Electrical Handbook Formula Book Sample

E EF O R M U L AB O O K

S A M P L EC O P Y

Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

HANDBOOK & FO RM U LA B OO K for G A TE , IE S , JTO , P S U’ s & S S C

ELECTRICAL ENGINEERING Published by Engineers Institute of India



S A M P L EC O P Y

© 2016 By Engineers Institute of Ind ia ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical & chemical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems.

Engineers Institute of India

28-B/7, Jia Sarai, Near IIT Hauz Khas New Delhi-110016 Tel: 011-26514888 For publication information, visit www.engineersinstitute.com/publication ISBN: 978-93-5156-854-4

Price: Rs. 349/-



S A M P L EC O P Y

A WORD TO THE STUDENTS

GATE and Engineering Services Examinations are the most prestigious competitive examinations conducted for graduate engineers. Over the past few years, they have become more competitive as more and more numbers of aspirants are increasingly becoming interested in post graduate qualifications & government jobs for a secured and bright career. This Formula Book consists of well-illustrated concepts, important formulae and diagrams, which will be highly beneficial at the last leg of candidate’s preparation. It includes all the subjects of Electrical Engineering, which are required for all type of competitive examinations. Adequate emphasis has been laid down to all the major topics in the form of Tips / Notes, which will be highly lucrative for objective and short answer type questions. Proper strategy and revision is a mandatory requirement for clearing any competitive examination. This book covers short notes and formulae for Electrical Engineering. This book will help in quick revision before the GATE, IES & all other PSUs. This book has been designed after considering the current demand of examinations. It would be very fruitful if the students go through this book every day. We are presenting this book by considering all the facts which is required to get success in the competition.

With best wishes for future career R. K. Rajesh Director Engineers Institute of India [email protected]



S A M P L EC O P Y

This book isdedicated to all ElectricalEngineers Preparing for GATE, IES, J TO, SSC & Public sector examinations.



S A M P L EC O P Y

CONTENTS

1.

NET WORK TH EORY ....... ...... ...... ...... ...... ...... ...... ... 01 -40

2.

CONT ROL SYSTEM S.... ...... ...... ...... ...... ..... ....... ...... 41 -74

3.

DIGITAL EL EC TRONICS AND CIRC UI TS .. .. .. .. .. .. .. 75-118

4.

MI CRO PRO CES SOR S ... ... ... .... .... .... .... ... ... .... .... ... .. 11 9-136

5.

EL EC TRONIC DE VICES & CIRCUITS

6.

ANAL OG EL EC TRONICS

.. .. .. .. .. .. .. .. .. .. .. ... ... .. .. .. .. .. 169 -204

7.

SIGNAL S AND SYSTEMS

.. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. 205 -230

8.

CO MMUN ICATION SYS TEMS .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. 231 -264

9.

EL EC TROMAG NETIC THEORY .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 265 -286

.. .. .. .. .. .. .. .. .. .. 137 -168

1 0 . ME AS URE ME NTS AND INSTR UME NTATIO N .. .. .. . 287- 308 1 1 . EL EC TRICAL MACHINES .. .. .. .. .. .. .. .. .. .. .. ... ... .. .. .. .. . 309 -392 1 2 . POW ER SYSTEMS ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 39 3-448 1 3 . POW ER ELE CTRONICS ... .... ... ... ... .... .... .... .... ... ... .. 44 9-504 1 4 . EL EC TRICAL MA TERIAL S .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. ..

505 -518



S A M P L EC O P Y

Why IES? Indian engineering services (IES) constitute of engineers that work under the govt. of India to manage a large segment of public sector economy which constitutes of Railroads, Public works, Power, Telecommunications, etc. IES remain the most sought-after careers for the engineering graduates in India. A combined competitive examination is conducted by UPSC for recruitment to the Indian Engineering Services. The exam constitutes of a written exam followed by an interview for personality test.

Why GATE? In the present competitive scenario, where there is mushrooming of universities and engineering colleges, the only yardstick to measure and test the calibre of engineering students is the GATE.

The GATE Advantage Many public sector undertakings such as BHEL, IOCL, NTPC, BPCL, HPCL, BARC and many more PSUs are using the GATE score for selecting candidates for their organizations. Students who qualify in GATE are entitled to a stipend of Rs 8,000 per month during their M.Tech. course. Better remuneration is being offered for students of M.Tech./ME as compared to those pursuing B.Tech/B.E. A good rank assures a good job. After joining M.Tech. at IITs and IISc, one can look at a salary package ranging from Rs 7lakh to 30lakh per annum depending upon specialization and performance. Qualifying GATE with good marks is also an eligibility clause for the award of JRF in CSIR Laboratories.



S A M P L EC O P Y

1 N E T W OR K T H E OR Y CONTENTS 1.

NE TWO RK BA SIC S ………………………………………………. 02- 05

2.

ME THO D S O F A NA L YS IS A ND THE O R E MS ……………. . 06 -10

3.

A C F UN D A ME NT A L S A ND R , L , C C IR C UI TS …………. .

4.

RE SO NA NCE ……………………………………………………….

16- 18

5.

TR AN S IE NTS ………………………………………………………

19- 22

6.

G R A P H THEO R Y ………………………………………………….

23- 26

7.

TW O P O R T NE TW O R KS ……………………………………….

27 -30

8.

MA G NE TIC C O UP L E D C IR C UIT S …………………………. .

31 -32

9.

F IL TE R S …………………………………………………………….

33- 36

10.

NE TW O R K S YNTHE S IS ……………………………………….

37- 40

11 -15



S A M P L EC O P Y

1. N ETWOR K BAS ICS Current: Electric current is the time rate of change of charge flow. dq i (Ampere) dt t

Charge transferred between time to and t



q  idt to

Sign Convention: A negative current of –5A flowing in one direction is same as a current of +5A in opposite direction. Voltage: Voltage or potential difference is the energy required to move a unit charge through an element, measured in volts.

Power: It is time rate of expending or absorbing energy.

 

Law of conservation of energy must be obeyed in any electric circuit. Algebraic sum of power in a circuit, at any instant of time, must be zero. i.e. P = 0 Circuit Elements: Resistor: Linear and bilateral (conduct from both direction) In time domain V(t) = I(t)R In s domain V(s) = RI(s)

R= l = length of conductor,



ρl A

ohm

 = resistivity, A = area of cross section

Extension of wire to n times results in increase in resistance:

R '  n2R





S A M P L EC O P Y

R'

Compression of wire results in decrease in resistance:

R n2

Capacitor: All capacitors are linear and bilateral, except electrolytic capacitor which is unilateral. Time Domain:

i(t)=

Cdv(t) dt

t

1

i(t)dt C

v(t) 



1 I(s) sC  Capacitor doesn’t allow sudden change of voltage, until impulse of current is applied.  It stores energy in the form of electric field and power dissipation in ideal capacitor is zero. 1  Impedance Zc =-jXc  &X c = ; Xc  Capacitive reactance ;  = 2f ωC Inductor: Linear and Bilateral element In s-domain:

I(s) = sCV(s)

Time Domain:

vt ( )L

Impedance

 

(vtdt) 

ti

dt

t

1

L

()



&

 XL ωL

I(s) = 1 V(s) sL Inductor doesn’t allowed sudden change of current, until impulse of voltage is applied. It stores energy in the form of magnetic field. Power dissipation in ideal inductor is zero.

