week102

week102 - R C Circuit Response Kirchoff Law u H t L = R Q L...

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Unformatted text preview: R C Circuit Response Kirchoff Law u H t L = R Q L H t L + G Q H t L , t > B G = 1 C F R > 0; C > R ' Resistance' is measured in ' Ohms'. C ~ ' Condensor'. ' Capacitance' C is measured in ' Farads'. G ' Elastance' v H t L = G Q H t L = ' Output' voltage u H t L source H ' Input' L voltage t ‡ ** ** ** ** ** ** ** ** ** ** ** ** ** k = G R = 1 RC Q H t L = e- k t Q H L + 1 R t e- k H t- s L u H s L s, t ‡ v H t L = e- kt GQ H L + k t e- k H t- s L u H s L s t > 0 . GQ H L = v H L = e- k H t-Τ L GQ H Τ L + k Τ t e- k H t- s L u H s L s, t > Τ . GQ H Τ L = v H Τ L ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** Printed by Mathematica for Students Rewrite as Q L H t L = - G R Q H t L + 1 R u H t L Differential Equation : x L H t L = - k x H t L + 1 R u H t L , k = G R = 1 RC SOLVE Technique of Solution Details Multiply both sides by e kt H a nonzero number ! called ' Integrating Factor' L : and get : e kt x L H t L + k e kt x H t L = 1 R e kt u H t L Left- side = d dt I e kt x H t LM Hence d ds I e ks x H s LM = 1 R e ks u H s L s > Take Τ Τ £ t Then integrate from Τ to t on both sides Τ t d ds I e ks x H s LM s = e kt x H t L- e k Τ x H Τ L = Τ t 1 R e ks u H s L s Or, x H t...
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This note was uploaded on 10/15/2009 for the course EE 10 taught by Professor Chang during the Spring '07 term at UCLA.

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week102 - R C Circuit Response Kirchoff Law u H t L = R Q L...

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