Coupling Matrix Extraction for Computer-Aided Tuning of Narrowband Coupled Resonator Networks

Coupled resonator networks are widely used in wireless communication systems as frequency-selective components. One of the major challenges in the mass production of coupled resonator components arises from the extreme sensitivity of their electrical performance to dimensional errors and material variations. Tuning is necessary to realize desired frequency responses in the simulation phase and is of paramount importance after fabrication. Several effective tuning strategies have been developed in the past decades. This article focuses on a computer-aided tuning (CAT) technique based on coupling matrix extraction. The technical framework involves first de-embedding the frequency-dependent phases at the terminals using pole-zero analysis. Then, the phase de-embedded S-parameter data are converted into Y-parameters. Model-based vector fitting (MVF) is used to fit the Y-parameter data. By properly setting the numerator degrees and applying suitable weighting, MVF can enhance robustness against measurement noise. A transversal coupling matrix can be constructed from the rational function approximation to the Y-parameters. After coupling matrix transformation, the matrix can indicate the coupling coefficients that correspond to the current tuning state and guide subsequent tuning operations. Experiments have validated the effectiveness of the coupling matrix extraction technique. Challenges and future works are discussed at the end of the article.