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

Abstract

AbstractThis 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.