Odd Mathieu Functions Application to Synthesize a Multi-element Radiator Flat-topped Radiation Pattern

The paper studies synthesizing capabilities of a flat-topped radiation pattern when using the expansion of the target radiation pattern into a series in terms of odd Mathieu functions. As parameters for comparing the target and synthesized radiation patterns, we used a main-lobe width at a level of -1 dB and an irregularity of the top of the main-lobe of the radiation pattern. The sector-shaped radiation pattern has been synthesized for linear radiators of various lengths. The convergence of the coefficients of the Mathieu series in the synthesis of the sector-shaped radiation pattern has been estimated. It is shown that the use of piecewise-linear approximation of the target radiation pattern in the synthesis using a series expansion into odd Mathieu functions allows us to improve the quality of the radiation pattern formed.The task that involved finding the amplitude-phase distribution for a linear emitter with a length of 3λ, 4λ and 5λ (λ is operation wavelength) for a target radiation pattern was solved. The target amplitude distribution has the following electrical characteristics: the main-lobe width is 37.5° at a level of -1 dB and the side lobe level (SLL) is -20 dB. The synthesis procedure was performed for two cases. In the first case, the target radiation pattern is represented by a piecewise constant function with a given width. In the second case, the target pattern was specified using piecewise linear approximation of the top and slopes of the main lobe.Comparison of the radiation patterns obtained shows that in the first case, the main-lobe width of the radiation pattern at a level of -1 dB is 34°, the SLL varies from -15.6 to -17 dB, and the irregularity of the main-lobe top of the radiation pattern lies within 0.9 ... 1.2 dB. In the second case, the main-lobe width of the antenna radiation pattern at a level of -1 dB is 36.5°, the SLL is -17.5 dB, and the irregularity of the main-lobe top is 0.4 dB at most. When used, the considered under consideration enables us to obtain both the synthesized patterns for linear radiators of various lengths, and the corresponding amplitude-phase distributions and coefficients of the Mathieu series. An estimate of the convergence of the Mathieu series shows that the use of linear approximation of the target radiation pattern in some cases allows up to 2.7-fold increase in acceleration of the convergence of the Mathieu series. The accuracy of reproducing the sector-shaped pattern by the synthesis method using the expansion into odd Mathieu functions gives good results when synthesizing the amplitude-phase distribution for the linear radiators with an electric length of 5λ or more.