Is it possible to derive complex impedance (magnitude + phase) from VNA 1-port network?

Question

With the scattering parameters of a 2 port network I can measure reflection and transmission by a network analyzer and calculate complex impedance, via S-parameters.

Now I've heard (no source) that one can also measure amplitude and phase with a 1 port network, where we have a ac voltage source, a complex impedance in series and a load impedance of 50 Ohm at the end to terminate it on the wafer surface correctly (for example microprobes connected to coplanar waveguide terminated on-wafer). Is this possible, does this need a special kind of VNA or measurement procedure. Does this give same accuracy compared to a "normal" 2-port reflection and transmission parameters measurement?

Answer 1

If you have a one-port network, you can measure the input impedance of that network with a VNA. If you have an n-port network, you can measure the input impedance of each of the ports one at a time, by terminating the other ports with the correct impedance and considering the result as a one-port network.

Essentially you measure only S₁₁, which is also known as \$\Gamma\$, the reflection coefficient.

The reflection coefficient is related to the input impedance of the network by

\$ \Gamma = \dfrac{Z_L - Z_0}{Z_L + Z_0}\$,

where Z₀ is the system characteristic impedance and Z_L is the input impedance of the one-port that you are trying to measure.

The relationship can be reversed to get

\$ Z_L = \dfrac{1+\Gamma}{1-\Gamma}Z_0\$.

Having measured \$\Gamma\$ you can either calculate this relationship numerically, or you can estimate it graphically using a Smith chart. Your VNA can probably either display the reflection results on a Smith chart background, or actually do the conversion to impedance internally and display Z_L in polar coordinates or magnitude/phase graphs.

You can do this measurement using the standard type of VNA. In fact it is quicker to do than a 2-port measurement because you only need to do an open-short-load (3 measurements) calibration on a single port rather than the open-short-load-through (8 measurements) that you do for a two-port measurement.

Does this give same accuracy compared to a "normal" 2-port reflection and transmission parameters measurement?

This is actually the exact same measurement that the VNA is doing when it gives you the S₁₁ results as part of a 2-port measurement.

Edit in reply to your comments:

can you give me minimum example for a non-terminating circuit part after the load impedance,

To be honest I might have confused myself. When you are measuring Z-parameters, and you want to measure Z₁₁ you need to leave all of the other ports open-circuited. So if you want the Z₁₁ of your n-port circuit, you should probably measure S₁₁ with the other port open, rather than properly terminated.

But if you want to know what is the Z_in when the other port is properly terminated, you should measure S₁₁ with the other port properly terminated.

If you can't do this, then I think you need to measure all four S-parameters. But if you can measure all four S-parameters that means you can connect your VNA to the second port. Which will properly terminate that port (assuming your circuit is designed for a 50-Ohm system)...so just make that connection, but only do the S₁₁ measurement.

... that makes all 4 S necessary to measure for Z_load

Not sure what you mean here. You only need S11 to get the Zin of your circuit. You only need all four S parameters if you want to get all four Z parameters.