Optimal primary spectra for parametric transmitting arrays

Abstract

The use of more than two spectral components in the primary signal of a parametric endfire array is considered. Equations are developed for the spectra of N components which maximize the farfield SPL for shock-free primaries in dispersionless media. Effects of the variation of attenuation with frequency are shown to have a considerable influence on the shape of the optimal spectra. For the case of attenuation proportional to the square of the frequency, the optimal spectra are functions only of the downshift ratio R and the number of components N, and not functions of the absolute value of the frequencies. The optimal spectra and waveforms for several sets of R and N values are shown. It is found that a 3-dB increase over a two-component primary can be obtained with three or four components for a wide range of downshift ratios. At extremely high primary powers, an increased tendency toward shock formation may negate this gain. Beamwidths were found to be essentially unaffected. Subject Classification: 25.35; 60.10.