John Ferrell wrote in
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BTW, I think my next lesson will be to understand Hairpin Matching. I
plan to start with the page on your website.

My page shows how to do it more thay why it works.

If you are interested in why it works, consider an L network to transform
a 20+j0 ohm antenna up to 50+j0. Think of a hi-pass configuration (series
C, shunt L), and find values for C and L. Understanding the L match is
essential to truly understanding the hairpin or beta match.

When you have worked that out, you will realise that you can create the
series capacitive reactance by shortening the antenna (DE) a little. Yes,
that also changes feedpoint R, but only very slowly compared to X.

The inductive reactance could be supplied by a coil, but at VHF it is
more practical to use a s/c stub (which is the hairpin).

Back to how rather than why, if you use 4NEC2 to model antennas, it
displays a parallel equivalent of the feedpoint impedance. If you shorten
the antenna so that the parallel equivalent is 50 ohms // -X (Y=1/50
+j/X), then the hairpin has to supply X (B=-j/X) to cancel the -X
(B=j/X).

Another application of the same concept is to shorten a loaded 80m mobile
whip (which has low feedpoint R) so that the parallel equivalent is 50
ohms // -X, and shunt it with an inductor of reactance X to cancel -X.

Owen