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ANALOG ELECTRONICS
DEVICES AND CIRCUITS
(Revised Edition)
Bishnu Charan Sarkar
Retired Professor, Physics Department
Burdwan University
Burdwan-713104
Suvra Sarkar
Associate Professor, Electronics Department
Burdwan Raj College
Burdwan-713104
Damodar Group
2019
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Analog Electronics: Devices and Circuits [Revised Edition]
By Bishnu Charan Sarkar and Suvra Sarkar
Published on: October 8, 2019 (Bijaya Dashami)
ⓒ Debdeep Sarkar
All rights reserved. No part of this publication may be reproduced or copied
in any form by any means without prior permission from the authors. The
views expressed in this publication are purely personal judgment of the
authors. All efforts are made to ensure that the published information is
correct.
ISBN: 978-93-85775-15-4
For distribution and marketing please contact authors
Price: Rs. 500.00
Printed & Published by
Damodar Group
54/1 Kachari Road
Burdwan-713101
West Bengal, India
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To the beloved memories of our parents
Late Radhakinkar Sarkar and Late Niharbala Sarkar
Late Sunil Sarkar and Late Sandhyarani Sarkar
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v
PREFACE TO REVISED EDITION
____________________________________________________________________
The revised edition of the book, “Analog Electronics: Devices and Circuits”, is
now published. As its first edition, this one is also self-financed and limited number
of copies is printed. In this edition, the book is thoroughly revised correcting
typographical errors and redrawing most of the figures. Also it has been abridged to
cover mainly the CBCS syllabus of the UGC for Physics and Electronic Science
(Honours and Generic) courses. Moreover care has been taken to include additional
materials to cater the needs of M Sc (Physics) students covering some of their
Electronics course. It would be useful for BE and B Tech students studying basic
courses on Analog Electronics. A good number of solved problems have been added
in different chapters, some of them deal with advanced topics. New chapters on
op amp design and filter theory are included. As before a collected set of objective
questions, short explanatory questions and model question papers are given for
self study.
We express our humble gratitude to the teachers from whom we learnt every bits
of the subject. We are thankful to our students, well wishers and friends who
extended active support in circulating the first edition of the book and hope they
would continue their support. We acknowledge the discussions we had with
Dr Tanmoy Banerjee, Physics department, Burdwan University, regarding the
content of the book. Affectionate encouragement from our son Dr Debdeep Sarkar to
take up this tiresome exercise of revision is fondly remembered.
Thanks are due to Damodar Group, Burdwan, publishers and printers of the
book. We hope that the new book would be useful for the students as a text book and
for others as a reference book.
October 8, 2019 (Bijaya Dashami) Bishnu Charan Sarkar
University Teachers Co-op Housing Suvra Sarkar
Plot - II
Krishnapur Road
Burdwan 713104
October, 2019
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vi
SOME REFERENCE BOOKS
R L. Boylested and L Nashelsky, Electronic Devices and Circuit Theory, Prentice
Hall, India, 2009.
A S Sedra and K C Smith, Microelectronic Circuits Theory and Applications,
Oxford Univ Press, 2010.
B G Streetman and S K Banerjee, Solid State Electronic Devices, Prentice-Hall,
India, 2006.
T H Lee, The design of CMOS radio frequency Integrated circuits, Cambridge
Univ Press, 2002.
P Bhattacharya, Semiconductor Optoelectronic Devices, Prentice Hall, India, 1999.
J Millman and A Grabel, Microelectronics: Digital and Analog Circuits and
Systems, McGraw-Hill International Student Edition, 1979.
J D Ryder, Electronic Fundamentals and Applications, , Prentice Hall, India, 1976.
D Roddy and J Coolen, Electronic Communions, Prentice-Hall, India, 2000.
K Leaver, Microelectronic Devices, Allied Publishers and World Scientific, 2003.
D K Roy, Physics of Semiconductor Devices, Universities Press, India, 2004.
H Taub, D L Schilling, G Saha, Principles of Communication Systems,Tata
McGraw Hill, 2008.
J D Ryder, Network works, Lines and Fields, Prentice-Hall, India, 2007.
I S Gonorovsky, Radio Circuits and Signals, Mir Publishers, Moscow, 1997.
G J Deboo and C N Burrous, Integrated Circuits and Semiconductor Devices, Tata
McGraw-Hill, 1995.
A K Maini and V Agrawal, Electronic Devices and Circuits, Wiley, 2015.
R A Gayakwad, Op amps and linear Integrated Technology, PHI Learning, 2002.
J G Proakis and D G Manolakis, Digital Signal Processing : Principles,
Algorithms and Applications, Pearson, 2014
R E Collin, Foundations for Microwave Engineering, McGraw-Hill International
Editions, 1966.
