I've been doing more work on the low frequency tuned loop antenna and
have two problems. One is that I can't find any info on how effective
the antenna will be in relation to the design parameters. That would be
the diameter of the loop, the number of turns and the spacing of the
turns. From the formulas I find for inductance, I would guess that the
spacing of the turns will want to be as small as possible, but I'm not
sure the factors that optimize self inductance are the same as what will
optimize antenna effectiveness.

What equations determine the signal strength from a low frequency tuned
loop antenna?

The other problem is finding an accurate formula for the inductance of
this design. I've found a number of equations for coil inductance, but
most are for coils with length longer than diameter. One I found
doesn't say what it's limitations are and doesn't agree with the others.
In fact, I can't find two formulas that approximate each other over
the range of interest which is 1 to 20 turns or d/l from 4 on up.

I've consulted the Radiotron Designer's Guide, Nagaoka's and Lundin's
papers on inductance of coils as well as a number of web pages. I'm
getting tired of looking... Is there a reasonable formula for
calculating the inductance of a short coil that works for a number of
turns from 1 to 20?

Rick

Just to give an update...

I got a response from Randy Yates in the comp.dsp group who gave me a
formula for the loop antenna signal strength which I'm including below
for reference. He said it came from the ARRL Handbook.

They dedicate an entire chapter (5) to loop antennas. Equation one
is the voltage at the loop terminals:

V = (2 * pi * A * N * E * cos(theta)) / lambda,

where

A = area of loop, in m^2
N = number of turns in loop
E = RF field strength in V/m
theta = angle between plane of the loop and the signal source
lambda = wavelength in meters.

Note that I know nothing about antennas - just acting as a scribe...
This is the expression for an untuned antenna. Shortly after this, they
provide the equation for a tuned antenna, which is identical except for
the addition of a Q in the numerator.
-- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com

I did the calculations and at 100 uV/m with 50 foot of coax in a two
turn loop I get a bit over 1 uV, not so good. I'm going to see what I
can find about the signal level from ferrite cores. I had the
impression they would be lower, but I seem to recall better numbers than
this in the ones I've seen before.

Rick