電性–磁性–電性（EME）微帶線之分析與應用

Abstract

本文提出一種新穎的光子能帶結構。此種週期結構單元乃由連續且相互耦合的金屬線圈所構成，故可傳導直流電流；但於某些禁止頻帶內，將因具有高阻抗而無法傳導交流電流。利用有限元素法來計算此種二維週期能帶結構的表面波色散特性，將可發現其在8.8至12.4 GHz及21.4至23.6 GHz的高頻微波頻段將具有全方向性的禁止頻帶。 而運用此種週期能帶結構，已成功地據以設計出一低損耗，且具有慢波特性的新式微帶線。此種微帶線以平行並排的電性與磁性複合表面金屬來取代傳統微帶線的金屬線。磁性表面乃由一群前文所述的二維週期能帶結構連結耦合而成。此表面在禁止頻帶內具有高阻抗狀態；而在低於禁止頻帶的操作頻率，將可藉由調整電性與磁性表面的尺寸來控制其傳播特性。本文採用由全波場論法配合矩陣數值演算法來得到此種微帶線的色散曲線，其值與由傳統習知的散射參數萃取法所得到之值近乎一致。而經由實驗驗證的理論結果指出，運用此種複合結構將可輕易地使微帶線的慢波值增加達60%之多，且不增加傳導損耗。此種複合電磁表面微帶線可用傳統的印刷電路板製程技術來完成，且在主模傳播時對製程上可能造成的週期結構的相對排列位置誤差並不敏感。此新型微帶線亦具有連續的均勻金屬接地面，故易與其它微波元件整合於多層板電路中而不致互相干擾。本文亦利用此種微帶線設計成一可消除諧波頻率響應的微小化帶通濾波器。相較於利用相同介質基板的傳統微帶線帶通濾波器，此種週期結構濾波器的長度可縮小達26%，且量測的數值顯示將不會犧牲傳導損耗與濾波頻寬來達成這些優點。 本文更進一步地探討具有不同週期結構組成比例的複合表面微帶線之第一高階模色散特性。同時成功地設計出具有傳統洩漏波型的微小化雙頻洩漏波天線。相較於具有相同洩漏波截止頻率的傳統微帶線，此種複合微帶線的線寬可縮小達47.5%。此種微帶線的高階模色散曲線亦可利用矩陣數值運算法得到，且已由量測到的洩漏波輻射場型加以驗證。色散曲線與模電流分佈皆顯示此微小化雙頻天線在5.25 GHz及12.35 GHz這兩個頻帶，具有相似的洩漏波掃頻特性與扁平輻射場型。故此種複合微帶線未來將可廣泛地用以設計各式微小化，且高性能的微波電路元件與洩漏波陣列天線。

This thesis presents a new type of photonic bandgap (PBG) structure that is characterized by having high surface impedance. Although it is made of continuous metal coils, and conducts dc currents, it does not conduct ac currents within a forbidden frequency range. The surface-wave dispersion diagram of the two-dimensional PBG substrate has been numerically computed by the finite-element method and found to have a complete stopband in the frequency range of 8.8-12.4 and 21.4-23.6 GHz, respectively. This PBG structure is successfully used to design a novel integrated microstrip low-loss, slow-wave line. The new microstrip replaces the conventional metal strip by composite metals paralleling the electric and magnetic surfaces. The magnetic surface made of an array of coupled inductors shows a high-impedance state in the stopband, below which the propagation properties can be well controlled by varying the dimensions of the electric and magnetic surfaces. The dispersion curves obtained by matrix-pencil analyses closely correspond to those obtained by scattering parameters extraction. Theoretical results, as confirmed experimentally, indicate that an increase of more than 60% in the slow-wave factor can be achieved without sacrificing propagation losses, using the proposed structure. This electric-magnetic-electric (EME) microstrip is insensitive to the alignment position of the periodical structure, and can be constructed using conventional printed-circuit-board (PCB) fabrication processes and integrated with other microwave components in a multi-layered circuit. A compact EME band pass filter (BPF) with suppressed harmonic responses is presented. The length of the filter is reduced by 26%, and the measured insertion loss and fractional bandwidth is comparable to that of a conventional microstrip BPF on the same substrate. Furthermore, the dispersion characteristics of the EME microstrip, with different PBG filling percentages, at the first higher order (EH1) are presented. A compact, dual-band leaky-mode antenna of similar radiation characteristics is successfully designed. The line width is reduced by 47.5%, compared to that of the conventional microstrip for the same onset frequency of the leaky mode. The dispersion curves of the EME microstrip, obtained by matrix-pencil analyses and validated experimentally by measured radiation patterns, indicates the strong radiation behavior with fan beam patterns at two frequency bands of 5.25 GHz and 12.35 GHz. The EME microstrip is potentially useful for compact microstrip component and leaky-mode antenna array design.