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Inductance (fwd)
---------- Forwarded message ----------
Date: Mon, 30 Mar 1998 17:35:43 EST
From: ESchulz531 <ESchulz531-at-aol-dot-com>
To: tesla-at-pupman-dot-com
Subject: Inductance
Maximizing the inductance for a cylinder coil.
L : inductance in uH, r : radius in inches, N : number of turns,
b : length of coil in inches, d : turns per inch, w : length of wire in inches
L = (r * r * N * N) / (9 * r + 10 * b)
Using this and solving for L in terms of r. and using
(N = b / d and b = w / (2 * Pi * r * d))
we get
L = w / (4 * Pi * Pi * (9 * r + (10 * w) / (2 * Pi * r * d)))
Now I took the derivative in respects to r
- (d * w * w * (9 * d * Pi * r * r - 5 * w)) / (4 * Pi * (9 * d * Pi * r * r +
5 * w) ^ 2)
Set this to 0 and solve.
So the most inductance for a cylinder coil is when
r = sqrt((5 * w) / d) / (3 * sqrt( Pi ))
or
w = r * r * Pi * d * 9 / 5
Can somebody check to see if this is right?
Just having fun with some old fashioned calculus. :)
Erik Schulz
ESchulz531-at-aol-dot-com