Negative group delay in lumped-element C-L transmission lines

Superluminal group velocities, i. e., velocities greater than the speed of light in vacuum, infinite or even negative, have been experimentally observed in the optical, electronic, and microwave domains. Such velocities in no way contradict special relativity because group velocity does not represent, in general, the velocity of a signal or information. Although it may seem counterintuitive, superluminal phenomena and the resulting negative-group-delay (NGD) effects find a variety of applications such as ultra-wide-band phase shifters, high-speed microelectronic interconnections, pulse shaping, delay control, dispersion compensations, and wave-packet switching, for instance. This paper reports on negative group velocities in a lumped C-L line, where capacitors C and inductors L connected to resistors are placed, respectively, in the series and shunt branches of the periodic line. The NGD effects are induced by 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 a 180 kHz modulated Gaussian pulse, with a full width at half maximum of 22.20 μs, for which the negative time delay of -1.26 μs determined from the numerical solution of circuit equations is in good agreement with that predicted by the analytical dispersion relation of the periodic structure.