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Lecture 14 - Lecture 14 2nd-order RC circuits 2nd order RC...

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Lecture 14 2 nd -order RC circuits
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2 nd order RC circuit: intuition V1 can’t change instantly, so Vin appears all across R1, generates large, decaying I1 I2=0 until voltage builds up on C1, then starts to charge C2, As V1 assymptotes, V2 starts to catch up, I2 decreases again + V in - V in t 0 t 1 I1 V1 I2 V2 R1 C1 R2 C2 I 1 t 0 t 1 V 1 t 0 t 1 I 2 t 0 t 1 V 2 t 0 t 1 V h /R1 V h V h
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2 nd order RC circuit: math Write KCL for two nodes Set up as two differential equations Look for natural response (Vin=0): guess two exponentials/time constants Implies four magnitude constants (A,B,C,D) Initial conditions also need to be met + V in - I1 V1 I2 V2 R1 C1 R2 C2 ( 29 ( 29 ( 29 ( 29 D B V C A V t D t B t V t C t A t V C R V V dt dV C R V V C R V V dt dV dt dV C R V V I I dt dV C R V V R V V I I I in C in C + = + = - + - = - + - = - = - - - = - - = - = - - - - = - - = 0 0 exp exp exp exp 0 0 2 1 2 1 2 2 1 1 2 2 2 1 2 1 2 2
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