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

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?

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 ZL 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 ZL 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.

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 Zin 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.

• +1 thanks. I always wait a bit before accepting. What additional info is than actually in the S<sub>21</sub> parameter, because I always see S<sub>11</sub> and S<sub>21</sub> used when deriving Z in an RLCG circuit, for instance jap.aip.org/resource/1/japiau/v95/i11/p7034_s1 Complex permeability is derived from real and imaginary Z here. According to your answer it would be sufficient to measure S<sub>11</sub>? S<sub>21</sub> basically carries some kind of physical absorption in the complex impedance load? But do some people use it for determining complex Z because they only Commented Jun 4, 2013 at 20:07
• know this more complicated mathematical method from 2 port network or is there additional info in S21? Basically S11 and S21 are linked, as reflection + transmission must equal 1... so intuitively I agree with you :) Commented Jun 4, 2013 at 20:09
• S21 tells you about transmission. S11 tells you about reflection. They measure different things and one doesn't have more information than the other. But it happens that S11 is enough to tell you about the input impedance (Z11 or v1 / i1). If you need a full 2-port Z-parameter model (all four Z-parameters), you will have to measure all four S-parameters. Commented Jun 4, 2013 at 21:53
• I found a website that has some formulas for converting between S- and Z-parameters. rfcafe.com/references/electrical/s-h-y-z.htm Unfortunately it tells how to convert Z-parameters to S-parameters but not the other way around --- you'll need to do a bunch of algebra to invert the formulas. Commented Jun 4, 2013 at 21:54
• Here's another link that gives (I think) all the conversions between S, Z, Y, T, and ABCD matrices: electron.frba.utn.edu.ar/~jcecconi/Bibliografia/… Commented Jun 4, 2013 at 21:58