宽带超声换能器电阻抗匹配网络设计研究
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摘要
超声技术近些年来由于其具有无损检测,在某些媒介中衰减速度慢等特性,正愈来愈引起人们的重视并且已经在能源,医疗,军事,通讯等各个行业得到应用。随着超声技术的飞速发展和实际中不断增长的技术需求,宽带超声技术具有非常广阔的前景。
一般来说,超声设备由发射系统,换能器或换能器阵列,信号采集系统和信号处理系统等几个组成部分。作为发射系统和接收系统中的重要组成部分,阻抗匹配网络是换能器和电子学模块连接的桥梁。在发射系统中,阻抗匹配网络的目的是提高信号源传输给换能器的有效功率,避免过大的反射波可能对激励源造成的损坏,降低带宽内声源级的起伏程度。在接收系统中,阻抗匹配网络除了防止信号反射外还可以避免采集的电信号变形。
早期的超声设备中,换能器往往工作于单一频率,工作带宽窄,阻抗匹配网络原理和计算都比较直观,匹配网络的拓扑结构也只需要很少的元件即可。随着超声技术的飞速发展,超声设备也越来越复杂,很多应用往往生成频带很宽甚至多个频带的超声波,这种情况下,简单的匹配网络已经不满足需求,往往经过复杂的计算过程,其最终的网络拓扑结构也变的越来越复杂。
从发展历程上看,宽带匹配网络设计方法主要是为了解决射频和微波领域的系统设计中的经常遇到的宽带阻抗匹配问题而发展起来的。对超声换能器来说,尽管其工作频率以及绝对带宽比射频电路低很多,但并不代表为其设计匹配网络是一个简单的任务。因为无论其电阻抗特性还是应用环境等很多方面与射频电路中碰到的问题不同,如果不考虑这些特殊因素,而直接将现有的方法应用于宽带换能器的匹配网络设计,得到匹配效果可能无法令人满意,为了有效解决宽带超声换能器的匹配网络设计问题,应该以现有的匹配网络设计方法为基础,结合宽带换能器本身的特有性质,寻找一种有效的宽带换能器匹配网络设计方法。
本文的主要目的是研究应用宽带超声换能器的时候会普遍遇到的宽带匹配网络设计问题,它包括理论研究和实验测试两个部分。在理论研究中,本文从宽带阻抗匹配的基本知识着手,讨论了目前工程实践中应用比较广泛的方法,并且讨论了不同类型的算法对结果的影响。在分析了现有算法的特性和不足之后,本文提出了一种基于遗传算法的宽带匹配网络设计方法,这种方法结合了实频法和直接优化方法的优点,不需要预先指定拓扑结构。在这之后,本文利用遗传算法对现有方法中存在的一些不足进行了改进。最后,本文通过解决一个实际工程中的多路宽带换能器的匹配网络设计问题验证算法的性能并且比较了不同算法之间的性能差异。本文各章的内容安排如下：
第一章介绍了给出了课题的选择原因和一些需要了解的背景知识,包括超声系统结构,压电超声换能器及匹配网络的原理,和宽带匹配网络设计方法的发展和现状。
第二章介绍了匹配网络设计涉及到的数学工具,包括赫尔维茨多项式,阻抗和频率归一化,正实函数,网络函数及其性质。在以上概念的基础上介绍了双端口网络综合的方法。
第三章研究了宽带匹配网络设计的主要方法,主要有两大类方法,包括解析方法,和计算机辅助设计法。首先,讨论了三种著名解析理论,即Bode理论,Fano理论和Youla理论。在分析了解析法的缺陷和不足的基础上,论述了弥补这些缺点的方法,即计算机辅助设计法,并主要包含的三类方法：实频法及其改进方法,史密斯图法和直接优化方法。这些方法共同点都是利用实测的负载数据,无需负载的拓扑形式。讨论直接优化法的过程中,提出基于全局优化算法的直接优化设计方法,并选择两种典型的全局优化算法：模拟退火法和粒子群算法作为实现实例。通过为一个实际的宽带换能器机电等效模型设计匹配网络,比较了三类直接优化方法的性能。
第四章在分析前文提出的方法的基础上,提出了一种基于遗传算法的宽带匹配网络设计方法,其最大特点是,和直接优化法不同,这个算法无需指定拓扑,可以通过优化过程搜索出拓扑结构及元件值。之后,结合上一章介绍的匹配网络设计方法的不足,给出了基于遗传算法改进方法。最后,对这种新方法通过仿真进行了验证。
第五章基于一个实际超声测井系统的需要,为某超声测井系统中使用的多路宽带换能器进行匹配。该测井系统采用三个工作在不同频带的换能器覆盖其工作频段,需要设计一个宽带匹配网络使其能够对三个换能器同时匹配。本章采用上文介绍的多种方法进行了设计,并通过详细仿真比较了这些算法的性能。最后,选择性能较好的几类电路做成实际电路进行了测试并验证匹配网络的有效性。
第六章为总结和展望。
Ultrasound is getting more and more attention for it's unique characteristics. It has played an important role in many fields such as communication, energy and medical treatment.
