本論文探討有限時域差分法（Finite Difference Time Domain ，FDTD）應用於平面天線結構的分析。首先，對於激發源的設置方式，本論文探討由微帶線饋入的結構中，以更新方程式建立穩定的入射電場，並對於兩種不同的激發方式進行比較，一是在微帶線與完美匹配層(PML)的介面處激發，叧一是在微帶線上某處做激發，比較二種激發方式的異同。 FDTD在計算天線遠場輻射的理論源自電磁場的等效原理，本論文詳盡地回顧了FDTD在頻域和時域的近遠場變換所需的公式，並針對於自由空間中以球座標描述的電磁場輻射公式進行座標轉換，以順利計算源自等效磁流及等效電流的輻射電磁場。 當要進一步分析天線的S11參數，其過程需經二次（two passes）的計算，第一次（first pass）的計算只模擬天線的傳輸線結構部分，以在觀測點處獲取記錄入射波隨時間的波形變化，第二次（second pass）的計算則是對包含天線的完整結構進行分析，此次的目的在觀測點處記錄反射波隨時間的波形變化，再由傅立葉轉換進而得到兩者的比值（即S11值）。 最後，本論文將前述的FDTD方法應用於三種平面天線的S11以及輻射場型之計算，再與商用模擬軟體HFSS及IE3D的計算結果以及實測天線的量測值做比較，我們發現，當天線所在的FR4基板直接深入PML層內時，其S11的模擬結果與IE3D軟體非常的接近，這證明了FDTD是用於分析平面天線非常有效的方法。 In this thesis the method of finite difference time domain (FDTD) is applied for the analysis of several structures of the planar antenna. First of all, about the establishment of the stimulating sources to excite the antenna structures, two modeling methods are examined and compared in this thesis for the microstrip feed line structures by using the FDTD updating equations in order to set up steady incidence electric field. One is set up the stimulating source at interface of the perfectly matched layer (PML) and the microstrip line, while the other is to set up the stimulating source at a certain place of the microstrip line. The similarities and differences of the above two stimulating sources are examined.
The profound theory for the FDTD method to calculate the radiated far field of the antennas is based the equivalent principle of the electric magnetic field. In this thesis, the frequently-used formulas employed for the near-field to far-field transformation in either frequency domain and time domain is exhaustively reviewed. The needed coordinate transformation from spherical coordinate to rectangular coordinate is carried out in order to execute the integration to sum up the far field contribution in the free space in terms of the equivalent magnetic currents and the equivalent electric currents. The calculation of the S11 parameter of the antenna is regularly required, the course needs to pass for twice calculation (two passes) usually. The first pass is to analyze the structure of the transmission line part only such that at an observation point the incident wave is calculated and saved for later usage. The second pass is to analyze the structure of the whole structure that include antenna. The purpose of this time is to calculate the reflection wave from the antenna at the same observation point. The Fouries transforms for both the incident and reflected waves are then performed, while the ratio of the two results in value of the S11 parameter. Finally, in this thesis the above-mentioned FDTD method is applied to calculate the S11 and the far field patterns of three kinds of plane antennas. Then, the simulated results are compared with those obtained with the commercial EM softwares HFSS and IE3D, and with the measured results. It is found that when the planar substrate of the antennas extends into the PML to model an infinite substrate, the results could match quite well with those obtained by using the software IE3D which justify the effectiveness of applying the FDTD method for the planar antennas structures.
