А.Y. Grinev – Dr.Sc. (Eng.), Professor, Moscow Aviation Institute (National Research University) (Moscow) E-mail: grinevau@yandex.ru
А.А. Izmaylov – Post-graduate Student, Moscow Aviation Institute (National Research University) (Moscow) E-mail: yustas1993@yandex.ru
А.А. Tsitovich – Engineer of the 1st category, FSUE «RPS «Istok» (Fryazino) E-mail: alekseytsitovich@gmail.com

The technique of analytical estimates of the main parameters and characteristics of two-dimensional antennas based on frequencyselective structures with partially reflecting surface properties (structure and geometry, working frequency band, gain, directivity pattern, etc.) is considered. The paper contains summarizes of the results obtained as an equivalent circuits based on the T-wave model, and on the model of a two-dimensional leaky-wave antenna.
The article proposes a method of analytical evaluation of the main parameters and characteristics of antenna systems based on frequency selective structures (structure and geometry, operating frequency band, gain, radiation pattern, etc.), summarizing the results obtained by the method of equivalent circuits based on the transverse equivalent network-wave model and the model of twodimensional leaky-wave antenna. The advantages of two-dimensional antenna systems based on frequency-selective structures with properties of partially reflecting surface are: low price, simplicity and manufacturability of design, high gain (with a reasonable compromise with the operating frequency band), high aperture efficiency. Such as are promising in the development of flat effective microwave and HF antenna arrays for frequencies of the order of 30…40 GHz and above, sparse antenna arrays (scanning in a limited sector), combined AP in one aperture (for example, X and C; and), etc.

1. Felsen L.B., Marcuvitz N. Radiation and Scattering of Waves. 2-nd ed. New York. 2003.
2. Vajnshtejn L.A. Otkry'ty'e rezonatory' i otkry'ty'e volnovody'. M.: Sov. radio. 1966. 474 s.
3. Shestopalov V.P., Kirilenko A.A., Masolov S.A.,Sirenko Yu.K. Rezonansnoe rasseyanie voln. T. 1. Difrakczionny'e reshetki. Kiev: Naukova Dumka. 1986. 232 s.
4. Galishnikova T.N., Il'inskij A.S. Metod integral'ny'x uravnenij v zadachax difrakczii voln. M.: MAKS Press. 2013. 248 s.
5. E'lektrodinamika antenn s poluprozrachny'mi poverxnostyami: metody' konstruktivnogo sinteza / Pod red. B.Z. Kaczenelenbauma i A.N. Sivova. M.: Nauka.1989. 176 s.
6. Kontorovich M.I., Astraxin M.I., Akimov V.P., Fersman G.A. E'lektrodinamika setchaty'x struktur. M.: Radio i svyaz'. 1987. 135 s.
7. Electromagnetic Theory of Gratings / Ed. R. Petit. New York: Springer-Verlag. 1980.
8. Applications of Metamaterials. Edited by F. Capolino. CRC Press. 2005.
9. Modern antenna handbook / Ed. C.A. Balanis. John Wiley & Sons. 2008. Ch. 7. P. 325−367.
10. Frontiers in antennas: next generation, design & engineering. Ed. Frank B. Gross. McGrow-Hill. 2011. Ch. 9. P. 339−409.
11. Pozar D.M. Microwave Engineering. NJ (USA): JohnWiley & Sons. 2012. 732 p.
12. Yang F., Rahmat-Samii Y. Electromagnetic Band Gap Structures in Antenna Engineering. Cambridge University Press. 2009. 266 p.
13. Tretyakov S. Analytical modeling in applied electromagnetics. Artech House. 2003. 272 p.
14. Vardaxoglou J.C. Frequency-Selective Surfaces: Analysis and Design. Taunton. U.K.: Res. Studies Press. 1997. 298 p.
15. Munk B.A., Frequency Selective Surfaces: Theory and Design. First Edition. Wiley, New York. 2000. 440 p.
16. Trentini G.V. Partially reflecting sheet arrays // IRE Trans. Antennas Propagation. 1956. № 4. P. 666−671.
17. Feresidis A.P., Vardaxoglou J.C. High gain planar antenna using optimized partially reflective surfaces // IEE Proceedings Microwaves. Antennas and Propagation. 2001. V. 148. № 6. P. 345−350.
