# ps4 soln - ECE 218A/145A Fall 2012 PS#4 Solutions 1...

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ECE - 218A/145A - Fall 2012PS #4 - Solutions1Problema)(a) Smith Chart S11(b) Simulation CircuitFigure 1: First CaseFrom the Smith chart in Fig.1a, it is seen that the quarter wavelength frequency is 105 GHz. The corre-sponding impedance at 105 GHz,Zin=Z0*(3.412-j0.009)Using the formula for a quarter-wavelength line,Zline=ZinZL. Here,ZL=Z0.Zline=pZ0*Z0*(3.412) =92.357Ωb) Z parameters are calculated by shorting one of the ports and forcing a voltage at the other port. Theconcept used here to calculatevwaveis that, a shorted microstrip line has aZin=jtan(βd), whereβ=2πλ=2π*fvwave. When,βd=odd*π2,tan(βd) =, which represent poles.From Fig.2a, we find that the first pole occurs atf=105GHz.2πfvwave*d=π21
vwave=4*f*d=4*105*109*500*10-6=2.1*108m/s(a) Imag( Z11) vs. Frequency(b) Simulation CircuitFigure 2: Second Case2Problem
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