In s-domain



di(t )

  jX L

ZL

V(s) =

V(s) = sL I(s)

Transformer: 4 terminal or 2-port devices. I1

I2

+

+

Input V1 port

N1

N2

V2

– N1

–

 N 2 : Step down transformer V1 V2

Output port



N2

N1

I1

N2

I2

 N1 : Step up transformer



N2 N1



Where

N1 N2

S A M P L EC O P Y

 K  Turns ratio .

Transformer doesn’t work as amplifier because current decreases in same amount power remain constant. Gyrator: I1

I2

Ro

V2

V1

Ro V1

  

 Coefficient of Gyrator  R o I2

V2

  Ro

I1

If load is capacitive then input impedance will be inductive and vice versa. If load is inductive then input impedance will be capacitive. It is used for simulation of equivalent value of inductance.

Voltage Source:

In practical voltage source, there is small internal resistance, so voltage across the element varies with respect to current.



Ideal voltmeter, RV → ∞ (Internal resistance)

Current Source:

In practical current source, there is small internal resistance, so current varies with respect to the voltage across element. Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888




S A M P L EC O P Y

Ideal Ammeter, Ra → 0 (Internal resistance)

Dependent and Independent Source: Independent Source: Voltage or current source whose values doesn’t depend on any other parameters. E.g. Generator etc. Dependent Source: Voltage or current source whose values depend upon other

parameters like current, voltage. The handling of independent and dependent voltage source is identical except. (i) In Thevenin and Norton Theorem (ii) Superposition Theorem Where, (i) All independent voltage sources are short circuited. (ii) All independent current sources are open circuited. (iii) All dependent voltage and current sources are left as they are.  A network in which all network elements are physically separable is known as lumped network.  A network in which the circuit elements like resistance, inductance etc, are not physically separate for analysis purpose, is called distributed network. E.g. Transmission line.



S A M P L EC O P Y

2 CO N T RO L SYSTEM S

CONTENTS

1.

BL OC K DIA GR AM ………………………………………………… 42- 44

2.

MA THE MA TIC A L MO D E L L ING ………………………………. 45 -46

3.

TIM E R E S P O NS E A NA L YS IS …………………………………

47 -52

4.

S TA B IL ITY ………………………………………………………….

53- 55

5.

RO O T LO CU S ……………………………………………………… 56- 58

6.

F R E Q UE NC Y D O MA IN A NA L YS IS ………………………….

59 -60

7.

P O L A R PL O TS ……………………………………………………

61 -64

8.

B O D E P L O TS ……………………………………………………. .

65 -68

9.

C O MP EN S A TO R S ………………………………………………. .

69- 72

10.

S TATE SP AC E ANA LYS IS …………………………………….

73- 74



S A M P L EC O P Y

1. BLOCK DIAGRAM Open Loop Control System:

 

In this system the output is not fedback for comparison with the input. Open loop system faithfulness depends upon the accuracy of input calibration.

When a designer designs, he simply design open loop system. Closed Loop Control System: It is also termed as feedback control system. Here the output has an effect on control action through a feedback. Ex. Human being Transfer Function:

Transfer function =

C(s) R(s)



G(s) 1 + G(s)H(s)

Comparison of Open Loop and Closed Loop control systems: Open Loop:

1. 2. 3. 4.

Accuracy of an open loop system is defined by the calibration of input. Open loop system is simple to construct and cheap. Open loop systems are generally stable. Operation of this system is affected due to presence of non-linearity in its elements.

Closed Loop: 1. As the error between the reference input and the output is continuously measured through feedback. The closed system works more accurately. 2. Closed loop systems is complicated to construct and it is costly. 3. It becomes unstable under certain conditions. 4. In terms of performance the closed loop system adjusts to the effects of nonlinearity present. Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

Transfer Function: The transfer function of an LTI system may be defined as the ratio of Laplace transform of output to Laplace transform of input under the assumption G(s)=

Y(s) X(s)



The transfer function is completely specified in terms of its poles and zeros and



the gain factor. The T.F. function of a system depends on its elements, assuming initial conditions as zero and is independent of the input function.



To find a gain of system through transfer function put s = 0

Example:

G(=s)

s2

s4 Gain =  6s  9

4 9

If a step, ramp or parabolic response of T.F. is given, then we can find Impulse Response directly through differentiation of that T.F.

d dt

(Parabolic Response) = Ramp Response

d (Ramp Response) = Step Response dt d dt

(Step Response) = Impulse Response

Block Diagram Reduction: Rule OriginalDiagram X1G1G2 1. Combining X1G1 X1 blocks in G1 G2 cascade

EquivalentDiagram X1 G 1 G 2 X1 G1G2



S A M P L EC O P Y

2. Moving a summing point after a block

3. Moving a summing point ahead of block

X1

4. Moving a take off point after a block

X1G

X1

X1 X1

5. Moving a take off point ahead of a block

G

1/G

X1 G

X1 G

X1

X1G

X1 G

6. Eliminating a feedback loop

X1G

G

X1

X1G

G

G

G

X2

1GH

(GX ±X ) 1

2

Signal Flow Graphs:  It is a graphical representation of control system.



Signal Flow Graph of Block Diagram:



Mason’s Gain Formula:

pk

S A M P L EC O P Y

Transfer function =

 pk  k 

 Path gain of k th forward path

  1 – [Sum of all individual loops] + [Sum of gain products of two non-touching loops] – [Sum of gain products of 3 non-touching loops] + ………..

 k  Value of  obtained by removing all the loops touching k thforward path as well as non-touching to each other



S A M P L EC O P Y

3 DIGI T AL EL EC T RONI CS AND C IRC U I TS CONTENTS

1.

NUMB E R S YS TE M & CO D E S …………………………………. 76- 78

2.

B INA R Y AI RT HME TIC …………………………………………. . 79- 82

3.

L OG IC G ATE S ……………………………………………………..

4.

D IG ITA L LO G IC C IR C UITS ……………………………………. 90- 95

5.

S E Q UE NTIA L C IR C UITS ……………………………………….

96- 100

6.

