R=50 ohms, L=10uH, C=100nF. Find Tv(s)=Vout(s)/Vin(s). ECE 202 Electric Circuits

Question

R=50 ohms, L=10uH, C=100nF. Find Tv(s)=Vout(s)/Vin(s).

ECE 202 Electric Circuits & Systems II Problem Set #6 Hand out: Friday, 04/06/2012 Due: Friday, 04/13/2012 Please include UNIT in your answer. Given a transfer function: Sketch the magnitude and phase angle Bode-diagrams of T(s) using the follow semi-log graph. Plot with straight lines and label all critical frequencies. Slops levels.(20) Given the following second-order linear circuit, answer questions. Find TV(s) = Vout(s) / Vin(s) Identify the type of filter and justify your answer Find the resonant frequency omega0 and quality Q0 find the Fourier series for the following waveform using Fourier coefficients

Explanation / Answer

knowing that :

Zc(s) = 1/ Cs and ZL(s) = Ls u have :

Zc // ZL = (1/Cs) (Ls) / [1/Cs + Ls] = (L/C) / [1/Cs + Ls] x [Cs / Cs]

=> Zeq = Ls / [LCs^2 + 1]

using voltage divider u get :

Vout = (Zeq / [Zeq + R] ) Vin

=> Vout/Vin = (Ls / [LCs^2 + 1]) / { ( Ls / [LCs^2 + 1 ]) + R }

=> Vo/Vi = Ls / { Ls + RLCs^2 + R) }

dividing by RLC up and down u will get :

Vo/Vi = (1/RC) s / [ s^2 + (1/RC)s + (1/LC) ]

with R = 50 , L = 10uH , C = 100nF u will get

T(s) = (2x105) s / [ s2 + 2x105 s + 1012]

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