# 28.5: Measurement of Polarisation

Polarisation may be defined as:

$P = \frac{Q}{A}$

where Q is the charge developed on the plates (Coulombs) and A is the area of the plates (m2).

A good ferroelectric has 10 μC cm-2 < P < 100 μC cm-2.

We can measure the polarisation by using the classic Sawyer-Tower circuit:

In this experiment, the voltage is cycled by the signal generator. Its direction is reversed at high frequency, and the voltage across the reference capacitor is measured. The charge on the capacitor must be the same as the charge over the ferroelectric capacitor, as they are in series. This means the charge on the ferroelectric can be found by:

$Q = C * V$

where C is the capacitance of the reference capacitor, and V is the voltage measured over this capacitor. We can therefore represent the polarisation of a material in an oscillating electric field, by plotting the voltage applied to the material on the x-axis of the oscilloscope, and the surface charge on the y-axis. This can be done because the capacitance of the reference capacitor is much higher than the capacitance of the ferroelectric, so most of the voltage lies over the ferroelectric. It is only possible to measure P by cycling the polarisation through cycling the voltage across the ferroelectric. We cannot measure absolute values instantaneously , but can deduce absolute values from the changes measured when cycling the polarisation.