

748 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



When the development program on deep sea repeatered .submarine 

 telephone cable systems was reactivated at the close of World War II, 

 one of the first problems to present itself was the detei-mination of the 

 delay distortion of a transatlantic repeatered cable system. The only | 

 means then known of obtaining an answer to this problem was by com- 

 puting the minimum phase of the system from its predictable attenua- 

 tion characteristic, using Bode's straight line approximation method,* 

 and then determining the delay distortion from the non-linear portion of 

 this minimum phase. However, the non-linear phase is such a small part 

 of the total phase, that a five figure accuracy tabulation of Integral (1) 

 was needed for a satisfactory determination of the non-linearity. The 

 necessary table was therefore compiled. A mmierical computation was 

 used to evaluate the integral because of the simplicity of its integrand. 

 The minimum phase of the projected transatlantic repeatered telephone 

 cables was then computed using this table and the anticipated delay dis- 

 tortion was determined from the non-linear portion of this minimum 

 phase. 



About this time the delay ecjualization of coaxial cable systems for 

 television transmission became a pressing problem. Bode's techniciue 

 proved to be the simplest means for determining the delay to be equal- i 

 ized and so the existing phase table was immediately put to use in the ji 

 coaxial cable delay ecjualization program. 



The increasing use of the tables led to a decision to publish them in in 

 The Bell System Technical Journal.^ In order to make the tables 

 more generally useful, the published paper included a tabulation of the 

 phase in radians as well as in degrees. The radian tables can, for example, I 

 be used to determine the reactance characteristic associated with a given 

 resistance characteristic of a minimum reactance impedance function. 



Because of the demand for higher accuracy which occasionally arose 

 after the publication of the five place tables, it was decided to undertake 

 the computation of seven-place tables. These tables were also computed 

 lunnerically using intervals selected to give at least ±1 accuracy in the 

 final figure. The complete tables require forty-nine pages for tabulation. 

 Since it is probable that only a fraction of the Journal readers would 

 need these tables, it did not seem desirable to publish the actual tables iti 

 the Journal. They are therefore being put)lished in original monograph 

 form as Bell System Monograph 2550 entitled "Tal)les of Phase of a 

 Semi-Infinite Unit Attenuation Slope." The phase is tabulated in the 



■' Ibid : Chap. XV. 



■* Tliomas, D. K., Tables of I'liase Associated willi a Semi Inliiiile I'nil Slope 

 of Attenuation, B. S.T.J. , 26, pp. 870-899, Oct., 1947. 



^ This Monograph will be available about June 15, 1956. 



