# Vol 24, No 3 (2021)

**Year:**2021**Articles:**12**URL:**https://journals.ssau.ru/pwp/issue/view/510

## Articles

### Entanglement of two dipole-couples qubits induced by a thermal field of a cavity with Kerr medium

#### Abstract

In the present work, we investigated the dynamics of two identical superconducting qubits interacting with the mode of the quantum electromagnetic field of a microwave coplanar cavity with a Kerr medium in the presence of an effective dipole-dipole interaction of the qubits. We have found an exact solution of the quantum Liouville equation for the complete density matrix of the system under consideration for the Fock and thermal chaotic initial states of the cavityr field. The exact solution for the full density matrix was used to determine the reduced qubit density matrix and to calculate the entanglement parameter – concurrence. Computer simulation of the time dependence of the concurrshowed that for certain initial states of qubits, their entanglement can be significantly increased in the presence of a Kerr medium and direct dipole-dipole interaction.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):9-17

### The method of simple iterations with correction of convergence and the minimal discrepancy method for plasmonic problems

#### Abstract

The problem of searching for complex roots of the dispersion equations of plasmon-polaritons along the boundaries of the layered structure-vacuum interface is considered. Such problems arise when determining proper waves along the interface of structures supporting surface and leakage waves, including plasmons and polaritons along metal, dielectric and other surfaces. For the numerical solution of the problem, we consider a modification of the method of simple iterations with a variable iteration parameter leading to a zero derivative of the right side of the equation at each step, i.e. convergent iterations, as well as a modification of the minimum residuals method. It is shown that the method of minimal residuals with linearization coincides with the method of simple iterations with the specified correction. Convergent methods of higher orders are considered. The results are demonstrated by examples, including complex solutions of dispersion equations for plasmon-polaritons. The advantage of the method over other methods of searching for complex roots in electrodynamics problems is the possibility of ordering the roots and constructing dispersion branches without discontinuities. This allows you to classify modes.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):18-27

### Advanced research directions in gravitational wave detectors

#### Abstract

The general principles of gravitational waves detection are considered in this paper. Current gravitational wave detectors represent modernized Michelson interferometer – LIGO-detector. Reduction of vibrations in the system and high stabilization of the reflective mirrors is one of the technical problem of the LIGO. It is proposed to study the features of the LIGO-detector with movable mirrors. The software simulating the operation of the LIGO and providing an opportunity to study its characteristics and capacity is developed and named «LIGO-RM». The primary goal of the modelling is to study the signal of the gravitational waves detector with oscillating mirrors. The «LIGO-RM» contains graphic user interface (GUI) that provides interactive control of mirrors movement nature and monitoring of detector signal change. The software simulates the presence of gravitational wave of a requested type and makes it able to monitor its effect on the operation results of the LIGO interferometer in interactive mode or as a numerical outcome. A range of numerical experiments is conducted and the signals on the detector with and without mirrors oscillations are shown. The results of calculations and a possibility of the registration of the gravitational waves using the LIGO-detector with movable mirrors are discussed.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):28-45

### Parametrical synthesis of radio devices with the set quantity of identical cascades for variants of inclusion of jet two-port networks between a source of a signal and a nonlinear part

#### Abstract

The algorithm of parametrical synthesis of various radio devices with any quantity of cascades of type «the jet two-port network – a nonlinear part» by criterion of maintenance of the set frequency characteristics is developed. Nonlinear parts are presented in the form of a nonlinear element and parallel either consecutive on a current or pressure of a feedback. According to this criterion systems of the algebraic equations are generated and solved. Models of optimum two-port networks in the form of mathematical expressions for definition of interrelations between elements of their classical matrix of transfer and for search of dependences of resistance of two-poles from frequency are as a result received. It is shown, that frequency characteristics of investigated radio devices from identical cascades are identical or similar to frequency characteristics of radio devices from one cascade, but with resistance of a source of a signal and the loading, changed definitely. Such schemes are named by equivalent. The comparative analysis of the theoretical results received by mathematical modelling in system «MathCad», and the experimental results received by circuit simulation in systems «OrCad» and «MicroCap», shows their satisfactory coincidence.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):46-55

