I have cause to convert some Z parameters to S parameters and vice versa. Here is the conversion for \$Z_{11}\$;

$$Z_{11} = {((1 + S_{11}) (1 - S_{22}) + S_{12} S_{21}) \over \Delta_S} Z_0$$


$$\Delta_S = (1 - S_{11}) (1 - S_{22}) - S_{12} S_{21}.$$

I thought I'd start nice and simple with an ideal short transmission line of impedance \$Z_0\$. Now \$S_{11}=0\$, \$S_{21}=1\$, \$S_{12}=1\$ and \$S_{22}=0\$. Therefore \$\Delta_S=0\$, so \$Z_{11}\$ diverges (as do the other Z parameters) and something has gone wrong somewhere.

Where have I messed up?


1 Answer 1


You didn't mess up.

\$Z_{11}\$ is the input impedance when the other port is terminated with an open circuit.

Since your device is just a bit of wire, it has infinite input impedance when the other end is not connected to anything, and thus infinite \$Z_{11}\$.

This is an example of why we need different two port representations (S-parameters, Y-parameters, Z-parameters, H-parameters). There's certain devices that can't be represented in any particular representation.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.