Debye Models, Three Ideal Components

Usually the two-component circuit is too simple to mimic with sufficient precision the frequency dependence of the variables measured. The three-component model combines features of both the series and parallel models. It may consist of two capacitors and one resistor (dielectrics with bound electric charges) or two resistors and one capacitor (conductors with free charge carriers). Detailed equations can be found in Section 12.2. 

The parallel version is best characterized by admittance because the time constant then is uniquely defined (Section 12.2). It has been used for cells and living tissue, with C for cell membranes, R for intracellular, and G for extracellular liquids. 

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Electrical circuits with lumped components are often used as models mimicking the electrical properties of tissue. The simplest models are with three components. If all components are ideal (not frequency-dependent values), the model is a Debye model. 

The similarity between the spectra of a model with just three components and a complex material such as tissue is of course limited. The first step of refinement is often to replace an ideal capacitor found in the Debye models of Figures 10.3 and 10.4 with a CPE. They are then called Cole impedance models (Cole 1940) and Cole-Cole permittivity models (Cole and Cole 1941). 

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