Technical Note:

Exploring the secrets of the Smith chart* - an indispensable tool

Copyright 1997 Chris Scott

Note: Real Smith charts and related items are available from Analog Instruments Company, P.O. Box 808, New Providence, NJ 07974. Their telephone number is (908)-464-4214.

An article appeared in the January, 1939 issue of Electronics that changed forever the way radio engineers think about transmission lines. Phil Smith devised an extraordinarily clever circular chart that revealed graphically the complex impedance anywhere along a line. The chart also functioned as a units converter. No math and minimum fuss. There's a marvelous symmetry in it's design - everything fits together neatly. So ingenious was his invention that it has been the standard of the industry - for over fifty years.

If you're a Radio Engineer wannabee, you need to understand transmission lines. It's impossible to really understand transmitters and antennas without understanding lines. Using the Smith chart is far easier than the really understanding the math. The chart gives you a way to think about impedance matching and line loss. You will have a clear understanding of VSWR - a very misunderstood subject.

This note is not really a chart primer. I will just touch on some key elements. You must spend the three hours with one of the excellent tutorials available. One good one is chapter 28 of the ARRL antenna book, available from arrl.org. A very simple program is available from the same organization called MicroSmith; it presents a Smith representation of simple matching networks, and allows you to play "what if" with the component values. The Motorola software available here for free is similar, oriented toward RF amplifier impedance matching.

Let's discuss just a few things to get you started. The center of the chart is always a perfect match. This normally represents fifty ohms, but can be any impedance line you want- it's normalized to 1.0 units. Everything is scaled relative to whatever unit you pick. The nature of impedance is that of a real or resistive portion, and an imaginary, or reactive portion, combined Pythagorean style.

VSWR, or voltage standing wave RATIO, is depicted as a circle around the chart, once around is a half wavelength. The smaller this circle is, the lower the VSWR, the better the impedance match. Understanding this alone will prove that VSWR does indeed not change with varying lengths of transmission line but the reactive / resistive ratios do. Line loss reduces VSWR- by swamping it with a resistive component. This too is covered by the chart.

The last items I'll mention are the "goalposts" - four of them spaced ninety degrees graphically and 45 degrees electrically apart. Two goalposts are resistive, one a short and the other an open. These are the left and right respective sides. The top and bottom posts are reactive, either inductive, or capacitive. Every point in between represents the various combinations resulting from a mismatched condition, and shows what will be required to form the conjugate matching circuit.

Pretty neat eh? The files available below should be of interest.

Files:

Motorola's matching program download (96K .zip)

And now for the chart - not really Smith, but very nice download (250K .gif)

This flavor is Postscript - great programming download (24K .ps)


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