Generally speaking, ultrasound system has several components including transmitter system, transducer or transducer array, data acquisition system and signal processing system. As an important part of transmitter system and data acquisition system, impedance matching network is a bridge connecting the transducer and electrical modules. In transmitter system, the impedance matching network is designed for improving effective power sent to transducer from the power souce and avoiding the damage of components of source caused by reflected pulse.
Most traditional ultrasound devices are narrowband which can only work within a narrow range near resonant frequency. The topology of the impedance matching networks of these devices is simple. As the development of ultrasound technology, wideband ultrasound or multiband ultrasound is needed in some applications. A simple matching network cannot meet these needs anymore. Complicated calculating process is always needed before a satisfactory result is brought to and the final structure of matching networks becomes more and more complicated.
Through the history of the development of the broadband matching network designing method, it is mainly used for designing broadband impedance matching networks of microwave and radio systems. Although the working frequency is low and the bandwidth is narrow for most of ultrasound systems, it is still not a simple mission to design impedance matching networks for them. The impedance and application environment of a broadband ultrasound transducer are usually different from those of a microwave system, and the performance of the matching networks will not be satisfactory without considering the difference.
The main goal of this dissertation is to study the impedance matching network that will be used in the broadband ultrasound systems. Theory and experiment are all included. In theory part, beginning from basic knowledge of broadband impedance matching, methods that are widely applied to the engineering practice and the results of different methods are discussed. Based on the analysis of characteristics and shortcomings of broadly used methods A new method based on genetic algorithm is developed, which combines the advantage of real frequency method and direct optimization method. Then, some deficiencies of current methods are improved by the genetic algorithm. Finally, a impedance matching network for a multi-transducers system is designed and results of different methods are compared.
In chapter one, the reasons for selecting the subject and some background knowledge are introduced, including the architecture of typical ultrasound systems, principle of piezoelectric ultrasound transducer and impedance matching network, development and current situation of designing method of broadband impedance matching network.
In chapter two, some mathematical concepts that will be used in this dissertation are discussed.
In chapter three, two classes of methods of designing broadband impedance matching network are discussed. First, three popular analytic theory are introduced. Second, three computer aided designing methods,including real frequency method, Smith chart and direct optimization method, are introduced. The characteristic the CAD methods have in common is that the topology of the load is not necessary. Finally, global optimization algorithms are introduced in direct optimization method. As examples, simulated annealing algorithm and particle swarm optimizer are used for designing and the results of different methods are compared.
In chapter four, a new method based on genetic algorithm is introduced. The basic feature of this method is that both the topology and parameters if components can be optimized.
In chapter five, a real impedance matching network for a multi-transducer ultrasound logging system is designed by different methods and results of simulation are compared. To prove the effectiveness of the network, actual circuits are made and tested.
At last, in chapter six, a summary and prospect are made.
