This paper presents a conceptual design of the compact SC230 superconducting cyclotron that accelerates a beam of protons to 230 MeV and is intended for proton therapy and biomedical research. SC230 is an isochronous four-sector cyclotron based on a shell-type magnet with a magnetic field in the center of 1.7 T. Superconducting coils will be enclosed in a cryostat; all other parts of the cyclotron are warm. Acceleration is carried out at the fourth harmonic mode of the accelerating high-frequency (HF) system consisting of four resonators located in the cyclotron valleys. The accelerator employs an internal Penning-type hot cathode source. Extraction is carried out using an electrostatic deflector located in the gap between the sectors and two passive magnetic channels.