volume | PIER Journals

2018-02-25

Analytical Solution of Impedance Synthesis Problem for a 2D Array of Thin Vibrators

Yuriy M. Penkin,

Dr. Yuriy M. Penkin

Department of Radiophysics

V. N. Karazin Kharkov National University

Ukraine

Homepage

Victor A. Katrich,

Dr. Victor A. Katrich

Department of Radiophysics

V. N. Karazin Kharkov National University

Ukraine

Homepage

Mikhail Nesterenko,

Dr. Mikhail Nesterenko

Department of Radiophysics

V. N. Karazin Kharkov National University

Ukraine

Homepage

Sergey L. Berdnik

Dr. Sergey L. Berdnik

Department of Radiophysics

V.N. Karazin Kharkov National University

Ukraine

Homepage

Progress In Electromagnetics Research M, Vol. 65, 43-49, 2018

doi:10.2528/PIERM17111501

Abstract

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.

Citation

Copy Export

Yuriy M. Penkin, Victor A. Katrich, Mikhail Nesterenko, and Sergey L. Berdnik, "Analytical Solution of Impedance Synthesis Problem for a 2D Array of Thin Vibrators," Progress In Electromagnetics Research M, Vol. 65, 43-49, 2018.
doi:10.2528/PIERM17111501

References

1. Bakhrakh, L. D. and S. D. Kremenetsky, Synthesis of Radiation Systems (Theory and Methods of Calculation), Sov. Radio, 1974 (in Russian).

2. Skobelev, S. P., Phased Array Antennas with Optimized Element Patterns, Artech House, 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.
doi:10.2528/PIERM16091605

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, 2011.
doi:10.1007/978-1-4419-7850-9

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.
doi:10.2528/PIERM17031602

6. Amitay, N. V. Galindo, and C. P. Wu, Theory and Analysis of Phased Array Antennas, John Wiley & Sons Inc, 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.
doi:10.2528/PIERM15120105