THIRD YEAR LABORATORY SEE3732 SESION 2010/2011 SEMESTER 1 BASIC ELECTRONICS LABTORARY LONG REPORT: AMPLIFIER FREQUENCY RESPONSE (BJT)
NAME
: MUHAMMAD SAUKANI BIN ABDUL HALIM AZIZI
IC
: 881230085891
MATRIX NO
: BE090138
COURSE
: 3SEC
SECTION
:8
GROUP
: 15
GROUP MEMBER: WONG KING KIAT & LIEW SHAN SUNG SUPERVISOR
: DR. RUBITA SUDIRMAN
DATE
: 23 SEPTEMBER 2010
TITLE
:AMPLIFIER FREQUENCY RESPONSE (BJT)
Title: Amplifier Frequency Response (BJT) Objectives 1. To obtain the frequency response of a BJT amplifier circuit. 2. To determine the lower cutoff frequency and the upper cutoff frequency of a BJT amplifier circuit. 3. To determine the midband gain, A mid of a BJT amplifier circuit. 4. To determine the input resistance, r in and the output resistance, r o of a BJT amplifier circuit.
List of Apparatus Components 1. Transistor: BC109 (or equivalent general purpose npn) 2. Resistor: 150kΩ, 33kΩ, 4.7kΩ, 680Ω(2) 3. Capacitor: 0.22μF (2), 0.047μF, 470μF, 0.01μF(2)
Equipments 1. Power Supply (TW63414) 2. Oscilloscope (B019785) 3. Function Generator (4020024535) 4. Digital Multimeter (3146A25078)
Power Supply Oscilloscope
Function Generator
Digital Multimeter
Introduction The input frequency of an amplifier is not only one fixed frequency; it can be in a range from low to high frequency. The ideal amplifier is supposed to operate at all frequency with the same output gain. The input resistance, r in and the output resistance, r o of an ideal amplifier will not change with input frequency. The phase different between input and output of an ideal amplifier will not be affected by frequency changes. Practical amplifiers do not exhibit the features of the ideal amplifier because of the coupling and bypass capacitor effect in low frequency range, and stray capacitance and transistor capacitance effects in high frequency range. The midband range is the r egion where coupling and bypass capacitors act as short circuits, and stray and transistor capacitances act as open circuits. In this region, the gain is almost a constant. The gain at f=f L and at f=f H is 3dB less than the maximum midband gain. The bandwidth of the amplifier (in Hz) is defined as f BW=f H-f L. Av(dB)
Low-frequency range
Midband
High-frequency range
Amid 3dB
f(Hz)
f L
f H
Frequency response of a practical amplifier
The frequency response begins with the low-frequency range designated between 0Hz and lower cutoff frequency. The output gain is equal to 0.707A mid, where Amid is the constant midband gain. The higher frequency range covers frequency between upper cutoff frequency and above. The output gain at f H is similarly 0.707Amid. The gain increase in low-frequency range until the maximum value in minband frequency and decrease in high-frequency range which dies off eventually.
The Lower Frequency Response
The reactance of capacitor, X C
1 2 fC
. The impedance of coupling and bypass capacitor
decrease as the frequency increase. Thus the voltage gain of BJT amplifier increase as the frequency increase. At very low frequencies, the capacitive reactance may become large enough to drop some of the input voltage and output voltage. Also the emitter-bypass capacitor may no longer short the emitter resistor to ground. The following equation can be use to approximate the lower-cutoff frequency of the amplifier . f 1
1 2 r in C 1
where, f 1 = lower cutoff frequency due to C 1 C1=input coupling capacitance (C 11 //C12) rin=input resistance of the amplifier f 2
1 2 r o C 2
where, f 2 = lower cutoff frequency due to C 2 C2=output coupling capacitance ro=output resistance of the amplifier f 1 and f 2 are not close in value. The actual lower cutoff frequency is approximately the larger frequency.
The Midband Response
In this range all capacitors are assumed to have very small effect on the circuit. Capacitors are considered as short circuit or no voltage drop over them. Stray and transistor capacitive reactance is still at a very large value and considered to be open circuit. Hence, the gain in this range will be constant and not affected by frequency changes. The gain in midband is the largest and is known as A mid.
