The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems

LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency–domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files. Using known ideal nonlinear circuits, the method extraction technique was tested for nonlinearities up to seventh order. The Volterra nonlinear transfer functions of an equalizing circuit were extracted from the results of transient simulations which utilized the shooting method. The resulting tables were then used to simulate an arbitrary waveform and the results closely matched the equivalent time domain circuit simulation.

[1]  Leon O. Chua,et al.  Measuring volterra kernels III: How to estimate the highest significant order , 1991, Int. J. Circuit Theory Appl..

[2]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[3]  C. S. Aitchison,et al.  Power Charcterisation of a MESFET Amplifier Using Small Signal Measurements and Volterra Series , 1985, 1985 IEEE MTT-S International Microwave Symposium Digest.

[4]  G. Kompa,et al.  Automatic Large-Signal Measurement System for Nonlinear Device Modeling and Model Verification , 1989, 1989 19th European Microwave Conference.

[5]  James W. Graham,et al.  Nonlinear System Modeling and Analysis with Applications to Communications Receivers , 1973 .

[6]  Functional analysis of nonlinear circuits: a generating power series approach , 1986 .

[7]  T. Neill.  Improved method of analysing nonlinear electrical networks , 1969 .

[8]  A. A. Wolf,et al.  Volterra-Wiener functionals for the analysis of nonlinear systems , 1966 .

[9]  Michael B. Steer,et al.  Generalized Power Series Analysis of Intermodulation Distortion in a MESFET Amplifier: Simulation and Experiment , 1987 .

[10]  S. Narayanan.  Transistor distortion analysis using volterra series representation , 1967 .

[11]  R. G. Sea,et al.  An algebraic formula for amplitudes of intermodulation products involving an arbitrary number of frequencies , 1968 .

[12]  W. Reiss.  Nonlinear distortion analysis of p-i-n diode attenuators using Volterra series representations , 1984 .

[13]  Y. Chow,et al.  Intermodulation distortion analysis using a frequency-domain harmonic balance technique , 1988 .

[14]  Michael B. Steer,et al.  Simulation of nonlinear microwave circuits-an historical perspective and comparisons , 1991, 1991 IEEE MTT-S International Microwave Symposium Digest.

[15]  A. Prochazka.  Degradation of Performance Parameters in a Television Relay System -I , 1979, IEEE Transactions on Broadcasting.

[16]  S. A. Maas,et al.  Minimization of intermodulation distortion in GaAs MESFET small-signal amplifiers , 1989 .

[17]  Michael B. Steer,et al.  Frequency-domain spectral balance using the arithmetic operator method , 1989 .

[18]  Hans Wilhelm Schüßler,et al.  A New Method for Measuring the Performance of Weakly Nonlinear and Noisy Systems , 1990 .

[19]  M. Steer,et al.  Nonlinear circuit analysis using the method of harmonic balance—A review of the art. Part I. Introductory concepts , 1991 .

[20]  Russell R. Barton,et al.  Large-signal MESFET characterization using harmonic balance , 1988, 1988., IEEE MTT-S International Microwave Symposium Digest.

[21]  A S French,et al.  Nonlinear mechanisms for gain adaptation in locust photoreceptors. , 1990, Biophysical journal.

[22]  Michael B. Steer,et al.  Extraction of the parameters of equivalent circuits of microwave transistors using tree annealing , 1990 .

[23]  Michael B. Steer,et al.  Simulation of Intermodulation Distortion in MESFET Circuits with Arbitrary Frequency Separation of Tones , 1986, 1986 IEEE MTT-S International Microwave Symposium Digest.

[24]  H. Thapar,et al.  Transform-domain and time- domain characterization of nonlinear systems with Volterra series , 1984 .

[25]  W. R. Curtice.  Nonlinear Analysis of GaAs MESFET Amplifiers, Mixers, and Distributed Amplifiers Using the Harmonic Balance Technique , 1987 .

