Lecture 13_14_2011 - Spring 2011 ECE 2100, Cornell Univ.,...

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Unformatted text preview: Spring 2011 ECE 2100, Cornell Univ., A. Molnar 1 Lecture 13+14 2 nd-order RC circuits, RLC part 1 Spring 2011 ECE 2100, Cornell Univ., A. Molnar 2 2 nd order RC circuit: intuition V1 cant 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 Spring 2011 ECE 2100, Cornell Univ., A. Molnar 3 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 + = + = - + - = - + - =- =--- =-- =- =---- =-- = exp exp exp exp 2 1 2 1 2 2 1 1 2 2 2 1 2 1 2 2 1 1 1 1 1 2 2 2 2 1 2 2 1 1 2 2 1 1 1 1 2 1 Note that sign rule still applies: V1 always has same sign, even when differentiated!...
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This note was uploaded on 06/10/2011 for the course ECE 2100 taught by Professor Kelley/seyler during the Spring '05 term at Cornell University (Engineering School).

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Lecture 13_14_2011 - Spring 2011 ECE 2100, Cornell Univ.,...

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