Approximation of Current on a Thin Tubular Vibration Antenna Using the Eigenfunction Method

Табаков, Д П; Mayorov, Andrey G.

doi:10.31854/1813-324x-2019-5-4-58-64

Cited by 5 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When studying the application of this approach to the problems of electrodynamics, the author could not find references to any significant works. As a result, papers [5,7] were written. In [7], the eigenvalues of the singular integral operator were studied as functions of the frequency and geometric dimensions of the tubular dipole.…”

Section: The Eigenfunction Methodsmentioning

confidence: 99%

“…It was concluded that the studied dependences allow a simple polynomial approximation, whereas the approximation with harmonic functions is advantageous for the eigenfunctions of the integral operator. Paper [5] presents the results of approximating the solution of the inner problem for a tubular dipole on the basis of the eigenfunction method. In both papers, the eigenfunctions were assumed to be frequency-independent.…”

Section: The Eigenfunction Methodsmentioning

confidence: 99%

“…The columns of the matrix T contain vectors that are close in form to the eigenvectors of the matrix Ẑ of a rectilinear thin wire [5], which was also obtained by segmentation, and TT T = D(1). Thus, using the matrix T we obtain a lower-dimension SLAE with better spectral characteristics, such that…”

Section: The Eigenfunction Methodsmentioning

confidence: 99%

“…In this case, the PFS can be found not at all frequencies. In particular, it was found in [5] that for a thin tubular dipole, the form of the eigenfunctions depends only slightly on the frequency. This is also confirmed by the results of numerical calculations presented in that work.…”

Section: Introductionmentioning

confidence: 99%

“…Third, knowing the frequency dependence of the elements Z k one can approximate the solution of the inner problem with a given accuracy in a wide frequency band [5].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Describing the Radiation and Diffraction of Electromagnetic Waves by the Eigenfunction Method

Табаков

2021

Radiophys Quantum El

View full text Add to dashboard Cite

We consider applicability of the eigenfunctions of the integral operator to solution of the inner problem of electrodynamics (finding the source function of the electromagnetic field) by the method of moments. It is shown that the eigenfunctions can be determined on the basis of solving the complete eigenvalue problem for the moment matrix. In this case, this procedure has a better computation stability compared with the procedure for calculating the characteristic modes of the integral operator, which is based on the same scheme and has gained a wider spread at present. As an example, we consider the problem of diffraction of a plane electromagnetic wave by a helical particle, which is solved by the eigenfunction method. The results of numerical modeling are presented.

show abstract

Section: The Eigenfunction Methodsmentioning

confidence: 99%

Section: The Eigenfunction Methodsmentioning

confidence: 99%

Section: The Eigenfunction Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Third, knowing the frequency dependence of the elements Z k one can approximate the solution of the inner problem with a given accuracy in a wide frequency band [5].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Describing the Radiation and Diffraction of Electromagnetic Waves by the Eigenfunction Method

Табаков

2021

Radiophys Quantum El

View full text Add to dashboard Cite

show abstract

Spectral characteristics of the integral operator of the internal problem of electrodynamics for elliptical frame structure

Табаков

Mayorov

2023

Physics of Wave Processes and Radio Systems

View full text Add to dashboard Cite

The article is devoted to the analysis of electrodynamic properties elliptical frame structure. Taking into account double symmetry internal problem of electrodynamics for the structure under consideration in the framework of the thin-wire approximation is reduced to four integral Fredholm equations of the first kind, written with respect to independent current functions. A study of spectral characteristics of the integral operators of the corresponding integral equations for various values of the electrical length and ellipticity of the frame. It is shown that the eigenfunctions of integral operators for close values of these parameters have a high degree of correlation, with In this case, the eigenfunctions are close in form to trigonometric functions. Features of the frequency dependence of the eigenvalues integral operators. The conclusion is made about the resonant nature of these dependences, what makes an elliptical frame structure in many respects similar to the previously considered tubular vibrator and spherical spiral particle. The results presented in the article form an in-depth understanding of the processes occurring in the structure under consideration, and also serve as a guideline in the construction of approximation models for solving the internal tasks.

show abstract

Solution of the internal and external problems of electrodynamics for a symmetrical vibrator with a reflector made of parallel straight conductors

Tabakov,

Al-Nozaili

2024

Physics of Wave Processes and Radio Systems

View full text Add to dashboard Cite

Background. The work is aimed at the development and research of rigorous methods for calculating multi-element emitting and re-emitting structures, consisting mainly of the same type of elements, as well as studying the physical processes occurring in them. An iterative approach to solving the internal problem is proposed, which allows minimizing the cost of computer time and computer memory. Aim. In this work, using the proposed approach, we solve the internal and external problems of electrodynamics for a symmetrical vibrator with a reflector made of parallel straight conductors. The convergence of the iterative process is studied, the currents on the elements of the structure, its input resistance and radiation characteristics are calculated. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a radiating structure is proposed, which is a symmetrical vibrator with a reflector made of parallel straight conductors. The internal and external problems of electrodynamics are formulated and solved for given parameter values. An effective algorithm for calculating the block matrix of SLAEs is proposed. Recommendations are given for the selection of systems of projection functions within the framework of the method of moments. The convergence of the iterative process for solving an internal problem of electrodynamics has been studied. The input resistance of the structure and the basic characteristics of its radiation are determined. Conclusion. A rational choice of systems of projection functions, based on the properties of the structure and its constituent elements, makes it possible to significantly reduce the size of the SLAE matrix and, accordingly, reduce computational costs. Taking into account the properties of the structure and its constituent elements also makes it possible to construct effective algorithms for calculating the SLAE matrix. It is shown that the convergence of the iterative process may be absent near resonant frequencies, therefore, when solving the internal problem, a combined approach should be used, which involves the use of both rigorous and approximate methods for solving SLAEs. At non-resonant frequencies, the iterative approach demonstrates its effectiveness. It is concluded that for such structures it is advisable to distinguish between resonant and non-resonant operating modes. In the non-resonant mode, the current functions have a fairly smooth dependence on frequency; in the resonant mode, these dependences become quite sharp and difficult to predict. In this regard, the task of developing an iterative approach to solving the internal problem of electrodynamics in resonant operating modes seems relevant.

show abstract

Approximation of Current on a Thin Tubular Vibration Antenna Using the Eigenfunction Method

Cited by 5 publications

References 4 publications

On Describing the Radiation and Diffraction of Electromagnetic Waves by the Eigenfunction Method

On Describing the Radiation and Diffraction of Electromagnetic Waves by the Eigenfunction Method

Spectral characteristics of the integral operator of the internal problem of electrodynamics for elliptical frame structure

Solution of the internal and external problems of electrodynamics for a symmetrical vibrator with a reflector made of parallel straight conductors

Contact Info

Product

Resources

About