# Impedance mathing and Smith charts

#### mojo_risin

Joined Jul 3, 2013
35
Hello

I have a homework which involves impedance matching using Smith charts. I have made an attempt to solve the problems, and actually I think I got them right. However, this has happened many times before and I have learned to double check everything. So I would like to post my problem and solution here and let people who are more experienced take a look and tell me if I am on the right track.

The task is to match two FET amplifiers. The schematic is here: FET A Input matching: The input needs to see impedance equal to Γopt and is driven by a generator with 50 Ω impedance. The input of the FET needs to be matched using a quarter-wave transformer (QWT) and a piece ot transmission line (TL).
My solution: I have plotted Γopt on a Smith chart and assume the center of the chart is where the load Z lies; everything is normalized to 50 Ω. Next, I have rotated the impedance corresponding to Γopt towards a constant VSWR circle towards the load (which is plotted at the center). The VSWR circle intersects the horizontal line after a length of 0.112 λ at point B. Impedance at point B is 0.315 * 50 = 15.75 Ω unnormalized. To go from point A to B, a QWT is used; its impedance is equal to ZT=√(50*15.75) = 28 Ω. Here is the Smith chart: FET A Output matching: The circuit shows the S values which need to be used. The input of FET B has S22 = 0.75∠-140° and needs to be matched to the input of FET A which has S11 = 0.5∠-70°. Method is TL + open-circuited stub.
My solution: Plot point A* = complex conjugate of the source impedance; point B is the load impedance. Rotate point B towards the generator A* on a constant VSWR circle to point C. This corresponds to adding a length of TL. Point C has the same conductance as point A*. Next, add an open-circuit stub with susceptance equal to the opposite of point C.
Here is the Smith chart: The last thing to to is match the 50 Ω load to the output of FET B. I think I could not go wrong on this one, but anyway. I plot point B*, which is the complex conjugate of the S22 parameter of the amplifier, and plot the 50 Ω load at the center. I rotate point B* towards the load on a constant VSWR circle, which corresponds to adding a length of TL, until it intersects the circle with admittance = 1 at point A. The susceptance of point A is -j0.95 mho, so I add an open-circuit stub with susceptance +0.95 mho. Here's the chart (for some reason it is rotated): Well, that's it. I hope I got everything right. If not, please point out my errors. Thanks for reading.[/plain]