Analytical method and device for average electric polarizability density of small holes in any shape and medium

Abstract

The invention discloses an analytical method and device for average electric polarizability density of small holes in any shape and medium, and the method comprises the steps: building a contour function Rho (Theta) based on polar coordinates according to the contour of a small hole to be analyzed on a conductive screen, and setting the geometric gravity center of the small hole to be analyzed asthe original point of the polar coordinates; repeating small holes with circular holes with radii is Rho (Theta2), Rho (Theta 3)to Pho (Theta n=2Phi), replacing the center of a circle of each circularhole on the geometric center of gravity of the small hole to be analyzed, calculating the electric polarizability corresponding to each circular hole according to a circular hole electric polarizability formula, and carrying out the limit operation of the arithmetic mean value on the electric polarizability corresponding to each circular hole to obtain the corresponding arithmetic mean value of the electric polarizability; Taking the arithmetic mean value of the electric polarizability as an approximate value of the electric polarizability of the small hole to be analyzed, and calculating theaverage electric polarizability density of the small hole to be analyzed according to a first formula. According to the method, on the premise that the precision is not lost, the calculation step ofthe average polarizability density of the small holes in any shape can be simplified, and meanwhile the solution efficiency of the small hole coupling problem is remarkably improved.

Description

technical field [0001] The invention relates to the technical field of microwave systems, in particular to an analysis method, equipment and medium for the average electric susceptibility density of small holes with arbitrary shapes. Background technique [0002] In microwave engineering, it is often necessary to know the coupling of a small hole to the electromagnetic field, for example, to quantitatively calculate the coupling of two waveguides of different sizes through the small hole on their common waveguide wall, which is very important for designing microwave systems. [0003] As early as 1944, H.A. Bathe first proposed the famous small hole coupling theory, but the theory only calculated the average electric susceptibility density of circular small holes, so the theory could only be used to calculate the Electromagnetic coupling problem. Since then, many scholars have devoted themselves to solving the average electric susceptibility density of small holes of various...

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Problems solved by technology

Okon et al. developed a method based on the method of moments that can calculate the average electric susceptibility density of small holes of any shape, but this method needs to model and subdivide the small holes, and generally needs to use professional simulation software for calculation. very convenient

Scholar Fabricant developed a method to solve the average polarizability density of small holes based on hypergeometric functions, and obtained the formulas for calculating the average polarizability density of pentagons, rectangles, rhombuses, crosses, and sectors through this method, but The mathematical derivation process of this method is extremely complicated, and a new analytical formula needs to be re-deduced for each shape of the small hole. The derivation is very complicated, and the solution obtained by this method is still not an exact solution. When the length and width of the small hole When the ratio is relatively large, the difference between the obtained average susceptibility density and the measured value is large. For non-mathematical engineers, it is necessary to directly analyze and calculate the average electric susceptibility density and the average The magnetic susceptibility density is a very difficult task, which makes the method very restrictive in practical application

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