# Vol 25, No 4 (2022)

## Articles

### Approaches to mathematical modeling of coatings that protect against electromagnetic radiation in the soft X-ray range

#### Abstract

The objects of study are composite structures that protect agaist electromagnetic radiation in the soft X-ray range. The purpose of this work is to propose approaches to the mathematical modeling of coatings based on these structures, to calculate the reflection and transmission characteristics of a homogeneous plane wave incident at different angles on such coatings. Research methods - electrodynamic modeling, graph theory, three-dimensional electromagnetic modeling in CAD. Mathematical models of multilayer structures obtained on the basis of the electrodynamic approach and using graph theory, the results of calculations of the reflection and transmission characteristics of a homogeneous plane wave incident at different angles on such structures are presented. The prospects for the use of film coatings with air holes are considered. The results obtained in the course of the work may be used to create coatings that protect electronic equipment from the effects of X-rays.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):9-26

### Discrete time model of self-oscillations with spectral line widening

#### Abstract

An algorithm for generating quasi-harmonic self-oscillations with a uniformly widened spectral line is presented. The algorithm is based on the equation of motion of the Thomson-type DT-oscillator, which introduced a random effect in the form of band-pass white noise. Two types of effects are implemented: additive and parametric. Spectral characteristics of generated self-oscillations were analyzed by numerical experiment. The additive algorithm is shown to generate self-oscillations with amplitude-frequency fluctuations. Frequency fluctuations set the Lorentz (resonant) shape of the central part of the self-oscillation power spectrum, amplitude fluctuations form a noise pedestal of the spectral line. Based on the analysis of statistical characteristics of fluctuations in the frequency of the DT-oscillator with additive noise impact, a parametric algorithm for generating quasi-harmonic self-oscillations is proposed. In it, the resonance frequency of the oscillating system of the Thomson DT-oscillator is subject to random perturbations. The results of numerical experiments with generators of quasi-harmonic oscillations are given.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):27-32

### Spectral solution for a delay system with hyper-Erlang distributions

#### Abstract

The article is devoted to the construction of a mathematical model for delaying claims in a queue in the form of a queuing system described by two flows with the laws of distribution of time intervals shifted to the right by hyper-Erlang distributions of the second order. In the queuing theory, the study of systems G/G/1 is relevant because there is no solution in the final form for the general case. Therefore, various partial distribution laws are used as an arbitrary distribution law G in the study of such systems. In this case, the use of the shifted hyper-Erlang distribution law provides the coefficient of variation of the input flow arrival intervals and service time over the entire interval (0, ∞). To solve the problem, we used the method of spectral solution of the Lindley integral equation, which plays an important role in the queuing theory. This method made it possible to obtain a solution for the average delay of requests in the queue for the considered system in a closed form. As is known, the remaining characteristics of the queuing system are derivatives of the average delay of requests in the queue.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):33-38

### Increasing of bit error rate performance for OFDM systems over fading channels

#### Abstract

A method for increasing performance of OFDM systems in multipath channels is proposed. The proposed method uses Kalman filter based channel estimator with block type pilot structure. Performance of the proposed method has been demonstrated for GSCM/EDGE channel models, typical for urban area and very small cells. The characteristics of the proposed algorithm are compared with other well-known methods. The impact of Doppler spread is considered. A computer simulation has been carried out to evaluate the required signal-to-noise ratio in case of fixed bit error probability. It is shown, that proposed method leads to lower bit error ratio for slow fading case, but its performance degrades with increasing Doppler frequency.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):39-45

### Phase frequency characteristics evaluation for E-class devices output circuits

#### Abstract

Based on the unitarity of the E-class device circuit [S]-matrix, the phase frequency characteristics are estimated for the output circuit at any harmonic of the fundamental frequency. Formulas are derived for approximate phase frequency characteristics of an E-class device model with a switch that operates in two states corresponding to either zero or infinite active resistances. Using the example of the presented phase-frequency characteristics of the E-class power amplifier layout, the validity of the formulas obtained is confirmed. Taking into account the conclusions drawn from the formulas, recommendations are formulated for making additions to the well-known methods of designing E-class devices. These techniques can be supplemented by the introduction of parameter settings of the elements of the output circuits, for which the established estimated values of the phase frequency characteristics of the output circuit on harmonics are most respected with the maximum possible number of them.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):46-51

### Modeling of electrodynamic parameters of microwave sterilizer

#### Abstract

For the sterilization of medical instruments, a technology for their immersion heat treatment with intense microwave radiation at the frequency of 2,45 GHz is analyzed. The advantages of this technology in comparison with traditional methods are shown. An electromagnetic model of a microwave sterilizer for surgical tools was built, taking into account the temperature dependence of the complex dielectric permittivity of the immersion medium (water). A rectangular cavity with a waveguide excitation was used as its basic unit. With the help of a numerical model on the finite element method, the values of the reflected and absorbed power, as well as the heating rate of water in the sterilizer for an operating power of 600 W, were determined. The analysis of thermal processes, performed according to a simplified method, showed a rather high efficiency of such device, which provides a high heating rate at a given frequency.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):52-58

### Analysis of heating of printed circuit board conductors on a metal base for spacecraft devices at pulsed current

#### Abstract

The article presents the results of the analysis of heating of printed circuit conductors of printed circuit boards mounted on a metal base, on-board device of spacecraft when pulsed current flows through them. Thermal transient and impulse characteristics of a system consisting of a printed conductor and a printed circuit board are considered. The analysis of the dependence of the temperature rise rate of printed conductors and the duration of transient processes on the linear dimensions of the system elements is given. It is noted in the article that the time of transient processes most strongly depends on the thickness of the layer of insulating materials. All the results were obtained in the process of modeling transients in the ANSYS 2019 R1 Transient Thermal module. Practical recommendations on the consideration of thermal transients in printed conductors in the design of printed circuit boards are given.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):59-66

