FERROMAGNETIC DISTORTION OF A WAVE 323 



The very simplicity which sometimes makes sinusoidal waves valu- 

 able 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. When two 

 waves are used, one may be thought of as the carrier, modulated by 

 the other, whose amplitude is chosen proportionate to the square root 

 of the energy in the more complex modulating wave it represents, or 

 both may be thought of as component waves in the same channel, or 

 as carriers in different channels, producing interference in certain other 

 channels. The amplitudes of the several product frequencies then 

 give a measure of the energy falling in their respective regions of the 

 spectrum under actual operation. The effect of the presence of one 

 fundamental upon the transmission of the other can also be ascertained. 

 Increasing the complexity of the test wave by the superposition of 

 additional frequencies can be seen to afford little added advantage at 

 the cost of much complication, unless the character of the waves 

 actually transmitted is simulated, in which case statistical methods of 

 study can perhaps be applied. 



From the foregoing circumstances the utility of information per- 

 taining to the application of two-frequency inputs as well as single- 

 frequency inputs to non-linear circuit elements is apparent; many 

 investigations have been conducted in this field to provide such 

 information. When the current-voltage relation is not single-valued 

 a more intricate treatment is necessary in carrying out the analysis. 

 A general method of attack for double-valued characteristics has been 

 provided and applied to hysteresis loops by E. Peterson ^ to determine 

 the flux in ferromagnetic materials under single-frequency magnet- 

 izing forces. The fundamental dependence of loop form upon wave 

 shape precludes immediate extension of Peterson's results to the case 

 of a multi-frequency force except for certain harmonic combinations, 

 one of which he considers.^ A study of flutter effect has been published 

 by Walter Deutschmann,^ who analyzed a complex loop made up of 

 straight lines. Both instances serve to emphasize the desirability of 

 a broader investigation of the theoretical aspects of two-frequency 

 magnetization including hysteresis. While no general and rigorous 



1 B. S. T. J., Vol. 7, pp. 762-796, Oct. 1928. 



2 Ibid., p. 773. 



3 Wiss. Ver. a.d. Siemens-Konzern, Vol. 8, No. 2, pp. 22-44, 1929; E. N. T., Vol. 6, 

 pp. 80-86, Feb. 1929. 



