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Date: Mon,  8 Apr 2002 08:25:25 +0100
From: "Claudio Girardi" <in3otd@qsl.net>
Subject: Re: LF: still more loop inductance formulas
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Hello to everybody,
regarding the loops inductance, Terman Radio Engineers' Handbook has formulas for 
single turn loops of many different shapes and also notes that these formulas have 
all the same general form; it references two articles in the Proceedings of the 
I.R.E. of 1927 and 1936, that should contain the formulas derivation, maybe I could 
be able to find one of them...
It gives also a formula for the inductance of a single turn rectangle: said a and b 
the rectangle sides length, d the wire diameter, g the diagonal of the loop (g = 
a^2+b^2) (all in meters) the inductance is:
  
  L = 0.4*((a+b)*ln(4.0*a*b/d) - a*ln(a+g) - b*ln(b+g)) + 0.4*(2*g+d-2*(a+b));

Rik first formula agrees well with the one from Terman, at least for side ratios up 
to the stated limit of six, where the error is around 10% depending on the wire 
diameter. I performed some comparison of that formula with the one from Terman and 
with computer simulations, you can find some results on 
http://www.qsl.net/in3otd/rlsim.html

I have also put on my site some forms for the inductance calculation of single turn 
loops of regular polygonal shape and of rectangular shape, they are at 
http://www.qsl.net/in3otd/ind1calc.html and http://www.qsl.net/in3otd/ind2calc.html

I have seen the new Rik formula just this morning, hope to have the time soon to 
compare also that with the inductance simulations made...

               73 de Claudio, IN3OTD