This paper introduces an original study of low-pass (LP) negative group delay (NGD) circuit. The family of the proposed passive network cross-topology was rarely investigated in the literature. It acts as a tri-port passive circuit presenting a cross-shaped topology. The present study of tri-port passive circuit is originally based on S-matrix modelling. The identification method of LP-NGD function type is established. The considered passive tri-port topology is innovatively constituted by a resistorless LC-passive network. Thanks to the impedance 3-D matrix modelling, the cross-circuit S-parameters are analytically expressed. Then, the NGD analysis at very low-frequencies is presented. The LP-NGD behavior existence condition of the cross-circuit in function of the L and C components is established. The relevance of the tri-port NGD circuit theory is verified by a proof-of-concept of resistorless cross-circuit. Analytical modelling, simulation, and experimentation confirmed the LP-NGD design feasibility with NGD value of about −2 ns and 6.67 MHz cut-off frequency.

Purpose The purpose of this paper is to introduce an innovative theoretical, numerical and experimental investigations on the HP NGD function. The identified HP NGD topology under study is constituted by first order passive RC-network. The simulations and measurements confirm in very good agreement the HP NGD behaviors of the tested circuits. NGD responses with optimal values of about -1 ns and cut-off frequencies of about 20 MHz are obtained. Design/methodology/approach The identified HP NGD topology understudy is constituted by a first-order passive Resistor-capacitor RC network. An innovative approach to HP NGD analysis is developed. The analytical investigation from the voltage transfer function showing the meaning of HP properties is established. Findings This paper introduces innovative theoretical, numerical and experimental investigations on the HP NGD function. Originality/value The NGD characterization as a function of the resistance and capacitance parameters is investigated. The feasibility of the HP NGD function is verified with proofs of concept constituted of lumped surface mounted components on printed circuit boards. The simulations and measurements confirm in very good agreement the HP NGD behaviors of the tested circuits. NGD responses with optimal values of about −1 ns and cut-off frequencies of about 20 MHz are obtained.

Most of the recent studies on unfamiliar negative group delay (NGD) circuit were focused on the classes of low-pass (LP) and bandpass (BP) topologies. So far, few research works are currently available in the literature on the highpass (HP) NGD class. This paper introduces an original HP-NGD circuit theory of four-port passive topology constituted by a single lumped capacitor. The S-matrix equivalent model of the innovative topology is established from the admittance matrix. The basic analytical frequency-dependent responses are expressed. Then, the GD model is derived in function of the capacitor. It was analytically found that the four-port mono-capacitor passive circuit is susceptible to behave as an unfamiliar class of HP-NGD function. An innovative HP-NGD analysis is explored in addition to the expression of synthesis design equation in function of the expected NGD cut-off frequency which is linked to NGD optimal value. The validity of the established HP-NGD theory is verified with a proof of concept (POC) circuit. As expected, the POC enables HP-NGD behavior to show a good correlation between analytical model which is confirmed by the simulation.

Purpose This paper aims to develop high-pass (HP) negative group delay (NGD) investigation based on three-port lumped circuit. The main particularity of the proposed three-port passive topology is the consideration of only a single circuit element represented by a capacitor. Design/methodology/approach The methodology of the paper is to consider the S-matrix equivalent model derived from admittance matrix approach. So, an S-matrix equivalent model of a three-port circuit topology is established from admittance matrix approach. The frequency-dependent basic expressions are explored to perform the HP-NGD analysis. Then, the existence condition of HP-NGD function type is analytically demonstrated. The specific characteristics and synthesis equations of HP-NGD circuit with respect to the desired optimal NGD value are established. Findings After computing the frequency expressions to perform the HP-NGD analysis, this study demonstrated the existence condition of HP-NGD function type analytically. The validity of the HP-NGD theory is verified by a prototype of three-port circuit. The proof-of-concept (POC) single capacitor three-port circuit presents an NGD response and characteristics from analytical calculation and simulation is in very good correlation. Originality/value An innovative theory of HP-NGD three-port circuit is studied. The proposed HP-NGD topology is constituted by only a single capacitor. After the topological description, the S-matrix model is established from the Y-matrix by means of Kirchhoff voltage law and Kirchhoff current law equations. A POC of single capacitor three-port circuit was designed and simulated with a commercial tool. Then, a prototype with a surface-mounted device component was fabricated and tested. As expected, simulation and measurement results in very good agreement with the calculated model show the feasibility of the HP-NGD behavior. This work is compared to other NGD-type function with diverse number of ports and components.