We theoretically study the temporal dynamics of a semiconductor optical amplifier (SOA) based double-stage wavelength converter in co-propagative configuration. The impact of the SOA number in the device is analyzed. In this work, we are concerned with the gain recovery time shortening while keeping a low level of noise. We also study the pump and probe power influence on a 10 Gbit/s NRZ sequence output extinction ratio and undertake a systematic study when varying the input extinction ratio.