Session 8:

INTRODUCTION TO FEED-BACK AMPLIFIERS, FEEDBACK

CHARACTERISTICS, NEED FOR FEEDBACK,

FEEDBACK TOPOLOGIES

Introduction of feedback Amplifier:

An amplifier is an electronic device that can increase the power of a signal. It

does this by taking energy from power supply and controlling the output to match the

input signal shape but with larger amplitude. In this sense, an amplifier modulates the

output of the power supply to make the output signal stronger than the input signal. An

amplifier is effectively the opposite of an attenuator, while an amplifier provides gain,

an attenuator provides loss. If some percentage of an amplifier’s output signal is

connected to the input, so that the amplifier amplifies part of its own output signal, we

have what is known as feedback. Such types of amplifiers are called as feedback

Amplifiers. Feedback circuit is essentially a potential divider consisting of resistances

R1 & R2. The purpose of feedback circuit is to return a fraction of the output voltage to

the input of the amplifier circuit.

Feedback amplifier contains two component namely feedback circuit and

amplifier circuit. For example consider the feedback amplifier circuit shown in Fig1. In

this A f is closed-loop gain of the amplifier, A is open-loop gain of the amplifier gain

andβ is called as feedback factor or gain of the feedback.

Fig 1: (a) Feedback amplifier (b) Feedback circuit

If Vf= 0 (There is no feedback)

A=V 0

V f=

V 0

V i

If feedback signal V f is connected in series with the input, then V i=V s−V f

V 0=AV i=A (V s−V f )But V f=βV 0

V 0=A(V s−βV 0 )V 0 (1+ βA )=AV s

V 0=AV s

(1+βA )

A f=V 0

V s=A

(1+βA )−−−−−−−−−Eq .(1)

The feedback gain is reduced by 1+βA times of the open loop gain. For negative

feedback βA>0 and for positive feedback βA<0 .

Feedback:

Feedback comes in two varieties: positive (also called regenerative),

and negative (also called degenerative). Positive feedback reinforces the direction of an

amplifier’s output voltage change, while negative feedback does just the opposite.

Feedback network is a passive network, which consists of only resistances in case of

negative feedback and combination of RLC in case of positive feedback.

A familiar example of feedback happens in public-address (“PA”) systems

where someone holds the microphone too close to a speaker: a high-pitched “whine” or

“howl” ensues, because the audio amplifier system is detecting and amplifying its own

noise. Specifically, this is an example of positive or regenerative feedback, as any

sound detected by the microphone is amplified and turned into a louder sound by the

speaker, which is then detected by the microphone again; and so on . . . the result being

a noise of steadily increasing volume until the system becomes “saturated” and cannot

produce any more volume.

Consider an example of a closed-loop system, shown in Fig 2, is a temperature-

control system in a room. For this system we wish to maintain, automatically, the

temperature of the room at a desired value. To control any physical variable, which we

usually call a signal, we must know the value of this variable, that is, we must measure

this variable. We call the system for the measurement of a variable a sensor. In this

system, the sensor is a thermistor. Thermistor is a device which has a resistance that

varies with temperature. By measuring this resistance, we obtain a measure of the

temperature.

Fig 2: Room temperature control system

Characteristics of feedback:

The feedback amplifiers have the following characteristics

a. Effect on gain

From the Eq.(1) the gain of the negative feedback amplifier, shown in Fig

1, is reduced by 1+βA times when 1+βA is greater than one.

b. Effect on gain stability

From Eq.(1) if βA >> 1 then

A f≃1β

Where β depends on the components used in feedback network and is

independent of transistor parameters. So, negative feedback network consists of

only resistors, which are more stable with respect to temperature and ageing.

Hence gain becomes more stable.

