h20_lecture14_2

# h20_lecture14_2 - Lecture 14 Stability Analysis of Feedback...

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EE 214 Lecture 14 (HO#20) B. Murmann 1 Lecture 14 Stability Analysis of Feedback Circuits Boris Murmann Stanford University [email protected] Copyright © 2004 by Boris Murmann EE 214 Lecture 14 (HO#20) B. Murmann 2 Overview Reading – 9.3 (Stability) – 8.8 (Return Ratio Analysis) – Supplementary Handout "Feedback Systems" by Tom Lee (see web, optional) Introduction – This lecture covers basics on the analysis of feedback amplifiers. Using a simple OTA with capacitive feedback as an example, we will study the so called "Return Ratio" method as a tool to assess stability and calculate the bandwidth of feedback amplifiers. Interestingly, most relevant performance metrics follow directly from the "return ratio" or loop gain of the circuit, which highlights the significance of this parameter in feedback system design.

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EE 214 Lecture 14 (HO#20) B. Murmann 3 Stability Most general criterion: BIBO – Bounded input – bounded output – Applies to any system A continuous time linear system is BIBO stable if all its poles are in the left half of the s-plane – Can calculate roots of 1+T(s) to check stability • Tedious and hard to do in general a(s) f(s) Σ v i v o - ) s ( T ) s ( a ) s ( f ) s ( a ) s ( a v v ) s ( A i o + = + = = 1 1 EE 214 Lecture 14 (HO#20) B. Murmann 4 Methods for Checking Stability Nyquist Criterion – Based on evaluating T(s) in a polar plot – Works for arbitrary T(s) • Even if T(s) itself is unstable – See books on control theory for details Bode Criterion – A subset of the general Nyquist criterion that can be applied when T(s) itself is stable • Safe to use in most electronic circuits • Beware of exceptions – System is unstable when |T(j ω )| > 1 at the frequency where Phase(T(j ω )) = -180° – Can use simple bode plot to check for stability
EE 214 Lecture 14 (HO#20) B. Murmann 5 Stability Measures ω c ω 180 ω c ω 180 |T(j ω )| Phase[T(j ω )] () [ ] c j T Phase PM ω = ° = 180 180 1 = = j T GM Typically want GM 3…5 Typically want PM 60…70° EE 214 Lecture 14 (HO#20) B. Murmann 6 Closed Loop Peaking ω / ω c [Text, p.632] Closed-loop gain, normalized to 1/f

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EE 214 Lecture 14 (HO#20) B. Murmann 7 OTA with Capacitive Feedback Important questions – Is this circuit stable? What is its phase margin?
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## This note was uploaded on 04/17/2008 for the course EE 214 taught by Professor Murmann,b during the Fall '04 term at Stanford.

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h20_lecture14_2 - Lecture 14 Stability Analysis of Feedback...

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