Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 9

Full text in Russian (pdf)

Russian page


DOI https://doi.org/10.30898/1684-1719.2020.9.2

UDC 621.396.677




M. V. Indenbom

All-Russian Scientific Research Institute of Radio Engineering, 105082, Moscow, Bolshaya Pochtovaya, 22, Moscow 105082, Russia


 The article is received on August 20, 2020


Abstract. In this paper, axisymmetric spherical phased array antennas (SPAA) for circle wide-angle electric scanning are explored. Slot radiators of SPAA are placed in rectangular or triangular grid on shifted on equal angle meridians with equal distances between slots and have impedance matching networks in its inputs.

Earlier developed by author asymptotic method for analysing quasi-periodic convex antenna array with interaction of the slot elements is used to study axisymmetric SPAA. It is applicable because unit cell form and sizes are slow functions of point on SPAA surface. In the paper, relationships of asymptotic method were further developed. Integral equation for distribution of slots voltages on SPAA surface were got and studied. The element patterns (in array environment) for large sphere radius are presented as Fourie series with asymptotic expression for coefficients. The simple asymptotic expressions for calculation of reflected waves in element inputs were also deduce in case of narrow-directed radiation. Numerical calculations of obtained asymptotic solutions were carried out. Good agreement with results obtained by strict method of eigenfunctions is established for SPAA with about 4λ radius. As a result of calculations, the practical applicability of a simple approximate solution is shown, for which the solution of the integral equation for the voltage distribution over the surface of the antenna array is not required. The characteristics of large sized SPAA with a radius of 13,5λ and a number of elements of about 104 are numerically studied. It is shown that the spherical PAR of the axial slots provides circular wide-angle scanning up to the hemisphere. In this case, the loss of the gain and EIRP when the beam is deflected by the elevation angle of 85º is about 4 dB (with a distance between the elements within half the wavelength).

Key words: spherical axisymmetric phased antenna array, slot elements interaction, asymptotic methods, wide-angle scanning, radiation pattern, realized gain, reflection waves, scattering matrix.


1. Voskresensky D.I., Ponomarev L.I., Filippov V.S. Vypuklyye skaniruyushchiye antenny [Convex scanning antennas]. Moscow, Sovetskoye Radio Publ. 1978. 304 p. (In Russian)

2. Indenbom M.V., Skuratov S.A. Modal approach in the method of calculating axisymmetric antenna arrays taking into account the interaction of slot radiators based on the decomposition of the electromagnetic field in terms of the eigenfunctions of the external area of ​​the antenna surface. Antenny - Antennas. 2020. No.4. (In Russian)

3. Indenbom M.V. Antennyye reshetki podvizhnykh obzornykh RLS. Teoriya, raschet, konstruktsii [Antenna arrays of mobile surveillance radars. Theory, calculation, designs]. Moscow, Radiotekhnika Publ. 2015. 416 p. (In Russian)

4. Indenbom M.V. Effects of mutual coupling of slot emitters in a convex quasi-periodic phased antenna array of large electrical size. Antenny - Antennas. 2017. No.3 (235). P.3-23. (In Russian)

5. Indenbom M.V. Asymptotic method for calculating the radiation pattern of a convex axisymmetric antenna array taking into account the interaction of slot radiators. Antenny - Antennas. 2018. No.1(245). P.9-22. (In Russian)

6. Amitei N., Galindo V., Wu Ch. Theory and analysis of phased array antennas. Wiley-Interscience. 1972. 443 p.

7. Verlan A.F., Sizikov V.S. Integral'nyye uravneniya: Metody, algoritmy, programmy. Spravochnoye posobiye [Integral equations: Methods, algorithms, programs. Reference manual]. Kiev, Naukova Dumka Publ. 1986. 544 p. (In Russian)

8. Indenbom M.V., Kurochkin N.Yu. Ring antenna arrays with maximum potential and multi-lobe directional pattern. Antenny - Antennas. 2019. No.1(255). P. 14-23. (In Russian)

9. Korn G.A., Korn M.A. Mathematical Handbook for scientists and engineers, second editionMcGraw-Hill Book Company, 1968. 1130 p.

10. Fedoryuk M.V. Asimptotika. Integraly i ryady [Asymptotics. Integrals and Series]. Moscow, Nauka Publ. 1987. 544 p. (In Russian)

11. Lee S.-W., Safavi-Naini S. Approximate Asymptotic Solution of Surface Field due to a Magnetic Dipole on a Cylinder. IEEE Trans. on AP. 1978. Vol.26. No.4. P.593-598.

12. Gradshtein I.S., Ryzhik I.M. Tablitsy integralov, summ, ryadov i proizvedeniy [Tables of integrals, sums, series and products]. Moscow, Nauka Fizmatgiz Publ. 1971. 1108 p. (In Russian)


For citation:

Indenbom M.V. Research of the characteristics of spherical axisymmetric phased antenna arrays taking into account the interaction of slit radiators. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No.9. https://doi.org/10.30898/1684-1719.2020.9.2 (In Russian)