Differentiate the Eq.(1) with respect to A

dA f

dA= 1

(1+ β . A )2=A f

A(1+βA )

dA f

A f=dA

A ( 11+ βA )−−−−−−−Eq .(2 )

From Eq.(2), in case of negative feedback, it is obvious that the

relative change in gain with feedback ( dA f

A f)

is less than the relative

change in gain without feedback ( dA

A )by the amount 1+βA

( dA f

A f)<( dA

A )−−−−−−−−Eq. (3 )

c. Sensitivity

The sensitivity of the feedback is given by

S=

dA f

A f

dAA

= 11+βA

d. Desensitivity

Desensitivity is a measure of the ability of the negative feedback to

desensitize or stabilize the circuit. Higher D indicates higher stability. The

desensitivity of the feedback is reciprocal of the sensitivity. It is given by

D= 1S=1+βA

e. Effect on bandwidth

The lower cut off frequency of the feedback amplifier is

ALf=A L

1+ βAL where

AL=Am

1−( jf L

f )ALf =

Am

1−( jf L

f )+βAm

=Am

(1+βAm)(1−( jf L

f (1+βAm )))

Where

Am

1+ βAm is the mid band gain with feedback denoted by Amf

f L

1+ βAm is the lower cut off frequency with feedback denoted by f Lf

f L=f L

1+βAm−−−−−−Eq .( 4 )

ALf =Amf

1−( jf Lf

f )FromEq .(4 ) , it is stated thatf Lf < f L . Hence negative feedback will

decrease the lower cut off frequency.

Similarly the higher cut off frequency is given by

f Hf =f H (1+βAm)−−−−−−−Eq .(5)

From Eq .(5) , it is stated that f Hf >f H . Hence negative feedback will

increase the higher cut off frequency.

From Eq .(4 ) and Eq .(5) , it is stated that the resultant bandwidth of the

negative feedback amplifier is increased by the factor1+βAm if the negative

feedback is used. It is shown in Fig 3. Graphically.

Fig 3: Bandwidth of the feedback amplifier with and without feedback.

f. Effect on frequency distortion

Negative feedback increases mid band range. Hence greater range of

frequencies can receive uniform amplification and this reduces frequency distortion.

Due to decrease in lower cut off percentage of tilt will be decreased, which indicates

decrease in frequency distortion. The increase in higher cut off frequency will

decrease rise time and fall time, which indicates decrease in high frequency

distortion.

Need for feedback:

The use of the feedback concept simplifies the process and provides better insight

into the working of amplifier circuits. Furthermore, the design of amplifiers becomes

systematic and simplified. This is another important motivation. The feedback is

frequently used in most areas of electrical engineering. The text of the exercise is made

relatively comprehensive in order to give general information about feedback and aim

therefore at the practical part of this special laboratory exercise. Feedback in amplifiers

gives better performance in several important ways, including:

a) Increased stability in the amplification. The gain is less dependent on the parameters of

the amplifier elements.

b) Feedback reduces distortion in the amplifier.

c) The bandwidth of the amplifier is increased.

d) It is easier to achieve desired input and output impedances.

These advantages are achieved at the expense of gain which is less than the

amplifier gain without feedback. Stability, nonlinear distortion, bandwidth requirements

and impedance matching are very important concepts that are part of a long list of

problems, for example in telecommunications.

Feedback topologies:

Depending on the input signal (voltage or current) to be amplified and form of the

output (voltage or current), amplifiers can be classified into four categories. Depending

on the amplifier category, one of four types of feedback structures should be used (series-

shunt, series-series, shunt-shunt, or shunt-series)

i. Series-shunt feedback

This type of feedback is also called as voltage series feedback or voltage-

voltage feedback. This is a voltage amplifier. The feedback of this is as shown in

Fig 4(a). It is a voltage controlled voltage source (VCVS).

ii. Shunt-series feedback

This type of feedback is also called as current shunt feedback or current-

current feedback. This is a current amplifier. The feedback of this is as shown in

Fig 4(d). It is a current controlled current source (CCCS).

iii. Series-series feedback

This type of feedback is also called as current series feedback or current-

voltage feedback. This is a trans conductance amplifier. The feedback of this is as

shown in Fig 4(b). It is a voltage controlled current source (VCCS).

iv. Shunt-shunt feedback

This type of feedback is also called as voltage shunt feedback or voltage-

current feedback. This is a trans resistance amplifier. The feedback of this is as

shown in Fig 4(c). It is a current controlled voltage source (CCVS).

