So I've been trying to design a matching network for a VHF mosfet. The problem that I am encountering is that I can find many calculators and formulas for making matching networks online, however, they all require you to know the source and load impedance. I know I want to match the transistor to 50ohms, but I don't know how to determine what the source impedance of the device is. In the datasheet, they give s-parameters, but I don't know how I can turn these s-parameters into some source ohms so I can use the formulas to calculate matching.

So my question is what do I do to find the impedance given s-parameters? I'm not even sure if that's all the data I need to calculate it. Do I need more than that?

Please explain to me clearly and simply because I've never done this before and I'm not entirely sure what I'm doing.

Thanks!

 

Normally what you would do in practice is use a network analyzer to characterize several devices of the type you intend to use. That way you can design the network to cover a range of known device parameters. Given that a network analyzer with an s-parameter test set costs about the same amount of money as a beachfront condo on S. Atlantic Ave. in Daytona Beach Shores, I recommend that you dig out your textbook and really try to understand what the s-parameters are telling you.

For example S11 will give you the input return loss in dB:

\(\text RL_{in} \math \;=\; 10log_{10}|\frac{1}{S_{11}^2}|\;=\;-20log_{10}|S_{11}|\)

-40 dB of return loss would represent a pretty good match.

If you don't have a textbook, you can always try the wiki:
https://en.wikipedia.org/wiki/Scattering_parameters

 

So I've been trying to design a matching network for a VHF mosfet. The problem that I am encountering is that I can find many calculators and formulas for making matching networks online, however, they all require you to know the source and load impedance. I know I want to match the transistor to 50ohms, but I don't know how to determine what the source impedance of the device is. In the datasheet, they give s-parameters, but I don't know how I can turn these s-parameters into some source ohms so I can use the formulas to calculate matching.

So my question is what do I do to find the impedance given s-parameters? I'm not even sure if that's all the data I need to calculate it. Do I need more than that?

Please explain to me clearly and simply because I've never done this before and I'm not entirely sure what I'm doing.

Thanks!

The easiest way to translate from S-Parameters to impedances in rectangular form is to plot S11 and S22 on a Smith Chart if your computer program will not do it for you.

Example: S22: Mag= 0.80 Angle = 100 degrees.

The circular perimeter of the chart graph is the 'Unit Circle' ie it has a value of '1'. Since printed charts vary in dimension you need to measure the distance from the center of the Smith Chart (The nomralised point labeled '1.0') to the edge of the chart. If your chart measured 40 mm from the center point '1.0' to the edge of the circle then you would plot you line from the center of the Smith Chart to a distance of 32 mm. Locate on the edge of the chart the value of the angle from the above posted Example value and line up a straight rule from the Chart Center to the tick mark on the edge of the Circle where you find 100 degrees. Then using your scale measure 32 mm from the Chart Center along the line you drew (vector) and place a dot at 32 mm from the Chart Center. Where the dot is located on the vector line you drew is the impedance in rectangular form (Re) ohms + (Im) ohms. Another form that may be more familiar is X Ohms = jY Ohms.

Do not construe or confuse the Smith Chart 1.0 ohm normalised Chart Center with the Unit Circle Value of 1. They are two different animals. Also if you have not been warned do not try to plot S21 or S12 on the Smith Chart. The Polar Chart is the appropriate medium to use for those two values.

RF Circuit Design by Chris Boswick provides sort of a cookbook approach to the use of Scattering Parameters and includes examples. However it is reported there are errors in the book and one needs to locate an addendum. I believe I found one of those errors as all calculations went fine including Stability Factor, Ds calculation, conjugate input matching impedance but no matter how I try to figure out the output matching network value I keep calculating the same value but different than the example.

I believe your plan is to simply determine the input and output impedance of the active device and build simple matching networks. While that is one approach ignoring the stability calculations is a good way to realize an oscillator when you want an amp. The calculations seem tedious but if you plug them into an Excel spreadsheet things clear up pretty fast.

Lastly you can check the following link for a site which has an online spreadsheet where you can plug in the S Parameter values and voila, it pumps out data needed for building your amp. Links are displayed below:

https://www.microwaves101.com/encyclopedias/s-parameter-utilities-spreadsheet#smith

The site provides good skinny on calculating some limited device values using only the Magnitude component of the parameter.

 

It is always helpful to periodically practice converting complex numbers from rectangular form to polar form and back again. That way you wont lose sight of what you are dealing with. When some function of an s-parameter represents a complex impedance or admittance then the magnitude of the complex number has units of ohms or siemens(aka mhos). What they give you directly is reflection coefficient (S11 & S22) and voltage gain (S21 & S12).

You might gain some insight from the following article:
https://www.maximintegrated.com/en/app-notes/index.mvp/id/2866

 

Incidentally, this is a link to download the 2nd edition of RF Circuit Design by Chris Boswick

 

Incidentally, this is a link to download the 2nd edition of RF Circuit Design by Chris Boswick

Thank you for the link to the pdf. As it turned out, upon revisiting the problem on page 129 in the first edition there was no error. Specifically when calculating the input load polar values the angle kept coming up -18 degrees using a handheld calculator and the arctangent function in Excel’s spreadsheet. It turns out that the arctangent for -18 or 162 degrees is the same. If using a calculator one needs to note the quadrant the resulting value occurs in so the correct angle can be chosen. In Excel the function ‘ATAN2’ is available and once both the real component is fed into the function with the reactive part the correct angle of 162 degrees is returned. My apology to Mr Bowick.