In new generation of more electric aircrafts, dc-bus voltage is variable due to the variable speed generator. This implies constrains to design the actuator for the lowest dc voltage value. In case of permanent magnet synchronous machine (PMSM) starter supplied by a conventional power topology (LC input filter-voltage-source inverter), the torque constant should be low enough to ensure the controllability of the phase currents. This leads to increase rated current and so to oversize the inverter heat sink. In this paper, an optimal design procedure for a quasi-Z-source inverter with coupled inductors is presented for a PMSM starter application. This topology allows boosting the inverter input voltage at high speeds. Therefore, a motor with higher torque constant and lower rated current can be designed for this application. In addition, the input current ripple is canceled by a structural modification allowing a smaller input filter. The global optimization of the power conversion chain shows a whole volume reduction of 20% without decreasing the global efficiency compared to the conventional solution. Experimental results illustrate this conclusion and show the effectiveness of the proposed approach.