Fig 4: Four feedback configurations (a) Series-shunt (VCVS). (b) Series-series (VCCS). (c) Shunt-shunt (CCVS). (d) Shunt-series (CCCS).

Let’s examine a simple amplifier circuit and see how we might introduce negative

feedback into it, starting with Fig 5.

Fig 5: Common-emitter amplifier without feedback.

The amplifier configuration shown above is a common-emitter, with a resistor

bias network formed by R1 and R2. The capacitor couples Vinput to the amplifier so that the

signal source doesn’t have a DC voltage imposed on it by the R1/R2 divider network.

Resistor R3 serves the purpose of controlling voltage gain. We could omit it for maximum

voltage gain, but since base resistors like this are common in common-emitter amplifier

circuits, we’ll keep it in this schematic.

Like all common-emitter amplifiers, this one inverts the input signal as it is

amplified. In other words, a positive-going input voltage causes the output voltage to

decrease, or move toward negative, and vice versa. The oscilloscope waveforms are

shown in Fig 6.

Fig 6: Common-emitter amplifier, no feedback, with reference waveforms for comparison.

Because the output is an inverted, or mirror-image, reproduction of the input

signal, any connection between the output (collector) wire and the input (base) wire of

the transistor in Fig 7 will result in negative feedback.

Fig 7: Negative feedback, collector feedback, decreases the output signal.

The resistances of R1, R2, R3, and Rfeedback function together as a signal-mixing

network so that the voltage seen at the base of the transistor (with respect to ground) is a

weighted average of the input voltage and the feedback voltage, resulting in signal of

reduced amplitude going into the transistor. So, the amplifier circuit in Figure above will

have reduced voltage gain, but improved linearity (reduced distortion) and increased

bandwidth.

A resistor connecting collector to base is not the only way to introduce negative

feedback into this amplifier circuit. Another method, although is more difficult to

understand at first, involves the placement of a resistor between the transistor’s emitter

terminal and circuit ground in Fig 8.

Fig 8: Emitter feedback: A different method of introducing negative feedback into a circuit.

This new feedback resistor drops voltage proportional to the emitter current

through the transistor, and it does so in such a way as to oppose the input signal’s

influence on the base-emitter junction of the transistor. Let’s take a closer look at the

emitter-base junction and see what difference this new resistor makes in Fig 9.

With no feedback resistor connecting the emitter to ground in Fig 9(a) , whatever

level of input signal (Vinput) makes it through the coupling capacitor and R1/R2/R3 resistor

network will be impressed directly across the base-emitter junction as the transistor’s

input voltage (VB-E). In other words, with no feedback resistor, VB-E equals Vinput.

Therefore, if Vinput increases by 100 mV, then VB-E increases by 100 mV: a change in one

is the same as a change in the other, since the two voltages are equal to each other.

Now let’s consider the effects of inserting a resistor (Rfeedback) between the

transistor’s emitter lead and ground in Fig 9(b).

Fig 9: (a) No feedback vs (b) emitter feedback. A waveform at the collector is inverted

with respect to the base. At (b) the emitter waveform is in-phase (emitter follower) with

base, out of phase with collector. Therefore, the emitter signal subtracts from the

collector output signal.

Note how the voltage dropped across Rfeedback adds with VB-E to equal Vinput. With

Rfeedback in the Vinput—VB-E loop, VB-E will no longer be equal to Vinput. We know that

Rfeedback will drop a voltage proportional to emitter current, which is in turn controlled by

the base current, which is in turn controlled by the voltage dropped across the base-

emitter junction of the transistor (VB-E). Thus, if Vinput were to increase in a positive

direction, it would increase VB-E, causing more base current, causing more collector

(load) current, causing more emitter current, and causing more feedback voltage to be

dropped across Rfeedback. This increase of voltage drop across the feedback resistor,

though, subtracts from Vinput to reduce the VB-E, so that the actual voltage increase for VB-

E will be less than the voltage increase of Vinput. No longer will a 100 mV increase in

Vinput result in a full 100 mV increase for VB-E, because the two voltages are not equal to

each other.

