高速VLSI电路中传输线瞬态响应的灵敏度分析
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摘要
随着集成电路尺寸的减小和信号速度的不断提高，高速VLSI电路中信号连接线的传输线效应(延迟、畸变、反射等)已成为限制系统信号完整性的主要原因。分析电路瞬态响应随传输线参数以及终端负载元件参数的变化规律，即分析瞬态响应的灵敏度，可以寻找到影响传输线效应的关键因素。本文提出了三种方法来求解传输线电路瞬态响应的灵敏度，分别是合同变换法、分段分解法和Chebyshev配点法。前两种方法是以传统传输线数学模型为基础，并在数值拉氏逆变换方法上进行深化和发展，它们分别应用于大规模线性传输线电路和非线性传输线电路。最后一种方法则是应用Chebyshev配点法对传输线建立新的数学分析模型，然后结合改进节点法对传输线电路进行瞬态响应分析和响应的灵敏度分析。最后通过实例分析，将应用三种方法得到的仿真波形和SPICE扰动法波形进行比较，波形吻合程度良好，说明精度较高。
With the reduction of the size of the integrate circuit and the advance of the speed of the signal, the transmission line effects (Delay, Reflection, Distortion etc) of the signal connection in the high speed VLSI circuit become the main cause of the restriction to the signal integrity analysis. Analyzing the transformation rule of the circuit transient response to the transmission line parameter and terminal load parameter, namely analyzing the sensitivity of the transient response, can find the key factors impacting the transmission line effect. This paper presents three methods to solve the sensitivity of the transient response of transmission line circuit. They are congruent transformation method, piecewise decomposition method and Chebyshev collocation method. The first two methods are based on the usual math model of the transmission line, and are developed from the NILT method. They are used in the complex linear transmission line circuit and. nonlinear transmission line circuit seperately. The last method applies the pseudo-spectral method to form the new math model of the transmission line, and then using the MNA method to progress the transisent response analysis and sensitivity analysis. From the comparison of the simulation wave and the SPICE perturbation method wave, the precision of the methods is good.
With the reduction of the size of the integrate circuit and the advance of the speed of the signal, the transmission line effects (Delay, Reflection, Distortion etc) of the signal connection in the high speed VLSI circuit become the main cause of the restriction to the signal integrity analysis. Analyzing the transformation rule of the circuit transient response to the transmission line parameter and terminal load parameter, namely analyzing the sensitivity of the transient response, can find the key factors impacting the transmission line effect. This paper presents three methods to solve the sensitivity of the transient response of transmission line circuit. They are congruent transformation method, piecewise decomposition method and Chebyshev collocation method. The first two methods are based on the usual math model of the transmission line, and are developed from the NILT method. They are used in the complex linear transmission line circuit and. nonlinear transmission line circuit seperately. The last method applies the pseudo-spectral method to form the new math model of the transmission line, and then using the MNA method to progress the transisent response analysis and sensitivity analysis. From the comparison of the simulation wave and the SPICE perturbation method wave, the precision of the methods is good.
