Time periodic EM fields in linear conducting media are usually determined by using time Fourier series of non-sinusoidal periodic waveforms. We present a method leading to a time periodic solution involving space eigenfunction expansion. For transient problems, the method leads to a very elegant form of the analytical solution. For time-periodic problems, if the space eigenfunctions can be easily determined, the method may be an interesting alternative to Fourier series decomposition, when the periodic excitation has a wide harmonic spectrum. The solution may be obtained as a product between a matrix depending only by the domain properties, and a matrix describing the coil current. These two approaches are complementary, the later one proving an accelerated convergence. An illustrative example concerning an aluminium cylindrical case for both sinusoidal and triangular waveform is included.

Keywords: Analytical method, Space eigenfunctions expansion, Eddy current problem