Synthesising a Fixed-Length Equispaced Linear Array to Produce Dolph–Chebyshev Patterns with Deep Nulls, a Desired Side Lobe Level and Different Beamwidths

A method for the synthesis of equally spaced antenna arrays based on the extension of the Orchard-Elliott-Stern technique to radiation patterns with three roots on the negative real axis of the Shelkunoff unit circle is presented. One of these roots is placed on the unit circle and the other two are off the unit circle with coordinates <i>r</i> and 1/r. For a desired side lobe level (SLL), the synthesis of patterns with these roots allows for a multiplicity of solutions with different amplitude ratios, obtained by varying the value of r, each of which presents radiation patterns with different beamwidths and directivity, but with two fewer side lobes than the patterns obtained without these restrictions in the roots. The technique has been thoroughly applied to Dolph-Chebyshev patterns of 10, 18 and 40 elements, with a λ/2 spacing and an SLL that guarantees maximum directivity in both cases. This approach ensures the study of examples of all sizes, from small to large. The findings derived from this technique would be applicable in the domain of wireless communications, where the necessity arises for radiation patterns that exhibit low SLL and adaptive beamwidth.