We present a small-signal model of the multiple quantum well (MQW) reflective semiconductor optical amplifier (RSOA) with the accompanying parasitic circuit, followed by a numerical simulation of its modulation response. We analyze the corresponding -3dB bandwidth's dependence on the bias current, optical power of the input signal and the RSOA's active region length. Material, electrical and optical parameters, and the overall design of MQW RSOA, are derived bottom-up from the fundamental principles. It is shown that the modulation response, resulting from either intrinsic or parasitic-like model (including transport effects), usually provides high -3dB bandwidth, which is clamped by the chip's parasitics, leading to a relatively poor external modulation bandwidth. This issue can be overcome by an advanced design of the RSOA structure, as the one proposed in this paper and with the optimized bonding, which may improve the external modulation bandwidth significantly through the inductive peaking effect (IPE). Moreover, IPE's efficiency increases if the intrinsic or parasitic-like modulation bandwidth is in the proximity of the parasitic circuit resonant frequency.