基于RF CMOS工艺的平面螺旋差分电感的参数化等效电路模型
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摘要
CMOS射频集成电路中,平面螺旋差分电感是一种必不可少的无源片上元件。但是在高频阶段,这类电感会受到四种高频效应的影响:趋肤效应和邻近效应,导体间的寄生电容,容性衬底耦合,感性衬底耦合。这些效应降低了差分电感的高频特性,特别是品质因素,并且也给精确建模带来了困难。目前工业界缺乏差分电感的参数化等效电路模型,特别是详细的模型参数抽取过程分析。
本文首先分析了差分电感的线圈参数对电感性能的影响,给出了电感线圈参数优化的方法;然后从差分电感的四种高频效应的物理含义出发,建立八角形平面螺旋差分电感的参数化等效电路模型。等效电路模型只有与差分电感的物理意义紧密结合才能实现参数化,才能适用于不同的晶圆代工厂、不同工艺的电感,才能预测工艺改变后的电感性能。建模时首先对平面螺旋差分电感建立一个能正确模拟端口特性的“2-π”等效电路拓扑;然后提出一套解析公式使得电路中每个元件值跟工艺参数和器件的几何尺寸建立解析关系;适当引入到公式里的一组模型参数需要根据几个特定的测试电感的实测数据来优化与校准,以往没有文献对平面螺旋差分电感的“2-π”等效电路模型的模型参数的抽取方法进行详细的分析,因此我在实验过程中发展了一套模型参数抽取的方法并对其进行了分析。
经实测数据验证,本论文的参数化等效电路模型的模拟精度和速度都令人满意;并且该参数化等效电路模型与差分电感的物理意义结合紧密,因此具有较宽的应用范围。
Differential spiral inductors are one kind of on-chip passive components, which plays a critical role in modern CMOS RFICs. However, at high frequencies, such inductors suffer from four kinds of high frequency effects: skin and proximity effects, parasitic capacitances between metal windings, capacitive substrate coupling, and inductive substrate coupling. These high frequency effects not only degrade performances of inductors at high frequencies, especially quality factor (Q), but also make the modeling work quite difficult. Now industry lacks a physically-based scalable compact circuit model, especially the detailed analysis of extracting model parameters.
In this thesis, the effects of varying geometrical parameters on the performance of differential spiral inductors was investigated and the method of optimizing dimension quantities was given; And then based on the physical insights of the above high frequency effects, I have developed a scalable compact circuit model for octagonal differential spiral inductors. Only combined closely with the physical meaning of the differential inductors, the compact circuit model can achieve scalable, can be applied to different foundries and processes, and can be used to predict performances of differential inductors even the processes are changed. The first step of making a model is that a 27-element“2-π”circuit topology is proposed which includes all four kinds of effects, and provides correct port behaviors vs. frequencies. And then I developed a set of analytical formulas which correlates the values of circuit elements in circuit topology with the technology parameters and device’s geometric dimensions. Some model parameters properly introduced to the formulas need to be optimized and calibrated based on the fitting to the measurement data of several testing devices. In the past, there was no literature gave detailed analysis of the model parameter extraction method of“2-π”scalable compact circuit model for differential inductors. So I developed the method of model parameter extraction during the experiment and gave analysis about it in this paper.
Through the validation of measurement data, the speed and accuracy of the scalable compact circuit model are satisfying, and because of its close combination with the physical insights of the differential inductors, the scalable compact circuit model has a wide scope of application.
本文首先分析了差分电感的线圈参数对电感性能的影响,给出了电感线圈参数优化的方法;然后从差分电感的四种高频效应的物理含义出发,建立八角形平面螺旋差分电感的参数化等效电路模型。等效电路模型只有与差分电感的物理意义紧密结合才能实现参数化,才能适用于不同的晶圆代工厂、不同工艺的电感,才能预测工艺改变后的电感性能。建模时首先对平面螺旋差分电感建立一个能正确模拟端口特性的“2-π”等效电路拓扑;然后提出一套解析公式使得电路中每个元件值跟工艺参数和器件的几何尺寸建立解析关系;适当引入到公式里的一组模型参数需要根据几个特定的测试电感的实测数据来优化与校准,以往没有文献对平面螺旋差分电感的“2-π”等效电路模型的模型参数的抽取方法进行详细的分析,因此我在实验过程中发展了一套模型参数抽取的方法并对其进行了分析。
经实测数据验证,本论文的参数化等效电路模型的模拟精度和速度都令人满意;并且该参数化等效电路模型与差分电感的物理意义结合紧密,因此具有较宽的应用范围。
Differential spiral inductors are one kind of on-chip passive components, which plays a critical role in modern CMOS RFICs. However, at high frequencies, such inductors suffer from four kinds of high frequency effects: skin and proximity effects, parasitic capacitances between metal windings, capacitive substrate coupling, and inductive substrate coupling. These high frequency effects not only degrade performances of inductors at high frequencies, especially quality factor (Q), but also make the modeling work quite difficult. Now industry lacks a physically-based scalable compact circuit model, especially the detailed analysis of extracting model parameters.