Consequently, the input voltage has less control over the transistor than before,

and the voltage gain for the amplifier is reduced: just what we expected from negative

feedback. In practical common-emitter circuits, negative feedback isn’t just a luxury; its a

necessity for stable operation. In a perfect world, we could build and operate a common-

emitter transistor amplifier with no negative feedback, and have the full amplitude of

Vinput impressed across the transistor’s base-emitter junction. This would give us a large

voltage gain. Unfortunately, though, the relationship between base-emitter voltage and

base-emitter current changes with temperature, as predicted by the “diode equation.” As

the transistor heats up, there will be less of a forward voltage drop across the base-emitter

junction for any given current. This causes a problem for us, as the R1/R2 voltage divider

network is designed to provide the correct quiescent current through the base of the

transistor so that it will operate in whatever class of operation we desire (in this example,

I’ve shown the amplifier working in class-A mode). If the transistor’s voltage/current

relationship changes with temperature, the amount of DC bias voltage necessary for the

desired class of operation will change. A hot transistor will draw more bias current for the

same amount of bias voltage, making it heat up even more, drawing even more bias

current. The result, if unchecked, is called thermal runaway.

Common-collector amplifiers, (Fig 10) however, do not suffer from thermal

runaway. Why is this? The answer has everything to do with negative feedback.

Fig 10: Common collector (emitter follower) amplifier.

Note that the common-collector amplifier (Fig 10) has its load resistor placed in

exactly the same spot as we had the Rfeedback resistor in Fig 9(b): between emitter and

ground. This means that the only voltage impressed across the transistor’s base-emitter

junction is the differencebetween Vinput and Voutput, resulting in a very low voltage gain

(usually close to 1 for a common-collector amplifier). Thermal runaway is impossible for

this amplifier: if base current happens to increase due to transistor heating, emitter current

will likewise increase, dropping more voltage across the load, which in

turn subtracts from Vinput to reduce the amount of voltage dropped between base and

emitter. In other words, the negative feedback afforded by placement of the load resistor

makes the problem of thermal runaway self-correcting. In exchange for a greatly reduced

voltage gain, we get superb stability and immunity from thermal runaway.

By adding a “feedback” resistor between emitter and ground in a common-emitter

amplifier, we make the amplifier behave a little less like an “ideal” common-emitter and

a little more like a common-collector. The feedback resistor value is typically quite a bit

less than the load, minimizing the amount of negative feedback and keeping the voltage

gain fairly high.

Another benefit of negative feedback, seen clearly in the common-collector

circuit, is that it tends to make the voltage gain of the amplifier less dependent on the

characteristics of the transistor. Note that in a common-collector amplifier, voltage gain is

nearly equal to unity (1), regardless of the transistor’s β. This means, among other things,

that we could replace the transistor in a common-collector amplifier with one having a

different β and not see any significant changes in voltage gain. In a common-emitter

circuit, the voltage gain is highly dependent on β. If we were to replace the transistor in a

common-emitter circuit with another of differing β, the voltage gain for the amplifier

would change significantly. In a common-emitter amplifier equipped with negative

feedback, the voltage gain will still be dependent upon transistor β to some degree, but

not as much as before, making the circuit more predictable despite variations in transistor

