[Lowfer] loop shape

[John Andrews]

Dave,

A few additional thoughts:

1. The radiation resistance formula you gave provides similar results to the
one presented by Kraus (and derived by Andrew Alford). For a 185 kHz square
loop 50 feet on a side, I get about 250 uOhm, neglecting the ground. You may
want to check my math.

2. Your analysis is correct for the lossless condition, but develops some
significant errors in the real world. Consider the above loop, made with
RG-8. The RF resistance of the 200 foot conductor is 0.38 ohms. Bill
Ashlock's experimental work in determining the equivalent ground loss
resistance gives an average of about 0.28 ohms for such a loop with the
bottom conductor 6 feet above the ground. This predicts a feedpoint
resistance of:
0.38 + 0.28 + .00025 = 0.66 ohms. Assuming 1 watt and lossless coupling (we
come very close in practice), that gives an antenna current of 1.23 Amp. The
sobering thought at this point is that you will radiate 380 microwatts.

3. Now consider adding a second conductor for a 2-turn loop. As you say, you
gain 6 dB, but you have to subtract 3 dB for the extra conductor and ground
loss, so the net gain is 3 dB (for the E or H far-field). BTW - I have no
data here on spacing of turns. Perhaps Bill can weigh in on that.

4. On the other hand, your lossless scenario is closer if you string that
same 400 feet of wire into a 100 by 100 foot loop. In that case, you gain 12
dB from area, and lose the same 3 dB in loss, for a gain of 9 dB. That's not
an exact figure, as Bill's research on ground losses has been confined to
the 50 foot square loops.

John Andrews, W1TAG