Lecture 13 - Lecture 13 Driven RC circuits Step response...

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Lecture 13 Driven RC circuits Step response
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Driven RC circuit ( 29 ( 29 ( 29 ( 29 ( 29 - = + = RC t V t V t V t V t V out outn outd outn out exp 0 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 RC t V RC t V C t I dt dV R t V t V t I in out out out in + - = = - = + V in - RC, but now with an input R C + V out - Solution has two parts: natural + driven Driven: look at a step input: V 1 V in t 0 t 1 ( 29 ( 29 ( 29 ( 29 1 0 0 0 1 1 = = < - = t u t t u t t t u V t V in
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Step response: RC circuit ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 - - - = - - = - = - = - = - = - = - = = = < = - + - = τ t t V t t u t V t t V V V t V t V t t V t t t V V RC t V dt dV dt dV dt dV t V V t V t t t V t V t t RC t V RC t t u V RC t V dt dV out R in out R R R out R out R R out R out out 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 exp 1 exp exp exp 0 , 0 + V in - Driven response: Vout(0)=0 R C + V out - First solve V R (t), then V out (t) v 1 t V out =V 1 u(t-t 1 )(1-exp[(t 1 -t)/ τ ]) v 1 0 t v
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Lecture 13 - Lecture 13 Driven RC circuits Step response...

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