18. Wang N., Liu Q., Wu C., et.al. Wideband Fabry-Perot resonator antenna with two somplementary FSS layers // IEEE Trans. Antennas Propag. 2014.V. 62. № 5. P. 2463−2471.
19. Wu Z-H., Zhang W-X. Broadband printed compound air-feed array antennas // IEEE antennas and wireless propagation letters. 2010. V. 9. P. 187−190.
20. David F., Rafael F.S., Caldeirinha I.C. and et.al. Square loop and slot Frequency selective surfaces study for equivalent circuit model optimization // IEEE Trans. on Antennas Propagation. 2015. V. 63. № 9. P. 3947−3955.
21. Hosseini S.A., Capolino F., Flaviis F. Q-band single-layer planar Fabry–Pérot cavity antenna with single integrated-feed // Progress In Electromagnetics Research. V. 52. 2014. P. 135−144.
22. Gardelli R., Albani M., Capolino F. Array thinning by using antennas in a Fabry–Perot cavity for gain enhancement // IEEE Trans. on Antennas Propagation. 2006. V. 54. № 7. P. 1979−1989.
23. Hosseini S.A., Capolino F., Flaviis F.D. A new formula for the pattern bandwidth of Fabry–Perot cavity antennas covered by thin frequency selective surfaces // IEEE Trans. Antennas Propagation. 2011. V. 59. № 7. P. 2724−2727.
24. Hosseini S.A., Capolino F., Flaviis F.D. and et.al. Improved bandwidth formulas for Fabry–Pérot cavity antennas formed by using a thin partially-reflective surface // IEEE Trans. Antennas Propagation. 2014. V. 62. № 5. P. 2361−2367.
25. Hosseini S.A., Flaviis F.D., Capolino F. Design formulas for planar Fabry–Pérot cavity antennas formed by thick partially reflective surfaces // IEEE Trans. Antennas Propagation. 2016. V. 64. № 12. P. 5487−5491.
26. Hosseini S.A., Capolino F., Flaviis F. Q-band single-layer planar Fabry–Pérot cavity antenna with single integrated-feed // Prog. Electromagn. Res. 2014.V. 52. P. 135−144.
27. Debogović T., Perruisseau-Carrier J. Array-Fed Partially Reflective Surface Antenna with Independent Scanning and Beam width Dynamic Control // IEEE Trans. Antennas Propagation. 2014. V. 62. № 1. P. 446−449.
28. Lu Y.F., Lin Y.C. A hybrid approach for finite-size Fabry–Pérot antenna design with fast and accurate estimation on directivity and aperture efficiency // IEEE Trans. Antennas Propagation. 2013. V. 61. № 11. P. 5395−5401.
29. Kyun R. Mikrovolnovy'e antenny'. L.: Sudostroenie 1967.
30. Tamir T. Leaky wave antennas // Antenna Theory / Eds. R.E. Collin, F.J. Zucker. Part 2. Ch. 20. New York: McGraw-Hill. 1969.
31. Jackson D.R., Oliner A.A. Leaky-Wave Antennas // Modern antenna handbook / Ed. C.A. Balanis. John Wiley & Sons. 2008. P. 325−369.
32. Lovat G., Burghignoli P., Jackson D.R. Fundamental properties and optimization of broadside radiation from uniform leaky-wave antennas // IEEE Trans. Antennas Propagation. 2006. V. 54. № 5. P. 1442−1452.
33. Burghignoli P., Lovat G., Capolino F., Jackson D.R., Wilton D.R. Directive leaky-wave radiation from a dipole source in a wire-medium slab // IEEE Trans. Antennas Propag. 2008. V. 56. № 5. P. 1329−1339.
34. Ip A., Jackson D.R. Radiation from cylindrical leaky waves// IEEE Trans. Antennas Propagation. 1990. V. 38. № 6. P. 482−488.