S HIF T R E G IS TE R S ………………………………………………

101- 102

7.

C O UNTE R S …………………………………………………………

103- 105

8.

D IG ITA L L O G IC F A MIL Y ………………………………………

106 -11 2

9.

A D C s A ND D A C s ………………………………………………

11 3- 11 6

10.

ME MO RIE S ………………………………………………………..

83- 89

117- 118



S A M P L EC O P Y

1. NUMBE R S YSTE M & CO DE S Number System and Codes:

A number system with base ‘ r’, contents ‘r’ different digits and they are from 0 to r – 1. Decimal to other codes conversions: To convert decimal number into other system with base ‘r’, divide integer part by r and multiply fractional part with r.

Other codes to Decimal Conversions: ( x2 x1 x0 . y1 y 2 ) r A x r2 2 x  r 1 x

y 0r

y r1

 (A)10 2

1

2

Hexadecimal to Binary: Convert each Hexadecimal digit into 4 bit binary.

(5 AF )16



(0101 1010 1111)2 5

A

F

Binary to Hexadecimal: Grouping of 4 bits into one hex digit. (110101.11) 2

 00110 101. 1100  (35.C)16   

Octal to Binary and Binary to Octal: Same procedure as discussed above but here group of 3 bits is made.



S A M P L EC O P Y

Codes: Binary coded decimal (BCD):



In BCD code each decimal digit is represented with 4 bit binary format.

Eg : (943)10



  1001 0100 4  9



0011

  

9

 BCD

It is also known as 8421 code Invalid BCD codes Total Number possible Valid BCD codes



24



16

10

Invalid BCD codes 16  10  6 These are 1010, 1011, 1100, 1101, 1110, and 1111

Excess-3 code: (BCD + 0011)

 

It can be derived from BCD by adding ‘3’ to each coded number. It is unweighted and self-complementing code.

Gray Code:

It is also called minimum change code or unit distance code or reflected code.

Binary code to Gray code:

+ + MSB 10010

MSB 11011

+

+

Binary

Gray

Gray code to Binary code: Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

Alpha Numeric codes: EBCDIC (Extended BCD Interchange code)

It is 8 bit code. It can represent 128 possible characters.

  

Parity Method is most widely used schemes for error detection. Hamming code is most useful error correcting code. BCD code is used in calculators, counters.

Complements: If base is r then we can have two complements.

(i) (r – 1)’s complement. (ii) r’s complement. To determine (r–1)’s complement: First write maximum possible number in the given system and subtract the given number. To determine r’s complement: (r–1)’s complement + 1

First write (r–1)’s complement and then add 1 to LSB Example: Find 7’s and 8’s complement of 2456

7777 7'sc omplement

2456 5321

5321 8'sc omplement

1 5322

Find 2’s complement of 101.110 1’s complement 010.001 For 2’s complement add 1 to the LSB

010.001 2'scomplement

1 010.010



S A M P L EC O P Y

4 MICROPROCESSORS

CONTENTS

1.

MIC R O P RO C E S S O R BA S IC S …………………………………. 120- 124

2.

808 5 INS TRU C TIO NS …………………………………………… 125- 132

3.

8086 B AS ICS ………………………………………………………. 133- 136



S A M P L EC O P Y

1. MI CROP ROC ESSO R BASICS A Microprocessor includes ALU, register arrays and control circuits on a single chip. Microcontroller:

A device that includes microprocessor, memory and input and output signal lines on a single chip, fabricated using VLSI technology.

Architecture of 8085 Microprocessor

1. 8085 MPU:



8 bit general – purpose microprocessor capable of addressing 64 K of memory.





S A M P L EC O P Y

It has 40 pins, requires a +5V single power supply and can operate with 3 – MHz single phase clock.

2. 8085 programming model:

It has six general purpose reg ister to store – 8 bit data. These are B, C, D, E, H and L. It can be combined as BC, DE, and HL to perform 16 bit operations. B, D, H

 high order register and C, E, L low order register.

Accumulator: Is an 8 bit register that is used to perform arithmetic and logic functions. Flags: 5 flags Flag Register:

DDDDDDDD 76543210 S

Z

AC

P

CY

Carry Flag (CY): If an arithmetic operation result in a carry or borrow, the CY flag is set, otherwise it is reset. Parity Flag (P):

If the result has au even number of 1s, the flag is set, otherwise the flag is reset. Auxiliary Carry (AC): In an arithmetic operation  If carry is generated by D 3 and passed to D4 flag is set.



Otherwise it is reset. Zero Flag (Z): Zero Flag is set to 1, when the result is zero otherwise it is reset. Sign Flag (S): Sign Flag is set if bit D 7 of the result is 1. Otherwise it is reset. Program counter (PC): It is used to store the l6 bit address of the next byte to be fetched from the memory or address of the next instruction to be executed. Stack Pointer (SP): It is 16 bit register used as a memory pointer. It points to memory location in Read/Write memory which is called as stack.



S A M P L EC O P Y

8085 Signals: Address lines:

There are l6 address lines AD0

 AD7 and A8  A15

to identify the memory

locations.

This book is available at all major book stalls.

For online purchase visit www.engineersinstitute.com/publication

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S A M P L EC O P Y

5 EL EC T RONI C D EVI CE S & CIRCUITS CONTENTS

1.

S E MIC O ND UC TO R B A S IC S & ENE R G Y BA ND S … ……… 138- 144

2.

JUNCTION

3.

VA R IO US SE MIC O ND UC TO R DIO D E S ……………………… 149- 152

4.

CL IPP ER S AND CL AMP ER S … …………………………………. 153- 154

5.

B JT ( B IP O L A R JUN C TIO N TRA NS IS TO R) ……………….. 155- 157

6.

F ET ( F IEL D E FF EC T TRA NS ISTO R) ………………………… 158- 164

7.

F A B R IC A TIO N OF INT E G R A TE D C IR C UIT S ……………. . 165 -16 5

8.

THYRIS TOR ……………………………………………………….. . 166- 168

DIO DE …………………………………………………. 145- 148



S A M P L EC O P Y

1. SEMI CONDUCTOR BA SICS & ENERG Y BANDS Thermal Voltage: VT (Voltage Equivalent of Temperature)

VT



T 11600

volt

Standard room temperature (300 K) VT

 0.0256v olt

VT

 26mV

The standard room temperature corresponds to a voltage of 26 mV. Leakage Current (I ) o

    

Also called minority carrier current or thermally generated current. In silicon it is in nano ampere range and in germanium it is in micro ampere range. Io doubles for every 10ºC. For 1ºC, Io increases by 7%.

