RF-MEMS天线理论、建模仿真及特性研究
|
摘要
近年来，微机电系统(MEMS)研究得到了迅猛的发展。用于射频通信领域中的MEMS技术，即 RF-MEMS (Radio Frequency Micro-electro-mechanical System)技术，蕴藏着巨大的市场潜力，已经成为研究的热点，受到学术界和政府部门的高度重视。采用微机械技术研制的RF-MEMS天线是RF-MEMS系统的关键器件之一，它不但具有体积小、重量轻、性能稳定等优点外，还能和其他电路元件集成在一起。
本文在分析了国内外RF-MEMS天线研究现状的基础上，对微尺度下微机械天线的电磁辐射与耦合理论、数学建模与数值仿真、参数优化、加工、测试及应用等方面进行了深入系统的理论分析和实验研究，成功地研制出了多种结构的微机械天线，在微机械天线的理论、数值模拟、参数优化和制造上取得了突破和创新。
本文研究的主要内容包括：从麦克斯韦方程和波动方程出发，分析了RF-MEMS天线的电磁辐射和耦合机理、准静态特征参数，讨论了色散和表面波效应及相关的电磁特性；对微机械天线进行了数学建模，着重优化了时域有限差分法（FDTD），用优化的FDTD法对微机械天线进行了数值计算和仿真，并通过傅里叶变换将时域计算所得结果转换到频域中，然后进行有关参数计算；采用理论分析和实验研究相结合的方法，对微机械天线进行参数优化，提出用新颖的结构和复合基片介质材料来实现微机械天线的小型化和宽带化，解决了多层混合基片介质相对介电常数、输入阻抗等参数的计算，采用短路结构实现四分之一波长贴片天线，并推导了其长度计算公式；结合微机械天线的特点对材料选取、制作工艺进行了研究，提出了材料的选用标准，在硅基片介质加工工艺上，提出用双面刻蚀法进行狭缝刻蚀以提高腐蚀因子；介绍了微机械天线测试场，对天线参数进行了误差分析；在微机械天线的应用方面，首先设计了蓝牙计算机无线通信演示装置，并在该系统上使用了微机械天线试验样品，该系统可以成功地进行无线互连，然后在Motorola G18无线通信平台上使用了微机械天线，可以成功地收发短信息；最后提出了微机械天线阵列、多芯片组装等下一步的研究计划。
本论文的创新点主要体现在：
(1) 将传输线法、空腔模型法及FDTD法用于微尺度下微机械天线的建模和仿真。重点对FDTD法进行了合理的优化，用以进行微机械天线的数值仿真，并用实验对其结果进行验证，表明这种优化方法是合理的，可以用以指导微机械天线的设计。
通过贴片和接地板间添加短接柱的理论分析和实验研究表明，短路针可降低微带天线的频率，根据微机械天线的工艺特性，首次提出了用短路壁结构代替短路针的结构，将天线变为四分之一波长结构，其长度减小了一半，并提出了四分之
(2) 一波长天线长度的计算公式。还采用C型折叠贴片等结构将天线尺寸进一步缩小，最小尺寸只有自由空间波长的。
(3) 针对高介电常数基片介质对天线性能的负面影响，提出将贴片下方的高介电常数介质腐蚀掉一部分，或在硅片和接地板间添加一层介电常数较低的媒质，可有效抑制表面波激励，提高天线效率、增加带宽。
(4) 采用添加寄生贴片、附加微带振子方案，通过电磁耦合作用有效地增加了天线带宽。
本论文对微尺度下微机械天线的电磁辐射和耦合理论、微型化和宽带化等方面做了有益的探索，为微尺度下电磁场理论的完善、天线的集成化制造奠定了理论和技术基础。
In recent years, Micro-electro-mechanical System (MEMS) has been developed drastically. MEMS technology applied in radio frequency communication field, which is known as RF-MEMS (Radio Frequency Micro-electro-mechanical System), has great potentials. RF-MEMS research has become very important in application of radio frequency, and drawn attention of academe and governments greatly. Micromachined RF-MEMS antenna, one of the key devices in RF-MEMS, has small size, light weight, stable quality and other merits; it can be integrated with other circuit element.
Rest on present research status of RF-MEMS antenna, systematically theoretical analysis and profoundly experimental research on electromagnetic radiation and coupling, mathematical modeling and numerical simulation, parameter optimization, machining and measuring of micromachined antenna in micro-scale have been presented in this thesis. Several types of micromachined antennas have been fabricated successfully. Innovation and breakthrough have been obtained in theory, numerical simulation, parameter optimization and fabrication.
The main contents of the thesis are shown as follow: analysis on electromagnetic radiation and coupling mechanics, quasi-static characteristic parameter of RF-MEMS antenna, discuss on the related electromagnetic character of dispersion and surfacewave effect; optimization of Finite-Difference-Time-Domain (FDTD), numerical simulation of micromachined antenna using optimized FDTD, and related parameter calculation; parameter optimization by theoretical analysis associated with experimental research, realization downsize and broadband by novel structure and hybrid substrate, resolution of calculations on relative dielectric constant and input impedance, realization of a quarter wavelength antenna by shorted wall. Material selection standard and fabrication process of micromachined antenna are presented. The antenna measurement fields are introduced, then error analysis of parameters developed. We applied the micromachined antennas in Bluetooth computer Demo devices and Motorola G18 wireless communication system, both can communicate with other devices. In the end some research plan such as micromachined array and multi-chip module are put forward.
Following are the important achievement and innovation:
To model and simulate micromachined antenna in micro-scale using TLM, cavity model and FDTD. To simulate micromachined antenna by optimized FDTD, and
(1) verify it by experiment. It indicates that the optimized method is rational, and the optimized FDTD can be used to design micromachined antenna.
(2) By theoretical analysis and experimental research of shorting stubs between patch and ground, it indicates that the shorting stub could lower frequency of microstrip antenna. Shorting wall in place of shorting stub, which can turn the antenna to a quarter wavelength antenna, has been put forward. The antenna dimensions will be downsized further if C folded structure is used; the length of the antenna is only 1/12 wavelength in free space.
(3) According to deficiency of high index substrate to antenna, some of the substrate beneath the patch should be partially removed, or some low index substrate should be sandwiched between the ground and the high index substrate, so the surfacewave would be suppressed greatly, then the efficiency and bandwidth would be increased.
