Miniaturized microstrip filters using quarter-wave or quasi-quarter-wave resonators with cross-coupling are presented. The quarter-wavelength resonators enable very compact positively or negatively cross-coupled filters to be realized. The combination of quarter-wave and quasi-quarter-wave resonators facilitates the cross-coupling with a proper coupling phase. A new explanation for the coupling phase between the main-coupling and cross-coupling paths is proposed. Different filters that use the proposed resonators are realized and may have either quasi-elliptical or flat group-delay responses. Measurement results correlate well with theoretical predictions.
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Chen et al. (2003) studied this question.
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