Design of standards of inductance, and the proposed use of model reactors in the design of air-core iron-core reactors

Abstract

After a brief discussion of the various uses of reactors and the general characteristics of formulas for the self-inductance of coils, a number of useful general relations concerning the self and mutual inductance of geometrically similar coils are given with illustrative derivations of some of these relations. Three applications of some of these relations are developed in the remainder of the paper. The first is a simple and straightforward procedure for the design of air-core coils to serve as standards of self-inductance and is believed to be the first such design procedure for this specific purpose to be published. The second application proposes that the self and mutual inductance of the large current-limiting reactors used in power systems may be advantageously predetermined, or their computed values checked, by laboratory tests made on small-scale models. The third application proposes to use models for the checking or predetermination of the properties of iron-core air-gap reactors. In developing the theory of this application it is shown that such reactors have their desirable optimum performance that is, minimum power factor-when the relative length of the air gap is such as to make the copper loss equal to the core loss for the desired maximum magnetic flux density in the core. CONTENTS Page * Maxwell, Electricity and Magnetism, 2, sec. 706. 8 The geometric mean distance of a rectangle of sides b and c may be taken to be equal to 0.2236 '(b+c).

Inductor coil of the highest possible $$\mathbf {Q}$$

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Figure 2 Cross-sections of the optimal coils. ( a ) Designs proposed by Gauss 3 , Maxwell 4 , and Brooks 6 . ( b ) Results obtained in this work.

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“…1 b. Maxwell’s analysis was improved by Rosa and Grover 5 . Building on their work, Brooks proposed that the mean radius of the optimal coil is approximately 3/2 of the side of the square 6 . The inductance of this coil is , where …”

(Invited) Passive Component Technologies for Advanced Power Conversion Enabled by Wide-Band-Gap Power Devices

“…Nonetheless, it has advantages over a spiral coil in that the flux is somewhat contained and is largely parallel to the planar conductors, and, compared to a toroid, it has more closely coupled turns, and as a result it can achieve higher inductance for the same resistance. This advantage of the solenoid is well established for low-frequency, wire-wound air-core inductors 23,24,25 . We wish to examine quantitatively how much of an advantage in performance the solenoid offers in high-frequency, height-constrained applications, in order to evaluate whether it is worth considering, even though it has a higher external field.…”

Interfacing transformer for a pulsed load current exceeding 1 MA

“…For the same winding volume, the use of a thin-walled solenoidal design results in a lower magnetizing inductance than does the alternative of a Brookes geometry [6]. However, the many inter-leaved and parallel-connected layers that are required by the much thicker windings then lead to the necessity for an isolating transformer to avoid high circulating currents and correspondingly increased losses, and numerous interconnections would be required.…”