A general model for an irreversible solar-driven Brayton multi-step heat engine is presented. The model incorporates a regenerator, an arbitrary number of turbines (Nt) and compressors (Nc) and the corresponding reheating and intercooling pro cesses; thus the solar-driven Ericsson cycle is a particular case where NtNc . For the so lar collector we assume linear heat losses and for the Brayton multi-step cycle irreversibilities arising from the non-ideal behavior of turbines and com pressors, pressure drops in the heat input and heat release, heat leakage through the plant to the sur roundings, and non-ideal couplings of the working uid with the external heat reservoirs. We obtain the collector temperatures at which maximum over all e ciency max is reached as a function of the thermal plant pressure ratio and a detailed com parison for several plant con gurations is given.