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A n al o g
El ect r o n i c
C i r cu i t s
Pr i n ci p l es & Fu n d am en t al s

K u m ar Raj a D R
Sy ed T h o u h eed A h m ed | Sy ed M u zam i l B ash a
ANALOG ELECTRONIC CIRCUITS
Principles and Fundamentals
First Edition

Kumar Raja D R
REVA University, Bengaluru, India

Syed Thouheed Ahmed

REVA University, Bengaluru, India

Syed Muzamil Basha

REVA University, Bengaluru, India

MileStone Research Publications

2022
The author(s) and publisher of this book have used their best efforts in preparing this book. these efforts include the
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Copyrights © 2022 by MileStone Research Publications, Inc.

This edition is published by arrangement with MileStone Research Foundation, Inc.

This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise
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prior written permission of both the copyright owner and the above mentioned publisher of this book.

ISBN 978-93-5636-178-2

First Edition Reprint, 2022

Published by MileStone Research Publications, Inc. India.

This edition is manufactured, printed and distributed in India and is authorised for sale in India, Bangladesh, Pakistan,
Nepal Sri Lanka and the Maldives.

Printed in India.
JOHN FORD

ELECTRONICS
Is clearly the winner of the dat
CONTENTS

Chapter-1: DIODE CIRCUITS

Introduction 1
Insulator 1
Conductors 2
Semiconductor 2
Semiconductor Types 2
EXTRINSIC SEMICONDUCTOR 3
N type semiconductor 3
P type semiconductor 3
Zero Biased PN Junction Diode 5

i
 Reverse Biased PN Junction Diode 5
Reverse Characteristics Curve for a Junction
Diode 6
Forward Biased PN Junction Diode 6
Forward Characteristics Curve for a Junction
Diode 7
Junction Diode Summary 7
Junction Diode Ideal and Real Characteristics
8
RECTIFIERS 8
INTRODUCTION 8
Characteristics of a Rectifier Circuit 9
CLASSIFICATION OF RECTIFIERS 11
HALF-WAVE RECTIFIER 11
Operation 12
DISADVANTAGES OF HALF-WAVE
RECTIFIER 12
FULL WAVE RECTIFIER 13
Advantages 16
Disadvantages 16
BIPOLAR JUNCTION TRANSISTOR 16

ii
INTRODUCTION 16
CONSTRUCTION OF BJT AND ITS
SYMBOLS 16
Bipolar Transistor Construction 17
TRANSISTOR CURRENT
COMPONENTS 18
Bipolar Transistor Configurations 19
COMMON-BASE CONFIGURATION 19
TRANSISTOR AS AN AMPLIFIER 21
Common-Emitter Configuration 21
Relationship analysis between α and β 23
COMMON – COLLECTOR CONFIGURATION
23
Limits of operation 24
BJT HYBRID MODEL 25
Z-parameters 25
Y-parameters 26
Hybrid parameters (h-parameters) 26
THE HYBRID MODEL FOR TWO
PORT 27

iii
 Analysis of a Transistor amplifier circuit using h-
parameters 31
Current Gain or Current Amplification (Ai) 31
Input Impedance (Zi) 31
Voltage Gain or Voltage Gain
Amplification Factor(Av) 32
Output Admittance (Yo) 33
Voltage Amplification Factor(Avs) taking into
account the resistance (Rs) of the
source 33
Current Amplification (Ais) taking into account
the source Resistance(RS) 34
Operating Power Gain (AP) 34
NEED FOR TRANSISTOR BIASING: 34
DC LOAD LINE 35
AC LOAD LINE 36
STABILITY FACTOR (S) 37
Stability factor S’ and S’’ 37
METHODS OF TRANSISTOR BIASING 38
Fixed bias (base bias) 38
Merits 38

iv
 Demerits 38
EMITTER-FEEDBACK BIAS 39
Merits 39
Demerits 39
COLLECTOR TO BASE BIAS OR
COLLECTOR FEED-BACK BIAS 40
Merits 41
Demerits 41
COLLECTOR –EMITTER FEEDBACK BIAS
41
VOLTAGE DIVIDER BIAS OR SELF BIAS
OR EMITTER BIAS 42
Merits 44
Demerits 44

Chapter-2: MOSFET CIRCUITS

INTRODUCTION 45
CLASSIFICATION OF FET 45
CONSTRUCTION AND OPERATION OF N-
CHANNEL FET 46
OPERATION OF N-CHANNEL JFET
46

v
 By varying the value of Vgs 47
Varying the value of Vds holding
Vgs constant 47
When both Vgs and Vds is applied
48
CHARACTERISTICS OF N-CHANNEL
JFET 48
Drain Characteristics 49
PINCH OFF Region 49
BREAKDOWN REGION 49
TRANSFER
CHARACTERISTICS 50
DIFFERENCE BETWEEN Vp
AND Vgsoff 50
Why the gate to source junction of
a JFET be always reverse biased? 50
JFET PARAMETERS 51
THE FET SMALL SIGNAL MODEL 51
MOSFET 52
CONSTRUCTION OF AN N-
CHANNEL MOSFET 53
DEPLETION MOSFET 53

vi
 Depletion mode operation 53
Enhancement mode operation of the D-
MOSFET 54
Characteristics of Depletion MOSFET
54
TRANSFER CHARACTERISTICS 55
E-MOSFETS 55
CHARACTERISTICS OF E MOSFET
56
DRAIN CHARACTERISTICS 56
TRANSFER CHARACTERISTICS 56
APPLICATION OF MOSFET 57
Field Effect Transistor 57
INTRODUCTION 57
Common Source (CS) Amplifier 58
Common Drain Amplifier 58
Voltage Gain 59
Input Impedance 59
Output Impedance 59

Chapter-3: MULTISTAGE AND POWER

AMPLIFIERS

vii
CLASSIFICATION OF AMPLIFIERS
61
DECIBEL NOTATION 61
MULTISTAGE AMPLIFIERS 62
DISTORTION IN AMPLIFIERS 63
NON – LINEAR DISTORTION 63
FREQUENCY DISTORTION 64
PHASE DISTRIBUTION 64
INTERMODULATION DISTORTION
64
FREQUENCY RESPONSE OF AN
AMPLIFIER 64
LOW FREQUENCY RESPONSE 66
HIGH FREQUENCY RESPONSE 66
FREQUENCY RESPONSE PLOTS 66
BANDWIDTH 66
RC COUPLED AMPLIFIER 67
ANALYSIS OF TWO STAGE RC
COUPLED AMPLIFIER 67
Current gain (Ai2) 68
Input resistance (Ri2) 68

viii
 Voltage gain (Av2) 68
Current gain (Ai1) 68
Input resistance (Ri1) 68
Voltage gain (Av1) 69
Overall gain (Av ) 69
Darlington Transistor 69
POWER AMPLIFIERS 69
Power Transistor 70
Difference between Voltage and Power
Amplifiers 70
Classification Based on
Frequencies 71
Classification Based on Mode of
Operation 71
Terms Considering Performance 72
Collector Efficiency 72
Power Dissipation Capacity 72
Distortion 72
CLASS A POWER AMPLIFIER 72
Advantages of Class A Amplifiers 75
Disadvantages of Class A Amplifiers 75

ix
TRANSFORMER COUPLED 75
CLASS-A POWER AMPLIFIER 75
Transformer Action 76
Circuit Analysis 77
Advantages 77
Disadvantages 77
Applications 77
CLASS –B POWER AMPLIFIER 78
Class B Operation 78
Class B Push-Pull Amplifier 78
Construction 78
Operation 79
Power Efficiency of Class B Push-Pull
Amplifier 79
Complementary Symmetry Push-Pull
Class B Amplifier 80
Advantages 80
Disadvantages 81
Cross-over Distortion 81
Class AB Power Amplifier 82

x
 Class C Power Amplifier 83

Chapter-4: FEEDBACK AMPLIFIERS

INTRODUCTION TO FEEDBACK
AMPLIFIERS 84
CLASSIFICATION OF AMPLIFIERS 84
VOLTAGE AMPLIFIER 84
CURRENT AMPLIFIER 85
TRANSCONDUCTANCE AMPLIFIER
85
TRANSRESISTANCE AMPLIFIER 85
THE FEEDBACK CONCEPT 86
SAMPLING NETWORK 86
FEEDBACK NETWORK 87
MIXER 87
GAIN OR TRANSFER RATIO 87
TYPES OF FEEDBACK 87
FEATURE OF NEGATIVE FEEDBACK
AMPLIFIERS 88
ANALYSIS OF FEEDBACK
AMPLIFIER 88
GAIN WITH FEEDBACK 89

xi
GAIN STABILITY 89
REDUCTION IN FREQUENCY DISTORTION
90
NON LINEAR DISTORTION 90
NOISE 90
OSCILLATORS 90
Amplifier vs. Oscillator 91
Alternator vs. Oscillator 91
Classification of Oscillators 91
Nature of Sinusoidal Oscillations 92
Practical Oscillator Circuit 93
Frequency Stability of an Oscillator 93
The Barkhausen Criterion 94
Principle of Feedback Amplifier 94
Types of Tuned Circuit Oscillators 95
Hartley Oscillator 95
Construction 95
Tank Circuit 96
Operation 96
Frequency 96

xii
 Advantages 97
Disadvantages 97
Applications 97
Colpitts Oscillator 97
Construction 97
Tank Circuit 98
Operation 98
Frequency 98
Advantages 98
Applications 99
RC Phase shift oscillator 99
Drawbacks of LC circuits 99
Principle of Phase-shift oscillators 99
Phase-shift Oscillator Circuit 100
Construction 100
Operation 101
Advantages 101
Disadvantages 101
Wien bridge oscillator 101
Construction 101

xiii
 Operation 102
Advantages 103
Disadvantages 103

Chapter-5: OPERATIOANL AMPLIFIERS

Introduction to Operational amplifiers 104

Integrated Circuit 104
Advantages of Integrated Circuits 104
Types of Integrated Circuits 104
Analog Integrated Circuits 104
Linear Integrated Circuits 105
Radio Frequency Integrated Circuits 105
Digital Integrated Circuits 105
Construction of Operational Amplifier 105
Characteristics of Operational Amplifier 105
Open loop voltage gain 105
Output offset voltage 105
Common Mode Rejection Ratio 105
Slew Rate 106
Types of Operational Amplifiers 106

xiv
 Ideal Op-Amp 106
Practical Op-Amp 106
Inverting Amplifier 107
Non-Inverting Amplifier 108
Integrator and Differentiator 109
Waveform Generators 110
Square Wave Generator 110
Triangular Wave Generator 112
Bibliography 113

xv
 1

Chapter-1
DIODE CIRCUITS

P-N junction diode, I-V characteristics of a diode; review of half-wave and full-wave rectifiers,
clamping and clipping circuits. Input output characteristics of BJT in CB, CE, CC configurations,
biasing circuits,Load line analysis, common emitter, common base and common collector amplifiers;
Small signal equivalent circuits.

INTRODUCTON
Based on the electrical conductivity all the materials in nature are classified as
insulators,semiconductors, and conductors.

Insulator: An insulator is a material that offers a very low level (or negligible) of conductivity when
voltage is applied. Eg: Paper, Mica, glass, quartz. Typical resistivity level of an insulator is of the order
of 1010 to 1012 Ω-cm. The energy band structure of an insulator is shown in the fig.1.1. Band structure
ofa material defines the band of energy levels that an electron can occupy. Valance band is the range
of electron energy where the electron remain bended too the atom and do not contribute to the electric
current. Conduction bend is the range of electron energies higher than valance band where electrons
are free to accelerate under the influence of external voltage source resulting in the flow of charge.
The energy band between the valance band and conduction band is called as forbidden band
gap. It is the energy required by an electron to move from balance band to conduction band i.e. the
energy required for a valance electron to become a free electron.
1 eV = 1.6 x 10-19 J
For an insulator, as shown in the fig.1.1 there is a large forbidden band gap of greater than 5Ev.
Becauseof this large gap there a very few electrons in the CB and hence the conductivity of insulator
is poor. Even an increase in temperature or applied electric field is insufficient to transfer electrons
from VB to CB.

CB
CB CB

Forbidden band o
Eo =≈6eV
gap Eo ≈6eV

VB
VB
VB

Insulator Semiconductor Conductor

Fig:1.1 Energy band diagrams insulator, semiconductor and
conductor
 2

Conductors: A conductor is a material which supports a generous flow of charge when a voltage is applied
across its terminals. i.e. it has very high conductivity. Eg: Copper, Aluminum, Silver, Gold. The resistivity
of a conductor is in the order of 10-4 and 10-6 Ω-cm. The Valance and conduction bands overlap (fig1.1)
and there is no energy gap for the electrons to move from valance band to conduction band. This implies
that there are free electrons in CB even at absolute zero temperature (0K). Therefore at room temperature
when electric field is applied large current flows through the conductor.

Semiconductor: A semiconductor is a material that has its conductivity somewhere between the insulator
and conductor. The resistivity level is in the range of 10 and 104 Ω-cm. Two of the most commonly used
are Silicon (Si=14 atomic no.) and germanium (Ge=32 atomic no.). Both have 4 valanceelectrons. The
forbidden band gap is in the order of 1eV. For eg., the band gap energy for Si, Ge and GaAs is 1.21, 0.785
and 1.42 eV, respectively at absolute zero temperature (0K). At 0K and at low temperatures, the valance
band electrons do not have sufficient energy to move from V to CB. Thus semiconductors act a insulators
at 0K. as the temperature increases, a large number of valance electrons acquire sufficient energy to leave
the VB, cross the forbidden bandgap and reach CB. These are now free electrons as they can move freely
under the influence of electric field. At room temperature there are sufficient electrons in the CB and
hence the semiconductor is capable of conducting some current at room temperature.
Inversely related to the conductivity of a material is its resistance to the flow of charge or current.
Typical resistivity values for various materials’ are given as follows.

Semiconductor Types

A pure form of semiconductors is called as intrinsic semiconductor. Conduction inintrinsic

sc is either due to thermal excitation or crystal defects. Si and Ge are the two most important
semiconductors used. Other examples include Gallium arsenide GaAs, Indium Antimonide (InSb) etc.
Let us consider the structure of Si. A Si atomic no. is 14 and it has 4 valance electrons. These 4
electrons are shared by four neighboring atoms in the crystal structure by means of covalent bond. Fig.
1.2a shows the crystal structure of Si at absolute zero temperature (0K). Hence a pure SC acts has poor
conductivity (due to lack of free electrons) at low or absolute zero temperature.
The absence of electrons in covalent bond is represented by a small circle usually referred to as
hole which is of positive charge. Even a hole serves as carrier of electricity in a manner similar to that
of free electron. In a pure semiconductor, the number of holes is equal to the number of free electrons.
 3

EXTRINSIC SEMICONDUCTOR

Intrinsic semiconductor has very limited applications as they conduct very small amounts of
current at room temperature. The current conduction capability of intrinsic semiconductor can beincreased
significantly by adding a small amounts impurity to the intrinsic semiconductor. By adding impurities it
becomes impure or extrinsic semiconductor. This process of adding impurities is called as doping. The
amount of impurity added is 1 part in 106 atoms.

N type semiconductor: If the added impurity is a pentavalent atom then the resultant semiconductor is
called N-type semiconductor. Examples of pentavalent impurities are Phosphorus, Arsenic, Bismuth,
Antimony etc.

P type semiconductor: If the added impurity is a trivalent atom then the resultant semiconductor is called
P-type semiconductor. Examples of trivalent impurities are Boron, Gallium , indium etc. Thus inP type
sc , holes are majority carriers and electrons are minority carriers. Since each trivalent impurity atoms are
capable accepting an electron, these are called as acceptor atoms. The following fig 1.5b shows the
pictorial representation of P type sc

 The conductivity of N type sc is greater than that of P type sc as the mobility of electron is
greater than that of hole.

 For the same level of doping in N type sc and P type sc, the conductivity of an N type sc
is around twice that of a P type sc.

A PN Junction Diode is one of the simplest semiconductor devices around, and which has
the characteristic of passing current in only one direction only. However, unlike a resistor, a diode does
not behave linearly with respect to the applied voltage as the diode has an exponential current- voltage (
I-V ) relationship and therefore we cannot described its operation by simply using an equation such as
Ohm’s law.
If a suitable positive voltage (forward bias) is applied between the two ends of the PN junction, it
can supply free electrons and holes with the extra energy they require to cross the junction as the width of
the depletion layer around the PN junction is decreased.
By applying a negative voltage (reverse bias) results in the free charges being pulled away from
the junction resulting in the depletion layer width being increased. This has the effect of increasing or
decreasing the effective resistance of the junction itself allowing or blocking current flow through the
diode.
Then the depletion layer widens with an increase in the application of a reverse voltage and
narrows with an increase in the application of a forward voltage. This is due to the differences in the
electrical properties on the two sides of the PN junction resulting in physical changes taking place. One
of the results produces rectification as seen in the PN junction diodes static I-V (current-voltage)
characteristics. Rectification is shown by an asymmetrical current flow when the polarity of bias voltage
is altered as shown below.
 4

Junction Diode Symbol and Static I-V Characteristics

But before we can use the PN junction as a practical device or as a rectifying device we need to
firstly bias the junction, ie connect a voltage potential across it. On the voltage axis above, “Reverse Bias”
refers to an external voltage potential which increases the potential barrier. An external voltage which
decreases the potential barrier is said to act in the “Forward Bias” direction.
There are two operating regions and three possible “biasing” conditions for the standard
Junction Diode and these are:
1. Zero Bias – No external voltage potential is applied to the PN junction diode.
2. Reverse Bias – The voltage potential is connected negative, (-ve) to the P-type material and
positive, (+ve) to the N-type material across the diode which has the effect of Increasing the PN junction
diode’s width.
3. Forward Bias – The voltage potential is connected positive, (+ve) to the P-type material and
negative, (-ve) to the N-type material across the diode which has the effect of Decreasing the PN junction
diodes width.
Zero Biased Junction Diode
When a diode is connected in a Zero Bias condition, no external potential energy is applied to the
PN junction. However if the diodes terminals are shorted together, a few holes (majority carriers) in the
P-type material with enough energy to overcome the potential barrier will move across the junction against
this barrier potential. This is known as the “Forward Current” and is referenced as IF

Likewise, holes generated in the N-type material (minority carriers), find this situation favourable
and move across the junction in the opposite direction. This is known as the “Reverse Current” and is
referenced as IR. This transfer of electrons and holes back and forth across the PN junction is known as
diffusion, as shown below.
 5

Zero Biased PN Junction Diode

The potential barrier that now exists discourages the diffusion of any more majority carriers across
the junction. However, the potential barrier helps minority carriers (few free electrons in the P- region and
few holes in the N-region) to drift across the junction.
The minority carriers are constantly generated due to thermal energy so this state of equilibrium
can be broken by raising the temperature of the PN junction causing an increase in the generation of
minority carriers, thereby resulting in an increase in leakage current but an electric current cannot flow
since no circuit has been connected to the PN junction.
Reverse Biased PN Junction Diode
When a diode is connected in a Reverse Bias condition, a positive voltage is applied to the N- type
material and a negative voltage is applied to the P-type material.
The positive voltage applied to the N-type material attracts electrons towards the positive electrode
and away from the junction, while the holes in the P-type end are also attracted away from the junction
towards the negative electrode.
The net result is that the depletion layer grows wider due to a lack of electrons and holes and
presents a high impedance path, almost an insulator. The result is that a high potential barrier is created
thus preventing current from flowing through the semiconductor material.
Increase in the Depletion Layer due to Reverse Bias
 6

This condition represents a high resistance value to the PN junction and practically zero current
flows through the junction diode with an increase in bias voltage. However, a very small leakagecurrent
does flow through the junction which can be measured in micro-amperes, ( μA ).
One final point, if the reverse bias voltage Vr applied to the diode is increased to a sufficiently
high enough value, it will cause the diode’s PN junction to overheat and fail due to the avalanche effect
around the junction. This may cause the diode to become shorted and will result in the flow of maximum
circuit current, and this shown as a step downward slope in the reverse static characteristics curve below.
Reverse Characteristics Curve for a Junction Diode

Sometimes this avalanche effect has practical applications in voltage stabilizing circuits where a
series limiting resistor is used with the diode to limit this reverse breakdown current to a presetmaximum
value thereby producing a fixed voltage output across the diode. These types of diodes are commonly
known as Zener Diodes and are discussed in a later tutorial.
Forward Biased PN Junction Diode
When a diode is connected in a Forward Bias condition, a negative voltage is applied to the N-
type material and a positive voltage is applied to the P-type material. If this external voltage becomes
greater than the value of the potential barrier, approx. 0.7 volts for silicon and 0.3 volts for germanium,
the potential barriers opposition will be overcome and current will start to flow.
This is because the negative voltage pushes or repels electrons towards the junction giving them
the energy to cross over and combine with the holes being pushed in the opposite direction towards the
junction by the positive voltage. This results in a characteristics curve of zero current flowing up to this
voltage point, called the “knee” on the static curves and then a high current flow through the diode with
little increase in the external voltage as shown below.
 7

Forward Characteristics Curve for a Junction Diode

The application of a forward biasing voltage on the junction diode results in the depletion layer
becoming very thin and narrow which represents a low impedance path through the junction thereby
allowing high currents to flow. The point at which this sudden increase in current takes place is represented
on the static I-V characteristics curve above as the “knee” point.
Reduction in the Depletion Layer due to Forward Bias

This condition represents the low resistance path through the PN junction allowing very large
currents to flow through the diode with only a small increase in bias voltage. The actual potential
difference across the junction or diode is kept constant by the action of the depletion layer at
approximately 0.3v for germanium and approximately 0.7v for silicon junction diodes.
Since the diode can conduct “infinite” current above this knee point as it effectively becomes a
short circuit, therefore resistors are used in series with the diode to limit its current flow. Exceeding its
maximum forward current specification causes the device to dissipate more power in the form of heat than
it was designed for resulting in a very quick failure of the device.
Junction Diode Summary
 The PN junction region of a Junction Diode has the following important characteristics:
 Semiconductors contain two types of mobile charge carriers, “Holes” and “Electrons”.
 The holes are positively charged while the electrons negatively charged.
 A semiconductor may be doped with donor impurities such as Antimony (N-type doping),
so that it contains mobile charges which are primarily electrons.
 A semiconductor may be doped with acceptor impurities such as Boron (P-type doping),
 8

so that it contains mobile charges which are mainly holes.