(4) By using parasitic patch and additive microstrip vibrator, the coupling effect with drive patch could enlarge bandwidth of the antenna.
The research of electromagnetic radiation, miniaturization and broadband of micromachined antenna in micro-scale has benefits, and found theoretical and technical base for improvement of electromagnetic field theory in micro-scale and antenna integrated fabrication.
本文在分析了国内外RF-MEMS天线研究现状的基础上，对微尺度下微机械天线的电磁辐射与耦合理论、数学建模与数值仿真、参数优化、加工、测试及应用等方面进行了深入系统的理论分析和实验研究，成功地研制出了多种结构的微机械天线，在微机械天线的理论、数值模拟、参数优化和制造上取得了突破和创新。
本文研究的主要内容包括：从麦克斯韦方程和波动方程出发，分析了RF-MEMS天线的电磁辐射和耦合机理、准静态特征参数，讨论了色散和表面波效应及相关的电磁特性；对微机械天线进行了数学建模，着重优化了时域有限差分法（FDTD），用优化的FDTD法对微机械天线进行了数值计算和仿真，并通过傅里叶变换将时域计算所得结果转换到频域中，然后进行有关参数计算；采用理论分析和实验研究相结合的方法，对微机械天线进行参数优化，提出用新颖的结构和复合基片介质材料来实现微机械天线的小型化和宽带化，解决了多层混合基片介质相对介电常数、输入阻抗等参数的计算，采用短路结构实现四分之一波长贴片天线，并推导了其长度计算公式；结合微机械天线的特点对材料选取、制作工艺进行了研究，提出了材料的选用标准，在硅基片介质加工工艺上，提出用双面刻蚀法进行狭缝刻蚀以提高腐蚀因子；介绍了微机械天线测试场，对天线参数进行了误差分析；在微机械天线的应用方面，首先设计了蓝牙计算机无线通信演示装置，并在该系统上使用了微机械天线试验样品，该系统可以成功地进行无线互连，然后在Motorola G18无线通信平台上使用了微机械天线，可以成功地收发短信息；最后提出了微机械天线阵列、多芯片组装等下一步的研究计划。
本论文的创新点主要体现在：
(1) 将传输线法、空腔模型法及FDTD法用于微尺度下微机械天线的建模和仿真。重点对FDTD法进行了合理的优化，用以进行微机械天线的数值仿真，并用实验对其结果进行验证，表明这种优化方法是合理的，可以用以指导微机械天线的设计。
通过贴片和接地板间添加短接柱的理论分析和实验研究表明，短路针可降低微带天线的频率，根据微机械天线的工艺特性，首次提出了用短路壁结构代替短路针的结构，将天线变为四分之一波长结构，其长度减小了一半，并提出了四分之
(2) 一波长天线长度的计算公式。还采用C型折叠贴片等结构将天线尺寸进一步缩小，最小尺寸只有自由空间波长的。
(3) 针对高介电常数基片介质对天线性能的负面影响，提出将贴片下方的高介电常数介质腐蚀掉一部分，或在硅片和接地板间添加一层介电常数较低的媒质，可有效抑制表面波激励，提高天线效率、增加带宽。
(4) 采用添加寄生贴片、附加微带振子方案，通过电磁耦合作用有效地增加了天线带宽。
本论文对微尺度下微机械天线的电磁辐射和耦合理论、微型化和宽带化等方面做了有益的探索，为微尺度下电磁场理论的完善、天线的集成化制造奠定了理论和技术基础。
In recent years, Micro-electro-mechanical System (MEMS) has been developed drastically. MEMS technology applied in radio frequency communication field, which is known as RF-MEMS (Radio Frequency Micro-electro-mechanical System), has great potentials. RF-MEMS research has become very important in application of radio frequency, and drawn attention of academe and governments greatly. Micromachined RF-MEMS antenna, one of the key devices in RF-MEMS, has small size, light weight, stable quality and other merits; it can be integrated with other circuit element.
Rest on present research status of RF-MEMS antenna, systematically theoretical analysis and profoundly experimental research on electromagnetic radiation and coupling, mathematical modeling and numerical simulation, parameter optimization, machining and measuring of micromachined antenna in micro-scale have been presented in this thesis. Several types of micromachined antennas have been fabricated successfully. Innovation and breakthrough have been obtained in theory, numerical simulation, parameter optimization and fabrication.
The main contents of the thesis are shown as follow: analysis on electromagnetic radiation and coupling mechanics, quasi-static characteristic parameter of RF-MEMS antenna, discuss on the related electromagnetic character of dispersion and surfacewave effect; optimization of Finite-Difference-Time-Domain (FDTD), numerical simulation of micromachined antenna using optimized FDTD, and related parameter calculation; parameter optimization by theoretical analysis associated with experimental research, realization downsize and broadband by novel structure and hybrid substrate, resolution of calculations on relative dielectric constant and input impedance, realization of a quarter wavelength antenna by shorted wall. Material selection standard and fabrication process of micromachined antenna are presented. The antenna measurement fields are introduced, then error analysis of parameters developed. We applied the micromachined antennas in Bluetooth computer Demo devices and Motorola G18 wireless communication system, both can communicate with other devices. In the end some research plan such as micromachined array and multi-chip module are put forward.
Following are the important achievement and innovation:
To model and simulate micromachined antenna in micro-scale using TLM, cavity model and FDTD. To simulate micromachined antenna by optimized FDTD, and
(1) verify it by experiment. It indicates that the optimized method is rational, and the optimized FDTD can be used to design micromachined antenna.
(2) By theoretical analysis and experimental research of shorting stubs between patch and ground, it indicates that the shorting stub could lower frequency of microstrip antenna. Shorting wall in place of shorting stub, which can turn the antenna to a quarter wavelength antenna, has been put forward. The antenna dimensions will be downsized further if C folded structure is used; the length of the antenna is only 1/12 wavelength in free space.
(3) According to deficiency of high index substrate to antenna, some of the substrate beneath the patch should be partially removed, or some low index substrate should be sandwiched between the ground and the high index substrate, so the surfacewave would be suppressed greatly, then the efficiency and bandwidth would be increased.
