art,

Wideband antennas already are available with no need for the "tank
circuit/equilibrium" concepts, design methods and limited band segments you
think must apply.

The link below describes one: a commercial HF antenna that has essentially
the same radiation pattern from 2-30 MHz with an SWR less than 2.5:1 without
a tuner, and is nearly 100% efficient throughout that range.

Not too usable for most hams, but that will be due to economic and real
estate issues, not to the (real) laws of physics.

http://www.antenna.be/tci-501.pdf

RF