利用漸近解分析內嵌週期性金屬圓柱介質波導之色散特性

Abstract

近來，有非常多的研究著重於電磁能隙結構(Electromagnetic Bandgap, EBG)，其特性最廣為人知便是在頻率截止帶相當於一高阻抗表面，有著抑制表面波的效果。除此之外，電磁能隙結構有些甚至放置在平行板波導的空隙中去實現高頻率波導特性。[1] 類似的概念也可以從矩形波導中發現。而還有一種新的複合材料，人們稱之為”針床”也已經被廣泛研究。其特性就類似於上述我們所說的EBG結構。不僅如此，我們可以發現此種結構應用在中脊波導，其原因在於此結構可近似模擬出高阻抗邊界條件；當我們放置一脊面於平行板波導中間、並讓周圍環繞著無限多(假想)的週期性金屬圓柱，當空氣隙小於四分之一波長時，那些規律無限多金屬圓柱形成了相當於理想磁導體(PMC)的平面，使得TEM波只會隨著中脊(ridge)而傳。 而這些年來，也有許多的研究是將一些填充物放置在空波導中，藉此量測波導的傳播特性、並且填充方式從最簡單的放置介質到插入一些介質層去做阻抗匹配並探討其特性。在此篇論文中，我們主要採用將空波導兩旁的介質放置入規律的金屬長柱（理想導體），並且利用漸近解的方式去分析其特徵方程式；分析出特徵方程式之後再用模擬軟體去跑出其色散圖。由HFSS及CST吻合的色散圖來推斷其模擬結果是正確的，搭配MATLAB結果，來分析其特性。

在分析此結構之前，我們會先介紹另一較單純結構：在介質基座裡，想像其中嵌有無限週期性排列金屬柱、利用電磁場的概念下去分析推導，並用漸近解取得其特徵方程式；接著用模擬軟體CST、HFSS跑出其色散圖，並將其結果與橫向共振技術(Transverse Resonance Technique, TRT)得到的特性方程式用MATLAB模擬出的色散圖做比較，藉此來證明其漸近解的可靠性與準確性，同時解釋選擇此種場論分析的目的。

There are so many researches focusing on Electromagnetic band-bap structure (EBG) recently; for their well-known characteristic of being as a high-impedance surface in frequency stop-band that can suppress surface waves. Besides, EBG structure can be used to realize a new high-frequency waveguide in the gap between the parallel plate waveguides. The similar concept can also be found in the rectangular waveguide. [1] Recently, a new type of novel meta-surfaces, which is called “pin-lattice” or “bed-of-nails” is being widely researched.[2] Its characteristics are similar to those of EBG structures. [3][4] Furthermore, we can see that the “bed-of-nails” structure is also applied in ridge gap waveguide. The reason of this structure being used is because that can usually mimic the ideal impedance boundary. When we put a ridge in the parallel plate and surrounded infinitely periodic pins, the “bed-of-nails” structure would be similar with PMC (Perfectly Magnetic Conducting) surface when the air gap is smaller than quarter-wavelength and let TEM wave propagate following on the ridge.[5] In recent years, the insertion of additional structures into empty waveguide has been practiced a lot, which can discuss about the characteristics of the propagation through the measurement of the waveguides. Furthermore, the insertion has ranging from the simplest use of dielectric fillings for reduction of cutoff frequency to the plugging in of dielectric layers to serve as impedance match-tunners. In this paper, we use the structure that is a waveguide filling the dielectric in the sidewall and loading with uniform embedded lattice of metallic pins (Perfect Electric Conductor, PEC). Next, we analyzed its characteristic equation by asymptotic solution, and simulated with the tools to get the dispersion diagrams. By agreements of simulating results in CST and HFSS, we can assume its accuracy, and we will analyze the characteristics with the MATLAB tool. On the other hand, we will introduce another simpler structure before the sidewall loaded with embedded pins waveguide; first, we imagine that there is a dielectric grounded plane filling with infinitely periodic array of metallic pins. Next, we derive it by the concept of electromagnetics and get the characteristic equation through the asymptotic solution. Then, we compare the result through the simulated tools with the result of the Transverse Resonance Technique (TRT), and we can get the agreement of the results and the dependability of the asymptotic solution.[2] Meanwhile, we will explain the objective of choosing this field analyzing method.