Transmission properties of doubly periodic LC ladder networks

On the basis of a general formulation described by a system of ordinary differential equations in the time domain, the present work examines filtering and transmission processes that occur in doubly periodic LC transmission lines. The formulation developed herein allows to include an arbitrary number of sections, where even and odd numbered sections are identified by two sets of reactive elements {L₂, C₂} and {L_1; Q}, respectively. It is shown that lumped-element transmission lines exhibit strong spatial dispersion whereby each line node shows a distinct frequency spectrum. Numerical results by considering inductors and capacitors with typical values of 1μH and 1μF and driving rectangular pulses of 5-μβ width are given and discussed by highlighting the spatial filtering features that occur on such LC lines.