引文
[1] 王志功，沈永朝．集成电路设计基础[M]．电子工业出版社．2005
[2] 朝来发，朱正堂．中国集成电路现状．科技情报开发与经济[J]．2004，14(2)，PP．191-192
[3] 杨之廉．集成电路导论[M]．清华大学出版社．2003
[4] 张洁萍．高速电路板设计中传输效应的抑制与分析[J]．机电工程技术．2005，34(7)，pp．51-52
[5] 李征帆，毛军发．微波与高速电路理论[M]．上海交通大学出版社．2001
[6] 梁宝娟，张少波．高速电路板设计的信号完整性分析[J]．西安文理学院学报．2006年4月，9(2)，pp．66-68
[7] Chiariello A. G, Maffucci A. and Miano G. Signal integrity analysis of high-speed interconnects through a full-wave transmission line model [C]. IEEE Workshop on Signal Propagation on Interconnects. 2005 Proceedings 9th. 10-13, May 2005, pp.47-50
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[14] Ling Y. Li, Greg E. Bridges and loan R. Ciric. Efficient Simulation of Interconnect Networks with Frequency-Dependent Lossy Transmission Lines [J]. IEEE Microwave and Wireless Components Letters. 2002, 12(4), pp. 131-133
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[21] Qinwei Xu, Mazumder. P. Efficient and passive modeling of transmission lines by using differential quadrature method[C]. Design, Automation and Test in Europe. 2001. Conference and Exhibition 2001 Proceedings. 2001, 13(16), pp. 437-444
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[31] Das. S. K. and Smith. W. T.. Application of asymptotic waveform evaluation for analysis of skin effect in lossy interconnects[J]. IEEE Transactions on Electromagnetic Compatibility. 1997, 39(2), pp. 138-146
[32] Lawrence T. Pillage and Ronald A. Rohrer. Asymptotic Waveform Evaluation for Timing Analysis[J]. IEEE Trans CAD. 1990, 9(4), pp. 352-366
[33] C. L. Ratzlaff and L. T. Pillage. RICE: Rapid interconnect circuit evaluation using AWE[J]. IEEE Trans. Computer-Aided Design. 1994, 13(6), pp. 763-776
[34] M. Celik and A. C. Cangellaris. Efficient transient simulation of lossy packaging interconnects using moment-matching techniques[J]. IEEE Trans Comp Packag., Manufact. Tech. B. 1996, 19(1), pp. 64-73
[35] 邵维，王秉中．二维FDTD法互连线分析的非均匀网格实现[J]．电子科技大学学报．2003，32(4)，pp．385-388
[36] Clayton. Incorporation of terminal constraints in the FDTD analysis of transmission lines[J]. IEEE Trans EC. 1992, 36(5), pp. 85-91
[37] 王承民，蒋传文．基于支路电流状态变量的灵敏度分析方法研究[J]．电工技术学报．2006，21(1)，pp．42-46
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[44] Nakhla M. S. A piecewise decomposition technique for analysis of nonlinear networks with distributed components[J]. IEEE International Symposium on Circuits and Systems. vol. 1, May 1989, pp. 606-609
[45] A. R. Djordjevic and T. K. Sarkar. Analysis of time response of lossy multiconductor transmission line networks[J]. IEEE Trans. Microwave Theory Tech. vol. MTT-35, No. 10, Oct. 1987, pp. 898-908
[46] T. K. Tang and M. S. Nakhla. Analysis of High-speed VLSI Interconnect Using the Asymptotic Waveform Evaluation Technique[j]. IEEE Trans. CAD. 1992, 11(3), pp. 341-351
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[3] 杨之廉．集成电路导论[M]．清华大学出版社．2003
[4] 张洁萍．高速电路板设计中传输效应的抑制与分析[J]．机电工程技术．2005，34(7)，pp．51-52
[5] 李征帆，毛军发．微波与高速电路理论[M]．上海交通大学出版社．2001
[6] 梁宝娟，张少波．高速电路板设计的信号完整性分析[J]．西安文理学院学报．2006年4月，9(2)，pp．66-68
[7] Chiariello A. G, Maffucci A. and Miano G. Signal integrity analysis of high-speed interconnects through a full-wave transmission line model [C]. IEEE Workshop on Signal Propagation on Interconnects. 2005 Proceedings 9th. 10-13, May 2005, pp.47-50
[8] Rubinstein J., Penfield P., Horowitz M. A.. Signal Delay in RC Tree Networks[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. July 1983, 2(3), pp. 202-211
