

250

300

350

400

Figure B.59 !.&)$#()0%.($'-)$(%-4%&%,&$,&*(%-4%0/-%CBQ%6&0($%#)0(.,-))(,0(*%=2%&%@;d<3%,&=:(%"&1#)6%&%,"&.&,0(.< #$0#,%#3'(*&),(%-4%JOO% ;%!"(%0(.3#)&0#-)%.($#$0&),(%'<@%R$((%F#6;%?;dTS%/&$%L('0%5),"&)6(*%&0%dO% ;%Z-0(%0"(%,"&)6(% #)%0#3(%$,&:(%-4%0"(%':-0;

@45,**<:% +)% ($046<% +#$% 5$$&% 6)0% 20)2$0*<% +$0145,+45-% +#$% +0,5.14..4)5% *45$:% +#$% &<5,14'% ,5,*<.4.% 4. 0$2$,+$&:%+#4.%+41$%;4+#%+#$%\D3 %'),C4,*%',9*$%0$2*,'$&%;4+#%,%HDD3 %+;4.+$&32,40%',9*$%;#4*$%S$$245-%+#$ +$0145,+4)5%0$.4.+,5'$%/5'#,5-$&!%"#$%0$./*+.%,0$%+#$%.*);%04.45-%,5&%6,**45-%,5&%*)5-3&$*,<$&%;,($6)01. .#);5%45%@4-!%A!\b!%>V)+$%+#$%'#,5-$%)6%2*)++45-%.',*$!?

Example PS.16.1 Verification of the Design of a Fifth-Order Chebyshev Filter =5%+#4.%$C,12*$%;$%.#);%#);%NQ=EK%',5%9$%/+4*4T$&%+)%($046<%+#$%&$.4-5%)6%,%646+#3)0&$0%E#$9<.#$(%64*+$0! N2$'464',**<:%;$%.41/*,+$%+#$%)2$0,+4)5%)6%+#$%'40'/4+%;#).$%')12)5$5+%(,*/$.%;$0$%)9+,45$&%45%KC$0'4.$ 77!8D!% "#$% ')12*$+$% '40'/4+% 4.% .#);5% 45% @4-!% A!MD>,?!% =+% ')5.4.+.% )6% ,% ',.',&$% )6% +;)% .$')5&3)0&$0 .41/*,+$&3_EG%0$.)5,+)0.%/.45-%+#$%O5+)54)/%'40'/4+%,5&%,%640.+3)0&$0%)2%,12PGE%'40'/4+!%d.45-%QN24'$: ;$% ;)/*&% *4S$% +)% ')12,0$% +#$% 1,-54+/&$% )6% +#$% 64*+$0% 0$.2)5.$% ;4+#% +#,+% ')12/+$&% &40$'+*<% 60)1% 4+. +0,5.6$0% 6/5'+4)5!% Y$0$:% ;$% 5)+$% +#,+% QN24'$% ',5% ,*.)% 9$% /.$&% +)% 2$06)01% +#$% *,++$0% +,.S% 9<% /.45-% +#$ _,2*,'$%+0,5.6$036/5'+4)5%9*)'S%45%+#$%,5,*)-39$#,(4)0,*31)&$*45-%>OAF?%*490,0IEIN?%;4+#%, -,45%)6%7DM%IJI:%,.%.#);5%45%@4-!%A!MD>9?!7M @g

87ABC%3-*(:$%4-.%0"(%-'%&3'%&.(%*($,.#=(*%#)%8(,0#-)%?;@;@

B-69

B-70 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.16.1 continued

A11 " !

R51 10 k)

C41 R31 2.43 nF 10 k)

" !

Vin

R62 55.6 k)

C61 2.43 nF

A12 ! "

R22 10 k)

R52 10 k)

C42 R32 10 k) 1.6 nF

" ! A22

C62 1.6 nF

! A31 "

R61 14 k)

A21

R12 10 k)

! A32 "

R11 10 k)

R21 10 k)

R23 10 k) R13 10 k)

C13 5.5 nF ! A13 "

" Vout !

(a)

Vo " Vid !

" A !

" Vo

Vid

" AV id !

! (b)

Figure B.60 B#.,5#0$%4-.%C+&3':(%78;@g;@%4"5%F#40"<-.*(.%B"(=2$"(1%4#:0(.%,#.,5#0%#3':(3()0(*%&$%&%,&$,&*(%-4%0/$(,-)*<-.*(.%$#35:&0(*%QBP%.($-)&0-.%,#.,5#0$%&)*%&%$#)6:(%4#.$0<-.*(.%-'%&3'cPB%,#.,5#0;%4J5 [B[8%.('.($()0&0#-) -4%&)%#*(&:%-'%&3'%/#0"%6&#)%+;

=5% NQ=EK:% ;$% ,22*<% ,% 73I% ,'% .4-5,*% ,+% +#$% 64*+$0% 452/+:% 2$06)01% ,5% ,'3,5,*<.4.% .41/*,+4)5% )($0% +#$ 0,5-$%7 YT%+)%8D SYT:%,5&%2*)+%+#$%)/+2/+%()*+,-$%1,-54+/&$%($0./.%60$B/$5'<:%,.%.#);5%45%@4-!%A!M7!

B.2 PSpice Examples

dB

0.0

!0.5

!1.0

0

5

10

15

20

Frequency (kHz) (a) dB

0

!50

0

5

10

15

20

Frequency (kHz) (b) Figure B.61 9&6)#05*(%.($'-)$(%-4%0"(%4#40"<-.*(.%:-/'&$$%4#:0(.%,#.,5#0%$"-/)%#)%F#6;%?;gO>%4"5 &)%(+'&)*(*%1#(/% -4%0"(%'&$$=&)*%.(6#-)j%4J5%&%1#(/%-4%=-0"%0"(%'&$$=&)*%&)*%$0-'=&)*%.(6#-)$;%

A)+#%,5%$C2,5&$&%(4$;%)6%+#$%2,..9,5&%,5&%,%(4$;%)6%+#$%$5+40$%1,-54+/&$%0$.2)5.$%,0$%.#);5!%"#$.$ 0$./*+.%,0$%,*1).+%4&$5+4',*%+)%+#).$%')12/+$&%&40$'+*<%60)1%+#$%4&$,*%+0,5.6$0%6/5'+4)5:%+#$0$9<%($046<45+#$%')00$'+5$..%)6%+#$%&$.4-5!%

Example PS.16.2 Effect of Finite Op-Amp Bandwidth on the Operation of the Two-Integrator-Loop Filter =5%+#4.%$C,12*$:%;$%45($.+4-,+$%+#$%$66$'+%)6%+#$%6454+$%9,5&;4&+#%)6%20,'+4',*%)2%,12.%)5%+#$%0$.2)5.$%)6%, +;)345+$-0,+)03*))2%9,5&2,..%64*+$0%/+4*4T45-%+#$%");3"#)1,.%94B/,&%'40'/4+%)6%@4-! 77!8\>9?!%"#$%'40'/4+ 4.%&$.4-5$&%+)%20)(4&$%,%9,5&2,..%0$.2)5.$%;4+#%-D% %7D%SYT:%W% %8D:%,5&%,%/54+<%'$5+$0360$B/$5'<%-,45! "#$%)2%,12.%,0$%,../1$&%+)%9$%)6%+#$%`L7%+<2$!%N2$'464',**<:%;$%1)&$*%+#$%+$0145,*%9$#,(4)0%)6%+#$%)2 ,12%;4+#%+#$%.45-*$3+41$3')5.+,5+%*45$,0%5$+;)0S%.#);5%45%@4-!%A!M8!%N45'$%+#$%,5,*<.4.%2$06)01$&%#$0$ 4.%,%.1,**3.4-5,*%>,'?%,5,*<.4.%+#,+%4-5)0$.%5)5*45$,04+4$.:%5)%5)5*45$,04+4$.%,0$%45'*/&$&%45%+#4.%)23,12

B-71

B-72 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.16.2 continued

Ro " Vid

2Ricm Rid

Gm Vid

2Ricm

!

A0 # GmR1

Rb

Cb

" Vb !

" !

Vo1

" Vo !

,b # 1/RbCb

Figure B.62 E)(<'-:(%(M5#1&:()0<,#.,5#0%3&,.-3-*(:%-4%&)%-'%&3'%-'(.&0(*%/#0"#)%#0$%:#)(&.%.(6#-);

R1 # 10 k) Rd # 200 k) Rg # 200 k)

Vin

C1 # 1.59 nF ! A1 "

C2 # 1.59 nF R2 # 10 k) ! A2 "

R3 # 10 k)

R4 # 10 k) ! A3 "

" Vout ! Figure B.63 B#.,5#0%4-.%C+&3':(%78;@g;H%8(,-)*<-.*(.%=&)*'&$$%4#:0(.%#3':(3()0(*%/#0"%&%!-/
1,'0)1)&$*!%>=6%+#$%$66$'+.%)6%)23,12%5)5*45$,04+4$.%,0$%+)%9$%45($.+4-,+$&:%,%+0,5.4$5+%,5,*<.4.%.#)/*& 9$%2$06)01$&!?%"#$%6)**);45-%(,*/$.%,0$%/.$&%6)0%+#$%2,0,1$+$0.%)6%+#$%)23,12%1,'0)1)&$*%45%@4-!%A!M8e '(!% %8%F

'()*% %\DD%F

'2% %`\%

S*% %D!7b%1OJI

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0.% %HD%2@

"#$.$%(,*/$.%0$./*+%45%+#$%.2$'464$&%452/+%,5&%)/+2/+%0$.4.+,5'$.%)6%+#$%`L73+<2$%)2%,12!%@/0+#$0:%+#$< 20)(4&$%,%&'%-,45%+D% %8!\8% %7D\%IJI%,5&%,%H3&A%60$B/$5'<%-.%)6%L%YT:%,-,45%$B/,*%+)%+#$%(,*/$.%.2$'464$& 6)0%+#$%`L7!%V)+$%+#,+%+#$%.$*$'+4)5%)6%+#$%45&4(4&/,*%(,*/$.%)6%S*:%'.:%,5&%0.%4.%411,+$04,*%,.%*)5-%,.%S*'. %+D%,5&% 0 . ' . @ H -. ; "#$%");3"#)1,.%'40'/4+%.41/*,+$&%4.%.#);5%45%@4-!%A!MH!%"#$%'40'/4+%4.%.41/*,+$&%45%QN24'$%6)0%+;) ',.$.e%>7?%,../145-%`L73+<2$%)2%,12.%,5&%/.45-%+#$%*45$,0%1,'0)1)&$*%45%@4-!%A!M8R%,5&%>8?%,../145g 4&$,*%)2%,12.%;4+#%&'%-,45%)6% + O @O %[a[ %,5&%/.45-%+#$%5$,034&$,*%1)&$*%45%@4-!%A!MD!%=5%9)+#%',.$.:

B.2 PSpice Examples

dB

20

10

741 op amp

0

!10

!20 8.0

Ideal op amp

10 Frequency (kHz)

Figure B.64 B-3'&.#)6%0"(%3&6)#05*(%.($'-)$(%-4%0"(%!-/
;$%,22*<%,%73I%,'%.4-5,*%,+%+#$%64*+$0%452/+:%2$06)01%,5%,'3,5,*<.4.%.41/*,+4)5%)($0%+#$%0,5-$%W%SYT%+)%78 SYT:%,5&%2*)+%+#$%)/+2/+3()*+,-$%1,-54+/&$%($0./.%60$B/$5'7b`W?n!%N/'#%,5%,5,*<.4.%.#);.%+#,+%W3$5#,5'$1$5+%)''/0.%,.%, 0$./*+%)6%+#$%$C'$..%2#,.$%*,-%45+0)&/'$&%9<%+#$%6454+$%)23,12%9,5&;4&+#!%"#$%+#$)0<%,*.)%.#);.%+#,+ +#$%W3$5#,5'$1$5+%$66$'+%',5%9$%')12$5.,+$&%6)0%9<%45+0)&/'45-%2#,.$%*$,&%,0)/5&%+#$%6$$&9,'S%*))2! "#4.% ',5% 9$% ,'')12*4.#$&% 9<% ')55$'+45-% ,% .1,**% ',2,'4+)0:% 0):% ,'0)..% 0$.4.+)0% '8!% ")% 45($.+4-,+$% +#$ 2)+$5+4,*%)6%./'#%,%')12$5.,+4)5%+$'#54B/$:%;$%0$2$,+%+#$%QN24'$%.41/*,+4)5%;4+#%(,04)/.%',2,'4+,5'$ (,*/$.!%"#$%0$./*+.%,0$%&4.2*,<$&%45%@4-!%A!M\>,?!%a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a$%5)+$%+#,+%,*+#)/-#%+#$%64*+$0%W%#,.%9$$5%0$.+)0$&%+) 4+.%4&$,*%(,*/$:%+#$0$%0$1,45.%,%&$(4,+4)5%45%+#$%'$5+$0%60$B/$5'
B-73

B-74 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.16.2 continued

6/0+#$0% #$0$R% )/0% )9X$'+4($% 4.% 5)+% +)% 20$.$5+% ,% &$+,4*$&% .+/&<% )6% +#$% &$.4-5% )6% +;)345+$-0,+)03*))2 94B/,&.R%0,+#$0:%4+%4.%+)%4**/.+0,+$%+#$%,22*4',+4)5%)6%NQ=EK%45%45($.+4-,+45-%+#$%5)54&$,*%2$06)01,5'$%)6 ,'+4($364*+$0%'40'/4+.:%-$5$0,**
dB

20 15 Cc # 0 pF 10 Cc # 20 pF 5

Cc # 40 pF Ideal

Cc # 60 pF 0

!5

!10

Cc # 80 pF

9.0

9.2

9.6

10.0

10.4

10.8

Frequency (kHz) (a) dB

4 0 Ideal

Cc # 64 pF !4

!8

!12

!16

!20

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

Frequency (kHz) (b)

Figure B.65 4"5% 9&6)#05*(% .($'-)$(% -4% 0"(% !-/
B.2 PSpice Examples

Example PS.17.1 Wien-Bridge Oscillator @)0%)/0%640.+%$C,12*$%)5%).'4**,+)0.:%;$%.#,**%.41/*,+$%+#$%)2$0,+4)5%)6%+#$%a4$53904&-$%).'4**,+)0%;#).$ .'#$1,+4'%',2+/0$%4.%.#);5%45%@4-!%A!MM!%"#$%')12)5$5+%(,*/$.%,0$%.$*$'+$&%+)%<4$*&%).'4**,+4)5.%,+%7 SYT! a$% ;)/*&% *4S$% +)% 45($.+4-,+$% +#$% )2$0,+4)5% )6% +#$% '40'/4+% 6)0% &466$0$5+% .$++45-.% )6% '7H% ,5&% '7.:% ;4+# ' @H ' @. dO%L !% N45'$% ).'4**,+4)5% X/.+% .+,0+.% ;#$5% ' H ' @. ' @H H % >.$$% KC$0'4.$% 78!L?:% +#,+% 4.: ;#$5%'7H% %8D%S %,5&%'7.% %HD%S :%;$%')5.4&$0%+#0$$%2)..49*$%.$++45-.e%>,?%'7H% %7\%S :%'7.% %H\%S R >9?%'7H% %7W%S :%'7.% %H8%S R%,5&%>'?%'7H% %8\ S :%'7.% %8\%S !%"#$.$%.$++45-.%')00$.2)5&%+)%*))2%-,45. )6%7!HH:%7!7:%,5&%D!W:%0$.2$'+4($*,?%.#);.%+#$ OUT D1

PARAMETERS: C3 # 16n C4 # 16n

D1N4148 {R1a}

R1a # 18K R1b # {50K!{R1a}} R2 # 10K R3 # 10K R4 # 10K

{R1b}

{R2}

0

D2 D1N4148

VCC # 15 VEE # !15

VCC A1

VCC

V" OS2

"

VEE

A

OUT !

V! OS1

uA741 " {VCC} !

"

VEE

{VEE}

{C4}

!

{R4}

IC # 0 {C3} 0

0

{R3}

IC # 0 0

0

Figure B.66 C+&3':(%78;@T;@>%8,"(3&0#,%,&'05.(%-4%&%_#()<=.#*6(%-$,#::&0-.; @T

!"(%87ABC%3-*(:$%4-.%0"(%TU@%-'%&3'%&)*%0"(%@ZU@U^%*#-*(%&.(%&1&#:&=:(%#)%78'#,(;%!"(%TU@%-'%&3'%/&$ ,"&.&,0(.#I(*%#)%C+&3':(%78;H;H;%!"(%@ZU@U^%*#-*(%/&$%5$(*%#)%C+&3':(%78;U;@;

B-75

B-76 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example PS.17.1 continued 15 V 10 V

0V

!10 V !15 V

0

5

10

V (OUT)

15

20

Time (ms) (a) R1a # 15 k), Loop Gain # 1.33

8.0 V

4.0 V

0V

!4.0 V

!8.0 V

0

5

10

V (OUT)

15

20

Time (ms) (b) R1a # 18 k), Loop Gain # 1.1

5.0 mV

2.5 mV

0V

!2.5 mV

0

5 V (OUT)

10

15

20

Time (ms) (c) R1a # 25 k), Loop Gain # 0.8

Figure B.67 80&.0<5'%0.&)$#()0%=("&1#-.%-4%0"(%_#()<=.#*6(%-$,#::&0-.%$"-/)%#)%F#6;%?;gg%4-.%1&.#-5$%1&:5($%-4%:--'% 6&#);

B.2 PSpice Examples

)/+2/+%;,($6)01%)9+,45$&%6)0%,%*))2%-,45%)6%7!HH%"U"!%[9.$0($%+#,+%,*+#)/-#%+#$%).'4**,+4)5.%-0);%,5& .+,94*4T$%0,24&*<:%+#$%&4.+)0+4)5%4.%')5.4&$0,9*$!%"#$%)/+2/+%)9+,45$&%6)0%,%*))2%-,45%)6%7!7:%.#);5%45%@4-! A!M`>9?:%4.%1/'#%*$..%&4.+)0+$&!%Y);$($0:%,.%$C2$'+$&:%,.%+#$%*))2%-,45%4.%0$&/'$&%+);,0&%/54+<:%4+%+,S$. *)5-$0%6)0%+#$%).'4**,+4)5.%+)%9/4*&%/2%,5&%6)0%+#$%,12*4+/&$%+)%.+,94*4T$!%@)0%+#4.%',.$:%+#$%60$B/$5'<%4. bWM!M%YT:%;#4'#%4.%0$,.)5,9*<%'*).$%+)%+#$%&$.4-5%(,*/$%)6%7%SYT:%,5&%+#$%,12*4+/&$%4.%`!H`%I!%@45,**<:%6)0 ,%*))2%-,45%)6%D!W:%+#$%)/+2/+%.#);5%45%@4-!%A!M`>'?%')56401.%)/0%$C2$'+,+4)5%+#,+%./.+,45$&%).'4**,+4)5. ',55)+%9$%)9+,45$&%;#$5%+#$%*))2%-,45%4.%*$..%+#,5%/54+()*+,-$% v+?:% ,% "YU% )6 8!\`h%4.%)9+,45$&:%;#4'#:%,.%$C2$'+$&:%4.%#4-#$0%+#,5%+#,+%6)0%+#$%()*+,-$%v[d":%9/+%5)+%9<%($0<%1/'#!%"#$ )/+2/+%+$0145,*%)6%+#$%)2%,12%4.%)6%')/0.$%,%1/'#%1)0$%')5($54$5+%2*,'$%+)%+,S$%+#$%)/+2/+!

Example PS.17.2 Active-Filter-Tuned Oscillator =5%+#4.%$C,12*$:%;$%/.$%QN24'$%+)%($046<%)/0%')5+$5+4)5%+#,+%,%./2$04)0%)2%,12P).'4**,+)0%',5%9$ 0$,*4T$& /.45-%+#$%,'+4($364*+$03+/5$&%'40'/4+%)6%@4-!%78!77!%a$%,*.)%45($.+4-,+$%+#$%$66$'+%)6%'#,5-45-%+#$%(,*/$%)6 +#$%64*+$0%W%6,'+)0%)5%+#$%.2$'+0,*%2/04+<%)6%+#$%)/+2/+%.45$%;,($! E)5.4&$0%+#$%'40'/4+%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45%@4-!%A!MW!%@)0%+#4.%'40'/4+:%+#$%'$5+$0%60$B/$5'< 4.%7%SYT:%,5&%+#$%64*+$0%W%4.%\%;#$5%'7% %\D%S %,5&%8D%;#$5%'7% %8DD%S !%O.%45%+#$%',.$%)6%+#$%a4$53 904&-$% '40'/4+% 45% KC,12*$% QN!7`!7:% `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b!%"#$%/22$0%-0,2#%.#);.%+#$%.45/.)43 &,*%;,($6)01%,+%+#$%)/+2/+%)6%)2%,12%+7%>()*+,-$%v7?!%"#$%*);$0%-0,2#%.#);.%+#$%;,($6)01%,'0).. +#$% &4)&$% *414+$0% >()*+,-$% v8?!% "#$% 60$B/$5'<% )6% ).'4**,+4)5% 4.% 6)/5&% +)% 9$% ($0<% '*).$% +)% +#$% &$.4-5 (,*/$%)6%7%SYT!%"#$%,12*4+/&$%)6%+#$%.45$%;,($%4.%&$+$0145$&%/.45-%Q0)9$%>+#$%-0,2#4',*%45+$06,'$%)6 QN24'$?%+)%9$%7!7\%I%>)0%8!H%I%232?!%V)+$%+#,+%+#4.%4.%*);$0%+#,5%+#$%H!M%I%$.+41,+$&%45%KC$0'4.$%78!`! "#$%*,++$0%(,*/$:%#);$($0:%;,.%9,.$&%)5%,5%$.+41,+$%)6%D!`3I%&0)2%,'0)..%$,'#%')5&/'+45-%&4)&$%45 +#$%*414+$0!%"#$%*);$0%;,($6)01%45%@4-!%A!Mb%45&4',+$.%+#,+%+#$%&4)&$%&0)2%4.%'*).$0%+)%D!\%I%6)0%,%7 I 2$,S3+)32$,S% ,12*4+/&$% )6% +#$% 2.$/&)3.B/,0$% ;,($!% a$% .#)/*&% +#$0$6)0$% $C2$'+% +#$% 2$,S3+)32$,S ,12*4+/&$%)6%+#$%)/+2/+%.45/.)4&%+)%9$%*);$0%+#,5%H!M%I%9<%+#$%.,1$%6,'+)0:%,5&%45&$$&%4+%4.%,220)C43 1,+$*<%+#$ ',.$! =5%QN24'$:%+#$%@)/04$0%,5,*<.4.%)6%+#$%)/+2/+%.45$%;,($%45&4',+$.%+#,+%"YU% %7!M7h!%G$2$,+45-%+#$ .41/*,+4)5% ;4+#% W% 45'0$,.$&% +)% 8D% >9<% 45'0$,.45-% '7% +)% 8DD% S ?:% ;$% 645&% +#,+ +#$% (,*/$% )6% "YU% 4. 0$&/'$&% +)% 7!D7h!% "#/.:% )/0% $C2$'+,+4)5.% +#,+% +#$% (,*/$% )6% +#$% 64*+$0% W% ',5% 9$% /.$&% ,.% ,5% $66$'+4($ 1$,5.%6)0%')5.+0)**45-%+#$%"YU%)6%+#$%)/+2/+%;,($6)01%,0$%')56401$&!

B-77

0

{VEE} !

"

VEE

0

2

0

D1 D1N4148

IC # 0

{C1}

{R1}

0 OS2 {R6}

V"

A1

0

D2 D1N4148

VCC OUT

{C2}

OS1

V! VEE

IC # 0 uA741 " !

{R2}

VEE

OUT

1

{R4}

V"

OS2

"

uA741

!

{R3}

V!

A2

OS1

0

{R5}

VCC

Figure B.68 C+&3':(%78;@T;H>%8,"(3&0#,%,&'05.(%%-4%&)%&,0#1(<4#:0(.<05)(*%-$,#::&0-.%4-.%/"#,"%0"(%W%-4%0"(%4#:0(.%#$%&*X5$0&=:(%=2%,"&)6#)6%'@;

" {VCC} !

VCC

VCC # 15 VEE # !15

R1 # 200K R2 # 10K R3 # 10K R4 # 10K R5 # 10K R6 # 10K

PARAMETERS: C1 # 16n C2 # 16n

B-78 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

B.3 Multisim Examples

B.3 Multisim Examples

2.0 V

0V

!2.0 V V (1) 500 mV

0V

SEL>> !500 mV

45

46

47

V (2)

48

49

50

Time (ms)

Figure B.69 E50'50%/&1(4-.3$%-4%0"(%&,0#1(<4#:0(.<05)(*%-$,#::&0-.%$"-/)%#)%F#6;%?;g^%4-.%W% %d%R'@% %dO%L S;%

B.3 Multisim Examples Example MS.5.1 The CS Amplifier =5%+#4.%$C,12*$:%;$%;4**%/.$%F/*+4.41%+)%'#,0,'+$04T$%,%EN%,12*464$0%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45 @4-!%A!`D!%a$%;4**%,../1$%,%D!7W3 1%EF[N%+$'#5)*)-<%6)0%+#$%F[N@K"%,5&%/.$%+<24',*%NQ=EK%*$($*37 1)&$*% 2,0,1$+$0.% 6)0% +#4.% +$'#5)*)-<:% ,.% 20)(4&$&% 45% ",9*$% A!L!% a$% ;4**% ,*.)% ,../1$% ,% .4-5,*3.)/0'$ 0$.4.+,5'$%'.4-%Z%7D%S :%,%*),&%0$.4.+,5'$%'?%Z%\D%S :%,5&%9<2,..%,5&%')/2*45-%',2,'4+)0.%)6%7D% @!%"#$ +,0-$+$&%.2$'464',+4)5.%6)0%+#4.%EN%,12*464$0%,0$%,%()*+,-$%-,45%o+vo%Z%7D%IJI%,5&%,%1,C41/1%2);$0%')53 ./12+4)5%O%Z%D!L\%1a!%O.%.#)/*&%,*;,<.%9$%+#$%',.$%;4+#%')12/+$0%.41/*,+4)5:%;$%;4**%9$-45%;4+#%,5 ,220)C41,+$%#,5&3,5,*<.4.%&$.4-5!%a$%;4**%+#$5%/.$%F/*+4.41%+)%645$3+/5$%)/0%&$.4-5%,5&%+)%45($.+4-,+$ +#$%2$06)01,5'$%)6%+#$%645,*%&$.4-5!% !"(%&3':#4#(.%$'(,#4#,&0#-)$%&.(%$533&.#I(*%#)%!&=:(%?;@J;

Hand Design a4+#%,%7!W3I%2);$0%./22*<:%+#$%&0,45%'/00$5+%)6%+#$%F[N@K"%1/.+%9$%*414+$&%+)%%4%Z%OJ"44%Z%D!L\%1aJ 7!W%I Z D!8\%1O%+)%1$$+%+#$%2);$0%')5./12+4)5%.2$'464',+4)5!%E#)).45-%"#"%Z%D!7\%I%,5&%"4$%Z%"44%JH%Z D!M I%>+)%,'#4$($%,%*,0-$%.4-5,*%.;45-%,+%+#$%)/+2/+?:%+#$%F[N@K"%',5%5);%9$%.4T$&%,.

B-79

B-80 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.5.1 continued DEVICE PARAMETERS Q1:NMOS NAME 15.48u W 0.2u L 291u KP 0.01u LD 0.45 VID 0.08 LAMBDA 0.3 GAMMA

VDD

VDD 1.8 V

1.8 V

RG1 1.2 M) 5%

RD 3.41k) 5%

CCO

VD CCI

Rsig vsig

10 k) vsig

Q1

VIN

10 &F RL 50 k)

10 &F VS

0 Vrms 1 kHz 0+

RG2 600 k) 5%

RS 0) 5%

CS 10 &F

Figure B.70 B&'05.(%$,"(3&0#,%-4%0"(%B8%&3':#4#(.; Table B.13 CS Amplifier Specifications 7&.&3(0(.$

[&:5(

7-/(.

O;Ud%3_

'$#6

@O%L

'?

dO%L

o+vo

@O%[a[

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B-81

B-82 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.5.1 continued

Amplifier Gain a$%',5%,*.)%($046<%46%)/0%&$.4-5%20)(4&$.%+#$%&$.40$&%-,45!%"#4.%',5%9$%&)5$%9<%2$03 6)0145-%+0,5.4$5+%0$.2)5.$%,5,*<.4.:%,.%.$+%/2%45%E#\pENpO12*464$0pKCp-,45!1.7D!%O.%',5%9$%.$$5%60)1 @4-!%%A!`8:%oSvo%$%o+vo%$%77%IJI!%V)+$%+#$%(,*/$.%)6%)($0,**%()*+,-$%-,45%Sv%,5&%+v%,0$%'*).$%.45'$%'(31Y >'SZ[['S\?1(1'.4-!%=5%+#$%',.$%;#$0$%+#$%',2,'4+)0%0$%4.%5)+%45'*/&$&%>0$1Z%D?:%+#$%-,45%&0)2.%9<%,%6,'+)0%)6 \!MH%>,220)C41,+$*<%$B/,*%+)%7%l%9*'$?%+)%7!b\!%"#4.%4.%,.%$C2$'+$&%60)1%)/0%.+/&<%)6%+#$%EN%,12*464$0 ;4+#%,%.)/0'$3&$-$5$0,+4)5%0$.4.+,5'$! 15 m 10 m

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B-83

B-84 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

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B.3 Multisim Examples

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B-85

B-86 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

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B.3 Multisim Examples

"#/.:1 ')E% $% 'E% Z% 7HD !% N/9.+4+/+45-% +#4.% (,*/$% 45% +#$% $B/,+4)5.% 6)/5&% 6)0% [+v[% ,5&% '45% .#);.% +#,+% '45 45'0$,.$.%60)1%M!7%S %+)%8D!b%S %;#4*$%[+v[%&0)2.%60)1%HW!8%IJI%+)%7W!W%IJI! _(%/#::%)-/%5$(%95:0#$#3%0-%1(.#42%-5.%*($#6)%&)*%#)1($0#6&0(%0"(%'(.4-.3&),(%-4%0"(%BC%&3':#4#(.; _(%=(6#)%=2%'(.4-.3#)6%&%=#&$<'-#)0%$#35:&0#-)%0-%1(.#42%0"&0%0"(%?G!%#$%'.-'(.:2%=#&$(*%#)%0"(%&,0#1( .(6#-)% &)*% 0"&0% 0"(% *,% 1-:0&6($% &)*% ,5..()0$% 3((0% 0"(% *($#.(*% $'(,#4#,&0#-)$;% ?&$(*% -)% 0"#$% $#35:&0#-) 4-./&.*D%/(%"&1(%#),.(&$(*%0"(%1&:5(%-4%'&%0-%JUO%L %#)%-.*(.%0-%:#3#0%%0%0-%&=-50%O;d%3N%/"#:(%5$#)6%& $0&)*&.*%@k%.($#$0-.%1&:5(;%Z(+0D%0-%3(&$5.(%0"(%6&#)%+vD%/(%,-)*5,0%&%0.&)$#()0%.($'-)$(%&)&:2$#$D%&$%$(0 5'%#)%B"ghBChN3':#4#(.hC+;3$@O;%N,,-.*#)6:2D%/#0"%)-%(3#00(.%*(6()(.&0#-)D%0"(%6&#)%#$%[+v[1W%J^;d%[a [;%Y$#)6%')E1W%@JO %.($5:0$%#)%&%*.-'%#)%0"(%6&#)%=2%&%4&,0-.%-4%H%R&$%,&)%=(%$(()%4.-3%F#6;%?;TgS;% 60.0 m 50.0 m

Output voltage (V)

40.0 m 30.0 m 20.0 m 10.0 m 0 –10.0 m –20.0 m –30.0 m –40.0 m –50.0 m 0

500.0000 &

1.0000 m

1.5000 m Time (s)

2.0000 m

2.5000 m

Figure B.76 %!.&)$#()0%&)&:2$#$%-4%0"(%BC%&3':#4#(.%/#0"%')E%W%O%&)*%')E%W%@JO ;

!"5$%4&.%#)%0"#$%(+&3':(D%/(%"&1(%&$$53(*%0"&0%0"(%1-:0&6(%6&#)%-4%0"(%?G!%&3':#4#(.%#$%,-)$0&)0%&)* #)*('()*()0%-4%0"(%4.(M5(),2%-4%0"(%#)'50%$#6)&:;%V-/(1(.D%&$%3()0#-)(*%#)%8(,0#-)%U;^;gD%0"#$%#$%)-0%0.5(D $#),(%#0%#3':#($%0"&0%0"(%&3':#4#(.%"&$%#)4#)#0(%=&)*/#*0";%!-%#::5$0.&0(%0"(%4#)#0(%=&)*/#*0"D%/(%,-3'50( 0"(% 4.(M5(),2% .($'-)$(% -4% 0"(% &3':#4#(.;% !"(% ':-0% -4% 0"(% -50'50<1-:0&6(% 3&6)#05*(% R#)% *?S% 1(.$5$% 4.(< M5(),2%#$%$"-/)%#)%F#6;%?;TT;%_#0"%)-%(3#00(.%*(6()(.&0#-)D%0"(%3#*=&)*%6&#)%#$%o+Po%W%J^;d%[a[%W%J@;T *?%&)*%0"(%J<*?%=&)*/#*0"%#$%&@%W%-V%c%-?%W%@Ud;T%LVI;%Y$#)6%&)%')E%-4%@JO %%.($5:0$%#)%&%*.-'%#)%0"( 3#*=&)*%6&#)%o+Po%=2%&%4&,0-.%-4%H%R,-)$#$0()0%/#0"%/"&0%/(%-=$(.1(*%'.(1#-5$:2%#)%-5.%0.&)$#()0%&)&:2$#$S; A)0(.($0#)6:2D%"-/(1(.D%&@%"&$%)-/%#),.(&$(*%=2%&''.-+#3&0(:2%0"(%$&3(%4&,0-.%&$%0"(%*.-'%#)%o+Po;%N$ /(%:(&.)(*%#)%B"&'0(.%fD%0"(%(3#00(.<*(6()(.&0#-)%.($#$0-.%')E%'.-1#*($%)(6&0#1(%4((*=&,LD%/"#,"%&::-/$ 5$%0-%0.&*(%-44%6&#)%4-.%-0"(.%*($#.&=:(%'.-'(.0#($%$5,"%&$%&%:&.6(.%#)'50%.($#$0&),(%&)*%&%/#*(.%=&)*/#*0"; !-%,-),:5*(%0"#$%(+&3':(D%/(%/#::%*(3-)$0.&0(%0"(%#3'.-1(*%=#&$<'-#)0%R-.%*,%-'(.&0#)6%'-#)0S%$0&< =#:#02%&,"#(1(*%/"()%&)%(3#00(.%.($#$0-.%',%#$%5$(*;%8'(,#4#,&::2D%/(%/#::%#),.(&$(a*(,.(&$(%0"(%1&:5(%-4%0"( '&.&3(0(.%&Q%R#;(;D%0"(%#*(&:%3&+#353%4-./&.*%,5..()0%6&#)S%#)%0"(%87ABC%3-*(:%4-.%'&.0%nHZJfOU%=2%& 4&,0-.%-4%H%&)*%.(&*%0"(%=#&$<'-#)0%'.-=($;%!"(%,-..($'-)*#)6%,"&)6(%#)%?G!%'&.&3(0(.%R *,S%&)*%=#&$< '-#)0%R%0%&)*%"0,S%&.(%'.($()0(*%#)%!&=:(%?;@T%4-.%0"(%,&$(%-4%',1W%g%L ;%

B-87

B-88 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Magnitude (dB)

Example MS.6.2 continued 35.0

20.0

5.0

–10.0 1.0000

10.0000

100.0000

1.0000 k

10.0000 k 100.0000 k 1.0000 M

Frequency (Hz) Figure B.77 %F.(M5(),2%.($'-)$(%-4%0"(%BC%&3':#4#(.%/#0"%')E%W%O%&)*%')E%W%@JO ; Table B.17 Variations in the Bias Point of the CE Amplifier with the SPICE Model Parameter BF of BJT RE = 6 k

BF (in SPICE)

RE = 0

.dc

IC (mA)

.dc

IC (mA)

VC (V)

HO^

fU;f

O;UdH

U@g;U%R)-3#)&:%1&:5(S

@HJ

O;UfU

O;U^U

fg;f

O;JTT

@;HHT

O;OgH

@HT

O;UfU

O;OgO

^JH

@UU

O;d@^


@d@

O;d^^


VC (V)

F-.%0"(%,&$(%/#0"-50%(3#00(.%*(6()(.&0#-)D%/(%/#::%5$(%',%W%O%#)%0"(%$,"(3&0#,%-4%F#6;%?;Td;%F5.0"(.< 3-.(D%0-%3&#)0&#)%0"(%$&3(%%0%&)*%"0%#)%=-0"%,&$($%&0%0"(%1&:5($%-=0&#)(*%4-.%)-3#)&:%&QD%/(%5$(%'&%W @;@H%9 %0-%:#3#0%%0%0-%&''.-+#3&0(:2%O;d%3N;%!"(%,-..($'-)*#)6%1&.#&0#-)$%#)%0"(%?G!%=#&$%'-#)0%&.(%&:$$"-/)% #)% !&=:(% ?;@T;% N,,-.*#)6:2D% /(% $((% 0"&0% (3#00(.% *(6()(.&0#-)% 3&L($% 0"(% =#&$% '-#)0% -4% 0"(% BC &3':#4#(.%35,"%:($$%$()$#0#1(%0-%,"&)6($%#)% ;%V-/(1(.D%5):($$%&%:&.6(%=2'&$$%,&'&,#0-.%0,%#$%5$(*D%0"#$ .(*5,(*%=#&$%$()$#0#1#02%,-3($%&0%0"(%(+'()$(%-4%&%.(*5,0#-)%#)%6&#)%R&$%/(%-=$(.1(*%#)%0"#$%(+&3':(%/"() /(%$#35:&0(*%0"(%0.&)$#()0%.($'-)$(%-4%0"(%BC%&3':#4#(.%/#0"%&)%')E%W%@JO S;

Example MS.7.1 The CMOS CS Amplifier =5%+#4.%$C,12*$:%;$%;4**%/.$%F/*+4.41%+)%'#,0,'+$04T$%+#$%EF[N%EN%,12*464$0%;#).$%.'#$1,+4'%',2+/0$%4. .#);5% 45% @4-!% A!`W!% a$% ;4**% ,../1$% ,% D!7W3 1% EF[N% +$'#5)*)-<% 6)0% +#$% F[N@K"% ,5&% /.$% +<24',* NQ=EK%*$($*37%1)&$*%2,0,1$+$0.%6)0%+#4.%+$'#5)*)-<%,.%-4($5%45%",9*$%A!L!%a$%;4**%9$-45%;4+#%,5%,220)C3 41,+$%#,5&3,5,*<.4.%&$.4-5!%a$%;4**%+#$5%/.$%F/*+4.41%+)%45($.+4-,+$%+#$%2$06)01,5'$%)6%+#$%645,*%&$.4-5! "#$% +,0-$+$&% .2$'464',+4)5.% 6)0% +#4.% EF[N% EN% ,12*464$0% ,0$% ,% ()*+,-$% -,45% oSvo% Z% \D% IJI% ,5&% ,% 94,. '/00$5+%%4%)6%7DD% O!

B.3 Multisim Examples

!"(%&3':#4#(.%$'(,#4#,&0#-)$%&.(%$533&.#I(*%#)%!&=:(%?;@^; Table B.18 CMOS CS Amplifier Specifications 8'(,#4#,&0#-)

[&:5(

%4

@OO%sN

oSvo

dO%[a[

"44

@;^%[

NMOS Vtn |VAn| kn' I L W

0.5 V 12.5 V 246.2uA/V^2 0.1 mA 0.2 um 0.523 um

VDD 1.8 V

VDD 1.8 V

M=9 Q3

M=9 Q2

PMOS Vtp |VAp| kp' I L W

–0.5 V 9V –86.1 uA/V^2 0.1 mA 0.2 um 0.46 um

I1 100 uA

vOUT vIN

vin

M=6 Q1

+ 0.707 mVrms – 1000 Hz 0º

0.71 V

Figure B.78 %8,"(3&0#,%,&'05.(%-4%0"(%B9E8%B8%&3':#4#(.;

Hand Design @)0%+#$%&$.4-5%)6%+#4.%,12*464$0%;$%'#)).$%?%Z%D!8D% 1:%.)%+#,+%.414*,0%+)%KC,12*$%FN!\!7:%;$%#,($%?$66%Z D!7W% 1!%@)0%+#4.%'#,55$*%*$5-+#:%,5&%45%D!7W3 1%EF[N%+$'#5)*)-<:%+#$%1,-54+/&$.%)6%+#$%K,0*<%()*+,-$. )6%+#$%VF[N%,5&%QF[N%+0,5.4.+)0.%,0$%"+3%Z%78!\%I%,5&%["+6o%Z%b%I:%0$.2$'+4($*
9E8FC!%@%,&)%)-/%=(%$#I(*%R=2%#6)-.#)6%0"(%,"&))(:<:()60"%3-*5:&0#-)S%&$ @ %4 <<<<<<<@< Z <<<<<<<<<<<<<<<<<<< < Z ? (44 @ <<< D 3 " H#"@ H

Pg

@OO @O <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < $ @^;UH @<<< Pg H O;H@ HUg;H @O H

B-89

B-90 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.7.1 continued

;#$0$:%,.%1$5+4)5$&:%?$66%%Z%D!7WD% 1:%,5&%.414*,0%+)%KC,12*$%FN!\!7:%D3 %Z%8LM!8% OJIH!%"#4.%<4$*&. @7 Z%7W!L8%?E--% H!H8% 1!%")%.2$'46<%+#$%&41$5.4)5.%)6%+#$%F[N@K".%45%F/*+4.41:%;$%;4**%/.$%+#$%1/*3 +42*4',+4($%6,'+)0%*R%4+.%&$6,/*+%(,*/$%4.%7:%,5&%4+%4.%/.$&%45%NQ=EK%+)%.2$'46<%+#$%5/19$0%)6%F[N@K".%')53 5$'+$&%45%2,0,**$*!%O.%&$24'+$&%45%@4-!%A!`b:%,%+0,5.4.+)0%;4+#%'#,55$*%*$5-+#%?%,5&%'#,55$*%;4&+#% * @ ',5%9$%412*$1$5+$&%/.45-%*%5,00);$0%+0,5.4.+)0.%45%2,0,**$*:%$,'#%#,(45-%,%'#,55$*%*$5-+#%?%,5&%,%'#,53 5$*%;4&+#%@!%=5%+#4.%$C,12*$:%,%/54+3.4T$%VF[N%+0,5.4.+)0%4.%/.$&%;4+#% @ @ ? @ Z O;dH 3 O;H 3 !%"#/.: ;$%645&% * @ Z J;JH O;dH $ g;

iD iD Q1

Aspect ratio of mW/L

Q2

Q3

Aspect ratio of each transistor W/L

Figure B.79 !.&)$#$0-.%(M5#1&:(),2;

F5.0"(.3-.(D%9E8FC!$%H%&)*%J%35$0%=(%$#I(*%0-%"&1(%.(&$-)&=:2%$3&::%"#"%4-.%0"(%=#&$%,5..()0%%41-4 @OO%sN;%!"#$%&::-/$%:&.6(%$#6)&:<$/#)6%&0%0"(%-50'50%-4%0"(%&3':#4#(.;%8#3#:&.%0-%-5.%'.(1#-5$%&''.-&,"D t =2%,"--$#)6%o"#"\o%W%O;J%[D%&)*%)-0#)6% 4 4$DH $ " 44 H Z O;f[ %R3#*c.&#:%1-:0&6(S> Pg %4 @ @OO @O <<<<<<
;#$0$%?E--%%Z%D!7W% 1%,5&% D 6 Z ^g;@ N [ ; %"#4.%<4$*&. @ H Z HJ;d ? (44 Z U;HJ 3; %=5%+#4.%$C,12*$: /54+3.4T$% QF[N% +0,5.4.+)0.% ,0$% /.$&% ;4+#% @ H ? H Z @ J ? J Z O;Ug 3 O;H 3 ; % "#/.:% ;$% 645& * H Z * J Z U;HJ O;Ug $ f !

