在微波电路CAD中采用神经网络方法的研究
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摘要
神经网络在微波电路CAD和微波电路优化中的应用是目前非线性微波电路研究领域中的前沿课题之一。神经网络的出现为一类输入输出关系呈高度非线性的系统提供了建模的有效工具。通过对射频微波电路测量或仿真，可得到微波电路的输入和输出数据，利用该数据可以对神经网络进行训练，而神经网络一旦训练成功，就能够瞬时地对在微波电路设计所学习的任务提供准确答案。经过训练后的神经网络模型可广泛用于解决射频微波电路的各种问题。如用于微波电路CAD，可用所建立的模型结构来描述这么一类微波电路的非线性行为特征；如用于微波电路设计，则可进行如共面波导、晶体管、传输线、滤波器和放大器等的设计；如用于微波电路优化，则可用所建立的电路模型优化电路参数，进行阻抗匹配等。
本文工作正是在这样的应用背景下，基于电子科技大学青年科技基金《无线非线性信道建模及特性分析方法研究》，对神经网络在非线性微波电路建模和优化中的应用，展开了一些研究工作，作者的主要贡献和创新如下：
1） 将神经网络应用于微波电路的时域非线性特性建模，通过分析了一个功率放大器的时域瞬态和稳态的非线性特性，并用HP-ADS对其非线性特性进行了仿真，然后把其仿真输入和输出数据来训练神经网络。计算机仿真结果表明所建立的神经网络模型和非线性放大器的输出基本一致。
2） 研究了一个建立在Volterra级数基础上的一般的分析方法，包括非线性参数和交调、频率中的谱分量之间的相互影响。对于Volterra级数而言，用于实际系统建模时的主要困难是其核函数的辨识。本文通过神经网络和Volterra级数的等价性，用训练后的神经网络确定出Volterra级数的核函数。
3） 把基于小波的神经网络训练方法用于微波电路的优化，通过对由微带线组成的低通滤波器参数的仿真和优化，表明了在得到较好优化结果的情况下，其优化时间大大降低。
Researching the applications of neural network techniques in the area of microwave circuits CAD and optimization design is one of the front edge issues in nonlinear microwave electronics domains. The emergence of neural network provide effective tools for a system with highly nonlinear input-output relations. A neural network model for a device/circuit can be developed by learning and abstracting from measured-simulated microwave data, through a process called training. Once be trained, the neural network model can be used during microwave design to provide instant answers to any pre-assigned task. The trained neural network model can be used to solve a variety of problems emerged in RF/microwave circuit design, such as in microwave circuit CAD, the established model structure can be used to characterize the nonlinear behavior of microwave circuits. And in microwave circuit design, the model can be used for the design of coplanar waveguides, transistors, transmission line, filters and amplifiers, etc. Besides, after in microwave circuit optimization, a neural network model can be used to optimize circuit parameters and match the microwave impedances, etc.
Under this background, with the support of the project entitled "Modeling of Wireless Nonlinear Channel and Analysis of Its Characteristics" of of UESTC Youth Funddation, this dissertation is intended to develop some techniques for application of neural networks in the fields of nonlinear microwave circuit modeling and optimization. The main contributions of the dissertation are as following:
1. Modeling time-domain nonlinear characteristics of microwave circuits by using the neural network techniques, then analyzing the time-domain transient and steady states of a power-amplifier and in collarboration with the HP-ADS. The results of computer simulation show that the output of the neural network model output is concidede with the output of a real nonlinear power-amplifier.
2. The nonlinear input-output characteristics of a GaAs MESFET is modeled by the use of Volterra series in the frequency domain. Based on this frequency domain model, after an MLP network training, the input-output characteristics of the device as well as the Volterra series Kernal function, which is hard to be determined by traditional approaches, is obtained with satisfactory accuracy.
3. A wavelet neural network training method is used for the optimization of a microwave circuit. This technique is used for the simulation and optimization
of the low-pass filter parameter. Simulation results indicate that this training algorithm is able to give solutions with high quality and remarkably reduced computation time.
