HO13_214W09_Feedback_2pp

HO13_214W09_Feedback_2pp - Handout #13 EE 214 Winter 2009...

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B. Murmann, B. Wooley EE214 Winter 2008-09 1 Feedback Handout #13 EE 214 Winter 2009 B. Murmann and B. A. Wooley Stanford University Update 2/27/09: corrections to equations on page 9 B. Murmann, B. Wooley EE214 Winter 2008-09 2 Benefits and Costs of Negative Feeback Reduced sensitivity (improved precision) Reduced distortion Scaling of impedance levels (up or down) Increased bandwidth Lower gain Potential instability Negative feedback provides a means of exchanging gain for improvements in other performance metrics Benefits Costs
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B. Murmann, B. Wooley EE214 Winter 2008-09 3 Ideal Feedback ! a f S i S o S fb + S " S o = a ! S " S fb = f ! S o S " = S i # S fb ! S o = (S i " S fb ) = a(S i " f # S o ) Assumptions for an ideal feedback system: 1. No loading 2. Unilateral transmission in both the forward amplifier and feedback network B. Murmann, B. Wooley EE214 Winter 2008-09 4 The feedback loop acts to minimize the error signal, S " , thus forcing S fb to track S i . In particular, S ! = S i " f # S o = S i " f # a 1 + af $ % ( ) S i = 1 " af 1 + af $ % ( ) # S i ! S " S i = 1 # T 1 + T = 1 1 + T S fb S i = a ! f S " S i # $ % ( = T 1 + T and If T >> 1 , then A ! a T = 1/ f T ! af = S fb S ! Closed-Loop Gain: Loop Gain: ! A = a 1 + T A ! S o S i = a 1 + af
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B. Murmann, B. Wooley EE214 Winter 2008-09 5 Gain Sensitivity The feedback network is typically a precision passive network with an insensitive, well-defined transfer function f. The forward amplifier gain is generally large, but not well controlled. Feedback acts to reduce not only the gain, but also the relative, or fractional, gain error by the factor 1+T dA da = d da a 1 + af ! " # $ % = 1 1 + af + a d da 1 1 + af ! " # $ % = (1 + af) af (1 + af) 2 = 1 (1 + af) 2 = 1 (1 + T) 2 For a change # a in a ! a = dA da ! a = ! a (1 + T) 2 ! " A
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This note was uploaded on 08/13/2009 for the course EE EE214 taught by Professor Borismurmann during the Winter '08 term at Stratford.

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HO13_214W09_Feedback_2pp - Handout #13 EE 214 Winter 2009...

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