How do I convert S-parameters for impedance matching?

How do I derive the Z-parameters to calculate a matching network for a device? I'm not sure what terms to even search for as I get all sorts of information I am not familiar with.

My task is to construct a matching network for the MRF1535NT1 FET from the provided S-parameters in the datasheet [PDF].

Frequency: 150MHz, |S11|:0.91 Θ:-175, |S21|:2.429 Θ:63, |S12|:0.011 Θ:-23, |S22|:0.82 Θ:-170

I started off by realizing that the given impedance data is for their already developed networks and not for the device itself so the only data I have is the S-parameters.

What I have gathered so far is that S-parameters cannot be directly converted to impedance since the ports differ from input to output impedance. [ref]

I tried out the formula given by biff44 - EDA Board

Zin = 50*(1 + S11)/(1 - S11)

Zout = 50*(1 + S22)/(1 - S22)

Where Zin and Zout are the impedances looking INTO the device. You have to multiply by 50 to convert the normalized impedance into ohms (assuming your S parameters were measured on a 50 ohm network analyzer).

However utilizing this formula I get very weird results. ~573-j598 after converting the polar form to rectangular and then performing the operation for Zin.

I'm not sure if I'm even doing this right, or if using the Z-parameters for this match will be helpful. Utilizing the Z-parameters for matching such as an L-match[4] are the only method I am aware of how to calculate. I am aware there is smith chart matching but I don't understand how to get there utilizing S-Parameters. I've tried reading some application notes such as those by Maxim, but they are a bit over my head.

The steps that I think I need to perform to make this match would be the following:

Covert S-parameters to Z domain for Zin and Zout -> Calculate L-Match given formulas in [Bowick] -> Simulate and test network in ADS.

References:

• [4] RF Circuit Design 2nd Ed. [Chris Bowick] - Chapter 4: Impedance Matching

• Suppose you take hParams, or zParams, and bury them inside the device behind phase-shifters. Then describe the 2 ports (in, out) in 2 directions (forward, reflected), thus 4 total sParams at each frequency. That is the behavior of sParams. Commented Jun 4, 2017 at 23:54
• Look at your Zin calculation again. S11 in rectangular form is roughly -0.907-j0.079. Entered into your equation for Zin is about 2.4-j2.2. By the way, that's not the general equation for Zin, but it will provide a ballpark. The datasheet impedances are probably from load-pull, intended for PA design. Commented Jun 7, 2017 at 21:19
• Calculation to get S param. to impedance is the most complicate. What I'm doing is: firts convert S to Z (and Δs) in ohms Zo), then using Z calculate Zin and Zout Commented Aug 18, 2019 at 19:57