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

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Lecture 18 Series RLC Some intuition Step responses
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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 dt C I dt dI L t 1 , 2 2 0 0 0 2 0 2 2 2 2 0 = = + + = + + = + + = ϖ α + V R - - V L + L C R V C + -
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Intuition, part 1: sketching solns • Under damped: 2 exponentials – Can say fast one decays to slow one. – 2 nd -order: only two curvatures (only one inflection point) • Over 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
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Intuition, part 2: cheesy water analogies Resistor constricted pipe Capacitor tank Inductor propeller with flywheel RLC
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This note was uploaded on 11/21/2011 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 18 - Lecture 18 Series RLC Some intuition Step...

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