本文工作正是在这样的应用背景下，基于电子科技大学青年科技基金《无线非线性信道建模及特性分析方法研究》，对神经网络在非线性微波电路建模和优化中的应用，展开了一些研究工作，作者的主要贡献和创新如下：
1） 将神经网络应用于微波电路的时域非线性特性建模，通过分析了一个功率放大器的时域瞬态和稳态的非线性特性，并用HP-ADS对其非线性特性进行了仿真，然后把其仿真输入和输出数据来训练神经网络。计算机仿真结果表明所建立的神经网络模型和非线性放大器的输出基本一致。
2） 研究了一个建立在Volterra级数基础上的一般的分析方法，包括非线性参数和交调、频率中的谱分量之间的相互影响。对于Volterra级数而言，用于实际系统建模时的主要困难是其核函数的辨识。本文通过神经网络和Volterra级数的等价性，用训练后的神经网络确定出Volterra级数的核函数。
3） 把基于小波的神经网络训练方法用于微波电路的优化，通过对由微带线组成的低通滤波器参数的仿真和优化，表明了在得到较好优化结果的情况下，其优化时间大大降低。
Researching the applications of neural network techniques in the area of microwave circuits CAD and optimization design is one of the front edge issues in nonlinear microwave electronics domains. The emergence of neural network provide effective tools for a system with highly nonlinear input-output relations. A neural network model for a device/circuit can be developed by learning and abstracting from measured-simulated microwave data, through a process called training. Once be trained, the neural network model can be used during microwave design to provide instant answers to any pre-assigned task. The trained neural network model can be used to solve a variety of problems emerged in RF/microwave circuit design, such as in microwave circuit CAD, the established model structure can be used to characterize the nonlinear behavior of microwave circuits. And in microwave circuit design, the model can be used for the design of coplanar waveguides, transistors, transmission line, filters and amplifiers, etc. Besides, after in microwave circuit optimization, a neural network model can be used to optimize circuit parameters and match the microwave impedances, etc.
Under this background, with the support of the project entitled "Modeling of Wireless Nonlinear Channel and Analysis of Its Characteristics" of of UESTC Youth Funddation, this dissertation is intended to develop some techniques for application of neural networks in the fields of nonlinear microwave circuit modeling and optimization. The main contributions of the dissertation are as following:
1. Modeling time-domain nonlinear characteristics of microwave circuits by using the neural network techniques, then analyzing the time-domain transient and steady states of a power-amplifier and in collarboration with the HP-ADS. The results of computer simulation show that the output of the neural network model output is concidede with the output of a real nonlinear power-amplifier.
2. The nonlinear input-output characteristics of a GaAs MESFET is modeled by the use of Volterra series in the frequency domain. Based on this frequency domain model, after an MLP network training, the input-output characteristics of the device as well as the Volterra series Kernal function, which is hard to be determined by traditional approaches, is obtained with satisfactory accuracy.
3. A wavelet neural network training method is used for the optimization of a microwave circuit. This technique is used for the simulation and optimization
of the low-pass filter parameter. Simulation results indicate that this training algorithm is able to give solutions with high quality and remarkably reduced computation time.
引文
[1]高葆新，洪兴楠等. 微波电路计算机辅助设计. 清华大学出版社. 北京，1988年.
[2]Fang Wang, and Qi-Jun Zhang. "Knowledge-based neural models for microwave design", IEEE Trans. Microwave theory Tech, vol. 45, NO. 12, pp.2333-2343, December 1997.
[3]Zaabab, A.H., Qi-Jun Zhang;, and Nakhla, M."A neural network modeling approach to circuit optimization and statistical design". IEEE Trans. Microwave theory Tech, vol. 43, NO. 6, pp.1349-1358, June, 1995.
[4]Watson, P.M.; Gupta, K.C. "EM-ANN models for microstrip vias and interconnects in dataset circuits". IEEE Trans. Microwave theory Tech, vol. 47, NO. 12, pp.2495-2503, December, 1996.
[5]Watson, P.M.; Gupta, K.C. "Design and optimization of CPW circuits using EM-ANN models for CPW components, IEEE Trans. Microwave theory Tech 47 (1997), NO. 12, pp.2515-2523.