Simulation Amplifier Biasing Z-/%-5.%*($#6)%,&)%=(%1(.#4#(*%5$#)6%0"(%$#35:&0#-)%0--:;%!"(%$,"(3&0#,%#$%#) B"ThB9E8hB8hN3':#4#(.h% C+h[!B;3$@O;% ?&$(*% -)% 0"(% $#35:&0#-)% .($5:0$D% oSvo% W% dU% [a[% &)* %4 W @O@%sN;%!"(.(4-.(D%0"(%$#35:&0#-)%.($5:0$%,-)4#.3%0"&0%0"(%*($#6)(*%B9E8%B8%&3':#4#(.%3((0$ 0"(%$'(,#4#,&0#-)$; DC Voltage Transfer Characteristic !-%,-3'50(%0"(%*,%0.&)$4(.%,"&.&,0(.#$0#,%-4%0"(%B8%&3':#< 4#(.D%/(%'(.4-.3%&%*,%&)&:2$#$%#)%95:0#$#3%/#0"%"AZ%$/('0%-1(.%0"(%.&)6(%O%0-%"44%&)*%':-0%0"(%,-..(< $'-)*#)6%-50'50%1-:0&6(%"EY!;% F#65.(%?;^OR&S%$"-/$%0"(%.($5:0#)6%0.&)$4(.%,"&.&,0(.#$0#,;%!"(%$:-'(%-4%0"(%[!B%,5.1(%&0%"S$Z%W%O;T@ [ ,-..($'-)*$%0-%0"(%*($#.(*%6&#)%-4%0"(%&3':#4#(.;%!-%(+&3#)(%0"(%"#6"<6&#)%.(6#-)%3-.(%,:-$(:2D%/(%.('(&0 0"(%*,%$/(('%4-.%"AZ%=(0/(()%O;g%[%&)*%O;^%[;%!"(%.($5:0#)6%0.&)$4(.%,"&.&,0(.#$0#,%#$%':-00(*%#)%F#6;%?;^O= R3#**:(%,5.1(S;%Y$#)6%0"(%,5.$-.%-4%0"(%].&'"(.%#)%95:0#$#3D%/(%4#)*%0"&0%0"(%:#)(&.%.(6#-)%-4%0"#$%*,%0.&)$< 4(.%,"&.&,0(.#$0#,%#$%=-5)*(*%&''.-+#3&0(:2%=2%"AZ1%W%O;gf^%[%&)*%"AZ1%W%O;TH@%[;%!"(%,-..($'-)*#)6%1&:5($ -4%"EY!%&.(%@;d@J%[%&)*%O;HJT%[;%!"($(%.($5:0$%&.(%,:-$(%0-%0"(%(+'(,0(*%1&:5($;%8'(,#4#,&::2D%0.&)$#$0-.$%WZ

B.3 Multisim Examples

DC transfer characteristic 2.00

V(out)

1.25

500.00 m

–250.00 m

0

500.0 m

1.0

1.5

2.0

VIN (V) Traces:

V(v[out]),

Figure B.80 4"5%[-:0&6(%0.&)$4(.%,"&.&,0(.#$0#,%-4%0"(%B9E8%B8%&3':#4#(.;

DC transfer characteristic 1.850

VOUT (V)

1.233

616.667 m

0

600 m

Traces:

625 m

650 m

W = Wnom,

675 m

700 m

725 m

VIN (V) W = Wnom +15%

750 m

775 m

800 m

W = Wnom –15%

Figure B.80 4J5%C+'&)*(*%1#(/%-4%0"(%0.&)$4(.%,"&.&,0(.#$0#,$%#)%0"(%"#6"<6&#)%.(6#-)%4-.%@%W%@)-3#)&:%u@dk;

B-91

B-92 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.7.1 continued

&)*%W\% /#::% .(3&#)% #)% 0"(% $&05.&0#-)% .(6#-)% &)*D% "(),(D% 0"(% &3':#4#(.% /#::% -'(.&0(% #)% #0$% :#)(&.% .(6#-)% #4 " #"@ " EY! " 44 P " #"H %-.%O;H@[% " EY! @;d%[; %F.-3%0"(%.($5:0$%&=-1(D%0"(%1-:0&6(%6&#)%Sv%R#;(;D 0"(%$:-'(%-4%0"(%:#)(&.%$(63()0%-4%0"(%*,%0.&)$4(.%,"&.&,0(.#$0#,S%#$%&''.-+#3&0(:2%cdU%[a[D%/"#,"%(+,((*$ =50%#$%.(&$-)&=:2%,:-$(%0-%0"(%0&.6(0(*%6&#); Z-0(D%4.-3%0"(%*,%0.&)$4(.%,"&.&,0(.#$0#,%#)%F#6;%^OR=SD%0"&0%4-.%&)%#)'50%*,%=#&$%-4%"AZ%W%O;T@O%[D%0"( -50'50%*,%=#&$%#$%"EY!1%W%O;^T@%[;%!"#$%,"-#,(%-4%"AZ%3&+#3#I($%0"(%&1&#:&=:(%$#6)&:%$/#)6%&0%0"(%-50'50%=2 $(00#)6%"EY!%&0%&''.-+#3&0(:2%0"(%3#**:(%-4%0"(%:#)(&.%$(63()0%-4%0"(%*,%0.&)$4(.%,"&.&,0(.#$0#,;

Using Transient Analysis to Verify Gv "#4.%',5%9$%&)5$%9<%')5&/'+45-%+0,5.4$5+%0$.2)5.$%,5,*<3 .4.:%,.%.$+%/2%45%E#`pEF[NpENpO12*464$0p%KCp-,45!1.7D!%O.%',5%9$%.$$5%60)1%@4-!%A!W7:%oSvo%$%o+vo%$ \L IJI! Transient analysis

60 m 40 m

Voltage (V)

20 m 0 –20 m –40 m –60 m

0

500.0 & Traces:

1.0 m

1.5 m Time (s) V(vin)

2.0 m

2.5 m

3.0 m

V(v[out])–0.873

Figure B.81 %Sv -4%0"(%B9E8%B8%&3':#4#(.%R0.&)$#()0%&)&:2$#$S;

Sensitivity to Process Variations A$',/.$%)6%+#$%#4-#%0$.4.+,5'$%,+%+#$%)/+2/+%5)&$%>)0:%$B/4(,3 *$5+*<:%9$',/.$%)6%+#$%#4-#%()*+,-$%-,45?:%+#$%(,*/$%)6%"[d"%4.%#4-#*<%.$5.4+4($%+)%+#$%$66$'+%)6%20)'$..%,5& +$12$0,+/0$%(,04,+4)5.%)5%+#$%'#,0,'+$04.+4'.%)6%+#$%+0,5.4.+)0.!%")%4**/.+0,+$%+#4.%2)45+:%')5.4&$0%;#,+%#,23 2$5.%;#$5%+#$%;4&+#%)6%WZ%>4!$!:%%@Z?%'#,5-$.%9<%q7\h!%"#$%')00$.2)5&45-%&'%+0,5.6$0%'#,0,'+$04.+4'.%,0$ .#);5%45%@4-!%A!WD>9?!%O'')0&45-*<:%;#$5%"=V1 %Z%D!`7%I:%"[d"%;4**%&0)2%+)%D!7WD%I%46%@Z%45'0$,.$.%9< 7\h:%,5&%;4**%04.$%+)%7!\\M%I%46%@Z%&$'0$,.$.%9<%7\h!%=5%20,'+4',*%'40'/4+%412*$1$5+,+4)5.:%+#4.%20)9*$1 4.%,**$(4,+$&%9<%/.45-%5$-,+4($%6$$&9,'S%+)%,''/0,+$*<%.$+%+#$%&'%94,.%()*+,-$%,+%+#$%)/+2/+%)6%+#$%,12*464$0 ,5&:%#$5'$:%+)%0$&/'$%+#$%.$5.4+4(4+<%)6%+#$%'40'/4+%+)%20)'$..%(,04,+4)5.!%a$%.+/&4$&%+#$%+)24'%)6%5$-,+4($ 6$$&9,'S%45%E#,2+$0%b!

B.3 Multisim Examples

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B-93

B-94 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

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B-95

B-96 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

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B-97

B-98 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

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!"(%.(1#$(*%*($#6)%#$%(1&:5&0(*%=2%.(&*#)6%'.-=($D%&$%$(0%5'%#)%B"^h!/-h80&6(hE'hN3'h.(1#$(*h C+;3$@O;%%!"(%$#35:&0#-)%.($5:0$%$"-/%o+@o%W%dU%[a[D%o+Ho%W%d^;H%[a[D%o+vo%W%J@Ud%[a[D%%RW@M1WHM1WJM1,5&1WUS%W @OJ%sND%%Wd1W%HOg%sND%%RWgM1WTS1%W%HOd%sND%&)*%%W^1%W%HOO%sND%4.-3%/"#,"%/(%$((%0"&0%0"(%1-:0&6(%6&#)$%&.( ,:-$(.%0-%0"(%0&.6(0(*%$'(,#4#,&0#-)$;% E)(%$"-5:*%)-0(%0"&0%0"(%*#$,.('&),#($%=(0/(()%0"(%"&)*<*($#6)%&)*%$#35:&0#-)%.($5:0$%#)%0"#$%$#35:&< 0#-)%(+&3':(%&.(%3-.(%&''&.()0%=(,&5$(%(..-.$%#)%(&,"%$0&6(%&**%5'; Z(+0D%/(%/#::%(+':-.(%$-3(%#3'-.0&)0%,"&.&,0(.#$0#,$%-4%0"(%*($#6)(*%0/-<$0&6(%B9E8%-'%&3';

Input Common-Mode Range "#$% /22$0% *414+% )6%+#$%452/+% ')11)531)&$% 0,5-$% 4.% +#$% (,*/$%)6 452/+%()*+,-$%,+%;#4'#%W7%,5&%W8%*$,($%+#$%.,+/0,+4)5%0$-4)5!%"#4.%)''/0.%;#$5%+#$%452/+%()*+,-$%$C'$$&.

B.3 Multisim Examples

1.0

VGD of Q and Q5 (V)

500.0 m 0 –500.0 m Q1 leaves saturation –1.0 Q5 leaves saturation –1.5 –2.0 –1

–500 m

0 vv1 Voltage (V)

500 m

Figure B.85 A)'50%,-33-)c3-*(%.&)6(%-4%0"(%0/-<$0&6(%B9E8%-'%&3';

+#$%&0,45%()*+,-$%)6%W7%9<%"/3%Z%D!\%I!%N45'$%+#$%&0,45%)6%W7%4.%,+%7%P%>D!87 l D!\? Z D!8b I:%+#$5%+#$%/22$0 *414+%)6%+#$%452/+%')11)531)&$%0,5-$%4.% v %0P3&+ Z O;Hf l O;d Z O;Tf[; !"(%:-/(.%:#3#0%-4%0"(%#)'50%,-33-)<3-*(%.&)6(%#$%0"(%1&:5(%-4%#)'50%1-:0&6(%&0%/"#,"%Wd%:(&1($%0"( $&05.&0#-)%.(6#-);%8#),(%4-.%Wd%0-%-'(.&0(%#)%$&05.&0#-)%0"(%1-:0&6(%&,.-$$%#0%R#;(;D%"4$dS%$"-5:*%&0%:(&$0%=( (M5&:%0-%0"(%-1(.*.#1(%1-:0&6(%&0%/"#,"%#0%#$%-'(.&0#)6%R#;(;D%O;H@%[SD%0"(%"#6"($0%1-:0&6(%'(.3#00(*%&0%0"( *.&#)%-4%Wd%$"-5:*%=(%cO;Tf%[;%A0%4-::-/$%0"&0%0"(%:-/($0%1&:5(%-4%v%0P%$"-5:*%=(% v %0P3#) Z P O;O^ [; ) !-%1(.#42%0"(%.($5:0$%5$#)6%0"(%$#35:&0#-)%0--:D%/(%$/('0%0"(%#)'50%,-33-)<3-*(%1-:0&6(%vAB9%4.-3%c @ [% 0-% @% [% &)*% ':-00(*% 0"(% .($5:0#)6% vS4% -4% W@% &)*% Wd% R&$% $(0% 5'% #)% B"^h!/-h80&6(hE'hN3'h C+hB9hP&)6(;3$@OS;%N$%,&)%=(%$(()%4.-3%F#6;%?;^dD%=-0"%0.&)$#$0-.$%W@%&)*%Wd%$0&2%#)%$&05.&0#-)%4-.%0"( #)'50%,-33-)<3-*(%.&)6(%-4% P O;O^ [ v %0P O;Tf%[D %&$%#)*#,&0(*%=2%,5.$-.$;

Common-Mode Rejection Ratio (CMRR) of the First Stage "#$%(,*/$%)6%+#$%EFGG%)6%+#$ 640.+% .+,-$% >+#$% ,'+4($3*),&$&% F[N% &466$0$5+4,*% ,12*464$0?% 4.% &$+$0145$&% 60)1% KB!% A!7L`!% V)+$% +#,+% +#$ (,*/$%)6%'$$%45%+#$%20)(4&$&%$B/,+4)5%')00$.2)5&.%+)%+#$%)/+2/+%0$.4.+,5'$%)6%W\%>4!$!:%72\?!%"#/.: B9PP

Pg +@ %@H;d %H @OO @O dO <<<<<<<<<<< < Z dfdH;U Z Td;d%*? Z <<<<<<<<<<<<<<<<<<<<<<<<<< Z @OO9 *J 7 2d Z @OO <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< <<<<<<<<<<<<<<<<<<<<<<<< Pg + )* O;H@ @ H9 *J 7 2d HOO @O

d.45-%+#$%.41/*,+4)5%+))*:%+#$%(,*/$%)6%EFGG%4.%',*'/*,+$&%9<%&4(4&45-%+#$%20$(4)/.*<%)9+,45$&%+7%(,*/$ >\L% IJI?% 9<% +#$% ')11)531)&$% -,45% )6% +#$% 640.+% .+,-$% ,.% 1$,./0$&% 45% E#Wp";)pN+,-$p[2pO12p KCpEFGG!1.7D!%"#4.%<4$*&. B9PP

+@ dU <<<<<<<<<<< Z <<<<<<<<<<<<<<<<<<<<< < Z gfHJ Z Tg;^%*? PJ + )* T^ @O

Output Voltage Range "#$%*);$.+%,**);,9*$%)/+2/+%()*+,-$%4.%+#$%(,*/$%,+%;#4'#%g`%*$,($.%+#$%.,+3 /0,+4)5%0$-4)5:%;#4'#%4.% P " $$ l " #"T Z P @ l O;H@ Z O;Tf%[; %"#$%#4-#$.+%,**);,9*$%)/+2/+%()*+,-$%4.%+#$ (,*/$%,+%;#4'#%WM%*$,($.%.,+/0,+4)5:%;#4'#%4.% " 44 P P " #"g Z @ P O;H@ Z O;Tf%[; %"#/.:%+#$%)/+2/+3()*+3 ,-$%0,5-$%4.%PD!`b%I%+)%D!`b%I! N$%$(0%5'%#)%B"^h!/-h80&6(hE'hN3'hC+hE50'50hP&)6(;3$@OD%0-%1(.#42%0"(%,&:,5:&0(*%-50'50%1-:0< &6(%.&)6(D%/(%$/('0%0"(%#)'50%1-:0&6(%4.-3%cH%3[%0-%H%3[%R/(%5$(*%&%$3&::%#)'50%1-:0&6(%*5(%0-%"#6"

B-99

B-100 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.8.1 continued

Output voltage swing 1.0

Voltage (V)

500.0 m

Output Swing

0

–500.0 m

–1.0

–1.5 –2 m

–1 m

0 vvin Voltage (V)

1m

Figure B.86 E50'50<1-:0&6(%.&)6(%-4%0"(%0/-<$0&6(%B9E8%-'%&3';

6&#)S;%N$%,&)%=(%$(()%4.-3%F#6;%?;^gD%0"(%-50'50%:(1(:%,"&)6($%4.-3%cO;Tfd%[%0-%O;T^U%[D%&%.&0"(.%$23< 3(0.#,&:%.&)6(;%!"(.(4-.(D%0"(%$#35:&0#-)%.($5:0$%,-)4#.3%-5.%"&)*<&)&:2$#$%,&:,5:&0#-)$;%

Input Offset Voltage O*+#)/-#:%+#$)0$+4',**<:%+#$0$%.#)/*&%9$%5)%.<.+$1,+4'%)66.$+:%;$%&)%)9.$0($ ,5%)/+2/+%)66.$+%()*+,-$%")!%O.%&$645$&%9<%KB!%`!7D8:%+#$%452/+%)66.$+%()*+,-$:%"[N:%',5%9$%)9+,45$&%,. " " #$ Z <<<<<#< +v Input offset of the op amp

1.0

500.0 m

Voltage (V)

Input Offset 0

–500.0 m

–1.0

–1.5 –750 &

–375 &

0 vvin voltage (V)

–375 &

Figure B.87 A)'50%-44$(0%1-:0&6(%-4%0"(%0/-<$0&6(%B9E8%-'%&3';

B.3 Multisim Examples

CM5#1&:()0:2D%#4%/(%&'':2%&%1-:0&6(%c"E8%=(0/(()%0"(%#)'50%0(.3#)&:$%-4%0"(%*#44(.()0#&:%&3':#4#(.D%0"( -50'50% 1-:0&6(% $"-5:*% =(% .(*5,(*% 0-% I(.-;% !"#$% (M5#1&:(),2% ,&)% =(% 1(.#4#(*% 5$#)6% 0"(% $#35:&0#-)% 0--: RB"^h!/-h80&6(hE'hN3'hC+hE50'50hP&)6(;3$@OS;%_"()%=-0"%0"(%#)'50%0(.3#)&:$%&.(%6.-5)*(*D%0"( '.-=(% &0% 0"(% -50'50% .(&*$% 0"(% *,% 1-:0&6(% O;dTU% [;% N:$-D% /"()% /(% &'':2% 0"(% 1-:0&6( " #$ Z O;dTU J@Ud $ @^J [ D%=(0/(()%0"(%#)'50%0(.3#)&:$D%0"(%-50'50%1-:0&6(%#$%.(*5,(*%0-%I(.-%RF#6; ?;^TS;%V(),(D%0"(%-'%&3'%"&$%&)%#)'50%-44$(0%1-:0&6(%-4%"E8%%W%@fd%s[D%/"#,"%&''.-+#3&0(:2%,-..($'-)*$ 0-%&)%-50'50%-44$(0%1-:0&6(%-4%"E%%W%O;dTU%[;

Example MS.9.1 Frequency Response of the Discrete CS Amplifier A)%0"#$%(+&3':(D%/(%/#::%#)1($0#6&0(%0"(%4.(M5(),2%.($'-)$(%-4%0"(%B8%&3':#4#(.%-4%C+&3':(%98;d;@;%?2 5$#)6%95:0#$#3%0-%'(.4-.3%p&,%&)&:2$#$q%-)%0"(%*($#6)(*%B8%&3':#4#(.D%/(%&.(%&=:(%0-%3(&$5.(%0"(%3#*< =&)*%6&#)%+P %&)*%0"(%J<*?%4.(M5(),#($%-?%&)*%-VD%&)*%0-%':-0%0"(%-50'50<1-:0&6(%3&6)#05*(%R#)%*?S%1(.$5$ 4.(M5(),2;%F#65.(%?;^^%$"-/$%0"(%$,"(3&0#,%,&'05.(%-4%0"(%B8%&3':#4#(.; DEVICE PARAMETERS

NAME W L KP LD VT0 LAMBDA GAMMA

Q1:NMOS 15.48u 0.2u 246u 0.01u 0.45 0.08 0.3

VDD

1.8 V

RG1 852.5 k)

RD1 3.41 k) CCO1

Rsig1

CCI1

10 k)

10 µF

V1

VDD 1.8 V

Q1

vout

10 µF RL1 50 k)

" 0.707 mVrms 1 kHz ! 0˚

RG2 947.5 k)

RS1 1.39 k)

CS1 10 µF

Figure B.88 8,"(3&0#,%,&'05.(%-4%*#$,.(0(%B8%&3':#4#(.;

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J

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B-101

B-102 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.9.1 continued

Low-Frequency Poles and Zero 6)**);.e

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@ @ < - O@ Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< Pg J J H 0 0% ' $#6 l ' #) @O @O l UU^;Td @O H @O @O - O@ Z O;OJUT%VI @ @ - OH Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < Pg J J H 0 0# ' 4 l ' ? H @O @O J;U@ @O l dO @O - OH Z O;JO%VI @ @ @ Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < J;JJ - OJ Z <<<<<<<<<<<<<<<<<<< 9 * l <<<<< Pg H 0$ '$ H @O @O

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B.3 Multisim Examples

30 fP2 = fL

fH

20

Magnitude

10

fP2 fz

fP1

0 –10 –20 –30 –40 10 m

1

100

10 k Frequency (Hz)

1M

100 M

10 G

100.0 M

10.0 G

Figure B.89 F.(M5(),2%.($'-)$(%-4%0"(%B8%&3':#4#(.; 30.0 20.0

Magnitude

10.0 0 !10.0 !20.0 !30.0 !40.0 10.0 m

1.0

100.0

10.0 k Frequency (Hz)

1.0 M

Figure B.90 F.(M5(),2%.($'-)$(%-4%0"(%B8%&3':#4#(.%/#0"%0$%W%@O%sF%&)*%0$%W%O;

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B-103

B-104 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.9.1 continued

$05*2% -4% 0"(% B8% &3':#4#(.% /#0"% &% $-5.,(<*(6()(.&0#-)% .($#$0&),(;% Z-0(% 0"&0% 0"(% =&)*/#*0"% &@% "&$ #),.(&$(*%=2%&''.-+#3&0(:2%0"(%$&3(%4&,0-.%&$%0"(%*.-'%#)%6&#)%+P;%N$%/(%:(&.)(*%#)%B"&'0(.%f%#)%-5. $05*2%-4%)(6&0#1(%4((*=&,LD%0"(%$-5.,(<*(6()(.&0#-)%.($#$0-.%'$%'.-1#*($%)(6&0#1(%4((*=&,LD%/"#,"%&::-/$ 5$%0-%0.&*(%-44%6&#)%4-.%&%/#*(.%=&)*/#*0";

Example MS.9.2 The Frequency Response of CMOS CS Amplifier and the Folded-Cascode Amplifier =5%+#4.%$C,12*$:%;$%;4**%45($.+4-,+$%+#$%60$B/$5'<%0$.2)5.$%)6%+#$%EF[N%EN%,12*464$0%,5&%+#$%6)*&$&3 ',.')&$%,12*464$0%.+/&4$&%45%KC,12*$.%FN!`!7%,5&%FN!`!8!%"#$%'40'/4+%&4,-0,1%)6%+#$%EF[N%EN%,12*43 64$0%4.%-4($5%45%@4-!%A!b7!% ?2%5$#)6%95:0#$#3%0-%'(.4-.3%p&,%&)&:2$#$q%-)%0"(%*($#6)(*%B9E8%B8%&3':#4#(.D%/(%&.(%&=:(%0-%3(&< $5.(%0"(%3#*=&)*%6&#)%+P%&)*%0"(%J<*?%4.(M5(),2%-VD%&)*%0-%':-0%0"(%-50'50<1-:0&6(%3&6)#05*(%R#)%*?S%1(.< $5$%4.(M5(),2%4-.%0/-%*#44(.()0%,&$($%-4%'$#6%R@OO% %&)*%@%9 SD%&$%$"-/)%#)%F#6;%?;fH; E=$(.1(% 0"&0% -V% *(,.(&$($% /"()% '$#6% #$% #),.(&$(*;% !"#$% #$% &)0#,#'&0(*% 4.-3% -5.% $05*2% -4% 0"(% "#6"< 4.(M5(),2%.($'-)$(%-4%0"(%B8%&3':#4#(.;%8'(,#4#,&::2D%&$%'$#6%#),.(&$($D%0"(%'-:(% @ @ - 6D#) Z <<<<<< <<<<<<<<<<<<<<<< H ' $#6 0 #)

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!"(%1&:5(%-4%0#)%,&)%=(%,&:,5:&0(*%=2%5$#)6%0"(%-1(.:&'%,&'&,#0&),($%09:M2vZ%&)*%6&0(<0-<,"&))(:%09:%&)* 09!M2vZ%&$%4-::-/$> 0 9: :2v@ Z * @ @ @ 0S$# Z d 0 9! :2v@ Z * @ @ @ 0S4# Z d

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@O

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@O

Pg

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@O

Pf

@O

Pf

F-.%09:D%/(%/.#0( H H 0 9:h,"&))(: Z <<< * @ @ @ ?0 2A Z <<< d J J

Pg

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@O

Pg

0 9:h,"&))(: Z H;U^%4F 0 9: Z H;U^%4F l O;^^O%4F Z J;Jg%4F

"#4.%0$./*+.%45%045%Z%L\!`W%6@%;#$5%oSvo%Z%\D%IJI!%O'')0&45-*<: @ @ < Z J;U^%9VI - V $ <<<<<< <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< H @ @O g UJ;J @O P@d

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Z O;^^O%4F Z O;^^O%4F P@H

J;f ^;^d @O <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < Pf U;O^ @O

B.3 Multisim Examples

Vtn |VAn| kn' IREF L W

NMOS 0.5 V 12.5V 246.2uA/V^2 0.1mA 0.2 um 0.48 um

Vtp |VAp| kp' IREF L W

PMOS –0.5 V 9V –86.1 uA/V^2 0.1mA 0.2 um 0.64 um

VDD

VDD 1.8 V

1.8 V M = 10 Q3

M = 10 Q4

Iref 100 uA

vout

Rsig 100 )

" !

Vsig 1 Vac

M=5 Q1

Iref2 100 uA

CS 1F

Figure B.91 8,"(3&0#,%,&'05.(%-4%0"(%B9E8%B8%&3':#4#(.;

Magnitude (dB)

40.0

10.0

–20.0

–50.0 1.0

100.0

10.0 k 1.0 M Frequency (Hz)

100.0 M

10.0 G

Figure B.92 F.(M5(),2%.($'-)$(%-4%0"(%B9E8%B8%&3':#4#(.%/#0"%'$#61W%@OO% %&)*%'$#61W%@%9 ;

B-105

B-106 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.9.2 continued

The Folded-Cascode Amplifier V$C+:% ;$% ;4**% 45($.+4-,+$% +#$% 60$B/$5'<% 0$.2)5.$% )6% +#$% 6)*&$&3 ',.')&$%,12*464$0%,5&%')12,0$%4+.%2$06)01,5'$%;4+#%+#,+%)6%+#$%EN%,12*464$0!%@4-/0$%A!bH%.#);.%+#$%'403 '/4+%&4,-0,1%)6%+#$%6)*&$&3',.')&$%,12*464$0!

Vtn |VAn| kn' IREF L W Vtp |VAp| kp' IREF L W

NMOS 0.5 V 12.5V 246.2uA/V^2

0.1mA 0.2 um 0.48 um

PMOS –0.5 V 9V –86.1 uA/V^2

0.1mA 0.2 um 0.64 um

VDD 1.8 V

VDD 1.8 V

VDD 1.8 V

M = 20 Q3

M = 10 Q4

M = 10 Q7

Iref 100uA VDD 1.8 V Rsig 1 M) " !

Vsig 1V ac

M=5 Q1

Iref2 100uA

M = 10 Q2

Iref3 100uA CS 1F M=5 IC = 0 V Q6

M = 10 Q8 VOUT

Iref4 100uA

M=5 Q5

Figure B.93 8,"(3&0#,%,&'05.(%-4%0"(%F-:*(*
@4-/0$%A!bL%.#);.%+#$%60$B/$5'<%0$.2)5.$%)6%+#$%6)*&$&3',.')&$%,12*464$0%,.%.41/*,+$&%9<%F/*+4.41%6)0 +#$%',.$.%)6%'.4-%Z%7DD %,5&%7%F !%"#$%')00$.2)5&45-%(,*/$.%)6%+#$%H3&A%60$B/$5'<%-V%)6%+#$%,12*464$0 ,0$%-4($5%45%",9*$%A!8L! 50.0

Magnitude (dB)

30.0

10.0

–10.0

–30.0

–50.0 1.0

100.0

10.0 k

1.0 M

100.0 M

10.0 G

Frequency (Hz)

Figure B.94 F.(M5(),2%.($'-)$(%-4%0"(%4-:*(*<,&$,-*(%&3':#4#(.%/#0"%'$#61W%@OO% %&)*%'$#61W%@%9 ;

B.3 Multisim Examples

Table B.24 Dependence of fH for the Designed Amplifiers 11111111111111111111111111111-V ':(91

B8%N3':#4#(.

F-:*(*
@OO%

d@O;T%9VI

Hfg;H%9VI

@%9

J;Jf%9VI

HU;O%9VI

F#.$0D%)-0(%0"&0%4-.%0"(%*($#6)(*%4-:*(*<,&$,-*(%&3':#4#(.D%'-5011W%@Hd%L %&)*%oSvo%W%@OO%[a[;%!"5$D%'-50 &)*%Sv%&.(%:&.6(.%0"&)%0"-$(%-4%0"(%B8%&3':#4#(.%R=2%&%4&,0-.%-4%HS;%Z-0(%0"&0%0"($(%,&:,5:&0#-)$%,&)%=( 4-5)*%#)%C+&3':($%98;T;@%&)*%98;T;H; N:$-D%-=$(.1(%0"&0%/"()%'$#6%#$%$3&::D%-V%-4%0"(%4-:*(*<,&$,-*(%&3':#4#(.%#$%:-/(.%0"&)%0"&0%-4%0"(%B8 &3':#4#(.%=2%&%4&,0-.%-4%&=-50%@;^D%&''.-+#3&0(:2%(M5&:%0-%0"(%4&,0-.%=2%/"#,"%0"(%6&#)%#$%#),.(&$(*;%!"#$%#$ =(,&5$(%/"()%'$#6%#$%$3&::D%0"(%4.(M5(),2%.($'-)$(%-4%=-0"%&3':#4#(.$%#$%*-3#)&0(*%=2%0"(%'-:(%4-.3(*%&0 0"(%-50'50%)-*(D%0"&0%#$D -V $ -6

-50

@ @ Z <<<<<< <<<<<<<<<<<<<<<<<<< H ' -50 0 -50

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oo%7 OJ %oo%' #)H

;#$0$%'45\%4.%+#$%452/+%0$.4.+,5'$%)6%+#$%')11)53-,+$%+0,5.4.+)0%W8%,5&%',5%9$%)9+,45$&%/.45-%,5%,220)C43 1,+4)5%)6%+#$%0$*,+4)5.#42%6)/5&%6)0%452/+%0$.4.+,5'$%)6%+#$%')11)53-,+$%,12*464$0e 7 2H l 7 2d < ' #)H $ <<<<<<<<<<<<<<<<<<< 9 *H 7 2H

"#/.: 7 2H l 7 2d H < Z <<<<<<< ' !@ $ 7 2@ %oo%7 2J %oo% <<<<<<<<<<<<<<<<<<< < 9 *H 7 2H 9 *H

!"(.(4-.(D%'!@%#$%35,"%$3&::(.%0"&)% ' ? %R#)%0"(%B8%&3':#4#(.%$%72@%oo%72JS;%V(),(D%0#)%-4%0"(%*($#6)(* 4-:*(*<,&$,-*(% &3':#4#(.% #$% #)*((*% 35,"% $3&::(.% 0"&)% 0"&0% -4% 0"(% B8% &3':#4#(.% =(,&5$(% 0"(% R@% e% 9*'`S 35:0#':#(.% #$% $3&::(.% 4-.% 0"(% 4-:*(*<,&$,-*(% *(1#,(;% !"#$% ,-)4#.3$% 0"&0% 0"(% 4-:*(*<,&$,-*(% &3':#4#(.% #$ 35,"%:($$%#3'&,0(*%=2%0"(%9#::(.%(44(,0%&)*D%0"(.(4-.(D%,&)%&,"#(1(%&%35,"%"#6"(.%-V%/"()%'$#6%#$%:&.6(; !"(%3#*=&)*%6&#)%-4%0"(%4-:*(*<,&$,-*(%&3':#4#(.%,&)%=(%$#6)#4#,&)0:2%#),.(&$(*%=2%.(':&,#)6%0"(%,5.< .()0%3#..-.%Wd ^Wg%/#0"%&%,5..()0%3#..-.%"&1#)6%&%:&.6(.%-50'50%.($#$0&),(D%$5,"%&$%0"(%,&$,-*(%,5..()0%3#.< .-.%#)%F#6;%g;JHD%/"-$(%-50'50%.($#$0&),(%#$%&''.-+#3&0(:2%9*72\;%A)%0"#$%,&$(D%"-/(1(.D%'#)H%&)*D%"(),(D%'!@ #),.(&$(D%,&5$#)6%&)%#),.(&$(*%9#::(.%(44(,0%&)*%&%,-..($'-)*#)6%.(*5,0#-)%#)%-V; F#)&::2D%#0%#$%#)0(.($0#)6%0-%-=$(.1(%0"&0%0"(%4.(M5(),2%.($'-)$(%-4%0"(%4-:*(*<,&$,-*(%&3':#4#(.%$"-/) #)%F#6;%?;fU%*.-'$%=(2-)*%-V%&0%&''.-+#3&0(:2%cHO%*?a*(,&*(%/"()%'$#6%W%@OO %&)*%&0%&''.-+#3&0(:2 cUO%*?a*(,&*(%/"()%'$#6%W%@9 ;%!"#$%#$%=(,&5$(%/"()%'$#6%#$%$3&::D%0"(%4.(M5(),2%.($'-)$(%#$%*-3#)&0(* =2%0"(%'-:(%&0%-6M-50;%V-/(1(.D%/"()%'$#6%#$%#),.(&$(*D%-6M#)1#$%3-1(*%,:-$(.%0-%-6M-50D%&)*%=-0"%'-:($%,-)0.#=50( 0-%0"(%6&#)%4&::-44;

B-107

B-108 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.10.1 A Two-Stage CMOS Op Amp with Series–Shunt Feedback =5%+#4.%$C,12*$:%;$%;4**%45($.+4-,+$%+#$%$66$'+%)6%,22*<45-%,%.$04$.P.#/5+%6$$&9,'S%+)%+#$%+;)3.+,-$%EF[N )2%,12%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45%@4-!%A!b\!% !"(%4#.$0%$0&6(%#$%&%*#44(.()0#&:%'&#.%W@^WH%R/"#,"%#$%&,0#1(:2%:-&*(*%/#0"%0"(%,5..()0%3#..-.%4-.3(*%=2 WJ%&)*%WUS%/#0"%=#&$%,5..()0%$5'':#(*%=2%&%,5..()0%3#..-.%4-.3(*%=2%W^%&)*%WdD%/"#,"%50#:#I($%0"(%.(4(.< (),(%=#&$%,5..()0%%PCF;%!"(%$(,-)*%$0&6(%,-)$#$0$%-4%WgD%/"#,"%#$%&%,-33-)<*.&#)%&3':#4#(.%&,0#1(:2%:-&*(* /#0"%&%,5..()0%$-5.,(%:-&*%R0.&)$#$0-.%WTS; F-.% 0"(% #3':(3()0&0#-)% -4% 0"#$% B9E8% -'% &3'D% /(% /#::% 5$(% &% O;@^
Vtn |VAn| kn' L W

NMOS 0.5 V 12.5V 246.2uA/V^2 0.2 um 0.48 um

VDD

VDD

VDD 1V

PMOS

1REF 200 µA

–0.5 V 9V –86.1 µA/V^2 0.2 um 0.64 um

Q6 Q1

vid

1V

Q4

Q3 Vtp |VAp| kp' L W

VDD 1V

1V

Q2

" 0.707µVrms 1 MHz ! 0º

vOUT

Q5 Q8

Q7

VSS –1 V

VSS –1 V

–1 V

VSS

Figure B.95 %8,"(3&0#,%,&'05.(%-4%0"(%0/-<$0&6(%B9E8%-'%&3';

,&'&,#0&),(%1&:5($;%!"(%0&.6(0(*%$'(,#4#,&0#-)$%&.(%&)%5):-&*(*%*,%-'()<:--'%1-:0&6(%6&#)%o+vo%W%dO%[a[D &)*%,:-$(*<:--'%1-:0&6(%6&#)%o+-o%W%@O%[a[D%/#0"%(&,"%-4%0.&)$#$0-.$%W@D%WHD%WJD%&)*%WU%=#&$(*%&0%&%*.&#) ,5..()0%-4%@OO%sN; !-%&,"#(1(%0"(%0&.6(0(*%$'(,#4#,&0#-)$D%&%=#&$#)6%,5..()0%%PCF%%W%HOO%sN%#$%5$(*D%&)*%0"(%0.&)$#$0-.$%WdD WgD%WTD%&)*%W^%/#::%=(%$#I(*%0-%,-)*5,0%*.&#)%,5..()0$%-4%HOO%sN;%!"(%*,%-'()<:--'%1-:0&6(%6&#)%4-.%0"#$ &3':#4#(.%#$%0"(%'.-*5,0%-4%0"(%1-:0&6(%6&#)$%-4%0"(%0/-%$0&6($;%8#),(%0"(%6&#)%-4%0"(%$(,-)*%$0&6(%R$-5.,( 4-::-/(.S% #$% &''.-+#3&0(:2% @% [a[D% 0"(% 4#.$0% $0&6(% 35$0% =(% *($#6)(*% 0-% '.-1#*(% 0"(% 45::% 1-:0&6(% 6&#)% -4 dO [a[%0-%&,"#(1(%0"(%$'(,#4#(*%-'()<:--'%1-:0&6(%6&#); !"(%&3':#4#(.%$'(,#4#,&0#-)$%&.(%$533&.#I(*%#)%!&=:(%?;Hd;

B.3 Multisim Examples

Table B.25 Two-Stage CMOS Op-Amp Specifications 7&.&3(0(.$

[&:5(

ARW@D%WHD%WJD%&)*%WUS

@OO%sN

ARWdD%WgD%WTD%&)*%W^S

HOO%sN

o+@o

dO%[a[

o+Ho

@%[a[

o+4o

@O%[a[

"44

%@%[

"$$

c@%[

Hand Design Design of the Two-Stage Op Amp !"(%4#.$0%$0&6(%-4%0"#$%B9E8%-'%&3'%#$%#*()0#,&:%0-%0"( 4#.$0%$0&6(%-4%0"(%-'%&3'%/(%*($#6)(*%#)%C+&3':(%98;^;@D%0-%/"#,"%0"(%.(&*(.%#$%.(4(..(*;%N:$-D%0.&)< $#$0-.$%Wg%&)*%WT%&.(%$#I(*%0-%'.-1#*(%0"(%=#&$%,5..()0%-4%HOO%sN%#)%0"(%$(,-)*%$0&6(; N$% &% .($5:0D%5$#)6% 5)#0<$#I(% Z9E8% 0.&)$#$0-.$%/#0"% @ 3 ? 3 Z O;U^ 3 O;HO 3D % &)*%5)#0<$#I(% 79E8 0.&)$#$0-.$%/#0"% @ 6 ? 6 Z O;gU 3 O;HO 3D %0"(%,-..($'-)*#)6%35:0#':#,&0#1(%4&,0-.%*%4-.%(&,"%0.&)$#$0-. ,&)%=(%,&:,5:&0(*%&$%4-5)*%#)%C+&3':(%98;^;@%R/#0"%0"(%*#44(.(),(%"(.(%0"&0%Wg%%&)*%WT%"&1(%0"(%$&3(%*#3()< $#-)$S;%!&=:(%?;Hg%$533&.#I($%0"(%.(:(1&)0%#)4-.3&0#-)%&)*%0"(%,&:,5:&0(*%*%1&:5($%4-.%0"(%0.&)$#$0-.; Table B.26 Transistor Sizes !.&)$#$0-.