(4) By using parasitic patch and additive microstrip vibrator, the coupling effect with drive patch could enlarge bandwidth of the antenna.
The research of electromagnetic radiation, miniaturization and broadband of micromachined antenna in micro-scale has benefits, and found theoretical and technical base for improvement of electromagnetic field theory in micro-scale and antenna integrated fabrication.
引文
[1]、 张方英. 天线及馈电设备. 第一版. 北京. 国防工业出版社. 1984. 7~10.
[2]、 刘泽文，李志坚，刘理天.用于通信领域中的MEMS器件.电子科技导报.1999.Vol.11(7)23~27.
[3]、 潘武、钟先信、巫正中. 无线通信系统中的微尺度射频元件. 光学 精密工程.2001.Vol.9(5)
[4]、 王广龙、周照英.RF MEMS技术的发展及应用研究.压电与声光.20001.5增刊.2～4
[5]、 Clark T. Nguyen. Microelectromechanical devices wireless communications. Proceedings of IEEE. Heidelberg.Germany. Jan.1998. 1~7
[6]、 Clark T. Nguyen. Communication application of microelectromechanical systems. 1998 Sensors Expro. San Jose. CA.1998.5. 447~455
[7]、 钟先信等.微光机电系统集成技术的新进展.'97微系统研讨会·重庆.12~16
[8]、 I.J.Bahl、P.Bhartia. Microstrip antennas. Artech House. London. 1980. 50~150
[9]、 Ioannis Papapolymerou, Rhonda Franklin Drayton, Linda P. B. Katehi. Micromachined patch antennas. IEEE Transactions on Antennas and Propagation. 1998.Vol.46(2). 275~283.
[10]、 Mark J. Vaughan, Katerina Y. Hur, et al. Improvement of microstrip patch antenna radiation patterns. IEEE. AP. 1994. Vol.42(6). 882~884
[11]、 钟顺时.微带天线理论与应用. 西安.西安电子科大出版社. 1991.125
[12]、 M. Zheng, Q. Chen, P. S. Hall and V. F. Fusco. Broadband microstrip patch antenna on micromachined silicon substrates. Electronics Letters, 1998.Vol.34(1).3~4
[13]、 S. D. Targonski, et al. Design of wideband aperture-stacked patch microstrip antennas. IEEE. AP. 1998. Vol.46 (9). 1245~1250
[14]、 巫正中、钟先信、潘武等.用于便携式通信设备的集成微带天线. 压电与声光.20001.5增刊.235~238
[15]、 巫正中、钟先信、潘武等.新型微机械微带天线的研究. 压电与声光.20001.5增刊.328~331
[16]、 潘英俊、邹建.光电子技术. 重庆.重庆大学出版社. 2000. 1~10
[17]、 楼仁海、符果行等.电磁理论.电子科技大学出版社.成都.1996.1~19
[18]、 Kai Chang. Antenna for radar and communications. New York. John Wiley & Sons press. 1992. 1~200
[19]、 康行健.天线原理与设计.北京.国防工业出版社.1986.1~48
[20]、 DiPaolo, Franco. Networks and Devices Using Planar Transmission Lines. CRC Press. Boca Raton.2000
[21]、 林昌禄.陈海等.近代天线设计.人民邮电出版社.北京.1990.1~50
[22]、 宋开宏等. 矩形微带贴片天线辐射边缘间的互耦. 无线电工程. Vol. 30 (2). 38~39
[23]、 K. C. Guptaetal. Computer-aided design of microwave circuits. London Artech House.1981
[24]、 H. Pues and A. Van. de Capelle. A simple accurate formula for the radiation conductance of a rectangular microstrip antenna. IEEE Trans. AP. 1981. Vol.29(9)
[25]、 吴万春.微波毫米波与光波集成电路的理论基础.西安.西北电讯工程学院出版社.第一版.1985.
[26]、 清华大学《微带电路》编写组. 第一版.微带电路.人民邮电出版社.北京.1975.
[27]、 A.R.N.Farias，et.al. The Microstrip Antenna Analysis and Design. Journal of Microwaves and Optoelectronics. 1998.Vol.1(2).24~28
[28]、 http://www.fdtd.org
[29]、 A.R.N.Farias，et.al. The Microstrip Antenna Analysis and Design. Journal of Microwaves and Optoelectronics. 1998.Vol.1(2).24~28
[30]、 康行健.天线原理与设计.北京.国防工业出版社.1986.1~48
[31]、 A.R.N.Farias，et.al. The Microstrip Antenna Analysis and Design. Journal of Microwaves and Optoelectronics. 1998.Vol.1(2).24~28
[32]、 Kane S.Yee. Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equation in Istropic Media. Mathematics of the Computation. 1977.Vol.31(139). 629-651.
[33]、 祝西礼等.电磁场时域有限差分法.电子工业出版社.北京.1995.23~50
[34]、 庞敏. MEMS层叠式微带贴片天线的建模、分析.重庆.重庆大学.2002.20~45
[35]、 藤本共荣 J.R.詹姆斯.移动天线系统手册.人民邮电出版社.北京. 1993. 340~395
[36]、 http://www.tcl.com
[37]、 任朗.天线理论基础. 北京.人民邮电出版社. 1988. 40~85
[38]、 Rebekka Porath. Theory of Miniaturized Shorting-Post Microstrip Antennas. IEEE AP.2000.Vol.48 (l). 87~93
[39]、 梁福生、王广学. 飞机天线工程手册. 北京.国防工业出版社.1989. 35～120
[40]、 潘武，钟先信，巫正中等.微带天线的宽带化、微型化进展及微机械天线.微米/纳米科学与技术.2000. Vol.5(1).201~204
[41]、 巫正中，钟先信，李晓毅等. 微机械多层短接式蓝牙天线.光学 精密工程.2001.Vol.9(2).572~576
[42]、 邓次平.现代微波网络导论.第一版.北京.国防工业出版社.1987.35~89
[43]、 D.R.Jackson and N.G.Alexopoulos. Gain Enhancement Methods for Microstrip Antennas. IEEE AP.1985 Vol.33(9). 976~978
[44]、 http://www.usf.edu
Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi, et.al. Broadband micromachined antenna for bluetooth device. Jinan, China. 2002.Harbin. Institute of Technology Press. Proceedings of ISIST'2002
[45]、 Vol.2.pp728~731.
