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研究生:李芳錡
論文名稱:積體電路多線串音之分析
論文名稱(外文):Crosstalk analysis for multiple coupled transmission lines
指導教授:李肇嚴
指導教授(外文):Jau-Yien Lee
學位類別:碩士
校院名稱:長庚大學
系所名稱:半導體研究所
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:2001
畢業學年度:89
語文別:中文
中文關鍵詞:串音
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近年來,隨著製程技術的迅速進步,超大型積體電路的設計也朝向高速度、高密度的趨勢而發展。因此,在超大型積體電路之中彼此相鄰的金屬連線越來越近,導致不可忽視的串音效應。所以,如何在增進電路的效能的情況下又要兼顧降低線與線之間的串音雜訊,及延遲時間等問題是值得注意的。由於SPICE是以Lumped架構對傳輸線作近似性的模擬,無法精確地分析出確實的傳輸效應,以致使用SPICE模擬的結果會與最後佈局模擬的結果不一樣。本文以簡單的梯形電路建立在S域多項式的ABCD傳輸函數,使系統分析可充分應用Laplace轉換的長處,而輕易地處理頻率響應與波形變化的問題,此方法亦可計算非均性的傳輸線使其更能切合各種環境實際的需要,另外本文經由M矩陣的轉換更可使多傳輸線簡化為單一傳輸線,透過此種轉換我們將多線間的互感與互耦效應吸收變成單線的分佈電感與電容電路,使複雜的多線干擾問題變成單純的傳輸線問題。因此,透過此公式可以得知線與線之間干擾的程度,提供給IC設計者一個更快速、更準確的資料,以作為電路設計的參考,最後本文應用在Routing、Packaging、DRAM等設計驗證此方法之可行。

Developing in the tendency toward high speed and high density, the counting of delay time and the analysis of crosstalk noise on interconnection for high speed VLSI has become very important. So, we will pay more attention to increase the efficiency of IC and decrease the crosstalk noise.
For the simulation of coupling effect among multi-transmission line, in this paper, we introduce a diagonalization matrix that transforms multiple coupled transmission lines into a set of uncoupled lines. And use the M matrix as the basis to transform the coupled transmission line mode into the uncoupled transmission line. Additionally, thus through ABCD matrix to establish the S-domain polynomial of single-transmission line. And final from the signal of time-domain with inverse Laplace transforms, we get the effect of signals disturbing among each other of multiple lines.

第一章 簡介…………………………………………………………….1
1.1 研究動機…………………………………………………….. 1
1.2 研究內容………………………………………………………1
1.3 章節概要………………………………………………………2
第二章 單線傳輸原理…………………………………………………3
2.1 雙埠網路…………………………………………………….. 3
2.2 傳輸線模型的建立……………………………………………4
2.2.1 RC傳輸線分析………………………………………… 7
2.2.2 頻率響應……………………………………………...14
2.2.3 RLCG傳輸線分析…………………………………….15
第三章 多線傳輸原理……………………………………………… .18
3.1 多線方程式………………………………………………….18
3.2 均性多線-單線矩陣轉換………………………………….19
3.3 Eigenvalues與Eigenvectors求法…………………………..20
3.4 非均性多線-單線矩陣轉換………………………………..26
第四章 應用……………………………………………………….. …32
4.1 串音分析…………………………………………………….32
4.2 均性應用…………………………………………………….34
4.3 非均性應用………………………………………………….36
第五章 結論與未來計畫……………………………………………..38
參考資料………………………………………………………………..41

[1]Jau-Yien Lee and Sen-Chang Hwang "Problems and Solutions of Nonuniform Transmission Lines", Int’l conf. on Microwave and Comm. pp. 12-17 1992. Nanjin China.
[2]Jau-Yien Lee "Chain Matrices of Polynomial Coefficients of Long Ladder Networks", IEEE proc colloquium on circuit and systems, pp. 100-104, 1999.
[3]Sadahiko Yamamoto, Takashi Azakami, Kiyoyasu Itakura "Coupled Nonuniform Transmission Line and Its Applications". IEEE Transactions on Microwave Theory and Techniques, VOL. MTT-15, NO. 4, pp. 220-231, APRIL 1967.
[4]Jau-Yien Lee, Chia-Chi Chu, Hien-Chang Wang "Matrix Trains for Rational S-polynomials of Nonuniform RLCG Transmission Lines", Cross strait 2000 conf. on wireless comm.. pp, 290-293, 2000 Hefei China.
[5]Prashant Saxena and C. L. Liu, “ A Postprocessing Algorithm for Crosstalk-Driven Wire Perturbation ”. IEEE Transactions on Computer-Aided design of integrated circuits and systems, VOL. 19, NO. 6, pp. 691-702, JUNE 2000.
[6]ASHOK K, GOEL “High-Speed VLSI Interconnections : Modeling, Analysis, and Simulation”. WILEY, 1994
[7]Tong Gao and C. L. Liu, “Minimum Crosstalk Channel Routing”. IEEE Transactions on computer-aided design of integrated circuits and systems, VOL. 15, NO. 5, pp, 465-474, MAY 1996.
[8]Rubio, N. Itazaki, X. Xu, and K. Kinoshita, “An Approach to the Analysis and Detection of Crosstalk Faults in Digital VLSI Circuits” IEEE Transaction on Computer-Aided Design of Integrated Circuits and System, VOL. 13, NO. 3, pp. 387-395, MARCH 1994.
[9]Alan Jennings, J.J. Mckeown “MATRIX COMPUTATION”
[10]Carl D. Meyer “Matrix Analysis and Applied Linear Algebra”
[11]Ashok Vittal, Lauren Hui Chen, Malgorzata Marek-Sadowska, Kai-Ping Wang, and Sherry Yang “Crosstalk in VLSI Interconnections” IEEE Transactions on computer-aided design of integrated circuits and systems. VOL. 18, NO. 12. pp. 1817-1824 December 1999.
[12]David S. Gao, Andrew t. Yang, and Sung Mo Kang, “Modeling and Simulation of Interconnection Delays and Crosstalks in High-Speed Integrated Circuits” IEEE Transactions on Circuits system, VOL. 37, NO. 1 pp. 1-9, January 1990.
[13]Wendemagegnehu T. Beyene, Jose E. Schutt-Aine, “Effcient Transient Simulation of High-Speed Interconnects Characterized by Sampled Data” IEEE Transactions on Components, Packaging, and Manufacturing Technology VOL.21, NO. 1, pp 105-114, February 1998.
[14]W.M. Kanfman and S.J. Garret "Tapered distributed filters," IRE Trans. Circuit Theory, vol. CT-9, pp. 1540-1545, 1962
[15]Lee Jau-Yien, Lin Sheng-Ping “Delay Time and Crosstalk Noise Simulation of Interconnections for High Speed VLSI”master thesis Chang Gung University June 2000.

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