Practical Models of Antenna Systems

130 Pages·2022·3.841 MB·English

by  Amur B. Khashimov, Rinat R. Salikhov

Springer Aerospace Technology
Amur B. Khashimov
Rinat R. Salikhov
Practical Models of
Antenna Systems
Springer Aerospace Technology
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Amur B. Khashimov Rinat R. Salikhov
Practical Models of Antenna
Systems
Amur B. Khashimov Rinat R. Salikhov
Department of Design and Manufacture NPO RTS LLC
of Radio Equipment Chelyabinsk, Russia
School of Electronic Engineering
and Computer Science
South Ural State University (National
Research University)
Chelyabinsk, Russia
ISSN 1869-1730 ISSN 1869-1749 (electronic)
Springer Aerospace Technology
ISBN 978-981-19-6218-9 ISBN 978-981-19-6219-6 (eBook)
https://doi.org/10.1007/978-981-19-6219-6
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Introduction
Mathematical modeling occupies an important place in the design of antenna systems.
This is due to a significant complication of the structure of antenna systems and their
functional characteristics, primarily for phased antenna arrays, where the issues of
mutual influence of radiators should be considered both for a given frequency band
and in the scanning sector, taking into account polarization characteristics. This
leads to the need to use mathematical models of real radiators of antenna systems,
built on the basis of strict electrodynamic relationships and taking into account the
installation object. In this case, the developers of antenna systems have the possibility
of a detailed analysis of the electromagnetic radiation field of antenna systems and the
synthesis of corrective functions of the amplitude-phase distribution to compensate
for the influence
Particular attention in the practice of mathematical modeling of complex antenna
systems is given to the reliability of the results obtained. Therefore, the main results
presented in the book have undergone a detailed verification by solving test problems
that admit a rigorous analytical solution. At the same time, it should be noted that such
solutions are most often represented as infinite Fourier series in special functions,
the calculation of which, in turn, is associated with certain errors. Consequently,
a slight discrepancy between the results of analytical and numerical results of the
study of mathematical models is often associated not only with the approximation
and discretization of a real electrodynamic problem but also with approximations
of finite series, especially in the field of asymptotic estimates of special functions.
Therefore, a high degree of agreement between numerical results and analytical solu-
tions indicates the reliability of mathematical models and the possibility of their use
in the design of antenna systems. In the absence of rigorous analytical solutions to
the corresponding boundary value problems, one of the ways to verify the results
obtained is an experimental study of the developed antenna system. It is impor-
tant that antenna measurements have their own specific features, but the qualitative
agreement of the results is also a criterion for the adequacy of mathematical models.
It should also be noted here that numerous variants of antenna systems developed
using the mathematical models proposed by the authors have received appropriate
experimental confirmation.
v
vi Introduction
The materials of the book may be useful to developers of antenna systems and
students of radio engineering specialties.
In Chap. 1, questions of the asymptotic correspondence of two-dimensional and
three-dimensional problems of antenna technology are considered. It is shown that,
for solving many practical problems, the establishment of such a correspondence
leads to the possibility of a significant simplification of the mathematical modeling
of complex antenna systems installed near various scattering objects. The formulation
of mathematical models in the form of integral equations and the use of effective
numerical methods for solving them makes it possible to obtain a large number
of results that can be used as estimates of the parameters of the designed antenna
systems.
Chapter 2 presents a technique for the formation of mathematical models of
dipole antennas of vertical polarization, installed near extended cylindrical objects
(metal, dielectric, combined). It is shown that the asymptotic correspondence of two-
dimensional and three-dimensional electrodynamic problems, described in Chap. 1,
leads to the possibility of calculating the radiation field of such antenna systems in
the far zone using effective mathematical models in a scalar formulation. The legit-
imacy of the transition from vector problems to much simpler scalar problems has
been proved by computational experiments.
Chapter 3 considers the problems of practical application of methods for correcting
the synthesized excitation of an antenna system, when the actual operating conditions
suggest the possible influence of various scattering objects. As a rule, the influence
of such objects leads to the formulation of incorrect problems, since the specified
requirements for correction lead to unrealizable excitation functions. It is shown
that the variational formulation of the correction problem leads to the possibility of
