Ferromagnetic Distortion of a Two-Frequency Wave

T ? O R precisely evaluating the performance of communication circuits containing ferromagnetic materials, methods for taking into account the non-linear effects of these materials are needed. To this end there have been devoted certain investigations of the behavior of such materials at the low flux densities usual in communication. These early disclosed t h a t hysteresis is a governing factor for weak fields and led to attempts to solve the problem of its bearing on speech. The complexity of speech and of hysteretic phenomena has made desirable the use of simple testing methods, which in turn require for their interpretation a quantitative theory. Since tests of this sort are usually made with one or more sinusoidal test waves, a theory of single-frequency magnetic performance has already been evolved as a first step toward fulfilling this need. For m a n y purposes singlefrequency tests are inadequate, and two-frequency waves are often used to obtain better information bearing on the design or performance of communication systems. It is the purpose of the present paper to take a further step by furnishing the theory of magnetic behavior under a two-frequency force. 322 FERROMAGNETIC DISTORTION OF A WA VE 323 The very simplicity which sometimes makes sinusoidal waves valuable for analyzing or testing the non-linear properties of channels of communication makes such waves worthless when applied in other instances, and more complex test waves must then be employed. The harmonics produced by a sine wave furnish an index of the distorting properties of a system, but the side frequencies produced by two such waves are needed to indicate its modulating properties or to give a measure of the interference between carrier channels.