## Vol 23, No 4 (2020)

**Year:**2020**Articles:**11**URL:**https://journals.ssau.ru/pwp/issue/view/455

###### Abstract

In the electrodynamic calculation of microwave (EHF) devices using methods that lead to algorithms in an open form, strict integral relations (representations) are very useful: Lorentz lemma, reciprocity theorem, orthogonality condition for eigenwaves, etc. of the results obtained, their convergence improves, and in some cases the calculation of characteristics that cannot be calculated without the indicated representations. Integral representations are a record of the equations of electrodynamics (in any unified form) and their solutions in one or another generalized form, linking in general the electromagnetic fields in electrodynamic structures described by boundary value problems. Integral views are used to control the results obtained; in some cases, they allow obtaining analytical solutions; lead to self-consistent problems that take into account the reverse effect of the radiation field on the primary sources; allow obtaining a priori information about the spectrum of possible solutions; solve associated problems as specific problems of arousal. Consideration of the phenomenon of complex resonance in this work shows that integral representations make it possible to establish a connection between non-self-adjointness and self-consistency of boundary value problems.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):8-18

###### Abstract

Various forms of integral representations of the electromagnetic field are considered. It is shown that the use of analytically developed integral representations of the electromagnetic field instead of the vector potential method makes it possible to significantly simplify the formulation of the internal and external electrodynamic problem for specific structures. The numerical results of solving problems of radiation and diffraction of electromagnetic waves are presented. It is shown that taking into account the peculiarities of the geometry and using projection functions close to the eigenfunctions of the integral operator of the internal electrodynamic problem for basic elements make it possible to construct effective algorithms for the electrodynamic analysis of metastructures. A mathematical model of a multistage chiral frame is proposed. By the example of a tubular vibrator, the possibility of approximating the solution of an internal electrodynamic problem using eigenfunctions is demonstrated. The prospects for further development of the integral representations of the electromagnetic field method are considered.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):19-35

###### Abstract

In the article, the features of using the barycentric method in solving problems of electrodynamic analysis of mirror antennas are considered. The solution of the internal problem of electrodynamics is the basis of the study. The problem of electrodynamic analysis of a mirror antenna is formulated in the classical representation of the problem of diffraction of an electromagnetic wave on a system of infinitely thin perfectly conducting screens of arbitrary shape and reduced to a system of integro-differential equations. The solution of the latter is performed numerically in the projection formulation of the Galerkin method when determining the approximation of the desired surface current density function in the system of global basis functions formed in the approximation of the barycentric method for the analyzed screen. The integral representation of the electromagnetic field of the mirror antenna, taking into account the properties of the introduced basic functions, is given. The features of the algorithmic implementation of the developed solutions are clarified. The efficiency and comparative preference of the use of the barycentric method in the problems of electrodynamic analysis of mirror antennas are tested on test examples.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):36-47

###### Abstract

Cylindrical Lunebeg lenses allow azimuthal scanning in a wide sector of angles. The article discusses a cylindrical Luneberg lens with an out-of-focus parallel printed circuit boards made of thin fiberglass (FR-4) with an etched H-shaped metamaterial structure. The distribution of the electric field in the azimuthal plane is shown when a linearly polarized plane wave is incident on the lens surface parallel to the printed circuit boards. The dependence of the focal length on the frequency is shown. Conclusions are drawn about the effect of dispersion on the focal length. To clarify the value of the focal length, the directional characteristics of the antenna system are considered when the focal length is changed. Directional characteristics are investigated when the feed is rotated in the azimuthal plane. The results presented in the article are planned to be used to create broadband Luneberg lenses from metamaterials.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):48-55

###### Abstract

The article presents the theoretical foundations for constructing invariant and quasi-invariant relative to the disturbing influences of measuring systems. A historical reference which shows the emergence, evolution and spread of methods of the theory of invariance from automatic control and regulation systems to information and measuring systems and measurements in general is given. The possibilities of new applications of the formulated by academician B.N. Petrov of the two-channel principle are shown. On its basis, methodological signs of the physical feasibility of structural and technological methods are formulated. Theoretical foundations and the method of linearization of principally nonlinear transformation functions of parametric measuring transducers, which are also based on the principle of two-channel, are given. All theoretical positions are supported by practical examples that extend the capabilities of the considered methods to the entire class of parametric measuring transducers as part of non-equilibrium measuring bridges and voltage dividers.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):56-67

