Steady state analysis of electronic circuits by cubic and exponential splines

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7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)287-299
Number of pages13
JournalElectrical Engineering
Issue number4-5
Publication statusPublished - Dec 2009


  • Harmonic Balance
  • MPDE
  • Multitone steady state analysis
  • Spline basis

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