COMPUTER-AIDED DESIGN OF THE VIVALDI ANTENNA FOR ULTRA-WIDEBAND ELECTROMAGNETIC PULSE RADIATION Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

УДК 004.832.2

doi:10.21685/2307-4205-2021-2-8

COMPUTER-AIDED DESIGN OF THE VIVALDI ANTENNA FOR ULTRA-WIDEBAND ELECTROMAGNETIC PULSE RADIATION

A.I. Mel'nichuk1, N.V. Goryachev2, N.K. Yurkov3

1 Aviation Base of the Krasnodar Higher Military Aviation School of Pilots of Russian Ministry of Defense, Rtishchevo, Russia 2' 3 Penza State University, Penza, Russia 1 [email protected], 2 [email protected], 3 [email protected]

Abstract. Background. Unmanned and remotely piloted aerial vehicles (UAVs and RPVs, respectively) have already found wide application in various areas of human life. Materials and methods. UAVs are actively used in agriculture, monitoring, logistics, control of hazardous objects. But, as often happens with technological progress, advanced developments are beginning to be actively used for military purposes. And today UAVs, including small ones, have become a real threat, not only to the military, but also to civilians. The purpose of this work is to substantiate the methods and means of countering strike UAVs, as well as to assess the damaging capabilities of the ammunition with the choice of the shape, mass and material of the striking elements. Results and conclusions. The concept of a universal ammunition capable of providing a prompt response to air threats to equipment and personnel emanating from unmanned aerial vehicles has been proposed and substantiated.

Keywords: drone, countermeasures, functional suppression, unmanned, apparatus, electromagnetic weapons

For citation: Mel'nichuk A.I., Goryachev N.V., Yurkov N.K. Computer-aided design of the Vivaldi antenna for ultrawideband electromagnetic pulse radiation. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2021;2:78-91. (In Russ.). doi:10.21685/2307-4205-2021-2-8

АВТОМАТИЗИРОВАННОЕ ПРОЕКТИРОВАНИЕ АНТЕННЫ ВИВАЛЬДИ ДЛЯ СВЕРХШИРОКОПОЛОСНОГО ЭЛЕКТРОМАГНИТНОГО ИМПУЛЬСНОГО ИЗЛУЧЕНИЯ

А. И. Мельничук1, Н. В. Горячев2, Н. К. Юрков3

1 Учебная авиационная база Краснодарского высшего военного авиационного училища летчиков МО РФ, Ртищево, Россия 2' 3 Пензенский государственный университет, Пенза, Россия 1 [email protected], 2 [email protected], 3 [email protected]

Аннотация. Актуальность и цели. Беспилотные и дистанционно пилотируемые летательные аппараты (БПЛА и ДПЛА соответственно) уже сегодня нашли широкое применение в различных областях жизнедеятельности человека. Материалы и методы. БПЛА активно используются в сельском хозяйстве, мониторинге, логистике, контроле за опасными объектами. Но как часто бывает при техническом прогрессе передовые разработки начинают активно применяться в военных целях. И сегодня БПЛА, в том числе малые, стали реальной угрозой, не только для военных, но и для мирных граждан. Целью данной работы является обоснование способов и средств противодействия ударным БПЛА, а также оценка поражающей возможности боеприпаса с выбором формы, массы и материала поражающих элементов. Результаты и выводы. Предложена и обоснована концепция универсального боеприпаса, способного обеспечить оперативный ответ на воздушные угрозы техники и личному состава, исходящие от беспилотных летательных аппаратов.

Ключевые слова: дрон, противодействие, функциональное подавление, беспилотный, аппарат, электро-магнитное оружие.

Для цитирования: Мельничук А. И., Горячев Н. В., Юрков Н. К. Автоматизированное проектирование антенны Вивальди для сверхширокополосного электромагнитного импульсного излучения // Надежность и качество сложных систем. 2021. № 2. С. 78-91. doi:10.21685/2307-4205-2021-2-8

© Melnichuk A.I., Goryachev N.V., Yurkov N.K., 2021. Контент доступен по лицензии Creative Commons Attribution 4.0 License / This work is licensed under a Creative Commons Attribution 4.0 License.

