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ELECTRONICS. RADIO ENGINEERING
ANALYSIS OF THE DISPERSION CHARACTERISTICS OF THE SLOW-WAVE STRUCTURES USED IN THE TERAHERTZ RANGE DEVICES
Natalia P. Kravchenko,
National Research University "Higher School of Economics", MIEM, Moscow, Russia, natkrav@inbox.ru
Yury V. Stromov,
National Research University "Higher School of Economics", MIEM, Moscow, Russia, stromov.y@gmail.com
Agata A. Chkheidze,
National Research University "Higher School of Economics", MIEM, Moscow, Russia, aachkheidze@edu.hse.ru
Sergey V. Mukhin,
Moscow University of Finanses and Law, Moscow, Russia, mukhin_sergey@yahoo.com
Keywords: resonator axially-symmetric slow-wave structures, electrodynamic characteristics, program HFSS, millimeter range, TWT modeling, discrete approach.
Models of slow-wave structures are used in simulating millimetre band devices are considered in the research. It is reasonable to use axially-symmetric slow-wave structures (SWS) for designing millimetre band traveling wave tubes (TWT). Simulating of considered slow-wave structure's 3D model produced in HFSS software package [1]. The program that is outlined in [2] is used for calculation of dispersion characteristics. The model of slow-wave structure cell bases on the results of calculation. The nature of the distribution of the electromagnetic field in the system depends on the interaction features of electrons and the field in the TWT with slow-wave structure. The discrete approach described in [3] is the most common for solving this type of problems.
It is electrodynamically justified to use difference equation for description of the discrete interaction in a traveling wave tube, in which the phase of the field in the interaction gaps in the longitudinal direction remains constant. The difference form of the electrodynamic theory of excitation allows to justify the use of one or another mathematical model for constructing a finite-difference equation [4].
The coefficients of the finite-difference equation Have a certain electrodynamic significance because they are calculated through the transmission matrix coefficients of the 2-N pole. Mathematical model of discrete interaction becomes more accurate when accuracy of coefficients of the finite-difference equation increases. In the research the 2-N pole is sextopole that appears form octopole in case of excitation current absence. The resulting sextopole is a mathematical model of the slow-wave structure cell. Coefficients of the obtained 2-N pole justifies accuracy, realism and recuperation of Electrodynamic characteristics of the simulated resonator slow-wave structure. Specification of discrete interaction processes in traveling wave tubes, and electrodynamic processes in the SWS is ensured by the correct selection of the transmission matrix coefficients.
Information about authors:
Natalia P. Kravchenko, Associate Professor, Candidate of Technical Sciences, National Research University
"Higher School of Economics", MIEM, Moscow, Russia.
Yury V. Stromov, student, National Research University "Higher School of Economics", MIEM, Moscow, Russia.
Agata A. Chkheidze, student, National Research University "Higher School of Economics", MIEM, Moscow, Russia.
Sergey V. Mukhin, Professor, Doctor of Technical Sciences, Moscow University of Finanses and Law, Moscow, Russia.
Для цитирования:
Кравченко Н.П., Стромов Ю.В., Чхеидзе А.А., Мухин С.В. Моделирование ЛБВ миллиметрового диапазона // T-Comm: Телекоммуникации
и транспорт. 2017. Том 1 1. №4. С. 81-86.
For citation:
Kravchenko N.P., Stromov Yu.V., Chkheidze A.A., Mukhin S.V. (2017). Analysis of the dispersion characteristics of the slow-wave
structures used in the terahertz range devices. T-Comm, vol. 1 1, no.4, pр. 81-86.
Intrudaction
Development of radar systems, communications and control in 8 millimeter wave band puts forward new requirements to amplifier characteristics of this range in terms of power and bandwidth of amplified frequencies.
There was the transition of satellite and other communication systems to higher frequencies, due to the overflow of satellite communication channels operating in the centimcter wavelength hand. Frequencies 20...30 GHz are intended for civilian needs and 20...44 GHz is used lbr military communication systems. The shift in lire range of higher frequencies necessitates the development of traveling-wave tube (TWT) amplifying devices that have high level of output power (more than 1000 W) in frequency hand more than 5... 10%.
