Simulink model for EDFA dynamics applied to gain modulation

Bononi and Rusch (1998) developed an approach for investigating erbium-doped fiber amplifier (EDFA) dynamics based on the one-dimensional ordinary nonlinear differential equation derived by Sun et al. (1996) for the time-dependent population of excited-state erbium atoms in EDFAs. Bononi and Rusch then applied their approach to the investigation of transients (1998). In this paper, we implement the same nonlinear ordinary differential equation as a MATLAB Simulink model and we use harmonic and random-noise inputs to investigate gain modulation, referred to also as overmodulation. This is the low-frequency (~kHz) amplitude modulation of the EDFA pump and the communication signal used for propagating line monitoring information [(Freeman and Conradi, 1993), (Murakami et al., 1996), (Shimizu et al., 1993), (Gieske and Bystrowski, 2001)]. Freeman and Conradi (1993) showed that the EDFA transfer function from overmodulated pump to output communication signal was effectively a low-pass filter response. They also showed that the transfer function from overmodulated communication input signal to output signal was effectively a high-pass filter response similar to a lead compensator with one zero followed in frequency by one pole. They developed a numerical model (Freeman and Conradi, 1993) to predict the shape of these transfer functions and compared their predictions with experiment. However, their model was not sufficiently developed in Freeman and Conradi (1993) to be directly applicable to the design of line monitoring systems. Using a Simulink simulation of the nonlinear differential equation due to Sun et al. (1996) and using standard signal processing techniques for calculating the pump-to-signal and signal-to-signal transfer functions, we obtain the low-pass filter response to pump overmodulation and the high-pass filter response to signal overmodulation. We compare our results with experiment for a given set of EDFA parameters (Gieske and Bystrowski, 2001). Our approach is straightforward and easy to implement as a MATLAB Simulink model