PHASE DISTORTION AND PHASE DISTORTION CORRECTION 211 



where r is a constant. It follows immediately that 



J5'(co) = T. 



Thus, when the steady state value of phase propagation is in linear 

 relation with the frequency, all signals of any frequency whatever 

 reach their proximate steady state in the same interval of time r. 

 These propositions make it possible to calculate two important 

 criteria of the transmission properties of the line: (1) the variation 

 with respect to frequency of the time interval r required for the current 

 to build up to its proximate steady state value and (2) its rate of 

 building-up at time t = r. The first is very important in telephony 

 but has no significance in telegraphy since only one frequency is 

 transmitted, whereas the second is important in both telephony and 

 telegraphy. While the formulas underlying these propositions are 

 approximate, they are sufficiently accurate for a study of the com- 

 parative merit of different types of transmission systems or for the 

 design of loaded lines. 



For the purpose of reducing transient distortion on a long loaded 

 cable of N sections, the loading and critical frequency ajc/27r may be 

 designed on the basis that the two time intervals, 



h = 2iV/co, (19) 



and 



, = 2iY(^^^_l). (20) 



should be less than given quantities determined by experience. The 

 two expressions h and t^ represent, respectively, (1) the time of 

 transmission of d.c. current or the nominal time of transmission and 

 (2) the excess of the time of building-up of the frequency aj/27r to 

 approximately one half the steady state value over the nominal time 

 of transmission. 1^ The right hand member of formula (20), although 

 initially determined by Carson by a method entirely dissimilar to that 

 in his later investigation, is, it will be noted, given by 



h= B'{iS) - B'iO) = T - To (21) 



and 



h = B\0) = To. (22) 



The nominal time of transmission ti is significant from the standpoint 

 of echo efifects but, with regard to phase distortion correction alone, 

 emphasis is placed upon the quantity h= T — To as the more 

 important factor. The enormous improvement in this respect of the 

 ^^ See reference 2. 



