Simple,fast, and accurate parametric modeling of the coupling and external quality factor for microstrip filter design using active learning method

In the realization step of any microstrip filter according to the required electrical characteristics, coupling factors and external quality factor (Q_ext) are related to the physical parameters of the structure using time consuming full wave simulations. This paper presents a simple, fast, and accurate parametric model of the coupling between the coupled square open loop resonators (SOLRs) and Q_ext of these resonators versus physical parameters of the structure and substrate characteristics utilizing active learning method (ALM). In the modeling process the multi-dimensional functions of coupling factor and Q_ext are broken down into their simpler aspects, their behaviors are extracted and then final model will be constructed by combining these simpler aspects. ALM allows the overall model for coupling factor and Q_ext to be developed through the use of small number of initial data. Once the modeling process is completed it provides a fast and accurate prediction of the required physical parameters for a given coupling factor and Q_ext. Using the constructed model for a distinct SOLR, which its accuracy was validated by comparison with the full wave simulation results a filter was designed and fabricated. Good agreement between measured and simulated response confirms the accuracy of the modeling procedure.