Time-Domain Simulation of Sampled Weakly Nonlinear Systems Using Analytical Integration and Orthogonal Polynomial Series

This paper presents a novel method for simulation of sampled systems with weakly nonlinear behavior. These systems can be characterized by adding weakly nonlinear terms to the linear state-space equations of the system resulting in an extended state-space model. Perturbation theory is used to split...

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Vydáno v:Design, Automation and Test in Europe s. 120 - 125
Hlavní autoři: Martens, Ewout, Gielen, Georges
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: Washington, DC, USA IEEE Computer Society 07.03.2005
IEEE
Edice:ACM Conferences
Témata:
Analytical models
Application specific integrated circuits
Clocks
Hardware > Hardware validation > Functional verification > Simulation and emulation
Jitter
Mathematics of computing > Mathematical analysis > Functional analysis > Approximation
Mathematics of computing > Mathematical analysis > Nonlinear equations
Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on polynomials
Nonlinear equations
Nonlinear systems
Numerical simulation
Polynomials
Theory of computation > Design and analysis of algorithms > Approximation algorithms analysis
Time domain analysis
Time series analysis
ISBN:9780769522883, 0769522882
ISSN:1530-1591
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Abstract This paper presents a novel method for simulation of sampled systems with weakly nonlinear behavior. These systems can be characterized by adding weakly nonlinear terms to the linear state-space equations of the system resulting in an extended state-space model. Perturbation theory is used to split these equations in an ideal linear behavior and a non-ideal small perturbation. The linear equations are solved analytically which reduces simulation time compared to numerical evaluation. The solution of the perturbation equations is approximated by orthogonal polynomials. This methodology not only reduces simulation time compared to traditional numerical simulations, but also deals naturally with clock jitter and the discontinuous behavior ofsampled systems. An implementation of the methodology has been used to analyze systems including switched filters and continuous-time ΔΣ modulators.
AbstractList This paper presents a novel method for simulation of sampled systems with weakly nonlinear behavior. These systems can be characterized by adding weakly nonlinear terms to the linear state-space equations of the system resulting in an extended state-space model. Perturbation theory is used to split these equations in an ideal linear behavior and a non-ideal small perturbation. The linear equations are solved analytically which reduces simulation time compared to numerical evaluation. The solution of the perturbation equations is approximated by orthogonal polynomials. This methodology not only reduces simulation time compared to traditional numerical simulations, but also deals naturally with clock jitter and the discontinuous behavior ofsampled systems. An implementation of the methodology has been used to analyze systems including switched filters and continuous-time ΔΣ modulators.
This paper presents a novel method for simulation of sampled systems with weakly nonlinear behavior. These systems can be characterized by adding weakly nonlinear terms to the linear state-space equations of the system resulting in an extended state-space model. Perturbation theory is used to split these equations in an ideal linear behavior and a non-ideal small perturbation. The linear equations are solved analytically which reduces simulation time compared to numerical evaluation. The solution of the perturbation equations is approximated by orthogonal polynomials. This methodology not only reduces simulation time compared to traditional numerical simulations, but also deals naturally with clock jitter and the discontinuous behavior of sampled systems. An implementation of the methodology has been used to analyze systems including switched filters and continuous-time /spl Delta//spl Sigma/ modulators.
This paper presents a novel method for simulation of sampled systems with weakly nonlinear behavior. These systems can be characterized by adding weakly nonlinear terms to the linear state-space equations of the system resulting in an extended state-space model. Perturbation theory is used to split these equations in an ideal linear behavior and a non-ideal small perturbation. The linear equations are solved analytically which reduces simulation time compared to numerical evaluation. The solution of the perturbation equations is approximated by orthogonal polynomials. This methodology not only reduces simulation time compared to traditional numerical simulations, but also deals naturally with clock jitter and the discontinuous behavior ofsampled systems. An implementation of the methodology has been used to analyze systems including switched filters and continuous-time ?? modulators.
Author Martens, Ewout
Gielen, Georges
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SubjectTerms Analytical models
Application specific integrated circuits
Clocks
Hardware -- Hardware validation -- Functional verification -- Simulation and emulation
Jitter
Mathematics of computing -- Mathematical analysis -- Functional analysis -- Approximation
Mathematics of computing -- Mathematical analysis -- Nonlinear equations
Mathematics of computing -- Mathematical analysis -- Numerical analysis -- Computations on polynomials
Nonlinear equations
Nonlinear systems
Numerical simulation
Polynomials
Theory of computation -- Design and analysis of algorithms -- Approximation algorithms analysis
Time domain analysis
Time series analysis
Title Time-Domain Simulation of Sampled Weakly Nonlinear Systems Using Analytical Integration and Orthogonal Polynomial Series
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