本論文提出兩種時域演算法，可萃取高速耦合互連結構的SPICE相容等效寬頻模型。第一種演算法主要針對多導體互連結構，以一傳輸線導向的模型單元串接來合成其等效模型。第二種演算法則是針對差動貫穿孔，探討其等效寬頻π模型，此模型的三個模組分別以最佳化的極點-餘數(pole-residue)的形式表示。配合集總元件萃取技術(SLET)，可將此三模組的極點-餘數分別轉換成相對應的集總電路模型。並在時域與頻域的角度上，分別與全波模擬(3D-FDTD)的結果比較，以驗證所提出的演算法的正確性。

This dissertation proposed two time-domain algorithms for extracting the broadband SPICE-compatible models of high-speed coupled interconnects. The first approach is proposed to synthesized the equivalent models of multi-conductor interconnects by cascading multiple configuration-oriented coupled transmission line (CCTL) units. The second approach focuses on the modeling of differential via based on a broadband macro-π model with three modules represented by the optimum pole-residue forms. Using a systematic lumped-model extraction technique (SLET), all the pole-residue rational functions can transfer into a corresponding lumped model. The accuracy of the two algorithms is demonstrated both in time- and frequency -domain responses comparison with the direct 3D-FDTD simulation.

Contents

Abstract i
Contents iii
List of Figure v
List of Tables x

1 Introduction 1
1.1 Research Motivations 1
1.2 Literature Survey 1
1.3 Contributions 3
1.4 Chapter Outline 5

2 Time-Domain Measurement and FDTD Method 6
2.1 Time-Domain Reflectometry (TDR) Theory 6
2.1.1 One-port measurement 6
2.1.2 Two-port measurement 10
2.1.3 Differential measurement 12
2.2 Finite-Difference Time-Domain (FDTD) Method 15

3 Broad-Band Models Extraction of the Multi-Conductor Coupled Interconnect 21
3.1 Layper Peeling Technique (LPT) 21
3.2 Multi-Dimensional Deconvolution Theory (MDA) 25
3.3 Examples 33
3.3.1 Asymmetric differential pair 33
3.3.2 Symmetric differential pair 37
3.3.3 Three parallel traces 41
3.4 Summary 46

4 Broadband Macro-Models of Differential Via 47
4.1 Simulation and Measurement Setup 47
4.2 Step Responses and Mode Extraction 49
4.3 Synthesis of Equivalent Macro-π Model 50
4.4 Order Reduction 51
4.5 Systematic lumped-model extraction technique (SLET) 52
4.6 Stability and Passivity 55
4.7 Examples 57
4.7.1 Asymmetric Through-Hole Vias 57
4.7.2 Differential Via 65
4.8 Summary 70

5 Conclusion 72


Bibliography 73
Biography 81
Publication List 82

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