[46]、 毛康侯，方振民.飞行器天线工程设计指南. 第一版北京.国防工业出版社.1988.
[47]、 毛康侯. 防空导弹天线. 第一版.北京.兵器工业出版社. 1992.
[48]、 http://www.ericsson.com
[49]、 Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi, et.al. Broad micromachined Bluetooth antenna. Proceedings of Pacifc Rim Workshop on Micro/Nano Technologies. Xiamen, China. July 2002.
[50]、 黄景熙，范治波. 锥削开槽天线的分析.武汉大学学报（自然科学版）.1989（1）.12~16
[51]、 范治波，黄景熙.具有一层空气隙的矩形微带天线谱域导抗法.武汉大学学报（自然科学版）.1995（2）.56~60
[52]、 王阳元等.微电子学概论.第一版.北京.北京大学出版社.1995. 235~255
[53]、 黄庆安.硅微细加工技术.第一版.北京.电子工业出版社. 1996. 125~260
[54]、 毛乃宏，俱新德. 天线测量手册.第一版. 北京.机械工业出版社.1987.
[55]、 Reimar Marg and Arne F. Jacob.Radiation Pattern of Microstrip Antennas on Finite Grounded Substrates. http://www.iht.edu/Annual report.pdf
[56]、 http://www.mmic.org
[57]、 Raymond L. Brown，et al., Embedded Passive Functions for RF and Mixed-Signal Circuits, http://www.mmic.org/presentation
[58]、 陈迪.非硅三维加工技术. 电子科技导报.1999.Vol.11(9)32~40.
[59]、 张兴, 郝一龙等.跨世纪的新技术—微机电系统(MEMS). 电子科技导报.1999.Vol.11(4)2~6.
[60]、 徐涛, 武国英.微结构气体传感器的研究现状及展望. 电子科技导报.1999.Vol.11(6)23~28.
[61]、 林守远, 顾墨琳.微机电系统的微波应用. 微波学报. 2000.Vol.16(4).416~422.
[62]、 郝一龙, 李志宏等.硅表面牺牲层技术. 电子科技导报.1999.Vol.11(12)23~28.
[63]、 尹家贤, 谭怀英等.FDTD中微带线激励源设置的新方法.电波科学学报.2000.Vol.15(2).204~207
[64]、 尹家贤, 谭怀英等.FDTD中微带线激励源分析.国防科技大学学报.2000. Vol.22(5).60~63.
[65]、 S.S.Zhong, Y.T.Lo, Single-Element Rectangular Microstrip Antenna for Dual - Frequency Operation, Electronics Letters. 1983, 19(18): 298～300
[66]、 G.Kumar, Directly Coupled Multiple Resonator Wideband Microstrip Antennas. IEEE Trans. Antennas Propagat. 1985,33(3):588～593
[67]、 K.R.Garver, Microstrip Antenna Technology. IEEE Trans. Antennas and Propagat.,1988,36(11): 1519～1525
[68]、 J.Yao, S.Chen, S.Eshelman, et al., Micromachined Low-Loss Microwave Switches. IEEE Journal of Microelectromechanical Systems, 1999,8(2): 129～134
M.Kim, J.B.Hacher, R.E.Mihailovich, et al., A Monolithic MEMS Switch Dual-Path Power
[69]、 Amplifier. IEEE Microwave and Wireless Components Letters, 2001, 11(7): 285～287
[70]、 R.E.Mihailovich, M.Kim, J.B.Hacker, et al., MEM Relay for Reconfigurable RF Circuits. IEEE Microwave and Wireless Components Letters, 2001, 11(2): 53～55
[71]、 J.G.Yook, L.P.B. Katchi, Micromachined Microstrip Patch Antenna with Controlled Mutual Coupling and Surface Waves. IEEE Trans. Antennas and Propagat., 2001, 49(9): 1282～1289
[72]、 V.Vigayak, W.O. Keese, C.Lam, A 2.4GHz Radio Solution for Bluetooth and Wireless Home Networking. Electronic Engineering, 2001, 73(889): 42～43
[73]、 K.S.Yee, Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media. IEEE Trans. Antennas and Propagat., 1966,14(5): 302～307
[74]、 K.S.Yee, D.Ingham, K.Shlager, Time-Domain Extrapolation to the Far Field Based on FDTD calculations. IEEE Trans. Antennas Propagat., 1991,39(3):410～413
[75]、 X. Zhang and K. K. Mei, Time-Domain Finite Difference Approach to the Calculation of Frequency-Dependent Characteristics of Microstrip Discontinuities. IEEE Trans. Microwave Theory Tech., 1988, 36(12): 1775～1783
[76]、 Reineix, B. Jecko, Analysis of Mircostrip Patch Antennas Using Finite Difference Time Domain Method. IEEE Trans. Antennas Propagat., 1989,37(11): 1361～1369
[77]、 A.Taflove, K.R.Umashankar, The Finite-Difference Time-Domain (FD-TD) Method for Numerical Modeling of Electromagnetic Scattering. IEEE Trans. Magnetics, 1989,25(4): 3086～3091
[78]、 W.L.Ko, R.Mittra, A Combination of FD-TD and Prony's Methods for Analyzing Microwave Integrated Circuits. IEEE Trans. Microwave Theory Tech., 1991,39(12): 2176～2181
[79]、 C.M.Furse, D.H.Roper, D.N.Buechler, et al., The Problem and Treatment of DC offsets in FDTD Simulations. IEEE Trans. Antennas and Propagat. 2000, 48(8): 1198～1201
[80]、 C.Q.Wang, O.P.Gandhi, Numerical Simulation of Annular Phased Arrays for Anatomically Based Models Using the FDTD Method. IEEE Trans. Microwave Theory Tech., 1989,37(1): 118～126
[81]、 阮成礼﹒毫米波理论与技术﹒第一版﹒成都﹒电子科技大学出版社﹒2001.3
[82]、 陈雅娟,龙云亮﹒宽带微带贴片天线的研究进展﹒电波科学学报﹒1999﹒14(3): 357～361
[83]、 林昌禄，陈海，吴为公﹒近代天线设计﹒第一版﹒北京﹒人民邮电出版社﹒1990.8
[84]、 刘庭华，章文勋﹒双层微带贴片天线单元的实验研究﹒现代雷达﹒1997﹒19(1): 54～60
[85]、 Z.F.Liu, P.S. Kooi, L.W.Li, et al, A Method for Designing Broad-band Microtrip Antennas in Multiplayered Planar Structures. IEEE Trans. Antennas and Propat. 1999,47(9): 1416～1420
G.P.Gauthier, A.Courtay, G. M. Rebeiz, Microstrip Antennas on Synthesized Low
