Every figure and number in the earlier notes can be checked in a tool I built, Smith Match. It runs in the browser, with nothing to install and no sign-up. This note walks through how to use it.
The layout
The Smith chart is on the left, with Schematic and Frequency response tabs below it. On the right are the Elements palette and the Settings.
Along the top is the current state:
f0 1 GHz Zin 50 + j0 Ω Target 3 + j0 Ω VSWR 1.000 RL ∞ |Γ| 0.0000Where Zin is now, and where the target is. Keeping those two in view at all times is the basic way to read it. The leading f0 is the design frequency, and the chart and all of these values are at that one frequency.
At the top right are Tour (a 9-step walkthrough that opens automatically the first time), Reset, and the language switch.
A first design — 200 Ω to 50 Ω
Let us retrace the design from the L-section note.
1. Set the load and the target
Under Settings → Impedance, set
- Load ZL: R to
200, X to0 - Target impedance Zt: R to
50, X to0 - Design frequency f0:
1 GHz
Values accept engineering notation: 1G, 1.4p, 13.8n and so on are understood. Input is committed only when you finish editing, so typing 1.35G will not briefly apply the 1 and send the design flying.
2. Add an element
Pick Shunt C from the palette. A dot appears on the chart, free to move along a constant-conductance circle.
3. Drag it
Drag the dot and it moves only along the path that element can physically produce, with the element value solved as you go. Take it to where it meets the constant-resistance circle and you are near 50 − j86.6 Ω.
Then add a Series L and drag it into the center, and the match is done. The values should come out at 1.378 pF and 13.78 nH.
If you drag in a direction the element cannot go, the tool says so and suggests an alternative. For example, pull a shunt C the wrong way and you get "That direction is unreachable — switch to Shunt L". It is built to tell you, on the spot, when the choice of element itself is wrong.
Editing from the schematic
The Schematic tab below the chart draws the design as a ladder. You can type values directly here and delete with ✕. Drag a symbol to change the order of the elements (or select it and use ← →). The same elements in a different order give a different result, so this is how you try out which way round an L-section goes.
The left end is the source side (the terminal looking into Zin); the right end is the load ZL. In practice the usual order is rough it out on the chart, then refine values in the schematic.
Looking at the response
Switch to the Frequency response tab and |S11| and |S21| are shown side by side.
One of them alone is not enough, so both are there from the start. Add a series R to a matching network and you can watch the point on the chart move toward the center while |S21| drops.
The sweep range is set under Settings → Frequency sweep. As the two-stage note says, make it a habit to widen it to two or three times the design band. A narrow sweep will not tell you what it is not showing.
Judging with spec limits
The same Frequency sweep tab is where spec limits are drawn. There are three kinds:
- Reflection — an upper limit on
|S11|(match) - Loss — a lower limit on
|S21|(insertion loss) - Attenuation — an upper limit on
|S21|(rejection)
You can have as many as you need (up to 20). "Add a limit line" adds a row, so when there are several stopbands — the second and third harmonics, say — draw one for each. Each row's type can be changed independently.
Give each one a band and a dB value, and the line on the plot is colored by whether it is met. A limit whose band lies outside the sweep is never colored as a pass — the distinction between "pass" and "cannot judge".
Out of the box there is one line of each kind, but all are disabled. A pass/fail verdict on placeholder numbers set before you have chosen f0 would mean nothing, so rewrite them to your own requirements before ticking them on.
If the design contains a Series tank / Shunt trap, its resonant frequency is drawn on the plots as a purple dashed line, so you can match a notch in |S21| to the element that causes it.
Changing what the chart shows
The button at the top left of the chart opens Chart display, where you choose what to overlay:
| Overlay | Use |
|---|---|
| Impedance grid | When working with series elements |
| Admittance grid | When working with shunt elements |
| Zin frequency locus | To see how wide the band is |
| VSWR circle | To see the margin to a spec at a glance |
| Q circle | To estimate the network Q |
The locus is especially useful. As reading the Smith chart explains, depth and width are separate questions, and the locus shows both at once. It follows along while you drag a matching element.
Note that the locus bandwidth is a separate setting from the frequency sweep. The locus is for looking around f0, the sweep for looking at the whole band; they answer different questions.
The target need not be the center
The chart reference Z0 and the target Zt are independent. With the chart normalized to 50 Ω, you can set the target to 75 Ω or to 25 − j40.
As the conjugate matching note explains, a PA output match usually does not target 50 Ω. The target is drawn as a marker away from the center, and how well the match is achieved is judged by the distance from that point.
The default target is deliberately set off center so that the difference between the two is clear from the start.
Switching the load model
Under Settings → Load ZL → Model, besides R + jX (constant vs frequency) you can choose R-L or R-C in series or in parallel.
R + jX (constant vs frequency) comes with a warning, because as an unphysical model it makes the bandwidth look wider than it really is. Keep the same design, switch only the model, and the shape of the sweep changes.
Saving designs
Designs are saved in your browser automatically. Close the tab and open it again, and you carry on where you left off.
Under Settings → Data I/O you can export and import designs as JSON. Use this to hand a design to someone, or to compare several alternatives.
Designs are stored in the browser (localStorage) and never sent to a server. The details are in the Privacy Policy.
It works on a phone too
The same screen works on a smartphone. Add it to your home screen and it launches like an app. It is perfectly usable for trying out a topology that occurs to you on the move.
Why I built it
Commercial simulators are powerful, but they are too heavy when all you want is to check which way the point moves when you add this element. A paper Smith chart, on the other hand, cannot follow the frequency response.
I wanted something in between — a tool that shows the intuition of the chart and the frequency response at the same time — so I built one. Almost everything in the earlier notes can be checked in it.