108 BELL SYSTEM TECHNICAL JOURNAL 



mediate values they decrease, becoming zero when the two carriers 

 are in phase quadrature. The phase lag, h q, is that due to trans- 

 mission alone; that is, the phases of the reproduced components are 

 independent of the phase of the local carrier. Since the phase of the 

 local carrier affects only the amplitudes and affects these the same for 

 all components, it does not alter the wave form of the reproduced 

 signal, but does affect its magnitude very materially. 



Thus in a carrier telephone system fluctuations in the phase of the 

 local carrier are much more serious when both side-bands are trans- 

 mitted than when one is suppressed, the only effect then being an 

 unimportant phase distortion. In a carrier telegraph system, how- 

 ever, the amplitude fluctuations which occur when both side-bands 

 are transmitted may not be particularly troublesome since telegraph 

 receiving apparatus is designed to operate over quite a range of signal 

 intensity. The phase distortion occurring in single side-band trans- 

 mission is however serious. It may perhaps be considered fortunate 

 that the requirements as to phase regulation are least severe in tel- 

 ephony with a single side-band and in telegraphy with both side- 

 bands, since these modes of operation appear on other grounds to be 

 the most practical for the two cases. 



In comparing single and double side-band transmission it is inter- 

 esting to note that for equal sending power, the power of the repro- 

 duced signal component is twice as great with two side-bands as with 

 one. However, the power of the same frequency resulting from 

 static is also twice as great, so that the ratio of signal to interference 

 is the same in both cases. To show this, let Bi be the amplitude of a 

 component of the single side-band and B 2 that of each of the cor- 

 responding components of the double side-band. Then equality of 

 power gives 



BS = 2B 2 \ (31) 



For the single side-band the amplitude of the reproduced component is 



Rx = gB u (32) 



where g is a constant of proportionality. The power, 



P x = \g*BS = g*B 2 \ (33) 



(The resistance is here omitted as it is assumed constant thruout.) 



For the double side-band, since the two components are in phase, 

 the resultant amplitude, 



R 2 = 2gB 2 , (34) 



and the power, 



P 2 = 2 g* B 2 * = 2 P y . (35) 