### The dynamics of synchronization of two-stage van der Pol generator

#### Abstract

Results of numerical simulation of self-oscillations synchronization process in two-cascade ring generator van der Pol by harmonic signal are presented. Studies were carried out within the framework of the DT- model of the dynamic system. The model was developed on the basis of the principle of compliance within the framework of the method of slowly changing amplitudes of characteristics of a discrete system with characteristics of an analog prototype. Shortened equations for complex oscillation amplitudes in generator stages are obtained. It was found that in an autonomous system there is an effect of bistability of amplitudes. In the synchronization mode with an external harmonic signal, solutions of shortened equations made it possible to calculate amplitude-frequency and phase-frequency characteristics of synchronous oscillations. It is shown that transitions between bistable states are observed in the synchronous oscillation holding band. Differences of frequency characteristics of synchronization of classical and two-stage oscillators van der Pol were analyzed.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):56-62

### Parametrical synthesis of radio devices with the set quantity of unequal cascades for variants of inclusion of jet two-port networks between a nonlinear part and loading

#### Abstract

The algorithm of parametrical synthesis of various radio devices with any quantity of cascades of type «a nonlinear part – the jet two-port network» by criterion of maintenance of the set frequency characteristics is developed. Nonlinear parts are presented in the form of a nonlinear element and parallel either consecutive on a current or pressure of a feedback. According to this criterion systems of the algebraic equations are generated and solved. Models of optimum two-port networks of one of cascades in the form of mathematical expressions for definition of interrelations between elements of their classical matrix of transfer and for search of dependences of resistance of two-poles from frequency are as a result received. It is spent mathematical and circuit simulation of the two-cascade amplifier. It is shown, that the increase in quantity of cascades with the optimised parametres leads to substantial growth of a working strip of frequencies. The comparative analysis of the theoretical results received by mathematical modelling in system «MathCad», and the experimental results received by circuit simulation in systems «OrCad» and «MicroCap», shows their satisfactory coincidence.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):63-70

### Mathematical model of a communication channel with an unmanned aerial vehicle

#### Abstract

In this paper, a mathematical model of a communication channel with an unmanned aerial vehicle and taking into account the specifics of the locations of a ground communication point when determining the effects of refraction, diffraction and interference of electromagnetic waves is proposed. A meaningful statement of the problem based on the mathematical relationship between the energy parameters of the first transmission equation and the quality indicators (BER) of the second transmission equation has been formed. The main features of calculating the parameters of the first equation are to determine the rules for calculating the level of attenuation due to the influence of the earth’s surface. The calculation of attenuations for cases of removal of an unmanned aerial vehicle from a ground communication point within the areas of line of sight, partial shade and shadow has been clarified. The second transmission equation is based on the mathematical model of the Rice communication channel. With respect to the energy parameters and the selected communication quality indicator for the formed mathematical model, examples of graphical dependencies are given in the study of typical computational problems. With respect to the energy parameters and the selected communication quality indicator for the formed mathematical model, examples of graphical dependencies in the study of typical computational problems are given.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):71-79

### Refinement of the method for selecting the width of the conductor of printed circuit boards on a metal base, working in the absence of convection

#### Abstract

The article proposes a refined method for calculating the width of the conductors of printed circuit boards on a metal base for the onboard devices of spacecraft, depending on the current flowing. The constructed refined mathematical model of the process of conductive heat exchange between the conductors and the metal base is described. The results of calculations of various, most common, locations of layers of printed circuit boards are presented. An analysis was carried out and a refined methodology was developed based on the results obtained. It allows you to easily (without complicate calculations) calculate the necessary values of the width of conductors. This technique is based on graphical methods, but allows you to perform technical calculations with sufficient accuracy. Accuracy is achieved by using special formulas that simplify the determination of the value of a physical quantity on a logarithmic scale. The disadvantages of the proposed method are indicated.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):80-91

