Vol 23, No 4 (2020)

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.

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.

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.

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.

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.

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.