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研究生:何仁堯
研究生(外文):JEN-YAO HO
論文名稱:利用遞迴迴旋積分分析頻率相關之VLSI傳輸線
論文名稱(外文):Using the Recursive Convolution Integration for Transient Simulation of VLSI Interconnect Characterized with Frequency Dependent Parameters
指導教授:張逢猷
指導教授(外文):F.Y.Chang
學位類別:碩士
校院名稱:國立交通大學
系所名稱:電信工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:52
中文關鍵詞:VLSI
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在現代的超大型積體電路(VLSI)中,積體電路包含大量的電路元件,其相互連結的金屬線便是實際的傳輸線(Transmission Line).
本論文介紹一種快速的離散時間分析法:遞迴迴旋積分(Recursive Convolution Integration);來分析非均勻耦合傳輸線的暫態模擬;其電容及電感參數皆為頻率相關.離散時間暫態摸擬是實行時變的特徵模式(Time-Verying Characteristic Model).其模式是由一般模式(Generalized Characteristic Model.)所轉換過來的.
這個模式是建構成二個不相交的時變阻抗網路,可表示成戴維寧或是諾頓型電路,而其電流/電壓源及端點的電流/電壓則成為遞迴迴旋積分輸入;而脈衝響應偶合傳輸線的阻抗函數(Immittance Function)和波型傳輸函數(Wave Propagation Function)則由Laguerre’s正交集來表示.
從實驗數據中可得知我們所使用的遞迴迴旋積分(Recursive Convolution Integration)比其它的演算法如波型鬆弛(waveform relaxation)及數值積分(numerical integration)來的更快. 而其結果跟實際的測量數據也只差了5%以內.

With the advent of Very Large Scale Integrated (VLSI) circuit technology, an integrated circuit (IC) nowadays consists of a very large number of circuit components interconnected by metal strips which in reality are transmission lines.
In this thesis we present an efficient discrete-time method of simulating the transient response of nonuniform coupled transmission lines that are characterized with frequency-dependent parameters. The discrete-time transient simulation is carried out from a time-verying characteristic model converted from the generalized characteristic model.
The time-varying characteristic model is constructed with two disjoint time-varying resistive networks connected with Norton/Thevanin’s current/voltage sources , which are generated by recursive convolution integration with the terminal currents/voltages and the Norton/Thevenin’s sources being the excitation and the impulse response functions are derived from the Laguerre’s orthonormal expansion of the characteristic immittance functions and the exponential wave propagation function of the coupled transmission line system.
The experimental results show that our proposed algorithm has more timing improvements than other algorithm such as the waveform relaxation and numerical integration. The experimental results are practically identical and differ from the analytical solutions by less than 5%.

Contents……………………………………………………………………………….1
List of Tables…….…………………………………………………………………....3
List of Figures….……………………………………………………………………..4
Chapter1:Introduction…………………………………………………………………5
Chapter2:Generalized Characteristics for the Transient Analysis of Transmission
Lines………………………………………………………………………..6
2-1 Transmission Lines Characteristic Model Equivalent Circuit…………..7
2-1-1 Thevenin Structures Characteristic Model…………………..7
2-1-2 Norton Structures Characteristic Model…..…………………9
2-2 Decouple Parameter of Transmission Lines……………………………10
Chapter3: Numerical Inversion of Laplace Transforms……………………………...12
3-1 Formal Statement of the Problem………………………………………12
3-2 Expansion of the Inverse Transform……………………………………13
3-3 Expansion of the Laplace Transform…………………………………...14
3-4 Computation Procedure………………………………………………...14
3-5 Numerical Examples……………………………………………………16
Chapter4 :Recursive Convolution Integration………………………………………..17
4-1 Convolution with Exponentially Decayed Polynomial Impulse Response
…………………………………………………………………………..17
4-2 Numerical Examples……………………………………………………19
Chapter5 :Time-Domain Synthesis of Characteristic Immittances and Exponential Wave Propagation using Recursive Convolution with Lagguerre’s Impulse
Response Function………………………………………………………..21
5-1 Synthesis of Exponential Wave Propagation Function…………………21
5-2 Synthesis of Characteristic Impedance Function……………………….26
Chapter6 : Circuit Simulation………………………………………………………..28
6-1 Recursive Convolution Integration v.s. Waveforms Relaxation Analysis
…………………………………………………………………………..28
6-1-1 Cascade Uniform Transmission Line……………………….28
6-1-2 Uniform Tri-Conductor System……………………………..31
6-2 Recursive Convolution Integration v.s. Numerical Integration………...38
Chapter7 :Conclusions and Future Work…………………………………………….42
Reference……………………………………………………………………………..43
Appendix A…………………………………………………………………………45
Resume……………………………………………………………………………..47

1 A.Semlyen and A.Dabuleanu : “Fast and accurate switching transient calculation on transmission lines with ground return using recursive convolution” IEEE Trans. Power App. Syst. Vol.94 pp.561-571 1975
2 F.Y.Chang : “Transient simulation of nonuniform coupled lossy transmission lines characteriszed with frequency-dependent parameters,Part I:Waveform relaxation analysis” IEEE Trans. Circuits Syst. Vol.39 pp.585-603 1992
3 A.E.Ruehli : “Circuit Analysis, Simulation and Design” NORTH HOLLAND
4 F.Y.Chang : “Waveform Relaxation Analysis of Nonuniform Lossy Transmission Lines Characterized with Frequency-Dependent Parameters” IEEE Trans. Circuits Syst. Vol.38 pp1484-1500 1991
5 E.C.Bertnolli : ”Exact and numerical analysis of distributed parameter RC networks ” Ph.D dissertation , Kansas State Univ. Manhattan. Sept. 1965
6 E.N.Protonotarios and O.Wing : “Theory of nonuniform RC lines ,Part I:Analytic properties and realizability conditions in the frequency domain ,PartII:Analytic properties in the time-domain” IEEE Trans. Circuit Theory Vol.14 pp2-20 Mar. 1967
7 C.R.Paul : “Useful matrix chain parameter identities for the analysis of multiconductor transmission lines” IEEE Trans .Microwave Theory Tech Vol. MIT-23 pp 756-780 Sept 1975
8 F.Y.Chang , “Tranient analysis of lossless coupled transmission lines in a nonhomogeneous dielectric medium ” IEEE Trans. Microwave Theory Tech Vol.MIT-18 pp 616-626 Sept 1970
9 F.Mesa R.Marques and M.Hrno “An efficient numerical spectral domain method to analyze a large clas of nonreciprocal planar transmission lines ” IEEE Trans. Microwave Theory Tech. Vol.40 pp1630-1641 Aug 1992
10 W.T.Weeks : “Numerical inversion of Laplace transforms using Laguerre functions” J.Assoc .Computing Machinery Vol13. pp419-426 July 1966
11 W.Magnus and F.Oberhettinger : “Formulas and Theorems for the Functions of Mathematical Physiscs” Chelsea ,New York 1954
12 F.B.Hildebrand : “Introduction to Numerical Analysis” McGraw-Hill New York 1956
13 F.Y.Chang : “Waveform relaxation analysis of RLCG transmission lines” IEEE Trans Circuits Syst. Vol.37 pp1394-1415 Nov 1990
14 Edward C. Chang and Sung-Mo Kaug: “Efficient modeling and simulation of coupled transmission lines”IEEE Trans Circuits Syst. Vol.24 pp152-156 1994
15 F.Y.Chang : “Transient Analysis of Lossy Transmission Lines with Arbitrary Initial Potenial and Current Distributions” IEEE Trans Circuits Syst. Vol.39 1991

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