%K%RsNS

*

@

@OO

g

H

@OO

g

J

@OO

@U

U

@OO

@U

d

HOO

@J

g

HOO

@J

T

HOO

@J

^

HOO

@J

Design of the Feedback Network F#.$0%/(%)((*%0-%*(0(.3#)(%0"(%1&:5(%-4%0"(%4((*=&,L%4&,0-. % 4-.% 0"#$% $(.#($c$"5)0% 4((*=&,L% &3':#4#(.;% !"(% % )(0/-.L% ,&)% =(% #3':(3()0(*% 5$#)6% &% 1-:0&6( *#1#*(.D%&$%$"-/)%#)%F#6;%?;fg;%!"(%.($#$0-.%1&:5($%&.(%,"-$()%:&.6(%()-56"%R#)%,-3'&.#$-)%0-%0"( -50'50%.($#$0&),(%-4%0"(%*($#6)(*%0/-<$0&6(%-'%&3'S%0-%3#)#3#I(%0"(%(44(,0%-4%:-&*#)6;%!"(.(4-.(D (44(,0#1(:2D% + $ +v

/"(.(%+%#$%0"(%-'()<:--'%6&#)%-4%0"(%&3':#4#(.%R/#0"%:-&*#)6S;%Z-/%/(%,&)%,&:,5:&0(%0"(%.(M5#.(*%4((*< =&,L%4&,0-.D% D%&$%4-::-/$> +v dO < Z @O[a[ Z <<<<<<<<<<<<<<<<<< + - Z <<<<<<<<<<<<<<<<<< @ l +v @ l dO Z O;O^

B-109

B-110 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.10.1 continued

!"(%.($#$0-.%1&:5($%-4%0"#$%1-:0&6(%*#1#*(.%&.(%$(:(,0(*%0-%'.-1#*(%1-:0&6(%*#1#$#-)$%-4%O;O^%R'@%W%fH%L &)*%'H%W%^L S; R1 vOUT

negative_input 92 k) R2 8 k)

Figure B.96 % Z(0/-.L;

Simulation Z-/%/(%/#::%$#35:&0(%-5.%*($#6)(*%,#.,5#0%0-%1(.#42%-5.%"&)*%*($#6)%&)*%$05*2%0"(%(44(,0%-4%4((*=&,L%-) 0"(%*,<6&#)D%=&)*/#*0"D%&)*%-50'50%.($#$0&),(%-4%0"(%&3':#4#(.;

Verifying Av "#$%.'#$1,+4'%',2+/0$%)6%+#$%+;)3.+,-$%EF[N%,12*464$0%4.%45%@4-!%A!b\!%a$%',5%($046< +#$% &'% ()*+,-$% -,45% )6% +#4.% ,12*464$0% 9<% 2$06)0145-% 60$B/$5'<30$.2)5.$% ,5,*<.4.% ,.% .$+% /2% 45 E#7Dp[2O12pKCpO(!1.7D! N$%,&)%=(%$(()%4.-3%F#6;%?;fTD%o+vo%W%Jd;O%*?%$%dg;H%[a[D%/"#,"%#$%,:-$(%0-%0"(%0&.6(0(*%$'(,#4#,&0#-); Verifying A

"#$%.'#$1,+4'%',2+/0$%)6%+#$%+3'40'/4+%4.%-4($5%45%@4-!%AbW! AC analysis

Magnitude

40 30 20 10 0 1M

10 M

100 M

1G

Frequency (Hz) 25

Phase (deg)

0 –25 –50 –75

–100 –125 1M

10M

100M Frequency (Hz)

1G

Figure B.97 F.(M5(),2%.($'-)$(%-4%0"(%0/-c$0&6(%B9E8%-'<&3'%&3':#4#(.;

B.3 Multisim Examples

Vtn |VAn| kn' L W

NMOS 0.5 V 12.5V 246.2µA/V^2 0.2 um 0.48 um

VDD 1V

1V

VDD 1V

Q4

Q3 IREF 200 uA

PMOS Vtp |VAp| kp' L W

VDD 1V

VDD

–0.5 V 9V –86.1 uA/V^2 0.2 um 0.64 um

Q6 Q2

Q1 vid

" 0.707uVrms 1 MHz ! 0˚

R3

R1 R2 8 k) 92 k)

92 k) vOUT

R4 8 k)

Q5 Q8

Q7

VSS –1 V

–1 V

VSS

–1 V

VSS

Figure B.98 8,"(3&0#,%,&'05.(%-4%0"(%+%,#.,5#0;

_(%,&)%1(.#42%0"(%-'()<:--'%1-:0&6(%6&#)%-4%0"#$%,#.,5#0%=2%'(.4-.3#)6%&%4.(M5(),2<.($'-)$(%&)&:2$#$ &$%$(0%5'%#)%B"@OhE'N3'hC+hN;3$@O;%N$%,&)%=(%$(()%4.-3%F#6;%?;ffD%o+o%W%JU;f%*?%$%dd;g%[a[D%/"#," #$%,:-$(%0-%0"(%1&:5(%-4%+v;%!"#$%$5''-.0$%-5.%&$$53'0#-)%-4% + $ + v ; AC analysis 40 Magnitude

30 20 10 0 –10 1M

10 M

100 M Frequency (Hz)

1G

25

Phase (deg)

0 –25 –50 –75 –100 –125 –155 1M

10 M

100 M

1G

Frequency (Hz)

Figure B.99 %8,"(3&0#,%,&'05.(%-4%0"(%+<%,#.,5#0;

Verifying Af "#$%.'#$1,+4'%',2+/0$%)6%+#$%'*).$&3*))2%'40'/4+%4.%-4($5%45%@4-!%A!7DD!%O.%',5%9$%.$$5 60)1%+#4.%.'#$1,+4':%+#$% 35$+;)0S%$.+,9*4.#$.%,%.$04$.%')55$'+4)5%,+%+#$%452/+%,5&%,%.#/5+%')55$'+4)5%,+ +#$%)/+2/+%)6%+#$%)04-45,*%+;)3.+,-$%EF[N%)2%,12!

B-111

B-112 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.10.1 continued

_(%,&)%1(.#42%0"(%,:-$(*<:--'%1-:0&6(%6&#)%=2%'(.4-.3#)6%&%4.(M5(),2<.($'-)$(%&)&:2$#$%&$%$(0%5'%#) B"@OhE'N3'hC+hN4;3$@O;%N$%,&)%=(%$(()%4.-3%F#6;%?;@O@D%o+-o%W%HO;H%*?%$%@O;H%[a[D%/"#,"%#$%,:-$( 0-%0"(%0&.6(0(*%$'(,#4#,&0#-)%4-.%+- ;

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0.2 um 0.48 um

L W

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Q4

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Figure B.100 %8,"(3&0#,%,&'05.(%-4%0"(%,:-$(*<:--'%,#.,5#0; AC analysis

Magnitude

25 10 –5 –20 1M

10 M

100 M Frequency (Hz)

1G

10 M

100 M Frequency (Hz)

1G

25

Phase (deg)

0 –25 –50 –75 –100 –125 –150 1M

Figure B.101 F.(M5(),2%.($'-)$(%-4%0"(%,:-$(*<:--'%,#.,5#0;

VSS

B.3 Multisim Examples

Investigating the Effect of Feedback =5% ,&&4+4)5% +)% +#$% 60$B/$5'<30$.2)5.$% ,5,*<.4.:% ;#4'# 20)(4&$&%456)01,+4)5%)5%+#$%&'%()*+,-$%-,45%,5&%+#$%H3&A%9,5&;4&+#:%;$%/.$&%F/*+4.41%+)%645&%+#$%)/+3 2/+%0$.4.+,5'$.%)6%+#$%)2$53*))2%,5&%'*).$&3*))2%'40'/4+.%>,.%.$+%/2%45%E#7Dp[2O12pKCpO!1.7D%,5& E#7Dp[2O12pKCpO6!1.7D?!% ",9*$% A!8`% ./11,04T$.% )/0% 645&45-.% 6)0% )2$53*))2% >+% '40'/4+?% ,5& '*).$&3*))2%'40'/4+.! Table B.27 Effect of Feedback on Gain, 3-dB Bandwidth, and Output Resistor B#.,5#0

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Example MS.11.1 Class B Bipolar Output Stage =5%+#4.%$C,12*$:%;$%;4**%&$.4-5%,%'*,..%A%)/+2/+%.+,-$%+)%&$*4($0%,5%,($0,-$%2);$0%)6%8D%a%+)%,5%W3 %*),&! "#$%.'#$1,+4'%',2+/0$%)6%,%'*,..%A%)/+2/+%.+,-$%412*$1$5+$&%/.45-%Af".%4.%.#);5%45%@4-!%A!7D8!%a$%+#$5 ;4**% 45($.+4-,+$% (,04)/.% '#,0,'+$04.+4'.% )6% +#$% &$.4-5$&% '40'/4+% ./'#% ,.% '0)..)($0% &4.+)0+4)5% ,5&% 2);$03 ')5($0.4)5%$664'4$5'
QN IN

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Figure B.102 8,"(3&0#,%,&'05.(%-4%,:&$$%?%-50'50%$0&6(;

RL 8)

B-113

B-114 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.11.1 continued

!"(%,#.,5#0%$'(,#4#,&0#-)$%&.(%$533&.#I(*%#)%!&=:(%?;H^; Table B.28 Class B Output Stage Specifications 8'(,#4#,&0#-)

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B.3 Multisim Examples

Load Power PL !-% 3(&$5.(% 0"(% &3-5)0% -4% '-/(.% *(:#1(.(*% 0-% 0"(% :-&*D% /(% /#::% 50#:#I(% !.&)$#()0 N)&:2$#$% #)% 95:0#$#3% &$% $(0% 5'% #)% B"@@hB:&$$h?hC+;3$@O;% !"(% 0.&)$#()0% &)&:2$#$% $#35:&0#-)% #$% '(.< 4-.3(*%-1(.%0"(%#)0(.1&:%O%3$%0-%H%3$D%&)*%0"(%/&1(4-.3$%-4%0"(%1-:0&6(%&0%0"(%-50'50%)-*(%&)*%0"(%-50'50 ,5..()0%&.(%':-00(*%#)%F#6;%?;@OJ;% N$%,&)%=(%$(()%#)%F#6;%?;@OJD%0"(%'(&L%1-:0&6(%&3':#05*(%#$%&''.-+#3&0(:2%@g;f%[%&)*%0"(%'(&L%,5.< .()0%&3':#05*(%#$%H;@%N;%Y'-)%&%,:-$(.%:--L%&0%0"(%,5..()0%&)*%1-:0&6(%/&1(4-.3$D%/(%,&)%-=$(.1(%0"&0 =-0"% (+"#=#0% ,.-$$-1(.% *#$0-.0#-);% !"(% =-00-3% 6.&'"% #)% F#6;% ?;@OJ% $"-/$% 0"(% #)$0&)0&)(-5$% &)*% 0"(

Voltage V (OUT)

20

10

0

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0

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1.0 m

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Time (s) 3

Current (A) I(RL)

2 1 0 –1 –2 –3

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Time (s) 40

25

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Figure B.103 Q-&*%1-:0&6(D%,5..()0D%&)*%#)$0&)0&)(-5$%&)*%&1(.&6(%:-&*%'-/(.;

B-115

B-116 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.11.1 continued

&1(.&6(%'-/(.%*#$$#'&0(*%#)%0"(%:-&*%.($#$0&),(;%!"($(%/&1(4-.3$%/(.(%-=0&#)(*%=2%35:0#':2#)6%0"(%,5.< .()0%&)*%1-:0&6(%/&1(4-.3$D%&)*%=2%0&L#)6%0"(%%.5))#)6%&1(.&6(%4-.%0"(%&1(.&6(%'-/(.D%O?L1!"(%0.&)$#()0 =("&1#-.%-4%&1(.&6(%'-/(.%(1()05&::2%$(00:($%#)0-%&%M5&$#,-)$0&)0%$0(&*2<$0&0(%1&:5(%-4%@T;g%_;%

Supply Power, PS 8#3#:&.:2D%/(%,&)%':-0%#)$0&)0&)(-5$%1-:0&6(%&)*%,5..()0%&0%0"(%"00%&)*%",,%)-*($ 0-%3(&$5.(%0"(%1&:5(%-4%O$ ;%F#65.(%?;@OU%$"-/$%0"(%1-:0&6(D%,5..()0D%#)$0&)0&)(-5$D%&)*%&1(.&6(%'-/(.%4-. a"001 ;%_(%,&)%':-0%0"($(%M5&)0#0#($%4-.1^",,1 %&$%/(::;%V-/(1(.D%-/#)6%0-%$233(0.2D%/(%*-%)-0%)((*%06()(.&0(%':-0$%4-.%0"(%)(6&0#1(%1-:0&6(%$5'':2;%!"(%&1(.&6(%'-/(.%'.-1#*(*%=2%a"00 M1O$aD11#$%@d%_;%!"(.(< 4-.(D%0"(%0-0&:%'-/(.%'.-1#*(*%=2%=-0"%1-:0&6(%$5'':#($%#$%JO%_; 26

VCC (V)

25 24 23 22 21 20

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2.0 m

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I (VCC) A

3

2

1

Instantaneous and Avg Power (W)

0

60 50 40 30 20 10 0 –10

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B.3 Multisim Examples

Power-Conversion Efficiency, h .41/*,+$&%'40'/4+%,.%6)**);.!% O Z <<<<
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Transistor Power Dissipation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dD%#$%&''.-+#3&0(:2%g%_;%!"(.(4-.(D%0"(%0-0&:%'-/(.%*#$$#'&0(*%#)%0"(%0.&)$#$0-.$%#$%@H%_; 0

VCE (QP) A

–13

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0

500.0 &

1.0 m

1.5 m Time (s)

2.0 m

2.5 m

3.0 m

0

500.0 &

1.0 m

1.5 m Time (s)

2.0 m

2.5 m

3.0 m

0

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IC (QP) A

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Instantaneous and Avg Power of QP (W)

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20 15 10 5 0

Figure B.105 [-:0&6(D%,5..()0D%&)*%#)$0&)0&)(-5$%&)*%&1(.&6(%'-/(.%4-.%W6;

B-117

B-118 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.11.1 continued

!"(%$#35:&0#-)%.($5:0$%&)*%"&)*<*($#6)%,&:,5:&0#-)$%&.(%$533&.#I(*%#)%!&=:(%?;Hf;%E=$(.1(%0"&0%0"( 1&:5($%&.(%M5#0(%,:-$(D%/"#,"%1(.#4#($%-5.%*($#6)%-4%0"(%,:&$$%?%%-50'50%$0&6(;% Table B.29 Summary of Simulation and Hand-Design Results 9(&$5.(3()0

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Voltage (V)

10 5 0 –5 –10 –15 –10

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vv1 Voltage (V)

Figure B.106 [!B%-4%,:&$$%?%-50'50%$0&6(;

Total Harmonic Distortion (THD) "#4.%,5,*<.4.%&$')12).$.%+#$%;,($6)01%-$5$0,+$&%(4,%+0,5.4$5+ ,5,*<.4.% 45+)% 4+.% @)/04$03.$04$.% ')12)5$5+.!% @/0+#$01)0$:% F/*+4.41% ')12/+$.% +#$% "YU% )6% +#$% )/+2/+ ;,($6)01:%,5&%+#$%0$./*+.%,0$%.#);5%45%@4-!%A!7D`!%

B.3 Multisim Examples

Fourier Analysis

Magnitude (dB)

30 0 –30 –60

0

2k

4k

6k

8k

10 k

Frequency (Hz)

Figure B.107 F-5.#(.<$(.#($%,-3'-)()0$%-4%0"(%-50'50%1-:0&6(%&)*%,:&$$%?%-50'50%$0&6(%!VK;

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Example MS.12.1 A Two-Stage CMOS Op Amp with Frequency Compensation =5%+#4.%$C,12*$:%;$%;4**%/.$%F/*+4.41%+)%,4&%45%&$.4-545-%+#$%60$B/$5'<%')12$5.,+4)5%)6%+#$%+;)3.+,-$ EF[N%'40'/4+%;#).$%.'#$1,+4'%4.%.#);5%45%@4-!%A!7DW!%F/*+4.41%;4**%+#$5%9$%$12*)<$&%+)%&$+$0145$%+#$ 60$B/$5'<%0$.2)5.$%,5&%+#$%.*$;%0,+$%)6%+#$%)2%,12!%a$%;4**%,../1$%,%D!\3 1%EF[N%+$'#5)*)-<%6)0%+#$ F[N@K".%,5&%/.$%+<24',*%NQ=EK%*$($*37%1)&$*%2,0,1$+$0.%6)0%+#4.%+$'#5)*)-
B-119

B-120 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.12.1 continued NMOS 0.7 V Vtn 0.1 LAMBDA 246.2uA/V^2 kn' IREF L W

0.09 mA 0.6 um 1.25 um

VDD

VDD 3.3 V

3.3 V

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M=16 Q5

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D

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0–5 v/v 0v0v

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B.3 Multisim Examples

Magnitude (dB)

75.0 50.0 25.0 0 ft

!25.0 !50.0 1.0000

100.0000

10.0000 k Frequency (Hz)

1.0000 M

100.0000 M

100.0000

10.0000 k Phase (deg)

1.0000 M

100.0000 M

Phase (degrees)

0 !45.0 !90.0 !135.0 !180.0 1.0000

Figure B.109 9&6)#05*(%&)*%'"&$(%.($'-)$(%-4%0"(%-'<&3'%,#.,5#0%/#0"%'%W%@;dJ%LD%00%W%O%R)-%4.(M5(),2%,-3'()< $&0#-)SD%&)*%00%W%@;^%'F%R79%W%Td-S;

/&$%4-5)*%0"&0D%/#0"%'%W%@;dJ%L D%/(%)((*(*%00%W%O;g%'F%&)*%00%W%@;^%'F%0-%$(0%OP%W%dd-%&)*%OP%W%Td-D .($'(,0#1(:2;%_(%)-0(%0"&0%0"($(%1&:5($%&.(%.(&$-)&=:2%,:-$(%0-%0"-$(%'.(*#,0(*%=2%"&)*%&)&:2$#$;%!"(%,-..(< $'-)*#)6%4.(M5(),2%.($'-)$($%4-.%0"(%,-3'()$&0(*%-'%&3'$%&.(%':-00(*%#)%F#6$;%?;@Of%&)*%?;@@O;%F-.%,-3'&.< #$-)D%/(%&:$-%$"-/%0"(%4.(M5(),2%.($'-)$(%-4%0"(%5),-3'()$&0(*%-'%&3'%R00%W%OS;%E=$(.1(%0"&0%0"(%5)#02<6&#) 4.(M5(),2%-/%*.-'$%4.-3%TO;^%9VI%0-%Hg;U%9VI%&$%00%#$%#),.(&$(*%0-%#3'.-1(%OP;% P&0"(.%0"&)%#),.(&$#)6%0"(%,-3'()$&0#-)%,&'&,#0-.%001 0-%#3'.-1(%0"(%'"&$(%3&.6#)D%0"(%1&:5(%-4%0"( $(.#($%.($#$0-.%'%,&)%=(%#),.(&$(*>%4-.%&%6#1()%00D%#),.(&$#)6%'%&=-1(% @ S *H %':&,($%0"(%0.&)$3#$$#-)%I(.&0%&%)(6&0#1(%.(&:<&+#$%:-,&0#-)%RCM;%@O;J^SD%/"(.(%0"(%'"&$(%#0%#)0.-*5,($%H!!:%0-%0"(%'"&$(%3&.6#);%!"5$D OP%,&)%=(%#3'.-1(*%/#0"-50%&44(,0#)6%-/;%%!-%1(.#42%0"#$%'-#)0D%/(%$(0%00%0-%O;g%'F%&)*%$#35:&0(%0"(%-'< &3'% ,#.,5#0% #)% 95:0#$#3% 4-.% 0"(% ,&$($% -4% '% W% @;dJ% L % &)*% '% W% J;H% L ;% !"(% ,-..($'-)*#)6% 4.(M5(),2 .($'-)$(% #$% ':-00(*% #)% F#6;% ?;@@@;% E=$(.1(% "-/% -/% #$% &''.-+#3&0(:2% #)*('()*()0% -4% ';% V-/(1(.D% =2 #),.(&$#)6%'D%/(%,&)%#3'.-1(%OP%4.-3%dd-%0-%Td-; A),.(&$#)6%0"(%OP%#$%*($#.&=:(%=(,&5$(%#0%.(*5,($%0"(%-1(.$"--0%#)%0"(%$0('%.($'-)$(%-4%0"(%-'%&3';%!1(.#42%0"#$%'-#)0D%/(%$#35:&0(%#)%95:0#$#3%0"(%$0('%.($'-)$(%-4%0"(%-'%&3'%4-.%OP%W%dd-%&)*%OP%W%Td-;%!*-%0"&0D%/(%,-))(,0%0"(%-'%&3'%#)%&%5)#02<6&#)%,-)4#65.&0#-)D%&'':2%&%$3&::%R@O<3[S%'5:$(%$#6)&:%&0%0"( #)'50%/#0"%1(.2%$"-.0%R@<'$S%.#$(%&)*%4&::%0#3($%0-%(35:&0(%&%$0('%#)'50D%'(.4-.3%&%0.&)$#()0%&)&:2$#$%$#35< :&0#-)%R&$%$(0%5'%#)%B"@Hh!/-h80&6(hB9E8hE'N3'hC+h83&::<8#6)&:;3$@OSD%&)*%':-0%0"(%-50'50%1-:0< &6(% &$%$"-/)% #)%F#6;%?;@@H;% E=$(.1(%0"&0%0"(%-1(.$"--0%#)% 0"(% $0('%.($'-)$(%*.-'$%4.-3%@dk% 0-%@;Uk /"()%0"(%'"&$(%3&.6#)%#$%#),.(&$(*%4.-3%dd-%0-%Td-; _(%,-),:5*(%0"#$%(+&3':(%=2%,-3'50#)6%$'D%0"(%$:(/%.&0(%-4%0"(%-'%&3';%F.-3%CM;%R@O;UOSD%/(%"&1( S *@ < " Z @gg;d%[a : $' Z H - / " #" Z <<<<<<<< 0 0 #"

B-121

B-122 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.12.1 continued

Magnitude (dB)

60.0 40.0 20.0 0

ft

!20.0 !40.0 1.0000

100.0000

10.0000 k Frequency (Hz)

1.0000 M

100.0000 M

100.0000

10.0000 k

1.0000 M

100.0000 M

Phase (deg)

0 !45.0 !90.0 !135.0 !180.0 1.0000

Phase (deg)

Magnitude (dB)

Figure B.110 9&6)#05*(%&)*%'"&$(%.($'-)$(%-4%0"(%-'<&3'%,#.,5#0%/#0"%'%W%@;dJ%L D%00%W%O%R)-%4.(M5(),2%,-3'()< $&0#-)SD%&)*%00%W%@;^%'F%ROP%W%Td-S; 60.000 50.000 40.000 30.000 20.000 10.000 0 !10.000 !20.000 !30.000 !40.000 1.00

1.00 k

Frequency (Hz)

1.00 M

Phase (deg)

0 !45.0 !90.0 !135.0 !180.0 1.000

100.0000

10.0000 k Phase (deg)

1.0000 M

Figure B.111 9&6)#05*(%&)*%'"&$(%.($'-)$(%-4%0"(%-'%&3'%,#.,5#0%/#0"%00%W%O;g%'FD%'%W%@;dJ%L %ROP%W%dd-SD%&)*% ' W J;H%L %ROP%W%Td-S;

B.3 Multisim Examples

1.6570

1.6550

1.6530

1.6510

1.6490 500 n

550 n

600 n

650 n Time (s)

700 n

750 n

800 n

Figure B.112 83&::<$#6)&:%$0('%.($'-)$(%R4-.%&%@O<3[%$0('%#)'50S%#4%0"(%-'<&3'%,#.,5#0%#$%,-))(,0(*%#)%&%5)#02<6&#)% ,-)4#65.&0#-)>%OP%W%dd-%R00%W%O;g%'FD%'%W%@;dJ%L S%&)*%OP1W%Td-%R00%W%O;g%'FD%'%W%J;H%L S;

3.5

Voltage (V)

2.5

1.5

500.0 m

!500.0 m 500 n

550 n

600 n

650 n Time (s)

700 n

750 n

Figure B.113 Q&.6(<$#6)&:%$0('%.($'-)$(%R4-.%&%H;H<[%$0('%#)'50S%#4%0"(%-'<&3'%,#.,5#0%#$%,-))(,0(*%#)%&%5)#02<6&#)% ,-)4#65.&0#-);%!"(%$:-'(%-4%0"(%.#$#)6%&)*%4&::#)6%(*6($%-4%0"(%-50'50%/&1(4-.3%,-..($'-)*%0-%0"(%$:(/%.&0(%-4%0"(%-'% &3';

/"()%00%W%O;g%'F;%Z(+0D%0-%*(0(.3#)(%8P%5$#)6%95:0#$#3D%/(%&6&#)%,-))(,0%0"(%-'%&3'%#)%&%5)#02<6&#)%,-)< 4#65.&0#-)% &)*% '(.4-.3% &% 0.&)$#()0% &)&:2$#$% $#35:&0#-)% R&$% $(0% 5'% #)% B"@Hh!/-h80&6(hB9E8h E'N3'hC+hQ&.6(<8#6)&:;3$@OS;%V-/(1(.D%/(%)-/%&'':2%&%:&.6(%'5:$(%$#6)&:%RH;H%[S%&0%0"(%#)'50%0-%,&5$( $:(/<.&0(%:#3#0#)6%&0%0"(%-50'50;%!"(%,-..($'-)*#)6%-50'50%1-:0&6(%/&1(4-.3%#$%':-00(*%#)%F#6;%?;@@J;%!"( $:-'(%-4%0"(%$:(/<.&0(<:#3#0(*%-50'50%/&1(4-.3%,-..($'-)*$%0-%0"(%$:(/%.&0(%-4%0"(%-'%&3'%&)*%#$%4-5)*%0-%=( $'%W%@gO%[as$%&)*%gO%[as$%4-.%0"(%)(6&0#1(<%&)*%'-$#0#1(<6-#)6%-50'50D%.($'(,0#1(:2;%!"($(%.($5:0$D%/#0"%0"(

B-123

B-124 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.12.1 continued

5)(M5&:%1&:5($%-4%$'%#)%0"(%0/-%*#.(,0#-)$D%*#44(.%4.-3%0"-$(%'.(*#,0(*%=2%0"(%$#3':(%3-*(:%4-.%0"(%$:(/<.&0( :#3#0#)6%-4%0"(%0/-<$0&6(%-'<&3'%,#.,5#0;%!"(%*#44(.(),(%,&)%'(."&'$%=(%$&#*%0-%=(%&%.($5:0%-4%0.&)$#$0-.%WU ()0(.#)6% 0"(% 0.#-*(% .(6#-)% &)*% #0$% -50'50% ,5..()0% R/"#,"% #$% $-5.,(*% 0".-56"% 00S% =(#)6% ,-..($'-)*#)6:2 .(*5,(*;%E4%,-5.$(D%0"(%&1&#:&=#:#02%-4%95:0#$#3%$"-5:*%()&=:(%0"(%.(&*(.%0-%(+':-.(%0"#$%'-#)0%45.0"(.;

Example MS.13.1 The CMOS Inverter =5%+#4.%$C,12*$:%;$%;4**%/.$%F/*+4.41%+)%&$.4-5%,%EF[N%45($0+$0%;#).$%.'#$1,+4'%',2+/0$%4.%.#);5%45%@4-! A!77L!%a$%;4**%,../1$%,%D!7W3 1%EF[N%+$'#5)*)-<%6)0%+#$%F[N@K".%,5&%/.$%+<24',*%NQ=EK%*$($*37 1)&$*%2,0,1$+$0.%6)0%+#4.%+$'#5)*)-<:%45'*/&45-%+#$%45+045.4'%',2,'4+,5'$%(,*/$.!%"#4.%1)&$*%&)$.%5)+%+,S$ 45+)%,'')/5+%+#$%.#)0+3'#,55$*%$66$'+.%6)0%+#4.%+$'#5)*)-0$./*+45-%60)1%+#$%;4045-%,5&%+#$%452/+%',2,'4+,5'$%)6%+#$%&04($5 -,+$.?:%;#$0$%+#$%(,*/$%/.$&%45%+#4.%$C,12*$%4.%7\%6@!%a$%;4**%9$-45%;4+#%,5%,220)C41,+$%#,5&3,5,*<.4. &$.4-5!%a$%;4**%+#$5%/.$%F/*+4.41%+)%($046<%+#,+%+#$%&$.4-5$&%'40'/4+%1$$+.%+#$%.2$'464',+4)5.!%"#$%+,0-$+$& .2$'464',+4)5%6)0%+#4.%45($0+$0%4.%,%#4-#3+)3*);%20)2,-,+4)5%&$*,<%>/OV??%)6%*$..%+#,5%L\%2.!%[5'$%&$.4-5$&: +#$%)+#$0%'#,0,'+$04.+4'.%)6%+#4.%45($0+$0%./'#%,.%*);3+)3#4-#%20)2,-,+4)5%&$*,<%>/O?V?:%5)4.$%1,0-45.:%,5& +#0$.#)*&%()*+,-$%;4**%9$%45($.+4-,+$&!% !"(%#)1(.0(.%$'(,#4#,&0#-)$%&.(%$533&.#I(*%#)%!&=:(%?;JO; Table B.30 CMOS Inverter Specifications 7&.&3(0(.$

[&:5(

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Figure B.114 8,"(3&0#,%,&'05.(%-4%0"(%B9E8%#)1(.0(.;

B.3 Multisim Examples

Hand Design F-.%0"(%*($#6)%-4%0"#$%#)1(.0(.%/(%,"--$(%?%W%O;H%s3D%$-%/(%"&1(%?(4411W%O%;@^O%s3;%N$%3()0#-)(*%(&.:#(.D 0-% 3#)#3#I(% &.(&D% &::% ,"&))(:$% &.(% 5$5&::2% 3&*(% (M5&:% 0-% 0"(% 3#)#353% :()60"% '(.3#00(*% =2% 0"(% 6#1() 0(,")-:-62;% !-% 3((0% 0"(% $'(,#4#(*% /OV?D% /(% )((*% 0-% $#I(% @ ?(44 3 % ,&.(45::2;% E),(% $#I(*D% @ ? (44 6 Z H @ ? (44 3 #$%,"-$()D%/"#,"%#$%&%,-3'.-3#$(%=(0/(()%&.(&D%)-#$(%3&.6#)$D%&)*%/O?V;% !"(%1&:5(%-4%/OV?%,&)%=(%($0#3&0(*%5$#)6%CM;%R@U;gUS%&$ P @d

@d @O 30 3 / OV? Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< < Z <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< @ Pg @ D 3 <<<<<<<< " 44 HUg;H @O <<<<<<<< @;^ ? (44 ? (44

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Table B.31 Transistor Sizes !.&)$#$0-.%

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Simulation Verifying Propagation Delay%")%45($.+4-,+$%+#$%&<5,14'%)2$0,+4)5%)6%+#$%45($0+$0%,5&%+)%($046<%+#,+ +#$%&$.4-5%1$$+.%+#$%.2$'464$&%/OV?:%;$%,22*<%,5%4&$,*%2/*.$%.4-5,*%,+%+#$%452/+%,5&%2$06)01%,%+0,5.4$5+%,5,*<3 .4.:%,.%.$+%/2%45%E#7HpEF[Np=5($0+$0p+QY_pKC!1.7D!%"#$5:%;$%2*)+%+#$%452/+%,5&%)/+2/+%;,($6)01.%,. .#);5%45%@4-!%A!77\!%%A,.$&%)5%+#$%.41/*,+$&%0$.2)5.$:%/OV?1Z%LD!\%2.%>,.%45&4',+$&%45%@4-!%A!77\?!%N414*,0*<: ;$%)9+,45%/O?V1%Z%MD!H%2.:%0$./*+45-%45%+#$%45($0+$0%20)2,-,+4)5%&$*,<%>/O?%)6%\D!L%2.!%"#$0$6)0$:%+#$%.2$'464$& #4-#3+)3*);%20)2,-,+4)5%&$*,<%.2$'464',+4)5%4.%1$+:%,5&%/O%+,S$.%,%0$,.)5,9*$%(,*/$! Voltage Transfer Characteristic (VTC) ")%')12/+$%9)+#%+#$%I"E%)6%+#$%45($0+$0%,5&%4+.%./22*< '/00$5+%,+%(,04)/.%(,*/$.%)6%+#$%452/+%()*+,-$%"45:%;$%,22*<%,%&'%()*+,-$%.)/0'$%,+%+#$%452/+%,5&%2$06)01%, &'%.;$$2%;4+#%"45%.;$2+%)($0%+#$%0,5-$%D%+)%"44:%,.%.$+%/2%45%E#7HpEF[Np=5($0+$0pI"Ep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`M%I%,5&%BPV%Z%D!W7I!%V)+$%+#,+ +#$%&$.4-5%20)(4&$.%#4-#%+)*$0,5'$%+)%5)4.$:%.45'$%5)4.$%1,0-45.%,0$%0$,.)5,9*<%#4-#%>BP?%,5&%BPV%,0$ L8h%,5&%L\h%)6%+#$%./22*<%()*+,-$?!%"#4.%412*4$.%+#,+%+#$%45($0+$0%;)/*&%20)(4&$%+#$%')00$'+%*)-4'%)/+2/+ 6)0%,5%452/+%5)4.$%(,04,+4)5%)6%/2%+)%,220)C41,+$*<%LDh%)6%+#$%"44!

B-125

B-126 Appendix B SPICE Device Models and Design Simulation Examples Using PSpice and Multisim

Example MS.13.1 continued 1.897

Voltage (V)

1.504

1.112

718.961 m

326.249 m

–66.462 m 490.018 p

577.367 p

664.716 p

752.064 p

839.413 p

926.762 p

Time (s)

Figure B.115 !#3(%*-3&#)%.($'-)$(%-4%0"(%B9E8%#)1(.0(.%0-%3(&$5.(%/OV?;

2

Voltage (V)

1

500 m

–250 m 0

500.0 m

1.0 vvin Voltage (V)

1.5

Figure B.116 E50'50%1-:0&6(%1(.$5$%#)'50%1-:0&6(%4-.%0"(%#)1(.0(.%R0-%3(&$5.():-/%&)*%"#6"%)-#$(%3&.6#)$%BP? &)*%BPVS;

!"(%0".($"-:*%1-:0&6(%"P%-4%0"(%B9E8%#)1(.0(.%#$%*(4#)(*%&$%0"(%#)'50%1-:0&6(%vAZ%0"&0%.($5:0$%#)%&) #*()0#,&:%$/#0,"#)6%-50'50%1-:0&6(%vEY!D%0"&0%#$D " P Z v AZ v #X< Z v %B

!"5$D%&$%$"-/)%#)%F#6;%?;@@TD%"P%#$%&0%0"(%#)0(.$(,0#-)%-4%0"(%[!B%/#0"%0"(%$0."0%:#)(%,-..($'-)*#)6 0-%vEY! Y vAZ;%!"#$%:#)(%,&)%=(%$#3':2%6()(.&0(*%=2%':-00#)6%vAZ%-)%0"(%1(.0#,&:%&+#$D%#)%&**#0#-)%0-%vEY!; Z-0(%0"&0%"P%W%O;^T%[D%/"#,"%#$%1(.2%,:-$(%0-%0"(%*($#.(*%1&:5(%-4%"44 aH W O;f[D%&$%*($#.(*;

B.3 Multisim Examples

2.00

Voltage (V)

1.25

–500.00 m

–250.00 m

0

500.0 m

1.0 vvin Voltage (V)

1.5

Figure B.117 E50'50%1-:0&6(%1(.$5$%#)'50%1-:0&6(%4-.%0"(%#)1(.0(.%R0-%0"(%0".($"-:*%1-:0&6(%3(&$5.(%"/;S;

30 µ 25 µ

Current (A)

20 µ 15 µ 10 µ 5µ 0 !5 µ

0

500.0m

1.0 vvin Voltage (V)

1.5

Figure B.118 85'':2%,5..()0%1(.$5$%#)'50%1-:0&6(%4-.%0"(%#)1(.0(.;

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B-127

!"#$%&''()*+,,-%.",/,,01"2#%34,56789"$,:;4,:;;<,,=>=;,-?

APPENDIX C

TWO-PORT NETWORK PARAMETERS

Introduction At various points throughout the text, we make use of some of the different possible ways to characterize linear two-port networks. A summary of this topic is presented in this appendix.

C.1 Characterization of Linear Two-Port Networks A two-port network (Fig. C.1) has four port variables: V1, I1, V2, and I2. If the two-port network is linear, we can use two of the variables as excitation variables and the other two as response variables. For instance, the network can be excited by a voltage V1 at port 1 and a voltage V2 at port 2, and the two currents, I1 and I2, can be measured to represent the network response. In this case, V1 and V2 are independent variables and I1 and I2 are dependent variables, and the network operation can be described by the two equations ! 1 = " 11 # 1 + " 12 # 2

(C.1)

! 2 = " 21 # 1 + " 22 # 2

(C.2)

Here, the four parameters y11, y12, y21, and y22 are admittances, and their values completely characterize the linear two-port network. Depending on which two of the four port variables are used to represent the network excitation, a different set of equations (and a correspondingly different set of parameters) is obtained for characterizing the network. We shall present the four parameter sets commonly used in electronics. I1 " V1 !

I2 Linear two-port network

" V2 !

Figure C.1 The reference directions of the four port variables in a linear two-port network.

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C-1

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C-2 Appendix C Two-Port Network Parameters

C.1.1 y Parameters The short-circuit admittance (or y-parameter) characterization is based on exciting the network by V1 and V2, as shown in Fig. C.2(a). The describing equations are Eqs. (C.1) and (C.2). The four admittance parameters can be defined according to their roles in Eqs. (C.1) and (C.2). Specifically, from Eq. (C.1) we see that y11 is defined as ! " 11 = @@@@@1 #1

.

(C.3)

# 2 =0

Thus y11 is the input admittance at port 1 with port 2 short-circuited. This definition is illustrated in Fig. C.2(b), which also provides a conceptual method for measuring the input short-circuit admittance y11. The definition of y12 can be obtained from Eq. (C.1) as ! " 12 = @@@@@1 #2

(C.4) # 1 =0

Thus y12 represents transmission from port 2 to port 1. Since in amplifiers, port 1 represents the input port and port 2 the output port, y12 represents internal feedback in the network. Figure C.2(c) illustrates the definition of and the method for measuring y12.

Figure C.2 Definition of and conceptual measurement circuits for the y parameters. ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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C.1 Characterization of Linear Two-Port Networks C-3

The definition of y21 can be obtained from Eq. (C.2) as ! " 21 = @@@@@2 #1

(C.5) # 2 =0

Thus y21 represents transmission from port 1 to port 2. If port 1 is the input port and port 2 the output port of an amplifier, then y21 provides a measure of the forward gain or transmission. Figure C.2(d) illustrates the definition of and the method for measuring y21. The parameter y22 can be defined, based on Eq. (C.2), as ! " 22 = @@@@@2 #2

(C.6) # 1 =0

Thus y22 is the admittance looking into port 2 while port 1 is short-circuited. For amplifiers, y22 is the output short-circuit admittance. Figure C.2(e) illustrates the definition of and the method for measuring y22.

C.1.2 z Parameters The open-circuit impedance (or z-parameter) characterization of two-port networks is based on exciting the network by I1 and I2, as shown in Fig. C.3(a). The describing equations are # 1 = $ 11 ! 1 + $ 12 ! 2

(C.7)

# 2 = $ 21 ! 1 + $ 22 ! 2

(C.8)

Figure C.3 Definition of and conceptual measurement circuits for the z parameters. ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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C-4 Appendix C Two-Port Network Parameters Owing to the duality between the z- and y-parameter characterizations, we shall not give a detailed discussion of z parameters. The definition and the method of measuring each of the four z parameters are given in Fig. C.3.

C.1.3 h Parameters The hybrid (or h-parameter) characterization of two-port networks is based on exciting the network by I1 and V2, as shown in Fig. C.4(a) (note the reason behind the name hybrid). The describing equations are # 1 = % 11 ! 1 + % 12 # 2

(C.9)

! 2 = % 21 ! 1 + % 22 # 2

(C.10)

from which the definition of the four h parameters can be obtained as # ! % 11 = @@@@@1 % 21 = @@@2@ ! 1 # 2 =0 ! 1 # 2 =0 # % 12 = @@@@@1 #2

! 1 =0

! % 22 = @@@@@2 #2

! 1 =0

(e) Figure C.4 Definition of and conceptual measurement circuits for the h parameters.

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C.1 Characterization of Linear Two-Port Networks C-5

Thus, h11 is the input impedance at port 1 with port 2 short-circuited. The parameter h12 represents the reverse or feedback voltage ratio of the network, measured with the input port open-circuited. The forward-transmission parameter h21 represents the current gain of the network with the output port short-circuited; for this reason, h21 is called the short-circuit current gain. Finally, h22 is the output admittance with the input port open-circuited. The definitions and conceptual measuring setups of the h parameters are given in Fig. C.4.

C.1.4 g Parameters The inverse-hybrid (or g-parameter) characterization of two-port networks is based on excitation of the network by V1 and I2, as shown in Fig. C.5(a). The describing equations are ! 1 = & 11 # 1 + & 12 ! 2

(C.11)

# 2 = & 21 # 1 + & 22 ! 2

(C.12)

The definitions and conceptual measuring setups are given in Fig. C.5.

C.1.5 Equivalent-Circuit Representation A two-port network can be represented by an equivalent circuit based on the set of parameters used for its characterization. Figure C.6 shows four possible equivalent circuits corresponding I

I

Figure C.5 Definition of and conceptual measurement circuits for the g parameters. ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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C-6 Appendix C Two-Port Network Parameters

Figure C.6 Equivalent circuits for two-port networks in terms of (a) y, (b) z, (c) h, and (d) g parameters.

to the four parameter types just discussed. Each of these equivalent circuits is a direct pictorial representation of the corresponding two equations describing the network in terms of the particular parameter set. Finally, it should be mentioned that other parameter sets exist for characterizing two-port networks, but these are not discussed or used in this book.

EXERCISE C.1

Figure EC.1 shows the small-signal, equivalent-circuit model of a transistor. Calculate the values of the h parameters. Ans. h11 ! 2.6 kΩ; h12 ! 2.5 × 10−4; h21 ! 100; h22 ! 2 × 10−5 Ω

Figure EC.1

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C.1 Characterization of Linear Two-Port Networks C-7

PROBLEMS

C.1 (a) An amplifier characterized by the h-parameter equivalent circuit of Fig. C.6(c) is fed with a source having a voltage Vs and a resistance Rs, and is loaded in a resistance RL. Show that its voltage gain is given by #2 – % 21 @ @@@@@@ = @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ #' ( % 11 + ( ' ) ( % 22 + 1 ⁄ ( ) ) – % 12 % 21

the current in the output is 0.2 mA and the voltage measured at the input is 2.5 mV. Find values for the h parameters of this network. C.3 Figure PC.3 shows the high-frequency equivalent circuit of a BJT. (For simplicity, rx has been omitted.) Find the y parameters.

