Negative group velocity in resistive lossy left‐handed transmission lines

Abstract

This study reports on negative group velocities in a lumped transmission line, where capacitors and inductors connected to resistors are placed in the series and shunt branches of the periodic line, respectively. The propagation characteristics of the left-handed transmission line are examined along with two methods. The first method consists of analysing the lumped-element ladder network by solving in the time domain a system of differential equations derived from the Kirchhoff's voltage and current laws. In the second method, transmission matrix of the unit cell is applied to obtain the dispersion diagram from which the time group delay induced by the periodic network is derived as a function of frequency. Also, non-analytical input signals are considered, whereby transient effects occur at both ends of modulated half-sine wave packets propagating under negative group delay (NGD) regime of the left-handed line. NGD effects arise from ohmic dissipation due to the resistors which establish a frequency range in which NGD propagation is allowed. This finding is numerically demonstrated by injecting into the line modulated Gaussian wave packets, for which the negative time delays determined from the numerical solution of circuit equations and from the dispersion relation are in good agreement.