[9] J. Jr. Wyatt. Signal delay in RC mesh networks [J]. IEEE Trans. Circuits syst. 1985, 32(5), pp. 507-510
[10] R. Achar and M. Nakhla. Simulation of high-speed interconnects [C]. Proc. IEEE. 2001, 89(5), pp. 693-728
[11] E. Chiprout and M. Nakhla. Analysis of interconnect networks using complex frequency hopping (CFH) [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 1995, 14(2), pp. 186-200
[12] Giulio Antonini and Giuseppe Ferri. A New Approach for Closed-Form Transient Analysis of Multiconductor Transmission Lines [J]. IEEE Trans. On Electromagnetic Compatibility. 2004, 46(4), pp. 529-543
[13] P. K. Gunupudi, M. Nakhla and R. Achar. Simulation of high-speed distributed interconnects using Krylov-space techniques [J]. IEEE Trans. Computer-Aided Design. 2000, 19(7), pp. 799-808
[14] Ling Y. Li, Greg E. Bridges and loan R. Ciric. Efficient Simulation of Interconnect Networks with Frequency-Dependent Lossy Transmission Lines [J]. IEEE Microwave and Wireless Components Letters. 2002, 12(4), pp. 131-133
[15] Linchao Lui, M. S. Nakhla and Q. J. Zhang. A resetting algorithm for transient analysis of coupled transmission line circuits[J]. IEEE Trans MTT, 1994, 42(3), pp. 494-500
[16] 张希，刘宗行，孙韬．传输线方程的一种数值解法[J]．重庆大学学报．2004，27(2)， PP．116-119
[17] Mao J F, Li Z F. Analysis of the time-response of multiconductor transmission lines with frequency-dependent losses by the method of convolution[J]. IEEE Trans on MTT. 1992, 40(4), pp. 637-644
[18] Z. F. Li, Q. W. Xu and J. Z. Zhu. Fast simulation of lossy transmission lines by the modified method of characteristics[J]. Electronics Letters. 1997, 33(11), pp. 942-944
[19] J. F. Mao and E. S. Kuh. Fast simulation and sensitivity analysis of lossy transmission lines by the method of characteristics[J]. IEEE Trans on CAS. 1997, 44(5), pp. 391-401
[20] Qin-Wei Xu, Zheng-FanLi, Jun Wang and Jun-Fa Mao. Transient Analysis of Lossy Interconnects by Modified Method of Characteristecs[J]. IEEE transactions on circuits and systems-Ⅰ. 2000, 47(3), pp. 363-375
[21] Qinwei Xu, Mazumder. P. Efficient and passive modeling of transmission lines by using differential quadrature method[C]. Design, Automation and Test in Europe. 2001. Conference and Exhibition 2001 Proceedings. 2001, 13(16), pp. 437-444
[22] 辛丙松，赵进全，杨拴科．基于精细积分法的耦合传输线瞬态分析[J]．光纤与电缆及其应用技术．2005年1期，PP．15-17
[23] 赵进全，马西奎，邱关源．任意负载有损传输线时域的精细积分法[J]．微电子学．2001，(31)6，pp．431-433
[24] 赵进全，马西奎，邱关源．传输线时域响应灵敏度分析的精细积分法[J]．无线电通信技术．2000，26(4)，pp．53-54
[25] 赵进全，马西奎，邱关源．有损传输线时域响应的精细积分法[J]．微电子学．1997，27(3)，pp．181-185
[26] R. Griffith and M. Nakhla. Time-domain analysis of lossy coupled transmission lines[J]. IEEE Trans. Microwave Theory and Tech.. vol. 38, Oct, 1990, pp. 1480-1487
[27] 郭裕顺．用NILT导出的传输线瞬态分析模型[J]．电子学报．2002，30(3)，pp．381-385
[28] 毛军发，李征帆．传输线时域响应分析中的改进NILT方法[J]．电子学报．1995，23(3)，pp．55-57
[29] 孙韬，刘宗行．传输线方程解析解求解方法的探讨[J]．华北电力大学学报．2005，32(B 12)，pp．25-28
[30] EY Chang. Waveform relaxation analysis of RLCG transmission lines[J]. IEEE Trans Circuits Syst. 1990, 37(11), pp. 1394-1415
[31] Das. S. K. and Smith. W. T.. Application of asymptotic waveform evaluation for analysis of skin effect in lossy interconnects[J]. IEEE Transactions on Electromagnetic Compatibility. 1997, 39(2), pp. 138-146
[32] Lawrence T. Pillage and Ronald A. Rohrer. Asymptotic Waveform Evaluation for Timing Analysis[J]. IEEE Trans CAD. 1990, 9(4), pp. 352-366
