"art" wrote
... I have always stated and proved. "The radiator can be
any shape or size or angle etc.as long as it is in equilibrium
and resonant which is buried in the laws of the masters"
____________

A distinction needs to be made between the ability of a conductor of any
size/shape to efficiently produce EM fields from the r-f current flowing
along it, and the capability of the associated transmitter and transmission
line to deliver that r-f current.

A good conductor of EVERY size/shape (including even a point source) will
radiate virtually ALL the r-f power that can be made to flow into it --
which quantity equals the product of the square of the r-f current at the
feedpoint, and the resistive term of the impedance there (ie, the radiation
resistance).

If the radiating structure (antenna) is not self-resonant, there will be an
impedance mismatch between it and the transmission line connected to its
feedpoint. This means that the antenna will not accept all of the
transmitter power that could be delivered it to by the transmission line.
But whatever power does transfer into the antenna will be radiated with the
same high efficiency as if the match was perfect.

There are many examples of non-resonant (highly reactive) antenna structures
that, with proper system design, radiate a very high percentage the power
available from the transmitter. Common examples of this are the monopole
radiators used by MW AM broadcast stations -- very few of which are
self-resonant.

High radiation efficiency is achieved in these non-resonant antennas by the
use of a matching network at the antenna feedpoint, which cancels the
reactance of the monopole, and transforms the r-f resistance term there to
match the Zo of the transmission line in use.

This results in an impedance match capable of passing nearly all the power
available from the transmission line, despite the fact that the antenna
itself remains non-resonant, and without setting up high standing waves on
the transmission line.

The only significant losses.then are the attenuation of the transmission
line, the loss in the matching network, and the loss in the r-f ground
system. In normal broadcast station practice these losses are small enough
for the groundwave field at 1 km to be 90% or better of the theoretical
value for a perfect radiator of that electrical height and applied power,
over a perfect ground plane.

Bottom line (N.B. Art): antennas do not need to be resonant to perform as
very efficient radiators.

RF