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ANALYSIS OF THE SLOW-WAVE STRUCTURES USED IN THE MILLIMETER RANGE DEVICES
Natalja P. Kravchenko,
National research University "Higher school of Economics" (HSE), Associate Professor, Candidate of Technical Sciences, Moscow, Russia, natkrav@inbox.ru
Sergey V. Mukhin,
National research University "Higher school of Economics" (HSE), Professor, Doctor of Technical Sciences, Moscow, Russia, mukhin_sergey@yahoo.com
Semyon A. Presnyakov,
National research University "Higher school of Economics" (HSE), student, Moscow, Russia, pressnyak@gmail.com
Alexander D. Kasatkin,
National research University "Higher school of Economics" (HSE), student, Moscow, Russia, sanchezonok@mail.ru
Keywords: resonator rectangular and axially-symmetric slow-wave structures, electrodynamic characteristics, program HFSS, millimeter range, TWT modeling, discrete approach.
In this paper the slow-wave structures and their models, which are used for development of the millimeter range devices, are considered. The travelling-wave tubes (TWTs) of the millimeter range use rectangular and axially-symmetric resonator slow-wave structures. Analysis of these slow-wave structures was performed using HFSS program for 3D-modeling [1]. Dispersion characteristics were calculated by program outlined in the paper [2]. These characteristics are used to build the model of the slow-wave structure's cell. The peculiarities of the interaction between the electrons and the field in the TWT with resonator slow-wave structures are determined by the nature of the field distribution in such structure. The discrete approach is the most common for solving problems of this type [3]. The difference form of the electrodynamic excitation theory applied to the description of the discrete interaction is justifying the use of a mathematical model.
For a description of the TWT with the discrete interaction, in which the phase of the field in the interaction gaps in the longitudinal remains constant, the use of the difference equation is electrody-namically reasonable.
The more precisely defined the coefficients of the finite difference equations, the more accurate the mathematical model of the discrete interaction becomes. These coefficients have a certain electro-dynamic meaning and are defined via coefficients of the quadripole transmission matrix derived from the sextopole if there is no the exciting current. The accuracy of the restoration of the electrody-namic characteristics of the modeled resonator slow-wave structures is determined by the coefficients of the quadripole obtained. Therefore, the correct selection of these coefficients provides a correct description of the discrete processes of interaction in travelling-wave tubes as well as the electrodynamic processes in the slow-wave structures.
Для цитирования:
Кравченко Н.П., Мухин С.В., Пресняков С.А., Касаткин А.Д. Анализ замедляющих систем, используемых в приборах миллиметрового диапазона // T-Comm: Телекоммуникации и транспорт. - 2016. - Том 10. - №8. - С. 83-88.
For citation:
Kravchenko N.P., Mukhin S.V., Presnyakov S.A., Kasatkin A.D. Analysis of the slow-wave structures used in the millimeter range devices. T-Comm. 2016. Vol. 10. No.8, рр. 83-88. (in Russian)
Я
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1. Introduction
The development of the radar, communication, and control systems in the 8-mm wavelength range puts forward new power and working bandwidth requirements on the amplifiers characteristics for this range.
Due the overflow of the satellite communication channels operating in the centimeter wavelength range, there was a transition of the satellite and other communication systems to a higher frequencies. The 20...30 GHz frequencies are intended for civil communication systems, while the 20...44 GHz frequencies are intended for a military communication systems. This shift to higher frequencies causes the need for the amplifying devices such as travelling-wave tubes (TWTs) with the high level of the output power in this range, more than 1000 W in the frequency range more than 5... 10% to be exact.
When creating a modem and advanced military control systems of the precision weapons and the radiovisión, the combination of a high power and a wide amplification band of the microwave amplifier is required. In particular, it is important in the development of a missile guidance systems with a radar homing and a goals recognition systems involving the use of the radar maps and the radio images of the observed objects. The need to create powerful broadband microwave amplifiers is also caused by the development needs of the radar weapons systems, for example, the airborne radars. Basic requirements for a new perspective radar weapon systems are following; the broad frequency band, the use of superresolutión signals, the combined use of a wide set of the probing signals, the solutions of the electronic warfare problems, the increased range on targets, including barely visible ones. The fulfillment of these requirements with the use of traditional microwave amplifiers is virtually impossible to implement, and therefore the problem of searching for a new ways and methods of their construction rises.
The currently achieved level of oulput power and the 8-mm range TWT frequency bandwidth are determined by the selection of the optimal parameters of used periodic slow-wave structures (SWSs) of "chain of coupled resonators" - type.
