Abstract
This paper introduces an innovative passive topology of bandpass (BP) negative group delay (NGD) electrical circuit implemented with symmetric H-tree network. The multi-port topology of BP NGD circuit is originally represented by a resistorless H-tree constituted by lumped LC-passive network. Until now, the NGD electronic circuits available in the literature are implemented by two-port circuits which are using either resistive elements or distributed microstrip topologies. In the present investigation, the feasibility of the modelling, design, fabrication and test of unfamiliar BP NGD original H-tree circuits. The main objective of the study is to identify analytically the existence of the BP NGD function with the resistorless H-tree circuit. Because of its simplicity and the analytical equation compactness, the uncommon approach of tensorial analysis of networks (TAN) is used in the paper. After the branch and mesh analyses, the impedance matrix of the resistorless H-tree is elaborated. Hence, the resistorless H-tree equivalent S-matrix is established by means of impedance to scattering matrix transform. The BP NGD analysis in function of the inductance and capacitance parameters constituting the H-tree circuit is presented. Then, the main steps of the BP NGD investigation are described. The existence of BP NGD behavior in function of the adequate transmission parameters is identified by the consideration of the canonical form. To validate the BP NGD behavior, a proof of concept (POC) of LC-network based resistorless and symmetrical tree prototype is designed, fabricated and measured. Comparison results between well-correlated TAN calculation, simulation and experimentation are discussed. INDEX TERMS Tensorial analysis of networks (TAN), Kron's formalism, bandpass negative group delay (NGD), resistorless topology, lumped H-tree, symmetric multi-port circuit, S-parameter modeling, LC-network passive circuit.