"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 11, 2019

contents of issue      DOI  10.30898/1684-1719.2019.11.14    full text in Russian (pdf)  

UDC 537.86

Efficiency Calculation of Reflector Antennas and Beam-Waveguides Considering Random Surface Errors and BWG Shroud Using the Riemann-Silberstein Vectors


I. V. Belkovich

JSC “Special Research Bureau of Moscow Power Engineering Institute”,

Krasnokazarmennaya str., 14, Moscow 111250, Russia


The paper is received on Saptember 10, 2019, after correction - on November 18, 2019


Abstract. At present, large antennas of deep space deep space communication with beam-waveguides are being designed and developed in response to the surge of interest in deep space exploration. Electromagnetic analysis of such structures traditionally causes difficulties and requires powerful computers to obtain an accurate solution. The results of vector EM field calculation and efficiency evaluation of electrically large reflector antennas and beam-waveguides (BWG) using the Riemann-Silberstein (RS) vectors are presented in this paper. Electromagnetic field propagation and radiation are analyzed considering distorted mirrors and BWG metal enclosure. This allows to obtain a more accurate solution for such systems and determine requirements for mirrors and enclosures in order to minimize distortions. It is shown that for a system of scattering structures it is enough to take into account only one RS vector to obtain a full field. Theoretical characteristics of the dual-reflector Cassegrain antenna are compared to the simulated and experimental results.

Key words: Antennas, aperture antennas, beam-waveguide, computational electromagnetics, electromagnetic fields, electromagnetic radiation, Riemann-Silberstein vectors, spherical harmonics, spherical wave expansion.


  1. Imbriale William A. Large Antennas of the Deep Space Network. John Willey & Sons Inc., 2003.

  2. Formaggi Marco. Enhanced Modeling and Design of Ground Station Antennas. PhD thesis. Pavia University, 2007.

  3. Kogan B.L., Belkovich I.V., Seleznyov V.N. Design of Dual-Reflector Offset Antennas and Beam-Waveguides with a Pattern Symmetry and Zero Cross-polarization. 13th European Conference on Antennas and Propagation, 2019.

  4. Kogan B.L. Application of Faraday's vectors in antenna theory. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2008. No. 7. URL: http://jre.cplire.ru/mac/jul08/1/text.html (In Russian)

  5. Kogan B.L., Belkovich I.V. Theory and practical application of Riemann-Zilberstein vectors for the tasks of antenna technology. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 12. Available at http://jre.cplire.ru/jre/dec18/11/text.pdf. DOI  10.30898/1684-1719.2018.12.11 (In Russian)

  6. Varshalovich D.A., Moskalev A.N., Khersonskii V.K. Quantum Theory of Angular Momentum. Singapore. World Scientific, 1988.

  7. Gelfand I.M., Minlos R.A., Shapiro Z.Y. Representations of the rotation and Lorentz group and their applications. Oxford, Pergamon Press, 1963.

  8. Fukushima T. Numerical computation of Wigner’s d-function of arbitrary high degree and orders by extending exponent of floating point numbers. Technical Report, National Astronomical Observatory of Japan, 2016.

  9. Kogan B.L. Elektromagnitnyye volny krugovoy polyarizatsii [Electromagnetic waves of a circular polarization in antenna theory]. Doctor of technical science dissertation. Moscow Power Engineering Institute, 2004.  (In Russian)

  10. Ludwig A. The definition of cross polarization.  IEEE Transactions on Antennas and Propagation. 1973. Vol.21. No.1. P.116–119.

  11. Belkovich I.V., Kogan B.L. Application of the Riemann-Silberstein vectors for the analysis of electromagnetic fields in reflector antennas. Radiation and Scattering of Electromagnetic Waves, 2017. DOI: 10.1109/RSEMW.2017.8103570

  12. Poperechenko B. A. Bol'shiye zerkal'nyye antenny. Problemy antennoy tekhniki [Large reflector antennas. Problems of antenna technology]. Moscow. Radio i Svyaz’ Publ. 1989. 368 p.  (In Russian)

  13. Bathker D.A., Veruttipong W., Otoshi T.Y., Cramer P.W., Jr. Beam Waveguide Antenna Performance Predictions with Comparisons to Experimental Results.  Microwave Theory and Techniques, Special Issue (Microwaves in Space). 1992. Vol. MTT-40. No.6. P.1274-1285.

  14. Imbriale W., Veruttipong W., Otoshi T., Franco M. Determining Noise Temperatures in Beam Waveguide Systems. TDA Progress Report, Feb. 1994.

  15. Kogan B.L., Belkovich I.V. Theory and practical application of the method of field expansion into a series of the Riemann-Silberstein vector spherical harmonics. Source matching method. VI Vserossijskaya Mikrovolnovaya konferenciya [6th All-Russian Microwave conference]. Moscow, 2018. (In Russian)

  16. Kogan B.L., Belkovich I.V. Physical optics method for calculation of aperture antenna electromagnetic fields using the Riemann-Silberstein vectors. VI Vserossijskaya Mikrovolnovaya konferenciya [6th All-Russian Microwave conference], Moscow, 2018. (In Russian)

  17. Mohamed Said A. Sanad. Aperture Blocking of a Symmetric Parabolic Reflector Antennas. Master’s Thesis, University of Manitoba, 1982.

  18. Ruze J. Antenna tolerance theory, a review. Proceedings of the IEEE. 1966. Vol.54.No. 4. P.633–640.

  19. Shifrin Ya.S. Voprosy statisticheskoj teorii antenn [Problems of Statistical Theory of Antennas]. Moscow. Sov. Radio Publ., 1970. 384 p.  (In Russian)

  20. Siwaphong Boonsalee. Effects of Random Surface Errors on the Performance of Paraboloidal Reflectors. Master’s Thesis, Massachusetts Institute of Technology, 2001.

  21. Frolov O.P., Wald V.P. Zerkal'nye antenny dlya zemnyh stancij sputnikovoj svyazi [Reflector antennas for satellite communication earth stations]. Moscow. Goryatchaya liniya-Telecom Publ. 2012. 496 p.  (In Russian)

  22. Cha A.G., Imbriale W.A. A New Analysis of Beam Waveguide Antennas Considering the Presence of the Metal Enclosure. IEEE Transactions on Antennas and Propagations. 1992. Vol. AP-40. No.9. P.1041-1046.


For citation:

Belkovich I.V. Efficiency Calculation of Reflector Antennas and Beam-Waveguides Considering Random Surface Errors and BWG Shroud Using the Riemann-Silberstein Vectors. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No. 11. Available at http://jre.cplire.ru/jre/nov19/14/text.pdf

DOI  10.30898/1684-1719.2019.11.14