一般来说,超声设备由发射系统,换能器或换能器阵列,信号采集系统和信号处理系统等几个组成部分。作为发射系统和接收系统中的重要组成部分,阻抗匹配网络是换能器和电子学模块连接的桥梁。在发射系统中,阻抗匹配网络的目的是提高信号源传输给换能器的有效功率,避免过大的反射波可能对激励源造成的损坏,降低带宽内声源级的起伏程度。在接收系统中,阻抗匹配网络除了防止信号反射外还可以避免采集的电信号变形。
早期的超声设备中,换能器往往工作于单一频率,工作带宽窄,阻抗匹配网络原理和计算都比较直观,匹配网络的拓扑结构也只需要很少的元件即可。随着超声技术的飞速发展,超声设备也越来越复杂,很多应用往往生成频带很宽甚至多个频带的超声波,这种情况下,简单的匹配网络已经不满足需求,往往经过复杂的计算过程,其最终的网络拓扑结构也变的越来越复杂。
从发展历程上看,宽带匹配网络设计方法主要是为了解决射频和微波领域的系统设计中的经常遇到的宽带阻抗匹配问题而发展起来的。对超声换能器来说,尽管其工作频率以及绝对带宽比射频电路低很多,但并不代表为其设计匹配网络是一个简单的任务。因为无论其电阻抗特性还是应用环境等很多方面与射频电路中碰到的问题不同,如果不考虑这些特殊因素,而直接将现有的方法应用于宽带换能器的匹配网络设计,得到匹配效果可能无法令人满意,为了有效解决宽带超声换能器的匹配网络设计问题,应该以现有的匹配网络设计方法为基础,结合宽带换能器本身的特有性质,寻找一种有效的宽带换能器匹配网络设计方法。
本文的主要目的是研究应用宽带超声换能器的时候会普遍遇到的宽带匹配网络设计问题,它包括理论研究和实验测试两个部分。在理论研究中,本文从宽带阻抗匹配的基本知识着手,讨论了目前工程实践中应用比较广泛的方法,并且讨论了不同类型的算法对结果的影响。在分析了现有算法的特性和不足之后,本文提出了一种基于遗传算法的宽带匹配网络设计方法,这种方法结合了实频法和直接优化方法的优点,不需要预先指定拓扑结构。在这之后,本文利用遗传算法对现有方法中存在的一些不足进行了改进。最后,本文通过解决一个实际工程中的多路宽带换能器的匹配网络设计问题验证算法的性能并且比较了不同算法之间的性能差异。本文各章的内容安排如下：
第一章介绍了给出了课题的选择原因和一些需要了解的背景知识,包括超声系统结构,压电超声换能器及匹配网络的原理,和宽带匹配网络设计方法的发展和现状。
第二章介绍了匹配网络设计涉及到的数学工具,包括赫尔维茨多项式,阻抗和频率归一化,正实函数,网络函数及其性质。在以上概念的基础上介绍了双端口网络综合的方法。
第三章研究了宽带匹配网络设计的主要方法,主要有两大类方法,包括解析方法,和计算机辅助设计法。首先,讨论了三种著名解析理论,即Bode理论,Fano理论和Youla理论。在分析了解析法的缺陷和不足的基础上,论述了弥补这些缺点的方法,即计算机辅助设计法,并主要包含的三类方法：实频法及其改进方法,史密斯图法和直接优化方法。这些方法共同点都是利用实测的负载数据,无需负载的拓扑形式。讨论直接优化法的过程中,提出基于全局优化算法的直接优化设计方法,并选择两种典型的全局优化算法：模拟退火法和粒子群算法作为实现实例。通过为一个实际的宽带换能器机电等效模型设计匹配网络,比较了三类直接优化方法的性能。
第四章在分析前文提出的方法的基础上,提出了一种基于遗传算法的宽带匹配网络设计方法,其最大特点是,和直接优化法不同,这个算法无需指定拓扑,可以通过优化过程搜索出拓扑结构及元件值。之后,结合上一章介绍的匹配网络设计方法的不足,给出了基于遗传算法改进方法。最后,对这种新方法通过仿真进行了验证。
第五章基于一个实际超声测井系统的需要,为某超声测井系统中使用的多路宽带换能器进行匹配。该测井系统采用三个工作在不同频带的换能器覆盖其工作频段,需要设计一个宽带匹配网络使其能够对三个换能器同时匹配。本章采用上文介绍的多种方法进行了设计,并通过详细仿真比较了这些算法的性能。最后,选择性能较好的几类电路做成实际电路进行了测试并验证匹配网络的有效性。
第六章为总结和展望。
Ultrasound is getting more and more attention for it's unique characteristics. It has played an important role in many fields such as communication, energy and medical treatment.
