Negative Group Delay Theory on Li Topology

Abstract

This paper investigates an innovative negative group delay (NGD) theory of ''li'' geometrical shape topology. The li-topology is an outstandingly simple and fully distributed circuit comprised of a coupled line (CL). The li S-parameter model taking into account the CL coupling coefficient, delay and attenuation is established. The NGD analysis showing the possibility to generate NGD condition with respect to the li topology parameters is developed. The NGD characteristics as NGD value, center frequency, bandwidth, transmission and reflection coefficient are expressed. The li-NGD theory is validated with two proofs-of-concept implemented in microstrip technology. Calculated models, simulations and measurements are in good correlation. As expected, bandpass NGD presenting center frequency at approximately 2.56 GHz and 0.92 GHz with NGD level of approximately −0.9 ns and −3.7 ns were realized with the small and large li prototypes. Outstanding time-domain analyses explaining the bandpass NGD meaning, with innovatively low attenuation output, were also presented. The time-domain results highlight li-output pulse signal envelopes in time advance without violating the causality. INDEX TERMS Distributed circuit, li-topology, microwave theory, negative group delay (NGD), S-matrix modelling.

Experimental Time-Domain Study for Bandpass Negative Group Delay Analysis With Lill-Shape Microstrip Circuit

“…TOPOLOGY LEADING TO INSPIRATION OF THE lill-CIRCUIT Fig. 3(a) represents the circuit diagram of the "li" topology [22]. It acts as one of the elementary NGD topology which can built with a single CL.…”

“…For the case of li microstrip circuit with effective permittivity, reff  , the NGD center frequency can be defined with the equation [22]:…”

“…It has been found since the early of 2000s that innumerable microwave circuit topologies [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] are susceptible to behave as an NGD function. In 2010s, one of the most explored NGD circuits are based on the microstrip transmission line (TL) [8][9][15][16][17][21][22][23]. Among the TLbased NGD topologies, the circuits designed with coupledline (CL) ones [22][23][24] seem to be the best candidate against the issues related to the attenuation loss.…”

“…In 2010s, one of the most explored NGD circuits are based on the microstrip transmission line (TL) [8][9][15][16][17][21][22][23]. Among the TLbased NGD topologies, the circuits designed with coupledline (CL) ones [22][23][24] seem to be the best candidate against the issues related to the attenuation loss. Until now, the degree of freedom of topologies using CL structure motivates the NGD researchers to exploit the structure.…”

“…Despite the progressive development of the research works on the NGD circuit design [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], the NGD functions are not still open to most of non-specialist electronic design, fabrication and sale engineers. Many questions remain technically open about the meaning and the interpretation of the NGD effect.…”