寬頻縮小化電磁能隙結構於電源完整性設計之應用

Abstract

本論文著重於電磁能隙結構之等效電路模型、原理以及設計於抑制接地彈跳雜訊之應用，並藉以提出一縮小與寬頻化之電磁能隙結構。首先，我們提出計算電磁能隙之低頻與高頻截止頻率的方法。此方法不僅可幫助我們預測低頻與高頻的截止頻率，也提供我們了解電磁能隙的產生原理。低頻與高頻截止頻率可藉由單位元與適合之邊界條件的共振頻率求得而不用解其色散關係。基於此方法，我們分別針對一維與二維電磁能隙結構發展其等效電路模型的建構方法。針對一維電磁能隙結構，我們利用傳輸線段建立單位元之等效電路模型。至於二維電磁能隙結構，我們利用單位元及其相對應低頻、高頻截止頻率之邊界條件建立其等效電路模型，而其中之個別元件值則可利用所推導的共振腔模型求得。這些等效電路模型可給我們較清楚的物理觀點來連結電磁能隙結構之幾何形狀與電磁能隙的關係。 此論文提出兩種新穎電磁能隙結構之設計。首先是多連通柱電磁能隙結構。此結構之低頻與高頻截止頻率已可被解釋。藉由調整連通柱的間距，我們可以發現此多連通柱電磁能隙結構有最大頻寬比例之最佳化設計。在相同的幾何大小的條件之下與蘑菇型電磁能隙結構相比，多連通柱電磁能隙結構可改善絕對頻寬與頻寬比例的特性。另一種為以交錯型電磁能隙結構達成較大寬頻與較小面積之設計。藉由縮小電源/接地連通柱對之間距，此電磁能隙結構的低頻與高頻截止頻率可同時被改善，並利用此設計概念，多電源/接地連通柱對的設計可更進一步的增加頻寬。以單一電源/接地連通柱對為例，其單位元邊長的電氣大小與頻寬比例分別為0.071 λgL 以及139 %，與過去文獻上之蘑菇型電磁能隙結構相比較，此設計多增加51.1 %的頻寬並同時節省61.2 %的面積。至於四對電源/接地連通柱對為例，其頻寬則可多增加115.2 %並同時減少30.5 %的面積。

This dissertation focuses on the equivalent circuit model, mechanism, and design of the electromagnetic bandgap (EBG) structures for the suppression of ground bounce noise. Developing a miniaturized and stopband-enhanced EBG structure is the main goal of this dissertation. In the beginning, we propose a method for determining the lower- and upper-bound cutoff frequencies of bandgaps. The method helps us not only to predict where the bandgap is but also to understand what mechanisms of the lower- and upper-bound cutoff frequencies are. Instead of solving the dispersion relation, we propose that the lower- and upper-bound cutoff frequencies can be determined by the resonant frequencies of the unit cell with appropriate boundary conditions. Based on the proposed method, two approaches are developed for constructing the physics-based models of one- and two-dimensional EBG structures, respectively. For the case of one-dimensional EBG structure, we can use an equivalent circuit model consisting of transmission-line sections to electrically characterize the electromagnetic behavior of a unit cell. As regards the two-dimensional EBG structure, an equivalent circuit model for the unit cell is developed to predict the lower- and upper-bound cutoff frequencies. The values of the circuit elements can be extracted by using the derived cavity models. The equivalent circuit models can provide us a design concept for relating the geometry of the EBG structure to the corresponding bandgap behavior. Two novel designs of EBG structures are proposed in this dissertation. The first one is the multiple vias EBG structures. The mechanisms of lower- and upper-bound cutoff behaviors and the corresponding frequencies of the EBG structure are investigated and explained. By sweeping the via pitch of the multiple vias EBG structure, we can find an optimized design for achieving the maximum bandwidth ratio. Under the assumption of the same dimension, the absolute bandwidth and bandwidth ratio are enhanced by the multiple vias EBG structure when compared with the mushroom EBG structure. The other design is the interleaved EBG structure for the wider bandwidth and smaller area. The improvements on lower- and upper-bound cutoff frequencies of the interleaved EBG structure can be achieved at the same time by reducing the pitch of power/ground vias pair. Based on the design concept, the interleaved EBG structures with multiple pairs of power/ground vias are also proposed to enhance the bandwidth of bandgap further. For the interleaved EBG structure with single pair of power/ground vias as an example, the electrical size of the unit-cell length, which is normalized to the wavelength in the substrate, and bandwidth ratio are 0.071 λgL and 139 %, respectively. Compared with the conventional mushroom EBG structure proposed in the past literatures, the interleaved EBG structure with single pair of power/ground vias simultaneously shows substantial improvements on bandwidth of 51.1 % and miniaturization of 61.2 %. With regard to the interleaved EBG structure with four pairs of power/ground vias, the bandwidth has an increase of 115.2 % wider than that of the conventional mushroom EBG structure and the required layout area can be reduced by 30.5 % simultaneously.