The design of broadband constant beamwidth and constant beam pattern transducers

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The broadband constant beamwidth (CBT) and the constant beam pattern (CBP) transducers attracted much attentions, because of their main lobes or even the whole beam patterns (CBP case) are independent of frequencies. For a spherical (or hemispherical) design, the far field angular beam patterns are the same as the normal directional radial particle velocity, or shading, distribution on the surface of the spherical transducer, if the ka product for the wave number and the sphere radius is greater than one, per spherical Hankel function asymptotic approximation to the solution of the Helmholtz wave equation. Any arbitrary velocity shading functions can be expanded by series of Legendre polynomials for optimization beamwidth and sidelobe levels. This paper introduced a new transducer or array design, where the methodology by CBP is employed, while the geometry of CBT spherical cap is applied, such that the shading functions are no longer confined by only one Legendre polynomial P(cos(θ)) of the CBT case. Here, the shading examples by various Legendre polynomials of P(z0*cos(θ)) and the classic Dolph-Chebyshev T(z1*cos(θ)) of different orders have been successfully simulated, where the z0 and the z1 are the design control parameters of the beams.