[26]  Françoise Lamnabhi-Lagarrigue,et al.  An algebraic approach to nonlinear functional expansions , 1983 .

[28]  M. Schetzen.  Measurement of the Kernels of a Non-linear System of Finite Order† , 1965 .

[29]  I. W. Sandberg,et al.  Expansions for nonlinear systems , 1982, The Bell System Technical Journal.

[30]  M. Lamnabhi.  Functional Analysis of Nonlinear Circuits , 1985, 1985 15th European Microwave Conference.

[31]  성단근.  고무의 힘-변위 관계를 나타내는 모델링에의 볼테라 급수의 응용 ( Application of Volterra Series to Modeling an Elastomer Force-Displacement Relation ) , 1989 .

[32]  Ping Zhang,et al.  An algorithm to measure high order Volterra kernels , 1990, IEEE International Symposium on Circuits and Systems.

[33]  Existence of Volterra series in the design of feedback systems for nonchaotic motion , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[34]  M. Steer,et al.  Relationship between Volterra series and generalized power series , 1983, Proceedings of the IEEE.

[35]  S. Parker,et al.  A discrete ARMA model for nonlinear system identification , 1981 .

[36]  S. J. Nightingale,et al.  Determination of the Transfer Function of a Nonlinear Circuit for Prediction of Intermodulation Characteristics , 1986, 1986 IEEE MTT-S International Microwave Symposium Digest.

[37]  A. Papoulis,et al.  The Identification Of Certain Nonlinear Systems By Only Observing The Output , 1989, Workshop on Higher-Order Spectral Analysis.

[38]  T. N. Trick,et al.  Fast periodic steady-state analysis for large-signal electronic circuits , 1973 .

[39]  Miroslav Morhác.  A fast algorithm of nonlinear Volterra filtering , 1991, IEEE Trans. Signal Process..

[40]  D. Hente,et al.  Frequency domain continuation method for the analysis and stability investigation of nonlinear microwave circuits , 1986 .

[41]  V. J. O H N M A T H.  Adaptive Polynomial Filters , 2022 .

[42]  G. Ramponi.  Bi-impulse response design of isotropic quadratic filters , 1990 .

[43]  L. Chua,et al.  Measuring Volterra kernels (II) , 1989 .

[44]  R. Gilmore,et al.  Design of a Novel FET Frequency Doubler Using a Harmonic Balance Algorithm , 1986, 1986 IEEE MTT-S International Microwave Symposium Digest.

[45]  Ping Zhang,et al.  IEEE Pacific Rim Conference on Communications, Computers and Signal Processing June 1st - 2nd, 1989 Discrete Frequency-domain Modeling and Measuring of Mildly Nonlinear of Volterra Transfer functions with a set of Special Sinusoid Signals(*) , 1989 .

[46]  L. Zadeh,et al.  Frequency Analysis of Variable Networks , 1950, Proceedings of the IRE.

[47]  R. B. Swerdlow.  Analysis of Intermodulation Noise in Frequency Converters by Volterra Series , 1978 .

[48]  Vincent Fusco,et al.  Large-signal FET simulation using time domain and harmonic balance methods , 1986 .

[49]  S. Rice.  Volterra systems with more than one input port — distortion in a frequency converter , 1973 .

[50]  Michael B. Steer,et al.  Nonlinear circuit analysis using the method of harmonic balance—a review of the art. II. Advanced concepts , 1991 .

[51]  K. Sam Shanmugan,et al.  Computer-Aided Modeling, Analysis, and Design of Communication Systems: Introduction and Issue Overview , 1984, IEEE Journal on Selected Areas in Communications.

[52]  Amar G Bose,et al.  A theory of nonlinear systems , 1956 .

[53]  Johan Schoukens,et al.  Parameter estimation in rational volterra models , 1987 .

