advertisement

Lecture 25 ANNOUNCEMENTS • 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 EE105 Fall 2007 Lecture 25, Slide 1 Prof. Liu, UC Berkeley Negative Feedback System • A negative feedback system consists of four components: 1) feedforward system, 2) sense mechanism, 3) feedback network, and 4) comparison mechanism. VY A1 • Closed loop transfer function: V X 1 KA1 EE105 Fall 2007 Lecture 25, Slide 2 Prof. Liu, UC Berkeley 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. VY VX 1 EE105 Fall 2007 Lecture 25, Slide 3 A1 R2 A1 R1 R2 Prof. Liu, UC Berkeley 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. VX E 1 A1 K E EE105 Fall 2007 Lecture 25, Slide 4 Prof. Liu, UC Berkeley Comparison Error Example VY R1 1 VX R2 EE105 Fall 2007 Lecture 25, Slide 5 Prof. Liu, UC Berkeley 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: VX 0 EE105 Fall 2007 VN KA1 Vtest Lecture 25, Slide 6 Prof. Liu, UC Berkeley 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%. A1 K 1 EE105 Fall 2007 VY 1 VX K Lecture 25, Slide 7 Prof. Liu, UC Berkeley 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. EE105 Fall 2007 Lecture 25, Slide 8 Prof. Liu, UC Berkeley Example Open Loop Gain A1 g m RD EE105 Fall 2007 Closed Loop Gain vout vin Lecture 25, Slide 9 g m RD R2 1 g m RD R1 R2 Prof. Liu, UC Berkeley Desensitization to Load Variation w/o Feedback with Feedback Large Difference Small Difference g m RD g m RD / 3 EE105 Fall 2007 g m RD g m RD R2 R2 1 g m RD 3 g m RD R1 R2 R1 R2 Lecture 25, Slide 10 Prof. Liu, UC Berkeley Benefit #2: Bandwidth Enhancement • Although negative feedback lowers the gain by (1+KA1), it increases the bandwidth by the same factor. Open Loop A1 j A0 j 1 0 EE105 Fall 2007 Closed Loop Negative Feedback A0 1 KA0 VY j j VX 1 1 KA0 0 Lecture 25, Slide 11 Prof. Liu, UC Berkeley Bandwidth Enhancement Example • As the loop gain increases, the low-frequency gain decreases and the bandwidth increases. EE105 Fall 2007 Lecture 25, Slide 12 Prof. Liu, UC Berkeley Benefit #3: Modification of I/O Impedances Open Loop 1 Rin gm EE105 Fall 2007 Closed Loop R2 1 1 Rin g m RD g m R1 R2 Lecture 25, Slide 13 Prof. Liu, UC Berkeley Modification of I/O Impedances (cont’d) Open Loop Rout RD EE105 Fall 2007 Closed Loop Rout Lecture 25, Slide 14 RD R2 1 g m RD R1 R2 Prof. Liu, UC Berkeley Benefit #4: Linearity Improvement w/o feedback with feedback EE105 Fall 2007 Lecture 25, Slide 15 Prof. Liu, UC Berkeley Sensing a Voltage • In order to sense a voltage across two terminals, a voltmeter with ideally infinite impedance is used. EE105 Fall 2007 Lecture 25, Slide 16 Prof. Liu, UC Berkeley 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 R1 R2 EE105 Fall 2007 Lecture 25, Slide 17 Prof. Liu, UC Berkeley 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. EE105 Fall 2007 Lecture 25, Slide 18 Prof. Liu, UC Berkeley Example (cont’d) Vout Vin EE105 Fall 2007 g mN ( rON || rOP ) R2 1 g mN ( rON || rOP ) R1 R2 Lecture 25, Slide 19 Prof. Liu, UC Berkeley Input Impedance with Feedback • Negative feedback raises the input impedance. Vin Rin (1 A0 K ) I in EE105 Fall 2007 Lecture 25, Slide 20 Prof. Liu, UC Berkeley Output Impedance with Feedback • Negative feedback lowers the output impedance. Rout VX I X 1 KA0 EE105 Fall 2007 Lecture 25, Slide 21 Prof. Liu, UC Berkeley Example Rout,closed EE105 Fall 2007 roN roP R2 1 g mN roN R1 R2 R1 1 1 R2 g mN roP Lecture 25, Slide 22 Prof. Liu, UC Berkeley Summary: Benefits of Negative Feedback 1) Gain desensitization to variations in gm, RD, RL 2) Bandwidth enhancement by the factor (1 + loop gain) 3) Modification of I/O impedances – Rin is increased by the factor (1 + loop gain) – Rout is decreased by the factor (1 + loop gain) 4) Linearity improvement – Gain is more uniform for different signal levels. EE105 Fall 2007 Lecture 25, Slide 23 Prof. Liu, UC Berkeley