ECE201_Lecture22 - ECE201 Linear Circuit Analysis I Lecture...

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1 ECE201 Linear Circuit Analysis I Lecture 22 Topic: Second-order circuits: LC undamped case 1. Introduction to 2 nd -order linear circuits * 2 nd -order linear circuits usually contain two energy-storage elements (e.g. L & C, L & L, or C & C), in addition to linear resistors, independent and dependent input sources. * Circuit equations are 2 nd -order linear differential equations. 2. An LC 2 nd -order circuit and its analysis (1) Determine initial conditions at t = 0 and t = 0 + . According to the continuity property for i L : i L (0 + ) = i L (0 ) = 0 According to the continuity property for v c : v c (0 + ) = v c (0 ) KVL gives V o = v c (0 ) thus v c (0 + ) = V o (2) circuit equation for i L (t), t ≥ 0 and v c (t), t ≥ 0. KCL : i c = − i L KVL v c = v L C : = d v c dt L : v L = i L 2 2 = 1 dv = 1 = 1 LC = − 1 i.e., 2 2 = − 1 Similarly: 2 v 2 = − 1 C L i c i L + v L + v c
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2 (3) Intuitive solutions for i L (t) and v c (t): * Both L and C are lossless elements.
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This note was uploaded on 11/13/2009 for the course PHYS 17200 taught by Professor Gaboracsathy during the Spring '09 term at Purdue University.

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ECE201_Lecture22 - ECE201 Linear Circuit Analysis I Lecture...

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