**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.

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

From the sample capacitors impedance spectrum

the complex sample capacity

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

where C_{0} is the capacity of the empty electrodes
without sample material in between. If the electrodes are arranged parallel

where *A* denotes the area of one electrode, *d* the spacing
between the electrodes and *ε*_{0}=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)*.