β. The fact that we have to introduce negative feedback into a common-emitter amplifier

to avoid thermal runaway is an unsatisfying solution. Is it possibe to avoid thermal

runaway without having to suppress the amplifier’s inherently high voltage gain? A best-

of-both-worlds solution to this dilemma is available to us if we closely examine the

problem: the voltage gain that we have to minimize in order to avoid thermal runaway is

the DC voltage gain, not the AC voltage gain. After all, it isn’t the AC input signal that

fuels thermal runaway: its the DC bias voltage required for a certain class of operation:

that quiescent DC signal that we use to “trick” the transistor (fundamentally a DC device)

into amplifying an AC signal. We can suppress DC voltage gain in a common-emitter

amplifier circuit without suppressing AC voltage gain if we figure out a way to make the

negative feedback only function with DC. That is, if we only feed back an inverted DC

signal from output to input, but not an inverted AC signal. The Rfeedback emitter resistor

provides negative feedback by dropping a voltage proportional to load current. In other

words, negative feedback is accomplished by inserting an impedance into the emitter

current path. If we want to feed back DC but not AC, we need an impedance that is high

for DC but low for AC. What kind of circuit presents a high impedance to DC but a low

impedance to AC? A high-pass filter, of course!

By connecting a capacitor in parallel with the feedback resistor in Fig 11, we

create the very situation we need: a path from emitter to ground that is easier for AC than

it is for DC.

Fig 11: High AC voltage gain reestablished by adding Cbypass in parallel with Rfeedback

The new capacitor “bypasses” AC from the transistor’s emitter to ground, so that

no appreciable AC voltage will be dropped from emitter to ground to “feed back” to the

input and suppress voltage gain. Direct current, on the other hand, cannot go through the

bypass capacitor, and so must travel through the feedback resistor, dropping a DC voltage

between emitter and ground which lowers the DC voltage gain and stabilizes the

amplifier’s DC response, preventing thermal runaway. Because we want the reactance of

this capacitor (XC) to be as low as possible, Cbypass should be sized relatively large.

Because the polarity across this capacitor will never change, it is safe to use a polarized

(electrolytic) capacitor for the task.

Another approach to the problem of negative feedback reducing voltage gain is to

use multi-stage amplifiers rather than single-transistor amplifiers. If the attenuated gain of

a single transistor is insufficient for the task at hand, we can use more than one transistor

to make up for the reduction caused by feedback. An example circuit showing negative

feedback in a three-stage common-emitter amplifier is Fig 12.

Fig 12: Feedback around an “odd” number of direct coupled stages produce negative feedback.

The feedback path from the final output to the input is through a single resistor,

Rfeedback. Since each stage is a common-emitter amplifier (thus inverting), the odd number

of stages from input to output will invert the output signal; the feedback will be negative

(degenerative). Relatively large amounts of feedback may be used without sacrificing

voltage gain, because the three amplifier stages provide much gain to begin with.

At first, this design philosophy may seem inelegant and perhaps even counter-

productive. Isn’t this a rather crude way to overcome the loss in gain incurred through the

use of negative feedback, to simply recover gain by adding stage after stage? What is the

point of creating a huge voltage gain using three transistor stages if we’re just going to

attenuate all that gain anyway with negative feedback? The point, though perhaps not

apparent at first, is increased predictability and stability from the circuit as a whole. If the

three transistor stages are designed to provide an arbitrarily high voltage gain (in the tens

of thousands, or greater) with no feedback, it will be found that the addition of negative

feedback causes the overall voltage gain to become less dependent of the individual stage

gains, and approximately equal to the simple ratio Rfeedback/Rin. The more voltage gain the

circuit has (without feedback), the more closely the voltage gain will approximate

Rfeedback/Rin once feedback is established. In other words, voltage gain in this circuit is

fixed by the values of two resistors, and nothing more.

This is an advantage for mass-production of electronic circuitry: if amplifiers of

predictable gain may be constructed using transistors of widely varied β values, it eases

the selection and replacement of components. It also means the amplifier’s gain varies

little with changes in temperature. This principle of stable gain control through a high-

gain amplifier “tamed” by negative feedback is elevated almost to an art form in

electronic circuits called operational amplifiers, or op-amps. You may read much more

about these circuits in a later chapter of this book!

