Novel engineered step-chirped gratings (SCG) for broadband frequency converters based on quasi-phase matched second harmonic generation in MgO-doped lithium niobate waveguides have been theoretically modeled and simulated. It is shown mathematically that engineered apodized gratings can flatten the efficiency response. Also, it is verified that the bandwidth and flatness of an apodized SCG can be improved extensively with decreasing the number of segments and increasing the apodization ratio, respectively. Further, we show enhancing the minimum width of the line of the gratings to 1 micron for easing fabrication, almost all the beneficial effect on the efficiency response of an apodized SCG are maintained. The possibility of increasing the width of the poled lines and the increase in the chirp step due to use of the SCG structure, may provide more convenient route for fabrication and poling.