Modeling a Phased Array of Parametric Array Loudspeakers Using the Spherical Wave Expansion

Parametric array loudspeakers (PALs) that utilize the phased array technique are receiving considerable attention because of their ability to electronically control and manipulate highly directional audio beams with great flexibility. However, accurately modeling the phased array PAL poses significant challenges due to the complex nature of the nonlinear processes involved, which results in the demodulated audio sound generated by the array not simply being a superposition of that generated by each individual array element. In addition, the nonlinear interaction between the ultrasound generated by any two distinct elements creates a coupled audio sound component that also contributes to the total audio sound field. Based on the quasilinear solution of the Westervelt equation as well as the spherical wave expansion method, this paper proposed a computationally efficient and accurate method to include the coupled audio sound component. Both simulations and experiments for a uniform linear PAL array are conducted to validate the method. The proposed method paved the way for simulating and designing phased array PAL systems.