 The junction region itself has no charge carriers and is known as the depletion region.
 The junction (depletion) region has a physical thickness that varies with the applied
voltage.
 When a diode is Zero Biased no external energy source is applied and a natural Potential
Barrier is developed across a depletion layer which is approximately 0.5 to 0.7v for silicon
diodes and approximately 0.3 of a volt for germanium diodes.
 When a junction diode is Forward Biased the thickness of the depletion region reduces and
the diode acts like a short circuit allowing full current to flow.
 When a junction diode is Reverse Biased the thickness of the depletion region increases and
the diode acts like an open circuit blocking any current flow, (only a very small leakage
current).
We have also seen above that the diode is two terminal non-linear device whose I-V characteristic
are polarity dependent as depending upon the polarity of the applied voltage, VD the diode is either
Forward Biased, VD > 0 or Reverse Biased, VD < 0. Either way we can model these current- voltage
characteristics for both an ideal diode and for a real silicon diode as shown:

Junction Diode Ideal and Real Characteristics

RECTIFIERS:

INTRODUCTION
For the operation of most of the electronics devices and circuits, a d.c. source is required. So it is
advantageous to convert domestic a.c. supply into d.c voltages. The process of converting a.c. voltage into
d.c. voltage is called as rectification. This is achieved with i) Step-down Transformer, ii) Rectifier,
iii) Filter and iv) Voltage regulator circuits.
These elements constitute d.c. regulated power supply shown in the fig 1 below.
 9

Fig 2.1: Block Diagram of regulated D.C Power Supply

 Transformer – steps down 230V AC mains to low voltage AC.

 Rectifier – converts AC to DC, but the DC output is varying.
 Smoothing – smooth the DC from varying greatly to a small ripple.
 Regulator – eliminates ripple by setting DC output to a fixed voltage.

The block diagram of a regulated D.C. power supply consists of step-down transformer, rectifier,
filter, voltage regulator and load. An ideal regulated power supply is an electronics circuit designed to
provide a predetermined d.c. voltage Vo which is independent of the load current and variations in the
input voltage ad temperature. If the output of a regulator circuit is a AC voltage then it is termed as voltage
stabilizer, whereas if the output is a DC voltage then it is termed as voltage regulator.

RECTIFIER
Any electrical device which offers a low resistance to the current in one direction but a high resistance to
the current in the opposite direction is called rectifier. Such a device is capable of converting a sinusoidal
input waveform, whose average value is zero, into a unidirectional Waveform, with a non- zero average
component. A rectifier is a device, which converts a.c. voltage (bi-directional) to pulsating
d.c. voltage (Unidirectional).

Characteristics of a Rectifier Circuit:

Any electrical device which offers a low resistance to the current in one direction but a high resistance to
the current in the opposite direction is called rectifier. Such a device is capable of converting a sinusoidal
input waveform, whose average value is zero, into a unidirectional waveform, with a non- zero average
component.
A rectifier is a device, which converts a.c. voltage (bi-directional) to pulsating d.c..Load currents: They
are two types of output current. They are average or d.c. current and RMS currents.
Average or DC current: The average current of a periodic function is defined as the area of one cycle of
the curve divided by the base.
 10

i) Effective (or) R.M.S current:

The effective (or) R.M.S. current squared ofa periodic function of time is given by the area of one cycle
of the curve, which represents the square of the function divided by the base.

1T
T
Vrms  V d (wt)

ii) Peak factor:

It is the ratio of peak value to Rms value

peakvalue
Peak factor =
rmsvalue
iii) Form factor:

It is the ratio of Rms value to average value

Rmsvalue
Form factor=
averagevalue

iv) Ripple Factor:

It is defined as ration of R.M.S. value of a.c. component to the d.c. component in the output is known
as “Ripple Factor”.

v) Efficiency :
It is the ratio of d.c output power to the a.c. input power. It signifies, how efficiently the rectifier circuit
converts a.c. power into d.c. power.

  o / p power
i / p power

vi) Peak Inverse Voltage (PIV):

It is defined as the maximum reverse voltage that a diode can withstand without destroying the
junction.
 11

vii) Transformer Utilization Factor (UTF):

The d.c. power to be delivered to the load in a rectifier circuit decides the rating of the
Transformer used in the circuit. So, transformer utilization factor is defined as

Pdc
TUF 
pac(rated)
viii) % Regulation:

The variation of the d.c. output voltage as a function of d.c. load current is called regulation. The
percentage regulation is defined as

VNL  VFL
% Re gulation  *100
VFL

For an ideal power supply, % Regulation is zero.

CLASSIFICATION OF RECTIFIERS
Using one or more diodes in the circuit, following rectifier circuits can be designed.
1) Half - Wave Rectifier
2) Full – Wave Rectifier
3) Bridge Rectifier
HALF-WAVE RECTIFIER:
A Half – wave rectifier as shown in fig 1.2 is one, which converts a.c. voltage into a pulsating voltage
using only one half cycle of the applied a.c. voltage.

Fig 1.2: Basic structure of Half-Wave Rectifier

 12

The a.c. voltage is applied to the rectifier circuit using step-down transformer-rectifying element i.e., p-
n junction diode and the source of a.c. voltage, all connected is series. The a.c. voltage is applied to the
rectifier circuit using step-down transformer

V=Vm sin (wt)

The input to the rectifier circuit, Where Vm is the peak value of secondary a.c. voltage.

Operation:
For the positive half-cycle of input a.c. voltage, the diode D is forward biased and hence it conducts.
Now a current flows in the circuit and there is a voltage drop across RL.
For the negative half-cycle of input, the diode D is reverse biased and hence it does not
Conduct. Now no current flows in the circuit i.e., i=0 and Vo=0. Thus for the negative half- cycle
no power is delivered to the load.

Let a sinusoidal voltage Vi be applied to the input of the rectifier.

Then V=Vm sin (wt) Where Vm is the maximum value of the secondary voltage. Let the diode be
idealized to piece-wise linear approximation with resistance Rf in the forward direction i.e., in the ON
state and Rr (=∞) in the reverse direction i.e., in the OFF state. Now the current ‘i’ in the diode (or) in
the load resistance RL is given by V=Vm sin(wt)

DISADVANTAGES OF HALF-WAVE RECTIFIER:

1. The ripple factor is high.

2. The efficiency is low.
3. The Transformer Utilization factor is low.
 13

FULL WAVE RECTIFIER:

A full-wave rectifier converts an ac voltage into a pulsating dc voltage using both half cycles of the
applied ac voltage. In order to rectify both the half cycles of ac input, two diodes are used in this circuit.
The diodes feed a common load RL with the help of a center-tap transformer. A center-tap transformer
is the one, which produces two sinusoidal waveforms of same magnitude and frequency but out of
phase with respect to the ground in the secondary winding of the transformer.

Fig. 5 shows the input and output wave forms of the ckt.
During positive half of the input signal, anode of diode D1 becomes positive and at the
same time the anode of diode D2 becomes negative. Hence D1 conducts and D2 does not
conduct. The load current flows through D1 and the voltage drop across RL will be equal to
the input voltage.
During the negative half cycle of the input, the anode of D1 becomes negative and the anode of
D2 becomes positive. Hence, D1 does not conduct and D2 conducts. The load current flows through D2
and the voltage drop across RL will be equal to the input voltage. It is noted that the load current flows in
the both the half cycles of ac voltage and in the same direction through the load resistance.
i) AVERAGEVOLTAGE
 14

ii) AVERAGE CURRENT

iii) RMS VOLTAGE:

1T
Vrms
V d (wt)

2
1
Vrms
2  (V sim(wt)) d (wt)
m

IV) RMS CURRENT

2Im

rms


vi) FORM FACTOR

Rms value
Form factor=
averagevalue

Form factor= (Vm / 2)

2Vm /

Form Factor =1.11

 15

vii) Ripple Factor:

V) Efficiency:

viii) Transformer Utilization Factor (TUF):

The d.c. power to be delivered to the load in a rectifier circuit decides the rating of the transformer used
in the circuit. So, transformer utilization factor is defined as
pdc
TUF
Pac(rated)
 16

ix) Peak Inverse Voltage (PIV):

It is defined as the maximum reverse voltage that a diode can withstand without destroying the junction.
The peak inverse voltage across a diode is the peak of the negative half- cycle. For half- wave rectifier,
PIV is 2Vm.
x) % Regulation

Advantages:

1) Ripple factor = 0.482 (against 1.21 for HWR)

2) Rectification efficiency is 0.812 (against 0.405 for HWR)
3) Better TUF (secondary) is 0.574 (0.287 for HWR)
4) No core saturation problem
Disadvantages:
1) Requires center tapped transformer.

BIPOLAR JUNCTION TRANSISTOR

INTRODUCTION
A bipolar junction transistor (BJT) is a three terminal device in which operation depends on the
interaction of both majority and minority carriers and hence the name bipolar. The BJT is analogues to
vacuum triode and is comparatively smaller in size. It is used as amplifier and oscillator circuits, and as
a switch in digital circuits. It has wide applications in computers, satellites and other modern
communication systems.

CONSTRUCTION OF BJT AND ITS SYMBOLS

The Bipolar Transistor basic construction consists of two PN-junctions producing three connecting
terminals with each terminal being given a name to identify it from the other two. These three terminals
are known and labelled as the Emitter ( E ), the Base ( B ) and the Collector ( C ) respectively. There are
two basic types of bipolar transistor construction, PNP and NPN, which basically describes the physical
arrangement of the P-type and N-type semiconductor materials from which they are made.
 17

Transistors are three terminal active devices made from different semiconductor materials that can act as
either an insulator or a conductor by the application of a small signal voltage. The transistor's ability to
change between these two states enables it to have two basic functions: "switching" (digital electronics)
or "amplification" (analogue electronics). Then bipolar transistors have the ability to operate within three
different regions:

1. Active Region - the transistor operates as an amplifier and Ic = β.Ib

2. Saturation - the transistor is "fully-ON" operating as a switch and Ic = I(saturation)
3. Cut-off - the transistor is "fully-OFF" operating as a switch and Ic = 0

Bipolar Transistors are current regulating devices that control the amount of current flowing through
them in proportion to the amount of biasing voltage applied to their base terminal acting like a
current-controlled switch. The principle of operation of the two transistor types PNP and NPN, is
exactly the same the only difference being in their biasing and the polarity of the power supply for
each type.
Bipolar Transistor Construction

Fig 3.1 Bipolar Junction Transistor Symbol

 18

The construction and circuit symbols for both the PNP and NPN bipolar transistor are given
above with the arrow in the circuit symbol always showing the direction of "conventional
current flow" between the base terminal and its emitter terminal. The direction of the arrow
always points from the positive P-type region to the negative N-type region for both transistor
types, exactly the same as for the standard diode symbol.
TRANSISTOR CURRENT COMPONENTS:

Fig 3.2 Bipolar Junction Transistor Current Components

The above fig 3.2 shows the various current components, which flow across the forward biased emitter
junction and reverse- biased collector junction. The emitter current IE consists of hole current IPE (holes
crossing from emitter into base) and electron current InE (electrons crossing from base into emitter).The
ratio of hole to electron currents, IpE / InE , crossing the emitter junction is proportional to the ratio of the
conductivity of the p material to that of the n material. In a transistor, the doping of that of the emitter is
made much larger than the doping of the base. This feature ensures (in p-n-p transistor) that the emitter
current consists an almost entirely of holes. Such a situation is desired since the current which results from
electrons crossing the emitter junction from base to emitter do not contribute carriers, which can reach the
collector.

For a p-n-p transistor, ICO consists of holes moving across JC from left to right (base to collector) and
electrons crossing JC in opposite direction. Assumed referenced direction for ICO i.e. from right to left, then
for a p-n-p transistor, ICO is negative. For an n-p-n transistor, ICO is positive.The basic operation will be
described using the pnp transistor. The operation of the pnp transistor is exactly the same if the roles
played by the electron and hole are interchanged. One p-n junction of a transistor is reverse-biased,
whereas the other is forward-biased.
 19

Bipolar Transistor Configurations

As the Bipolar Transistor is a three terminal device, there are basically three possible ways to connect
it within an electronic circuit with one terminal being common to both the input and output. Each
method of connection responding differently to its input signal within a circuit as the static
characteristics of the transistor vary with each circuit arrangement.
1. Common Base Configuration - has Voltage Gain but no Current Gain.
2 Common Emitter Configuration - has both Current and Voltage Gain.
3. Common Collector Configuration - has Current Gain but no Voltage Gain.
COMMON-BASE CONFIGURATION

Common-base terminology is derived from the fact that the : base is common to both input and output of
t configuration. base is usually the terminal closest to or at ground potential. Majority carriers can cross
the reverse-biased junction because the injected majority carriers will appear as minority carriers in the n-
type material. All current directions will refer to conventional (hole) flow and the arrows in all electronic
symbols have a direction defined by this convention.

Note that the applied biasing (voltage sources) are such as to establish current in the direction indicated
for each branch.

Fig 3.4 CB Configuration

 20

To describe the behavior of common-base amplifiers requires two set of characteristics:

1. Input or driving point characteristics.

2. Output or collector characteristics

The output characteristics has 3 basic regions:

 Active region –defined by the biasing arrangements

 Cutoff region – region where the collector current is 0A
 Saturation region- region of the characteristics to the left of VCB = 0V

Fig 3.5 CB Input-Output Characteristics

 21

Fig 3.6 CE Configuration

TRANSISTOR AS AN AMPLIFIER
Common-Emitter Configuration

It is called common-emitter configuration since : emitter is common or reference to both input and
output terminals. Emitter is usually the terminal closest to or at ground potential. Almost amplifier
design is using connection of CE due to the high gain for current and voltage. Two set of
characteristics are necessary to describe the behavior for CE ;input (base terminal) and output
(collector terminal) parameters. Proper Biasing common-emitter configuration in active region.

Fig 3.8 CE Configuration

 22

Base-emitter junction is forward bias Increasing VCE will reduce IB for different values.

Fig 3.9a Input characteristics for common-emitter npn transistor

Fig 3.9b Output characteristics for common-emitter npn transistor

 23

Relationship analysis between α and β

COMMON – COLLECTOR CONFIGURATION

Also called emitter-follower(EF). It is called common-emitter configuration since both the signal
source and the load share the collector terminal as a common connection point. The output voltage is
obtained at emitter terminal. The input characteristic of common-collector configuration is similar
with common-emitter configuration. Common-collector circuit configuration is provided with the
load resistor connected from emitter to ground. It is used primarily for impedance- matching
purpose since it has high input impedance and low output impedance.

Fig 3.10 CC Configuration

 24

For the common-collector configuration, the output characteristics are a plot of IE vs VCE for a range
of values of

IB.
Fig 3.11 Output Characteristics of CC Configuration for npn Transistor
Limits of operation

Many BJT transistor used as an amplifier. Thus it is important to notice the limits of operations. At
least 3 maximum values is mentioned in data sheet.

There are:

a) Maximum power dissipation at collector: PCmax or PD

b) Maximum collector-emitter voltage: VCEmax sometimes named as VBR(CEO) orVCEO.

c) Maximum collector current: ICmax

There are few rules that need to be followed for BJT transistor used as an amplifier. The rules are:
transistor need to be operate in active region! IC < ICmax PC < PCmax
 25

Note: VCE is at maximum and IC is at minimum (ICMAX=ICEO) in the cutoff region. IC is at

maximum and VCE is at minimum (VCE max = Vcesat = VCEO) in the saturation region. The
transistor operates in the active region between saturation and cutoff.

BJT HYBRID MODEL

Small signal low frequency transistor Models:
All the transistor amplifiers are two port networks having two voltages and two currents. The positive
directions of voltages and currents are shown in fig. 1.

Fig. 1
A two-port network is represented by four external variables: voltage V1 and current I1 at the input port,
and voltage V2 and current I2 at the output port, so that the two-port network can be treated as a black box
modeled by the relationships between the four variables, V1,V2, I1,I2 . Out of four variables two can be
selected as are independent variables and two are dependent variables. The dependent variables can be
expressed interns of independent variables. This leads to various two port parameters out of which the
following three are important:

1. Impedance parameters (z-parameters)

2. Admittance parameters (y-parameters)
3. Hybrid parameters (h-parameters)
Z-parameters
A two-port network can be described by z-parameters as

In matrix form, the above equation can be rewritten as

Where
Input impedance with output port open circuited

Reverse transfer impedance with input port open circuited

 26

Forward transfer impedance with output port open circuited

Output impedance with input port open circuited

Y-parameters
A two-port network can be described by Y-parameters as

In matrix form, the above equation can be rewritten as

Input admittance with output port short circuited

Reverse transfer admittance with input port short circuited

Forward transfer admittance with output port short circuited

Output admittance with input port short circuited

Hybrid parameters (h-parameters)

If the input current I1 and output voltage V2 are taken as independent variables, the dependent
variables V1 and I2 can be written as

Where h11, h12, h21, h22 are called as hybrid parameters.

 27

Input impedance with o/p port short circuited

Reverse voltage transfer ratio with i/p port open circuited

Forward voltage transfer ratio with o/p port short circuited

output impedance with i/p port open circuited

THE HYBRID MODEL FOR TWO PORT

NETWORK:

Based on the definition of hybrid parameters the mathematical model for two pert networks known as
h-parameter model can be developed. The hybrid equations can be written as:

(The following convenient alternative subscript notation is recommended

by the IEEE Standards:
i=11= input o = 22 = output

f =21 = forward transfer r = 12 = reverse transfer)

 28

If these parameters are specified for a particular configuration, then suffixes e,b or c are also
included, e.g. hfe ,h ib are h parameters of common emitter and common collector amplifiers

Using two equations the generalized model of the amplifier can be drawn as shown in fig. 2.

ANALYSIS OF A TRANSISTOR AMPLIFIER USING H-PARAMETERS:

To form a transistor amplifier it is only necessary to connect an external load and signal source as

indicated in and to bias the transistor properly.

