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16A METHODOLOGY OF METAMATERIAL EFFECTIVE PERMITTIVITY AND PERMEABILITY VALUE MEASUREMENT
Kukharenko A. S.
technical science philosophy doctor, head researcher Branch of'VRSC" "ISDE".
МЕТОДИКА ИЗМЕРЕНИЯ ЭФФЕКТИВНЫХ ЗНАЧЕНИЙ ДИЭЛЕКТРИЧЕСКОЙ И МАГНИТНОЙ ПРОНИЦАЕМОСТИ МЕТАМАТЕРИАЛОВ
Кухаренко Александр Сергеевич, кандидат технических наук, старший научный сотрудник, Филиал ОАО «ОРКК» -«НИИ КП».
АННОТАЦИЯ
В настоящей работе предложена методика измерения эффективных значений диэлектрической и магнитной проницаемости этих структур, основанная на измерении их комплексных коэффициентов передачи и отражения. В основу представленного алгоритма положен приведенный математический аппарат, устанавливающий прямую зависимость диэлектрических параметров тестируемых образцов от измеренных значений их S-параметров. Непосредственно для проведения измерений предложен ряд конструкций оснасток. Подробно рассмотрена схема подключения оснасток к векторному анализатору цепей. Приведены практические результаты определения эффективных значений диэлектрической и магнитной проницаемости образца метаматериала, полученные по описанному алгоритму при помощи двух разных оснасток. Проведенный эксперимент показал хорошее совпадение данных между собой и с результатами математического моделирования.
ABSTRACT
In this paper a methodology of metamaterial effective permittivity and permeability determination, based on their complex reflecting and transmitting coefficient measurement, is suggested. The base of the presented algorithm is evaluations, shown here, which determine the dependence of dielectric parameters of the sample under test on its measured S-parameters. For practical measurement some constructions of measuring tools are suggested. The schema of connecting the measuring tools to a vector network analyzer is detail reviewed. Practical results of metamaterial sample effective permittivity and permeability determination, made using the described algorithm and two different measuring tools, are shown. The made experiment has shown a good correlation of the obtained data between each other and with the computed parameters of the sample.
Ключевые слова: диэлектрическая проницаемость, магнитная проницаемость, эффективное значение, метаматери-ал, полоса запирания, частотно-селективная поверхность.
Key words: permittivity, permeability, effective value, metamaterial, band gap, frequency-selective surface.
Introduction
In our days metamaterials are more and more applicable for various UHF devices design [1, 2]. They are used as elements of amplifiers [3], filters [4, 5], power couplers [5] and other applications. They are also widely used for antennas [6, 7] and antenna arrays [8] constructing. Their unusual properties, which are conditioned by the possibility of obtaining a negative reflective index value, allow significant improvement of characteristics of UHF devices, where they are implemented.
But the developers of such devices face a serious problem - self parameters of metamaterial can be determined only indirectly by analyzing the characteristics of the complete device. As metamaterials are periodical metal-dielectric structures, which properties are determined not only by the properties of its components, but the same time by its construction, such methods of their permittivity and permeability determination as method of complete resonance [9], method of dielectric resonator [10] and other traditional methods are not applicable.
At now several methods of metamaterial working band measurements are suggested, such as probe method [11] or method of directive antennas [12]. But they provide only a qualitative assessment of the band gap width and a suppression level, provided by the structures, and don't allow to evaluate permittivity and permeability values.
The paper presents a method of metameterial effective permittivity and permeability values measurement and construction of measuring tools, which are necessary for measurements in case of different electromagnetic field polarization.
Determination of structure effective values of permittivity and permeability with the help of complex transmission and reflection coefficients
Basically metamaterials can be considered as anisotropic environments. Their construction is a periodical metal-dielectric structure, which has at least one symmetry axes. As the size of metamaterial construction resonance elements are usually less than the tenth part of the wave length in the structure operating band, is can be considered as isotropic environment in case of electromagnetic wave propagates along the symmetry axes and has a linear (vertical or horizontal) polarization of electric field.
Let's consider metamaterial as a structure with the length d, with an electromagnetic wave normally falling on its surface (Fig. 1). Vectors E and H are electric and magnetic components of the field, P - Pointing vector. Indexes «f», «r» and «tr» marks components of electromagnetic field of falling, reflected and transmitted wave respectively.
Fig. 1. Electromagnetic wave normally falling on the metamaterial surface.
Such a structure can be represented as an equivalent S-type quadripole, which complex reflection S11 and transmission S21 coefficients can be presented in the following way [13, 14]:
R01 x(l - exp (i2nk0d))
S = ■
1 - x exp (i2nk0d)
S21 =
(l - R2 ) x exp ( i2nk0 d ) 1 - R2 x exp (i2nk0d)
(1)
(2)
Z -1
(3)
where:
Rl = Z+1
n - refraction coefficient;
R01 - multiplication coefficient in equations (1) and (2) [13, 14];
Z - complex wave resistance of equivalent quadripole; k0=2n/X - wave number; d - structure length.
