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Unformatted text preview: ECE231 Circuits and Systems I Fall 2011 Session 8 Dr. Stewart Personick Office: ECEC Room 331 sdp2@verizon.net 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) 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/ ) sin(200 t) + (20/3 ) sin(600 t) + (20/5 ) sin(1000 t) + i(t)  + Vab(t) Representing a square wave as a sum of sine waves and cosine waves Vs(t) t 10ms Vs(t) = (20/ ) sin(200 t) + (20/3 ) sin(600 t) + (20/5 ) sin(1000 t) + Reference: http://ptolemy.eecs.berkeley.edu/eecs20/week8/examples.ht 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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This note was uploaded on 03/01/2012 for the course ECE 231 taught by Professor Pietrucha during the Spring '08 term at NJIT.
 Spring '08
 PIETRUCHA
 Volt

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