Current gain:

For the transistor amplifier stage, Ai is defined as the ratio of output to input currents.

Input impedance:
The impedance looking into the amplifier input terminals ( 1,1' ) is the input impedance Zi
 29

Voltage gain:

The ratio of output voltage to input voltage gives the gain of the transistors.

Output Admittance:

It is defined as

Av is the voltage gain for an ideal voltage source (Rv = 0).

Consider input source to be a current source IS in parallel with a resistance RS as shown in fig. 3.

In this case, overall current gain AIS is defined as

 30

h-parameters:
To analyze multistage amplifier the h-parameters of the transistor used are obtained
from manufacture
data sheet. The manufacture data sheet usually provides h-parameter in CE
configuration. These parameters may be converted into CC and CB values. For
example fig. 4 hrc in terms of CE parameter can be obtained as follows.

hybrid model for transistor in three different configurations

Typical h-parameter values for a transistor

Parameter CE CC CB
hi 1100 Ω 1100 Ω 22 Ω
hr 2.5 × 10-4 1 3 × 10-4
hf 50 -51 -0.98
ho 25 µA/V 25 µA/V 0.49 µA/V
 31

Analysis of a Transistor amplifier circuit using h-parameters

A transistor amplifier can be constructed by connecting an external load and signal source and
biasing the transistor properly.

Fig.1.4 Basic Amplifier Circuit

The two port network of Fig. 1.4 represents a transistor in any one of its configuration. It is
assumed that h-parameters remain constant over the operating range. The input is sinusoidal and I1,V-
1,I2 and V2 are phase quantities.

Fig. 1.5 Transistor replaced by its Hybrid Model

Current Gain or Current Amplification (Ai)

For transistor amplifier the current gain Ai is defined as the ratio of output current to input
current.
Input Impedance (Zi)

In the circuit of Fig , RS is the signal source resistance .The impedance seen when looking into the
amplifier terminals (1,1’) is the amplifier input impedance Zi,

Zi = V1 / I1
From the input circuit of Fig V1 = hi I1 +

hrV2 Zi = ( hi I1 + hrV2) / I1

= hi + hr V2 / I1
 32

Substituting

V2 = -I2 ZL = A1I1ZL

Zi = hi + hr A1I1ZL / I1
= hi + hr A1ZL

Substituting for Ai

Zi = hi - hf hr ZL / (1+ hoZL)

= hi - hf hr ZL / ZL(1/ZL+ ho)

Taking the Load admittance as

YL =1/ ZL Zi = hi - hf hr / (YL + ho)

Voltage Gain or Voltage Gain Amplification Factor(Av)

The ratio of output voltage V2 to input voltage V1 give the voltage gain of the transistor i.e,

Av = V2 / V1

Substituting

V2 = -I2 ZL = A1I1ZL

Av = A1I1ZL / V1 = AiZL / Zi

Output Admittance (Yo)

Yo is obtained by setting VS to zero, ZL to infinity and by driving the output terminals from a generator
V2. If the current V2 is I2 then Yo= I2/V2 with VS=0 and RL= ∞.

From the circuit of fig

I2= hf I1 + hoV2

Dividing by V2,

I2 / V2 = hf I1/V2 + ho
 33

With V2= 0, by KVL in input circuit,

RSI1 + hi I1 + hrV2 = 0

(RS + hi) I1 + hrV2 = 0

Hence, I2 / V2 = -hr/ (RS + hi)

= hf (-hr/( RS + hi)+ho

Yo= ho- hf hr/( RS + hi)

The output admittance is a function of source resistance. If the source impedance is resistive then Yo is
real.

Voltage Amplification Factor(Avs) taking into account the resistance (Rs) of the source

Fig. 5.6 Thevenin’s Equivalent Input Circuit

This overall voltage gain Avs is given by

Avs = V2 / VS = V2V1 / V1VS = Av V1/ VS

From the equivalent input circuit using Thevenin’s equivalent for the source shown in Fig. 5.6

V1 = VS Zi / (Zi + RS)

V1 / VS = Zi / ( Zi + RS)

Then, Avs = Av Zi / ( Zi +

RS) Substituting Av = AiZL /

 34

Zi

Avs = AiZL / ( Zi + RS)

Avs = AiZL RS / ( Zi + RS) RS

Avs = AisZL / RS

Current Amplification (Ais) taking into account the source Resistance(RS)

Fig. 1.7 Norton’s Equivalent Input Circuit

The modified input circuit using Norton’s equivalent circuit for the calculation of Ais is shown in Fig.
1.7 Overall Current Gain, Ais = -I2 / IS = - I2I1 /I1 IS = Ai I1/IS
From Fig. 1.7 I1= IS RS / (RS +
Zi) I1 / IS = RS/ (RS +Zi)
and hence, Ais = Ai RS / (RS +Zi)

Operating Power Gain (AP)

The operating power gain AP of the transistor is defined as
AP = P2 / P1 = -V2 I2 / V1 I1 = AvAi = Ai AiZL/ Zi
AP = Ai 2(ZL/ Zi )

NEED FOR TRANSISTOR BIASING:

If the o/p signal must be a faithful reproduction of the i/p signal, the transistor must be operated
in active region. That means an operating point has to be established in this region . To establish an
operating point (proper values of collector current Ic and collector to emitter voltage VCE) appropriate
supply voltages and resistances must be suitably chosen in the ckt. This process of selecting proper supply
voltages and resistance for obtaining desired operating point or Q point is called as biasing and the ckt
used for transistor biasing is called as biasingckt.
 35

There are four conditions to be met by a transistor so that it acts as a faithful ampr:

1) Emitter base junction must be forward biased (VBE=0.7Vfor Si, 0.2V for Ge) and collector
base junction must be reverse biased for all levels of i/p signal.
2) Vce voltage should not fall below VCE (sat) (0.3V for Si, 0.1V for Ge) for any part of the i/p
signal. For VCE less than VCE (sat) the collector base junction is not probably reversebiased.
3) The value of the signal Ic when no signal is applied should be at least equal to the max. collector
current t due to signal alone.
4) Max. rating of the transistor Ic(max), VCE (max) and PD(max) should not be exceeded at any value of
i/p signal.

Consider the fig shown in fig1. If operating point is selected at A, A represents a condition when no
bias is applied to the transistor i.e, Ic=0, VCE =0. It does not satisfy the above said conditions necessary for
faithful amplification.

Point C is too close to PD(max) curve of the transistor. Therefore the o/p voltage swing in the positive
direction is limited.

Point B is located in the middle of active region .It will allow both positive and negative half cycles
in the o/p signal. It also provides linear gain and larger possible o/p voltages andcurrents

Hence operating point for a transistor amplifier is selected to be in the middle of active region.

DC LOAD LINE
Referring to the biasing circuit of fig 4.2a, the values of VCC and RC are fixed and Ic and VCE are
dependent on RB.

Applying Kirchhoff’s voltage law to the collector circuit in fig. 4.2a, we get

Fig 4.2a CE Amplifier circuit (b) Load line

 36

The straight line represented by AB in fig4.2b is called the dc load line. The coordinates of the end
point A are obtained by substituting VCE =0 in the above equation. Then . Therefore The
coordinates of A are VCE =0 and .

The coordinates of B are obtained by substituting Ic=0 in the above equation. Then Vce = Vcc.
Therefore the coordinates of B are VCE =Vcc and Ic=0. Thus the dc load line AB can be drawn if the values
of Rc and Vcc are known.

As shown in the fig4.2b, the optimum POINT IS LOCATED AT THE MID POINT OF THE
MIDWAY BETWEEN a AND b. In order to get faithful amplification, the Q point must be well within
the active region of the transistor.

Even though the Q point is fixed properly, it is very important to ensure that the operating point
remains stable where it is originally fixed. If the Q point shifts nearer to either A or B, the output voltage
and current get clipped, thereby o/p signal is distorted.

In practice, the Q-point tends to shift its position due to any or all of the following three main factors.

1) Reverse saturation current, Ico, which doubles for every 10oC raise in temperature
2) Base emitter Voltage ,VBE, which decreases by 2.5 mV per oC
3) Transistor current gain, hFE or β which increases withtemperature.
If base current IB is kept constant since IB is approximately equal to Vcc/RB. If the transistor is replaced
by another one of the same type, one cannot ensure that the new transistor will have identical parameters
as that of the first one. Parameters such as β vary over a range. This results in the variation ofcollector
current Ic for a given IB. Hence, in the o/p characteristics, the spacing between the curves might increase
or decrease which leads to the shifting of the Q-point to a location which might be completely
unsatisfactory.

AC LOAD LINE

After drawing the dc load line, the operating point Q is properly located at the center of the dc
load line. This operating point is chosen under zero input signal condition of the circuit. Hence the ac
load line should also pas through the operating point Q. The effective ac load resistance Rac, is a
combination of RC parallel to RL i.e. || . So the slope of the ac load line CQD will be .
To draw the ac load line, two end points, I.e. VCE(max) and IC(max) when the signal is applied are required.

, which locates point D on the Vce axis.

, which locates the point C on the IC axis.

 37

By joining points c and D, ac load line CD is constructed. As RC > Rac, The dc load line is less steep
than ac load line.

STABILITY FACTOR (S):

The rise of temperature results in increase in the value of transistor gain β and the leakage current
Ico. So, IC also increases which results in a shift in operating point. Therefore, The biasing network should
be provided with thermal stability. Maintenance of the operating point is specified by S, which indicates
the degree of change in operating point due to change in temperature.

The extent to which IC is stabilized with varying IC is measured by a stability factor S

For CE configuration

Differentiate the above equation w.r.t IC , We get

S should be small to have better thermal stability.

Stability factor S’ and S’’:

S’ is defined as the rate of change of IC with VBE, keeping IC and VBE constant.

S’’ is defined as the rate of change of IC with β, keeping ICO and VBE constant.
 38

METHODS OF TRANSISTOR BIASING

1) Fixed bias (base bias)

Fig 4.3 Fixed Biasing Circuit

This form of biasing is also called base bias. In the fig 4.3 shown, the single
power source (for example, battery) is used for both collector and base of a transistor,
although separate batteries can also be used.
In the given circuit, Vcc = IBRB + Vbe
Therefore, IB = (Vcc - Vbe)/RB
Since the equation is independent of current ICR, dIB//dICR =0 and the
stability factor is given by the equation….. reduces to
S=1+β
Since β is a large quantity, this is very poor biasing circuit. Therefore in
practice the circuit is not used fo biasing.
For a given transistor, Vbe does not vary significantly during use. As Vcc is
of fixed value, on selection of R the base current IB is fixed. Therefore this type is
called fixed bias type of circuit.
Also for given circuit, Vcc = ICRC + Vce
Therefore, Vce = Vcc - ICRC

Merits:
It is simple to shift the operating point anywhere in the active region by
merely changing the base resistor (RB).
A very small number of components are required.
Demerits:
The collector current does not remain constant with variation in temperature
or power supply voltage. Therefore the operating point is unstable.
Changes in Vbe will change IB and thus cause RE to change. This in turn
will alter the gain of the stage.
When the transistor is replaced with another one, considerable change in the
value ofβ can be expected. Due to this change the operating point will shift.
 39

EMITTER-FEEDBACK BIAS:

The emitter feedback bias circuit is shown in the fig 4.4. The fixed bias circuit
is modified by attaching an external resistor to the emitter. This resistor introduces
negative feedback that stabilizes the Q-point. From Kirchhoff's voltage law, the
voltage across the base resistor is
VRb = VCC - IeRe - Vbe.

Fig 4.4 Self Biasing Circuit

From Ohm's law, the base current is
Ib = VRb / Rb.
The way feedback controls the bias point is as follows. If Vbe is heldconstant
and temperature increases, emitter current increases. However, a larger Ie increases
the emitter voltage Ve = IeRe, which in turn reduces the voltage VRb across the base
resistor. A lower base-resistor voltage drop reduces the base current, which results in
less collector current because Ic = ß IB. Collector current and emitter current are
related by Ic = α Ie with α ≈ 1, so increase in emitter current with temperature is
opposed, and operating point is kept stable.
Similarly, if the transistor is replaced by another, there may be a change in IC
(corresponding to change in β-value, for example). By similar process as above, the
change is negated and operating point kept stable.
For the given circuit,
IB = (VCC - Vbe)/(RB + (β+1)RE).
Merits:
The circuit has the tendency to stabilize operating point against changes in
temperature and β-value.
Demerits:
In this circuit, to keep IC independent of β the following condition must be
met:
 40

which is approximately the case if ( β + 1 )RE >> RB.

As β-value is fixed for a given transistor, this relation can be satisfied either
by keeping RE very large, or making RB very low. If RE is of large value, high VCC
is necessary. This increases cost as well as precautions necessary while handling. If
RB is low, a separate low voltage supply should be used in the base circuit. Using two
supplies of different voltages is impractical. In addition to the above, RE causes ac
feedback which reduces the voltage gain of the amplifier.

COLLECTOR TO BASE BIAS OR COLLECTOR FEED-BACK BIAS:

Fig 4.5 Collector to Base Biasing Circuit

This configuration shown in fig 4.5 employs negative feedback to prevent
thermal runaway and stabilize the operating point. In this form of biasing, the base
resistor RB is connected to the collector instead of connecting it to the DC source Vcc.
So any thermal runaway will induce a voltage drop across the RC resistor that will
throttle the transistor's base current.
From Kirchhoff's voltage law, the voltage across the base resistor Rb is

By the Ebers–Moll model, Ic = βIb, and so

From Ohm's law, the base current , and so

Hence, the base current Ib is

 41

If Vbe is held constant and temperature increases, then the collector current
Ic increases. However, a larger Ic causes the voltage drop across resistor Rc to
increase, which in turn reduces the voltage across the base resistor Rb. A lower
base-resistor voltage drop reduces the base current Ib, which results in less collector
current Ic. Because an increase in collector current with temperature is opposed, the
operating point is kept stable.
Merits:
Circuit stabilizes the operating point against variations in temperature and β
(i.e. replacement of transistor)
Demerits:
In this circuit, to keep Ic independent of β, the following condition must be
met:

which is the case when

As β-value is fixed (and generally unknown) for a given transistor, this

relation can be satisfied either by keeping Rc fairly large or making Rb very low. If
Rc is large, a high Vcc is necessary, which increases cost as well as precautions
necessary while handling. If Rb is low, the reverse bias of the collector–base region
is small, which limits the range of collector voltage swing that leaves the transistor
in active mode. The resistor Rb causes an AC feedback, reducing the voltage gain of
the amplifier. This undesirable effect is a trade-off for greater Q-point stability.

Usage: The feedback also decreases the input impedance of the amplifier as
seen from the base, which can be advantageous. Due to the gain reduction from
feedback, this biasing form is used only when the trade-off for stability is warranted.

COLLECTOR –EMITTER FEEDBACK BIAS:

Fig 4.6 Collector-Emitter Biasing Circuit

 42

The above fig4.6 shows the collector –emitter feedback bias circuit that can
be obtained by applying both the collector feedback and emitter feedback. Here the
collector feedback is provided by connecting a resistance RB from the collector to the
base and emitter feedback is provided by connecting an emitter Re from emitter to
ground. Both feed backs are used to control collector current and base current IB in
the opposite direction to increase the stability as compared to the previous biasing
circuits.

VOLTAGE DIVIDER BIAS OR SELF BIAS OR EMITTER BIAS:

The voltage divider as shown in the fig 4.7 is formed using external resistors
R1 and R2. The voltage across R2 forward biases the emitter junction. By proper
selection of resistors R1 and R2, the operating point of the transistor can be made
independent of β. In this circuit, the voltage divider holds the base voltage fixed
independent of base current provided the divider current is large compared to the base
current. However, even with a fixed base voltage, collector current varies with
temperature (for example) so an emitter resistor is added to stabilize the Q-point,
similar to the above circuits with emitter resistor.

Fig 4.7 Voltage Divider Biasing Circuit

In this circuit the base voltage is given by:

voltage across

provided .

Also For the given circuit,

Let the current in resistor R1 is I1 and this is divided into two parts – current
through base and resistor R2. Since the base current is very small so for all practical
purpose it is assumed that I1 also flows through R2, so we have
 43

Applying KVL in the circuit, we have

It is apparent from above expression that the collector current is independent of ? thus the
stability is excellent. In all practical cases the value of VBE is quite small in comparison to the
V2, so it can be ignored in the above expression so the collector current is almost independent
of the transistor parameters thus this arrangement provides excellent stability.
Again applying KVL in collector circuit, we have

The resistor RE provides stability to the circuit. If the current through the collector rises, the
voltage across the resistor RE also rises. This will cause VCE to increase as the voltage V2 is
independent of collector current. This decreases the base current, thus collector current
increases to its former value.
Stability factor for such circuit arrangement is given by

If Req/RE is very small compared to 1, it can be ignored in the above

expression thus we have
 44

Which is excellent since it is the smallest possible value for the stability. In actual practice the value of stability
factor is around 8-10, since Req/RE cannot be ignored as compared to 1.
Merits:

 Unlike above circuits, only one dc supply is necessary.

 Operating point is almost independent of β variation.
 Operating point stabilized against shift in temperature.
 45

Chapter-2
MOSFET CIRCUITS

MOSFET structure and I-V characteristics. MOSFET as a switch. small signal equivalent circuits -
gain, input and output impedances, small-signal model and common-source, common-gate and
common-drain amplifiers, trans conductance, high frequency equivalent circuit.

INTRODUCTION
 The Field effect transistor is abbreviated as FET , it is an another semiconductor device like a BJT
which can be used as an amplifier or switch.
 The Field effect transistor is a voltage operated device. Whereas Bipolar junction transistor is a
current controlled device. Unlike BJT a FET requires virtually no input current.
 This gives it an extremely high input resistance , which is its most important advantage over a bipolar
transistor.
 FET is also a three terminal device, labeled as source, drain and gate.
 The source can be viewed as BJT’s emitter, the drain as collector, and the gate as the counter part of
the base.
 The material that connects the source to drain is referred to as the channel.

 FET operation depends only on the flow of majority carriers ,therefore they are called uni polar
devices. BJT operation depends on both minority and majority carriers.

 As FET has conduction through only majority carriers it is less noisy than BJT.

 FETs are much easier to fabricate and are particularly suitable for ICs because they occupy less space
than BJTs.

 FET amplifiers have low gain bandwidth product due to the junction capacitive effects and produce
more signal distortion except for small signal operation.

 The performance of FET is relatively unaffected by ambient temperature changes. As it has a negative
temperature coefficient at high current levels, it prevents the FET from thermal breakdown. The BJT
has a positive temperature coefficient at high current levels which leads to thermal breakdown.

CLASSIFICATION OF FET:
There are two major categories of field effect transistors:
1. Junction Field Effect Transistors
2. MOSFETs
These are further sub divided in to P- channel and N-channel devices.
MOSFETs are further classified in to two types Depletion MOSFETs and Enhancement. MOSFETs
When the channel is of N-type the JFET is referred to as an N-channel JFET, when the channel is of P-
type the JFET is referred to as P-channel JFET.
The schematic symbols for the P-channel and N-channel JFETs are shown in the figure.
 46

CONSTRUCTION AND OPERATION OF N- CHANNEL FET

If the gate is an N-type material, the channel must be a P-type material.

CONSTRUCTION OF N-CHANNEL JFET

A piece of N- type material, referred to as channel has two smaller pieces of P-type material attached to
its sides, forming PN junctions. The channel ends are designated as the drain and source . And the two
pieces of P-type material are connected together and their terminal is called the gate. Since this channel is
in the N-type bar, the FET is known as N-channel JFET.

