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MIT6_012s09_lec22

# MIT6_012s09_lec22 - MIT OpenCourseWare http/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Lecture 22 Frequency Response of Amplifiers (II) VOLTAGE AMPLIFIERS Outline 1. Full Analysis 2. Miller Approximation 3. Open Circuit Time Constant 6.012 Spring 2009 Lecture 22 1 Reading Assignment: Howe and Sodini, Chapter 10, Sections 10.1-10.4
Common Emitter Amplifier + BIAS + V + R S R L i SUP i OUT V s v OUT + Operating Point Analysis v s =0, R S = 0, r o → ∞ , r oc → ∞ , R L → ∞ Find V BIAS such that I C =I SUP with the BJT in the forward active region V BIAS 6.012 Spring 2009 Lecture 22 2

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(a) Frequency Response Analysis of the Common Emitter Amplifier V s r π R S C µ C π V π + V out R L + g m V π r o ⎢⎢ r oc + Frequency Response Set V BIAS = 0. Substitute BJT small signal model (with capacitors) including R S , R L , r o , r oc Perform impedance analysis 6.012 Spring 2009 Lecture 22 3
(a) 1. Full Analysis of CE Voltage Amplifier Replace voltage source and resistance with current source and resistance using Norton Equivalent V s r π R S C µ C π V π + V out R L + g m V π r o ⎢⎢ r oc + C µ + 6.012 Spring 2009 Lecture 22 4 Node 1: Node 2: ( ) out in s V V C j V C j R V I + + = π μ π π π ω ω ( ) out out out m V V C j R V V g = + π μ π ω I s R' in R' in = R S ⎢⎢ r π R' out = r o ⎢⎢ r oc ⎢⎢ R L R' out C π V π + V out g m V π

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Full Frequency Response Analysis (contd.) • Re-arrange 2 and obtain an expression for V π • Substituting it into 1 and with some manipulation, we can obtain an expression for V out / I s : V R g j ω C μ ) R in out ( m out = I 1 + j ω R R ) ω 2 R s ( out C μ + R in C μ + R in C π + g m out R in C μ out R in C μ C π Changing input current source back to a voltage source: μ g R r π 1 j ω C V out V s = g m R out R S + r π g m 1 + j ω R out C μ + R in C μ 1 + g m R out ( ) + R in C π ( ) ω 2 R out R in C μ C π V out V s = A vo 1 + j ω τ 1 ( ) 1 + j ω τ 2 ( ) = A vo 1 j ω τ 1 + τ 2 ( ) ω 2 τ 1 τ 2 The gain can be expressed as: where A vo is the gain at low frequency and τ 1 and τ 2 are the two time constants associated with the capacitors L oc o S R r r r R || || R and || R
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