ECE201_Lecture25

ECE201_Lecture25 - ECE201 Linear Circuit Analysis I Lecture...

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1 ECE201 Linear Circuit Analysis I Lecture 25 Topic: Second-order circuits: RLC constant inputs 1. Review of series or parallel source-free RLC circuits circuit equation characteristic equation σ and ω n damping coefficient (series) or (parallel) undamped oscillation frequency ω n = 1 LC 3 forms of responses (i) σ > ω n (overdamped) s 1 ≠ s 2 , real. If σ > 0, then s 1 < 0, s 2 < 0. (ii) σ = ω n (critically damped) s 1 = s 2 = – σ , real. If σ > 0, then s 1 , s 2 < 0. (iii) σ < ω n (underdamped) . A & B are real. final value of the response x(t) For all 3 forms of x(t), x( ) = 0 if σ > 0. In other words, without any inputs, any initial energy stored in the capacitor and/or inductor will eventually be dissipated by the resistor. d 2 x dt 2 + 2 σ dx + ω n 2 = 0 s 2 + 2 + 2 = 1 ( ) 2 ( ) = 0 1,2 = − ± 2 2 = R 2 L = 1 2 RC ( t ) = K 1 e 1 + 2 2 ( ) = 1 + 2 ( ) ( ) = A cos ( ) + B sin ( ) [ ] = 2 2 R L C OR R L C Circuit
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2 2. Now add a constant input to the RLC circuit circuit equation i.e. the only change is to add a constant F to the right side of the equation.
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This note was uploaded on 04/19/2011 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue.

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ECE201_Lecture25 - ECE201 Linear Circuit Analysis I Lecture...

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