# Vol 25, No 2 (2022)

**Year:**2022**Articles:**10**URL:**https://journals.ssau.ru/pwp/issue/view/547

## Articles

### Application of the thin-wire integral representation of the electromagnetic field to solving the problem of diffraction of electromagnetic waves on conducting bodies

#### Abstract

The article is devoted to numerical methods for solving the problem of diffraction of electromagnetic waves by conducting bodies. Two approaches to solving the problem are considered. The first one is based on the use of the thin-wire integral representation of the electromagnetic field (TP-method) for a grid model of the body surface. The second approach is associated with the use of the basis functions of Rao–Wilton–Glisson when solving a vector integral equation formulated with respect to the electric current density on the body surface (RWG-method). The diffraction of a plane linearly polarized electromagnetic wave by a sphere is considered as a test problem. The results of calculations of the normalized diagrams of the scattered field are presented. It is shown that there are practically no visual differences for the results obtained using both approaches. At the same time, it should be noted that the TP method is much simpler in numerical implementation than the RWG method.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):7-14

### Peculiarities of the Norton conversions application when matching impedances with different transformation coefficients

#### Abstract

The paper studies the features and consequences of the use of Norton conversions in the process of broadband and narrowband matching of circuit impedances based on filter theory in cases with different transformation ratios. For Norton circuits conversions with different transformation ratios (greater than and less than one), an additional rule is formulated. Using the generalized form of recording the Norton consequence conversions, two examples of reducing the number of elements in bandpass filters are demonstrated. In addition, the consequences that are characteristic of narrow-band applications of transformations are established. Formulas for calculating transformation ratios that depend on frequency are obtained for direct and mirror Г-shaped circuits with different reactivities. It is shown that these circuits can be combined with similar reactivities of Г-shaped circuits with frequency independent transformation ratios. On the basis of the established for the Norton conversions consequences, the step-up and step-down matching circuits of the combined type are synthesized.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):15-21

### The calculation of reflections of linear polarization plane electromagnetic wave from the boundary of the «air – wet soil» based on heterogeneous Maxwell Garnett and Brughehman models

#### Abstract

In this work we calculated the reflection coefficients modules of a linear polarization plane electromagnetic wave depending on soil moisture with a relative complex dielectric constant described by the heterogeneous Maxwell Garnett and Bruggeman models. A comparison is made of the calculated dependences of reflection coefficients for incident E- and H-polarization waves on soil moisture according to the two proposed heterogeneous two-component models. The correctness of the applied models is shown within the soil moisture content up to 10 %. Within the limits of soil moisture change from 10 to 50 %, there are slight discrepancies in the calculation results for two heterogeneous models. The reflection level of an electromagnetic wave from the soil surface in the case of its H-polarization is less than in the case of E-polarization. With an increase in soil moisture, a monotonous increase in the reflection level is observed. The proposed heterogeneous models of wet soil and the calculation method can be used for remote radar sensing of the Earth’s surface in order to determine the moisture content in the rooted layer of the soil.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):22-27

### Comparison of the main aspects of modern approaches to the development of surface acoustic wave filters: model of the coupling of mode and the finite element method

#### Abstract

This article discusses the main issues of designing filters based on surface acoustic waves. A type of band-pass filter based on longitudinal resonant modes is presented. The features of the calculation based on two approaches are considered: the coupled mode model and the finite element method. Practical recommendations are proposed for reducing the time of filter calculation in numerical simulation. The results of calculating and measuring the transmission coefficient of a filter on a leaky surface acoustic waves on a 36° YX-cut lithium tantalate substrate are presented and compared. The main aspects and directions in which the considered modeling methods can be compared are highlighted and analyzed. It is shown that the use of different modeling approaches increases the development efficiency, and fast analytical models are required for the synthesis and optimization of filter parameters.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):28-39

### Parametrical synthesis of dynamic links for variants of their inclusion between a nonlinear part and loading of automatic systems of radio management with the general feedback

#### Abstract

Introduction: the analysis of the known literature shows that the use of various types of matching quadripoles (reactive, resistive, complex, mixed) and the feedback circuit covering the non-linear element makes it possible to increase the area of physical feasibility of the given forms of frequency characteristics. The purpose of the work is to increase the area of physical feasibility of given forms of frequency responses by optimizing the parameters of matching mixed quadripoles and using an additional feedback circuit covering a nonlinear element and a mixed quadripole. One part of such quadripoles consists only of resistive elements, and the second – only of reactive elements. Materials and methods: theory of four-terminal networks, matrix algebra, decomposition method, method of synthesis of microwave control devices, circuit engineering method for analyzing the characteristics of radio devices. Results: Mathematical models of matching mixed quadripoles are obtained in the form of relationships between the elements of their transmission matrix and the dependences of the resistances of their two-terminals on frequency, which are optimal in terms of the criterion for providing specified forms of frequency characteristics. Conclusion: a comparative analysis of the theoretical results (frequency response and phase response of amplifiers) obtained by mathematical modeling in the MathCad system and experimental results obtained by circuit simulation in the OrCad and MicroCap systems shows their satisfactory agreement.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):40-50

