This article presents the design of bandpass filters with tunable transmission zeros (TZs) using frequency-dependent coupling (FDC) structures, which are introduced as cross-couplings in trisections. Theoretically, a bandpass filter with cross-coupling FDCs can achieve different filtering characteristics by changing the signs of the coupling coefficients. For this purpose, an FDC realized by a dual-post coupling structure is proposed, which contains two antipodal partial-height posts to couple two TE <tex-math notation="LaTeX">₁₀₁</tex-math> modes of rectangular resonators. An important feature of this coupling structure is that the coupling sign can be tuned from negative to zero and positive. Based on this structure, two trisection units with two TZs are designed. One can flexibly tune the positions of the TZs on the left and right sides of the passband, and the other introduces TZs on both sides of the passband. Using these two types of trisections, two fifth-order filters with different TZ distributions are designed, fabricated, and measured. The measurements show good agreement with the theoretical analysis and simulations.
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Yan et al. (2024) studied this question.
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