Cole–Cole equation

The Cole -Cole diagram (also: Cole -Cole circle or Cole -Cole plot) presents complex material parameters such as the impedance or permittivity of dielectric materials, as a locus in the Gaussian plane as a function of frequency is (see also: Vector diagram ). Thus, it has similarity to the (few years later designed as a tool for RF technology ) Smith chart. The name of the Cole -Cole diagram is derived from the two brothers, Kenneth S. Cole and Robert H. Cole, who performed around 1931 experimental studies on the impedance of biological tissue.

Features and Significance

A typical Cole -Cole diagram describes a semi- circle whose center lies on the real axis ( see picture). On the abscissa of the Cole-Cole plot of the real part of the relative permittivity ( dielectric constant ) and the ordinate represents its negative imaginary part ( dielectric loss ) is read.

The relative permittivity of materials depends on the temperature and the frequency. The frequency dependency can be represented as a Cole-Cole diagram according to the following relationship, where the angular frequency, and j is the imaginary unit.

As locus results in approximately a semicircle, whose position and size of four parameters depends which have approximately the following values ​​for the sample of water at room temperature or dielectrically very similar muscle tissue:

  • The static dielectric constant, which is the relative permittivity of the dielectric at the frequency 0 Hz
  • The permittivity at very high frequencies
  • The relaxation time constant
  • The Cole exponent, it is for muscle tissue and water

The Cole -Cole diagram can be found in some important characteristic parameters of the investigated dielectric. Serve this purpose the Cole exponent, the relaxation time or its reciprocal value. Cole -Cole circuit has two real points of intersection with the abscissa. At the resonance frequency, the locus is at its maximum. In the picture ( above) the locus of the relative permittivity of water for the temperature is 0 ° C shown. At this temperature and.

Electrical impedance RF engineering Properties of water Resonant frequency Datasheet Agilent Technologies Digital Object Identifier
196569
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