This document summarizes key concepts about feedback circuits: 1. It describes four types of feedback connections: voltage-series, voltage-shunt, current-series, and current-shunt. Negative feedback reduces gain but improves other properties. 2. Equations are provided for calculating gain, input impedance, and output impedance with feedback. Negative feedback increases input impedance for series connections and decreases it for shunt. It decreases output impedance for voltage feedback and increases it for current feedback. 3. Practical feedback circuits using op-amps in voltage-series configuration are discussed. The Nyquist stability criterion and gain/phase margins are introduced for analyzing feedback amplifiers.

1. Chapter 6 Feedback Circuits
Analogue Electronics 电子 2＋2

2. 6.1 Introduction
6.2 Types of feedback connection
Overall gain of the system
Input and output impedance
6.3 Practical feedback circuits
6.4 Feedback amplifier – phase and frequency considerations
Nyquist criterion
Ch 6 – Feedback circuits
Content

3. Introduction
A typical feedback connection is shown below. The input signal Vs is applied to a mixer
network, where it is combined with a feedback signal Vf. The difference of these signals Vi is
then the input voltage to the amplifier. A portion of the amplifier output Vo is connected to the
feedback network, which provides a reduced portion of the output as feedback signal to the
input mixer network.
Ch 6 – Feedback circuits

4. Introduction
Depending on the relative polarity of the signal being fed back into a circuit, one may have
negative or positive feedback. Negative feedback results in decreased voltage gain, for which a
number of circuit features are improved. Positive feedback drives a circuit into oscillation as in
various types of oscillator circuits
Ch 6 – Feedback circuits
• A(s)： open-loop amplifier or open-loop gain.
• β(s) ：feedback loop gain.
• A(s) β(s)：overall gain.
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5. Introduction
If the feedback signal is of opposite polarity to the input signal, negative feedback results.
Although negative feedback results in reduced overall voltage gain, a number of improvements
are obtained, among them being:
Ch 6 – Feedback circuits
1. Higher input impedance.
5. Reduced noise.
2. Better stabilized voltage gain.
3. Improved frequency response.
4. Lower output impedance.
6. More linear operation.

6. Feedback connection types
There are four basic ways of connecting the feedback signal. Both voltage and current can be
fed back to the input either in series or parallel. Specifically, there can be:
Ch 6 – Feedback circuits
1. Voltage-series feedback 2. Voltage-shunt feedback
Gain without feedback A
Feedback β
Gain with feedback Af
Gain without feedback A
Feedback β
Gain with feedback Af

7. Feedback connection types
3. Current-series feedback
Ch 6 – Feedback circuits
4. Current-shunt feedback
Gain without feedback A
Feedback β
Gain with feedback Af
Gain without feedback A
Feedback β
Gain with feedback Af

8. Feedback connection types
Ch 6 – Feedback circuits
Series feedback connections tend to increase the input resistance, whereas shunt feedback
connections tend to decrease the input resistance. Voltage feedback tends to decrease the
output impedance, whereas current feedback tends to increase the output impedance.
Typically, higher input and lower output impedances are desired for most cascade amplifiers.
Both of these are provided using the voltage-series feedback connection. We shall therefore
concentrate first on this amplifier connection.

9. Gain with Feedback - Voltage-Series Feedback
The circuit shows the voltage-series feedback connection with a part of the output voltage fed
back in series with the input signal. If there is no feedback (Vf = 0), the voltage gain of the
amplifier stage is
Ch 6 – Feedback circuits
If a feedback signal Vf is connected in series with the input, then
So that the overall voltage gain with feedback is
Therefore, an overall gain reduction is resulted.

10. Gain with Feedback - Voltage-Shunt Feedback
For the voltage-shunt feedback connection, we have
Ch 6 – Feedback circuits
Therefore, an overall gain reduction is resulted.

11. Input Impedance- Voltage-Series Feedback
For the voltage-series feedback connection, the input impedance can be determined as follows
Ch 6 – Feedback circuits
The input impedance with series feedback is the value of the input impedance without feedback
multiplied by the factor (1 + βA). This conclusion applies to both voltage-series and current-series
configurations.