The Upper Frequency Response
The capacitive reactance of a capacitor decrease as frequency increase. This can lead to problems for amplifiers used for high-frequency amplification. Transistor has inherent shunt capacitances between each pair of terminals. These capacitances effectively short the ac signal voltage
Signals lost through transistor capacitances
Part of signals lost through stray capacitances
For the circuit in Figure 2, the upper cutoff frequency, f H due to shunt capacitor C B and feedback capacitance C C, can be closely approximate using the following general equations: f H
1 1
f ' A
1
f ' B
where, f ' A
1 2 r s C ' A
and f ' B
1 2 r O C B
where, CA and CB are modified by adding the Miller-effect capacitance, which is the interelectrode feedback capacitance C CB modified by the gain A mid as follows: C’A = CA + (1-Amid) CC , C’B = CB + (1-1/Amid)CC
where, Amid = the voltage gain from input-to-load midband. However, capacitor Cp11 and Cp12 are used to subdue these shunt capacitance effects. So, f H can be evaluate approximately by 1 f ' H 2 r O C p ' where, Cp’ =Cp11//Cp12
Method Preliminary work 1. Simulated frequency response, voltage gain versus frequency of the amplifier circuit given in figure 2 was produced using MULTISIM or any equivalent software. 2. The response was printed, and observed to determine the midband gain, A mid, lower cutoff frequency, f L and upper cutoff frequency, f H. All value was recorded. Experimental procedure 1. Apparatus and all necessary connections was setup to carry out the required experimental work in determining the frequency response of the amplifier circuit as shown in figure 2. 2. Voltage was applied to the circuit. The base, the collector and the emitter voltage of the transistor was measured and recorded. 3. A sinusoidal input signal, Vi, with voltage of 1volt peak-to-peak value at frequency 5Hz was applied to test the circuit. 4. The output voltage, Vo was measured, recorded and the Av=Vo/Vi was calculated. The phase different between input and output signals were also measured and record in the table. 5. The signal frequency was increased with the input signal always constant to get another set of output voltage, Vo, voltage gain and signals phase difference. 6. A frequency response table was created to tabulate the readings with frequency, input voltage, output voltage, voltage gain, phase difference, and the phase angle. 7. All necessary readings to cover frequency band between 5Hz and 50 kHz was produced. The input voltage was maintained constant. 8. The frequency response of (i) voltage gain in dB versus frequency, and (ii) phase response versus frequency was plotted on a semi-log paper.
Figure2: Amplifier circuit for the frequency response experiment
Results Preliminary work (simulation) results
Mid band gain, A mid = 16.406dB
Lower cutoff frequency, f L =28.066 Hz
Upper cutoff frequency, f H =16.41 kHz
Experimental results A. Transistor Measured Voltages βfor transistor assumed to be 275
VB 2.059V
VC 7.04V
VE 1.445V
IC (calculated) 1.0553mA
IB (calculated) 5.2127μA
B. Frequency Response Table Freq(Hz) Vi(peakVo(peakpeak)(V) peak)(V)
Av=Vo/Vi Av(dB)= θ(phase (V) 20logvo/vi difference)
5 8 10 15 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 900 1000 2000 3000 4000 5000 10000 15000 18000 24000 27000 30000 40000 45000 50000
1.4021 2.0816 2.6186 3.5052 4.1649 4.8889 5.4433 5.6122 5.7143 5.7778 6.0206 6.0412 6.0619 6.2474 6.1837 6.2887 6.1818 6.3093 6.2245 6.0594 6.1200 6.0196 6.1212 6.0600 6.1429 5.8235 5.1731 4.6337 4.2157 3.5686 3.3592 3.0980 2.5243 2.1553 2.0762
0.97 0.98 0.97 0.97 0.97 0.99 0.97 0.98 0.98 0.99 0.97 0.97 0.97 0.97 0.98 0.97 0.99 0.99 0.98 1.01 1.00 1.02 0.99 1.00 0.98 1.02 1.04 1.01 1.02 1.02 1.03 1.02 1.03 1.03 1.05
1.36 2.04 2.54 3.40 4.04 4.84 5.28 5.50 5.60 5.72 5.84 5.86 5.88 6.06 6.06 6.10 6.12 6.12 6.10 6.12 6.12 6.14 6.06 6.06 6.02 5.94 5.38 4.68 4.30 3.64 3.45 3.16 2.60 2.22 2.18
2.9353 6.3681 8.3612 10.8941 12.3922 13.7846 14.7172 14.9827 15.1392 15.2353 15.5928 15.6225 15.6521 15.9140 15.8249 15.9712 15.8220 15.9996 15.8821 15.6486 15.7350 15.5914 15.7367 15.6495 15.7674 15.3037 14.2750 13.3185 12.4974 11.6500 10.5348 9.8217 8.0427 6.6703 6.3453
82.21 75.69 69.47 58.06 48080 38.94 28.78 23.66 21.74 19.14 16.37 11.99 9.329 4.520 2.560 0.920 -1.188 -1.020 -2.269 -1.674 -3.059 -4.899 -8.064 -10.42 -12.19 -16.23 -32.23 -44.05 -43.75 -56.87 -56.42 -65.66 -65.51 -68.23 -68.99
Phase angle= 180°+θ 262.21 255.69 249.47 238.06 228.80 218.94 208.78 203.66 201.74 199.14 196.37 199.99 189.33 184.52 182.56 180.92 178.81 178.98 177.73 178.32 176.94 175.10 171.93 169.58 167.81 163.77 147.77 135.95 136.25 123.13 123.58 114.34 114.49 111.77 111.01
Graph of frequency response Plotted using Microsoft Excel
Frequency Response
18 16 14 12 ) B10 d ( v A 8
6 4 2 0 1
10
100
1000
10000
100000
Frequency (Hz)
Phase Angel vs frequency 300
250 ) e e r 200 g e d ( l e 150 g n A e s 100 a h P
50
0 1
10
100
1000
Frequency (Hz)
10000
100000
C. Measured Frequency Response Parameters (from the plotted graph)
