Investigation of the Two-Mode Regime of Two-Gap Photonic-Crystal Resonance Systems Produced on a Printed Circuit Board with Fractal Elements "Minkowski Island

Introduction. The development of new amplifiers and generators of the Ku- and K-bands (12…27 GHz) for use in onboard equipment is increasingly attracting research interest. Low-voltage multi-beam klystrons (LMBK) can be a promising element base for such devices. Serious problems are associated with the need to suppress parasitic modes of oscillations in NMLK operating in the centimeter and millimeter range. A possible solution is to use double-gap photonic-crystal resonators (DPCR) in LMBK. Another promising direction for improving the characteristics of such resonators is to use resonant segments of strip lines with fractal elements. In this case, the strip lines are placed on a dielectric substrate in the interaction space. Such resonators exhibit new properties that are useful for klystrons (an increase in characteristic impedance, suppression of the spectrum of unwanted frequencies, a reduction in mass and dimensions).

Aim. Determination of an optimal set of electrodynamic and electronic parameters of double-gap photonic-crystal resonance systems with fractal elements "Minkowski Island" when operated as part of the LMBK resonator system, excited on π- and 2π-modes of oscillation.

Materials and methods. To calculate the electrodynamic parameters of resonators, the method of finite differences in the time domain was used. The well-known Wessel-Berg method was used to calculate electronic parameters, such as the G_e / G₀ electronic conductivity and the coupling coefficient M.

Results. The main electrodynamic parameters of the resonator – Q-factor, resonant frequency and characteristic impedance – were investigated. The electronic parameters of the resonator, the coefficient of coupling with the electron beam, and the relative electronic conductivity for π- and 2π-modes of oscillations were calculated. In this case, three variants of the resonator with zero, first and second iterations of the fractal element were investigated. The amplitude-frequency characteristics of the resonator were investigated with a change in the pitch of the photonic crystal lattice. An estimation of the inhomogeneity of the high-frequency field in the interaction spaces of the resonator was carried out. Operational conditions were determined simultaneously for two types of oscillations without self-excitation.

Conclusion. The results can find application in the development of resonator systems for klystron-type devices in the centimeter and millimeter ranges.

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