[33] C. L. Ratzlaff and L. T. Pillage. RICE: Rapid interconnect circuit evaluation using AWE[J]. IEEE Trans. Computer-Aided Design. 1994, 13(6), pp. 763-776
[34] M. Celik and A. C. Cangellaris. Efficient transient simulation of lossy packaging interconnects using moment-matching techniques[J]. IEEE Trans Comp Packag., Manufact. Tech. B. 1996, 19(1), pp. 64-73
[35] 邵维，王秉中．二维FDTD法互连线分析的非均匀网格实现[J]．电子科技大学学报．2003，32(4)，pp．385-388
[36] Clayton. Incorporation of terminal constraints in the FDTD analysis of transmission lines[J]. IEEE Trans EC. 1992, 36(5), pp. 85-91
[37] 王承民，蒋传文．基于支路电流状态变量的灵敏度分析方法研究[J]．电工技术学报．2006，21(1)，pp．42-46
[38] 孙林根，洪远丰．计算机辅助电路分析[M]．机械工业出版社．1985
[39] K. C.格普塔，R.加格，R.查德哈．微波电路的计算机辅助设计[M]．科学出版社．1986
[40] S. W. Director and R. A. Rohrer. The generalized adjoint network and network sensitivity[J]. IEEE Trans on circuit theory. 1969, 16(3), pp. 318-323
[41] S. Lum, M. Nakhla and Q. J. Zhang. Sensitivity analysis of lossy coupled transmission lines[J]. IEEE Trans. Microwave Theory Tech. vol. 39, Dec. 1991, pp. 2089-2099
[42] 李新，李征帆．高速集成电路互连线结构的时域波形灵敏度分析[J]．上海交通大学学报．1997，31(6)，pp．69-72
[43] A. Dounavis, R. Achar and M. Nakhla. Efficient sensitivity analysis of lossy multiconductor transmission lines with nonlinear terminations[C]. Microwave Symposium Digest, 2001 IEEE MTT-S International. Vol. 3, May 2001, pp. 2099-2102
[44] Nakhla M. S. A piecewise decomposition technique for analysis of nonlinear networks with distributed components[J]. IEEE International Symposium on Circuits and Systems. vol. 1, May 1989, pp. 606-609
[45] A. R. Djordjevic and T. K. Sarkar. Analysis of time response of lossy multiconductor transmission line networks[J]. IEEE Trans. Microwave Theory Tech. vol. MTT-35, No. 10, Oct. 1987, pp. 898-908
[46] T. K. Tang and M. S. Nakhla. Analysis of High-speed VLSI Interconnect Using the Asymptotic Waveform Evaluation Technique[j]. IEEE Trans. CAD. 1992, 11(3), pp. 341-351
[47] A. R. Djordjevic and T. K. Sarkar. Analysis of time response of lossy multiconductor transmission line networks[J]. IEEE Trans. Microwave Theory Tech. vol. MTT-35, No.10, Oct. 1987, pp. 898-908
[48] J．瓦拉赫，K．辛格尔．电路分析和设计的计算机方法[M]．科学出版社．1992
[49] S. Lum, M. Nakhla and Q. J. Zhang. Sensitivity analysis of lossy coupled transmission lines[J]. IEEE Trans. Microwave Theory Tech.. vol. 39, Dec. 1991, pp. 2089-2099
[50] R. W. Freund and P. Feldmann. Small-signal circuit analysis and sensitivity computations with the PVL algorithm[J]. IEEE Trans. Circuits Syst. I. vol. 43, Aug, 1996, pp.577-585
[51] J. Y. Lee, X. Huang and R. A. Roher. Pole and zero sensitivity calculation in asymptotic waveform evaluation[J]. IEEE Trans. Computer-Aided Design. vol. 11, May, 1992, pp. 586-597.
[52] 顾敦和，张弦，郁易生．线性代数[M]．高等教育出版社．2001
[53] J. E. Schutt-Aine and R. Mitra. Nonlinear transient analysis of coupled transmission lines[J]. IEEE Trans. Circuits Syst. CAS-36, July 1989, pp. 959-967
[54] A. R. Djordjevic, T. K. Sarkar and R. F. Harrington. Analysis of lossy transmission lines with arbitrary nonlinear terminal networks[J]. IEEE Trans. Microwave Theory Tech.. MTT-34, June 1986, pp. 660-666
[55] M. Nakhla and J. Vlach. A piecewise harmonic balance technique for determination of periodic response on nonlinear systems[J]. IEEE Trans. Circuits Syst. CAS-23, Feb, 1976, pp. 85-91
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