Estimating an Error of the Excitation-Field Model in the Form of a Delta Function in the Theory of Dipole Antennas
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Radiophysics and Quantum Electronics, Vol. 62, No. 11, April, 2020 (Russian Original Vol. 62, No. 11, November, 2019)
ESTIMATING AN ERROR OF THE EXCITATION-FIELD MODEL IN THE FORM OF A DELTA FUNCTION IN THE THEORY OF DIPOLE ANTENNAS A. V. Sochilin and S. I. Eminov ∗
UDC 621.396:517.9
We compare the values of the input impedance of a linear dipole antenna, which are obtained on the basis of solving integral equations by the exact and approximate methods. The expansions in terms of the weighted Chebyshev polynomials and trigonometric functions are used for solving the equations with exact kernels. The results obtained by our own methods are compared with those obtained using the well-known MMANA code, which is based on solving the integral equation with the approximate kernel and the delta-function model. The dependences of the input impedance on the primary-field distribution are studied theoretically and numerically. The errors resulting from replacing the exact kernel with an approximate one are determined.
1.
INTRODUCTION
The methods for calculating dipole antennas on the basis of solving integral equations have been developed since 1930s [1, 2]. With the advent of computers, these studies were intensified using such numerical techniques as Galerkin’s method, the collocation method, and the method of moments. An integral equation with the approximate kernel was used as a mathematical model of a dipole. The results of the studies in this field are systematized in [3]. The main achievement is that the values of the input impedance of the dipole antennas, which were obtained by numerical methods, are in good agreement with the experimental results. A new direction of studies, which is related to explicit isolation of the logarithmic singularity of the kernel of an exact integral equation, started in the 1980s [4, 5]. This approach allows one to use the experience gained in the theory of diffraction of electromagnetic waves by the screens. However, this approach involved serious difficulties related to the presence of a small parameter, i.e., the dipole-antenna radius and locality of the excitation region. Further development of the theory of dipole antennas is related to overcoming these difficulties. Interest in these studies is also due to the fact that such methods are employed to analyze the widely used microstrip and slot antennas. The works of the last two decades [6–9] deal with theoretical studies of equations and the development of various numerical methods for calculating the antenna input impedance. Nevertheless, these works lack a comparison with the results of other works and do not demonstrate the convergence rate. The efficiency of the numerical methods of these works when calculating the input impedance, which is the most sensitive to the antenna-parameter variations, remains undetermined. On the other hand, various software packages, such as MMANA [10], CST Microwave Studio, FEKO, Ansoft HFSS, etc., have been developed and are used at present. Therefore, the problem of comparing different methods is very
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