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We present an experimental and theoretical investigation into the low-frequency intensity noise characteristics of erbium-doped distributed feedback (DFB) fiber lasers. The intensity noise characteristics of six nonidentical erbium-doped DFB fiber lasers are presented along with the characteristics of the grating and doped fibers. An analytical model has been used to predict the intensity noise generated in a linear fiber laser and explain the observed noise characteristics. Overall we find good agreement between our analytical model and observations. In particular, we find the intensity noise at frequencies close to the relaxation oscillation frequency significantly elevated due to excess noise from either spontaneous emission or cavity loss modulation. These results can be used to optimize the fiber laser design for sensor applications.