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70

UNIT - IV FEEDBACK AMPLIFIERS & OSCILATTORS

OBJECTIVES

i)The basics of feedback.

ii)The properties of negative feedback.

iii)The basic feedback topologies.

iv)An example of the “ideal” feedback case.

v)Some realistic circuit examples and how to analyze them.

INTRODUCTION TO FEEDBACK

• There are two types of feedback: regenerative (positive feedback) and

degenerative

(negative feedback).

• Unless you want your circuit to oscillate, we usually use NEGATIVE

FEEDBACK...

• This idea came about in the late 1920’s when they were able to build

amplifiers with reasonable gains, but with gains that were difficult to

control from amplifier to amplifier...

• One day, while riding the Staten Island Ferry, Harold Black invented

negative feedback....

DEFINITION

By building an amplifier whose gain is made deliberately, say 40

decibels higher than necessary (10,000-fold excess on an energy basis)

and then feeding the output back to the input in such a way as to throw

away the excess gain, it has been found possible to effect extraordinary

improvement in constancy of amplification and freedom from non-

linearity. Harold Black, inventor of negative feedback, 1934

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PROPERTIES OF NEGATIVE FEEDBACK

• The gain of the circuit is made less sensitive to the values of individual

components.

• Nonlinear distortion can be reduced.

• The effects of noise can be reduced (but not the noise itself).

• The input and output impedances of the amplifier can be modified.

• The bandwidth of an amplifier can be extended.

• All you have to do to “get some feedback” (of the negative kind) is to

supply a scaled replica of the amplifier’s output to the inverting (negative)

input (more on this below) and presto!

• Of course, if you use negative feedback, overall gain of the amplifier is

always less than the maximum achievable by the amplifier without

feedback.

THE BASIC FEEDBACK CIRCUIT

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• With an input signal xs, an output signal xo, a feedback signal xf, and an

amplifier input

signal xi, let’s look at the basic feedback circuit illustrated above.

• The amplifier has a gain of A and the feedback network has a gain of

• The input to the amplifier is,

xi = xs - xf

• The output of the amplifier is,

xo = Axi

• So we can obtain an expression for the output signal in terms of the input

signal and the feedback gain...

xo = A xs - xf = A xs - β xo

• Rearranging,

xo = Axs - A β xo β o 1 + A β s

75

FROM BASIC BLOCK DIAGRAM TO ACTUALDIFFERENT

TYPES OF FEEDBACK CIRCUITS

76

The comparison of parameters of different types of amplifiers is given in

the form of tabular column which is shown below.

COMPARISON TABLE

77

BASIC STRUCTURE OF THE CIRCUIT

• Here we have assumed that there was an input “comparator” or “mixer”

and an output

“sampler” that provided us with a copy of the output signal for use as a

feedback signal.

• The form these devices take depends upon whether the amplifier’s input

and output

are current or voltage based...

78

SERIES-SHUNT FEEDBACK - VOLTAGE AMPLIFIER

80

SHUUNT-SERIES FEEDBACK - CURRENT AMPLIFIER

SERIES-SERIES FEEDBACK -TRANSCONDUCTANCE

AMPLIFIER

VOLTAGE -IN, CURRENT -OUT (SHUNT [VOLTAGE]

MIXING, CURRENT -SAMPLING)

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SHUNT-SHUNT FEEDBACK -TRANSRESISTANCE

AMPLIFIER

CURRENT-IN, VOLTAGE-OUT (SHUNT [CURRENT]

MIXING, VOLTAGE-SAMPLING)

84

SUMMARY OF STEPS YOU WILL

USE

85

LINEAR OSCILLATORS

• A linear oscillator ideally produces a pure sinusoidal output at a single

frequency

(hopefully).

• To achieve linear oscillation, a linear amplifier must oscillate without

external stimuli

(other than a start-up transient to get it going, perhaps).

• In order to understand this type of oscillator, a minor excursion into

theory will be

required (it’s worth it, since a little bit of intuitive understanding goes a

long way!).

• What is required to make a linear oscillator (that works, that is!) is the

arrangement

shown below (this is just POSITIVE feedback)...

86

• Actually, it is a necessary condition for this type of oscillator (linear) to

work.

