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Unformatted text preview: 1 1 Summary of Lecture #10 9/15/2010 Switching RLC circuits Construct the sdomain circuit for t > 0 . Account for initial conditions at t = 0 . Determine V c (s), I L (s), then v C (t), i L (t) etc. Switching at t = t 1 Construct the sdomain circuit for t 1 . Account for initial conditions at t 1 . Determine V c (s), I L (s), then v C (t), i L (t) etc. Initial and final value theorems Examples Impulse response and step response 2 C v c (t) i c (t) + v c (0 ) Cv c (0 ) I c (s) V c (s) + I c (s) V c (s) + + Cs 1 v c (0 ) s i L (t) v L (t) + L i L (0 ) I L (s) V L (s) + Ls i L (0 ) s + Ls I L (s) V L (s) + Li L (0 ) Cs 1 Circuit elements having nonzero initial conditions in time and frequency domains Current source in parallel Voltage source in series 3 Ex. 3. Switch S has been at B for a long time and it turns to A at t = 0 and returns to B at t = 2.7465 s . Find i L (t) for t > 2.7465 s . i L (0 ) = 0 A For 0 t <2.7465 s 4 . s 3 s 3 ) s 10 4 ( s 12 s 10 4 s / 12 ) s ( I L + = + = + = A . 2 e 3 3 ) 7465 . 2 ( i A ) t ( u ) e 3 3 ( ) t ( i 7465 . 2 4 . L t 4 . L = = =  4 For t 2.7465 s Write t = t  2.7465 In terms of t In terms of t 10 s 2 s 10 100 s 10 s 2 ) s ( I L + = + = A ) ' t ( u ) e 2 ( )...
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This document was uploaded on 01/13/2012.
 Spring '06

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