A theoretical threshold model based on the spherical wave assumption for a pulsed double-pass pumped singly resonant confocal positive-branch unstable optical parametric oscillator (OPO) has been proposed. It is demonstrated that this model is also applicable to the plane-parallel resonator in the special case. The OPO threshold as a function of important parameters such as the cavity magnification factor, cavity physical length, crystal length, pump pulsewidth, output coupler reflectance and crystal position inside the resonator has been presented. Experimental data show the good agreement with the results obtained from the theoretical model.