Parametric Modeling of EM Behavior of Microwave Components Using Combined Neural Networks and Pole-Residue-Based Transfer Functions

This paper proposes an advanced technique to develop combined neural network and pole-residue-based transfer function models for parametric modeling of electromagnetic (EM) behavior of microwave components. In this technique, neural networks are trained to learn the relationship between pole/residues of the transfer functions and geometrical parameters. The order of the pole-residue transfer function may vary over different regions of geometrical parameters. We develop a pole-residue tracking technique to solve this order-changing problem. After the proposed modeling process, the trained model can be used to provide accurate and fast prediction of the EM behavior of microwave components with geometrical parameters as variables. The proposed method can obtain better accuracy in challenging applications involving high dimension of geometrical parameter space and large geometrical variations, compared with conventional modeling methods. The proposed technique is effective and robust especially in solving high-order problems. This technique is illustrated by three examples of EM parametric modeling.

[1]  J.W. Bandler,et al.  Implicit space mapping optimization exploiting preassigned parameters , 2004, IEEE Transactions on Microwave Theory and Techniques.

[2]  M. Moraud.  Wavelet Networks , 2018, Foundations of Wavelet Networks and Applications.

[3]  M.C.E. Yagoub,et al.  Neural based dynamic modeling of nonlinear microwave circuits , 2002, 2002 IEEE MTT-S International Microwave Symposium Digest (Cat. No.02CH37278).

[4]  John W. Bandler,et al.  Tuning space mapping: A novel technique for engineering design optimization , 2008, 2008 IEEE MTT-S International Microwave Symposium Digest.

[5]  I. A. Maio,et al.  Parametric macromodels of digital I/O ports , 2002 .

[6]  J.W. Bandler,et al.  Space Mapping With Adaptive Response Correction for Microwave Design Optimization , 2009, IEEE Transactions on Microwave Theory and Techniques.

[7]  Yagyensh C. Pati,et al.  Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations , 1993, IEEE Trans. Neural Networks.

[8]  Qi-Jun Zhang,et al.  Artificial neural networks for RF and microwave design - from theory to practice , 2003 .

[9]  S. Koziel,et al.  A Space-Mapping Framework for Engineering Optimization—Theory and Implementation , 2006, IEEE Transactions on Microwave Theory and Techniques.

[10]  Qi-Jun Zhang,et al.  Ultra fast neural models for analysis of electro/optical interconnects , 1997, 1997 Proceedings 47th Electronic Components and Technology Conference.

[11]  S. Koziel,et al.  Space mapping , 2008, IEEE Microwave Magazine.

[12]  John W. Bandler,et al.  Cognition-Driven Formulation of Space Mapping for Equal-Ripple Optimization of Microwave Filters , 2015, IEEE Transactions on Microwave Theory and Techniques.

[13]  Russell Reed,et al.  Pruning algorithms-a survey , 1993, IEEE Trans. Neural Networks.

[14]  G. L. Creech,et al.  Artificial neural networks for fast and accurate EM-CAD of microwave circuits , 1997 .

[15]  C.G. Christodoulou,et al.  Neural network processing for adaptive array antennas , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[16]  Flavio Canavero,et al.  NARX approach to black-box modeling of circuit elements , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[17]  Qi-Jun Zhang,et al.  High-Dimensional Neural-Network Technique and Applications to Microwave Filter Modeling , 2010, IEEE Transactions on Microwave Theory and Techniques.

[18]  P. Vega,et al.  State-space neural network for modelling, prediction and control , 2000 .

[19]  James T. Kwok,et al.  Constructive algorithms for structure learning in feedforward neural networks for regression problems , 1997, IEEE Trans. Neural Networks.

[20]  Qi-Jun Zhang,et al.  Simple and Efficient High-Dimensional Parametric Modeling for Microwave Cavity Filters Using Modular Neural Network , 2011, IEEE Microwave and Wireless Components Letters.

[21]  Vicente E. Boria,et al.  Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping , 2015, IEEE Transactions on Microwave Theory and Techniques.

[22]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[23]  J.E. Rayas-Sanchez,et al.  EM-based optimization of microwave circuits using artificial neural networks: the state-of-the-art , 2003, IEEE Transactions on Microwave Theory and Techniques.

[24]  D. Wisell,et al.  Wide-band dynamic modeling of power amplifiers using radial-basis function neural networks , 2005, IEEE Transactions on Microwave Theory and Techniques.

[25]  Feng Feng,et al.  Parametric Modeling of Microwave Components Using Adjoint Neural Networks and Pole-Residue Transfer Functions With EM Sensitivity Analysis , 2017, IEEE Transactions on Microwave Theory and Techniques.

[26]  M.C.E. Yagoub,et al.  Exact adjoint sensitivity analysis for neural based microwave modeling and design , 2001, 2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157).