(b) Use the expression derived in (a) to find the voltage gain of the transistor in Exercise C.1 for Rs = 1 kΩ and RL = 10 kΩ. C.2 The terminal properties of a two-port network are measured with the following results: With the output shortcircuited and an input current of 0.01 mA, the output current is 1.0 mA and the input voltage is 26 mV. With the input open-circuited and a voltage of 10 V applied to the output,

Figure PC.3

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APPENDIX D

SOME USEFUL NETWORK THEOREMS

Introduction In this appendix we review three network theorems that are useful in simplifying the analysis of electronic circuits: Thévenin’s theorem, Norton’s theorem, and the source-absorption theorem.

D.1 Thévenin’s Theorem Thévenin’s theorem is used to represent a part of a network by a voltage source Vt and a series impedance Zt, as shown in Fig. D.1. Figure D.1(a) shows a network divided into two parts, A and B. In Fig. D.1(b), part A of the network has been replaced by its Thévenin equivalent: a voltage source Vt and a series impedance Zt. Figure D.1(c) illustrates how Vt is to be determined: Simply open-circuit the two terminals of network A and measure (or calculate) the voltage that appears between these two terminals. To determine Zt , we reduce all external (i.e., independent) sources in network A to zero by short-circuiting voltage sources and open-circuiting current sources. The impedance Zt will be equal to the input impedance of network A after this reduction has been performed, as illustrated in Fig. D.1(d).

D.2 Norton’s Theorem Norton’s theorem is the dual of Thévenin’s theorem. It is used to represent a part of a network by a current source In and a parallel impedance Zn, as shown in Fig. D.2. Figure D.2(a) shows a network divided into two parts, A and B. In Fig. D.2(b), part A has been replaced by its Norton’s equivalent: a current source In and a parallel impedance Zn. The Norton’s current source In can be measured (or calculated) as shown in Fig. D.2(c). The terminals of the network being reduced (network A) are shorted, and the current In will be equal simply to the short-circuit current. To determine the impedance Zn , we first reduce the external excitation in network A to zero: That is, we short-circuit independent voltage sources and open-circuit independent current sources. The impedance Zn will be equal to the input impedance of network A after this source-elimination process has taken place. Thus the Norton impedance Zn is equal to the Thévenin impedance Zt. Finally, note that ! " = # $ ⁄ % , where Z = Zn = Zt.!!

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D-1

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D-2 Appendix D Some Useful Network Theorems

Figure D.1 Thévenin’s theorem.

n

Figure D.2 Norton’s theorem.

Example D.1 Figure D.3(a) shows a bipolar junction transistor circuit. The transistor is a three-terminal device with the terminals labeled E (emitter), B (base), and C (collector). As shown, the base is connected to the dc power supply V + via the voltage divider composed of R1 and R2. The collector is connected to the dc supply V + through R3 and to ground through R4. To simplify the analysis, we wish to apply Thévenin’s theorem to reduce the circuit.

Solution Thévenin’s theorem can be used at the base side to reduce the network composed of V +, R1, and R2 to a dc voltage source VBB, + '2 ! B #&& = # BBBBBBBBBBBBBBBBB '1 + '2

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D.3 Source-Absorption Theorem D-3

Figure D.3 Thévenin’s theorem applied to simplify the circuit of (a) to that in (b). (See Example D.1.)

and a resistance RB,

' & = ' 1 ||(': where || denotes “in parallel with.” At the collector side, Thévenin’s theorem can be applied to reduce the network composed of V +, R3, and R4 to a dc voltage source VCC, + '4 ! #)) = # BBBBBBBBBBBBBBBBBB '3 + '4

and a resistance RC,

' ) = ' 3 || '? The reduced circuit is shown in Fig. D.3(b).

D.3 Source-Absorption Theorem Consider the situation shown in Fig. D.4. In the course of analyzing a network, we find a controlled current source Ix appearing between two nodes whose voltage difference is the controlling voltage Vx. That is, Ix = gmVx where gm is a conductance. We can replace this controlled source by an impedance % * = #* ⁄ !* = 1 ⁄ + , , as shown in Fig. D.4, because the current drawn by this impedance will be equal to the current of the controlled source that we have replaced.

Figure D.4 The source-absorption theorem. ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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D-4 Appendix D Some Useful Network Theorems

Example D.2 Figure D.5(a) shows the small-signal, equivalent-circuit model of a transistor. We want to find the resistance Rin “looking into” the emitter terminal E—that is, the resistance between the emitter and ground— with the base B and collector C grounded.

(a) Figure D.5 Circuit for Example D.2.

Solution From Fig. D.5(a), we see that the voltage vπ will be equal to –ve. Thus, looking between E and ground, we see a resistance rπ in parallel with a current source drawing a current gmve away from terminal E. The latter source can be replaced by a resistance D1 ⁄ + ,E, resulting in the input resistance Rin given by

' FG = - π || D1 ⁄ + ,E as illustrated in Fig. D.5(b).

EXERCISES D.1

A source is measured and found to have a 10-V open-circuit voltage and to provide 1 mA into a short circuit. Calculate its Thévenin and Norton equivalent source parameters. Ans. Vt = 10 V; Zt = Zn = 10 kΩ; In = 1 mA

D.2 In the circuit shown in Fig. ED.2, the diode has a voltage drop VD ! 0.7 V. Use Thévenin’s theo-

rem to simplify the circuit and hence calculate the diode current ID.

Ans. 1 mA

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D.3 Source-Absorption Theorem

D-5

Figure ED.2

D.3 The two-terminal device M in the circuit of Fig. ED.3 has a current IM ! 1 mA independent of the volt-

age VM across it. Use Norton’s theorem to simplify the circuit and hence calculate the voltage VM. Ans. 5 V

Figure ED.3

PROBLEMS

D.1 Consider the Thévenin equivalent circuit characterized by Vt and Zt. Find the open-circuit voltage Voc and the short-circuit current IsD (i.e., the current that flows when the terminals are shorted together). Express Zt in terms of Voc and IsD. D.2 Repeat Problem D.1 for a Norton equivalent circuit characterized by In and Zn.

D.3 A voltage divider consists of a 9-kΩ resistor connected to +10 V and a resistor of 1 kΩ connected to ground. What is the Thévenin equivalent of this voltage divider? What output voltage results if it is loaded with 1 kΩ? Calculate this two ways: directly and using your Thévenin equivalent.

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APPENDIX D PROBLEMS

D-6 Appendix D

Some Useful Network Theorems

D.4 Find the output voltage and output resistance of the circuit shown in Fig. PD.4 by considering a succession of Thévenin equivalent circuits.

! Vo "

Figure PD.4

D.5 Repeat Example D.2 with a resistance RB connected between B and ground in Fig. D.5 (i.e., rather than directly grounding the base B as indicated in Fig. D.5). D.6 Figure PD.6(a) shows the circuit symbol of a device known as the p-channel junction field-effect transistor (JFET). As indicated, the JFET has three terminals. When the gate terminal G is connected to the source terminal S, the twoterminal device shown in Fig. PD.6(b) is obtained. Its i–v characteristic is given by

v! v! . = ! )"" 2 BBBBBB – BBBBBB #/ #/ . = ! )""

2

+8%!v ≤ # / +8%!v ≥ # /

where IDSS and VP are positive constants for the particular JFET. Now consider the circuit shown in Fig. PD.6(c) and let VP = 2 V and IDSS = 2 mA. For V + = 10 V show that the JFET is operating in the constant-current mode and find the voltage across it. What is the minimum value of V + for which this mode of operation is maintained? For V + = 2 V find the values of I and V.

Figure PD.6

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APPENDIX E

SINGLE-TIME-CONSTANT CIRCUITS

Introduction Single-time-constant (STC) circuits are those circuits that are composed of or can be reduced to one reactive component (inductance or capacitance) and one resistance. An STC circuit formed of an inductance L and a resistance R has a time constant τ = ! ⁄ ". The time constant τ of an STC circuit composed of a capacitance C and a resistance R is given by τ = CR. Although STC circuits are quite simple, they play an important role in the design and analysis of linear and digital circuits. For instance, the analysis of an amplifier circuit can usually be reduced to the analysis of one or more STC circuits. For this reason, we will review in this appendix the process of evaluating the response of STC circuits to sinusoidal and other input signals such as step and pulse waveforms. The latter signal waveforms are encountered in some amplifier applications but are more important in switching circuits, including digital circuits.

E.1 Evaluating the Time Constant The first step in the analysis of an STC circuit is to evaluate its time constant τ.

Example E.1 Reduce the circuit in Fig. E.1(a) to an STC circuit, and find its time constant.

Solution The reduction process is illustrated in Fig. E.1 and consists of repeated applications of Thévenin’s theorem. From the final circuit (Fig. E.1c), we obtain the time constant as

τ = # { " 4 || !" 3 + ( " 1 || " 2 )"}

E.1.1 Rapid Evaluation of τ In many instances, it will be important to be able to evaluate rapidly the time constant τ of a given STC circuit. A simple method for accomplishing this goal consists first of reducing the excitation to zero; that is, if the excitation is by a voltage source, short it, and if by a current

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E-1

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E-2 Appendix E Single-Time-Constant Circuits

Figure E.1 The reduction of the circuit in (a) to the STC circuit in (c) through the repeated application of Thévenin’s theorem.

source, open it. Then, if the circuit has one reactive component and a number of resistances, “grab hold” of the two terminals of the reactive component (capacitance or inductance) and find the equivalent resistance Req seen by the component. The time constant is then either ! ⁄" "# or CReq. As an example, in the circuit of Fig. E.1(a), we find that the capacitor C “sees” a resistance R4 in parallel with the series combination of R3 and R2 in parallel with R1. Thus " "# = " 4 || $" 3 + ( " 2 || " 1 )% and the time constant is CReq. In some cases it may be found that the circuit has one resistance and a number of capacitances or inductances. In such a case, the procedure should be inverted; that is, “grab hold” of the resistance terminals and find the equivalent capacitance Ceq, or equivalent inductance Leq, seen by this resistance. The time constant is then found as CeqR or Leq / R. This is illustrated in Example E.2.!

Example E.2 Find the time constant of the circuit in Fig. E.2.

Figure E.2 Circuit for Example E.2.

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E.1 Evaluating the Time Constant E-3

Solution After reducing the excitation to zero by short-circuiting the voltage source, we see that the resistance R “sees” an equivalent capacitance C1 + C2. Thus, the time constant τ is given by

τ = ( # 1 + # 2 )" Finally, in some cases an STC circuit has more than one resistance and more than one capacitance (or more than one inductance). Such cases require some initial work to simplify the circuit, as illustrated by Example E.3.!

Example E.3 Here we show that the response of the circuit in Fig. E.3(a) can be obtained using the method of analysis of STC circuits.

Solution The analysis steps are illustrated in Fig. E.3. In Fig. E.3(b) we show the circuit excited by two separate but equal voltage sources. The reader should convince himself or herself of the equivalence of the circuits in Fig. E.3(a) and E.3(b). The “trick” employed to obtain the arrangement in Fig. E.3(b) is a very useful one.

Figure E.3 The response of the circuit in (a) can be found by superposition, that is, by summing the responses of the circuits in (d) and (e). ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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E-4 Appendix E Single-Time-Constant Circuits

Example E.3 continued

Application of Thévenin’s theorem to the circuit to the left of the line $$′ and then to the circuit to the right of that line results in the circuit of Fig. E.3(c). Since this is a linear circuit, the response may be obtained using the principle of superposition. Specifically, the output voltage vO will be the sum of the two components vO1 and vO2. The first component, vO1, is the output due to the left-hand-side voltage source with the other voltage source reduced to zero. The circuit for calculating vO1 is shown in Fig. E.3(d). It is an STC circuit with a time constant given by

τ = ( # 1 + # 2 ) ( " 1 || " 2 ) Similarly, the second component vO2 is the output obtained with the left-hand-side voltage source reduced to zero. It can be calculated from the circuit of Fig. E.3(e), which is an STC circuit with the same time constant τ. Finally, it should be observed that the fact that the circuit is an STC one can also be ascertained by setting the independent source vI in Fig. E.3(a) to zero. Also, the time constant is then immediately obvious.

E.2 Classification of STC Circuits STC circuits can be classified into two categories, low-pass (LP) and high-pass (HP) types, with each category displaying distinctly different signal responses. The task of finding whether an STC circuit is of LP or HP type may be accomplished in a number of ways, the simplest of which uses the frequency domain response. Specifically, low-pass circuits pass dc (i.e., signals with zero frequency) and attenuate high frequencies, with the transmission being zero at ω = ∞. Thus, we can test for the circuit type either at ω = 0 or at ω = ∞. At ω = 0 capacitors should be replaced by open circuits D1 ⁄ %ω # = ∞ E and inductors should be replaced by short circuits ( jωL = 0). Then if the output is zero, the circuit is of the high-pass type, while if the output is finite, the circuit is of the low-pass type. Alternatively, we may test at ω = ∞ by replacing capacitors with short circuits D1 ⁄ %ω # = 0E and inductors with open circuits ( jωL = ∞). Then if the output is finite, the circuit is of the HP type, whereas if the output is zero, the circuit is of the LP type. In Table E.1, which provides a summary of these results, s.c. stands for short circuit and o.c. for open circuit. Figure E.4 shows examples of low-pass STC circuits, and Fig. E.5 shows examples of highpass STC circuits. For each circuit we have indicated the input and output variables of interest. Note that a given circuit can be of either category, depending on the input and output variables. The reader is urged to verify, using the rules of Table E.1, that the circuits of Figs. E.4 and E.5 are correctly classified. ! Table E.1 Rules for Finding the Type of STC Circuit Test at

ω=0 ω=∞

Replace C by o.c. L by s.c. C by s.c. L by o.c.

Circuit is LP if

Circuit is HP if

output is finite

output is zero

output is zero

output is finite

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E.2 Classification of STC Circuits E-5

(a)

(c)

(b)

(f)

(e)

(d)

Figure E.4 STC circuits of the low-pass type.

(b)

(c)

(e) (d) Figure E.5 STC circuits of the high-pass type.

(f)

(a)

EXERCISES E.1

Find the time constants for the circuits shown in Fig. EE.1.

D! !|| ! E "

D! !|| ! E D"=!|| "2E

= 2 = 2 Ans. (a) GGGGGGGGGGGGGGGGGGGG F (b) GGGGGGGGGGGGGGGGGGGG

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E-6 Appendix E Single-Time-Constant Circuits

E.2 Classify the following circuits as STC high-pass or low-pass: Fig. E.4(a) with output iO in C to ground; Fig. E.4(b) with output iO in R to ground; Fig. E.4(d) with output iO in C to ground; Fig. E.4(e) with output iO in R to ground; Fig. E.5(b) with output iO in L to ground; and Fig. E.5(d) with output vO across C. Ans. HP; LP; HP; HP; LP; LP

E.3 Frequency Response of STC Circuits E.3.1 Low-Pass Circuits The transfer function T(s) of an STC low-pass circuit can always be written in the form ( (E.1) & ( ' ) = GGGGGGGGGGGGGGGGGGGGGGGGGG 1 + ( ' ⁄ ω0 ) which, for physical frequencies, where s = jω, becomes ( & ( % ω ) = GGGGGGGGGGGGGGGGGGGGGGGGGGGGGG (E.2) 1 + % ( ω ⁄ ω0 ) where K is the magnitude of the transfer function at ω = 0 (dc) and ω 0 is defined by

ω0 = 1 ⁄ τ

with τ being the time constant. Thus the magnitude response is given by ( & ( % ω ) = GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 2 1 + ( ω ⁄ ω0 ) and the phase response is given by –1

φ ( ω ) = – :)4 ( ω ⁄ ω 0 )

(E.3)

(E.4)

Figure E.6 sketches the magnitude and phase responses for an STC low-pass circuit. The magnitude response shown in Fig. E.6(a) is simply a graph of the function in Eq. (E.3). The magnitude is normalized with respect to the dc gain K and is expressed in decibels; that is, the plot is for 20!I;1 & ( % ω ) ⁄ ( 7 with a logarithmic scale used for the frequency axis. Furthermore, the frequency variable has been normalized with respect to ω 0. As shown, the magnitude curve is closely defined by two straight-line asymptotes. The low-frequency asymptote is a horizontal straight line at 0 dB. To find the slope of the high-frequency asymptote, consider Eq. (E.3) and let ω ⁄ ω 0 ! 1, resulting in

ω ω

& ( % ω ) !( GGGGG0G It follows that if ω doubles in value, the magnitude is halved. On a logarithmic frequency axis, doublings of ω represent equally spaced points, with each interval called an octave. Halving the magnitude function corresponds to a 6-dB reduction in transmission (20 log 0.5 = –6 dB). Thus the slope of the high-frequency asymptote is –6 dB/octave. This can be equivalently expressed as –20 dB/decade, where “decade” indicates an increase in frequency by a factor of 10. The two straight-line asymptotes of the magnitude–response curve meet at the “corner frequency” or “break frequency” ω 0. The difference between the actual magnitude–response curve

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E.3 Frequency Response of STC Circuits E-7

Figure E.6 (a) Magnitude and (b) phase response of STC circuits of the low-pass type.

and the asymptotic response is largest at the corner frequency, where its value is 3 dB. To verify that this value is correct, simply substitute ω = ω0 in Eq. (E.3) to obtain & ( % ω 0 ) = K/ 2 Thus at ω = ω 0 , the gain drops by a factor of 2 relative to the dc gain, which corresponds to a 3-dB reduction in gain. The corner frequency ω 0 is appropriately referred to as the 3-dB frequency. Similar to the magnitude response, the phase–response curve, shown in Fig. E.6(b), is closely defined by straight-line asymptotes. Note that at the corner frequency the phase is –45°, and that for ω ! ω 0 the phase approaches –90°. Also note that the –45°/decade straight line approximates the phase function, with a maximum error of 5.7°, over the frequency range 0.1ω 0 to 10ω 0.!

Example E.4 Consider the circuit shown in Fig. E.7(a), where an ideal voltage amplifier of gain µ = –100 has a small (10-pF) capacitance connected in its feedback path. The amplifier is fed by a voltage source having a source resistance of 100 kΩ. Show that the frequency response Vo /Vs of this amplifier is equivalent to that of an STC circuit, and sketch the magnitude response. ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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E-8 Appendix E Single-Time-Constant Circuits

Example E.4 continued

(b)

(a)

Figure E.7 (a) An amplifier circuit and (b) a sketch of the magnitude of its transfer function.

Solution Direct analysis of the circuit in Fig. E.7(a) results in the transfer function

) µ GGGGG* = GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG )' 1 + '"# + ( – µ + 1 ) which can be seen to be that of a low-pass STC circuit with a dc gain µ = –100 (or, equivalently, 40 dB) and a time constant τ = RCf (–µ + 1) = 100 × 103 × 10 × 10–12 × 101 ! 10–4 s, which corresponds to a frequency ω 0 = 1/τ = 104 rad/s. The magnitude response is sketched in Fig. E.7(b).

E.3.2 High-Pass Circuits The transfer function T(s) of an STC high-pass circuit can always be expressed in the form (' & ( ' ) = GGGGGGGGGGGGGGG ' + ω0

(E.5)

which for physical frequencies s = jω becomes ( & ( % ω ) = GGGGGGGGGGGGGGGGGGGGGGGGG 1 – % ω0 ⁄ ω

(E.6)

where K denotes the gain as s or ω approaches infinity and ω 0 is the inverse of the time constant τ,

ω0 = 1 ⁄ τ The magnitude response

and the phase response

( & ( % ω ) = GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 2 1 + ( ω0 ⁄ ω ) –1

φ ( ω ) = :)4 ( ω 0 ⁄ ω )

(E.7)

(E.8)

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E.3 Frequency Response of STC Circuits

(a)

Figure E.8 (a) Magnitude and (b) phase response of STC circuits of the high-pass type.

are sketched in Fig. E.8. As in the low-pass case, the magnitude and phase curves are well defined by straight-line asymptotes. Because of the similarity (or, more appropriately, duality) with the low-pass case, no further explanation will be given. !

EXERCISES E.3 Find the dc transmission, the corner frequency f0, and the transmission at f = 2 MHz for the lowpass STC circuit shown in Fig. EE.3.

Figure EE.3

Ans. –6 dB; 318 kHz; –22 dB E.4 Find the transfer function T(s) of the circuit in Fig. E.2. What type of STC network is it?

# " # 1 + # 2 " + [ 1#$# 1 + # 2 )$ ]

1 Ans. ! ( " ) = """""""""""""""""" ! """""""""""""""""""""""""""""""""""""""""""""" % HP

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E-9

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E-10 Appendix E Single-Time-Constant Circuits

E.5 For the situation discussed in Exercise E.4, if R = 10 kΩ, find the capacitor values that result in the circuit having a high-frequency transmission of 0.5 V/V and a corner frequency ω 0 = 10 rad/s. Ans. C1 = C2 = 5 µF E.6 Find the high-frequency gain, the 3-dB frequency f0, and the gain at f = 1 Hz of the capacitively coupled amplifier shown in Fig. EE.6. Assume the voltage amplifier to be ideal.

Figure EE.6

Ans. 40 dB; 15.9 Hz; 16 dB

E.4 Step Response of STC Circuits In this section we consider the response of STC circuits to the step-function signal shown in Fig. E.9. Knowledge of the step response enables rapid evaluation of the response to other switching-signal waveforms, such as pulses and square waves.

E.4.1 Low-Pass Circuits In response to an input step signal of height S, a low-pass STC circuit (with a dc gain K = 1) produces the waveform shown in Fig. E.10. Note that while the input rises from 0 to S at t = 0, the output does not respond immediately to this transient and simply begins to rise exponentially toward the final dc value of the input, S. In the long term—that is, for t ! τ — the output approaches the dc value S, a manifestation of the fact that low-pass circuits faithfully pass dc. The equation of the output waveform can be obtained from the expression , ( - ) = . ∞ – ( . ∞ – . 0M )/

–- ⁄ τ

(E.9)

where Y∞ denotes the final value or the value toward which the output is heading and Y0+ denotes the value of the output immediately after t = 0. This equation states that the output at any time t is equal to the difference between the final value Y∞ and a gap that has an initial value of Y∞ – Y0+ and is “shrinking” exponentially. In our case, Y∞ = S and Y0+ = 0; thus, ,(-) = 0( 1 – /

Figure E.9 A step-function signal of height S.

–- ⁄ τ

)

(E.10)

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E.4 Step Response of STC Circuits

Figure E.10 The output y(t) of a low-pass STC circuit excited by a step of height S.

Figure E.11 The output y(t) of a high-pass STC circuit excited by a step of height S.

The reader’s attention is drawn to the slope of the tangent to y(t) at t = 0, which is indicated in Fig. E.10.

E.4.2 High-Pass Circuits The response of an STC high-pass circuit (with a high-frequency gain K = 1) to an input step of height S is shown in Fig. E.11. The high-pass circuit faithfully transmits the transient part of the input signal (the step change) but blocks the dc. Thus the output at t = 0 follows the input, ! 0" = " and then it decays toward zero, !∞ = 0 Substituting for Y0+ and Y∞ in Eq. (E.9) results in the output y(t), # ( $ ) = "%

–$ ⁄ τ

(E.11)

The reader’s attention is drawn to the slope of the tangent to y(t) at t = 0, indicated in Fig. E.11.!

Example E.5 This example is a continuation of the problem considered in Example E.3. For an input vI that is a 10-V step, find the condition under which the output vO is a perfect step.

Solution Following the analysis in Example E.3, which is illustrated in Fig. E.3, we have

v &1 = ' ( [ 10 ( 1 – %

–$ ⁄ τ

)]

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E-11

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E-12 Appendix E Single-Time-Constant Circuits

Example E.5 continued

where

"2 1 2 ≡ GGGGGGGGGGGGGGGGGG "1 + "2 and

v 32 = 1 4 ( 10/

–- ⁄ τ

)

where

#1 1 4 ≡ GGGGGGGGGGGGGGGGGG #1 + #2 and

τ = ( # 1 + # 2 ) ( " 1 || " 2 ) Thus

v 3 = v 31 + v 32 = 101 2 + 10/

–- ⁄ τ

( 14 – 12 )

It follows that the output can be made a perfect step of height 10kr volts if we arrange that

14 = 12 that is, if the resistive voltage divider ratio is made equal to the capacitive voltage divider ratio. This example illustrates an important technique, namely, that of the “compensated attenuator.” An application of this technique is found in the design of the oscilloscope probe. The oscilloscope probe problem is investigated in Problem E.3.

EXERCISES E.7 For the circuit of Fig. E.4(f), find vO if iI is a 3-mA step, R = 1 kΩ, and C = 100 pF. Ans. 3 ( 1 – /

7

– 10 -

)

E.8 In the circuit of Fig. E.5(f), find vO(t) if iI is a 2-mA step, R = 2 kΩ, and L = 10 µH. Ans. 4/

8

– 2 × 10 -

E.9 The amplifier circuit of Fig. EE.6 is fed with a signal source that delivers a 20-mV step. If the source resistance is 100 kΩ, find the time constant τ and vO(t). Ans. τ = 2 × 10−2 s; vO(t) = 1 × e–50t E.10 For the circuit in Fig. E.2 with C1 = C2 = 0.5 µF, R = 1 MΩ, find vO(t) if vI (t) is a 10-V step. Ans. 5e−t E.11 Show that the area under the exponential of Fig. E.11 is equal to that of the rectangle of height S and width τ.

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E.5 Pulse Response of STC Circuits E-13

E.5 Pulse Response of STC Circuits Figure E.12 shows a pulse signal whose height is P and whose width is T. We wish to find the response of STC circuits to input signals of this form. Note at the outset that a pulse can be considered as the sum of two steps: a positive one of height P occurring at t = 0 and a negative one of height P occurring at t = T. Thus, the response of a linear circuit to the pulse signal can be obtained by summing the responses to the two step signals.

E.5.1 Low-Pass Circuits Figure E.13(a) shows the response of a low-pass STC circuit (having unity dc gain) to an input pulse of the form shown in Fig. E.12. In this case, we have assumed that the time constant τ is in the same range as the pulse width T. As shown, the LP circuit does not respond immediately to the step change at the leading edge of the pulse; rather, the output starts to rise exponentially toward a final value of P. This exponential rise, however, will be stopped at time t = T, that is, at the trailing edge of the pulse when the input undergoes a negative step change. Again, the output will respond by starting an exponential decay toward the final value of the input, which is zero. Finally, note that the area under the output waveform will be equal to the area under the input pulse waveform, since the LP circuit faithfully passes dc. A low-pass effect usually occurs when a pulse signal from one part of an electronic system is connected to another. The low-pass circuit in this case is formed by the output resistance (Thévenin’s equivalent resistance) of the system part from which the signal originates and the input capacitance of the system part to which the signal is fed. This unavoidable low-pass filter will cause distortion—of the type shown in Fig. E.13(a)—of the pulse signal. In a well-designed system such distortion is kept to a low value by arranging that the time constant τ be much smaller than the pulse width T. In this case, the result will be a slight rounding of the pulse edges, as shown in Fig. E.13(b). Note, however, that the edges are still exponential. The distortion of a pulse signal by a parasitic (i.e., unwanted) low-pass circuit is measured by its rise time and fall time. The rise time is conventionally defined as the time taken by the amplitude to increase from 10% to 90% of the final value. Similarly, the fall time is the time during which the pulse amplitude falls from 90% to 10% of the maximum value. These definitions are illustrated in Fig. E.13(b). By use of the exponential equations of the rising and falling edges of the output waveform, it can be easily shown that - 2 = - + ! 2.2 τ which can be also expressed in terms of f0 = ω 0 "2π = 1"2πτ as !?-CH! - 2 = - + ! GGGGGGGGGGGGG +0

(E.12)

(E.13)

Figure E.12 A pulse signal with height P and width T.

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E-14 Appendix E Single-Time-Constant Circuits

(c) Figure E.13 Pulse responses of three STC low-pass circuits.

Finally, we note that the effect of the parasitic low-pass circuits that are always present in a system is to “slow down” the operation of the system: To keep the signal distortion within acceptable limits, one has to use a relatively long pulse width (for a given low-pass time constant). The other extreme case—namely, when τ is much larger than T , is illustrated in Fig. E.13(c). As shown, the output waveform rises exponentially toward the level P. However, since τ ! T, the value reached at t = T will be much smaller than P. At t = T, the output waveform starts its exponential decay toward zero. Note that in this case the output waveform bears little resemblance to the input pulse. Also note that because τ ! T, the portion of the exponential curve from t = 0 to t = T is almost linear. Since the slope of this linear curve is proportional to the height of the input pulse, we see that the output waveform approximates the time integral of the input pulse. That is, a low-pass network with a large time constant approximates the operation of an integrator.

E.5.2 High-Pass Circuits Figure E.14(a) shows the output of an STC HP circuit (with unity high-frequency gain) excited by the input pulse of Fig. E.12, assuming that τ and T are comparable in value. As shown, the step transition at the leading edge of the input pulse is faithfully reproduced at the output of the HP circuit. However, since the HP circuit blocks dc, the output waveform immediately starts an exponential decay toward zero. This decay process is stopped at t = T, when the negative step transition of the input occurs and the HP circuit faithfully reproduces it. Thus, at t = T the output waveform exhibits an undershoot. Then it starts an exponential decay toward zero. Finally, note that the area of the output waveform above the zero axis will be equal to that below the axis for a total average area of zero, consistent with the fact that HP circuits block dc. In many applications, an STC high-pass circuit is used to couple a pulse from one part of a system to another part. In such an application, it is necessary to keep the distortion in the pulse shape as small as possible. This can be accomplished by selecting the time constant τ to be much longer than the pulse width T. If this is indeed the case, the loss in amplitude during the pulse period T will be very small, as shown in Fig. E.14(b). Nevertheless, the output waveform still swings negatively, and the area under the negative portion will be equal to that under the positive portion. Consider the waveform in Fig. E.14(b). Since τ is much larger than T, it follows that the portion of the exponential curve from t = 0 to t = T will be almost linear and that its slope will be ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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E.5 Pulse Response of STC Circuits E-15

Figure E.14 Pulse responses of three STC high-pass circuits.

equal to the slope of the exponential curve at t = 0, which is P"τ. We can use this value of the slope to determine the loss in amplitude ∆P as 5 ∆5 ! GGG &

τ

(E.14)

The distortion effect of the high-pass circuit on the input pulse is usually specified in terms of the per-unit or percentage loss in pulse height. This quantity is taken as an indication of the “sag” in the output pulse, ∆5 0"(9"4:)1"!5)1 ≡ GGGGGGG × 100 5

(E.15)

& 0"(9"4:)1"!5)1 = GGG × 100

(E.16)

Thus

τ

Finally, note that the magnitude of the undershoot at t = T is equal to ∆P. The other extreme case—namely, τ # T—is illustrated in Fig. E.14(c). In this case, the exponential decay is quite rapid, resulting in the output becoming almost zero shortly beyond the leading edge of the pulse. At the trailing edge of the pulse, the output swings negatively by an amount almost equal to the pulse height P. Then the waveform decays rapidly to zero. As seen from Fig. E.14(c), the output waveform bears no resemblance to the input pulse. It consists of two spikes: a positive one at the leading edge and a negative one at the trailing edge. Note that the output waveform is approximately equal to the time derivative of the input pulse. That is, for τ # T , an STC high-pass circuit approximates a differentiator. However, the resulting differentiator is not an ideal one; an ideal differentiator would produce two impulses. Nevertheless, high-pass STC circuits with short time constants are employed in some applications to produce sharp pulses or spikes at the transitions of an input waveform.! ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

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E-16 Appendix E Single-Time-Constant Circuits

EXERCISES E.12 Find the rise and fall times of a 1-µs pulse after it has passed through a low-pass RC circuit with a corner frequency of 10 MHz. Ans. 35 ns E.13 Consider the pulse response of a low-pass STC circuit, as shown in Fig. E.13(c). If τ = 100T, find the output voltage at t = T. Also, find the difference in the slope of the rising portion of the output waveform at t = 0 and t = T (expressed as a percentage of the slope at t = 0). Ans. 0.01P; 1% E.14 The output of an amplifier stage is connected to the input of another stage via a capacitance C. If the first stage has an output resistance of 10 kΩ, and the second stage has an input resistance of 40 kΩ, find the minimum value of C such that a 10-µs pulse exhibits less than 1% sag. Ans. 0.02 µF E.15 A high-pass STC circuit with a time constant of 100 µs is excited by a pulse of 1-V height and 100-µs width. Calculate the value of the undershoot in the output waveform. Ans. 0.632 V

PROBLEMS

E.1 Consider the circuit of Fig. E.3(a) and the equivalent shown in (d) and (e). There, the output, vO = vO1 + vO2, is the sum of outputs of a low-pass and a high-pass circuit, each with the time constant τ = (C1 + C2)(R1 || R2). What is the condition that makes the contribution of the low-pass circuit at zero frequency equal to the contribution of the highpass circuit at infinite frequency? Show that this condition can be expressed as C1R1 = C2R2. If this condition applies, sketch ! " ⁄ ! # versus frequency for the case R1 = R2. E.2 Use the voltage divider rule to find the transfer function Vo(s)/Vi(s) of the circuit in Fig. E.3(a). Show that the transfer function can be made independent of frequency if the condition C1R1 = C2R2 applies. Under this condition the circuit is called a compensated attenuator. Find the transmission of the compensated attenuator in terms of R1 and R2. **DE.3 The circuit of Fig. E.3(a) is used as a compensated attenuator (see Problems E.1 and E.2) for an oscilloscope probe. The objective is to reduce the signal voltage applied to the input amplifier of the oscilloscope, with the signal attenuation independent of frequency. The probe itself includes R1 and C1, while R2 and C2 model the oscilloscope input circuit. For an oscilloscope having an input resistance of 1 MΩ and an input capacitance of 30 pF,

design a compensated “10-to-1 probe”—that is, a probe that attenuates the input signal by a factor of 10. Find the input impedance of the probe when connected to the oscilloscope, which is the impedance seen by vI in Fig. E.3(a). Show that this impedance is 10 times higher than that of the oscilloscope itself. This is the great advantage of the 10:1 probe. E.4 In the circuits of Figs. E.4 and E.5, let L = 10 mH, C = 0.01 µF, and R = 1 kΩ. At what frequency does a phase angle of 45° occur? *E.5 Consider a voltage amplifier with an open-circuit voltage gain Avo = −100 V/V, Ro = 0, Ri = 10 kΩ, and an input capacitance Ci (in parallel with Ri) of 10 pF. The amplifier has a feedback capacitance (a capacitance connected between output and input) Cf = 1 pF. The amplifier is fed with a voltage source Vs having a resistance Rs = 10 kΩ. Find the amplifier transfer function Vo(s)/Vs(s) and sketch its magnitude response versus frequency (dB vs. frequency) on a log axis. E.6 For the circuit in Fig. PE.6, assume the voltage amplifier to be ideal. Derive the transfer function Vo(s)/Vi(s). What type of STC response is this? For C = 0.01 µF and R = 100 kΩ, find the corner frequency.

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E.5 Pulse Response of STC Circuits E-17

E.11 A pulse of 10-ms width and 10-V amplitude is transmitted through a system characterized as having an STC high-pass response with a corner frequency of 10 Hz. What undershoot would you expect? E.12 An RC differentiator having a time constant τ is used to implement a short-pulse detector. When a long pulse with T ! τ is fed to the circuit, the positive and negative peak outputs are of equal magnitude. At what pulse width does the negative output peak differ from the positive one by 10%? Figure PE.6

E.7 For the circuits of Figs. E.4(b) and E.5(b), find vO(t) if vI is a 10-V step, R = 1 kΩ, and L = 1 mH. E.8 Consider the exponential response of an STC low-pass circuit to a 10-V step input. In terms of the time constant τ , find the time taken for the output to reach 5 V, 9 V, 9.9 V, and 9.99 V. E.9 The high-frequency response of an oscilloscope is specified to be like that of an STC LP circuit with a 100MHz corner frequency. If this oscilloscope is used to display an ideal step waveform, what rise time (10% to 90%) would you expect to observe? E.10 An oscilloscope whose step response is like that of a low-pass STC circuit has a rise time of ts seconds. If an input signal having a rise time of tw seconds is displayed, the waveform seen will have a rise time td seconds, which can be found using the empirical formula $ % = $ 2& + $ 2' ) If ts = 35 ns, what is the 3-dB frequency of the oscilloscope? What is the

E.13 A high-pass STC circuit with a time constant of 1 ms is excited by a pulse of 10-V height and 1-ms width. Calculate the value of the undershoot in the output waveform. If an undershoot of 1 V or less is required, what is the time constant necessary? E.14 A capacitor C is used to couple the output of an amplifier stage to the input of the next stage. If the first stage has an output resistance of 2 kΩ and the second stage has an input resistance of 3 kΩ, find the value of C so that a 1-ms pulse exhibits less than 1% sag. What is the associated 3-dB frequency? DE.15 An RC differentiator is used to convert a step voltage change V to a single pulse for a digital-logic application. The logic circuit that the differentiator drives distinguishes signals above V/ 2 as “high” and below V/ 2 as “low.” What must the time constant of the circuit be to convert a step input into a pulse that will be interpreted as “high” for 10 µs? DE.16 Consider the circuit in Fig. E.7(a) with µ = –100, Cf = 100 pF, and the amplifier being ideal. Find the value of R so that the gain ! " ⁄ ! & has a 3-dB frequency of 1 kHz.

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APPENDIX E PROBLEMS

observed rise time for a waveform rising in 100 ns, 35 ns, and 10 ns? What is the actual rise time of a waveform whose displayed rise time is 49.5 ns?

SedraAppF.fm Page 1 Tuesday, October 20, 2009 8:27 PM

APPENDIX F

s-DOMAIN ANALYSIS: POLES, ZEROS, AND BODE PLOTS

In analyzing the frequency response of an amplifier, most of the work involves finding the amplifier voltage gain as a function of the complex frequency s. In this s-domain analysis, a capacitance C is replaced by an admittance sC, or equivalently an impedance 1 ⁄ sC , and an inductance L is replaced by an impedance sL. Then, using usual circuit-analysis techniques, one derives the voltage transfer function T ( s ) ≡ Vo ( s ) ⁄ Vi ( s ).

EXERCISE F.1

Find the voltage transfer function T ( s ) ≡ Vo ( s ) ⁄ Vi ( s ) for the STC network shown in Fig. EF.1.

R1 Vi

" ! R2

Figure EF.1

C

" Vo !

1 ⁄ CR s + 1 ⁄ C ( R 1 || R 2 )

1 Ans. T ( s ) = ------------------------------------------

Once the transfer function T(s) is obtained, it can be evaluated for physical frequencies by replacing s by jω. The resulting transfer function T( jω) is in general a complex quantity whose magnitude gives the magnitude response (or transmission) and whose angle gives the phase response of the amplifier. In many cases it will not be necessary to substitute s = jω and evaluate T( jω); rather, the form of T(s) will reveal many useful facts about the circuit performance. In general, for all

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F-1

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F-2 Appendix F s-Domain Analysis: Poles, Zeros, and Bode Plots the circuits dealt with in this book, T(s) can be expressed in the form + … + #0 # $ " + # $−1 " ! ! ( " ) = !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! % %−1 " + &%−1 " + … + & 0 $

$−1

(F.1)

where the coefficients a and b are real numbers, and the order m of the numerator is smaller than or equal to the order n of the denominator; the latter is called the order of the network. Furthermore, for a stable circuit—that is, one that does not generate signals on its own—the denominator coefficients should be such that the roots of the denominator polynomial all have negative real parts. The problem of amplifier stability is studied in Chapter 10.

F.1 Poles and Zeros An alternate form for expressing T(s) is ( " – '1 ) ( " – '2 ) … ( " – '$ ) ! ! ( " ) = # $ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ( " – (1 ) ( " – ( 2 ) … ( " – (% )

(F.2)

where am is a multiplicative constant (the coefficient of sm in the numerator), Z1, Z2, . . . , Zm are the roots of the numerator polynomial, and P1, P2, . . . , Pn are the roots of the denominator polynomial. Z1, Z2, . . . , Zm are called the transfer-function zeros or transmission zeros, and P1, P2, . . . , Pn are the transfer-function poles or the natural modes of the network. A transfer function is completely specified in terms of its poles and zeros together with the value of the multiplicative constant. The poles and zeros can be either real or complex numbers. However, since the a and b coefficients are real numbers, the complex poles (or zeros) must occur in conjugate pairs. That is, if 5 + j3 is a zero, then 5 − j3 also must be a zero. A zero that is purely imaginary (±jωZ) causes the transfer function T( jω) to be exactly zero at ω = ωZ. This is because the 2 numerator will have the factors (s + jωZ )(s − jωZ ) = (s2 + ω ' ), which for physical frequen2 2 cies becomes (−ω + ω ' ), and thus the transfer fraction will be exactly zero at ω = ωZ. Thus the “trap” one places at the input of a television set is a circuit that has a transmission zero at the particular interfering frequency. Real zeros, on the other hand, do not produce transmission nulls. Finally, note that for values of s much greater than all the poles and zeros, the %−$ transfer function in Eq. (F.1) becomes ! ( " ) ! # $ ⁄ " . Thus the transfer function has (n − m) zeros at s = ∞.

F.2 First-Order Functions Many of the transfer functions encountered in this book have real poles and zeros and can therefore be written as the product of first-order transfer functions of the general form #1 " + #0 ! ( " ) = !!!!!!!!!!!!!!!!!!! " + ω0

(F.3)

where −ω0 is the location of the real pole. The quantity ω0, called the pole frequency, is equal to the inverse of the time constant of this single-time-constant (STC) network (see Appendix E). The constants a0 and a1 determine the type of STC network. Specifically, we ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

"#$%&'(()*+,--.&/#-B--1#$2#3$&45-6789:#%-;<5-0==>--?@0;-.A

F.3 Bode Plots F-3

studied in Chapter 1 two types of STC networks, low pass and high pass. For the low-pass first-order network we have #0 (F.4) ! ( " ) = !!!!!!!!!!!!!!! " + ω0 In this case the dc gain is # 0 ⁄ω 0, and ω0 is the corner or 3-dB frequency. Note that this transfer function has one zero at s = ∞. On the other hand, the first-order high-pass transfer function has a zero at dc and can be written as #1 " ! ! ( " ) = !!!!!!!!!!!!!! (F.5) " + ω0 At this point the reader is strongly urged to review the material on STC networks and their frequency and pulse responses in Appendix E. Of specific interest are the plots of the magnitude and phase responses of the two special kinds of STC networks. Such plots can be employed to generate the magnitude and phase plots of a high-order transfer function, as explained below.

