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How to match an antenna to 50 ohms on a Smith chart

You have measured an antenna and it is not 50 ohms. Here is how to get from that reading to two components and a part number, using a Smith chart, in about a minute.

Start with the measurement

Say a 145 MHz whip reads 25 - j40 ohms at the feedpoint. That is a real number off a real analyser: a little under half the resistance you want, and capacitive, which is what a whip cut slightly short does.

Drop an RX chip on the load slot, type 25 and -40, set the frequency to 145 MHz, and the chart puts a dot where that impedance lives: below the centre line, left of centre. The readout says VSWR 3.49. Nobody is happy with that.

Open the bare antenna in QuickSmith

What matching actually means

The centre of the chart is 50 ohms. Matching is moving the dot there, and every component you add moves it along one particular curve and no other.

That constraint is the whole game. You are not steering freely, you are changing trains at stations. The standard two element recipe is: get onto the circle that passes through the centre, then ride that circle to the middle.

Let the program find it

You do not have to work out which train. Press Auto-match to 50 Ω and QuickSmith solves it in closed form, giving every two element network that lands exactly on 50 ohms:

There are always at most four, because there are two orders (series first or shunt first) and each has two solutions. All four are exact. All four give VSWR 1.0000 at 145 MHz. So how do you choose?

Choosing between them

Not on the match, because the match is identical. On everything else.

Bandwidth is the big one, and it is not obvious from the component values. Sweeping each of those four networks and asking where VSWR crosses 2:1:

A factor of three and a half between the narrowest and the widest, from networks that are identical at the design frequency. That is worth knowing before you order parts.

Then the practical things. Does the network need to pass DC to a bias tee, or block it? Series C blocks, series L passes. Is one of the values awkward? 16.46 nH is a few turns of wire and hard to hold accurately; 71.35 nH is a comfortable chip inductor. Do you want a low pass shape, which also helps with harmonics, or a high pass one, which keeps lightning and static off the front end?

For a 2 m whip the low pass version is the usual answer: series inductor, shunt capacitor, harmonics attenuated on the way out.

Open the matched antenna in QuickSmith

Doing it by hand instead

Auto-match is quick, but the chart is where the understanding lives, and QuickSmith will coach you through it. Under the chart there is a line that reads something like:

next: series L 71.4 nH, then shunt C 22.0 pF

That is the shortest way from wherever the dot is now to the centre, and it updates as you edit. Drop a series inductor in slot 2, and as you walk its value up with the spin buttons you can watch the dot climb the constant resistance circle. When it crosses the circle through the centre, stop. Add a shunt capacitor and walk that up until the dot lands in the middle.

You can also just grab the dot and pull it. Every component puts a handle on its node, and dragging one solves backwards for the value that puts the node under your pointer. Try dragging a series part and you will find it will only go round its own circle, which is the constraint above, made physical.

Check it before you build it

A match at one frequency is easy. Confirm it is a match across the band you care about:

If the bandwidth is too narrow, you generally need a lower Q transformation, which usually means a smaller impedance jump, which usually means fixing the antenna rather than the network. A matching network can transform an impedance. It cannot make a badly resonant antenna into a good one.