The potential of the millimeter range far from being exhausted, as the most of the radars and modem information and communication systems, including those related to the space communication, are operating in this range, which in itself speaks about the prospects of the microwave technology development. One of the most important tasks in the development of new devices and devices operating in the microwave range is the construction of mathematical and computer models, not only adequate in relation to the laws of physics and giving the results corresponding with a real systems, but also being economical in terms of computational burden.
This paper deals with the widely applied in the amplifying systems medium power all-metal resonator slow-wave structures used due to their substantial heat sink. These slow-wave structures are three-dimensional, so their computer simulation based on strict electro dynamic laws is extremely demanding on computing power, which makes the problem of constructing the exact and at the same time simple models for calculating of resonator slow-wave structures quite urgent.
2. Model of slow-wave structure cell
In the millimeter range traveling-wave tubes the rectangular and axjally-symmetric slow-wave structures (SWSs) presented in Figures 1 and 2 are used.
Fig. 1, Ax ¡ally-symmetric resonator s tow-wave structure (SWS): 1 -slot channel, 2 - transit channel, rl - resonator radius
"Â i
t
d
Fig. 2, Rectangular resonator SWS
The main features of these slow-wave structures are the small dimensions and the absence of protrusions on the diaphragms.
All-metal resonator slow-wave structures (SWS) are transmission lines obtained by connecting identical cells into a chain. These cells are coupled by waveguide channels. These channels can be divided into the input channels Sa', a=t,2,.,,k and output channels Sy:, a=l,2,.../. Due to the the periodicity of the investigated slow-wave structures, the distance between the sections S„' and Su~ equals the period of the slow-wave structure D, and the number of input channels is equal to ihe number of output channels (k=/=N).
The components of the electromagnetic fields at the boundaries of sections S,,1 are connected by the expression:
v 1 у
ь,
V - У
(1)
where 'PI, '<2I are vectors, which represent a set of complex amplitudes in the sections Su' AN is matrix linear operator of the form:
Aj? ''' 12N
An
■Ait "".A33N
I .A ;v' '"A ; ,
(2)
Using the operator As from (1), it is possible to obtain all possible operating modes ofthe considered SWS. ffthe elements of the operator AN are known to us, the SWS is completely formalized, therefore, we can calculate all of its electromagnetic characteristics [2].
The normal wave field in the volume of the considered cell is the completely determined by the tangential components of electromagnetic fields in sections S01(2), which obey the f'loquet conditions [2]:
(3)
where hr, is propagation constant ofthe normal wave within n-th cell having period D. Considering (1), rewrite the expression (3) relative to the vectors of complex amplitudes as:
У
У
ZZR2,
ZZllj 600
ZZRJ
ZZlh
Fig. 16. Transit channel's characteristic impedance of the millimeter range axial ly-symmetric SWS of "chain of coupled resonators"-type
As seen from the calculation results, the introduction of even small radius transit channel (r=0.05mm) affects the position of the passbands and attenuation bands as well as the characteristic impedance of the SWS's microwave energy transmission channels. Thus, when designing the millimeter range devices the SWS models with transit channel should be used.
3. Modeling of the TWT section excited by current
The interaction of electrons with the electromagnetic wave in traveling-wave tubes is determined by the Held distribution in the SWS, Due to the fact that the field amplitudes vary from maximum in the interaction gap to minimum in the transit channel, the electron beam actually interacts with the field in a limited area discretely. The discrete approach to problems of this type is the most common.
Studies carried out in the work [3] showed that using formal transformations the known equations of excitation are reduced to the finite difference equations of two types: Vn+l-(A,1 + Ai2)Vn+Vn.1=[(A]3A31 + A3,A23)-(All + A22)A33]jn +
+A,3(Jj,., + Jn+t)-[A3!(A^A^ - A2,A12)-A32(A„A21 - A23Am)]J„_|
(8)
Vk+1-(Alt + A22)Vk+Vk,=-A,A (9)
The coefficients of these equations can be expressed through the transmission matrix coefficients of the sextopolc modeling the resonator SWS ceil excited by current. To justify the choice of a mathematical model used for describing the process of discrete interaction the difference form of the electrodynamic excitation theory will be used [4].
For a description of the TWT with discrete interaction in which the phase of the field in the interaction gaps in the longitudinal direction remains constant the use of a differential equation (9)is electrodynamically justified. This equation corresponds to sextopole, in which the inputs of the excitation by current and the inputs of the excitation by field are combined. In this case, the TWT section excited by a given current is modeled by the chain of the sextopoles derived from the octopoles when the microwave energy transmission channels are combined (Figure 17), which makes it easy to take into account the boundary conditions
at the ends of the section, as well as the reflections arising from the merging in the section of the non-identical cells. The octopoles are obtained by the 3D-modeling of the slow-wave structures cells distinguished by the interaction gaps (Figures 9, 10).
