Beampattern design for the parametric array loudspeaker using mixed Gaussian directivity method

The parametric array loudspeaker (PAL) uses an array of ultrasonic transducers to transmit inaudible ultrasonic frequencies into air, in order for an audible difference frequency to be produced by the parametric acoustic array effect. The PAL is advantageous in possessing a much narrower sound beam as compared to the conventional loudspeaker with the same size. The beampattern of the PAL is described by the convolution model that the directivity of the difference frequency is calculated by the convolution between the Westervelt's directivity and the product directivity of the ultrasonic frequencies. Previous beampattern design methods of the PAL have failed to consider the effect of the Westervelt's directivity. This paper proposes to use the mixed Gaussian directivity method to approximate the Westervelt's directivity, such that the convolution model can be analytically decomposed into solvable equations. A beampattern design method is therefore established and then validated by k-wave numerical simulations.