EE 435 Lect 11 Spring 2010

EE 435 Lect 11 Spring 2010 - EE 435 Lecture 11 Cascaded...

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EE 435 Lecture 11 Cascaded Amplifiers -- Two-Stage Op Amp Design
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Current-Mirror Op Amps – Another Perspective ! + = 8 6 6 4 2 2 1 O O m m m V g g g g g A 8 6 1 4 6 8 6 1 2 2 O O m m m O O m VO g g g g g g g g M A + = + = Differential Half-Circuit Cascade of n-channel common source amplifier with p-channel common-source amplifier ! From Current Mirror Analysis : Review from Last Time
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Current-Mirror Op Amps – Another Perspective ! 1 4 1 C g p m ( ) 2 8 6 2 C g g p O O + Differential Half-Circuit Are there stability issues or concerns ? Large Large Small Small 2 1 p p >> -p 1 -p 2 No stability problems provided C 2 is sufficiently large ! Review from Last Time
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Current-mirror op amp offers no improvement in performance over the reference op amp Current-mirror op amp can be viewed as a cascade of two common-source amplifiers, one with a low gain and the other with a larger gain Current-mirror op amp is useful as an open-loop programmable transconductance amplifier (OTA) Current Mirror Op Amp Summary Review from Last Time
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Increasing Gain by Cascading A 1 A 2 X IN X OUT 2 1 IN OUT A A X X = 3 2 1 IN A A A X X = = = n 1 i i IN A X X Provided the stages are non-interacting Gain can be easily increased to almost any desired level ! Review from Last Time
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Review of Basic Concepts Theorem: A linear system is stable iff all poles lie in the open left half-plane Im Re Open Left Half Plane Stable with two negative real axis poles and two LHP CC poles Unstable with positive real axis pole Review from Last Time
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Consider Again the Frequency Response of a Feedback Amplifier n 0 n n 0 FB β A 1 p s A A + + = ~ β Example: Assume n=3 3 0 3 3 0 FB β A 1 p s A A β 1 A A + + = + = ~ X X X Re Im Note this amplifier is unstable !!! () p A β 1 p 1 - A β 1 p 0 3 1 3 1 0 3 1 3 1 F ~ ~ = The poles with feedback, p F , are given by Review from Last Time
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Consider Again the Frequency Response of Feedback Amplifier β Example: If n=3 and stages are identical 3 0 3 3 0 FB β A 1 p s A A β 1 A A + + = + = ~ X X X Re Im Routh-Hurwitz Stability Criteria: A third-order polynomial s 3 +a 2 s 2 +a 1 s+a 0 has all poles in the LHP iff all coefficients are positive and a 1 a 2 >a 0 Consider () 3 0 2 2 3 3 3 0 3 FB β A 1 p 3 s p 3 s p 1 s β A 1 p s (s) D + + + + = + + = ~ ~ ~ ~ ( ) ( ) 3 0 3 2 β A 1 p p 3 p 3 + > ~ ~ ~ 3 0 β A 8 > Not only is the 3-stage amplifier unstable, it is far from being stable!
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Routh-Hurwitz Stability Criteria: A third-order polynomial s 3 +a 2 s 2 +a 1 s+a 0 has all poles in the LHP iff all coefficients are positive and a 1 a 2 >a 0 Very useful in amplifier and filter design Can easily determine if poles in LHP without finding poles But tells little about how far in LHP poles may be RH exists for higher-order polynomials as well
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EE 435 Lect 11 Spring 2010 - EE 435 Lecture 11 Cascaded...

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