A four sector compact superconducting cyclotron for light ion beams with a maximum energy of 250 MeV/amu has been studied. This cyclotron is mainly designed to accelerate H²⁺ ions to be extracted by stripping. Ions like C, O or Ne can also be accelerated and extracted by stripping. Extraction by stripping allows to overcome many problems, especially if a certain beam intensity is requested. The preliminary design model of the magnet circuit has been accomplished with the 3D electromagnetic code OPERA. The design of the main coils and of the cryostat has been investigated, too. The features of beam dynamics of this cyclotron, including extraction trajectories, will be presented. Several fields of application have been envisaged for this cyclotron, namely nuclear physics, therapy treatment, interdisciplinary research and radioisotope production using low or medium intensity beams.