The distributed feedback (DFB) laser is widely used in sensing because of its portable size, simple fabrication and high sensitivity. Most theoretical design models are based on passive Bragg gratings. However, passive grating models cannot be used to predict sensor performance using the important indicator of figure of merit (FOM) through theoretical calculations. To solve this problem, we replaced the passive grating with an active grating by using the imaginary part of the coupling constant that represents the value of the gain. As a comparison, the influence of the full width at half maximum (FWHM) and sensitivity were analyzed for different grating duty cycles and depths in the passive grating sensors. To obtain a higher FOM in the active grating sensors, we systematically investigated the effects of duty cycle and gain value through numerical simulations. We found that the redshift caused by a duty cycle increase can improve the sensitivity of biomolecule detection by 1.7 times.