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Application of Vilenkin’s Additional Theorem in the Calculations of Mutual Coupling Between Circular Apertures on Conducting Sphere

The paper deal with an application of Vilenkin’s additional theorem to the mutual coupling calculations within Moment Method (MoM) between circular apertures on conducting sphere. When calculating the mutual coupling between the apertures one needs to calculate the vector-Legendre transforms of basis and test functions with the domain on the aperture located at an arbitrary position on the sphere. Clasical approach is to numerical calculate the need terms using Euler’s formulas for coordinate system rotation. This approach is very time consuming. Instead, significantly accelerating the calculation is achieved by rotation in theta direction in closed form by using of Vilekin’ additional theorem for associated Legendre functions.

Spherical antenna ; Circular aperture ; Vilenkin’s additional theorem ; Method of moments

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