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vii
CONTENTS
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PREFACE TO REVISED EDITION v
SOME REFERENCE BOOKS vi
CHAPTER 1: INTRODUCTION 1-26
1.1. Prelude 1
1.2. Introduction to Solid State Electronics 2
1.3. Physics of semiconductors 3
1.4. Classification of semiconductors 6
1.5 Intrinsic semiconductor 6
1.6. Extrinsic semiconductor 7
1.6.1. n-type semiconductor 8
1.6.2. p-type semiconductor 9
1.6.3. Degenerate semiconductor 10
1.7. Physics of current conduction in semiconductors 10
1.7.1. Drift Mechanism 11
1.7.2. Diffusion Mechanism 13
1.8. Hall Effect and its application in semiconductor physics 16
1.9. Haynes-Shockley experiment
1. A. Appendix: Equilibrium concentration of electrons and holes 19
1A.1. Density of states 19
1A.2. Electrons and holes in intrinsic semiconductor 20
1A.3. Continuity of Fermi level 21
1A.4. Electrons and holes in extrinsic semiconductor 22
Solved Problems and Important Points 24
Exercises: Review Questions and Problems 25
CHAPTER 2: ELEMENTARY CIRCUIT THEORY 27-46
2.1. Electrical circuit components 27
2.1.1. Resistance 27
2.1.2. Inductance ( 28
2.1.3. Capacitance 28
2.2. Voltage source 29
2.3. Current source 30
2.4. Laws for circuit analysis 30
2.4.1. Laws on combination of circuit elements 30
2.4.2. Division of current 31
2.4.3. Kirchhoff’s laws 31
2.5. Some useful theorems 33
2.5.1. Superposition theorem 33
2.5.2. Thevenin’s theorem 34
2.5.3. Norton’s theorem 35
2.5.4. Maximum power transfer theorem 36
2.6. LCR combination 37
2.6.1. Properties of LC tank circuit 37
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viii
2.6.2. Two equivalent forms of tank circuit 38
2.6.3. Impedance of a tank circuit 38
2.7. Circuit model of mutual inductance 39
2.8. Theory of coupled circuit 40
Solved Problems and Important points 42
Exercise: Review Questions and Problems 45
CHAPTER 3: SEMICONDUCTOR DIODES 47-62
3.1. p-n junction and its fabrication 47
3.2. Potential barrier at p-n junction 48
3.3. Some parameters of p-n junction 50
3.3.1. Contact potential 50
3.3.2. Electric field in the DR 51
3.3.3. Width of the DR 52
3.4. Current flow mechanism across p-n junction 52
3.4.1 Forward biased condition 53
3.4.2. Recombination in the neutral region 54
3.4.3. Recombination in the DR 55
3.4.4. Reverse bias condition 55
3.5. Current-voltage characteristics of p-n junction 57
3.5.1. Static and dynamic resistance 58
3.6. Junction capacitances 58
Solved Problems and Important Points 60
Exercises: Review Questions and Problems 61
CHAPTER 4: SPECIAL PURPOSE DIODES 63-86
4.1. Introduction 63
4.2. Light emitting diode (LED) 63
4.3. Photo diode 66
4.3.1. Avalanche photo diode 67
4.4. Solar cell 67
4.5. Laser diode 70
4.6. Reverse bias breakdown diodes 71
4.6.1. Zener diode 71
4.6.2. Avalanche breakdown diodes 72
4.6.3. Comparison between ZB and AB 72
4.7. Tunnel diode 73
4.8. IMPATT diode 75
4.9. Metal-Semiconductor junction 77
4.9.1. Junction between metal and n-type SC 77
4.9.2. Junction between metal and p-type SC 78
4.9.3. Effects of external biasing at metal-SC junction 79
4.10. Uni- junction transistor 81
4.11. Silicon controlled rectifier 82
Solved Problems and Important Points 84
Exercise: Review Questions and Problems 85
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ix
CHAPTER 5: RECTIFIERS AND POWER SUPPLY 87-104
5.1. Introduction 87
5.2. Rectifier circuits 87
5.2.1. Output dc current ( and dc voltage
89
5.2.2. Ripple factor 89
5.2.3. Rectification efficiency 89
5.2.4. Percentage regulation (
90
5.2.5. Peak inverse voltage (PIV) 90
5.3. Half wave rectifier without filter 90
5.4. Full wave rectifier without filter 91
5.5. Rectifier circuits with filters 93
5.5.1. Half wave rectifier with capacitor filter 93
5.5.2. Full wave rectifier with capacitor filter 94
5.6. Zener diode based voltage regulator (ZD-VR) 96
Solved Problems and Important Points 98
Exercise: Review Questions and Problems 102
CHAPTER 6: BJT STRUCTURE AND CHARACTERISTICS 105-120
6.1. Bipolar junction transistor (BJT) 105
6.2. Classification of BJT 105
6.3. Physical mechanism of current flow in a BJT 107
6.3.1. Energy band diagram of BJT 108
6.3.2. Distribution of injected minority carriers 109
6.3.3. Current gain parameters 109
6.4. Characteristics curves in CB configuration 111
6.5. Characteristics curves in CE configuration 112
6.6. Input-output current in CC Configuration 112
6.7. Early effect and Punch through 112
6.8. Enhanced performance BJTs 113
6.9. Planer transistor and IC 114
Solved Problems and Important Points 115
Exercise: Review Questions and Problems 119
CHAPTER 7: FET STRUCTURE AND CHARACTERISTICS 121-134
7.1. Introduction 121
7.2. Structure and operation of JFET 122
7.3. Current-voltage characteristics of JFET 123
7.4. Metal oxide semiconductor FET (MOSFET) 124
7.4.1. Enhancement MOSFET 125
7.4.2. Depletion MOSFET 126
7.5. Volt-ampere characteristics of MOSFET 126
7.5.1. Drain characteristics of E-MOSFET 127
7.5.2. Drain characteristics of D-MOSFET 128
7.5.3. ID-VGS characteristics of MOSFET 128
7.6. Mathematical relation between and
129
7.7. Band diagram of MOSFET 130
Solved Problems and Important Points 131
Exercise: Review Questions and Problems 133
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x
CHAPTER 8: GENERAL AMPLIFIER THEORY 135-144
8.1. Introduction 135
8.2. Amplifiers as two port active networks 135
8.3. Voltage amplifier 137
8.4. Current amplifier 137
8.5. Trans-conductance amplifier 138
8.6. Trans-resistance amplifier 138
8.7. Negative resistance amplifier 140
8. 8. Effect of nonlinearity in amplifiers 141
8.9. Noise in an amplifier and Noise Figure 142
Solved Problems and Important Points 143
Exercise: Review Questions and Problems 144
CHAPTER 9: LOW FREQUENCY AMPLIFIERS 145-172
9.1. Introduction 145
9.2. Operating point of BJT amplifiers 145
