### COIL02 Electrical Inductance Calculator

This program computes the electrical self inductance of various shapes and sizes of air core coils, using accurate formulas from National Bureau of Standards circulars and related sources. Archive includes C source code and an MSDOS executable. Calculations include inductance of single-layer circular solenoid of round wire, multi-layer circular solenoid, flat spiral, circular solenoidal current sheet, N-turn circular loop, straight round wire, circular toroid with circular winding, circular torus ring with rectangular winding, single-layer square solenoid, single-layer rectangular solenoid, multi-layer square solenoid, and wire gauge calculation.

Usage:

On startup, the following initial menu is displayed:

Geometry of coil:

• 1 Circular solenoidal current sheet
• 2 Straight round wire
• 3 N-turn circular loop
• 4 Circular toroid, circular winding
• 5 Multi-layer square solenoid (low precision)
• 6 Circular torus ring, rectangular winding
• 7 Multi-layer circular solenoid
• 8 Single-layer circular solenoid of round wire
• 9 Single-layer square solenoid
• 10 Single-layer rectangular solenoid
• 11 Wire gauge calculation
• 12 Select dimensions in inches or centimeters
• Choose geometry (1) ?

Select the desired coil geometry from the menu. Enter mean diameter, length, and thickness of winding, and total number of turns, as prompted. The program will display the inductance in henrys, then loop back for more input. "Mean diameter" is the arithmetic average of the inner and outer diameters of the winding; for a single layer coil it is measured to the center of the wire. "Thickness," for a single layer coil, is the wire diameter (see below for the correction for empty space in the winding).

For each item the previously entered value is displayed in parentheses and will be kept if you just hit the carriage return key.

Item 11, wire gauge calculation, prompts for the wire gauge and the dimensions of a rectangular area to be filled. It displays the wire diameter and the number of turns that will fit into the indicated space.

The formulas for a multi-layer circular solenoid were obtained from National Bureau of Standards publications and are very accurate. They work for arbitrary winding thickness and length. A flat spiral disc coil is obtained by setting the length = 0.

Also very precise is the NBS formula for a helical solenoid of round wire. It models the size of the wire and the nonuniform current density inside the wire. The only low precision formula included is the one for a multi-layer square solenoid; it is an approximation from the CRC handbook.

In the case of a single-turn loop or a straight piece of wire, a skin effect correction is computed. This requires that you enter the frequency of operation. The wire is then assumed to have the conductivity of copper.

If the wire diameter or winding thickness is not explicitly requested, the coil is modeled as a zero thickness current sheet. Except for the circular solenoid of round wire, the formulas assume uniform current density throughout the winding, modified only when skin effect is included.

In the cases that assume uniform current density, there is no correction for empty space in the winding. An approximate correction for close-wound coils is (Rosa, 1906)

dL = 0.00097 d N

where d is the mean diameter of the winding, in centimeters, and N is the total number of turns. This correction, in microhenrys, is added to the inductance.

All calculations assume both the core material and the wire are non-magnetic.

Files:

coil.c
main program for coil calculator
coil.doc
this file
coil.mak
MSDOS makefile
coil.nmk
MS Visual C nmake file
coil2_bc45.zip
Borland project file
coil.opt
VAX makefile
descrip.mms
VAX makefile
formulae.c
inductance formulas from NBS publications
lyle.h
approximations to Lyle's tables
makefile
Unix makefile
mathl.c
elliptic integrals and other math functions
tables.c
computes tables found in engineering handbooks
tables.ans
result of running tables.c
tables.opt
VAX makefile
bcb5.zip
Borland Code Builder scripts

References:

Butterworth 1915: S. Butterworth, "On the Coefficients of Self and Mutual Induction of Coaxial Coils," Philosophical Magazine, vol. 29 (1915), pp. 578-592

Dwight, 1918: Dwight, Electrical World 71, p. 300 (1918). Formulas for long coils.

Grover 1918: Frederick W. Grover, "Additions to Inductance Formulas," Sci. Pap. #320, Bulletin of the Bureau of Standards 14, 555-570.

Grover 1922a: Frederick W. Grover, "Tables for the calculation of the inductance of circular coils of rectangular cross section," Sci. Pap. #455, Scientific Papers of the Bureau of Standards 18, 451-487 (1922). Butterworth's expansions for thick circular coils.

Grover 1922b: Frederick W. Grover, "Formulas and tables for the calculation of the inductance of coils of polygonal form," Sci. Pap. #468, Scientific Papers of the Bureau of Standards 18, 737-762 (1922).

Grover 1946: Frederick W. Grover, _Inductance Calculations, Working Formulas and Tables_, Van Nostrand, 1946; Dover, 1962.

Lyle, 1914: T. R. Lyle, "On the self-inductance of circular coils of rectangular section." Philosophical Transactions of the Royal Society of London, Series A, Volume 213 (1914), 421-435.

Nagaoka 1909: Nagaoka, J. College of Science, Tokyo, 27, Art. 6, p. 18 (1909). Inductance of circular solenoidal current sheet.

Rosa 1906: Sci. Pap. #31, Bulletin of the Bureau of Standards 2, 161.

Skilling 1948: H. H. Skilling, _Fundamentals of Electric Waves_, Wiley, 1948, pp 99-101.

Snow 1952: Chester Snow, "Formulas for Computing Capacitance and Inductance," National Bureau of Standards Circular #544. Circular solenoid of round wire.

Niwa 1924: Formula for single-layer rectangular coil, quoted in Grover 1946.

Spielrein, 1915: Spielrein, Archiv fur Elektrotechnik 3, p. 182 (1915). Formula for wide disk coils.

See also the section "Radio Formulae" in _Handbook of Chemistry and Physics_, Chemical Rubber Publishing Co., for toroidal and rectangular coils, loops, straight wire, etc.

Program by Steve Moshier

moshier@na-net.ornl.gov

coil00.zip: December, 1992 (Original version)
coil01.zip: February, 1996 (Menu item to choose inches or centimeters)
coil02.zip: January, 2002 (Use Lyle if b/r <= 0.2)
November, 2004: Added single-layer rectangular solenoid.

Last update: 14 Nov 2004