Download 164_56809_Lecture notes on feedback amplifiers

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 Af is closed-loop gain of the amplifier, A is open-loop gain of the amplifier gain
and  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
V0 V0

V f Vi
If feedback signal V f is connected in series with the input, then Vi  Vs  V f
V0  AVi  A(Vs  V f ) But V f   V0
V0  A(Vs  V0 )
V0 (1  A)  AVs
AVs
(1  A)
V
A
Af  0 
         Eq.(1)
Vs (1  A)
V0 
The feedback gain is reduced by 1   A times of the open loop gain. For negative
feedback A  0 and for positive feedback  A  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 temperaturecontrol 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   A times when 1   A is greater than one.
b. Effect on gain stability
From Eq.(1) if  A  1 then
1
Af 

Where  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   . A)
2

Af
A(1  A)
dA f
Af

dA  1 

        Eq.(2)
A  1  A 
From Eq.(2), in case of negative feedback, it is obvious that the
 dA f
relative change in gain with feedback 
 A
 f

 is less than the relative


 dA 
change in gain without feedback   by the amount 1   A
 A
 dA f

 A
 f
  dA 
            Eq.(3)
  A

c. Sensitivity
The sensitivity of the feedback is given by
dA f
S
Af
dA
A

1
1  A
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
1
 1  A
S
e. Effect on bandwidth
The lower cut off frequency of the feedback amplifier is
ALf 
AL
where AL 
1   AL
ALf 
Where

1  

Am
 jf
1   L
 f



Am
Am

 
jf L 

jf L
  Am (1  Am )1  

  f (1  A )  
f 
m



Am
is the mid band gain with feedback denoted by Amf
1   Am
fL
is the lower cut off frequency with feedback denoted by f Lf
1  Am
fL 
fL
      Eq.(4)
1  Am
ALf 
Amf
 jf Lf 

1  
f


From Eq.( 4) , it is stated that f 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  Am )        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 factor 1  Am 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 (seriesshunt, series-series, shunt-shunt, or shunt-series)
i.
Series-shunt feedback
This type of feedback is also called as voltage series feedback or voltagevoltage 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 currentcurrent 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 currentvoltage 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 voltagecurrent 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 R 1/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 baseemitter 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 VBE
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 commonemitter 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 bestof-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 counterproductive. 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 highgain 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 R L 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:
I 0  A.Vi  A(Vs  V f )
V f   .I 0
A(Vs   .I 0 )  I 0
AVs  (1  A) I 0
Af 
I0
A

Vs 1   A
Input Impedance:
Z in 
Vs Vi  V f

Is
Is
Z in 
Vi  V0 Vi  AVi

Is
Is
Z in 
Vi (1  A)
 ri (1  A)
Is
Output Impedance:
Vi  V f  Vs  0
I0 
V0  A. .I 0
r0
Z out |Vs 0 
V0
V  A.Vi
; I0  0
I0
r0
Z out 
V0
r0

I 0 1  A.
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:
V0  A.I i  A( I s  I f )
I f   .V0
A( I s   .V0 )  V0
A.I s  (1  A)V0
Af 
V0
A

I s 1  A
Input Impedance:
Z in 
Vi
Vi

I s Ii  I f
Z in 
I i .ri
I i .ri

I i   .V0 I i   .. A.I i
Z in 
ri
(1  A)
Output Impedance:
Z out |Vs 0 
I0 
V0
I0
V0  A.I i
r0
From input port I i   I f    .V0
From output port I 0 
V0  A.I i V0   . A.V0

r0
r0
Z out 
V0
r0

I 0 1   .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:
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 seriesshunt 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:
V0  A.Vi  A(Vs  V f )
V f   .V0
A(Vs   .V0 )  V0
AVs  (1  A)V0
Af 
V0
A

Vs 1   A
Input Impedance:
Z in 
Vs Vi  V f

Is
Is
Z in 
Vi  V0 Vi  AVi

Is
Is
Z in 
Vi (1  A)
 ri (1  A)
Is
Output Impedance:
Z out |Vs 0 
I0 
V0
I0
V0  A.Vi
r0
Vi   .V0  Vs  0
Vi    .V0
I0 
V0  A. .V0
r0
Z out 
V0
r0

I 0 1  A.
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
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 Ve. 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
Vi  Ve
Rid
Rs  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 shuntseries 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:
I 0  A..I i  A( I s  I f )
I f   .I 0
A( I s   .I 0 )  I 0
A.I s  (1  A) I 0
Af 
I0
A

I s 1  A
Input Impedance:
Z in 
Vi
Vi

I s Ii  I f
Z in 
I i .ri
I i .ri

I i   .I 0 I i   .. A.I i
Z in 
ri
(1  A)
Output Impedance:
Ii  I f  I s  0
I i  I f
I 0  A.I i 
V0
r0
V0
 I 0  A.I i
r0
V0
 I 0  A.( I f )  I 0  A.I f  I 0  A. .I 0
r0
V0
 r0 .(1  A. )
I0
Z out | I s 0 
V0
 r0 .(1  A. )
I0
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.