R to justateraccon t 0 il vs note l il 0

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Unformatted text preview: ore acCon t = 0! R t=o just aTer acCon t = 0+ iL Vs Note! L iL (0 ! ) = io Inductor current can not change instantaneously !! iL (0 ! ) = iL (0 + )!! !! t = 0 ! !! t=o !! t = 0 + !! R R vR iL Vs L Vs vL iL L iL (0 ! ) = io iL (0 + ) = io 4 3/18/12 For !! t ! 0 + !! R vR KVL: Vs = iR R + vL Vs = vR + vL L iL (0 + ) = io ! di $ Vs = iL R + L # L & " dt % diL R V + iL = s dt L L vL iL Vs diL 1 V + iL = s dt ! L != L R First order non‐homogeneous D.E. First order non‐homogeneous D.E. D.E. diL 1 V + iL = s dt ! L != L R SoluCon: Note: For non homogeneous D.E the soluCon has two components! iL (t ) = in + iss in :! Natural response iss :! steady ! state in: due to energy stored within the circuit iss: due to sources in the circuit 5 3/18/12 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 connecCon: Vs ! R R R vR vR vL iL Vs vL iL Vs L L Inductor = short circuit Steady state ! iss = Vs ! R SoluCon 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 ! 6 3/18/12 First order homogeneous D.E. din 1 + in = 0 dt ! First order homogeneous D.E. ! = RC SoluCon: 1. Assume solution form as : in (t ) = A ! e A = constant where st s = constant 2. Substitute in the D.E. to get : " 1 ! iss = 1% " $ s+ ' = 0 # !&...
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This note was uploaded on 02/21/2013 for the course EEL 3004 taught by Professor Gong during the Spring '08 term at University of Central Florida.

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