In this Master's thesis the possibility of a multi-stage design of a centrifugal compressor for high rotational speeds and low flow rates, was examined by aerodynamic and thermodynamic analysis of airflow. The main part of the calculation of the airflow through the compressor was carried out using the finite volume method in commercial package Ansys Fluent, while the geometric domain was discretized with a unstructured Cartesian mesh, constructed in the CF-MESH+ tool, that is based on inside-out method. Calculation and dimensioning of individual components of the compressor was carried out in the programming language Python. The reconstruction of the precharger compressor is actually a reverse engineering process, but with the use of standard methods for designing rotor blades. The return channel and stator vanes are dimensioned according to recommendations from the literature, and with the aim of reducing losses as much as possible. By comparing the results of the simulations, it was shown that the addition of a return channel does not result in a large stagnation pressure and efficiency drop compared to the single-stage configuration with spiral volute.