[54]  Edward J. Powers,et al.  A digital method of modeling two-input quadratic systems with general random inputs , 1991, IEEE Trans. Signal Process..

[55]  Pol D. Spanos,et al.  Stochastic Response of a Tension Leg Platform to Viscous Drift Forces , 1991 .

[56]  I. Sandberg.  Volterra expansions for time-varying nonlinear systems , 1982, The Bell System Technical Journal.

[57]  Mathias Friese,et al.  Multitone signals with low crest factor , 1997, IEEE Trans. Commun..

[58]  Bruce W. Char,et al.  Maple User''s Guide , 1985 .

[59]  A. G. Vacroux,et al.  On the computation of intermodulation products for a power series nonlinearity , 1969 .

[60]  F. H. Branin,et al.  Determining the periodic response of nonlinear systems by a gradient method , 1977 .

[61]  G. Sorkin,et al.  Applying harmonic balance to almost-periodic circuits , 1988 .

[62]  SYMBOLIC CALCULUS AND VOLTERRA SERIES , 1990 .

[63]  S. A. Maas.  A general-purpose computer program for the Volterra-series analysis of nonlinear microwave circuits , 1988, 1988., IEEE MTT-S International Microwave Symposium Digest.

[64]  L. Chua,et al.  Frequency domain analysis of nonlinear systems: general theory , 1979 .

[65]  Franco Mastri,et al.  General-purpose harmonic balance analysis of nonlinear microwave circuits under multitone excitation , 1988 .

[66]  M. Vlach,et al.  Modeling and simulation with Saber , 1990, Third Annual IEEE Proceedings on ASIC Seminar and Exhibit.

[67]  I. Sandberg.  Series expansions for nonlinear systems , 1983 .

[68]  C. Rauscher,et al.  Modelling the 3rd-order intermodulation-distortion properties of a GaAs f.e.t. , 1977 .

[69]  William H. Press,et al.  Numerical recipes in C , 2002 .

[70]  H. A. Mantooth,et al.  Beyond SPICE with Saber and MAST , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[71]  D. Weiner,et al.  Identification of weakly nonlinear systems using input and output measurements , 1980 .

[72]  S. Maas.  Two-Tone Intermodulation in Diode Mixers , 1987 .

[73]  Ian W. Hunter,et al.  The identification of nonlinear biological systems: Wiener kernel approaches , 2006, Annals of Biomedical Engineering.

[74]  S. Narayanan.  Application of Volterra series to intermodulation distortion analysis of transistor feedback amplifiers , 1970 .

[75]  D. Schaefer,et al.  Volterra series and Picard iteration for nonlinear circuits and systems , 1978 .

[76]  Michael B. Steer,et al.  Frequency-domain nonlinear circuit analysis using generalized power series , 1988 .

[77]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[78]  Stephen P. Banks,et al.  Rational Expansion for Nonlinear Input-Output Maps , 1988 .

[79]  A. Saleh.  Matrix analysis of mildly nonlinear, multiple-input, multiple-output systems with memory , 1982, The Bell System Technical Journal.

[80]  S. H. Ardalan,et al.  CAPSIM: a graphical simulation tool for communication systems , 1988, IEEE Global Telecommunications Conference and Exhibition. Communications for the Information Age.

[81]  Yongcai Hu,et al.  Nonlinear analysis of microwave FET oscillators using Volterra series , 1989 .

[82]  L. Chua,et al.  Frequency-domain analysis of nonlinear systems: formulation of transfer functions , 1979 .

[83]  Yongcai Hu,et al.  A Nevv Method of Third-Order Intermodulation Reduction in Nonlinear Microwave Systems , 1986 .

[84]  C. S. Aitchison,et al.  Optimization of Third-Order Intermodulation Product and Output Power from an X-Band MESFET Amplifier Using Volterra Series Analysis , 1985 .

[85]  A. Javed,et al.  Intermodulation Distortion Analysis of Reflection-Type IMPATT Amplifiers Using Volterra Series Representation , 1977 .

