# le12 - 10/6/2009 E E 2315 Lecture 12 - Natural Response of...

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10/6/2009 1 E E 2315 Lecture 12 - Natural Response of Parallel RLC Circuits Natural Response of Parallel RLC Circuit (1/5) L R C t = 0 + v - i L KCL for t 0: 0 L dv v Ci dt R  but 0 0 1 t L L iv d t i L then 0 0 1 0 t L dv v Cv d t i dt R L Natural Response of Parallel RLC Circuit (2/5) L R C t = 0 + v - i L 2 2 1 0 dv dv v C dt R dt L Differentiate KCL: From experience with 1st order problems: at vV e

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10/6/2009 2 Natural Response of Parallel RLC Circuit (3/5) L R C t = 0 + v - i L into differentiated KCL at Ve Substitute equation: 2 0 at at at aV a CVe Ve e RL  Divide out at Ve 2 1 0 a aC Natural Response of Parallel RLC Circuit (4/5) L R C t = 0 + v - i L Solve for a: 22 11 1 24 a RC R C LC  1 2 RC 2 1 o LC Let and Natural Response of Parallel RLC Circuit (5/5) 1 2 o o a a      Then Three types of response: real and unequal (both negative) real and equal (negative) complex conjugate pair
10/6/2009 3 Overdamped Parallel RLC (1/5) 62.5 mH 1

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## This note was uploaded on 02/20/2010 for the course EE 2315 taught by Professor Staff during the Fall '08 term at UT Arlington.

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le12 - 10/6/2009 E E 2315 Lecture 12 - Natural Response of...

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