Investigation of signal distortion in cables caused by imperfections in cable manufacture

A complete theory of signal distortion caused by irregularities in the structure of coaxial cable is developed. The theory is general in the sense that it is developed in terms of the properties of an arbitrary reflection-density function r(x) of the cable. The formulas derived relate signal distortion to the statistics of the r(x) process and to its power-density spectrum. The use of the theory is illustrated by application to four classes of irregularity in cables: (i) periodic, (ii) random but approximately periodic, (iii) random, but with a power-density spectrum which is a slowly varying function of frequency, and (iv) random with a flat power-density spectrum. In particular, formulas are derived for the expected attenuation a and the phase-change coefficient ß. Signal distortion is studied in some detail, and the expected pulse distortion is calculated with particular reference to a cable with approximately periodic irregularities. The stability of statistical estimates is examined with particular reference to measurements on commercial cables. It is shown that, to determine certain cable parameters with a reasonable degree of certainty, it is necessary to have available for tests substantial lengths of cable.