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How to calculate impedance from 2port Sparameters

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GGAPBE96

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According to some reference books,impedance can be calculated by the following equations.

Z1 = (1+S11)*Z0/(1-S11)
Z2 = 2Z0*(1/S21-1)

where,S11 and S21 are Sparameters and Z0 is the characteristic impedance (50Ohm).

I simulate a resonator and plot Z1,Z2,but Z2 seems to be strange.
(There is no resonance point)

Why are the two impedance different ??
 

This equations are valid only if you have the circuit properly matched to the terminations (here 50ohm).

Do you really have a 50ohm characteristic impedance it this one?
 

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