Harmonic Production in Ferromagnetic Materials at Low Frequencies and Low Flux Densities

Abstract

When a multi-channel communication circuit includes a non-linear element such as a ferromagnetic core coil, distortion of the wave form impressed upon the circuit is produced. In terms of the single frequency components, this distortion is manifested in the appearance of new components. This distortion may give rise to the reduction of quality in any channel, and it may also introduce crosstalk and interference, which consists of new frequencies not present in the impressed wave of any channel under consideration, produced by independent channels. In view of the recent increased use of multi-channel systems, it has become necessary to investigate the effects of this type of distortion, to determine the dependence of this distortion upon the properties of the magnetic materials constituting the cores of inductance coils and transformers, as well as upon the circuit impedances, and to determine those constants of core materials which are significant in the distorting process. The behavior of magnetic materials to complex waves of magnetizing force is ordinarily a highly involved process, so that a direct correlation between distortion and some of the easily measured constants of materials is a matter of some difficulty. It has been established experimentally, as a confirmation of theoretical speculations, that the third harmonic e.m.f. generated by a sinusoidal wave of magnetizing force may serve as an index of the distortion with a complex wave of magnetizing force. This relation is valid for low flux densities and for frequencies at which the screening effect of eddy currents is not important. The paper is therefore devoted to an investigation of the third harmonic production in its dependence upon the properties of hysteresis loops. These loop constants in turn are shown to be deducible from AC bridge measurements on a coil of known dimensions having a core of the magnetic material under investigation. The loop constants for a few materials are included in the text. An analogy exists between the treatments of hysteresis loop and of three-element vacuum tube characteristics which enables us to compare simplifying relations introduced by Rayleigh and by H. J. van der Bijl in the two cases. The theoretical deductions are found to be in general agreement with experiment, and are applied to a number of cases of practical interest. These include the effects of air gaps and dilution, and the choice of core material in third harmonic production by inductance coils and transformers. Finally, the amount of third harmonic current flowing out of long lines is deduced with both lumped and continuous loading.