We propose a new practical analytical model to calculate the performance of amplitude-modulated systems, including semiconductor optical amplifiers (SOA). Lower and upper-performance bounds are given in terms of signal quality factor (Q) concerning the input signal pattern. The target is to provide a design tool for gain elements included in photonic integrated circuits (PIC) to compensate for their insertion loss. This subject is a critical issue, for example, in the arrays of optical transmitters with silicon photonics modulators used for interconnection applications. Due to implementation limitations, the design of an SOA embedded in a PIC is considerably different with respect to the use of SOAs as line amplifiers in optical networks. SOA amplified spontaneous emission (ASE) and gain saturation effects have been included in the model, together with the input signal extinction ratio and the receiver electrical filter. Each degradation effect provides its own contribution to the signal integrity in terms of signal-to-noise ratio (SNR) or inter-symbol interference (ISI). The model shows that the SOA operation at low extinction ratios, typical in optical interconnect applications, is substantially different from the operation at higher extinction ratios used in transport networks. The model is validated through numerical simulations and experiments. Finally, two examples are provided for dimensioning a PIC system and optimizing the SOA parameters.