Introduction

A technology for functional suppression of unmanned aerial vehicles (UAV) suggests using shortwave (fractions to tens of nanoseconds) electromagnetic radiation (EMR). There are two possible options for such EMR effect on electronic equipment, namely, in-band or out-of-band [6, 7].

Out-of-band functional suppression provides for the impact of radio electronic means (REM) on receivers at any frequencies outside their bandwidth, and does not require initial data on operating frequency range.

In-band functional suppression techniques provide for EMR energy losses when passing through the input circuitry of REM receiver, and depending on the ratio between the bandwidth of the reception path, and the EMR spectrum width. In-band methods are energetically most favorable, but they require initial data on technical characteristics of microwave radiation effect on UAV, and attacked or suppressed REM (e.g., the operating frequency and bandwidth of receiving devices; the clock frequency of special calculators and computers; the resonant frequency of fastener designs of radio circuit board components, etc.).

There are three fundamentally different areas for the implementation of functional suppression means using powerful short-wave EMR, and the third one being mostly widespread [1]:

1. Spark-gap and semiconductor video pulse generators.

2. Relativistic microwave radio pulse oscillators.

3. Transmitting multi-position radiation systems (MRS) and phased arrays with controlled EMR microwave focusing.

Here are the effects of ultra-short microwave radio pulses:

1. Interference: the radiation source creates electromagnetic field intensity in the operating frequency range of the target receiver. This intensity is the same or greater than the useful signal, since the receiver is unable to extract the useful signal.

2. False information: an induced electromagnetic signal sends false information into the receiver.

3. Transient destabilization: the induced voltage affects the logic state of an electronic component.

4. Permanent damage: semiconductor junctions are exposed to overvoltage, leading to their failure. However, this is due to the presence of an effective antenna system capable of transmitting power of ultrashort microwave pulses without losses [2].

Since the problem of ultra-wide range microwave radiation is associated with designing the device, it is advisable to consider an antenna operating in a wide frequency band. To create an antenna-feeder device, it is proposed to view a tapered slot antenna (TSA), which meets the requirements for creating a device for functional suppression of UAV systems by emitting an ultra-wideband and ultra-short electromagnetic pulse.

TSA, also called Vivaldi antennas (radiators based on symmetrical slot lines), posess important technical characteristics: 1) small overall dimensions; 2) small radiator weight; 3) the required radiation pattern over the entire range of operating frequencies; 4) the ability to emit ultra-short pulses.

Along with stated requirements, it is necessary to note a simple design of this type of radiators, and the ability to work in a wide range of frequencies. Based on these, it is advisable to calculate and consider such radiator for further modeling, and testing.

When calculating, the operating bandwidth mostly depends on the selected frequency, generally degrading the output matching, and on the change in the maximum of radiation pattern, beam expansion, and other parameters.

The operating bandwidth of wideband antennas should be 10 to 50% of the nominal frequency. A Vivaldi antenna is a broadband antenna, considered as a radiator of ultra-short pulses in a number of works. It should be noted that we have selected the operating frequency of 8 GHz for further calculations, as the frequency range from 5 to 8 GHz negatively affects electronic radio-elements [3].

Initially, it is appropriate to consider such radiator as an irregular transmission line harmonizing a regular line with free space. It is necessary to minimize the reflection coefficient at the input of the matching device, wherein the wave impedance and the transition length change. Thus, proper frequency characteristics (T-waves and quasi T-waves propagating in slot lines) are satisfied.

For a more accurate determination of characteristics, different calculation methods for the field along the entire slot antenna are used. A stepwise approximation by sections representing segments of a constant

width slot is applied to an expansion slot according to an exponential law. This technique presents an approximate, but more accurate calculation method. For such sections, the field distribution obtained by the Galerkin method in the spectral domain is used. Thus, the field of the entire slot antenna can be defined as the sum of fields of each section.

