From Dave G3YMC
Further to the discussion on loop inductance and various related matters, a
couple of
weeks ago Mike Underhill G3LHZ gave a talk at our Bracknell Amateur Radio Club
on
loops. Some of you may remember the similar lecture he gave at the HF
Convention a
couple of years ago. Mike has done a lot of work with loops, mainly 1-2m
diameter
ones on the hf bands, and probably knows more about them than anybody. Some of
his
theories are also rather contoversial, but they are all based on practical
results.
In subsequent mails with Mike he has supplied some of the formulae he uses in
his
design of loops.
Inductance of a circular loop L(microHenries) = pi D^1.16 / (160d)^0.16
where D is the loop diameter in metres and d is the diameter of the conductor
wire in
metres.
This can be extended to non circular loops ie rectangular ones if D is
calculated as
the loop circumference (ie length of wire) divided by pi. The ^ symbol in the
formula means 'raised to the power of'. This formula gives a value of 75uH for
my
loop (measured value 70uH).
Another interesting formula he uses is:
Q = 500/D
as a limiting value of the Q of a loop, and where D is the diameter in metres as
above. This is the value of Q if the other losses, ie series R, are negligible.
This relates to a Q of 35 for my own loop (effective D 14.3m). This shows that
there
is a limit to how far you can improve a loop by reducing the resistance, though
I
feel it is rather pessimistic in my case.
Even more bizarre is his formula for radiation resistance:
R(looprad) ~ = LoopArea * f (MHz) / 20.
When I put the figures in for my loop I got a value of 0.68 ohms, implying 50%
effiency (and hence rather over 1W erp!). But in fact Mike says you have to
include
the earth loss resistance in calculating the efficiency with this formula - for
my
very lossy 300 ohms ground it brings the efficiency down to 0.22%, a rather more
plausible figure. But it throws out of the window the theory that you can
largely
ignore earth resistance losses....
Not sure what to make of these figures, but they are food for thought and may
help.
Dave G3YMC
[email protected]
[email protected]
http://www.dsergeant.btinternet.co.uk
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