ho22.l19_fb1

# ho22.l19_fb1 - 1 Fundamentals of Feedback Fundamentals of...

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Unformatted text preview: 1 Fundamentals of Feedback Fundamentals of Feedback Part I R. Dutton, B. Murmann R. Dutton, B. Murmann 1 EE114 (HO #22) Stanford University Negative Feedback • Harold S. Black, 1927 ( ) out in out fv v a v − = af a v v in out + = 1 • Interesting case: R. Dutton, B. Murmann 2 EE114 (HO #22) f v v af in out 1 1 ≅ ⇒ >> 2 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 out in – 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 R. Dutton, B. Murmann 3 EE114 (HO #22) 1 ≅ in out v v 1 2 1 R R R v v in out + ≅ Example 5 2 1 . f R R = ⇒ = • Case 1: a=100 • Case 2: a=1000 ... . . f a v v in out 96078 1 5 100 1 1 1 1 = + = + = ... . v v in out 996007 1 5 1 1 1 1 = + = + = R. Dutton, B. Murmann 4 EE114 (HO #22) . f a 5 1000 + + • 10x variation in forward gain, and only about 1.8% change in closed loop gain! 3 Gain Sensitivity • Define af a A + = 1 • Can show that T a a af a a A A + Δ = + Δ = Δ 1 1 • Fractional change in gain is reduced by product of a and f, which can be made arbitrarily large (conceptually) – Loop gain T R. Dutton, B. Murmann 5 EE114 (HO #22) 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… Effect of Negative Feedback on Nonlinearity • Substitute (2) into (1), then compare coefficients to get...
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ho22.l19_fb1 - 1 Fundamentals of Feedback Fundamentals of...

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