Shape Optimization of Rectangular Horns for Directivity Control in Finite Enclosures

Rectangular horns are essential components in professional audio systems where precise directivity control is important. Although a horn’s directivity is known to be influenced by its finite mounting enclosure, a shape-optimization method to improve directivity control under these realistic conditions has been lacking. To address this, an optimization method based on a hybrid model is developed. The model couples the mode-matching method for the internal sound field of the horn with the boundary element method to accurately compute the modal radiation impedance at the mouth. This provides the mode-matching method with a realistic boundary condition that fully accounts for the enclosure. The optimization method then employs this hybrid model within a gradient-based procedure to design a rectangular horn that maintains constant coverage angles in both horizontal and vertical planes over a wide frequency band. A physical prototype was manufactured, and its directivity measurements show good agreement with simulations, validating the proposed method as a predictive tool for high-performance horn design.