Dec. 1931 / Jan. 1932 Short Wave Craft
[Table
of Contents]
Wax nostalgic about and learn from the history of early electronics. See articles
from Short Wave Craft,
published 1930  1936. All copyrights hereby acknowledged.

This is a nice
short article covering the calculation of inductances for coils wound on cores and wire
sizes. The author recognized that standard formulas, although concise and accurate, are
sometimes difficult to work with when calculations for a large number of values is needed
for a particular circuit design. To address the situation, he presents a handy nomograph,
chart, and a table of typical values. A smartphone app, a spreadsheet, or a desktop computer
program would be used today to calculate inductance values, number of turns, winding
spacing, etc., but back when mechanical slide rules were the order of the day, these
visual methods were a real benefit.
How Many Microhenrys in That Coil?
By James K. Clapp*Every radio student should know how to calculate the inductance
of a coil of given or known size. Here's a simplified method worked out by a leading
engineer.
Fig. 3  The graph at left gives the values of Nagaoka's constant
"K" for' different values of 2a over b = dn_{0} over n, on a logarithmic scale.
This chart will prove very useful in calculating the inductance of coils.

While much material has been published on the calculation of the inductance of coils.†
the formulae given are in general not convenient for engineering use. Two difficulties
are encountered in applying the results in engineering practice, one being the involved
computations and the other the fact that differences in form and wire sizes and errors
in the measurement of these factors introduce errors in the calculations which largely
vitiate the utility of precise formulae.
Fig. 1  The inductance of coils closely wound on General Radio, type
577 form, as a function of the number of turns and different sizes of doublesilk covered
wire. Table I gives number of turns.
For singlelayer coils at radio frequencies (and, with slight modification, for bankwound
coils), Nagaoka's formula probably is the best for general engineering use. While neglecting
the shape and size of the crosssection of the wire, the selfcapacity of the winding
and the variation of inductance due to skineffect, it may be shown that the formula
gives about as good results for highfrequency inductance as can be obtained.
Tables of the values of Nagaoka's correction factor have been prepared, but require
considerable time to use due to the necessity for interpolations. The table values may
be plotted in the form of a curve, but a more convenient interpolation is made possible
by plotting these values on logarithmic scales, as has been done in Figure 3. Where much
work of this type is done, the scales may be transferred to a sliderule so that no reference
to printed material is required.
The formulae given here, when carefully applied, give values of inductance to within
about two per cent. for singlelayer coils and to within about five per cent. for fourlayer
bankwound coils for frequencies where the coils would serve as normal tunedcircuit
elements.
The general formula is
where a is radius of a mean turn in inches, n is the number of turns, b is the length
of the winding in inches, and K is Nagaoka's correction factor which is a function of
or the ratio of diameter
to length of the winding.
If n_{0} is the number of turns per inch, the inductance and ratio of diameter
to length are more conveniently given by:
L = 0.1003a^{2}nn_{0}K, microhenrys (2)
or L = 0.0251d^{2}nn_{0}K, microhenrys (3)
where numeric (4)
and d is the diameter of the mean turn in inches.
Given the size of wire and its insulation and the diameter of the coil form, n_{0}
as wound, is found from Table I and is readily computed for any
desired number of turns. Read the corresponding value of K from the scales at the left.
The inductance is then easily computed by means of the sliderule.
For banked windings of not too great depth as compared with the diameter, a close
approximation for the inductance is obtained by using Nn_{0} for the turns per
inch (where N is the number of banks) and for the ratio of diameter
to length.
Then =
numeric (5) and L = 0.0251•d^{2}•N•n•n_{0}•K,
microhenries (6)
Fig. 2  Inductance of coils wound on General Radio, type 577 form,
with double silk covered, copper wire, in which the turns have been equally spaced in
order to fill the 2inch winding space. Here n_{0} = 1/2 n.
The number of turns required for a desired value of inductance cannot be directly
calculated since K varies as n is varied. With given types of windings experience will
indicate an approximate value for the number of turns. If the computations are carried
out and the inductance obtained is near the desired value, the correct number of turns
to give the desired value may be obtained by readjustment, since K does not vary rapidly
with n. Where many values are required it is simpler to calculate a sufficient number
of values for a curve. The required values may then be read off directly. (See Figures
1 and 2, for example.)
Examples of Calculations
Given: Form diameter = 2.75 inches (General Radio Company Type 577 Form). Wire size
= No. 20 doublesilkcovered. Find: The inductance for coil of 35 turns.
Procedure: In Table 1 find n_{0} = 25
From scales, opposite 1.99 for , read
K= 0.526
L = 0.0251 x (2.79)^{2} x 35 x 25 x 0.526 = 90.0 microhenrys.
For a rough estimate, the diameter of the form may often be taken as the diameter
of a turn. In the above example this procedure gives = 1.965, K = 0.530 and L =
88 microhenrys, which differs from the previous value by about 2.5 per cent.
For bankwound coils an example is as follows:
Given: d = 2.75, n_{0} =25, N = 4, and n = 200
Then = 1.455.
From Figure 3, K = 0.604
Then 4 x 25 x 200 x 0.604 = 2570 microhenries.
Table I  Winding Data for Closely Wound Coils
Many experimenters and many engineers "design" inductors by guessing at the number
of turns, then peeling off wire until the correct value of inductance is obtained rather
than go to the trouble of using the usual tables and formulas. Our experience with the
method described here proves conclusively that much time and effort are saved by calculating
the desired value of inductance before the coil is wound.  Courtesy "General Radio Experimenter."
*Engineer, General Radio Company
†See in particular the publications of the U. S. Bureau of Standards and the
Proceedings of the Institute of Radio Engineers.
Nomographs Available on RF Cafe: 
Decibel Nomograph 
Voltage and Power Level Nomograph
 Voltage, Current, Resistance,
and Power Nomograph  Resistor
Selection Nomogram  Resistance
and Capacitance  Capacitance
Nomograph  Earth Curvature Nomograph
 Coil Design Nomograph 
Coil Inductance Nomograph
 Antenna Gain Nomograph 
Resistance and
Reactance Nomograph
Posted January 23, 2015
