# Vol 24, No 1 (2021)

**Year:**2021**Articles:**11**URL:**https://journals.ssau.ru/pwp/issue/view/479

## Articles

### Influence of detuning and Kerr nonlinearity on atom-atom entanglement in the double two-photon Jaynes–Cummings model

#### Abstract

In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):9-14

### Point spread function of a four-wave radiation converter in a multimode waveguide with Kerr nonlinearity

#### Abstract

An expression is obtained for the point spread function of a four-wave radiation converter in a multimode waveguide with Kerr nonlinearity, taking into account the transfer of energy from the object wave to the signal wave and vice versa. For single-mode pump waves, the presence of «generation» points is shown and conditions are found on the waveguide parameters, characteristics of the interacting waves, under which the «generation» condition is realized. In the vicinity of the «generation» points, the shape of the point spread function is determined by one of the waveguide modes, the number of which coincides with the number of the pump wave mode. For a four-wave radiation converter in a waveguide with infinitely conducting surfaces, the quality of the wavefront conjugation near the second «generation» point coincides with the quality of the wavefront conjugation at a low reflection coefficient. For a four-wave radiation converter in a parabolic waveguide near the second and next «generation» points, the shape of the point spread function is determined by one of the waveguide modes.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):15-21

### Development of exact mathematic models for planar slotted traveling wave antennas using the dyadic Green function and their experiment foundation

#### Abstract

Exact mathematic models were developed for traveling wave antennas with a constant slot width based on the dyadic Green function, taking into account both the main and cross-polarization components of the field in the far radiation zone. The possibility of using these models as basic models for studying the electrodynamic properties of traveling wave antennas with a different slot configuration (linearly, exponentially tapering, etc.) is justified. The influence of the geometric parameters of the investigated traveling wave antennas on their characteristics was studied by means of using the established mathematic models. It has been found that in the electrodynamic E plane, with an increase of the length and width of the slot, the main beam of the radiation pattern narrows, which leads to an increase the directed properties of the antennas. In the electrodynamic H plane, the width of the main beam of radiation pattern decreases only as the length of the slot of traveling wave antennas increases and does not depend on its width in practice. It was shown that the established theory results of the study are well consistent with the results of experiments, which also revealed the limitations of the applicability of the developed models. Analysis of traveling wave antennas characteristics was carried out at central frequency of 10 GHz in the frequency range of 8-12 GHz.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):22-31

### Study of a hemispherical metamaterial lens made of parallel printed circuit boards with metal diffusers of small electrical dimensions

#### Abstract

Antenna systems based on hemispherical lenses allow full azimuth scanning or electronically controlled sector scanning. The article presents a numerical simulation of a broadband multi-beam antenna system based on a hemispherical metamaterial lens made of parallel printed circuit boards with metal diffusers of small electrical dimensions. The effective parameters of a metamaterial based on printed Jerusalem crosses with welded-in transverse metal pins are investigated. The selected geometric dimensions of the metamaterial made it possible to reduce the effect of anisotropy. Directional patterns are considered when a lens is excited by a system of broadband vibrators with two orthogonal polarizations. For each polarization, conclusions are drawn about the operating range and the magnitude of the losses. The results obtained in this work are planned to be used in the future in the design of wideband lens antennas from parallel printed circuit boards.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):32-38

### Development of predictive mathematical models of the quality of radio electronic equipment based on the results of autonomous tests

#### Abstract

The article discusses the methodology for developing a predictive model (forecasting operator) of the quality of onboard equipment using the extrapolation method. It is shown that the most efficient information about the quality and reliability of the equipment can be obtained from the results of autonomous tests. The choice of the test object was made. A microprocessor temperature controller was chosen as the object of autonomous tests. The transition resistance between the electrical circuits of the microprocessor temperature controller was chosen as a predicted parameter. The results of the training experiment are presented. To construct the forecasting operator, quasi-deterministic models of linear, logarithmic, exponential, and parabolic forms are used. When developing the models, the normalization of predicted parameter by mathematical expectation was used. The choice of predictive models was based on the criteria of minimum average variance, calculated at the test time points, and the minimum values of the probability of erroneous decisions and consumer risk. The research of the developed operator was carried out, probabilistic characteristics of its efficiency are obtained.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):39-47

### Flat Luneberg lens based on a printed circuit with curved conductors

#### Abstract

The use of a printed Luneberg lens is promising for powering ultra-wideband phased array antennas with full-azimuth scanning. This article describes in detail the model for constructing a flat Luneberg lens based on a printed circuit with curved conductors. A certain pattern(pattern) with a relative permittivity er ≈ 1 was etched on the copper-coated substrate. This was done in order to realize the value of the refractive index. By printing a grid of intersecting conducting lines, a refractive index of was achieved in the center of the lens. The diameter of the Luneburg lens antenna was chosen to be 28.6 cm, which corresponds to 12,4l0 (l0 is the wavelength of free space) to achieve a half-power beam width of ≈ 5° at an estimated frequency of up to 20 GHz. Since the design of the Luneberg lens is based on geometric optics, the lens diameter must be a multiple of the wavelength to limit diffraction effects. Operating frequencies up to 20 GHz were selected. The lens was sampled into single cells. If the unit cell size is small enough, the lens can be described as a medium with a certain effective refractive index. As a result, this propagation theory can be used for lens design. The substrate used for the lens was 1 mm thick, the material used was Rohacell 31HF, which has a permittivity of 1,046 and a loss tangent of tg(d) = 0,002.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):48-57

