Application of the Optical Perturbation Coupled-Mode Theory to the Design of a Microwave Coaxial Filter With a Support-Free Gradient Profile for Additive Manufacturing

The additive manufacturing (AM) technology requires compatible design and analysis theories to utilize its advantages in processing complex structures to produce high-performance microwave devices. Microwave devices designed based on traditional theories contain a large number of right-angle corners and abruptly varying structures, making them unsuitable for AM. The optical perturbation coupled-mode theory (PCMT) is adopted to analytically relate gradient geometric variations in coaxial microwave waveguides to multimode coupling behavior, resulting in a systematic design methodology for the synthesis, analysis, and fabrication of microwave filters suitable for AM. Derived from orthogonal mode expansion with first-order boundary perturbations, the proposed theory provides a unified framework that connects the geometry, modal evolution, and scattering response. The PCMT offers three advantages through the synergy of physical clarity, computational efficiency, and fabrication compatibility. It provides explicit insight into the local geometry’s influence on the amplitude and phase evolution, enables broadband prediction using only a few dominant modes, and yields right-angle-corner-free profiles well suited to support-free AM. By flexibly switching the inner conductor of different profiles, various frequency responses can be achieved, increasing the adaptability of the proposed methodology to multiple application scenarios. The proposed methodology enables rapid and efficient synthesis of gradient coaxial waveguide filters without parametric sweeping, offering a promising solution for the design and fabrication of lightweight, low-loss, low-cost, and modular microwave components by AM.