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Frequency Domain Measurement

The purpose is to measure the complex permittivity spectra ε*(ω) and conductivity spectra σ*(ω) of a sample material. The material may be solid or liquid and is usually placed between two electrodes which form a capacitor. 

measurement principle
Fig. 1: Principle of a frequency domain dielectric and conductivity measurement.

For compact formulas, complex notation is used and indicated by the asterisk.

From the sample capacitors impedance spectrum

Definition of Impedance

the complex sample capacity

Sample Capacity

is calculated. C*(ω) is directly related to the permittivity spectrum

Permittivity Spectrum

where C0 is the capacity of the empty electrodes without sample material in between. If the electrodes are arranged parallel

Empty Cell Capacity

where A denotes the area of one electrode, d the spacing between the electrodes and ε0=8.854*10-12 As/Vm is the vacuum permittivity. It should be noted that ε*(ω) generally includes a permittivity contribution from molecular dipoles and a conductivity contribution from free charge carriers. The same applies to the conductivity spectrum which is another representation of ε*(ω), i.e.,


The term −1 takes the charge contribution of the empty electrodes (vacuum permittivity)  into acount, resulting in ε*(ω) = 1 and σ*(ω) = 0 for the vacuum. Refer to Dielectric Spectroscopy and Impedance Spectroscopy of Materials for details and typical properties of ε*(ω) and σ*(ω).