DISTORTION CORRECTION 475 



The circuit assumed is a submarine cable whose length, /, is 1700 

 miles and whose parameters are to have the constant values per mile 



R' = 2.74 ohms; L' = .001 h.; 

 G' = ; C = .296 mf. 



It is terminated at the receiving end only by a resistance R = -ylL'/C 

 = 58.12 ohms. The transfer exponent, a + ib, of this circuit at the 

 terminal resistance is computed from the formula, easily derived, 



ga+ib = (^/j^) sinh yl + cosh yl, (66) 



where 



7 = V(i?' + iL'c^)iC'o>, 

 and 



k = -V(i?' + iL'oi)liC'o:. 



These results are shown in Fig. 12. 



It is desired to obtain distortion correction in this circuit from 

 to 25 cycles per second by introducing a terminal constant resistance 

 transducer which will approximately equalize the attenuation over 

 this range and make the resultant phase linear with frequency. Since 

 in practice there is interference between different cables at higher 

 frequencies, the correcting network should introduce increased attenua- 

 tion above this range. Calculations gave 



at/ = 0, a = 4.40 napiers; 

 and 



at/ = 25~, a = 14.10 napiers. 



Assuming arbitrarily that the network will have at / = 25~ an 

 attenuation of only .30 napier, the ideal total attenuation for the 

 frequency range is 



a' = 14.10 + .30 = 14.40 napiers. (67) 



The attenuation of the network should decrease from a maximum 

 value of (14.40 - 4.40) = 10.00 napiers at / = to a value of .30 

 napier at / = 25 ~ and then increase with frequency. If a linear 

 relation for the resultant phase is assumed so as to cross the b curve 

 at about/ = 25~, the phase which the network should give is negative 

 in the range with a minimum of about — 2.75 radians, and is zero at 

 / = Oand/ = 25~. 



A network having this desired general type of propagation constant 

 is Network 8, Appendix IV, with the characteristic 1, but a single 

 section will not be sufficient since its minimum phase is between 



