微帶線第一高階模在頻域與時域之特性阻抗和傳導特性之研究暨鄰近耦合洩漏模陣列天線之設計

Abstract

本論文主要分成兩部分：第一部份，依據N.K. Das博士所提之「微帶線第一高階模（洩漏模）特性阻抗的定義」。理論計算出其特性阻抗，並設計實驗證明其結果正確且合乎物理意義。第二部份，利用微帶線第一高階模洩漏之特性，設計鄰近耦合洩漏模陣列天線。 在第一部份□，利用嚴謹之全波積分方程式，求出微帶線第一高階模之正歸化傳導常數及複數特性阻抗。為能更瞭解洩漏模特性阻抗之物理意義，將所得頻域之特性阻抗，轉換至steepest decent plane並解釋、分析其意義。以傳導常數及複數特性阻抗，描述開路洩漏模傳輸線電路模型，並以反傅立葉轉換至時域所得的波形與TDR實驗所得波形比較，而其結果非常一致。反射回波在時域的擴展是由於群速度散色（群速度之大小隨頻率而變）的關係，利用理論所得之群速度，亦能精確推算出由開路反射回波的時間，而最低群速度是在洩漏模的頻段。由時域TDR測量之數據 轉換至頻域之頻譜，透露出EH1模同時存在反射、洩漏、傳導等三種頻段。假如衰減常數不是太大，亦可從此頻譜精確推算出其大小。以傅立葉轉換TDR反應的數據，亦能推算出頻域之反射係數，進而依此反射係數，推算出頻域之特性組抗，而其結果非常接近理論值。 在論文第二部分裡，提出串列饋送鄰近耦合洩漏模陣列天線之結構，本結構包含一個50歐姆饋送線及N條洩漏線。此一陣列天線的設計，其目標在於達成五度輻射波束，為此，本設計應用了三種解析方法：（一）利用二維全波解析法，求出洩漏模之傳導常數。（二）利用解三維空域積分方程式，求出耦合係數及向量電流分佈，並利用電流分佈確認輻射場形。（三）利用Matrix-Pencil方法，分析向量電流分佈，求出被激發洩漏模之大小。經由上述方法與步驟，實作後，測量其結果，證明確能達成設計目標。

This thesis consists of two parts, including 1) experimentally and theoretically confirms the validity of the definition proposed by N. K. Das [4] for computing the complex characteristic impedance of the first higher-order (EH1) microstrip mode. 2) theoretically and experimentally demonstrates to design a millimeter wave leaky-mode antenna array based on the first higher-order mode on the printed microstrip line. In the first part of the thesis, the normalized complex propagation constant and complex characteristic impedance of the microstrip obtained by the rigorous full-wave integral equation method is also presented. To better understand the circuit behavior of the leaky mode at the respective frequencies, the results are analyzed in both frequency and transformed steepest descent plane. A differential TDR (Time Domain Reflectometry) experiment shows that the experimental results agree excellently with the time-domain plots obtained theoretically by the Inverse Discrete Fourier Transform of the transmission line modeled by the dispersive characteristic. The propagation characteristics of the echoed signals in time-domain, which are reflected from the open-end of the leaky line, are analyzed in detail using the corresponding group velocity of the EH1 mode. The wide spread of the echoed signals in the time-domain is the direct result of the highly dispersive group velocity. The slowest group velocity is in the leaky region. The time-to-frequency conversion of the measured TDR data reveals that the reflection, leaky and propagation zones coexist simultaneously for the EH1 mode propagation. The conversion also accurately assesses the attenuation constant of the EH1 mode if the attenuation is not too high. The Fourier transform of the TDR responses also simultaneously yields the input reflection coefficient (S11) and the complex characteristic impedance. The complex characteristic impedance extracted from the TDR responses also agrees closely with the theoretical data. In the second part of the thesis, proposed a series-fed, proximity coupling, N-element, leaky-mode microstrip antenna array, consisting of one 50ohm series-feeding line and N leaky lines. The design explored three analytic methods, included 1): the 2D full-wave analysis to get the propagation constant of the leaky-mode, 2) 3D space-domain integral equation for validating parameter of field pattern, determining the coupling coefficient and providing the vector current distribution, 3) General matrix-pencil method for extracting the amplitude of leaky-mode excited by the feeding-line. The design goal of this demonstration approaches 5o pencil- beam that be reached by this presented and validated by experiment.