Analysis Of Rotman Lenses And Application Study Of Boundary Element Method

This paper is mainly consisted of two parts of research work: the numerical analysis of Rotman lenses and the application study of Boundary Element Method. First, the precise analysis and design for Rotnian lens, an important multiple beamforming network are accomplished by the Boundary Element Method respectively along with the Segmentation Method and the Mode Expansion Method. Then other important applications of BEM in electromagnetic problems especially in the metal resonators and cavity scattering problems are systematically studied. The author抯 main contributions are as follows: 1. 2-dimensional Boundary Element Method is used to the analysis of arbitrary planer circuits. A new kind of microstrip stub, the step radial stub is proposed. Comparisons show that the new stubs can work better than conventional straight stubs and common radial stubs when low impedance and a wide low-impedance frequency band are required. 2. The design equations derived by Geometry Optics for Rotman lenses are presented and the effective aperture theory is applied to investigate the effect of the seven parameters on the main performances of Rotman lenses. Attentions are focused on large lenses with multiple beam ports and array ports. 3. The precise analysis of Rotman lens is accomplished by the Boundary Element Method along with the Segmentation Method. All complex effects such as mutual couplings, internal reflections between ports and the discontinuity at every junction are taken into account. Some new techniques are proposed to make the method far more computationally efficient. The effects of the three individual design parameters on the shape and performance of Rotman lens are predicted. In addition, the effects of the dummy-loaded ports are investigated quantitatively and some general design principles are drawn out. 4. The multiple-mode scattering parameter of Rotman lens is computed by the Boundary Element Method combined with the planar waveguide mode expansion method. To reflect the actual performance of Rotman lens in the whole band, planar waveguide models considering the dispersion effect of the medium with frequencies are used in the analysis. When computing the diagonal elements of the Galerkin matrix, one will encounter the integral of Hankel function, the Green抯 function of 2-dimensional Helmholtz equation and the cosine weighting function, whose integrand is singular in the integration range. A new approach is proposed to deal with this kind of singular integrals, which is pivotal but have not been reported so far. 5. A method which combines 3-dimensional BEM and the connection scheme is proposed to study arbitrary metal resonators. In an innovatory way, we commence the analysis using the 3-dimensional version of the boundary integral formulation relating the magnetic field along the boundary and the electric and magnetic currents. After complicated manipulations the eigenvalue equation which determines the resonant frequencies of the resonator is derived. A connection scheme which allows the resonator to be divided into sections is introduced to alleviate computational constraints. Then the eigenvalue equation of the whole resonator is derived by matching the boundary conditions on each junction. The connection scheme make the method can be used to much larger resonators and complex resonators with stratified heterogeneous media. Furthermore, an efficient method is presented to compute the integrals of the Green抯 function and its derivat...