These formulas, developed by Wheeler at the (then) NBS, give approximate inductances for various coil configurations. They are primarily based on empirical measurements, and are accurate to a few percent.
L (uH) = r^2 * n^2 / (9 * r + 10 * l)
where
r = coil radius in inches
l = coil length in inches
n = number of turns
L (uH) = 0.8 * a^2 * n^2 / (6*a + 9*b + 10*c )
where
a = average radius of windings
b = length of the coil
c = difference between the outer and inner radii of the coil.
all dimensions in inches.
It states that it is accurate to 1% when the terms in the denominator are
about equal. This is also an equation by Wheeler. It applies as long as the
coil has a rectangular cross section.
L (uH) = r^2 * n^2 / (8 * r + 11 * w)
where
r = radius to center of windings in inches
w = width of windings (in inches)
n = number of turns
The original Wheeler papers:
An enormous compendium of inductance references compiled by Dr. Marc Thompson.
Dr Thompson has a new paper out that covers approximation techniques:
Thompson, M. , "Inductance Calculation Techniques -- Part II: Approximations and Handbook Methods", Power Control and Intelligent Motion, December 1999 http://www.pcim.com
http://members.aol.com/Marcttpapers2/Induct2.pdf - 26 April 2001
The above paper doesn't cover the parasitic C or R, though.
Someone has scanned the classic Grover reference which is out of print (but not out of copyright, so I hope that they got permission).
http://home.san.rr.com/bushnell/self_inductance.htm
http://home.san.rr.com/bushnell/inductance_table_3_grover.htm
Dr. Antonio Carlos M. de Queiroz at the University of Brazil has written a set of programs to calculate inductance (particularly mutual inductance) of coils of any shape from first principles. The INCA program is particularly useful, and can be found at http://www.coe.ufrj.br/~acmq/programs/. The program also computes capacitance, etc.
Copyright 2001, Jim Lux / wheeler.htm / 26 Jan 2004 / Back to HV Home / Back to home page / Mail to Jim