20_Lecutre - EE 114 Lecture 20 Fundamentals of Feedback...

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EE 114 Lecture 20 R. Dutton, B. Murmann 1 EE114 (HO #24) Fundamentals of Feedback Part II R. Dutton, B. Murmann Stanford University R. Dutton, B. Murmann 2 EE114 (HO #24) 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, but… We’ll look in detail at T(s) as easier-to-get “proxy” a(s) f(s) ! v i v o - ) s ( T ) s ( a ) s ( f ) s ( a ) s ( a v v ) s ( A i o + = + = = 1 1
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EE 114 Lecture 20 R. Dutton, B. Murmann 3 EE114 (HO #24) 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, or e.g. N. M. Nguyen and R. G. Meyer, "Start-up and Frequency Stability in High-Frequency Oscillators," IEEE JSSC, pp. 810- 820, May 1992. Hurst,Gray, Lewis, Meyer, Analysis and Design of Analog Integrated Circuits, Fourth Ed. Chapter 9. Im Re ω =0 " = # (-1,0) R. Dutton, B. Murmann 4 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 Bode Criterion EE114 (HO #24)
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EE 114 Lecture 20 R. Dutton, B. Murmann 5 EE114 (HO #24) Bode Plot View of Stability Measures ω c ω 180 ω c ω 180 |T(j ω )| Phase[T(j ω )] ( ) [ ] c j T Phase 180 PM ! ! ! = + ° = ( ) 180 1 ! ! ! = = j T GM Typically want GM 3…5 Typically want PM 60…70° R. Dutton, B. Murmann 6 EE114 (HO #24) Closed Loop Peaking ω / ω c [Gray, Hurst et al, p.632] Closed-loop gain, normalized to 1/f
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EE 114 Lecture 20 R. Dutton, B. Murmann 7 EE114 (HO #24) Solutions If all we needed was the closed loop transfer function, we could simply do a KCL/KVL based analysis Can be quite tedious, especially for more complex circuits Hard to assess stability and stability margin Two port feedback analysis (treated e.g. in EE214)
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