Lower cutoff frequency, f L =28 Hz Midband gain, Amid =15.9 dB Upper cutoff frequency, f H =16 kHz Phase angle at lower cutoff frequency =217.5° Phase angle at midband frequency =175 ° Phase angle at upper cutoff frequency =135 °
Question and Discussion 1. What are the simulated values of f L, Amid and f H for the common-emitter amplifier in figure 2? Compare these values with the cutoff frequencies obtained from the measured values -The simulated values of fl ,Amid and fh for common-emmiter amplifier are 25.632 Hz, 16.391 dB and 17.564 kH z respectively, meanwhile the measured values of fl, Amid and fh from the expirement are ,28 Hz,15.9 dB and 16 kHz. - By comparing these two set of data , it is observed that the measured on reading values are generally different than simulated results with percentage error for fl is 9.23% ,Av is 8.49% and fh is 8.88% .This may due to the instrumentation error in adjusting the precise values of Vc and input frequency as well as internal capacitance and resistance of the amplifier cir cuit 2. Which capacitor affects on the lower cutoff frequency and the upper cutoff frequency of the amplifier circuit? -Coupling capacitor (C11 and C12 ) and bypass capacitor (C E) affects on the lower cutoff frequency -Cp11 and Cp12, stray capacitor (wiring)and transistor terminal capacitance affects on the upper cutoff frequency. 3. With cutoff frequencies known, find the input resistance, r in, and the output resistance, rO , of the amplifier circuit ri calculated using simulation result: 1 1 1 f L 2 r i C 1 2 r i C 11 // C 12 2 r i (0.22 // 0.047 ) 25.632 Hz
r i
1 2 r i (0.22 // 0.047 )
23.255k
ri calculated using experimental result: 1 1 1 f L 2 r i C 1 2 r i C 11 // C 12 2 r i (0.22 // 0.047 ) 28 Hz
r i
1 2 r i (0.22 // 0.047 )
21.2888k
ro calculated using simulation result: 1 1 1 f H 2 r o C P ' 2 r o (C 11 // C 12 ) 2 r o (0.001 // 0.001 ) 17.564kHz
r o
1 2 r o (0.001 // 0.001 )
4.5307k
ro calculated using experimental result: 1 1 1 f H 2 r o C P ' 2 r o (C 11 // C 12 ) 2 r o (0.001 // 0.001 ) 16kHz
r o
1 2 r o (0.001 // 0.001 )
4.9736k
4. Obtain the empirical function to describe the measured frequency response of the amplifier circuit? -From the graph plotted ,the gain will drop 20 dB for eery decrease in frequency until the gain approachs zero. If the frequency drop in a factord of 2 ( (octave), the gain will drop dy 6 dB. The same thing happens for frequency higher than fh, whereby the gain drops by 20 dB per decade for the increase of frequency. - For midband frequency, the graphhremains constan without being affected by frequency changes -Also , by reffering to the graph plotted , the output signalis anti phase (in difference of 180°) to the input signalat midband frequency. The phase angle is decresing from lower to higher frequency. 5. Discuss your observation on the simulated and the measured frequency response - The measured results which obtain from the plotted graph are slightly different from the simulated results. This due to the errors from the instruments, environment and human. The instrument errors are due to the precision of value measured and supplies by the instrument. (Example: function generator and oscilloscope). The environment error its mainly due to the environment temperature. The human error is due to the adjustment made by human on asserting the input value. By referring to the plotted graph, it is observed that the graph pattern not as smooth as the simulated graph. There are certain points which deviate from the actual graph pattern. Thus, the values of Amid , fl and fh are different from the simulated results.
Conclusion The frequency response of a BJT amplifier circuits can be obtained through two method: by simulation and by experiment. The simulation of the BJT amplifier circuit is done by using Multism Software , meanwhile the measured values of frequency response for BJT amplifier circuit is obtained by measuring and calculating the amplifier gain for a specific frequency range, which is later plotted as bode plot to simplify the analysis of fr equency response of Bjt amplifier circuit. The lower cutoff frequency and the upper cutoff of BJT amplifier circuit are determined by determining the values of Amid first and later find the frequency when the amplifier gain is 0.707 Amid. The smaller values of the respective frequencies obtained is the lower cutoff frequency meanwhile the another would be upper cutoff fr equency. The midband gain, Amid of the BJT amplifier circuit is determinedby taking the highest values of amplifier gain for a specified frequency range applied to the amplifier circuit. The input resistance, r i of the BJT amplifier circuit is calculated by using the following equation: f L
1 2 r i C 1
Where
1 2 r i C 11 // C 12
fl = lower cutoff frequency C11,C12 =coupling capacitor
The output resistance ,r o of the BJT amplifier circuit is calculated by using the following equation f H
1 2 r o C P '
1 2 r o (C 11 // C 12 )
Where fh = upper cutoff frequency Cp11,Cp12=capacitor connected parallel to the output terminal
References Siti Hawa Ruslan, Puspa Inayat Khalid, Ismawati Abdul Ghani (2003): Elektronik 2 Modul Pengajaran Edisi ke-3, FKE UTM.
