The high conversion efficiency broadband broadband second harmonic generation (SHG) in the wavelength range of 1.06～1.08 μm can be achieved in the aperiodic optical superlattice (AOS),and the AOS was designed by simulated annealing algorithm under undepletion pump approximation (UPA).The applicability of error function proposed in a published literature for broadband SHG in AOS structure is investigated.Error function proposed in a published literature can well estimate application range of UPA in SHG and is only related to the conversion efficiency of SHG.The results show that error function curves presented in a published literature are not suitable for broadband SHG because the structure of broadband SHG can not reach good quasi phase matiching (QPM).Only under the condition of perfect QPM,error function curves presented in a published literature can completely be suitable for broadband SHG.Furthermore,error function is related to the conversion efficiency of SHG and is also related to the wavelength of incident fundamental wave.