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

2. Ch 6 – Feedback circuits Content 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

3. Ch 6 – Feedback circuits 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.

4. Ch 6 – Feedback circuits 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
A(s)： open-loop amplifier or open-loop gain.
β(s) ：feedback loop gain.
A(s) β(s)：overall gain.

5. Ch 6 – Feedback circuits 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:
1. Higher input impedance.
2. Better stabilized voltage gain.
3. Improved frequency response.
4. Lower output impedance.
5. Reduced noise.
6. More linear operation.

6. Feedback connection types
Ch 6 – Feedback circuits
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:
2. Voltage-shunt feedback
1. Voltage-series feedback
Gain without feedback A
Gain without feedback A
Feedback β
Feedback β
Gain with feedback Af
Gain with feedback Af

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

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

11. Input Impedance- Voltage-Series Feedback
Ch 6 – Feedback circuits
Input Impedance- Voltage-Series Feedback
For the voltage-series feedback connection, the input impedance can be determined as follows
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
Ch 6 – Feedback circuits
Input Impedance- Voltage-Shunt Feedback
For the voltage-shunt feedback connection, one can obtain
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
Ch 6 – Feedback circuits
Output Impedance- Voltage-Series Feedback
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
This equation shows that with voltage-series feedback the output impedance is reduced from that without feedback by the factor (1 + βA ).

14. Output Impedance- Current-Series Feedback
Ch 6 – Feedback circuits
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. - +
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
Ch 6 – Feedback circuits
Voltage gain and impedance with feedback
A summary of the effect of feedback on input and output impedance is provided in Table
Input impedance
Output impedance
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.

16. Voltage gain and impedance with feedback - Example
Ch 6 – Feedback circuits
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.

17. Reduction in Frequency Distortion
Ch 6 – Feedback circuits
Reduction in Frequency Distortion
For a negative-feedback amplifier having βA >> 1.
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
Ch 6 – Feedback circuits
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.
Differentiating the following equation leads to
This shows that magnitude of the relative change in gain is reduced by the factor compared to that without feedback

19. Gain Stability with Feedback – Example
Ch 6 – Feedback circuits
Gain Stability with Feedback – Example
If an amplifier with gain of and feedback of β = -0.1 has a gain change of 20% due to temperature, calculate the change in gain of the feedback amplifier
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
Ch 6 – Feedback circuits
Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
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
Ch 6 – Feedback circuits
Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
Step 1: Identify the feedback loop, the input, output and feedback variables
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.
Feedback loop

22. Practical feedback circuits
Ch 6 – Feedback circuits
Practical feedback circuits
Find the overall voltage gain of the following feedback circuit (rd can be ignored).
Voltage-series feedback connection √
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. ?
Feedback loop
Negative feedback:
Negative feedback:

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

24. Practical feedback circuits – Example
Ch 6 – Feedback circuits
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.

25. Practical feedback circuits - Voltage-Series Feedback
Ch 6 – Feedback circuits
Practical feedback circuits - Voltage-Series Feedback
A voltage-series feedback connection can also be built using an op-amp
Vi1 Vo
Vi2
Vo = A (Vi1 – Vi2)
Feedback loop
Without feedback the amplifier gain is A
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.
With feedback the overall gain is reduced by the feedback factor

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

27. Practical feedback circuits
Ch 6 – Feedback circuits
Practical 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
Feedback amplifier – phase and frequency considerations
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
Feedback amplifier – phase and frequency considerations
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. Ch 6 – Feedback circuits Nyquist Criterion
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. Ch 6 – Feedback circuits Nyquist Criterion
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.
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.

32. Ch 6 – Feedback circuits Nyquist Criterion
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
Nyquist Criterion - Gain and Phase Margins
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
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°.
Thus, 0 dB, equal to a value of βA = 1, is on the border of stability and any negative decibel value is stable.
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).