[Lowfer] loop Rr (2-turn loop)

[Lyle Koehler]

It is easy to show that at DC, an electromagnet made from 20 turns of a
given wire size in series has exactly the same efficiency as one made from
the same 20 turns connected in parallel. The only thing that matters is the
total cross section of copper.

At radio frequencies, skin effects and proximity effects make things
somewhat more complicated, but essentially the same thing holds true.
Theoretically it doesn't make any difference whether you use two #12 turns
in series or parallel. In practice, there are a number of other
considerations. With two turns in series, the series impedance is 4 times as
high as with the turns in parallel. This reduces the effect of the resistive
losses in the loop connections, the tuning capacitor, and the matching
transformer. But the higher impedance carries a penalty if the loop is not
mounted "in the clear". A LowFER transmitting loop may have an advantage
over a vertical if there is no way to keep the antenna out of the trees.
That's because a small loop is a very low-impedance antenna compared to a
small vertical. LowFER loop experiments have shown that the tree losses are
very low for a single-turn loop. However, as you increase the number of
turns, there has to be some point at which the tree losses become a
significant factor. I don't know just when that would happen, but tree
losses may have contributed to the higher than expected resistance of Bill's
experimental two-turn loop.

Getting back to radiation resistance and its usefulness: Bill Ashlock
prefers to use the current-area product, and he is correct that this
provides a figure of merit that is useful when comparing one loop antenna to
another. Actually, it should be (current * area * turns squared) to account
for multiturn loops. If you have the same (current * area * turns squared)
product in two loops, they should radiate the same amount of power,
regardless of their size (as long as they are much smaller than a
wavelength) or shape. But what if you want to know the antenna's efficiency,
or how much power it is radiating, or how it would compare to another type
of antenna such as a vertical. Radiation resistance provides those answers.
Once you have determined Rr, either by formula or with modeling software,
it's simply application of Ohm's law. Current squared times Rr tells how
many watts are being radiated. Power radiated divided by transmitter power
gives the efficiency. For example, my vertical presently has a current of
about 200 milliamps. Modeling results tell me that the Rr of my antenna is
0.061 ohms, so the radiated power is about 2.44 milliwatts, and the
efficiency is 0.24 per cent. Maybe better than average for a LowFER antenna,
but nowhere near what the TEXAS and OK verticals used to achieve!

Lyle, K0LR