EECE 213 HW 3

EECE 213 HW 3 - Matthew Thompson EECE 213 HW#3 ltr =...

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Unformatted text preview: Matthew Thompson EECE 213 HW #3 ltr = LaplaceTransform @ f_ @ t_ D , t_, s_ D : > Symbol @ ToUpperCase @ SymbolName @ f [email protected] s D Protect @ ltr D Off @ Clear:: wrsym , Remove:: rmptc D inSeries @ z__ D : = Plus 8 z < inParallel @ z__ D : = 1 Plus J 1 8 z < N 10 - 8 zeq = inSeries A inParallel A inSeries A 2 R, 1 c s E , 2 R E , 1 2 c s E Together 1 + 8 c R s + 8 c 2 R 2 s 2 2 c s H 1 + 4 c R s L Find the zeros: n = Numerator @ zeq D 1 + 8 c R s + 8 c 2 R 2 s 2 Solve @ n 0, s D :: s fi- 2- 2 4 c R > , : s fi- 2 + 2 4 c R >> Find the poles: d = Denominator @ zeq D 2 c s H 1 + 4 c R s L Solve @ d 0, s D :8 s fi < , : s fi - 1 4 c R >> 10 - 13 eq1 : = VA + is @ t D * R + iR @ t D * R eq2 : = VA + is @ t D * R + VA + 1 c t ic @ Τ D Τ Printed by Mathematica for Students eq3 : = is @ t D iR @ t D + ic @ t D Eliminate @8 eq1, eq2, eq3 < , 8 is @ t D , iR @ t D<D R ic @ t D- 3 VA- 2 t ic @ Τ D Τ c && c „ eq4 = - 3 VA- 2 t ic @ Τ D Τ c- R ic @ t D ==- 3 VA- R ic @ t D- 2 t ic @ Τ D Τ c slnT = LaplaceTransform @ eq4, t, s D . 8 ltr <- 3 VA s- R IC @ s D- 2 IC @ s D c s sln1 = Solve @ slnT, IC @ s DD Flatten : IC @ s D fi - 3 c VA 2 + c R s > sln2 = InverseLaplaceTransform @ IC @ s D . sln1, s, t D- 3 ª- 2 t c R VA R 10 -15 Clear @ "Global` * " D ; Remove @ "Global` * " D eq1 : = - VA s + Is @ s D * R + IR @ s D * R eq2 : = - VA s + Is @ s D * R + IL @ s D * L * s- L * iL @ D eq3 : = Is @ s D...
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EECE 213 HW 3 - Matthew Thompson EECE 213 HW#3 ltr =...

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