Io is proportional to the area of the device. Advantages of smaller Io: (i) Suitable for high temperature applications (ii) Good Thermal stability (iii) No false triggering Energy Gap: Difference between the lower energy level of conduction band (CB) E C and upper energy level of valance band (VB) E vis called as energy gap. Metals: VB and CB are overlap to each other.  This overlapping increases with temperature. 

 e is both in CB and VB. Insulators: Conduction band is always empty. Hence no current passes. gap: 5 eV – 15 eV. Semiconductor: Energy gap is small and it is in range of 1 eV.  At room temperature current can pass through a semi conductor. Energy Gap Si GaAs Ge Eg T  0 7.85eV 1.21eV XX Eg T  300K

0.72eV

1.1eV

1.47eV

Energy gap at temperature T 4

For Ge For Si

Eg(T)  0.785  7.2  10 T Eg(T)  1.21  3.6 104 T

Energy gap decreases with temperature. Electric Field Intensity

dv volt ε dx meter

Mobility of charge carriers



dri ft veloci ty electri c fiel d inte nsity



v

m2



sec


Band


Mobility V

ε

s

S A M P L EC O P Y

c u r ve

So drift velocity: V d  ε

 ε 1/2

Vd

  constant

 < 10 3 10 3    10 4

µ  ε

  10 4

µ

 1/ 2

1

ε

 constant

Vd 

 Mobility indicates how quick is the e or hole moving from one place to another.  Electron mobility > hole mobility  Mobility of charge carriers decreases with the temperature.

µ  T m Mass Action Law: In a semi conductor under thermal equilibrium (at constant temperature) the product of electrons and holes in a semiconductor is always constant and equal to the square of intrinsic concentration.

 ni2 ]

[ n o po 

no  Concentration of e in conduction band Po  Concentration of holes in valance band ni



Intrinsic concentration at given temperature

Majority carrier concentration =

ni2 Minority carrier concentration 3 ni2 A T o e

Intrinsic concentration



Eg 2 KT

ni is a function of temperature and energy gap. Einstein’s Equation: Relation between diffusion constant, mobility and thermal voltage.

Dn

µn Theunitof

D

isvolts.





DP

µP

 VT  KT

Where,

Dn

constant e  diffusion

Dp

 Hole diffusion constant

Diffusion and Drift Current: Diffusion Current: It is defined as migration of charge carriers from higher concentration to lower concentration due to concentration gradient. Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

Drift Current: It is flow of current through the material or device under the influence of voltage or electric field intensity. Total current density in a semi conductor



J

 

(Current carried by e )



J





J

n

current due to e

e  drift current density

dn

Jn

 nq µ n ε  qDn

Jp

 pq µ p ε  qDp

dx



dp dx

Ln

 Dnτ cm

Hole diffusion length

LP

 DP τ cm

–

e  diffusion current density

A / cm2

diffusion length

e

J n



For holes

(Current carried by holes)



n

 

Jp



(Total current)

For e



Jn



A / cm2

Conductivity 

In Metals: Metals are uni-polar, so current is carried only by e

σ  nqµ n

In metal, conductivity decreases with temperature. In Semi Conductors

σ  nqµ n  pq µ P



S A M P L EC O P Y

6 AN AL OG EL EC T RONI CS

CONTENTS

1.

VOL TAG E RE GUL ATO R & RE CTIF IER S …………………….. 170- 171

2.

BJT & TRA NSIS TOR BIA SING …………………………………. 172- 175

3.

MUL TISTA G E & P OW ER AM P LIF IER S ……………………… 176- 178

4.

SMA LL SIGNAL ANAL YSIS …... ... ... ... .. ... ... .. ... ... ... ... .. .. .. .

5.

FE ED BA CK AMPL IFIER S ………………………………………… 184- 187

6.

OS CILL ATOR S ………………………………………………………. 188-191

7.

OP ER ATIO NAL AMP LIF IER S …………………………………… 192- 204

179-183



S A M P L EC O P Y

1. V OLTAG E RE GULATOR & RE CTI FIERS Voltage Regulator Circuits:

% Regulation =

VNL -VFL VFL

Full load current = I FL =

×100%

VFL RL

VNL -No load VFL -Fullload Smaller the regulation better is the circuit performance.

Zener Voltage Regulator Circuit:

Since Zener diode is conducting VL  Vz  VBr VL  I L R L

Vz

 Iz

I  Iz

Rz

 IL

If Zener current is maximum then load current is minimum and vice versa. I

 I z m ax 

I L m in

For satisfactory operation of circuit

I

 I z m in 

I  I z min  I L

The power dissipated by the Zener diode is

Pz

Vi

I L m ax

 VL Rs

 I z min  I L

 Vz I z

Rectifier: To convert a bi-directional current or voltage into a unidirectional current or voltage



Ripple factor:

S A M P L EC O P Y

r

rms value of AC component DC value 2

r

V   rms   1  Vdc 

Vrms

rms value Form factor:

F

2

r

 dc value  V dc

F

1

Peak value

Crest factor =

RMS value

Rectifier Efficiency =

DC power output ACpower input

100%

TUF (Transformer utilization factor):

DC power output TUF = ACrating of transformer Half Wave Rectifier: Average value of current and voltage

Idc 

Im



,

RMS value of cu rrent and voltag e:

Efficiency

Vdc



Vm

I rms



Im

 40.6%

2

,

Vrms



Vm 2

Ripperfactor=1.21

Frequency of ripple voltage = f Peakinversevoltage=



Vm

Form factor = 1.57 TUF=0.286

Full Wave Rectifier: Average value of current and voltage:

Idc



2Im



, Vdc



2Vm





S A M P L EC O P Y

RMS value of current and voltage:

Vrms

Efficiency

 81.2%

Fromfactor=1.11



Vm 2

, I rms



Im 2

Ripperfactor=0.48 Crestfactor=

2

TUF = 0.692 Frequency of ripple voltage = 2f

Peak inverse voltage = 2 Vm

Bridge Rectifier: All the parameters are same as full wave rectifier except Peak inverse voltage = Vm Transformer utilization factor = 0.812 Advantage of Bridge Rectifier: 1. The current in both the primary and secondary of the transformer flows for entire cycle. 2. No center tapping is required in the transformer secondary. Hence it is a cheap device. 3. The current in the secondary winding of transformer is in opposite direction in two half cycles. Hence net DC current flow is zero. 4. As two diode currents are in series, in each of the cycle inverse voltage appear

across diode gets shared. Hence the circuit can be used for high voltage application.



S A M P L EC O P Y

7 S IG NAL S A ND S YS TE MS

CONTENTS 1.

B A S IC P R O P E R TIE S O F S IG NA L S …………………………. . 206 -20 9

2.

LTI SYS TEMS ………………………………………………………. 210- 212

3.

FO URIE R SE RIE S …………………………………………………. 213- 214

4.

