Analysis on acoustic directivity of spherical cap transducers

In order to study acoustic radiation from the spherical cap transducer, a theoretical model was used by solving the wave equation in spherical coordinates using the method of separation of variables, based on the spherical harmonic Fourier transform and boundary condition. The calculation formulas for far field radiated pressure and directivity of spherical cap are derived. Some theoretical results are presented in the form of far-field directivity patterns of the spherical cap transducer for various polar angle of spherical cap, radius of sphere baffle and operating frequency. Tile diameter of sphere baffle and wavelength in the media determine the directivity of acoustic radiation from a spherical cap. When the frequency is low or the wavelength is longer than the diameter of the sphere baffle, the acoustic radiation from a spherical cap is omnidirectional. With the increasing of the frequency or the diameter of the sphere baffle, the acoustic radiation from a spherical cap is more directional and the beamwidth more tends to spherical cap angle, furthermore the ripple in the beam is more obvious. Finally, the high frequency spherical cap transducer was fabricated and the directivity pattern were tested. As a result, the measurement data coincides with the theoretical calculation results and at the same time it verifies the correctness of theoretical formulas. This research can provide a guideline for designing the spherical cap transducers and arrays.