A combination of high power and a wide amplification hand of a microwave amplifier is necessary for the creation of modern and promising military systems for precision-guided weapons and radio control, in particular, on development stage of missile control systems with radar homing heads and target recognition systems which are involving the use of radar terrain maps and radio images of observable objects. The need of creating powerful broadband microwave amplifiers is also conditioned by the development requirements of radar weapons systems like airborne radars for example. The main requirements for new advanced radar systems are wide frequency band, the use of signals w ith a higher definition, the combined use of wide sets of sounding signals, solving electronic warfare problems, increase the range of action by targets including low-level objects. The fulfillment of these requirements is practically unrealizable with using traditional microwave amplifiers and requires the search for new ways and methods of amp! i fier construction.
Output power level and bandwidth of TWT of 8-mm range achieved nowadays are determined by the optimal parameters selection of used periodic slow-wave structures (SWS) chains of coupled cavity type.
Millimeter frequency range potential is far from exhausted. It is in this range that most of the radar stations and modem infocommunication systems operate, including those systems which are related to space communications. This is the evidence of the promising development of microwave technologies. Creation of mathematical and computer models of these devices which are appropriate to physical laws and to accordance of the predicted to the real results, but also as effective as possible in terms of computing resources is one of the most important problems in the development of new devices and instruments.
In this paper are considered the all-metal resonator slow-wave structures that are widely used in medium-power amplification systems because of their considerable heat removal. These SWS are three-dimensional, that is why their computer simulation based on strict electrodynamic laws is extremely demanding on computing power. What makes actual problem of obtaining sufficiently accurate and simultaneously simple models of cavity slow-wave structures.
Slow-wave structure cell model
Axially symmetric slow-wave structures (SWS) are necessary to design a TWT millimeter range. Model of this slow-wave structure type is shown on Fig. I.
All-metal resonator SWS are transmission lines obtained by connecting identical ceils in a chain. These cells are articulated
by waveguide channels. These channels can be conditionally divided into input S„l, a=l,2,,...k and output Sr,2, a=l,2,.,.' channels. The distance between cross-sections Su' and S«2 equals the slow-wave structure period D, and number of input channels equals number of output channels =N) because of periodicity of the slow-wave structures.
Components of electromagnetic fields at the boundaries of cross-sections S„' ~ arc related by equation:
( > S 5
«1 <h
A N = A
14 i b, \ -
(1)
Where , are vector set of complex amplitudes in cross-sections Sj':,
An is linear matrix operator:
All Ai; A|3n
A -
y A 2V1A 2K2 ' A V
(2)
Using the AN operator from (I) allows to obtain all possible operating modes of the considered SWS. SWS is completely formalized in case when all elements of As operator are known. It means that Calculation of all electrodynamic characteristics is possible [2].
The field of a normal mode in volume of the cell is completely determined by the tangential components of the electromagnetic lields in the cross-sections S«""1, which obey the Floquet conditions in the given cross-sections [2]:
£' (x,y,z)=£ (x,y,z+[))e
[I[ '(x.y.ztOJe*-"
(3)
Where h„ is the propagation constant of n-th normal mode inside the cell with D period. We rewrite equation (3) with relation to vectors of complex amplitudes considering equation ( I ):
( ^ ( -*}
a2 &
« £ ;
(4)
Removing and from ( 1 ) considering (4) we obtain:
/ >
ü\
, 1 J
P'ih.tl
(5)
The resulting equation (5) is an algcbraic formulation of the SWS eigenwaves problem. When cells of the SWS arc represented as a 2N-pole which is described by AN the operator.