Session 9:

ANALYSIS OF SERIES-SERIES FEEDBACK AMPLIFIERS USING BJT

Introduction of series-series feedback:It is basically a trans conductance amplifier. Here the input signal is a voltage and

the output signal is a current. It follows that the appropriate feedback topology is the

current-sampling series-mixing topology, illustrated in Fig 13. Hence it is known as the

series-series feedback configuration and is called as voltage controlled current source

(VCCS).

Concept of output sampling and mixing at input:

Sampling network represents the way feedback network is connected to amplifier

output. Mixing network represents the connection of feedback network to the amplifier

input side.

In this series-series feedback the feedback is connected in series with RL such that

full load current will act as input to the feedback network. At input side the feedback

network is in series with signal source by mixing the voltage. This is shown in Fig 13.

. Fig 13: Series-series feedback

Effect of feedback on characteristics of the amplifier:

For this consider the equivalent circuit of the series-series feedback shown in Fig

14. In that output resistance of the amplifier and output resistance of the feedback circuit

are in series hence effective output resistance of the feedback amplifier will increase.

Input resistance of the amplifier and feedback network are in series hence effective input

resistance will increase. Thus Current series feedback circuit behave like a voltage

controlled current source.

Fig 14: Equivalent circuit of the series-series feedback

Current Gain:

Input Impedance:

Zin=V s

I s=

V i+V f

I s

Zin=V i+ βV 0

I s=

V i+β AV i

I s

Zin=V i (1+βA )I s

=ri(1+βA )

Output Impedance:

I 0=A . V i=A (V s−V f )V f=β . I0

A(V s−β . I 0 )=I 0

AV s=(1+βA ) I0

A f=I 0

V s=A

1+βA

V i+V f=V s=0

I 0=V 0+ A . β . I0

r0

Zout|V s=0=V 0

I 0; I 0 =

V 0−A .V i

r 0

Zout=V 0

I 0=

r0

1+ A . β

Example for series-series feedback using BJT:

A series-series feedback BJT amplifier is shown in Fig 15. The input variable is

the voltage v1 and the output variable is the voltage v2. The feedback is from ie3 to the

emitter of Q1. Because the feedback does not connect to the input node, the input

summing is series. The output sampling is series because the feedback is proportional to

the current that flows in series with the output rather than the output voltage. The circuit

with feedback removed is shown in Fig 16.

Fig 15: Amplifier circuit.

The circuit looking out of the emitter of Q1 is a Thévenin equivalent made with

respect to the current ie3. The output current is proportional to this current, i.e. ic3 = αie3.

Because r0 = ∞ for Q3, the feedback does not affect the output resistance seen looking

down through R4 because it is infinite. For a finite r0, a test voltage source can be added

in series with R4 to solve for this resistance. It would be found that a finite r0 for Q3

considerably complicates the circuit equations and the flow graph.

Fig 16: Circuit with feedback removed.

Session 10:

ANALYSIS OF SHUNT-SHUNT FEEDBACK AMPLIFIERS USING FET

Introduction of shunt-shunt feedback:

It is basically a trans resistance amplifier. Here the input signal is current and the

output signal is voltage. It follows that the appropriate feedback topology is of the

voltage-sampling shunt-mixing type, shown in Fig 17. Hence it is called as shunt-shunt

feedback. It is a current controlled voltage amplifier (CCVS).

Concept of output sampling and mixing at input:

Sampling network represents the way feedback network is connected to amplifier

output. Mixing network represents the connection of feedback network to the amplifier

input side.

In this shunt-shunt feedback the feedback is connected in shunt with RL such that

full load voltage will act as input to the feedback network. At input side the feedback

network is in shunt with signal source. This is shown in Fig 17.

Fig 17: Shunt-shunt feedback

Effect of feedback on characteristics of the amplifier:

For this consider the equivalent circuit of the shunt-shunt feedback shown in Fig

18. In that output resistance of the amplifier and output resistance of the feedback circuit

are in parallel hence effective output resistance of the feedback amplifier will reduce.

