Hello group,
thanks to all who replied to my request, either direct or via the reflector.
The result is a nice collection of formulas, both for round as for square
single turn loops (3 formulas for round loops and 3 for square loops).
Apart from the very simple formula that was given by RA9MB all other
formulas were based on the natural logaritm of the loop circumreference vs.
wire diameter ratio, but all with other dimensions.
And surprisingly (or not so surprisingly ?) ... after converting everything
to a circumreference in meter and wire diameter in mm all 3 formulas were
very similar (only few % difference). So either several people came to the
same result independently from each other or all formulas were derived from
the same 'mother of all formulas" for loop inductance.
Anyway, for those interested :
Round loop : L = 0.2*W*(ln(W/d)+5.85)
Square loop : L = 0.2*W*(ln(W/d)+5.5)
L = loop inductance in uH
W = loop circumreference (perimeter) in m
d = wire diamter in mm
ln = natural logaritm
Further I found :
Octagonal loop : L = 0.2W*(ln(W/d)+5.73)
Hexagonal loop : L = 0.2W*(ln(W/d)+5.66)
Pentagonal loop : L = 0.2W*(ln(W/d)+5.59)
Triangular loop : L = 0.2W*(ln(W/d)+5.1)
(all the above for equilaterally shapes)
Rectangular triangle loop : L = 0.2W*(ln(W/d)+4.96)
Interesting constatation :
A. Round loop with 10m diameter (circumref.= 31.4m, area = 78.5m^2) = 48uH
B. differently shaped loops with same circumreference :
square = 46uH
rect. triangle = 43uH
B. diffently shaped loops with same area :
square = 53uH
rect. triangle = 61uH
So at first sight the loop inductance is more determined by the
circumreference than by the area.
So far I haven' found any formula for rectangular loops, unfortunately this
is the most common shape for big transmitting loops.
73, Rik ON7YD
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