9.2.1. Graphical method of finding Q-point 146
9.2.2. Algebraic method of finding Q-point 147
9.3. Transistor biasing 147
9.3.1. Temperature variation of BJT parameters 147
9.3.2. Sample-dependent variation 148
9.3.3. Requirements of a good biasing circuit 148
9.4. Common biasing circuits 148
9.4.1. Base bias or fixed bias circuit 148
9.4.2. Base bias circuit along with emitter resistor 149
9.4.3. Voltage divider biasing circuit 150
9.5. h-parameter equivalent circuit of BJT 151
9.5.1. Advantages and limitations 152
9.5.2. Determination of h-parameters 152
9.6. Analysis of BJT amplifier in CE configuration 154
9.6.1. Current gain 154
9.6.2. Input resistance ( 155
9.6.3. Voltage gain 155
9.6.4. Output resistance 155
9.6.5 Power gain 156
9.7. Simplified analysis 156
9.8. Biasing circuits for JFET amplifiers 157
9.8.1. DC bias point of a given JFET amplifier 159
9.9. Small signal analysis of JFET amplifier 160
9.9.1. -model and JFET parameters 161
9.9.2. FET amplifier as a voltage source 161
9.10. Different configurations of JFET amplifier 162
9.10.1. CS amplifier with bypassed 162
9.10.2. CS amplifier in presence of 162
9.10.3. CD amplifier 163
9.10.4. CG amplifier 164
9.11. E-MOSFET amplifiers 164
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xi
Solved Problems and Important Points 166
Exercise: Review Questions and Problems 170
CHAPTER 10: HIGH FREQUENCY & TUNED AMPLIFIERS 173-204
10.1. Introduction 173
10.2. High Frequency current gain of BJT 173
10.3. High frequency input admittance 175
10.4. Single stage R-C coupled amplifier 176
10.4.1. Mid-frequency response 176
10.4.2. Low frequency response 177
10.4.3. High frequency response 178
10.4.4. Approximate relations 179
10.5. Band-width and Figure of Merit 180
10.6. Coupling of multiple amplifying stages 180
10.7. Two stage coupled amplifier (TSCA) R-C-type 181
10.7.1. Mid frequency response 182
10.7.2. Low frequency response 182
10.7.3. High frequency response 183
10.8. Video amplifier 184
10.8.1. High frequency compensation 184
10.8.2. Low frequency compensation 186
10.9. Pulse Amplifier 187
10.10. Step response of amplifier 188
10.11. Single tuned amplifier 190
10.12. Inductively coupled amplifiers 192
10.13. Double tuned amplifier 192
10.14. Stagger tuned amplifier 195
10.15. Some novel applications of tuned amplifiers 196
Solved Problems and Important Points 197
Exercise: Review Questions and Problems 202
CHAPTER 11: POWER AMPLIFIERS 205-216
11.1. Introduction 205
11.2. Class-A power amplifier 206
11.2.1. Series-fed load 206
11.2.2. Transformer-fed load 207
11.3. Class-B Power Amplifier 209
11.3.1. Class B PA using transformer 209
11.3.2. Transformer-less class-B PA 210
11.4. Class C Power Amplifier 212
Solved Problems and Important Points 213
Exercise: Review Questions and Problems 216
CHAPTER 12: FEEDBACK AMPLIFIERS AND STABILITY 217-230
12.1. Introduction 217
12.2. Basic feedback principle 217
12.2.1. Different topologies of feedback amplifier 218
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xii
12.3. Effects of negative feedback 220
12.3.1. Improved stability of gain 220
12.3.2. Reduction of output distortion 220
12.3.3. Increased bandwidth 221
12.3.4. Effects on input resistance 222
12.3.5. Effects on output resistance 223
12.4. Stability of amplifiers with feedback 223
12.4.1. Condition of self-oscillation 224
12.4.2. Gain margin and phase margin of an amplifier 224
12.4.3. Routh-Hurwitz stability condition 224
12.4.4. Nyquist stability criterion 226
12.4.5. Comparison of stability calculation technique 227
Solved Problems and Important Points 228
Exercise: Review Questions and Problems 229
CHAPTER 13: OSCILLATORS 231-248
13.1. Introduction 231
13.2. Basic conditions of oscillator design 231
13.3. Barkhausen criterion 232
13.4. R-C Phase shift oscillator 233
13.5. Reactance Oscillators 235
13.5.1. Colpitts oscillator 236
13.5.2. Hartley oscillator 237
13.6. Tuned collector oscillator 237
13.7. Nonlinear analysis of tuned collector oscillator 239
13.7.1. NDE of oscillator 239
13.7.2. Solution of LDE 240
13.7.3. Solution of NDE 241
13.8. Voltage controlled oscillator 242
13.9. Negative resistance oscillator 244
Solved Problems and Important Points 245
Exercise: Review Questions and Problems 247
CHAPTER 14: OP AMP CHARACTERISTICS AND DESIGN 249-268
14.1. Introduction 249
14.2. Basic op-amp 249
14.3. Characteristics of an op-amp 249
14.4. Some important parameters 251
14.4.1. Common mode rejection ratio (CMRR) 251
14.4.2. Open-loop and closed-loop gain 251
14.4.3. Frequency response 252
14.4.4. Slew rate 252
14.5. Emitter coupled difference amplifier 253
14.5.1. DC analysis of ECDA 253
14.5.2. AC analysis of ECDA 254
14.6. Constant current sources 255
14.6.1. Basic current mirror 256
14.6.2. An improved current mirror 257
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xiii
14.6.3. Widlar current mirror 257
14.7. Voltage reference circuits (VRC) 258
14.7.1. Voltage divider reference circuit 259
14.7.2. Diode-based VRC 259
14.7. 3. VBE Multiplier type VRC 260
14.8. I-V characteristics of current source based ECDA 260
14.9. Active load in trans-conductance amplifier 262
14.10. Internal architecture of 741 263
Solved Problems and Important Points 264
Exercise: Review Questions and Problems 267
CHAPTER 15: OP AMP BASED CIRCUITS 269-294
15.1. Introduction 269
15.2. Inverting amplifier 269
15.2.1. Virtual ground 270
15.3. Non-inverting amplifier 270
15.4. Analog adder circuits 271
15.5. Analog subtractor circuits 273
15.6. Ideal differentiator circuit (inverting) 274
15.7. Imperfect differentiator circuit (inverting) 274
15.8. Ideal integrator circuit (inverting) 275
15.9. Imperfect integrator circuit (inverting) 275
15.10. Nonlinear op-amp circuits 276
15.10.1. Log amplifier 276
15.10.2. Exponential amplifier 277
15.10.3. Multiplier and divider circuits 278
