Chin. Phys. B, 2014, Vol. 23(8): 088401    DOI: 10.1088/1674-1056/23/8/088401
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Complete eigenmode analysis of a ladder-type multiple-gap resonant cavity

Zhang Chang-Qing (张长青), Ruan Cun-Jun (阮存军), Zhao Ding (赵鼎), Wang Shu-Zhong (王树忠), Yang Xiu-Dong (杨修东)
Key Laboratory of High Power Microwave Sources and Technologies, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China
Abstract  A theoretical model is developed for calculating the eigenmodes of the multi-gap resonant cavity. The structure of concern is a kind of ladder-type circuit, offering the advantages of easy fabrication, high characteristic impedance (R/Q), and thermal capacity in the millimeter wave to THz regime. The eigenfunction expansion method is used to establish the field expressions for the gaps and the coupling region. Then, the match conditions at the interface are employed, which leads to a group of complicate boundary equations in the form of an infinite series. To facilitate the mathematical treatments and perform a highly efficient calculation, these boundary equations are transformed into the algebraic forms through the matrix representations. Finally, the concise dispersion equation is obtained. The roots of the dispersion equation include both the axial modes in the gaps, which include the fundamental and the high-order modes, and the cavity modes in the coupling region. Extensive numerical results are presented and the behaviors of the multi-gap resonant cavity are examined.
Keywords:  multi-gap resonant cavity      ladder-type circuit      eigenfunction expansion      mode spectrum
Received:  29 October 2013      Revised:  06 March 2014      Accepted manuscript online:
 PACS: 84.40.Dc (Microwave circuits) 03.50.De (Classical electromagnetism, Maxwell equations) 41.20.-q (Applied classical electromagnetism) 84.40.Fe (Microwave tubes (e.g., klystrons, magnetrons, traveling-wave, backward-wave tubes, etc.))
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61222110 and 60971073).
Corresponding Authors:  Zhang Chang-Qing     E-mail:  c.q.zhang@163.com