Dear John, LF Group,

In principle, either method ought to work. To relate the current in the
"sensing" loop to the induced EMF (and therefore the flux) in the main loop,
you need to know the mutual inductance M brtween the loops. Then the induced
EMF is 2*pi*f*M*I, where I is the current in the sensing loop.

 In principle, this is easier if the sensing loop is a turn added to the
main winding, since then the coupling factor k will be close to 1, and M =
k*sqrt (L1*L2) where L1 and L2 are the inductances of the main and sensing
loops. So if you know or can measure the loop inductances, you can calculate
M. k will only be close to 1 if the turns of the main winding are not spaced
apart too much.

Using a smaller sensing loop has the advantage that it will have very little
effect on the performance of the main loop. If the sense loop is a seperate
smaller loop, you need to find the right formula to calculate M from the
geometry of the loops. I have the re-print of Grover's "Inductance
Calculations" (keep it on the bedside table...) which contains vast numbers
of tables and formulae for different cases - I could probably find the
appropriate calculation for you. It seems to be easiest to do this
calculation if the loops are co-axial, co-planar and the same shape, so bear
this in mind when designing the sensing loop!

Alternatively, you could measure M by injecting a known current into the
sensing loop and measuring the induced voltage in the main loop, e.g. with a
selective voltmeter. This probably needs to be done at a relatively low
frequency (VLF) in order to avoid the effects of the impedance and
distributed capacitance of the multi-turn winding. The same applies to
measuring the inductances; also if the sense loop is part of the main
winding it will probably affect the tuning for the same reason - care would
be needed to ensure the effect was the same when calibrating and in normal
use.

Methods that I have tried include comparing the loop output on a strong
signal (e.g. DCF39) with a small single turn loop, and using Helmholz coil
set-ups to produce a known magnetic field strength (only really practical
for small loops!)

I have used mainly single-turn loops for FS measurement, partly to avoid the
distributed capacity issues - I have found a good technique is to use a
"current transformer" to induce a known loop EMF. This can be a small
ferrite toroidal transformer with, say, 20 or 50 turns or some convenient
number that gives a high reactance, connected to a sig gen. The loop
conductor passes through the core to form a single turn secondary. The
secondary impedance is so low it doesn't significantly affect the loop, and
the induced EMF is just the sig gen output divided by the turns ratio. I
usually find this gives a result within a dB or so of other methods. With
all these measurements, you have to take care that errors are not caused by
stray coupling and ground loops between sig gen and receiver, or between the
loop antenna and other antennas or long bits of wire.

Cheers, Jim Moritz
73 de M0BMU