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Figures 8(a) and 8(b) depict 3D model of gain and directivity pattern. From all these, it is clear that the proposed design exhibits a reasonably high gain of around 27.3 dB at the frequency of 2.4 GHz with the beamwidth of 7.5 degrees at phi = 0 degrees.
Directivity pattern is one of the most important characteristics of the speaker in the design process which is defined based on the required SPL distribution from the customer.
Figure 7(a) shows the directivity pattern of the sectorized array with the conical reflector in the 360[degrees] configuration obtained by operating each element of the array in pulseecho mode (using the 5077 PR) and measuring the peak to peak amplitude of the echo originated by a 20 mm cylindrical reflector located at 200 mm away from the transducer/conical reflector axis.
The proposed method is based on the optimization of the array geometry in order to obtain a high directivity pattern. This optimization is performed by means of the PSO tool of program FEKO that takes into account the mutual coupling between all the parasitic and active elements as well as the presence of the dielectric substrate.
Although efficiency is not directly considered in this paper, the efficiency pattern will be equivalent to directivity pattern since the distance between the array elements is half-wavelength.
The aperture-power normalized directivity pattern of an electrically large aperture (with narrow beamwidth), for sum or difference in general, is thereby approximated by [[absolute value of [T.sup.norm]].sup.2]/[P.sup.norm.sub.ap], the squared magnitude of the area-normalized space factor divided by the area-normalized aperture power.
3-D directivity pattern at 2.4 GHz of the elliptical patch antenna, shown in Fig.
For instance, the approach in [8] provides a Convex Programming (CP) procedure for the synthesis of continuous aperture sources realizing a circularly-symmetric directivity pattern fulfilling the requirements represented in Fig.

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