# Solving an Equation by the Saddle Point Method for the Electromagnetic Field Scattered by the Opening Horn Emitter

## DOI:

https://doi.org/10.20535/RADAP.2023.91.28-36## Keywords:

asymptotic research methods, saddle point method, scattered electromagnetic field, horn emitter## Abstract

Horn emitters are widely used as part of antenna systems in modern radio-electronic equipment, radars, television, etc. The simplicity of their design and high-level technical characteristics are major advantages of the emitters. However, there are certain disadvantages. In order to assess and possibly eliminate them, we usually do electrodynamics calculations of the electromagnetic field scattered from the horn emitter when designing new antenna systems and take into account all the factors, which cause scattering in order to reduce it. The well-known calculation methods result in the appearance of algorithms in open form, which usually do not have any exact solutions. In the few cases where their strict solutions are known, the algorithms look rather complex and, even with the help of modern software packages of computing tools, do not allow us to understand physics or causes of such a process. In such cases, approximate asymptotic methods shall be widely applied.

It has been established that it is appropriate to use the saddle point method to solve boundary value problems in determining the electromagnetic field scattered from a horn emitter.

We carried out a detailed analysis of the saddle point method by solving an equation for the electromagnetic field scattered by an opening horn emitter, which was a causes of diffraction on the horn in order to reduce the diffraction.

The publication involves two tasks: a detailed analysis of the saddle point method for solving the integral electromagnetic field equation and determination of the field scattered by the opening horn emitter with application of the saddle point method.

The problem statement includes one of the cases of a plane wave free incidence, namely, when the wave is polarized normally to the plane of incidence (S-polarization), that is, the plane of wave polarization and the incidence plane are mutually perpendicular.

We have obtained an expression for the field scattered by the opening horn emitter with normal polarization of the incident wave to the plane of its incidence after taking integrals by the saddle point method.

Unlike complex modern software products, this solution will allow us to analyze physical processes that occur when the electromagnetic field is reflected by the opening horn emitter. For example, we have analysed the scattered field in two planes. These simple expressions may be used to easily make scattered field diagrams in Mathcad.

Further studies will take into account beyond cutoff reflection coefficients and the horn emitter load.

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (91), pp. 28-36. doi: 10.20535/RADAP.2023.91.28-36.

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Copyright (c) 2023 Оlha Sydorchuk, Сергій Соболенко, Людмила Марищук, Валентина Ковальчук

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