15.11. Zero crossing detector 278
15.12. Wien bridge oscillator 279
15.13. Converter circuits 280
15.14. Digital to Analog converter (DAC) 281
15.14.1. Weighted summer 281
15.14.2. R-2R ladder based DAC 282
15.15. Analog to Digital Converter (ADC) 283
15.15.1. Parameters of an ADC circuit 283
15.15.2. Successive approximation type ADC 283
15.15.3 Priority encoder–based ADC 284
15.15.4 Dual slope ADC 286
15.16. Op-amp based rectifier circuits 286
15.16.1. Precision half wave rectifier 287
15.16.2. Precision full wave rectifiers 287
Solved Problems and Important Points 288
Exercise: Review Questions and Problems 293
CHAPTER 16: SOME PASSIVE AND ACTIVE FILTERS 295-316
16.1. Introduction 295
16.2. Frequency selective two-port reactive network 296
16.2.1. PB determination from CI 297
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xiv
16.2.2. PB determination from PC 298
16.3. Proto type filter design 299
16.4. Variation of α and with frequency 303
16.4.1. Variation of with frequency in the PB 303
16.4.2. Variation of α with frequency in the AB 303
16.5. Introduction to active filters 304
16.5.1. Filters and their transfer functions 304
16.5.2. Multiple feedback active filters 306
16.6. Generalized Sallen-Key Filter 308
16.7. Design of higher order low pass filters 310
16.8. Universal bi-quad filter circuit 312
Solved Problems and Important Points 313
Exercise: Review Questions and Problems 315
CHAPTER 17: ANALOG AMPLITUDE MODULATION 317-338
17.1. Introduction 317
17.2. Overview of electronic communication systems 317
17.3. Necessity of up-ward frequency translation 318
17.4. Classification of modulation techniques 319
17.5. Analog amplitude modulation 321
17.5.1. Mathematical representation 321
17.5.2. Tone-modulated DSB-TC AM wave 322
17.5.3 AM by sum of two sinusoidal signals 325
17.5.4 SSB-TC AM wave 326
17.6. Principle of amplitude modulator design 326
17.6.1. Generation of DSB-TC AM signal 326
17.6.2 Generation of DSB-SC AM signal 327
17.6.3. Generation of SSB-TC AM signal 328
17.6.4. Generation of SSB-SC AM signal 329
17.7. Detection of transmitted carrier AM signals 330
17.7.1. Envelope detection scheme 331
17.7.2. Product detection scheme 332
17.7.3. Square-law detection scheme 333
17.8. Detection of suppressed carrier signals 333
17.8.1. Detection of DSB-SC signal 333
17.8.2. Detection of SSB-SC signal 334
17.9. Vestigial side band (VSB) AM Signal 334
Solved Problems and Important Points 335
Exercise: Review Questions and Problems 337
CHAPTER 18: ANALOG ANGLE MODULATION 339-360
18.1. Introduction 339
18.2. Frequency modulated (FM) signal 339
18.3. Phase modulated (PM) signal 341
18.4. Comparison between FM and PM signals 341
18.5. Frequency spectrum of FM wave 342
18.6. Transmission Bandwidth of FM Signal 343
18.7. NBFM Signal 344
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xv
18.8. Different techniques of FM Generation 345
18.8.1. NBFM by Balanced Modulator 345
18.8.2. WBFM by nonlinear amplifier 346
18.8.3. Direct Method of FM Generation 347
18.9. Techniques of FM Detection 348
18.9.1. FM Detection using limiter-discriminator 348
18.9.2. FM Detection using phase discriminator 351
Solved Problems and Important Points 352
Exercise: Review Questions and Problems 353
18A. Appendix 354
SOME QUESTIONS AND TABLES 361-372
INDEX 373-375
Commonly used Physical Constants
Physical constant Value Unit
Velocity of light in free space, c
m/s
Planck’s constant, h
!
"
#$
%
!
%
"
&'
J-s
eV- s
Magnitude of electronic charge, e
!
"
&(
C
Rest mass of free electron, m0
)
!
"
#&
kg
Boltzmann constant, k
!
*
"
+#
*
!
,
"
'
J/K
eV/K
Thermal energy at 300 K 0.0259 eV
Avogadro’s number, N
!
,
+#
Molecules/mole
Permittivity of free space,
-
.
*
!
*/
"
&+
F/m
Permeability of free space,
0
.
4
1
"
2
H/m
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xvi
Landmarks in Electronic Technology
Year Event
1864 Maxwell’s field equations
1886 Hertz’s experiment proved Maxwell’s predictions
1897 Discovery of Electron by J J Thompson
1899
Self-recovering “coherer” by J C Bose; used in Marconi’s experiment
1901 Marconi’s radio telegraphy experiment
1901
J C Bose got patent for solid state detector
1905
Pickard reported a crystal detector; Fleming’s vacuum diode
1906
Fessenden showed audio broadcasting ; L de forest invented triode
1912 E Armstrong designed regenerative amplifier using improved triode
1922 O Losev of Russia arguably invented solid state amplifier
1927 Negative feedback amplifier by H S Black
1945-46 Electronic computer ENIAC
1939-40 High power microwave tube, RADAR
1944 Fully electronic monochrome TV
1948 Transistor invention by Shockley, Bardeen and Brattain Bell Labs
1951 Commercial discrete transistor
1954 Patent granted for frequency modulation to E Armstrong
1953-54 NTSC Color television standard
1957-60 LASER; artificial satellite (Sputnik); MOS transistor; Integrated
circuit; satellite repeater,
1943 Pulse code modulation (PCM) technique
1964-65 Logic circuits on silicon chip, G Moore’s prediction
1967-69 Computer networks ARPANET made operational
1970 W S Boyle and G E Smith gave the idea of CCD at Bell labs
1970 Microprocessor designed in The Intel
1980 Personal computer of IBM launched; Analog mobile communication
1983 ARPANET adopts TCP/IP; birth of Internet;
1989 WWW invented at the CERN ; Came into public domain
1991 -01 Digital mobile communication (2G, 3G, 4G…) Pentium IV
Present
decade
High-speed, low-power, huge-storage technology invention continues
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CHAPTER 8
GENERAL AMPLIFIER THEORY
_______________________________________________________________________
Chapter outlines
Amplifiers as two port active networks; high frequency effect in amplifier model; negative
resistance amplifiers; nonlinearity and distortion in amplifiers; effect of noise in amplifiers
and noise figure.
