PHASE DISTORTION AND PHASE DISTORTION CORRECTION 217 



While 0(00) = TT, it is apparent from Fig. 15 that increases very 

 slowly for values of <^ > 2.5 and it is found that a distortion angle 

 of not more than about 2.5 radians can well be compensated for 

 with each section of lattice network. o-^/2.5 determines roughly the 

 number of sections required where am represents the maximum 

 distortion for the total length of line. It is only essential that the 

 total number of sections be included where correction is desired. 

 The corrective structure may be divided and one or more sections 

 located at convenient points throughout the length of the cable whose 

 phase is to be corrected. In the latter case a desirable arrangement 

 on a repeatered cable is to insert at each repeater point a sufficient 

 number of sections to correct the distortion on the cable length 

 between two successive repeaters. 



If the network is connected directly to the line, i.e., without the 

 interposition of a unilateral element such as a vacuum tube, the 

 necessary condition 



K(co) = R, 



where i? is a constant representing approximately the characteristic 

 impedance of the cable, imposes one limitation upon the constants 

 L and C, leaving one other to be fixed by the phase. For this condi- 

 tion, put 



^a(w) = — (Ta, 



where Ca is the value of o-(w) at a frequency /„ = Wa/27r near the 

 upper limiting frequency of the correction range and at which it is 

 desirable to have exactly (r{ui) = — ^(w). Substituting for K and 

 (j)a in (27) and (28) and solving, gives 



2R 1 

 L = tan - (Ta, 



^' ' (31) 



C = Btan^r ffa- 



OiaK L 



An application of this method of design to the 19-gauge H-44-25 

 cable is shown in Figs. 17 and 18. This design requires two sections 

 of lattice network at each repeater point of constants 



L = .116 henry, 



C = .181 microfarad 



per section, the distance between repeaters being 50 miles. 



While the design above effects considerable improvement, it is 



