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.

Radial stub based negative group delay circuit theory

“…Thanks to the phase expression defined in (28), the GD as a function of the resonance frequency is expressed as…”

“…Nevertheless, the available NGD circuit topologies are either implemented with passive complex structure or with lossy lumped elements. Therefore, the design of simpler NGD microwave circuits remains an attractive challenging research topic for NGD circuit researchers [28][29][30][31][32][33]. Acting as an unfamiliar research topic, it is always interesting to investigate more deeply the NGD circuits with any topologies.…”

“…In 2010s, NGD researches were more focused on low-attenuation passive topologies. A resistive lossy left-handed transmission line structure exhibiting NGD function was proposed in [28]. An NGD circuit built with absorptive band-stop filter was presented in [29].…”

Bandpass Negative Group Delay Theory of Fully Capacitive Δ-Network

“…The understanding curious questions about the NGV behaviors attracted also the attention of radio frequency (RF) and microwave design engineers in early 2000s. Some revolutionary designs were made with NGV structures based on the negative refractive index metamaterial and left-handed structures [13][14][15][16][17][18][19][20]. The metamaterial NGD circuits were usually implemented with split ring resonator (SRR) structures [13,18].…”

“…Some elementary topologies of low-pass (LP) [45], high-pass (HP) [46] and bandpass (BP) [47] NGD circuits were initiated. Following this innovative NGD theorization, we can understand that the previously described metamaterial inspired, coupled line and compact NGD microwave circuits [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] are classified as BP NGD function. However, in difference to the other electronic functions (filter, attenuators, phase shifters, amplifiers, power combiner, power dividers, …) if we summarize and classify all the NGD topologies existing in the literature , they are limited to the following characteristics:…”