• Intuitively, however the fact that the overall gain is infinity means that

the output of the

circuit is some signal (to be determined!), even with NO input at all!

• If one can arrange it so that the Barkhausen Criterion is met at only a

single frequency,

87

it is possible to obtain a very pure sinewave output (if it is met at multiple

frequencies,

you might get an interesting mix of frequencies).

TYPES OF OSCILLATORS

1. Non-sinusoidal Oscillator

These Oscillators produce other than sine wave. (eg.) Triangular

wave, square wave,sawtooth wave…They are generated by using

relaxation oscillator circuits. In this type of circuit, the V or I change

abruptly one or more times during each cycle and thus result in a non-

sinusoidal oscillation.

Application

Used as a timing circuit

A few non-sinusoidal oscillators are,

(i) Multivibrator

(ii) Saw-tooth wave generator

(iii) Rectangular wave generator

(iv) Triangular wave generator

2. Sinusoidal Oscillator

In a Sinusoidal Oscillator the voltage varies continuously with respect to

time. They are generated using any one of the following property.

(i) Negative resistance

(ii) Feedback

88

(iii) Heterodyne

(iv) Crystal

(v) Magnetostriction

(vi) Ultra high frequency

(vii)

Nature of sinusoidal oscillation

1. damped Oscillation

The electrical oscillation whose amplitude goes on decreasing with

time is known as damped Oscillation

2. Undamped Oscillation

89

The electrical oscillation whose amplitude remains constant with time

is known as undamped Oscillation

BARKHAUSEN CRITERION

The overall gain of a positive feedback amplifier is given by the relation

Af=A/(1-βA)

Where, Af is the voltage gain with feedback

βA is the loop gain

If βA is made equal to unity then Af is infinity. (i.e) the circuit had

stopped amplifying and started oscillating. To provide positive feddedback

the feedback network should produce a phase shift of 180º in addition to

180º phase shift produced by the amplifier.

Therefore the total phase shift should be 360º.

Hence the condition for oscillations is

(i) βA must be equal to one

(ii) The total phase shift should be 360º.

FREQUENCY STABILITY

The ability of the oscillator to maintain constant frequency is

called Frequency stability

Factors affecting Frequency stability

1. operating point

2. Parameters of active device

3. Power source

4. Temperature variation

90

5. Mechanical vibration

A. RC OSCILLATOR

1. WEIN BRIDGE OSCILLATOR

It consists of two transistors connected in cascade and a bridge

network used to provide positive feedback.

Transistor Q1 provides amplifications and phase shift of 180º.

Transistor Q2 provides further amplifications and a phase shift of 180º.

Signals at base Q1are amplified and they appear with a phase shift of 360º

at the collector of Q1. Though the signal at the output of Q2 is in phase

with the input of Q1 it cannot be directly fed as a feedback signal; since it

would affect the frequency stability.

Circuit operation

The bridge circuit consists of two arms, the resistive arm and

reactive arm. The resistive arm consists of swamping resistor which

introduces a negative feedback to Q1. Thus it improves bias stability since

the arm consists of only resistive components alone. The amount of

feedback is determined only by voltage divider R3 and R4.

The reactive arm consists of two RC networks, out of which one is

in shunt and another is in series . since capacitors are connected in this

arm they are frequency sensitive. Hence the feedback signal from this

arms changes w.r.to frequency and magnitude depends upon the voltage

divider formed by R3-R4. The bridge is said to be balanced if the voltage

at point A equals to voltage at point D and this occurs only at one

frequency.

The circuit consists if two RC coupled amplifier, which provides

phase shift of 360º.So the feedback network has no need to provide any

additional phase shift. When the circuit is energized by switching on the

supply a small random oscillations are produced at base1. They are further

amplified at Collector of Q2 .Since the oscillations at collector of Q2 have

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been inverted twice, the input signal is in phase with the output signal,

apart of output form the collector of Q2 is feedback to Wein Bridge which

is further amplified. The process continues still a sustained oscillation is

produced.

