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ECE 231 -8

# ECE 231 -8 - ECE-231 Circuits and Systems I Fall 2011...

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ECE-231 Circuits and Systems I Fall 2011 Session 8 Dr. Stewart Personick Office: ECEC Room 331 [email protected]

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Using sine waves to solve for currents and voltages in RLC networks
Using sine waves to solve for currents and voltages in RLC networks + - Vs(t) Rs = 100 a b From superposition , we can solve for i(t) and Vab(t) by representing Vs(t) as the sum of a number of voltage waveforms Vs(t) = V1(t) + V2(t) + …. + Vn(t) , and solving for the waveforms i(t) and Vab(t) that are produced by individually applying each of: V1(t), V2(t), etc. i(t) - + Vab(t)

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Using sine waves to solve for currents and voltages in RLC networks + - Vs(t) Rs = 100 a b From superposition, we can solve for i(t) and Vab(t) by representing Vs(t) as the sum of a number of voltage waveforms Vs(t) = V1(t) + V2(t) + …. + Vn(t) , and solving for the waveforms i(t) and Vab(t) that are produced by individually applying each of: V1(t), V2(t), etc. We can represent almost any waveform, Vs(t), as a sum of sine waves and cosine waves (Fourier analysis) i(t) - + Vab(t)
Using sine waves to solve for currents and voltages in RLC networks + - Vs(t) Rs = 100 a b From superposition , we can solve for i(t) and Vab(t) by representing Vs(t) as the sum of a number of voltage waveforms Vs(t) = V1(t) + V2(t) + …. + Vn(t) , and solving for the waveforms i(t) and Vab(t) that are produced by individually applying each of: V1(t), V2(t), etc. Example: We can represent a 5 volt (peak) square wave, that repeats every 10 milliseconds as: Vs(t) = (20/ π ) sin(200 π t) + (20/3 π ) sin(600 π t) + (20/5 π ) sin(1000 π t) + … i(t) - + Vab(t)

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Representing a square wave as a sum of sine waves and cosine waves Vs(t) t 10ms Vs(t) = (20/ π ) sin(200 π t) + (20/3 π ) sin(600 π t) + (20/5 π ) sin(1000 π t) + … Reference: http://ptolemy.eecs.berkeley.edu/eecs20/week8/examples.ht ml 5 V
Using sine waves to solve for currents and voltages in RLC networks 1. From superposition, we can solve for i(t) and Vab(t) by representing Vs(t) as the sum of a number of voltage waveforms Vs(t) = V1(t) + V2(t) + …. + Vn(t) , and solving for the waveforms i(t) and Vab(t) that are produced by individually applying each of: V1(t), V2(t), etc.

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ECE 231 -8 - ECE-231 Circuits and Systems I Fall 2011...

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