Paul Keinanen wrote:
. . .
When the antenna size is below perhaps 1/10 wavelength, the radiation
resistance drops by the square of frequency, so the radiation
resistance can quite easily be well below 1 ohm at LF and below. The
loss resistance (include grounding and loading coil losses) can be
several ohms, thus the majority of the generator power is dissipated
in the losses and only a very small part is actually radiated by the
very small radiation resistance.
. . .

Neglecting ground effects, the radiation resistance of a four-sided loop
100 meters on a side at 100 kHz is 45 milliohms. The radiation
resistance of a four-sided loop 10 meters on a side at 10 kHz is about
400 picoohms (4 X 10^-10 ohms). If you used 2 mm diameter wire to
construct the loops, the first would have an efficiency of 0.7%, and the
second of 0.00000016 percent. These are very optimistic, since they
don't account for the considerable loss you'd incur by induction into
the ground and objects for quite some distance around. They also don't
account for losses in the required impedance matching network. And a
receiving antenna would have the same efficiency.

You can easily get these numbers with the free EZNEC demo program from
http://eznec.com. Or use a calculator and the simple equations you'll
find in any antenna text.

The OP wondered if anybody had ever thought of this before. The answer
is yes, the first time probably well over a hundred years ago. Anyone
doing the simple calculations sees immediately why it's not a great idea.

Roy Lewallen, W7EL