According to this method, the field of a slot antenna with the obtained amplitude field distribution in the slot is determined. Based thereon, it is possible to consider the dielectric substrate (given a printed circuit board antenna), and the wave diffraction at the edges of an infinite height radiator.

These methods are cumbersome and inconvenient. For an approximate engineering calculation and electrodynamic modeling, software packages for calculating various types of antennas are quite suitable. For an approximate antenna calculation and simulation, it is advisable to use the CST Microwave Studio and HFSS Microwave Office computer-aided design (CAD) systems, since the theory of Vivaldi antennas is rather complicated in the field of electrodynamics (it is a traveling wave antenna). As a rule, antenna parameters are selected empirically. For further modeling of the Vivaldi antenna, it is appropriate to use the HFSS tool [4].

Approximate calculation and optimization in the CAD system

The calculation of the actual antenna length is carried out as follows:

L = Lf - 2AL,

W =-

"Total

2/°

(Er +1)

8 + 1 8 - 1 8 „ =—-+ —-

■eff

1 +12 W

LTotal

2/J 8

- 0,824

(( + °.з) W + 0,264

(8/ - °'258)[ "T" + 0

The aperture geometry is calculated according to the formulas:

W__ =

2 /min^[8r

Wmln =

2 /maxV87

where c is the speed of an electromagnetic wave propagating in a vacuum; fmin is the minimum operating frequency; fmax is the maximum operating frequency; er is the permittivity. The antenna slot width is determined by [5]:

W ( x) = W°exp

ln(WL )| L

-(W° + b ).

where W0 is the antenna length; WL is the total antenna width; b is the minimum aperture value of the taper; a = 0.7.

A screenshot of this calculation results is given in Fig. 1.

c

2

c

c

.&> Ansoft HFSS Antenna Design Kit — X

Fig. 1. Calculation program screenshot (geometric dimensioning obtained by approximate calculation)

Freq [GHz]

Fig. 2. Reflection coefficient versus frequency

As seen from the graph (Fig.2), the reflection coefficient is -10.5 dB at 8 GHz, being rather low. A good result is achieved from -20 dB, and it increases from 6 GHz [6].

It is necessary to perform antenna optimization (length, width, and size of the initial aperture) for its further consideration, wherein weight and size parameters should not go beyond the desired results. First, we consider the effect of the initial aperture size Ws[ot on the reflection coefficient.

Fig. 3. Reflection coefficient optimization by varying the initial antenna aperture

As seen from the plot (Fig.3), the reflection coefficient increases with an increase in the indicator, being undesirable.

After unsuccessful optimization of the previous parameter, we have carried out optimization of the antenna length LtoM (Fig. 4).

Fig. 4. Reflection coefficient optimization by varying the antenna length

In the above plot, one can distinguish a polygonal chain that meets the minimum requirements for the reflection coefficient. A genetic algorithm was chosen for the initial optimization.

It was found that the antenna length was 228.5 mm with the optimal coefficient, which satisfies the forthcoming operating conditions (Fig. 5).

Fig. 5. Approximate optimization results in the CAD system

Thus, it was possible to reduce the reflection coefficient at a frequency of 5.7 GHz. Since the antenna is supposed to be of ultra-wideband, therefore, it is advisable to carry out further optimization so that the reflection coefficient should become acceptable at other frequencies [7].

As can be seen from the optimization plots, the reflection coefficient decreases as the width of antenna reduces. Considering this, a polygonal chain of 39.5 mm was chosen. The graph shows a more acceptable size in the 5.6 GHz domain, wherein it does not meet the specified characteristics in the 7.5 GHz domain.

Thus, the geometric dimensioning has changed after optimization (Fig.6).

Fig. 6. The obtained antenna geometric dimensioning after optimization

Verification of the obtained results when simulating the antenna

Consider the following plot to verify the obtained antenna geometry (Fig. 7) [8].

Fig. 7. Reflection coefficient of an optimized antenna simulation

A shift in 5(1,1) was caused by a change in active and reactive resistance. The antenna gain was modified due to an increase in the antenna geometry parameters Ltota{.