Frequency calculation

Impendence of series arm 1C

1S s

1R)S(Z

1

11

sC

1CsR

Impendence of parallel arm 2

2p SC

1R)S(Z

92

22

22

SC1R

SC1xR

1CsR

R)S(Z

22

2P

Feedback Voltage

)S(Z)S(Z

)S(Z)S(V)S(V

Sp

p0p

1

11

22

2

222

0f

sC

1CsR

1CsR

R1CsR

R

)S(V)S(V

WKT,

)S(V

)S(V

0

f feedback fraction ratio.

122

221122112

12

222

sC1CsR

1CsRCsRCRCRsCsR

1CsRR

1CsRCsRCRCRsCsR

CsR

221122112

12

12

Let CCC&RRR 2121

1.....1sRC3CRs

sRC222

GAIN of op. amp 2....R

R1

)S(V

)S(VA

i

f

f

0

WKT, for oscillation to start,

93

3....1A

Sub 1 & 2 in 3

11sRC3CRs

sRC

R

R1

222i

f

replace s = js

where f2

f is the frequency of oscillation

j is the complex variable

11RCj3CRj

RCj

R

R1

2222i

f

Real part,

01CR 222

1CR 222

222

CR

1

RC

1

f2

RC2

1f

Imaginary part,

RC3jRCjR

R1

i

f

if R2R

Frequency Range

20Hz to 1MHz

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Advantages

1. Good Frequency stability

2. Good amplitude stability

3.

Application

Audio signal generator.

2. RC PHASE SHIFT OSCILLATOR

A fraction of output of a single stage amplifier is passed thro, a

phase shift network, before feeding back to the input. The phase shift

network provides a phase shift of 180º and another 180º phase shift is

produced by the amplifier.

Hence the total phase shift is 360º.

Circuit Diagram.

The feedback network consists of three identical RC section. Each

section produces a phase shift of 60º. Therefore the total phase shift of the

feedback network is180º and another 180º phase shift is produced by the

amplifier.

Therefore the total phase shift should be 360º.

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Circuit operation

When the circuit is energized by switching on the supply a small

random oscillations are produced .The oscillation may start due to minor

variation in d.c supply. The output form the collector is feedback to phase

shift network and finally applied to the base. The oscillation will be

maintained if loop gain is made equal to unity.

frequency calculation

Node 1

)S(I)S(I)S(I 321

C

211

C

10

s1

)S(V)S(V

R

)S(V

s1

)S(V)S(V

1....1sRC2

sRC)S(V)S(V)S(V 02

1

Node 2

)s(I)S(I)S(I 543

C

f22

C

21

s1

)S(V)S(V

R

)S(V

s1

)S(V)S(V

96

2....sRC

1sRC2

)S(V)S(V)S(V 02

2

Node 3

Since 0)S(IRR 7i

)S(I)6(I 65

3....)S(VsRC

1sRC)S(V f2

Sub 3 in 1

sRC

1sRC2

)S(V)S(VsRC

1sRC

)S(V0f

1

sRC1sRC2sRC

)S(sRcV)S(V1sRC)S(V 0f

1

4....1sRC2

)S(sRcV)S(V1sRC)S(V 0f

1

Now Sub 3 in 2

Equating 4 & 5

3330

222s333f CRs)S(VsRC5CR6CRs)S(V

WKT, ,)S(V

)S(V

0

f feedback fraction ratio

1sRC5CRs6CRs

CRs222333

333

Put js

6....1RCj5CR6CjR

CjR322333

333

Gain of opamp, 7....R

RA

i

f

WKT, condition for oscillation is 8....1A

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Sub 6, 7 in 8

11RCj5CR6CjR

CjR

R

R222333

333

i

f

Equating real and imaginary part to zero,

Real part,

01CR6 222

1CR6 222

222

CR6

1

RC6

1

f2

6RC2

1f

Imaginary part,

RCj533C3jR33C3jRiRfR

522C2R22C2RiRfR

5CR1R

R 222

i

f

29R

R

i

f

Frequency Range

20Hz to 1MHz

Advantages

98

4. Good Frequency stability

5. Good amplitude stability

Application

Audio signal generator.

B. LC Oscillators

They are also known as tuned Oscillators or tank circuit oscillator.

They are used to produce frequency in the range of 1MHz to 500MHz.

Hence they are also known as R.F oscillators.

