A detailed characterization and analysis of the acoustic field radiated by an active diffraction grating is presented. This is a spiral-shaped source of constant width of the spiral paths and spacing among them, built with flexible ferroelectrets, which is suitable to operate within a broad range of ultrasonic frequencies. The simultaneous airborne generation of multiple Bessel vortex beams with different topological charges along the propagation axis is thoroughly discussed in terms of the structure of the spiral source and the driving frequency, along with some technical details of the prototype. Finally, the quality of the experimentally generated Bessel vortices is discussed, including the phase structure and the amplitude of the acoustic pressure.