Group-Delay Engineered Noncommensurate Transmission Line All-Pass Network for Analog Signal Processing

Abstract

A group-delay engineered noncommensurate transmission line two-port all-pass network for analog signal-processing applications is presented, analytically modeled, and experimentally demonstrated. This network consists of transversally cascaded C-sections, which are distributed implementations of the bridged-T equalizer lumped circuit. It is obtained by interconnecting the alternate ports of adjacent lines of a 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -port coupled transmission line network with transmission line sections, and it is modeled using multiconductor transmission line theory with per-unit-length capacitance matrix <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> and inductance matrix <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</b> . By allowing the different C-sections of the network to exhibit different lengths, a generalized group-delay engineering procedure is proposed, where quasi-arbitrary group-delay responses are achieved by combining the group-delay responses of C-sections with different lengths. A computer design approach based on genetic algorithms is applied for synthesis, which consists of determining the structural parameters of the different C-section groups. Using this approach, noncommensurate networks are group-delay engineered in edge-coupled stripline technology, and Gaussian, linear and quadratic group-delay responses are realized. The theoretical results are validated by experiment. Finally, two application examples of analog signal processing-a tunable impulse delay line and a real-time frequency discriminator-using the proposed dispersive noncommensurate all-pass networks are presented.