[86]、 Dielectric-Constant Substrates. IEEE Trans. Antennas and Propagat., 1997, 45(8): 1310～1314
[87]、 M.Zheng, Q.Chen, P.S.Hall, et al., Broadband Microstrip Patch Antenna on Micromachined Silicon Substrates. Electronic Letters, 1998, 34(1): 3～4
[88]、 K.L.Wong, T.W.Chiou, Broad-Band Single-patch Circularly Polarized Microstrip Antenna with Dual Capacitively Coupled Feeds. IEEE Trans. Antennas and Propagat., 2001,49(1):41～44
[89]、 F.Tefiku, C.A.Grimes, Design of Broad Band and Dual-Band Antennas Comprised of Series-Fed Printed-Strip Dipole Pairs. IEEE Trans. Antennas and Propagat., 2000,48(6):895～900
[90]、 S.M.Duffy, An Enhanced Bandwidth Design Technique for Electromagnetically Coupled Microstrip Antennas. IEEE Trans. Antennas and Propagat., 2000,48(2): 161～164
[91]、 S.K.Palit, A.Hamadi, Design and Development of Wideband and Dual-Band Microstrip Antennas. IEE Proc. Microwave Antennas and Propagat., 1999,146(1): 35～39
[92]、 封建湖，车刚明，聂玉峰﹒数值分析原理﹒第一版﹒北京﹒科学出版社﹒2001.9
[93]、 颜庆津﹒数值分析﹒第一版﹒北京﹒北京航空航天大学出版社﹒2001.1
[94]、 李庆扬，关治，白峰杉﹒数值计算原理﹒第一版﹒北京﹒清华大学出版社﹒2000.9
[95]、 H.Pues, A.V.Cappele, Accurate Transmission-line Model for the Rectangular Microstrip Antenna. Proc. Inst. Elect. Eng. Microwave Antennas and Propagat., 1984,133(11): 334～340
[96]、 D.L.Sengupata, Transmission Line model Analysis of Rectangular Patch Antennas. Electromagnetics, 1984, 4(4): 355～376
[97]、 电子科技大学应用数学系编﹒实用数值计算方法﹒第一版﹒北京﹒高等教育出版社﹒2001.1
[98]、 F.Capalino, M.Albani, S.Maci, et al., Frequency-Domain Green's Funcion for a Planar Periodic Semi-Infinite Phased Array. IEEE Trans Antennas and Propagat., 2000, 48(1): 67～85
[99]、 A.Reineix, B.Jecko, Analysis of Microstrip Patch Antennas Using Finite Difference Time Domain Method. IEEE Trans. Antennas and Propagat., 1989,37(11):1361～1369
[100] D.M.Sheen, S.M.Ali, M.D.Abouzahra, et al., Application of the Three-Dimensional Analysis of Planar Microstrip Circuits. IEEE Trans. Microwave Theory Tech., 1990, 38(7): 847～857
[101] C.Wu, K.L.Wu, Z.Q.Bi, et al. Accurate Characterization of Planar Printed Antennas Using Finite-Difference Time-Domain Method. IEEE Trans. Antennas and Propagat., 1992,40(5): 526～534
[102]A.Taflove, M.E.Brodwin, Numerical Solution of Steady-state Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations. IEEE Trans. Microwave Theory Tech. 1975, 23(8): 623～630
[103] G.Mur, Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations. IEEE Trans. Electromagnetic Compatibility,
1981, 23(4): 1073～1077
[104] K.K.Mei, J.Y.Fang, Superabsorption-A Method to Improve Absorbing Boundary Conditions. IEEE Trans. Antennas Propagat., 1992, 40(9): 1001～1010
[105] J.P.Berenger, A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Physics, 1994, 114: 185～200
[106] 马双武，高攸纲﹒时域有限差分法中超吸收技术的改进及数值验证﹒电波科学学报﹒2000﹒15(1): 20～24
[107] F.Akleman, L.Sevgi, A novel Implementation of Berenger's PML for FDTD Applications. IEEE Microwave and Guided Wave Lett., 1998, 5(10): 324～326
[108] D.T.Prescott, N.V.Shuley, Reflection Analysis of FDTD boundary Conditions-Part II: Berenger's PML Absorbing Layers. IEEE Trans. Microwave Theory, 1997,45(8): 1171～1178
[109] G.X.Fan, Q.H.Lin, An FDTD Algorithm with Perfectly Matched Layers for General Dispersive Media. IEEE Trans. Antennas and Propagat., 2000, 48(5): 637～646
[110] H.Derudder, F.Olyslager, D.D.Zutter, et al., Efficient Mode-Matching Analysis of Discontinuities in Finite Planar Substrates Using Perfectly Matched Layers. IEEE Trans. Antennas and Propagat., 2001,49(2):185～195
[111] S.Winton, C.M.Rappaport, Specifying PML Conductivities by Considering Numerical Reflection Dependencies. IEEE Trans. Antennas and Propagat., 2000,48(7): 1055～1063
[112] 陈彬，方大纲﹒完全匹配层（PLM）吸收边界条件的理论分析﹒微波学报﹒1996﹒12(2): 110～115
[113] 马双武, 高攸纲﹒时域有限差分法中几种吸收边界条件的比较与数值验证﹒长沙大学学报﹒1999﹒13(4): 1～4
[114] B.Engquist, A.Majda., Absorbing Boundary Conditions for the Numerical Simulation of Waves. Math. Comp. , 1977, 31(139): 629～651
[115] A.P.Zhao, A.V.Raisanen , S.R.Cvetkovic, A Fast and Efficient FDTD Algorithm for the Analysis of Planar Microstrip Discontinuities by Using a Simple Source Excitation Scheme. IEEE Microwave and Guided Wave Lett. 1995, 5(10): 341～343
[116] X.Zhang, J.Fang, K.K.Mei, Calculations of the Dispersive Characteristics of Microstrips by the Time-Domian Finite Difference Method. IEEE Trans. Microwave Theory Tech., 1988, 36(2): 263～267
[2]、 刘泽文，李志坚，刘理天.用于通信领域中的MEMS器件.电子科技导报.1999.Vol.11(7)23~27.