TYPES OF LC OSCILLATORS

1.TUNED COLLECTOR OR ARMSTRONG OSCILLATOR

It uses inductive feedback

The LC circuit is in collector of transistor

Hartley Oscillator


Colpitt’s Oscillator

It uses capacitive feedback

Clapp Oscillator

It uses capacitive feedback

2. TUNED BASE OSCILLATOR


The LC circuit is in base of transistor

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1.TUNED COLLECTOR OSCILLATOR

It uses inductive feedback. The LC circuit is in collector of transistor.

The feedback signal is taken from the secondary winding L1and fed back

to the base terminal. There is phase shift of 180ºin the transformer and

another 180º phase shift is produced by transistor amplifier. Hence the

total phase shift is 360º.

Hence the feedback fraction β=M/L

M- Mutual inductance between primary and secondary winding.

L- self inductance between primary and secondary winding.

WKT,

βA=1

A=1/β

For the oscillation to start, voltage gain must be greater than 1/β

R1,R2 Re are used to produce d.c bias to the transistor. The capacitor C'

and Ce act as a bypass capacitor to the resistor R2 and Re respectively.

Operation

When the circuit is energized by switching on the supply small

random oscillations are produced, hence the collector current increase to

quiescent value. These current charges the capacitor C. when it is fully

charged it discharges thro, the primary winding of L producing a magnetic

field around it. When the capacitor I s fully discharged, magnetic field

collapses and charges the capacitor in reverse direction. The process

continues still a sustained oscillation is produced.

HARTLEY OSCILLATOR

It uses inductive feedback. The tank circuit consists of two coils L1

and L2. The L1 is inductively coupled to L2 and the combination works as

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auto transformer. The feedback between output and input is accomplished

thro; this autotransformer action which also introduces a phase shift of

180º and the transistor Q1 provides amplifications and a phase shift of

180º. Hence the total phase shift is 360º.

Hence the feedback fraction β=L2/L1

WKT,

βA=1

A=1/β


A= L1/L2

R1,R2 Re are used to produce d.c bias to the transistor. The capacitor Cc

permits only a.c current to pass thro, tank circuit.Cb acts as blocking

capacitor, which blocks the d.c current reaching the base terminal. and Ce

act as a bypass capacitor.

Operation



quiescent value. The oscillations are produced because of positive

feedback from the tank circuit. The process continues still a sustained

oscillation is produced.

101

COLPITTS OSCILLATOR

It uses capacitive feedback. The tank circuit consists of two capacitor

C1 and C2connected in series with each other which introduces a phase

shift of 180º and the transistor Q1 provides amplifications and a phase shift

of 180º. Hence the total phase shift is 360º.

Hence the feedback fraction β=C1/C2

WKT,

βA=1

A=1/β


A= C2/C1





Operation

When the circuit is energized by switching on the supply a small random

oscillation are produced, hence the collector current increase to quiescent

value. The oscillations are produced because of positive feedback from the

tank circuit. The process continues still a sustained oscillation is produced.

102

CLAPP OSCILLATOR

It uses capacitive feedback. The circuit differs from the colpitt only in

one respect, that it contained one additional capacitor C3 connected in

series with inductor. This additional capacitor eliminates the effect of

frequency stability and improves the frequency stability. The tank circuit

consists of two capacitor C1 and C2 connected in series with each other

which introduces a phase shift of 180º and the transistor Q1 provides

amplifications and a phase shift of 180º. Hence the total phase shift is

360º.

Hence the feedback fraction β=C1/C2

WKT,

βA=1

A=1/β


A= C2/C1





Operation

When the circuit is energized by switching on the supply small random

oscillations are produced, hence the collector current increase to quiescent

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value. The oscillations are produced because of positive feedback from the

tank circuit. The process continues still a sustained oscillation is produced.

2.TUNED BASE OSCILLATOR

It uses inductive feedback. The LC circuit is in base of transistor. The

feedback signal is taken from the secondary winding L1and fed back to

the base terminal. Thers is phase shift of 180ºin the transformer and

another 180º phase shift is produced by transistor amplifier. Hence the

total phase shift is 360º.

Hence the feedback fraction β=M/L

M- Mutual inductance between primary and secondary winding.

L- self inductance between primary and secondary winding.