###### Abstract

In modern systems of radiolocation, navigation and communication, the requirements for antennas are becoming higher requirements every year, namely: operation in a wide frequency range, the ability to change of direction of the main lobe of the radiation pattern. Antenna systems with similar characteristics can be built using dielectric antenna beamforming structures. One of these structures is the Luneberg lens, the peculiarity of which is its spherical symmetry. However, the curved surface of this lens significantly complicates the placement of transmitting and receiving elements along it, which increases the complexity of constructing the entire antenna system. This paper proposes an algorithm for constructing a Luneberg lens with a flat surface. The lens was synthesized using the method of quasi-conformal optical transformations, the mathematical algorithm of which is also described in this work. The paper also presents the results of mathematical modeling of the antenna system using a Luneberg lens with a flat surface at different positions of the emitter relative to the center of the lens, as well as different cut angles. The simulation results show that the synthesized lens can be used to construct a multi-beam antenna system that allows the direction of the main lobe of the antenna radiation pattern to be rearranged over a wide range of angles. However, the scanning angles of this system are limited by the lens geometry, the larger the maximum scanning angle we choose, the more significant the influence of the side lobes on the radiation pattern becomes.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):68-73

###### Abstract

The results of integrity of narrowband and wideband lumped element circulators design methodology to the computer aided design system of microwave devices AWR Microwave Office are presented in the article. The calculation method of narrow band circulators circuits which consist of serious and shunt tuning capacities is investigated. The simple and visual method of wideband ferrite isolators optimize design based on circulation impedance calculation is described here. The results of design of the ultra wideband circulator with shunt capacity, serious resonant matching circuit and serious resonant circuit between common terminal and ground are considered. The new theoretical results of calculation of two schematics of wideband high power circulators with serious tuning capacity are presented. The first schematic is formed with matching resonant network being connected in serious at each terminal. It is shown that double hump characteristic is realized. The second schematic is formed with serious resonant network connected between common terminal and the ground. It is shown that four-order Tchebycheff characteristic is realized.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):74-84

###### Abstract

Based on the phenomenological equations describing the dynamic processes of magnetization of ferromagnets of inductors and polarization of capacitor dielectrics, taking into account complex frequency-dependent dielectric constants e(jw) of capacitor dielectrics and magnetic permeabilities m(jw) of inductor cores, equivalent electrical structural-parametric and capacitor replacement circuits were obtained. The connection of parasitic elements of equivalent electric circuits of capacitors and inductors with the electrophysical characteristics of the material of the dielectric of the capacitor and the inductor core, which determine their frequency properties, structure and parameters of the elements of the equivalent circuit, is established. The features of the design of line radio interference filter taking into account the parasitic parameters of the inductors and capacitors of line radio interference filter, found as a result of the synthesis of equivalent electric circuits of the inductors and capacitors in a wide frequency range of 150 kHz – 30 MHz.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):85-96

###### Abstract

This article is devoted to the study of the possibilities of increasing spectral efficiency in MIMO systems by using antennas with substrates of biisotropic and bianisotropic chiral metamaterials and various types of fractal emitters, in particular, fractal structures in the form of a Sierpinski triangle, Koch and Gilbert curves, as well as a dipole triangular antenna of complex configuration – FRM. The spectral efficiency was calculated by using one of the variations of the Shannon formula, which includes a complete matrix of Z-parameters. In turn, this matrix was determined using the software package of electrodynamic modeling. It is shown that the use of such antennas with the fractal geometry of the emitters located on chiral substrates reduces the mutual influence between the emitters, and, in turn, increases the spectral efficiency in several frequency ranges compared to traditional solutions.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):97-110

###### Abstract

The paper presents the results of calculating the angular spectra of light reflection under the condition of excitation of surface plasmons in the Kretschman scheme. The silver layer in this scheme plays the role of a reference material, the minimum in the angular spectrum of which serves as a reference point for the shift of the minimum of the angular spectrum when a layer of the studied biological material is added to the considered layered system, which were melanin and biological tissue. As a result of the work, specific pronounced minima in the angular spectra were obtained, which make it possible to identify these materials with a high degree of accuracy due to the narrow resonance peaks in the angular reflection spectra, which are spaced from the peak in the reflection from the silver film by certain angles. The method contains all the characteristic features of the resonance spectroscopy method; the conditions for the excitation of a surface plasmon at the metal boundary act as resonance conditions.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):111-115

###### Abstract

The solution of the genetic-mathematical problem of interaction between the human population and the virus population in relation to the problem of the COVID-19 pandemic is presented. It is noted that the virus does not interact with the entire human body, as a set of complex organs, but with its individual cells. A mathematical model based on the Hardy–Weinberg law is used, consisting of two linear interdependent differential equations relatively to the frequency of an allele with different right sides. The equations reflect the time dynamics of human cells and virus populations during their interaction. In the equation for the virus population the right side is a constant value that characterizes the death of viruses due to the human immune system. In the equation for human cells population the right side depends linearly on the allele frequency of the virus population. The right side of this equation characterizes the death of a cell when a virus inserted in its DNA for its reproduction. Solutions of differential equations are found and the results of these solutions are analyzed. The duration of the pandemic was estimated using parameters of human liver cells and influenza virus.

**Physics of Wave Processes and Radio Systems**. 2020;23(4):116-122