12. Input Impedance- Voltage-Shunt Feedback
For the voltage-shunt feedback connection, one can obtain
Ch 6 – Feedback circuits
The input impedance with shunt feedback is the value of the input impedance without feedback
divided by the factor (1 + βA). This conclusion applies to both voltage-shunt and current-shunt
configurations.

13. Output Impedance- Voltage-Series Feedback
This equation shows that with voltage-series feedback the output impedance is reduced from
that without feedback by the factor (1 + βA ).
Ch 6 – Feedback circuits
The output impedance is determined by applying a voltage V, resulting in a current I, with Vs
shorted out (Vs = 0). So according to this, we have

14. Output Impedance- Current-Series Feedback
The output impedance with current-series feedback can be determined by applying a signal V
to the output with Vs shorted out, resulting in a current I, the ratio of V to I being the output
impedance.
Ch 6 – Feedback circuits
This equation shows that with current-series feedback the output impedance is increased from
that without feedback by the factor (1 + βA ).
+
-

15. Voltage gain and impedance with feedback
A summary of the effect of feedback on input and output impedance is provided in Table
Ch 6 – Feedback circuits
• The input impedance for the connections is dependent on whether series or shunt feedback
is used. For serious feedback, the input impedance is increased, whereas shunt feedback
decreases the input impedance.
• The output impedance for the connections is dependent on whether voltage or current
feedback is used. For voltage feedback, the output impedance is decreased, whereas current
feedback increases the output impedance.
Input impedance
Output impedance

16. Voltage gain and impedance with feedback - Example
Determine the voltage gain, input, and output impedance with feedback for voltage-series
feedback having A = -100, Ri = 10 k, and Ro = 20 k for feedback of β = -0.1.
Ch 6 – Feedback circuits

17. Reduction in Frequency Distortion
For a negative-feedback amplifier having βA >> 1.
Ch 6 – Feedback circuits
It follows from this that if the feedback network is purely resistive, the gain with feedback is
not dependent on frequency even though the basic amplifier gain is frequency dependent.
Practically, the frequency distortion arising because of varying amplifier gain with frequency is
considerably reduced in a negative-voltage feedback amplifier circuit

18. Gain Stability with Feedback
In addition to the β factor setting a precise gain value, we are also interested in how stable the
feedback amplifier is compared to an amplifier without feedback.
Ch 6 – Feedback circuits
This shows that magnitude of the relative change in gain is reduced by the factor
compared to that without feedback
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Differentiating the following equation leads to

19. Gain Stability with Feedback – Example
If an amplifier with gain of -1000 and feedback of β = -0.1 has a gain change of 20% due to
temperature, calculate the change in gain of the feedback amplifier
Ch 6 – Feedback circuits
The improvement is 100 times. Thus, whereas the amplifier gain |A| changes from 1000 to 800
by 20%, the gain with feedback |Af| only changes from 10 to 9.98 by only 0.2%.

20. Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
Ch 6 – Feedback circuits
Step 1: Identify the feedback loop, the input, output
and feedback variables
Step 2: Identify feedback connection type
Step 3: Calculate the overall gain

21. Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
Ch 6 – Feedback circuits
A part of the output signal (Vo) is obtained using a
feedback network of resistors R1 and R2. The
feedback voltage Vf is connected in series with the
source signal Vs, their difference being the input
signal Vi.
0
Feedback loop
Step 1: Identify the feedback loop, the input, output
and feedback variables

22. Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
Ch 6 – Feedback circuits
Step 2: Identify feedback connection type
A part of the output signal (Vo) is obtained using a
feedback network. The feedback voltage Vf is
connected in series with the source signal Vs, their
difference being the input signal Vi.
0
Feedback loop
Voltage-series feedback connection √
0
Negative feedback:
Negative feedback:
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i s f
V V V
 

23. Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
Ch 6 – Feedback circuits
Step 3: Calculate the overall gain
Without feedback the amplifier gain is
RL = RD||Ro||(R1+R2)
Negative feedback:

