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Kirt
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RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...
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Dec. 1931 / Jan. 1932 Short Wave Craft[Table of Contents]People old and young enjoy waxing nostalgic about and learning some of the history of early electronics. Short Wave Craft was published from 1930 through 1936. All copyrights are hereby acknowledged. See all articles from Short Wave Craft. 
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.
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.
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.
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)
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.
Nomographs Available on RF Cafe:

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Posted January 23, 2015