In this thesis, the effects of varying geometrical parameters on the performance of differential spiral inductors was investigated and the method of optimizing dimension quantities was given; And then based on the physical insights of the above high frequency effects, I have developed a scalable compact circuit model for octagonal differential spiral inductors. Only combined closely with the physical meaning of the differential inductors, the compact circuit model can achieve scalable, can be applied to different foundries and processes, and can be used to predict performances of differential inductors even the processes are changed. The first step of making a model is that a 27-element“2-π”circuit topology is proposed which includes all four kinds of effects, and provides correct port behaviors vs. frequencies. And then I developed a set of analytical formulas which correlates the values of circuit elements in circuit topology with the technology parameters and device’s geometric dimensions. Some model parameters properly introduced to the formulas need to be optimized and calibrated based on the fitting to the measurement data of several testing devices. In the past, there was no literature gave detailed analysis of the model parameter extraction method of“2-π”scalable compact circuit model for differential inductors. So I developed the method of model parameter extraction during the experiment and gave analysis about it in this paper.
Through the validation of measurement data, the speed and accuracy of the scalable compact circuit model are satisfying, and because of its close combination with the physical insights of the differential inductors, the scalable compact circuit model has a wide scope of application.
引文
[1] 施超,庄奕琪,CMOS射频集成电路中器件模型的研究,微电子学,2002,32(6):405-408
[2] Ansoft HFSS user's manual. Ansoft Corporation, PA, U.S., 2001
[3] Gharpurey R, Meyer R G. Modeling and Analysis of Substrate Coupling in Integrated Circuits. IEEE J. Solid-State Circuits, 1996, 31(3):344~353
[4] Niknejad A M, Gharpurey R, Meyer R G. Numerically stable green function for modeling and analysis of substrate coupling in integrated circuits. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, 1998, 17(4):305~315
[5] Advanced design system manuals, Momentum. Agilent Technologies, CA, U.S., 2004
[6] W. Gao and Z. Yu, Scalable compact circuit model and synthesis for RF CMOS spiral inductors. IEEE Trans. Microw. Theory Tech. 2006, 54(3): 1055–1064
[7] 王忠诚,《电子电路及元器件入门教程》,2006,324-334页
[8] 倪光正,《工程电磁场原理》,2002,159-169页
[9] Shiu P H, Lim S K. Multi-layer Floor planning for Reliable System-on-Package, Center for Experimental Research in Compurer System Technical Reports, 2003, 3(13)
[10] Nguyen N M, Meyer R G, Si IC-compatible inductors and LC passive filters, IEEE J. Solid-State Circuits, 1990, 25(4):1028–1031
[11] Astis G D, Cordeau D, Paillot J M, et al. A 5-GHz fully integrated full PMOS low-phase-noise LC VCO. IEEE J Solid-State Circuits, 2005, 40(10): 2087-2091
[12] Gierkink S L J, Levantino S, Frye R C, et al. A low-phase-noise 5-GHz CMOS quadrature VCO using superharmonic coupling. IEEE J Solid-State Circuits, 2003, 38 (7): 1148
[13] Li Xiaoyong, Shekhar S, Allstot D J. Gm-boosted common-gate LNA and differential colpitts VCO/QVCO in 0.18-μm CMOS. IEEE J Solid-State Circuits, 2005, 40(12): 2609
[14] Chen H C, Wang T, Lu S S, et al. A monolithic 5.9-GHz CMOS I/Q direct-down converter utilizing a quadrature coupler and transformer-coupled subharmonic mixers. IEEE Microw Wireless Comp on Lett, 2006, 16(4): 197