[86]  Jacob K. White,et al.  Relaxation Techniques for the Simulation of VLSI Circuits , 1986 .

[87]  T Kinoshita,et al.  PROBABILITY DENSITY FUNCTION OF A SLOW DRIFT MOTION OF A MOORED FLOATING STRUCTURE IN RANDOM SEAS , 1990 .

[89]  K. Current.  Optimization of forced nonlinear periodic circuits , 1976 .

[90]  R. J. Bowman,et al.  An intuitive behavioral modeling language for mixed signal ASIC simulation , 1990, IEEE International Symposium on Circuits and Systems.

[91]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[92]  Y. S. Cho,et al.  Nonlinear distortion analysis using digital higher-order coherence spectra , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[93]  J. J. Bussgang,et al.  Analysis of nonlinear systems with multiple inputs , 1974 .

[94]  A. Jimenez,et al.  Algorithms for ASTAP--A network-analysis program , 1973 .

[95]  Johan Schoukens,et al.  Steady-state analysis of a periodically excited nonlinear system , 1990 .

[96]  J. Duvernoy.  Volterra-Wiener partially coherent imaging systems : three-dimensional objects and generalized G functionals , 1990 .

[97]  R. Gilmore.  Nonlinear Circuit Design Using the Modified Harmonic Balance Algorithm , 1986 .

[99]  NECESSARY CONDITIONS FOR OPTIMALITY VIA VOLTERRA APPROXIMATIONS , 1990 .

[100]  R. D. DeGroat,et al.  Realizations of nonlinear systems , 1989 .

[101]  T. Aprille,et al.  Steady-state analysis of nonlinear circuits with periodic inputs , 1972 .

[102]  R. S. Tucker,et al.  Third-Order Intermodulation Distortion and Gain Compression in GaAs Fet's , 1979 .

[103]  W. Snelgrove,et al.  Nonlinear IIR adaptive filtering using a bilinear structure , 1989, IEEE International Symposium on Circuits and Systems,.

[104]  E. J. Powers,et al.  On the linearization of Volterra nonlinear systems using third-order inverses in the digital frequency-domain , 1990, IEEE International Symposium on Circuits and Systems.

[105]  Louis R. Hunt,et al.  Nonlinear filter design , 1987 .

[106]  Rob A. Rutenbar,et al.  Macromodeling of Integrated Circuit Operational Amplifiers , 2002 .

[107]  John W. Bandler,et al.  Efficient large-signal FET parameter extraction using harmonics , 1989 .

[108]  Leon O. Chua,et al.  Nonlinear oscillation via Volterra series , 1982 .

[109]  G. Tomlinson,et al.  Recent advances in the application of functional series to non-linear structures , 1989 .

[110]  M. Shensa,et al.  Cross modulation and intermodulation in amplifiers at high frequencies , 1972 .

[111]  R. Tymerski,et al.  Volterra series modelling of power conversion systems , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[112]  J. Vlach,et al.  A CAD-oriented nonlinear model of the operational amplifier in the frequency-domain , 1987 .

[113]  R. Hermann.  Volterra modeling of digital magnetic saturation recording channels , 1990, International Conference on Magnetics.

[114]  Georgios B. Giannakis,et al.  Linear and non-linear adaptive noise cancelers , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[115]  K. Sam Shanmugan,et al.  An update on software packages for simulation of communication systems (links) , 1988, IEEE J. Sel. Areas Commun..

[116]  Y. Volkov.  Analysis of nonlinear devices in a radio-receiving channel in the time domain , 1990 .

[117]  Michael B. Steer,et al.  Frequency-domain bivariate generalized power series analysis of nonlinear analog circuits , 1990 .

[118]  Adam Krzyzak,et al.  On estimation of a class of nonlinear systems by the kernel regression estimate , 1990, IEEE Trans. Inf. Theory.