[3]、 潘武、钟先信、巫正中. 无线通信系统中的微尺度射频元件. 光学 精密工程.2001.Vol.9(5)
[4]、 王广龙、周照英.RF MEMS技术的发展及应用研究.压电与声光.20001.5增刊.2～4
[5]、 Clark T. Nguyen. Microelectromechanical devices wireless communications. Proceedings of IEEE. Heidelberg.Germany. Jan.1998. 1~7
[6]、 Clark T. Nguyen. Communication application of microelectromechanical systems. 1998 Sensors Expro. San Jose. CA.1998.5. 447~455
[7]、 钟先信等.微光机电系统集成技术的新进展.'97微系统研讨会·重庆.12~16
[8]、 I.J.Bahl、P.Bhartia. Microstrip antennas. Artech House. London. 1980. 50~150
[9]、 Ioannis Papapolymerou, Rhonda Franklin Drayton, Linda P. B. Katehi. Micromachined patch antennas. IEEE Transactions on Antennas and Propagation. 1998.Vol.46(2). 275~283.
[10]、 Mark J. Vaughan, Katerina Y. Hur, et al. Improvement of microstrip patch antenna radiation patterns. IEEE. AP. 1994. Vol.42(6). 882~884
[11]、 钟顺时.微带天线理论与应用. 西安.西安电子科大出版社. 1991.125
[12]、 M. Zheng, Q. Chen, P. S. Hall and V. F. Fusco. Broadband microstrip patch antenna on micromachined silicon substrates. Electronics Letters, 1998.Vol.34(1).3~4
[13]、 S. D. Targonski, et al. Design of wideband aperture-stacked patch microstrip antennas. IEEE. AP. 1998. Vol.46 (9). 1245~1250
[14]、 巫正中、钟先信、潘武等.用于便携式通信设备的集成微带天线. 压电与声光.20001.5增刊.235~238
[15]、 巫正中、钟先信、潘武等.新型微机械微带天线的研究. 压电与声光.20001.5增刊.328~331
[16]、 潘英俊、邹建.光电子技术. 重庆.重庆大学出版社. 2000. 1~10
[17]、 楼仁海、符果行等.电磁理论.电子科技大学出版社.成都.1996.1~19
[18]、 Kai Chang. Antenna for radar and communications. New York. John Wiley & Sons press. 1992. 1~200
[19]、 康行健.天线原理与设计.北京.国防工业出版社.1986.1~48
[20]、 DiPaolo, Franco. Networks and Devices Using Planar Transmission Lines. CRC Press. Boca Raton.2000
[21]、 林昌禄.陈海等.近代天线设计.人民邮电出版社.北京.1990.1~50
[22]、 宋开宏等. 矩形微带贴片天线辐射边缘间的互耦. 无线电工程. Vol. 30 (2). 38~39
[23]、 K. C. Guptaetal. Computer-aided design of microwave circuits. London Artech House.1981
[24]、 H. Pues and A. Van. de Capelle. A simple accurate formula for the radiation conductance of a rectangular microstrip antenna. IEEE Trans. AP. 1981. Vol.29(9)
[25]、 吴万春.微波毫米波与光波集成电路的理论基础.西安.西北电讯工程学院出版社.第一版.1985.
[26]、 清华大学《微带电路》编写组. 第一版.微带电路.人民邮电出版社.北京.1975.
[27]、 A.R.N.Farias，et.al. The Microstrip Antenna Analysis and Design. Journal of Microwaves and Optoelectronics. 1998.Vol.1(2).24~28
[28]、 http://www.fdtd.org
[29]、 A.R.N.Farias，et.al. The Microstrip Antenna Analysis and Design. Journal of Microwaves and Optoelectronics. 1998.Vol.1(2).24~28
[30]、 康行健.天线原理与设计.北京.国防工业出版社.1986.1~48
[31]、 A.R.N.Farias，et.al. The Microstrip Antenna Analysis and Design. Journal of Microwaves and Optoelectronics. 1998.Vol.1(2).24~28
[32]、 Kane S.Yee. Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equation in Istropic Media. Mathematics of the Computation. 1977.Vol.31(139). 629-651.
[33]、 祝西礼等.电磁场时域有限差分法.电子工业出版社.北京.1995.23~50
[34]、 庞敏. MEMS层叠式微带贴片天线的建模、分析.重庆.重庆大学.2002.20~45
[35]、 藤本共荣 J.R.詹姆斯.移动天线系统手册.人民邮电出版社.北京. 1993. 340~395
[36]、 http://www.tcl.com
[37]、 任朗.天线理论基础. 北京.人民邮电出版社. 1988. 40~85
[38]、 Rebekka Porath. Theory of Miniaturized Shorting-Post Microstrip Antennas. IEEE AP.2000.Vol.48 (l). 87~93
[39]、 梁福生、王广学. 飞机天线工程手册. 北京.国防工业出版社.1989. 35～120
[40]、 潘武，钟先信，巫正中等.微带天线的宽带化、微型化进展及微机械天线.微米/纳米科学与技术.2000. Vol.5(1).201~204
[41]、 巫正中，钟先信，李晓毅等. 微机械多层短接式蓝牙天线.光学 精密工程.2001.Vol.9(2).572~576
[42]、 邓次平.现代微波网络导论.第一版.北京.国防工业出版社.1987.35~89
[43]、 D.R.Jackson and N.G.Alexopoulos. Gain Enhancement Methods for Microstrip Antennas. IEEE AP.1985 Vol.33(9). 976~978
[44]、 http://www.usf.edu
Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi, et.al. Broadband micromachined antenna for bluetooth device. Jinan, China. 2002.Harbin. Institute of Technology Press. Proceedings of ISIST'2002
[45]、 Vol.2.pp728~731.
[46]、 毛康侯，方振民.飞行器天线工程设计指南. 第一版北京.国防工业出版社.1988.
[47]、 毛康侯. 防空导弹天线. 第一版.北京.兵器工业出版社. 1992.
