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This paper introduces a coupling matrix synthesis method tailored for a class of tunable bandpass filters (BPFs) with reconfigurable filtering characteristics. The filter has symmetric transmission zeros (TZs) which can be reconfigured on the real or imaginary axis of the complex plane. Different filtering characteristics can be obtained by merely tuning resonant frequencies of certain resonators. The frequency tuning and reconfigurable states of the filter can be achieved simultaneously. The synthesis procedure mainly includes three steps. First, a transversal coupling matrix is synthesized according to the design specifications of one of the reconfigurable states. Second, the matrix is transformed to an intermediate configuration, in which some of the coupling coefficients on the mainline couplings are designated as the key coefficients. Tuning these key coefficients alone can change the locations of TZs to realize reconfigurable filtering characteristics. In this intermediate configuration, the coupling matrix is optimized based on the synthesized values to make all reconfigurable filter states meet their design requirements. Finally, the key coefficients are rotated to the diagonal entries of the coupling matrix, so that reconfigurable TZs are realized by merely tuning the resonant frequencies of certain resonators. The reconfigurable mechanism and the maximum number of TZs under different filter orders are investigated in detail for a variety of coupling diagrams. Two synthesis examples are presented to show the novel reconfigurable filter optimization procedure. For experimental verification, a fourth-order tunable BPF with a pair of reconfigurable symmetric TZs was fabricated and measured. The filter states with TZs on the real or imaginary axis of the complex plane can be switched solely by tuning resonant frequencies, which validates the proposed synthesis approach of tunable filters.

Tunable Bandpass Filters With Reconfigurable Symmetric Transmission Zeros on Real or Imaginary Axis