Adaptive Multi-rate Wavelet Method for Circuit Simulation

In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The circuit ordinary differential equations are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to deco...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Bittner, Kai, Brachtendorf, Hans Georg
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 25.04.2016
Subjects:
Adaptive algorithms
Boundary conditions
Boundary value problems
Circuit design
Computer simulation
Discretization
Galerkin method
Mathematical analysis
Mixers
Ordinary differential equations
Partial differential equations
Run time (computers)
Spline functions
Wavelet analysis
ISSN:2331-8422
Online Access:Get full text
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Summary:In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The circuit ordinary differential equations are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. Second, a semi-discretization by Rothe's method of the MPDEs results in a system of differential algebraic equations (DAEs) with periodic boundary conditions. These boundary value problems are solved by a Galerkin discretization using spline functions. An adaptive spline grid is generated, using spline wavelets for non-uniform grids. Moreover the instantaneous frequency is chosen adaptively to guarantee a smooth envelope resulting in large time steps and therefore high run time efficiency. Numerical tests on circuits exhibiting multi-rate behavior including mixers and PLL conclude the paper.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1604.07215