______________________________________________________________________
8.1. Introduction
Electronic amplifiers are designed to amplify amplitude level or power level of
electrical signals. Generally it is an active network comprising of input port and
output port. The signal to be amplified is applied at the input port and the amplified
signal is taken out from the output port. In general a linear amplifier circuit gives a
magnified replica of the input signal. Note that the operation of such circuit must
obey conservation of energy principle. So there must be some external source to
provide additional energy obtained at output to validate “energy conservation
principle”. An additional source of energy, often called power supply, is used in an
amplifier circuit. In our discussion here, for simplicity, we consider input and output
signals as ac signals and applied power supply as a dc voltage source. However,
amplification of dc voltage or current is also possible adopting special arrangements.
Also in some special type of amplifiers (like, parametric amplifiers), ac power
supplies are used. In amplifier circuits, output ac power is always less than or at best
equal to the power of applied dc supply. Two parameters, gain and efficiency, are
used to quantify the response of an amplifier. Gain is the ratio of output signal and
input signal. Efficiency of an amplifier determines the ability of amplifier in
converting dc energy into ac energy. To get higher efficiency, the output waveform
is deliberately deformed in some amplifiers. At first, we consider linear amplifiers
only where output signal is a linear function of input signal.
(a) (b)
Fig 8.1: (a) Block diagram of an amplifier as two port network (b) Equivalent circuit of the
amplifier with
and
as independent variables
8.2. Amplifiers as two port active networks
The block diagram of a typical amplifier is shown in Fig 8.1(a). It is an active
two port network (TPN), and is driven by a voltage source (VS) or current source
(CS) at its input port. Looking into the circuit from output port, we can describe it
as a dependent voltage source (DVS) or a dependent current source (DCS). Each of
these sources may depend on input voltage or current. TPN representation of
amplifier is a non-reciprocal type, i.e. response of the circuit is totally different if the
136 Analog Electronics: Devices and Circuits
output port and the input port are reversed. When this system is in dynamic
condition, we consider four instantaneous electrical variables at any instant of time,
two variables for input port and other two for output port. These are voltage and
current obtained at respective ports. Instantaneous values of these variables are sum
of their dc and ac values. DC values determine the operating condition of amplifier
and these values are appropriately chosen to keep the circuit in active condition. AC
values are taken small compared to respective dc values. This assumption is
necessary for an ac amplifier. We discuss ac linear amplifier theory to begin with.
Electrical variables of input port are denoted by
and
where they denote voltage
and current respectively. Similarly
and
are variables for output port. We can
take two of these four variables as independent at a time and express other two
variables as linear combination of independent variables. This helps us to formulate
a linear circuit model of amplifier. For example, let us choose input current
and
output voltage
as independent variables. This choice leads to a very popular
equivalent model of amplifier. We write
and
in terms of
and
as follows:
In these equations there are four parameters denoted by
,
,
and
. Note
that, we use one voltage variable and one current variable as independent and
parameters have different physical units. So we name these parameters as hybrid or
h-parameters. These parameters are defined as follows:
Note that, zero value of ac voltage at a particular port means short circuited
condition of the port; similarly zero value of ac current means open circuited
condition of the port. In definitions given above,
and
are short circuit input
resistance and open circuit voltage reverse feedback factor respectively.
Similarly
and
are short circuit forward current gain and open circuit output
admittance respectively.
Circuit representation of (8.1) and (8.2) are given in Fig 8.1(b). It shows input
port of amplifier is replaced by a DVS with input resistance in series with it. Output
port is replaced by a DCS with output admittance in shunt with it. Equivalent
representation of amplifiers can be made in a different way. The type of dependent
source representing output port is primarily determined by output resistance of
amplifiers. These equivalent dependent sources are controlled by concerned input
signal sources. Again the choice of input sources is made considering input
resistances of amplifier circuits. Thus we have four forms of output port, two as VSs
and two as CSs. VSs are of values
or
and CSs are of values
or
. Here,
and
are voltage and current at input port of the amplifier.
Input port of an amplifier can be driven by a VS or a CS. If the input port offers very
high resistance to applied signal source, then almost no current would flow into
input port. Full source voltage would appear at input port. In that case we consider
amplifier to be driven by a VS. In other extreme, if input resistance be very low,
effective voltage between two terminals of input port would be almost zero and an
appreciable current is injected into amplifier circuit from applied signal source. In
Chapter 8: General Amplifier Theory 137
that situation, we consider that the amplifier is driven by a CS. Ideal VS and ideal
CS are characterized by their internal resistances. For ideal VS, source resistance is
zero and for an ideal CS, source resistance is infinity. In practical situations, we take
a small value as zero value and a very large value as infinity. Thus when we
consider an amplifier as a VS, we take output resistance of amplifier as a small
resistance appearing in series with the equivalent DVS. For current source
representation of amplifier, output resistance is taken of large value appearing in
shunt with equivalent DCS. With these considerations in mind, we discuss four
classes of amplifiers.
8.3. Voltage amplifier
Fig 8.2(a) shows an amplifier considered as DVS driven by VS at input port. Here
and
are the effective input resistance and output resistance of the amplifier
respectively.
(a) (b)
Fig 8.2: Representation of (a) voltage amplifier, (b) current amplifier
The voltage at input port is
and the voltage DVS (VDVS) at output port is
,
is a parameter of the amplifier. We take
as source resistance of
input VS
. We take output voltage
across the load resistance
.
