CC BY
8
УДК 538.36.08
Method of Measuring Effective Dielectric Permittivity of Partially Filled Waveguides Using
a Mismatched T-Bridge
Karashchuk N. M.1, Manoilov V. P.2, ^Stdorchuk 0. L.\ Tarasenko S. M.\ Chukhov V. V.2
1Zhytomyr military institute named after S. P. Korolyov 2Zhytomyr State Technological University
E-mail: eidorchuk_ o&ukr.ncl■
Introduction. Waveguides, partially filled with dielectric material (partially filled waveguides) are widely-used in the super high frequency equipment.. They have certain advantages over hollow waveguides, including the possibility of reducing sizes of a cross-section, increasing the power of radiation and suppressing undesired types of waves. Following the production of diverse new dielectric materials intended for use in super high frequency range devices, there is a need to continuously develop methods of calculation and measuring characteristics of partially filled waveguides.
Statement of the problem. The theory of completely filled waveguides and waveguides with dielectric filling along narrow walls is developed quite thoroughly. However, its application to various waveguide devices requires the solution of transcendental equations, which is possible only using numerical methods. This makes it difficult, to obtain information about, any characteristics of a device. For the study of partially filled waveguides with different, sample height., among others, this paper presents an approach, which is based 011 the representation of the relative permittivity of the medium in the form of two real functions, each of which depends 011 the cross-section from one coordinate. The paper also introduces the method which allows calculating the propagation constant, at. any frequency, by measuring the value of effective dielectric permittivity.
Results and discussion. The results of the analysis shows that, known methods of measuring effective dielectric permittivity have certain shortcomings in relation to the modification of partially filled waveguides, bandlimit.edness, and a significant, relative error of measurement, with increasing effective dielectric permittivity. It. is necessary to match the bridge at. each frequency, reaching the absence of a signal in the arm E for identical loads that, are connected to the side arm. For this, bridges have tuning elements in the form of pins, diaphragms, etc. The method for measuring effective dielectric permittivity of partially filled waveguides using an unmatched T-bridge, which does not. have these deficiencies, is introduced. Conclusions. The scientific novelty of the proposed method for measuring effective permittivity of partially filled waveguides using an unmatched T-bridge gives the possibility of providing broadbandness, increasing the accuracy of measurements, and the universality through the use of a panoramic indicator of the standing wave ratio using the voltage and electron-computer. The results obtained should be used when designing new antenna systems, which include partly filled waveguides, as well as part, of teaching and learning activities for creating new workplaces or improving existing ones aimed at. laboratory and practical training using the above method of measurement..
Key words: effective dielectric permittivity: partial dielectric filling: method for measuring effective dielectric permittivity: partially filled waveguide: teaching and learning activities
DOI: 10.20535/RADAP.2019.78.6-12
1 Statement of the problem
Waveguides, partially filled with dielectric material - partially filled waveguides (PFWs) - are widely used in the super high frequency (SHF) equipment fl 5]. The increased interest to such waveguides is due to the fact that they have a number of advantages over hollow waveguides. Thus, changing the form of their filling and dielectric permittivity of a material, it is
possible to control the distribution of the power flow in a cross-section, the position of the circular polarization points of the SHF magnetic field, and other characteristics [0,7]. This enables increasing the power of radiation and suppressing undesired types of waves in waveguides [9.10].
At present, various dielectric materials are intended for the use in SHF range devices with small losses (with relative permittivity within er =
2 ... 20). Improvement of waveguide characteristics with frequency dielectric filling goes along with a decrease in their size and greater stability of characteristics in the frequency range, which is the basis for the creation of small size and broadband antennas [10.12].
Tims. PFWs are widely used in various SHF devices. Therefore, there is a need to continuously develop methods of calculation and measuring their characteristics.
2 Analysis of recent research and publications
The number of dielectrics that are nsed in the superhigh frequency (SHF) equipment is rapidly increasing now. The emergence of new dielectrics contributes to the creation of new transmission lines and SHF devices, snch as partially filled waveguides (PFWs). resonators, filters, phase shifters, etc. The practical application of snch devices without reference to their dielectric permittivities is impossible.