[6]M. Vai, S. Wu, B. Li, and S. Prasad, Microwave circuit analysis and design by a massively distributed computing network, IEEE Trans. Microwave theory Tech 43 (1995), 1087-1094.
[7]Y. Harkouss, J. Rousset, H. Chehade, D. Barataud, and J. P. Teyssier, The use of artificial neural networks in nonlinear microwave devices and circuits modeling: an application to telecommunication system design, Inc. Int Journal RF and Microwave CAE 9:198-215, 1999.
[8]A. H. Zaabab, Q. J. Zhang, and M. S. Nakhla, Analysis and optimization of microwave circuits and devices using neural network models, IEEE Int Microwave Digest, San Diego, CA, May 1994, pp. 393-396.
[9]李征帆，毛军发. 微波与高速电路理论. 上海交通大学出版社. 上海，2001年.
[10]李润旗，李国定等. 微波电路CAD软件应用技术. 国防工业出版社. 北京， 1996年.
[11]靳 番编著. 神经计算智能基础. 西南交通大学出版社, 成都, 2000年.
[12]Q. J. Zhang and M. S. Nakhla, Signal integrity analysis and optimization of VLSI interconnects using neural network models, IEEE Int Symp Circuits System, London, U.K.,1994, pp. 459-462.
[13]A .Veluswami, M. S. Nakhla, and Q. J. Zhang, The application of neural networks to EM based simulation and optimization of interconnects in high speed VLSI circuits, IEEE Trans. Microwave theory Tech 45 (1997), 712-723.
[14]T. Horng, C, Wang, and N. G. Alexopoulos, Microstrip circuit design using neural networks, IEEE Int Microwave Symp Digest, Altanta, GA, 1993, pp. 413-416.
[15]P. Burrascano, M. Dionigi, C. Fancelli, and M. Mongiardo. A neural network model for CAD and optimization of microwave filters, IEEE Int Microwave Symp Digest, Baltimore, MD, 1998, pp. 13-16.
[16]M. Vai. and S. Prasad, Automatic impedance matching with a neural network, IEEE Microwave Guided Wave Lett 3 (1993), 353-354.
[17]Fang Wang, Vijaya K. Devabhaktuni, Changgeng Xi, Qi-Jun Zhang. Neural networks and training algorithms for RF and microwave applications. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 216-240.
[18]Kwok, T. Y., and D. Y. Yeung, Constructive algorithms for structure learning in feedforward neural networks for regression problems. IEEE Trans. Neural Networks, Vol. 8, 1997, pp.630-645.
[19]Krzyzak, A., and T. Linder, Radial Basis Function Networks and Complexity Regularization in Function Learning. IEEE Trans. Neural Networks, Vol. 9, 1998, pp. 247-256.
[20]Garcia, J. A., et al., Modeling MESFETs and HEMts intermodulation distortion behavior using a generalized radial basis function network. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 261-276.
[21]陈哲，冯天瑾. 小波分析与神经网络结合的研究进展. 电子科学学刊，2000，22（3）：496－504.
[22]蔡念，胡匡祜等. 小波神经网络及其应用. 中国体视学与图象分析. 2001，6（4）：239-245.
[23]Zhang, Q. H., Using Wavelet Networks in Nonparametric Estimation. IEEE Trans. Neural Networks, Vol. 8, 1997, pp. 227-236.
[24]Zhang, Q. H., and A. Benvensite, Wavelet Networks. IEEE Trans. Neural Networks, Vol. 3, 1992, pp. 889-898.
[25]Pati, Y. C., and P. S. Krishnaprasad. Analysis and Synthesis of Fastforward Neural Networks using Discrete Affine Wavelet Transformations. IEEE Trans. Neural Networks, Vol. 4, 1993, pp. 73-85.
[26]Bila, S., et al., Accurate Wavelet Neural Network Based Model for Electromagnetic Optimization of Microwaves Circuits. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 297-306.
