## Wheeler Formulas for Inductance

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.

#### Single layer air core solenoid

`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

#### Multi layer air core solenoid

`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.

#### Flat "pancake" coil

`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

### References

The original Wheeler papers:

- Harold A. Wheeler, "Formulas for the Skin Effect,"
*Proceedings of the
I.R.E.*, September 1942, pp. 412-424
- Harold A. Wheeler, "Simple Inductance Formulas for Radio Coils,"
*Proceedings
of the I.R.E.*, October 1928, pp. 1398-1400.

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

### Numerically calculating inductance

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
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