### Investigation of electrical properties of photosensitive structures of reduced dimension based on silicon coated with rare earth fluorides

#### Abstract

In this paper, we consider the effect of porous silicon and dysprosium fluoride films on the current-voltage characteristics of low-dimensional photosensitive structures based on silicon. The processes of creating and studying the resulting photosensitive structures are described. The current-voltage characteristics of the structures before and after coating are given. The study found a positive effect of porous silicon and dysprosium fluoride coating on the current-voltage characteristics of structures both with and without porous silicon. Values of the optimal thickness of the dysprosium fluoride coating for porous photosensitive structures are obtained. It is shown that dysprosium fluoride coatings do not always have a positive effect on such parameters of photosensitive structures as short-circuit current and open-circuit voltage, since this is due to the non-uniformity of film deposition on the surface of the structure.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):67-73

### How the accuracy of mobile objects positioning with GNSS affects the energy characteristics of the communication channel in 5G networks

#### Abstract

The analytical relations determining the dependence between the accuracy of positioning objects-subscribers on the GNSS signals and the accuracy of pseudorange measurements were obtained. Based on these relationships, the relationship between positioning accuracy and the distribution of power radiated by the antennas into the space is revealed, which allows us to estimate the error of pointing the antenna beams in space. The correlations are based on the assumption of a Rayleigh channel for GNSS signal propagation. It is shown that the positioning accuracy of objects at the pseudo range error of 1 m and a beam width error of 2 degrees determines the average reduction in signal power in the radio channel, due to errors in positioning objects, not more than 0,25 dB, the normalized value of the standard deviation is equal to 13,5 dB. Due to positioning errors it is possible to reduce the signal strength in the radio channel by up to 1 dB.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):74-78

### Detection characteristics and features of signal processing of aerial objects on images of spacborne synthetic aperture radars

#### Abstract

The article considers the possibilities of detecting airborne moving targets by space radars with aperture synthesis using interferometry mode along the path. The method of calculating the signal-to-noise ratio, the characteristics of detecting aerial targets in the mode of selection of moving targets is described. Based on calculations, it is shown that the dynamics of the underlying surface caused by fluctuations in grass, foliage or an agitated sea surface significantly reduces the ability to detect aerial objects by space radars with aperture synthesis in the selection of moving targets mode. It is shown by the examples of existing space radars with aperture synthesis that when using the interferometry method along the path, at least 2 interferometric bases and refocusing on the marks of bright moving targets in the mode of selection of moving targets channel, the effectiveness of the detection procedure can be sufficient for practical applications. However, the region of small radial velocity values remains a «blind» zone for any multi-base circuit configurations and can only be reduced by increasing the energy potential of the space radars with aperture synthesis.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):79-87

### Excitation of a rectangular resonator through communication windows in the conveyor installation of microwave heating

#### Abstract

Based on the excitation theory of L.A. Vainstein obtained simple and convenient iterative relations for excitation of a resonator in the form of a rectangular parallelepiped with a dielectric layer through several coupling windows in its walls. The expansion of the field in terms of the complete system of solenoidal functions of a rectangular resonator is used. Solenoidality is due to the fact that the electric fields of excitation in the openings of rectangular waveguides on the resonator walls, fed through coaxial-waveguide transitions, are tangent to the boundaries of the heated dielectric layer. Simple formulas for expansion coefficients and calculation of fields are obtained. It is convenient to solve the obtained implicit formulas iteratively; in this case, it is possible to take into account both a linear dielectric and a nonlinear dielectric, the permittivity of which depends on the square of the electric field. The algorithm is implemented to simulate a conveyor installation of microwave heating. It is possible to modify the algorithm by introducing potential basic subsystems of functions for the case of modeling complex dielectric inclusions. The results are suitable for modeling other nonlinear inclusions, as well as in problems when using volumetric given sources instead of surface ones. For given electric fields in the coupling windows, the power entering the resonator is calculated on the basis of the Poynting vector.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):88-99

### Equivalent circuit of an inductor on a nanocrystalline core with a high magnetic permeability

#### Abstract

Based on the measured impedance of the inductors based on a toroidal core wound from a thin (18 μm) nanocrystalline tape, with a different number of winding turns, an equivalent high frequency (0 Hz - 500 MHz) circuit model was built. The equivalent circuit model was built taking into account the physical processes occurring in the inductor: effect of wire resistance, effect of core material, mutual effect of wire and core material. The attempt explaining why the frequency characteristics (modulus and phase) of the inductor complex impedance have such a character in a wide frequency band (up to 500 MHz) was made. It was shown that for constructing an equivalent circuit model (structure and parameters), measuring only the inductor’s resistance modulus is not enough. It is also necessary to measure the phase of the inductor complex resistance, which is ignored in many works on the synthesis of an e inductor equivalent circuit. The fundamental difference between the operation of a nanocrystalline core and a ferrite core as applied to high-frequency filters is shown.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):100-121

### Some features of a radio signal interaction with a turbulent atmosphere

#### Abstract

On the basis of the solution of Maxwell’s equations system for electromagnetic radiation in a turbulent atmosphere the differential effective section of scattering of this radiation on turbulence is found. Dependence of scattering section on wave length and an angle of scattering is investigated. It is shown that interaction of electromagnetic radiation and turbulence of an atmosphere is interaction of the determined electromagnetic wave process with stochastic turbulent wave process. It is marked, that the wave vector of scattering electromagnetic radiation is proportional to a wave vector of turbulence.

**Physics of Wave Processes and Radio Systems**. 2022;25(4):122-128