The electrodynamic problem solving for PFW reduces to finding the propagation constant in the waveguide [13.14]. The exact solution of the Helmholtz equation of the electromagnetic field for PFW is only possible in certain cases, for example, in layered waveguides, when the distribution limit is subject to the piecewise continuous law of the distribution of permittivities. The classical methods for determining the propagation constants in PFW are reduced to solving the dispersion equation obtained either by-comparing the tangential components of the electric and magnetic fields at the distribution limits of each layer, or by the theory of circles [15.16].
In [14]. for the study of PFWs with different sample height, an approach, based on the representation of the relative permittivity of the medium in the form of two real-valued functions, each of which depends in the cross-section from one coordinate, is introduced. This is an approximate method for determining proper scalar and vector functions of a PFW. At first, the approximation of the piecewise-inhomogeneons waveguide filling allowed the authors to reduce the problem to the Hill equation. Given only one member in these series, the solution of the problem was obtained in Mathien functions.
Any theory needs to be practically confirmed. This can be a fnll-scalc experiment (measurement) or a computer simulation with the help of modern software packages.
Measurements of effective dielectric permittivity are considered in many papers [13.14]. In [9]. a method for measuring effective dielectric permittivity e by a measuring line was introduced. One of the advantages of the method is its simplicity, and. among the disadvantages. there is the ability to nse only those
modifications of PFWs that do not interfere with the movement of a measuring line probe.
The studies [16.17] show that at extreme frequencies of the standing-wave ratio (SWR) characteristics on a panoramic indicator screen there is the possibility to fulfill the following condition:
'K
fti = X-,
H 2'
(1)
where ft - the wave number in the waveguide; i - the length of the dielectric sample; x = 2n - at the point of minimum and x = 2n + 1 at the point of maximum, n = 1, 2, 3 ....
The condition (1) is equivalent to the fact that along the sample of the dielectric that is being investigated. an integer of half-waves is inserted:
i
A
n—, 2'
(2)
where A is the wavelength in the waveguide with the dielectric that is being investigated, or. eqnivalently. the even number of quarters of the wavelengths:
i = 2n-. 4
(3)
The condition (1) can be rewritten in the following form:
"K
1 = 2n2
(4)
In [18]. for analysis of reflection coefficient it is shown that the following condition is fulfilled at the maxima frequencies:
fti = (2n +1) -,
(5)
that is. along the dielectric sample, an odd number of quarters of wavelengths is inserted:
fti =(2n +1) ±.
(6)
Consequently, in the general case, the conditions of extremnms can be rewritten in the form:
■k
fti = x-,
(7)
where x = 2n is at the point of minimum and x = 2n+l is at the point of maximum.
Tims, conditions (1) and (2) have a clear physical content, the frequency of the minimum is a resonant frequency, and the frequency of the maximum is the antiresonance frequency.
As the result of the measurement, the condition (7) is fulfilled, then one measured extremnm frequency is not enough, but it is still necessary to know the number of half waves (quarter waves) that are enclosed along the sample - n.
For this, condition (7) can bo written in the form analogous to the system as relating to er, then for a completely filled waveguide [17.18]:
n2\2 n0A0
* - (&)^
(no + q)2>H3 * - (è)2
4i2
4i2
(8)
(9)
where a is the size of the broad wall of the waveguide; Ao - wavelength of the generator; A - wavelength in the dielectric. For this it is believed that e (fo) = e (f) = e; q a, number of half-waves along dielectrics.
For the measurement of the frequency characteristic of SWR Kc (f) in [ , ], a measuring device was developed on the basis of a panoramic indicator of SWR. and the equations (8). (9) were solved as follows:
no = q +
\[(M)
2 - (i/a )2 (A2 - 1),
( t )2 [(1/ )+( T )
(10)
(11)
where A = f/fo .
In fig. , the dependences of the magnitude Je on the decay factor for the waveguide with two plates, respectively, at the different filling tx for the values a/X =0,6 Mid a/X =0,7 calculated by the expressions (10) and (11), are given. If a certain enrvo does not reach the value Je « 3, 5, this means that at given tx higher-order modes may occur in a rectangular waveguide.
All dependencies are developed for such values of tx, when only the wave of the main type (H1o) is applied to PFW.