The more precisely defined the coefficients of the finite difference equations, the more accurate the mathematical model of the discrete interaction becomes. These coefficients have a certain electrodynamic sense and are calculated through the transmission matrix coefficients of the quadripole derived from the sextopole provided that there is no exciting current. In turn, this quadripole is the mathematical model of the resonator slow-wave structure cell. The restoration accuracy of the modeled resonator SWS's electrodynamic characteristics is determined by the coefficients of the obtained quadripole. Therefore, the correct selection of these coefficients provides the correct description of the discrete interaction in traveling-wave tubes and electrodynamic processes in the slow-wave structures [5].
Of3
Fig. 17. Model of the TWT section
4. Conclusion
On the Figures 11-16 the dispersion characteristics of the millimeter range slow-wave structure of "chain of coupled resona-tors"-type with the transit channel (r = 0.05mm) are shown. It is easy to see that even such a small aperture has an impact on the dispersion characteristics, in particular on the characteristic impedance. This effect increases with the transit channel radius. Thus, the correct calculation of the dispersion characteristics wil I enable a more targeted selection of parameters and characteristics when designing the millimeter range traveling-wave tubes, built on the basis of these slow-wave structures.
References
1. Kurushin, 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 chained cavities. (2012). Radiotekhnika i Electronika [J, of Communication Technology and Electronics], 57( 12), pp. 1276-1286.
3. Mukhin. S. and Sotntsev 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 Electronics], 36(11), p. 2161.
5. Kravchenko, N.. Mukhin, S., and Presnyakov, S. Millimeter-band slow-wave structures. (2015), T-Comm, 9(6), pp. 57-63.
T-Comm Vol.10. #8-2016
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PUBLICATIONS IN ENGLISH
АНАЛИЗ ЗАМЕДЛЯЮЩИХ СИСТЕМ, ИСПОЛЬЗУЕМЫХ В ПРИБОРАХ МИЛЛИМЕТРОВОГО ДИАПАЗОНА
Кравченко Наталья Павловна, доцент, к.т.н., Национальный исследовательский университет "Высшая школа
экономики", Москва, Россия, natkrav@inbox.ru
Мухин Сергей Владимирович, профессор, д.т.н., Национальный исследовательский университет "Высшая школа экономики", Москва, Россия, mukhin_sergey@yahoo.com
Пресняков Семен Андреевич, студент, Национальный исследовательский университет "Высшая школа экономики", Москва, Россия, pressnyak@gmail.com)
Касаткин Александр Дмитриевич, студент, Национальный исследовательский университет "Высшая школа экономики", Москва, Россия, sanchezonok@mail.ru
Аннотация
Рассматриваются замедляющие системы и их модели, которые используются при проектировании приборов миллиметрового диапазона. В лампах бегущей волны миллиметрового диапазона используются прямоугольные и аксиально-симметричные резонаторные замедляющие системы (ЗС). Анализ этих замедляющих систем проводился с использованием 3D моделирования по программе HFSS [1]. Дисперсионные характеристики рассчитывались по программе, изложенной в [2]. Полученные в результате расчета характеристики используются для построения модели ячейки замедляющей системы. Особенности взаимодействия электронов и поля в ЛБВ с резонаторными замедляющими системами определяются характером распределения полей в такой системе. Наиболее общим при решении задач данного типа является дискретный подход [3]. При описании дискретного взаимодействия применение разностной формы электродинамической теории возбуждения [4] позволяет сделать выбор между той или иной математической моделью. Для описания ЛБВ с дискретным взаимодействием, в которых фаза поля в зазорах взаимодействия в продольном направлении остается постоянной, электродинамически обоснованным является использование разностного уравнения. Чем точнее заданы коэффициенты конечно-разностного уравнения, тем более адекватной становится и математическая модель дискретного взаимодействия. Эти коэффициенты обладают определенным электродинамическим смыслом и задаются через коэффициенты матрицы передачи четырехполюсника, получаемого из шестиполюсника при условии, что возбуждающего тока нет. Данный четырехполюсник, в свою очередь, является математической моделью ячейки резонаторной замедляющей системы. Точность восстановления электродинамических характеристик моделируемой резонаторной ЗС определяется коэффициентами полученного четырёхполюсника. Следовательно, верный подбор данных коэффициентов обеспечивает правильное описание и процессов дискретного взаимодействия в лампах бегущей волны, и электродинамических процессов в ЗС.
Ключевые слова: pезонаторные прямоугольные и аксиально-симметричные замедляющие системы, электродинамические характеристики, программа 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. 176 с. 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 Е^йпэп^ю 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 // T-Comm: Телекоммуникации и транспорт. 2015. Т. 9. №6 С. 57-63.
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