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 12.1-12.2,12.4,12.6.1

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:

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.

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

Comparison Error Example

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:

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%.

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.

Example Open Loop Gain Closed Loop Gain

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

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

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

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

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

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

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

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

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.

Example (cont’d)

Input Impedance with Feedback Negative feedback raises the input impedance.

Output Impedance with Feedback Negative feedback lowers the output impedance.

Example

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.