Journal of Radio Electronics. eISSN 1684-1719. 2024. №4

Contents

Full text in Russian (pdf)

Russian page

 

 

DOI: https://doi.org/10.30898/1684-1719.2024.4.7

 

 

THE METHOD OF APPROXIMATE CALCULATION
OF THE KIRCHHOFF'S INTEGRAL

 

N.V. Anyutin

 

Public joint-stock company “Research and Production Corporation “Almaz”
125190, Russia, Moscow, Leningrad Avenue, 80, b. 16

 

The paper was received August 7, 2023.

 

Abstract. The article proposes a method of approximate calculation of the wave field gradient by its distribution on the only one closed surface. This allows calculating the Kirchhoff's integral without additional calculations or measurements of the electromagnetic field and opens up the opportunity to use it in practice along with the field equivalence principle. The comparison of the Kirchhoff's integral calculation accuracy with its vector forms showed that the proposed approximation for the wave field derivative leads to additional methodological errors, which are equivalent to the stray signal at the level less then −40 dB. At the same time, the use of Kirchhoff's integral instead of a widespread field equivalence principle in the electromagnetic field transformation algorithms reduces their computing complexity to 20 times.

Key words: Kirchhoff’s integral, field equivalence principle, Stratton and Chu formulas, near field, far field, electromagnetic field transformation, antenna measurements, antenna diagnostics.

Corresponding author: Anyutin Nikolay Viktorovich, anyutinnv@mail.ru

 

References

1. Grinev A. YU. Chislennye metody resheniya prikladnykh zadach ehlektrodinamiki. Radiotekhnika. – 2012.

2. Tseitlin N. M. Metody izmereniya kharakteristik antenn SVCH. M.: Radio i svyaz'. – 1985.

3. Potekhin A. I. Nekotorye zadachi difraktsii ehlektromagnitnykh voln. M.: Sov. Radio. – 1948.

4. Love A. E. H. I. The integration of the equations of propagation of electric waves // Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. – 1901. – Vol. 197. – No. 287-299. – Pp. 1-45. (https://doi.org/10.1098/rsta.1901.0013)

5. Stratton J. A., Chu L. J. Diffraction theory of electromagnetic waves // Physical review. – 1939. – Vol. 56. – No. 1. – Pp. 99-107. (https://doi.org/10.1103/PhysRev.56.99)

6. Sun Q., Klaseboer E., Chan D. Y. C. Robust multiscale field-only formulation of electromagnetic scattering // Physical Review B. – 2017. – Vol. 95. – No. 4. – Pp. 045137. (https://doi.org/10.1103/PhysRevB.95.045137)

7. Anyutin N. V., Kurbatov K. I., Malay I. M., Ozerov M. A. Algorithm for Transforming Antenna Electromagnetic Near-Field Measured on Spherical Surface into Far-Field Based on Direct Calculation of Stratton and Chu Formulas // Radioelectronics and Communications Systems. – 2019. – Vol. 62. – No. 3. –
Pp. 109-118. (https://doi.org/10.3103/S0735272719030026)

8. Anyutin N., Malay I., Malyshev A. Advantage of Stratton and Chu Formulas for Electromagnetic Field Reconstruction // 2019 Radiation and Scattering of Electromagnetic Waves (RSEMW). – IEEE, 2019. – Pp. 293-296.

9. Yang X. New far-field extrapolation method for the computation of electric fields // Optica Applicata. – 2021. – Vol. 51. – No. 3. – Pp. 321-333.

10. Zhukov V. P., Fedoruk M. P. Vysokoehffektivnyi metod vychisleniya integrala Strehttona-Chu v zadachakh vzaimodeistviya lazernogo izlucheniya s veshchestvom // Vychislitel'nye tekhnologii. – 2021. – Vol. 26. – No. 3. – Pp. 42-60. (https://doi.org/10.25743/ICT.2021.26.3.004)

11. Balabukha N. P., Konyaev D. A., Shapkina N. E. Simulation of Bistatic RCS Based on a Calculated Electromagnetic Near-Field // Moscow University Physics Bulletin. – 2022. – Vol. 77. – No. 3. – Pp. 3-13. (https://doi.org/10.3103/S0027134922030055)

12. Zolotorev M. S. McDonald K. T. Time-Reversed Diffraction // arXiv preprint physics/0003058. – 2000.

13. Chan D. Y. C. et al. Efficient field-only surface integral equations for electromagnetics // arXiv preprint arXiv:1901.01602. – 2019. (https://doi.org/10.48550/arXiv.1901.01602)

14. Anyutin N. V. Metod priblizhennogo vychisleniya integrala Kirkhgofa // Trudy vserossiiskoi konferentsii REDS-IT – 2023. – 2023. – Pp. 17-22.

15. Ramahi O. M. Near- and far-field calculations in FDTD simulations using Kirchhoff surface integral representation // IEEE Transactions on Antennas and Propagation. – 1997. – Vol. 45. – No. 5. – Pp. 753-759. (https://doi.org/10.1109/8.575616)

16. Lai L. W. et al. Near-field to far-field transformation with non-contacting near-field measurement by using Kirchhoff surface integral representation // Microwave Conference (APMC), 2015 Asia-Pacific. – IEEE, 2015. – Vol. 1. – Pp. 1-3. (https://doi.org/10.1109/APMC.2015.7411688)

17. Eibert T. F. et al. Electromagnetic field transformations for measurements and simulations // Progress In Electromagnetics Research. – 2015. – Vol. 151. – Pp. 127-150. (https://doi.org/10.2528/PIER14121105)

18. Anyutin N. V. Electromagnetic Field Transformation from a Surface Closed Around the Antenna to its Aperture // Measurement Techniques. – 2021. – Vol. 64. – No. 1. – Pp. 51-59. (https://doi.org/10.1007/s11018-021-01895-4)

19. Newell A. C., Hindman G. E. Antenna pattern comparison using pattern subtrac-tion and statistical analysis // Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP). – IEEE, 2011. – Pp. 2537-2540.

20. Bakhrakh L. D., Kolosov YU. A., Kurochkin A. P. Opredelenie polya antenny v dal'nei zone cherez znacheniya polya v blizhnei zone // Antenny. – 1976. – No. 24. – Pp. 3-14.

21. Krivosheev YU. V., Shishlov A. V. Razvitie metoda vosstanovleniya diagramm napravlennosti antenn po izmereniyam v zone Frenelya // Radiotekhnika. – 2012. – No. 11. – Pp. 47-53.

For citation:

Anyutin N.V. The method of approximate calculation of the Kirchhoff’s integral. // Journal of Radio Electronics. – 2024. – №. 4. https://doi.org/10.30898/1684-1719.2024.4.7 (In Russian)