Calculation for frequency-tunable resonant cavities using a global homogeneous mode-matching matrix

Background Frequency-tunable high-power microwave oscillators require repeated cold-cavity calculations over a range of tuning parameters, while conventional port scattering-parameter peak/valley criteria may fail to identify weakly coupled target eigenmodes.

Purpose This work proposes a fast target-eigenmode calculation method for a three-period coaxial resonant cavity based on a global homogeneous mode-matching matrix.

Methods The cavity is decomposed into uniform coaxial sections and radial step discontinuities. Axisymmetric modes are expanded in each uniform section, and all internal forward and backward power-wave amplitudes are retained to assemble a global homogeneous matrix. Candidate eigenfrequencies are determined by a normalized minimum-singular-value criterion, and the target π/2 mode is selected using a period-center phase-advance criterion and a TM₀₁-like field-pattern check.

Results At a typical tuning length of 4.6 mm, conventional S₁₁ and S₂₁ responses do not provide a clear peak/valley indication of the target mode, whereas the proposed criterion gives distinct eigenmode candidates and enables target-mode identification. As the tuning length varies from 0 to 4.6 mm, the target-mode frequency increases monotonically from approximately 13.8 GHz to 15.2 GHz. Under the adopted CHIPIC eigenmode boundary conditions and model settings, the target-mode frequency difference is less than 0.65%, and the computation time for a typical tuning point is about 1 min.

Conclusion The method provides an efficient tool for rapid cold-cavity design and target-eigenmode tracking in frequency-tunable high-power microwave sources.