F OU RIE R TRA NSF O RM …………………………………………. 215- 218

5.

D IS C R E TE TIME S IG NA L S YS TE MS ………………………. . 219- 221

6.

L AP LA CE TRA NSF OR M ………………………………………… 222- 224

7.

Z TRA NS FO RM ……………………………………………………. 225- 228

8.

D IS C R E TE F O UR IE R TR AN S F O RM S ………………………. 229- 230



S A M P L EC O P Y

1. BA SIC PR OP ER TIES OF SIG NAL S Operations on Signals: y (t )  x (t Time Shifting:

 )

 Shift the signal towards right side by | | when   0. This is also called as time delay.

 Shift the signal left towards side by | | when   0. This is also called as time advance. Time Reversal y (t) = x (–t) Rotate the signal w.r.t. y-axis. It is mirror image of signal. y (t) = – x (t) Rotate the signal w.r.t. x-axis.

y (t )  x( t )  When   1, compress the signal.  When   1, expand the signal.

Time Scaling

Eg.  y(t) = x(–5t + 3)

   

y (t )  x  5  t 

3 



5 

Steps: 1. First rotate the signal w.r.t. y-axis. 2. Compress the signal by 5 times. 3 3. Shift the signal by unit towards right side.

5



S A M P L EC O P Y

Standard Signals: Continuous time signals Impulse signal (Direct Delta Functi on)

 0

δ (t )  

,

t 0

,

t 0

Properties of Impulse Signal (i) x(t ) (t )  x (0) (t )

(iii)



1



(ii) x (t ) ( t to )

x(t o ) (t

to )



1

[ (t  )]



&dt t δ ( )

  (t

||

)

(iv)

 (t ) dt  1





(v)

 x (t )  (t  t )  x (t ) o

o

(vi) x (t ) * (t to )

x (t to )



Unit Step signal:

u (t ) 

1, t  0 0, t  0

Unit Ramp signal: r (t ) t u t ( )

t , t  0 r (t )   0 , t  0

Parabolic signal: 2

x(t )  At u(t ) 2

 At 2 ,t0  x (t )   2  0 , t  0 Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


unit parabolic signal

S A M P L EC O P Y

t 2  x (t )   2 0

,

t0

,

t0

Unit Pulse signal:



1



π (t )u t   ut   2  

1 2

Triangular signal:

1  | t | , | t | a  x (t )   a  0, | t | a Signum Signal:

 1, t  0 1, t  0

x (t )  sgm(t )  

 2u ()t  1 sgn  u (t )  u t(  ) sgn()t



S A M P L EC O P Y

8 C O M M UN ICA TI O N SYS TEM S

CONTENTS

1.

A NA L O G M O D UL A TIO N ……………………………………….

232 -23 8

2.

P UL S E M O D UL A TI O N TE C HN IQ UE S …………………….

23 9- 24 4

3.

NO IS E ……………………………………………………………….

245- 246

4.

D IG IT A L MO D UL A TI O N SC HE ME S ……………………….

24 7- 24 8

5.

R A ND O M P R O C E SS E S .. .. . .. . . . .. . .. . ………………………….

249- 250

6.

IN F O R MA TI O N TH E O R Y ……………………………………. .

25 1- 25 2

7.

A NT E NN A TH E O R Y . ………………………………………….

25 3- 25 5

8.

R A D A R ………………… … … ……… ……… ……… …… … ……. .

256 -25 7

9.

S A TE L L IT E C O MM UN IC A TI O N ……………………………

25 8- 25 9

10 .

O P TI C A L C O MM UN IC A TI O N ………………………………

26 0- 26 4



S A M P L EC O P Y

1. AN ALO G MODULATION Modulation is the process of placing the message signal over some carrier signal to make it suitable for transmission. Need for Modulation:

1. Size of antenna required for receiving the wave is reduced if signal is transmitted at high frequency. 2. Many number of signals can be transmitted simultaneously by selecting the carriers of different frequencies. 3. The interference of noise and other signals can be reduced by changing the frequency of transmission. 4. Integration of different communication system is possible. Amplitude Modulation

Amplitude Modulated Signal: AM be defined as a system which the maximum amplitudeof ofthe themodulating carrier wavemay is made proportional to theininstantaneous value (amplitude) or base band signal. x m (t ) xc (t )

 Am cos ω m t  Ac cos ω c t where  = KaAm

x(t )  Ac [1 maK x (tc)]cos ω t

x (t )  Ac coscω tcam A K xc (t ) cos ω t where

 = modulation index x m (t )  message signal

c  tc x (t )  A c cos

m Ac  cos

t cos

t



S A M P L EC O P Y

Frequency spectrum of AM wave:

Bandwidth = 2 f m



Frequency band from f c to f c  f m is called as upper sideband



Frequencyb andf rom f c  f m to f c iscalledas lower sideband

µ

Amax  Amin

Amax

Amax  Amin

 AC [1  µ ]

Amin  AC [1  µ ]

Amax – maximum amplitude Amin – minimum amplitude Power Relations in AM wave:

Ptotal = Pcarrier + PLSB + PUSB

Ptotal



Ac2 2



µ 2 Ac2 8



µ 2 Ac2 8

Pcarrier

Ptotal



Ac2 2

PLSB

 PUSB 

µ 2 Ac2 8

 µ2   1   cP  2 

Maximum power dissipated in AM wave isPAM= 1.5 P c for µ=1 and this is maximum power that amplifier can handle without distortion. Efficiency of Amplitude Modulated System:

η AM 

PSB Pt

100%

 

η AM

 µ2   2   µ  2

100%



S A M P L EC O P Y

For satisfactory modulation 0    1 Current relations in AM wave:

Pt

 2   1   Pc  2 

IC

1

2 2

Multi-tone Modulation: When carrier is modulated simultaneously by more than one sinusoidal signal.

Resultant Modulation Index =  12   22 

2 3

............

Double side Band Suppressed Carrier modulation DSB-SC:

ts( )A µ

ctcos ωtc

  modulationindex

cos ω m

Ac

carrieramplitude

In DSB-SC the carrier signal is suppressed at the time of modulation. Only sidebands are transmitted in modulated wave. Bandwidth = 2 f m

Transmitted Power Pt



2 2

Pc

Power saving = 66.67% (for = 1)

Single Sideband Modulation (SSB): In this technique, along with modulation carrier one side band gets suppressed from AM modulated wave. st( )  Amtc

( ) cos ft c 2cπAmt  c

ftˆ ( ) sin 2π

 ( t ) is Hilbert transform of message signal. m

Bandwidth= f m

Power saving

TransmitterPower

Pt



µ2 4

PC

 83.3%



S A M P L EC O P Y

Vestigial Sideband (VSB) modulation: In this modulation one side band and vestige of another sideband is transmitted.

