應用模耦合逼近法設計被動/主動式微帶線洩漏模陣列天線

Abstract

本論文包含兩部分；內含(1)微帶線陣列洩漏模之模耦合物理特性研究與探討以及，(2)應用模耦合逼近法分析及設計被動式/主動式微帶線洩漏模陣列天線之實例介紹。 論文第一部份，詳列模耦合逼近法導式，以表述如何將傳統複數傳播常數全波計算法之非標準式特徵值問題，轉換成標準式特徵值問題，使吾人可同時計算獲得，存在於微帶線陣列之特徵值(耦合洩漏模)，以及特徵向量(耦合洩漏模電流分佈)，而不論微帶線數目之多寡，因此計算時間及容量均可大幅減少。再經由繁複推導導式，微帶線數目為二、三、四陣列中之電磁耦合係數可計算得之。理論數據證實，微帶線陣列中，電磁耦合係數之振幅，會隨微帶線間之距離增加而遞減。最後由一組共分饋送(corporate-fed)網路，及八條微帶線組成之陣列天線實例計算驗證，更進一步發現此構型陣列天線有八耦合洩漏模，其中僅四耦合洩漏模被激發，並經由測量的天線場形數據，驗證文中所提理論分析摸式之正確性。 第二部分提出兩種應用實例，其一為全新型緊密並排相鄰之微帶線洩漏模陣列天線設計，經由實例驗證，適當操作四個被激發耦合洩漏模結果，高效率微帶線洩漏模陣列天線得以達成。數值分析數據，顯現衰減常數略為增加，然相位常數幾乎維持不變，此結果會導致背後波束降低、效率提升，而不致於影響設計之波束指向。另一設計實例，展現一種新奇的注入鎖定主動積體微帶線洩漏模陣列天線設計方式，應用準光學空間功率合成技術，達成波束掃瞄。由前述電磁耦合係數理論值，再利用凡德波(Van Der Pol)方程式可精確摸擬非線性特性，進而掌握主動積體微帶線洩漏模陣列天線重要物理參數諸如波束指向、天線場形之分析。最後兩種設計實例，經由實驗驗證，其測量到數據和理論值相當吻合。

This thesis consists of two parts, including 1) investigation of the mode coupling of the complex-wave inhering in the microstrips array , and 2) analysis and design of the passive/active microstrip leaky-mode antenna array employing coupled-mode approach. The first part presents the coupled-mode approach to the analysis and design of large leaky-mode array, in which an N-element microstrip array supports N coupled leaky-modes at first higher order (leaky EH1 modes). The second part proposes a novel design of a closely coupled microstrip leaky-mode antenna array and an injection-locked coupled microstrip leaky-mode antenna array. In the first part of the dissertation, following a brief description of conventional, full-wave, non-standard eigenvalue problem for solving the complex propagation constants, we present the detailed formulation of the coupled-mode approach, clearly showing the transformation of the nonstandard eigenvalue problem into a standard one. Thus all the eigenvalues (complex propagation constants) and the eigenvectors (modal current distributions) are solved simultaneously, regardless of the size of the array (N). Closed-form expressions for obtaining the coupling coefficients of orders two, three, and four are presented. Theoretical studies of closely coupled microstrip arrays of two, three, and four elements show that the magnitude of the coupling coefficient Ci,i+j between element i and element i+j decreases at the order of 10-j. Finally, an example of applying the proposed coupled-mode approach for analyzing a corporate-fed, leaky-mode array of eight elements is reported, revealing that only four out of the eight leaky modes are excited. The coupled mode theory predicts the far-field radiation pattern in the main beam region in excellent agreement with the measured results. In the second part of the dissertation, two design examples are proposed. The first design example presents a novel design for a closely coupled microstrip leaky-mode antenna array. It demonstrates that high-efficiency printed array is achieved by employing closely coupled microstrip leaky-mode antenna array operating in four excited coupled EH1 modes. Numerical results of this study indicate that the attenuation constant □/ko is increasing –while the propagation constant □/ko is almost unchanged due to mode coupling between leaky lines. This phenomenon, in turn, reduces the backlobe and enhances radiation efficiency while maintaining the beam pointing direction in the desired direction. The second design example proposes a new design for beam scanning array based on the concept of quasi-optical power combining using the microstrip leaky-mode antenna array. It demonstrates that the coupling parameters can be obtained numerically, leading the analysis of the steady-state phase relationships of the coupled oscillators based on ven der pol equations for determining the excitation signals of the array. Finally prototypes of the proof-of-concept design examples are built for experimental validation, demonstrating excellent correlation between the measured results and theoretical predictions.