Methods of theoretical analysis and computer modelling of the shaping of electrical pulses by nonlinear transmission lines and lumped-element delay lines

Some theoretical aspects of shock wave formation on uniform LC ladder networks containing either nonlinear capacitors or nonlinear (saturable) inductors are discussed. It is shown that, if the ladder is unbiased, then in the low-frequency limit the tendency of a propagating pulse is to form a shock front. In a distributed line such a shock front can reach a steady state form, but in a lumped element network decomposition into a soliton array eventually occurs. There is consequently an optimum length for a pulse sharpening line which is a compromise consisting in the need to minimize the rise time of the pulse without allowing undue fragmentation of the propagation wave front. The time development of large amplitude pulses as they propagate along the ladder is accurately predicted by numerical solutions of the coupled equations for the currents and voltages