隨著系統級封裝(System In Package，SIP)或系統單晶片(System on chip，SOC)時脈速度快速的增加與互連結構佈局密度提高，在相鄰互連結構間的串音雜訊對於電路系統訊號完整度(Signal Integrity，SI)的影響也日益增加。全波模擬軟體如HFSS等經常被使用於傳輸系統的特性分析，但計算所需的時間較長，且對於主動電路的整合上較為困難。而電路模擬軟體如ADS因具有整合被動與主動元件的簡易性與較少的模擬時間等優點，是目前系統級高速電路設計最佳的工具。在現有文獻中通常以頻域的技術獲取尺寸化等效巨集模型，但是以時域的技
術來建構尺寸化等效巨集模型是一種比較直接、方便且低成本的方式。所以在考慮量測成本與實用性上，本論文發展一個系統化的方法應用時域的矩陣束法(method of Pencil Matrix)獲得高速互連耦合結構的尺寸化寬頻等效巨集模型(scalable broadband equivalent macro-model)，使其能應用於現有電路模擬軟體中，以快速、準確的分析模擬系統級封裝。

As the circuit density and clock rate in SIP or SOC getting higher, the crosstalk interference between interconnects becomes more and more serious. This results in the degradation of signal integrity. Full wave simulation softwares such as HFSS are often used to analyze the characteristics of the transmission system, but the computation time is relatively long and it is difficult to integrate with active circuits. On the other hand, circuit simulation softwares such as ADS has the advantages of simplicity and needs less simulation time. The circuit simulation softwares is so far the best tool of designing high speed circuits. Usually obtain scalable equivalent macro-model in the existing literature with the technology of the frequency-domain, but using the technology of the time-domain to construct scalable equivalent
macro-model have more direct, convenient and low-cost. Therefore, considering cost and practicability, this thesis develops a systematic method using the method of Pencil Matrix in time domain to obtain the scalable broadband equivalent macro-model of the components of high-speed interconnect structures. The developed macro-models can be applied to existing simulation softwares for a fast and accurate
analysis of systems such as SIP.

目錄…………………………………………………………………………………………..Ⅰ
圖表索引……………………………………………………………………………………..Ⅲ
第一章 序論…………………………………………………………………………………1
1.1 研究目的與方法..……..…………………………………………………………….1
1.2 論文大綱..……………..…………………………………………………………….2
第二章 時域響應波形的模擬與量測………………………………………………………4
2.1 FDTD 演算法介紹...……………...………………………………………………….4
2.1.1 FDTD 公式推導...…..………………………………………………………….4
2.1.2 Courant 穩定準則...…………………………………………………………….7
2.1.3 吸收邊界………………………………………………………………………7
2.1.4 FDTD 模擬……...…..………………………………………………………….8
2.2 TDR理論……………………………………………………………………………..9
2.2.1 TDR/TDT 波形量測…………………………………………………………..10
2.2.2 訊號完整性(signal integrity)的重要性……………………………………….15
第三章 矩陣束法與多埠寬頻巨集模型…………………………………………………..18
3.1 矩陣束法(Pencil Matrix Method)…..……………………………………………...18
3.1.1 簡介…………………………………………………………………………..18
3.1.2 矩陣束法理論………………………………………………………………..19
3.2 等效寬頻集種元件模型…………..………………..……………………………...23
3.2.1 電抗理論……………...………………………..…………………………….23
3.2.2 電路等效模型…………………………………..……………………………23
3.2.3 寬頻集總元件模型……...………..……………………………………….…26
3.3 多埠寬頻巨集模型………………………………………………………………...29
3.3.1 雙埠寬頻巨集模型...………………………………………………………...29
3.3.2 三埠寬頻巨集模型…...……………………………………………………...31
3.3.3 多埠寬頻巨集模型…...……………………………………………………...36
第四章 尺寸化巨集模型…………………………………………………………………..38
4.1 迴歸分析理論……………………………………………………...........................38
4.2 尺寸化巨集模型的建構…………………………………………………………...41
4.2.1 傳輸線巨集模型……………………………………………………………..42
4.2.2 過孔結構巨集模型…………………………………………………………..48
4.2.3 混合結構巨集模型…………………………………………………………..53
4.2.4 差動過孔結構巨集模型……………………………………………………..56
第五章 結論………………………….…………………………………………………….65
參考文獻……………………………………………………………………………………..66

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