542 BELL SYSTEM TECHNICAL JOURNAL 



characteristic impedance of any two elementary pieces. This repre- 

 sents a first approximation to the problem. It is fairly accurate for 

 pairs in ordinary cable in which the outstanding irregularities are devia- 

 tions, from the average, between whole reel lengths; and in which the 

 lengths of the successive spliced pieces (reel lengths) are at least 

 roughly the same. 



There are irregularities in some coaxial conductors in which the 

 impedance change is gradual rather than abrupt from one element to 

 the next, and in which the elements can vary in length along the line. 

 For these cases the approximation is a little over-simplified. However, 

 although this somewhat affects the echo wavelets as computed from 

 the impedance deviations along the line, Didlaukis and Kaden, as 

 referred to above, have shown that it does not affect the ratio between 

 the echo wavelets, suitably averaged, reaching the receiving end and 

 those, similarly averaged, returning to the sending end. 



With the above assumptions there will be some correlation between 

 the reflections at the two ends of an elementary length. If, for 

 example, this length happens to be high in characteristic impedance the 

 reflection at one end will tend greatly to be the negative of that at the 

 other end. For this reason we are going to break up the reflection into 

 two parts, at a point between any two successive elementary lengths of 

 circuit — one part from one length of the circuit to an infinitesimal 

 length of cable of average characteristics inserted between the two 

 elementary lengths — and the other from this infinitesimal piece to the 

 next elementary length of circuit. There is then 100 per cent correla- 

 tion between the reflections at the two ends of a given elementary 

 length (one being exactly the negative of the other) ; but there is no 

 correlation between the reflections from any one elementary length to 

 its adjacent infinitesimal piece of average cable, and the reflections 

 from any other elementary length to its adjacent piece. This same 

 treatment is used in the calculation of certain types of "reflection" 

 crosstalk. 



The departure in characteristic impedance in the usual transmitting 

 circuit in the higher frequency range, where the irregularities are most 

 important, results essentially from deviations in the two primary con- 

 stants of capacitance and inductance, each per unit length. There is a 

 certain correlation between these, inasmuch as the capacitance devia- 

 tion is contributed to both by differences in the dielectric constant of 

 the insulation and by differences in the geometrical size, shape, and 

 relative arrangement of the conductors; and the inductance deviation 

 is contributed to by the latter alone. If there were no deviation in 

 dielectric constant there would be no deviation in velocity of propaga- 