[48]、 http://www.ericsson.com
[49]、 Wu Zhengzhong, Zhong Xianxin, Li Xiaoyi, et.al. Broad micromachined Bluetooth antenna. Proceedings of Pacifc Rim Workshop on Micro/Nano Technologies. Xiamen, China. July 2002.
[50]、 黄景熙，范治波. 锥削开槽天线的分析.武汉大学学报（自然科学版）.1989（1）.12~16
[51]、 范治波，黄景熙.具有一层空气隙的矩形微带天线谱域导抗法.武汉大学学报（自然科学版）.1995（2）.56~60
[52]、 王阳元等.微电子学概论.第一版.北京.北京大学出版社.1995. 235~255
[53]、 黄庆安.硅微细加工技术.第一版.北京.电子工业出版社. 1996. 125~260
[54]、 毛乃宏，俱新德. 天线测量手册.第一版. 北京.机械工业出版社.1987.
[55]、 Reimar Marg and Arne F. Jacob.Radiation Pattern of Microstrip Antennas on Finite Grounded Substrates. http://www.iht.edu/Annual report.pdf
[56]、 http://www.mmic.org
[57]、 Raymond L. Brown，et al., Embedded Passive Functions for RF and Mixed-Signal Circuits, http://www.mmic.org/presentation
[58]、 陈迪.非硅三维加工技术. 电子科技导报.1999.Vol.11(9)32~40.
[59]、 张兴, 郝一龙等.跨世纪的新技术—微机电系统(MEMS). 电子科技导报.1999.Vol.11(4)2~6.
[60]、 徐涛, 武国英.微结构气体传感器的研究现状及展望. 电子科技导报.1999.Vol.11(6)23~28.
[61]、 林守远, 顾墨琳.微机电系统的微波应用. 微波学报. 2000.Vol.16(4).416~422.
[62]、 郝一龙, 李志宏等.硅表面牺牲层技术. 电子科技导报.1999.Vol.11(12)23~28.
[63]、 尹家贤, 谭怀英等.FDTD中微带线激励源设置的新方法.电波科学学报.2000.Vol.15(2).204~207
[64]、 尹家贤, 谭怀英等.FDTD中微带线激励源分析.国防科技大学学报.2000. Vol.22(5).60~63.
[65]、 S.S.Zhong, Y.T.Lo, Single-Element Rectangular Microstrip Antenna for Dual - Frequency Operation, Electronics Letters. 1983, 19(18): 298～300
[66]、 G.Kumar, Directly Coupled Multiple Resonator Wideband Microstrip Antennas. IEEE Trans. Antennas Propagat. 1985,33(3):588～593
[67]、 K.R.Garver, Microstrip Antenna Technology. IEEE Trans. Antennas and Propagat.,1988,36(11): 1519～1525
[68]、 J.Yao, S.Chen, S.Eshelman, et al., Micromachined Low-Loss Microwave Switches. IEEE Journal of Microelectromechanical Systems, 1999,8(2): 129～134
M.Kim, J.B.Hacher, R.E.Mihailovich, et al., A Monolithic MEMS Switch Dual-Path Power
[69]、 Amplifier. IEEE Microwave and Wireless Components Letters, 2001, 11(7): 285～287
[70]、 R.E.Mihailovich, M.Kim, J.B.Hacker, et al., MEM Relay for Reconfigurable RF Circuits. IEEE Microwave and Wireless Components Letters, 2001, 11(2): 53～55
[71]、 J.G.Yook, L.P.B. Katchi, Micromachined Microstrip Patch Antenna with Controlled Mutual Coupling and Surface Waves. IEEE Trans. Antennas and Propagat., 2001, 49(9): 1282～1289
[72]、 V.Vigayak, W.O. Keese, C.Lam, A 2.4GHz Radio Solution for Bluetooth and Wireless Home Networking. Electronic Engineering, 2001, 73(889): 42～43
[73]、 K.S.Yee, Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media. IEEE Trans. Antennas and Propagat., 1966,14(5): 302～307
[74]、 K.S.Yee, D.Ingham, K.Shlager, Time-Domain Extrapolation to the Far Field Based on FDTD calculations. IEEE Trans. Antennas Propagat., 1991,39(3):410～413
[75]、 X. Zhang and K. K. Mei, Time-Domain Finite Difference Approach to the Calculation of Frequency-Dependent Characteristics of Microstrip Discontinuities. IEEE Trans. Microwave Theory Tech., 1988, 36(12): 1775～1783
[76]、 Reineix, B. Jecko, Analysis of Mircostrip Patch Antennas Using Finite Difference Time Domain Method. IEEE Trans. Antennas Propagat., 1989,37(11): 1361～1369
[77]、 A.Taflove, K.R.Umashankar, The Finite-Difference Time-Domain (FD-TD) Method for Numerical Modeling of Electromagnetic Scattering. IEEE Trans. Magnetics, 1989,25(4): 3086～3091
[78]、 W.L.Ko, R.Mittra, A Combination of FD-TD and Prony's Methods for Analyzing Microwave Integrated Circuits. IEEE Trans. Microwave Theory Tech., 1991,39(12): 2176～2181
[79]、 C.M.Furse, D.H.Roper, D.N.Buechler, et al., The Problem and Treatment of DC offsets in FDTD Simulations. IEEE Trans. Antennas and Propagat. 2000, 48(8): 1198～1201
[80]、 C.Q.Wang, O.P.Gandhi, Numerical Simulation of Annular Phased Arrays for Anatomically Based Models Using the FDTD Method. IEEE Trans. Microwave Theory Tech., 1989,37(1): 118～126
[81]、 阮成礼﹒毫米波理论与技术﹒第一版﹒成都﹒电子科技大学出版社﹒2001.3
[82]、 陈雅娟,龙云亮﹒宽带微带贴片天线的研究进展﹒电波科学学报﹒1999﹒14(3): 357～361
[83]、 林昌禄，陈海，吴为公﹒近代天线设计﹒第一版﹒北京﹒人民邮电出版社﹒1990.8
[84]、 刘庭华，章文勋﹒双层微带贴片天线单元的实验研究﹒现代雷达﹒1997﹒19(1): 54～60
[85]、 Z.F.Liu, P.S. Kooi, L.W.Li, et al, A Method for Designing Broad-band Microtrip Antennas in Multiplayered Planar Structures. IEEE Trans. Antennas and Propat. 1999,47(9): 1416～1420
G.P.Gauthier, A.Courtay, G. M. Rebeiz, Microstrip Antennas on Synthesized Low
[86]、 Dielectric-Constant Substrates. IEEE Trans. Antennas and Propagat., 1997, 45(8): 1310～1314
