Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2021. №9
ContentsFull text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2021.9.12
UDC: 537.87
Approximate Asymptotic Expressions for the Electromagnetic Field and the Mutual Admittance of Slоts in a Conducting Convex Surface of Rotation in the Form of Series of Azimuthal Harmonics
M. V. Indenbom
All-Russian Scientific Research Institute of Radio Engineering, 105082, Moscow, Bolshaya Pochtovaya, 22.
The paper was received September 21, 2021
Abstract. In this paper, we obtain approximate asymptotic expressions for the electromagnetic field and the self and mutual admittances of "single-mode" slots in a smooth convex surface of rotation of large sizes in the form of a series of azimuthal harmonics. The coefficients of the series are expressed as integrals over the wave spectrum and can be calculated numerically or as a sum series of deductions (for mutual admittances). The expressions for the coefficients are uniformly valid in the boundary surface layer, except for the vicinity of the poles of the surface of rotation, and do not have discontinuities on the caustics of the surface rays. The resulting expressions can be directly used to calculate the fields and the self and mutual admittances of annular slots. In contrast to the eigenfunction method, asymptotic expressions allow us to cover the case of an arbitrary-shaped surface and avoid summing slowly converging double series. A comparison of the results of calculating the admittances of annular slots in a conducting spherical surface obtained by the proposed method and the method of eigenfunctions was executed, and their good agreement shown even for a small radius of the sphere equal to 3λ.
Key words: convex surface of rotation, slots, ring slots, electromagnetic field, boundary surface layer, mutual admittance, uniform asymptotic, caustic of surface ray.
1. Orlova N. S. Electromagnetic Fields of Dipoles Near a Metal Convex Body of Large Electrical Dimensions. Radiotechnica i electronica [Radio Engineering and Electronics]. 1974. Vol.19. No.7. P.1372-1377.
2. Pathak P.H., Kouyoumjian R.G. An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction. IEEE Proceedings. 1974. V.62. P.1438-1447.
3. Pathak P.H., Wang N., Burnside W.D., Kouyoumjian R.G. A Uniform GTD Solution for the Radiation from Sources on a Convex Surface. IEEE Transactions on Antennas and Propagation. 1981. V.29. №4. P.609-622.
4. Lee S.-W., Safavi-Naini S. Approximate Asymptotic Solution of Surface Field due to a Magnetic Dipole. IEEE Transactions on Antennas and Propagation 1978.V.26. №4. P.593-598.
5. Lee S.-W. Mutual Admittance of Slots on a Cone: Solution by Ray Technique. IEEE Transactions on Antennas and Propagation. 1978. V.26. №6. P.768-773.
6. Indenbom M. V., Skuratov V. A. A Modal Approach to the Method of Calculating Axisymmetric Phased Array Antenna Taking into Account the Interaction of Slot Elements Based on the Expansion of the Electromagnetic Field in Terms of the Eigenfunctions of the Outer Surface Region. Radiotekhnika. 2021. No. 5. P.117-131.
7. Weinstein L. A. Electromagnitnie volny [Electromagnetic waves]. Moscow, Radio i Svjase Pabl. 1988. 440 p.
8. Felsen L., Marcuvitz N. Radiation and Scattering of Waves. Vol. 1. Prentice Hall, Inc., Englewood Cliffs, New Jersey. 1973.
9. Maslov V. P. Operatorniye metody [Operator methods]. Moscow, Nauka. 1973. 543 p.
10. Fedoryuk M. V. Asymptotica. Integraly i rjady [Asymptotics. Integrals and series]. Moscow, Nauka. 1987. 544 p.
11. Markov G. T., Chaplin A. F. Vozbushdenie electromagnitnyh voln [Excitation of electromagnetic waves]. Moscow, Radio i Svjase Publ. 1983. 296 p.
12. Fok V. A. Problemy difractcii i rasprostraneniya electromagnitnyh voln [Problems of diffraction and propagation of electromagnetic waves]. Moscow, Sovetskoye Radio. 1970. 520 p.
13. Feld Y. N., Benenson L. S. Osnovy teorii antenn [Fundamentals of antenna theory]. Moscow, Drofa. 2007. 491 p.
14. Lee S.-W., Safavi-Naini S. Approximate asymptotic solution of surface field due to a magnetic dipole on a cylinder. IEEE Transactions on Antennas and Propagation. 1978. V.AP-26. №4. P.593-598.
For citation:
Indenbom M.V. Approximate Asymptotic Expressions for the Electromagnetic Field and the Mutual Admittance of Slоts in a Conducting Convex Surface of Rotation in the Form of Series of Azimuthal Harmonics. Zhurnal Radioelektroniki [Journal of Radio Electronics]. 2021. No.9. https://doi.org/10.30898/1684-1719.2021.9.12 (In Russian)