OPERATION OF N-CHANNEL JFET:-

The overall operation of the JFET is based on varying the width of the channel to control the drain current.
A piece of N type material referred to as the channel, has two smaller pieces of P type material
attached to its sites, farming PN –Junctions. The channel’s ends are designated the drain and the source. And
the two pieces of P type material are connected together and their terminal is called the gate. With the gate
terminal not connected and the potential applied positive at the drain negative at the source a drain current Id
flows. When the gate is biased negative with respective to the source the PN junctions are reverse biased and
depletion regions are formed. The channel is more lightly doped than the P type gate blocks, so the depletion
regions penetrate deeply into the channel. Since depletion region is a region depleted of charge carriers it
behaves as an Insulator. The result is that the channel is narrowed. Its resistance is increased and Id is reduced.
When the negative gate bias voltage is further increased, the depletion regions meet at the center and Id is cut
off completely.
There are two ways to control the channel width
 By varying the value of Vgs
 And by Varying the value of Vds holding Vgs constant
 47

1 By varying the value of Vgs :-

We can vary the width of the channel and in turn vary the amount of drain current.
This can be done by varying the value of Vgs. This point is illustrated in the fig below. Here we are dealing
with N channel FET. So channel is of N type and gate is of P type that constitutes a PN junction. This PN
junction is always reverse biased in JFET operation .The reverse bias is applied by a battery voltage Vgs
connected between the gate and the source terminal i.e positive terminal of the battery is connected to the
source and negative terminal to gate.

1) When a PN junction is reverse biased the electrons and holes diffuse across junction by leaving
immobile ions on the N and P sides , the region containing these immobile ions is known as depletion
regions.
2) If both P and N regions are heavily doped then the depletion region extends symmetrically on both
sides.
3) But in N channel FET P region is heavily doped than N type thus depletion region extends more in N
region than P region.
4) So when no Vds is applied the depletion region is symmetrical and the conductivity becomes Zero.
Since there are no mobile carriers in the junction.
5) As the reverse bias voltage is increases the thickness of the depletion region also increases. i.e. the
effective channel width decreases .
6) By varying the value of Vgs we can vary the width of the channel.

2 Varying the value of Vds holding Vgs constant :-

 When no voltage is applied to the gate i.e. Vgs=0 , Vds is applied between source and drain the
electrons will flow from source to drain through the channel constituting drain current Id .
 With Vgs= 0 for Id= 0 the channel between the gate junctions is entirely open .In response to a small
applied voltage Vds , the entire bar acts as a simple semi conductor resistor and the current Id increases
linearly with Vds .
 The channel resistances are represented as rd and rs as shown in the fig.

 This increasing drain current Id produces a voltage drop across rd which reverse biases the gate to
 48

source junction,(rd> rs) .Thus the depletion region is formed which is not symmetrical .
 The depletion region i.e. developed penetrates deeper in to the channel near drain and less towards
source because Vrd >> Vrs. So reverse bias is higher near drain than at source.
 As a result growing depletion region reduces the effective width of the channel. Eventually a voltage
Vds is reached at which the channel is pinched off. This is the voltage where the current Id begins to
level off and approach a constant value.
 So, by varying the value of Vds we can vary the width of the channel holding Vgs constant.

When both Vgs and Vds is applied:-

It is of course in principle not possible for the channel to close Completely and there by reduce the current
Id to Zero for, if such indeed, could be the case the gate voltage Vgs is applied in the direction to provide
additional reverse bias
 When voltage is applied between the drain and source with a battery Vdd, the electrons flow from
source to drain through the narrow channel existing between the depletion regions. This constitutes
the drain current Id, its conventional direction is from drain to source.
 The value of drain current is maximum when no external voltage is applied between gate and source
and is designated by Idss.

 When Vgs is increased beyond Zero the depletion regions are widened. This reduces the effective
width of the channel and therefore controls the flow of drain current through the channel.
 When Vgs is further increased a stage is reached at which to depletion regions touch each other that
means the entire channel is closed with depletion region. This reduces the drain current to Zero.

CHARACTERISTICS OF N-CHANNEL JFET :-

The family of curves that shows the relation between current and voltage are known as characteristic
curves.
There are two important characteristics of a JFET.
1) Drain or VI Characteristics
2) Transfer characteristics
 49

 Drain Characteristics:-

Drain characteristics shows the relation between the drain to source voltage Vds and
drain current Id. In order to explain typical drain characteristics let us consider the curve with Vgs=
0.V.
1. When Vds is applied and it is increasing the drain current ID also increases linearly up to knee
point.
2. This shows that FET behaves like an ordinary resistor. This region is called as ohmic region.
3. ID increases with increase in drain to source voltage. Here the drain current is increased slowly as
compared to ohmic region.

4) It is because of the fact that there is an increase in VDS .This in turn increases the reverse bias voltage
across the gate source junction .As a result of this depletion region grows in size thereby reducing the
effective width of the channel.
5) All the drain to source voltage corresponding to point the channel width is reduced to a minimum
value and is known as pinch off.
6) The drain to source voltage at which channel pinch off occurs is called pinch off voltage(Vp).

PINCH OFF Region:-

1. This is the region shown by the curve as saturation region.
2. It is also called as saturation region or constant current region. Because of the channel is occupied
with depletion region , the depletion region is more towards the drain and less towards the source,
so the channel is limited, with this only limited number of carriers are only allowed to cross this
channel from source drain causing a current that is constant in this region. To use FET as an
amplifier it is operated in this saturation region.
3. In this drain current remains constant at its maximum value IDSS.
4. The drain current in the pinch off region depends upon the gate to source voltage and is given by
the relation

Id =Idss [1-Vgs/Vp]2

This is known as shokley’s relation.

BREAKDOWN REGION:-
 The region is shown by the curve .In this region, the drain current increases rapidly as the drain to
source voltage is increased.
 It is because of the gate to source junction due to avalanche effect.
 The avalanche break down occurs at progressively lower value of VDS because the reverse bias
gate voltage adds to the drain voltage thereby increasing effective voltage across the gate junction
 50

This causes
o The maximum saturation drain current is smaller
o The ohmic region portion decreased.
 It is important to note that the maximum voltage VDS which can be applied to FET is the lowest
voltage which causes available break down.

 TRANSFER CHARACTERISTICS:-

These curves shows the relationship between drain current ID and gate to source voltage VGS
for different values of VDS.

i) First adjust the drain to source voltage to some suitable value , then increase the gate to source
voltage in small suitable value.
ii) Plot the graph between gate to source voltage along the horizontal axis and current ID on the
vertical axis. We shall obtain a curve like this.

iii) As we know that if Vgs is more negative curves drain current to reduce . where V gs is made
sufficiently negative, Id is reduced to zero. This is caused by the widening of the depletion region
to a point where it is completely closes the channel. The value of Vgs at the cutoff pointis
designed as Vgsoff
iv) While the lower end is indicated by a voltage equal to Vgsoff
v) If Vgs continuously increasing , the channel width is reduced , then Id =0
vi) It may be noted that curve is part of the parabola; it may be expressed as
Id=Idss[1-Vgs/Vgsoff]2
DIFFERENCE BETWEEN Vp AND Vgsoff –
Vp is the value of Vgs that causes the JFET to become constant current component, It is measured at
Vgs =0V and has a constant drain current of Id =Idss .Where Vgsoff is the value of Vgs that reduces Id to
approximately zero.

Why the gate to source junction of a JFET be always reverse biased ?

The gate to source junction of a JFET is never allowed to become forward biased because the gate
material is not designed to handle any significant amount of current. If the junction is allowed to become
forward biased, current is generated through the gate material. This current may destroy the component. There
is one more important characteristic of JFET reverse biasing i.e. JFET’s have extremely high characteristic gate
input impedance. This impedance is typically in the high mega ohm range. With the advantage of extremely
high input impedance it draws no current from the source. The high input impedance of the JFET has led to its
extensive use in integrated circuits. The low current requirements of the component makes it perfect for use in
ICs. Where thousands of transistors must be etched on to a single piece of silicon. The low current draw helps
the IC to remain relatively cool, thus allowing more components to be placed in a smaller physical area.
 51

JFET PARAMETERS
The electrical behavior of JFET may be described in terms of certain parameters. Such parameters are
obtained from the characteristic curves.
A C Drain resistance(rd):
It is also called dynamic drain resistance and is the a.c resistance between the drain and source terminal, when
the JFET is operating in the pinch off or saturation region. It is given by the ratio of small change in drain to
source voltage ∆Vds to the corresponding change in drain current ∆Id for a constant gate to source voltage Vgs.
Mathematically it is expressed as rd=∆Vds/ ∆Id where Vgs is held constant.
TRANCE CONDUCTANCE (gm):
It is also called forward transconductance . It is given by the ratio of small change in drain current (∆Id) to the
corresponding change in gate to source voltage (∆Vds)
Mathematically the transconductance can be written as
gm=∆Id/∆Vds
AMPLIFICATION FACTOR (µ)
It is given by the ratio of small change in drain to source voltage (∆Vds) to the corresponding change in gate
to source voltage (∆Vgs)for a constant drain current (Id).
Thus µ=∆Vds/∆Vgs when Id held constant
The amplification factor µ may be expressed as a product of transconductance (gm)and ac drain resistance (rd)
µ=∆Vds/∆Vgs=gm rd

THE FET SMALL SIGNAL MODEL:-

The linear small signal equivalent circuit for the FET can be obtained in a manner similar to that
used to derive the corresponding model for a transistor.
We can express the drain current iD as a function f of the gate voltage and drain voltage V ds.
Id =f(Vgs,Vds) ------------------ (1)
The transconductance gm and drain resistance rd:-
If both gate voltage and drain voltage are varied, the change in the drain current is approximated by
using taylors series considering only the first two terms in the expansion
∆id= |vds=constant .∆vgs |vgs=constant∆vds
we can write ∆id=id
∆vgs=vgs
∆vds=vds
Id=gm v Vds→(1)

Where gm= |Vds |Vds

gm= |Vds
Is the mutual conductance or transconductance .It is also called as gfs or yfs common source forward
conductance .
The second parameter rd is the drain resistance or output resistance is defined as

rd= |Vgs |Vgs= |Vgs

rd= |Vgs
The reciprocal of the rd is the drain conductance gd .It is also designated by Yos and Gos and called
the common source output conductance . So the small signal equivalent circuit for FET can be drawn in two
different ways.
 52

1. small signal current –source model

2.small signal voltage-source model.
This low frequency model for FET has a Norton’s output circuit with a dependent current generator
whose magnitude is proportional to the gate-to –source voltage. The proportionality factor is the
transconductance ‘gm’. The output resistance is ‘rd’. The input resistance between the gate and source is infinite,
since it is assumed that the reverse biased gate draws no current. For the same reason the resistance between
gate and drain is assumed to be infinite.
These small signal models for FET can be used for analyzing the three basic FET amplifier
configurations:
1.common source (CS) 2.common drain (CD) or source follower
3. common gate(CG).
(a)Small Signal Current source model for FET (b)Small Signal voltage source model for FET

MOSFET:-
We now turn our attention to the insulated gate FET or metal oxide semi conductor FET which is having
the greater commercial importance than the junction FET.
Most MOSFETS however are triodes, with the substrate internally connected to the source. The circuit
symbols used by several manufacturers are indicated in the Fig below.

(a) Depletion type MOSFET (b) Enhancement type MOSFET

Both of them are P- channel

Here are two basic types of MOSFETS
(1) Depletion type (2) Enhancement type MOSFET.
D-MOSFETS can be operated in both the depletion mode and the enhancement mode. E MOSFETS are
restricted to operate in enhancement mode. The primary difference between them is their physical
construction.
The construction difference between the two is shown in the fig given below.

As we can see the D MOSFET have physical channel between the source and drain terminals(Shaded area)
 53

The E MOSFET on the other hand has no such channel physically. It depends on the gate voltage to form
a channel between the source and the drain terminals.
Both MOSFETS have an insulating layer between the gate and the rest of the component. This
insulating layer is made up of SIO2 a glass like insulating material. The gate material is made up of metal
conductor .Thus going from gate to substrate, we can have metal oxide semi conductor which is where the term
MOSFET comes from. Since the gate is insulated from the rest of the component, the MOSFET is sometimes
referred to as an insulated gate FET or IGFET. The foundation of the MOSFET is called the substrate. This
material is represented in the schematic symbol by the center line that is connected to the source. In the symbol
for the MOSFET, the arrow is placed on the substrate. As with JFET an arrow pointing in represents an N-
channel device, while an arrow pointing out represents p-channel device.

CONSTRUCTION OF AN N-CHANNEL MOSFET:-

The N- channel MOSFET consists of a lightly doped p type substance into which two heavily doped n+
regions are diffused as shown in the Fig. These n+ sections, which will act as source and drain. A thin layerof
insulation silicon dioxide (SIO2) is grown over the surface of the structure, and holes are cut into oxide layer,
allowing contact with the source and drain. Then the gate metal area is overlaid on the oxide, covering the entire
channel region. Metal contacts are made to drain and source and the contact to the metal over the channel area
is the gate terminal. The metal area of the gate, in conjunction with the insulating dielectric oxide layer and the
semiconductor channel, forms a parallel plate capacitor. The insulating layer of sio2
Is the reason why this device is called the insulated gate field effect transistor. This layer results in an extremely
high input resistance (10 10 to 10power 15ohms) for MOSFET.

DEPLETION MOSFET
The basic structure of D –MOSFET is shown in the fig. An N-channel is diffused between source and
drain with the device an appreciable drain current IDSS flows foe zero gate to source voltage, Vgs=0.

Depletion mode operation:-

1. The above fig shows the D-MOSFET operating conditions with gate and source terminals shorted
together(VGS=0V)
2. At this stage ID= IDSS where VGS=0V, with this voltage VDS, an appreciable drain current IDSS
flows.
3. If the gate to source voltage is made negative i.e. VGs is negative .Positive charges are induced in the
channel through the SIO2 of the gate capacitor.
4. Since the current in a FET is due to majority carriers(electrons for an N-type material) , the induced
positive charges make the channel less conductive and the drain current drops as Vgs is made more
negative.
 54

5. The re distribution of charge in the channel causes an effective depletion of majority carriers , which
accounts for the designation depletion MOSFET.
6. That means biasing voltage Vgs depletes the channel of free carriers This effectively reduces the width
of the channel , increasing its resistance.
7. Note that negative Vgs has the same effect on the MOSFET as it has on the JFET.

8. As shown in the fig above, the depletion layer generated by Vgs (represented by the white space
between the insulating material and the channel) cuts into the channel, reducing its width. As a result
,Id<Idss. The actual value of ID depends on the value of Idss,Vgs(off) and Vgs.
Enhancement mode operation of the D-MOSFET:-
 This operating mode is a result of applying a positive gate to source voltage Vgs to the device.
 When Vgs is positive the channel is effectively widened. This reduces the resistance of the channel
allowing ID to exceed the value of IDSS
 When Vgs is given positive the majority carriers in the p-type are holes. The holes in the p type
substrate are repelled by the +ve gate voltage.
 At the same time, the conduction band electrons (minority carriers) in the p type material are
attracted towards the channel by the +gate voltage.
 With the build up of electrons near the channel , the area to the right of the physical channel
effectively becomes an N type material.
 The extended n type channel now allows more current, Id> Idss

Characteristics of Depletion MOSFET:-

The fig. shows the drain characteristics for the N channel depletion type MOSFET
1) The curves are plotted for both Vgs positive and Vgs negative voltages
2) When Vgs=0 and negative the MOSFET operates in depletion mode when Vgs is positive ,the
MOSFET operates in the enhancement mode.
3) The difference between JFET and D MOSFET is that JFET does not operate for positive values of
Vgs.
4) When Vds=0, there is no conduction takes place between source to drain, if Vgs<0 and Vds>0 then
Id increases linearly.
5) But as Vgs,0 induces positive charges holes in the channel, and controls the channel width. Thus the
conduction between source to drain is maintained as constant, i.e. Id is constant.
 55

6) If Vgs>0 the gate induces more electrons in channel side, it is added with the free electrons generated
by source. again the potential applied to gate determines the channel width and maintains constant
current flow through it as shown in Fig

TRANSFER CHARACTERISTICS:-

The combination of 3 operating states i.e. Vgs=0V, VGs<0V, Vgs>0V is represented by the D
MOSFET transconductance curve shown in Fig.

 Here in this curve it may be noted that the region AB of the characteristics similar to that of JFET.
 This curve extends for the positive values of Vgs
 Note that Id=Idss for Vgs=0V when Vgs is negative,Id< Idss when Vgs= Vgs(off) ,Id is reduced to
approximately omA.Where Vgs is positive Id>Idss.So obviously Idss is not the maximum possible
value of Id for a MOSFET.
 The curves are similar to JFET so thet the D MOSFET have the same transconductance equation.

E-MOSFETS
The E MOSFET is capable of operating only in the enhancement mode. The gate potential must be
positive w.r.t to source.

 when the value of Vgs=0V, there is no channel connecting the source and drain materials.
 As aresult , there can be no significant amount of drain current.
 56

 When Vgs=0, the Vdd supply tries to force free electrons from source to drain but the presence of p-
region does not permit the electrons to pass through it. Thus there is no drain current at Vgs=0,
 If Vgs is positive, it induces a negative charge in the p type substrate just adjacent to the SIO2 layer.
 As the holes are repelled by the positive gate voltage, the minority carrier electrons attracted toward
this voltage. This forms an effective N type bridge between source and drain providing a path for
drain current.
 This +ve gate voltage forma a channel between the source and drain.
 This produces a thin layer of N type channel in the P type substrate. This layer of free electrons is
called N type inversion layer.

 The minimum Vgs which produces this inversion layer is called threshold voltage and is designated
by Vgs(th).This is the point at which the device turns on is called the threshold voltage Vgs(th)
 When the voltage Vgs is <Vgs (th) no current flows from drain to source.
 How ever when the voltage Vgs > Vgs (th) the inversion layer connects the drain to source and we
get significant values of current.

CHARACTERISTICS OF E MOSFET:-
o DRAIN CHARACTERISTICS

The volt ampere drain characteristics of an N-channel enhancement mode MOSFET are given in the fig

o TRANSFER CHARACTERISTICS:-

 The current Idss at Vgs≤ 0 is very small beinf of the order of a few nano amps.
 As Vgs is made +ve , the current Id increases slowly at forst, and then much more rapidly with an
increase in Vgs.
 The standard transconductance formula will not work for the E MOSFET.
 To determine the value of ID at a given value of VGs we must use the following relation
Id =K[Vgs-Vgs(Th)]2
 57

Where K is constant for the MOSFET . found as

K=

From the data specification sheets, the 2N7000 has the following ratings.
Id(on)= 75mA(minimum).
And Vgs(th)=0.8(minimum)

APPLICATION OF MOSFET

One of the primary contributions to electronics made by MOSFETs can be found in the area of digital
(computer electronics). The signals in digital circuits are made up of rapidly switching dc levels. This signal
is called as a rectangular wave ,made up of two dc levels (or logic levels). These logic levels are0V and
+5V. A group of circuits with similar circuitry and operating characteristics is referred to as a logic family.
All the circuits in a given logic family respond to the same logic levels, have similar speed and power-
handling capabilities , and can be directly connected together. One such logic family is complementary
MOS (or CMOS) logic. This logic family is made up entirely of MOSFETs.

