Negative and zero group velocity in microstrip/negative-refractive-index transmission-line couplers

The existence of negative group velocity in the complex-mode region of an infinite length MS/NRI transmission-line coupler is shown. The negative group velocity is associated with only one of the complex modes (c-mode) and exists only when that mode is dominantly excited. The possibility of independently exciting either of the complex modes in an infinite coupler is discussed. A method is proposed for terminating a finite length coupler at one end with a two-port network which provides a matched boundary condition for the complex modes and extends the applicability of theorems and methods of infinite couplers to finite length MS/NRI-TL couplers. A circuit containing a 360° MS/NRI-TL coupler is designed and the presence of negative (and zero) group velocity is shown in design and experiment. Applications include constant with frequency phase shifters, dispersion compensation and broadside series-fed antennas with reduced-beam squinting.