STUDIES IX RADIO BROADCAST TRAXSMISSIOX 207 



residual \va\c form distortion and some further consequences of selec- 

 tive fading under the assumption that there is no frequency moduhi- 

 tion involved. 



The process of detecting audio signals from radio frequency signals 

 is, at least in its simpler aspects, well understood, but it may not be 

 generally appreciated that the action is such that the detected signals 

 ma\- be greatly modified by changes in the relative amplitudes and 

 phases of the carrier and side-band components such as may 

 result from their transmission through the medium. That the ampli- 

 tudes and phases of the carrier and side-band signals are not neces- 

 sarily received in the same relation that existed as they left the trans- 

 mitter has been pointed out earlier, in the discussion on selective 

 fading. 



The usual expression for a high-frequency carrier wave of frequency 

 p/2Tr modulated by a low-frequency wave of frequency v/'I-rr is 



e=A[l^a sin (r/ + (/>)] sin pt 



where A is the carrier amplitude, a, the percentage modulation and 

 <^ the starting phase of the modulating tone with reference to the 

 carrier. Expanded into its components this becomes 



e=^-^ cos {pt-\-vt-\-(j)i) (the upper side band) 



A "a 

 _•- cos (pt — I't — (1)2) (the lower side band) 



-^Az sin pi (the carrier) 



where 0i=<^2 = and Ai=A2=As = A as the waves leave the trans- 

 mitting antenna. 



In the receiving set this funct'on is squared by the action of the 

 detector and, neglecting direct currents and frequencies above the 

 audio range, the result is 



2 



^Az[A, sm (W + (/)i)+^2sin (r+0->)]+^4i^o — cos (2r/+0i + 0.) (17) 



of which the first term represents the fundamental frequency of the 

 original modulating tone and the second term the second harmonic. 



From this expression several conclusions can be immediately 

 drawn. Due to the action of the detector there is always some 

 slight wave fcrm distortion as is evidenced by the presence in rela- 

 tively small amplitude of the second harmonic. In the ordinary case 

 this is negligible. The first term contains the carrier amplitude as a 



