Abstract :
The paper gives a statistical treatment of line irregularities in which the correlation theory is briefly surveyed, and describes in detail an alternative treatment using ?unit irregularities,? which yields equivalent results. The reflection and transmitted echo coefficients are derived for families of lines, and it is shown that whilst the latter generally add on a random basis and increase with the square root of the cable length, the effects due to double reflections within the units add systematically and increase linearly with length. Formulae are developed for various types of unit irregularity, and the corresponding correlation functions are given. There is evidence that the unit irregularity and the correlation function for drum lengths of coaxial cable have an exponential character. The effects of reflections on the insertion loss are considered, and it is shown that double reflections within unit irregularities cause an increase in the mean attenuation. Reflections arising from the mismatch between cable and associated repeaters are evaluated, and the formulae are applied to compare the steady-state echoes from various sources in a 600-mile coaxial-cable link, with special reference to the requirements for broad-band telephony. An extension of the Didlaukis-Kaden quasi-steady-state method is used to study the time effect of irregularity echoes, and their effect on television. The unit-irregularity method is applied, and leads to the conclusion that there are relatively large initial transients due to double reflections within the units which decay very rapidly, whilst others due to reflections between units are initially smaller and last longer. The 600-mile link is considered with reference to the requirements for television, and the conclusion is drawn that, with recently developed repeaters, the reflection effects are well inside the tolerable limits. It is evident that whilst a suitable criterion for the regularity of repeater sections of coaxial cable- intended for broad-band telephony is the smoothness of the input-impedance/frequency characteristic, this needs to be supplemented by pulse-reflection observations if the cable is intended for television.