Generally speaking, ultrasound system has several components including transmitter system, transducer or transducer array, data acquisition system and signal processing system. As an important part of transmitter system and data acquisition system, impedance matching network is a bridge connecting the transducer and electrical modules. In transmitter system, the impedance matching network is designed for improving effective power sent to transducer from the power souce and avoiding the damage of components of source caused by reflected pulse.
Most traditional ultrasound devices are narrowband which can only work within a narrow range near resonant frequency. The topology of the impedance matching networks of these devices is simple. As the development of ultrasound technology, wideband ultrasound or multiband ultrasound is needed in some applications. A simple matching network cannot meet these needs anymore. Complicated calculating process is always needed before a satisfactory result is brought to and the final structure of matching networks becomes more and more complicated.
Through the history of the development of the broadband matching network designing method, it is mainly used for designing broadband impedance matching networks of microwave and radio systems. Although the working frequency is low and the bandwidth is narrow for most of ultrasound systems, it is still not a simple mission to design impedance matching networks for them. The impedance and application environment of a broadband ultrasound transducer are usually different from those of a microwave system, and the performance of the matching networks will not be satisfactory without considering the difference.
The main goal of this dissertation is to study the impedance matching network that will be used in the broadband ultrasound systems. Theory and experiment are all included. In theory part, beginning from basic knowledge of broadband impedance matching, methods that are widely applied to the engineering practice and the results of different methods are discussed. Based on the analysis of characteristics and shortcomings of broadly used methods A new method based on genetic algorithm is developed, which combines the advantage of real frequency method and direct optimization method. Then, some deficiencies of current methods are improved by the genetic algorithm. Finally, a impedance matching network for a multi-transducers system is designed and results of different methods are compared.
In chapter one, the reasons for selecting the subject and some background knowledge are introduced, including the architecture of typical ultrasound systems, principle of piezoelectric ultrasound transducer and impedance matching network, development and current situation of designing method of broadband impedance matching network.
In chapter two, some mathematical concepts that will be used in this dissertation are discussed.
In chapter three, two classes of methods of designing broadband impedance matching network are discussed. First, three popular analytic theory are introduced. Second, three computer aided designing methods,including real frequency method, Smith chart and direct optimization method, are introduced. The characteristic the CAD methods have in common is that the topology of the load is not necessary. Finally, global optimization algorithms are introduced in direct optimization method. As examples, simulated annealing algorithm and particle swarm optimizer are used for designing and the results of different methods are compared.
In chapter four, a new method based on genetic algorithm is introduced. The basic feature of this method is that both the topology and parameters if components can be optimized.
In chapter five, a real impedance matching network for a multi-transducer ultrasound logging system is designed by different methods and results of simulation are compared. To prove the effectiveness of the network, actual circuits are made and tested.
At last, in chapter six, a summary and prospect are made.
引文
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[11]B. S. Yarman and H. J. Carlin. A simplified real frequency technique applied to broad-band multistage microwave amplifiers. IEEE Transactions on Microwave Theory and Techniques,82:2216-2222, December 1982
[12]Haiying Huang and Daniel Paramo, "Broadband electrical impedance matching for piezoelectric ultrasound transducers ", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, December 2011, Volume:58, Issue:12.
[13]Reinhold Ludwig and Pavel Bretchko,“射频电路设计：理论与应用”,电子工业出版社；第1版,2002年.
[14]Dedieu, H., C.Dehollain, J.Neirynck, and G Rhodes, "A new method for solving broadband matching problems", IEEE Trans. Circuits Syst. I, Vol.41, No.9,561-570,1994.
[15]S. Kirkpatrick, CD Gelatt Jr., MP Vecchi, "Optimization by simulated annealing", Science,220 (1983), pp.671-680.
[16]J. Kennedy and R. Eberhart, "Particle swarm optimization." Proc. IEEE International Conf. on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ,1995 (in press).
[17]J. J. Liang, A. K. Qin,, Ponnuthurai Nagaratnam Suganthan, and S. Baskar, "Comprehensive learning particle swarm optimizer for global optimization of multimodal functions", IEEE Transactions on Evolutionary Computation,2006 Volume:10,Page(s):281 -295.
