This paper investigates the original circuit theory on stopband (SB) negative group delay (NGD) passive topology. The basic specifications of SB-NGD function are defined by considering the voltage transfer function (VTF) of the passive circuit. An original design method and experimentation tests of SB-NGD circuit are developed. The innovative theoretical analysis is elaborated from both magnitude and GD analytical expression of the VTF model from the resonant LC-series network passive topology. The mathematical existence condition of SB-NGD aspect is analytically explored in function of R, L, and C component parameters. The formulations of the basic equations enabling the calculation of the lumped components of the SB-NGD passive circuit in function of the desired specifications as NGD cut-off frequencies, NGD value and attenuation are established. To confirm the effectiveness of the original SB-NGD circuit theory, a proof-of-concept (POC) of SB-NGD circuit board is designed, simulated, fabricated, and experimented. As expected, despite the equivalent series resistor (ESR) effect of the inductor element, the theoretical modelling, simulation and measurement results are in good agreement. The SB-NGD behavior is confirmed with lower and upper cut-off frequencies, 0.7 kHz and 1.35 kHz, respectively. Furthermore, the corresponding NGD minimal values are −33 µs and −11 µs, respectively.

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.