There is a non-trivial solution for a given system in case when the condition (6) is satisfied [2]
det(AN —/LnE) = 0 (6)
ELECTRONICS. RADIO ENGINEERING
■
Modeling of the TWT section exited by current
The interaction of electrons with an electromagnetic wave in traveling wave tubes is determined by distribution of electromagnetic fields in SWS. According the fact that the field amplitudes vary from the maximum in the interaction gap to a minimum in transit channel and the electron beam interacts with the field discretely in a bounded region, a discrete approach in problems of this type is the most common way to solve it.
The researches carried out in [3] have shown that known excitation equations with help of formal transformations reduce to finite-difference equations of two types: V+l - (A,, + ) V + V = [(AtiAit + A3, )—( A,, + AH) Als ]in +
(8)
Vktl - ( A,, + A22)Vk + VM = -Al;Jk (9)
Each type of the difference equation is composed of 2N-pole transfer matrix coefficients, which is simulating the eel! of resonator slow-wave structure excited by current. Using the first or second type of finite-difference equation can be justified due to the difference form of the electrodynamic theory of excitation [4]. Inasmuch as in the TWT with discrete interaction, the phase of the field in interaction gaps in the longitudinal direction remains constant it is electrodynamically justified to use the difference equation (9). This equation corresponds to a sixtopole obtained from an octopolc by combining the microwave energy transmitted channels. Field and current excitation inputs are combined. The TWT section excited by current is in this case simulated by a chain of sixtopoles. what makes it possible to take into account the boundary conditions at the ends of the section and the reflections that arise when non-identical cells is combined in a section. Octopoles are obtained by 3D simulating of the SWS cells separated by interaction gaps (Tig. 6). Mathematical model of discrete interaction becomes more accurate, depending on the accuracy of finite-difference equation coefficients specifying. Consequently, the correct selection of these coefficients provides a correct description of the discrete interaction processes in traveling wave tubes and electrodynamic in slow-wave structures [5].
J
Fig. 13. Model of TWT section
Conclusion
Dispersion characteristics of chains of coupled cavity slow-wave structures in centimeter and millimeter ranges are shown on Fig.7-12. As it can be seen a decrease in the geometric dimensions of the resonators, as well as changes in the radius of the transit channel, has a significant effect on the dispersion characteristics of the SWS. Correct calculation of dispersion characteristics allows more accurate estimation of TWT characteristics which are designed on base of reviewed slow-wave structures.
References
!. K u rush in, A. and Titov, A. Designing of high frequency structures using HFSS. (2003), Moscow: Moscow Institute of Electronics and Mathematics.
2. Mukhin, S. Analysis of the dispersion characteristics in the vicinity of the passband boundaries of the slow-wave structures that represent cliaincd cavities. (2012). Radiotekhnika i Electronika [J, of Communication Technology and Electronics], 57(!2), pp. 1276-1286.
3. Mukhin, S. and Solntsev V. Comparative analysis of excitation models of O-type devices with a periodic structure. (1990). Abstracts of the X-th All-Union seminar "The wave and Oscillatory phenomena in O-type electronic devices". Leningrad, p. 99.
4. Solntsev, V. and Mukhin, S. Document Difference form of the periodic waveguides excitation theory. (1991). Radiotekhnika i Electronika [J. of Communication Technology and ElectronicsJ, 36( I 1), p. 2161.
