Cecil Moore wrote:
I have previously presented my thoughts about the
similarity between dual-Z0 stubs and base-loaded
mobile antennas. Here is an article on the subject
of "Dual-Z0 Stubs" that is directly applicable
to base-loaded mobile antennas.

If we can shorten a stub by using two Z0s, why
can't we shorten an antenna by using two Z0s?

http://www.w5dxp.com/shrtstub.htm

Congratulations, Cecil, you've just re-invented the electrical
analog of the Helmholtz resonator. Your analysis would be a lot
simpler if you'd first characterized each stub with T parameters
and then multiplied them together to get a two port you could use
to find the conditions for the resonance of the entire stub. You
could then use the differential calculus to find out what the
criteria was for the shortest overall stub. (It's true, both lengths
have to be the same.) If you want to take a stab at using your
discovery to deal with antennas, why don't you use two "dual Z0
stubs together to make a folded dipole. You could even do that in
EZNEC. Applying this to your favorite loaded dipole is a stretch,
but that probably won't stop you from trying.
73,
Tom Donaly, KA6RUH

(P.S. Where did you learn about "dual Z0" stubs?)