1. Lecture 25 ANNOUNCEMENTS OUTLINE
Reminder: Prof. Liu’s office hour is cancelled on Tuesday 12/4
OUTLINE
Feedback
General considerations
Benefits of negative feedback
Sense and return techniques
Voltage-voltage feedback
Reading: Chapter ,12.4,12.6.1

2. Negative Feedback System
A negative feedback system consists of four components: 1) feedforward system, 2) sense mechanism, 3) feedback network, and 4) comparison mechanism.
Closed loop transfer function:

3. Negative Feedback Example
The amplifier is the feedforward system, R1 and R2 provide the sensing and feedback capabilities, and comparison is provided by differential input to the amplifier.

4. Comparison Error
As A1K increases, the difference between the input and fed back signal decreases, i.e. the fed back signal becomes a good replica of the input. E

5. Comparison Error Example

6. Loop Gain
The loop gain is the product of the gain of the feedforward system (A1) and the feedback factor (K). It can be interpreted to be the gain if a signal “goes around the loop,” i.e. if we break the loop at an arbitrary location, then apply a test voltage at one end and determine the voltage that comes out at the other end, with the input grounded:

7. Benefit #1: Gain Desensitization
A large loop gain is needed to achieve a precise gain, one that does not depend on A1, which can vary by ±20%.

8. Ratio of Resistor Values
If two resistors are built using the same unit resistor, then the ratio of their resistances does not change with variations in the fabrication process and the circuit operating temperature. Thus, the ratio of two resistances can be more precisely controlled than the open loop gain (A1) of an amplifier.

9. Example
Open Loop Gain
Closed Loop Gain

10. Desensitization to Load Variation
w/o Feedback
Large Difference
with Feedback
Small Difference

11. Benefit #2: Bandwidth Enhancement
Although negative feedback lowers the gain by (1+KA1), it increases the bandwidth by the same factor.
Open Loop
Closed Loop
Negative
Feedback

12. Bandwidth Enhancement Example
As the loop gain increases, the low-frequency gain decreases and the bandwidth increases.

13. Benefit #3: Modification of I/O Impedances
Open Loop
Closed Loop

14. Modification of I/O Impedances (cont’d)
Open Loop
Closed Loop

15. Benefit #4: Linearity Improvement
w/o feedback
with feedback

16. Sensing a Voltage
In order to sense a voltage across two terminals, a voltmeter with ideally infinite impedance is used.

17. Sensing and Returning a Voltage
Similarly, for a feedback network to correctly sense the output voltage, its input impedance needs to be large.
R1 and R2 also provide a means to return the voltage.
To return a voltage, the output impedance of an ideal feedback network should be small.
Feedback
Network

18. Example: Sense and Return
R1 and R2 sense and return the output voltage to the feedforward network consisting of M1, M2, M3, and M4.
M1 and M2 also act as a voltage comparator.

19. Example (cont’d)

20. Input Impedance with Feedback
Negative feedback raises the input impedance.

21. Output Impedance with Feedback
Negative feedback lowers the output impedance.

22. Example

23. Summary: Benefits of Negative Feedback
Gain desensitization
to variations in gm, RD, RL
Bandwidth enhancement
by the factor (1 + loop gain)
Modification of I/O impedances
Rin is increased by the factor (1 + loop gain)
Rout is decreased by the factor (1 + loop gain)
Linearity improvement
Gain is more uniform for different signal levels.