### Asymmetrical dipole antenna based on a phase-correcting dielectric lens

#### Abstract

Problem. Modern mobile robotic systems are increasingly used in various fields of human activity. More and more stringent requirements are imposed on them to ensure high throughput, broadband and reliability of data transmission and control channels at the maximum distance from the control center. And what I would like to note separately is the requirement to reduce the cost of such complexes as much as possible. Therefore, the development of technologically advanced, economically feasible antenna systems that provide an increase in the energy potential of the radio channel in the interval of the robotic complex - control point is one of the ways to solve this problem. Formulation of the problem. It is required to develop a mechanically strong, technological antenna, built on the basis of lens structures of various configurations, made of modern dielectric materials, characterized by reduced weight and size characteristics and cost price, which will increase the level of radiated electromagnetic energy in a wide frequency band. Purpose of the article. Present the developed model of an asymmetric dipole antenna and the results of a numerical experiment. Result. The antenna design is made on a metallized round substrate and is a polystyrene cylinder with a funnel-shaped hole, inside which there is an asymmetrical conical vibrator arm. The results of calculations showed that in the frequency band, which is used to organize direct broadband radio communication channels with robotic complexes, the gain varies within 5.5-9 dB, which is superior in this parameter to the commonly used whip antennas. The calculated standing wave ratio confirms the performance of the developed antenna model in a wide frequency band. The impedance response and the Smith-Smith diagram showed a preliminary calculated spread of the input impedance of the antenna from 30 to 95 ohms. Practical significance. The proposed antenna model ensures manufacturability, mechanical strength, and low cost. The full-azimuth radiation mode and increased gain make it possible to predict the possibility of using this antenna as part of the equipment for the data transmission channel and control of robotic complexes such as unmanned aerial vehicles.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):92-99

### Antenna array with switching scanning in elevation plane

#### Abstract

It is known that the most reliable communication in hard-to-reach places such as the Arctic, Tundra, Taiga is satellite communication [1-5]. Therefore, for satellite communications, it is necessary to develop your own antenna arrays. This article discusses a waveguide-slot antenna array with a Luneburg lens for a mobile satellite communications terminal, which provides a continuous and stable signal. This antenna operates in the 10.9 to 14.5 GHz frequency range. Possesses vertical polarization. The overall dimensions of the antenna array are: diameter of the diagram-forming lens 256 mm (thickness 5 mm, material – FLAN 2.8 (epsilon 2.8, tangent delta – 0.0015)); waveguide length 600 mm (internal section – 10.5 mm by 5 mm, filling – FLAN 2.8). Slotted waveguide antennas and lens are made of standard FLAN 2.8 material (epsilon 2.8, tangent delta – 0.0015) 5 mm thick, foiled on both sides. There are 17 coaxial cables to the HF switch (equal lengths are not required), the scanning step in elevation is 5 degrees. When using 54 waveguide-slot antennas and 18 switch inputs, a scanning sector in elevation of 90 degrees is provided. All the nodes were pre-modeled separately – a cylindrical Luneburg lens with suitable waveguides, excited by slits; slotted waveguide antennas; coaxial-waveguide transitions.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):100-106

### Investigation of CIE color spaces for differences in color differentiation thresholds in different regions of the color locus

#### Abstract

The equidistance of the color space plays a significant role in determining the color difference in color transmission systems. Strictly equal contrasting color spaces can be considered only those color spaces in which equal changes in the visual perception of color are provided with an equal change in the color coordinates in this color space. Currently, the International Commission on Lighting (CIE) has adopted a number of color spaces called equal-contrast. The article presents the results of the study of color spaces adopted by CIE for equal contrast, i.e. on the differences in the thresholds of color differentiation in different areas of the color locus. The article investigated such color spaces as CIE 1931 (RGB), CIE 1931 (x, y), CIE 1960 (u, v), CIE 1976 (u*, v*), CIE LAB (a*, b*).

**Physics of Wave Processes and Radio Systems**. 2021;24(3):107-110

### Method for determining the authenticity of a document based on computer colorimetry

#### Abstract

Determining the authenticity of documents is an important task when conducting investigative measures. In practice, for the examination of documents to determine the prescription of their creation, a spectral method is used, in which it is necessary to make clippings from the document under study, which leads to damage to the document under study, and also requires the use of expensive equipment, which affects the price of the examination of the document. The article describes a method for determining the authenticity of a document based on computer colorimetry, which does not require expensive equipment for conducting an examination. This method for determining the authenticity of a document uses a change in the color of the strokes of a ballpoint pen over time, which is caused by the drying of the solvent in the ink of the pen, and also lacks the disadvantage of the need to damage the document under study.

**Physics of Wave Processes and Radio Systems**. 2021;24(3):111-116