Leakage Inductance

Author: Reuben Lee

Flux set up by the primary winding which does not link the secondary, or vice versa, gives rise to leakage or self-inductance in each winding without contributing to the mutual flux. The greater this leakage flux, the greater the leakage inductance, because the inductance of a winding equals the flux linkages with unit current in the winding. In Fig. 57, all flux which follows the core path l_c is mutual flux. Leakage flux is the relatively small flux which threads the secondary winding sections, enters the core, and returns to the other side of the secondaries, without linking the primary. The same is true of flux linking only the primary winding. But it is almost impossible for flux to leave the primary winding, enter the core, and re-enter the primary without linking part of the secondary also. The more the primary and secondary windings are interleaved, the less leakage flux there is, up to the limit imposed by flux in the spaces c between sections. These spaces contain leakage flux also; indeed, if there is much interleaving or if the spaces c are large, most of the leakage flux flows in them. Large coil mean turn length, short winding traverse b, and tall window height a all increase leakage flux.

Several formulas have been derived for the calculation of leakage inductance. That originated by Fortescue ¹ is generally accurate, and errs, if at all, on the conservative side:

where L_S = leakage inductance of both windings in henrys, referred to the winding having N turns

MT = mean length of turn for whole coil in inches

n = number of dielectrics between windings (n = 2 in Fig. 57)

c = thickness of dielectric between windings in inches

a = winding height in inches

b = winding traverse in inches.

The greatest gain from interleaving comes when the dielectric thickness c is small compared to the window height; when nc is comparable to the window height, the leakage inductance does not decrease much as n is increased. It is often difficult to reduce the leakage inductance which occurs in high-voltage transformers because of leakage flux in spaces c. A small number of turns, short mean turn, and low, wide core windows all contribute to a low value of leakage inductance.

1	See Standard Handbook for Electrical Engineers, McGraw-Hill Book Co., New York, 1922, 5th ed., p. 413.