Optimum Directivity Patterns for Linear Point Arrays

Abstract

The sharpest major lobe of a directivity pattern due to a linear array of equally-spaced point elements is achieved when the elements are excited in such a manner that all minor lobes in the pattern have the same relative amplitude. Methods of producing such equal-minor-lobe patterns originally given in the radio literature by C. L. Dolph and by H. J. Riblet are summarized briefly in this paper. In particular, the synthesis method indicated by Riblet is described in general terms, and the effect of the element spacing is discussed in detail. Included in this discussion is the subject of super-directivity. Results of numerical calculations based on these methods are presented as families of curves showing the relationships existing among angular width of the major lobe, relative amplitude of the equal minor lobes, directivity index, and number and spacing of the elements in the array for 5–13 odd numbers of elements. In addition, the synthesis methods are extended to compensated, or steered, arrays.

A general superdirectivity model for arbitrary sensor arrays

“…Linear arrays for superdirectivity have been extensively investigated [11,24,[32][33][34][35][36]. An endfire linear array has been proven to possess the highest superdirectivity for a given number of sensors, and its DI approaches 20logN (dB) when the inter-sensor spacing becomes infinitely small [2,23], where N is the number of sensors.…”

The sound field in the Fresnel zone of an axially symmetric plane emitter with nonuniform vibrational velocity distribution

“…For comparison, the dotted curve represents the function Φ e (θ)2/(ka) corre sponding to homogeneous distribution of the normal vibrational velocity components on the piston. As is clear, an increase in vibrational velocity toward the periphery of the piston leads to escalation of the beam characteristic, whereas in the case of a linear antenna, a drop in vibrational velocity toward the periphery is required [8] (however, this opposition does not lead to a contradiction, since in the projection onto any pis ton diameter, the integral vibrational velocity on the piston tends to zero when the coordinates on this diameter tend toward its ends). The dashed dotted curve represents the function P(θ)R 0 /a at ka = 3, R 0 /a = 2, and F(x) 1; the dashed curve represents the function corresponding to the distribution F(x) = 1 + 0.6x.…”

Transducer array excitations for optimum difference patterns

“…It is not surprising, therefore, that there has been a certain amount of cross pollination between these two disciplines. Soon after the monumental paper of Dolph (1946), the Chebyshev synthesis method was more fully discussed in the acoustic context by Pritchard ( 1953 ), with mori• complete: performance data being made available through the parametric study conducted. Similarly, numerical optimization methods for transducer arrays (Winkler and Schwartz, 1971 ) have been considered in discussions on the use of such techniques for the analogous electromagnetic problems (Kurth, 1974).…”