[27]  Yazi Cao,et al.  Passivity enforcement for passive component modeling subject to variations of geometrical parameters using neural networks , 2012, 2012 IEEE/MTT-S International Microwave Symposium Digest.

[28]  Qi-Jun Zhang,et al.  Smart Modeling of Microwave Devices , 2010, IEEE Microwave Magazine.

[29]  D.E. Root,et al.  A behavioral modeling approach to nonlinear model-order reduction for RF/microwave ICs and systems , 2004, IEEE Transactions on Microwave Theory and Techniques.

[30]  John W. Bandler,et al.  Space mapping with distributed fine model evaluation for optimization of microwave structures and devices , 2008, 2008 IEEE MTT-S International Microwave Symposium Digest.

[31]  Gaofeng Wang,et al.  A New Training Approach for Parametric Modeling of Microwave Passive Components Using Combined Neural Networks and Transfer Functions , 2009, IEEE Transactions on Microwave Theory and Techniques.

[32]  F.M. Ghannouchi,et al.  Dynamic behavioral modeling of 3G power amplifiers using real-valued time-delay neural networks , 2004, IEEE Transactions on Microwave Theory and Techniques.

[33]  J.W. Bandler,et al.  EM-based surrogate modeling and design exploiting implicit, frequency and output space mappings , 2003, IEEE MTT-S International Microwave Symposium Digest, 2003.

[34]  Q.J. Zhang,et al.  A Neural Network Approach to the Modeling of Heterojunction Bipolar Transistors from S-Parameter Data , 1998, 1998 28th European Microwave Conference.

[35]  Lei Zhang,et al.  Portable Space Mapping for Efficient Statistical Modeling of Passive Components , 2012, IEEE Transactions on Microwave Theory and Techniques.

[36]  Dominique Schreurs,et al.  Construction of behavioral models for microwave devices from time domain large-signal measurements to speed up high-level design simulations , 2003 .

[37]  Qinghua Zhang,et al.  Using wavelet network in nonparametric estimation , 1997, IEEE Trans. Neural Networks.

[38]  Feng Feng,et al.  Neural space mapping optimization for EM design , 2015, 2015 Asia-Pacific Microwave Conference (APMC).

[39]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[40]  Wei Zhang,et al.  Fast and simple technique for computing circuit noise figure from component noise model using artificial neural network , 2015, 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO).

[41]  J.W. Bandler,et al.  Adjoint techniques for sensitivity analysis in high-frequency structure CAD , 2004, IEEE Transactions on Microwave Theory and Techniques.

[42]  J.W. Bandler,et al.  New directions in model development for RF/microwave components utilizing artificial neural networks and space mapping , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[43]  John W. Bandler,et al.  Expanded space-mapping EM-based design framework exploiting preassigned parameters , 2002 .

[44]  John W. Bandler,et al.  Reliable Space-Mapping Optimization Integrated With EM-Based Adjoint Sensitivities , 2013, IEEE Transactions on Microwave Theory and Techniques.

[45]  J.W. Bandler,et al.  Neural space mapping EM optimization of microwave structures , 2000, 2000 IEEE MTT-S International Microwave Symposium Digest (Cat. No.00CH37017).

[46]  Chao Zhang,et al.  Parallel EM optimization approach to microwave filter design using feature assisted neuro-transfer functions , 2016, 2016 IEEE MTT-S International Microwave Symposium (IMS).

[47]  Qi-Jun Zhang,et al.  Parallel Automatic Model Generation Technique for Microwave Modeling , 2007, 2007 IEEE/MTT-S International Microwave Symposium.

[48]  José E. Rayas-Sánchez,et al.  Neural input space mapping optimization based on nonlinear two-layer perceptrons with optimized nonlinearity , 2010 .

[49]  Feng Feng,et al.  Parametric modeling of millimeter-wave passive components using combined neural networks and transfer functions , 2015, Global Symposium on Millimeter-Waves (GSMM).

[50]  Magdalena Salazar-Palma,et al.  Multilevel aggressive space mapping applied to coupled-resonator filters , 2016, 2016 IEEE MTT-S International Microwave Symposium (IMS).

[51]  Qi-Jun Zhang,et al.  Neural Networks for RF and Microwave Design , 2000 .

[52]  Fang Wang,et al.  Knowledge based neural models for microwave design , 1997, 1997 IEEE MTT-S International Microwave Symposium Digest.

[53]  M.C.E. Yagoub,et al.  Advanced microwave modeling framework exploiting automatic model generation, knowledge neural networks and space mapping , 2002, 2002 IEEE MTT-S International Microwave Symposium Digest (Cat. No.02CH37278).

[54]  Qi-Jun Zhang,et al.  A Combined State Space Formulation/Equivalent Circuit and Neural Network Technique for Modeling of Embedded Passives in Multilayer Printed Circuits , 2003 .