In order to reduce the reflection from the output ends of the dielectric plates, it is proposed to use the cutoffs, and the presence of higher-order modes can be detected with the help of the standing wave pattern.
Tims, by measuring the value of effective dielectric permittivity e, it's possible to calculate the propagation constant at any frequency. As the magnitude e increases, the deceleration rate m increases as well and its value approaches Je. As the size of the filling as well as the effective dielectric permittivity e increase, and the value of a/X decreases, the propagation of the main wave in the PFW becomes possible.
The waveguide width, normalized to the wavelength, depending on the filling, changes more rapidly with small fillings. The conducted experimental studies of measuring e with the help of a panoramic indicator of the voltage standing-wave ratio (VSWR) have proved that the relative error of measurement for dielectric permittivity e < 2 does not exceed ±2% in the frequency range (26 - 37,5) GHz.
The use of a panoramic indicator of VSWR in the case where the partial dielectric filling (PDF) has a relative effective dielectric permittivity that
changes within the limits e = 5... 15 has a relative ±l5%
this method [20].
Therefore, the purpose of the paper is to develop the method for measuring the effective dielectric permittivity of a PFW in order to improve the accuracy of measuring e.
3 R-Gsults
In order to increase the accuracy of measuring e of a PFW, it is proposed to apply a bridge measurement method based on the waveguide bridge [10].
The method of using bridge meters is to compare the unknown impedance of a SHF device with the reference one. Therefore, the reference impedance is a necessary part of a bridge meter. Various bridge coaxial and waveguide circuits are known. Consider one of them - the waveguide bridge [10] (fig. 2).
The wave from the SHF generator conies in the 4th bridge arm. If the bridge is strictly symmetrical (agreed), the wave is divided in half between arms 1 and 2 and does not pass in the arm 3 to which the detector and the indicator are connected. If the reference impedance (standard measure) is connected to the arm 1, the bridge will only be matched if the impedance (load), oqnal to the reference one, is connected to the arm 2. At that, the waves, reflected from both loads, at the input of the arm 3 are completely subtracted. In all other cases, if the module or phase of the reflection coefficient of the load in the arm 2 differs from the module or phase of the reflection coefficient of the standard measure, and a wave that is proportional to the difference between the amplitudes and phases of waves reflected from both loads will appear in the arm 3.
Tims, with the help of a bridge, one can estimate the difference between the impedances of two loads.
For graduation, it is possible to connect sequentially several loads with known VSWR to the arm 2, observed the indicator readings; and then mark the whole scale according to the keys received.
The disadvantage of bridge indicators is the very-narrow frequency range at which the bridge remains matched. In practice, it is necessary to match the bridge at each frequency, reaching the absence of a signal in the arm 3 with the same loads that are connected to the arms 1 and 2. For this bridge there are adjusting elements in the form of pins, diaphragms, etc. Sometimes matching transformers, which are activated between the inputs of the arms 1 and 2 and the loads, are nsod for adjusting.
In some cases, it is possible to exclude this procedure by applying a method of nsing a mismatched bridge to compare impedances, which is widely nsod in practice [20].
2
a 0,6
a/ X- 0,7
/0,2 /0,2 I/"131 5 0,4 ^ 0,6
/ / £
/ / //
V -1
W X
■y
-A, X < < >i
a x
0,025 / 0,05 / 0,75^ / / /u ^ 0,3//'/ AA
A !// / / 0,6
///
w. / tx - 0S
W
2,5 3 m
2,5 3 m
(a)
(b)
Fig. 1. The relationship between e mid m
reflection in it and from its flanges, and the reflection from the reference and regulated loads, equals to zero. If a short-circuited waveguide with PDF is connected to the arm 2. then the magnitude of the reflection coefficient of the waveguide with PDF can be found by moving a short-circuiting switch.
4
Fig. 2. Scheme of a waveguide bridge
Consider the method of measuring the parameters of SHF devices, consisting of a VSWR panoramic indicator and a mismatched bridge.
The composition of the diagram of measuring VSWR of partially filled waveguides by a computer includes:
OFG - oscillation frequency generator: D1 - direct-reading incident wave detector: D2 - direct-reading standing wave detector: ID - interface device: T - hybrid-t:
ECM - electronic computing machine: I - indicator.
