M.V. Indenbom, V.A. Skuratov

 JSC “All-Russian Scientific Research Institute of Radio Engineering” (Moscow, Russia)

Half-sphere scanning may be realized by using a convex axisymmetric phased array antenna (PAA) on a surface of rotation (cone, sphere, paraboloid of revolution, etc.). PAA radiating elements are placed on the surface in a rectangular or triangular grid.

Interaction of elements for convex PAA has even more important role than for planar PAA. For an antenna array of small and medium sizes, the surface shape of which allows the wave equation to be solved by the method of separation of variables, the calculation of characteristics taking into account the interaction of elements can be performed using representation of the electromagnetic field in the outer region of the antenna as an expansion in eigenfunctions of the field equations. Based on the element-wise approach, using this representation, the mutual admittances of the slots can be calculated, the voltages in the slots can be determined, and then the far field of the antenna array and the amplitudes of the reflected waves at the inputs of the radiated elements can be found.

However, with an increase in the number of array elements, the dimension of the matrix of mutual admittances increases, as a result of which the counting time of its elements and the inversion of the matrix grow rapidly. The size of the matrices can be radically reduced due to the axial symmetry of the antenna array using the modal approach used in the present work to analyze an arbitrary axisymmetric antenna array of slot radiators with matching input networks. The calculated ratios are specified for antenna arrays of axial and azimuthal slots on the surface of a sphere and a cone.

The distribution of the electric field in the slots was initially assumed to be known in shape (“single-mode” radiators). The complex field amplitude in the gaps was found using the matrix of mutual admittances, which is equivalent to using the well-known method of induced magnetomotive forces. For “single-mode” slotted radiators, the admittances matrix is presented as a linear combination (sum) with the known coefficients of modal matrices. The number of members of the sum is equal to the number of elements in the antenna array ring. Using this representation, the antenna array scattering matrix at the inputs of matching four-terminal devices located at the input of the elements is similarly obtained as the sum of modal scattering matrices. Since the size of the admittance and scattering matrices of the antenna array is equal to the number of elements of the entire antenna array, and the size of the modal matrices is equal to the number of rings of elements, the modal representation can significantly reduce the dimension of matrix operations.

The arbitrary element pattern and the antenna array pattern is presented in the form of the Fourier series in azimuthal harmonics, the coefficients of which are expressed through the radiation patterns of the harmonics of the circular filaments of the magnetic current on the surface of the antenna and the voltages in the slots under modal excitations, which are obtained using matrix operations from modal admittance matrices.

Using the obtained relations, elements pattern of axial and azimuthal slot radiators in spherical and conical antenna arrays containing from several tens to almost a thousand of elements are calculated in the single-mode approximation (with the cosine field distribution in the slots).

Indenbom M.V., Skuratov V.A. Modal approach to the method of calculating axisymmetric array antennas taking into account interaction of slot elements based on the electromagnetic field expansion in terms of the eigenfunctions of the outer region of the antenna surface. Radiotekhnika. 2021. V. 85. № 5. P. 117−131. DOI: https://doi.org/10.18127/j00338486-202105-11 (In Russian)

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