Yu. V. Yukhanov – Dr.Sc. (Eng.), Professor, Chief Research Scientist,

Head of Department of Antennas and Radio Transmitting Devices, Southern Federal University (Taganrog) E-mail: yu_yukhanov@mail.ru

T. Yu. Privalova – Ph.D. (Phys.-Math.), Associate Professor,

Department of General Physics, Southern Federal University (Rostov-on-Don)

E-mail: tatyana.privalova@gmail.com

E. V. Kryuk – Post-graduate Student,

Department of Antennas and Radio Transmitting Devices, Southern Federal University (Taganrog) E-mail: evkryuk@sfedu.ru

F. S. Topalov – Post-graduate Student,

Department of Antennas and Radio Transmitting Devices, Southern Federal University (Taganrog) E-mail: fzzavod@yandex.ru

I. V. Merglodov – Ph.D. (Eng.), Assistant,

Department of Antennas and Radio Transmitting Devices, Southern Federal University (Taganrog)

E-mail: ivmerglodov@sfedu.ru

The paper considers solution of a two-dimensional problem of diffraction of a plane wave on a waveguide Van Atta array, located on the surface of a circular perfectly conducting cylinder. Radiators in the form of slots on the surface of the cylinder are connected by plane-parallel waveguides of equal length. The problem is reduced to the Fredholm integral equations system of the first kind with respect to E-field vector in the apertures of the radiators. When calculating the auxiliary field, it was assumed that its source is in the presence of perfectly conducting cylinder (a cylinder on the surface of which the investigated Van Atta array is located).

The solution is obtained approximately under the assumption that only the main type of wave is excited in the waveguides, the radiators do not interact through the outer space, that is, the connection between the apertures is carried out only through the connecting waveguides. The curvature of the waveguides was not taken into account; it was assumed that they are straight. Thanks to the assumptions made, the system of integral equations has been reduced to the systems of second-order linear algebraic equations. Their number is equal to the number of pairs of radiators in the array. When calculating the kernel of equations, its asymptotics was used. The expressions for the E-field vectors in the apertures were found in the explicit form through the radiation pattern of the radiators. Approximate expressions have been obtained for the scattering diagram of the array, which in this case could be represented as the sum of the antenna component and structural component. The accuracy of the obtained formulas was estimated by comparing approximate results with an exact solution to the problem of plane wave scattering on a single-element Van Atta array obtained using the Ansoft HFSS package for different aperture sizes (kb = 1; 3; 6) of waveguides on electric radius cylinders ka = 20 and 40. It has been shown that for kb= 3, the discrepancy between the exact and approximate calculations of the DOR does not exceed 6 dB for a cylinder with ka = 20 and 1 dB for a cylinder with ka = 40. For kb = 1 an error of 10–25 dB is caused by the inaccuracy of the asymptotics of the kernel of integral equations, and for kb = 6 it is caused by occurrences of higher-type waves in connecting waveguides which are not taken into account in the approximate formulas.

Monostatic backscattering diagrams of the Van Atta array with different number of M pairs of radiators located on cylinders of various electrical sizes for different sizes of apertures and lengths of connecting waveguides have been calculated. The backscattering diagrams of arrays with path lengths that provide the in-phase addition of scattering fields of all pairs in array have been defined. In this case, the reflected field has the maximum possible RCS value, but its angular width has the same value as one pair of radiators (as with the Van Atta array). The influence of the cylinder curvature and the number of array radiators with the same length of waveguides on the width of the main lobe of backscattering diagram has been investigated. The optimal relations between the structural parameters of the array and the cylinder dimensions have been found by the criterion of the maximum RCS level and its width. It has been shown that for each of the cylinders there is a certain number of array elements, at which its backscattering diagram has the widest angular sector at an acceptable level of RCS reduction. In all the cases considered, this array has an angular sector on the cylinder corresponding to the first Fresnel zone.

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