Based on the microstructure and the domain reversal behavior of ferroelectric thin films

the ferroelectric domains are abstracted as a cluster of dipoles.Each dipole has self-independent coercive field

and the complicated mechanism of their polarization switching under random signal is considerably facilitated by a geometric interpretation.Then

we introduce the concept of polarization switching function to represent the relation between the macroscopical polarization and electric field.The polarization switching function also help to simply the computation and avoid the enhanced errors from the differentiations of experimental data.A model based on polarization reversal function is developed

which has explicit physical background and concise mathematical formalism.