  

It is used for transmission of video signal in television broadcasting. It is also used for high speed data signal and facsimile. Vocal signal transmission of T.V. via F.M.

AM Modulators:



For Generation of AM or DSB/Full carrier wave A. Product Modulator B. Square Law Modulator C. Switching Modulator



For Generation DSB-SC wave A. Filter method/frequency discrimination method B. Phase shift method/Phase discrimination method C. Third method/Weaver’s method



S A M P L EC O P Y

9 ELECTROMAGNETIC THEORY CONTENTS

1.

C O O R D INA TE S YS TE MS A ND V E C TO R C A L C UL US …. . 266 -26 7

2.

EL EC TROS TATIC FIEL DS ……………………………………..

3.

MA G NE TO S TA TIC F IE L D S …………………………………… 272 -27 4

4.

MA XW E LL ’S EQ UA TIO NS ……………………………………. .

275- 276

5.

E L E C TR O MA GN E TIC W A VE S ………………………………. .

277- 281

6.

TR AN S MIS S IO N L INE …………………………………………. .

282- 285

7.

A NTE NNA S …………………………………………………………

286- 286

268-271



S A M P L EC O P Y

1. C O O RD INATE S YSTE MS AND VEC TOR CALCULUS Vector Calculus:  Gradient: The gradient of scalar V is written as  V and result is vector quantity. V V V For Cartesian: V  aˆ x  aˆ y aˆ x y z z For Cylindrical:

V 1 V V V  aˆ ρ   aˆ   aˆ z    z

For Spherical:

V



V 1 V  aˆ  aˆ   r r  r 

A x A y   x y



. A 

For Cylindrical:

.A 

A z z

.A

rr





r  sin 

Curl of vector: The curl of vector A is defined as quantity.

For Cartesian:

and result is scalar

1



For Spherical:

.A

 1 A  A z  ( A )     z 1  2 1  (r A r )   (sin 2



aˆ  

Divergence: The divergence of vector A is written as quantity.

For Cartesian:



V

1 r sin



 A

aˆ x

aˆ y

aˆ z

  x

 y

 z

Ax

Ay

Az

a r

a 

A )

1

A 

 r sin   A and result is

a z

     A     z A  A  A z 

For Cylinderical:

a r r sin θ

a θ sinθ r

 r

 

2



For Spherical:

A 

Ar

rA

a  r

  r sinA 




vector


S A M P L EC O P Y



Laplacian of Scalar: Laplacian of scalar field V is written as divergence of gradient of V. The result is a scalar quantity.  2 V  2 V 2 V 2 V  2  2 For Cartesian: x y z2 For Cylinderical:

2

V r r r  r r  sin  Laplacian of Vector: It is a vector quantity. 2



2



2 A (

    

It is the

1

2V

For Spherical:



  V   1 2 V 2 V         2 2 z 2 1V 2  1  

 V .



 .A)

V

 sin

2

1

r

2

sin

2

V 2



A



. (  A) 0 Curl of gradient of a scalar field is always zero  ( V)  0  The vector field is said to be solenoidal or divergence less if . A  0  A vector field is said to be irrotational (or potential) if  A  0 A vector field is said to be harmonic if 2 V  0 Divergence of a curl of vector is always zero



( . A)     A    



2



A



    . (A B) B . (  A) A . (

B)

 through Divergence Theorem: It states that total outward flux of vector field A 

closed surface S is the same as volume integral of the divergence of A .  



 A.ds    . A dv s

v 

Stokes’ Theorem: It states that line integral of a vector field A over a closed path is 

equal to surface integral of curl of A. 



 A . dl   (  A) . ds l

s



S A M P L EC O P Y

10 MEASUREMENTS & INSTRUMENTATION CONTENTS

1.

ME A S UR IN G I NS TR UM E NT C HA R A C TE R IS TI C S ……. 28 8- 28 9

2.

C L A S S IF IC A TIO N OF E L E C TR IC A L IN S TR UME NTS … 290 -29 5

3.

AC BR IDG ES ……………………………………………………… 296- 298

4.

ME A S UR E ME NT O F P O W E R & WA TTM E TE R S ………. . 29 9- 30 1

5.

ME A S UR E ME NT OF R E S IS TA NC E ………………………. . 302 -30 2

6.

Q- ME TER ………………………………………………………….. 303- 303

7.

TR A NS D UC E R S …………………………………………………

8.

CR O ( C A THO D E R A Y O S CI L L O S C O P E) ………………… 307- 308

304- 306



S A M P L EC O P Y

1. MEAS URIN G INSTRUMENT CHARACTERISTICS Generalized Measuring Instrument: The block diagram of generalized measuring system may be represented as:

IMPORTANT DEFINITIONS: Accuracy: Closeness with which an instrument reading approaches the true value of

the variable being measured. It can be improved by recalibration. Precision: It is a measure of the degree to which successive measurement differ from

one another.



It is design time characteristic.

High precision does not mean high accuracy. A highly precise instrument may be inaccurate. Ex: If reading are 101, 102, 103, 104, 105. Most precise value is 103 Resolution: The smallest change in measured value to which the instrument will respond. It is improved by re-calibrating the instrument. Sensitivity: It is ratio of change in output per unit change in input quantity of the

instrument. It is design time characteristic. Drift: It means deviation in output of the instrument from a derived value for a

particular input. Reproducibility: It is degree of closeness with which a given value may be measured

repeatedly for a given period of time. Repeatability: It is degree of closeness with which a given input is repeatably indicated for a given set of recordings. Errors: 1. Absolute E rror/Static E rror/Limiting E rror: Am AT

 A  Am  AT  Measured value of quantity of actual value  True value of quantity or nominal value



S A M P L EC O P Y

2.

Relative Error:

 r

3.

Percent Error:

% r

A 

Am

AT



A AT

 AT

AT

 100

Instrument Error is generally given in percent error.

4.

Percentage E rror at r eading ‘x’:  Full Scale Reading  [%, %  r , x    x 

r

Full scale]

Error due to combination of quantities: 1. Error due to Sum/Difference of quantities X  x1  x 2

% r

X  X

x1  x1  X  x   1

x2 x2   X x    2 

2. Error due to product or quotient of quantities x1 Or or X  x1 x 2 x3 x 2 x3

1

x1x 2 x3

x x x3     1  2 X x3   x1 x2  x x  X  X  x1n . x2m    n 1 m 2  X x x2   1 X

3. Composite factors

CLASSIFICATION OF ERRORS:

Standards of EMF:

(a) Saturated Weston cell is used for Primary standard of emf. Its emf is 1.01864 volt, maximum current drawn is 100 CdSO 4 crystal and its internal resistance is 600

A.