F.3 Bode Plots A simple technique exists for obtaining an approximate plot of the magnitude and phase of a transfer function given its poles and zeros. The technique is particularly useful in the case of real poles and zeros. The method was developed by H. Bode, and the resulting diagrams are called Bode plots. A transfer function of the form depicted in Eq. (F.2) consists of a product of factors of the form s + a, where such a factor appears on top if it corresponds to a zero and on the bottom if it corresponds to a pole. It follows that the magnitude response in decibels of the network can be obtained by summing together terms of the form 20 log10 # 2 + ω 2 , and the phase response can be obtained by summing terms of the form tan−1(ω ⁄ # ). In both cases the terms corresponding to poles are summed with negative signs. For convenience we can extract the constant a and write the typical magnitude term in the form 20 log 1 + ( ω ⁄ # ) 2 . On a plot of decibels versus log frequency this term gives rise to the curve and straight-line asymptotes shown in Fig. F.1. Here the low-frequency asymptote is a horizontal straight line 20 log "######### 1 ! ("/a)2 (dB)

!6 dB/octave (!20 dB/decade)

Actual curve

3 dB

0 dB

"3dB # $a $ #

1 $

" (log scale)

Figure F.1 Bode plot for the typical magnitude term. The curve shown applies for the case of a zero. For a pole, the high-frequency asymptote should be drawn with a –6-dB/octave slope. ©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

"#$%&'(()*+,--.&/#-<--1#$2#3$&45-6789:#%-;<5-0==>--?@0;-.A

F-4 Appendix F s-Domain Analysis: Poles, Zeros, and Bode Plots at 0-dB level and the high-frequency asymptote is a straight line with a slope of 6 dB/octave or, equivalently, 20 dB/decade. The two asymptotes meet at the frequency ω = # , which is called the corner frequency. As indicated, the actual magnitude plot differs slightly from the value given by the asymptotes; the maximum difference is 3 dB and occurs at the corner frequency. For a = 0—that is, a pole or a zero at s = 0—the plot is simply a straight line of 6 dB/ octave slope intersecting the 0-dB line at ω = 1. In summary, to obtain the Bode plot for the magnitude of a transfer function, the asymptotic plot for each pole and zero is first drawn. The slope of the high-frequency asymptote of the curve corresponding to a zero is +20 dB/decade, while that for a pole is −20 dB/decade. The various plots are then added together, and the overall curve is shifted vertically by an amount determined by the multiplicative constant of the transfer function.-

Example F.1 An amplifier has the voltage transfer function

10" ! ! ( " ) = !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 2 5 ( 1 + " ⁄ 10 ) ( 1 + " ⁄ 10 ) Find the poles and zeros and sketch the magnitude of the gain versus frequency. Find approximate values for the gain at ω = 10, 103, and 106 rad/s.

Solution The zeros are as follows: one at s = 0 and one at s = ∞. The poles are as follows: one at s = –102 rad/s and one at s = –105 rad/s. Figure F.2 shows the asymptotic Bode plots of the different factors of the transfer function. Curve 1, which is a straight line intersecting the ω -axis at 1 rad/s and having a +20 dB/decade slope, corresponds to the s term (that is, the zero at s = 0) in the numerator. The pole at s = –102 results in curve 2, which consists of two asymptotes intersecting at ω = 102. Similarly, the pole at s = –105 is represented by curve 3, where the intersection of the asymptotes is at ω = 105. Finally, curve 4 represents the multiplicative constant of value 10.

Figure F.2 Bode plots for Example F.1.

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"#$%&'(()*+,--.&/#-?--1#$2#3$&45-6789:#%-;<5-0==>--?@0;-.A

F.3 Bode Plots F-5

Adding the four curves results in the asymptotic Bode diagram of the amplifier gain (curve 5). Note that since the two poles are widely separated, the gain will be very close to 103 (60 dB) over the frequency range 102 to 105 rad/s. At the two corner frequencies (102 and 105 rad/s) the gain will be approximately 3 dB below the maximum of 60 dB. At the three specific frequencies, the values of the gain as obtained from the Bode plot and from exact evaluation of the transfer function are as follows: ω

10 103 106

Approximate Gain

Exact Gain

40 dB 60 dB 40 dB

39.96 dB 59.96 dB 39.96 dB

We next consider the Bode phase plot. Figure F.3 shows a plot of the typical phase term tan–1(ω/a), assuming that a is negative. Also shown is an asymptotic straight-line approximation of the arctan function. The asymptotic plot consists of three straight lines. The first is horizontal at φ = 0 and extends up to ω = 0.1 # * The second line has a slope of –45°/decade and extends from ω = 0.1 # to ω = 10 # * The third line has a zero slope and a level of φ = –90°. The complete phase response can be obtained by summing the asymptotic Bode plots of the phase of all poles and zeros.-

Figure F.3 Bode plot of the typical phase term tan–1(ω/a) when a is negative.

Example F.2 Find the Bode plot for the phase of the transfer function of the amplifier considered in Example F.1.

Solution The zero at s = 0 gives rise to a constant +90° phase function represented by curve 1 in Fig. F.4. The pole at s = –102 gives rise to the phase function –1 ω φ 1- = – 8&2 !!!!!!!2!

10

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SedraAppF.fm Page 6 Tuesday, October 20, 2009 8:42 PM

F-6 Appendix F s-Domain Analysis: Poles, Zeros, and Bode Plots

Figure F.4 Phase plots for Example F.2.

(the leading minus sign is due to the fact that this singularity is a pole). The asymptotic plot for this function is given by curve 2 in Fig. F.4. Similarly, the pole at s = –105 gives rise to the phase function –1 ω φ 2 = – tan -------5-

10 whose asymptotic plot is given by curve 3. The overall phase response (curve 4) is obtained by direct summation of the three plots. We see that at 100 rad/s, the amplifier phase leads by 45° and at 105 rad/s the phase lags by 45°.

F.4 An Important Remark For constructing Bode plots, it is most convenient to express the transfer-function factors in the form (1 + s ⁄ a ). The material of Figs. F.1 and F.2 and of the preceding two examples is then directly applicable.

PROBLEMS

F.1 Find the transfer function T ( s ) = Vo ( s ) ⁄ Vi ( s ) of the circuit in Fig. PF.1. Is this an STC network? If so, of what type? For C1 = C2 = 0.5 µF and R = 100 kΩ, find the location of the pole(s) and zero(s), and sketch Bode plots for the magnitude response and the phase response.

C1 ! Vi

! "

C2

R

Vo "

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SedraAppF.fm Page 7 Tuesday, October 20, 2009 8:42 PM

F.4 An Important Remark

Rs

F.7 An amplifier has a voltage transfer function T ( s ) = 6 3 10 s ⁄ ( s + 10 ) ( s + 10 ). Convert this to the form convenient

C !

Vs ! "

an actual physical circuit, where must other poles and zeros be found?

RL

Vo

for constructing Bode plots [that is, place the denominator factors in the form (1+s/a)]. Provide a Bode plot for the magnitude response, and use it to find approximate values for the amplifier gain at 1, 10, 102, 103, 104, and 105 rad/s. What would the actual gain be at 10 rad/s? At 103 rad/s?

Figure PF.2

F.8 Find the Bode phase plot of the transfer function of the amplifier considered in Problem F.7. Estimate the phase angle at 1, 10, 102, 103, 104, and 105 rad/s. For comparison, calculate the actual phase at 1, 10, and 100 rad/s.

(b) In this circuit, capacitor C is used to couple the signal source Vs having a resistance Rs to a load RL. For Rs = 10 kΩ, design the circuit, specifying the values of RL and C to only one significant digit to meet the following requirements:

F.9 A transfer function has the following zeros and poles: one zero at s = 0 and one zero at s = ∞; one pole at s = −100 and one pole at s = −106. The magnitude of the transfer function at ω = 104 rad/s is 100. Find the transfer function T(s) and sketch a Bode plot for its magnitude.

(i) The load resistance should be as small as possible. (ii) The output signal should be at least 70% of the input at high frequencies. (iii) The output should be at least 10% of the input at 10 Hz.

F.10 Sketch Bode plots for the magnitude and phase of the transfer function

"

F.3 Two STC RC circuits, each with a pole at 100 rad/s and a maximum gain of unity, are connected in cascade with an intervening unity-gain buffer that ensures that they function separately. Characterize the possible combinations (of lowpass and high-pass circuits) by providing (i) the relevant transfer functions, (ii) the voltage gain at 10 rad/s, (iii) the voltage gain at 100 rad/s, and (iv) the voltage gain at 1000 rad/s. F.4 Design the transfer function in Eq. (F.5) by specifying a1 and ω 0 so that the gain is 10 V/V at high frequencies and 1 V/V at 10 Hz. F.5 An amplifier has a low-pass STC frequency response. The magnitude of the gain is 20 dB at dc and 0 dB at 100 kHz. What is the corner frequency? At what frequency is the gain 19 dB? At what frequency is the phase −6°? F.6 A transfer function has poles at (−5), (−7 + j10), and (−20), and a zero at (−1 − j20). Since this function represents

4

5

10 ( 1 + s ⁄ 10 ) T ( s ) = --------------------------------------------------------3 4 ( 1 + s ⁄ 10 ) ( 1 + s ⁄ 10 )

From your sketches, determine approximate values for the magnitude and phase at ω = 106 rad/s. What are the exact values determined from the transfer function? F.11 A particular amplifier has a voltage transfer function 2 6 T ( s ) = 10s ⁄ ( 1 + s ⁄ 10 ) ( 1 + s ⁄ 100 ) ( 1 + s ⁄ 10 ). Find the poles and zeros. Sketch the magnitude of the gain in dB versus frequency on a logarithmic scale. Estimate the gain at 100, 103, 105, and 107 rad/s. F.12 A direct-coupled differential amplifier has a differential gain of 100 V/V with poles at 106 and 108 rad/s, and a common-mode gain of 10−3 V/V with a zero at 104 rad/s and a pole at 108 rad/s. Sketch the Bode magnitude plots for the differential gain, the common-mode gain, and the CMRR. What is the CMRR at 107 rad/s? (Hint: Division of magnitudes corresponds to subtraction of logarithms.)

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APPENDIX F PROBLEMS

D*F.2 (a) Find the voltage transfer function T ( s ) = Vo ( s ) ⁄ Vi ( s ) , for the STC network shown in Fig. PF.2.

F-7

SedraAppG.fm Page 1 Tuesday, October 20, 2009 8:52 PM

APPENDIX G

BIBLIOGRAPHY

HISTORY OF EL ECTRONICS L. Berlin, The Man Behind the Microchip: Robert Noyce and the Invention of Silicon Valley, New York: Oxford University Press, 2005. T.R. Reid, The Chip, New York: Random House, 2001. J.N. Shurkin, Broken Genius: The Rise and Fall of William Shockley, Creator of the Electronic Age, New York, Macmillan, 2008. J. Williams, editor, Analog Circuit Design: Art, Science, and Personalities, Boston: ButterworthHeinemann, 1991. IEEE Solid-State Circuits Magazine, and its predecessor, IEEE Solid-State Circuits Newsletter, published quarterly by the IEEE Solid-State Circuits Society. GENERA L TEXTBOO KS ON ELECTRONIC CIRCUITS E.F. Angelo Jr., Electronics: BJTs, FETs, and Microcircuits, New York: McGraw-Hill, 1969. S.B. Burns and P.R. Bond, Principles of Electronic Circuits, St. Paul: West, 1987. M.S. Ghausi, Electronic Devices and Circuits: Discrete and Integrated, New York: Holt, Rinehart and Winston, 1985. P.E. Gray and C.L. Searle, Electronic Principles, New York: Wiley, 1969. A.R. Hambley, Electronics, 2nd ed., Upper Saddle River, NJ: Prentice-Hall, 1999. W.H. Hayt and G.W. Neudeck, Electronic Circuit Analysis and Design, 2nd ed., Boston: Houghton Mifflin Co., 1984. C.A. Holt, Electronic Circuits, New York: Wiley, 1978. M.N. Horenstein, Microelectronic Circuits and Devices, 2nd ed., Englewood Cliffs, NJ: PrenticeHall, 1995. R.T. Howe and C.G. Sodini, Microelectronics—An Integrated Approach, Englewood Cliffs, NJ: Prentice-Hall, 1997. R.C. Jaeger and T.N. Blalock, Microelectronic Circuit Design, 3rd ed., New York: McGraw-Hill, 2008. N.R. Malik, Electronic Circuits: Analysis, Simulation, and Design, Englewood Cliffs, NJ: Prentice-Hall, 1995.

J. Millman and A. Grabel, Microelectronics, 2nd ed., New York: McGraw-Hill, 1987. D.A. Neamen, Electronic Circuit Analysis and Design, 3rd ed., New York: McGraw-Hill, 2007. M.H. Rashid, Microelectronic Circuits: Analysis and Design, Boston: PWS, 1999. B. Ravazi, Fundamentals of Microelectronics, Hoboken, NJ: Wiley, 2008. D.L. Schilling and C. Belove, Electronic Circuits, 2nd ed., New York: McGraw-Hill, 1979. R.A. Spencer and M.S. Ghausi, Introduction to Electronic Circuit Design, Upper Saddle River, NJ: Pearson Education Inc. (Prentice-Hall), 2003. CIRCUIT AND SYSTEM AN ALYSIS L.S. Bobrow, Elementary Linear Circuit Analysis, 2nd ed., New York: Holt, Rinehart and Winston, 1987. A.M. Davis, Linear Circuit Analysis, Boston, PWS Publishing Company, 1998. S.S. Haykin, Active Network Theory, Reading, MA: Addison-Wesley, 1970. W.H. Hayt, G.E. Kemmerly, and S.M. Durbin, Engineering Circuit Analysis, 6th ed., New York: McGraw-Hill, 2003. D. Irwin, Basic Engineering Circuit Analysis, 7th ed., New York: Wiley, 2001. B.P. Lathi, Linear Systems and Signals, New York: Oxford University Press, 1992. J.W. Nilsson and S. Riedel, Electronic Circuits, 7th ed., Upper Saddle River, NJ: Prentice-Hall, 2005. DEVICES AND IC FABRICATION R.S.C. Cobbold, Theory and Applications of Field Effect Transistors, New York: Wiley, 1969. I. Getreu, Modeling the Bipolar Transistor, Beaverton, OR: Tektronix, Inc., 1976. R.S. Muller and T.I. Kamins, Device Electronics for Integrated Circuits, 3rd ed., New York: Wiley, 2003. J.D. Plummer, M.D. Deal, and P.B. Griffin, Silicon VLSI Technology, Upper Saddle River, NJ: Prentice-Hall, 2000. D.L. Pulfrey and N.G. Tarr, Introduction to Microelectronic Devices, Englewood Cliffs, NJ: PrenticeHall, 1989.

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G-1

!"#$%&''()*+,,-%.",/,,0$1#%23,45678"$,9:3,/;;<,,=>9=,-?

G-2 Appendix G Bibliography C.L. Searle, A.R. Boothroyd, E.J. Angelo, Jr., P.E. Gray, and D.O. Pederson, Elementary Circuit Properties of Transistors, Vol. 3 of the SEEC Series, New York: Wiley, 1964. B.G. Streetman and S. Banerjee, Solid-State Electronic Devices, 5th ed., Upper Saddle River, NJ: Prentice-Hall, 2000. Y. Tsividis, Operation and Modeling of the MOS Transistor, 2nd ed., New York: Oxford University Press, 1999. OPERATIO NAL AMPLIFIERS G.B. Clayton, Experimenting with Operational Amplifiers, London: Macmillan, 1975. G.B. Clayton, Operational Amplifiers, 2nd ed., London: Newnes-Butterworths, 1979. S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed., New York: McGraw-Hill, 2001. J.G. Graeme, G.E. Tobey, and L.P. Huelsman, Operational Amplifiers: Design and Applications, New York: McGraw-Hill, 1971. W. Jung, IC Op Amp Cookbook, Indianapolis: Howard Sams, 1974. E.J. Kennedy, Operational Amplifier Circuits: Theory and Applications, New York: Holt, Rinehart and Winston, 1988. J.K. Roberge, Operational Amplifiers: Theory and Practice, New York: Wiley, 1975. J.L. Smith, Modern Operational Circuit Design, New York: Wiley-Interscience, 1971. J.V. Wait, L.P. Huelsman, and G.A. Korn, Introduction to Operational Amplifiers: Theory and Applications, New York: McGraw-Hill, 1975. ANALOG CIRCUITS P.E. Allen and D.R. Holberg, CMOS Analog Circuit Design, 2nd ed., New York: Oxford University Press, 2002. K. Bult, Transistor-Level Analog IC Design. Notes for a short course organized by Mead, Ecole Polytechnique Féderal de Lausanne, 2002. M.J. Fonderic and J.H. Huising, Design of Low-Voltage Bipolar Operational Amplifiers, Boston: Kluwer Academic Publishers, 1993. R.L. Geiger, P.E. Allen, and N.R. Strader, VLSI Design Techniques for Analog and Digital Circuits, New York: McGraw-Hill, 1990. P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 5th ed., Hoboken, NJ: Wiley, 2008. A.B. Grebene, Bipolar and MOS Analog Integrated Circuit Design, New York: Wiley, 1984. R. Gregorian and G.C. Temes, Analog MOS Integrated Circuits for Signal Processing, New York: Wiley, 1986. J.H. Huising, Operational Amplifiers, Boston: Kluwer Academic Publishers, 2001. IEEE Journal of Solid-State Circuits, a monthly publication of the IEEE. D.A. Johns and K. Martin, Analog Integrated Circuit Design, New York: Wiley, 1997.

K. Laker and W. Sansen, Design for Analog Integrated Circuits and Systems, New York: McGraw-Hill, 1999. H.S. Lee, “Analog Design,” Chapter 8 in BiCMOS Technology and Applications, A.R. Alvarez, editor, Boston: Kluwer Academic Publishers, 1989. National Semiconductor Corporation, Audio/Radio Handbook, Santa Clara, CA: National Semiconductor Corporation, 1980. B. Razavi, Design of Analog CMOS Integrated Circuits, New York: McGraw-Hill, 2001. J.K. Roberge, Operational Amplifiers: Theory and Practice, New York: Wiley, 1975. S. Rosenstark, Feedback Amplifier Principles, New York: Macmillan, 1986. W.M.C. Sansen, Analog Design Essentials, Dordrecht, The Netherlands: Springer, 2006. A.S. Sedra and G.W. Roberts, “Current Conveyor Theory and Practice,” Chapter 3 in Analogue IC Design: The Current-Mode Approach, C. Toumazou, F.J. Lidgey, and D.G. Haigh, editors, London: Peter Peregrinus, 1990. R. Severns, editor, MOSPOWER Applications Handbook, Santa Clara, CA: Siliconix, 1984. Texas Instruments, Inc., Power Transistor and TTL Integrated-Circuit Applications, New York: McGraw-Hill, 1977. S. Soclof, Applications of Analog Integrated Circuits, Englewood Cliffs, NJ: Prentice-Hall, 1985. J.M. Steininger, “Understanding wideband MOS transistors,” IEEE Circuits and Devices, Vol. 6, No. 3, pp. 26–31, May 1990. DIGITAL CIRCUITS A.R. Alvarez, editor, BiCMOS Technology and Applications, 2nd ed., Boston: Kluwer Academic Publishers, 1993. S.H.K Embabi, A. Bellaour, and M.I. Elmasry, Digital BiCMOS Integrated Circuit Design, Boston: Kluwer, 1993. M.I. Elmasry, editor, Digital MOS Integrated Circuits, New York: IEEE Press, 1981. Also, Digital MOS Integrated Circuits II, 1992. D.A. Hodges, H.G. Jackson, and R.A. Saleh, Analysis and Design of Digital Integrated Circuits, 3rd ed., New York: McGraw-Hill, 2004. IEEE Journal of Solid-State Circuits, a monthly publication of the IEEE. S.M. Kang and Y. Leblebici, CMOS Digital Integrated Circuits, 3rd ed., New York: McGraw-Hill, 2003. R. Littauer, Pulse Electronics, New York: McGrawHill, 1965. K. Martin, Digital Integrated Circuit Design, New York: Oxford University Press, 2000. J. Millman and H. Taub, Pulse, Digital, and Switching Waveforms, New York: McGraw-Hill, 1965. Motorola, MECL Device Data, Phoenix, AZ: Motorola Semiconductor Products, Inc., 1989. Motorola, MECL System Design Handbook, Phoenix, AZ: Motorola Semiconductor Products, Inc., 1988.

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!"#$%&''()*+,,-%.",J,,0$1#%23,45678"$,9:3,/;;<,,=>9=,-?

Bibliography J.M. Rabaey, Digital Integrated Circuits, Englewood Cliffs, NJ: Prentice-Hall, 1996. Note: A 2nd ed., with A. Chandrakasan and B. Nikolic, also appeared in 2003. L. Strauss, Wave Generation and Shaping, 2nd ed., New York: McGraw-Hill, 1970. H. Taub and D. Schilling, Digital Integrated Electronics, New York: McGraw-Hill, 1977. N. Weste and K. Eshraghian, Principles of CMOS VLSI Design, Reading, MA: Addison-Wesley, 1985 and 1993. FILTERS AND TUNED AMPLIFIERS P.E. Allen and E. Sanchez-Sinencio, Switched-Capacitor Circuits, New York: Van Nostrand Reinhold, 1984. K.K. Clarke and D.T. Hess, Communication Circuits: Analysis and Design, Ch. 6, Reading, MA: Addison Wesley, 1971. G. Daryanani, Principles of Active Network Synthesis and Design, New York: Wiley, 1976. R. Gregorian and G.C. Temes, Analog MOS Integrated Circuits for Signal Processing, New York: WileyInterscience, 1986. C. Ouslis and A. Sedra, “Designing custom filters,” IEEE Circuits and Devices, May 1995, pp. 29–37. S.K. Mitra and C.F. Kurth, editors, Miniaturized and Integrated Filters, New York: Wiley-Interscience, 1989. R. Schaumann, M.S. Ghausi, and K.R. Laker, Design of Analog Filters, Englewood Cliffs, NJ: PrenticeHall, 1990.

R. Schaumann, M. Soderstand, and K. Laker, editors, Modern Active Filter Design, New York: IEEE Press, 1981. R. Schaumann and M.E. Van Valkenburg, Design of Analog Filters, New York: Oxford University Press, 2001. A.S. Sedra, “Switched-capacitor filter synthesis,” in MOS VLSI Circuits for Telecommunications, Y. Tsividis and P. Antognetti, editors, Englewood Cliffs, NJ: Prentice-Hall, 1985. A.S. Sedra and P.O. Brackett, Filter Theory and Design: Active and Passive, Portland, OR: Matrix, 1978. M.E. Van Valkenburg, Analog Filter Design, New York: Holt, Rinehart and Winston, 1981. A.I. Zverev, Handbook of Filter Synthesis, New York: Wiley, 1967. SPICE ?)@), A"$B16"$3, Schematic Capture with Cadence PSpice!"#$%"&%'!,C''"$,!%##D",E1F"$3,GH>,-$"B615"I A%DD3,/;;J) (),?%KK78$17,%B#,-),&B67.B"6613,Semiconductor Device Modeling with SPICE!, #$%" &%'!, G"L, M7$N> ?5($%LIA1DD3,9< O1D"23,/;;/) -)O),PQ1B"B.%3,SPICE: A Guide to Circuit Simulation & Analysis Using PSpice!" #$%" &%'!, @B.D"L77# RD1**K3,GH>,-$"B615"IA%DD3,9<
©2010 Oxford University Press, Inc. Reprinting or distribution, electronically or otherwise, without the express written consent of Oxford University Press, Inc. is prohibited.

G-3

APPENDIX H

STANDARD RESISTANCE VALUES AND UNIT PREFIXES !"#$%&'&(%&#"#')%#(*%&(*+*",*-,&().,/(".(#'*.0*%0(+*,1(3*-,&(425(6%)+"0&#('7&(81,'"6,"&%# 9)%('7&(#'*.0*%0(+*,1&#()9(:;<'),&%*.$&(*.0(5;<'),&%*.$&(%&#"#')%#2(371#=(".('7&(>",)78(

Table H.1 Standard Resistance Values !"#!$%&'&()*!+,-.%&!/0Ω1 2#!$%&'&()*!+,-.%&!/0Ω1

"334"56

"3 "" "; "8 "2 ": "7 ;3 ;; ;6 ;5 83 88 8: 89 68 65 2" 2: :; :7 52 7; 9"

"33 "3; "32 "35 ""3 ""8 ""2 ""7 ";" ";6 ";5 "83 "88 "85 "63 "68 "65 "23 "26 "27 ":; ":2 ":9 "56

"574839 "57 "7; "75 "9" "9: ;33 ;32 ;"3 ;"2 ;;" ;;: ;8; ;85 ;68 ;69 ;22 ;:" ;:5 ;56 ;73 ;75 ;96 83" 839

8":4269

2:;495:

8": 8;6 88; 863 867 825 8:2 856 878 89; 63; 6"; 6;; 68; 66; 628 6:6 652 675 699 2"" 2;8 28: 269

2:; 25: 293 :36 :"9 :86 :69 ::2 :7" :97 5"2 58; 523 5:7 575 73: 7;2 762 7:: 775 939 98" 928 95:

H-1

H-2 Appendix H Standard Resistance Values and Unit Prefixes %*.?&()9(:;(%&#"#')%#=().&(9".0#(%&#"#'*.$&#()9(52@=(525=(52A=(52B=(52:= 2 2 2 2(C.('7&(#*8&(%*.?&= ).&(9".0#(5;(%&#"#')%#()9(>",)78(+*,1&#()9(52@@=(52@A=(52@:=(52@D=(525@= 2 2 2 2 3*-,&(42A(6%)+"0&#('7&(EC(1."'(6%&9"F&#(1#&0(".('7"#(-))>(*.0(".(*,,(8)0&%.(G)%>#(". H.?,"#72 Table H.2 SI Unit Prefixes <,=%

>?=@)-

C%=()

C

D'B)

D

E,E)

E

='B*)

µ

='--'

=

0'-)

0

=%F,

G

F'F,

H

(%*,

I

D%(,

J

3*-,&(42B(6%)+"0&#('7&(8&'&%($).+&%#").(9*$')%#2 Table H.3 Meter Conversion factors "!µ=!K!"3−6!B=!K!"3−:!= "!=!K!"3;!B=!K!"3:!µ= 3L"!µ=!K!"33!E= "!M!K!"3−7!B=!K!"3−"3!=

A,B()*

×("3−"2 ×("3−"; ×("3−9 ×("3−: ×("3−8 ×("38 ×("3: ×("39 ×("3"; ×("3"2

APPENDIX I

ANSWERS TO SELECTED PROBLEMS CHAPTER 1 !"! #$% !&'()* #+% !&',Ω* #-% !&&'.* #/% &"!') !"0 #$% &"1'23'!'2* #-% &"&1'23 !/4'2* #5% &"!0!'23'!/4'2'+67'89:5:9$+;<'!/='2' !"= !>' !"> 0"1='.3'0"00',Ω*'0">?'.'7@' A"!='.3'0"!!',Ω'7@'0"AA',Ω !"1 !&"0'.*'BC6D7'7C:'!&E,Ω'9:BFB7@9'$'!?>E,Ω'9:BFB7@9*'$//'$' B:9F:B'9:BFB7@9'@5'0&&'Ω*'BC6D7'7C:'=">E,Ω'9:BFB7@9'GF7C'$'!?>',Ω'$D/'7C:'!&E,Ω'9:BFB7@9'GF7C' 1&',Ω !"!! 0?&'Ω !"!A HC6D7'!"'GF7C'$'!"!E,Ω'9:BFB7@9*'-699:D7'/FIF/:9' !"!? &">>'.' $D/'J"!?',Ω*'&"!'() !"!> !"44'µ)*'?"J='. !"!1 #$% !&−>'B3'!&>'KL3'J"04'×'!&>'KL* #5% !&A'9$/MB3'!"?1'×'!&0'KL3'J"04'×'!&−A'B !"0! #$% #!'− #!"?1%',Ω*'#-% #>!">0'−'#=?"&=%',Ω !"00 #+% &"!'.3'!&'µ)3'!&',Ω !"0= !&',Ω !"04 #$% !J?'.*'#+% 0='. !"A& &"?'.*'!'.* &'.*'!'.*'!&&&'KL*'!&−A'B !"A0 =',KL*'='KL' !"A= &3'!&!3'!&&&3'!!&&!3'!!!&&! !"AJ #-% !!*'=.1'(.*'0"='(. !"A4 >"&?J''×'!&?'+F7B'8:9'B:-@D/' !"=& !!'.M.'@9'0&"4' /N*'00')M)'@9'0J"4'/N*'0=0'2M2'@9'0A"4'/N*'!0&'(2*'1?"4'(2*'0&"0O' !"=0 1'(.*' ?>"?'(.*'&"?>A'. !"=A #$% 4"0J'.M.'@9'!4"A'/N* #+% 0"?'.M.'@9'4'/N* #-% &"&4A'.M.'@9' −0!"J'/N' !"=J &"4A'.*'−!"J'/N*'>1.0'/N*'A4"4'/N !"?! #$% A&&'.M.* #+% 1&',Ω3 A'×'!&=')M)3'1'×'!&J'2M2* #-% JJ>'Ω*'#/% ???">'.M.*'#:% !&&',Ω3'!&&'Ω3'AJA'.M. !"?> P9$DB-@D/6-7$D-:'$(8;F5F:9*'!&&',Ω*'!&&',Ω; !0!'.M. !"J? $/#$ + !/%!% !"J4 &"J='µQ !">! &"?!/%! !">0 !A"A'8Q*'&"0J'8Q !">? 0&'/N*'A>'/N*'=&'/N*'A>'/N*' 0&'/N*'&'/N*'−0&'/N*'11&&'KL !">J !/#$%!!!'+'!%*'!?"1'KL*'−&'$#!0MM!A%/($'+ !/#%0#!0 + !A%%%*'?A'KL*'!J'KL

CHAPTER 2 0"0 0&&0'.M. 0"? 0&3&&&'.M. 0"4 #$% −!&'.M.3'!&',Ω* #+% −!&'.M.3'!&',Ω* #-% −!&'.M.3'!&',Ω;'#/% −!&'.M.3'!&',Ω 0"!! #$% −! .M.* #+% −!&'.M.*''#-% −&"!'.M.*' #/% −!&&'.M.*'#:% −!&'.M.' 0"!0 #+% !!'='!&',Ω3'!0'='0&',Ω #/% !!'='!&',Ω3 !0'='!'RΩ' 0"!= !FD'='?&"!',Ω 0"!4 &'.3'?'.*'−="1'.'7@'−?"!'. 0"0& #+% −JJ"='.M. 0"0! ±?'(. 0"0J #+% 1&1'.M.' 0"01 !&&'Ω* !&&'Ω*'!&&',Ω 0"A! #$% !3'!3'!3'!* #+% (3'0(3'=(3'4(* #-% −(!3'−0(!3'−=(!3'−4(! 0"A= #$% !"!!',Ω*'#+% 0 Ω, ∞ 0"AJ v)'S'T#v!'U'V'v0)*'−!'. 0"=A !0"4',Ω 0"=J !'='!&&',Ω*'W@ 0"?& v*'='='BFD#0π'×' !&&&+%' 0"?A #$% &"&11'.*'&"&11'()*'&"&11'()* #+% !&'.*'!&'()*'&'()' 0"?= v) ⁄ v!''S'! ⁄ (1 + 1 ⁄Α)*'&"1113'−&"!O*'&"11&3'−!"&O*'&"1&13'−1"!O 0"?J 4"AA'.M.*'HC6D7' !!'GF7C'!$,'='AJ',Ω*'1"&1'.M.*'!!"!'.M. 0"?1 −!&">!='7@'+!&">!='.*'!"&>'. 0"J0 v)'S'v0'−'v!*'!*'0!*'0!*'! 0"J= !!'='!A' 0"JJ J4'/N 0"J4 #$% !3'&* #+% −?'.'7@'+?'.*''#-% !3'&3'−A&'7@'+A&'. 0">A #$%'−&"!='7@'+&"!='.*'−!='7@'+!='.' 0">J !!'='&"?',Ω'5FX:/*'!0'='?&',Ω 0">> #$% A'.M.3'−A"&'.M.* #+% J'.M.* #-% ?J'.' #8:$,E7@E8:$,%3'!1"4'.'#9(B%' 0"4! !&&',KL*'!"?1'µB 0"4? !&&'86;B:B 0"44 !"?1',KL*' !&'.'#8:$,E7@E8:$,%' 0"1> !"='(. 0"11 ?>"?'(.*'=0"?'7@'?>"?'(.*')//'$'?E,Ω'9:BFB7@9'FD' B:9F:B'GF7C'7C:'8@BF7FI:'FD867'7:9(FD$;*'±!&'(.*'$//'?E,Ω'9:BFB7@9'FD'B:9F:B'GF7C'7C:'D:Y$7FI:' FD867';@$/" 0"!&! ="?='(. 0"!&= #$% &"!'.*'#+% &"0'.* #-% !&',Ω3'!&'(.* #/% !!&'(. 0"!&4 =J'/N*'?&!'KL*'!&'RKL 0"!!! =>"J',KL*'!1"1'.M.*'!1"1'.M.

I-1

I-2 Appendix I Answers to Selected Problems 0"!!= A0'.M. 0"!!> #$% # 0 'T'!%!M0'-!*'#+% !&',KL* #-% J="=',KL3'$+@67'BFX'7F(:B' Y9:$7:9 0"!0& Q@9':$-C3'-A/N'S'-+'⁄ A 0"!0> #$% A!"4',KL* #+% &">1?'.* #-% &'7@'0&&',KL* #/% !'.'8:$,

CHAPTER 3 A"!''?"AA'×'!&T!4*'A"&?'×'!&T!=*'!">0'X'!&T!A*'0"4>'×'!&T!!*'1"=?'×'!&T!!''' A"=''!"?'×'!&!>'.' $7@(BM-(A' A"?''K@;:'-@D-:D79$7F@D'0"0?'×'!&=M-(A*'0"0A'×'!&1M-(A' A"1''="JA'×'!&!>M-(A' A"!&''&"=A0')M-(0' A"!!''/0Z'A?3'04"?3'!4"!3'1"A*'/1Z'!0"=3'!&"=3'J">3'A"1' A"!A''&"JAA'.*' &"1?!'µ(*'&"4J=0'µ(*'&"4J=0'µ(*'?"?A'×'!&T!='[' A"00''A"J'×'!&T!?')*'&"JJ=?'. A"0>''0?1'8H*'!'8Q

CHAPTER 4 ="! #$% &')*'!"?'.* #+% !"?')*'&'. ="0 #$% ?'.*'!'()* '#+%'?'.*'&'()* #-%'?'.*'!'()* #/% ?'.*'&'() ="4 ?&',Ω ="1 #$% &'.*'&"A'()* #+% &"='.*'&'()' ="!& #$% ="?'.*' &"00?'()* #+% 0'.*'&') ="!? 01"J>'.*'A">?'Ω*'&">?')*'0J"4A'.*'A&'.*'A'Ω*'0&"?O* !AJ'()*'!')*'0>'. ="!J 9:/';FYC7B*'D:F7C:9';FYC7*'Y9::D';FYC7B ="!4 &"A=?'.* !"=?'×'!&!0(2 ="0& ?A>'×'!&−!4')*'&">=J'()*'0>"A0'()*'&"AA?'()*'1"!>'µ)*'?>"?J'(. ="0A >"1'()*'−!&"!?'(.' ="0J !1='Ω ="01 ?&°[*'1'2*'?"?J°[M2 ="AA &"JJA?'.*' &"AAJ?'() ="A? !'='1=>'Ω ="A4 &"4J'()*'&'.*'&')*'A"J'. ="?! !?> µ)*'−4="A°'7@ −?">!° ="?4 −A&'(.M()*'−!0&'(.M()'' ="J& 4"1J'.*'1"&!'.*'1"=J'. ="JA 4"4A'.*' !1"!A'()*'A&&'Ω*'1"!='.*'±&"&!'.*''+&"!0'.*'?>4'Ω*'4"4A'.*'1&'(.M.*'−0>"A'()M() ="J4 !J"0>'.*'=4">O*'&"!A*'?"&J'.*'?"&J'() ="J1 !J"0>'.*'1>"=O*'!&"!0'.*'!&"!0'() =">& !?"?>'.*'1="4O*'1"=='.*'1"=='() =">0 ??'. =">? #$% !JJ">'µQ*'!?"='.*'>"!O* 0AA'()*'==1'()* #+% !JJ>'µQ*'!J"!1'.*'0"0?O*'>A?'()*'!=??'() =">J #$% 4A"A'µQ*' !?"?'.*'!="0O*'!0="='()*'0AA'()* #+% 4AA'µQ*'!J"!1'.*'="?O*'A>J'()*'>A?'() =">1 #$% 0A"J'.* #+% ==="='µQ* #-% A0">'.*'=1'.*'#/% &">A')* #:% !"AJ') ="1! !="!='.

CHAPTER 5 ?"0 !"4>?'5[ ?"> 0"A4'µ( ?"!0 31/30'='0"? ?"!A 0A4'Ω*'0A4'(.*'?& ?"!= #$% >"A'()* #+% !"J0'()*'!"J!'()*'!>">'() ?"!> A"?'.*'!"?'.*'?&&'Ω*'!&&'Ω ?"!4 !"&'.*'&"?'.*'!"?'.*'!"&'. ?"00 !&"A'. ?"0A !&&'Ω'7@'!&',Ω* #$% 0&&'Ω'7@'0&',Ω* #+% ?&'Ω'7@'?',Ω* #-% !&&'Ω'7@'!&',Ω ?"A! ?&&',Ω*'?&',Ω*'0O*'0O' ?"AA 40"!A'µ)*' 0">O*'6B:'"'='J'µ( ?"A4 &"0='()*'&"?0'()*'&"?='()*'&"?1'() ?"A1 −A'.*'+A'.* −='.*'+='.*'−!'.*'−?&'.*'−&"&0'.−!*'!"A1'()/.0 ?"=0 #+% '−&"AOM°[ ?"=J !'='!!"!',Ω*'!'='!"J>',Ω ?"=1 0?'µ(*'!"4>?',Ω ?"?& 0'µ(*'?"J'µ(*'0"4',Ω ?"?0 &"A1?'()*'>"J'. ?"?> #$% &"1'.*'−!"J'.* #+% ="!'.*'0"?'.*'&"1'. ?"?1 #$% >"?'µ)*' !"?'.* #+% ="J'µ)*'!"='.* #-% !"?'.*'>"?'µ) ?"J! #$% !'.*'!'.*'−!"A0'.* #+% &"0'.*'!"4'.* −!"A?'. ?"J? &"='.*'4"AA ?">! #$% !0?'\)*'&"4'.* #+% !'(H* #-% −4"&'.M.* #/% 4&',Ω*'−>"A'.M. ?">? ='µ(*'!"&'. ?">> −14"0'.M.*'!"0&>'.* −0A"J'.M.'' ?">4 WR]HZ'=0='\H3'!J&',Ω3'&"=>'.*'^R]HZ'0=?'\H3'0=&',Ω3'&"40'. ?"!&& A"A1'.*'&"4J'()'7@'&"AJ'()*'!"!',Ω ?"!&! !'()*'>"JO ?"!&0 0'.*'0"=&'.* 0"??'() ?"!&J #$% −!"?'.*'+0.?'.*'0'.* #+% −!"A>'.*'+0.?'.*'+!"4>'. ?"!&4 !?"1',Ω*' &"A!='()*'!"40'. ?"!!& −!!"0'.M.

CHAPTER 6 J"! $-7FI:*'B$769$7F@D*'$-7FI:*'B$769$7F@D*'FDI:9B:/'$-7FI:*'$-7FI:*'-67@55*'-67@55 J"4 ?A"A*' &"140 J"!& &"?*'&"JJ>*'&"1&1*'&"1?0*'&"11!3'&"11?*'&"111*'&"111? J"> &"1&>'()*'&"?4>'.

Answers to Selected Problems

J"!0 A'7@'!?'()*'A"&?'7@'!?"&?'()*'!A?'(2 J"!> −&">!4'.*'="&J'.*'&"&A'() J"00 −0'.*' &"40'()*'−&"?>'. J"0= &"1!'()*'1"&1'()*'&"4&A'.*'1"11'() J"04 #$% !'()* #+% −0'.*''#-% !'()*'!'.* #/% &"1J?'()*'&"A?'. J"A4 &">='.*'&"?='. J"=& A"A?'µ) J"=A AA"A',Ω*'!&&'.*'A"A',Ω J"=? !">0'()*'J'.*'A='.*'0&',Ω J"=> !?&*'!0?*'!"=>='() J">& −AJ&'.M.*'&">'.3'0'(. J">? −!&&'.M. J">4 A'()*'−!0&'.M.*'−&"JJ'.*'−&"J'.*' &"?='.*'&"J'. J"?! #$% !"A'.3'A">'.* #+% &"A'.3'=">'.* #-% &'.3'+?'. J"?= −&">'.*' +=">'.*'−&"?'.''#−!'.* +?'.%*''+0"J'.'#!"1'.3'0"J'.% J"?J &"A'.*'!?'µ)*'&"4'()* &">4?'()*'−!"&>?'.*'?0"A*'&"14 J"J! #$% −&">'.3'!"4'.*'#+% !"4>0'.3'!"1??'()* #-% −&">'.3'&'.3'!"4>0'.* #/% !"1'.3'−&"0&1'.* #:% !"00='.3'!"10='.3'−&"0=J'. J"J= !"&4',Ω*'7C:'79$DBFB7@9'B$769$7:B" J"1= !"0?'.*'0&'()M.*'!?&'.M. J"!&0 !A?*' =!"4'Ω*'0A'()M.*'!"&1',Ω*'−&">J'.M. J"!&? 1"A',Ω*'04"J',Ω*'!=A'.M. J"!&J !'()*'&"11J'.M.*'&"JA'.M. J"!?0 #$% !">A'()3'J4"?'()M.3'!="?'Ω3'!"=J',Ω* #+% !=4"0',Ω3'&"1A'.M.*'#-% !4"0!',Ω3'&"J='.M.

