Dual-mode patch resonator-based microstrip filters with finite real or imaginary transmission zeros are discussed by combining the analytical studies with numerical investigations. The analytical study presents the coupling scheme of a dual-mode patch resonator, while the numerical simulation discusses the coupling nature between the source (input) and load (output), which constitutes the presented half-analytical model. Furthermore, the difference of in-band losses between the two different responses can also be qualified based on this model. The contribution and novelty of this work is the coupling nature between the source and load which is explained for the first time, and based on this, the half-analytical model can further estimate the transmission zeros of the microstrip patch resonator filter. For demonstration purposes, two prototype filters that exhibit transmission zeros at the real and imaginary frequencies, respectively, are developed and confirmed experimentally. The measurements agree closely with the predications.

中文翻译：

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具有实部或虚部传输零点的双模贴片谐振器滤波器的分析和数值研究

通过将分析研究与数值研究相结合，讨论了具有有限实部或虚部传输零点的基于双模贴片谐振器的微带滤波器。分析研究提出了双模贴片谐振器的耦合方案，而数值模拟讨论了源（输入）和负载（输出）之间的耦合性质，构成了所提出的半分析模型。此外，两个不同响应之间的带内损耗差异也可以基于该模型进行限定。这项工作的贡献和新颖之处在于首次解释了源和负载之间的耦合性质，在此基础上，半解析模型可以进一步估计微带贴片谐振器滤波器的传输零点。出于演示目的，两个原型滤波器分别在实部和虚部频率处显示传输零点，并通过实验进行了验证。测量结果与预测非常吻合。