Electromagnetic coils are ubiquitously used in the modern world in motors, antennas, etc. In many applications (magnetic field coil calibration and nuclear magnetic resonance spectroscopy and imaging) there is a strong need for a homogeneous magnetic field. In this paper, we propose a simple modelling based on serial Fourier decomposition allowing the determination of the electrical conductor distribution to make the magnetic field homogeneous. The method is valid both for plane and axisymmetric geometries. The method allows the retrieval of the classical configurations of saddle coil for the plane geometry and Helmholtz coil for the axisymmetric one. The method is generalized for any number of electrical conductors and brings the perspective of new homogeneous magnetic resonance imaging (MRI) coil configuration.