MIT6_012S09_lec22

# MIT6_012S09_lec22 - Lecture 22 Frequency Response of...

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Unformatted text preview: 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 + V 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 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 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 ′ 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 − ω C V out V s = − g m R out R S + r π 1 − j ω 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 ωτ 1 ( ) 1 + j ωτ 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...
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MIT6_012S09_lec22 - Lecture 22 Frequency Response of...

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