Hence, there is a growing request for reduced order modeling of nonlinear problems. Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This increases development time and costs for the design of new circuits. Modern model order reduction mor techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. These algorithms let you control the absolute or relative approximation error, and are all based on the hankel singular values of the system. This allows the efficient accurate simulation of frequencydependent coupled transmission lines characterized by scattering parameters and an optimal reference system.
Model order reduction for coupled systems using lowrank approximationsa. Existing model order reduction techniques 1, however, stamp. Simulation acceleration of highfidelity nonlinear power electronic. Reduced order model validation even the 3 rd order model gives good accuracy. Model reduction techniques for speeding up the thermal simulation of printed circuit boards lon. Krylovsubspace methods for reducedorder modeling in circuit.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Modeling software for rf, microwave, and millimeterwave. Model order reduction techniques for circuit simulation core. Fem models in system simulations using model order reduction. Simulation based on mathematical models plays a major role in computer. Introduction to model order reduction virginia tech. In addition, the proposed multiterminal model reduction methods make circuit. Proceedings in applied mathematics and mechanics, 30 october 2007 model order reduction for nonlinear problems in circuit simulation a. Model reduction can also ameliorate problems in the correlation of widely used finiteelement analyses and test analysis models produced by excessive system complexity.
The basic idea of mor techniques is to reduce the size of a system described by circuit equations, but preserve the dominant behavior of the original system. Fem models in system simulations using model order. Chi shui a a department of electrical and control engineering, national chiao. Computeraided circuit simulation and verification lecture note 3 model order reduction 1 spring 2008 prof. Linear and nonlinear model order reduction for numerical. Abstract model order reduction techniques represent an advanced simulation tool for a large variety of problems of practical and fundamental interest in both industrial and research applications. Model order reduction techniques for circuit simulation.
Citeseerx model order reduction techniques for circuit. Model order reduction mor is here understood as a computational technique to reduce the order of a dynamical system described by a set of ordinary or differentialalgebraic equations odes or. Simulation of the resulting partial differential equations using various popular software tools will be introduced with selected topics on numerical issues. We present the software mor4ansys that allows engineers to employ modern model reduction techniques to finite element models developed in ansys. Advanced model order reduction techniques in vlsi design. Model order reduction technique applied on harmonic. Model reduction for circuit simulation peter benner springer. Gunupudi p and nakhla m model reduction of nonlinear circuits using krylovspace techniques proceedings of the 36th annual acmieee design automation conference, 16 yang z and zwolinski m fast, robust dc and transient fault simulation for nonlinear analogue circuits proceedings of the conference on design, automation and test in europe. Given the system matrices at different values of the parameters, we introduce a simple method of extracting system matrices which are independent of the parameters, so that parametric models of a. Simplified techniques of model order reduction with. Model order reduction, proper generalized decomposition, reduced basis method, proper generalized decomposition.
In numerical linear algebra, it covers both general and more specialized model order reduction techniques for linear and nonlinear systems, and it discusses the use of model order reduction techniques in a variety of practical applications. Multipoint fullwave model order reduction for delayed. Model order reduction for large systems in computational. Read model order reduction and equivalent circuit extraction for fit discretized electromagnetic systems, international journal of numerical modelling. Robust control toolbox software offers several algorithms for model approximation and order reduction.
Model order reduction for multiterminal systems with. The new model reduction method for circuit simulation preserves passivity by interpolating dominant spectral zeros. Model order reduction for nonlinear problems in circuit simulation a. In this paper, we describe the use of krylovsubspace methods for generating reducedorder models of systems of linear daes, such as the ones arising in circuit simulation. Model reduction for circuit simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the eumarie curie action tok project omoorenice members in belgium, the netherlands and germany, the eumarie curie action rtnproject comson members in the netherlands, italy, germany, and. The results from both applications are encouraging and demonstrate that model order reduction techniques can be an extremely useful tool for circuit simulation problems and can lead to substantial savings in the simulation of many types of circuits. Order reduction of large scale secondorder systems using krylov. In order reduction of largescale linear time invariant systems, krylov. A trajectory piecewiselinear approach to model order. The basic idea of model order reduction of a circuit system is to replace the original system by an approximating system with much smaller statespace dimension. This paper investigates two alternative, simple model order reduction techniques and argues that the ready availability of digital simulation languages to test the time frequency response characteristics of pro. Chapter 2 elementbased model reduction in circuit simulation. The method is demonstrated on a dcdc boost converter with a saturated inductor. Recursive convolution is used to speedup the transient simulation.