[1]Hollan J H.,"Conceming Efficient Adaptive Systems." InYovits, M.C., Eds, Self-Organizing Systems,1962,215-230
[2]Lucasius, and C. B. & Kateman G. "Applications of genetic algorithms in chemometrics."Proc. of the Third International Conference on Genetic Algorithms, J. David Schaffer (Ed.),1989,170-176.
[3]Nicol.N.Schraudolph, Richard K. Belew, "Dynamic Parameter Encoding For Genetic Algorithms", Machine Learning,1992,9:9-21
[4]Samir W. Mahfoud,and David E. Goldberg, "Parallel recombinative simulated annealing: a genetic algorithm." Parallel Computing,21,1995,1-28.
[5]任子武,伞冶,“自适应遗传算法的改进及在系统辨识中应用研究”,系统仿真学报,2006年01期.
[6]M.A.Potter, K.A.De Jong,"A cooperative coevolutionary approach to function optimization." Lecture Notes in Computer Science Volume 866,1994, pp 249-257
[7]郭建龙,张维明,曹阳,徐磊,“应用机器学习制定的入侵检测专家系统规则集”,计算机工程,2002年07期
[8]吴奇石,邱家驹,“基于GIS的配电网规划人工智能方法(二)遗传算法在配电网初级布线系统中的应用”电力系统自动化,1998年11期.
[9]JR Koza, "Hierarchical genetic algorithms operating on populations of computer programs" In Proceedings of the 11th International Joint Conference on Artificial Intelligence. San Mateo:Morgan Kaufman 1989.
[10]Koza, John R. "Automated synthesis of analog electrical circuits by means of genetic programming" IEEE Transactions on Evolutionary Computation,1997,Volume:1,Issue:2
[11]John R. Koza, Martin A. Keane, Matthew J. Streeter, William Mydlowec, Jessen Yu, Guido Lanza, "Genetic programming Ⅳ:Routine human-competitive machine intelligence" Springer; 2nd edition (July 2003)
[12]Riccardo Poli, "A Simple but Theoretically-Motivated Method to Control Bloat in Genetic Programming" 6th European Conference, EuroGP 2003 Essex, UK, April 14-16, 2003 Proceedings.
[13]W. B. Langdon, Wolfgang Banzhaf,"A SIMD Interpreter for Genetic Programming on GPU Graphics Cards" 11th European Conference, EuroGP 2008, Naples, Italy, March 26-28, 2008. Proceedings.
[14]Fernando E. B. Otero, Monique M. S. Silva, Alex A. Freitas, Julio C. Nievola "Genetic Programming for Attribute Construction in Data Mining" 6th European Conference, EuroGP 2003 Essex, UK, April 14-16,2003 Proceedings.
[15]John R. Koza, Forrest H. Bennett Ⅲ, David Andre, Martin A. Keane "Genetic Programming Ⅲ:Darwinian Invention and Problem Solving" Morgan Kaufmann; 1st edition (May 14,1999)
[16]Jason D. Lohn, Silvano P. Colombano, "A Circuit Representation Technique for Automated Circuit Design" IEEE Transactions on Evolutionary Computation,1999, Volume: 3, Issue:3
[17]Dedieu, H., Dehollaini, C.; Neirynck, Jacques; Rhodes, G. "A new method for solving broadband matching problems." IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Applications,1994 Volume:41,Issue:9
[18]F. Herrera, M. Lozano, J.L. Verdegay,"Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis" Artificial Intelligence Review,Volume 12, Issue 4, pp 265-319
[19]Petrowski, A., "A clearing procedure as a niching method for genetic algorithms", Proceedings of IEEE International Conference on Evolutionary Computation,1996,pp 798-803.
[20]Shu-Kai S.Fana, Yun-Chia Lianga, Erwie Zahara,"A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search" Computers& Industrial Engineering, Volume 50, Issue 4, August 2006, Pages 401-425
[21]M.M. Raghuwanshi, O.G. Kakde "Survey on multiobjective evolutionary and real coded genetic algorithms" The 8th Asia Pacific Symposium on Intelligent and Evolutionary Systems, December,2004
[22]K.A. De Jong, "An analysis of the behavior of a class of genetic adaptive systems", Doctoral dissertation, University of Michigan, Ann Arbor, Michigan 1975.
