ECE201_Lecture23

ECE201_Lecture23 - ECE201 Linear Circuit Analysis I Lecture...

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1 ECE201 Linear Circuit Analysis I Lecture 23 Topic: Second-order circuits: RLC source free case (with real characteristic roots) 1. Review of 2 nd -order Source Free LC Circuits v c i circuit equations C C v LC dt v d 1 2 2 = d 2 i L dt 2 = − 1 LC solution (general) v c ( t ) = K cos( ω + θ ) i L ( ) = cos( + ω ω = 1 ω = 1 K, θ determined by v c (t o + ) and i L (t o + v c o + ), v c (t o + i L (t o + ), i L (t o + + v c i L L + v L i c C
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2 2. Source-free 2 nd -order linear networks with real characteristic roots (over-damped & critically-damped responses) In other words: Add a resistor to the LC circuit. Two cases: 3. Circuit Equations (1) Series RLC circuit Expand in terms of i L : (i R = i L = i c ) 0 ) ( 1 = + + t L L L d i C dt di L i R τ Differentiate: R di L dt + d 2 i 2 + 1 C = 0 Divide both sides by L and rearrange terms: 2 2 + + 1 LC = 0 L C R R L C R L + C v c i L kVL: v R + v L + v c = 0
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3 Expand KVL in terms of v c : i R = i L = C dv c dt RC dv c dt + LC d 2 v 2 + = 0 2 2 + R L + 1 = 0 Same 2 nd -order differential equation as for i L .
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This note was uploaded on 04/19/2011 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue.

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ECE201_Lecture23 - ECE201 Linear Circuit Analysis I Lecture...

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