The sun never sets on distributed networks

Abstract

As is well known, at high frequencies, when the physical dimensions of an electrical network are comparable to the wavelength, the network dynamics necessarily involves space variables, in addition to the time variable. Such networks form the general class of distributed networks, of which the transmission line is a common example. This lecture will trace the personal involvements of the author in exploring some of the interesting aspects of such networks, LC (bar denotes distributed) as well as RC. The latter type is encountered in integrated circuits and their interconnections, and in modelling some physical processes. The hitherto unsolved problem of general nonuniformity and the occurrence of irrational functions will be particularly highlighted. In the area of LC networks, two problems which will be given some emphasis are those of voltage compression and impedance matching with Ruthroff connection. The inadequacies of existing mathematical formulations of transmission line theory will be brought out with reference to the latter problem, and some others, and the current research in this direction will be mentioned. Finally, the natural occurrence of RC concepts in neural networks will be briefly touched upon.