lecture 10

lecture 10 - 1 1 Summary of Lecture#10 • Switching RLC...

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Unformatted text preview: 1 1 Summary of Lecture #10 9/15/2010 • Switching RLC circuits • Construct the s-domain 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 s-domain 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 non-zero 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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lecture 10 - 1 1 Summary of Lecture#10 • Switching RLC...

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