Intrinsic-analysis method for assigned frequency of periodic structure

Abstract

The invention relates to an intrinsic-analysis method for assigned frequency of a periodic structure, which includes steps: A, setting a functional equation which can consider boundary value of an electromagnetic field in conductors and medium loss periodic structure and can obtain the boundary value of the electromagnetic field by means of standard variation principle of the finite element method; B, solving solution domain by gridding subdivision of a tetrahedron and guaranteeing gridding matching of a primary side and a secondary side of the periodic boundary; C, selecting primary function, expanding electric-field intensity vector in all grids by the primary function and obtaining a matrix equation of expansion coefficient by Ritz method; D, writing the matrix equation of the expansion coefficient into a linear generalized intrinsic equation about propagation constant; E, solving the linear generalized intrinsic equation by setting a frequency, obtaining attenuation constant and phase constant corresponding to the set frequency according to the propagation constant, and obtaining interaction impedance through after treatment; and F, repeating the step of E to obtain attenuation constants, phase constants and interaction impedance corresponding to different frequency.

Description

technical field [0001] The invention belongs to the technical field of three-dimensional electromagnetic field numerical solution, and in particular relates to an eigenanalysis method of a specified frequency of a periodic structure. Background technique [0002] Periodic structures are widely used in microwave tubes, including periodic changes in waveguide cross-section, periodic loading of diaphragms in waveguides, and periodic filling of dielectrics. In microwave tubes, periodic structures are commonly used as the high-frequency circuit of the device, forming a place where electron beams interact with high-frequency fields for energy exchange to realize microwave oscillation or amplification. The high-frequency characteristics of the periodic structure directly affect the device's operating frequency, frequency bandwidth, conversion efficiency, output power, and a series of other performances of the whole tube. It is extremely important to obtain high-frequency character...

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Problems solved by technology

[0005] Specified phase-shift eigenanalysis of periodic structures with loss (finite conductivity conductor and non-ideal medium) compared to specified phase-shift eigenanalysis of periodic structures without losses (conductor is assumed to be perfect conductor and medium is ideal medium) The method will be much more complicated, and the accuracy and efficiency will be much lower

Taking the finite element method as an example, first of all, due to the existence of the periodic boundary, the introduction of the dielectric constant considering the dielectric loss, or the surface impedance boundary considering the conductor loss, will make the finite element matrix generated by the periodic structure finite element analysis from the lossless case The Hermitian symmetric matrix becomes complex asymmetric matrix, thus increasing the solution time and memory

Second, in the case of loss considerations, the surface impedance of the conductor is a function of frequency, and the eigenanalysis method using the specified phase shift needs to solve a nonlinear generalized eigenproblem with respect to frequency, which is more complex than solving the linear generalized eigenproblem in the case of no loss Intrinsic problems are much more complex

Finally, in the case of considering the loss, the loss tangent of the medium varies with frequency, and there is no definite functional relationship

Therefore, when using the eigenanalysis method with a specified phase shift, only the estimated dielectric loss tangent can be used for eigenanalysis of the periodic structure, and the accuracy of the estimated dielectric loss tangent will seriously affect the eigenanalysis of the periodic structure the accuracy of

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