Single-layer Coil Research Articles

Distributed Capacity of Single-Layer Coils

The results of previous work done on the distributed capacity of single-layer coils are briefly outlined. Previous theory and experiment do not agree. The reasons for this disagreement are discussed. Two important parameters were omitted from previous theory. The theoretical part of the present paper yields a formula which includes these two additional parameters. This formula is substantiated by experimental evidence and gives the internal capacity of short single-layer coils. By a short single-layer coil, the author means one whose length of winding is, at most, of about the order of the diameter of winding. Any capacity due to leads or terminals should not be considered as part of the internal coil capacity but should be treated separately.

Tables for the Calculation of the Mutual Inductance of Any Two Coaxial Single-Layer Coils

Absolute formulas for the calculation of the mutual inductance of coaxial solenoids, although they are required for work of the great precision necessary in absolute measurements, are not convenient for routine calculations. Series formulas, although simpler, are limited in the range of their convergence, thus requiring the choice of the proper formula for any given problem. The tables and formulas here presented enable the mutual conductance of any two coaxial solenoids whatever to be calculated from a single formula. Examples make clear that a five-figure accuracy may be attained with concentric coils and even with poorly coupled coils the error does not exceed a few parts in ten thousand.

The Effect of Displacement Currents on the High-Frequency Resistance of Circular Single-Layer Coils

In existing theoretical formulas for obtaining the high-frequency resistance of circular single-layer coils, the effect of displacement currents has been neglected. It was thought that the displacement currents in going from one turn of the coil to another through the dielectric, would affect the distribution of current over the cross section of the conductor and, consequently, the effective resistance at high frequencies. The present paper shows that this effect is of minor importance by applying, for the first time, the similitude principle to circular single-layer coils. The paper also experimentally substantiates the results predicted by the similitude principle.

Supplementary note to the "Study of the High-Frequency Resistance of Single Layer Coils"

Since the publication of the above paper in the December, 1930, number of the Proceedings of the IRE, the attention of the authors has been called to two articles on the alternating-current resistance of solenoidal coils, by S. Butterworth, which they regret to state were overlooked in the preparation of the original paper. In the first of these articles (Phys. Rev., 11, 752-755; June, 1924) Butterworth has explained the disagreement of results, calculated by a formula derived by him in 1921, and the experimental results of Hickman (US Bureau of Standards Scientific Paper No. 472) as being due to a misinterpretation by the latter of the scope of this formula. The measurements of Hickman were carried out with long coils, while the constants in the formula cited apply only to coils whose length is less than their diameter. Butterworth shows that, properly extended, his formula correctly represents Hickman's experimental values of the resistance ratio. In the second of these articles Butterworth gives the derivation of this extended expression, formula together with that of two other formulas. In conclusion, the general agreement of the above-named paper's measured values and the values of resistance ratio computed by Butterworth's formulas may be regarded as satisfactory in all cases where the assumptions of the formulas are fulfilled. For a more rigid comparison, measurements are necessary with coils of more open winding and with greater attention paid to obtaining uniformity of spacing over the length of the coil.

A Study of the High-Frequency Resistance of Single Layer Coils

Existing formulas for the high-frequency resistance of single layer coils have all been obtained by making simplifying assumptions. The errors due to these assumptions are difficult to estimate and the data available are not conclusive. This paper gives the experimental results of a systematic study of the highfrequency resistance of single layer coils of the forms and sizes usual in radio circuits in the broadcast range of frequency. New formulas are derived by expanding Hickman's low-frequency formulas in asymptotic series, thus making the formulas applicable to high frequencies. An empirical formula for coils of intermediate lengths is also found. These formulas are compared with the experimental results.

The Calculation of the Inductance of Single-Layer Coils and Spirals Wound with Wire of Large Cross Section

Formulas are given for both wires of round cross section and wires of rectangular cross section. These are obtained by an extension of the Rosa Method. Tables are given from which the geometric mean distances of rectangles which enter in the formulas may be readily obtained.

On the alternating current resistance of solenoidal coils

In a paper published some time ago by the present writer a formula was given for computing the alternating current resistance of single-layer coils in which the spacing of the wires is not too close. Recently Mr. C. N. Hickman has made a comparison between the measured and computed values of the resistance of solenoidal coils and has used the above formula. Owing mainly to a misconception in regard to the scope of the formula, he came to the conclusion that the formula could be in error by as much as 300 per cent. It has been pointed out, however, that when the formula is legitimately applied the discrepancy is reduced to 30 per cent. In order to account for the outstanding difference it is necessary to extend the theory so as to include closely wound coils. This extension has been made in the present paper, with the result that the difference between theory.

Note on the Alternating Current Resistance of Single Layer Coils

Note on the Alternating Current Resistance of Single Layer Coils

Formulas and Tables for the Calculation and Design of Single-Layer Coils

A set of tables for the simple calculation of the inductance of single layer helical and polygonal coils and their design is given; together with full illustrations of their use.

Self Inductance and Natural Wave Length of Single Layer Coils for Radio Use

Self Inductance and Natural Wave Length of Single Layer Coils for Radio Use

Alternating-current resistance and inductance of single-layer coils

Alternating-current resistance and inductance of single-layer coils

Simplified Inductance Calculations, with Special Reference to Thick Coils

The method of calculation advocated in the Paper is based on an extension of Nagaoka's formula for single layer coils, to include as well all ordinary forms of thick coils. Rosa's formula for thick coils is put into the same from as Nagaoka's, and its use enables a series of correction factors to be calculated for various coil thicknesses. By the aid of a single sheet of curves giving values of these correction factors the inductance of any form of coil likely to be met with in practice may be readily calculated, using only one simple standard formula for all cases. Reasonable accuracy is obtained even in the limiting example of a single turn of wire. The results arrived at agree well with other published charts, which are usually of more limited application, while the use of a single formula for all cases lessens the liability to error. It is also shown that Rayleigh and Niven's formula enables the calculation of the correction factors for very short coils to be carried out without having recourse to Nagaoka's more complicated expressions.

Calculation of the self-inductance of single-layer coils

Calculation of the self-inductance of single-layer coils