It contains

 to 800 .



S A M P L EC O P Y

(b) Unsaturated Weston cell is used for secondary standards. Its emf is 1.0180 to 1.0194 volt and does not have CdSO 4 crystal. Standard of Resistance: Maganin (Ni + Cu + Mn) Nickel 4%

Magnese 12% [High Resistivity and low temperature coefficient] Copper 84% Inductive effect of resistance can be eliminated, using Bifilar winding. Standard of Time and F requency: Atomic clock is used as primary standard of time and frequency. Quartz, Rubidium crystal is used as secondary standard of time and frequency. Example: Cesium 133, hydrogen maser etc.



S A M P L EC O P Y

11 EL EC T I CA L M AC H I N ES

CONTENTS

1.

TRANS FO RMER …………………………………………………… 310-330

2.

DC MAC HINE …… ………………………………………………… 331- 346

3.

SYNC HRO NOUS MAC HINES… ……………………………… 347-364

4.

INDUC TION MAC HINES … ……………………………………. 365- 381

5.

FR AC TIONAL KW MA CHINES ………………………………. 382- 392



S A M P L EC O P Y

1. TRANSFORMER

Definition: A transformer is a static device that transfers electrical energy from one electrical circuit to another electrical circuit through the medium of magnetic field and without the change of frequency.

Construction of Transformer: Core Type:

1. In core type construction, both the limbs are provided with windings and the core is surrounded by windings. 2. For a given output and voltage rating, it requires less iron but more copper. 3. Cross-section area of both limbs is equal. 4. These are used for high power applications. 5. These are suited for high voltage, small kVA rating. For example: 15 kVA, 2200 / 1100V 6. Cost of insulation is less.

Shell Type:

1. In shell type, only middle limb is provided with winding and the windings are surrounded by core. 2. Amount of copper required is less. 3. Cross-sectional area of the middle limb is twice to that of outer limbs. 4. These are used for low power applications. Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

5. These are suited for large kVA ratings but low voltage. For Example: 150 kVA, 400/230 V

Principle of Transformer Action:

Figure (i)

  

A transformer works on the principle of electromagnetic induction between two (or more) coupled circuits or coils. According to Faraday’s law of electromagnetic induction, an emf is induced in a coil if it links to changing flux. The direction of induced emf is given by Lenz’s law which states that emf will be induced in such a way that it opposes the cause which has produced it. In transformer electrical energy is transferred due to mutual induction between primary and secondary winding.

Emf equation of Transformer: Referring to figure (i), E1 = emf induced in the primary winding E 2 = emf induced in the secondary winding N1 , N 2 are the winding turns.

and Let the flux



  m sin t

is represented as,

By Faraday’s law of electromagnetic induction, Emf induced in primary winding,



E1

 N1

d dt

E1

 N1

d dt E1  N 1 

(m sin t )

m

 t cos

E1in primary (E1 ) m sin(winding t  90º ) rms value of emf induced (E ) (E1 )rms  1 m 2 (E1 ) rms



2 f N1 m

Similarly, emf induced in secondary winding

…(i) E2

 N2

d dt



S A M P L EC O P Y

 N 2  m sin(   t 90º )  N  m  (E 2 ) rms   2  2   (E 2 ) rms  2  f N 2 m E2

E1

From equation (i) and (ii),

N1



…(ii)

E2 N2

i.e., voltage per turns are equal in primary and secondary windings. From figure (i) we have, E1  V1 and E2  V2 Hence,

V1 V2

E

N1

I2

E2

N2

I1

 1

 a

Key Points:

   radians ahead by the core flux.  2

1. Emf induced in the windings are 

2. Any change in the secondary current of the transformer causes a change in primary current so that the flux remains constant. 3. Infinite permeability of the core signifies that no magnetizing current is required for establishment of flux. Ideal Transformer: Properties (i) Resistance of the windings of transformer is zero. (ii) Magnetic leakage flux is zero. (iii) The permeability of the core of transformer is infinite. (iv) Efficiency is 100%.



S A M P L EC O P Y

12 PO WE R SYST EMS CONTENTS 1.

F UND A ME NTA L O F E L E C TR IC A L P O W E R S YS TE M …

2.

P ER UNIT RE PR ES ENTA TIO N ……………………………

397- 397

3.

TR ANS MISS ION LI NE ……………………………………….

398- 405

4.

TRA VEL LING WA VES ……………………………………….

406- 406

5.

CA BL E & INSUL ATO R ………………………………………

407- 409

6.

A D M IT TA NC E & IM P E D E NC E MO D E L O F NE TW O R K

7.

LO AD FL OW STUD IES ……………………………………….

414- 416

8.

E CO NOM IC L OA D DIS P AC TCH ………………………….

417- 418

9.

FA ULT ANA LYS IS ……………………………………………

419- 426

10.

PO WE R SYS TEM STA BIL ITY …………………………….

427- 430

11.

SA G AND TENSION

431-432

12.

COR ONA ………………………………………………………….

433 -438

13.

PO WE R SYS TEM PR OTE CTIO N ………………………….

439- 442

14.

CIRC UIT BR EA KER …………………………………………..

443-444

15.

HVDC -HIGH VOL TAG E DC TRA NSMIS SIO N ………….

445- 448

…………………………………………..

39 4- 396

41 0- 41 3



S A M P L EC O P Y

1. FUNDAMENT AL OF ELE CTRICAL POW ER SYSTEM

Work done = F.d cos 

Where F= force applied ,

d = displacement,

 = angle between F & d

Energy: It is capacity to do the work. Unit : watt second 1w s

1Joule  

1N

m Newton

meters



Electrical energy : It is energy that is in charged particles in an electric field.

Electrical energy generally expressed in kilo watt hours (kwh)

1 kwh

 3.6 10 6J

Kinetic energy (KE):

1 2

mv2 (Jules)

Potential Energy (PE): Mgh (Jules) Thermal Energy: Internal energy present in system by virtue of its temperature. Unit : Calories 1 Cal



4.186 J

Power: it is time rate of change of energy

P

dw dt



du

u = work,

dt

Unit : Watt

1 Watt



w = energy

1J/s

Note: Electric motor ratings are expressed in horse power (hp) 1hp = 7 45.7 W and also 1 metric horse power = 735 Watt.