Field Effect Transistor:

INTRODUCTION
Field Effect Transistor (FET) amplifiers provide an excellent voltage gain and high input impedance.
Because of high input impedance and other characteristics of JFETs they are preferred over BJTs for certain
types of applications.
There are 3 basic FET circuit configurations:
i)Common Source ii)Common Drain iii)Common Gain
Similar to BJT CE,CC and CB circuits, only difference is in BJT large output collector current is
controlled by small input base current whereas FET controls output current by means of small input voltage.
In both the cases output current is controlled variable.
FET amplifier circuits use voltage controlled nature of the JFET. In Pinch off region, ID depends only
on VGS.
 58

Common Source (CS) Amplifier

Fig. 7.1 (a) CS Amplifier (b) Small-signal equivalent circuit

A simple Common Source amplifier is shown in Fig. 7.1(a) and associated small signal equivalent circuit
using voltage-source model of FET is shown in Fig. 7.1(b)
Voltage Gain
Source resistance (RS) is used to set the Q-Point but is bypassed by CS for mid-frequency operation. From the
small signal equivalent circuit ,the output voltage
VO = -RDµVgs(RD + rd)
Where Vgs = Vi , the input voltage,
Hence, the voltage gain,
AV = VO / Vi = -RDµ(RD + rd)
Input Impedance
From Fig. 7.1(b) Input Impedance is
Zi = RG
For voltage divider bias as in CE Amplifiers of BJT
RG = R1 ║ R2
Output Impedance
Output impedance is the impedance measured at the output terminals with the input voltage V I = 0
From the Fig. 7.1(b) when the input voltage Vi = 0, Vgs = 0 and hence
µ Vgs = 0
The equivalent circuit for calculating output impedance is given in Fig. 7.2.
Output impedance Zo = rd ║ RD
Normally rd will be far greater than RD . Hence Zo ≈ RD
Common Drain Amplifier
A simple common drain amplifier is shown in Fig. 7.2(a) and associated small signal equivalent circuit using
the voltage source model of FET is shown in Fig. 7.2(b).Since voltage Vgd is more easily determined than Vgs,
the voltage source in the output circuit is expressed in terms of Vgs and Thevenin’s theorem.
 59

Fig. 7.2 (a)CD Amplifier (b)Small-signal equivalent circuit

Voltage Gain
The output voltage,
VO = RSµVgd / (µ + 1) RS + rd
Where Vgd = Vi the input voltage.
Hence, the voltage gain,
Av = VO / Vi = RSµ / (µ + 1) RS + rd
Input Impedance
Input Impedance Zi = RG
Output Impedance
From Fig. 7.2(b), Output impedance measured at the output terminals with input voltage Vi = 0 can be
calculated from the following equivalent circuit.
As Vi = 0: Vgd = 0: µvgd / (µ + 1) = 0
Output Impedance
ZO = rd / (µ + 1) ║RS When µ » 1
ZO = ( rd / µ) ║RS = (1/gm) ║RS
 60

Chapter-3
MULTISTAGE AND POWER AMPLIFIERS

Classification of Amplifiers, Distortion in amplifiers, Different coupling schemes

used in amplifiers, Frequency response and Analysis of multistage amplifiers,
Cascade amplifier, Darlington pair. Transistor at High Frequency: Hybrid -
model of Common Emitter transistormodel, fα, β and unity gain bandwidth, Gain
band width product. Differential Amplifiers, Power amplifiers - Class A, Class B,
Class C, Class AB.

In order to realize the function of amplification, the transformer may appear to be a potential
device. However, in a transformer, though there is magnification of input voltage or current,
the power required for the load has to be drawn from the source driving the input of the
transformer. The output power is always less than the input power due to the losses in the core
and windings. The situation in amplification is that the input source is not capable of supplying
appreciable power. Hence the functional block meant for amplification should not draw any
power from the input source but should deliver finite out power to the load.
Thus the functional block required should have input power
Pi = Vi Ii = 0
And give the output
P0 = V0 I0 = finite

Such a functional block is called an ideal amplifier, which is shown in Fig.1 below.

Power gain is G = P0/Pi

The power gain of an ideal amplifier being infinite may sound like witchcraft in that something
can be produced from nothing. The real fact is that the ideal amplifier requires dc input power.
It converts dc power to ac power without any demand on the signal source to supply the power
for the load.
 61

CLASSIFICATION OF AMPLIFIERS

Amplifiers are classified in many ways based on different criteria as given below.
I In terms of frequency range:
1. DC amplifiers. (0 Hz to 20 Hz)
2. Audio amplifiers (20 Hz to 20 KHz)
3. Radio frequency amplifiers (Few KHz to hundreds of KHz)
4. Microwave amplifiers (In the range of GHz)
5. Video amplifiers (Hundreds of GHz)

II In terms of signal strength:

1. Small signal amplifiers.

2. Large signal mplifiers
III. In terms of coupling:

1. Direct coupling.
2. Resistance – capacitance (RC) coupling.
3. Transformer coupling.

IV. In terms of parameter:

1. Voltage amplifiers.
2. Current amplifiers.
3. Power amplifiers.

V. In terms of biasing condition:

1. Class A amplifier
2. Class B amplifier
3. Class AB amplifier
4. Class C amplifier.

VI. In terms of tuning:

1. Single tuned amplifier
2. Double tuned amplifier
3. Stagger tuned amplifier.

DECIBEL NOTATION:

The power gain of an amplifier is expressed as the ratio of the output power to the input power.
When we have more than one stage of amplification i.e. when the output of one stage becomes the
input to the next stage, the overall gain has to be obtained by multiplying the gains of the
 62

individual stages. When large numbers are involved, this calculation becomes cumbersome.
Also, when we have passive coupling networks between amplifier stages, there will be attenuation
of the signal that is gain less than unity. To find the overall gain of a typical multistage amplifier
such as the one given below.

We have to multiply the various gains and attenuations. Moreover, when we wish to plot the gain
of an amplifier versus frequency, using large numbers for plotting is not convenient. Hence it has
been the practice to use a new unit called the decibel (usually abbreviated as dB) for measuring
the power gain of a four terminal network. The power gain in decibels is given by

G = 10 log10 P0 / Pi dB

This new notation is also significant in the field of acoustics as the response of the human ear
to sound intensity is found to be following this logarithmic pattern. The overall gain in decibel
notation can be obtained for the amplifier gain of the figure1 by simply adding the decibel
gains of the individual networks. If any network attenuates the signal, the gain will beless than
the unity and the decibel gain will be negative. Thus the overall gain for the amplifier chain
shown above is given by
Overall gain = 10 – 6 + 30 – 10 + 20 = 44 dB
The absolute power level of the output of an amplifier is sometimes specified in dBm, i.e. decibels
with reference to a standard power power level, which is usually, 1 Mw dissipated in a 600 load.
Therefore, if an amplifier has 100 Mw, its power level in dBm is equal to 10 log 100/1 = 20 dBm.

MULTISTAGE AMPLIFIERS:

In real time applications, a single amplifier can’t provide enough output. Hence, two or more
amplifier stages are cascaded (connected one after another) to provide greater output Such an
arrangement is known as multistage amplifier Though the basic purpose of this arrangement is
increase the overall gain, many new problems as a consequence of this, are to be taken care. For
e.g. problems such as the interaction between stages due to impedance mismatch, cumulative hum
& noise etc.
 63

DISTORTION IN AMPLIFIERS:

In any amplifier, ideally the output should be a faithful reproduction of the input. This is called
fidelity. Of course there could be changes in the amplitude levels. However in practice this never
happens. The output waveform tends to be different from the input. This is called as thedistortion.
The distortion may arise either from the inherent non – linearity in the transistor characteristics or
from the influence of the associated circuit.

The distortions are classified as:

1. Non – linear or amplitude distortion

2. Frequency distortion
3. Phase distortion
4. Inter modulation distortion
NON – LINEAR DISTORTION:

This is produced when the operation is over the non-linear part of the transfer characteristics of the
transistor. (A plot between output v/s input is called as the transfer characteristics). Since the
amplifier amplifies different parts of the input differently. For example, there can be compression
of the positive half cycle and expansion of the negative half cycle. Sometimes, the waveform can
become clipped also. (Flattening at the tips). Such a deviation from linear amplification produces
frequencies in the output, which are not originally present in the output. Harmonics (multiples) of
the input signal frequency are present in the output. The percentage harmonic distortion for the nth

Harmonic is given by

Dn = An (amplitude of the n the harmonic) 100%

A1(amplitude of the fundamental)

And the total harmonic distortion by

DT =

Where D2, D3 are harmonic components.

 64

A distortion factor meter measures the total distortion. The spectrum or wave analyzer can be used
to measure the amplitude of each harmonic.

FREQUENCY DISTORTION:

A practical signal is usually complex (containing many frequencies). Frequency distortion occurs
when the different frequency components in the input signal are amplified differently. This is due
to the various frequency dependent reactances (capacitive & inductive) present in the circuit or the
active devices (BJT or FET).

PHASE DISTRIBUTION:

This occurs due to different frequency components of the input signal suffering different phase
shifts. The phase shifts are also due to reactive effects and the active devices. This causes problems
in TV picture reception. To avoid this amplifier phase shift should be proportional to the frequency.

INTERMODULATION DISTORTION:

The harmonics introduced in the amplifier can combine with each other or with the original
frequencies to produce new frequencies to produce new frequencies that are not harmonics of the
fundamental. This is called inter modulation distortion. This distortion results in unpleasant
hearing.

FREQUENCY RESPONSE OF AN AMPLIFIER:

Frequency response of an amplifier is a plot between gain & frequency. If the gain is constant
(same) for all frequencies of the input signal, then this plot would be a flat line. But this never
happens in practice.

As explained earlier, there are different reactive effects present in the amplifier circuit and the
active devices used. Infact there are external capacitors used for blocking, capacitors etc. Also, in
tuned amplifiers, resonant LC circuits are connected in the collector circuits of the amplifier to get
narrow band amplification around the resonant frequencies.

Fig below shows a frequency response of a typical amplifier.

 65

Where Amid = mid band voltage gain (in dB)

fL = Lower cut – off frequency. (in Hz)

fH = Upper cut - off frequency (in Hz)

Usually the frequency response of an amplifier is divided into three regions. (i) The mid band
region or flat region, over which the gain is constant (ii) The lower frequency region. Here the
amplifier behaves like a high pass filter, which is shown below.

At high frequencies, the reactance of C1 will be small & hence it acts as a short without any
attenuation (reduction in signal voltage) (iii) In the high frequency region above mid band, the
circuit often behaves like the low pass filter as shown below.
 66

As the frequency is increased, the reactance of C2 decreases. Hence more voltage is dropped across
Rs and less is available at the output. Thus the voltage gain of the amplifier decreases at high
frequencies.

LOW FREQUENCY RESPONSE:

In the frequency below the mid band, the High pass filter as shown above can approximate the
amplifier. This is equal to 3 dB in log scale. For higher frequencies f >> f L, AL tends to unity.
Hence, the magnitude of AVL falls of to 70.7 % of the mid band value at f = fL, Such a frequency is
called the lower cut-off or lower 3 dB frequency.

HIGH FREQUENCY RESPONSE:

In the high frequency region, above the mid band , the amplifier stage can be approximated by the
low pass circuit.

FREQUENCY RESPONSE PLOTS:

The gain & phase plots versus frequency can be approximately sketched by using straight-line
segments called asymptotes. Such plots are called Bode plots. Being in log scale, these plots are
very convenient for evaluation of cascaded amplifiers.

BANDWIDTH:

The range of frequencies from fL to fH is called the bandwidth of the amplifier. The product of mid
band gain and the 3dB Bandwidth of an amplifier is called the Gain-bandwidth product. It is figure
of merit or performance measure for the amplifier.
 67

RC COUPLED AMPLIFIER:

Fig. (1) above shows a two stage RC coupled CE amplifier using BJTs where as fig.(2) shows the
FET version. The resistors RC & RB ( = R1R2 / (R1 + R2 ) and capacitors CC form the coupling
network. Because of this, the arrangement is called as RC coupled amplifier. The bypass capacitors
CE (= CS) are used to prevent loss of amplification due to –ve feedback. The junction capacitance
Cj should be taken into account when high frequency operation is considered.
When an ac signal is applied to the input of the I stage, it is amplified by the active device (BJT or
FET) and appears across the collector resistor RC / drain resistor RD. this output signal is connected
to the input of the second stage through a coupling capacitor CC. The second stage doesn’t further
amplification of the signal. In this way, the cascaded stages give a large output & the overall gain
is equal to the product of this individual stage gains.

ANALYSIS OF TWO STAGE RC COUPLED AMPLIFIER:

This analysis is done using h parameter model. Assuming all capacitors are arbitrarily large and
act as ac short circuits across RE. The dc power supply is also replaced by a short circuit. Their h
parameter approximate models replace the transistors.
 68

The parallel combination of resistors R1 and R2 is replaced by a single stage resistor RB.

RB = R1 || R2 = R1R2/ (R1 + R2)

For finding the overall gain of the two stage amplifier, we must know the gains of the individual
stages.

Current gain (Ai2):

Ai = - hfe / (1 + hoe RL)

Neglecting hoe as it is very small, Ai = -hfe

Input resistance (Ri2):

We know that Ri = hie + hreAi RL

Hence, Ri = hie and Ri2 = hie

Voltage gain (Av2):

We know that Av = Ai RL/ Ri

Av2 = - hfe RC2 / Ri2

Current gain (Ai1):
Ai1 = -hfe

Input resistance (Ri1):

Ri1 = hie
 69

Voltage gain (Av1):

AV = Ai RL / Ri1
Here RL = RC1 || RB || Ri2
AV1 = - hfe (RC1 || RB || Ri2 ) / Ri1
Overall gain (Av ):
AV = AV1 X AV2

A Darlington Transistor configuration, also known as a “Darlington pair” or “super-alpha circuit”,

consist of two NPN or PNP transistors connected together so that the emitter current of the first
transistor TR1 becomes the base current of the second transistor TR2. Then transistor TR1 is connected
as an emitter follower and TR2 as a common emitter amplifier as shown below. Also note that in this
Darlington pair configuration, the collector current of the slave or controltransistor, TR1 is “in-
phase” with that of the master switching transistor TR2.

Basic Darlington Transistor Configuration

Using the NPN Darlington pair as the example, the collectors of two transistors are connected
together, and the emitter of TR1 drives the base of TR2. This configuration achieves β multiplication
because for a Base current ib, the collector current is β*ib where the current gain is greater than one,
or unity and this is defined as:
But the base current, IB2 is equal to transistor TR1 emitter current, IE1 as the emitter of TR1 is
connected to the base of TR2.
This means that the overall current gain, β is given by the gain of the first transistor multiplied by
the gain of the second transistor as the current gains of the two transistors multiply. In other words, a
pair of bipolar transistors combined together to make a single Darlington transistor pair can be
regarded as a single transistor with a very high value of β and consequently a high input resistance.
POWER AMPLIFIERS
After the audio signal is converted into electrical signal, it has several voltage amplifications done,
after which the power amplification of the amplified signal is done just before the loud speaker stage.
This is clearly shown in the below figure.
 70

While the voltage amplifier raises the voltage level of the signal, the power amplifier raises the power
level of the signal. Besides raising the power level, it can also be said that a power amplifier is a
device which converts DC power to AC power and whose action is controlled by the input signal.
The DC power is distributed according to the relation,
DC power input = AC power output + losses

Power Transistor
For such Power amplification, a normal transistor would not do. A transistor that is manufactured to
suit the purpose of power amplification is called as a Power transistor.
A Power transistor differs from the other transistors, in the following factors.
 It is larger in size, in order to handle large powers.
 The collector region of the transistor is made large and a heat sink is placed at the collector-
base junction in order to minimize heat generated.
 The emitter and base regions of a power transistor are heavily doped.
 Due to the low input resistance, it requires low input power.
Hence there is a lot of difference in voltage amplification and power amplification. So, let us now try
to get into the details to understand the differences between a voltage amplifier and a power amplifier.

Difference between Voltage and Power Amplifiers

Let us try to differentiate between voltage and power amplifier.

Voltage Amplifier
The function of a voltage amplifier is to raise the voltage level of the signal. A voltage amplifier is
designed to achieve maximum voltage amplification.
The voltage gain of an amplifier is given by
Av=β(RcRin)Av=β(RcRin)
The characteristics of a voltage amplifier are as follows −
 The base of the transistor should be thin and hence the value of β should be greater than 100.
 The resistance of the input resistor Rin should be low when compared to collector load RC.
 The collector load RC should be relatively high. To permit high collector load, the voltage
amplifiers are always operated at low collector current.
 The voltage amplifiers are used for small signal voltages.
 71

Power Amplifier
The function of a power amplifier is to raise the power level of input signal. It is required to deliver
a large amount of power and has to handle large current.
The characteristics of a power amplifier are as follows −
 The base of transistor is made thicken to handle large currents. The value of β being (β > 100)
high.
 The size of the transistor is made larger, in order to dissipate more heat, which is produced
during transistor operation.
 Transformer coupling is used for impedance matching.
 Collector resistance is made low.
The Power amplifiers amplify the power level of the signal. This amplification is done in the last
stage in audio applications. The applications related to radio frequencies employ radio power
amplifiers. But the operating point of a transistor, plays a very important role in determining the
efficiency of the amplifier. The main classification is done based on this mode of operation.
The classification is done based on their frequencies and also based on their mode of operation.

Classification Based on Frequencies:

Power amplifiers are divided into two categories, based on the frequencies they handle. They are as
follows.
 Audio Power Amplifiers − The audio power amplifiers raise the power level of signals that
have audio frequency range (20 Hz to 20 KHz). They are also known as Small signal power
amplifiers.
 Radio Power Amplifiers − Radio Power Amplifiers or tuned power amplifiers raise the
power level of signals that have radio frequency range (3 KHz to 300 GHz). They are also
known as large signal power amplifiers.

Classification Based on Mode of Operation

On the basis of the mode of operation, i.e., the portion of the input cycle during which collector
current flows, the power amplifiers may be classified as follows.
 Class A Power amplifier − When the collector current flows at all times during the full cycle
of signal, the power amplifier is known as class A power amplifier.
 Class B Power amplifier − When the collector current flows only during the positive half
cycle of the input signal, the power amplifier is known as class B power amplifier.
 Class C Power amplifier − When the collector current flows for less than half cycle of the
input signal, the power amplifier is known as class C power amplifier.
There forms another amplifier called Class AB amplifier, if we combine the class A and class B
amplifiers so as to utilize the advantages of both.
Before going into the details of these amplifiers, let us have a look at the important terms that have
to be considered to determine the efficiency of an amplifier.
 72

Terms Considering Performance

The primary objective of a power amplifier is to obtain maximum output power. In order to achieve
this, the important factors to be considered are collector efficiency, power dissipation capability and
distortion. Let us go through them in detail.

Collector Efficiency
This explains how well an amplifier converts DC power to AC power. When the DC supply is given
by the battery but no AC signal input is given, the collector output at such a condition is observed as
collector efficiency.
The collector efficiency is defined as
η=averagea.cpoweroutputaveraged.cpowerinputtotransistorη=averagea.cpoweroutputaveraged.cpow
erinputtotransistor
For example, if the battery supplies 15W and AC output power is 3W. Then the transistor
efficiency will be 20%.
The main aim of a power amplifier is to obtain maximum collector efficiency. Hence the higher the
value of collector efficiency, the efficient the amplifier will be.

Power Dissipation Capacity

Every transistor gets heated up during its operation. As a power transistor handles large currents, it
gets more heated up. This heat increases the temperature of the transistor, which alters the operating
point of the transistor.
So, in order to maintain the operating point stability, the temperature of the transistor has to be kept
in permissible limits. For this, the heat produced has to be dissipated. Such a capacity is called as
Power dissipation capability.
Power dissipation capability can be defined as the ability of a power transistor to dissipate the
heat developed in it. Metal cases called heat sinks are used in order to dissipate the heat produced in
power transistors.

Distortion
A transistor is a non-linear device. When compared with the input, there occur few variations in the
output. In voltage amplifiers, this problem is not pre-dominant as small currents are used. But in
power amplifiers, as large currents are in use, the problem of distortion certainly arises.
Distortion is defined as the change of output wave shape from the input wave shape of the
amplifier. An amplifier that has lesser distortion, produces a better output and hence considered
efficient.
CLASS A POWER AMPLIFIER:
We have already come across the details of transistor biasing, which is very important for the
operation of a transistor as an amplifier. Hence to achieve faithful amplification, the biasing of the
transistor has to be done such that the amplifier operates over the linear region.
A Class A power amplifier is one in which the output current flows for the entire cycle of the AC
input supply. Hence the complete signal present at the input is amplified at the output. Thefollowing
figure shows the circuit diagram for Class A Power amplifier.
 73

From the above figure, it can be observed that the transformer is present at the collector as a load.
The use of transformer permits the impedance matching, resulting in the transference of maximum
power to the load e.g. loud speaker.The operating point of this amplifier is present in the linear region.
It is so selected that the current flows for the entire ac input cycle. The below figure explains the
selection of operating point.

