19_Lecutre

19_Lecutre - Lecture 19 EE 114 Lecture 19 Fundamentals of...

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EE 114 Lecture 19 R. Dutton, B. Murmann 1 EE114 (HO #23) Lecture 19 Fundamentals of Feedback Part I R. Dutton, B. Murmann Stanford University R. Dutton, B. Murmann 2 Negative Feedback Harold S. Black, 1927 a f ! v in v out - ( ) out in out fv v a v ! = af a v v in out + = 1 Interesting case: f v v af in out 1 1 ! " >> EE114 (HO #23)
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EE 114 Lecture 19 R. Dutton, B. Murmann 3 Interpretation As long as we have "large" gain in the forward path a, the overall gain will depend only on f Since v out /v in ~1/f, we often make f 1 – E.g. for a "closed loop" gain of two, we need f=0.5 f 1 is easy to implement, and ratiometric! – A "wire" (f=1) or resistive or capacitive voltage divider a ! v in v out - a ! v in v out - R 2 R 1 1 ! in out v v 1 2 1 R R R v v in out + ! EE114 (HO #23) R. Dutton, B. Murmann 4 Example Case 2: a=1000 5 0 2 1 . f R R = ! = Case 1: a=100 ... . . f a v v in out 96078 1 5 0 100 1 1 1 1 = + = + = ... . . f a v v in out 996007 1 5 0 1000 1 1 1 1 = + = + = 10x variation in forward gain, and only about 1.8% change in closed loop gain! EE114 (HO #23)
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EE 114 Lecture 19 R. Dutton, B. Murmann 5 Gain Sensitivity Define af a A + = 1 Can show that T a a af a a A A + ! = + ! = ! 1 1 Fractional change in gain is reduced by product of a and f, which can be made arbitrarily large (conceptually) – Loop gain T We will find that loop gain is a very meaningful parameter that will also appear in bandwidth and impedance calculations – More later… EE114 (HO #23) R. Dutton, B. Murmann 6 Effect of Negative Feedback on Nonlinearity
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19_Lecutre - Lecture 19 EE 114 Lecture 19 Fundamentals of...

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