本論文提出利用時域演算法，萃取封裝級電源層與接地層間具共振效應的SPICE 相容等效寬頻模型。此演算法可針對一般互連結構與電源接地層，探討其等效寬頻巨集模型，此巨集模型的每個模組分別有最佳化的極點-餘數(pole-residue)的形式表示。配合系統化的集總元件萃取技術，可將模組最佳化的極點-餘數分別轉換成相對應的集總電路模型。並從時域與頻域的角度上，分別與全波模擬(3D-FDTD)及量測的結果比較，以驗證所提出的演算法的正確性。此外，這些模型能夠有效的與主動電路利用現有的商用電路模擬軟體如HSpice 進行封裝級地彈雜訊的分析。

This dissertation proposed a novel time-domain algorithm for extracting the broadband SPICE-compatible models of power/ground planes with resonance effect. The time-domain algorithm approach can focus on the modeling of interconnectors and power/ground planes based on a broadband macro model. Every module of the
broadband macro model is represented by the optimum pole-residue forms. Using a systematic lumped-model extraction technique, all the optimum pole-residue rational functions can be transferred into a corresponding lumped circuit model. The accuracy
of the time-domain algorithms is demonstrated both in time- and frequency-domain responses comparison by the 3D-FDTD simulation and measurement. In addition, these models can be efficiently incorporated into the currently available circuit simulator such as HSpice for the consideration of power/ground bouncing noise with active devices in high-speed circuits.

Abstract.................................................................................................... i
Contents ................................................................................................. iii
List of Figure ...........................................................................................v
1 Introduction..............................................................................1
1.1 Research Motivations.......................................................................................1
1.2 Literature Survey and Contributions................................................................2
1.3 Chapter Outline................................................................................................5
2 Time-Domain Reflectometry Theory ...............................................7
2.1 Numerical Time-Domain Reflectometry (TDR) Method ................................7
2.2 Time-Domain Reflectometry (TDR) Theory on measurement......................13
2.2.1 TDR measurement ................................................................................13
2.2.2 TDR/TDT measurement .......................................................................20
3 Broadband Model Extraction of Power/Ground Planes with
Resonance Effect ............................................................................... 24
3.1 Measurement and Simulation Setup ..............................................................24
3.2 Step Response and Matrix Pencil Method (MPM) ........................................25
3.3 Broadband Equivalent Lumped Modules ......................................................28
3.4 Lumped Circuits Extraction Method .............................................................30
3.5 Examples........................................................................................................33
3.5.1 Solid power/ground planes by simulation.............................................34
3.5.2 Solid power/ground planes by measurement ........................................42
3.5.3 Electromagnetic Band-gap by measurement ........................................46
iv
3.6 Summary........................................................................................................51
4 Synthesizing Marco-Model of Power/Ground Planes with
Resonance Effect ............................................................................... 52
4.1 Simulation and Measurement Setup ..............................................................52
4.2 Step Responses and Mode Extraction............................................................54
4.3 Order Reduction.............................................................................................54
4.4 Synthesis of Equivalent Macro-π Model .......................................................55
4.5 Lumped Model Extraction Technique............................................................56
4.6 Examples........................................................................................................61
4.6.1 35mm × 35mm power/ground planes by simulation...........................61
4.6.2 30mm × 30mm power/ground planes by measurement ......................69
4.7 Summary........................................................................................................75
5 Conclusion .......................................................................................... 77
Reference................................................................................................ 79
Vita ......................................................................................................... 87
Publication List ..................................................................................... 88

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