Application Study On Fourier's Expansion-Differential Method (FEDM) In Waveguide And Resonance Cavity Problems

The problems of the transmission electromagnetic wave in waveguides and the electromagnetic resonance in resonance cavities are important ones in the application of electromagnetic theory, microwave and millimeter wave technology. With the complicacy of microwave engineering, more and more questions of this kind need to be solved simplely and efficiently. There are plenty of subjects and practical values to discuss these problems conveniently. Not only does it enrich the contents of the theory of electromagnetism, but also the reference can be provided for analyzing and solving the problem in microwave engineering field. So far, there are many kinds of methods to analyze the wave guide and resonance cavitie problem. Some very complicated ones have not been solved conveniently and efficiently, however. The new method of Fourier's expansion-difference method that was presented newly for analyzing arbitrary-shaped grooveguide is adopted in order to solve some practical application problems of wave guide in this paper. This method gathers the analytical and numerical calculation. It is amended and perfected so that it can be used to analyze the transmission characteristics of the arbitrary metallic waveguide filled with symmetrical and non-symmetrical dielectric, metallic resonance cavity with the arbitrary shapes, and other boundary value problems of the electromagnetic field.Several methods for improving calculation precision are provided in this paper. Just as modifying the matrix elements, adding progression items and approaching boundary. Through calculating cut-off wave numbers of several tipical kinds of guide, waveguide wavelengths of several tipical kinds of grooveguide, resonance wavelenghts of several tipical kinds of resonance cavities, and comparing the results with the theoretic walues, the validity of these methods are proved.The cut-off characteristic and dispersion characteristic of several new types of regtangular waveguide filled with sheet of metal and several new kinds of grooveguide are analyzed in this paper. The bandwidth characteristic and dispersion characteristic are attained. For example, enhancing bandwidth or restraining some modes can be realized by loading sheet of metal properietly. So the theoretical guidance is provided for applying microwave engineering.The transmission characteristics of the ragular waveguide with non-symmetrical dielectric, waveguide of H-shape, non-symmetrical guide H-shape are analyzed in this paper, too. It is shown that application area of this new method is expanded and the correctness is verified also. At the same time, the influencing relationship of the transmission characteristics with the dielectric is obtained.In addition, the waveguide of arbitrary metal groove with the periodic structure and slow wave system formed by the comb-shape metal surface are analyzed in this paper. The dispersion relation is abtained. It is shown that some three-dimensional and non-symmetrical problem can be solved using this new method. So the significance of academic and application is illuminated, too.Above all, it is shown that the new Fourier's expansion-difference method not only can be used to solve the problems of waveguides and resonance cavities with the regular shapes and malformed shapes, but also can be used to solve the problems with the arbitrary shapes and some malformed shapes, even some three-dimensional and non-symmetrical problem can be solved more efficiently and conveniently. Furthermore, the calculation precision can be satisfied the need of engineering application in waveguide. So it is of important application values that producing and improving of the new method and application in waveguide and resonance cavity for enriching guide theory, analysis and calculation of guide performances in engineering applications.