WKT,

βA=1

A=1/β

104


R1,R2 Re are used to produce d.c bias to the transistor. The capacitor C'

and Ce act as a bypass capacitor to the resistor R2 and Re respectively.

Operation



quiescent value. These current charges the capacitor C. when it is fully

charged it discharges thro, the primary winding of L producing a magnetic

field around it. When the capacitor I s fully discharged, magnetic field

collapses and charges the capacitor in reverse direction. The process

continues still a sustained oscillation is produced.

C. CRYSTAL OSCILLATOR

It is basically a tuned oscillator. It uses a piezoelectric crystal in the

tank circuit. The crystal is usually made up of quartz crystal and provides

a high frequency of stability and accuracy. Therefore the crystal oscillators

are used in applications where frequency stability is very essential. They

are widely used in digital watches and clocks.

Quartz crystal

It has a very peculiar property known as piezoelectric effect. When an

a.c voltage is applied to the crystal, it stars vibrating at a frequency of

applied voltage. Conversely if a force is applied to the crystal, it generates

the a.c voltage.

Electric equivalent of a crystal

105

It consists of series R-L-C1 circuit in parallel with a capacitance

C2.When the crystal is not vibrating, it is equivalent to capacitance C2.

When the crystal is vibrating , it is equivalent to series R-L-C1 circuit.

The series resonant frequency (fs) occurs when reactance of inductance

equals to the reactance of capacitance C2.

12

1

LCsf

The parallel resonant frequency occurs when reactance of inductance

equals to the reactance of series R-L-C1 circuit.

LCfp

2

1

where C=C1*C2/(C1+ C2)

Q=Factor of the crystal is given by

Q=(2*∏* sf *L)/R

Crystal Oscillator circuit

The crystal is connected as a series element in the feedback path from

collector to base.R1,R2 Re are used to produce d.c bias to the transistor.

The capacitor Cc permits only a.c current to pass thro, tank circuit.Cb acts

as blocking capacitor, which blocks the d.c current reaching the base

terminal and Ce act as a bypass capacitor. he coupling capacitor C has a

negligible impedance at the circuit operating frequency.

106

The circuit operating frequency of oscillation is set by series resonant frequency

of crystal and its value is given by relation,

OSCILLATORS USING OP-AMP

RC –PHASE SHIFT OSCILLATOR

An example of a sinewave generator is shown in Figure 21. This is a

phase-shift oscillator, and amongst other things demonstrates that negative

feedback becomes positive feedback if there is enough phase-shift around

the feedback loop. Here, the opamp is connected as an inverting amplifier,

but the connection between output and input of three RC sections in

cascade introduces 180 phase shift at some particular frequency. If the

gain of the amplifier section is sufficient to make up for the attenuation of

the phase-shift network at that frequency, then the system will oscillate. If

the gain is too high, the oscillations build up until the amplifier output

reaches its maximum values and the system “saturates” (that is it becomes

non-linear). If the gain is too low, the system may show resonance, but it

will not oscillate. In fact, the diode network provides controlled non-

linearity to keep the overall loop gain at unity, and so provide stable

oscillation. Note that at least three RC sections are required, since each

section can produce only just under 90 phase-shift at most, so that two

cannot provide the necessary 180 shift. This circuit is quite tricky to

analyse, just because each RC section loads the preceding section. A

sinewave oscillator based on the Wien bridge, somewhat easier to analyse

and also rather better in performance, appears in the tutorial exercises. The

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circuit in Figure 21 was in fact “designed” by adjusting values in a PSpice

model.

C

_

+ R

R2

Sinewave R

C C R1

V(Sinewave)

-3

-2

-1

0

1

2

3

0.06 0.07 0.08 0.09 0.1

Time (s)

Ou

tpu

t (V

)

108

Phase-shift oscillator voltages

-3

-2

-1

0

1

2

3

0.1 0.101 0.102 0.103 0.104 0.105

Time (s)

Wav

efo

rms

(V)

V(Sinewave) V(C2:1) V(C3:1)

Figure 21. Phase-shift oscillator. Waveforms are calculated for R = 10 k,

R1 = R2 = 200 k, C = 10 nF. Note the initial exponential rise of

oscillation amplitude, followed by levelling off as the diode limiter

operates. Note also the phase-shifted waveforms at each stage of the

phase-shift network.

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