Design manual for a constant beamwidth transducer
Abstract
The theory of a broadband constant beamwidth transducer (CBT) which is based on Legendre function amplitude shading of a spherical cap was described in a previous report, J. Acoust. Soc. Am. 64:3843 (1978). Theoretical calculations showed the CBT to have uniform acoustic loading, extremely low sidelobes, virtually no nearfield, an essentially constant beam pattern for all frequencies above a certain cutoff frequency, and a flat transmitting current response over a broad band for piezoelectric drive. In this report formulas suitable for the design of a CBT which is to be used as a transmitter and/or receiver are developed. The formulas involve simple algebraic and trigonometric expressions and can be readily evaluated using a pocket calculator. Formulas are developed for the required velocity distribution, limiting beam patterns, directivity index, equivalent twoway beam widths for volume and surface reverberation, shading coefficients for a stepwise implementation of the velocity distribution, size, ceramic mass, bandwidth, source level, transmitting voltage and current responses, and receiving voltage sensitivity. The report concludes with an example illustrating the procedure used to design a CBT with a specified  3 dB halfangle beam pattern, source level, and receiving voltage sensitivity.
 Publication:

Naval Research Lab. Report
 Pub Date:
 October 1979
 Bibcode:
 1979nrl..reptR....V
 Keywords:

 Beams (Radiation);
 Electrical Engineering;
 Manuals;
 Transducers;
 Acoustics;
 Legendre Functions;
 Piezoelectricity;
 Radiation Distribution;
 Velocity Distribution;
 Electronics and Electrical Engineering