L09 lecture

# L09 lecture - Feedback Benefits Reduced sensitivity to Gain...

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EECS 240 Lecture 9: Feedback B. Boser 1 Feedback Benefits – Reduced sensitivity to Gain variations • Nonlinearity – Increased bandwidth Caveat: potential instability Stability test – Bounded input, bounded output: no general test available – Linear system: • Poles in LHP (“left half-plane”) • Nyquist criterion • Bode criterion – Hand-analysis – SPICE EECS 240 Lecture 9: Feedback B. Boser 2 Generic Feedback Circuit 1 for 1 1 1 1 1 : gain loop - closed : gain loop : factor feedback : gain loop - open 1 >> + = + = = = T f f T a V V A f a T f a T i o v v

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EECS 240 Lecture 9: Feedback B. Boser 3 Electronic Feedback Circuit f T R R R R T R R R R V V A f a T R R R f a i o v v 1 1 for 1 1 1 : gain loop - closed : gain loop isolate) to difficult (sometimes : factor feedback : gain loop - open 1 2 1 2 2 1 1 2 2 1 1 >> + = = = + = EECS 240 Lecture 9: Feedback B. Boser 4 Stability Analysis Depends on T(s) – NOT a(s) Finding T(s): – Hand analysis: Break loop at controlled source (e.g. g m ) •T = - s r / s t – SPICE: Controlled sources not accessible a) Break loop, model load (approximation), or b) Determine T from T v and T i (exact)
EECS 240 Lecture 9: Feedback B. Boser 5 Simple Circuit Example freq, Hertz C 1 r o C GS Vi C 2 Vo C 1 C 2 g m v gs v i v o v gs Small Signal Equivalent Loop Gain = ? Feedback Amplifier (Biasing for V gs not shown) EECS 240 Lecture 9: Feedback B. Boser 6 Return Ratio Analysis [HLGM 01] freq, Hertz r o C GS C 2 g m v gs v gs C 1 i test i return 1. Set all independent sources to zero (v i =0) 2. Disconnect (ideal) controlled source from circuit 3. Replace with test source 4. Find ratio return signal/test signal = “Return Ratio“ = Loop Gain GS GS o GS m C C C C C C r p C C C C F p s r g F s T + + + = + + = + = 1 2 1 2 1 2 1 2 1 0 ) ( 1 1 1 ) ( Easy! Why not do the same thing in SPICE?

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EECS 240 Lecture 9: Feedback B. Boser 7 MOSFET AC Simulation Model freq, Hertz Small-signal model not accessible in SPICE! EECS 240 Lecture 9: Feedback B. Boser 8 Popular Simulation Approach freq, Hertz An ideal loop gain test circuit would: - not alter node impedances - not affect the DC bias point Vo 1Gig v return v test Mock Load C 1 C 2 test return v v s T ) ( • Inaccurate • Cumbersome • Different results for different breakpoints
EECS 240 Lecture 9: Feedback B. Boser 9 Problem Generalization freq, Hertz Breakpoint at ideal source is not available. But there is a breakpoint “between finite impedances“ Any “single loop“ feedback circuit can be represented as: g m v x v x Z 1 Z 2 available breakpoint 2 1 2 1 ) ( Z Z Z Z g s T m + = EECS 240 Lecture 9: Feedback B. Boser 10 Middlebrook Double Injection [Middlebrook 75] freq, Hertz Z 1 Z 2 i

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L09 lecture - Feedback Benefits Reduced sensitivity to Gain...

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