[15] Kuhn W B, Ibrahim N M. Analysis of current crowding effects in multi-turn spiral inductors. IEEE Trans. Microwave Theory Tech., 2001, 49(1):31~38
[16] Kim S, Neikirk, D P. Compact equivalent circuit model for the skin effect. IEEE MTT-S International Microwave Symposium Digest, 1996, 3:1815~1818
[17] Zheng J, Hahm Y-C, Tripathi V K, et al. CAD-oriented equivalent-circuit modeling of on-chip interconnects on lossy silicon substrate. IEEE Trans. Microwave Theory Tech., 2000, 48(9):1443~1451
[18] Melendy D, Francis P, Pichler C, et al. A new wide-band compact model for spiral inductors in RFICs. IEEE Electron Device Lett., 2002, 23(5):273~275
[19] 高巍,潘桃,刘佳扬等. 考虑衬底涡旋电流的CMOS 射频电路电感元件的快速提取算法及实现,电子学报,2006, 34(8):1361~1366
[20] Cao Y, Groves R A, Huang X, et al. Frequency-independent equivalent circuit model for on-chip spiral inductors. IEEE J. Solid-State Circuits, 2003, 38(3):419~426
[21] Koutsoyannopoulos Y K and Papananos Y. Systematic analysis and modeling of integrated inductors and transformers in RF IC design, IEEE Trans Circuit and Systems-II: Analog and Digital signal processing, CSII-47 (2000), 699–713.
[22] Long J R, Copeland M A. The modeling, characterization, and design of monolithic inductors for silicon RF IC’s, IEEE J Solid-State Circ SSC-32 (1997), 357–369
[23] 王新稳,李萍,微波技术与天线[M],电子工业出版社,2003,pp.85-86
[24] Danesh M, Long J R. Differentially driven symmetric microstrip inductors, IEEE Trans. Microwave Theory Tech., 2002, 50(1): 332-341
[25] Nguyen N M, Meyer R G. Si IC-compatible inductors and LC passive filters. IEEE J. Solid-State Circuits, 1990, 25(4):1028~1031
[26] Yue C P, Wong S S. Physical modeling of spiral inductors on silicon. IEEE Trans. Electron Devices, 2000, 47(3):560~568
[27] Burghartz J N, Rejaei B. On the design of RF spiral inductors on silicon. IEEE Trans. Electron Devices, 2003, 50(3):718~729
[28] Chao C-J, Wong S-C, Kao C-H, et al. Characterization and modeling of on-chip spiral inductors for Si RFICs. IEEE Trans. Semiconductor Manufact., 2002, 15(1): 19-29
[29] Watson A C, Melendy D, Francis P., et al. A comprehensive compact-modeling methodology for spiral inductors in silicon-based RFICs. IEEE Trans. Microwave Theory Tech., 2004, 52(3):849~857
[30] Yu Cao, Robert A G, Noah D Z. Frequency-Independent Equivalent Circuit Model for On-chip Spiral Inductors, EECS Department, University of California, Berkeley, CA' IBM Microelectronics Division, Hopewell Junction, NY
[31] Wei Gao, Chao Jiao, Tao Liu, Scalable compact circuit model for differential spiral transformers in CMOS RFICs, IEEE Tr. Electron Devices, 2006, 53(9):2181-2194
[2] Ansoft HFSS user's manual. Ansoft Corporation, PA, U.S., 2001
[3] Gharpurey R, Meyer R G. Modeling and Analysis of Substrate Coupling in Integrated Circuits. IEEE J. Solid-State Circuits, 1996, 31(3):344~353
[4] Niknejad A M, Gharpurey R, Meyer R G. Numerically stable green function for modeling and analysis of substrate coupling in integrated circuits. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, 1998, 17(4):305~315
[5] Advanced design system manuals, Momentum. Agilent Technologies, CA, U.S., 2004
[6] W. Gao and Z. Yu, Scalable compact circuit model and synthesis for RF CMOS spiral inductors. IEEE Trans. Microw. Theory Tech. 2006, 54(3): 1055–1064
[7] 王忠诚,《电子电路及元器件入门教程》,2006,324-334页
[8] 倪光正,《工程电磁场原理》,2002,159-169页
[9] Shiu P H, Lim S K. Multi-layer Floor planning for Reliable System-on-Package, Center for Experimental Research in Compurer System Technical Reports, 2003, 3(13)