[23]J.H. Holland, "Adaptation in Natural and Artificial Systems", The MIT Press,1992 (1st ed.:1975).
[24]Goldberg DE, J Richardson. "Genetic Algorithms with Sharing for Multimodal Function Optimization." Proceedings of 9th Conference Electronic Computation, ASCE[C], New York,1986:471-482.
[25]肖宏峰,“基于单纯形多向搜索的大规模进化优化算法”中南大学博士论文,2009.
[1]汪钢,“小直径壁井超声成像系统的研究与实现”哈尔滨工程大学硕士论文,2010.
[2]“4294A精密阻抗分析仪简介及操作指南”,Agilent Technologies.
[3]梁志国,张大治,孙璟宇,李新良,“四参数正弦波曲线拟合的快速算法”,计测技术；2006年01期.
[4]"AWG5000 Series Data Sheet", Tektronix.
[5]“MSO5000和DPO5000系列示波器用户手册”,Tektronix.
[2]孔权,“压电换能器自动阻抗匹配系统的设计”,重庆医科大学硕士论文,2009年.
[3]王胜超,“水声宽带换能器匹配技术研究”,哈尔滨工程大学硕士论文,2008年.
[4]吴运发,“水声宽带换能器匹配技术研究”,声学技术,2000,19(2)
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[6]HF Pues, AR Van De Capelle, "An impedance-matching technique for increasing the bandwidth of microstrip antennas", IEEE Transactions on Antennas and Propagation, Volume: 37. Issue:11, Nov 1989.
[7]AJ Kerkhoff, H Ling, "Design of a band-notched planar monopole antenna using genetic algorithm optimization", IEEE Transactions on Antennas and Propagation, Volume: 55 Issue:3, March 2007.
[8]刘国权,“高性能超声成像测井仪研究”,西安石油大学硕士论文,2008年.
[9]刘菲菲,“多功能超声成像测井仪声系设计研究”,中国石油大学硕士论文,2003年.
[10]鲍静,“医学超声成像系统的编码激励技术研究”,天津大学硕士论文,2007年.
[11]徐威,“宽带发射机设计实现”,哈尔滨工程大学硕士论文,2012年.
[12]倪磊,“D类音频功率放大器的分析和设计要素”,ELECTRONICS AND PACKAGING,2008,8(6).
[13]冯常顺,“一种紧凑化长脉冲Marx型脉冲功率源的初步研究”,国防科学技术大学硕士论文,2009年.
[14]栾桂冬,张金铎,王仁乾,“压电换能器和换能器阵”,北京大学出版社,2005年.
[15]"Oilfield Review", Schlumberger,2008
[16]Binboga Siddik Yarman, "Design of Ultra Wideband Power Transfer Networks", WILEY,2010.
[17]H.W.Bode, "Network Analysis and Feedback Amplifier Design", NewYork, Van Nostrand, 1945.
[18]RM.Fano, " Theoretical Limitation on The Broadband Matching of Arbitrary impedances", Jourual of the Franklin Institute,1950, Vol.249, PP.57-83,139-154.
[19]D.C.Youla,"A New Theory of Broad-Band Matching", IEEE Trans. On Circuit Thcory, Mar.1964,Vol11,pp.30-50.
[20]H.J.Carlin, P.J.Crepeau, "Theoretical Limlitations on The Broadband Matching of Arbitrary ImPedances", IRE Trans.onCircut Theory,1961, Vol.8, No.2, PP.165.
[21]J.Pandel, A.Fettweis," Broadband Matching Using Parametric Representations ", IEEE International Symposium on Circuits and Systems.1985. pp.143-149.
[22]H.Dedieu, C.Dehollain, J-Neirynck and GRhodes, " New Broadband-Matching Circuit", International Journal of Circuit Theory and Applications,1994, Vol.22, PP.61-69.
[23]A. Colorni, M. Dorigo, and V. Maniezzo. "Distributed optimization by ant colonies", In Proceedings of the First European Conference on Artificial Life, pages 134-142 Elsevier,1992.
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[1]罗胜钦,刘芳,韩志刚,“网络综合原理(第2版)”,同济大学出版社,2009年.
[2]上海铁道学院主编,“网络综合理论”,中国铁道出版社,1980年.