The output characteristics with operating point Q is shown in the figure above. Here (Ic)Q and
(Vce)Q represent no signal collector current and voltage between collector and emitter respectively.
When signal is applied, the Q-point shifts to Q1 and Q2. The output current increases to (Ic)max and
decreases to (Ic)min. Similarly, the collector-emitter voltage increases to (Vce)max and decreases to
(Vce)min.
D.C. Power drawn from collector battery Vcc is given by
Pin=voltage×current=VCC(IC)QPin=voltage×current=VCC(IC)Q
This power is used in the following two parts −

 Power dissipated in the collector load as heat is given by

PRC=(current)2×resistance=(IC)2QRCPRC=(current)2×resistance=(IC)Q2RC
 74

 Power given to transistor is given by

Ptr=Pin−PRC=VCC−(IC)2QRCPtr=Pin−PRC=VCC−(IC)Q2RC
When signal is applied, the power given to transistor is used in the following two parts −
 A.C. Power developed across load resistors RC which constitutes the a.c. power output.

(PO)ac=I2RC=V2RC=(Vm2–

√)21RC=V2m2RC(PO)ac=I2RC=V2RC=(Vm2)21RC=Vm22RC
Where I is the R.M.S. value of a.c. output current through load, V is the R.M.S. value of a.c.
voltage, and Vm is the maximum value of V.
 The D.C. power dissipated by the transistor (collector region) in the form of heat, i.e., (PC)dc
We have represented the whole power flow in the following diagram.

This class A power amplifier can amplify small signals with least distortion and the output will be
an exact replica of the input with increased strength.
Let us now try to draw some expressions to represent efficiencies.

Overall Efficiency
The overall efficiency of the amplifier circuit is given by
(η)overall=a.cpowerdeliveredtotheloadtotalpowerdeliveredbyd.csupply(η)overall=a.cpowerdelivered
totheloadtotalpowerdeliveredbyd.csupply
=(PO)ac(Pin)dc=(PO)ac(Pin)dc
Collector Efficiency
The collector efficiency of the transistor is defined as
(η)collector=averagea.cpoweroutputaveraged.cpowerinputtotransistor(η)collector=averagea.cpowero
utputaveraged.cpowerinputtotransistor
=(PO)ac(Ptr)dc=(PO)ac(Ptr)dc
Expression for overall efficiency
(PO)ac=Vrms×Irms(PO)ac=Vrms×Irms
=12–√[(Vce)max−(Vce)min2]×12–
√[(IC)max−(IC)min2]=12[(Vce)max−(Vce)min2]×12[(IC)max−(IC)min2]
=[(Vce)max−(Vce)min]×[(IC)max−(IC)min]8=[(Vce)max−(Vce)min]×[(IC)max−(IC)min]8
 75

Therefore
(η)overall=[(Vce)max−(Vce)min]×[(IC)max−(IC)min]8×VCC(IC)Q(η)overall=[(Vce)max−(Vce)mi
n]×[(IC)max−(IC)min]8×VCC(IC)Q
Advantages of Class A Amplifiers
The advantages of Class A power amplifier are as follows −

 The current flows for complete input cycle

 It can amplify small signals
 The output is same as input
 No distortion is present
Disadvantages of Class A Amplifiers
The advantages of Class A power amplifier are as follows −

 Low power output

 Low collector efficiency

TRANSFORMER COUPLED CLASS-A POWER AMPLIFIER

The class A power amplifier as discussed in the previous chapter, is the circuit in which the output
current flows for the entire cycle of the AC input supply. We also have learnt about the disadvantages
it has such as low output power and efficiency. In order to minimize those effects, the transformer
coupled class A power amplifier has been introduced.
The construction of class A power amplifier can be understood with the help of below figure.
This is similar to the normal amplifier circuit but connected with a transformer in the collector load.

Here R1 and R2 provide potential divider arrangement. The resistor Re provides stabilization, Ce is
the bypass capacitor and Re to prevent a.c. voltage. The transformer used here is a step-down
transformer. The high impedance primary of the transformer is connected to the high impedance
collector circuit. The low impedance secondary is connected to the load (generally loud speaker).
 76

Transformer Action
The transformer used in the collector circuit is for impedance matching. R L is the load connected in
the secondary of a transformer. RL’ is the reflected load in the primary of the transformer.
The number of turns in the primary are n1 and the secondary are n2. Let V1and V2 be the primary and
secondary voltages and I1 and I2 be the primary and secondary currents respectively. The below figure
shows the transformer clearly.

We know that
V1V2=n1n2andI1I2=n1n2V1V2=n1n2andI1I2=n1n2
Or
V1=n1n2V2andI1=n1n2I2V1=n1n2V2andI1=n1n2I2
Hence
V1I1=(n1n2)2V2I2V1I1=(n1n2)2V2I2
But V1/I1 = RL’ = effective input resistance
And V2/I2 = RL = effective output resistance
Therefore,
R′L=(n1n2)2RL=n2RLRL′=(n1n2)2RL=n2RL
Where
n=numberofturnsinprimarynumberofturnsinsecondary=n1n2n=numberofturnsinprimarynumberoftur
nsinsecondary=n1n2
A power amplifier may be matched by taking proper turn ratio in step down transformer.

Circuit Operation
If the peak value of the collector current due to signal is equal to zero signal collector current, then
the maximum a.c. power output is obtained. So, in order to achieve complete amplification, the
operating point should lie at the center of the load line.
The operating point obviously varies when the signal is applied. The collector voltage varies in
opposite phase to the collector current. The variation of collector voltage appears across theprimary
of the transformer.
 77

Circuit Analysis
The power loss in the primary is assumed to be negligible, as its resistance is very small.
The input power under dc condition will be
(Pin)dc=(Ptr)dc=VCC×(IC)Q(Pin)dc=(Ptr)dc=VCC×(IC)Q
Under maximum capacity of class A amplifier, voltage swings from (Vce)max to zero and current
from (Ic)max to zero.
Hence
Vrms=12–√[(Vce)max−(Vce)min2]=12–√[(Vce)max2]=2VCC22–√=VCC2–
√Vrms=12[(Vce)max−(Vce)min2]=12[(Vce)max2]=2VCC22=VCC2
Irms=12–√[(IC)max−(IC)min2]=12–√[(IC)max2]=2(IC)Q22–√=(IC)Q2–
√Irms=12[(IC)max−(IC)min2]=12[(IC)max2]=2(IC)Q22=(IC)Q2
Therefore,
(PO)ac=Vrms×Irms=VCC2–√×(IC)Q2–
√=VCC×(IC)Q2(PO)ac=Vrms×Irms=VCC2×(IC)Q2=VCC×(IC)Q2
Therefore,
Collector Efficiency = (PO)ac(Ptr)dc(PO)ac(Ptr)dc
Or,

(η)collector=VCC×(IC)Q2×VCC×(IC)Q=12(η)collector=VCC×(IC)Q2×VCC×(IC)Q=12
=12×100=50%=12×100=50%
The efficiency of a class A power amplifier is nearly than 30% whereas it has got improved to 50%
by using the transformer coupled class A power amplifier.

Advantages
The advantages of transformer coupled class A power amplifier are as follows.

 No loss of signal power in the base or collector resistors.

 Excellent impedance matching is achieved.
 Gain is high.
 DC isolation is provided.
Disadvantages
The disadvantages of transformer coupled class A power amplifier are as follows.

 Low frequency signals are less amplified comparatively.

 Hum noise is introduced by transformers.
 Transformers are bulky and costly.
 Poor frequency response.
Applications
The applications of transformer coupled class A power amplifier are as follows.
 This circuit is where impedance matching is the main criterion.
 These are used as driver amplifiers and sometimes as output amplifiers.
 78

CLASS –B POWER AMPLIFIER:

Class B Operation
The biasing of the transistor in class B operation is in such a way that at zero signal condition, there
will be no collector current. The operating point is selected to be at collector cut off voltage. So,
when the signal is applied, only the positive half cycle is amplified at the output.
The figure below shows the input and output waveforms during class B operation.

When the signal is applied, the circuit is forward biased for the positive half cycle of the input and
hence the collector current flows. But during the negative half cycle of the input, the circuit is reverse
biased and the collector current will be absent. Hence only the positive half cycle is amplified at the
output.
As the negative half cycle is completely absent, the signal distortion will be high. Also, when the
applied signal increases, the power dissipation will be more. But when compared to class A power
amplifier, the output efficiency is increased.
Well, in order to minimize the disadvantages and achieve low distortion, high efficiency and high
output power, the push-pull configuration is used in this class B amplifier.

Class B Push-Pull Amplifier

Though the efficiency of class B power amplifier is higher than class A, as only one half cycle of the
input is used, the distortion is high. Also, the input power is not completely utilized. In order to
compensate these problems, the push-pull configuration is introduced in class B amplifier.

Construction
The circuit of a push-pull class B power amplifier consists of two identical transistors T1 and
T2 whose bases are connected to the secondary of the center-tapped input transformer Tr1. The
emitters are shorted and the collectors are given the VCC supply through the primary of the output
transformer Tr2.
The circuit arrangement of class B push-pull amplifier, is same as that of class A push-pull
amplifier except that the transistors are biased at cut off, instead of using the biasing resistors. The
figure below gives the detailing of the construction of a push-pull class B power amplifier.
 79

The circuit operation of class B push pull amplifier is detailed below.

Operation
The circuit of class B push-pull amplifier shown in the above figure clears that both the transformers
are center-tapped. When no signal is applied at the input, the transistors T1 and T2 are in cut off
condition and hence no collector currents flow. As no current is drawn from VCC, no power is wasted.
When input signal is given, it is applied to the input transformer Tr1 which splits the signal into two
signals that are 180o out of phase with each other. These two signals are given to the two identical
transistors T1 and T2. For the positive half cycle, the base of the transistor T1 becomes positive and
collector current flows. At the same time, the transistor T2 has negative half cycle, which throws the
transistor T2 into cutoff condition and hence no collector current flows. The waveform is produced
as shown in the following figure.

For the next half cycle, the transistor T1 gets into cut off condition and the transistor T2 gets into
conduction, to contribute the output. Hence for both the cycles, each transistor conducts alternately.
The output transformer Tr3 serves to join the two currents producing an almost undistorted output
waveform.

Power Efficiency of Class B Push-Pull Amplifier

The current in each transistor is the average value of half sine loop.
For half sine loop, Idc is given by
 80

Idc=(IC)maxπIdc=(IC)maxπ
Therefore,
(pin)dc=2×[(IC)maxπ×VCC](pin)dc=2×[(IC)maxπ×VCC]
Here factor 2 is introduced as there are two transistors in push-pull amplifier.
R.M.S. value of collector current = (IC)max/2–√(IC)max/2
R.M.S. value of output voltage = VCC/2–√VCC/2
Under ideal conditions of maximum power
Therefore,
(PO)ac=(IC)max2–√×VCC2–√=(IC)max×VCC2(PO)ac=(IC)max2×VCC2=(IC)max×VCC2
Now overall maximum efficiency
ηoverall=(PO)ac(Pin)dcηoverall=(PO)ac(Pin)dc
=(IC)max×VCC2×π2(IC)max×VCC=(IC)max×VCC2×π2(IC)max×VCC
=π4=0.785=78.5%=π4=0.785=78.5%
The collector efficiency would be the same.
Hence the class B push-pull amplifier improves the efficiency than the class A push-pull amplifier.

Complementary Symmetry Push-Pull Class B Amplifier

The push pull amplifier which was just discussed improves efficiency but the usage of center- tapped
transformers makes the circuit bulky, heavy and costly. To make the circuit simple and to improve
the efficiency, the transistors used can be complemented, as shown in the following circuit diagram.

The above circuit employs a NPN transistor and a PNP transistor connected in push pull
configuration. When the input signal is applied, during the positive half cycle of the input signal,
the NPN transistor conducts and the PNP transistor cuts off. During the negative half cycle, the NPN
transistor cuts off and the PNP transistor conducts. In this way, the NPN transistor amplifies during
positive half cycle of the input, while PNP transistor amplifies during negative half cycle of the input.
As the transistors are both complement to each other, yet act symmetrically while being connected
in push pull configuration of class B, this circuit is termed as Complementary symmetry push pull
class B amplifier.

Advantages
The advantages of Complementary symmetry push pull class B amplifier are as follows.
 As there is no need of center tapped transformers, the weight and cost are reduced.
 Equal and opposite input signal voltages are not required.
 81

Disadvantages
The disadvantages of Complementary symmetry push pull class B amplifier are as follows.
 It is difficult to get a pair of transistors (NPN and PNP) that have similar characteristics.
 We require both positive and negative supply voltages.

Cross-over Distortion
In the push-pull configuration, the two identical transistors get into conduction, one after the other
and the output produced will be the combination of both. When the signal changes or crosses over
from one transistor to the other at the zero voltage point, it produces an amount of distortion to the
output wave shape. For a transistor in order to conduct, the base emitter junction should cross 0.7v,
the cut off voltage. The time taken for a transistor to get ON from OFF or to get OFF from ON state
is called the transition period. At the zero voltage point, the transition period of switching over the
transistors from one to the other, has its effect which leads to the instances where both thetransistors
are OFF at a time. Such instances can be called as Flat spot or Dead band on the outputwave shape.

The above figure clearly shows the cross over distortion which is prominent in the output waveform.
This is the main disadvantage. This cross over distortion effect also reduces the overall peak to peak
value of the output waveform which in turn reduces the maximum power output. This can be more
clearly understood through the non-linear characteristic of the waveform as shown below.

It is understood that this cross-over distortion is less pronounced for large input signals, where as it
causes severe disturbance for small input signals. This cross over distortion can be eliminated if the
conduction of the amplifier is more than one half cycle, so that both the transistors won’t be OFF at
the same time. This idea leads to the invention of class AB amplifier, which is the combination of
both class A and class B amplifiers, as discussed below.
 82

Class AB Power Amplifier

As the name implies, class AB is a combination of class A and class B type of amplifiers. As class A
has the problem of low efficiency and class B has distortion problem, this class AB is emerged to
eliminate these two problems, by utilizing the advantages of both the classes.
The cross over distortion is the problem that occurs when both the transistors are OFF at the same
instant, during the transition period. In order to eliminate this, the condition has to be chosen for more
than one half cycle. Hence, the other transistor gets into conduction, before the operating transistor
switches to cut off state. This is achieved only by using class AB configuration, as shown in the
following circuit diagram.

Therefore, in class AB amplifier design, each of the push-pull transistors is conducting for slightly
more than the half cycle of conduction in class B, but much less than the full cycle of conduction of
class A. The conduction angle of class AB amplifier is somewhere between 180o to 360o depending
upon the operating point selected. This is understood with the help of below figure.

The small bias voltage given using diodes D1 and D2, as shown in the above figure, helps the operating
point to be above the cutoff point. Hence the output waveform of class AB results as seenin the above
figure. The crossover distortion created by class B is overcome by this class AB, as well the
inefficiencies of class A and B don’t affect the circuit.

So, the class AB is a good compromise between class A and class B in terms of efficiency and
linearity having the efficiency reaching about 50% to 60%. The class A, B and AB amplifiers are
called as linear amplifiers because the output signal amplitude and phase are linearly related to the
input signal amplitude and phase.
 83

Class C Power Amplifier

When the collector current flows for less than half cycle of the input signal, the power amplifier is
known as class C power amplifier. The efficiency of class C amplifier is high while linearity is poor.
The conduction angle for class C is less than 180o. It is generally around 90o, which means the
transistor remains idle for more than half of the input signal. So, the output current will be delivered
for less time compared to the application of input signal. The following figure shows the operating
point and output of a class C amplifier.

This kind of biasing gives a much improved efficiency of around 80% to the amplifier, but introduces
heavy distortion in the output signal. Using the class C amplifier, the pulses produced at its output
can be converted to complete sine wave of a particular frequency by using LC circuits in its collector
circuit.
 84

Chapter-4
FEEDBACK AMPLIFIERS
Concepts of feedback: Classification of feedback amplifiers, general characteristics of Negative
feedback amplifiers, effect of feedback on amplifier characteristics, voltage series, voltage shunt,
current series and current shunt feedback configurations, simple problems; Oscillators: Condition for
Oscillations, RC type Oscillators RC phase shift and Wien-bridge Oscillators, LC type Oscillators,
generalized analysis of LC Oscillators, Hartley and Colpitts oscillators.

INTRODUCTION TO FEEDBACK AMPLIFIERS

Feedback is a common phenomenon in nature. It plays an important role in electronics & control
systems. Feedback is a process whereby a portion of the output signal of the amplifier is feedback
to the input of the amplifier. The feedback signal can be either a voltage or a current, being applied
in series or shunt respectively with the input signal.
CLASSIFICATION OF AMPLIFIERS:
Before analyzing the concept of feedback, it is useful to classify amplifiers based on the magnitudes
of the input & output impedances of an amplifier relative to the sources & load impedances
respectively as (i) voltage (ii) current (iii) Tran conductance (iv) Tran resistanceamplifiers.

VOLTAGE AMPLIFIER:
The above figure shows a Thevenin’s equivalent circuit of an amplifier. If the input resistance of the
amplifier Ri is large compared with the source resistance Rs, then Vi = Vs. If the external load RL is
large compared with the output resistance R0 of the amplifier, then V0 = AV VS .This type

of amplifier provides a voltage output proportional to the input voltage & the proportionality factor
doesn’t depend on the magnitudes of the source and load resistances. Hence, this amplifier is known
as voltage amplifier. An ideal voltage amplifier must have infinite resistance Ri and zero output
resistance.
 85

CURRENT AMPLIFIER:

Above figure shows a Norton’s equivalent circuit of a current amplifier. If the input resistance of
the amplifier Ri is very low compared to the source resistance RS, then Ii = IS. If the output resistance
of the amplifier R0 is very large compared to external load RL, then IL = AiIi = Ai IS. This amplifier
provides an output current proportional to the signal current and the proportionally is dependent
of the source and load resistance. Hence, this amplifier is called a current amplifier. An ideal current
amplifier must have zero input resistance & infinite output resistance.
TRANSCONDUCTANCE AMPLIFIER:

The above figure shows the equivalent circuit of a transconductance amplifier. In this circuit, the
output current I0 is proportional to the signal voltage VS and the proportionality factor is independent
of the magnitudes of source and load resistances. An ideal transconductance amplifier must have an
infinite resistance Ri & infinite output resistance R0.
TRANSRESISTANCE AMPLIFIER:
Figure above shows the equivalent circuit of a transconductance amplifier. Here, the output voltage
V0 is proportional to the signal current IS and the proportionality factor is independent of magnitudes
of source and loads resistances. If RS >>Ri , then Ii = IS , Output voltage V0 = RmIS
An ideal transconductance amplifier must have zero input resistance and zero output resistance.
 86

THE FEEDBACK CONCEPT:

In each of the above discussed amplifiers, we can sample the output voltage or current by means of
a suitable sampling network & this sampled portion is feedback to the input through a feedback
network as shown below.

RL

All the input of the amplifier, the feedback signal is combined with the source signal through a unit
called mixer. The signal source shown in the above figure can be either a voltage source VS or a
current source. The feedback connection has three networks.
1. Sampling network
2. Feedback network
3. Mixer network
SAMPLING NETWORK:
There are two ways to sample the output, depending on the required feedback parameter. The output
voltage is sampled by connecting the feedback network in shunt with the output. This is called as
voltage sampling.
 87

FEEDBACK NETWORK:
This is usually a passive two-port network consisting of resistors, capacitors and inductors. In case
of a voltage shunt feedback, it provides a fraction of the output voltage as feedback signal Vf to the
input of the mixer.
MIXER:
There are two ways of mixing the feedback signal with the input signal with the input signal as shown
in figure . below.