As seen from the plot (Fig. 7), the minima values are achieved at 5.6 GHz and 7.5 GHz. The indicated frequencies lie in the range of desired ones, which are negatively affect radio-electronic devices. To construct the radiation pattern, the following formulas are used in the #-plane (9 = 0):

^ (0 ) =

and in the E-plane (ф = п/2):

^ (0 )=-

2cos0

f

J

sin (0,5k0 • a sin 0)

0,5k0 • a sin 0

cos" 0 + ((ctg2k0d )

22, cos 0 • cos ( 0,5k°b sin 0 )

+ ( cos 0 • ctg^k° d )2

-f

1 -| k0—sin(

bv

П

2

where d is the thickness; a is the width; b is the length; k = p/s^; P is the propagation constant; s is the permittivity; ^ is the permeability; = yjs^ - sin2 0. The directivity is defined as follows:

d=44nU,

P

rad

where U is the radiation intensity; Prad is the radiation power. The intense radiation power is calculated by:

U (0,9 )= M. r2, no

where | E | is the E-plane module; r is the distance from the antenna; n is the impedance of free space being 376.7 dB.

3D visualization of the radiation pattern is presented in Fig. 8 [9].

Fig. 8. Three-dimensional radiation pattern

Based on the results, the radiation pattern is wide enough, and the maximum gain is 8.7 dB for the area marked in red.

2D visualization of the radiation pattern is presented in Fig. 9.

Fig. 9. Two-dimensional radiation pattern

It follows from the plot of polar coordinates that half power beamwidth (HPBW) corresponds to 60 degrees, being rather high. The side-lobe level is very low, being less than 13%.

Polarization plots in the £-plane and the #-plane are presented in Fig.10 and Fig. 11, respectively.

<nnn ff_2D_Gain Total Vivaldi _Antenna_ADKv1 ^ FT

Curve Info

- dB(GainTotal) Setup 1 : LastAdaptive

Freq=TGHz" Phi=X)deg'

- dB(GainTotal)_1 Setup 1 : La^tAdaptive

Freq=TGHz" Phi=-90deg

1 4s

T---

.00

-20 С ).0 ' -15(1 .00 Vo( ' -50 00 T o.bo' heta [deg] 50 'oo ' ' ioo .00 50 .00 30(

Fig. 10. Plot of polarization in the ¿-plane

The plot follows the radiation pattern in polar coordinate system, but it is presented in a rectangular shape for convenience. The main lobe gain is 8.7 dB [10].

ff 2D GainTotal Vivaldi_Antenn.a_ADKv1 At

Curve Info

- dB(GainTotal) Setup 1 : LastAdaptive

/ Freq^BGHz" Phi^deg1

ПП - dB[Gai nTo1al)_1 Setup 1 : LastAdaptive

Freq^BGHz" Phi^deg1

П nn .00

/

\

/ \

T>- l

/ \ /

I I

/ 44

> г ч ✓ /

I

-in nn

u

4

с ПП

-20( Î.0 15Ù.00 V>l i.0( t -50 00 o.bo' Theta [deg] 50. 00 100 .00 150 .00 ' 20(

T

Fig. 11. Plot of polarization in the ^-plane The Smith chart is presented in Fig. 12.

Fig. 12. The Smith chart

Simulation of antenna radiation patterns in the E-plane is shown in Fig. 13 and Fig. 14 [11, 12].

0 50 100 {mm)

■ —

Fig. 13. Antenna radiation pattern in the E-plane

0 50 100 (mm)

Fig. 14. Antenna radiation pattern in the E-plane

As shown in the above simulation screenshot in the E-plane, there is a strong radiation of electromagnetic field, marked in orange and yellow [13, 14].

A similar picture is observed in the H-plane radiation pattern shown in Fig. 15 [15, 16].

Fig. 15. Antenna radiation pattern in the H-plane

Conclusion

Using the finite element method, it was possible to analyze the results, calculations, and simulation of the Vivaldi antenna. Having used a genetic algorithm for optimizing the resulting Vivaldi antenna (due to changing geometric dimensioning), we have managed to achieve the acceptable characteristics of a radiator. Based on practical experience, a simplified idealized model considering mutual influence of electronic radio-elements and characteristics of filters and coils would be sufficient [17].

