788 BELL SYSTEM TECHNICAL JOURNAL 



which clearly indicates that no change is produced in the secondary 

 third harmonic current by introducing air-gaps or by diluting the core 

 material, the change in core area being negligible. This relation has 

 been verified experimentally. 



The discussion above considers a constant potential applied to a 

 transformer circuit and the relations derived are somewhat changed 

 when we consider constant current or constant potential transformers. 

 We seldom have to do with constant current transformers but constant 

 potential transformers are met with frequently in vacuum tube circuits 

 as input transformers or interstage transformers. The above discus- 

 sion may be applied to this case by taking the primary generator 

 resistance much lower than its nominal value — a condition, inci- 

 dentally, which works toward the suppression of harmonic. 



The conclusions are also somewhat altered when we have networks 

 offering different impedances to the harmonic and the fundamental. 

 Thus it is evident that the third harmonic current can be eliminated 

 from both primary and secondary circuits by inserting a high series im- 

 pedance to the harmonic frequency, or by encircling the core with a 

 winding connected to a network which has a very low impedance to the 

 third harmonic and high impedance to the fundamental. Further, in 

 single frequency transmission the result may be equally well obtained 

 by shunting a series tuned circuit around the primary or secondary 

 winding. 



Applications to Harmonic Production in Loaded Lines 



If distortion takes place at any one point of a loaded line, the amount 

 of distorted current received at the far end depends upon the ampli- 

 tudes of the currents producing it, and upon the line attenuation from 

 the point of origin to the far end. The phase similarly depends upon 

 the phase of the fundamentals, and upon the phase shift of the line. 

 When we have a number of distorting sources at different points along 

 the line, the net distorted output is obtained by combining vectorially 

 the currents due to the individual centers of distortion, since it may 

 be assumed that no interaction exists. In a uniformly loaded line 

 we may think of these sources of distortion as being uniformly dis- 

 tributed, but the amount of distortion introduced is, on the contrary, 

 not distributed uniformly on account of the line attenuation which 

 reduces the distortion generated at the far end of the line. 



It is apparent, then, that if we are to calculate the net distortion 

 introduced by the line, a complete specification of the phase shift 

 and attenuation is required, together with a knowledge of the law of 

 production of the distortion. This last also requires a specification of 



