E source 0 dil r v il s dt l l din r in 0 dt

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Unformatted text preview: circuit Steady state component ( iss) : Steady state D.E. 0+ diL R V + iL = s dt L L R V iss = s L L iss = From circuit connec;on: R R vR vR vL iL Vs vL iL Vs L L Steady state Vs R Inductor = short circuit iss = Vs R 7 3/12/14 Solu;on for Natural response component ( in ) : D.E. Source = 0 diL R V + iL = s dt L L din R + in = 0 dt L First order homogeneous D.E. din 1 + in = 0 dt τ First order homogeneous D.E. din 1 + in = 0 dt τ First order homogeneous D.E. τ = RC Solu;on: 1. Assume solution form as : in (t ) = A ⋅ es t A = constant where s = constant 2. Substitute in the D.E. to get : 1 s A es t + A es t = 0 τ for A e s t ≠ 0, ⎛ 1⎞ A es t ⎜ s + ⎟ = 0 ⎝ τ⎠ 1⎞ ⎛ ⎜ s+ ⎟ = 0 ⎝ τ⎠ s= − 1 τ 8 3/12/14 iss = Vs R − t in = A e τ Adding the two components to get: iL (t ) = in + iss iL (t ) = Finding the constant (A): iL (t ) = t − Vs + A e τ R Ini;al Condi;on! t − Vs + A e τ R iL...
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This document was uploaded on 03/16/2014 for the course EEL 3004C at University of Central Florida.

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