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Transactions on Machine Design (TMD)
 

Vilekin’s Additional Theorem for Legendre Functions and Rotation-based Measurements
Slavko Rupcic, Vanja Mandri-Radivojevic and Nataša Nešic
Department of Communications Faculty of Electrical Engineering Osijek 31000, Croatia., College of Applied Technical Sciences Niš Aleksandra Medvedeva 20 Niš 18000, Serbia
Abstract: In this work, we applied Vilenkin’s additional theorem among the circular apertures to measure the coupling calculations. We measure the vector-Legendre transformations of basis and test functions by keeping the domain over the aperture at an arbitrary level. With the help of Euler’s formula for rotating the coordinate system, we used the classical approach for the numerical measurements, which is more time intensive. With Vilekin’s additional theorem for Legendre functions, we increased the rotation-based measurements.
Keywords: Spherical Antenna, Circular Aperture, Vilenkin’s Additional Theorem, Method of Moments Vilekin’s Additional Theorem for Legendre Functions and Rotation-based Measurements
DOI:https://doi.org/10.6025/tmd/2023/11/2/33-42
Full_Text   PDF 2.65 MB   Download:   66  times
References:

[1]Ja, N. (1968). Vilenkin. Special Functions and the Theory of Group Representation, American Mathematical Society, Providence.
[2] Sipus, Z., Kildal, P.S., Leijon, R., Johansson, M. (1998). An Algorithm for Calculating Green's functions for planar, circular czlindrical and spherical multilazer substrates@, Applied Computational Electromagnetics Societz Journal, Volume 13, p 243- 245.
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[4] Bailey, M.C. Analysis of finite-size phased arrays of circular waveguide elements, NASA TR R-408, National Aerunautics and Space Administration, Washington, DC.
[5] Bailey, M.C., Bostian, C.W. (1974). Mutual Coupling in a Finite Planar Array of Circular Apertures, IEEE Transactions on Antennas and Propagation, Volume AP-22 (2), p 178-184, March.
[6] Rupcic, S. (2009). Circular Waveguide Antenna Arrays on Spherical Structures, PhD Thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb.
[7] Sipus, Z., Skokic, S. Applications of Vilenkin's additional theorem in the analysis of spherical antennas and periodic structures, First European Conference on Antennas and Propagation EUCAP, Proceedinsg of EUCAP, 6-10 November, 2006, Nice, France.
[8] Sipus, Z., Bosiljevac, M., Skokic, S. (2004).Analysis of Conformal Waveguide Antennas Using Hybrid Spectral Domain UTDMethod, Proceedings of JINA 2004 International Symposium on Antennas / Guiraud, Jean-Louis, editor(s). Nica : JINA, p 92-93.


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