週期擾動微帶線之散射特性

Abstract

本論文探討平面週期傳輸線散射特性之理論與分析技巧。為了節省本質傳導特性之計算量，提出具週期電感性負載或週期電容性負載之單一微帶線模型，利用全波積分方程分析週期結構接地面上之電流分佈，藉由模態萃取法（Matrix-Pencil）萃取存在之模態。此結果與根據Floquet’s theorem所得之週期結構空間諧波展開具相當之類似性。布林圖形（Brillouin diagram，或稱k-b diagram）中之基本模態 與 分別表示正向傳輸波與背向傳輸波，此與全波模型法所得之散射曲線吻合。高階空間諧波彼此間距一歸一單位 ，b0表示自由空間中之波數，d表示單一傳輸線擾動週期。於布林圖形中之截止帶（Stopband），如 與 耦合處，明確地顯示一對複數模之存在。此外，布林圖形亦清楚描繪空間諧波如何進入輻射區域並轉變成洩漏波。由散射參數得到之相對能量吸收係數（RPA，Relative Power Absorbed）於此波段損耗之突然上升亦印證此輻射現象。

Theory and technique for resolving the dispersion characteristics of a periodic planar transmission line are presented. A simplified model made of a uniform mi-crostrip loaded periodically with either inductive notch or capacitive stub is proposed to save computational efforts while explicitly demonstrating the intrinsic guiding properties. After invoking the full-wave integral equation method for scattering analyses of the periodical structure, the excited currents flowing on the smoothed metal surface, i.e., the ground plane of the model, are subject to the matrix-pencil mode extraction algorithm. The solutions agree excellently with the well-known space harmonics expansion (of a periodic structure) based on Floquet’s theorem. The fundamental and waves as shown in Brillouin dia-gram (or the diagram), representing the forward traveling wave and backward traveling wave, respectively, fall into the dispersion curves dictated by the full-wave modal solutions. The higher space harmonics are thus separated by one normalized unit, , where is the free-space wavenumber and d is the period of the per-turbations on the uniform line. A pair of complex modes are explicitly shown to ex-ist in the stopband where and , for example, couple. Additionally the Bril-louin diagram depicts clearly how the space harmonics enter the radiation region and become leaky waves. The RPA (relative power absorbed) values obtained by the scattering analyses confirm that a sudden rise in losses is closely related to the radia-tion.