We present here a detailed investigation of a commercial-core Erbium-doped fiber-based femtosecond laser optical frequency comb equipped with an intra-cavity Electro-Optics modulator. This device allows rapid feed-back on the laser's repetition rate, enabling reaching the narrow-linewidth regime when locked to a ultra-high spectral purity optical continuous wave reference. Our study makes use of transfer functions analysis to characterize the laser dynamic response and the residual unavoidable cross talks. In a second part, we also present some results which show how to combine the signals from two photodetector to obtain a very low amplitude-phase conversion detection of the repetition rate, which is very useful in the context of low phase noise microwave generation with optical frequency combs.