An amplified closed-Sagnac loop interferometric fiber optic gyroscope (AC-IFOG) has been proposed and demonstrated in our earlier work. This paper reports the theoretical analysis of its operation. The analysis has been focused on the effect of the erbium-doped fiber amplifier (EDFA) inserted within the reentrant path. The analysis shows that the sensitivity can be improved by at least two orders of magnitude as compared to a conventional IFOG if the EDFA is an ideal device. The simulated open-loop response coincides well with that of the experimental data. Further analysis shows that the detection limit is restricted by the beat noise that build ups rapidly in successive circulations. The rate of noise build-up depends greatly on the optical bandwidth of the closed-Sagnac loop.
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