Tables for the calculation of the inductance of circular coils of rectangular cross section

Abstract

Multilayer coils with spaced layers or banked or honeycomb windings for reducing the capacity of the coil find an extensive use in radio circuits where a greater induc- tance is required than can readily be obtained from a single-layer coil. The inductance of these varied types of multilayer coil may be accurately calcu- lated from the known formulas for the inductance of circular coils of rectangular cross section, provided a relatively small correction is applied to take into account the fact that a part of the cross section is occupied by insulation. These formulas (the most important of which are given in the appendix for reference) are rather complicated, calculations made by them are time consuming, and some uncertainty is often experienced in making a choice of the most suitable formula for a given case. When many calculations have to be made, there is an imperative need for some means for simplifying the calculations and for rendering unnecessary a choice among formulas. Such aids which have previously appeared have taken the form of a single empirical formula to cover the whole range of coils, or of charts from which the inductance, or some function simply related to the inductance, can be interpolated. These methods do not allow of an accuracy greater than about I per cent at best, and in some instances the curves have been based on unsuitable formulas and give only a rough accuracy. Tables are presented in this paper which are based on accurate formulas for the inductance. By the use of these tables the calculation of the inductance is reduced to the simplest of arithmetical operations. The tabulated values give directly an accuracy in the value of the inductance of one part in ten thousand. In the case of the most unfavorable interpolation the error should not be as great as a part in a thousand. Examples are given to illustrate and explain the use of the tables, and the further application of the tables to the calculation of mutual inductance in certain cases is treated.