A Basic Study on an Optimum Design of a High Permittivity Dielectric Disk Resonator in Milli-meter Wave Band Mobile Communication

本课题由两部分组成，即1、高介电常数介质圆盘谐振器上回音壁模式的谐振频率研究、2、矩形截面高介电常数介质波导的传播特性研究1)谐振频率的研究引入近似分离变量法和有效介电常数，分析了高介电常数圆盘谐振器上回音壁模式的谐振频率。结果表明，该方法对传统方法的结果有很大的改善。我们还实验地给出了圆盘附近的电磁场分布，以定义语音廊模式的模数。在不久的将来，我们将提出一种新的分析方法，该方法是由应用点匹配方法导出的。我们可以同时得到圆盘谐振器的谐振频率和空载Q因子。2)传播特性的研究由于高介电常数介质波导中的电磁场倾向于向周围区域弯曲，我们考虑了所有的场分量来获得传播常数。首先，我们求解由主场分量的连续性导出的本征值方程。我们还考虑了与波导边界上二次场分量的连续性不同的情况。在我们分析的下一步，我们将最小化差异以选择正确的传播常数。计算结果与前人的数值计算结果吻合较好。我们发现，我们的简单的解析方法不仅给出了传输常数，而且给出了很好的近似场表达式。

A subject of our research consists of 2 parts, namely 1 ; A study on resonance frequencies of a Whispering Gallery Mode on a high permittivity dielectric disk resonator, 2 ; A study on propagation characteristics of a high permittivity dielectric waveguide which has a rectangular cross section.1) A study on resonance frequenciesIntroducing an approximate separation of variables method and a effective dielectric constant, we analyze resonance frequencies of the Whispering Gallery Mode on the resonator. As the result, it is found that our method improves results come from conventional methods very much. We also show experimentally electromagnetic field distribution near the disk to define a mode number of the Whispering Gallery Mode.In a near future, we will present a new analytical method derived by applied Point Matching Method. It is possible for us to obtain the resonance frequencies and an unloaded Q factor of the disk resonator at the same time.2) A study on propagation characteristicsAs electromagnetic fields in a high permittivity dielectric waveguide tend to bend toward surrounding area, we take account of the all field components to obtain an propagation constant. First, we solve an eigenvalue equation derived from a continuity of main field components. We also consider a difference from the continuity in the secondary field components on the waveguide boundary. Next step of our analysis, we minimize the difference to select a correct the propagation constant. Our results show a good agreement with a previous numerical work. It is found that our simple analytical method gives us not only propagation constant but also well approximated field expression.