When the feedback voltage is applied in series with the input voltage through the feedback network
as shown in figure 6.7 (a) above, it is called series mixing. Otherwise, when the feedback voltage is
applied in parallel to the input of the amplifier as shown in figure (b) above, it is called shunt
feedback.
GAIN OR TRANSFER RATIO:
The ratio of the output signal to the input signal of the basic amplifier is represented by the symbol
A , with proper suffix representing the different quantities.
TYPES OF FEEDBACK:
Feedback amplifiers can be classified as positive or negative feedback depending on how the
feedback signal gets added to the incoming signal. If the feedback signal is of the same sign as the
incoming signal, they get added & this is called as positive feedback. On the other hand, if the
feedback signal is in phase inverse with the incoming signal, they get subtracted from each other; it
will be called as negative feedback amplifier. Positive feedback is employed in oscillators whereas
negative feedback is used in amplifiers.
 88

FEATURE OF NEGATIVE FEEDBACK AMPLIFIERS:

 Overall gain is reduced
 Bandwidth is improved
 Distortion is reduced
 Stability is improved
 Noise is reduced
ANALYSIS OF FEEDBACK AMPLIFIER:
The analysis of the feedback amplifier can be carried out by replacing each active element (BJT,
FET) by its small signal model and by writing Kirchoff’s loop or nodal equations. Consider the
schematic representation of the feedback amplifier as shown below.
 89

The four basic types of feedback are:

 Voltage –Series feedback
 Current – Series feedback
 Current – Shunt feedback
 Voltage – Shunt feedback
GAIN WITH FEEDBACK:
Consider the schematic representation of negative feedback amplifier as shown in fig.6.8.The source
resistance RS to be part of the amplifier & transfer gain A (AV,Ai ,Gm ,Rm ) includes the effect of
the loading of the network upon the amplifier.The input signal XS, the output signal X0, the feedback
signal Xf and the difference signal Xd , each represents either a voltage or a current and also the
ratios A and as summarized below.
The gain, A = X0 / XS (1)The
output of the mixer,
Xd = Xs + (-Xf ) = Xi (2)
The feedback ratio , = Xf / X0 (3)
The overall gain (including the feedback)
Af = X0 / XS (4)
From equation (2), XS = Xi + Xf Af = X0 / (Xi + Xf)
Dividing both numerator and denominator by Xi and simplifying, we get Af = A / (1 + A) (5)
Equation (5) indicates that the overall gain Af is less the open loop gain. The denominator term (1
+ A) in equation (5) is called the loop gain. The forward path consists only of the basic amplifier,
whereas the feedback is in the return path.
GAIN STABILITY:
Gain of an amplifier depends on the factors such as temperature, operating point aging etc. It can be
shown that the negative feedback tends to stabilize the gain. The ratio of fractional change in
amplification with feedback to the fractional change in without feedback is called the sensitivity
of the gain
 90

REDUCTION IN FREQUENCY DISTORTION:

If the feedback network is purely resistive, the overall gain is then not a function of frequency even
though the basic amplifier gain is frequency dependent. Under such conditions a substantial reduction
in frequency & phase distortion is obtained.
NONLINEAR DISTORTION:
Negative feedback tends to reduce the amount of noise and non-linear distortion. Suppose that a large
amplitude signal is applied to an amplifier, so that the operation of the device extends slightly beyond
its range of linear operation and as a consequence the output signal is distorted. Negative feedback is
now introduced and the input signal is increased by the same amount by which the gain is reduced,
so that the output signal amplitude remains the same. Assume that the second harmonic component,
in the absence of feedback is B2. Because of feedback, a component B2f actually appears in the
output. To find the relationship that exists between B2f& B2, it is noted that the output will contain
the term –AβB2f , which arises from the component –βB2f that is feedback to the input. Thus the
output contains two terms: B2, generated in the transistor and –AβB2f , which represents the effect
of the feedback. Thus, it is seen that, the negative feedback tends to reduce the second harmonic
distortion by the factor (1+βA).
NOISE:
Noise or hum components introduced into an amplifier inside the feedback loop are reduced by the
feedback loop. Suppose there are two stages of amplifier with gains A1 & A 2 and noise or hum pick-
up is introduced after the amplifier with gain A1 as shown in the fig. below

The overall gain of the two stage amplifier is reduced by the factor 1 + A1A2β. In addition the
noise output is reduced by the additional factor A1 which is the gain that precedes the introduction
of noise. In a single stage amplifier, noise will be reduced by the factor 1/(1 + Aβ) just like distortion.
But if signal-to-noise ratio has to improve, we have to increase the signal level at the input by the
factor (1 + Aβ) to bring back the signal level to the same value as obtained without feedback. If we
can assume that noise does not further increase when we increase the signal input, we can conclude
that noise is reduced by the factor 1/(1+Aβ) due to feedback while the signal level is maintained
constant.
OSCILLATORS:
An oscillator generates output without any ac input signal. An electronic oscillator is a circuit which
converts dc energy into ac at a very high frequency. An amplifier with a positive feedback can be
understood as an oscillator.
 91

Amplifier vs. Oscillator

An amplifier increases the signal strength of the input signal applied, whereasan
oscillator generates a signal without that input signal, but it requires dc for its operation. This is the
main difference between an amplifier and an oscillator. Take a look at the following illustration. It
clearly shows how an amplifier takes energy from d.c. power source and converts it into a.c. energy
at signal frequency. An oscillator produces an oscillating a.c. signal on its own.

The frequency, waveform, and magnitude of a.c. power generated by an amplifier, is controlled by
the a.c. signal voltage applied at the input, whereas those for an oscillator are controlled by the
components in the circuit itself, which means no external controlling voltage is required.

Alternator vs. Oscillator

An alternator is a mechanical device that produces sinusoidal waves without any input. This a.c.
generating machine is used to generate frequencies up to 1000Hz. The output frequency depends on
the number of poles and the speed of rotation of the armature.
The following points highlight the differences between an alternator and an oscillator −
 An alternator converts mechanical energy to a.c. energy, whereas the oscillator converts d.c.
energy into a.c. energy.
 An oscillator can produce higher frequencies of several MHz whereas an alternator cannot.
 An alternator has rotating parts, whereas an electronic oscillator doesn’t.
 It is easy to change the frequency of oscillations in an oscillator than in an alternator.
Oscillators can also be considered as opposite to rectifiers that convert a.c. to d.c. as these convert
d.c. to a.c. You can get a detailed description on rectifiers in our Electronic Circuits tutorial.

Classification of Oscillators
Electronic oscillators are classified mainly into the following two categories −
 Sinusoidal Oscillators − The oscillators that produce an output having a sine waveform are
called sinusoidal or harmonic oscillators. Such oscillators can provide output at frequencies
ranging from 20 Hz to 1 GHz.

 Non-sinusoidal Oscillators − The oscillators that produce an output having a square,

rectangular or saw-tooth waveform are called non-sinusoidal or relaxation oscillators. Such
oscillators can provide output at frequencies ranging from 0 Hz to 20 MHz.
 92

 Sinusoidal Oscillators
Sinusoidal oscillators can be classified in the following categories −
 Tuned Circuit Oscillators − These oscillators use a tuned-circuit consisting of inductors
(L) and capacitors (C) and are used to generate high-frequency signals. Thus they are also
known as radio frequency R.F. oscillators. Such oscillators are Hartley, Colpitts, Clapp-
oscillators etc.
 RC Oscillators − There oscillators use resistors and capacitors and are used to generate low
or audio-frequency signals. Thus they are also known as audio-frequency (A.F.) oscillators.
Such oscillators are Phase –shift and Wein-bridge oscillators.
 Crystal Oscillators − These oscillators use quartz crystals and are used to generate highly
stabilized output signal with frequencies up to 10 MHz. The Piezo oscillator is an example of
a crystal oscillator.
 Negative-resistance Oscillator − These oscillators use negative-resistance characteristic of
the devices such as tunnel devices. A tuned diode oscillator is an example of a negative-
resistance oscillator.

Nature of Sinusoidal Oscillations

The nature of oscillations in a sinusoidal wave are generally of two types. They
are damped and undamped oscillations.

Damped Oscillations
The electrical oscillations whose amplitude goes on decreasing with time are called as Damped
Oscillations. The frequency of the damped oscillations may remain constant depending upon the
circuit parameters.

Damped oscillations are generally produced by the oscillatory circuits that produce power losses and
doesn’t compensate if required.

Undamped Oscillations
The electrical oscillations whose amplitude remains constant with time are called as Undamped
Oscillations. The frequency of the Undamped oscillations remains constant.
 93

Undamped oscillations are generally produced by the oscillatory circuits that produce no power losses
and follow compensation techniques if any power losses occur. An Oscillator circuit is a complete
set of all the parts of circuit which helps to produce the oscillations. These oscillations should sustain
and should be Undamped as just discussed before. Let us try to analyze a practical Oscillator circuit
to have a better understanding on how an Oscillator circuit works.

Practical Oscillator Circuit

A Practical Oscillator circuit consists of a tank circuit, a transistor amplifier, and a feedback circuit.
The following circuit diagram shows the arrangement of a practical oscillator.

Let us now discuss the parts of this practical oscillator circuit.

 Tank Circuit − The tank circuit consists of an inductance L connected in parallel with
capacitor C. The values of these two components determine the frequency of the oscillator
circuit and hence this is called as Frequency determining circuit.
 Transistor Amplifier − The output of the tank circuit is connected to the amplifier circuit
so that the oscillations produced by the tank circuit are amplified here. Hence the output of
these oscillations are increased by the amplifier.
 Feedback Circuit − The function of feedback circuit is to transfer a part of the output energy
to LC circuit in proper phase. This feedback is positive in oscillators while negative in
amplifiers.

Frequency Stability of an Oscillator

The frequency stability of an oscillator is a measure of its ability to maintain a constant frequency,
over a long time interval. When operated over a longer period of time, the oscillator frequency may
have a drift from the previously set value either by increasing or by decreasing.
The change in oscillator frequency may arise due to the following factors −
 Operating point of the active device such as BJT or FET used should lie in the linear region
of the amplifier. Its deviation will affect the oscillator frequency.
 The temperature dependency of the performance of circuit components affect the oscillator
frequency.
 The changes in d.c. supply voltage applied to the active device, shift the oscillator frequency.
This can be avoided if a regulated power supply is used.
 A change in output load may cause a change in the Q-factor of the tank circuit, thereby causing
a change in oscillator output frequency.
 The presence of inter element capacitances and stray capacitances affect the oscillator output
frequency and thus frequency stability.
 94

The Barkhausen Criterion

With the knowledge we have till now, we understood that a practical oscillator circuit consists of a
tank circuit, a transistor amplifier circuit and a feedback circuit. so, let us now try to brush up the
concept of feedback amplifiers, to derive the gain of the feedback amplifiers.

Principle of Feedback Amplifier

A feedback amplifier generally consists of two parts. They are the amplifier and the feedback
circuit. The feedback circuit usually consists of resistors. The concept of feedback amplifier can be
understood from the following figure below.

From the above figure, the gain of the amplifier is represented as A. The gain of the amplifier is the
ratio of output voltage Vo to the input voltage Vi. The feedback network extracts a voltage Vf = β Vo
from the output Vo of the amplifier.
This voltage is added for positive feedback and subtracted for negative feedback, from the signal
voltage Vs.
So, for a positive feedback,
Vi = Vs + Vf = Vs + β Vo
The quantity β = Vf/Vo is called as feedback ratio or feedback fraction.
The output Vo must be equal to the input voltage (Vs + βVo) multiplied by the gain A of the
amplifier.
Hence,
(Vs+βVo)A=Vo(Vs+βVo)A=Vo Or
AVs+AβVo=VoAVs+AβVo=Vo Or
AVs=Vo(1−Aβ)AVs=Vo(1−Aβ)
Therefore , VoVs=A1−AβVoVs=A1−Aβ
Let Af be the overall gain (gain with the feedback) of the amplifier. This is defined as the ratio of
output voltage Vo to the applied signal voltage Vs, i.e.,
Af=OutputVoltageInputSignal
Voltage=VoVsAf=OutputVoltageInputSignalVoltage=VoVs
from the above two equations, we can understand that, the equation of gain of the feedback
amplifier with positive feedback is given by
Af=A1−AβAf=A1−Aβ
Where Aβ is the feedback factor or the loop gain.
 95

If Aβ = 1, Af = ∞. Thus the gain becomes infinity, i.e., there is output without any input. In another
words, the amplifier works as an Oscillator.
The condition Aβ = 1 is called as Barkhausen Criterion of oscillations. This is a very important
factor to be always kept in mind, in the concept of Oscillators.

Tuned circuit oscillators are the circuits that produce oscillations with the help of tuning circuits.
The tuning circuits onsists of an inductance L and a capacitor C. These are also known as LC
oscillators, resonant circuit oscillators or tank circuit oscillators.

The tuned circuit oscillators are used to produce an output with frequencies ranging from 1 MHz to
500 MHz Hence these are also known as R.F. Oscillators. A BJT or a FET is used as an amplifier
with tuned circuit oscillators. With an amplifier and an LC tank circuit, we can feedback a signal
with right amplitude and phase to maintain oscillations.

Types of Tuned Circuit Oscillators

Most of the oscillators used in radio transmitters and receivers are of LC oscillators type. Depending
upon the way the feedback is used in the circuit, the LC oscillators are divided as the following types.

 Tuned-collector or Armstrong Oscillator − It uses inductive feedback from the collector

of a transistor to the base. The LC circuit is in the collector circuit of the transistor.

 Tuned base Oscillator − It uses inductive feedback. But the LC circuit is in the base circuit.

 Hartley Oscillator − It uses inductive feedback.

 Colpitts Oscillator − It uses capacitive feedback.

 Clapp Oscillator − It uses capacitive feedback.

Hartley Oscillator:
A very popular local oscillator circuit that is mostly used in radio receivers is the Hartley
Oscillator circuit. The constructional details and operation of a Hartley oscillator are as discussed
below.

Construction
In the circuit diagram of a Hartley oscillator shown below, the resistors R1, R2and Re provide
necessary bias condition for the circuit. The capacitor Ce provides a.c. ground thereby providing any
signal degeneration. This also provides temperature stabilization. The capacitors Cc and Cb are
employed to block d.c. and to provide an a.c. path. The radio frequency choke (R.F.C) offers very
high impedance to high frequency currents which means it shorts for d.c. and opens for a.c. Hence
it provides d.c. load for collector and keeps a.c. currents out of d.c. supply source
 96

Tank Circuit
The frequency determining network is a parallel resonant circuit which consists of the inductorsL1
and L2 along with a variable capacitor C. The junction of L1and L2 are earthed. The coil L1 has its
one end connected to base via Cc and the other to emitter via Ce. So, L2 is in the output circuit. Both
the coils L1 and L2 are inductively coupled and together form an Auto-transformer. The following
circuit diagram shows the arrangement of a Hartley oscillator. The tank circuit is shunt fed in this
circuit. It can also be a series-fed.

Operation
When the collector supply is given, a transient current is produced in the oscillatory or tank circuit.
The oscillatory current in the tank circuit produces a.c. voltage across L1. The auto- transformer
made by the inductive coupling of L1 and L2 helps in determining the frequency and establishes the
feedback. As the CE configured transistor provides 180o phase shift, another 180o phase shift is
provided by the transformer, which makes 360o phase shift between the inputand output voltages.
This makes the feedback positive which is essential for the condition of oscillations. When the loop
gain |βA| of the amplifier is greater than one, oscillations aresustained in the circuit.

Frequency
The equation for frequency of Hartley oscillator is given as
f=12πLTC−−−−√f=12πLTC
LT=L1+L2+2MLT=L1+L2+2M
Here, LT is the total cumulatively coupled inductance; L1 and L2 represent inductances of 1st and
2nd coils; and M represents mutual inductance. Mutual inductance is calculated when two windings
are considered.
 97

Advantages
The advantages of Hartley oscillator are
 Instead of using a large transformer, a single coil can be used as an auto-transformer.
 Frequency can be varied by employing either a variable capacitor or a variable inductor.
 Less number of components are sufficient.
 The amplitude of the output remains constant over a fixed frequency range.

Disadvantages
The disadvantages of Hartley oscillator are

 It cannot be a low frequency oscillator.

 Harmonic distortions are present.
Applications
The applications of Hartley oscillator are

 It is used to produce a sine wave of desired frequency.

 Mostly used as a local oscillator in radio receivers.
 It is also used as R.F. Oscillator.
Colpitts Oscillator:
A Colpitts oscillator looks just like the Hartley oscillator but the inductors and capacitors are replaced
with each other in the tank circuit. The constructional details and operation of a colpitts oscillator are
as discussed below.

Construction
Let us first take a look at the circuit diagram of a Colpitts oscillator.
 98

The resistors R1, R2 and Re provide necessary bias condition for the circuit. The capacitor Ce
provides a.c. ground thereby providing any signal degeneration. This also provides temperature
stabilization. The capacitors Cc and Cb are employed to block d.c. and to provide an a.c. path. The
radio frequency choke (R.F.C) offers very high impedance to high frequency currents which means
it shorts for d.c. and opens for a.c. Hence it provides d.c. load for collector and keeps a.c. currents
out of d.c. supply source.

Tank Circuit
The frequency determining network is a parallel resonant circuit which consists of variable capacitors
C1 and C2 along with an inductor L. The junction of C1and C2 are earthed. The capacitor C1 has its
one end connected to base via Cc and the other to emitter via Ce. the voltage developed across C1
provides the regenerative feedback required for the sustained oscillations.

Operation
When the collector supply is given, a transient current is produced in the oscillatory or tank circuit.
The oscillatory current in the tank circuit produces a.c. voltage across C1 which are applied to the
base emitter junction and appear in the amplified form in the collector circuit and supply losses to
the tank circuit. If terminal 1 is at positive potential with respect to terminal 3 at any instant, then
terminal 2 will be at negative potential with respect to 3 at that instant because terminal 3 is grounded.
Therefore, points 1 and 2 are out of phase by 180o. As the CE configured transistor provides 180o
phase shift, it makes 360ophase shift between the input and output voltages. Hence, feedback is
properly phased to produce continuous Undamped oscillations. When the loop gain
|βA| of the amplifier is greater than one, oscillations are sustained in the circuit.

Frequency
The equation for frequency of Colpitts oscillator is given as
f=12πLCT−−−−√f=12πLCT
CT is the total capacitance of C1 and C2 connected in series.
1CT=1C1+1C21CT=1C1+1C2
CT=C1×C2C1+C2CT=C1×C2C1+C2
Advantages
The advantages of Colpitts oscillator are as follows −

 Colpitts oscillator can generate sinusoidal signals of very high frequencies.

 It can withstand high and low temperatures.
 The frequency stability is high.
 Frequency can be varied by using both the variable capacitors.
 Less number of components are sufficient.
 The amplitude of the output remains constant over a fixed frequency range.
 99

The Colpitts oscillator is designed to eliminate the disadvantages of Hartley oscillator and is known
to have no specific disadvantages. Hence there are many applications of a colpitts oscillator.

Applications
The applications of Colpitts oscillator are as follows −

 Colpitts oscillator can be used as High frequency sine wave generator.

 This can be used as a temperature sensor with some associated circuitry.
 Mostly used as a local oscillator in radio receivers.
 It is also used as R.F. Oscillator.
 It is also used in Mobile applications.
 It has got many other commercial applications.
RC Phase shift oscillator:
One of the important features of an oscillator is that the feedback energy applied should be in correct
phase to the tank circuit. The oscillator circuits discussed so far has employed inductor (L) and
capacitor (C) combination, in the tank circuit or frequency determining circuit. We have observed
that the LC combination in oscillators provide 180o phase shift and transistor in CE configuration
provide 180° phase shift to make a total of 360o phase shift so that it would make a zero difference
in phase.

Drawbacks of LC circuits
Though they have few applications, the LC circuits have few drawbacks such as

 Frequency instability
 Waveform is poor
 Cannot be used for low frequencies
 Inductors are bulky and expensive
We have another type of oscillator circuits, which are made by replacing the inductors with resistors.
By doing so, the frequency stability is improved and a good quality waveform is obtained. These
oscillators can also produce lower frequencies. As well, the circuit becomes neither bulkynor
expensive. All the drawbacks of LC oscillator circuits are thus eliminated in RC oscillator circuits.
Hence the need for RC oscillator circuits arise. These are also called as Phase–shift Oscillators.

Principle of Phase-shift oscillators

We know that the output voltage of an RC circuit for a sine wave input leads the input voltage. The
phase angle by which it leads is determined by the value of RC components used in the circuit. The
following circuit diagram shows a single section of an RC network.
 100

The output voltage V1’ across the resistor R leads the input voltage applied input V1 by some phase
angle ɸo. If R were reduced to zero, V1’ will lead the V1 by 90o i.e., ɸo = 90o. However, adjusting R
to zero would be impracticable, because it would lead to no voltage across R. Therefore, in practice,
R is varied to such a value that makes V1’ to lead V1 by 60o. The following circuit diagramshows the
three sections of the RC network.

