ho23.l20_fb2

# ho23.l20_fb2 - Fundamentals of Feedback of Feedback Part II...

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1 Fundamentals of Feedback Part II R. Dutton, B. Murmann Stanford University R. Dutton, B. Murmann 1 EE114 (HO #23) Stability T ) s ( a ( f ) s ( a v ) s ( A o = = = 1 1 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 ) s ( ) s ) s ( a v i + + R. Dutton, B. Murmann 2 EE114 (HO #23) 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”

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2 Methods for Checking Stability Nyquist Criterion Im ω = ∞ (-1,0) – 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 Re ω =0 R. Dutton, B. Murmann 3 EE114 (HO #23) Hurst,Gray, Lewis, Meyer, Analysis and Design of Analog Integrated Circuits, Fourth Ed. Chapter 9. Bode Criterion 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 R. Dutton, B. Murmann 4 – Can use simple bode plot to check for stability EE114 (HO #23)
3 Bode Plot View of Stability Measures |T(j ω )| ( ) 1 ω = j T GM ω c ω 180 ω c ω 180 Phase[T(j ω )] () [ ] c j T Phase 180 PM = + ° = 180 = Typically want GM 3…5 R. Dutton, B. Murmann 5 EE114 (HO #23) Typically want PM 60…70° Closed Loop Peaking Closed loop gain ω / ω c Closed-loop gain, normalized to 1/f R. Dutton, B. Murmann 6 EE114 (HO #23) [Gray, Hurst et al, p.632]

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4 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) – "Shunt-series, shunt-shunt, series-shunt, series-series" feedback configurations – Attempts to identify amplifier (a) and feedback network (f) with loading effects included
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ho23.l20_fb2 - Fundamentals of Feedback of Feedback Part II...

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