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A general time-domain transfer matrix model is presented which is able to handle waves perturbed by a locally uniform medium and which is particularly well adapted to equivalent circuit implementations. We use this model for the simulation of a picosecond pulse propagating through a semiconductor optical amplifier (SOA). The signal propagation through the SOA is described by an envelope propagation equation, taking into account the optical carrier's wavelength evolution (modulated wavelenght division multiplexing spectrum consideration). We present the SOA equivalent circuit and its implementation under a commercially available software. The SOA is described through the wideband definition of all parameters which makes it comparable to a real component. Simulations have been validated with experimental results over at least 60 nm. We simulate both amplitude and phase evolutions of a picosecond pulse and a continuous-wave probe at various pulse's optical carrier wavelengths. We show a strong influence of the imaginary part of the complex time delay on the phase variations, and as a consequence on the additional spectral red or blue shift.