[27]Stephane Mallat著，杨力华，戴道清，黄文良等译. 信号处理的小波导引. 机械工业出版社. 北京. 2002年.
[28]程正兴. 小波分析算法与应用. 西安交通大学出版社. 1998年.
[29]崔锦泰著，程正兴译. 小波分析导论. 西安交通大学出版社. 1997年.
[30]P. Buerraacano, S. Fiori, M. Mongiardo. A Review of Artificial Neural Networks Applications in Microwave Computer-Aided Design. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 158-174.
[31]Bandler, J.W.; Ismail, M.A.; Rayas-Sanchez, J.E.; Qi-Jun Zhang. "Neuromodeling of microwave circuits exploiting space-mapping technology", IEEE Trans. Microwave theory Tech, vol. 47, NO. 12,pp.2417-2427, December, 1999.
[32]Yonghua Fang, Yagoub, M.C.E, Fang Wang, and Qi-Jun Zhang. "A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks", IEEE Trans. Microwave theory Tech, vol. 48, NO. 12, pp.2335-2344, December 2000
[33]阎平凡，张长水. 人工神经网络与模拟进化计算. 清华大学出版社. 2001年.
[34]K.S.Narendra and K.Parthasarthy, "Gradient Methods for the optimization of Dynamical
System containing neural networks," IEEE. Trans. On Neural Networks, vol.2(1991).pp. 252-262.
[35]Schilling, R.J., Carroll, J.J., Jr., and Al-Ajlouni, A.F. "Approximation of nonlinear systems with radial basis function neural networks", IEEE Ttrans. Neural networks, Volume. 12 Issue: 1 pp.1-15. Jan. 2001.
[36]J.Park. and I.W.Sandberg, "Universal approximation using radial-basis-function networks," Neural Comput., vol 3,pp.246-257, 1991.
[37]Steve C. cripps. "RF Power Amplifiers for Wireless Communications". Artech House Boston. London. 1999.
[38]Tri. T. Ha. Solid-State Microwave-Amplifier Design. A Wiley-Interscience Publication. JOHN WILEY & SONS, NEW YORK. 1981.
[39]HP-ADS 2001.The User's guides and Help files.2001.
[40]Zhang Guanglan, udantha R. Abeyratne, and P. Saratchandran,. "Comparing RBF and BP neural networks in Dipole Localization", Proceedings of The First Joint NMES/EMBS Conference Serving Humanity, Advancing Technology. Oct.13-16. 99, Atlanta,Ga.USA
[41]Sang Yun Lee; Cetiner, B.A.; Torpi, H.; Cai, S.J.; Jiang Li; Alt, K.; Chen, Y.L.; Wen, C.P.; Wang, K.L.; Itoh, T. "An X-band GaN HEMT power amplifier design using an artificial neural network modeling technique". IEEE Trans.on Electron Devices., vol. 48, NO. 3, pp.495-501,March , 2001.
[42]Marcelino. Lazaro, Ignacio Santamaria, Carlos. Pantaleon. Neural Networks for Large- and Small-Signal Modeling of MESFET/HEMT Transistors. IEEE Trans.on Instrumentation and measurement., vol. 56, NO. 6, pp.1587-1593, December, 2001.
[43]Sebastien. Goasguen, Samir M. El-Ghazaly. A Practical Large-Signal Global Modeling Simulation of a Microwave Amplifier Using Artificial Neural Network. IEEE Trans.on microwave and guided wave letters, vol. 10, NO. 7, pp.273-275, July, 2000.
[44]David. M. Pozar. Microwave and RF Design of Wireless Systems.
[45]Ulrich. L. Rohde, David. P. Newkirk.RF/Microwave Circuit Design for Wireless Applications.
[46]Jose Carlos Pedro, Jorge Perez. Accurate Simulation of GaAs MESFET's Intermodulation Distortion Using a New Drain-Soure Current Model. IEEE Trans. Microwave theory Tech, vol. 42, NO.1, pp.25-33, January, 1994.
[47]R. S. Tucker. Third-order intermodulation distortion and gain compression in GaAs FET's. IEEE Trans. Microwave theory Tech, vol. MTT-28, pp.400-408, may.1979.
