A combination of asymptotic and numerical methods in calculating the characteristics of a convex quasi-periodic phased antenna array with account the interaction of elements of an arbitrary type

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Abstract

Approximate asymptotic expressions are obtained for the partial radiating elements pattern and the active reflection coefficient of a large-sized quasi-periodic convex phased array antenna (PAA), using as a basis the results of a numerical solution for the electromagnetic field in a single PAA cell under periodic boundary conditions on the lateral surface of the cell. These expressions can be used to create mathematical software for modelling such phased arrays, taking into account the interaction of radiating elements, based on a combination of direct numerical methods, such as the finite element method, to analyse the field in a single cell of the phased array with the calculation of the characteristics of the phased array as a whole using analytical asymptotic expressions. Numerical results of applying the method are presented for calculating the characteristics of multi-element spherical phased array of slot radiating elements and conical phased array of slot and director radiating elements.

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About the authors

M. V. Indenbom

All-Russian Research Institute of Radio Engineering

Author for correspondence.
Email: mindenbom@mail.ru
Russian Federation, st. Bolshaya Pochtovaya, 22, Moscow, 105082

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Supplementary files

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2. Fig. 1. Schematic representation of a convex phased array.

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3. Fig. 2. Single cell of a convex phased array.

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4. Fig. 3. Partial diagram of the axial slot element of a spherical phased array located at ϑₙ = 72.3°, in sections θ = 44.3° (a) and θ = 50° (b) for φ-polarization (1, 2) and θ-polarization (3, 4): 1, 3 – according to formula (32); 2, 4 – according to formula (32) at ResM = 0.

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5. Fig. 4. Partial diagram of the axial slot element of the spherical antenna array, located at ϑₙ = 72.3° (dᵩ = 0.986λ), for θ = 90° (a) and θ = 60° (b) for φ-polarization (1, 3, 5) and θ-polarization (2, 4, 6): 1, 2 – spatial wave (8); 3, 4 – asymptotics of integrals (32); 5, 6 – asymptotics and DFT (46).

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6. Fig. 5. Partial diagram of the azimuthal slot element of a conical antenna array at θ = 90° (a) and θ = 60° (b) for φ-polarization (1, 2) and θ-polarization (3, 4): 1, 2 – rigorous method; 3, 4 – asymptotics and DFT (46).

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7. Fig. 6. Partial diagram of the axial director radiator of a conical phased array with a triangular grid (section θ = 90°); aₙ = 11.5λ for φ-polarization (1, 2) and θ-polarization (3, 4): 1, 3 – spatial wave (8); 2, 4 – asymptotics and DFT (46).

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8. Fig. 7. Effective reflection coefficient of the conical phased array of axial director radiators at θ₀ = 90°: curve 1 – aₙ = 11.5λ (dᵩ = 1.2λ); curve 2 – aₙ = 9.2λ (dᵩ = λ).

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