Formulations in AC conduction
AC conduction analysis is the study of electric field, current and losses arising in conductors and imperfect (lossy) dielectrics from the application of an alternating (AC) voltage or external current to electrodes. Similar to problems of AC magnetics, variation of the field with respect to time is assumed to be sinusoidal.
Complex arithmetic is used to represent harmonic time-dependency. The problem formulation combines equations for Electrostatics (∇·εE = ρ) and DC conduction (∇·j = -iω/σ), taking into account the Ohm's law, j = σE. Final equation with respect to electric potential U is
∇( [ε - i·σ/ω] ∇U ) = 0
where electric conductivity σ and components of electric permittivity tensor εz and εy (εz and εr) are constants within each block of the model.