Lecture 25 ANNOUNCEMENTS. Reminder: Prof. Liu s office hour is cancelled on Tuesday 12/4 OUTLINE. General considerations Benefits of negative feedback

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1 Lecture 25 ANNOUNCEMENTS eminder: Prof. Liu s office hour is cancelled on Tuesday 2/4 Feedback OUTLINE General considerations Benefits of neative feedback Sense andreturn techniques Voltae voltae feedback eadin: Chapter ,2.4,2.6., EE05 Fall 2007 Lecture 25, Slide Prof. Liu, UC Berkeley

2 Neative Feedback System A neative feedback system consists of four components: ) feedforward system, 2) sense mechanism, 3) feedback network, and 4) comparison mechanism. V Closed loop transfer function: Y A = V X KA EE05 Fall 2007 Lecture 25, Slide 2 Prof. Liu, UC Berkeley

3 Neative Feedback Example The amplifier is the feedforward system, and 2 provide the sensin and feedback capabilities, and comparison is provided by differential input to the amplifier. V Y A = V X 2 A 2 EE05 Fall 2007 Lecture 25, Slide 3 Prof. Liu, UC Berkeley

4 Comparison Error As A K increases, the difference between the input and fed back sinal decreases, i.e. the fed back sinal becomes a ood replica of the input. E E = VX A K EE05 Fall 2007 Lecture 25, Slide 4 Prof. Liu, UC Berkeley

5 Comparison Error Example V V X Y 2 EE05 Fall 2007 Lecture 25, Slide 5 Prof. Liu, UC Berkeley

6 Loop Gain The loop ain is the product of the ain of the feedforward system (A ) and the feedback factor (K). It can be interpreted to be the ain if a sinal oes around the loop, i.e. if we break the loop at an arbitrary location, then apply a test voltae at one end and determine the voltae that comes out at the other end, with the input rounded: V X = 0 KA = V V N test EE05 Fall 2007 Lecture 25, Slide 6 Prof. Liu, UC Berkeley

7 Benefit #: Gain Desensitization A lare loop ain is needed to achieve a precise ain, one that does not depend on A, which can vary by ±20%. A K >> V Y K EE05 Fall 2007 Lecture 25, Slide 7 Prof. Liu, UC Berkeley V X

8 atio of esistor Values If two resistors are built usin the same unit resistor, then the ratio of their resistances does not chane with variations in the fabrication process and the circuit operatin temperature. Thus, the ratio of two resistances can be more precisely controlled than the open loop ain (A ) of an amplifier. EE05 Fall 2007 Lecture 25, Slide 8 Prof. Liu, UC Berkeley

9 Example Open Loop Gain A m D v v out in Closed Loop Gain = m 2 2 D m D EE05 Fall 2007 Lecture 25, Slide 9 Prof. Liu, UC Berkeley

10 Desensitization to Load Variation w/o Feedback Lare Difference with Feedback Small Difference 3 / D m D m D m D m D m D m EE05 Fall 2007 Lecture 25, Slide 0 Prof. Liu, UC Berkeley 2 2

11 Benefit #2: Bandwidth Enhancement Althouh neative feedback lowers the ain by (KA ), it increases the bandwidth by the same factor. Open Loop A jω ω 0 ( jω) Neative Feedback Closed Loop A0 V KA Y jω = V X j ω KA A = ( ) 0 0 ( 0 ) 0 ω EE05 Fall 2007 Lecture 25, Slide Prof. Liu, UC Berkeley

12 Bandwidth Enhancement Example As the loop ain increases, the low frequency ain decreases andthe bandwidth increases. EE05 Fall 2007 Lecture 25, Slide 2 Prof. Liu, UC Berkeley

13 Benefit #3: Modification of I/O Impedances Open Loop Closed Loop = in m = m m 2 2 in = D EE05 Fall 2007 Lecture 25, Slide 3 Prof. Liu, UC Berkeley

14 Modification of I/O Impedances (cont d) Open Loop Closed Loop out = D out = 2 D 2 m D EE05 Fall 2007 Lecture 25, Slide 4 Prof. Liu, UC Berkeley

15 Benefit #4: Linearity Improvement w/o feedback with feedback EE05 Fall 2007 Lecture 25, Slide 5 Prof. Liu, UC Berkeley

16 Sensin a Voltae In order to sense a voltae across two terminals, a voltmeter with ideally infinite impedance is used. EE05 Fall 2007 Lecture 25, Slide 6 Prof. Liu, UC Berkeley

17 Sensin and eturnin a Voltae Similarly, for a feedback network to correctly sense the output voltae, its input impedance needs to be lare. and 2 also provide a means to return the voltae. To return a voltae, the output impedance of an ideal feedback network should be small. Feedback Network 2 EE05 Fall 2007 Lecture 25, Slide 7 Prof. Liu, UC Berkeley

18 Example: Sense and eturn and 2 sense and return the output voltae to the feedforward network consistin of M, M 2, M 3, and M 4. M and M 2 also act as a voltae comparator. EE05 Fall 2007 Lecture 25, Slide 8 Prof. Liu, UC Berkeley

19 Example (cont d) V V out in = mn 2 ( r 2 ON mn r ( r OP ON ) r OP ) EE05 Fall 2007 Lecture 25, Slide 9 Prof. Liu, UC Berkeley

20 Input Impedance with Feedback Neative feedback raises the input impedance. Vin = in ( A 0 K I in ) EE05 Fall 2007 Lecture 25, Slide 20 Prof. Liu, UC Berkeley

21 Output Impedance with Feedback Neative feedback lowers the output impedance. V X out = I X KA 0 ( ) EE05 Fall 2007 Lecture 25, Slide 2 Prof. Liu, UC Berkeley

22 Example out = r r on op, closed 2 mn on op 2 2 ( r r ) mn EE05 Fall 2007 Lecture 25, Slide 22 Prof. Liu, UC Berkeley

23 Summary: Benefits of Neative Feedback ) Gain desensitization to variations iti in m, D, L 2) Bandwidth enhancement by the factor ( loop ain) 3) Modification of I/O impedances in is increased by the factor ( loop ain) out is decreased by the factor ( loop ain) 4) Linearity improvement Gain is more uniform for different sinal levels. EE05 Fall 2007 Lecture 25, Slide 23 Prof. Liu, UC Berkeley

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