Home conferences aspdac proceedings aspdac 19 efficient sparsification of dense circuit matrices in model order reduction. Model reduction of an elastic crankshaft for elastic. Efficient sparsification of dense circuit matrices in. Model order reduction for multiterminal systems with applications to circuit simulation. Model order reduction techniques have been studied by several authors as these techniques offer. Given the system matrices at different values of the parameters, we introduce a simple method of extracting system matrices which are independent of the parameters, so that. Model order reduction of nonlinear systems in circuit simulation. A fast block structure preserving model order reduction for. Electronic networks, devices and fields on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. First, an algorithm for the efficient simulation of clocked. I k v 3 e 1 e e 2 3 v 3 0 r 1 r 2 r 3 r 4 0 spice file i0 1 0 1m r1 1 2 1k r2 2 0 1. In this work, we discuss the parametric modeling for the electrothermal analysis of components of nanoelectronic structures and automatic model order reduction of the consequent parametric models. Efficient sparsification of dense circuit matrices in model order reduction.
The need for novel model order reduction techniques in the electronics industry. This paper examines classical model order reduction mor strategies in view of the. In this paper, we describe the use of krylovsubspace methods for generating reduced order models of systems of linear daes, such as the ones arising in circuit simulation. Chungkuan cheng slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Circuit simulation on a computer must be e cient in terms of cpu time especially for large circuits. Model order reduction techniques with applications in finite element analysis. Krylovsubspace methods for reducedorder modeling in. Model reduction for circuit simulation peter benner. Model order reduction techniques with applications in. Products, components, and devices can always be improved. White, a linear timeinvariant model for solidphase diffusion in. With model reduction for circuit simulation we survey the state of.
Modern model order reduction mor techniques present a way out of this. Fem models in system simulations using model order reduction and functional mockup interface andreas godecke, monika muhlbauer, jorg nieveler, iason vittorias, thomas vontz siemens ag, corporate technology ottohahnring 6 81739 munich, germany abstract the integration of a threedimensional fem model. Simulation acceleration of highfidelity nonlinear power electronic circuits using model order reduction. New techniques are needed to shorten timetomarket and to reduce the cost of producing a correct analog integrated circuit. A trajectory piecewiselinear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. Model order reduction for linear and nonlinear systems. Review of model order reduction methods for numerical.
Sparsi cation and model order reduction mor are hence both needed to reduce a large scale rlc circuit. Theoretical and practical aspects of model order reduction techniques for use in the context of circuit simulation are investigated, with particular attention to problems involving clocked analog circuitry and to interconnect and packaging applications. A variety of reduction techniques based on momentmatching with. Pdf this chapter offers an introduction to model order reduction mor. Computer methods for circuit analysis and design guide books. Model order reduction techniques explains and compares such methods focusing. Model order reduction for large scale engineering models. In this work a method is presented in which real time performance is achieved by means of the offline solution of a high dimensional parametric problem that provides a sort of response surface or computational vademecum. Model order reduction is one of the most appealing choices for realtime simulation of nonlinear solids. Model reduction for circuit simulation request pdf. This paper presents a comparison between the full ansys harmonic response and the reduced order model, and shows excellent agreement. An error estimator for realtime simulators based on model.
This leads to very high dimensional problems which nowadays require simulation times too. Model reduction via proper orthogonal decomposition rene pinnau. Currently, reduction techniques based on modal reduction, condensation and component mode synthesis cms are often used in industrial environments. The increase of operating frequencies requires 3d electromagnetic em methods, such as the partial element equivalent circuit peec method, for the analysis and design of highspeed circuits. Model reduction for circuit simulation springerlink. Parametric modeling and model order reduction for electro. Fluid dynamics mechanics computational biology circuit design control theory many heuristics available. Furthermore, this work is somewhat limited since mor methods for some special systems are not included, e.
