In this work we study the factors affecting the linewidth of a swept laser source. A ring fiber laser source based on EDFA and a Fabry-Perort resonator is used for this purpose. With this setup a swept source with a linewidth of better than 0.1 nm is obtained over a tuning range of about 47 nm limited by the spectral gain of the EDFA amplifier used. The factors affecting the source linewidth are then examined by modeling the EFDA amplifier and the swept source and then compared to the practical measured results of an EDFA swept laser source. The measurements and simulations both show that the swept laser linewidth is about 10 times narrower than the Fabry-Perot filter 3dB linewidth.