Transmission Characteristics of the 

 Submarine Cable^ 



By JOHN R. CARSON and J. J. GILBERT 



Synopsis: The present paper presents an extensive theoretical investiga- 

 tion of the impedance of the "sea return" of various types of submarine 

 cables. In the case of the cables used for submarine telegraphy the im- 

 pedance of the sea return has been practically negligible because of the low 

 frequencies involved. For these low frequencies the cross-section of the re- 

 turn path is very large and its resistance low, even though the specific 

 resistance of sea water is of the order of ten million times that of copper. 

 As the frequency of the cable current is raised, however, the return cur- 

 rents crowd in nearer the cable and the resistance of the return path is 

 increased. For frequencies in and above the telephone range, the return 

 currents are forced into the steel armor wires around the cable and into the 

 water just outside of the insulation. The small cross-section of the water 

 involved and the loss in the armor wires cause the resistance of the return 

 path to become a very large part of the total resistance of the circuit. 



The present investigation led to the conclusion that the resistance of 

 the return path could be greatly diminished by winding a low resistance 

 conductor in the form of a copper tape immediately around the gutta 

 percha insulation applied to the core of the cable. The concentric, cylin- 

 drical conductor thus formed lies within the armor wires but is not insu- 

 lated from them and the sea water. Estimates of the sea return which 

 would have been obtained in the Key West-Havana cable if no copper 

 tape had been provided give values of 4, 6.5, and 8 ohms per nautical mile 

 at 1,000, 3,000 and 5,000 cycles. The resistance actually obtained with 

 the copper tape does not exceed 1.7 ohms at 5,000 cycles. The greater 

 values would have increased the attenuation by approximately 30% at 

 1,000 cycles and by 50% at the two higher frequencies. The present 

 cable permits of the operation of a carrier telegraph channel at 3,800 cycles, 

 this lying above the range of telephone frequencies. 



The paper gives a comparison of the theoretical conclusions with ex- 

 perimental data and the agreement is so satisfactory as to indicate that 

 the theory is a reliable guide in the design of such a cable. — Editor. 



I 



THE transmission characteristics of a conducting system, such as 

 a submarine cable circuit, are determined by its propagation 

 constant, F, and characteristic impedance, K, which may be calcu- 

 lated for the frequency p 12-k from the formulas: 



r = V {R^-ip L) {G + ipO, (1) 



^^ \R±ipL 

 \ G + ipC' 



where R, L, G and C are the four fundamental line parameters, re- 

 sistance, inductance, leakance, and capacity, all per unit length. These 

 formulas are rigorous for all types of transmission systems; but the 

 determination of the line parameters is not always possible by ele- 

 mentary methods, and may indeed be a matter of considerable com- 



' Reprinted from the Journal of the Franklin Institute, December, 1921. 



88 



