Design and Tuning of Extracted-Pole Filters With Non-Resonant Nodes by Circuit Model Extraction

This article proposes an analytical circuit model extraction technique for extracted-pole filters with nonresonant nodes (NRNs). The circuit model is described by a generalized coupling matrix incorporating both resonant nodes and NRNs. It is shown that, in most cases, Y-parameter polynomials of extracted-pole filters with NRNs take the same form as those of coupled-resonator filters. Thus, the model-based vector fitting technique can be applied to obtain legitimate rational function approximation to measured or simulated S-parameter data, and then, a circuit model in the correct form can be synthesized accordingly. This article discusses different possible arrangements of extracted-pole sections to develop a general solution to the circuit model extraction problem. It also defines a standard circuit form to rule out multiple solutions in the circuit model extraction problem for guiding the computer-aided design and tuning process. A combline filter design and a waveguide filter tuning example are presented to demonstrate the application of the circuit model extraction technique. These examples show that simple mapping relationships exist between extracted circuit parameters and physical elements. Thus, accurate dimensioning of extracted-pole filters can be accomplished without electromagnetic optimization in the design phase. Filter fine-tuning can be done by inexperienced operators or an automatic tuning machine with the circuit model extraction technique.