Electric parameter: Let

v

2V sin ω t



S A M P L EC O P Y

i  2sI in(ω t  φ) where v = instantaneous value voltage

i = instantaneous value current V = rms value of voltage I = rms value of voltage

In Phasor representation

vV  0 , i I

 

S = P+jQ = VI cos lagging VAR)



φ

+ jVI sin  = VI* (for this relation Q will be positive for

Where S = complex power or apparent power P = Active power Q = Reactive power

For balanced 3 phase system

P V3I|

||

P P

| Pcos φVI  L L 3|

||

| cos φP



Q V3I|

||

P P

S A M P L EC O P Y

| Psin φVI  L L 3|

| sin φP

||

where VL = line voltage VP = phase voltage Note:

in  connection VP



VL 3

 IL

& IP

 connection VP  VL & I P 

IL 3

Hyrdo power: P = gWh(watt) Where  = water density (100 kg/m3) g = 9.81 m/s2 W = discharge rate (m3/sec) h= head of water Tidal power

P =  gh2 A/T (watt) Where h = tidal head A = area of basin T = period of tidal cycle Wind power

P = 0.5  AV3 (watt)

 = air density (1201 g/m3 at NTP) V = Wind speed in (m/s) A = Swept area by blade (m 2) Load Curve: It is graph between the power demands of the system w.r.t. to time. Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

Figure: Typical daily load curve

(i) (ii)

Base Load: The unvarying loads which occur almost the whole day. Peak load: The various peak demands of load over and above the base load.

Designation capacity

Capital cost

Fuel cost

Base load

High

Low

Peak load

Low

High

Typical annual load factor 65-75

5-10

Type of plant

Nuclear, thermal Gas based, small hydro, pump storage

Operational factors : Maximum demand

1.

Demand Factor =

2.

Average load 

3.

Load factor 

4.

Diversity factor

5.

Plant Capacity factor

6.

Reserve Capacity = Plant capacity - max. demand

7.

Plant use factor 

Connected load

energy consumed is a given period Hours in that time period

Average demand Maximum load



sum of individual max demands Maximum demand on power station



Average demand Installed capcity

Actual energy produced Plant capacity

 hours (the plant has been in operation)



S A M P L EC O P Y

Note: 1.

Load factor can be defined for a period such daily load factor, monthly load factor, annual load factor etc.

2.

Practically load factor is less than 1.

3.

Practically diversity factor is greater than 1.

4.

Both factors should be high for economical use.



S A M P L EC O P Y

13 POW ER ELE CT RON I CS

CONTENTS

16.

PO WE R SE MICONDUCTO R DE VICES… ………………….. 450-461

17.

PHAS E CONTRO LLE D RECTIFIER S… ……………………. 46 2- 477

18.

INV ERTER S …………… ………………………………………… 478 -490

19.

CHOPP ERS ………………………………………………………. 491 -496

20.

A C VO L TA G E C O NTR O LL E R A ND CYCLO- CONVERT ERS

21.

……………………………………..

PO WE R ELE CTRO NICS DR IVES ... ... ... .. ... ... .. .. ... .. ... ..

49 7-500 501-504



S A M P L EC O P Y

1. POWER SEMICONDUCTOR DEVICES

Definition: Power electronics deals with control and conversion of high power applications. Key Points:

1. Power semiconductor devices should be capable to withstand large magnitudes of power with high efficiency. 2. In power electronics, the devices are utilized as switch while in signal electronics devices are used as switch and amplifiers. Four Modes of Switching Action: 1. Forward Blocking Mode

2. Forward Conduction Mode



S A M P L EC O P Y

3. Reverse Blocking Mode

4. Reverse Conduction Mode

Note: TRIAC supports all 4 modes of switch. So it is used as AC switch. Power Diode



Heavily doped layer

  Lightly doped layer Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y

VI Characteristic:

Reverse Recovery Characteristics of Power Diode:

Important Points:

(1) Q R

(2)

di dt

1

  trr  I RM 2



I RM

trr

[ta  trr ]



S A M P L EC O P Y

(3) The reverse recovery time (trr ) decides the switching frequency of diode. f Silicon Controlled Rectifier (SCR)

VI Characteristic:



I L = Latching current



IH = Holding current




1

trr


S A M P L EC O P Y

Important Point: SCR supports three modes of switchingi.e. forward blocking, forward conduction and reverse blocking mode. Important Terms used with SCR: 1. Latching current (I L ) : It is defined as the minimum value of anode current which

must be reached so that SCR remains on even after the gate signal is removed. 2. Holding Current (IH ) : It is that value of the anode current below which SCR is

turned off. (i.e., it regains it’s forward blocking capability) Note:

* IL  2.4 I H



S A M P L EC O P Y

14 EL EC T RI CAL M ATERI AL S

CONTENTS

22.

S TRUC TUR E OF MA TER IAL S …………………………… 506- 507

23.

E L E C TR IC MA TE RI A LS & PR O P E R TIE S …………….

508 -511

24.

C O ND UC TIVE MA TE R IA L S ………………………………

512 -514

25.

MA G NE TIC MA TE R IA LS ………………………………….

515 -518



S A M P L EC O P Y

1. S TRUCTUR E O F MATE RIA LS

1.

2.

Simple Cubic (SC):

  

Distance between adjacent atoms d SC  a  2 r



Packing efficiency = 52% Example Polonium, Fluorspar

Coordination number = 6

1

No of atoms per unit cell = 8 corners 

8

part  1

Body Centered Cubic (BCC):



Distance between adjacent atom d BCC






No of atoms per unit cell = 8 



Packing efficiency = 68%

1 8

 2r 

3 2

a

 1 2

Example  Fe, Cr, Na 3.

Face Centered Cubic (FCC):



Distance between adjacent atoms d FCC







1 8

 2r 

a 2

 3 4



Packing efficiency = 74% Example  Cu, Silver, Gold

Hexagonal Closed Pack (HCP):  Coordination number = 12




1 12

 3 4



Packing efficiency = 74% Example  Cd, Mg



S A M P L EC O P Y

Different types of unit cell Type of unit cell Cubic Tetragonal Orthorhombic

Volume of unit cell a3 a2c abc

Hexagonal

2

3 3a c 2

Crystallographic Plane and Miller Indices: Miller indices are used to specify directions and planes and it could be in lattices or in crystals.

Miller Indices for plane A  B  C 

h

OA OA 

,k



OB OB 

,

OC OC 

Example: 1.

h

OA OA

k

OB



OC

2

2

 

0 0

( h, k , )  (2, 0, 0)



S A M P L EC O P Y

2.

h

OA



OB



OC

k

1

OA

OB

OC

1

1

( h, k , )  (1, 1, 1) 3.

h k



l

OA OA OB

 OC

1 0 0

(h, k , l )  (1,0 ,0 )

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For online purchase visit www.engineersinstitute.com/publication

Call us at +91-9990357855 Published by: ENGINEERS INSTITUTE OF INDIA . © ALL RIGHTS RESERVED www.engine ersinstitu te.com Ph. 011-26514888


S A M P L EC O P Y



S A M P L EC O P Y

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