CHAPTER 7 >"!? &"1&?'.*'!"='.0' >"!1 #$% &"?'()* #+% !&&',Ω3'!&&',Ω3'?&',Ω* #-% 0"?',Ω3'0&'()M.*' #/% 0"?',Ω3'?&',Ω3'−!&&&'.M. >"=J !&"?',Ω*'&"0?'.*'?&',Ω*'!&'µ) >"=1 !&&'µ)*' &"0'.*'&">'.*'?'µ) >"?0 =Z'0?3'?&3'0&&3'=&&'µ)*'AZ'!J">3'=&3'!AA'µ)*'!"&?'. >"?= #$% !&'µ)'7@'10'()*' &"JAA'7@'&"4&J'. >"?> &"0 (Α; 10% >"J& #$% !"& (Α, −&">'.3'A'.3'&">'.3'−?">'.3'−A"0'.* #+% &"!'()3'−&">'.3'A'.3'&">'.3'−&">'.3'−A"0'. >"JA !"?J'\) >"J= 4"1A'RΩ*'&"1?'.*'!"=?'.*'!&&"='\) >"J1 ?&&'Ω >">& 0'µ)*'&"0O >">J #$% ?">',Ω* #+% !J"='RΩ3'&"A'µ) >">4 >"=J'RΩ >">1 #$% J4"?',Ω* #+% !!0"?'RΩ >"4& J"=0',Ω >"4= !0*'A= >"4? 0"44 >"44 &"?'()*'='()M. >"1A !J">'_KL*'0A"1'_KL*'+:-$6B:'7C:'@I:9;$8'-$8$-F7$D-:'FB'D:Y;:-7:/" >"1= !?'.M.*' !J="0'RKL*'0"?'_KL3'&"!??'()*'`6$/968;:/'7@'&"J0'()*'>"?'.M.*'J?J"4'RKL >"1> ?"A'RKL*'A1!'RKL

CHAPTER 8 4"1 &">0='.* A"?>'()M.*'&"A!>'.*'!"J'() 4"!! −!"?'.* +&"?'.*':`6$;'FD'+@7C'-$B:B*' &"&?'.* −&"&?'.*'&"?AJ'.' 4"A0 −!"JJ?'.*'0"?0'. 4"A= −!"?A'.'7@' 0"10'. 4"A4 #$% 4%%'−'#(/0%!%*'#+% −#(/0%!%3'+#(/0%!%* #-% ='.* #/% &"='()3'!&',Ω 4"=! #$% 0&(!%'.M.* #+% 4%%5− &"&0>?675 4"=A (8!'='0'()3'(80'='!'()3'(%!'='0'()3 (%0'='!'()*'!>"A'(. 4"=? ='()M.*'>?"?',Ω 4"=4 #$% &"0'()3'!&'(.* #+% &">'()3 &"A'()* #-% −0"='.3'+0"='.* #/% =4'.M. 4"?1 ?&'.M.*'?&"?',Ω 4"J& ?&'.M.* ?&"?',Ω 4"JA 0?'.M.*'=&"=',Ω*'&"&&!'.M.*'J"?J'RΩ 4"J= #$% 0&&'.M.* #+% 0&"0',Ω* #-% &"&&&?'.M.* #/% !!0'/N* #:% 1">J'(Ω 4"J> !"4'()*'AJ&'.M.*'!"4'BFD'ω+'. 4"J4 !8'='0?'Ω*5!%'='!&',Ω*'!)'!?&',Ω*'!9:''='?'RΩ*'±!0'.'G@6;/'/@3'±!?'.'G@6;/'+:' +:77:9" 4"J1 0O' 4">& &"&&4'.M. 4">> −!0?'µ. 4">1 !">'(.R 4"4! #$% &"A*' #+% &'4"!!?' !9;!'S'=&"=',Ω*'!9;0'S'!&"!',Ω*'0&"0'.M.*'A40A'.M.'/:-9:$B:'4"!!J !?'='>"A=',Ω* =!&='.M.*'!='='!"!!',Ω 4"!!> #$% !>A"!'×'!&A'.M.'#+% ??4A'.M.' 4"!!4 #$% &"1>'()*' #+% 0"0A',Ω3'!01'Ω*'#-% 0"4J'×'!&='.M.'

CHAPTER 9 1"! 1.43'.M.3'1"A'µQ 1"= −!J'.M.*'%%!'='0!"0'DQ3'%25='1"J'µQ*'%%0'='&"?'µQ*'?&'KL 1"!> J"A'_KL 1"!1 ?"='_KL 1"0= ?&&'RKL3'J&&'RKL3'0?!"1'8B3'&"=A?'8Q 1"0? &"J1'8Q*'=&'()M.*'=',Ω*'?&'RKL' 1"AA #$% −!?"1'.M.*'#+% =&"!',KL 1"=? #$% 0"&>* #+% >"&0 1"=J #$% !&='9$/MB*'#+% !&"!'Κ9$/MB' 1"=> ?"J>'×'!&J'9$/MB

I-3

I-4 Appendix I Answers to Selected Problems 1"?= =&"J'.M.*'0=A">?'DB*'A!&&'DB*'A&&'DB*'=A">',KL 1"?4 #$% −!&&&'.M.3'%9'='!"&&!'DQ3' %)'='!"&&!'8Q* #+% −!&'.M.3'%9'='!!&'8Q3'%)'='!!'8Q* #-% −!'.M.3'%9'='0&'8Q3'%)'='0&'8Q*' #/% !'.M.3'%9'='&'8Q3'%)'='&'8Q* #:% !&'.M.3'%9'='−1&'8Q3'%)'='1'8Q 1"J0 J"A>'_KL*' J>A"0A',KL*'0!"A1'RKL*'J>A"0A',KL' 1"JJ !A1'.M.*'0!"00'_KL*'!"11'RKL*'4A"00'RKL*' !"11'RKL 1"J4 −4&'.M.*'A">1'RKL*'A&A"0'RKL 1">0 !?1"!'5Q 1">? !J'.M.* A14'RKL*'A">1'RKL*'A">1'RKL 1"44 &"1J='.M.*'?1A"4'RKL 1"!&A #$% 0"?'RΩ3 −A1=A"J'.M.* #+% !&>"4',KL3'#%"'U'%µ0%'/@(FD$7:B3'%µ0'@9'%<5FB'7C:'B:-@D/'(@B7'BFYDF5F-$D7

CHAPTER 10 !&"! 1"11'×'!&−A*'1!">=*'−4"0JO !&"!= 6=-'='6= ⁄#!'+'6=β%*'3"-'='3" ⁄#!'+'6=β%' !&"!J !'RKL*'!'KL !&"A= #$% ,!!'='!!!0 /#!!'+'!0%'Ω3',!0'=5!0/#!!'+'!0%'.M.3 ,0!'='−!0'/#!!'+'!0%')M)3',00'='!/#!!'+'!0%'Ω* #+% ,!!'='!&'Ω3',!0'='&"&!'.M.3',0!'='−&"&!')M.3 ,00'='&"11'×'!&−A'Ω !&"A? !&&'.M.*'!"&&!'RΩ !&"J0 #$% BC6D7TB:9F:B* #+% B:9F:BT B:9F:B* #-% BC6D7TBC6D7 !&"4& !&='9$/MB*' β'='&"&&0* ?&&'.M. !&"40 >'<'&"&&4 !&"4= 1"1'.M.*'!"&!'RKL*'!&'RKL*'!&! !&"4? #$% ?"?'×'!&?'KL3'β'='0"&0?'×'!&−A* #+% AA&"J'.M.* #-% !JJ"A'.M.3'!⁄ 0* #/% !"AA !&"4> ω&'='!/%!*'?'='!/#0"!'−'>%*'&"!*' &"J4J*'>'='0"! !&"41 !'RKL*'1&° !&"1! ?J"4>°; ?="&>°; ?1"0=°; ?0"1A° !&"1A !?1"0'µB*'A1"A°;'0&'/N !&"1? A'aKL !&"1J !?'aKL*'0&& !&"1> !/!&%!*'!/%!*' !/#!&&'X'%-55X'!%*'1"!/%! !&"14 !&&'KL*'!"?1'DQ !&"11 ?4"4'8Q*'A>"1?'RKL'

CHAPTER 11 !!"! b88:9';F(F7'#B$(:'FD'$;;'-$B:B%Z'=">'.3'?"='.*';@G:9';F(F7BZ'−="A'.3'−A"J'.*'−0"!?'.3 −!"=?'. !!"= !?0'Ω*'&"114'.M.*'&"11J'.M.*'&"1>4'.M.*'0O !!"J 4%%( !!"4 ?'. !!"!& ="?'.*'J"=O*'J0?'Ω !!"!0 ?"&'.'8:$,*'A"!4'.'8:$,*'A"=0?'Ω*'="4A'Ω*'A"J?'2* &"J=>'2 !!"!1 !0"? !!"0! 0&">'()*'>44'(2*'>"1°[*'A>"J'() !!"00 !"A=',Ω* !"&=',Ω !!"A& ?&'2*'0"?') !!"A0 !=&°[*'&"?>'.' !!"A= !&&'2*'&"=°[M2 !!"=? !A'Ω*'=AA'(.*'&"AA'µ) !!"=> !!'='J&',Ω*'!2'='?',Ω*'&"&!'µ) !!"=1 (8!'='(80'!'!>'µ)*'(8A'='(8='!'A?4'µ)*'(8?'!'(8J'='A=!'µ)*'!&"?'. !!"?& !='.*'!"1'2* !!'. !!"?! !A'='!='='=&'Ω*'!!'='!0'='0"0',Ω !!"?A =&',Ω*'?&',Ω !!"?? "'='µ0#v&2'−'4+% ⁄ @B$7*'A'µ(*'A')*'!')M.

CHAPTER 12 !0"0= AJ"A'µ) !0"0? &"J0?'.*'5@9')3'>"A'()M.3'!A="A'Ω3'J"4?',Ω3'0>=',Ω*'5@9'N3 0!"1'()M.3'==">'Ω3'0"04',Ω3'1!"A',Ω !0"01 ?1A'(.*'?!4'(.*'>"?',Ω !0"A! =">?'µ)*' !"1=',Ω !0"AA ?J"?',Ω*'1"A?A'µ) !0"AJ ?"J'(.' !0"A4 J"A>',Ω*'0>&'µ) !0"=& !"J4'()*'?&"='(2 !0"=0 c$FB:'!′!3'!′05+)'="JA',Ω !0"=? !"='(. !0"?& A"!'RΩ*'1"A4'()M. !0"?0 ="0'.'7@'−A"J'. !0"?= !&?"J'/N*'d4)d'<'='.*'0!"&'()' !0"?J !&4'/N*'J!"1'Ω !0"?4 >"J'RKL !0"J& A!4',Ω' !0"J0 !?1"0',KL*'!?"1'RKL '

CHAPTER 13 !A"J !"?'.*'!"?'.*'!"?'.*'&'.*'A'.*'!"?'.*'!"?'.*'∞ !A"4 &"A=1'7@'&"=?!'.*'&">=1'7@ &"4?0'.*'&'.*'!"0'.*'&"A=1'7@'&"=?0'.*'&"A=4'7@'&"=?!'. !A"!1 ="AJ'(2* !"=4'(2 !A"0! #$% +."A'='!"J'DB3'+.A"'='&"4'DB* #+% %'='!"=A'8Q* #-% %)'='&"4J'8Q3 %9'='&"?>'8Q' !A"0? #$% &"JJ3'&"=A?'#+% &"=AJ3'&"=A? !A"01 1"&1'(.*'?&'(.' !A"=J 0= !A"?A 16'='1'Z'1B'='1%'='1/'='01*'$D/'06'='0B'='00'Z'0%'='0/'='0#00%'='=0 !A"?? '+.A"'FB'='7F(:B';$9Y:9*'+."A'FB'7C:'B$(:

Answers to Selected Problems

CHAPTER 14 !="! #$% &"J1A'!/%* #+% &"?!/%3'5@9'$'0!"?O'9:/6-7F@D !="0 !"?0*'&"1>'.*'!"J1'.* !"0'.*'0"?'.*'&"04'.*'&"4!'.*'&"J1'. !="= C5!'0"!*'D="($X'&">A!'. !="J !"AA !="0A 1"A4'DB !="A& A'(B*'AAA'KL !="AA 0"0>'_KL' !="A?'AA"A'RKL*'CFYC'!A'DB* ;@G'!>'DB' !="A4 &"AA'.M.*'4"1?'.M.*'&"A>'.M. !="A1 #$% −!"A>?'.3'−!"0J?'.* #+% −!"=1A'.3'−!"!=>'. !="=! 0!"0' !="=A >'-( !="=? #3'⁄ 'e%'='?'µ('⁄ !'µ(* J"?'µ) !="=J 0"A0'.*'A"44'() !="=> Q@9'!!Z'?&O*'AJ"?',Ω*'0&O*'1!"!',Ω*'5@9'!0Z'?&O*' J">&',Ω*'0&O*'!J">',Ω*'?&O*'!! ⁄ !0'='?"=?*'0&O*'!! ⁄ !0'='?"=? !="=4 4A"0'8B*'?&">'8B*' J>"&'8B !="?& #3/"%D6'S'#3/"%DB'S'0#3/"%D*'#3/"%.6'S'#3/"%.B'S'#3/"%.

CHAPTER 15 !?"!& 0"0AJ'.*'!&&'.M. !?"!0 !&0=*'!&0=*'=&&'8Q*'00?'8Q*'00&'5QM+F7*'0"4'7F(:B' !?"!A J&O !?"01 =!'(. !?"A! &"='8) !?"A0 !"?41'()M.*'!!"AJ'µ(*'A="!'µ(* !"?J'DB !?"AA J4&'µ)M.*'&"=40'.*'&"0&J'.*'?&O*'>"?'DB !?"A4 1*'?!0*'!4*'=J&4'WR]H' $D/'?!0'^R]H'79$DBFB7@9B !?"A1 1*'!&0=*'=J&4*'?!0*'?J=!*'?0!' !?"== &!&&3'&&&&3' !&&&3'!&&!3'&!&!3'&&&!3'&!!&3'$D/'&&!& !?"=J 0"=0'DB*'0A'DB3'A"!J'.*'!"1&'DB

CHAPTER 16 !J"! !'.M.3'&°3'&'/N3'&'/N*'&"41='.M.3'−0J"J°3'−&"1>'/N3'&"1>'/N*'&">&>'.M.3'−=?"&°3 −A"&!'/N3'A"&!'/N*'&"==>'.M.3'−JA"=°3'−J"11'/N3'J"11'/N*'&"!1J'.M.3'−>4">°3'−!="!'/N3' !="!'/N*'&"!&&'.M.3'−4="A°3'−0&"&'/N3'0&"&'/N*'&"&!&'.M.3'−41"=°3'−=&"&'/N3'=&"&'/N' !J"? &"?&44'9$/MB*'A'9$/MB*'?"1' !J"1 <#$%'='&"000?'#$0'+'=% ⁄ f#$'+'!%#$0'+'$'+'&"41%g' !J"!! <#$%'='&"? ⁄ $A'+'0$0'U'0$'U'!*'8@;:B'$7'$'='−!3'−!M0'h'# A'⁄ 03'A5L:9@B'$7'$'S'" !J"!A 04"J'/N' !J"!1 !!'='!&',Ω*'!0'='!&&',Ω*'%'='!?1'8Q !J"0! 40 /Β !J"0A <#$%'='T#H'T'ω& ⁄ 'H'U'ω&%*'0"J4',Ω3'?">>',Ω3'!&',Ω3'!>"A',Ω3'A>"A',Ω !J"0? <#$%'='!&J ⁄ #$0'+'!&A$'+'!&J%*'&">&>'9$/MB*'!"!?'.M.*'!"0!'/N !J"AA "'='?&&'(K* %'='0&'DQ' !J"A? '$0 ⁄ #$0'+'$ ⁄ !%'+'! ⁄ "%% !J"A1 "! ⁄ "0'='&"0A=J*'|<|'='"0 ⁄ #"!'+'"0%* |<|'='! !J"=A !!'='!0'='!A'='!?'='A"1>1',Ω*'!J'='A1">1',Ω*'%J!'='J"='DQ*'%J0'='A"J'DQ !J"== %='='%J'='!'DQ*'!!'='!0'='!A'='!?'='!J'='!?1"!J',Ω !J"=1 %'='!&'DQ*'!'='!?"10',Ω*' !!'='!-'='!&',Ω*'!0'='!&',Ω*'!A'='A1&',Ω*'A1'.M. !J"?! h!O !J"?? !A'='!=!"=',Ω* !='='>&">',Ω !J"?> = ⁄ !%*'0*'4'.M. !J"?1 KFYCE8$BB*'!'.M.*'!A'='!=!"=',Ω* !='='>&">',Ω !J"J= &*'0?0M6

CHAPTER 17 !>"! #$% ω'='ω&3'6>'='!* #+% '−0? ⁄ ω&* #-% ∆ω& ⁄ ω&'='−∆φ ⁄ 0? !>"? '0&'/N*' h!4&° !>"1 '! ⁄ !%*!*!' !>"!& !"!? ⁄ !% !>"!? 0&"A'. !>"!> E*'01!*'&"&J?/!% !>"0A '0"&!J!0'RKL'7@'0"&!>0'RKL !>"0? #$% 4<"'='4!5#!'−'!! ⁄ !0%'−'"+!! ⁄ !03'4"04 #$% +!0'.'@9'−!0'.' !>"01 4F'='J"4'.*'!!'='!0'='A>"?',Ω*'!'='="!',Ω !>"AA 4F'='J"4'.*5!!'='!0'=5!A'='!='= !?'=5!J'='0&&',Ω*'!>'='?"!',Ω*'79F$DY;:'GF7C'8:9F@/'@5'!&&'µB'$D/'±>"?'.'8:$,B !>"A? 1J'µB !>"A4 #$% 1"!',Ω* #+% !A"A'. !>"A1 !6'=''0!"0',Ω*'!B'='!&">',Ω !>"=! 4'='!"&11J'.*'!'='=&&'Ω*'P$+;:'9@GB3'5@9'vG3'θ3'&">'BFD'θ3':99@9'O'$9:Z'&">&'.3'1&°3' &">&&'.3'&O*'&"J?'.3'JA"J°3'&"J0>'.3'A">O*'&"J&'.3'?0"=°3'&"??='.3'4"0O*'&"??'.3'=J"!°3' &"?&='.3'1"!O*'&"?&'.3'=!"A°3'&"=J0'.3'4"AO*'&"=&'.3'A0"4°3'&"A>1'.3'?"JO*'&"A&'.3'0="J°3' &"01!'.3'A"!O*'&"0&'.3'!J"=°3'&"!1>'.3'!"?O*'&"!&'.3'4"0°3'&"!&&'.3'&O*'&"&&'.3'&°3 &"&'.3'&O" !>"=0 0"?'. !>"?? !&'(.3'0&'(.3'!&&'(.*'?&'86;B:B3'!&&'86;B:B3 0&&'86;B:B

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J F ETs, G a A s D E VI C ES A N D C IR C U ITS, A N D T TL C IR C U ITS

5.11 THE JUNCTION FIELD-EFFECT TRANSISTOR (JFET) The junction field-effect transistor, or JFET, is perhaps the simplest transistor available. It has some important characteristics, notably a very high input resistance. Unfortunately, however (for the JFET), the MOSFET has an even higher input resistance. This, together with the many other advantages of MOS transistors, has made the JFET virtually obsolete. Currently, its applications are limited to discrete-circuit design, where it is used both as an amplifier and as a switch. Its integrated-circuit applications are limited to the design of the differential input stage of some operational amplifiers, where advantage is taken of its high input resistance (compared to the BJT). In this section, we briefly consider JFET operation and characteristics. Another important reason for including the JFET in the study of electronics is that it helps in understanding the operation of gallium arsenide devices, the subject of the next section.

Device Structure As with other FET types, the JFET is available in two polarities: n-channel and p-channel. Fig. 5.69(a) shows a simplified structure of the n-channel JFET. It consists of a slab of n-type silicon with p-type regions diffused on its two sides. The n region is the channel, and the p-type regions are electrically connected together and form the gate. The device operation is based on reverse-biasing the pn junction between gate and channel. Indeed, it is the reverse bias on this junction that is used to control the channel width and hence the current flow from drain to source. The major role that this pn junction plays in the operation of this FET has given rise to its name: Junction Field-Effect Transistor (JFET).

Channel

n

(a)

(b)

(c)

FIGURE 5.69 (a) Basic structure of n-channel JFET. This is a simplified structure utilized to explain device operation. (b) Circuit symbol for the n-channel JFET. (c) Circuit symbol for the p-channel JFET.

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It should be obvious that a p-channel device can be fabricated by simply reversing all the semiconductor types, thus using p-type silicon for the channel and n-type silicon for the gate regions. Figures 5.69(b) and (c) show the circuit symbols for JFETs of both polarities. Observe that the device polarity (n-channel or p-channel) is indicated by the direction of the arrowhead on the gate line. This arrowhead points in the forward direction of the gate–channel pn junction. Although the JFET is a symmetrical device whose source and drain can be interchanged, it is useful in circuit design to designate one of these two terminals as source and the other as drain. The circuit symbol achieves this designation by placing the gate closer to the source than to the drain.

Physical Operation Consider an n-channel JFET and refer to Fig. 5.70(a). (Note that to simplify matters, we will not show the electrical connection between the gate terminals; it is assumed, however, that the two terminals labeled G are joined together.) With vGS = 0, the application of a voltage vDS causes current to flow from the drain to the source. When a negative vGS is applied, the depletion region of the gate–channel junction widens and the channel becomes correspondingly narrower; thus the channel resistance increases and the current iD (for a given vDS) decreases. Because vDS is small, the channel is almost of uniform width. The JFET is simply operating as a resistance whose value is controlled by vGS. If we keep increasing vGS in the negative direction, a value is reached at which the depletion region occupies the entire channel. At this value of vGS the channel is completely depleted of charge carriers (electrons); the channel has in effect disappeared. This value of vGS is therefore the threshold voltage of the device, Vt , which is obviously negative for an n-channel JFET. For JFETs the threshold voltage is called the pinch-off voltage and is denoted VP. Consider next the situation depicted in Fig. 5.70(b). Here vGS is held constant at a value greater (that is, less negative) than VP, and vDS is increased. Since vDS appears as a voltage drop across the length of the channel, the voltage increases as we move along the channel from source to drain. It follows that the reverse-bias voltage between gate and channel varies at different points along the channel and is highest at the drain end. Thus the channel acquires a tapered shape and the iD!vDS characteristic becomes nonlinear. When the reverse bias at the drain end, vGD , falls below the pinch-off voltage VP, the channel is pinched off at the drain end and the drain current saturates. The remainder of the description of JFET operation follows closely that given for the depletion MOSFET. The description above clearly indicates that the JFET is a depletion-type device. Its characteristics should therefore be similar to those of the depletion-type MOSFET. This is true with a very important exception: While it is possible to operate the depletion-type MOSFET in the enhancement mode (by simply applying a positive vGS if the device is n channel) this is impossible in the JFET case. If we attempt to apply a positive vGS, the gate–channel pn junction becomes forward biased and the gate ceases to control the channel. Thus the maximum vGS is limited to 0 V, though it is possible to go as high as 0.3 V or so since a pn junction remains essentially cut off at such a small forward voltage.

Current–Voltage Characteristics The current–voltage characteristics of the JFET are identical to those of the depletion-mode MOSFET studied in Section 5.3 except that for the JFET the maximum vGS allowed is

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J F ETs, G a A s D E VI C ES A N D C IR C U ITS, A N D T TL C IR C U ITS

(a)

(b)

FIGURE 5.70 Physical operation of the n-channel JFET: (a) For small vDS the channel is uniform and the device functions as a resistance whose value is controlled by vGS. (b) Increasing vDS causes the channel to acquire a tapered shape and eventually pinch-off occurs. Note that, though not shown, the two gate regions are electrically connected.

normally 0 V. Furthermore, the JFET is specified in terms of the pinch-off voltage VP (equal to Vt of the MOSFET) and the drain-to-source current with the gate shorted to the source, 2 IDSS, which corresponds to 1--2- k n" V t for the MOSFET. With these substitutions, the n-channel JFET characteristics can be described as follows: Cutoff: v GS # VP , i D = 0

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Triode region: VP # v GS # 0, v DS # v GS – VP

v GS( ' v DS ( ' v DS( 2 i D = I DSS 2 ' 1 – ------- --------- – -------% VP & % – VP & % VP &

(5.116)

Saturation (pinch-off) region: VP # v GS # 0, v DS ) v GS – VP

v GS( i D = I DSS ' 1 – ------- ( 1 + $ v DS ) % VP & 2

(5.117)

where $ is the inverse of the Early voltage; $ = 1/ VA, and VA and $ are positive for n-channel devices. Recalling that for an n-channel device, VP is negative, we see that operation in the pinch-off region is obtained when the drain voltage is greater than the gate voltage by at least |VP |. Since the gate–channel junction is always reverse-biased, only a leakage current flows through the gate terminal. From Chapter 3, we know that such a current is of the order of 10!9 A. Although iG is very small, and is assumed zero in almost all applications, it should be noted that the gate current in a JFET is many orders of magnitude greater than the gate current in a MOSFET. Of course the latter is so tiny because of the insulated gate structure. Another complication arises in the JFET because of the strong dependence of gate leakage current on temperature—approximately doubling for every 10°C rise in temperature, just as in the case of a reverse-biased diode (see Chapter 3).

The p-Channel JFET The current–voltage characteristics of the p-channel JFET are described by the same equations as the n-channel JFET. Note, however, that for the p-channel JFET, VP is positive, 0 # v GS # VP, vDS is negative, $ and VA are negative, and the current iD flows out of the drain terminal. To operate the p-channel JFET in pinch-off, v DS # v GS – VP , which in words means that the drain voltage must be lower than the gate voltage by at least |VP |. Otherwise, with v DS ) v GS – VP , the p-channel JFET operates in the triode region.

The JFET Small-Signal Model The JFET small-signal model is identical to that of the MOSFET [see Fig. 5.34(b)]. Here, gm is given by 2IDSS ( ' VGS ( - 1 – -------gm = ' -----------% VP & % VP &

(5.118a)

2IDSS ( ID - --------gm = ' -----------% VP & IDSS

(5.118b)

or alternatively by

where VGS and ID are the dc bias quantities, and VA ro = -------ID

(5.119)

At high frequencies, the equivalent circuit of Fig. 5.67(c) applies with Cgs and Cgd being both depletion capacitances. Typically, Cgs = 1 to 3 pF, Cgd = 0.1 to 0.5 pF, and fT = 20 to 100 MHz.

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J F ETs, G a A s D E VI C ES A N D C IR C U ITS, A N D T TL C IR C U ITS

EXERCISES In Exercises 5.43 to 5.46, let the n-channel JFET have VP = –4 V and IDSS = 10 mA, and unless otherwise specified assume that in pinch-off (saturation) the output resistance is infinite. 5.43 For vGS = !2 V, find the minimum vDS for the device to operate in pinch-off. Calculate iD for vGS = !2 V and vDS = 3 V. Ans. 2 V; 2.5 mA 5.44 For vDS = 3 V, find the change in iD corresponding to a change in vGS from !2 to !1.6 V. Ans. 1.1 mA 5.45 For small vDS, calculate the value of rDS at vGS = 0 V and at vGS = !3 V. Ans. 200 *; 800 * 5.46 If VA = 100 V, find the JFET output resistance ro when operating in pinch-off at a current of 1 mA, 2.5 mA, and 10 mA. Ans. 100 k*; 40 k*; 10 k* D5.47 The JFET in the circuit of Fig. E5.47 has VP = !3 V, IDSS = 9 mA, and $ = 0. Find the values of all resistors so that VG = 5 V, ID = 4 mA, and VD = 11 V. Design for 0.05 mA in the voltage divider.

FIGURE E5.47

Ans. RG1 = 200 k*; RG2 = 100 k*; RS = 1.5 k*; RD = 1 k* 5.48 For the JFET circuit designed in Exercise 5.47, let an input signal vi be capacitively coupled to the gate, a large bypass capacitor be connected between the source and ground, and the output signal vo be taken from the drain through a large coupling capacitor. The resulting common-source amplifier is shown in Fig. E5.48. Calculate gm and ro (assuming VA = 100 V). Also find Ri, A v + ( v o ⁄ v i ), and Ro. VDD

RG1

RD #

#

" vo !

"

vi ! Ri

RG2

RS

#

Ro

FIGURE E5.48

Ans. 4 mA/V; 25 k*; 66.7 k*; !3.8 V/V; 962 *

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5.12 GALLIUM ARSENIDE (GaAs) DEVICES—THE MESFET 10 The devices discussed thus far, and indeed the devices used in most of the circuits studied in this book, are made of silicon. This reflects the situation that has existed in the microelectronics industry for at least three decades. Furthermore, owing to the advances that are continually being made in silicon device and circuit technologies, the dominance of silicon as the most useful semiconductor material is expected to continue for many years to come. Nevertheless, another semiconductor material has been making inroads into digital applications that require extremely high speeds of operation and analog applications that require very high operating frequencies. We refer to gallium arsenide (GaAs), a compound semiconductor formed of gallium, which is in the third column of the periodic table of elements, and arsenic, which is in the fifth column; thus GaAs is known as a III-V semiconductor. The major advantage that GaAs offers over silicon is that electrons travel much faster in n-type GaAs than in silicon. This is a result of the fact that the electron drift mobility µn (which is the constant that relates the electron drift velocity to the electric field; velocity = µnE) is five to ten times higher in GaAs than in silicon. Thus for the same input voltages, GaAs devices have higher output currents, and thus higher gm, than the corresponding silicon devices. The larger output currents enable faster charging and discharging of load and parasitic capacitances and thus result in increased speeds of operation. Gallium arsenide devices have been used for some years in the design of discretecomponent amplifiers for microwave applications (in the 109 Hz or GHz frequency range). More recently, GaAs has begun to be employed in the design of very-high-speed digital integrated circuits and in analog ICs, such as op amps, that operate in the hundreds of MHz frequency range. Although the technology is still relatively immature, suffering from yield and reliability problems and generally limited to low levels of integration, it offers great potential. Therefore, this book includes a brief study of GaAs devices and circuits. Specifically, the basic GaAs devices are studied in this section; their basic amplifier circuit configurations are discussed in Section 6.8; and GaAs digital circuits are studied in Section 14.8.

The Basic GaAs Devices Although there are a number of GaAs technologies currently in various stages of development, we shall study the most mature of these technologies. The active device available in this technology is an n-channel field effect transistor known as the metal semiconductor FET or MESFET. The technology also provides a type of diode known as the Schottkybarrier diode (SBD). (Recall that the SBD was briefly introduced in Section 3.9.) The structure of these two basic devices is illustrated by their cross sections, depicted in Fig. 5.71. The GaAs circuit is formed on an undoped GaAs substrate. Since the conductivity of undoped GaAs is very low, the substrate is said to be semi-insulating. This turns out to be an advantage for GaAs technology as it simplifies the process of isolating the devices on the chip from one another, as well as resulting in smaller parasitic capacitances between the devices and the circuit ground. As indicated in Fig. 5.71, a Schottky-barrier diode consists of a metal–semiconductor junction. The metal, referred to as the Schottky-barrier metal to distinguish it from the different kind of metal used to make a contact (see Long and Butner (1990) for a detailed explanation of the difference), forms the anode of the diode. The n-type GaAs forms the 10

The material in this section is required only for the study of the GaAs circuits in Sections 6.8 and 14.8. Otherwise, this section can be skipped without loss of continuity.

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SBD

MESFET

Schottky-barrier metal Cathode Source (S)

Anode

Gate (G)

Drain (D)

Contact metal n

n n"

n"

n" L Channel

Isolation regions Semi-insulating GaAs substrate

FIGURE 5.71 Cross-section of a GaAs Schottky-barrier diode (SBD) and a MESFET.

cathode. Note that heavily doped n-type GaAs (indicated by n+) is used between the n region and the cathode metal contact in order to keep the parasitic series resistance low. The gate of the MESFET is formed by Schottky-barrier metal in direct contact with the n-type GaAs that forms the channel region. The channel length L is defined by the length of the gate electrode, and similarly for the width W (in the direction perpendicular to the page). To reduce the parasitic resistances between the drain and source contacts and the channel, the two contacts are surrounded with heavily doped (n+) GaAs. Since the main reason for using GaAs circuits is to achieve high speed/frequency of operation, the channel length is made as small as possible. Typically L = 0.2!2 µm. Also, usually all the transistors on the IC chip are made to have the same length, leaving only the width W of each device to be specified by the circuit designer. Only n-channel MESFETs are available in GaAs technology. This is because holes have a relatively low drift mobility in GaAs, making p-channel MESFETs unattractive. The lack of complementary transistors is a definite disadvantage of GaAs technology. Correspondingly, it makes the task of the circuit designer even more challenging than usual.

Device Operation The MESFET operates in a very similar manner to the JFET, with the Schottky metal playing the role of the p-type gate of the JFET (refer to Fig. 5.69). Basically, a depletion region forms in the channel below the gate surface, and the thickness of the depletion region is controlled by the gate voltage vGS. This in turn effects control over the channel dimensions and thus on the current that flows from drain to source in response to an applied vDS. The latter voltage causes the channel to have a tapered shape, with pinch-off eventually occurring at the drain end of the channel. The most common GaAs MESFETs available are of the depletion type with a threshold voltage Vt (or, equivalently, pinch-off voltage VP) in the range of !0.5 to !2.5 V. These devices can be operated with vGS values ranging from the negative Vt to positive values as high as a few tenths of a volt. However, as vGS reaches 0.7 V or so, the Schottky-barrier diode between gate and channel conducts heavily and the gate voltage no longer effectively

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controls the drain-to-source current. Gate conduction, which is not possible in MOSFETs, is another definite disadvantage of the MESFET. Although less common, enhancement-mode MESFETs are available in certain technologies. These normally-off devices are obtained by arranging that the depletion region existing at vGS = 0 extends through the entire channel depth, thus blocking the channel and causing iD = 0. To cause current to flow from drain to source the channel must be opened by applying to the gate a positive voltage of sufficient magnitude to reduce the thickness of the depletion region below that of the channel region. Typically, the threshold voltage Vt is between 0.1 and 0.3 V. The above description of MESFET operation suggests that the iD!vDS characteristics should saturate at vDS = vGS ! Vt, as is the case in a silicon JFET. It has been observed, however, that the iD!vDS characteristics of GaAs MESFETs saturate at lower values of vDS and, furthermore, that the saturation voltages vDSsat do not depend strongly on the value of vGS. This “early saturation” phenomenon comes about because the velocity of the electrons in the channel does not remain proportional to the electric field (which in turn is determined by vDS and L; E = vDS / L) as is the case in silicon; rather, the electron velocity reaches a high peak value and then saturates (that is, becomes constant independent of vDS). The velocitysaturation effect is even more pronounced in short-channel devices (L # 1 µm), occurring at values of vDS lower than (vGS ! Vt). Finally, a few words about the operation of the Schottky-barrier diode. Forward current is conducted by the majority carriers (electrons) flowing into the Schottky-barrier metal (the anode). Unlike the pn-junction diode, minority carriers play no role in the operation of the SBD. As a result, the SBD does not exhibit minority-carrier storage effects, which give rise to the diffusion capacitance of the pn-junction diode. Thus, the SBD has only one capacitive effect, that associated with the depletion-layer capacitance Cj.

Device Characteristics and Models A first-order model for the MESFET, suitable for hand calculations, is obtained by neglecting the velocity-saturation effect, and thus the resulting model is almost identical to that of the JFET though expressed somewhat differently in order to correspond to the literature: iD = 0

for v GS < V t

i D = , [ 2 ( v GS – V t ) v DS – vDS ] ( 1 + $ v DS ) 2

i D = , ( v GS – V t ) ( 1 + $ v DS ) 2

for v GS ) V t, v DS < v GS – V t

for v GS ) V t, v DS ) v GS – V t

(5.120)

The only differences between these equations and those for the JFETs are (1) the channellength modulation factor, 1 + $ vDS, is included also in the equation describing the triode region (also called the ohmic region) simply because $ of the MESFET is rather large and including this factor results in a better fit to measured characteristics; and (2) a transconductance parameter , is used so as to correspond with the MESFET literature. Obviously, , is related to IDSS of the JFET and k" (W/ L) of the MOSFET. (Note, however, that this , has absolutely nothing to do with , of the BJT!) A modification of this model to account for the early saturation effects is given in Hodges and Jackson (1988). Figure 5.72(a) shows the circuit symbol for the depletion-type n-channel GaAs MESFET. Since only one type of transistor (n channel) is available, all devices will be drawn the

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(a)

(b)

FIGURE 5.72 Circuit symbols for (a) an n-channel depletiontype GaAs MESFET, and (b) a Schottky-barrier diode (SBD).

same way, and there should be no confusion as to which terminal is the drain and which is the source. The circuit symbol of the Schottky-barrier diode is depicted in Fig. 5.72(b). In spite of the fact that the physical operation of the SBD differs from that of the pn-junction diode, their i!v characteristics are identical. Thus the i!v characteristic of the SBD is given by the same exponential relationship studied in Chapter 3. For the GaAs SBD, the constant n is typically in the range of 1 to 1.2. The small-signal model of the MESFET is identical to that of other FET types. The parameter values are given by g m = 2 , ( VGS – V t )(1 + $VDS )

-i D r o + ----------v DS

(5.121)

–1

= 1 /$, ( V GS – Vt )

2

(5.122)

The MESFET, however, has a rather high value for $ (0.1 to 0.3 V!1) which results in a small output resistance ro. This turns out to be a serious drawback of GaAs MESFET technology, resulting in low voltage-gain obtainable from each stage. Furthermore, it has been found that ro decreases at high frequencies. Circuit design techniques for coping with the low ro will be presented in Section 6.8. For easy reference, Table 5.2 gives typical values for device parameters in a GaAs MESFET technology. The devices in this technology have a channel length L = 1 µm. The values given are for a device with a width W = 1 µm. The parameter values for actual devices can be obtained by appropriately scaling by the width W. This process is illustrated in the following example. Unless otherwise specified, the values of Table 5.2 are to be used for the exercises and the end-of-chapter problems.

TABLE 5.2

Typical Parameter Values for GaAs MESFETS and Schottky Diodes in L = 1 µm Technology, Normalized for W = 1 µm V t = – 1.0 V

, = 10

–4

A/V

$ = 0.1 V I S = 10

– 15

2

–1

A

n = 1.1

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EXAMPLE 5.11 Figure 5.73 shows a simple GaAs MESFET amplifier, with the W values of the transistors indicated. Assume that the dc component of vI, that is VGS1, biases Q1 at the current provided by the current source Q2 so that both devices operate in saturation and that the dc output is at half of the supply voltage. Find: (a) the , values for Q1 and Q2; (b) VGS1; (c) gm1, ro1, and ro2; and (d) the small-signal voltage gain.

FIGURE 5.73 Circuit for Example 5.11: a simple MESFET amplifier.

Solution (a) The values of , can be obtained by scaling the value given in Table 5.2 using the specified values of W,

, 1 = 100 . 10 , 2 = 50 . 10

–4

–4

= 10

–2

= 5 . 10

2

A/V = 10 mA/V –3

2

2

A/V = 5 mA/V

2

(b) 2

I D2 = , 2 (VGS2 – V t ) (1 + $VDS2 ) 2

= 5 ( 0 + 1 ) ( 1 + 0.1 . 5 ) = 7.5 mA I D1 = ID2 = 7.5 mA 2

7.5 = , 1 ( VGS1 – Vt ) (1 + $VDS1) 2

= 10 ( VGS1 + 1 ) ( 1 + 0.1 . 5 ) Thus, VGS1 = – 0.3 V

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(c) gm1 = 2 . 10 ( – 0.3 + 1 ) ( 1 + 0.1 . 5 ) = 21 mA/V 1 ro1 = -----------------------------------------------2- = 2 k* 0.1 . 10 ( – 0.3 + 1 ) 1 ro2 = -----------------------------------2- = 2 k* 0.1 . 5 ( 0 + 1 ) (d) A v = – gm1 ( ro1 // ro2 ) = – 21 . ( 2 // 2 ) = – 21 V/V

EXERCISE 5.49 For a MESFET with the gate shorted to the source and having W = 10 µm, find the minimum voltage

between drain and source to operate in saturation. For VDS = 5 V, find the current ID. What is the output resistance of this current source? Ans. 1 V; 1.5 mA; 10 k*

As already mentioned, the main reason for using GaAs devices and circuits is their high frequency and high speed of operation. A remark is therefore in order on the internal capacitances and fT of GaAs transistors. For a particular GaAs technology with L = 1 µm, Cgs (at VGS = 0 V) is 1.6 fF/µm-width, and Cgd (at VDS = 2 V) is 0.16 fF/µm-width. Thus for a MESFET with W = 100 µm, Cgs = 0.16 pF and Cgd = 0.016 pF. fT typically ranges from 5 to 15 GHz.

6.8 GaAs AMPLIFIERS 3 Gallium arsenide (GaAs) technology makes possible the design of amplifiers having very wide bandwidths, in the hundreds of megahertz or even gigahertz range. In this section we shall study some of the circuit design techniques that have been developed over the last few years for the design of GaAs amplifiers. As will be seen, these techniques aim to circumvent the major problem of the MESFET, namely, its low output resistance in saturation. Before proceeding with this section the reader is advised to review the material on GaAs devices presented in Section 5.12.

Current Sources Current sources play a fundamental role in the design of integrated-circuit amplifiers, being employed both for biasing and as active loads. In GaAs technology, the simplest way to implement a current source is to connect the gate of a depletion-type MESFET to its source, 3

This section can be omitted with no loss in continuity.