From (1) - (3) equations for complex wave resistance and refraction coefficient determination can be obtained [13 - 16]:
Z=
\
(1+Sil )2 - S:
(1 - S11 )2 - S,
(4)
n=
kod
x cos
—x(1 - S121 + s22 ) 2S„ 1 11 21 '
+-
2nm kd
(5)
where m - an integer number, equal to a number of wave half on the measurement frequency, which can be arranged along the structure length d [16].
If we know the metamaterial complex wave resistance and
refraction coefficient its effective values of permittivity (e) and permeability can be determined using the equations:
£=nZ; (6)
^=nxZ. (7)
So effective values of metamaterial structure permittivity and permeability can be determined by measuring its complex reflection and transmission coefficients.
Metamaterial complex reflection and transmission coefficient measurement
As generally the metamaterial structure is not symmetrical along all main coordinate axes [2], its properties in different directions and in case of different falling electromagnetic wave polarization can be not the same. According to the reason it is expedient to make structure measurements for each field polarisation separately.
The case of propagating of electromagnetic wave with vertical polarization of electric field along the metamaterial working surface
In this case to determine the complex reflection and transmission coefficients values the method of measurement with the use of microstrip line can be implemented [17, 18].
The idea of the method is that between microstrip line conductor (1) and its ground plane (2) a thin plate of the material under test (3) is placed (Fig. 2a). The direction of electromagnetic wave propagation is shown on the Fig. 2a by an arrow. The electric field in the construction is mostly concentrated between the line conductor and the ground plane and has a vertical polarisation in the area [19] (Fig. 2b). The advantage of the method is the possibility of the used microstrip line coupling in a wide frequency band [18], what allows creating a universal measuring tool.
The example of such a construction realization is shown on the Fig. 3. A microstrip line conductor with the width a and length b is placed on the high c above the ground plane with the length is b and width d.
A fabricated measuring tool sample (Fig. 3b) is an FR4 PCB with dimensions b=200 mm and d=100 mm fixed on the high c=5 mm above the ground plane of the same size with the help of dielectric stages. On the PCB side facing the ground plane a microstrip line conductor wit dimentiones a=20 mm and b=200 mm is made. There is no metallization on the opposite side of the PCB. The measuring tool connection to a network analyzer
is realized by coaxial cables, which central wires are connected to opposite edges of the microstrip line conductor and their shield is connected to the ground plane. The measured complex reflection and transmission coefficients of the tool (Fig. 3c) show, that the construction is coupled in the frequency band 1 - 2 GHz.
ä
о
a)
b)
Su, S21 0 IdB] .
15
-20
-25 -30 -35 -40 -45
Sil \--^-i--
JT p Г Ь / \ r
7 = Su f P Д / \J
/----------r--------- b "/" "----Г-------- P - ----------Г---------- г---------
Г ь J ? ¥ fe
Tl Г* ■ »V ■ r F"---------Ii----- " " j-
1 P ■e H ■ p H
1 * *" в H к
1.2
1.4 1.6
1.8
2.2 2.4
c)
2.6 2.8 3 F [GHz]
Fig. 3. Construction of the tool for measuring metamaterial parameters with the help of microstrip line (a), its manufactured sample (b) and the dependence of the sample reflection and transmission coefficients on the frequency (c).
The case of propagating of electromagnetic wave with horizontal polarization of electric field along the metamaterial working surface
To measure the values of complex reflection and transmission coefficients values in this case, a construction, presented on the Fig. 4, is suggested. It contains two dielectric substrates (1), placed one against another on the distance b,
with T-shape conductors (2) with the width a, made on their top side. Conducting ground planes (3) with dimensions c*d are placed from the top and from the bottom of the substrates on the distance e between each other in the way, that T-shape conductors appear right in the center between them. The sample under test (4) should be plased on the bottom ground plane between dielectric substrates. Top and bottom ground
planes are connected one to another by conducting stages (5).
The electric field distribution in the structure is presented on Fig. 4b and is close to a distribution of the gap line electric field [19]. In the area between two T-shape conductors the electric field polarization can be considered as horizontal. The sample under test should be placed directly in this area.
The manufactured sample of the construction (Fig. 4c) has the following dimensions: a=80 mm, b=150 mm, c=100 mm, d=200 mm, e=5 mm. The dielectric substrate material (1) is
FR4. The conducting stages (5) are metal stages for PCB with the high 5 mm. The measuring tool connection to a network analyzer is realized by coaxial cables, which central wires are connected to a horizontal part of the T-shape conductors, and their shield is connected to a bottom ground plane. Complex reflection and transmission coefficients, presented on the Fig. 4d, shou, thet the sample is coupled only in a respectively narrow band 1.52 - 1.58 GHz.
