392 BELL SYSTEM TECHNICAL JOURNAL 



length and the characteristic impedance, K, which quantities are 

 defined at the frequency pjiir by the formulas 



r = ^{R+jpmG+jpC), (5) 



R+jpL 

 ^ - \G+jpC • ^^^ 



Knowing these two quantities at any frequency, the values of the 

 four parameters can be readily computed. 



The propagation constant and the characteristic impedance of 

 telephone cables lOO miles or less in length have been determined by 

 measuring the input impedance of the cable with the distant end in 

 turn insulated and grounded. These two impedances are determined 

 for a cable of length 5 by the formulas 



Zr = K coth Vs 

 Zg = K tanh Ts, 



and given the values oi Zr and Za it is an easy matter to compute 

 the corresponding values of propagation constant and characteristic 

 impedance, the accuracy of this determination depending upon the 

 difference between Zj and Zg- In the case of a submarine telegraph 

 cable of the order of 2000 miles in length, the value of Ts is so large 

 that Zi and Z g differ by less than one part in 10,000 in the frequency 

 range in which we are interested. This means physically that the 

 remote parts of the cable have little effect upon the terminal impedance 

 of the cable and the values of input impedance are determined almost 

 entirely by the parameters of the 400 or 500 miles of cable adjacent to 

 the terminal. It is true that by going to extremely low frequencies, 

 perhaps fractional cycles per second, the method above described 

 could be used to determine the characteristic impedance and the 

 propagation constant of long cables, but at such frequencies these 

 quantities are determined almost entirely by the d.c. resistance and 

 capacity of the cable and no information regarding the quantities in 

 which we are particularly interested would be obtained. 



The method that has actually been employed to determine the 

 parameters of several of the continuously loaded cables which have 

 recently been laid is to measure separately at a number of frequencies 

 the real and imaginary parts of the propagation constant, the capacity 

 of the cable at various frequencies being determined by correlating 

 the results of laboratory tests with d.c measurements of capacity 

 made on the laid cable. 



