洩漏波於斜角饋入方形貼片暨具反對稱週期微擾之微帶線之探討

Abstract

本論文主要分成三部分：第一部份，作者提出以電路模型的觀點來說明洩漏模在斜角饋入方形貼片天線中所扮演之角色。第二部分，作者提出了一種新型的週期結構之微帶線輻射狀天線陣列。此天線陣列具有圓錐狀(conical)輻射場型，而其輻射機制乃為週期結構中空間諧波(space harmonic)之洩漏。 在第一部份□，作者提出一連串的舉證來說明斜角饋入方形貼片天線中洩漏模之洩漏特性。首先，作者觀察雙埠斜角饋入方形貼片天線之相對功率吸收值(RPA, Relative Power Absorbed )。當中RPA之定義為1-|S11|2-|S21|2。在觀察此雙埠結構之RPA時，作者發現RPA之峰值具有週期性，且隨著頻率的升高，此雙埠結構的損耗亦增加。如此之損耗現象讓我們與洩漏模之洩漏特性產生聯想。此外，在觀察此雙埠結構之最大獲得功率增益(maximum available power gain)時可發現：在微帶線洩漏區之外幾乎是沒有能量損耗，而在洩漏區之內卻有相當之能量損耗。當作者觀察單埠斜角饋入方形貼片天線時亦可發現：天線之(0,N)及(N,0)模(N=1,2,3,4)之輻射頻率分別坐落於第一至第四高階洩漏模之洩漏區，且在第四高階洩漏區中其輻射場型具有與洩漏波相似之頻率掃描(frequency scanning)特性。最後作者提出了一種二維傳輸線模型(two-dimensional transmission-line model)：以互相垂直之模電流(modal current)來模擬單埠斜角饋入方形貼片天線之激發。當工作頻率在第四高階洩漏區之22.6 GHz時，由此模型所獲得之電流分佈與全波(full-wave)解相當接近。另外，此單埠斜角饋入方形貼片天線亦可發現其減幅振盪(damped oscillation)之電流分佈。此減幅振盪之電流分佈是洩漏模在方形貼片天線中多次反射所造成。尤須注意的是在方形貼片天線中也會激發出束縛模(bound mode)之共振，在此共振頻率時，束縛模共振卻也增強了洩漏模之洩漏。 在第二部份中，作者提出了一種新型週期結構：一微帶線置於具有反對稱性(anti-symmetric)排孔之接地面上。此洩漏微帶線主要輻射出一對向前及向後之波束並應用了週期結構中空間諧波調變(space-harmonic modulation)之概念。其中，每一個空間諧波以其複數傳波參數 表示，並且表現在Brillouin diagram上；而 之意義為：第m個微帶線模(EHm)之第n個空間諧波。 中上標之正負其意義為：上標為正時，表示向前傳導波(forward traveling wave)；上標為負時，表示向後傳導波(backward traveling wave)。在此單一天線中 及 空間諧波均表現出奇對稱(odd-symmetric)之電場極化，而且皆在Brillouin diagram之三角形區域外，分別形成背向洩漏波(backward leaky wave)及正向洩漏波(forward leaky wave)。利用此洩漏特性而設計之輻射狀天線陣列，在工作頻率為11.5 GHz時具有圓錐狀輻射場型，其張角為31度，且3-dB之波束為24度。 在第三部份中，作者提出了一種毫米波反射陣列天線的觀念；此反射陣列使用了第二高階洩漏模。另外，作者並對上述之反對稱週期微擾之微帶線的止帶(stopband)作進一步的探討。

The thesis mainly consists of three parts. In the first part, the author proposes a circuit-modeling perspective of leaky-mode leakages in a corner-fed square patch. The second part demonstrates a periodic microstrip radial antenna array with a conical beam. The radiation mechanisms of the antenna array are the leakages of the space harmonics. The first part chronicles the leaky-mode leakages in a corner-fed square patch. First, the measured peak RPA (relative power absorbed, 1-|S11|2-|S21|2) values of the two-port corner-fed square patch (two-port test circuit) are reported. The peak values are occurred periodically. Such periodicity of frequencies and the phenomenon of increasing losses at higher frequencies enable us to link these peak frequencies to leaky-mode excitations. The maximum available power gain (GA,max), obtained by simultaneously complex conjugate matched impedance at the referenced two ports of the test circuit, depicts that 1) nearly loss-free transmission parameter outside the leaky-mode regions and 2) substantial losses inside the leaky-mode regions. This result suggests that the leaky modes are the main sources causing losses for the two-port test circuit. The one-port properties of the two-port patch with the second port opened are then investigated. The degenerated (0,N) and (N,0) modes (N=1, 2, 3 and 4), calculated by the cavity model method, fall into the strong leakage regions from the first to the fourth higher-order leaky modes. The well-known leaky line’s frequency-scanning characteristics also appear in the one-port test circuit. Lastly, a two-dimensional (2-D) transmission-line model of the one-port test circuit is proposed. This model uses two orthogonal modal currents as excitations to stimulate the corner-fed square patch. At 22.60 GHz, in the fourth higher-order leaky mode (EH4) region, the current distributions obtained by the 2-D transmission-line model closely agree with those of the full-wave simulation. This consistency shows that the damped-oscillation current distributions of the corner-fed square patch at 22.60 GHz are caused significantly by the multiple reflections of the leaky mode. Furthermore, at the resonant frequencies of the patch, the tangled bound-mode resonance of the EH0 mode can enhance the leaky-mode leakages. In the second part, the author proposes a periodic structure derived from a microstrip on a perforated ground plane with anti-symmetric perturbations. The leaky microstrip radiates mainly a pair of forward and backward beams. The new leaky line design employs the concept of space-harmonic modulation. The dispersion characteristics of space harmonics are established and shown in a Brillouin diagram. Each space harmonic is denoted by its complex propagation constant . represents a traveling-wave component of the nth higher-order spatial component in association with the EHm mode: the superscript, +(-), signifies a forward (backward) traveling wave. For the particular leaky line design, and space harmonics, both showing odd-symmetric field polarization, and both outside the triangular Brillouin region, form the backward and forward leaky waves, respectively. When the leaky lines are evenly and collinearly tied, an 11.5 GHz radial antenna array prototype is formed, and emits a conical beam, showing a 3-dB beamwidth of 24o at the flare angle of 31o. In the third part, the author would propose a concept of a millimeter-wave microstrip reflectarray incorporating higher-order EH2 leaky mode. Additionally, the stop-band characteristic of the periodic microstrip with anti-symmetric perturbations is further studied.