[48]George. M. Lambrianou, Conlin. S. Aitchison. Optimization of Third-Order Intermodulation Product and Output Power From an X-Band MESFET Amplifier Using Volterra Series Analysis. IEEE Trans. Microwave theory Tech, vol. MTT-33, No. 12, pp.1395-1403, 1985.
[49]S. A. Maas and D. Neilson. Modeling the gate I/V characteristic of a GaAs MESFET for Volterra-series analysis. IEEE Trans. Microwave theory Tech, vol. MTT-37, pp.1134-1136,1989.
[50]Robert Aram Minasian. Intermodulation Distortion Analysis of MESFET Amplifiers Using
the Volterra Series Representation. IEEE Trans. Microwave theory Tech, vol. MTT-28, NO.1. pp.1-8, January 1980.
[51]H. Southall, J.A. Simmers, and T. O'Donnell, Direction finding in phased arrays with a neural network beamformer, IEEE Trans Antennas Propagation 43 (1995),1369-1374.
[52]A. Patnaik, R.K. Mishra, G..K. Patra, and S.K. Dash, An artificial neural network model for effective dielectric constant of microstrip line, IEEE Trans Antennas Propagation 45 (1997), 1697.
[53]清华大学《微带电路》编写组. 微带电路. 1980.
[54]顾其诤. 项家桢. 袁孝康. 微波集成电路设计. 1980.
[55]美. Reinhold Ludwig. Pavel Bretchko 著. 王子宇等译. 射频电路设计－理论和应用. 电子工业出版社. 北京. 2002年.
[56]Y. Harkouss, E. Ngoya. J. Rousset. and D. Argollo. Accurate radial wavelet neural-network model for efficient CAD modeling of microstrip discontinuities. IEE. Proc-Microw. Antennas Propag. Vol, 147. No. 4, pp:277-283. Auguet. 2000.
[57] Devabhaktuni, V.K, Yagoub, M.C.E, and Qi-Jun Zhang. A robust algorithm for automatic development of neural-network models for microwave applications. IEEE Trans. Microwave theory Tech, vol. 49, NO. 12, pp.2282-2291, December 2001.
[58]V.K.Devabhaktuni, M.C.E.Yagoub, Y.Fang, J.Xu, and Q.J.Zhang, Neural networks for microwave modeling: Model development issues and nonlinear modeling techniques. Int. J. RF Microwave CAE, vol.11, pp.4-21,2001.
[59]Creech, G.L.,Paul, B.J.,Lesniak, C.D, Jenkins,T.J., and Calcatera, M.C. Artificial neural networks for fast and accurate EM-CAD of microwave circuits. IEEE Trans. Microwave theory Tech, vol. 45, NO. 5, pp.794-802, May, 1997.
[60] Karayiannis, N.B. "Reformulated radial basis neural networks trained by gradient descent". IEEE. Trans. On Neural Networks, vol.10.No.3 .pp. 657-671. May 1999.
[61]刘荧. 林嘉宇. 毛均杰. 基于神经网络的微波电路建模与优化. 微波学报，2001，16（3）：242－248.
[62]Q. J. Zhang. Neural Networks for RF and Microwave Design. Norwood, MA: Artech House. 2000.
[63]李海涛, 邓樱. MATLAB 6.1基础及应用技巧. 国防工业出版社. 2002年.
[64]Mankuan. Vai. Sheila. Prasad. Neural networks in microwave circuit design －beyond black-box moduls. Int. J. RF Microwave CAE, vol.9, pp.187-197, 1999.
[2]Fang Wang, and Qi-Jun Zhang. "Knowledge-based neural models for microwave design", IEEE Trans. Microwave theory Tech, vol. 45, NO. 12, pp.2333-2343, December 1997.
[3]Zaabab, A.H., Qi-Jun Zhang;, and Nakhla, M."A neural network modeling approach to circuit optimization and statistical design". IEEE Trans. Microwave theory Tech, vol. 43, NO. 6, pp.1349-1358, June, 1995.
