202 nr.I.J. SYSTEM TECUSIC.II. JOI'RX.IL 



H. J. Vander Bijl in his analysis'' of this circuit gives the natural 

 frequency of oscillation as 



I 



=^\ 



LX 



(14) 



when r/p is the plate resistance and the remaining constants are given 

 in the illustration. 



Direct modulation by the usual method involves a cyclic change in 

 the value of plate resistance. Hence, according to the above equa- 

 tion, there results a cyclic change in frequency which, though rela- 

 tively small, becomes of the utmost importance when subjected to 

 the peculiar phenomena of night-time transmission. 



By making certain assumptions concerning the nature of frequency 

 variation as amplitude modulation takes place, it is possible to work 

 out distorted waves corresponding to various assumed wave inter- 

 ference conditions at the receiver. Perhaps the most simple and 

 instructive means for producing these distorted waves is by a graph- 

 ical method. 



The equation for modulation of a high-frequency wave by a single 

 tone may be written 



e = (A+kA cosvt) sin pt (15) 



When A represents the unmodulated amplitude of the wave, fe is a 

 factor determined by degree of modulation, v is an angular velocity 

 of the tone wave and p is the angular velocity of the high-frequency 

 wave. The amplitude factor in this equation may be considered as a 

 vector which is undergoing a change in length in accordance with 

 the term included in the brackets. For the purpose of our analysis 

 we shall include the angular velocity imparted to this vector by the 

 last term in the above equation, since we are interested in the en- 

 velope of the resultant high-frequency wave at the receiver and the 

 relative phase relations for two waves directly and indirectly trans- 

 mitted combining to form this resultant. Since both carrier waves 

 are of the same mean frequency only the relative position need be 

 considered. 



Now in our graphical determinations for the case of two trans- 

 mission paths different in length, we represent the two effective fields 

 by vectors varying in length in accordance with the amplitude factor 

 of equation (15). However, due to the difference in length of path, 



^"Theniiionic X'.icuum Tube," l)y \'an der Bijl, i age 274. 