[87]、 M.Zheng, Q.Chen, P.S.Hall, et al., Broadband Microstrip Patch Antenna on Micromachined Silicon Substrates. Electronic Letters, 1998, 34(1): 3～4
[88]、 K.L.Wong, T.W.Chiou, Broad-Band Single-patch Circularly Polarized Microstrip Antenna with Dual Capacitively Coupled Feeds. IEEE Trans. Antennas and Propagat., 2001,49(1):41～44
[89]、 F.Tefiku, C.A.Grimes, Design of Broad Band and Dual-Band Antennas Comprised of Series-Fed Printed-Strip Dipole Pairs. IEEE Trans. Antennas and Propagat., 2000,48(6):895～900
[90]、 S.M.Duffy, An Enhanced Bandwidth Design Technique for Electromagnetically Coupled Microstrip Antennas. IEEE Trans. Antennas and Propagat., 2000,48(2): 161～164
[91]、 S.K.Palit, A.Hamadi, Design and Development of Wideband and Dual-Band Microstrip Antennas. IEE Proc. Microwave Antennas and Propagat., 1999,146(1): 35～39
[92]、 封建湖，车刚明，聂玉峰﹒数值分析原理﹒第一版﹒北京﹒科学出版社﹒2001.9
[93]、 颜庆津﹒数值分析﹒第一版﹒北京﹒北京航空航天大学出版社﹒2001.1
[94]、 李庆扬，关治，白峰杉﹒数值计算原理﹒第一版﹒北京﹒清华大学出版社﹒2000.9
[95]、 H.Pues, A.V.Cappele, Accurate Transmission-line Model for the Rectangular Microstrip Antenna. Proc. Inst. Elect. Eng. Microwave Antennas and Propagat., 1984,133(11): 334～340
[96]、 D.L.Sengupata, Transmission Line model Analysis of Rectangular Patch Antennas. Electromagnetics, 1984, 4(4): 355～376
[97]、 电子科技大学应用数学系编﹒实用数值计算方法﹒第一版﹒北京﹒高等教育出版社﹒2001.1
[98]、 F.Capalino, M.Albani, S.Maci, et al., Frequency-Domain Green's Funcion for a Planar Periodic Semi-Infinite Phased Array. IEEE Trans Antennas and Propagat., 2000, 48(1): 67～85
[99]、 A.Reineix, B.Jecko, Analysis of Microstrip Patch Antennas Using Finite Difference Time Domain Method. IEEE Trans. Antennas and Propagat., 1989,37(11):1361～1369
[100] D.M.Sheen, S.M.Ali, M.D.Abouzahra, et al., Application of the Three-Dimensional Analysis of Planar Microstrip Circuits. IEEE Trans. Microwave Theory Tech., 1990, 38(7): 847～857
[101] C.Wu, K.L.Wu, Z.Q.Bi, et al. Accurate Characterization of Planar Printed Antennas Using Finite-Difference Time-Domain Method. IEEE Trans. Antennas and Propagat., 1992,40(5): 526～534
[102]A.Taflove, M.E.Brodwin, Numerical Solution of Steady-state Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations. IEEE Trans. Microwave Theory Tech. 1975, 23(8): 623～630
[103] G.Mur, Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations. IEEE Trans. Electromagnetic Compatibility,
1981, 23(4): 1073～1077
[104] K.K.Mei, J.Y.Fang, Superabsorption-A Method to Improve Absorbing Boundary Conditions. IEEE Trans. Antennas Propagat., 1992, 40(9): 1001～1010
[105] J.P.Berenger, A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Physics, 1994, 114: 185～200
[106] 马双武，高攸纲﹒时域有限差分法中超吸收技术的改进及数值验证﹒电波科学学报﹒2000﹒15(1): 20～24
[107] F.Akleman, L.Sevgi, A novel Implementation of Berenger's PML for FDTD Applications. IEEE Microwave and Guided Wave Lett., 1998, 5(10): 324～326
[108] D.T.Prescott, N.V.Shuley, Reflection Analysis of FDTD boundary Conditions-Part II: Berenger's PML Absorbing Layers. IEEE Trans. Microwave Theory, 1997,45(8): 1171～1178
[109] G.X.Fan, Q.H.Lin, An FDTD Algorithm with Perfectly Matched Layers for General Dispersive Media. IEEE Trans. Antennas and Propagat., 2000, 48(5): 637～646
[110] H.Derudder, F.Olyslager, D.D.Zutter, et al., Efficient Mode-Matching Analysis of Discontinuities in Finite Planar Substrates Using Perfectly Matched Layers. IEEE Trans. Antennas and Propagat., 2001,49(2):185～195
[111] S.Winton, C.M.Rappaport, Specifying PML Conductivities by Considering Numerical Reflection Dependencies. IEEE Trans. Antennas and Propagat., 2000,48(7): 1055～1063
[112] 陈彬，方大纲﹒完全匹配层（PLM）吸收边界条件的理论分析﹒微波学报﹒1996﹒12(2): 110～115
[113] 马双武, 高攸纲﹒时域有限差分法中几种吸收边界条件的比较与数值验证﹒长沙大学学报﹒1999﹒13(4): 1～4
[114] B.Engquist, A.Majda., Absorbing Boundary Conditions for the Numerical Simulation of Waves. Math. Comp. , 1977, 31(139): 629～651
[115] A.P.Zhao, A.V.Raisanen , S.R.Cvetkovic, A Fast and Efficient FDTD Algorithm for the Analysis of Planar Microstrip Discontinuities by Using a Simple Source Excitation Scheme. IEEE Microwave and Guided Wave Lett. 1995, 5(10): 341～343
[116] X.Zhang, J.Fang, K.K.Mei, Calculations of the Dispersive Characteristics of Microstrips by the Time-Domian Finite Difference Method. IEEE Trans. Microwave Theory Tech., 1988, 36(2): 263～267