Modeling and Analysis of Ladder-Network Transmission Lines with Capacitive and Inductive Lumped Elements

Abstract

This paper examines the properties of wave propagation in transmission lines with periodic LC and CL cells, taking into account ohmic losses in resistors connected in series to lumped capacitors and inductors. First order time differential equations are derived for current and charge, thus allowing analysis of transient regimes of the lines being excited by a pulse of arbitrary shape. In particular we examine the propagation characteristics of periodic lines in which identical unit cells are repeated periodically and also discuss the interpretation of positive and negative phase velocities associated with the LC and CL topologies. Loss effects on the propagation bandwidths of both lines are also discussed, and it is shown that in the left-handed transmission line (CL configuration) the phase advance of the crest of the transmitted signal with respect to the source signal is due to the intrinsic dispersive nature of the CL line which, in contrast to the LC line, is highly dispersive at low propagation factors.