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Measuring Differential Impedances with a Two-Port Network Analyzer

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pancho_hideboo

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I think differential Impedances, Zd can be calculated by the following.
Code:
Gamma_d = (S11-S12-S21+S22)/2
Zd = 2*R0 * (1+Gamma_d)/(1-Gamma_d)

However, I found different equation in https://www.maximintegrated.com/en/app-notes/index.mvp/id/915
Code:
Gamma_d = {(2*S11-S21)*(1-S22-S12) + (1-S11-S21)*(1+S22-2*S12)} / {(2-S21)*(1-S22-S12) + (1-S11-S21)*(1+S22)}

Zd = R0 * (1+Gamma_d)/(1-Gamma_d)
I can not understand how to derive this equation.

How can I derive this equation ?
 
Last edited:

This is what I use: Zdiff = Z(1,1) – Z(1,2) – Z(2,1) + Z(2,2)
 

This is what I use: Zdiff = Z(1,1) - Z(1,2) - Z(2,1) + Z(2,2)
Thanks for response.

"z11 + z22 - z12 - z21" gives an impedance at floating drive where "current of port1" is equal to "-current of port2".

On the other hand, Sdd by Vector Network Analyzer gives "(s11 - s12 - s21 + s22)/2"
In this case, Zdiff=(z11-z12-z21-2*z12*z21+z22+2*z11*z22) / (2+z11+z12+z21+z22).
This is not floating drive.
https://www.designers-guide.org/Forum/YaBB.pl?num=1205240723#9

Which value should I adopt as differential impedance ?
https://www.edaboard.com/showthread.php?t=365152
 

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