A design of broadband constant beam pattern transducers

Abstract

A constant beam pattern (CBP) transducer is an acoustic transducer, where its beam patterns are independent of frequency. The theory and numerical simulations for constant beam pattern transducer design are introduced. For a hemispherical design, if the radial velocity distribution on the surface of a conventional hemisphere transducer is a single complete Legendre polynomial, the far field angular beam pattern shows the same Legendre polynomial distribution for all frequencies above its cut-off frequency, based on spherical Hankel function asymptotic approximation to the solutions from Helmholtz wave equation. Because of orthogonality, Legendre polynomials form a complete set, per Sturm-Liouville theory that an arbitrary velocity shading function can be expanded by Legendre series. Each polynomial within this Legendre series contributes its share to the far field, such that the converging acoustic beam pattern displays the same shape as the original shading function itself. Numerical simulations with various samples include (cos(theta))^3 and Gaussian, a well as equal sidelobe suppression classic Dolph-Chebyshev functions used as shading and achievable as beam patterns for a broadband frequency range.