Based on the obtained results, one can judge the relevance of using such types of antennas in the radiation of ultra-wideband systems. Construction of a phased array based on the Vivaldi antenna, emitting in the indicated range, would be interesting from an engineering point of view [18, 19].

References

1. Gross F.B. Frontiers in Antennas: Next Generation Design & Engineering, 1st ed. McGraw-Hill Companies, 2011.

2. Bobreshov A.M., Meshcheryakov I.I., Uskov G.K. Modeling generator of ultrashort pulses with the Vivaldi antenna. Proceedings of Voronezh State University. Ser.: Systems analysis and information technologies. 2014;3:81-85

3. Voskresensky D.I. Microwave Devices and Antennas. Phased Array Design. Moscow: Radiotekhnika, 2012.

4. Mitelman Yu.E. Design of Antenna Systems in Ansoft HFSS. Yekaterinburg: Ural Federal University, 2012.

5. Chernyshev S.L., Vilensky A.R. Development of radiators for ultra-short-pulse antenna arrays. XVII International Scientific and Technical Conference on Radiolocation, Navigation, Communications (RLNC-2011) (Voronezh, 12-14 April, 2011). Voronezh, 2011:2159-2170.

6. Patent RU2700206C1. Method of two-factor functional suppression of unmanned aerial vehicle. Yurkov N.K., Goryachev N.V., Kuzina E.A. Sept. 13, 2019, bull. No. 26.

7. Patent RU2700207C1. Method for functional suppression of an unmanned aerial vehicle. Yurkov N.K., Goryachev N.V., Kuzina E.A. Sept. 13, 2019, bull. No. 26.

8. Soghomonyan K.E., Yurkov N.K. Effects of ultra-short pulses of electromagnetic radiation on unmanned aerial vehicles. Proceedings of the International Symposium on Reliability and Quality. 2019;2:315-317.

9. Melnichuk A.I., Goryachev N.V., Yurkov N.K. Ways and means of countering an unmanned aerial vehicle. Reliability & Quality of Complex Systems. 2020;4(32):131-138. doi: 10.21685/2307-4205-2020-4-14.

10. Grishko A.K. Optimal control of frequency resource in radio electronic systems on the basis of probability analysis of information conflict dynamics. Vestnik of Ryazan State Radio Engineering University. 2016;(57):21-28. doi: 10.21667/1995-4565-2016-57-3-21-28.

11. Grishko A.K., Goryachev N.V., Yurkov N.K. Analysis of mathematical models for calculating the fields of electro and range radar systems by sequential analysis. Engineering Journal of Don. 2015;2:16.

12. Andreev P.G., Yakimov A.N., Yurkov N.K. [et al.]. Methods of calculating the strength of electric component of electromagnetic field in difficult conditions. International Conference on Actual Problems of Electron Devices Engineering (APEDE) (Saratov, Russia, Sept. 22-23, 2016). Saratov, 2016:1-7. doi: 10.1109/ APEDE.2016.7878895.

13. Grishko A.K. Optimizing the placement elements of RES based multilevel geoinformation model. Vestnik of Samara State Technical University. Technical Sciences Series. 2015;3(47):85-90.

14. Grishko A.K., Zhumabaeva A.S., Yurkov N.K. The electromagnetic resistance of electronic systems based on probabilistic analysis of the dynamics of the information conflict. Measuring. Monitoring. Management. Control. 2016;4(18):49-58.

15. Grishko A.K. Parameter control of radio-electronic systems based of analysis of information conflict. 13th International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE) (Novosibirsk, Russia, Oct. 03-06, 2016). Novosibirsk, 2016:107-111. doi: 10.1109/APEIE.2016.7806423.

16. Grishko A., Goryachev N., Kochegarov I. [et al.]. Management of structural components complex electronic systems on the basis of adaptive model. 13th International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET) (Lviv, Ukraine, Feb. 23-26, 2016). Lviv, 2016:214-218. doi: 10.1109/TCSET.2016.7452017.