The output voltage
is negative, because the output port current goes into the
circuit. So
is 180
0
output phase with respect to
. If
source be an ideal type
then
and
. Also for ideal VS representation of amplifier, the output
port resistance
. This makes
Hence, parameter
is
and it is voltage gain (VG) of the amplifier. For
practical circuits
has finite value; similarly
would not be zero. However, the
approximations made earlier are valid if
. Thus when
is
large and
is small, these conditions nearly satisfied and the amplifier is driven by
a VS and the output port is replaced by a VDVS.
8.4. Current amplifier
The equivalent circuit of a current amplifier is shown in Fig 8.2(b). Here the
input CS
has an internal resistance
. Also the current DCS (CDCS) at the output
port is of magnitude
and it has output resistance
. In ideal case
∞and
∞ . Applying KCL at the output node, we have
. Moreover,
in terms of
we write
and
as,
138 Analog Electronics: Devices and Circuits
In ideal case
∞ and so
and
. These relations
can also be written when
. Similarly, we write input current and input
voltage as
and
=
.For an ideal or nearly
ideal input CS,
∞and
. These conditions give
=
and
=
. So we get current gain and voltage gain as,
Negative sign in these expressions implies the phase reversal of output voltage with
respect to input voltage.
8.5. Trans-conductance amplifier
Next, consider the amplifier as a DCS driven by a VS and this gives voltage DCS
(VDCS). The equivalent circuit for such amplifier is given in Fig 8.3.
Fig 8.3: Representation of trans-conductance amplifier
The output CS is shown as
. Then we write from basic circuit laws the
expressions of input voltage, load current and output voltage as,
For ideal situation,
and
∞. Also in nearly ideal condition,
. These give,
=
;
=
. So we have a parameter
that
connects output load current with input voltage of the amplifierIt has got dimension
of conductance. So this amplifier is called trans-conductance amplifier.
Moreover, the output voltage is,
=
. The voltage gain of trans-
conductance amplifier is,
This expression indicates that the gain of this amplifier is the product of the trans-
conductance parameter and the load impedance.
8.6. Trans-resistance amplifier
Fig 8.4: Representation of trans-resistance amplifier
Finally, we consider an amplifier which appears from output port as a DVS
driven by a CS at input port. Output DVS is written as
. Equivalent circuit for
Chapter 8: General Amplifier Theory 139
this amplifier is shown in Fig 8.4. Consideration of ideal type of sources is same as
before i.e.
and
∞ In practical circuit we get
and
.
The input current and then input voltage are obtained.
Using the conditions mentioned for this amplifier, we can get approximate relation
and
. The relations for output port are,
and
. So load current is
and output voltage
is
. Applying the conditions of ideal source or
practical source, we get
and
. Note that the
parameter connecting output voltage with input current is
and it has got the
dimension of resistance. So this amplifier is called trans-resistance amplifier.
Voltage gain of the amplifier is
We summarize these properties in Table 8.1.
Table 8.1: Classification of Amplifiers
Sl no
Input driven by Output port Amplifier name
1. Voltage signal, v
i
VDVS, v
0
Voltage,
2. Current signal i
i
CDCS, i
0
Current;
3. Voltage signal, v
i
VDVS, i
0
Trans-conductance;
4. Current signal, i
i
CDVS, v
0
Trans-resistance;
The proportionality constants for four different types of amplifiers are called
voltage gain (
), current gain (
), trans-conductance (G
M
) and trans-resistance
(R
M
) respectively. Out of these,
and
are dimensionless quantities or numbers,
but
and
have dimensions of conductance and resistance respectively.
Amplifiers are treated as a VS or a CS when
is zero or infinity respectively in
ideal cases. In practical situation, relative magnitudes of
and
determine the
type of amplifier output variable, When,
, the amplifier is considered as a
VS but if
, amplifier is a CS.
Table 8.2: Classification of amplifiers based on input and output resistances
.
Sl no
Amplifier type
and
and
1. Voltage
>>
2. Current
3. Trans-conductance
>>
4 Trans-resistance
In Table 8.2, we have enlisted the relative magnitudes of
and
of amplifier
compared to
and
respectively. Values of input and output resistance of an
amplifier are to be obtained in dynamic condition of amplifier. Input resistance of an
amplifier is defined as the ratio of input voltage measured at input port and injected
current to input port. Thus, we write,
.
In an ideal amplifier, R
i
is either zero or infinity. For a practical amplifier, R
i
is of
low or high magnitude depending on type of amplifier. Generally for BJT
amplifiers, it is of low value and for MOSFET amplifiers it is of high value. in
absence of R
L
the value of R
0
can be obtained in the following way. First, R
L
is
removed from circuit and input excitation signal source is replaced by a short circuit.
140 Analog Electronics: Devices and Circuits
Then, a voltage source v
x
is applied at the output port. The current (i
x
) going into the
port is measured. In this situation the ratio of v
x
and i
x
is output resistance
of
amplifier, i.e.
.We note that dependent voltage source considered at
output port of amplifier is replaced by a short circuit when input excitation signal is
zero. On the other hand, dependent current source at output port is replaced by an
open circuit for zero input excitation signals. R
0
appears in series with dependent
voltage source and ideally it is zero. For a dependent current source, R
0
appears in
parallel to source and is infinity in ideal case. In practice, output resistance of
amplifier is considered in presence of
.The effective value is denoted by
and
it is a parallel combination of
and
.
8.7. Negative resistance amplifier
So far we have discussed amplifiers as active TPN. The devices used in these
amplifiers are operated as externally controlled VS or CS when kept in proper
biasing condition. There is a different class of amplifiers where active devices
operate as negative resistive components under proper biasing. These are called
negative resistance amplifiers (NRA). Since positive resistances consume power, it
is expected that a negative resistance is capable of generating power.
Tunnel diode (TD) is one such device. Its volt current-voltage characteristic and
ac equivalent circuit are shown in Fig 4.8(a) and Fig 4.10 of chapter 4. In Fig 4.10
,
and C represent lead resistance and lead inductance and diode capacitance
respectively. In simplified model we may ignore the effects of lead inductance and
lead resistance at the operating frequency of the amplifier.