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V DD I

"

vDS

$Vt2

ro

! iD

I

(a)

(c)

(b)

!VSS (d)

FIGURE 6.39 (a) The basic MESFET current source; (b) equivalent circuit of the current source; (c) the current source connected to a positive power supply to source currents to loads at voltages #VDD ! |Vt|; (d) the current source connected to a negative power supply to sink currents from loads at voltages )!VSS + |Vt|.

as shown in Fig. 6.39(a). Provided that vDS is maintained greater than |Vt|, the MESFET will operate in saturation and the current iD will be i D = , V t ( 1 + $ v DS ) 2

(6.126)

Thus the current source will have the equivalent circuit shown in Fig. 6.39(b), where the output resistance is the MESFET ro, r o = 1 /$, V t

2

(6.127)

In JFET terminology, , V t = I DSS and $ = 1 / V A ; thus 2

r o = V A ⁄ I DSS

(6.128)

Since for the MESFET, $ is relatively high (0.1 to 0.3 V!1) the output resistance of the current source of Fig. 6.39(a) is usually low, rendering this current-source realization inadequate for most applications. Before considering means for increasing the effective output resistance of the current source, we show in Fig. 6.39(c) how the basic current source can be connected to source currents to a load whose voltage can be as high as VDD ! |Vt |. Alternatively, the same device can be connected as shown in Fig. 6.39(d) to sink currents from a load whose voltage can be as low as !VSS + |Vt |.

EXERCISE 6.23 Using the device data given in Table 5.2 (page 456), find the current provided by a 10-µm-wide MESFET connected in the current-source configuration. Let the source be connected to a !5-V supply and find the current when the drain voltage is !4V. What is the output resistance of the current source? What change in current occurs if the drain voltage is raised by +4V? Ans. 1.1 mA; 10 k*; 0.4 mA

A Cascode Current Source The output resistance of the current source can be increased by utilizing the cascode configuration as shown in Fig. 6.40. The output resistance Ro of the cascode current source can be

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Ro

I VBIAS

Q2

Q1

!VSS

FIGURE 6.40 Adding the cascode transistor Q2 increases the output resistance of the current source by the factor gm2ro2; that is, Ro = gm2ro2ro1.

found by using Eq. (6.116), R o ! gm2 ro2 ro1

(6.129)

Thus, adding the cascode transistor Q2 raises the output resistance of the current source by the factor gm2ro2, which is the intrinsic voltage gain of Q2. For GaAs MESFETs, gm2ro2 is typically 10 to 40. To allow a wide range of voltages at the output of the cascode current source, VBIAS should be the lowest value that results in Q1 operating in saturation.

EXERCISE D6.24 For the cascode current source of Fig. 6.40 let VSS = 5 V, W1 = 10 µm, and W2 = 20 µm, and assume that the devices have the typical parameter values given in Table 5.2. (a) Find the value of VBIAS that will result in Q1 operating at the edge of the saturation region (i.e., VDS1 = |Vt |) when the voltage at the output is !3 V. (b) What is the lowest allowable voltage at the current-source output? (c) What value of output current is obtained for VO = !3 V? (d) What is the output resistance of the current source? (e) What change in output current results when the output voltage is raised from !3 V to +1 V? Ans. (a) !4.3 V; (b) !3.3 V; (c) 1.1 mA; (d) 310 k*; (e) 0.013 mA

Increasing the Output Resistance by Bootstrapping Another technique frequently employed to increase the effective output resistance of a MESFET, including the current-source-connected MESFET, is known as bootstrapping. The bootstrapping idea is illustrated in Fig. 6.41(a). Here the circuit inside the box senses the voltage at the bottom node of the current source, vA, and causes a voltage vB to appear at the top node of a value v B = VS + / v A (6.130) where VS is the dc voltage required to operate the current-source transistor in saturation ( VS ) V t ) and / is a constant #1. The incremental output resistance of the bootstrapped current source can be found by causing the voltage vA to increase by an increment va. From Eq. (6.130) we find that the resulting increment in vB is vb = /va. The incremental current through the current source is therefore (va ! vb) ⁄ro or (1 ! /)va ⁄ro. Thus the output resistance Ro is ro va - = -----------R o = -----------------------------( 1 – / ) va ⁄ r o 1 – /

(6.131)

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B

Bootstrapping circuit

Q1

I

A

Ro (a) Bootstrapping circuit Q3 VDD

ro3 1/gm3

I/2 Q3 (W)

E

B ro1

B

D1 A ia Q1 (W)

D2

va

Q2 ro2 " !

1/gm2 C

I

A

Q2 (W/2) C

Ro " va/ia I

(b)

(c)

FIGURE 6.41 Bootstrapping of a MESFET current source Q1: (a) basic arrangement; (b) an implementation; (c) small-signal equivalent circuit model of the circuit in (b), for the purpose of determining the output resistance Ro.

Thus, bootstrapping increases the output resistance by the factor 1/ (1 ! /), which increases as / approaches unity. Perfect bootstrapping is achieved with / = 1, resulting in Ro = 0. From the above we observe that the bootstrapping circuit senses whatever change occurs in the voltage at one terminal of the current source and causes an almost equal change to occur at the other terminal, thus maintaining an almost constant voltage across the current source and minimizing the change in current through the current-source transistor. The

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action of the bootstrapping circuit can be likened to that of a person who attempts to lift himself off the ground by pulling on the straps of his boots (!), the origin of the name of this circuit technique, which, incidentally, predates GaAs technology. Bootstrapping is a form of positive feedback; the signal vb that is fed back by the bootstrapping circuit is in phase with (has the same polarity as) the signal that is being sensed, va. Feedback will be studied formally in Chapter 8. An implementation of the bootstrapped current source is shown in Fig. 6.41(b). Here transistor Q2 is a source follower used to buffer node A, whose voltage is being sensed. The width of Q2 is half that of Q1 and is operating at half the bias current. (Transistors Q1 and Q2 are said to operate at the same current density.) Thus VGS of Q2 will be equal to that of Q1—namely, zero—and hence VC = VA. The two Schottky diodes behave as a battery of approximately 1.4 V, resulting in the dc voltage at node E being 1.4 V higher than VC. Note that the signal voltage at node C appears intact at node E; only the dc level is shifted. The diodes are said to perform level shifting, a common application of Schottky diodes in GaAs MESFET technology. Transistor Q3 is a source follower that is operating at the same current density as Q1, and thus its VGS must be zero, resulting in VB = VE. The end result is that the bootstrapping circuit causes a dc voltage of 1.4 V to appear across the current-source transistor Q1. Provided that |Vt| of Q1 is less than 1.4 V, Q1 will be operating in saturation as required. To determine the output resistance of the bootstrapped current source, apply an incremental voltage va to node A, as shown in Fig. 6.41(c). Note that this small-signal equivalent circuit is obtained by implicitly using the T model (including ro ) for each FET and assuming that the Schottky diodes act as a perfect level shifter (that is, as an ideal dc voltage of 1.4 V with zero internal resistance). Analysis of this circuit is straightforward and yields ro3 gm2 ro2 + -----gm3ro3 -----------------------v gm2ro2 + 1 ro1 / + -----b = ----------------------------------------------------va ro3 gm3ro3 + ------ +1 ro1 which is smaller than, but close to, obtained as v R o + -----a = ia

(6.132)

unity, as required. The output resistance Ro is then

ro1 -----------1–/ gm3 ro3 + (ro3 ⁄ ro1 ) + 1 = ro1 --------------------------------------------------------gm3 ro3 ⁄ ( gm2 ro2 + 1 ) + 1

(6.133)

For ro3 = ro1, assuming that gm3ro3 and gm2ro2 are %1, and using the relationships for gm and ro for Q2 and Q3, one can show that R o ! ro1 ( g m3 ro3 ⁄ 2 )

(6.134)

which represents an increase of about an order of magnitude in output resistance. Unfortunately, however, the circuit is rather complex.

A Simple Cascode Configuration–The Composite Transistor The rather low output resistance of the MESFET places a severe limitation on the performance of MESFET current sources and various MESFET amplifiers. This problem can be alleviated by using the composite MESFET configuration shown in Fig. 6.42(a) in place of a

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D

G Q2

D "

vgs

G Q1

Composite MESFET

S (a)

gm1 vgs

gm2 ro2 ro1

!

S (b)

FIGURE 6.42 (a) The composite MESFET and (b) its small-signal model.

single MESFET. This circuit is unique to GaAs MESFETs and works only because of the early-saturation phenomenon observed in these devices. Recall from the discussion in Section 5.12 that early saturation refers to the fact that in a GaAs MESFET the drain current saturates at a voltage vDSsat that is lower than vGS ! Vt. In the composite MESFET of Fig. 6.42(a), Q2 is made much wider than Q1. It follows that since the two devices are conducting the same current, Q2 will have a gate-to-source voltage vGS2 whose magnitude is much closer to |Vt| than |vGS1| is (thus, |vGS2| % |vGS1|). For instance, if we use the devices whose typical parameters are given in Table 5.2 and ignore for the moment channel-length modulation ($ = 0), we find that for W1 = 10 µm and W2 = 90 µm, at a current of 1 mA, vGS1 = 0 and v GS2 = – 2--3- V. Now, since the drain-tosource voltage of Q1 is vDS1 = !vGS2 + vGS1, we see that vDS1 will be positive and close to but lower than vGS1 ! Vt ( 2--3- V in our example compared to 1 V). Thus in the absence of early saturation, Q1 would be operating in the triode region. With early saturation, however, it has been found that saturation-mode operation is achieved for Q1 by making Q2 5 to 10 times wider. The composite MESFET of Fig. 6.42(a) can be thought of as a cascode configuration, in which Q2 is the cascode transistor, but without a separate bias line to feed the gate of the cascode transistor (as in Fig. 6.40). By replacing each of Q1 and Q2 with their smallsignal models one can show that the composite device can be represented with the equivalent circuit model of Fig. 6.42(b). Thus while gm of the composite device is equal to that of Q1, the output resistance is increased by the intrinsic gain of Q2, gm2ro2, which is typically in the range 10 to 40. This is a substantial increase and is the reason for the attractiveness of the composite MESFET. The composite MESFET can be employed in any of the applications that can benefit from its increased output resistance. Some examples are shown in Fig. 6.43. The circuit in Fig. 6.43(a) is that of a current source with increased output resistance. Another view of the operation of this circuit can be obtained by considering Q2 as a source follower that causes the drain of Q1 to follow the voltage changes at the current-source terminal (node A), thereby bootstrapping Q1 and increasing the effective output resistance of the current source. This alternative interpretation of circuit operation has resulted in its alternative name: the self-bootstrapped current source. The application of the composite MESFET as a source follower is depicted in Fig. 6.43(b). Assuming the bias-current source I to be ideal, we can write for the gain of

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VDD

VDD

VDD

Q2

Q2

Q4

Q1

Q3

vi Q1

vo

A I

vo

I

Q2

vi Q1

(a)

(b)

(c)

FIGURE 6.43 Applications of the composite MESFET: (a) as a current source; (b) as a source follower; and (c) as a gain stage.

this follower ro , eff vo ----- = ------------------------------------v i ro , eff + (1 ⁄ gm1) gm2 ro2 ro1 = -----------------------------------------------gm2 ro2 ro1 + (1 ⁄ gm1)

(6.135)

which is much closer to the ideal value of unity than is the gain of a single MESFET source follower.

EXERCISE 6.25 Using the device data given in Table 5.2, contrast the voltage gain of a source follower formed using a single MESFET having W = 10 µm with a composite MESFET follower with W1 = 10 µm and W2 = 90 µm. In both cases assume biasing at 1 mA and neglect $ while calculating gm (for simplicity). Ans. Single: 0.952 V/V; composite: 0.999 V/V

A final example of the application of the composite MESFET is shown in Fig. 6.43(c). The circuit is a gain stage utilizing a composite MESFET (Q1, Q2) as a driver and another composite MESFET (Q3, Q4) as a current-source load. The small-signal gain is given by

vo ----- = – g m1 R o vi

(6.136)

where Ro is the output resistance, R o = ro , eff ( Q 1, Q 2 ) //ro , eff ( Q 3, Q 4 ) = gm2 ro2 ro1 // gm4 ro4 ro3

(6.137)

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VDD Q4

vo " vi !

Q1

Q2

Q3

!VSS

FIGURE 6.44 A simple MESFET differential amplifier.

Differential Amplifiers The simplest possible implementation of a differential amplifier in GaAs MESFET technology is shown in Fig. 6.44. Here Q1 and Q2 form the differential pair, Q3 forms the bias current source, and Q4 forms the active (current-source) load. The performance of the circuit is impaired by the low output resistances of Q3 and Q4. The voltage gain is given by

vo ----- = – gm2 ( ro2 // ro 4 ) vi

(6.138)

The gain can be increased by using one of the improved current-source implementations discussed above. Also, a rather ingenious technique has been developed for enhancing the gain of the MESFET differential pair. The circuit is shown in Fig. 6.45(a). While the drain

(a)

(b)

FIGURE 6.45 (a) A MESFET differential amplifier whose gain is enhanced by the application of positive feedback through the source follower Q3; (b) small-signal analysis of the circuit in (a).

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of Q2 is loaded with a current-source load (as before), the output signal developed is fed back to the drain of Q1 via the source follower Q3. The small-signal analysis of the circuit is illustrated in Fig. 6.45(b) where the current sources I and I/ 2 have been assumed ideal and thus replaced with open circuits. To determine the voltage gain, we have grounded the gate terminal of Q2 and applied the differential input signal vi to the gate of Q1. The analysis proceeds along the following steps: 1. 2. 3. 4.

From the output node we see that id2 = 0. From the sources node, since id2 = 0, we find that id1 = 0. From the node at the drain of Q1, since id1 = 0, we find that id3 = 0. Writing for each transistor i d = gmvgs + vds ⁄ ro = 0 we obtain three equations in the three unknowns vd1, vs, and vo. The solution yields

v -----o = g m1 ro1 vi

gm3 ro3 gm1 ro1 + 1 -----------------------– -----------------------gm2ro2 + 1 gm3 ro3 + 1

(6.139)

If all three transistors have the same geometry and are operating at equal dc currents, their gm and ro values will be equal and the expression in Eq. (6.139) reduces to vo 2 ----- ! ( gm ro ) (6.140) vi Thus application of positive feedback through follower Q3 enables one to obtain a gain equal to the square of that naturally available from a single stage!

EXERCISE 6.26 Using the device data given in Table 5.2, find the gain of the differential amplifier circuit of Fig. 6.45(a) for I = 10 mA and W1 = W2 = W3 = 100 µm. Ans. 784 V/V

14.8 GALLIUM-ARSENIDE DIGITAL CIRCUITS We conclude our study of digital-circuit families with a discussion of logic circuits implemented using the emerging technology of gallium arsenide. An introduction to this technology and its two basic devices, the MESFET and the Schottky-barrier diode (SBD), was given in Section 5.12. We urge the reader to review Section 5.12 before proceeding with the study of this section. The major advantage that GaAs technology offers is a higher speed of operation than currently achievable using silicon devices. Gate delays of 10 to 100 ps have been reported for GaAs circuits. The disadvantages are a relatively high power dissipation per gate (1 to 10 mW); relatively small voltage swings and, correspondingly, narrow noise margins; low packing density, mostly as a result of the high-power dissipation per gate; and low manufacturing yield. The present state of affairs is that a few specialized manufacturers produce SSI, MSI, and some LSI digital circuits performing relatively specialized functions, with a cost per gate considerably higher than that of silicon digital ICs. Nevertheless, the very high

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FIGURE 14.47 A DCFL GaAs gate implementing a two-input NOR function. The gate is shown driving the input transistor Q3 of another gate.

speeds of operation achievable in GaAs circuits make it a worthwhile technology whose applications will possibly grow. Unlike the CMOS logic circuits that we have studied in Chapter 13, and the bipolar logic families that we have studied in earlier sections of this chapter, there are no standard GaAs logic-circuit families. The lack of standards extends not only to the topology of the basic gates but also to the power-supply voltages used. In the following we present examples of the most popular GaAs logic gate circuits.

Direct-Coupled FET Logic (DCFL) Direct-coupled FET logic (DCFL) is the simplest form of GaAs digital logic circuits. The basic gate is shown in Fig. 14.47. The gate utilizes enhancement MESFETs, Q1 and Q2, for the input switching transistors, and a depletion MESFET for the load transistor QL. The gate closely resembles the now obsolete depletion-load MOSFET circuit. The GaAs circuit of Fig. 14.47 implements a two-input NOR function. To see how the MESFET circuit of Fig. 14.47 operates, ignore input B and consider the basic inverter formed by Q1 and QL. When the input voltage applied to node A, vI , is lower than the threshold voltage of the enhancement MESFET Q1, denoted VtE, transistor Q1 will be off. Recall that VtE is positive and for GaAs MESFETs is typically 0.1 to 0.3 V. Now if the gate output Y is open circuited, the output voltage will be very close to VDD. In practice, however, the gate will be driving another gate, as indicated in Fig. 14.47, where Q3 is the input transistor of the subsequent gate. In such a case, current will flow from VDD through QL and into the gate terminal of Q3. Recalling that the gate to source of a GaAs MESFET is a Schottky-barrier diode that exhibits a voltage drop of about 0.7 V when conducting, we see that the gate conduction of Q3 will clamp the output high voltage (VOH) to about 0.7 V. This is in sharp contrast to the MOSFET case, where no gate conduction takes place. Figure 14.48 shows the DCFL inverter under study with the input of the subsequent gate represented by a Schottky diode Q3. With vI < VtE, i1 = 0 and iL flows through Q3 resulting in vO = VOH ! 0.7 V. Since VDD is usually low (1.2 to 1.5 V) and the threshold voltage of QL, VtD, is typically !0.7 to !1 V, QL will be operating in the triode region. (To simplify matters, we shall ignore in this discussion the early-saturation effect exhibited by GaAs MESFETs.) As vI is increased above VtE, Q1 turns on and conducts a current denoted i1. Initially, Q1 will be in the saturation region. Current i1 subtracts from iL, thus reducing the current in Q3. The voltage across Q3, vO, decreases slightly. However, for the present discussion we shall assume that vO will remain close to 0.7 V as long as Q3 is conducting. This will continue until vI reaches the value that results in i1 = iL. At this point, Q3 ceases conduction

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FIGURE 14.48 The DCFL gate with the input of the subsequent gate represented by a Schottky diode Q3.

and can be ignored altogether. Further increase in vI results in i1 increasing, vO decreasing, and iL = i1. When (VDD – vO) exceeds VtD , QL saturates; and when vO falls below vI by VtE, Q1 enters the triode region. Eventually, when vI = VOH = 0.7 V, vO = VOL, which is typically 0.1 to 0.2 V. From the description above we see that the output voltage swing of the DCFL gate is limited by gate conduction to a value less than 0.7 V (typically 0.5 V or so). Further details on the operation of the DCFL gate are illustrated by the following example.

EXAMPLE 14.3 Consider a DCFL gate fabricated in a GaAs technology for which L = 1 µm, VtD = !1 V, VtE = 0.2 V, , (for 1-µm width) = 10!4 A/V2, and $ = 0.1 V!1. Let the widths of the input MESFETs be 50 µm, and let the width of the load MESFET be 6 µm. VDD = 1.5 V. Using a constant-voltagedrop model for the gate-source Schottky diode with VD = 0.7 V, and neglecting the earlysaturation effect of GaAs MESFETs (that is, using Eqs. 5.120 to describe MESFET operation), find VOH, VOL , VIH, NMH, NML , the static power dissipation, and the propagation delay for a total equivalent capacitance at the gate output of 30 fF.

Solution From the description above of the operation of the DCFL gate we found that VOH = 0.7 V. To obtain VOL, we consider the inverter in the circuit of Fig. 14.48 and let vI = VOH = 0.7 V. Since we expect vO = VOL to be small, we assume Q1 to be in the triode region and QL to be in saturation. (Q3 is of course off.) Equating i1 and iL gives the equation 2

2

, 1 [ 2 ( 0.7 – 0.2 )VOL – V OL ] ( 1 + 0.1VOL ) = , L [ 0 – ( – 1 ) ] [ 1 + 0.1 ( 1.5 – VOL ) ] To simplify matters, we neglect the terms 0.1VOL and substitute ,L ⁄ ,1 = WL ⁄ W1 = 6 ⁄ 50 to obtain a quadratic equation in VOL whose solution gives VOL ! 0.17 V. Toward obtaining the value of VIL we shall first find the value of vI at which i1 = iL, the diode Q3 turns off, and vO begins to decrease. Since at this point vO = 0.7 V, we assume that Q1 is in saturation. Transistor QL has a vDS of 0.8 V, which is less than VtD and is thus in the triode region. Equating i1 and iL gives 2

2

, 1 ( v I – 0.2 ) ( 1 + 0.1 . 0.7 ) = , L [ 2 ( 1 ) ( 1.5 – 0.7 ) – ( 1.5 – 0.7 ) ] [ 1 + 0.1 ( 1.5 – 0.7 ) ] Substituting ,L ⁄ ,1 = WL ⁄ W1 = 6 ⁄ 50 and solving the resulting equation yields v I = 0.54 V. Figure 14.49 shows a sketch of the transfer characteristic of the inverter. The slope dvO ⁄ dvI at

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vO (V)

SE D R A / S M IT H

NML & 0.37 V

A

0.7

VOH & 0.7 V

0.6 0.5 0.4 Slope & !1

0.3 B

0.2

VOL & 0.17 V

0.1 NMH & 0.07 V 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 vI (V)

VIL & 0.54 V VIH & 0.63 V FIGURE 14.49 Transfer characteristic of the DCFL inverter of Fig. 14.48.

point A can be found to be !14.2 V/V. We shall consider point A as the point at which the inverter begins to switch from the high-output state; thus VIL ! 0.54 V. To obtain VIH, we find the co-ordinates of point B at which dvO ⁄ dvI = !1. This can be done using a procedure similar to that employed for the MOSFET inverters and assuming Q1 to be in the triode region and QL to be in saturation. Neglecting terms in 0.1vO, the result is VIH ! 0.63 V. The noise margins can now be found as NM H + V OH – V IH = 0.7 – 0.63 = 0.07 V NM L + V IL – V OL = 0.54 – 0.17 = 0.37 V The static power dissipation is determined by finding the supply current IDD in the outputhigh and the output-low cases. When the output is high (at 0.7 V), QL is in the triode region and the supply current is 2

I DD = , L [ 2 ( 0 + 1 ) ( 1.5 – 0.7 ) – ( 1.5 – 0.7 ) ] [ 1 + 0.1 ( 1.5 – 0.7 ) ] Substituting ,L = 10!4 . WL = 0.6 mA/V2 results in I DD = 0.61 mA When the output is low (at 0.17 V), QL is in saturation and the supply current is 2

IDD = , L ( 0 + 1 ) [ 1 + 0.1 ( 1.5 – 0.17 ) ] = 0.68 mA Thus the average supply current is I DD = 1--2- ( 0.61 + 0.68 ) = 0.645 mA

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FIGURE 14.50 Circuits for calculating the propagation delays of the DCFL inverter: (a) tPHL; (b) tPLH.

and the static power dissipation is PD = 0.645 . 1.5 ! 1 mW The propagation delay tPHL is the time for the output voltage of the inverter to decrease from VOH = 0.7 V to 1--2-(VOH + VOL ) = 0.435 V. During this time vI is at the high level of 0.7 V, and the capacitance C (assumed to be 30 fempto Farads [fF]) is discharged by (i1 ! iL); refer to Fig. 14.50(a). The average discharge current is found by calculating i1 and iL at the beginning and at the end of the discharge interval. The result is that i1 changes from 1.34 mA to 1.28 mA and iL changes from 0.61 mA to 0.66 mA. Thus the discharge current (i1 ! iL ) changes from 0.73 mA to 0.62 mA for an average value of 0.675 mA. Thus – 15

C 1V 30 . 10 ( 0.7 – 0.435 )tPHL = ------------ = -------------------------------------------------------= 11.8 ps –3 I 0.675 . 10 To determine tPLH we refer to the circuit in Fig. 14.50(b) and note that during tPLH, vO changes from VOL = 0.17 V to 1--2- (VOH + VOL) = 0.435 V. The charging current is the average value of iL, which changes from 0.8 mA to 0.66 mA. Thus i L average = 0.73 mA and – 15

30 . 10 . ( 0.435 – 0.17 ) - = 10.9 ps tPLH = ----------------------------------------------------------------–3 0.73 . 10 The propagation delay of the DCFL gate can now be found as t P = 1--2- ( tPHL + tPLH ) = 11.4 ps

As a final remark, we note that the analysis above was done using simplified device models; our objective is to show how the circuit works rather than to find accurate performance measures. These can be obtained using SPICE simulation with more elaborate models [see Roberts and Sedra (1997)].

Logic Gates Using Depletion MESFETs The DCFL circuits studied above require both enhancement and depletion devices and thus are somewhat difficult to fabricate. Also, owing to the fact that the voltage swings and noise margins are rather small, very careful control of the value of VtE is required in fabrication. As an alternative, we now present circuits that utilize depletion devices only.

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VDD & "3 V Subsequent gate

QL

vO v 'O vI

QS

D1

D2

QS2 QPD

!VSS & !2 V FIGURE 14.51 An inverter circuit utilizing depletion-mode devices only. Schottky diodes are employed to shift the output logic levels to values compatible with the input levels required to turn the depletion MESFET QS on and off. This circuit is known as FET logic (FL).

Figure 14.51 shows the basic inverter circuit of a family of GaAs logic circuits known at FET logic (FL). The heart of the FL inverter is formed by the switching transistor QS and its load QL—both depletion-type MESFETs. Since the threshold voltage of a depletion MESFET, VtD, is negative, a negative voltage
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!1.27 V

0.7 V IH

FIGURE 14.52 Transfer characteristic of the FL inverter of Fig. 14.51.

The segment BC of the transfer curve corresponds to QS operating in the triode region. Here QL and QPD continue to operate in saturation and D1 and D2 remain conducting. Finally, for vI = VOH = 0.7 V, vO = VOL, which for the case VtD = !0.9 V can be found to be !1.3 V.

EXERCISE 14.30 Verify that the co-ordinates of points A, B, and C of the transfer characteristic are as indicated in Fig. 14.52. Let VtD = !0.9 V and $ = 0.

As indicated in Fig. 14.52, the FL inverter exhibits much higher noise margins than those for the DCFL circuit. The FL inverter, however, requires two power supplies. The FL inverter can be used to construct a NOR gate by simply adding transistors with drain and source connected in parallel with those of QS.

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VDD " #3 V

VDD " #3 V

D1A A

QL

QL B

D1

vO

D2

vI

D1B

Y"A#B

D2

QS QPD

!VSS " !2 V

QPD

!VSS " !2 V

(a)

(b)

FIGURE 14.53 (a) An SDFL inverter. (b) An SDFL NOR gate.

Schottky Diode FET Logic (SDFL) If the diode level-shifting network of the FL inverter is connected at the input side of the gate, rather than at the output side, we obtain the circuit shown in Fig. 14.53(a). This inverter operates in much the same manner as the FL inverter. The modified circuit, however, has a very interesting feature: The NOR function can be implemented by simply connecting additional diodes, as shown in Fig. 14.53(b). This logic form is known as Schottky diode FET logic (SDFL). SDFL permits higher packing density than other forms of MESFET logic because only an additional diode, rather than an additional transistor, is required for each additional input, and diodes require much smaller areas than transistors.

Buffered FET Logic (BFL) Another variation on the basic FL inverter of Fig. 14.51 is possible. A source follower can be inserted between the drain of QS and the diode level-shifting network. The resulting gate, shown for the case of a two-input NOR, is depicted in Fig. 14.54. This form of GaAs logic circuit is known as buffered FET logic (BFL). The source-follower transistor QSF increases the output current-driving capability, thus decreasing the low-to-high propagation time. FL, BFL, and SDFL feature propagation delays of the order of 100 ps and power dissipation of the order of 10 mW/gate.

FIGURE 14.54 A BFL two-input NOR gate. The gate is formed by inserting a source-follower transistor QSF between the inverting stage and the level-shifting stage.

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14.3 TRANSISTOR–TRANSISTOR LOGIC (TTL OR T 2 L) For more than two decades (late 1960s to late 1980s) TTL enjoyed immense popularity. Indeed, the bulk of digital systems applications employing SSI and MSI packages were designed using TTL. We shall begin this section with a study of the evolution of TTL from DTL. In this way we shall explain the function of each of the stages of the complete TTL gate circuit. Characteristics of standard TTL gates will be studied in Section 14.4. Standard TTL, however, has now been virtually replaced with more advanced forms of TTL that feature improved performance. These will be discussed in Section 14.5.

Evolution of TTL from DTL The basic DTL gate circuit in discrete form was discussed in the previous section (see Fig. 14.6). The integrated-circuit form of the DTL gate is shown in Fig. 14.7 with only one input indicated. As a prelude to introducing TTL, we have drawn the input diode as a diodeconnected transistor (Q1), which corresponds to how diodes are made in IC form. This circuit differs from the discrete DTL circuit of Fig. 14.6 in two important aspects. First, one of the steering diodes is replaced by the base–emitter junction of a transistor (Q2) that is either cut off (when the input is low) or in the active mode (when the input is high). This is done to reduce the input current and thereby increase the fan-out capability of the gate. A detailed explanation of this point, however, is not relevant to our study of TTL. Second, the resistance RB is returned to ground rather than to a negative supply, as was done in the earlier discrete circuit. An obvious advantage of this is the elimination of the additional power supply. The disadvantage, however, is that the reverse base current available to remove the excess charge stored in the base of Q3 is rather small. We shall elaborate on this point below.

FIGURE 14.7 IC form of the DTL gate with the input diode shown as a diode-connected transistor (Q1 ). Only one input terminal is shown.

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EXERCISE 14.4 Consider the DTL gate circuit shown in Fig. 14.7 and assume that ,(Q2) = ,(Q3) = 50. (a) When vI = 0.2 V, find the input current. (b) When vI = +5 V, find the base current of Q3. Ans. (a) 1.1 mA; (b) 1.6 mA

Reasons for the Slow Response of DTL The DTL gate has relatively good noise margins and reasonably good fan-out capability. Its response, however, is rather slow. There are two reasons for this: first, when the input goes low and Q2 and D turn off, the charge stored in the base of Q3 has to leak through RB to ground. The initial value of the reverse base current that accomplishes this “base discharging” process is approximately 0.7 V/RB, which is about 0.14 mA. Because this current is quite small in comparison to the forward base current, the time required for the removal of base charge is rather long, which contributes to lengthening the gate delay. The second reason for the relatively slow response of DTL derives from the nature of the output circuit of the gate, which is simply a common-emitter transistor. Figure 14.8 shows the output transistor of a DTL gate driving a capacitive load CL. The capacitance CL represents the input capacitance of another gate and/or the wiring and parasitic capacitances that are inevitably present in any circuit. When Q3 is turned on, its collector voltage cannot instantaneously fall because of the existence of CL. Thus Q3 will not immediately saturate but rather will operate in the active region. The collector of Q3 will therefore act as a constant-current source and will sink a relatively large current (,IB). This large current will rapidly discharge CL. We thus see that the common-emitter output stage features a short turn-on time. However, turnoff is another matter. Consider next the operation of the common-emitter output stage when Q3 is turned off. The output voltage will not rise immediately to the high level (VCC). Rather, CL will charge up to VCC through RC. This is a rather slow process, and it results in lengthening the DTL gate delay (and similarly the RTL gate delay). Having identified the two reasons for the slow response of DTL, we shall see in the following how these problems are remedied in TTL.

Input Circuit of the TTL Gate Figure 14.9 shows a conceptual TTL gate with only one input terminal indicated. The most important feature to note is that the input diode has been replaced by a transistor. One can

FIGURE 14.8 The output circuit of a DTL gate driving a capacitive load CL.

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FIGURE 14.9 Conceptual form of TTL gate. Only one input terminal is shown.

FIGURE 14.10 Analysis of the conceptual TTL gate when the input is high.

think of this simply as if the short circuit between base and collector of Q1 in Fig. 14.7 has been removed. To see how the conceptual TTL circuit of Fig. 14.9 works, let the input vI be high (say, vI = VCC). In this case current will flow from VCC through R, thus forward-biasing the base! collector junction of Q1. Meanwhile, the base!emitter junction of Q1 will be reverse-biased. Therefore Q1 will be operating in the inverse active mode—that is, in the active mode but with the roles of emitter and collector interchanged. The voltages and currents will be as indicated in Fig. 14.10, where the current I can be calculated from V CC – 1.4 I = ---------------------R In actual TTL circuits Q1 is designed to have a very low reverse , (,R ! 0.02). Thus the gate input current will be very small, and the base current of Q3 will be approximately equal to I. This current will be sufficient to drive Q3 into saturation, and the output voltage will be low (0.1 to 0.2 V). Next let the gate input voltage be brought down to the logic-0 level (say, vI ! 0.2 V). The current I will then be diverted to the emitter of Q1 . The base!emitter junction of Q1 will become forward-biased, and the base voltage of Q1 will therefore drop to 0.9 V. Since Q3 was in saturation, its base voltage will remain at +0.7 V pending the removal of the excess charge stored in the base region. Figure 14.11 indicates the various voltage and current values immediately after the input is lowered. We see that Q1 will be operating in the normal

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FIGURE 14.11 Voltage and current values in the conceptual TTL circuit immediately after the input voltage is lowered.

RE

CL FIGURE 14.12 An emitter-follower output stage with capacitive load.

active mode3 and its collector will carry a large current (,FI). This large current rapidly discharges the base of Q3 and drives it into cutoff. We thus see the action of Q1 in speeding up the turn-off process. As Q3 turns off, the voltage at its base is reduced, and Q1 enters the saturation mode. Eventually the collector current of Q1 will become negligibly small, which implies that its VCEsat will be approximately 0.1 V and the base of Q3 will be at about 0.3 V, which keeps Q3 in cutoff.

Output Circuit of the TTL Gate The above discussion illustrates how one of the two problems that slow down the operation of DTL is solved in TTL. The second problem, the long rise time of the output waveform, is solved by modifying the output stage, as we shall now explain. First, recall that the common-emitter output stage provides fast discharging of load capacitance but rather slow charging. The opposite is obtained in the emitter-follower output stage shown in Fig. 14.12. Here, as v I goes high, the transistor turns on and provides a low output resistance (characteristic of emitter followers), which results in fast charging of CL. On the other hand, when vI goes low, the transistor turns off and CL is then left to discharge slowly through RE. 3

Although the collector voltage of Q1 is lower than its base voltage by 0.2 V, the collector–base junction will in effect be cut off and Q1 will be operating in the active mode.

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FIGURE 14.13 The totem-pole output stage.

It follows that an optimum output stage would be a combination of the common-emitter and the emitter-follower configurations. Such an output stage, shown in Fig. 14.13, has to be driven by two complementary signals vI1 and vI2. When v I1 is high vI2 will be low, and in this case Q3 will be on and saturated, and Q4 will be off. The common-emitter transistor Q3 will then provide the fast discharging of load capacitance and in steady state provide a low resistance (RCEsat ) to ground. Thus when the output is low, the gate can sink substantial amounts of current through the saturated transistor Q3. When vI1 is low and vI2 is high, Q3 will be off and Q4 will be conducting. The emitter follower Q4 will then provide fast charging of load capacitance. It also provides the gate with a low output resistance in the high state and hence with the ability to source a substantial amount of load current. Because of the appearance of the circuit in Fig. 14.13, with Q4 stacked on top of Q3, the circuit has been given the name totem-pole output stage. Also, because of the action of Q4 in pulling up the output voltage to the high level, Q4 is referred to as the pull-up transistor. Since the pulling up is achieved here by an active element (Q4), the circuit is said to have an active pull-up. This is in contrast to the passive pull-up of RTL and DTL gates. Of course, the common-emitter transistor Q3 provides the circuit with active pull-down. Finally, note that a special driver circuit is needed to generate the two complementary signals vI1 and vI2.

EXAMPLE 14.1 We wish to analyze the circuit shown together with its driving waveforms in Fig. 14.14 to determine the waveform of the output signal vO. Assume that Q3 and Q4 have , = 50.

Solution Consider first the situation before vI1 goes high—that is, at time t < 0. In this case Q3 is off and Q4 is on, and the circuit can be simplified to that shown in Fig. 14.15. In this simplified circuit we have replaced the voltage divider (R1, R2) by its Thévenin equivalent. In the steady state, CL will be charged to the output voltage vO, whose value can be obtained as follows: 5 = 10 . I B + VBE + I E . 0.5 + 2.5 Substituting VBE ! 0.7 V and IB = IE ⁄ (, + 1) = IE ⁄ 51 gives IE = 2.59 mA. Thus the output voltage vO is given by

v O = 2.5 + I E . 0.5 = 3.79 V

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0V FIGURE 14.14 Circuit and input waveforms for Example 14.1.

FIGURE 14.15 The circuit of Fig. 14.14 when Q3 is off.

We next consider the circuit as vI1 goes high and vI2 goes low. Transistor Q3 turns on and transistor Q4 turns off, and the circuit simplifies to that shown in Fig. 14.16. Again we have used the Thévenin equivalent of the divider (R1, R2). We shall also assume that the switching times of the transistors are negligibly small. Thus at t = 0+ the base current of Q3 becomes 5 – 0.7 I B = ---------------- = 0.43 mA 10 Since at t = 0 the collector voltage of Q3 is 3.79 V, and since this value cannot change instantaneously because of CL, we see that at t = 0+ transistor Q3 will be in the active mode. The collector current of Q3 will be ,IB , which is 21.5 mA, and the circuit will have the equivalent shown in Fig. 14.17(a). A simpler version of this equivalent circuit, obtained using Thévenin’s theorem, is shown in Fig. 14.17(b). The equivalent circuit of Fig. 14.17 applies as long as Q3 remains in the active mode. This condition persists while CL is being discharged and until vO reaches about +0.3 V, at which time Q3 enters saturation. This is illustrated by the waveform in Fig. 14.18. The time for the output

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FIGURE 14.16 The circuit of Fig. 14.14 when Q4 is off.

FIGURE 14.17 (a) Equivalent circuit for the circuit in Fig. 14.16 when Q3 is in the active mode. (b) Simpler version of the circuit in (a) obtained using Thévenin’s theorem.

FIGURE 14.18 Details of the output voltage waveform for the circuit in Fig. 14.14.

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voltage to fall from +3.79 V to +0.3 V, which can be considered the fall time tf , can be obtained from – 8.25 – ( – 8.25 – 3.79 )e

–t f ⁄ 2

= 0.3

which results in tf ! 0.34 2 where

2 = C L . 0.5 k* = 10 ns Thus tf = 3.4 ns. After Q3 enters saturation, the capacitor discharges further to the final steady-state value of VCEsat (!0.2 V). The transistor model that applies during this interval is more complex; since the interval in question is quite short, we shall not pursue the matter further. Consider next the situation as vI1 goes low and vI2 goes high at t = T. Transistor Q3 turns off as Q4 turns on. We shall assume that this occurs immediately, and thus at t = T+ the circuit simplifies to that in Fig. 14.15. We have already analyzed this circuit in the steady state and thus know that eventually vO will reach +3.79 V. Thus vO rises exponentially from +0.2 V toward +3.79 V with a time constant of CL{0.5 k*//[10 k* / (, + 1)]}, where we have neglected the emitter resistance re. Denoting this time constant 21, we obtain 21 = 2.8 ns. Defining the rise time tr as the time for vO to reach 90% of the final value, we obtain 3.79 – ( 3.79 – 0.2 )e –t r ⁄ 21 = 0.9 . 3.79, which results in tr = 6.4 ns. Figure 14.18 illustrates the details of the output voltage waveform.

The Complete Circuit of the TTL Gate Figure 14.19 shows the complete TTL gate circuit. It consists of three stages: the input transistor Q1, whose operation has already been explained, the driver stage Q2, whose function is to generate the two complementary voltage signals required to drive the totem-pole circuit,

FIGURE 14.19 The complete TTL gate circuit with only one input terminal indicated.

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which is the third (output) stage of the gate. The totem-pole circuit in the TTL gate has two additional components: the 130-* resistance in the collector circuit of Q4 and the diode D in the emitter circuit of Q4. The function of these two additional components will be explained shortly. Notice that the TTL gate is shown with only one input terminal indicated. Inclusion of additional input terminals will be considered in Section 14.4. Because the driver stage Q2 provides two complementary (that is, out-of-phase) signals, it is known as a phase splitter. We shall now provide a detailed analysis of the TTL gate circuit in its two extreme states: one with the input high and one with the input low.

Analysis When the Input Is High When the input is high (say, +5 V), the various voltages and currents of the TTL circuit will have the values indicated in Fig. 14.20. The analysis illustrated in Fig. 14.20 is quite straightforward, and the order of the steps followed is indicated by the circled numbers. As expected, the input transistor is operating in the inverse active mode, and the input current, called the input high current IIH, is small; that is, IIH = , R I ! 15 µ A where we assume that , R ! 0.02 . The collector current of Q1 flows into the base of Q2, and its value is sufficient to saturate the phase-splitter transistor Q2. The latter supplies the base of Q3 with sufficient current to drive it into saturation and lower its output voltage to VCEsat (0.1 to 0.2 V). The voltage at the collector of Q2 is VBE3 + VCEsat(Q2), which is approximately +0.9 V. If diode D were not included, this voltage would be sufficient to turn Q4 on, which is contrary to the proper operation of the totem-pole circuit. Including diode D ensures that both Q4 and D remain off.

FIGURE 14.20 Analysis of the TTL gate with the input high. The circled numbers indicate the order of the analysis steps.

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FIGURE 14.21 The vO–iL characteristic of the TTL gate when the output is low.

The saturated transistor Q3 then establishes the low output voltage of the gate (VCEsat) and provides a low impedance to ground. In the low-output state the gate can sink a load current iL, provided that the value of iL does not exceed ! " 2.6 mA, which is the maximum collector current that Q3 can sustain while remaining in saturation. Obviously the greater the value of iL, the greater the output voltage will be. To maintain the logic-0 level below a certain specified limit, a corresponding limit has to be placed on the load current iL. As will be seen shortly, it is this limit that determines the maximum fan-out of the TTL gate. Figure 14.21 shows a sketch of the output voltage vO versus the load current iL of the TTL gate when the output is low. This is simply the vCE#iC characteristic curve of Q3 measured with a base current of 2.6 mA. Note that at iL = 0, vO is the offset voltage, which is about 100 mV.

