104 BELL SYSTEM TECHNICAL JOURNAL 



nately the quality of telephone reproduction is not seriously impaired 

 by shifting the phases of the various components by even as much as 

 several cycles. In telegraphy, however, the shape of the signal current 

 which operates the relay depends very much on the preservation of 

 the proper phase relations of the components, and the entire nature 

 of the signal may be changed by phase shifts of even a fraction of a 

 cycle. 



It is worth while then to examine some of the phase shifts which 

 are likely to occur in practice. Transmission of a sinusoidal wave 

 thru the free ether involves a phase lag proportional to the distance 

 and to the frequency. Hence the phase lags, 4> + and $, due to this 

 cause, will be proportional to p-\-q and p respectively, and their 

 difference, ^, will be proportional to q. Replacing ^ by h q in equa- 

 tion (12) and regrouping terms gives 



r = Rcos[q(t-h)+o\. (18) 



By displacing the origin of time by h this becomes identical with 

 the original signal component. Also, since h is independent of q, the 

 same time shift brings all the components into agreement; that is, 

 a phase shift proportional to the frequency does not distort the wave, 

 but merely delays it by the corresponding time of transmission. 6 

 In considering the terminal circuits then it is only the departure of 

 their phase lag versus frequency curve from a straight line that need 

 be considered as a source of distortion. It is of interest to note here 

 that for most filters this relation is approximately linear thruout 

 the range of free transmission. The actual curves for a particular 

 band filter are shown in Fig. 5, where there is plotted against frequency 

 the relation of the amplitude and phase of the current at the third 

 section of an infinite filter to those of the voltage applied to the first 

 section. It will be noticed how the phase curve departs abruptly 

 from a straight line at the edges of the band where the sudden drop 

 in the amplitude curve occurs. Similarly Fig. 6 shows how in the cur- 

 rent-voltage relation of a simple resonant circuit, the distortion of 

 phase and of amplitude occur together. 



In case both side-bands are transmitted, a simple relation is found 

 if the distortion is symmetrical with respect to the carrier frequency. 

 By this is meant that, however, the different components are distorted 

 relative to each other, for every signal component the two corre- 

 sponding side-band components are equal in amplitude and are 



6 For a fuller discussion of this point see a paper by T. C. Fry on "Theorie des 

 binauralen Horens nebst einer Erklarung der empirischen Hornbostel-Wertheimer- 

 schen Konstanten," " Physikalische Zeitschrift," 23, page 273, 1922. 