Review of model order reduction methods for numerical simulation of nonlinear circuits. Model reduction via proper orthogonal decomposition. Lutowska 2012 model order reduction for multiterminal systems with applications to circuit simulation. Model order reduction of nonlinear systems in circuit. The heterogeneous reduction techniques are woven into a unified method by using network partitioning techniques. Thanks to model order reduction, achieve simpler models for a given accuracy compared to traditional techniques such as inverse fast fourier transform. This solution is then evaluated in realtime at feedback rates.
Particular emphasis is on projection techniques that, when applied to a passive circuit, preserve the passivity of the circuit. Simulation based on mathematical models plays a major role in computer aided design of integrated circuits ics. Pdf model order reduction of electrical circuits with nonlinear. Jacob white and associate member, title a trajectory piecewiselinear approach to model order reduction and fast simulation of nonlinear circuits and. Model order reduction using spice simulation traces. Such methods exist for some classes of models typically linear. One of the most used model reduction techniques in circuit simulation is moment matching approximation. Finally, it is shown that the proposed model order reduction technique is. In order to speed up the simulations, a model order reduction technique based on krylov subspaces is implemented. Model order reduction techniques have been studied by several authors as these techniques offer a method to reduce the number of degrees of freedom while an accurate description of the dominant dynamic behaviour may be preserved.
Model order reduction techniques for circuit simulation by luis miguel silveira submitted to the department of electrical engineering and computer science on may 16, 1994, in partial fulfillment of the requirements for the degree of doctor of philosophy abstract. Model reduction techniques model reduction guyanirons condensation dynamic condensation improved reduced system system equivalent reduction expansion process hybrid reduction kammer generally, it may be necessary to reduce a finite element model to a smaller size especially when correlation studies are to be performed. Users may download and print one copy of any publication from the public portal for the. Model order reduction for nonlinear problems in circuit. Compared to the dense partial inductance matrix l, l 1 matrix is easier to sparsify 3,4, where l 1 elements are related to the drop of the branch vector potential 4. A fast block structure preserving model order reduction. Sadayappan p and visvanathan v parallelization and performance evaluation of circuit simulation on a sharedmemory. Ionutiu 2011 model order reduction and sensitivity analysis. Model order reduction mor is a technique for reducing the computational complexity of mathematical models in numerical simulations. Model order reduction technique applied on harmonic analysis. Model order reduction is an approach used to reduce the computational. Time and frequencydomain model order reduction techniques, system identification, parameter estimation, filtering, and control theory will be covered and applied to state of charge, state.
This book presents a systematic introduction to, and treatment of, the key mor methods employed in general linear circuits, using realworld examples to illustrate the advantages and disadvantages of. Model reduction for power electronics systems with multiple heat. Ansys mor techniques model order reduction mor for linear problems transfer function based or lti method system matrix based. Casa model order reduction for multiterminal systems. Very large systems of equations are often produced by 3d em methods and model order reduction mor techniques are used to reduce such a high complexity. Model singleended and differential highspeed transmission lines and channels using rational functions or characterize linear frequency dependent analog components such as ctle. Decreasing structure sizes, increasing packing densities and driving frequencies requi. A trajectory piecewiselinear approach to model order reduction and.
Model order reduction techniques with applications in finite. In this section, we present a model reduction technique for nonlinear circuits with. In order to modelsimulate such problems eciently, developing compact model representation via model order reduction mor 4,5 is desirable for peec modeling. Dounavis a, nakhla m and achar r passive model order reduction of multiport distributed interconnects proceedings of the 37th annual design automation conference, 526531. Model order reduction mor techniques, which are able to reduce the size of a dynamical system description, were recently applied to nd smaller and faster models of electronic circuits 2, 3. We also go into somewhat more detail about the question as to what model order reduction is. Many different model reduction approaches have been developed in computational. With model reduction for circuit simulation we survey the state of the art in the challenging research field of. As such it is closely related to the concept of metamodeling with applications in all areas of mathematical modelling. Hence, there is a strong need for model reduction techniques to reduce the computational costs and. We discuss the computational cost with examples related to structural mechanics.
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