5. Kravehenko, N., Mukhin, S., and Presnyakov, S. Millimeter-band slow-wave structures. (2015). T-Comm. 9(6), pp. 57-63.
ELECTRONICS. RADIO ENGINEERING
МОДЕЛИРОВАНИЕ ЛБВ МИЛЛИМЕТРОВОГО ДИАПАЗОНА
Кравченко Наталья Павловна, МИЭМ национальный исследовательский университет "Высшая школа экономики",
Москва, Россия, natkrav@inbox.ru
Стромов Юрий Васильевич, МИЭМ национальный исследовательский университет "Высшая школа экономики",
Москва, Россия, stromov.y@gmail.com
Чхеидзе Агата Андреевна, МИЭМ национальный исследовательский университет "Высшая школа экономики",
Москва, Россия, aachkheidze@edu.hse.ru
Мухин Сергей Владимирович, Московский финансово-юридический университет, Москва, Россия, ukhin_sergey@yahoo.com Аннотация
Данная работа рассматривает модели замедляющих систем, используемых при проектировании приборов миллиметрового диапазона. Для конструирования ламп бегущей волны (ЛБВ), работающей в миллиметровом диапазоне, следует выбирать аксиально-симметричные резонаторные замедляющие системы (ЗС). Построения 3D моделей рассматриваемой замедляющей системы производиться в программном пакете HFSS [1]. Для расчета дискретных характеристик используется программа, изложенная в [2]. На основе результатов расчета строится модель ячейки замедляющей системы. Характер распределения электромагнитного поля в системе определяется по особенностям взаимодействия электронов и поля в ЛБВ с замедляющей системой. Для решения задач данного типа наиболее общим является дискретный подход, описанный в [3].
Для описания дискретного взаимодействия в лампе бегущей волны, при котором фаза поля в зазорах взаимодействия в продольном направлении остается постоянной, электродинамически обоснованным является использование разностного уравнения. Обосновать использование той или иной математической модели построения конечно-разностного уравнения, позволяет разностная форма электродинамической теории возбуждения [4].
Коэффициенты конечно-разностного уравнения рассчитываются через коэффициенты матрицы передачи 2-N полюсника, благодаря чему имеют определенный электродинамический смысл. Чем точнее заданы коэффициенты конечно-разностного уравнения, тем более точной становится и математическая модель дискретного взаимодействия. 2-N полюсник в данной задаче является шести полюсником, полученном из восмиполюсника при условии отсутствия тока возбуждения. Полученный шестиполюсник - это математическая модель ячейки замедляющей системы. Точность данной модели и ее реалистичность, восстановления электродинамических характеристик моделируемой резонаторной замедляющей системы определяется коэффициентами полученного 2-N полюсника. А значит, верный подбор коэффициентов матрицы передачи обеспечивает и правильное описание процессов дискретного взаимодействия в лампах бегущей волны, и электродинамических процессов в ЗС.
Ключевые слова: pезонаторные аксиально-симметричные замедляющие системы, электродинамические характеристики, программный пакет HFSS, миллиметровый диапазон, моделирование ЛБВ, дискретный подход.
Литература
1. Курушин А.А., Титов А.П. Проектирование СВЧ структур с помощью HFSS. Утверждено Редакционно-издательским советом института в качестве учебного пособия. Моск.гос. ин-т электроники и математики. М., 2003. С. 176. ISBN 5-94506-067-4.
2. Mukhin S.V. Analysis of the Dispersion Characteristics in the Vicinity of the Passband Boundaries of the Slow-Wave Structures That Represent Chained Cavities // Journal of Communications, Technology and Electronics - 2012, Vol. 57, No. 12, pp. 1276-1286.
3. Мухин С.В., Солнцев В.А. Сравнительный анализ моделей возбуждения приборов О-типа с периодической структурой // Тезисы докладов Х Всесоюзного семинара "Волновые и колебательные явления в электронных приборах О-типа". Ленинград, 1990. С. 99.
4. Солнцев В.А., Мухин С.В. Разностная форма теории возбуждения периодических волноводов // Радиотехника и электроника, 1991. Т. 36. №1 1. С. 2161.
5. Кравченко Н.П., Мухин С.В., Пресняков С.А. Замедляющие системы миллиметрового диапазона 6 // T-Comm: Телекоммуникации и транспорт. 2015. Т.9. №6. С. 57-63.
Информация об авторах:
Кравченко Наталья Павловна, доцент, к.т.н., МИЭМ национальный исследовательский университет "Высшая школа экономики", Москва, Россия.
Стромов Юрий Васильевич, студент, МИЭМ национальный исследовательский университет "Высшая школа экономики", Москва, Россия.
Чхеидзе Агата Андреевна, студент, МИЭМ национальный исследовательский университет "Высшая школа экономики", Москва, Россия.
Мухин Сергей Владимирович, профессор, д.т.н., Московский финансово-юридический университет, Москва, Россия.
