# Vol 24, No 2 (2021)

## Articles

### Generalization of the Fourier problem of temperature waves in half-space

#### Abstract

The problem of asymptotic fluctuations of temperature and moisture content in a half-space whose boundary is blown by an air flow with a temperature varying according to the harmonic law is solved by the method of complex amplitudes. The material filling the half-space consists of a solid base (capillary-porous body) and water. The well-known Fourier solution for temperature fluctuations in half-space in the absence of moisture and under the boundary conditions of heat exchange of the first kind is generalized to the case of a wet material under the boundary conditions of Newton for temperature and Dalton for moisture content. The results of the work can be used in geocryology to model seasonal changes in the thermophysical state of frozen rocks and soils, in the theory of building structures to study the thermal regime of indoor premises with fluctuations in ambient temperature, in the theory of drying by electromagnetic radiation to study the processes of heat and mass transfer in oscillating modes.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):13-21

### Interaction of electromagnetic wave and metamaterial with inductive type chiral inclusions

#### Abstract

The principle of calculation of a plate from a metamaterial with inductive type chiral inclusions is submitted. It is shown that distribution of an electromagnetic wave to such substance can be investigated with the help of introduction of a chiral parameter and on the basis of a detailed method of calculation. By comparison of two methods the dependence of chiral parameter from frequency of electromagnetic radiation falling on a plate is found. With the help of a detailed method the nonlinear differential equation for potential on the chiral plate is found. It is shown that this equation has solutions as traveling solitary and standing waves but not traveling sine waves. The analysis of the received solutions of the nonlinear equation is carried out. Transition from the multiwave solution to the solution as standing waves is graphically shown at reduction of distance between the chiral elements.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):22-31

### Assessment of the resistance of technical means of space systems and complexes to the effects of electrostatic discharges

#### Abstract

In order to further improve the methods of protecting the onboard spacecraft equipment from the effects of electrostatic discharges, based on a comprehensive study of the problem of the occurrence of electrostatic discharges, the authors carried out the studies described in this article to analyze the functioning of the onboard spacecraft equipment under the influence of electrostatic discharges. In the course of the research, the methodology for assessing the resistance of the onboard equipment of the spacecraft to the effects of electrostatic discharges was refined, based on the generalization of the calculation and analytical work. The analysis of the resistance of the onboard equipment of the spacecraft was carried out taking into account the main mechanisms of the effect of electrostatic discharges on the onboard space network. Taking into account the need to assess the resistance of the onboard space network equipment to electrostatic discharges outside real operating conditions, the authors assess the resistance of the onboard space network equipment on the basis of mathematical and physical modeling. As a result of the study, an algorithm was developed for assessing the resistance of the onboard equipment of a spacecraft to the effects of electrostatic discharges, which is described in detail in this article.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):32-40

### Determination of the crystal lattice parameters based on the fast Fourier transform

#### Abstract

In this work, it is shown that the image formed as a result of the passage of coherent radiation through the crystal has certain characteristic features. When the crystal is rotated with respect to the propagation axis of the investigated beam, the formation of the intensity distribution of a complex structure associated with the transformation of the «flat image» into «volumetric» was detected at the output. Crystalline plates can be used to form the distribution of a continuous «flat» light field in the implementation of a real 3D scene, which can provide a three-dimensional image on a television screen, as well as on a computer monitor screen. It can also be used in billboards. The three-dimensional image obtained in this way can be observed directly with the eyes of a person (without using special glasses. Thus, the information capacity of the image on the screen increases, and the perception of the picture approaches real conditions.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):41-48

### Calculated estimation of electromagnetic compatibility of radio-electronic means of space systems and complexes

#### Abstract

This article presents the methods of complex computational and analytical assessment of ensuring electromagnetic compatibility of technical means (electrical, electronic and radio-electronic means of launch vehicles and spacecraft). These methods allow us to conduct a comprehensive computational and analytical assessment of the electromagnetic compatibility of the technical means of rocket and space technology, which in its essence allows us to assess the mutual influence of the technical means of rocket and space technology already at the design stage of rocket and space technology objects. The analysis of the results of the assessment of the electromagnetic compatibility of the technical means of rocket and space technology allows us to develop organizational and technical measures aimed at ensuring the electromagnetic compatibility of the technical means of rocket and space technology at all stages of the life cycle of objects of rocket and space technology. To assess the electromagnetic compatibility of the technical means of rocket and space technology, an integrated approach was chosen due to the large dimension of the initial data and the variety of possible variants of interference penetration.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):49-54