EXERCISE 14.5 Assume that the saturation portion of the vO#iL characteristic shown in Fig. 14.21 can be approximated by a straight line (of slope = 8 $) that intersects the vO axis at 0.1 V. Find the maximum load current that the gate is allowed to sink if the logic-0 level is specified to be %0.3 V. Ans. 25 mA

Analysis When the Input Is Low Consider next the operation of the TTL gate when the input is at the logic-0 level (!0.2 V). The analysis is illustrated in Fig. 14.22, from which we see that the base#emitter junction of Q1 will be forward-biased and the base voltage will be approximately +0.9 V. Thus the current I can be found to be approximately 1 mA. Since 0.9 V is insufficient to forward-bias the series combination of the collector–base junction of Q1 and the base#emitter junction of Q2 (at least 1.2 V would be required), the latter will be off. Therefore the collector current of Q1 will be almost zero and Q1 will be saturated, with VCEsat ! 0.1 V. Thus the base of Q2 will be at approximately +0.3 V, which is indeed insufficient to turn Q2 on. The gate input current in the low state, called input-low current IIL, is approximately equal to the current I (! 1 mA) and flows out of the emitter of Q1. If the TTL gate is driven

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VCC & "5 V 5 ! 0.9 2 4 # 1 mA

I&

130 (

1.6 k(

4 k( Q4 "0.9 V 1

vI & "0.2 V IIL # 1 mA 3

Q1

5 "0.3 V

Q2

(off)

iL

D

vo

0 mA 4 Q3

6 0V 1 k(

(off)

0 mA 7

FIGURE 14.22 Analysis of the TTL gate when the input is low. The circled numbers indicate the order of the analysis steps.

by another TTL gate, the output transistor Q3 of the driving gate should sink this current IIL. Since the output current that a TTL gate can sink is limited to a certain maximum value, the maximum fan-out of the gate is directly determined by the value of IIL.

EXERCISES 14.6 Consider the TTL gate analyzed in Exercise 14.5. Find its maximum allowable fan-out using the value of IIL calculated above. Ans. 25 14.7 Use Eq. (4.114) to find VCEsat of transistor Q1 when the input of the gate is low (0.2 V). Assume that ,F = 50 and ,R = 0.02. Ans. 98 mV

Let us continue with our analysis of the TTL gate. When the input is low, we see that both Q2 and Q3 will be off. Transistor Q4 will be on and will supply (source) the load current iL. Depending on the value of iL, Q4 will be either in the active mode or in the saturation mode. With the gate output terminal open, the current iL will be very small (mostly leakage) and the two junctions (base!emitter junction of Q4 and diode D) will be barely conducting. Assuming that each junction has a 0.65-V drop and neglecting the voltage drop across the 1.6-k* resistance, we find that the output voltage will be

v O ! 5 – 0.65 – 0.65 = 3.7 V

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As iL is increased, Q4 and D conduct more heavily, but for a range of iL, Q4 remains in the active mode, and vO is given by iL - . 1.6 k* – VBE4 – VD v O = VCC – ----------,+1

(14.4)

If we keep increasing iL, a value will be reached at which Q4 saturates. Then the output voltage becomes determined by the 130-* resistance according to the approximate relationship

v O ! VCC – iL . 130 – VCEsat ( Q 4 ) ! VD

(14.5)

Function of the 130-* Resistance At this point the reason for including the 130-* resistance should be evident: It is simply to limit the current that flows through Q4, especially in the event that the output terminal is accidentally short-circuited to ground. This resistance also limits the supply current in another circumstance, namely, when Q4 turns on while Q3 is still in saturation. To see how this occurs, consider the case where the gate input was high and then is suddenly brought down to the low level. Transistor Q2 will turn off relatively fast because of the availability of a large reverse current supplied to its base terminal by the collector of Q1. On the other hand, the base of Q3 will have to discharge through the 1-k* resistance, and thus Q3 will take some time to turn off. Meanwhile Q4 will turn on, and a large current pulse will flow through the series combination of Q4 and Q3. Part of this current will serve the useful purpose of charging up any load capacitance to the logic-1 level. The magnitude of the current pulse will be limited by the 130-* resistance to about 30 mA. The occurrence of these current pulses of short duration (called current spikes) raises another important issue. The current spikes have to be supplied by the VCC source and, because of its finite source resistance, will result in voltage spikes (or “glitches”) superimposed on VCC. These voltage spikes could be coupled to other gates and flip-flops in the digital system and thus might produce false switching in other parts of the system. This effect, which might loosely be called crosstalk, is a problem in TTL systems. To reduce the size of the voltage spikes, capacitors (called bypass capacitors) should be connected between the supply rail and ground at frequent locations. These capacitors lower the impedance of the supply-voltage source and hence reduce the magnitude of the voltage spikes. Alternatively, one can think of the bypass capacitors as supplying the impulsive current spikes.

EXERCISES 14.8 Assuming that Q4 has , = 50 and that at the verge of saturation VCEsat = 0.3 V, find the value of iL at which Q4 saturates. Ans. 4.16 mA 14.9 Assuming that at a current of 1 mA the voltage drops across the emitter!base junction of Q4 and the diode D are each 0.7 V, find vO when iL = 1 mA and 10 mA. (Note the result of the previous exercise.) Ans. 3.6 V; 2.7 V 14.10 Find the maximum current that can be sourced by a TTL gate while the output high level (VOH) remains greater than the minimum guaranteed value of 2.4 V. Ans. 12.3 mA; or, more accurately, taking the base current of Q4 into account, 13.05 mA

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14.4 CHARACTERISTICS OF STANDARD TTL Because of its historical popularity and continued importance, TTL will be studied further in this and the next sections. In this section we shall consider some of the important characteristics of standard TTL gates. Special improved forms of TTL will be dealt with in Section 14.5.

Transfer Characteristic Figure 14.23 shows the TTL gate together with a sketch of its voltage transfer characteristic drawn in a piecewise-linear fashion. The actual characteristic is, of course, a smooth curve. We shall now explain the transfer characteristic and calculate the various break-points and slopes. It will be assumed that the output terminal of the gate is open. Segment AB is obtained when transistor Q1 is saturated, Q2 and Q3 are off, and Q4 and D are on. The output voltage is approximately two diode drops below VCC. At point B the phase splitter (Q2) begins to turn on because the voltage at its base reaches 0.6 V (0.5 V + VCEsat of Q1). Over segment BC, transistor Q1 remains saturated, but more and more of its base current I gets diverted to its base!collector junction and into the base of Q2, which operates as a linear amplifier. Transistor Q4 and diode D remain on, with Q4 acting as an emitter follower. Meanwhile the voltage at the base of Q3, although increasing, remains insufficient to turn Q3 on (less than 0.6 V). Let us now find the slope of segment BC of the transfer characteristic. Let the input vI increase by an increment 1vI. This increment appears at the collector of Q1, since the saturated Q1 behaves (approximately) as a three-terminal short circuit as far as signals are

(a)

(b)

FIGURE 14.23 The TTL gate and its voltage transfer characteristic.

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concerned. Thus at the base of Q2 we have a signal 1vI. Neglecting the loading of emitter follower Q4 on the collector of Q2, we can find the gain of the phase splitter from

v c2 –/2 R1 ------ = -----------------r e2 + R 2 v b2

(14.6)

The value of re2 will obviously depend on the current in Q2. This current will range from zero (as Q2 begins to turn on) to the value that results in a voltage of about 0.6 V at the emitter of Q2 (the base of Q3). This value is about 0.6 mA and corresponds to point C on the transfer characteristic. Assuming an average current in Q2 of 0.3 mA, we obtain re2 ! 83 *. For / = 0.98, Eq. (14.6) results in a gain value of 1.45. Since the gain of the output follower Q4 is close to unity, the overall gain of the gate, which is the slope of the BC segment, is about !1.45. As already implied, breakpoint C is determined by Q3 starting to conduct. The corresponding input voltage can be found from

v I ( C ) = VBE3 + VBE2 – VCEsat ( Q 1 ) = 0.6 + 0.7 – 0.1 = 1.2 V At this point the emitter current of Q2 is approximately 0.6 mA. The collector current of Q2 is also approximately 0.6 mA; neglecting the base current of Q4, the voltage at the collector of Q2 is

v C2 ( C ) = 5 – 0.6 . 1.6 3 4 V Thus Q2 is still in the active mode. The corresponding output voltage is

v O ( C ) = 4 – 0.65 – 0.65 = 2.7 V As vI is increased past the value of vI(C) = 1.2 V, Q3 begins to conduct and operates in the active mode. Meanwhile, Q1 remains saturated, and Q2 and Q4 remain in the active mode. The circuit behaves as an amplifier until Q2 and Q3 saturate and Q4 cuts off. This occurs at point D on the transfer characteristic, which corresponds to an input voltage vI(D) obtained from

v I ( D ) = VBE3 + VBE2 + VBC1 – VBE1 = 0.7 + 0.7 + 0.7 – 0.7 = 1.4 V Note that we have in effect assumed that at point D transistor Q1 is still saturated, but with VCEsat ! 0. To see how this comes about, note that from point B on, more and more of the base current of Q1 is diverted to its base!collector junction. Thus while the drop across the base!collector junction increases, that across the base!emitter junction decreases. At point D these drops become almost equal. For vI > vI(D) the base!emitter junction of Q1 cuts off; thus Q1 leaves saturation and enters the inverse active mode. Calculation of gain over the segment CD is a relatively complicated task. This is due to the fact that there are two paths from input to output: one through Q3 and one through Q4. A simple but gross approximation for the gain of this segment can be obtained from the coordinates of points C and D in Fig. 14.23(b), as follows:

vO ( C ) – vO ( D ) Gain = – -----------------------------------vI ( D ) – vI ( C ) 2.7 – 0.1 = – --------------------- = – 13 V/V 1.4 – 1.2

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From the transfer curve of Fig. 14.23(b) we can determine the critical points and the noise margins as follows: VOH = 3.7 V; VIL is somewhere in the range of 0.5 V to 1.2 V, and thus a conservative estimate would be 0.5 V; VOL = 0.1 V; VIH = 1.4 V; NMH = VOH ! VIH = 2.3 V; and NML = VIL ! VOL = 0.4 V. It should be noted that these values are computed assuming that the gate is not loaded and without taking into account power-supply or temperature variations.

EXERCISE 14.11 Taking into account the fact that the voltage across a forward-biased pn junction changes by about !2 mV/°C, find the coordinates of points A, B, C, and D of the gate transfer characteristic at !55°C and

at +125°C. Assume that the characteristic in Fig. 14.23(b) applies at 25°C, and neglect the small temperature coefficient of VCEsat. Ans. At !55°C: (0, 3.38), (0.66, 3.38), (1.52, 2.16), (1.72, 0.1); at +125°C: (0, 4.1), (0.3, 4.1), (0.8, 3.46), (1.0, 0.1)

Manufacturers’ Specifications Manufacturers of TTL usually provide curves for the gate transfer characteristic, the input i!v characteristic, and the output i!v characteristic, measured at the limits of the specified operating temperature range. In addition, guaranteed values are usually given for the parameters VOL, VOH, VIL, and VIH. For standard TTL (known as the 74 series) these values are VOL = 0.4 V, VOH = 2.4 V, VIL = 0.8 V, and VIH = 2 V. These limit values are guaranteed for a specified tolerance in power-supply voltage and for a maximum fan-out of 10. From our discussion in Section 14.3 we know that the maximum fan-out is determined by the maximum current that Q3 can sink while remaining in saturation and while maintaining a saturation voltage lower than a guaranteed maximum (VOL = 0.4 V). Calculations performed in Section 14.3 indicate the possibility of a maximum fan-out of 20 to 30. Thus the figure specified by the manufacturer is appropriately conservative. The parameters VOL, VOH, VIL, and VIH can be used to compute the noise margins as follows: NM H = VOH – VIH = 0.4 V NM L = VIL – VOL = 0.4 V

EXERCISES 14.12 In Section 14.3 we found that when the gate input is high, the base current of Q3 is approximately

2.6 mA. Assume that this value applies at 25°C and that at this temperature VBE ! 0.7 V. Taking into account the !2-mV/°C temperature coefficient of VBE and neglecting all other changes, find the base current of Q3 at !55°C and at +125°C. Ans. 2.2 mA; 3 mA

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14.13 Figure E14.13 shows sketches of the iL!vO characteristics of a TTL gate when the output is low. Use these characteristics together with the results of Exercise 14.12 to calculate the value of , of transistor Q3 at !55°C, +25°C, and +125°C.

FIGURE E14.13

Ans. 16; 25; 28

Propagation Delay The propagation delay of TTL gates is defined conventionally as the time between the 1.5-V points of corresponding edges of the input and output waveforms. For standard TTL (also known as medium-speed TTL) tP is typically about 10 ns. As far as power dissipation is concerned it can be shown (see Exercise 14.14) that when the gate output is high the gate dissipates 5 mW, and when the output is low the dissipation is 16.7 mW. Thus the average dissipation is 11 mW, resulting in a delay-power product of about 100 pJ.

EXERCISE 14.14 Calculate the value of the supply current (ICC), and hence the power dissipated in the TTL gate, when the output terminal is open and the input is (a) low at 0.2 V (see Fig. 14.22) and (b) high at +5 V (see Fig. 14.20). Ans. (a) 1 mA, 5 mW; (b) 3.33 mA, 16.7 mW

Dynamic Power Dissipation In Section 14.3 the occurrence of supply current spikes was explained. These spikes give rise to additional power drain from the VCC supply. This dynamic power is also dissipated in the gate circuit. It can be evaluated by multiplying the average current due to the spikes by VCC, as illustrated by the solution of Exercise 14.15.

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EXERCISE 14.15 Consider a TTL gate that is switched on and off at the rate of 1 MHz. Assume that each time the gate is turned off (that is, the output goes high) a supply-current pulse of 30-mA amplitude and 2-ns width occurs. Also assume that no current spike occurs when the gate is turned on. Calculate the average supply current due to the spikes, and the dynamic power dissipation. Ans. 60 µA; 0.3 mW

The TTL NAND Gate Figure 14.24 shows the basic TTL gate. Its most important feature is the multiemitter transistor Q1 used at the input. Figure 14.25 shows the structure of the multiemitter transistor. It can be easily verified that the gate of Fig. 14.24 performs the NAND function. The output will be high if one (or both) of the inputs is (are) low. The output will be low in only

FIGURE 14.24 The TTL NAND gate.

FIGURE 14.25 Structure of the multiemitter transistor Q1.

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FIGURE 14.26 A TTL AND-OR-INVERT gate.

one case: when both inputs are high. Extension to more than two inputs is straightforward and is achieved by diffusing additional emitter regions. Although theoretically an unused input terminal may be left open-circuited, this is generally not a good practice. An open-circuit input terminal acts as an “antenna” that “picks up” interfering signals and thus could cause erroneous gate switching. An unused input terminal should therefore be connected to the positive power supply through a resistance (of, say, 1 k*). In this way the corresponding base–emitter junction of Q1 will be reverse-biased and thus will have no effect on the operation of the gate. The series resistance is included in order to limit the current in case of breakdown of the base–emitter junction due to transients on the power supply.

Other TTL Logic Circuits On a TTL MSI chip there are many cases in which logic functions are implemented using “stripped-down” versions of the basic TTL gate. As an example we show in Fig. 14.26 the TTL implementation of the AND-OR-INVERT function. As shown, the phase-splitter transistors of two gates are connected in parallel, and a single output stage is used. The reader is urged to verify that the logic function realized is as indicated. At this point it should be noted that the totem-pole output stage of TTL does not allow connecting the output terminals of two gates to realize the AND function of their outputs (known as the wired-AND connection). To see the reason for this, consider two gates whose outputs are connected together, and let one gate have a high output and the other have a low output. Current will flow from Q4 of the first gate through Q3 of the second gate. The current value will fortunately be limited by the 130-* resistance. Obviously, however, no useful logic function is realized by this connection. The lack of wired-AND capability is a drawback of TTL. Nevertheless, the problem is solved in a number of ways, including doing the paralleling at the phase-splitter stage, as illustrated in Fig. 14.26. Another solution consists of deleting the emitter-follower transistor

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altogether. The result is an output stage consisting solely of the common-emitter transistor Q3 without even a collector resistance. Obviously, one can connect the outputs of such gates together to a common collector resistance and achieve a wired-AND capability. TTL gates of this type are known as open-collector TTL. The obvious disadvantage is the slow rise time of the output waveform. Another useful variant of TTL is the tristate output arrangement explored in Exercise 14.16.

EXERCISE 14.16 The circuit shown in Fig. E14.16 is called tristate TTL. Verify that when the terminal labeled Third state is high, the gate functions normally and that when this terminal is low, both transistors Q3 and Q4 cut off and the output of the gate is an open circuit. The latter state is the third state, or the high-outputimpedance state.

FIGURE E14.16

Tristate TTL enables the connection of a number of TTL gates to a common output line (or bus). At any particular time the signal on the bus will be determined by the one TTL gate

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that is enabled (by raising its third-state input terminal). All other gates will be in the third state and thus will have no control of the bus.

14.5 TTL FAMILIES WITH IMPROVED PERFORMANCE The standard TTL circuits studied in the two previous sections were introduced in the mid1960s. Since then, several improved versions have been developed. In this section we shall discuss some of these improved TTL subfamilies. As will be seen the improvements are in two directions: increasing speed and reducing power dissipation. The speed of the standard TTL gate of Fig. 14.24 is limited by two mechanisms: first, transistors Q1, Q2, and Q3 saturate, and hence we have to contend with their finite storage time. Although Q2 is discharged reasonably quickly because of the active mode of operation of Q1, as already explained, this is not true for Q3, whose base charge has to leak out through the 1-k* resistance in its base circuit. Second, the resistances in the circuit, together with the various transistor and wiring capacitances, form relatively long time constants, which contribute to lengthening the gate delay. It follows that there are two approaches to speeding up the operation of TTL. The first is to prevent transistor saturation and the second is to reduce the values of all resistances. Both approaches are utilized in the Schottky TTL circuit family.

Schottky TTL In Schottky TTL, transistors are prevented from saturation by connecting a low-voltagedrop diode between base and collector, as shown in Fig. 14.27. These diodes, formed as a metal-to-semiconductor junction, are called Schottky diodes and have a forward voltage drop of about 0.5 V. We have briefly discussed Schottky diodes in Section 3.9. Schottky diodes4 are easily fabricated and do not increase chip area. In fact, the Schottky TTL fabrication process has been designed to yield transistors with smaller areas and thus higher , and fT than those produced by the standard TTL process. Figure 14.27 also shows the symbol used to represent the combination of a transistor and a Schottky diode, referred to as a Schottky transistor.

(a)

4

(b)

FIGURE 14.27 (a) A transistor with a Schottky diode clamp. (b) Circuit symbol for the connection in (a), known as a Schottky transistor.

Note that silicon Schottky diodes exhibit voltage drops of about 0.5 V, whereas GaAs Schottky diodes (Section 5.12) exhibit voltage drops of about 0.7 V.

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

9.7 DATA CONVERTERS—AN INTRODUCTION In this section we begin the study of another group of analog IC circuits of great importance; namely, data converters.

9.7.1 Digital Processing of Signals Most physical signals, such as those obtained at transducer outputs, exist in analog form. Some of the processing required on these signals is most conveniently performed in an analog fashion. For instance, in instrumentation systems it is quite common to use a highinput-impedance, high-gain, high-CMRR differential amplifier right at the output of the transducer. This is usually followed by a filter whose purpose is to eliminate interference. However, further signal processing is usually required, which can range from simply obtaining a measurement of signal strength to performing some algebraic manipulations on this and related signals to obtain the value of a particular system parameter of interest, as is usually the case in systems intended to provide a complex control function. Another example of signal processing can be found in the common need for transmission of signals to a remote receiver. Many such forms of signal processing can be performed by analog means. In earlier chapters we encountered circuits for implementing a number of such tasks. However, an attractive alternative exists: It is to convert, following some initial analog processing, the signal from analog to digital form and then use economical, accurate, and convenient digital ICs to perform digital signal processing. Such processing can in its simplest form provide us with a measure of the signal strength as an easy-to-read number (consider, e.g., the digital voltmeter). In more involved cases the digital signal processor can perform a variety of arithmetic and logic operations that implement a filtering algorithm. The resulting digital filter does many of the same tasks that an analog filter performs—namely, eliminate interference and noise. Yet another example of digital signal processing is found in digital communications systems, where signals are transmitted as a sequence of binary pulses, with the obvious advantage that corruption of the amplitudes of these pulses by noise is, to a large extent, of no consequence. Once digital signal processing has been performed, we might be content to display the result in digital form, such as a printed list of numbers. Alternatively, we might require an analog output. Such is the case in a telecommunications system, where the usual output may be audible speech. If such an analog output is desired, then obviously we need to convert the digital signal back to an analog form. It is not our purpose here to study the techniques of digital signal processing. Rather, we shall examine the interface circuits between the analog and digital domains. Specifically, we shall study the basic techniques and circuits employed to convert an analog signal to digital form (analog-to-digital or simply A/D conversion) and those used to convert a digital signal to analog form (digital-to-analog or simply D/A conversion). Digital circuits are studied in Chapters 10 and 11.

9.7.2 Sampling of Analog Signals The principle underlying digital signal processing is that of sampling the analog signal. Figure 9.36 illustrates in a conceptual form the process of obtaining samples of an analog signal. The switch shown closes periodically under the control of a periodic pulse signal (clock). The closure time of the switch, τ, is relatively short, and the samples obtained are

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9.7 DATA CONVERTERS—AN INTRODUCTION

vO vI

" !

C

(a)

(b) vI

t

(c) vS

#

T

t

(d) vO

t

FIGURE 9.36 The process of periodically sampling an analog signal. (a) Sample-and-hold (S/H) circuit. The switch closes for a small part (τ seconds) of every clock period (T). (b) Input signal waveform. (c) Sampling signal (control signal for the switch). (d) Output signal (to be fed to A/D converter).

stored (held) on the capacitor. The circuit of Fig. 9.36 is known as a sample-and-hold (S/H) circuit. As indicated, the S/H circuit consists of an analog switch that can be implemented by a MOSFET transmission gate (Section 10.5), a storage capacitor, and (not shown) a buffer amplifier. Between the sampling intervals—that is, during the hold intervals—the voltage level on the capacitor represents the signal samples we are after. Each of these voltage levels is then fed to the input of an A/D converter, which provides an N-bit binary number proportional to the value of signal sample. The fact that we can do our processing on a limited number of samples of an analog signal while ignoring the analog-signal details between samples is based on the Shannon’s sampling theorem [see Lathi (1965)].

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

9.7.3 Signal Quantization Consider an analog signal whose values range from 0 to +10 V. Let us assume that we wish to convert this signal to digital form and that the required output is a 4-bit digital signal.4 We know that a 4-bit binary number can represent 16 different values, 0 to 15; it follows that the resolution of our conversion will be 10 V ⁄ 15 = 2--3- V. Thus an analog signal of 0 V will be represented by 0000, --23- V will be represented by 0001, 6 V will be represented by 1001, and 10 V will be represented by 1111. All these sample numbers are multiples of the basic increment ( --23- V). A question now arises regarding the conversion of numbers that fall between these successive incremental levels. For instance, consider the case of a 6.2-V analog level. This falls between 18/ 3 and 20 / 3. However, since it is closer to 18 / 3 we treat it as if it were 6 V and code it as 1001. This process is called quantization. Obviously errors are inherent in this process; such errors are called quantization errors. Using more bits to represent (encode or, simply, code) an analog signal reduces quantization errors but requires more complex circuitry.

9.7.4 The A/D and D/A Converters as Functional Blocks Figure 9.37 depicts the functional block representations of A/D and D/A converters. As indicated, the A/D converter (also called an ADC) accepts an analog sample vA and produces an N-bit digital word. Conversely, the D/A converter (also called a DAC) accepts an n-bit digital word and produces an analog sample. The output samples of the D/A converter are often fed to a sample-and-hold circuit. At the output of the S/H circuit a staircase waveform, such as that in Fig. 9.38, is obtained. The staircase waveform can then be smoothed by a

FIGURE 9.37 The A/D and D/A converters as circuit blocks.

vA

t

FIGURE 9.38 The analog samples at the output of a D/A converter are usually fed to a sample-and-hold circuit to obtain the staircase waveform shown. This waveform can then be filtered to obtain the smooth waveform, shown in color. The time delay usually introduced by the filter is not shown. 4

Bit stands for binary digit.

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9.8 D/A CONVERTER CIRCUITS

low-pass filter, giving rise to the smooth curve shown in color in Fig. 9.38. In this way an analog output signal is reconstructed. Finally, note that the quantization error of an A/D converter is equivalent to ± 1--2- least significant bit (bN).

EXERCISE 9.31 An analog signal in the range 0 to +10 V is to be converted to an 8-bit digital signal. What is the resolu-

tion of the conversion in volts? What is the digital representation of an input of 6 V? What is the representation of an input of 6.2 V? What is the error made in the quantization of 6.2 V in absolute terms and as a percentage of the input? As a percentage of full scale? What is the largest possible quantization error as a percentage of full scale? Ans. 0.0392 V; 10011001; 10011110; −0.0064 V; −0.1%; −0.064%; 0.196%

9.8 D/A CONVERTER CIRCUITS 9.8.1 Basic Circuit Using Binary-Weighted Resistors Figure 9.39 shows a simple circuit for an N-bit D/A converter. The circuit consists of a reference voltage VREF, N binary-weighted resistors R, 2R, 4R, 8R, . . . , 2N−1R, N single-pole double-throw switches S1, S2, . . . , SN, and an op amp together with its feedback resistance Rf = R / 2. The switches are controlled by an N-bit digital input word D, b b b D = -----11 + -----22 + . . . + -----NN2 2 2

(9.109)

where b1, b2, and so on are bit coefficients that are either 1 or 0. Note that the bit bN is the least significant bit (LSB) and b1 is the most significant bit (MSB). In the circuit in Fig. 9.39, b1 controls switch S1, b2 controls S2, and so on. When bi is 0, switch Si is in position 1, and when bi is 1 switch Si is in position 2. Since position 1 of all switches is ground and position 2 is virtual ground, the current through each resistor remains constant. Each switch simply controls where its corresponding current goes: to ground (when the corresponding bit is 0) or to virtual ground (when the corresponding bit is 1). The currents flowing into the virtual ground add up, and the sum flows VREF

FIGURE 9.39 An N-bit D/A converter using a binary-weighted resistive ladder network.

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

through the feedback resistance Rf. The total current iO is therefore given by V REF V REF V REF - bN - b + ---------- b + . . . + --------------i O = ---------N –1 R 1 2R 2 2 R 2V REF ⎛ b 1 b 2 . . . b N⎞ ----- + ----- + = -------------+ -----NR ⎝ 21 22 2 ⎠ Thus, 2V REF i O = --------------D R

(9.110)

vO = −iORf = −VREF D

(9.111)

and the output voltage vO is given by which is directly proportional to the digital word D, as desired. It should be noted that the accuracy of the DAC depends critically on (1) the accuracy of VREF, (2) the precision of the binary-weighted resistors, and (3) the perfection of the switches. Regarding the third point, we should emphasize that these switches handle analog signals; thus their perfection is of considerable interest. While the offset voltage and the finite on resistance are not of critical significance in a digital switch, these parameters are of immense importance in analog switches. The use of MOSFETs to implement analog switches will be discussed in Chapter 10. Also, we shall shortly see that in practical circuit implementations of the DAC, the binary-weighted currents are generated by current sources. In this case the analog switch can be realized using the differential-pair circuit, as will be shown shortly. A disadvantage of the binary-weighted resistor network is that for a large number of bits (N > 4) the spread between the smallest and largest resistances becomes quite large. This implies difficulties in maintaining accuracy in resistor values. A more convenient scheme exists utilizing a resistive network called the R-2R ladder.

9.8.2 R-2R Ladders Figure 9.40 shows the basic arrangement of a DAC using an R-2R ladder. Because of the small spread in resistance values, this network is usually preferred to the binary-weighted scheme discussed earlier, especially for N > 4. Operation of the R-2R ladder is straightforward. First, it can be shown, by starting from the right and working toward the left, that the

VREF

FIGURE 9.40 The basic circuit configuration of a DAC utilizing an R-2R ladder network.

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9.8 D/A CONVERTER CIRCUITS

resistance to the right of each ladder node, such as that labeled X, is equal to 2R. Thus the current flowing to the right, away from each node, is equal to the current flowing downward to ground, and twice that current flows into the node from the left side. It follows that I1 = 2I2 = 4I3 = . . . = 2N−1IN

(9.112)

Thus, as in the binary-weighted resistive network, the currents controlled by the switches are binary weighted. The output current iO will therefore be given by V REF -D i O = ---------R

(9.113)

9.8.3 A Practical Circuit Implementation A practical circuit implementation of the DAC utilizing an R-2R ladder is shown in Fig. 9.41. The circuit utilizes BJTs to generate binary-weighted constant currents I1, I2, . . . , IN, which are switched between ground and virtual ground of an output summing op amp (not shown). We shall first show that the currents I1 to IN are indeed binary-weighted, with I1 corresponding to the MSB and IN corresponding to the LSB of the DAC. Starting at the two rightmost transistors, QN and Qt , we see that if they are matched, their emitter currents will be equal and are denoted (IN /α). Transistor Qt is included to provide proper termination of the R-2R network. The voltage between the base line of the BJTs and node N will be I VN = VBE N + ⎛ ----N-⎞ ( 2R ) ⎝ α⎠ To virtual ground of output op amp

···

iO

··· VREF

!0 A

S1

IREF

S3

SN

RREF I1

!0 V "

S2

QREF

A1

!

Q1

IREF $ 2R

I2 Q2

I1 $

2R

R 3

IN QN

IN! 1 $ 2R

R 2

QN ! 1

I3 $ 2R

R 1

B ···

Q3 I2 $

2R

IN! 1

I3

··· N!1

Qt IN $

2R

IN $ 2R

R 2IN $

N

!VEE FIGURE 9.41 A practical circuit implementation of a DAC utilizing an R-2R ladder network.

927

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

where VBEN is the base–emitter voltage of QN. Since the current flowing through the resistor R connected to node N is (2IN /α), the voltage between node B and node (N − 1) will be 2I 4I N VN – 1 = VN + ⎛ --------N⎞ R = VBEN + --------R ⎝ α ⎠ α Assuming, for the moment, that VBE N –1 = VBE N , we see that a voltage of (4IN /α)R appears across the resistance 2R in the emitter of QN−1. Thus QN−1 will have an emitter current of (2IN /α) and a collector current of (2IN), twice the current in QN. The two transistors will have equal VBE drops if their junction areas are scaled in the same proportion as their currents, which is usually done in practice. Proceeding in the manner above we can show that I1 = 2I2 = 4I3 = . . . = 2N−1IN

(9.114)

under the assumption that the EBJ areas of Q1 to QN are scaled in a binary-weighted fashion. Next consider op amp A1, which, together with the reference transistor QREF, forms a negative-feedback loop. (Convince yourself that the feedback is indeed negative.) A virtual ground appears at the collector of QREF forcing it to conduct a collector current IREF = VREF / RREF independent of whatever imperfections QREF might have. Now, if QREF and Q1 are matched, their collector currents will be equal, I1 = IREF Thus, the binary-weighted currents are directly related to the reference current, independent of the exact values of VBE and α. Also observe that op amp A1 supplies the base currents of all the BJTs.

9.8.4 Current Switches Each of the single-pole double-throw switches in the DAC circuit of Fig. 9.41 can be implemented by a circuit such as that shown in Fig. 9.42 for switch Sm. Here Im denotes the current flowing in the collector of the mth-bit transistor. The circuit is a differential pair with the iO

VBIAS

VBIAS

FIGURE 9.42 Circuit implementation of switch Sm in the DAC of Fig. 9.41. In a BiCMOS technology, Qms and Qmr can be implemented using MOSFETs, thus avoiding the inaccuracy caused by the base current of BJTs.

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9.9 A/D CONVERTER CIRCUITS

base of the reference transistor Qmr connected to a suitable dc voltage VBIAS, and the digital signal representing the mth bit bm applied to the base of the other transistor Qms. If the voltage representing bm is higher than VBIAS by a few hundred millivolts, Qms will turn on and Qmr will turn off. The bit current Im will flow through Qms and onto the output summing line. On the other hand, when bm is low, Qms will be off and Im will flow through Qmr to ground. The current switch of Fig. 9.42 is simple and features high-speed operation. It suffers, however, from the fact that part of the current Im flows through the base of Qms and thus does not appear on the output summing line. More elaborate circuits for current switches can be found in Grebene (1984). Also, in a BiCMOS technology the differential-pair transistors Qms and Qmr can be replaced with MOSFETs, thus eliminating the base current problem.

EXERCISES 9.32 What is the maximum resistor ratio required by a 12-bit D/A converter utilizing a binary-weighted

resistor network? Ans. 2048 9.33 If the input bias current of an op amp, used as the output summer in a 10-bit DAC, is to be no more than that equivalent to 1--4- LSB, what is the maximum current required to flow in Rf for an op amp whose bias current is as great as 0.5 µA? Ans. 2.046 mA

9.9 A/D CONVERTER CIRCUITS There exist a number of A/D conversion techniques varying in complexity and speed. We shall discuss four different approaches: two simple, but slow, schemes, one complex (in terms of the amount of circuitry required) but extremely fast method, and, finally, a method particularly suited for MOS implementation.

9.9.1 The Feedback-Type Converter Figure 9.43 shows a simple A/D converter that employs a comparator, an up/down counter, and a D/A converter. The comparator circuit provides an output that assumes one of two

FIGURE 9.43 A simple feedback-type A/D converter.

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

distinct values: positive when the difference input signal is positive, and negative when the difference input signal is negative. We shall study comparator circuits in Chapter 13. An up/down counter is simply a counter that can count either up or down depending on the binary level applied at its up/down control terminal. Because the A/D converter of Fig. 9.43 employs a DAC in its feedback loop it is usually called a feedback-type A/D converter. It operates as follows: With a 0 count in the counter, the D/A converter output, vO, will be zero and the output of the comparator will be high, instructing the counter to count the clock pulses in the up direction. As the count increases, the output of the DAC rises. The process continues until the DAC output reaches the value of the analog input signal, at which point the comparator switches and stops the counter. The counter output will then be the digital equivalent of the input analog voltage. Operation of the converter of Fig. 9.43 is slow if it starts from zero. This converter however, tracks incremental changes in the input signal quite rapidly.

9.9.2 The Dual-Slope A/D Converter A very popular high-resolution (12- to 14-bit) (but slow) A/D conversion scheme is illustrated in Fig. 9.44. To see how it operates, refer to Fig. 9.44 and assume that the analog input signal vA is negative. Prior to the start of the conversion cycle, switch S2 is closed, thus discharging capacitor C and setting v1 = 0. The conversion cycle begins with opening S2 and connecting the integrator input through switch S1 to the analog input signal. Since vA is negative, a current I = vA/R will flow through R in the direction away from the integrator. Thus v1 rises linearly with a slope of I/ C = vA/RC, as indicated in Fig. 9.44(b). Simultaneously, the counter is enabled and it counts the pulses from a fixed-frequency clock. This phase of the conversion process continues for a fixed duration T1. It ends when the counter has accumulated a fixed count denoted nREF. Usually, for an N-bit converter, nREF = 2N. Denoting the peak voltage at the output of the integrator as VPEAK, we can write with reference to Fig. 9.44(b) vA V PEAK -------------- = ------T1 RC

(9.115)

At the end of this phase, the counter is reset to zero. Phase II of the conversion begins at t = T1 by connecting the integrator input through switch S1 to the positive reference voltage VREF. The current into the integrator reverses direction and is equal to VREF / R. Thus v1 decreases linearly with a slope of (VREF/RC). Simultaneously the counter is enabled and it counts the pulses from the fixed-frequency clock. When v1 reaches zero volts, the comparator signals the control logic to stop the counter. Denoting the duration of phase II by T2, we can write, by reference to Fig. 9.44(b), V PEAK V REF -------------- = ---------T2 RC

(9.116)

Equations (9.115) and (9.116) can be combined to yield vA ⎞ T2 = T1 ⎛ ---------⎝ VREF ⎠

(9.117)

Since the counter reading, nREF, at the end of T1 is proportional to T1 and the reading, n, at the end of T2 is proportional to T2, we have vA ⎞ n = n REF ⎛ ---------⎝ V REF ⎠

(9.118)

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9.9 A/D CONVERTER CIRCUITS

" VREF

(a)

VPEAK VREF RC

FIGURE 9.44 The dual-slope A/D conversion method. Note that vA is assumed to be negative.

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

VR 1

VR 2

VR (2 N ! 1)

Comparator 1

Bit 1

Comparator 2

Bit 2 Digital output

Logic ···

Analog input

···

932

Comparator 2N ! 1

Bit N

FIGURE 9.45 Parallel, simultaneous, or flash A/D conversion.

Thus the content of the counter,5 n, at the end of the conversion process is the digital equivalent of vA. The dual-slope converter features high accuracy, since its performance is independent of the exact values of R and C. There exist many commercial implementations of the dualslope method, some of which utilize CMOS technology.

9.9.3 The Parallel or Flash Converter The fastest A/D conversion scheme is the simultaneous, parallel, or flash conversion process illustrated in Fig. 9.45. Conceptually, flash conversion is very simple. It utilizes 2N − 1 comparators to compare the input signal level with each of the 2N − 1 possible quantization levels. The outputs of the comparators are processed by an encoding-logic block to provide the N bits of the output digital word. Note that a complete conversion can be obtained within one clock cycle. Although flash conversion is very fast, the price paid is a rather complex circuit implementation. Variations on the basic technique have been successfully employed in the design of IC converters.

9.9.4 The Charge-Redistribution Converter The last A/D conversion technique that we shall discuss is particularly suited for CMOS implementation. As shown in Fig. 9.46, the circuit utilizes a binary-weighted capacitor array, a voltage comparator, and analog switches; control logic (not shown in Fig. 9.46) is also required. The circuit shown is for a 5-bit converter; capacitor CT serves the purpose of terminating the capacitor array, making the total capacitance equal to the desired value of 2C. Operation of the converter can be divided into three distinct phases, as illustrated in Fig. 9.46. In the sample phase (Fig. 9.46a) switch SB is closed, thus connecting the top plate of all capacitors to ground and setting vO to zero. Meanwhile, switch SA is connected to the analog input voltage vA. Thus the voltage vA appears across the total capacitance of 2C, resulting in a stored charge of 2CvA. Thus, during this phase, a sample of vA is taken and a proportional amount of charge is stored on the capacitor array. 5

Note that n is not a continuous function of vA, as might be inferred from Eq. (9.118). Rather, n takes on discrete values corresponding to one of the 2N quantized levels of vA.

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9.9 A/D CONVERTER CIRCUITS

SB

Comparator

vO % 0 C 2

C S1

C 4 S2

C 8 S3

C 16 S4

C 16 S5

Control logic

" !

CT

ST SA

vA VREF

(a) SB

vO % ! vA C S1

C 2 S2

C 4 S3

C 8

C 16

S4

S5

C 16

" !

CT

ST SA

vA VREF

(b) SB

vO % 0 C S1

C 2

C 4

C 8

S2

S3

S4

C 16 S5

C 16

" !

CT

ST SA

vA VREF

(c) FIGURE 9.46 Charge-redistribution A/D converter suitable for CMOS implementation: (a) sample phase, (b) hold phase, and (c) charge-redistribution phase.

During the hold phase (Fig. 9.46b), switch SB is opened and switches S1 to S5, and ST are thrown to the ground side. Thus the top plate of the capacitor array is open-circuited while their bottom plates are connected to ground. Since no discharge path has been provided, the capacitor charges must remain constant, with the total equal to 2CvA. It follows that the voltage at the top plate must become −vA. Finally, note that during the hold phase, SA is connected to VREF in preparation for the charge-redistribution phase.

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CHAPTER 9 OPERATIONAL-AMPLIFIER AND DATA-CONVERTER CIRCUITS

Next, we consider the operation during the charge-redistribution phase illustrated in Fig. 9.46(c). First, switch S1 is connected to VREF (through SA). The circuit then consists of VREF, a series capacitor C, and a total capacitance to ground of value C. This capacitive divider causes a voltage increment of VREF ⁄ 2 to appear on the top plates. Now, if vA is greater than VREF ⁄ 2 , the net voltage at the top plate will remain negative, which means that S1 will be left in its new position as we move on to switch S2. If, on the other hand, vA was smaller than VREF ⁄ 2 , then the net voltage at the top plate would become positive. The comparator will detect this situation and signal the control logic to return S1 to its ground position and then to move on to S2. Next, switch S2 is connected to VREF, which causes a voltage increment of VREF ⁄ 4 to appear on the top plate. If the resulting voltage is still negative, S2 is left in its new position; otherwise, S2 is returned to its ground position. We then move on to switch S3, and so on until all the bit switches S1 to S5 have been tried. It can be seen that during the charge-redistribution phase the voltage on the top plate will be reduced incrementally to zero. The connection of the bit switches at the conclusion of this phase gives the output digital word; a switch connected to ground indicates a 0 value for the corresponding bit, whereas connection to VREF indicates a 1. The particular switch configuration depicted in Fig. 9.46(c) is for D = 01101. Observe that at the end of the conversion process, all the charge is stored in the capacitors corresponding to 1 bits; the capacitors of the 0 bits have been discharged. The accuracy of this A/D conversion method is independent of the value of stray capacitances from the bottom plate of the capacitors to ground. This is because the bottom plates are connected either to ground or to VREF; thus the charge on the stray capacitances will not flow into the capacitor array. Also, because both the initial and the final voltages on the top plate are zero, the circuit is also insensitive to the stray capacitances between the top plates and ground.6 The insensitivity to stray capacitances makes the charge-redistribution technique a reasonably accurate method capable of implementing A/D converters with as many as 10 bits.

EXERCISES 9.34 Consider the 5-bit charge-redistribution converter in Fig. 9.46 with VREF = 4 V. What is the voltage

increment appearing on the top plate when S5 is switched? What is the full-scale voltage of this converter? If vA = 2.5 V, which switches will be connected to VREF at the end of conversion? ------ V; S1 and S3 Ans. 1--8- V; 31 8 9.35 Express the maximum quantization error of an N-bit A/D converter in terms of its least-significant bit (LSB) and in terms of its full-scale analog input VFS. N Ans. ± 1--2- LSB; VFS ⁄ 2(2 – 1 )

9.10 SPICE SIMULATION EXAMPLE We conclude this chapter with an example to illustrate the use of SPICE in the simulation of the two-stage CMOS op amp. 6

More precisely, the final voltage can deviate from zero by as much as the analog equivalent of the LSB. Thus, the insensitivity to top-plate capacitance is not complete.