Yu. I. Choni – Ph.D. (Eng.), Associate Professor, Kazan National Research Technical University n.a. A.N. Tupolev – KAI
Interest in the phase structure of the radiation field of antennas was associated primarily with the development and enhancement of horn or other types of feeds for parabolic reflectors. It is very important that the feed forms a spherical wave, the center of which, so-called phase center, should be placed in the focus of the reflector. Wide analytical studies were carried out, methods and means for ex-perimental determination of the phase center position were developed many years ago. With the advent of satellite positioning systems, high accuracy of which is due to phase measurements on the carrier frequency, the requirements for the stability of the phase center and the accuracy of its control have multiplied. This gave rise to a second wave of research on this subject these days using digital modeling and modern antenna measurement tools.
For real antennas, with rare exceptions, there is no phase center in the strict sense of the word. Therefore, they introduce the concept of a local phase center as the center of a spherical surface that reproduces a sufficiently small portion of the phase front of the emitted field in the vicinity of the remote observation point. In most works, the local phase center is identified with the center of curvature of the phase-front curve in the main cross sections of the radiation pattern. This is far from always applicable, since the curvature of the phase front in mutually perpendicular cross sections can differ significantly. The article is devoted to the analysis of methodological and computational aspects of the universal computing algorithm to find the position of a local phase center by the best mean square approximation. In it, there are closed expressions for the coefficients of the corresponding set of linear algebraic equations of the fourth order: three coordinates of the local phase center and the radius of the approximating sphere. While the angular coordinates (θ, φ) of the observation point change, the local phase center moves, forming a surface in three-dimensional space, called a 3D hodograph. In some cases (a linear antenna, for example), this hodograph is a surface of rotation and one can confine ourselves to analyzing the principal curve, that is a 2D hodograph.
A circle antenna array, whose elements have the cardioids pattern, used as a test example to compare several computational algorithms. For cases of zero and first phase variations of the excitation distribution, 3D hodographs are presented for a different number of antenna elements. They are shown by an axonometric projection of the set of local phase center points that correspond to directions (θi, φj) with spacing of 5 degree. The shape of many of these hodographs is unpredictable and curious. It is found that the calculation of the local phase center as the center of curvature of the phase front curve leads to erroneous results that contradict the physical meaning.
- Carter D. Phase centers of microwave antennas // IRE Trans. on Antennas and Propagation. 1956. V. 4. P. 597–600.
- Sander S., Cheng D. Phase center of helical beam antennas // IRE Internat. Convention Record. 1958. V. 6. P. 152–157.
- Vol'pert A.R. O fazovom tsentre antenny // Radiotekhnika. 1961. T. 16. № 3. S. 3−12.
- Muehldorf E.I. The phase center of horn antennas // IEEE Trans. on Antennas and Propagation 1970. V. 18. P. 753–760.
- Kildal P.S. Combined E- and H-plane phase centers of antenna feeds // IEEE Trans. on Antennas and Propagation. 1983. V. 31. P. 199–202.
- Rao K.S., Shafai L. Phase centre calculation of reflector antenna feeds // IEEE Trans. on Antennas and Propagation. 1984. V. 32. P. 740–742.
- Teichman M. Precision phase center measurements of horn antennas // IEEE Trans. on Antennas and Propagation. 1970. V. 18. P. 689–690.
- Patent № 1350625 SSSR. Sposob opredeleniya fazovogo tsentra antenny / I.N. Gvozdev, V.V. Ivanov, A.V. Sosnin, V.P. Chernoles. Opubl. 07.11.1987.
- Patent № 1702325 SSSR. Sposob opredeleniya fazovogo tsentra antenny / I.A. Vinter, A.S. Pautov. Opubl. 30.12.1991.
- Hussein Z.A., Rengarajan S.R. Ground plane effects on quadrifilar helix antenna phase center and radiation characteristics for GPS applications // Antennas and Propagation Society Internat. Symp. Digest. 1991. P. 1594–1597.
