I finally took the time to do some modeling using EZNEC v4 of a loop
I'm going to build. I used the loop facility in EZNECv4 to construct a
circular loop approximated by 32 linear pieces each of a single
segment. I placed a lossless 23.2pf capacitor (series RLC with R,L as
shorts) in the center of the topmost segment. The "wire size" for this
portion was 0.875" corresponding to the 3/4" soft copper I'm using. The
loop size was 5.25ft in diameter just short of a 1/4 wave at 20M.

I then constructed a 1/5 diameter loop of #12 copper and placed it
within 0.1ft of the outer loop at the bottom.

The base of the whole assembly was placed 10ft above a medium ground.

The results were consistent with most of the calculators found on the
web. The loop resonated at 14.02Mhz with a SWR around 1.1. The size of
the coupling loop needed to be reduced a bit from the 1/5 diameter.
EZNEC has a nice facility for changing the loop sizes to make this
easy.

The far field pattern was better than I had expected. The gain at
around 25° was just short of 4dBi and the side lobe was down 12dB.
Written descriptions I have read led me to believe that a 1/4wave loop
would have poorer sidelobes than that. I had not expected to see 4dBi
either which compares favorably to a dipole.

Much more puzzling however was the performance at 40M. I changed the
tuning capacitor to 110pf and swept the SWR around 7Mhz. Min SWR was in
the right frequency range but around 3, too high but fixable with the
coupling loop. More disappointing however was the farfield pattern.
Probably due to the fact that it is now half the height above ground in
fractional wavelengths the antenna is much more of a cloud warmer. This
increased upward radiation comes at the expense of directional gain and
the sidelobes minima while still present are nearly at ground level
providing little suppression to incoming waves at "normal heights. The
pattern is basically that of a dome.

The reason that this bothers me is that descriptions of small loops
suggest that as the loop size approaches 0.1wavelength the pattern
directional performance improves rather than degrades. At 7Mhz this
loop is an 1/8 wave and I would think would show improvement.

Any ideas?

jim

Talking to myself...

Did a bit more modeling to get rid of the segmentation check warning
about the coupling loop having segments too small on 40M. I had to
change down to an octal loop for the coupling loop to give me wiggle
room on the loop size.

I found that playing with coupling loop diameter and placement distance
from the bottom loop interacted and changed the coupling loop impedence
presented to the source. In general lowering the loop will make it more
capacitive and lower the resistive portion. Making the loop smaller
raises the resistive portion and raises the capacitance as well. So I
moved it up until the reactance got pretty small then fiddled with the
size until the resistance approached 50ohms then moved it up or down to
again reduce the reactance. Lots of fiddling. I suspect that indicates
a similar level of sensitivity to size and placement in the real world
as well.

After playing a bit I got the SWR down to 1.3 or so.

Retuning the capacitor back to the 23pf and retesting at 20M shows a
reasonable match (1.2) there as well.

So it seems that a likely approach for tuning the match loop would be
to do it on 40M then test at 20M where it appears to be a bit less
critical.