The measurement method IS ctS follows: the reference load 7 is connected to the arm 2 (fig. 3). to the arm 1 the special load C with reflection coefficient varying in module and phase (the oscillator 5 is connected to the arm 4). With the help of the adjustment controls of this load, zero indicator readings are achieved. For this, the sum of the waves in the arm 3 due to the asymmetry of the hybrid-t, the
OFG
D1
D2
6
ll
4 T 3
2
7
ID
ECM
Fig.
3. The block diagram of measuring VSWR of partially filled waveguides by a computer
In this device, the detected signals from the detectors of the directional couplers of the incident D1 and the reflected D2 waves instead of the panoramic indicator PI are fed to the interface device ID where they are amplified and converted into binary code. The basis of the oscillation frequency generator of such a device most typically is a digital frequency synthesizer controlled by its computer. Since the accuracy of frequency synthesizers is constantly improving, in such a panoramic indicator there is no need to use an external frequency meter.
The functions of displaying, controlling oscillator frequency generator and calculating are performed by a personal computer.
The results of measurements can be automatically generated in the form of a report, for example, in MS Excel format.
Fig. shows the dependencies of the value e on the ratio tx/a , calculated from the expressions ( ) and (11) and measured experimentally by the proposed
2.5
2,5
1.5
1,5
0.5 1
1.5
0,5 1
1,5
1
5
I
method based on a mismatched bridge (where n is the motion distance of a short-circuiting switch).
14
12
10
0 0,2 0,4 0,6 0,8 1
tja
Fig. 4. Dependence of the waveguide with two dielectric plates adjacent to the walls of the waveguide (1 - experiment. 2 - measurement)
The transition from the reflection coefficient of the PFW to SWR can be carried out either according to the known formula [7.18] or according to the diagram [9].
The use of the expressions (10) and (11) for calculation allows determining e of the PFW, and the use of a bridge meter allows precise measuring e in the required frequency band. The calculation and experimental studies conducted for a waveguide with two plates for £ have a little variation between the curves. The relative error for the dielectric permittivity £ < 15 does not exceed ±0, 7% in the range (26 - 37.5) GHz.
The proposed method with the use of a bridge, in which measure is a controlled short-circuiting switch, is widely used to measure dielectric properties of materials, since compared with other methods in many practical cases, it is relatively simpler and more universally applicable for preparing and conducting measurements.
Conclusions
Consequently, clS ct result of the conducted research, a method for measuring the effective dielectric permittivity of a PFW with the help of a mismatched T-bridge with increased accuracy of measurement of £ is proposed.
An expression £ for the effective dielectric permittivity of a partially filled waveguide is obtained. The curves of the dependence of effective dielectric permittivity on the slowness factor /ё (то) for a waveguide with two dielectric plates with a different value of filling factor tx for fixed electric sizes of the cross section of a rectangular waveguide a/A for the condition of propagation of the wave of the main type (Hю) are given.
The graphs obtained by the expressions derived for the measuring unit on the basis of the panoramic indicator of the standing wave ratio give an opportunity to analyze the effect of waveguide filling, taking into account their effective dielectric permittivity, on the change of their cross-section sizes and the type of waves in a waveguide. The relative error of measurement for effective dielectric permittivity £ < 2 did not exceed ±2% in the frequency range (26 - 37.5) GHz according to the results of experimental measurements.
Thus, a more precise method of measuring the effective dielectric permittivity of a PFW in the frequency range based on the application of a mismatched T-bridge has been developed.
An electron-computer was used to increase the efficiency of measuring the effective dielectric permittivity of a PFW.
The calculated and experimental curves of the dependences of the effective dielectric permittivity on the location of the plates in the waveguide £ (tx/a ) are given. The relative error for the dielectric permittivity £ < 15 does not exceed ±0, 7% in the frequency range (26 - 37.5) GHz.
The advantage of the proposed measurement method is the use of a personal computer that controls the oscillation frequency generator, performs calculations and displays their results on the monitor. This increases the flexibility of the use of the device to measure VSWR of a PFW with acomputer and decreases the risk of its obsolete depreciation.
The software of such a device allows receiving dependencies of measurement parameters on frequency or power, filtering them, carrying out statistical processing with different software-installed parameters, identifying characteristic points on the graphs (for example, search of the minima and maxima required in this case) and calculating other derivative parameters [13 16].