24. Practical feedback circuits – Example
Find Af, Zif, Zof of the following feedback circuit using these values: R1 = 80 k, R2 = 20 k, Ro = 10 k,
RD = 10 k, and gm = 4000 μS.
Ch 6 – Feedback circuits
1 2
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25. Practical feedback circuits - Voltage-Series Feedback
Ch 6 – Feedback circuits
A voltage-series feedback connection can also be built using an op-amp
Without feedback the amplifier gain is A
Vo = A (Vi1 – Vi2)
Vo
Vi1
Vi2
With feedback the overall gain is reduced by the
feedback factor
0
Feedback loop
A part of the output signal (Vo) is obtained using a
feedback network. The feedback voltage Vf is
connected in series with the source signal Vs, their
difference being the input signal Vi.

26. Practical feedback circuits - Voltage-Series Feedback
Ch 6 – Feedback circuits
A voltage-series feedback connection can also be built using an op-amp
0
Feedback loop
Calculate Af if A = 100,000 and R1 = 1.8 k and R2 = 200

27. Practical feedback circuits
Ch 6 – Feedback circuits
If we take the input voltage and R1 as the current source, and the output voltage is fed back into the
input in terms of current. Then we have built a voltage-shunt feedback connection using the
constant-gain op-amp.
Voltage-shunt feedback

28. Feedback amplifier – phase and frequency considerations
Ch 6 – Feedback circuits
Because of the RL branch, the performance of the following connection is dependent
upon the frequency of the signal source. And the gain is a complex, which is actually
a combination of an amplitude and angle.

29. Feedback amplifier – phase and frequency considerations
Ch 6 – Feedback circuits
Since the feedback amplifier is also consisted of a number of RL branches, the overall gain will
change with frequency.
If, as the frequency increases, the phase shift changes, then some of the feedback signal will add to
the input signal. It is then possible for the amplifier to break into oscillations due to positive
feedback. Proper feedback-amplifier design requires that the circuit be stable at all frequencies, not
merely those in the range of interest. Otherwise, a transient disturbance could cause sudden
oscillating.

30. Nyquist Criterion
Ch 6 – Feedback circuits
• In judging the stability of a feedback amplifier as a function of frequency, the βA product and the
phase shift between input and output are the determining factors.
• One of the most popular techniques used to investigate stability is the Nyquist method. A Nyquist
diagram is used to plot gain and phase shift as a function of frequency on a complex plane.

31. Nyquist Criterion
Ch 6 – Feedback circuits
Thus points on this plot can represent both gain magnitude of βA and phase shift. If the points
representing gain and phase shift for an amplifier circuit are plotted at increasing frequency, then a
Nyquist plot is obtained.
As a start, consider the complex plane. A few points of various gain (βA) values are shown at a few
different phase-shift angles. By using the positive real axis as reference (0°), we see a magnitude of
βA = 2 at a phase shift of 0° at point 1. Additionally, a magnitude of βA =3 at a phase shift of
135° is shown at point 2 and a magnitude/ phase of βA = 1 at 180° is shown at point 3.

32. Nyquist Criterion
Ch 6 – Feedback circuits
The amplifier is unstable if the Nyquist curve encloses (encircles) the –1 point, and it
is stable otherwise.
(a) stable (b) unstable

33. Nyquist Criterion - Gain and Phase Margins
Ch 6 – Feedback circuits
Gain margin (GM) is defined as the negative of the
value of |βA| in decibels at the frequency at which
the phase angle is 180°.
Phase margin (PM) is defined as the angle of 180°
minus the magnitude of the angle at which the value
|βA| is unity (0 dB).
From the Nyquist criterion, we know that a feedback amplifier is stable if the loop gain (b A ) is less
than unity (0 dB) when its phase angle is 180°. We can additionally determine some margins of
stability to indicate how close to instability the amplifier is
Thus, 0 dB, equal to a value of βA = 1, is on the
border of stability and any negative decibel value is
stable.