### Improving noise immunity of homography superposition for television signals

#### Abstract

The algorithm of homography superposition of the television signals was shown in this article. The algorithm allows improving noise immunity for homography parameters of television signal with textural fragments. The core of the estimation procedure of homography parameters for image superposition is the matching of the feature points. The feature points are local extremes of the pixel brightness of the image. The matching is defined by the maximum correlation coefficient between a region of the image of a neighbor area of the feature point. The log-polar system of the images provides an invariant correlation of scale and rotate are proportional offsets along the axis in this coordinate system. The noise immunity is provided due to the developing procedure of removing feature points in the textural region. This procedure leads to decreasing probability of error matching of the feature points. The numerical modeling shows high noise immunity of the developed procedure in comparing the current researches.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):58-66

### Algorithm for filtering coordinates of a ground source unauthorized radio emission in a satellite communication system with direct retransmission

#### Abstract

In the article, an algorithm for filtering the coordinates of a ground source of unauthorized radio emission in a satellite communication system with direct retransmission is developed. The content statement of the problem of filtering the coordinates of a ground source of unauthorized radio emission is initially formulated for its formation when selecting a system of restrictions and assumptions. On the basis of its mathematical model is developed, which unlike the well-known allows you to perform collaborative problem solving filtration coordinates of ground source unauthorized radio emission in conditions of a priori uncertainty about the position coordinates and velocity vector of the perturbed orbital motion of the primary and adjacent satellites-repeaters. The basis of the final algorithm for filtering the coordinates of a ground source of unauthorized radio emission is the rule of recursive estimation of the state vector, defined when using the extended Kalman filter to minimize the root-mean-square error of the state vector. The efficiency of the developed algorithm is checked on specific examples. The efficiency of the developed algorithm is checked. Based on the results of a posteriori studies, it was determined that the algorithm on average reduces the root-mean-square error of the estimate by 1,34 times.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):67-77

### Design features of negative feedback and power smoothing filter of the DC / DC converter with pulse loads for transmitter-receiver modules of active electronically scanned arrays

#### Abstract

The fundamental difference of the voltage converter of the secondary power supply source for the transmitter-receiver modules of active electronically scanned arrays with impulse load and variable duty cycle from traditional voltage converters that constantly consume power from the primary network is shown. Methods for improving the quality of transient processes in voltage converter with constant power consumption during start-up by soft start are not applicable to improve the quality of transients in periodic current pulses caused by a pulsed load. Since any ripples, noises, instabilities in the power supply of the transmitter-receiver modules of active electronically scanned arrays operating in a linear mode lead to parasitic amplitude modulation of the emitted signal and to a deterioration in the quality of selection and target tracking, very strict requirements are imposed on the quality of the transmitter-receiver modules supply voltage (voltage ripple kп ≤ 0,5 %, the amount of overshoot of the output voltage sU ≤ 2 %, etc.). The article shows that such a quality of the output voltage with a pulsed load of the transmitter-receiver modules of active electronically scanned arrays can be obtained using a lower-type voltage converter, with a double-circuit negative feedback for the output voltage and current of the inductor, with a storage capacitor and with a power smoothing filter with the characteristics of Chebyshev and Butterworth. The work investigated the influence of the negative feedback depth on the output voltage and current of the smoothing filter choke, the value of the storage capacitor capacity, the type and parameters of the smoothing filter, and recommendations were given to select their optimal values, at which the required quality of the supply voltage for the transmitter-receiver modules of active electronically scanned arrays was ensured, taking into account the minimization of their dimensions.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):78-88

### Software applications in modeling of physical processes in radio engineering and electronics in the context of distance learning

#### Abstract

This article examines the existing software applications for electronic circuit prototyping that can help evaluate the operation of the entire circuit based on specified parameters and find the best options. Using the TAC application and the Arduino library components, projects and instructions for creating and testing electronic circuits were developed. The resulting application was tested for capabilities and efficiency. The interface design and settings were also assessed to determine whether they simulate real conditions. The functionality of TAC application made it possible to generate alternate circuits. The results of software testing showed that using the application speeds up the learning process significantly when compared to traditional methods and helps eliminate problems that may emerge when designing and assembling circuits. The application may be useful in designing complex electronic circuits and developing teaching aids for students in technical fields.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):89-97

### Determining the color of a multi-colored object with relatively large dimensions

#### Abstract

The use of standard instruments (colorimeters) when measuring the color coordinates and chromaticity of multicolored objects and having relatively large dimensions is practically impossible. This is due to the fact that ordinary colorimeters, no matter what method is implemented in them, are designed to determine the color of a specific point of the measured object. This article discusses a method for determining the color of a multicolored and relatively large object, for example, a car, color photography, art painting, etc. Let us call this method computer colorimetry. A practical solution to this method can be used in such areas of the national economy, as, for example, repainting a car after damage to certain parts of the body with damage to the paintwork, automatic control and video surveillance of forest and peatland areas to detect fires, in the examination of the authenticity of documents and works of art, and other areas of the national economy.

**Physics of Wave Processes and Radio Systems**. 2021;24(1):98-104