Tensorial-Analysis-of-Networks Applied to Bandpass Negative-Group-Delay Analysis of Resistorless LC-Coupler-Network

This paper develops a bandpass (BP) negative-group-delay (NGD) analysis of multi-port topology. The circuit under study consists of resistorless symmetric coupler constituted by passive LC-networks. By using the tensorial-analysis-of-networks (TAN) formalism, an innovative study enables to verify if the four-port circuit is susceptible to exhibit the unfamiliar BP-NGD function. Using the TAN formalism, the different steps of the method is described from the branch and mesh spaces via the tensor connectivity to determine the equivalent S-parameters. The general methodology of the S-matrix modeling is expressed in the function of the coupler L and C parameters. To validate the BP-NGD behavior, an arbitrary parametrized lumped four-port coupler is considered as a proof-of-concept. The feasibilities of the TAN S-parameter modeling added by the BP-NGD function is validated comparison results between TAN mathematical calculations and simulations from a commercial tool. Excellent correlations between the calculated and simulated results are confirmed with BP-NGD behavior of the connections between port 1 and port 2 with −30 ns NGD value at the center frequency, 124 MHz, and between port 1 and port 4 with −27 ns NGD value at the center frequency, 92 MHz. The present results confirm a scientific result never being found before, the first time, which demonstrates the possibility to generate the BP-NGD function with a four-port resistorless circuit. The TAN method flexibility advantages are the flexibility to lumped and distributed circuits. However, the sensitivity to the component inaccuracies constitute the main drawbacks.