17. Grishko A.K., Goryachev N.V., Kochegarov I.I., Yurkov N.K. Dynamic analysis and optimization of parameter control of radio systems in conditions of interference. International Siberian Conference on Control and Communications (SIBCON) (Moscow, Russia, May 12-14, 2016). Moscow, 2016:1-4. doi: 10.1109/SIBC0N.2016.7491674.

18. Grigor'ev A.V., Grishko A.K., Goryachev N.V. [et al.]. Contactless three-component measurement of mirror antenna vibrations. International Siberian Conference on Control and Communications (SIBCON) (Moscow, Russia, May 12-14, 2016). Moscow, 2016:1-5. doi: 10.1109/SIBC0N.2016.7491673.

19. Grishko A., Goryachev N., Yurkov N. Adaptive control of functional elements of complex radio electronic systems. Int. J. Appl. Eng. Res. 2015;10(23):43842-43845.

Список литературы

1. Gross F. G. Frontiers in Antennas: Next Generation Design &Engineering. The McGraw-Hill Companies, 2011. 526 р.

2. Бобрешов А. М., Мещеряков И. И., Усков Г. К. Моделирование генератора сверхкоротких импульсов совместно с антенной Вивальди // Вестник Воронежского государственного университета. Сер.: Системный анализ и информационные технологии. 2014. № 3. С. 81-85.

3. Устройства СВЧ и антенны. Проектирование фазированных антенных решеток / под ред. Д. И. Воскресенского. М. : Радиотехника, 2012. 744 с.

4. Мительман Ю. Е. Проектирование антенных систем в ansoft hfss. Екатеринбург, 2012.

5. Чернышев С. Л., Виленский А. Р. Разработка излучателей для сверхкороткоимпульсных антенных решеток // Радиолокация. Навигация. Связь : докл. XVII Междунар. науч.-техн. конф. Воронеж, 2011. С. 2159-2170.

6. Патент 2700206 Российская Федерация, B64C 99/00(2019.09) H04K 3/00(2019.09) F41H 13/00(2019.09). Способ двухфакторного функционального подавления беспилотного летательного аппарата / Н. К. Юрков, Н. В. Горячев, Е. А. Кузина. № 2018114720 ; заявл. 20.04.2018 ; опубл. 13.09.2019, Бюл. № 26.

7. Патент 2700207 Российская Федерация, МПК B64C 99/00(2019.09) H04K 3/00(2019.09) F41H 13/00(2019.09) F42B 12/36(2019.09). Способ функционального подавления беспилотного летательного аппарата / Н. К. Юрков, Н. В. Горячев, Е. А. Кузина. № 2018142886 ; заявл. 05.12.2018 ; опубл. 13.09.2019, Бюл. № 26.

8. Согомонян К. Э. Воздействие ультракоротких импульсов электромагнитного излучения на беспилотные летательные аппараты // Труды Международного симпозиума Надежность и качество. 2019. Т. 2. С. 315-317.

9. Мельничук А. И., Горячев Н. В., Юрков Н. К. Способы и средства противодействия // Надежность и качество сложных систем. 2020. № 4. С. 131-138.

10. Гришко А. К. Оптимальное управление частотным ресурсом радиотехнических систем на основе вероятностного анализа динамики информационного конфликта // Вестник Рязанского государственного радиотехнического университета. 2016. № 57. С. 21-28. doi: 10.21667/1995-4565-2016-57-3-21-28

11. Гришко А. К., Горячев Н. В., Юрков Н. К. Анализ математических моделей расчета электроакустических полей и дальности действия радиолокационных систем методом последовательного анализа // Инженерный вестник Дона. 2015. Т. 35, № 2-1. С. 16.

