Dale Parfitt wrote:

In addition to the end Z varying radically with frequency, you will also

find the classic 9:1 toroidal transformer only functions as a 9:1 over a
relatively narrow frequency range- whereas a binocular core will behave as a
9:1 over almost 2 decades. Somewhere here I have a network analyzer plot
comparing a toroidal vs binocular transformer.

It depends a lot on the size of the transformer. You can get two decades
from a tiny one made with a TV balun toroid. One trick is to keep the
total length of wire in the transformer below about 5% of a wavelength
at the highest frequency of interest.

The antenna's Z does indeed vary a great deal, from 10's to 1000's of
ohms. If you plot it in the complex plane, it makes a spiral centered at
the antenna's *characteristic* Z, which for an inverted L is generally
in the range of 300-700 ohms. Matching to an impedance near the center
of the spiral yields a system that is not perfectly matched at any
frequency, but is adequately matched over a wide range of frequencies.

-jpd