Lecture 15_16 - Spring 2011 ECE 2100, Cornell Univ. Prof....

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Unformatted text preview: Spring 2011 ECE 2100, Cornell Univ. Prof. A. Molnar 1 Lecture 15 + 16 RLC: finding the natural response different kinds of damping Spring 2011 ECE 2100, Cornell Univ. Prof. A. Molnar 2 Parallel RLC circuit KCL gave us a 2 nd order differential equation Can reformulate in a general form Subbing in an exponential gives a quadratic equation Solve for roots Question: how does behavior change as a function of , ? 3 cases of interest ( ) 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 1 exp 1 , 2 1 2 1 = = + + = + + = = = = + + = + + = LC RC RC s V s s LC RC s s st V LC RC V dt dV dt V d LC V dt dV RC dt V d + V- L C R I L I C I R Spring 2011 ECE 2100, Cornell Univ. Prof. A. Molnar 3 Case 1: over damped If > 0, then Has two real roots, specifically: Note that 1> 2 Solution takes the form: Where initial conditions dictate that 2 2 2 2 1 2 2 1 1 1 =...
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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 15_16 - Spring 2011 ECE 2100, Cornell Univ. Prof....

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