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Steady state analysis of electronic circuits by cubic and exponential splines

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Abstract

Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady state of RF circuits. HB is based on a Fourier expansion of the unknown waveforms and is state-of-the-art. Unfortunately, trigonometric polynomials exhibit poor convergence properties in cases where the signal is not quasi-sinusoidal which leads to a prohibitive run-time even for small circuits. Moreover, the approximation of sharp transients leads to the well-known Gibbs phenomenon, which cannot be reduced by an increase of Fourier coefficients. In this paper, we present an alternative approach based on alternatively cubic or exponential splines for a (quasi-) periodic steady state analysis. Unlike trigonometric basis function, a spline basis solves for a variational problem, i.e., the cubic spline minimizes the curvature. Because of their compact support, spline bases are better suited for waveforms with sharp transients. Furthermore, we show that the amount of work for coding of splines is negligible if an implementation of HB is available. In general, designers are mainly interested in spectra and not in waveforms. Therefore, a method for calculating the spectrum from a spline basis is derived too.

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Authors and Affiliations

  1. University of Applied Science of Upper Austria, Wels, Austria

    Hans Georg Brachtendorf

  2. University of Bremen, Bremen, Germany

    Angelika Bunse-Gerstner, Barbara Lang & Siegmar Lampe

Authors
  1. Hans Georg Brachtendorf
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  2. Angelika Bunse-Gerstner
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  3. Barbara Lang
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  4. Siegmar Lampe
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Corresponding author

Correspondence to Hans Georg Brachtendorf.

Additional information

This paper is dedicated to Prof. Dr.-Ing. Rainer Laur, University of Bremen, on the occasion of his 65th birthday. This work has been partly supported by the ICESTARS project of the European Community under grant 214911.

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Brachtendorf, H.G., Bunse-Gerstner, A., Lang, B. et al. Steady state analysis of electronic circuits by cubic and exponential splines. Electr Eng 91, 287–299 (2009). https://doi.org/10.1007/s00202-009-0137-7

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  • DOI: https://doi.org/10.1007/s00202-009-0137-7

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