Novel Tee-Shaped Topology Theory of Low- and High-Pass NGD Double-Type Function

Abstract

Recent investigation reports that certain electronic circuits operate with the unfamiliar negative group delay (NGD) function. It is fundamentally stated that the NGD circuits can be classified in different types. For example, we have the simplest ones as LP and HP NGD circuit types. So far, all the NGD studies are focused on simple type function. In step up of the research about the NGD electronic circuit engineering, this paper develops an original theory of electronic circuit topology operating with double NGDtype behavior. The study consists in the theorization of three-port circuit simultaneously generating LP and HP NGD function types. The proposed three-port innovative circuit under study is innovatively composed of resistive-capacitive (RC) network of Tee-shaped topology. Moreover, the LP and HP double-NGD circuit is a first order cell which does not contain any inductive component. The LP and HP NGD analyses of the Tee-topology is based on the 3-D S-matrix modelling. Analytical investigation based on classical circuit theory is elaborated to determine the S-matrix model from the equivalent admittance matrix. The identification of the double-NGD function is established from the LP-and HP-NGD canonical forms. Hence, the specific double-NGD characteristics are defined in function of the R and C elements constituting the three-port topology. To validate the developed double-NGD theory, a proof-of-concept (PoC) of SMD lumped component-based three-port circuit is designed, simulated, fabricated and tested. The calculated, simulated and measured results from the three-port circuit PoC prototype in very good agreement confirm the double-NGD behavior. The proposed innovative NGD three-port circuit design is useful in the future for the synchronization of signals propagating through multi-way communication system.INDEX TERMS Negative group delay (NGD), low-pass (LP) NGD function, high-pass (HP) NGD function, RC-network, circuit theory, three-port topology, LP-HP double-NGD analysis.

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“…In the past two year, more general topologies of NGD circuit with multi-port accesses were performed [71][72][73][74][75][76][77][78]. The design feasibility was verified with three-port topologies as Y-or T-shape circuits [71][72][73][74]. The BP-NGD function was also verified with ∆-shape lumped circuit [75].…”

New Analytical Approach to Estimate the Electromagnetic Spectrum From Devices Submitted to High Voltages

“…At the beginning, all the research work on LP-, HP-and BP-NGD circuit design was focused on two-port topologies . In the past two year, more general topologies of NGD circuit with multi-port accesses were performed [71][72][73][74][75][76][77][78]. The design feasibility was verified with three-port topologies as Y-or T-shape circuits [71][72][73][74].…”

High-pass negative group delay analysis of single capacitor three-port circuit

“…The S-matrix of our three-port topology is established by considering reference impedance R 0 = 50 Ω. According to the S-matrix theory, we have the Y-to-S matrix transform (Nebhen and Ravelo, 2021; Wan et al , 2021; Jia et al , 2022; Sambatra et al , 2022; Ravelo et al , 2021c, 2022e): with the 3D identity matrix: Substituting the Y-matrix given in equation (5) into matrix equation (7), we have the expression of S-matrix in function of R and Z : where the reflection coefficients are: and the transmission coefficients are: where: …”

“…The S-matrix of our three-port topology is established by considering reference impedance R 0 = 50 X. According to the S-matrix theory, we have the Y-to-S matrix transform (Nebhen and Ravelo, 2021;Wan et al, 2021;Jia et al, 2022;Sambatra et al, 2022;Ravelo et al, 2021c:…”