Steady state solution of NFC model with nonlinear load using PEEC

Samuel Kvasnicka, Thomas Bauernfeind, Paul Baumgartner, Riccardo Torchio

Research output: Contribution to journalArticlepeer-review


Purpose: The purpose of this paper is to show that the computation of time-periodic signals for coupled antenna-circuit problems can be substantially accelerated by means of the single shooting method. This allows an efficient analysis of nonlinearly loaded coupled loop antennas for near field communication (NFC) applications. Design/methodology/approach: For the modelling of electrically small coupled field-circuit problems, the partial element equivalent circuit (PEEC) method shows to be very efficient. For analysing the circuit-like description of the coupled problem, this paper developed a generalised modified nodal analysis (MNA) and applied it to specific NFC problems. Findings: It is shown that the periodic steady state (PSS) solution of the resulting differential-algebraic system can be computed very time efficiently by the single shooting method. A speedup of roughly 114 to conventional transient approaches can be achieved. Practical implications: The proposed approach appears to be an efficient alternative for the computation of time PSS solutions for nonlinear circuit problems coupled with discretised conductive structures, where the homogeneous solution is not of interest. Originality/value: The present paper explores the implementation and application of the shooting method for nonlinearly loaded coupled antenna-circuit problems based on the PEEC method and shows the efficiency of this approach.

Original languageEnglish
Pages (from-to)840-851
Number of pages12
JournalCOMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Issue number3
Early online date31 Jan 2022
Publication statusPublished - 14 Apr 2022


  • Near Field Communication (NFC)
  • partial element equivalent circuit (PEEC)
  • modified nodal analysis
  • nonlinearity
  • single shooting method
  • Transient analysis
  • Backward differentiation formula
  • Nonlinear resistive loads
  • Field circuit models
  • Modified nodal analysis
  • Single shooting method
  • Circuit analysis
  • Differential-algebraic equation
  • Near field communication
  • Computational electromagnetics
  • Equivalent circuit model
  • Partial element equivalent circuit method
  • Full-wave rectifier
  • Time-domain modelling

ASJC Scopus subject areas

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


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