EECS240 – Spring 2009Lecture 12: FeedbackElad AlonDept. of EECSEECS240 Lecture 12 2Feedback• Assume you are familiar with feedback benefits, issues• Review: G&M Ch. 8 & 9, Razavi Ch. 8• Focus here on:• Stability• Analysis and simulation• Settling• Often amplifying pulses and not sinusoids• More next lectureEECS240 Lecture 12 3Generic Feedback Circuit11 11== = ≈+1oviTVaAV1+Tf f+Vi+-avfVoVerr• Open-loop gain: av• Feedback factor: f• Loop gain: T = avf• Closed-loop gain:EECS240 Lecture 12 4Electronic Feedback CircuitViVo+-R1R2-av+Vi+-avfVoVerr+• Careful with mapping circuit feedback to generic diagram…=?=+112RfRREECS240 Lecture 12 5Stability• Nearly all circuits are actually non-linear and time-varying• “Poles” only accurate for given bias, temp., etc. • What we usually mean by stability:• Circuit always converges to the “origin” for zero input within finite time• (Exponential stability)• Another common definition: BIBO stabilityVinVbpVoutEECS240 Lecture 12 6Stability In Practice• Linearize the circuit and look at its poles• Remember: this is only an approximation!• Perform linear analysis over several corners, temps, supplies, etc.• May want to do a couple of transient sims tooVinVbpVoutEECS240 Lecture 12 7Linear Circuit StabilityVinVoutCfCsCL• Stability set by T(s)• T(s) is an open-loop parameter - need to break the loop• Easy to do in hand analysis: break at controlled source• Not as easy in simulation…EECS240 Lecture 12 8Simulating StabilityVinVoutCfCsCLEECS240 Lecture 12 9Common ApproachEECS240 Lecture 12 10Middlebrook Method (1975)freq, HertzZ1Z2iyvxZ1Z2vyvtest(ac)itest(ac)ix221yvmxvZTgZvZ≡= ⋅+211ZZZgTiimixy+⋅=≡2121ZZZZgTm+⋅=True Loop Gain:Solving yields:21++−=ivivTTTTT• Measure Tvand Ti, then calculate actual TEECS240 Lecture 12 11Phase Margin• Approximate method to evaluate stability: phase margin• Works well for most circuits of interest• Sometimes have to use Nyquiststability testEECS240 Lecture 12 12Multi-Loop FeedbackEECS240 Lecture 12 13Multi-Loop Feedback EECS240 Lecture 12 14Multi-Loop Feedback
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