[119]  S. Maas.  A GaAs MESFET Mixer with Very Low Intermodulation , 1987 .

[120]  Mohammad Maqusi,et al.  Analysis and Modeling of Intermodulation Distortion in Wide-Band Cable TV Channels , 1987, IEEE Trans. Commun..

[121]  Martin Schetzen.  Multilinear theory of nonlinear networks , 1985 .

[122]  George W. Hart,et al.  Memoryless nonlinear system identification with unknown model order , 1991, IEEE Trans. Inf. Theory.

[123]  Rob A. Rutenbar,et al.  Simulated annealing algorithms: an overview , 1989, IEEE Circuits and Devices Magazine.

[124]  E. Bedrosian,et al.  The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs , 1971 .

[125]  S. Narayanan,et al.  Noise Loading Analysis of a Third-Order Nonlinear System with Memory , 1968 .

[126]  K. Hecox,et al.  Nonlinear system identification by m-pulse sequences: application to brainstem auditory evoked responses , 1991, IEEE Transactions on Biomedical Engineering.

[127]  Ikuo Oka,et al.  Error probability for digital transmission over nonlinear channels with application to TCM , 1990, IEEE Trans. Inf. Theory.

[128]  The relationships between different measures of nonlinear distortion in single-amplifier active filters , 1983 .

[129]  Alberto L. Sangiovanni-Vincentelli,et al.  Simulation of Nonlinear Circuits in the Frequency Domain , 1986, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[130]  D. A. Kabanov,et al.  Method of analysis of non-linear systems on the basis of generalization of the volterra functional series relative to complex envelopes , 1991, Int. J. Circuit Theory Appl..

[131]  S. A. Maas,et al.  Modeling the gate I/V characteristic of a GaAs MESFET for Volterra-series analysis , 1989 .

[132]  Michael B. Steer,et al.  A New Frequency Domain Approach to the Analysis of Nonlinear Microwave Circuits , 1985, 1985 IEEE MTT-S International Microwave Symposium Digest.

[133]  S. Billings,et al.  Interpretation of non-linear frequency response functions , 1990 .

[134]  Edward J. Powers,et al.  On the identification of a third-order Volterra nonlinear system using a frequency-domain block RLS adaptive algorithm , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[135]  M. Korenberg,et al.  Orthogonal approaches to time-series analysis and system identification , 1991, IEEE Signal Processing Magazine.

[136]  M Lamnabhi.  A new symbolic calculus for the response of nonlinear systems , 1982 .

[137]  E. J. Powers,et al.  Testing for Gaussianity in nonlinear system identification , 1990, IEEE International Symposium on Circuits and Systems.

[138]  A. Halme,et al.  Polynomial operators in non-linear systems theory , 1971 .

[139]  T.K. Biswas,et al.  Volterra series analysis of semiconductor laser diode , 1991, IEEE Photonics Technology Letters.

[140]  M. Steer,et al.  An algebraic formula for the output of a system with large-signal, multifrequency excitation , 1983, Proceedings of the IEEE.

[141]  S.W. Nam,et al.  Adaptive algorithms for the frequency-domain identification of a second-order Volterra system with random input , 1990, Fifth ASSP Workshop on Spectrum Estimation and Modeling.

[142]  Jiri Vlach,et al.  A piecewise harmonic balance technique for determination of periodic response of nonlinear systems , 1976 .

[143]  A. Nassirharand,et al.  FREQUENCY-DOMAIN MODELING OF NONLINEAR MULTIVARIABLE SYSTEMS , 1989 .

[144]  R. W. Miksad,et al.  Stabilization of Moored Vessels Using a Second-Order Volterra Filter and Feedforward Compensator , 1991 .

[145]  R. de Figueiredo.  The Volterra and Wiener theories of nonlinear systems , 1982, Proceedings of the IEEE.

