The theoretical model for erbium-dc^ed phosphate glass waveguide amplifiers pumped at 980 nm wavelength is studied in this paper. This model is usually simplified as two models with upconversion and without upconversion. The comparison study of the two simplified models is carried out by the effect of erbium-doped concentration on amplifier gain. Numerical results demonstrate that when the erbium-doped concentration is less than 10^{26} m-3 the upconversion may be neglected or upconversion may be considered.