Determination of biconical cavity eigenfrequencies using method of partial intersecting regions and approximation by rational fractions

The paper considers the problem of determining the eigenfrequencies of biconical cavity making it possible to simplify the eigenfrequency-based design of devices. We used the solving of the excitation problem for biconical cavity using the method of partial intersecting regions in combination with the collocation method. Based on the concept of the search of quasisolution for determining eigenfrequencies, it was proposed to apply the fractionally rational approximation of cavity response obtained as a result of solving the problem of resonator excitation. The efficiency of finding eigenfrequencies of biconical cavity was substantiated by using the fractionally rational approximation based on the chain fraction interpolation of cavity response calculated only at collocation points. Using the above approach, we have obtained the relationship of eigenfrequencies of azimuth-symmetric oscillations of biconical cavity as a function of the aperture angle, and the typing of lower azimuth-symmetric transverse electric modes of biconical cavity has been performed

Simple technique for biconical cavity eigenfrequency determination

A number of features of biconical cavities make them attractive for various applications. Expressions for the calculation of the eigenfrequencies of a biconical cavity with large cone angles can be derived using the overlapping domain decomposition method in combination with the collocation method; however, the expressions reported in the literature involve only a single pair of collocation points, thus giving no way to estimate the eigenfrequency determination accuracy. The aim of this paper is to calculate the biconical cavity eigenfrequencies for an arbitrary number of collocation point pairs. An equation in the biconical cavity eigenfrequencies for an azimuthally symmetric transverse electric field at an arbitrary number of collocation point pairs is derived. The equation reduces to two equations, whose solution requires far less computational effort in comparison with the original equation. The solution of one of the two equations are based on modes symmetric about the cavity symmetry plane, and the solutions of the other are based on antisymmetric modes. The calculated eigenfrequencies converge rapidly with increasing number of collocation point pairs, while the use of only one collocation point pair may introduce noticeable error. The proposed technique may be used in the development of components and units on the basis of biconical cavities