[146]  Choi Look Law,et al.  Prediction of Wide-Band Power Performance of MESFET Distributed Amplifiers Using the Volterra Series Representation , 1986 .

[147]  Patrick Duvaut,et al.  Geometrical properties of optimal Volterra filters for signal detection , 1990, IEEE Trans. Inf. Theory.

[148]  Michael K. Sain,et al.  A VOLTERRA METHOD FOR NONLINEAR CONTROL DESIGN , 1990 .

[149]  T. Poggio,et al.  The Volterra Representation and the Wiener Expansion: Validity and Pitfalls , 1977 .

[150]  S. Billings,et al.  Describing functions, Volterra series, and the analysis of non-linear systems in the frequency domain , 1991 .

[151]  G. Mazzarella,et al.  Reconstruction of one-dimensional dielectric profiles , 1991 .

[152]  T. Aprille,et al.  A computer algorithm to determine the steady-state response of nonlinear oscillators , 1972 .

[153]  G. Gielen,et al.  Symbolic simulation of harmonic distortion in analog integrated circuits with weak nonlinearities , 1990, IEEE International Symposium on Circuits and Systems.

[154]  Ezio Biglieri,et al.  Analysis and compensation of nonlinearities in digital transmission systems , 1988, IEEE J. Sel. Areas Commun..

[155]  Leon O. Chua,et al.  Measuring Volterra kernels , 1983 .

[156]  Viktor Krozer,et al.  A novel analytical approach for the nonlinear microwave circuits and experimental characterisation of the nonlinear behaviour of a new MESFET device structure , 1989, IEEE MTT-S International Microwave Symposium Digest.

[157]  R. Jones,et al.  Phase spaces from experimental time series , 1989 .

[158]  Willy Sansen,et al.  Analog Circuit Design Optimization based on Symbolic Simulation and Simulated Annealing , 1989, ESSCIRC '89: Proceedings of the 15th European Solid-State Circuits Conference.

[159]  Tapani Narhi.  Multi-Frequency Analysis of Nonlinear Circuits using One and Two-Dimensional Series Expansions , 1989, 1989 19th European Microwave Conference.

[160]  A recursive solution for strongly nonlinear systems by combining Volterra principles with the harmonic balance technique , 1989, IEEE International Symposium on Circuits and Systems,.

[161]  Vito Volterra,et al.  Theory of Functionals and of Integral and Integro-Differential Equations , 2005 .

[162]  K. W. Lang,et al.  A 16-Mbit/s adapter chip for the IBM token-ring local area network , 1989 .

[163]  A. Mircea,et al.  Distortion noise in frequency-dependent nonlinear networks , 1969 .

[164]  R. Schaumann,et al.  Effects of weak nonlinearities in transconductance-capacitor filters , 1989, IEEE International Symposium on Circuits and Systems,.

[165]  Stephen A. Maas,et al.  Nonlinear microwave circuits , 1988 .

[166]  E. Powers,et al.  On modeling the nonlinear relationship between fluctuations with nonlinear transfer functions , 1980, Proceedings of the IEEE.

[167]  W. X. Zhang.  Estimation Of Frequency Response And Intermodulation Distortion From Bispectra , 1989, Workshop on Higher-Order Spectral Analysis.

[168]  S B Kim,et al.  SPECTRAL ESTIMATION OF SECOND ORDER WAVE FORCES ON A TLP SUBJECT TO NONGAUSSIAN IRREGULAR SEAS , 1990 .

[169]  N. Ishii,et al.  Estimation of kernel function of non-linear system by gaussian non-white noise , 1991 .

[170]  Erik Eisen.  Tech talk. , 1985, Pennsylvania dental journal.

[171]  Ali H. Nayfeh,et al.  Parametric identification of nonlinear dynamic systems , 1985 .

[172]  R. Minasian.  Intermodulation Distortion Analysis of MESFET Amplifiers Using the Volterra Series Representation , 1980 .