Fig 8.5: The equivalent circuit of tunnel diode based amplifier
The equivalent circuit of tunnel diode based NRA is shown in Fig 8.5. Here, an
input signal source
of internal resistance
is connected with the load
and
resistive equivalent of the TD. The diode is biased in the NDR region and at the
operating point it offers an NDR taken as
. We assume power gain of the
amplifier as
and the voltage across the load as. The power output across the
load
is written as
where
Thus power taken from input source
and power across the diode
are,
So we can write using principle of conservation of power
Thus the power gain of the amplifier is obtained as
Chapter 8: General Amplifier Theory 141
This relation indicates that large power gain can be obtained at the load
when
its magnitude is close to
but less than that. From the above discussion we get
that signal amplification is possible with a one port device which is properly biased
and enhanced power is obtained from the source used to keep the device in proper
bias condition.
8. 8. Effect of nonlinearity in amplifiers
When output voltage (
) of an amplifier is a nonlinear function of input voltage
(
), the amplifier is called a nonlinear amplifier. Generally,
is written as a
polynomial function of
as given below.
Here
’s are constants determining the property of the amplifier. The nonlinear
response of an amplifier can have different origins. It can be dc supply voltage
dependent limiting type nonlinearity or circuit and device parameter dependent
nonlinearity. Since
of an amplifier would be within dc supply voltage level, one
can have
up to a level dependent on supply voltage. This nonlinearity would
takes place for higher values of
. Again, when we use nonlinear circuit elements
like diodes, transistors etc in an amplifier, the gain of the amplifier becomes
dependent on the effective applied voltage level across those elements. In that case
we have circuit element dependent nonlinearity. Finally, all electronic devices are
inherently nonlinear in their response to external excitation. Keeping the level of
excitation low, one can have linear response of the device. But as excitation level
becomes high, one gets nonlinear response of the device. This results into device
dependent nonlinearity of an amplifier. For simple amplifiers, nonlinearity is treated
as disturbance by a circuit designer. It causes change in the waveform and output of
the amplifier is not a faithful reproduction of the input signal. However, nonlinearity
of an amplifier has several positive effects. Many applications of electronic circuits
are not possible using linear amplifiers only. We briefly discuss some applications of
nonlinear amplifiers (NLAs).
Changing of the shape of a given waveform from one type to the other is
necessary in several applications and in such cases, NLAs are only solution. To get
square wave or saw tooth wave, for example, from sinusoidal waveform, we use
NLAs. In mathematical operations on electrical signals one often requires logarithm
or antilogarithm of a given signal. Similarly, to have trigonometric functions of a
given signal is necessary for signal processing applications. All these operations are
done using different nonlinear amplifiers. A special group of amplifiers called
operational amplifiers have been designed to perform such nonlinear operations on
signals. We have discussed such applications of operational amplifiers as NLAs in a
proper chapter.
Linear amplifiers are used to increase the amplitude level of a given signal. But
suppose we have to multiply the frequency of a signal by a given factor. In that case
NLA is only solution. Let
be a quadratic function of
for a particular NLA i.e.,
we have
. If a signal of frequency f be applied to this amplifier we could
get a signal of frequency 2f from this NLA. In this application NLA is being used as
a “frequency multiplier”; besides the NLA, we have to use tuned circuit having
centre frequency 2f at the output of NLA. To get multiplying factor as n in place of
2, we require an NLA having n-th degree of nonlinearity. In that case we take
142 Analog Electronics: Devices and Circuits
and a tune circuit whose centre frequency is tuned at frequency. Frequency
multipliers have many applications in signal processing. Again we consider that two
sinusoidal signals of different frequencies say f
1
and f
2
are simultaneously applied to
an NLA having quadratic transfer function. In that case we get a group of signals of
frequencies 2f
1
, 2f
2
, (f
1
+f
2
), (f
1
-f
2
) besides a dc signal and signals having frequencies
f
1
and f
2
. Applying suitable frequency selective network at the output of the
amplifier, we can extract different groups of signals having new frequencies. This
feature of an NLA is applied in the design of frequency mixers, modulators,
demodulators etc. These circuits are widely used in electronic communication
systems and so importance of NLAs is easily understood.
In power amplifiers basic intension is to convert dc power of the supply voltage
into useful ac power. In these circuits conversion efficiency of dc power to ac power
is most important. To achieve this goal, output signal waveforms are deliberately
deformed. The design principle of class B, class C, class D type of power amplifiers
is very common example in this respect. Consider the case of class C amplifier
where output signal is obtained during a fraction of half cycle of the input signal
period. The active device used in the amplifier remains in non- conducting state
during most of the signal period and in the absence of output signal the loss of dc
power is minimized. This gives higher efficiency of the amplifier. Using suitable
frequency selective load for the amplifier in this group of amplifiers we get full
signal output. This is the principle of efficient power amplifier in simple words. We
have elaborately discussed theory and technique of power amplifier in a suitable
chapter. We thus observe that power amplifiers of high efficiency are special type of
NLAs.
Nonlinearity of amplifiers due to inherent nonlinear response of active devices
provides the basis of self-sustained oscillations in oscillator circuits. In a self-
oscillator building up of oscillation starts from very small amplitude noise signals
and this requires a gain element in the form of an amplifier. But the gain of the
amplifier must be a function of input signal appearing at its input and for larger input
the gain should decrease to provide a finite amplitude oscillation. Thus the amplifier
used in an oscillator must be nonlinear type. Besides this amplitude limiting feature
NLA-based oscillators shown several interesting phenomena. Frequency
synchronization is one such phenomenon where an oscillator gets synchronized to an
injected signal applied to it. During synchronized state, the driven oscillator follows
the frequency and phase of the driving signal of very low amplitude. This physical
phenomenon has been applied to design lock-in amplifiers, tracking filters,
synchronous modulators and detectors etc. Synchronous communication system is
developed around nonlinear oscillators and amplifiers. Using the nonlinearity of an
electronic system, we can design several hardware models of several physical events
of nonlinear dynamics like bifurcation and chaos. For this reason NLAs have
attracted the interest of researchers of different branches of knowledge.
