Exploiting the T(x) function in fast hysteresis models for transient circuit simulations

Johann Wilhelm*, Werner Renhart

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Purpose: The purpose of this paper is to investigate an alternative to established hysteresis models. Design/methodology/approach: Different mathematical representations of the magnetic hysteresis are compared and some differences are briefly discussed. After this, the application of the T(x) function is presented and an inductor model is developed. Implementation details of the used transient circuit simulator code are further discussed. From real measurement results, parameters for the model are extracted. The results of the final simulation are finally discussed and compared to measurements. Findings: The T(x) function possesses a fast mathematical formulation with very good accuracy. It is shown that this formulation is very well suited for an implementation in transient circuit simulator codes. Simulation results using the developed model are in very good agreement with measurements. Research limitations/implications: For the purpose of this paper, only soft magnetic materials were considered. However, literature suggests, that the T(x) function can be extended to hard magnetic materials. Investigations on this topic are considered as future work. Originality/value: While the mathematical background of the T(x) function is very well presented in the referenced papers, the application in a model of a real device is not very well discussed yet. The presented paper is directly applicable to typical problems in the field of power electronics.

Original languageEnglish
Pages (from-to)1427-1440
Number of pages14
JournalCOMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Issue number5
Publication statusPublished - 2 Sept 2019


  • Magnetic hysteresis
  • Transient analysis
  • Transient simulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Applied Mathematics


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