### Parametrical synthesis of the complex two-port networks for variants of their inclusion between a source of a signal and a nonlinear part by criterion of maintenance of the set characteristics amplifiers with the general feedback

#### Abstract

Introduction: the analysis of known literature shows that the use of various types of matching quadripoles (reactive, resistive, complex, mixed) and a feedback circuit covering a non-linear element makes it possible to increase the area of physical feasibility of given forms of frequency characteristics. The purpose of the work is to increase the area of physical feasibility of given forms of frequency characteristics by optimizing the parameters of matching complex quadripoles and using an additional feedback circuit covering a nonlinear element and a mixed quadripole. Each two-terminal network of such four-terminal networks consists of both resistive and reactive elements. Materials and methods: theory of four-terminal networks, matrix algebra, decomposition method, method of synthesis of microwave control devices, circuit engineering method for analyzing the characteristics of radio devices. Results: Mathematical models of matching complex quadripole networks are obtained in the form of relationships between the elements of their transmission matrix and the dependences of the resistances of their two-terminal circuits on frequency, which are optimal in terms of the criterion for providing specified forms of frequency characteristics. Conclusion: a comparative analysis of the theoretical results (frequency response and phase response of amplifiers) obtained by mathematical modeling in the MathCad system and experimental results obtained by circuit simulation in the OrCad and MicroCap systems shows their satisfactory agreement.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):51-59

### Description of digital systems by various construction schemes

#### Abstract

The article discusses ways of describing digital systems with various schemes, provides a comparative characteristic of these schemes, indicates the advantages and disadvantages of different schemes. The four schemes for constructing digital systems described in the article are equivalent, since with the same input signal, the output signal for all circuits will be the same, although different signals will circulate inside these circuits. To build adaptive digital systems, preference should be given to state-space circuits, since in them it is easier to adjust the parameters of the digital system. When choosing between serial and parallel circuits, preference should be given to the parallel circuit if the coefficients in it are valid. With complex coefficients, the implementation of the parallel scheme becomes more complicated, therefore, in this case, one should choose a sequential scheme in the state space, all the coefficients are real.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):60-66

### The effect of fast relay fading and frequency mismatch of the frequencies of the receiving and transmitting channels on the characteristics of the OFDM signal

#### Abstract

In this paper, we consider the negative simultaneous effect of fast relay fading in the channel and mutual frequency shifts of subcarriers between the transmitting and receiving sides of the channel, causing violation of orthogonality between the signals of individual subchannels of OFDM system. Violation of orthogonality is manifested in the appearance of mutual interference signal at the receiving end of the channel in each OFDM subchannel. The paper evaluates the joint effect of fast fading and frequency shifts on the magnitude of the transient interference between subchannels and investigates in sufficient detail the manifestation of transient interference between individual subchannels caused by orthogonality violations each of the two factors cited separately. In this paper, we consider the simultaneous effect of both factors and their influence on the value of the interchannel transient interference.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):67-72

### Study of digital diagram formation for optimum interference and noise reduction in antenna arrays of different shapes with directional radiators

#### Abstract

In the paper the digital beamforming is examined in azimuth and elevation, which allows more accurate formation of nulls and maximum of the radiation pattern. The minimum variance distortionless response beamformer, the sample matrix inversion algorithm using regularization, and the null steering algorithms at the output of cylindrical, hemispherical and planar lattices are considered. The ratio of the useful signal power to the active interference plus noise resulting power and the bit error ratio at the output of digital antenna arrays are estimated depending on the directivity of the antenna elements and the number of averaging samples. It has been established that a hemispherical antenna array can significantly increase the transmission reliability in comparison with the considered ones, which will reduce the computational load without using complicated diagramming algorithms.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):73-82

### Receiving and transmitting feed of reflector antennas for satellite communication systems

#### Abstract

The performance indicators of the antenna-feed path of a multiband reflector antenna are formulated and analyzed in the form of partial coefficients of the complex amplitude of the input signal, vectors of the polarization signal and noise in the input signal in each of the combined ranges. Examples of implementation of antenna-feed path multiband antennas based on various layouts are considered. Conclusions are drawn about the advantages and disadvantages of the presented methods.

**Physics of Wave Processes and Radio Systems**. 2022;25(2):83-90