[3]吕玉琴,俎云霄,“网络分析与综合”,机械工业出版社,2008年.
[4]黄香馥,“宽带匹配网络”,西北电讯工程学院,1986.
[1]H.W.Bode, "Network Analysis and Feedback Amplifier Design". NewYork, Van Nostrand, 1945.
[2]R.M.Fano," Theoretical Limitation on The Broadband Matching of Arbitrary impedances", Jourual of the Franklin Institute,1950, Vol.249, PP.57-83,139-154.
[3]D.C.Youla," A New Theory of Broad-Band Matching", IEEE Trans. On Circuit Thcory, Mar.1964,Vol11,pp.30-50.
[4]吕玉琴,俎云霄,“网络分析与综合”,机械工业出版社,2008年.
[5]CHARLES M:SON GEWERTZ, "SYNTHESIS OF A FINITE, FOUR-TERMINAL NETWORK FROM ITS PRESCRIBED DRIVING-POINT FUNCTIONS AND TRANSFER FUNCTION", THE WILLIAMS & WILKINS COMPANY,1933.
[6]黄香馥,“宽带匹配网络”,西北电讯工程学院,1986.
[7]Binboga Siddik Yarman, " DESIGN OF ULTRA WIDEBAND POWERTRANSFER NETWORKS", WILEY.2010.
[8]H.J.Carlin, P.J.Crepeau, "Theoretical limitations on The Broadband Matching of Arbitrary Impedances", IRE Trans, on Circuit Theory,1961, Vol.8, No.2, PP.165.
[9]H.J.CARLIN and B.S.YARMAN, The double matching problem:analytic and real frequency solutions. IEEE Trans. Circuits and Sys.1983,1(30):15-28.
[10]B.S.Yarman and A.Fettweis, " Computer-aided double matching via parametric representation of Brune functions", IEEE Trans Circuits Sys.37 (1990),212-222.
[11]B. S. Yarman and H. J. Carlin. A simplified real frequency technique applied to broad-band multistage microwave amplifiers. IEEE Transactions on Microwave Theory and Techniques,82:2216-2222, December 1982
[12]Haiying Huang and Daniel Paramo, "Broadband electrical impedance matching for piezoelectric ultrasound transducers ", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, December 2011, Volume:58, Issue:12.
[13]Reinhold Ludwig and Pavel Bretchko,“射频电路设计：理论与应用”,电子工业出版社；第1版,2002年.
[14]Dedieu, H., C.Dehollain, J.Neirynck, and G Rhodes, "A new method for solving broadband matching problems", IEEE Trans. Circuits Syst. I, Vol.41, No.9,561-570,1994.
[15]S. Kirkpatrick, CD Gelatt Jr., MP Vecchi, "Optimization by simulated annealing", Science,220 (1983), pp.671-680.
[16]J. Kennedy and R. Eberhart, "Particle swarm optimization." Proc. IEEE International Conf. on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ,1995 (in press).
[17]J. J. Liang, A. K. Qin,, Ponnuthurai Nagaratnam Suganthan, and S. Baskar, "Comprehensive learning particle swarm optimizer for global optimization of multimodal functions", IEEE Transactions on Evolutionary Computation,2006 Volume:10,Page(s):281 -295.
[1]Hollan J H.,"Conceming Efficient Adaptive Systems." InYovits, M.C., Eds, Self-Organizing Systems,1962,215-230
[2]Lucasius, and C. B. & Kateman G. "Applications of genetic algorithms in chemometrics."Proc. of the Third International Conference on Genetic Algorithms, J. David Schaffer (Ed.),1989,170-176.
[3]Nicol.N.Schraudolph, Richard K. Belew, "Dynamic Parameter Encoding For Genetic Algorithms", Machine Learning,1992,9:9-21
[4]Samir W. Mahfoud,and David E. Goldberg, "Parallel recombinative simulated annealing: a genetic algorithm." Parallel Computing,21,1995,1-28.
[5]任子武,伞冶,“自适应遗传算法的改进及在系统辨识中应用研究”,系统仿真学报,2006年01期.
