A semi-phenomenological wideband model is proposed for both the material gain and the gain coefficient of a multi-quantum well semiconductor optical amplifier (MQW-SOA). This analytical model is integrated in a SOA-dedicated simulation tool and validated experimentally over a wide range of bias currents, input powers and wavelengths. We demonstrate the ability of multi-electrode configurations to increase the saturation power of MQW-SOA without sacrificing either their noise figure or their optical gain bandwidth. A tri-electrode configuration permits to obtain an enhancement of the MQW-SOA output saturation power of more than 3 dB over 100 nm while maintaining its optical bandwidth (defined at -1 dB) at about 76 nm.