Playing with S-parameters and the Smith chart in Qucs



I'm not an EE graduate, but practical electronics has always been my hobby (albeit typically on the back burner) and I also happen to wade into antenna and RF technology on my job every now and then. On a recent encounter with WiFi antennas and directional couplers, as I was simulating some stuff in Qucs, I came across the S-parameters and the Smith chart (once again). I got intrigued, because this stuff seemd related to my "research into directional couplers". (Well... not all that useful, as I later concluded, but anyway.)

I felt I had to "start from someplace in the middle", as I didn't have enough of a maths background to start "properly from the ground up".
I started out by spending some time reading primers on the
S-parameters and the Smith chart (kudos to what variables are on each axis, why the grid is curved, the distinction between the impedance vs. admittance version of the Smith chart. I was wondering what some typical circuits looked like in the Smith chart - and the interwebs provided surprisingly few answers. That's when I started to squint back at Qucs: "Oh wait... I can sketch some circuits in Qucs. And, Qucs contains some Smith charts in the graphing tabs. Now how do I go about this, does it actually work? I could then try fiddling with some component values to see the effect of my changes..."

The current version of Qucs (0.0.19 RC as of this writing) turns out to be an excellent educational toy when it comes to S-parameters and the Smith chart.

Essentially, you need a "power source" for each port of your circuit. This component looks like a voltage source with a series resistor in one package. Next, you need an "S-parameter simulation". This will automatically set up the matrix of N by N ports. Once you compute the simulation, in the graphing tab you can select the two versions of the Smith chart, or a "cartesian" Bode plot. You will be offered the S-matrix members for use in your charts/plots.


The following is an LC circuit, coupled by two different series resistors to two different power sources. Note the resulting shape on the Smith chart, the differences and similarities between the impedance and admittance version of the Smith chart, and the differences vs. similarities among the various S-parameters.
I've taken screenshots of two, slightly different versions of the schematic: the difference is in the L and C values, both versions resonate at 50 MHz, but each one with a different Q. Note how this affects the shape of the Bode plot and the "spacing of nodes" in the Smith chart :-)

Schematic with a higher impedance resonator (lower Q)

Charts with a higher impedance resonator (lower Q)
Impedance chart on the left, admittance chart on the right

Schematic with a lower impedance resonator (higher Q)

Charts with a lower impedance resonator (higher Q)
Impedance chart on the left, admittance chart on the right

Note: speaking of Q, this is affected by the resistors in the schematic. The resonant cell itself consists of ideal L and C, but the resistance from the signal sources (and also the one intrinsic to the signal sources) plays a role in the Q.
Try playing with the values yourselfs (
data download follows below).

Lessons learned

I have an itching to summarize, in lay man terms, some of the stuff I've gleaned from all the tutorials I've read. Stuff that has some practical use, without you knowing all the background maths by heart. As a consequence, some of my statements below are likely incorrect :-) or need to be further qualified by conditions.
Use with a grain of salt.

Example Qucs data

My experiments in Qucs have resulted in some trivial example circuits and simulations = a Qucs project directory containing some ready files. Have them :-) and use them as a basis for your own tweaks/experiments.


Qucs project homepage

Microwaves101 on S-parameters

Wikipedia on S-Parameters

Wikipedia on Admittance (and its relationship to Impedance)

Microwaves101 on the Smith chart, including a "nomogram trick" to calculate a matching compensation TML stub

Wikipedia on the Smith chart

Wikipedia's Smith chart (a beautiful vector image in SVG format)

By: Frank Rysanek [ rysanek AT fccps DOT cz ] in January 2017