35. Zhao T., Jackson D.R., Williams J.T. and et.al. 2-D periodic leaky-wave antennas. Part I: Metal patch design // IEEE Trans. Antennas Propag. 2005. V. 53. № 11. P. 3505−3514.
36. Guo X., Jackson D.R., Chen J., Capolino F., Wilton D.R. Leaky-wave analysis of Fabry–Pérot resonant cavity antennas // 2013 URSI Electromagnetic Theory Symposium. Japan. 2013.
37. Guo X., Jackson D.R., Chen Ji, Capolino F., Wilton D.R. Leaky-Wave analysis of Fabry–Pérot resonant cavity antennas // Proceedings of the Intern. Symposium on electromagnetic theory. 2013. P. 1091−1093.
38. Luukkonen O., Simovski C., Granet G., et. all. Simple and Accurate Analytical Model of Planar Grids and High-Impedance Surfaces Comprising Metal Strips or Patches // IEEE Trans. Antennas Propag. 2008. V. 56. № 6. P. 1624−1632.
39. Taflove A., Hagness S.C. Computational electromagnetics: The finite-difference time-domain method. Artech House. 2005. 853 p.
40. Volakis J.L., Chatterjee A., Kempel L.C. Finite element method for electromagnetic. New York: IEEE Press. 1998. 344 p.
41. Sadiku M.N.O. Numerical technique in electromagnetics with MATLAB. CRC Press. 2009. 710 p.
42. Costa F., Monorchio A., Manara G. Efficient analysis of frequency selective surfaces by a simple equivalent-circuit model // IEEE Transactions on antennas and propagation magazine. 2012. V. 54. № 4. P. 35−48.
43. Sarabandi K., Behdad N. A frequency selective surface with miniaturized elements // IEEE Trans. Antennas Propag. 2007. V. 55. № 5. P. 1239−1245.
44. Bayatpur F., Sarabandi K. Single-layer high-order miniaturized-element frequency-selective surfaces // IEEE Trans. on microwave theory and techniques. 2008. V. 56. № 4. P. 774−781.
45. Al-Joumayly M., Behdad N. A new technique for design of low-profile, second-order, bandpass frequency selective surfaces // IEEE Trans. Antennas Propagation. Magazine. 2009. V. 57. № 2. P. 452−4459.
46. Al-Joumayly M., Behdad N. A generalized method for synthesizing low-profile, band-pass frequency selective surfaces with nonresonant constituting elements// IEEE Trans. Antennas Propag. 2010. V. 58. № 12. P. 4033−4041.
47. Kashanianfard M., Sarabandi K. Metamaterial inspired optically transparent Band-Selective ground planes for antenna application // IEEE Trans. Antennas Propag. 2013. V. 61. № 9. P. 4624−4631.
48. Mingyun L., Minjie H., Zhe W. Design of multi-band frequency selective surfaces using multi-periodicity combined elements // Journal of Systems Engineering and Electronics. 2009. V. 20. № 4. P. 675−680.
49. Zhang J.C., Yin Y.C., Zheng A.F. Double screen FSSs with multi-resonant elements for multiband, broadband applications // J. of Electromagn. Waves and Appl. 2009. V. 23. P. 2209−2218.
50. Bayer H., Krauss A., Zaiczek T. and et. al. Ka-Band User Terminal Antennas for Satellite scommunications // IEEE Antennas & Propagation Magazine. 2016. № 2. P. 76−88.
51. Chaharmir M.R., Shaker J. Design of a multilayer X-/Ka-band frequency-selective surface-backed reflect array for satellite applications // IEEE Trans. on Antennas Propagation. 2015. V. 63. № 4. P. 1255−1262.
52. Qin F., Gao S., Luo Qi, Mao C-X. and et. al. A simple low-cost shared-aperture dual-band dual-polarized high-gain antenna for synthetic aperture radars // IEEE Trans. on Antennas Propagation. 2016. V. 64. № 7. P. 2914−2922.
53. Zhong S.S., Sun Z., Kong L.B., Gao C., Wang W., Jin M.P. Tri-band dual-polarization shared-aperture microstrip array for SAR applications // IEEE Trans. Antennas Propagation. 2012. V. 60. № 9. P. 4157−4165.