Similarly overall input resistance of the feedback amplifier will reduce due to parallel

connection of amplifier and feedback resistor. Since effective input resistance is small

hence input should be a current. For ideal voltage source – input resistance is very high

compare to internal source resistance, if not then, lot of voltage will be dropped at

internal source resistance and voltage source won’t be an ideal voltage source.

Effective output resistance is also small compare to the resistance of amplifier

without feedback hence less voltage will drop at effective output resistance and most of

the voltage occurs at load resistor. Hence output circuit will behave like a voltage source.

Thus voltage shunt feedback circuit behave like a current controlled voltage source.

Fig 18: Equivalent circuit of the Shunt-shunt feedback

Voltage Gain:

Input Impedance:

V 0=A . I i=A ( I s−I f )I f=β .V 0

A( I s−β . V 0 )=V 0A . I s=(1+ βA )V 0

A f=V 0

I s=A

1+βA

Zin=V i

I s=

V i

I i+ I f

Zin=I i .ri

I i+β . V 0=

I i .r i

I i+β . . A . I i

Zin=ri

(1+ βA )

Output Impedance:

From input port I i=−I f =−β . V 0

From output port I 0=

V 0− A . Ii

r0=

V 0+β . A .V 0

r0

Zout=V 0

I 0=

r0

1+β . A

Example for shunt-shunt feedback using FET:

A shunt-shunt feedback FET amplifier is shown in Fig 19.

Fig 19: (a) Amplifier circuit. (b) Circuit with feedback removed.

Session 11:

Zout|V s=0=V 0

I 0

I 0=V 0−A . I i

r0

ANALYSIS OF SERIES-SHUNT FEEDBACK AMPLIFIERS USING OP-AMP

Introduction of series-shunt feedback:

Here the input signal is voltage and the output signal is also voltage. Hence it is

also called as voltage amplifier. It follows that the appropriate feedback topology is of

the voltage-sampling series-mixing type, shown in Fig 20. Hence it is called as series-

shunt feedback. It is a voltage controlled voltage source (VCVS).

Concept of output sampling and mixing at input:

Sampling network represents the way feedback network is connected to amplifier

output. Mixing network represents the connection of feedback network to the amplifier

input side.

In this series-shunt feedback the feedback is connected in shunt with RL

such that full load voltage will act as input to the feedback network. At input side the

feedback network is in series with signal source. This is shown in Fig 20.

Fig 20: Series-shunt feedback

Effect of feedback on characteristics of the amplifier:

For this consider the equivalent circuit of the series-shunt feedback shown in Fig

21. In that Input resistance of the amplifier and feedback network are in series hence

effective input resistance will increase. Output resistance of the amplifier and output

resistance of the feedback circuit are in parallel hence effective output resistance of the

feedback amplifier will reduce.

Fig 21: Equivalent circuit of the series-shunt feedback.

Voltage Gain:

Input Impedance:

Zin=V s

I s=

V i+V f

I s

Zin=V i+ βV 0

I s=

V i+β AV i

I s

Zin=V i (1+βA )I s

=ri(1+βA )

V 0=A .V i=A (V s−V f )V f=β . V 0

A(V s− β . V 0 )=V 0

AV s=(1+βA )V 0

A f=V 0

V s=A

1+βA

Output Impedance:

Example for series-shunt feedback using Op-Amp:

A series-shunt feedback Op-Amp amplifier is shown in Fig 22. A series-shunt

feedback amplifier is a non-inverting amplifier in which the input signal x is a voltage

and the output signal y is a voltage. If the input source is a current source, it must be

converted into a thevenin source for the gain. Because the input is a voltage and the

output is a voltage, the gain A represents a dimensionless voltage gain. Because feedback

gain must be dimensionless, the feedback factor is also dimensionless.

