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Medical and Biological Engineering and Computing

, Volume 40, Issue 5, pp 542–545 | Cite as

Sauer's non-linear voltage division

  • H. P. Schwan
  • E. T. McAdams
  • J. Jossinet
Article

Abstract

The non-linearity of the electrode-tissue interface impedance gives rise to harmonics and thus degrades the accuracy of impedance measurements. Also, electrodes are often driven into the non-linear range of their polarisation impedance. This is particularly true in clinical applications. Techniques to correct for electrode effects are usually based on linear electrode impedance data. However, these data can be very different from the non-linear values needed. Non-linear electrode data suggested a model based on simple assumptions. It is useful in predicting the frequency dependence of non-linear effects from linear properties. Sauer's treatment is a first attempt to provide a more general and rigorous basis for modelling the non-linear state. The paper reports Sauer's treatment of the non-linear case and points out its limitations. The paper considers Sauer's treatment of a series arrangement of two impedances. The tissue impedance is represented by a linear voltage-current characteristic. The interface impedance is represented by a Volterra expansion. The response of this network to periodic signals is calculated up to the second-order term of the series expansion. The resultant, time-dependent current is found to contain a DC term (rectification), as well as frequency-dependent terms. Sauer's treatment assumes a voltage clamp across the impedances and neglects higher-order terms in the series expansion. As a consequence, it fails adequately to represent some experimentally observed phenomena. It is therefore suggested that Sauer's expressions for the voltage divider should be combined with the non-linear treatments previously published by the co-authors. Although Sauer's work on the non-linear voltage divider was originally applied to the study of the non-linear behaviour of the electrode-electrolyte interface and biological tissues, it is stressed, however, that the work is applicable to a wide range of research areas.

Keywords

Non-linearity Harmonics Impedance Electrodes 

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References

  1. McAdams, E. T., andJossinet, J. (1991): ‘DC nonlinearity of the solid electrode-electrolyte interface impedance’,Innov. Tech. Biol. Med.,12–3, pp. 329–343Google Scholar
  2. McAdams, E. T., andJossinet, J. (1992): ‘A physical interpretation of Schwan's limit current of linearity’,Ann. Biomed. Eng.,20, pp. 307–319Google Scholar
  3. Moussavi, M., Schwan, H. P., andSun, H. H. (1994): ‘Harmonic distortion caused by electrode polarisation’,Med. and Biol. Eng. and Comput.,32, pp. 121–125Google Scholar
  4. Schwan, H. P. (1992): ‘Linear and nonlinear electrode polarization and biological material’,Ann. Biomed. Eng.,20, pp. 269–288Google Scholar
  5. Simpson, R. W., Berberian, J. G., andSchwan, H. P. (1980): ‘Nonlinear AC and DC polarization of platinum electrodes’,IEEE Trans. Biomed. Eng.,27, pp. 166–171Google Scholar

Copyright information

© IFMBE 2002

Authors and Affiliations

  1. 1.Bioengineering DepartmentUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Max Planck Institute for BiophysicsFrankfurt a.M.Germany
  3. 3.Northern Ireland Bio-Engineering CentreUniversity of Ulster at JordanstownN. IrelandUK
  4. 4.National Institute for Health & Medical ResearchINSERM U556LyonFrance

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