EE 435 Lect 17 Spring 2010

EE 435 Lect 17 Spring 2010 - EE 435 Lecture 17 Two-Stage Op...

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EE 435 Lecture 17 Two-Stage Op Amp with LHP Zero Loop Gain - “Breaking the Loop”
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Nyquist and Gain-Phase Plots -40 -30 -20 -10 0 10 20 30 40 50 60 70 Nyquist and Gain-Phase Plots convey identical information but gain-phase plots often easier to work with -300 -250 -200 -150 -100 -50 0 Note: The two plots do not correspond to the same system in this slide Mag Phase ω ω Review from last lecture
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-80 -60 -40 -20 0 20 40 60 80 -300 -250 -200 -150 -100 -50 0 Magnitude in dB 1 β Phase Margin ω ω Angle in degrees Gain and Phase Margin Examples () ( ) 20 s 1 s 1581 T(s) + + = 2 Review from last lecture
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In general, the relationship between the phase margin and the pole Q is dependent upon the order of the transfer function and on the location of the zeros In the special case that the open loop amplifier is second-order low- pass, a closed form analytical relationship between pole Q and phase margin exists and this is independent of A 0 and β .. ) sin( φ ) cos( φ Q M M = + = 2 4 1 M 2Q 1 4Q 1 1 cos φ The region of interest is invariable only for 0.5 < Q < 0.7 larger Q introduces unacceptable ringing and settling smaller Q slows the amplifier down too much Relationship between pole Q and phase margin Review from last lecture
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Phase Margin vs Q 0 1 2 3 4 5 6 7 0 2 04 06 08 0 1 0 0 Phase Margin Pole Q Second-order low-pass Amplifier Review from last lecture
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Phase Margin vs Q 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 40 50 60 70 80 Phase Margin Pole Q Second-order low-pass Amplifier Review from last lecture
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Magnitude Response of 2 nd -order Lowpass Function Q 2 1 = ξ From Laker-Sansen Text Q MAX for no peaking = 707 2 1 . = Review from last lecture
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Step Response of 2 nd -order Lowpass Function Q MAX for no overshoot = 1/2 From Laker-Sansen Text Q 2 1 = ξ Review from last lecture
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Compensation Summary • Gain and phase margin performance often strongly dependent upon architecture • Relationship between overshoot and ringing and phase margin were developed only for 2 nd -order lowpass gain characteristics and differ dramatically for higher-order structures • Absolute gain and phase margin criteria are not robust to changes in architecture or order • It is often difficult to correctly “break the loop” to determine the loop gain A β with the correct loading on the loop (will discuss this more later) Review from last lecture
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Basic Two-Stage Op Amp , 356 17 T 13 6 7 5 WWW WW ,,,,, I θ LL L L L ⎩⎭ { P, θ , V EB1 , V EB3 , V EB5 ,V EB6 , V EB7 } 7 Degrees of Freedom .• • • Review from last lecture .•
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1. Choose channel length 2. V EB3 , V EB5 , V EB6 V imax =V DD + V EB3 + V T1 + V T3 V omax =V DD + V EB5 V omin =V EB6 3. V EB1 4. V EB7 V imin =V EB1 + V EB7 + V T1 5. Choose P to satisfy power constraint () | | 4 5 1 2 EB EB p n O V V A λ λ+ = P I= T V1 + θ DD Example for Design Procedure {P, θ , V EB1 , V EB3 , V EB5 , V EB6 , V EB7 } {P, θ , V EB1 , V EB3 , V EB5 , V EB6 , V EB7 } {P, θ , V EB1 , V EB3 , V EB5 , V EB6 , V EB7 } {P, θ , V EB1 , V EB3 , V EB5 , V EB6 , V EB7 } .• • • Review from last lecture .•
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6.
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EE 435 Lect 17 Spring 2010 - EE 435 Lecture 17 Two-Stage Op...

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