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EE 435 Lect 12 Spring 2010

# EE 435 Lect 12 Spring 2010 - EE 435 Lecture 12 Cascaded...

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EE 435 Lecture 12 Cascaded Amplifiers -- Two-Stage Op Amp Design

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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 Review from Last Time
Similar implications on amplifier even if not a basic voltage feedback amplifier 1 2 OUT 1 VF IN 2 V 1 R 1+ V R A = = V R 1+ 1+ A R 1 2 OUT 1 VF IN 2 V 1 R - V R A = = V R 1+ 1+ A R 1 2 1 R β = R +R OUT V VF IN 1 V 2 1 V A A = = V R 1+A R R + 2 V 1 OUT VF IN 1 V 2 1 -R A R V A = = V R 1+A R R + These circuits have • same β same dead network same characteristic polynomial same poles different zeros ( ) D s =1+A β (expressed as polynomial) Review from Last Time

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Cascaded Amplifier Issues Four or more amplifier cascades - problems even larger than for three stages -- seldom used in industry ! -- seldom used in industry ! Two amplifier cascades 0TOT 0TOT A 2 β k A 4 β > > -- widely used in industry but compensation is essential ! Three amplifier cascades - for ideally identical stages 3 0 β A 8 > Single-stage amplifiers -- widely used in industry, little or no concern about compensation Note: Some amplifiers that are termed single-stage amplifiers in many books and papers are actually two-stage amplifiers and some require modest compensation. Some that are termed two- stage amplifiers are actually three-stage amplifiers. These invariable have a very small gain on the first stage and a very large bandwidth. The nomenclature on this summary refers to the number of stages that have reasonably large gain. Review from Last Time
Fundamental Amplifier Design Issues Single-Stage Low Gain Op Amps Single-Stage High Gain Op Amps Two-Stage Op Amp – Compensation Breaking the Loop Other Basic Gain Enhancement Approaches Other Issues in Amplifier Design Summary Remarks

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Two-stage op amp design It is essential to know the poles of the op amp since there are some rather strict requirements about the relative location of the poles
Poles and Zeros of Amplifiers V DD M 1 M 2 V B2 M 3 M 4 V IN V IN M 5 V DD M 6 M 7 V B2 M 8 M 9 C L M 10 V OUT C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 There are a large number of parasitic capacitors in an amplifier (appprox 5 for each transistor) Many will appear in parallel but the number of equivalent capacitors can still be large Order of transfer function is equal to the number of non-degenerate energy storage elements Obtaining the transfer function of a high-order network is a lot of work !

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EE 435 Lect 12 Spring 2010 - EE 435 Lecture 12 Cascaded...

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