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 = 0.0251d^{2}Nnn_{0}K, microhenrys
(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.
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.
Table I  Winding Data for Closely Wound Coils
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
