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Solving circuits directly using Laplace

EE 230 Laplace circuits 1 Solving circuits directly using LaplaceThe Laplace method seems to be useful for Solving the differential equations that arise with circuits that have capacitors and inductors and sources that vary with time (steps and sinusoids.) The approach has been to: the circuit in the time domain using familiar circuit analysis techniques to arrive at a differential equation for the time-domain quantity of interest ( voltage or current). a Laplace transform on the differential equation to arrive a frequency-domain form of the quantity of interest. the frequency-domain algebra expression.

voltage divider. = 1 sC R+ 1 sC +sL V i (s) V C (s) = Z C Z R +Z C +Z L V i (s) V C (s) = (1 1+sRC+s2LC)(V f s) = V f LC s(s2 +s R L + 1 LC) – + + – Z R V i (s) Z C V C (s) Z L Convert to the frequency domain. Z R = R

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