The results of measurements can be automatically generated in the form of a report, for example, in MS Excel format. Moreover, in some of these devices, the software interface is open and documented.
The scientific novelty of the proposed method for measuring the effective dielectric permittivity of a PFW with the help of a mismatched T-bridge is the ability to provide broadbandness, increase the accuracy of measurements, universality through the use of a panoramic indicator of the PFW and a computer. One more distinguishing feature of this method is the ability to measure effective dielectric permittivity of such a PFW, where other measurement methods are not suitable.
The results obtained should be used during the design of new antenna systems, which include a PFW, as well as in the learning process in order to create new or improve existing environment for laboratory-arid practical training using the above method of measurement.
к
2
0.8
Г = 0.1
0.6
0
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Метод вим!рювання ефективно!" д!еле-ктрично!" проникност! частково запов-нених хвилевод!в за допомогою не-узгодженого Т-мосту
Каращук Н. М., Манойлов В. П., СиОорчук О. Л., Тарасенко С. М., Чухов В. В.
Вступ. У техшц! падвисоких частот широко засто-совуються хвилеводи. що частково заповпеш д!електри-чпим матер1алом частково-заповпеш хвилеводи. Вопи мають переваги пор1впяпо 1з порожпистими хвилево-дамп. зокрема можливост! щодо змепшмшя розм!р!в поперечного перетипу, збглынеппя потужпост! випро-мшювашш та подавления пебажапих тгш!в хвиль. У зв'язку з вгшуском пових р1зпомаштпих д!електричпих матер!ал1в. призпачепих для використаппя в пристро-ях д!апазопу падвисоких частот з малими втратами. мае м!сце пеобх!дшсть пост1йпо розвгшати методи розра-хупку та методи вим1рюваппя характеристик частково-заповпепих хвилевод!в.
Постановка проблеме. Теор1я хвилевод!в. запов-пепих повшетю i хвилевод!в з д1електричпим запов-пеппям вздовж вузьких етток. розроблепа достатпьо повпо. Проте И застосуваппя до р!зпих хвилеводпих пристрош потребуе розв'язку трапецепдептпих р1впяпь. що можливо лише чиселышми методами. Це ускла-дшое отримаппя ¡пформ£иц1 про будь-яку характеристику пристрою. Також впливае велика к!льк1сть фа-ктор1в. в!д яких залежать характеристики частково-заповпепих хвилевод!в (ступшь заповпмшя. положения пластшш у хвилевод!. величгша д1електричпо1 протш-кпост! тощо). Розв'язок електродипам1чпо1 задач! для частково-заповпепих хвилевод!в зводиться до пошуку стало! поширмшя в хвилевод!. Точпий розв'язок р!в-пя1шя Гельмгольца електромагп1тпого поля для таких
хвилевод!в можливий лише в окремих випадках, папри-клад, в шаруватих хвилеводах, коли межа розподшу шдкоряеться кусково-неперервним законом розподшу проникностей. Класичш методи визначення сталих по-ширення в частково-заповнених хвилеводах зводяться до розв'язку дисперсшного р!вняння, отриманого або методом прпр1внювання тангешцйних складових еле-ктричного та магштного пол!в на межах розподшу кожного шару, або методом теори кш. Для доондження частково-заповнених хвилевод!в з р!зною висотою зраз-ка, серед шших, иропонуеться шдх!д, який базуеться на поданш в1дносно! д1електрпчно! пронпкноста середо-вища у вигляд! двох дшсних функцш, кожна з яких залежить у поперечному перетиш в!д одше! координати. Це наближена методика визначення власних скаляр-них \ векторпих функцш частково-заповнених хвиле-вод!в. Отже, розв'язок електродинам!чно! задач! для частково-заповнених хвилевод!в зводиться до пошуку стало! поширення в хвилевод! точпими або наближени-ми методами. У статл розглядаеться метод, який дозволяв, вим!рявши значения ефективно! д!електрично! проникноста, розрахувати сталу поширення за будь-яко! частотп.