Each section produces a phase shift of 60o. Consequently, a total phase shift of 180o is produced,
i.e., voltage V2 leads the voltage V1 by 180o.

Phase-shift Oscillator Circuit

The oscillator circuit that produces a sine wave using a phase-shift network is called as a Phase-
shift oscillator circuit.

Construction
The phase-shift oscillator circuit consists of a single transistor amplifier section and a RC phase- shift
network. The phase shift network in this circuit, consists of three RC sections. At the resonant
frequency fo, the phase shift in each RC section is 60o so that the total phase shift produced by RC
network is 180o. The following circuit diagram shows the arrangement of an RC phase-shiftoscillator.
 101

The frequency of oscillations is given by

fo=12πRC6–√fo=12πRC6
Where
R1=R2=R3=RR1=R2=R3=R
C1=C2=C3=CC1=C2=C3=C
Operation

The circuit when switched ON oscillates at the resonant frequency fo. The output Eo of the amplifier
is fed back to RC feedback network. This network produces a phase shift of 180o and a voltage
Ei appears at its output. This voltage is applied to the transistor amplifier.

The feedback applied will be

m=Ei/Eom=Ei/Eo
The feedback is in correct phase, whereas the transistor amplifier, which is in CE configuration,
produces a 180o phase shift. The phase shift produced by network and the transistor add to form a
phase shift around the entire loop which is 360o.

Advantages
The advantages of RC phase shift oscillator are as follows −

 It does not require transformers or inductors.

 It can be used to produce very low frequencies.
 The circuit provides good frequency stability.
Disadvantages
The disadvantages of RC phase shift oscillator are as follows −

 Starting the oscillations is difficult as the feedback is small.

 The output produced is small.
Wien bridge oscillator
Another type of popular audio frequency oscillator is the Wien bridge oscillator circuit. This is mostly
used because of its important features. This circuit is free from the circuit fluctuations and the
ambient temperature.
The main advantage of this oscillator is that the frequency can be varied in the range of 10Hz to about
1MHz whereas in RC oscillators, the frequency is not varied.

Construction
The circuit construction of Wien bridge oscillator can be explained as below. It is a two-stage
amplifier with RC bridge circuit. The bridge circuit has the arms R1C1, R3, R2C2 and the tungsten
lamp Lp. Resistance R3 and the lamp Lp are used to stabilize the amplitude of the output. The following
circuit diagram shows the arrangement of a Wien bridge oscillator.
 102

The transistor T1 serves as an oscillator and an amplifier while the other transistor T2 serves as an
inverter. The inverter operation provides a phase shift of 180o. This circuit provides positive
feedback through R1C1, C2R2 to the transistor T1 and negative feedback through the voltage divider
to the input of transistor T2. The frequency of oscillations is determined by the series element
R1C1 and parallel element R2C2 of the bridge.
f=12πR1C1R2C2−−−−−−−−−√f=12πR1C1R2C2
If R1 = R2 and C1 = C2 = C
Then,
f=12πRCf=12πRC
Now, we can simplify the above circuit as follows −

The oscillator consists of two stages of RC coupled amplifier and a feedback network. The voltage
across the parallel combination of R and C is fed to the input of amplifier 1. The net phase shift
through the two amplifiers is zero. The usual idea of connecting the output of amplifier 2 to amplifier
1 to provide signal regeneration for oscillator is not applicable here as the amplifier 1 willamplify
signals over a wide range of frequencies and hence direct coupling would result in poor frequency
stability. By adding Wien bridge feedback network, the oscillator becomes sensitive to a particular
frequency and hence frequency stability is achieved.

Operation
When the circuit is switched ON, the bridge circuit produces oscillations of the frequency stated
above. The two transistors produce a total phase shift of 360o so that proper positive feedback is
ensured. The negative feedback in the circuit ensures constant output. This is achieved by
temperature sensitive tungsten lamp Lp. Its resistance increases with current. If the amplitude of the
output increases, more current is produced and more negative feedback is achieved. Due to this, the
output would return to the original value. Whereas, if the output tends to decrease, reverse action
would take place.
 103

Advantages
The advantages of Wien bridge oscillator are as follows −
 The circuit provides good frequency stability.
 It provides constant output.
 The operation of circuit is quite easy.
 The overall gain is high because of two transistors.
 The frequency of oscillations can be changed easily.
 The amplitude stability of the output voltage can be maintained more
accurately, byreplacing R2 with a thermistor.

Disadvantages
The disadvantages of Wien bridge oscillator are as follows −
 The circuit cannot generate very high frequencies.
 Two transistors and number of components are required for the circuit construction.
 104

Chapter-5
OPERATIOANL AMPLIFIERS
Ideal op-amp, Output offset voltage, input bias current, input offset current, slew rate, gain
bandwidth product, Inverting and non-inverting amplifier, Differentiator, integrator, Square-
wave and triangular-wave generators.
Introduction to Operational amplifiers:
An electronic circuit is a group of electronic components connected for a specific purpose.
A simple electronic circuit can be designed easily because it requires few discrete electronic
components and connections. However, designing a complex electronic circuit is difficult, as it
requires more number of discrete electronic components and their connections. It is also time
taking to build such complex circuits and their reliability is also less. These difficulties can be
overcome with Integrated Circuits.

Integrated Circuit (IC)

If multiple electronic components are interconnected on a single chip of semiconductor material,
then that chip is called as an Integrated Circuit (IC). It consists of both active and passive
components.
This chapter discusses the advantages and types of ICs.

Advantages of Integrated Circuits

Integrated circuits offer many advantages. They are discussed below −
 Compact size − For a given functionality, you can obtain a circuit of smaller size using
ICs, compared to that built using a discrete circuit.
 Lesser weight − A circuit built with ICs weighs lesser when compared to the weight of a
discrete circuit that is used for implementing the same function of IC. using ICs, compared
to that built using a discrete circuit.
 Low power consumption − ICs consume lower power than a traditional circuit,because
of their smaller size and construction.
 Reduced cost − ICs are available at much reduced cost than discrete circuits because of
their fabrication technologies and usage of lesser material than discrete circuits.
 Increased reliability − Since they employ lesser connections, ICs offer increased
reliability compared to digital circuits.
 Improved operating speeds − ICs operate at improved speeds because of theirswitching
speeds and lesser power consumption.

Types of Integrated Circuits

Integrated circuits are of two types − Analog Integrated Circuits and Digital Integrated
Circuits.

Analog Integrated Circuits

Integrated circuits that operate over an entire range of continuous values of the signal amplitude
are called as Analog Integrated Circuits. These are further classified into the two types as
discussed here −
 105

 Linear Integrated Circuits − An analog IC is said to be Linear, if there exists a linear

relation between its voltage and current. IC 741, an 8-pin Dual In-line Package(DIP)op-
amp, is an example of Linear IC.
 Radio Frequency Integrated Circuits − An analog IC is said to be Non-Linear, if there
exists a non-linear relation between its voltage and current. A Non-Linear IC is also called
as Radio Frequency IC.

Digital Integrated Circuits

If the integrated circuits operate only at a few pre-defined levels instead of operating for an entire
range of continuous values of the signal amplitude, then those are called as Digital Integrated
Circuits.
Operational Amplifier, also called as an Op-Amp, is an integrated circuit, which can be usedto
perform various linear, non-linear, and mathematical operations. An op-amp is a direct coupled
high gain amplifier. You can operate op-amp both with AC and DC signals. This chapter
discusses the characteristics and types of op-amps.

Construction of Operational Amplifier

An op-amp consists of differential amplifier(s), a level translator and an output stage. A
differential amplifier is present at the input stage of an op-amp and hence an op-amp consists of
two input terminals. One of those terminals is called as the inverting terminal and the other
one is called as the non-inverting terminal. The terminals are named based on the phase
relationship between their respective inputs and outputs.

Characteristics of Operational Amplifier

The important characteristics or parameters of an operational amplifier are as follows −

 Open loop voltage gain

 Output offset voltage
 Common Mode Rejection Ratio
 Slew Rate
This section discusses these characteristics in detail as given below −

Open loop voltage gain

The open loop voltage gain of an op-amp is its differential gain without any feedback path.
Mathematically, the open loop voltage gain of an op-amp is represented as −
Av=v0v1−v2Av=v0v1−v2
Output offset voltage
The voltage present at the output of an op-amp when its differential input voltage is zero is
called as output offset voltage.

Common Mode Rejection Ratio

Common Mode Rejection Ratio (CMRR) of an op-amp is defined as the ratio of the closed
loop differential gain, AdAd and the common mode gain, AcAc.
Mathematically, CMRR can be represented as −
CMRR=AdAcCMRR=AdAc
 106

Note that the common mode gain, AcAc of an op-amp is the ratio of the common mode
output voltage and the common mode input voltage.
Slew Rate
Slew rate of an op-amp is defined as the maximum rate of change of the output voltage dueto a
step input voltage.
Mathematically, slew rate (SR) can be represented as −
SR=MaximumofdV0dtSR=MaximumofdV0dt
Where, V0V0 is the output voltage. In general, slew rate is measured in
either V/μSecV/μSec or V/mSecV/mSec.
Types of Operational Amplifiers
An op-amp is represented with a triangle symbol having two inputs and one output.
Op-amps are of two types: Ideal Op-Amp and Practical Op-Amp.
They are discussed in detail as given below −

Ideal Op-Amp
An ideal op-amp exists only in theory, and does not exist practically. The equivalentcircuit
of an ideal op-amp is shown in the figure given below −

An ideal op-amp exhibits the following characteristics −

 Input impedance Zi=∞ΩZi=∞Ω
 Output impedance Z0=0ΩZ0=0Ω
 Open loop voltage gaine Av=∞Av=∞
 If (the differential) input voltage Vi=0VVi=0V, then the output voltage willbe
V0=0VV0=0V
 Bandwidth is infinity. It means, an ideal op-amp will amplify the signals of any
frequency without any attenuation.
 Common Mode Rejection Ratio (CMRR) is infinity.
 Slew Rate (SR) is infinity. It means, the ideal op-amp will produce a change in the
output instantly in response to an input step voltage.

Practical Op-Amp
Practically, op-amps are not ideal and deviate from their ideal characteristics because of some
imperfections during manufacturing. The equivalent circuit of a practical op-amp is shown in
the following figure −
 107

A practical op-amp exhibits the following characteristics −

 Input impedance, ZiZi in the order of Mega ohms.
 Output impedance, Z0Z0 in the order of few ohms..
 Open loop voltage gain, AvAv will be high.

When you choose a practical op-amp, you should check whether it satisfies the following
conditions −
 Input impedance, ZiZi should be as high as possible.
 Output impedance, Z0Z0 should be as low as possible.
 Open loop voltage gain, AvAv should be as high as possible.
 Output offset voltage should be as low as possible.

 The operating Bandwidth should be as high as possible.

 CMRR should be as high as possible.
 Slew rate should be as high as possible.

A circuit is said to be linear, if there exists a linear relationship between its input and the output.
Similarly, a circuit is said to be non-linear, if there exists a non-linear relationship between its
input and output. Op-amps can be used in both linear and non-linear applications. The following
are the basic applications of op-amp −

 Inverting Amplifier
 Non-inverting Amplifier
 Voltage follower
Inverting Amplifier
An inverting amplifier takes the input through its inverting terminal through a resistor R1R1,and
produces its amplified version as the output. This amplifier not only amplifies the input but also
inverts it (changes its sign).
 108

Note that for an op-amp, the voltage at the inverting input terminal is equal to the voltage at its
non-inverting input terminal. Physically, there is no short between those two terminalsbut
virtually, they are in short with each other. In the circuit shown above, the non- inverting input
terminal is connected to ground. That means zero volts is applied at the non- inverting input
terminal of the op-amp. According to the virtual short concept, the voltage at the inverting input
terminal of an op-amp will be zero volts.
The nodal equation at this terminal's node is as shown below −
0−ViR1+0−V0Rf=00−ViR1+0−V0Rf=0
=>−ViR1=V0Rf=>−ViR1=V0Rf
=>V0=(−RfR1)Vt=>V0=(−RfR1)Vt
=>V0Vi=−RfR1=>V0Vi=−RfR1
The ratio of the output voltage V0V0 and the input voltage ViVi is the voltage-gain or gain of the
amplifier. Therefore, the gain of inverting amplifier is equal to −RfR1−RfR1.
Note that the gain of the inverting amplifier is having a negative sign. It indicates that there exists
a 1800 phase difference between the input and the output.

Non-Inverting Amplifier
A non-inverting amplifier takes the input through its non-inverting terminal, and producesits
amplified version as the output. As the name suggests, this amplifier just amplifies the input,
without inverting or changing the sign of the output. The circuit diagram of a non- inverting
amplifier is shown in the following figure −

In the above circuit, the input voltage ViVi is directly applied to the non-inverting input terminal
of op-amp. So, the voltage at the non-inverting input terminal of the op-amp willbe ViVi. By
using voltage division principle, we can calculate the voltage at the inverting input terminal of
the op-amp as shown below −
=>V1=V0(R1R1+Rf)=>V1=V0(R1R1+Rf)
According to the virtual short concept, the voltage at the inverting input terminal of an op-amp
is same as that of the voltage at its non-inverting input terminal.
=>V1=Vi=>V1=Vi
=>V0(R1R1+Rf)=Vi=>V0(R1R1+Rf)=Vi
=>V0Vi=R1+RfR1=>V0Vi=R1+RfR1
=>V0Vi=1+RfR1=>V0Vi=1+RfR1
 109

Now, the ratio of output voltage V0V0 and input voltage ViVi or the voltage-gain or gain ofthe
non-inverting amplifier is equal to 1+RfR11+RfR1. Note that the gain of the non- inverting
amplifier is having a positive sign. It indicates that there is no phase difference between the input
and the output.
Integrator and Differentiator:
The electronic circuits which perform the mathematical operations such as differentiation and
integration are called as differentiator and integrator, respectively. This chapter discusses in detail
about op-amp based differentiator and integrator. Please note that these also come under linear
applications of op-amp.
Differentiator
A differentiator is an electronic circuit that produces an output equal to the first derivativeof
its input. This section discusses about the op-amp based differentiator in detail.
An op-amp based differentiator produces an output, which is equal to the differential ofinput
voltage that is applied to its inverting terminal. The circuit diagram of an op-amp based
differentiator is shown in the following figure −

In the above circuit, the non-inverting input terminal of the op-amp is connected to ground.That
means zero volts is applied to its non-inverting input terminal.
According to the virtual short concept, the voltage at the inverting input terminal of opampwill
be equal to the voltage present at its non-inverting input terminal. So, the voltage at the inverting
input terminal of op-amp will be zero volts.
The nodal equation at the inverting input terminal's node is −
Cd(0−Vi)dt+0−V0R=0Cd(0−Vi)dt+0−V0R=0
=>−CdVidt=V0R=>−CdVidt=V0R
=>V0=−RCdVidt=>V0=−RCdVidtIf
RC=1secRC=1sec, then the output voltage V0V0 will be −
V0=−dVidtV0=−dVidt
Thus, the op-amp based differentiator circuit shown above will produce an output, which is the
differential of input voltage ViVi, when the magnitudes of impedances of resistor and capacitor
are reciprocal to each other.
Note that the output voltage V0V0 is having a negative sign, which indicates that there exists a
1800 phase difference between the input and the output.
Integrator
An integrator is an electronic circuit that produces an output that is the integration of the
applied input. This section discusses about the op-amp based integrator.
 110

An op-amp based integrator produces an output, which is an integral of the input voltage applied
to its inverting terminal. The circuit diagram of an op-amp based integrator is shown in the
following figure −

In the circuit shown above, the non-inverting input terminal of the op-amp is connected to ground.
That means zero volts is applied to its non-inverting input terminal. Accordingto virtual
short concept, the voltage at the inverting input terminal of op-amp will be equal to the voltage
present at its non-inverting input terminal. So, the voltage at the invertinginput terminal of op-
amp will be zero volts.
The nodal equation at the inverting input terminal is −
0−ViR+Cd(0−V0)dt=00−ViR+Cd(0−V0)dt=0
=>−ViR=CdV0dt=>−ViR=CdV0dt
=>dV0dt=−ViRC=>dV0dt=−ViRC
=>dV0=(−ViRC)dt=>dV0=(−ViRC)dt
Integrating both sides of the equation shown above, we get −
∫dV0=∫(−ViRC)dt∫dV0=∫(−ViRC)dt
=>V0=−1RC∫Vtdt=>V0=−1RC∫Vtdt
If RC=1secRC=1sec, then the output voltage, V0V0 will be −
V0=−∫VidtV0=−∫Vidt
So, the op-amp based integrator circuit discussed above will produce an output, which is the
integral of input voltage ViVi, when the magnitude of impedances of resistor and capacitor are
reciprocal to each other.
Note − The output voltage, V0V0 is having a negative sign, which indicates that there exists1800
phase difference between the input and the output.

Waveform Generators:
A waveform generator is an electronic circuit, which generates a standard wave. There aretwo
types of op-amp based waveform generators −

 Square wave generator

 Triangular wave generator
Square Wave Generator:
A square wave generator is an electronic circuit which generates square wave. This section
discusses about op-amp based square wave generators.
The circuit diagram of a op-amp based square wave generator is shown in the following figure
 111

Observe that in the circuit diagram shown above, the resistor R1R1 is connected between the
inverting input terminal of the op-amp and its output of op-amp. So, the resistor R1R1 isused
in the negative feedback. Similarly, the resistor R2R2 is connected between the noninverting
input terminal of the op-amp and its output. So, the resistor R2R2 is used inthe positive
feedback path. A capacitor C is connected between the inverting input terminal of the op-amp
and ground. So, the voltage across capacitor C will be the input voltage at this inverting terminal
of op-amp. Similarly, a resistor R3R3 is connected between the non- inverting input terminal
of the op-amp and ground. So, the voltage acrossresistor R3R3 will be the input voltage
at this non-inverting terminal of the op-amp.
The operation of a square wave generator is explained below −
 Assume, there is no charge stored in the capacitor initially. Then, the voltage present at
the inverting terminal of the op-amp is zero volts. But, there is some offset voltageat non-
inverting terminal of op-amp. Due to this, the value present at the output of above circuit
will be +Vsat+Vsat.
 Now, the capacitor C starts charging through a resistor R1R1. The value present at the
output of the above circuit will change to −Vsat−Vsat, when the voltage across the
capacitor C reaches just greater than the voltage (positive value) across resistor R3R3.
 The capacitor C starts discharging through a resistor R1R1, when the output of above
circuit is −Vsat−Vsat. The value present at the output of above circuit will change to
+Vsat+Vsat,when the voltage across capacitor C reaches just less than (more negative)
the voltage (negative value) across resistor R3R3.
Thus, the circuit shown in the above diagram will produce a square wave at the output as shown
in the following figure −

From the above figure we can observe that the output of square wave generator will haveone
of the two values: +Vsat+Vsat and −Vsat−Vsat. So, the output remains at one value for some
duration and then transitions to another value and remains there for some duration. In this way, it
continues.
 112

Triangular Wave Generator:

A triangular wave generator is an electronic circuit, which generates a triangular wave. The
block diagram of a triangular wave generator is shown in the following figure −

The block diagram of a triangular wave generator contains mainly two blocks: a squarewave
generator and an integrator. These two blocks are cascaded. That means, the output of square
wave generator is applied as an input of integrator. Note that the integration of a square wave is
nothing but a triangular wave. The circuit diagram of an op-amp based triangular wave generator
is shown in the following figure −

We have already seen the circuit diagrams of a square wave generator and an integrator. Observe
that we got the above circuit diagram of an op-amp based triangular wave generator by replacing
the blocks with the respective circuit diagrams in the block diagram of a triangular wave
generator.
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ix
Textbook on
Analog Electronic Circuits
Principles & Fundamentals
Kumar Raja D R
Syed Thouheed Ahmed
Syed Muzamil Basha

ISBN: 978-93-5636-178-2

FIRST EDITION - AUG 2022

MileStone Research Publications,
India

Open Access Book

Declaration - The content, information and representation is derived solely for

understand-ability of reader and the author (s) claim no copyrights on content.