Abstract: In this paper, neglecting amplified spontaneous emission(ASE) and upconversion process, the rate equation for Erbium-Doped Waveguide amplifiers (EDWA's) pumped with 980 nm wavelength is studied using overlapping factors method, and an analytical implicit gain solution is derived. Based on which an analytical threshold expression of pumping power is also obtained. Effects of overlapping factors on the gain and pumping threshold power are discussed in detail.