現今封裝電源供應系統，運作速度以提升到GHz階段，當邏輯閘快速切換時，瞬間的電流變化會經由IC接腳，傳至電源供應系統的動力平面造成電源面電壓波動之現象進而導致電磁輻射(EMI)的問題產生。
在本論文中，將用在二維時域有限差分法的快速方法去分析對封裝電源供應系統裡的電磁輻射效應分為三部分探討。第一部分，利用時域有限在差分法在二維結構計算EMI；第二部分，在時域有限差分法二維結構去探討更複雜的電源供應面結構如EBG的研究；第三部分，把實際上常用的去耦合電容降低EMI的特性加到二維結構的研究。
經由以上的研究，期待能夠建立出快速的方法去計算電磁輻射效應以解決現今比較常用的全波模擬軟體的冗長運算時間，以利工程師能夠更有效率的解決封裝系統的類似問題。

The operation speed of power delivery system of packages has been upgraded to GHz. The instant current will pass to the power plane of the mother board by way of the IC pins and result in electromagnetic wave propagation between the power plane and the ground plane, then to produce the programs of electromagnetic interference.
In this thesis, we will analyze the EMI of power delivery system of packages by finite-difference time-domain in two dimensions structure in three sections. In firist section, to computing EMI in finite-difference time-domain in two dimensions structure. In second section, to analyze more complicated power delivery plane, ex: EBG, in finite-difference time-domain in two dimensions structure. In three section, to add property of capacitors on power plane to reduce EMI in two dimensions structure.
Above all, we hope to built a fast computing method to compute EMI to solve the time-consuming problems of full-wave simulated software. And to supply the engineer to deal with the similar problems in packages efficiently.

目錄
第一章 序論………………………………………………………………………………………………………….1
1.1 研究目的與方法..……..………………………………………………………………………………1
1.2 論文大綱..……………..………………………………………………………………………………….3
第二章 FDTD演算法……………………………………………………………………………………………4
2.1馬克斯威爾方程式………………...……..………...………………………………………………….4
2.2三維方程式.………………………………..…..………………………………….……………………….4
2.2.1中央差分法與Yee網格配置……………………………………………………..………5
2.2.2 邊界條件…………………………………………………………………………………..………8
2.3 二維方程式………………………………………………………………………………………………...9
2.3.1 模態之中央差分法與網格配置………………………………………………..10
2.3.2 TMz模態之邊界條件…………………………………………………………………..….12
2.4 Courant穩定準則…………………………………………………………………………….………...12
2.5集總電路元件…………………………………………………………………………………….….…..13
2.5.1電阻………………………………………………………………………………………………....14
2.5.2阻抗性電壓源……………………………………………………………………………..…..14
2.5.3電感…………………………………………………………………………………………….…...15
2.5.4電容…………………………………………………………………………………………….…...15
2.6程式執行流程……………………………………………………………………………………….…….16
第三章 二維時域近遠場轉換……………………………………………………………………………17
3.1二維時域有限差分法對封裝系統結構的描述…..……………………………………...17
3.1.1利用2D-FDTD模擬電源供應系……………………………………………………..17
3.2近遠場轉換方法…………..………………..……………………………................................19
3.2.1三維時域有限差分法計算空間分……………………..…………………………….19
3.2.2二維時域有限差分法計算遠場分析…………………..……………………………22

第四章 槽孔修正理論與模擬………………………………………………………………….30
4.1二維時域有限差分法狹縫槽孔修正式…………………………………………………….30
4.2電源供應平面開槽孔模擬…………………………………………………………….………...34
4.3電磁能隙結構之模擬…………………………………………………………….………...........40
第五章 去耦合電容數值模擬方法………………………….………………………………………….45
5.1 FDTD單網格的RLC串聯方法………………………………………………………………45
5.2模擬結果…………………………………………………………….………...............................50
第六章 結論………………………………………………………………………………………………………..58
參考文獻……………………………………………………………………………………………………………….60

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