Integro-differential equation of an impedance curvilinear vibrator antenna
https://doi.org/10.34680/2076-8052.2025.1(139).514-521
Abstract
In this paper we study a wire antenna of arbitrary configuration. An impedance boundary condition is applied on the surface of the antenna. This condition relates the tangential components of the electric and magnetic fields. The use of the boundary condition and the representation of the electric field through the Green’s function lead to a two-dimensional integral equation for the surface current density. A direct numerical solution of the integral equation is problematic, since the kernel of the equation becomes singular when the observation point coincides with the source point. Therefore, the singularity is isolated in the kernel, and the equation is transformed into a form that allows for efficient numerical solution on a computer. The operator describing the integral equation is investigated. Appropriate functional spaces are chosen, and it is shown that the operator can be represented as the sum of an invertible operator and a compact operator. Therefore, the integral equation corresponds to a well-set problem in the respective spaces.
About the Authors
S. I. Eminov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
A. V. Sochilin
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
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Review
For citations:
Eminov S.I., Sochilin A.V. Integro-differential equation of an impedance curvilinear vibrator antenna. Vestnik of Novgorod State University. 2025;(3(141)):514-521. (In Russ.) https://doi.org/10.34680/2076-8052.2025.1(139).514-521
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