348 BELL SYSTEM TECHNICAL JOURNAL 



Intermodulation Products 



Generated Modulation Voltages 



From the foregoing results the voltage generated in a coil of N turns 

 on a closed ferromagnetic core of cross-sectional area A can be found 

 by the use of 



^(/) - 7V^ 10-«^. (52) 



Components of this voltage segregated according to frequency are of 

 the type 



emn{t) = {7np + nq)NA 10~^ [c,„„ cos {mp + nq)t 



— dmn sin (?np + «g)/], (53) 



each proportional to its frequency and in general having two com- 

 ponents in quadrature. The amplitudes of these will be designated by 



Emn = {mp + nq)NA IQ-^ c^n, (54) 



Emn" = (mp + nq)NA IQ-Mmn. (55) 



The amplitude of their resultant is 



E^n = (mp -f nq)NA lO'^c^J + dmn^. (56) 



One component, if it greatly exceeds the other, may be taken as the 

 generated distortion voltage. The various coefficients to which the 

 components of the voltage are proportional have already been cal- 

 culated, and also given in tabular or graphical form for specific 

 instances. The relations 



OAwNI OAttNJ 



I ' ^~ / 



where I is the mean length of magnetic path, may be used to convert 

 these results into terms of the current amplitudes / and /. Where 

 r-m-s quantities are used, they will be distinguished by bars over them. 

 Several features of the distortion are particularly outstanding. 

 Perhaps chief among these is the dissimilarity of corresponding upper 

 and lower side-frequency voltages. Inasmuch as these are products 

 of a reactance modulator, they might be expected to be in the ratio of 

 their frequencies, as they are found to be for one component. Often, 

 however, a predominating component appears at each lower side 

 frequency with no counterpart at the upper side frequency. This 