[10] Nguyen N M, Meyer R G, Si IC-compatible inductors and LC passive filters, IEEE J. Solid-State Circuits, 1990, 25(4):1028–1031
[11] Astis G D, Cordeau D, Paillot J M, et al. A 5-GHz fully integrated full PMOS low-phase-noise LC VCO. IEEE J Solid-State Circuits, 2005, 40(10): 2087-2091
[12] Gierkink S L J, Levantino S, Frye R C, et al. A low-phase-noise 5-GHz CMOS quadrature VCO using superharmonic coupling. IEEE J Solid-State Circuits, 2003, 38 (7): 1148
[13] Li Xiaoyong, Shekhar S, Allstot D J. Gm-boosted common-gate LNA and differential colpitts VCO/QVCO in 0.18-μm CMOS. IEEE J Solid-State Circuits, 2005, 40(12): 2609
[14] Chen H C, Wang T, Lu S S, et al. A monolithic 5.9-GHz CMOS I/Q direct-down converter utilizing a quadrature coupler and transformer-coupled subharmonic mixers. IEEE Microw Wireless Comp on Lett, 2006, 16(4): 197
[15] Kuhn W B, Ibrahim N M. Analysis of current crowding effects in multi-turn spiral inductors. IEEE Trans. Microwave Theory Tech., 2001, 49(1):31~38
[16] Kim S, Neikirk, D P. Compact equivalent circuit model for the skin effect. IEEE MTT-S International Microwave Symposium Digest, 1996, 3:1815~1818
[17] Zheng J, Hahm Y-C, Tripathi V K, et al. CAD-oriented equivalent-circuit modeling of on-chip interconnects on lossy silicon substrate. IEEE Trans. Microwave Theory Tech., 2000, 48(9):1443~1451
[18] Melendy D, Francis P, Pichler C, et al. A new wide-band compact model for spiral inductors in RFICs. IEEE Electron Device Lett., 2002, 23(5):273~275
[19] 高巍,潘桃,刘佳扬等. 考虑衬底涡旋电流的CMOS 射频电路电感元件的快速提取算法及实现,电子学报,2006, 34(8):1361~1366
[20] Cao Y, Groves R A, Huang X, et al. Frequency-independent equivalent circuit model for on-chip spiral inductors. IEEE J. Solid-State Circuits, 2003, 38(3):419~426
[21] Koutsoyannopoulos Y K and Papananos Y. Systematic analysis and modeling of integrated inductors and transformers in RF IC design, IEEE Trans Circuit and Systems-II: Analog and Digital signal processing, CSII-47 (2000), 699–713.
[22] Long J R, Copeland M A. The modeling, characterization, and design of monolithic inductors for silicon RF IC’s, IEEE J Solid-State Circ SSC-32 (1997), 357–369
[23] 王新稳,李萍,微波技术与天线[M],电子工业出版社,2003,pp.85-86
[24] Danesh M, Long J R. Differentially driven symmetric microstrip inductors, IEEE Trans. Microwave Theory Tech., 2002, 50(1): 332-341
[25] Nguyen N M, Meyer R G. Si IC-compatible inductors and LC passive filters. IEEE J. Solid-State Circuits, 1990, 25(4):1028~1031
[26] Yue C P, Wong S S. Physical modeling of spiral inductors on silicon. IEEE Trans. Electron Devices, 2000, 47(3):560~568
[27] Burghartz J N, Rejaei B. On the design of RF spiral inductors on silicon. IEEE Trans. Electron Devices, 2003, 50(3):718~729
[28] Chao C-J, Wong S-C, Kao C-H, et al. Characterization and modeling of on-chip spiral inductors for Si RFICs. IEEE Trans. Semiconductor Manufact., 2002, 15(1): 19-29
[29] Watson A C, Melendy D, Francis P., et al. A comprehensive compact-modeling methodology for spiral inductors in silicon-based RFICs. IEEE Trans. Microwave Theory Tech., 2004, 52(3):849~857
[30] Yu Cao, Robert A G, Noah D Z. Frequency-Independent Equivalent Circuit Model for On-chip Spiral Inductors, EECS Department, University of California, Berkeley, CA' IBM Microelectronics Division, Hopewell Junction, NY
[31] Wei Gao, Chao Jiao, Tao Liu, Scalable compact circuit model for differential spiral transformers in CMOS RFICs, IEEE Tr. Electron Devices, 2006, 53(9):2181-2194