[55]  P. Gil.  State-Space Neural Networks and the Unscented Kalman Filter in On-line Nonlinear System Identification , 2001 .

[56]  S. Manetti,et al.  Design of cylindrical posts in rectangular waveguide by neural network approach , 2000, IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (C.

[57]  V. Rizzoli,et al.  Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation , 2004, IEEE Transactions on Microwave Theory and Techniques.

[58]  S. Brisset,et al.  Three-Level Output Space Mapping Strategy for Electromagnetic Design Optimization , 2012, IEEE Transactions on Magnetics.

[59]  J. Bandler,et al.  Constrained parameter extraction for microwave design optimisation using implicit space mapping , 2011 .

[60]  Q.J. Zhang,et al.  A new nonlinear transient modelling technique for high-speed integrated circuit applications based on state-space dynamic neural network , 2004, 2004 IEEE MTT-S International Microwave Symposium Digest (IEEE Cat. No.04CH37535).

[61]  Fang Wang,et al.  A new macromodeling approach for nonlinear microwave circuits based on recurrent neural networks , 2000, IMS 2000.

[62]  Feng Feng,et al.  Parallel Space-Mapping Approach to EM Optimization , 2014, IEEE Transactions on Microwave Theory and Techniques.

[63]  Feng Feng,et al.  Parallel gradient-based local search accelerating particle swarm optimization for training microwave neural network models , 2015, 2015 IEEE MTT-S International Microwave Symposium.

[64]  Jacques de Villiers,et al.  Backpropagation neural nets with one and two hidden layers , 1993, IEEE Trans. Neural Networks.

[65]  Feng Feng,et al.  Knowledge-based coarse and fine mesh space mapping approach to EM optimization , 2014, 2014 International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO).

[66]  Klaus Iglberger,et al.  Parallel Computing. Numerics, Applications, and Trends , 2009 .

[67]  V. Gutierrez-Ayala,et al.  EM-Based Monte Carlo Analysis and Yield Prediction of Microwave Circuits Using Linear-Input Neural-Output Space Mapping , 2006, IEEE Transactions on Microwave Theory and Techniques.

[68]  Gaofeng Wang,et al.  A Wideband and Scalable Model of Spiral Inductors Using Space-Mapping Neural Network , 2007, IEEE Transactions on Microwave Theory and Techniques.

[69]  Qi Jun Zhang,et al.  Automated Knowledge-Based Neural Network Modeling for Microwave Applications , 2014, IEEE Microwave and Wireless Components Letters.

[70]  Adam Krzyzak,et al.  Radial Basis Function Networks and Complexity Regularization in Function Learning , 2022 .

[71]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

[72]  R. Lewis,et al.  An Overview of First-Order Model Management for Engineering Optimization , 2001 .

[73]  Q.J. Zhang,et al.  Transient electromagnetic modeling using recurrent neural networks , 2005, IEEE MTT-S International Microwave Symposium Digest, 2005..

[74]  Qi-Jun Zhang,et al.  A Broadband and Parametric Model of Differential Via Holes Using Space-Mapping Neural Network , 2009, IEEE Microwave and Wireless Components Letters.

[75]  Weicong Na,et al.  A Unified Automated Parametric Modeling Algorithm Using Knowledge-Based Neural Network and ${l}_{1}$ Optimization , 2017, IEEE Transactions on Microwave Theory and Techniques.

[76]  J.W. Bandler,et al.  Space mapping: the state of the art , 2004, IEEE Transactions on Microwave Theory and Techniques.

[77]  Q.J. Zhang,et al.  An adjoint dynamic neural network technique for exact sensitivities in nonlinear transient modeling and high-speed interconnect design , 2003, IEEE MTT-S International Microwave Symposium Digest, 2003.

[78]  John W. Bandler,et al.  Fast EM Modeling Exploiting Shape-Preserving Response Prediction and Space Mapping , 2014, IEEE Transactions on Microwave Theory and Techniques.

[79]  M.C.E. Yagoub,et al.  A robust algorithm for automatic development of neural network models for microwave applications , 2001, 2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157).

[80]  John W. Bandler,et al.  Computer-aided design of RF and microwave circuits and systems , 2002 .

[81]  M. Salazar-Palma,et al.  Efficient electromagnetic optimization of microwave filters and multiplexers using rational models , 2004, IEEE Transactions on Microwave Theory and Techniques.

[82]  J.W. Bandler,et al.  A space-mapping interpolating surrogate algorithm for highly optimized EM-based design of microwave devices , 2004, IEEE Transactions on Microwave Theory and Techniques.

[83]  T.J. Brazil,et al.  RF Power Amplifier Behavioral Modeling using a Globally Recurrent Neural Network , 2006, 2006 IEEE MTT-S International Microwave Symposium Digest.

