An explicit analytical expression for the transmission of pump and sig
nal power through an erbium-doped fibre in the presence of background
loss is given. Because the solution is explicit, it can easily be fitt
ed to measurement results. This leads to a simple method for determini
ng the erbium absorption constant, saturation power and fibre backgrou
nd absorption constant. The technique is demonstrated for wavelengths
of the signal range.