In this paper new magnitudes for DC side capacitors’ voltages of a multi level voltage source inverter (MLVSI) are presented. Using these magnitudes of DC side capacitors voltages allow generation of steps of AC output voltage by cascade connection of only N single-phase full bridge inverter (FBI). This subject has resulted in almost sinusoidal output voltage waveform. Approximated equal area pulse amplitude modulation (AEAPAM) technique is used to calculate the duration of each step of voltage, which has resulted in reduction of complexity of control circuit. A simple closed-loop controller is developed for controlling the voltages of DC side capacitors. Harmonic analysis and capacitor calculations are presented, too. Simulation results have been used to verify the overall operation of the proposed MLVSI in feeding a R-L load with a stepped sinusoidal waveform.