A synthesis problem of a 2D array of thin linear vibrators, whose geometric centers are located at the nodes of a flat rectangular grid with double periodicity solved. The problem can be formulated as follows. A 2D antenna array radiates monochromatic electromagnetic waves into free space. Suppose that the array radiation pattern (RP) can be scanned in space by varying complex surface impedances of separate vibrators. Then, it is necessary to determine vibrator surface impedances to control the direction of the RP maximum. The analytical solution of the impedance synthesis problem, as an alternative to a numerical solution of a two-dimensional equation system, was obtained under two assumptions: the vibrators are excited by electric currents of equal amplitudes, and the RP of each radiator does not differ from that of an isolated radiator. Verification of theoretical formulas will be done by comparing them with relations known for one-dimensional equidistant arrays.
2. Skobelev, S. P., Phased Array Antennas with Optimized Element Patterns, Artech House, Boston, 2011.
3. Berdnik, S. L., V. A. Katrich, M. V. Nesterenko, and Y. M. Penkin, "Electromagnetic waves radiation by a vibrators system with variable surface impedance," Progress In Electromagnetics Research M, Vol. 51, 157-163, 2016.
4. Nesterenko, M. V., V. A. Katrich, Yu. M. Penkin, V. M. Dakhov, and S. L. Berdnik, Thin Impedance Vibrators. Theory and Applications, Springer Science+Business Media, New York, 2011.
5. Penkin, Yu. M., V. A. Katrich, and M. V. Nesterenko, "Formation of radiation fields of linear vibrator arrays by using impedance synthesis," Progress In Electromagnetics Research M, Vol. 57, 1-10, 2017.
6. Amitay, N. V. Galindo, and C. P. Wu, Theory and Analysis of Phased Array Antennas, John Wiley & Sons Inc, New York, 1972.
7. Penkin, Yu. M., V. A. Katrich, and M. V. Nesterenko, "Development of fundamental theory of thin impedance vibrators," Progress In Electromagnetics Research M, Vol. 45, 185-193, 2016.