[84]  Chao Zhang,et al.  EM optimization using coarse and fine mesh space mapping , 2013, 2013 Asia-Pacific Microwave Conference Proceedings (APMC).

[85]  Diego Masotti,et al.  A new family of neural network-based bidirectional and dispersive behavioral models for nonlinear RF/microwave subsystems(invited paper) , 2002 .

[86]  John W. Bandler,et al.  Neural space-mapping optimization for EM-based design , 2000 .

[87]  Naofumi Okubo,et al.  Structural determination of multilayered large-signal neural-network HEMT model , 1998 .

[88]  Qi-Jun Zhang,et al.  State-space dynamic neural network technique for high-speed IC applications: modeling and stability analysis , 2006, IEEE Transactions on Microwave Theory and Techniques.

[89]  Qi-Jun Zhang,et al.  Neural Network Inverse Modeling and Applications to Microwave Filter Design , 2008, IEEE Transactions on Microwave Theory and Techniques.

[90]  James Aweya,et al.  A direct adaptive neural controller for flow control in computer networks , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[91]  Feng Feng,et al.  Parametric modeling using sensitivity-based adjoint neuro-transfer functions for microwave passive components , 2015, 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO).

[92]  Servaas Vandenberghe,et al.  Straightforward and accurate nonlinear device model parameter-estimation method based on vectorial large-signal measurements , 2001 .

[93]  Weicong Na,et al.  Recent advances in parallel EM optimization approaches , 2016, 2016 IEEE International Conference on Microwave and Millimeter Wave Technology (ICMMT).

[94]  Chao Zhang,et al.  Parallel Decomposition Approach to Gradient-Based EM Optimization , 2016, IEEE Transactions on Microwave Theory and Techniques.

[95]  Michel S. Nakhla,et al.  Signal integrity analysis and optimization of VLSI interconnects using neural network models , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[96]  Qi-Jun Zhang,et al.  Evolutionary Neuro-Space Mapping Technique for Modeling of Nonlinear Microwave Devices , 2011, IEEE Transactions on Microwave Theory and Techniques.

[97]  Slawomir Koziel,et al.  Tuning space mapping design framework exploiting reduced electromagnetic models , 2011 .

[98]  J.W. Bandler,et al.  Neuromodeling of microwave circuits exploiting space mapping technology , 1999, 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282).

[99]  Venu-Madhav-Reddy Gongal-Reddy,et al.  Efficient design optimization of microwave circuits using parallel computational methods , 2012, 2012 7th European Microwave Integrated Circuit Conference.

[100]  Sushanta K. Mandal,et al.  ANN- and PSO-Based Synthesis of On-Chip Spiral Inductors for RF ICs , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[101]  Mauro Mongiardo,et al.  A review of artificial neural networks applications in microwave computer-aided design , 1999 .

[102]  Wei Zhang,et al.  Distributed parallel computing technique for EM modeling , 2015, 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO).

[103]  M.C.E. Yagoub,et al.  Neural-network approaches to electromagnetic-based modeling of passive components and their applications to high-frequency and high-speed nonlinear circuit optimization , 2004, IEEE Transactions on Microwave Theory and Techniques.

[104]  M.C.E. Yagoub,et al.  Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling , 2005, IEEE Transactions on Microwave Theory and Techniques.

[105]  John W. Bandler,et al.  Distributed fine model evaluation for rapid space-mapping optimisation of microwave structures , 2009 .

[106]  K. C. Gupta,et al.  Design and optimization of CPW circuits using EM-ANN models for CPW components , 1997 .

[107]  Qi-Jun Zhang,et al.  Parametric Modeling of Microwave Passive Components Using Sensitivity-Analysis-Based Adjoint Neural-Network Technique , 2013, IEEE Transactions on Microwave Theory and Techniques.

[108]  D. Depriest,et al.  Understanding Industrial Designed Experiments , 1993 .

[109]  Shin'ichi Tamura,et al.  Capabilities of a four-layered feedforward neural network: four layers versus three , 1997, IEEE Trans. Neural Networks.

[110]  Michel Nakhla,et al.  A neural network modeling approach to circuit optimization and statistical design , 1995 .

[111]  Venu-Madhav-Reddy Gongal-Reddy,et al.  Parallel Computational Approach to Gradient Based EM Optimization of Passive Microwave Circuits , 2016, IEEE Transactions on Microwave Theory and Techniques.

[112]  Qi-Jun Zhang,et al.  Automated time domain modeling of linear and nonlinear microwave circuits using recurrent neural networks , 2008 .

[113]  P. A. Newman,et al.  Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models , 2001 .

[114]  Feng Feng,et al.  Recent advances in space mapping approach to EM optimization , 2015, 2015 Asia-Pacific Microwave Conference (APMC).