Harmonic Production in Ferromagnetic Materials at Low 

 Frequencies and Low Flux Densities 



By EUGENE PETERSON 



Synopsis: When a multi-channel communication circuit includes a non- 

 linear element sucn 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 com- 

 ponents. 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 wa\'e 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 in- 

 vestigate 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 foice. 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 hav- 

 ing a core of the magnetic material under investigation. The loop con- 

 stants for a few materials are included in the text. An analogy exists be- 

 tween 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 ot 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. 



Part 1, Hysteresis Loops and their Mathematical 

 Representation 



NEW and improved systems of multi-channel communication which 

 have come into use during the past few years have imposed 

 rigorous requirements on the circuit elements constituting the com- 

 municating link, and have made it necessary to investigate the degree 

 of distortion which arises from the use of ferromagnetic apparatus. 

 The distortion introduced may have two general effects: distortion 

 of the signal in any one channel, which is usually the minor effect, 

 and production of crosstalk and interference between the various 



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