- Prata A. Misaligned antenna phase-center determination using measured phase patterns // IPN Progress Report 42-150. 2002. P. 1–9.
- Akrour B., Santerre R., Geiger A. Calibrating antenna phase centers. A tale of two methods // GPS World. February 2005. P. 49–53. URL: http://www2.unb.ca/gge/Resources/gpsworld.february05.pdf (data obrashcheniya: iyul' 2017 g.).
- Choni Yu.I. Hodograph of antenna’s local phase center: computation and analysis // IEEE Trans. on Antennas and Propagation. 2015. V. 63. P. 2819–2823.
- Protsenko M.B., Nesteruk S.V. Osobennosti rascheta i analiz mestopolozheniya lokal'nogo fazovogo tsentra antenny s e'llipticheskoj polyarizatsiej // Naukovі pratsі ONAZ іm. O.S. Popova. 2006. № 2. S. 6–10.
- Chen A., Su D. The effects of near-field factors on rectangular horn antenna's phase center // 7th Internat. Symp. Antennas, Propagation & EM Theory. 2006. P. 1–4.
- Deboux P., Verdin B., Pichardo S. Calculation of the phase-center offset from 2D antenna radiation patterns // Proc. SPIE 9461. Radar Sensor Technology XIX; Active and Passive Signatures VI, 946102. May, 2015.
- Podkorytov A.N. Matematicheskaya model' smeshcheniya fazovykh tsentrov antenn pri vysokotochnom mestoopredelenii v global'nykh navigatsionnykh kompleksakh // E'lektronnyj zhurnal «Trudy MAI». 2012. Vyp. 50. URL: http://trudymai.ru/publish¬ed.php?ID=28680.
- Zhang C., Lin S. UWB antipodal Vivaldi antennas with protruded dielectric rods for higher gain, symmetric patterns and minimal phase center variations // Proc. IEEE Antennas Propagation Soc. Int. Symp. 2007. P. 1973–1976.
- Vladimirov V.M., Markov V.V., Shepov V.N. Shchelevaya poloskovaya antenna krugovoj polyarizatsii s dopolnitel'nymi spiral'nymi shchelyami v izluchatele // Izv. VUZov. Fizika. 2013. T. 56. № 8/2. S. 97–101.
- Wang X., Yao J., Lu X., Lu W. Research on phase center stability of circularly polarized patch antennas for GPS applications // IEEE 4th Asia-Pacific Conf. Antennas and Propagation (APCAP). 2015. P. 362–365.
- Patent № 2326393 RF. Sposob opredeleniya polozheniya fazovogo tsentra antenny / P.V. Milyaev, A.P. Milyaev, V.L. Morev, Yu.N. Kalinin. Opubl. 10.06.2008.
- Padilla1 P., Fernandez J.M., Padilla1 J.L., Exposito-Domınguez G., Sierra-Castaner M., Galocha B. Comparison of different methods for the experimental antenna phase center determination using a planar acquisition system. // Progress in Electromagnetics Research. 2013. V. 135. P. 331–346.
- Chen Y., Vaughan R.G. Determining the three-dimensional phase center of an antenna // 2014 XXXIth URSI General Assembly and Scien. Symp. 2014. P. 1–4.
- Kalinin Yu.N. Izmerenie koordinat fazovogo tsentra antenny // Antenny. 2014. № 4. S. 54−62.
- Khabirov D.O., Udrov M.A. Metodika opredeleniya koordinat tsentra izlucheniya antenny i prakticheskie aspekty ee primeneniya // Izvestiya VUZov Rossii. Radioe'lektronika. 2015. № 3. S. 30–33.
- Choni Yu.I. Sintez antenn po zadannoj amplitudnoj diagramme napravlennosti // Radiotekhnika i e'lektronika. 1971. T. 15. № 5. S. 726–734.