8.9. Noise in an amplifier and Noise Figure
In any electronic circuit, presence of noise is inevitable. This is an unwanted
signal. It arises due to random fluctuations of charge carriers in circuit components
due to thermal agitation. Noise in a component is expressed in terms of absolute
temperature of the said component. The noise voltage is always present in an
Chapter 8: General Amplifier Theory 143
electronic circuit at nonzero temperature of operation. We know that electrons
present on a conductor or in a cavity wall are always in random thermal motion. In
macroscopic time scale there is no drift current in any direction due to these moving
electrons. But in microscopic time scale one observes fluctuating currents in
conductors with non-zero average value. This current produces a fluctuating voltage
drop across any resistive component. Since this voltage is random in time domain,
its frequency domain representation would have all possible frequency components
of equal power. This is the characteristics of white noise spectrum.
The overall effects of different noise sources in an electronic system are generally
specified by means of noise figure (NF) of the circuit. There are different ways of
defining NF. In our discussion we define it for a linear TPN in the following way.
For this purpose we take a standard noise source as reference. This noise source is
considered to have a bandwidth (BW) and it is kept at normal
temperature. Thus we have the available noise power from this source
where is Boltzman’s constant (
joules per Kelvin). Suppose
and
are the signal powers at the input and the output of the TPN respectively
and we take
as the available noise power at the output. Taking
as the
input noise power we write input signal-to-noise ratio ()
and output
. Then NF in dB of the TPN is defined as “ten times of the logarithm of
the ratio of input SNR to output SNR”. Thus,
We put as the power gain of the TPN. The noise performance of an amplifier can
be given in terms of NF defined above. Applying intuitive argument we write output
noise of the amplifier
as
The inherent noise of the amplifier is often expressed in terms of noise
temperature
. It is the absolute temperature of a matched load at the input of the
amplifier that would produce noise power
at its output when the amplifier
itself is considered to be an ideal system (i.e. it does not produce any noise itself). In
that case we write,
. For the amplifier, we take the standard noise
source mentioned earlier as the same matched load applied at the input of the real
amplifier at room temperature 300 K. So,
. Using these values for
and
we get NF of a practical amplifier as
Also we use the parameter
i.e. noise temperature of the amplifier defined in terms
of as
Solved problems
SP8.1. An amplifier with gain has noise figure. If its input signal power
and input noise power are respectively and then calculate output
noise power, output signal power and output signal to noise ration in .
144 Analog Electronics: Devices and Circuits
(
Then using given
data, ,
,
,
. Using
One get output noise power as
and output signal power as
SP8.2. In a three stage cascade amplifier individual gain of 1
st
stage, 2
nd
stage and
3
rd
stage are respectively, and , corresponding noise factors are
, and . Find out the total noise factor of the cascaded amplifier.
1
st
stage, 2
nd
stage and 3
rd
stage the value of noise factors are
gain of 1
st
stage of the amplifier then
, So
. Similarly for 2
nd
and 3
rd
stage
10,
According to Friiss’ formula, total noise factor of the cascaded amplifier is
So using above values
Important points
From the output port amplifiers can be treated as dependent voltage or current
sources. The amplifier can be driven by a voltage source or current source.
There are four different types of amplifiers: voltage, current, trans-conductance and
trans-resistance types.
Negative feedback has important role in the response of a generalized amplifier.
Nonlinearity in amplifiers has important role in several applications. Modulators,
demodulators, frequency multipliers, power amplifiers, synchronizers etc are
examples of such applications.
Exercise
Review Questions
R8.1.A trans-conductance amplifier is driven by a voltage source and it drives
current to the load at the output port-Justify the statement.
R8.2.How do we model a general amplifier in the high frequency operation? What is
Miller effect?
R8.3. What is gain-frequency figure of merit in an amplifier? Show that it is nearly
constant for a typical amplifier and it depends on device parameters.
R8.4.What is negative resistance amplifier? Obtain an expression for power gain of
a Tunnel diode based negative resistance amplifier.
R8.5. What do you mean by a nonlinear amplifier? Mention a few applications of a
nonlinear amplifier.
R8.6. Show that amplitude modulators could be designed using a special class of
nonlinear amplifiers.
R8.7. Define noise-figure of a typical amplifier.
Problem
1. Calculate noise temperature of an amplifier. Given its input signal to noise ratio
and the output signal to noise ratio are and respectively.
----- -----
About the book
————————————————————————————————
This book is a text-book on Analog Electronics according to the UGC CBCS
syllabus on B.Sc. (Honours and Generic) in Physics and Electronic Science and a
part of Electronics course of M Sc syllabus in Physics. It presents semiconductor
device physics and solid state electronic circuits. Some relevant advanced topics are
discussed as solved problems. Review questions and numerical problems are
included in each chapter. A set of objective questions (MCQ) and model question
papers are given for the benefit of the students. Chapters on integrated circuit design,
filter design are included in this revised second edition of the book.
About the authors
————————————————————————————————-
Prof. Bishnu Charan Sarkar (Retd)
had served Physics department, Burdwan
University for nearly 38 years. He was Head of the Department, In-charge of
Electronics section and Coordinator of M Tech in ECE (Microwave) program. He
was the Dean of Science of the University. He has a long research experience and
has published more than 200 technical papers in different journals and conference
proceedings.. He also supervised PhD works of 15 students. He has written or edited
7 technical books and contributed 4 book chapters (Springer, Nova Publishers)
Dr. (Mrs.) Suvra Sarkar
completed her B.Sc. and M.Sc. courses from the
University of Burdwan securing University Gold Medals in both cases. She received
her PhD degree from the same university. She was a CSIR research associate. Till
date she has published more than 60 technical papers and co-authored one book
chapter (Springer). Her teaching experience is more than 20 years and currently she
is Associate Professor and Head of the Department of Electronics, Burdwan Raj
College.