[4]Watson, P.M.; Gupta, K.C. "EM-ANN models for microstrip vias and interconnects in dataset circuits". IEEE Trans. Microwave theory Tech, vol. 47, NO. 12, pp.2495-2503, December, 1996.
[5]Watson, P.M.; Gupta, K.C. "Design and optimization of CPW circuits using EM-ANN models for CPW components, IEEE Trans. Microwave theory Tech 47 (1997), NO. 12, pp.2515-2523.
[6]M. Vai, S. Wu, B. Li, and S. Prasad, Microwave circuit analysis and design by a massively distributed computing network, IEEE Trans. Microwave theory Tech 43 (1995), 1087-1094.
[7]Y. Harkouss, J. Rousset, H. Chehade, D. Barataud, and J. P. Teyssier, The use of artificial neural networks in nonlinear microwave devices and circuits modeling: an application to telecommunication system design, Inc. Int Journal RF and Microwave CAE 9:198-215, 1999.
[8]A. H. Zaabab, Q. J. Zhang, and M. S. Nakhla, Analysis and optimization of microwave circuits and devices using neural network models, IEEE Int Microwave Digest, San Diego, CA, May 1994, pp. 393-396.
[9]李征帆，毛军发. 微波与高速电路理论. 上海交通大学出版社. 上海，2001年.
[10]李润旗，李国定等. 微波电路CAD软件应用技术. 国防工业出版社. 北京， 1996年.
[11]靳 番编著. 神经计算智能基础. 西南交通大学出版社, 成都, 2000年.
[12]Q. J. Zhang and M. S. Nakhla, Signal integrity analysis and optimization of VLSI interconnects using neural network models, IEEE Int Symp Circuits System, London, U.K.,1994, pp. 459-462.
[13]A .Veluswami, M. S. Nakhla, and Q. J. Zhang, The application of neural networks to EM based simulation and optimization of interconnects in high speed VLSI circuits, IEEE Trans. Microwave theory Tech 45 (1997), 712-723.
[14]T. Horng, C, Wang, and N. G. Alexopoulos, Microstrip circuit design using neural networks, IEEE Int Microwave Symp Digest, Altanta, GA, 1993, pp. 413-416.
[15]P. Burrascano, M. Dionigi, C. Fancelli, and M. Mongiardo. A neural network model for CAD and optimization of microwave filters, IEEE Int Microwave Symp Digest, Baltimore, MD, 1998, pp. 13-16.
[16]M. Vai. and S. Prasad, Automatic impedance matching with a neural network, IEEE Microwave Guided Wave Lett 3 (1993), 353-354.
[17]Fang Wang, Vijaya K. Devabhaktuni, Changgeng Xi, Qi-Jun Zhang. Neural networks and training algorithms for RF and microwave applications. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 216-240.
[18]Kwok, T. Y., and D. Y. Yeung, Constructive algorithms for structure learning in feedforward neural networks for regression problems. IEEE Trans. Neural Networks, Vol. 8, 1997, pp.630-645.
[19]Krzyzak, A., and T. Linder, Radial Basis Function Networks and Complexity Regularization in Function Learning. IEEE Trans. Neural Networks, Vol. 9, 1998, pp. 247-256.
[20]Garcia, J. A., et al., Modeling MESFETs and HEMts intermodulation distortion behavior using a generalized radial basis function network. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 261-276.
[21]陈哲，冯天瑾. 小波分析与神经网络结合的研究进展. 电子科学学刊，2000，22（3）：496－504.
[22]蔡念，胡匡祜等. 小波神经网络及其应用. 中国体视学与图象分析. 2001，6（4）：239-245.
[23]Zhang, Q. H., Using Wavelet Networks in Nonparametric Estimation. IEEE Trans. Neural Networks, Vol. 8, 1997, pp. 227-236.
[24]Zhang, Q. H., and A. Benvensite, Wavelet Networks. IEEE Trans. Neural Networks, Vol. 3, 1992, pp. 889-898.