using methods for minimizing variational functionals and the iterative regularization
method. Computational experiments show high efficiency of iterative regularization
in the presence of random errors in the input data.
In Chap. 4, statistical modeling of the accuracy of the functioning of the localizer
antenna system of the radio navigation system was carried out. The need for such
a study is due to the multifactorial influence of various random errors that occur
in the dividers and cable paths of the emitters, and the instability of the transmitter
frequency. The obtained statistical estimates of accuracy can be used in the design
of antenna systems and in the practice of operating radio navigation systems.
Chapter 5 discusses the practical application of orthogonal bases for the decom-
position of polarization vectors for the synthesis of excitation of a promising radio
navigation system VDB (Very High Frequency Data Broadcast). The application of
methods for optimizing the residual functional of the solution in the frequency band
leads to the possibility of constructing an antenna system that meets the specified
requirements for both the directional properties and the polarization characteristics
of the radiation field. Experimental studies confirm the reliability of the adopted
design solutions.
Chapter 6 provides a consistent method for forming a mathematical model of a
DME (Distance Measuring Equipment) antenna system. The use of integral equations
of the second kind provides a stable numerical solution for thin metal reflectors
Introduction vii
using special quadrature formulas. To optimize the shape of the reflector, a nonlinear
function is used, the minimization of which leads to acceptable characteristics of
the radiation field. An example of the practical use of the developed mathematical
model for designing an antenna system is given, the simulation results are confirmed
by experimental studies in the coverage area of the antenna system.
In Chap. 7, based on the asymptotic correspondence of two-dimensional and
three-dimensional problems, using a rigorous electrodynamic approach, methods for
solving the ill-posed problem of reconstructing the radiation field from the results of
measurements in the near field are considered. This assumes the presence of statistical
measurement errors that affect the accuracy of the reconstruction. The mathematical
reconstruction model takes into account the influence of nearby scattering objects. A
series of computational experiments were carried out using iterative regularization
of an ill-posed reconstruction problem.
At the end of the book is a bibliographic list, which does not claim to be complete.
All calculations were carried out on the basis of the supercomputing center of the
South Ural State University (National Research University, http://supercomputer.
susu.ac.ru. South Ural State University (National Research University).
Amur B. Khashimov
Rinat R. Salikhov
Gratitude
The authors of the book express their deep gratitude for many years of coopera-
tion and work on joint projects: Candidate of Technical Sciences M.S. Vorobyov,
Associate Professor of the Department of Infocommunication Technologies, South
Ural State University, and Candidate of Technical Sciences L. P. Kudrin, Associate
Professor of the Department of Design and Production of Radio Equipment, South
Ural State University. Thanks to the participation of colleagues, a number of results
were obtained, which are reflected in the book.
The authors will always remember with warmth and gratitude: A. I. Gromov,
senior engineer, leading specialist in antenna arrays of the USSR and the Russian
Federation; G. N. Pirogov, chief designer of the air navigation and landing system of
civil aviation of the USSR and the Russian Federation; A. M. Baidikov, a specialist
in air navigation systems, a participant in the Buran project.
The authors of the book are grateful for many years of communication, advice,
support to the staff of the Institute of Radio Electronics and Information Technology-
RTF of the Federal State Autonomous Educational Institution of Higher Education
“Ural Federal University named after the first President of Russia B. N. Yeltsin”:
Doctor of Technical Sciences B. A. Panchenko, Professor of the Depart-
ment of High-Frequency Radio Communications and Television, Doctor of Tech-
nical Sciences S. T. Knyazev, Professor of the Department of Radioelectronics
and Telecommunications, Vice-Rector for Academic Affairs; Doctor of Tech-
nical Sciences S. N. Shabunin, Associate Professor, Head of the Department of
Radioelectronics and Telecommunications.
Separately, the authors note the contribution to the creation of the book and thank
E. G. Popova, Head of the project to popularise Russian aviation science and tech-
nology abroad. Thanks to her motivation, dedication, perseverance, this book was
written.
The authors are grateful to the translator of the book A. V. Kudryashova.
The authors thank their family and friends for the opportunity to devote enough
time to writing the book.
The authors are grateful and thankful to their employers:
ix
x Gratitude
Federal State Autonomous Educational Institution of Higher Education “South
Ural State University (National Research University)”
“SUSU (NIU)”; www.susu.ru
NPO “RTS” LLC, www.nports.ru.