Roy Lewallen wrote:

We can use the inductor as an autotransformer. If we tap up on the
inductor some fraction k of the whole way up, the impedance we'll see
at
that tap will be very nearly 1275 * k^2, and it'll be purely
resistive
(no reactance) because the impedance across the whole coil is purely
resistive. For example, half way up the coil we'll see 1275 * (.5)^2
=
1275 / 4 = 319 ohms. So to get 50 ohms, we tap up sqrt(50/1275) = 20%
of
the way up the coil.

Roy Lewallen, W7EL

Hi Roy, I'm OK with 319+j0 half way up the coil, but at 20% of the way
up I keep getting 50+j50. I did it on the Smith Chart, and on a Spice
based circuit analysis program. Too old to do this stuff by hand.
That's not a real good match for 50 ohm coax. The are other taps that
will provide a better match, but no where did I find 50+j0.
In an earlier post I stated that it looked like the real part of the
antenna impedance needed to be less than 50 ohms to get a perfect
match, using this method.
The impedance across the whole coil is not purely resistive, it is at
the 50% point. Apparently I am modeling incorrectly, or missing
something.
Gary N4AST