210 BELL SYSTEM TECHNICAL JOURNAL 



function of eliminating terminal reflection, accomplished in the former' 

 by the vacuum tube, is accomplished in the latter by the additional 

 impedance elements. 



2. Loading Systems 



The use of loaded cable circuits for the transmission of programs 

 and for the transmission of pictures introduced some interesting 

 problems in connection with phase correction at the higher frequencies. 

 In this connection, a study of the building-up of sinusoidal oscilla- 

 tions in long loaded cables led to the establishment of two propo- 

 sitions which are of great value in comparing communication systems 

 with respect to the quality of transmission.^' These two propositions 

 relate the variation with frequency of the steady state phase to the 

 duration and nature of the transient distortion. They are applicable 

 to all types of periodic loading, with or without terminal phase com- 

 pensators under two restrictions; namely, (1) the line must comprise 

 at least 100 loading sections and (2) the transducer as a whole must 

 be approximately equalized as regards absolute steady state values 

 of the received current in the neighborhood of the applied frequency. 

 The successive derivatives of the total phase angle B{o)) with respect 

 to o) will be denoted by B'{o:), B"{oi), B"'{w). B{w) may be under- 

 stood to represent the sum of the phase differences due to transmission 

 over the line and a terminal distortion corrective network, as well as 

 the phase difference on the line alone. The propositions follow. 



Case I: 5"(co) 9^ and <B"{(^)I2\ large compared with a5'"(co)/3!. 



The envelope of the oscillations in response to an e.m.f. E cos uit 

 applied at time t = reaches 50 per cent, of its ultimate steady value 

 at time t = B'{u>) and its rate of huildijig-up is inversely proportional 

 to <B%S). 



Case II: B"{(S) = 0, B'"{iS) 7^ and V5'"(co)/3! large compared 

 with <lB^^{oi)lM 



The envelope of the oscillations in response to an e.m.f. E cos co/ 

 applied at time t = reaches 1/3 of its ultimate steady value at time 

 t = B'{w) and its rate of building-up is inversely proportional to ^B"'{ui). 



These propositions furnish supplementary verification of the 

 condition with regard to phase variation already established as a 

 requirement for distortionless transmission; namely, that the phase 

 vary linearly with the frequency or 



B{(ji) = COT, 



^^ See reference 4. 



