Enhancing Model Order Reduction for Nonlinear Analog Circuit Simulation

Traditionally, model order reduction methods have been used to reduce the computational complexity of mathematical models of dynamic systems, while preserving their functional characteristics. This technique can also be used to fasten analog circuit simulations without sacrificing their highly nonlinear behavior. In this paper, we present an iterative approach for reducing the computational complexity of nonlinear analog circuits using piecewise linear approximations, k-means clustering, and Krylov space projection techniques. We model primary circuit inputs, design initial conditions, and circuit parameters as fuzzy variables with different distributions in qualitative simulations. We then iteratively fine-tune the reduced models until a model is achieved that meets a predefined performance and accuracy conformance criteria. We demonstrate the effectiveness of our method using several key nonlinear circuits: 1) a transmission line; 2) a ring oscillator; 3) a voltage controlled oscillator; 4) a phase-locked loop; and 5) an analog comparator circuit. Our experiments show that the reduced model simulations are fast and accurate compared with the existing techniques.

[1]  Chenjie Gu,et al.  QLMOR: A Projection-Based Nonlinear Model Order Reduction Approach Using Quadratic-Linear Representation of Nonlinear Systems , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[2]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[3]  Sofiène Tahar,et al.  Towards improving simulation of analog circuits using model order reduction , 2012, 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[4]  Charlie Chung-Ping Chen,et al.  Hierarchical model order reduction for signal-integrity interconnect synthesis , 2001, GLSVLSI '01.

[5]  R. Freund.  Krylov-subspace methods for reduced-order modeling in circuit simulation , 2000 .

[6]  Gianluca Bontempi.  Simulating continuous dynamical systems under conditions of uncertainty: the probability and the possibility approaches , 2004 .

[7]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control) , 2005 .

[8]  Janne Roos,et al.  Hierarchical Model-Order Reduction Flow , 2010 .

[9]  Jacob K. White,et al.  A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[10]  Sheldon X.-D. Tan,et al.  Advanced Model Order Reduction Techniques in VLSI Design , 2007 .

[11]  Sofiène Tahar,et al.  Enablingy the DC solutions characterization using a fuzzy approach , 2014, 2014 IEEE 12th International New Circuits and Systems Conference (NEWCAS).

[12]  Yan Li,et al.  Compact Modeling of Nonlinear Analog Circuits Using System Identification via Semidefinite Programming and Incremental Stability Certification , 2009, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[13]  Georges G. E. Gielen,et al.  Characterization of Analog Circuits Using Transfer Function Trajectories , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  R. W. Kelsall,et al.  The Monte Carlo method for semiconductor device simulation , 1995 .

[15]  Michael Hinze,et al.  POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks , 2011 .

[16]  Sofiène Tahar,et al.  A qualitative simulation approach for verifying PLL locking property , 2014, GLSVLSI '14.

[17]  Likun Xia,et al.  Automated Model Generation of Analog Circuits through Modified Trajectory Piecewise Linear Approach with Cheby Shev Newton Interpolating Polynomials , 2013, 2013 4th International Conference on Intelligent Systems, Modelling and Simulation.

[18]  Jaijeet Roychowdhury,et al.  Model reduction via projection onto nonlinear manifolds, with applications to analog circuits and biochemical systems , 2008, ICCAD 2008.

[19]  Ning Dong,et al.  General-Purpose Nonlinear Model-Order Reduction Using Piecewise-Polynomial Representations , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[20]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[21]  Qing Wang,et al.  Fast nonlinear model order reduction via associated transforms of high-order Volterra transfer functions , 2012, DAC Design Automation Conference 2012.

[22]  P. R. Bevington,et al.  Data Reduction and Error Analysis for the Physical Sciences , 1969 .

[23]  Sofiène Tahar,et al.  Generation of reduced analog circuit models using transient simulation traces , 2014, GLSVLSI '14.

[24]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[25]  R. Jacob Baker,et al.  CMOS Circuit Design, Layout, and Simulation , 1997 .

[26]  Joel R. Phillips.  Automated extraction of nonlinear circuit macromodels , 2000, Proceedings of the IEEE 2000 Custom Integrated Circuits Conference (Cat. No.00CH37044).

[27]  Lihong Feng,et al.  Review of model order reduction methods for numerical simulation of nonlinear circuits , 2005, Appl. Math. Comput..

[28]  Yong Chen.  Model order reduction for nonlinear systems , 1999 .

[29]  M. Nabi,et al.  Adaptive sampling of nonlinear system trajectory for Model Order Reduction , 2012, 2012 Proceedings of International Conference on Modelling, Identification and Control.

[30]  Shahkar Ahmad Nahvi,et al.  Nonlinearity-aware sub-model combination in trajectory based methods for nonlinear Mor , 2013, Math. Comput. Simul..

[31]  L. Sirovich.  TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I : COHERENT STRUCTURES , 2016 .