enee204Lecture23_Gomez

enee204Lecture23_Gomez - 1 Lecture 23 1 Welcome to ENEE 204...

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Unformatted text preview: 1 Lecture 23 1 Welcome to ENEE 204 Basic Circuit Theory Lecture 23 Chap. 7, Transfer Functions Lecture 23 2 Transfer Functions! This is a technique to circumvent the derivation of the differential equation, immediately determine the characteristic equation and the particular solution. (ONE STOP SHOP) Lecture 23 3 Transfer function is the ratio of the output signal to the input signal An example: Network + v in − + v out − We can define For ac signals (with frequency ω ) it is often useful to define the transfer function for phasors ) ( ) ( ) ( t V t V t H in out = ) ( ˆ ) ( ˆ ) ( ˆ ω ω ω j V j V j H in out = Lecture 23 4 Simple examples of transfer functions L R v s (t) + v out − s out V V (j ω H ˆ ˆ ) 1 = C L R v S (t) i R (t) s R V I (j ω H ˆ ˆ ) 2 = L j R (j ω H ω + = 1 ) 2 L j R R j H ω ω + = ) ( ˆ 2 Lecture 23 5 A little review: Growing and decaying oscillations can be represented by phasors with complex frequencies v(t) = V m e σ t cos ( ω t + φ v ) v(t) = V m e σ t Re {e (j ω t+ φ v) } s = σ + j ω σ > 0 growing oscillations σ < 0 decaying oscillations =Re { V m e j φ v e ( σ + j ω) t } { } e V ˆ Re v t s (t) = s = complex radial frequency Lecture 23 6 Exponentially growing and decaying oscillations are very important class of signals σ = 0 v(t) = V m e σ t cos ( ω t + φ v ) σ < 0 Decaying oscillations σ > 0 Growing oscillations Lecture 23 7 Procedure for solving transients...
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This note was uploaded on 04/07/2008 for the course ENEE 204 taught by Professor Gomez during the Fall '04 term at Maryland.

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enee204Lecture23_Gomez - 1 Lecture 23 1 Welcome to ENEE 204...

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