[25]Pati, Y. C., and P. S. Krishnaprasad. Analysis and Synthesis of Fastforward Neural Networks using Discrete Affine Wavelet Transformations. IEEE Trans. Neural Networks, Vol. 4, 1993, pp. 73-85.
[26]Bila, S., et al., Accurate Wavelet Neural Network Based Model for Electromagnetic Optimization of Microwaves Circuits. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 297-306.
[27]Stephane Mallat著，杨力华，戴道清，黄文良等译. 信号处理的小波导引. 机械工业出版社. 北京. 2002年.
[28]程正兴. 小波分析算法与应用. 西安交通大学出版社. 1998年.
[29]崔锦泰著，程正兴译. 小波分析导论. 西安交通大学出版社. 1997年.
[30]P. Buerraacano, S. Fiori, M. Mongiardo. A Review of Artificial Neural Networks Applications in Microwave Computer-Aided Design. Int Journal RF and Microwave CAE, Special Issue on Applications of ANN to RF and Microwave Design, Vol. 9, 1999, pp. 158-174.
[31]Bandler, J.W.; Ismail, M.A.; Rayas-Sanchez, J.E.; Qi-Jun Zhang. "Neuromodeling of microwave circuits exploiting space-mapping technology", IEEE Trans. Microwave theory Tech, vol. 47, NO. 12,pp.2417-2427, December, 1999.
[32]Yonghua Fang, Yagoub, M.C.E, Fang Wang, and Qi-Jun Zhang. "A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks", IEEE Trans. Microwave theory Tech, vol. 48, NO. 12, pp.2335-2344, December 2000
[33]阎平凡，张长水. 人工神经网络与模拟进化计算. 清华大学出版社. 2001年.
[34]K.S.Narendra and K.Parthasarthy, "Gradient Methods for the optimization of Dynamical
System containing neural networks," IEEE. Trans. On Neural Networks, vol.2(1991).pp. 252-262.
[35]Schilling, R.J., Carroll, J.J., Jr., and Al-Ajlouni, A.F. "Approximation of nonlinear systems with radial basis function neural networks", IEEE Ttrans. Neural networks, Volume. 12 Issue: 1 pp.1-15. Jan. 2001.
[36]J.Park. and I.W.Sandberg, "Universal approximation using radial-basis-function networks," Neural Comput., vol 3,pp.246-257, 1991.
[37]Steve C. cripps. "RF Power Amplifiers for Wireless Communications". Artech House Boston. London. 1999.
[38]Tri. T. Ha. Solid-State Microwave-Amplifier Design. A Wiley-Interscience Publication. JOHN WILEY & SONS, NEW YORK. 1981.
[39]HP-ADS 2001.The User's guides and Help files.2001.
[40]Zhang Guanglan, udantha R. Abeyratne, and P. Saratchandran,. "Comparing RBF and BP neural networks in Dipole Localization", Proceedings of The First Joint NMES/EMBS Conference Serving Humanity, Advancing Technology. Oct.13-16. 99, Atlanta,Ga.USA
[41]Sang Yun Lee; Cetiner, B.A.; Torpi, H.; Cai, S.J.; Jiang Li; Alt, K.; Chen, Y.L.; Wen, C.P.; Wang, K.L.; Itoh, T. "An X-band GaN HEMT power amplifier design using an artificial neural network modeling technique". IEEE Trans.on Electron Devices., vol. 48, NO. 3, pp.495-501,March , 2001.
[42]Marcelino. Lazaro, Ignacio Santamaria, Carlos. Pantaleon. Neural Networks for Large- and Small-Signal Modeling of MESFET/HEMT Transistors. IEEE Trans.on Instrumentation and measurement., vol. 56, NO. 6, pp.1587-1593, December, 2001.
[43]Sebastien. Goasguen, Samir M. El-Ghazaly. A Practical Large-Signal Global Modeling Simulation of a Microwave Amplifier Using Artificial Neural Network. IEEE Trans.on microwave and guided wave letters, vol. 10, NO. 7, pp.273-275, July, 2000.
[44]David. M. Pozar. Microwave and RF Design of Wireless Systems.