### Spectral expansion method for analysis of a system with shifted Erlang and hyper-Erlang distributions

#### Abstract

In this paper, we obtained a spectral expansion of the solution to the Lindley integral equation for a queuing system with a shifted Erlang input flow of customers and a hyper-Erlang distribution of the service time. On its basis, a calculation formula is derived for the average waiting time in the queue for this system in a closed form. As you know, all other characteristics of the queuing system are derivatives of the average waiting time. The resulting calculation formula complements and expands the well-known unfinished formula for the average waiting time in queue in queuing theory for G/G/1 systems. In the theory of queuing, studies of private systems of the G/G/1 type are relevant due to the fact that they are actively used in the modern theory of teletraffic, as well as in the design and modeling of various data transmission systems.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):55-61

### Mathematical model of delay based on a system with gamma distribution

#### Abstract

This article is devoted to the analysis of a queuing system formed by two flows with density functions of the gamma distribution law in order to derive a solution for the average delay of requests in the queue, which is the main characteristic for any queuing system. According to this characteristic, for example, packet delays in packet-switched networks are estimated when they are modeled using the queuing system. In queuing theory, studies of G/G/1 systems are especially relevant because there is no solution in the final form for the general case. Therefore, in the study of such systems, various particular distribution laws are used as an arbitrary distribution law for G. In the study of G/G/1 systems, an important role is played by the method of spectral decomposition of the solution of the Lindley integral equation, and most of the results in the theory of queuing were obtained using this method. The article presents the derivation of the calculation formula for the average delay of requests in the queue in the system under consideration, also based on the spectral decomposition method.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):62-67

### Electrophysical characteristics of germanium MIS structures with rare-earth element fluorides

#### Abstract

The electrical properties of MIS structures with rare-earth element fluorides on germanium substrates were studied to analyze the possibility of using these materials as gate dielectrics of devices. The structures are also studied from the point of view of assessing the degradation of their electrophysical properties under the action of electric fields of ~108 V/m, which act on the dielectric during electroforming, since the MIS structures with rare-earth element fluorides have the property of bistable switching. Studies of the I-V and C-V characteristics show that all structures have approximately the same value of the density of surface states at the rare-earth element / Ge fluoride interface. The leakage currents in the MIS structures with TmF3 and SmF3 film are less than in the MIS structures with NdF3 film of greater thickness. There is also no effect of reducing the current density when using the double film structure CeF3/DyF3. The most promising material with a low leakage current at a fairly high value of the dielectric constant in germanium MIS structures is thin-film samarium fluoride.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):68-72

### Reflection of waves from a mobile elastic layer in a multimode waveguide

#### Abstract

Waveguide structures are used to transmit energy and information signals in a wide range of wavelengths and, in terms of wave-guiding physical properties, usually have mutual (identical) properties in forward and backward directions. The asymmetry of the structure and external influences can often cause non-reciprocity of structures for waves, propagating in mutually opposite directions (this property, although limited, is already used in the so-called nonreciprocal devices of microwave, EHF and optical ranges such as ferrite valves, circulators, phase shifters). At the same time, the nonreciprocal properties of wave-guiding structures, independent of their physical nature, were not considered. It is found, that the motion of the medium filling the acoustic waveguide leads to nonreciprocity of its parameters in the forward and backward directions. The degree of nonreciprocity is proportional to the velocity of the medium. The velocity of the medium also affects the propagation velocity of acoustic waves and leads to a change in the critical frequencies or critical wavelengths of the waveguide modes. As the velocity of the medium increases, the number of modes for which the propagation condition is satisfied increases as well.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):73-78