12. Andreev P. G., Yakimov A. N., Yurkov N. K. [et al.]. Methods of Calculating the Strength of Electric Component of Electromagnetic Field in Difficult Conditions // 12th International Conference on Actual Problems of Electron Devices Engineering (APEDE 2016). Saratov, Russia. 2016. Vol. 1. P. 1-7. doi: 10.1109/ APEDE.2016.7878895

13. Гришко А. К. Оптимизация размещения элементов РЭС на основе многоуровневой геоинформационной модели // Вестник Самарского государственного технического университета. Сер.: Технические науки.

2015. № 3. С. 85-90.

14. Гришко А. К., Жумабаева А. С., Юрков Н. К. Управление электромагнитной устойчивостью радиоэлектронных систем на основе вероятностного анализа динамики информационного конфликта // Измерение. Мониторинг. Управление. Контроль. 2016. № 4. С. 49-58.

15. Grishko A. K. Parameter control of radio-electronic systems based of analysis of information conflict // 13th International Scientific Тechnical Conference on Actual Problems of Electronic Instrument Engineering (APEIE 2016). Novosibirsk, Russia. 2016. Р. 107-111. doi: 10.1109/APEIE.2016.7806423

16. Grishko A., Goryachev N., Kochegarov I. [et al.]. Management of Structural Components Complex Electronic Systems on the Basis of Adaptive Model // 13 th International Conference on Modern Problems of Radio Engineering, Telecommunications, and Computer Science (TCSET). Lviv-Slavsko, Ukraine, 2016. P. 214-218. doi: 10.1109/TCSET.2016.7452017

17. Grishko A., Goryachev N., Kochegarov I., Yurkov N. Dynamic Analysis and Optimization of Parameter Control in Radio Systems in Conditions of Interference // International Siberian Conference on Control and Communications (SIBCON). Moscow, Russia, 2016. Р. 1-4. doi: 10.1109/SIBC0N.2016.7491674

18. Grigor'ev A., Grishko A., Goryachev N. [et al.]. Contactless Three-Component Measurement of Mirror Antenna Vibrations // International Siberian Conference on Control and Communications (SIBCON). Moscow, Russia,

2016. P. 1-5. doi: 10.1109/SIBC0N.2016.7491673

19. Grishko A., Goryachev N., Yurkov N. Adaptive Control of Functional Elements of Complex Radio Electronic Systems // International Journal of Applied Engineering Research. 2015. Vol. 10, № 23. P. 43842-43845.

Информация об авторах / Information about the authors

Антон Иванович Мельничук

инженер группы обслуживания и ремонта бортовой контрольно-записывающей аппаратуры, Учебная авиационная база Краснодарского высшего военного авиационного училища летчиков МО РФ (Россия, Саратовская область, г. Ртищево, ул. Котовского, 1/1) E-mail: [email protected]

Anton I. Mel'nichuk

Engineer of the service and repair group

of on-board recording equipment training,

Aviation Base of the Krasnodar Higher Military

Aviation School of Pilots

of Russian Ministry of Defense

(1/1 Kotovsky street, Rtishchevo,

Saratov Region, Russia)

Николай Владимирович Горячев

кандидат технических наук, доцент кафедры конструирования и производства радиоаппаратуры, Пензенский государственный университет (Россия, г. Пенза, ул. Красная, 40) E-mail: [email protected]

Николай Кондратьевич Юрков

доктор технических наук, профессор, заслуженный деятель науки РФ, заведующий кафедрой конструирования и производства радиоаппаратуры, Пензенский государственный университет (Россия, г. Пенза, ул. Красная, 40) E-mail: [email protected]

Nikolay V. Goryachev

Candidate of technical sciences,

associate professor of sub-department

of radio equipment design

and production,

Penza State University

(40 Krasnaya street, Penza, Russia)

Nikolay K. Yurkov

Doctor of technical sciences, professor,

the honoured worker of science

of the Russian Federation,

head of sub-department

of radio equipment design and production,

Penza State University

(40 Krasnaya street, Penza, Russia)

Авторы заявляют об отсутствии конфликта интересов / The authors declare no conflicts of interests.

Поступила в редакцию/Received 15.04.2021 Поступила после рецензирования/Revised 30.04.2021 Принята к публикации/Accepted 15.05.2021