E. V. Zakharov1, A. I. Skorodumov2, Yu. Ya. Kharlanov3
1 Lomonosov Moscow State University (Moscow, Russia)
2, 3 16th CSR-TI MoD of Russia (Mytishchi, Russia)

Investigations and optimization of the characteristics of lens antennas based on a multilayer spherical Luneberg lens have been carried out. The maximum value of the antenna gain is taken as the optimization criterion. The dependences of the antenna characteristics on the methods of dividing the lens into layers, the number of layers, the geometric dimensions of the lens, the losses in the dielectric and the radiation patterns of the irradiator have been obtained.

To conduct the research, a mathematical model of a lens antenna has been used. This model is based on a strict solution of the problem of diffraction of electromagnetic waves on a multilayer dielectric ball with losses at the arbitrary amplitude-phase distribution of the exciting field. The central place in the algorithm for the numerical solution of the problem is occupied by algorithms for solving systems of ordinary differential equations for radial functions. The specificity of the obtained systems is such that standard matrix run methods cannot be used directly to solve them. An analog of the counter nonmonotonic run method has been developed and implemented for a two-point vector system of equations the leading element selection by line.

Based on the research results, the following recommendations have been formulated for the optimal design of antennas with multilayer spherical Luneberg lenses:

the use of multilayer Luneberg lenses is most appropriate when it is necessary to achieve gain values of more than 42...45 dB, as well as in cases where it is necessary to ensure operation in a continuous frequency band with a width of more than 15...20%;

the advantages of multilayer Luneberg lenses in comparison with a two-layer lens of optimal design are realized when the values of losses in the dielectric are not exceed tgδj ≈ (2...5)∙10–4;

when the number of layers is more 15...20, the methods of dividing the lens into layers are similar in efficiency, with a smaller number of layers the best way of splitting is to ensure the same difference in the dielectric permittivity of neighboring layers;

if the maximum number of lens layers is less 30…50 which is real in practical implementation, for each value of tgδ for a given D/λ, there is an optimal number of layers, an increase beyond which is impractical.

Zakharov E.V., Skorodumov A.I., Kharlanov Yu.Ya. Antennas based on a multilayer spherical Luneberg lens: investigation and optimization of characteristics. Antennas. 2022. № 4. P. 46–58. DOI: https://doi.org/10.18127/j03209601-202204-05 (in Russian)

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