[45]Ulrich. L. Rohde, David. P. Newkirk.RF/Microwave Circuit Design for Wireless Applications.
[46]Jose Carlos Pedro, Jorge Perez. Accurate Simulation of GaAs MESFET's Intermodulation Distortion Using a New Drain-Soure Current Model. IEEE Trans. Microwave theory Tech, vol. 42, NO.1, pp.25-33, January, 1994.
[47]R. S. Tucker. Third-order intermodulation distortion and gain compression in GaAs FET's. IEEE Trans. Microwave theory Tech, vol. MTT-28, pp.400-408, may.1979.
[48]George. M. Lambrianou, Conlin. S. Aitchison. Optimization of Third-Order Intermodulation Product and Output Power From an X-Band MESFET Amplifier Using Volterra Series Analysis. IEEE Trans. Microwave theory Tech, vol. MTT-33, No. 12, pp.1395-1403, 1985.
[49]S. A. Maas and D. Neilson. Modeling the gate I/V characteristic of a GaAs MESFET for Volterra-series analysis. IEEE Trans. Microwave theory Tech, vol. MTT-37, pp.1134-1136,1989.
[50]Robert Aram Minasian. Intermodulation Distortion Analysis of MESFET Amplifiers Using
the Volterra Series Representation. IEEE Trans. Microwave theory Tech, vol. MTT-28, NO.1. pp.1-8, January 1980.
[51]H. Southall, J.A. Simmers, and T. O'Donnell, Direction finding in phased arrays with a neural network beamformer, IEEE Trans Antennas Propagation 43 (1995),1369-1374.
[52]A. Patnaik, R.K. Mishra, G..K. Patra, and S.K. Dash, An artificial neural network model for effective dielectric constant of microstrip line, IEEE Trans Antennas Propagation 45 (1997), 1697.
[53]清华大学《微带电路》编写组. 微带电路. 1980.
[54]顾其诤. 项家桢. 袁孝康. 微波集成电路设计. 1980.
[55]美. Reinhold Ludwig. Pavel Bretchko 著. 王子宇等译. 射频电路设计－理论和应用. 电子工业出版社. 北京. 2002年.
[56]Y. Harkouss, E. Ngoya. J. Rousset. and D. Argollo. Accurate radial wavelet neural-network model for efficient CAD modeling of microstrip discontinuities. IEE. Proc-Microw. Antennas Propag. Vol, 147. No. 4, pp:277-283. Auguet. 2000.
[57] Devabhaktuni, V.K, Yagoub, M.C.E, and Qi-Jun Zhang. A robust algorithm for automatic development of neural-network models for microwave applications. IEEE Trans. Microwave theory Tech, vol. 49, NO. 12, pp.2282-2291, December 2001.
[58]V.K.Devabhaktuni, M.C.E.Yagoub, Y.Fang, J.Xu, and Q.J.Zhang, Neural networks for microwave modeling: Model development issues and nonlinear modeling techniques. Int. J. RF Microwave CAE, vol.11, pp.4-21,2001.
[59]Creech, G.L.,Paul, B.J.,Lesniak, C.D, Jenkins,T.J., and Calcatera, M.C. Artificial neural networks for fast and accurate EM-CAD of microwave circuits. IEEE Trans. Microwave theory Tech, vol. 45, NO. 5, pp.794-802, May, 1997.
[60] Karayiannis, N.B. "Reformulated radial basis neural networks trained by gradient descent". IEEE. Trans. On Neural Networks, vol.10.No.3 .pp. 657-671. May 1999.
[61]刘荧. 林嘉宇. 毛均杰. 基于神经网络的微波电路建模与优化. 微波学报，2001，16（3）：242－248.
[62]Q. J. Zhang. Neural Networks for RF and Microwave Design. Norwood, MA: Artech House. 2000.
[63]李海涛, 邓樱. MATLAB 6.1基础及应用技巧. 国防工业出版社. 2002年.
[64]Mankuan. Vai. Sheila. Prasad. Neural networks in microwave circuit design －beyond black-box moduls. Int. J. RF Microwave CAE, vol.9, pp.187-197, 1999.