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Lecture 17_v2 - Lecture 18 Series RLC Some intuition Step...

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Spring 2011 ECE 2100, Cornell Univ. Professor A. Molnar 1 Lecture 18 Series RLC Some intuition Step responses
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Spring 2011 ECE 2100, Cornell Univ. Professor A. Molnar 2 Series RLC circuit K VL gives us a 2 nd order differential equation Can reformulate in a general form Just like before, but with different alpha (same ω o ) Note: α looks like -1/(2 τ ) For parallel, α =1/(2RC) like τ for RC circuit For series, α =R/(2L) like τ for LR circuit LC L R I dt dI dt I d LC I dt dI L R dt I d IR Vc d C I dt dI L t 1 2 2 0 0 0 0 2 0 2 2 2 2 0 = = + + = + + = + + + = ω α ω α τ , ) ( + V R - - V L + L C R V C + -
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Spring 2011 ECE 2100, Cornell Univ. Professor A. Molnar 3 Intuition, part 1: sketching solns Over damped: 2 exponentials Can say fast one decays to slow one. 2 nd -order: only two curvatures (only one inflection point) Under damped: Period is 2 π / ω d Envelope decays as exp(- α t) -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 1 2 3 4 5 tau1 tau2 tot -1.5 -1 -0.5 0 0.5 1 1.5 0 1 2 3 4 5 Period, T= 2 π / ω d Long term, larger tau dominates smaller tau sets initial decay to longer exponential
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