Результати. За результатами проведеного анал!зу показано, що в!дом! методи вим!рювання ефективно! д!електрично! ироникноста (за допомогою вим!рюваль-но! лш, панорамного вим!рювача, мостового вим!рю-вача) мають недолши щодо залежноста в!д модифша-цп частково-заповнених хвилевод!в, вузькосмуговоста, значно! в1дносно! похибки вим!рювання за зб1лынення ефективно! д!електрично! проникноста. Зокрема, недо-л!ком мостових вим!рювач!в е дуже вузький частотний д!апазон, в якому м!ст залишаеться узгодженим. Практично необх!дно узгоджуватп м!ст на кожшй частот!, досягаючп в!дсутност! сигналу в плеч! Е за однакових навантажень, що шдключеш до бокових плечей. Для цього мости мають налаштувальш елементи у вигляд! штир!в, д!афрагм та ш. Запроионовано метод вим!рю-вання ефективно! д!електрично! проникноста частково заповнених хвилевод!в за допомогою неузгодженого Т-мосту, який вказаних недолшв не мае.
Висновки. Наукова новизна запропонованого методу вим!рювання ефективно! д!електрично! проникно-ста частково-заповнених хвилевод!в за допомогою неузгодженого Т-мосту полягае у можливоста забезпе-чення широкосмуговоста, шдвшценш точноста вим!рю-вань, ушверсальноста за рахунок застосування панорамного вим!рювача коефкцента стоячо! хвшн за на-иругою та електронно-обчислювально! машини. Осо-блив!стю також е можливють вим!рювання ефективно! д!електрично! проникноста у випадках такого частково-заповненого хвилеводу, де шпп методи вим!рювань не шдходять. Отримаш результати доцшьно застосовува-ти шд час проектування нових антенних систем, до складу яких входять частково-заповнеш хвилеводи, а також у навчальному процес! для створення нових або удосконалення ¡снуючих робочих м!сць для проведения лабораториях та практичних занять з використанням наведеного методу впм!рювання.
Ключовг слова: ефективна д!електрпчна прони-кшсть; часткове д!електричне заповнення; метод вимь рювання ефективно! д!електрично! ироникноста; частково заповнений хвилев!д
Метод измерения эффективной диэлектрической проницаемости частично заполненных волноводов с помощью несогласованного Т-моста
Каращук Н. Н., Манойлов В. Ф., Сидорчук О. Л., Тарасенко С. М., Чухов В. В.
В технике сверхвысоких частот широко используются волноводы, которые частично заполнены диэлектрическим материалом - частично-заполненные волноводы. Они имеют преимущества по сравнению с полыми волноводами, состоящие в возможности уменьшения размеров их поперечного сечения, увеличения мощности излучения и подавления нежелательных типов электромагнитных волн. В связи с выпуском новых разнообразных диэлектрических материалов, предназначенных для использования в устройствах диапазона сверхвысоких частот с малыми потерями, возрастает необходимость развивать методы расчета и методы измерения характеристик частично-заполненных волноводов. Решение электродинамической задачи для частично-заполненных волноводов сводится к поиску постоянной распространения электромагнитной волны в волноводе точными или приближенными методами. В статье рассмотрен метод, позволяющий измерить значение эффективной диэлектрической проницаемости и рассчитать постоянную распространения волны на любой частоте. Показано, что известные методы измерения (с помощью измерительной линии, панорамного измерителя, мостового измерителя) имеют недостатки в зависимости от модификации частично-заполненных волноводов, узкополосности, значительной относительной погрешности измерения. Предложенный метод измерения эффективной диэлектрической проницаемости частично-заполненных волноводов основан на применении несогласованного Т-моста, что обеспечивает высокую точность и широкополосность измерения. Для увеличения быстродействия измерения применена электронно-вычислительная машина. С ее помощью, благодаря различным программно-установленным компонентам, осуществляется статистическая обработка результатов, определяются характерные точки на графиках или рассчитываются другие производные параметры. Предложенный метод можно использовать для разработки и изготовления новых антенных систем, в состав которых входят частично-заполненые волноводы, а также в учебном процессе для подготовки специалистов соответствующей отрасли.
Ключевые слова: эффективная диэлектрическая проницаемость; частичное диэлектрическое заполнение; метод измерения эффективной диэлектрической проницаемости; частично заполненный волновод