Fig 22(a) shows an op amp with a feedback network consisting of a voltage

divider connected between its output and inverting input. The input signal is connected to

the non-inverting input. Because the feedback does not connect to the same terminal as

the input signal, the summing is series. The feedback network connects in shunt with the

output node, thus the sampling is shunt. To analyze the circuit, we replace the circuit seen

looking out of the op-amp inverting input with a thevenin equivalent circuit with respect

to Vo and the circuit seen looking into the feedback network from the Vo node with a

thevenin equivalent circuit with respect to i1. We replace the op amp with a simple

controlled source model which models the differential input resistance, the open-loop

voltage gain, and the output resistance. A test source it is added at the output in order to

Zout|V s=0=V 0

I 0

I 0=V 0−A .V i

r0V i+β .V 0=V s=0V i=−β . V 0

I 0=V 0+ A . β .V 0

r0

Zout=V 0

I 0=

r0

1+ A . β

calculate the output resistance. The circuit is shown in Fig 22(b), where Rid is the

differential input resistance, A0 is the open-loop gain; R0 is the output resistance of the op

amp. The feedback factor b is given by

b=R1

R1+RF

The error signal z in Fig 22(b) is a voltage which we denote by V e. It is the difference

between the two voltage sources in the input circuit and is given by

Ve = Vs − bVo

By voltage division, the voltage Vi which controls the op amp output voltage is

V i=V e

Rid

R s+Rid+R1||RF

Fig 22: (a) Series-shunt feedback Op-Amp (b) Circuit with feedback removed

Session 12:

ANALYSIS OF SHUNT-SERIES FEEDBACK AMPLIFIERS USING OP-AMP,

STABILITY ANALYSIS AND COMPENSATION TECHNIQUES

Introduction of shunt- series feedback:

Here the input signal is current and the output signal is also current. Hence it is

also called as current amplifier. It follows that the appropriate feedback topology is of

the current-sampling series-mixing type, shown in Fig 23. Hence it is called as shunt-

series feedback. It is a current controlled current source (CCCS).

Concept of output sampling and mixing at input:

Sampling network represents the way feedback network is connected to amplifier

output. Mixing network represents the connection of feedback network to the amplifier

input side.

In this shunt- series feedback the feedback is connected in series with RL

such that full load current will act as input to the feedback network. At input side the

feedback network is in shunt with signal source. This is shown in Fig 23.

Fig 23: Shunt- series feedback

Effect of feedback on characteristics of the amplifier:

For this consider the equivalent circuit of the shunt- series feedback shown in Fig

24. In that effective output resistance of the feedback amplifier will increase. Effective

input resistance will decrease. Thus current shunt feedback circuit behave like a current

controlled current source.

Fig 24: Equivalent circuit of shunt- series feedback.

Current Gain:

Input Impedance:

Zin=V i

I s=

V i

I i+ I f

Zin=I i .ri

I i+β . I 0=

Ii . ri

Ii+ β . . A . Ii

Zin=ri

(1+ βA )

I 0=A . . Ii=A( I s−I f )I f=β . I 0

A( I s−β . I 0 )=I 0A . I s=(1+ βA )I 0

A f =I 0

I s=A

1+ βA

Output Impedance:

I i+ I f=I s=0I i=−I f

I 0=A . I i+V 0

r0V 0

r0=I 0−A . I i

V 0

r0=I 0−A .(−I f )=I 0+ A . I f=I 0+ A . β . I 0

V 0

I 0=r 0 .(1+ A . β )

Zout|Is=0=V 0

I 0=r0 .(1+ A . β )

Example for shunt-series feedback using Op-Amp:

A shunt-series feedback Op-Amp amplifier is shown in Fig 25. A shunt-series feedback

amplifier is an inverting amplifier in which the input signal is a voltage signal and the output

signal is a current signal. If the input source is a voltage source, it must be converted into a

Norton source for the gain. Because the input is a current and the output is a current, the gain A

represents a dimensionless current gain. Because feedback gain must be dimensionless, the

feedback factor is dimensionless.

Fig 25: Shunt-series feedback amplifier.