# Time Domain Measurement

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

At time *t=0*, voltage step from 0 V to *U _{0}* is applied to the sample capacitor. The response current

*I(t)*is measured as a function of time. From this, the time dependent capacity is calculated from

It is directly related to the time dependent permittivity function by

where *C _{0}* is the
capacity of the empty electrodes without sample material in between. If the
electrodes are arranged in 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(t)* generally contains a permittivity contribution from molecular dipoles and a conductivity contribution from free charge carriers. The same
applies to the time dependent conductivity function, which is another
representation of ε(t)

The delta function *δ(t)* takes the current peak of the empty electrodes (vacuum permittivity) at t=0 into acount, resulting in *ε(t)*
= 1 and *σ(t)* = 0 for the vacuum. Refer to Dielectric Spectroscopy and Impedance Spectroscopy of Materials for details
and typical properties of *ε(t)* and *σ(t)*.