[6]M.A.Potter, K.A.De Jong,"A cooperative coevolutionary approach to function optimization." Lecture Notes in Computer Science Volume 866,1994, pp 249-257
[7]郭建龙,张维明,曹阳,徐磊,“应用机器学习制定的入侵检测专家系统规则集”,计算机工程,2002年07期
[8]吴奇石,邱家驹,“基于GIS的配电网规划人工智能方法(二)遗传算法在配电网初级布线系统中的应用”电力系统自动化,1998年11期.
[9]JR Koza, "Hierarchical genetic algorithms operating on populations of computer programs" In Proceedings of the 11th International Joint Conference on Artificial Intelligence. San Mateo:Morgan Kaufman 1989.
[10]Koza, John R. "Automated synthesis of analog electrical circuits by means of genetic programming" IEEE Transactions on Evolutionary Computation,1997,Volume:1,Issue:2
[11]John R. Koza, Martin A. Keane, Matthew J. Streeter, William Mydlowec, Jessen Yu, Guido Lanza, "Genetic programming Ⅳ:Routine human-competitive machine intelligence" Springer; 2nd edition (July 2003)
[12]Riccardo Poli, "A Simple but Theoretically-Motivated Method to Control Bloat in Genetic Programming" 6th European Conference, EuroGP 2003 Essex, UK, April 14-16, 2003 Proceedings.
[13]W. B. Langdon, Wolfgang Banzhaf,"A SIMD Interpreter for Genetic Programming on GPU Graphics Cards" 11th European Conference, EuroGP 2008, Naples, Italy, March 26-28, 2008. Proceedings.
[14]Fernando E. B. Otero, Monique M. S. Silva, Alex A. Freitas, Julio C. Nievola "Genetic Programming for Attribute Construction in Data Mining" 6th European Conference, EuroGP 2003 Essex, UK, April 14-16,2003 Proceedings.
[15]John R. Koza, Forrest H. Bennett Ⅲ, David Andre, Martin A. Keane "Genetic Programming Ⅲ:Darwinian Invention and Problem Solving" Morgan Kaufmann; 1st edition (May 14,1999)
[16]Jason D. Lohn, Silvano P. Colombano, "A Circuit Representation Technique for Automated Circuit Design" IEEE Transactions on Evolutionary Computation,1999, Volume: 3, Issue:3
[17]Dedieu, H., Dehollaini, C.; Neirynck, Jacques; Rhodes, G. "A new method for solving broadband matching problems." IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Applications,1994 Volume:41,Issue:9
[18]F. Herrera, M. Lozano, J.L. Verdegay,"Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis" Artificial Intelligence Review,Volume 12, Issue 4, pp 265-319
[19]Petrowski, A., "A clearing procedure as a niching method for genetic algorithms", Proceedings of IEEE International Conference on Evolutionary Computation,1996,pp 798-803.
[20]Shu-Kai S.Fana, Yun-Chia Lianga, Erwie Zahara,"A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search" Computers& Industrial Engineering, Volume 50, Issue 4, August 2006, Pages 401-425
[21]M.M. Raghuwanshi, O.G. Kakde "Survey on multiobjective evolutionary and real coded genetic algorithms" The 8th Asia Pacific Symposium on Intelligent and Evolutionary Systems, December,2004
[22]K.A. De Jong, "An analysis of the behavior of a class of genetic adaptive systems", Doctoral dissertation, University of Michigan, Ann Arbor, Michigan 1975.
[23]J.H. Holland, "Adaptation in Natural and Artificial Systems", The MIT Press,1992 (1st ed.:1975).
[24]Goldberg DE, J Richardson. "Genetic Algorithms with Sharing for Multimodal Function Optimization." Proceedings of 9th Conference Electronic Computation, ASCE[C], New York,1986:471-482.
[25]肖宏峰,“基于单纯形多向搜索的大规模进化优化算法”中南大学博士论文,2009.
[1]汪钢,“小直径壁井超声成像系统的研究与实现”哈尔滨工程大学硕士论文,2010.
[2]“4294A精密阻抗分析仪简介及操作指南”,Agilent Technologies.
[3]梁志国,张大治,孙璟宇,李新良,“四参数正弦波曲线拟合的快速算法”,计测技术；2006年01期.
[4]"AWG5000 Series Data Sheet", Tektronix.
[5]“MSO5000和DPO5000系列示波器用户手册”,Tektronix.