Tony,

The key to improving the loop is to
-increase the induced voltage; and / or to
-improve its efficiency.

Increasing the induced voltage means increasing the size of the loop.
With a small loop, doubling the size of the side will win nearly 6dB of
induced voltage, but it also increases the inductance of the loop which
might degrade impedance matching and defeat most of the increased induced
voltage.

Improving the efficiency means addressing conductor / transmission line
losses and better impedance matching. Most of the 50 some dB of loss is
attributable to impedance matching.

I expressed surprise at the shunt tuning capacitor in an earlier posting.
I know it is a popular circuit, and it features in the ARRL Antenna
Handbook, but that doesn't make it a good circuit. Try the variable
capacitor in series with the coax inner conductor, you should improve the
gain by around 20dB.

Then try a shunt capacitor on the receiver side of the variable
capacitor, start with 1000pF, you should see further improvement in gain
but with a narrower bandwidth.

This is not a new circuit, you will find it in books, certainly at least
where the tuning / matching network is right at the loop gap. The
relocation of the capacitors by a length of transmission line does change
things a little, and it is more complicated to solve, but behaviour is
soemwhat similar.

Should you try this, your findings would be interesting.

The mathematically based approach might not be popular, and I am no
mathemetician, but the approach does reveal why the antenna is
inadequate, and suggests what can be done to improve it.

Owen