### Formation of additional virtual reception channels when processing signals at the outputs of elements of the antenna array of a promising cellular base station

#### Abstract

The results of research on the layout of the antenna array for a promising cellular base station in the frequency range 1,8–1,88 GHz, which includes a linear antenna array of 12 slotted elements with rectangular directors, the diagram – forming scheme of which uses a modification of the Rotman lens, characterized in that for the sake of reducing its overall dimensions, the lens is folded in half – the earth is located in the center, and on both sides of it-the halves of the lens body with exponential strip transformers. It is shown that to reduce the level of the side lobes of the antenna system in the reception mode, interpolation and extrapolation antenna arrays can be used. An extrapolation array can also be formed in order to increase the directional coefficient of the receiving antenna system and resolve radio sources that are not resolved by the «real» antenna array.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):79-87

### Development of a phased array antenna powered by Rotman printed lens for a mobile satellite communication terminal

#### Abstract

Connecting to the Internet whenever and wherever you travel is no longer a luxury. All people have the ability to connect to the Internet and share data away from home. Satellite communications are now an integral part of successful and high-quality communications. Satellite communications antennas are usually installed on mobile ground terminals. Due to its wide coverage and versatility, satellite communications are continuously improving and adapting to the telecommunications needs of many countries, despite the fact that broadband, Internet and fiber - optic communications are used almost everywhere. We know that more than 50 % of all satellites in orbit are communications satellites.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):88-102

### Influence of the switching frequency of the switch and the amplitude of the reference voltage of a pulsed voltage regulator of the lowering type on its stability

#### Abstract

On the basis of classical stability criteria, using the expressions of the transfer function, according to the block diagram, the stability of the impulse controller with feedback is estimated. The influence of the switching frequency of the switch and the amplitude of the reference voltage on the stability of a pulsed voltage regulator of a lowering type with deterministic parameters of the system is analyzed. In accordance with the Nyquist criterion for the transfer function of an open-loop system, both stability and phase stability margins for a closed-loop system can be estimated. When simulating the operation of the device, the phase stability margin was obtained, according to the Nyquist criterion, which is γс = Н = 7°. An increase in the sawtooth voltage is not a desirable phenomenon, which, although it increases the margin of stability, however, reduces stability. Moreover, the dependence of the ripple, affecting the stability of operation, on the amplitude of the sawtooth voltage is not a predictable value and takes on a random value

**Physics of Wave Processes and Radio Systems**. 2021;24(2):103-108

### Bifurcation processes in pulse voltage regulator

#### Abstract

Analysis of a pulse voltage regulator from the point of view of transition to an unstable position and possible bifurcation states. Calculation of the stability condition when changing the parameters of the system. Obtaining the pulse voltage regulator stability surface. This voltage stabilizer can have the basic intrinsic parameters of the system, such as, for example, the load resistance, the value of which can change over time according to unknown laws. In the course of the work, the stability limits for static and dynamic bifurcations were obtained with respect to many parameters of the system, including with respect to the value of the load conductivity. To obtain numerical results, a system with the following main parameters was used: U = 4,1 V, d′0 = 0,4, C = 600 μF, L = 2 mH, f1 = 0,8 Ohm, G = 0,5 V–1, RL = 2 Ohm.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):109-112

### Historical aspects of fractal theory appearance

#### Abstract

In paper short definition of a fractal is made, its basic properties are resulted, historical preconditions of origination fractal theories in a context of terms «assemblage» and «function» which development is observed from the moment of their origination before formation of their notional apparatus are in detail observed. Names, years of life and a photo of the scientists who have brought in the basic contribution to development of observed terms are resulted. As result of the retrospective analysis, it is shown that appearance of the fractal theory is the integral stage in evolution of mathematics and physics. Short listed the main routes of the fractal theory practical application in the field of radio engineering and electronics among which some scientists who have brought in a practical mite in development of a modern science and its practical applications are gated out. In particular, pioneers of fractal theory which application found wide practical application are resulted.

**Physics of Wave Processes and Radio Systems**. 2021;24(2):113-126