Solving an Equation by the Saddle Point Method for the Electromagnetic Field Scattered by the Opening Horn Emitter
Keywords:asymptotic research methods, saddle point method, scattered electromagnetic field, horn emitter
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.
Dubrovka F. F., Ovsianyk Yu. A. (2009). Dual- And Multiband Horns of feed systems for reflector-type antennas. Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, Vol. 38, pp. 130-147. doi: 10.20535/RADAP.2009.38.130-147.
Benenson L. S., Feld Ya. N. (1988). Rasseyanie elektromagnitnyih voln antennami (obzor) [Scattering of electromagnetic waves by antennas (review)]. Radiotehnika i elektronika [Radio engineering and electronics], Vol. 33, Iss. 2, pp. 225–246.
Sirenko Yu. K, Suharevskiy I. V., Suharevskiy O. I., Yashina N. P. (2000). Fundamentalnyie i prikladnyie zadachi teorii rasseyaniya elektromagnitnyih voln [Fundamental and applied problems of the theory of scattering of electromagnetic waves]. Harkov: Krok [Kharkov: Krok], 344 p.
Sydorchuk О. L., Zalevskiy V. Y. (2022). Investigation of Electromagnetic Wave Diffraction at the Edges of the Pyramidal Horn Irradiator of the Antenna, as One of the Causes of Scattering. Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, Vol. 89, pp. 11-20. doi: 10.20535/RADAP.2022.89.11-20.
Sydorchuk O. L. (2011). Calculation of effective surface of dispersion of megaphone aerial at falling on it of wave of free-form with the use of lemma of Lorenca. The Journal of Zhytomyr State Technological University / Engineering, Vol. 2(57), pp. 103–113. doi:10.26642/tn-2011-2(57)-103-113.
Zalevskiy G. S. (2007). Otsinka vidstani mizh obiektamy, pry yakii yikh elektromahnitnoiu vzaiemodiieiu mozhna znevazhyty, provedena metodom intehralnykh rivnian [Estimation of the distance between objects, at which their electromagnetic interaction can be neglected, carried out by the method of integral equations]. Systemy ozbroiennia i viiskova tekhnika [Weapon systems and military equipment], Vol. 2, pp. 59–63.
Mittra R., Lee S. W. (1971). Analytical Techniques in the Theory of Guided Waves. NewYork: Macmillan, 302 p.
Kuznetsov V. L., Filonov P. V. (2010). Uravnenie pogruzheniya dlya obobschennoy matritsyi rasseyaniya v teorii neregulyarnyih volnovodov [The immersion equation for the generalized scattering matrix in the theory of irregular waveguides]. Nauchnyiy vestnik MGTU GA [Scientific Bulletin of MSTU GA], Vol. 157, pp. 5–11.
Konnikov I. A. (2017). Raschet polya v ploskosloistyih sredah mikroelektroniki [Calculation of the field in plane-layered media of microelectronics]. Zhurnal tehnicheskoy fiziki [Journal of technical physics], Vol. 87, pp. 1615–1623.
Grinchik N. N. (2008). Modelirovanie elektricheskih i teplovyih protsesov v sloistyih sredah [Modeling of electrical and thermal processes in layered media]. Minsk, 252 p.
Li L.-W., Lee C.-K., Yeo T.-S. and Leong M.-S. (2004). Wave mode and path characteristics in a four-layered anisotropic forest environment. IEEE Transactions on Antennas and Propagation, Vol. 52, No. 9, pp. 2445-2455. doi: 10.1109/TAP.2004.834021.
Sautbekov S., Bourgiotis S., Chrysostomou A., Frangos P. (2018). A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic Field Expressions and the Emergence of the Surface Waves. Progress In Electromagnetics Research M, Vol. 64, pp. 9-22. DOI: 10.2528/PIERM17082806.
Michalski, K. A., and H.-I. Lin (2017). On the far-zone electromagnetic field of a vertical Hertzian dipole over an imperfectly conducting half-space with extensions to plasmonics. Radio Science, Vol. 52, Iss. 7, pp. 798–810. doi:10.1002/2017RS006299.
Christie L., Mondal P. (2016). Mode Matching Method for the Analysis of Cascaded Discontinuities in a Rectangular Waveguide. Proceedings of the 6th International Conference on Advances in Computing and Communications, Vol. 93, P. 251–258. doi: 10.1016/j.procs.2016.07.208.
Vorob'ev S. N., Litvinenko L. N., Prosvirnin S. L. (2005). Operatornyiy metod v zadache difraktsii elektromagnitnyih voln na polubeskonechnyih lentochnyih reshetkah [Operator method in the problem of diffraction of electromagnetic waves on semi-infinite strip gratings]. Radiofizika i radioastronomiya [Radiophysics and radio astronomy], Vol. 10, No. 3, pp. 273–283.
How to Cite
Copyright (c) 2023 Оlha Sydorchuk, Сергій Соболенко, Людмила Марищук, Валентина Ковальчук
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).