Transmission Line Elements on Smith Chart Web App

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I've successfully added transmission line elements to the Smith Chart matching web app here on These include series, shorted shunt section, and open shunt section. There's a trick you can use to have these transmission line elements use an arbitrary characteristic impedance. The elements adopt the same characteristic impedance as the chart normalization impedance (default is 50 Ohms). So, if you change the Chart normalization impedance to the value you would like to use for your transmission line section, then add whichever transmission line element you want, it will be added with that characteristic impedance. You can then change the chart impedance back to whatever it was beforehand and the transmission line elements will remain unchanged.

The series transmission line drawing routine has been improved and tracks the mouse input more smoothly now. If the characteristic impedance of the series transmission line is the same as the chart impedance, then the arc that is drawn simply rotates around the center of the chart, which is pretty easy to code. However, if the impedance of the line is not the same as the chart, then figuring out the center of the circle that it traces out is much more complicated.

In the olden days of paper charts, to use a series line with a different impedance, you would have to read off the impedance of your termination or network at the point where you are about to insert the line. Then switch to another Smith Chart that you normalize to the impedance of the line and plot the impedance there. Then you could add the line length, which would now rotate about the center of the chart by a certain number of degrees, where you could read off the new impedance, which you could transfer back to the first chart and continue matching. I'm frankly not sure if this was a technique that was used, or more likely there were tricks to get around this hassle (i.e. Only using a 1/4 wavelength transformer, etc.).

Nonetheless a variation of this approach is used to find the center of the circle for arbitrary impedance series transmission lines, and it works more smoothly than the routine that was used in the old Java version. Now that transmission line elements are included, the old Java applet version can be retired and the web app can be used in its place.

Have fun making matching networks with transmission lines!