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 VY 1 VX K A1 K 1 EE105 Fall 2007 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 1 Lecture 25 Slide 9 g m RD R2 g m RD R1 R2 Prof Liu UC Berkeley Desensitization to Load Variation with Feedback w o Feedback Small Difference Large 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 A A1 j 0 j 1 0 EE105 Fall 2007 Closed Loop Negative Feedback Lecture 25 Slide 11 A0 1 KA0 VY j j VX 1 1 KA0 0 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 Rin 1 g m RD g m R1 R2 Lecture 25 Slide 13 Prof Liu UC Berkeley Modification of I O Impedances cont d Open Loop Closed Loop Rout RD EE105 Fall 2007 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 1 EE105 Fall 2007 Lecture 25 Slide 19 g mN rON rOP R2 g mN rON rOP R1 R2 Prof Liu UC Berkeley Input Impedance with Feedback Negative feedback raises the input impedance Vin Rin 1 A 0 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 1 EE105 Fall 2007 roN roP R2 g mN roN roP R1 R2 Lecture 25 Slide 22 R1 1 1 R2 g mN 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
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