0)
a)
b)
c)
Sii^Su s idB] o
-10
-40-
-B5
I- » ■! ! 1
Sn j/Fh \ ■ 1 1 / 1 t i 1
1 / JT X i
Sil 1 \ 1 \ ■ V
1 1
»■ I-■ 1
-- - I-1- - - - - 1 -1- -
1-45
1.43 L5 1 52 1.54 1.56 i.5Ö 1.6
d)
LW 1.65
F[GH*]
Fig. 4. Construction of the tool for metamaterial parameter measurement in case of horizontally polarized wave propagation along its surface (a), electric field distribution in it (b), manufactured sample (c) and the dependence of reflection and transmission coefficients on frequency (r).
Measuring stand construction and its calibration
The measurement of complex reflection and transmission coefficients can be made by using the vector network analyzer. The analyzer software should provide a possibility of uploading the complex values of reflection and transmission coefficients in a convenient form (.txt or .dat files for example) for further calculations using formulas (4) - (7). Fig. 5a illustrates the measuring tool connecting schema. Fig. 5b shows a schema of signal distribution in a network analyzer [20]. The properties of distorting adapters are determined by their complex reflection and transmission coefficients, which are marked on the Fig. 5d as ED, ES, ER, ET and EL. Additional index «F» marks the direct signal propagation and «R» - the reverse one. The parasite signal penetration from the generator is marked as EX.
As it is seen from the Fig. 5b the measuring schema shows not only reflection and transmission coefficients of the structure under test, but also some internal losses. So to obtain self reflection and transmission coefficients of the sample,
the measuring stand, assembled according to the schema on the Fig. 5a, should be calibrated. The calibration of output connectors and connecting cables should be made according to a user manual of the network analyzed, used for measuring. But the influence of the measuring tool can't be compensated using the standard calibration procedures.
According to [20, 21] and as it is shown on the Fig. 5b, the measuring tool can be considered as a distorting adapter, serially connected with the sample under test in the schema. So the metamaterial self complex reflection and transmission coefficients can be obtained using equations [21]:
(8) (9)
where S11 - complex reflection coefficient; S21 - complex transmission coefficient; bydex «tr» the true value of the coefficient; index «m1» - the measured value of the tool without the sample under test inside; index «m2» - the measured value of the tool with the sample under test inside.
C tr_C m2 C ml. S11 =S11 "S11 > C tr_C m2 C m1 S21 S21 "S21 >
a)
b) Fig.
Ideal network analyzer
Distorting adapter
SarnpEe under test
Distorting adapter
5. Schema of connecting a measuring tool to a network analyzer (a) and vector network analyzer model (b).
So to obtain self (true) values of metamaterial complex reflection and transmission coefficients the sample and measuring tool should be measured, and calculations according to equations (8) and (9) should be made.
Practical measurement of metamaterial parameters
A sample of a dual band mushroom-type metamaterial [7, 22-24], which overall view is shown on the Fig. 6a, was taken for the experiment. The structure parameters were chosen in the way to provide signal suppression in frequency bands L1(1223 - 1236 MHz) and L2 (1575 - 1590 MHz) (Fig. 6b).
Su 0
im -5
a)
Î
nr
b)
1.2 1.25 1.3 L35 M 1.45 1.5 I.S5 1.6
F IG Hi)
Fig. 6. Metamaterial sample under test (a) and the result of its transmission coefficient simulation (b).
The metamaterial sample effective permittivity and permeability values determination was made according to the following algorithm:
Calibration of a vector network analyzer with connected cables.
Connecting of the measuring tool and its complex transmission and reflection coefficients measured values obtaining.
Installing the sample under test in to the tool and its complex transmission and reflection coefficients measured values obtaining.
Calculation according to (8) and (9) of the self (true) values of the complex transmission and reflection coefficients of the sample under test.
Calculation of the permittivity and permeability effective values according to (4) - (7) for each measuring point.
Fig.7 (a - d) presents the results of the complex reflection and transmission coefficient measurements according to the points 1 - 3 of the algorithm, made with the help of measuring tools, intended for cases of propagating along the metamaterial working surface of the electromagnetic wave with vertical and horizontal polarization of electric field. It is seen, that in both cases the measured structure band gap positions corresponds well with the result of simulation.
a)
IdR]
-1 HJ
-U№
- JJ3J
^—■'
Y
r*- .....
- t -F /
i w
c)
1.575 1.6
F[GH*I
S>1 ■ [dB]
-5 -lfl -1i
-K
1 F" — P ** 1»
If F " y' *
J B Cr
v
V 1
b)
L 2 L2J 13 LW 14 1.(5 1.5 1.55 LS
F [GHz]
1-
t
9 L*- •V3 1 \ 1 1 |l i r * f 1 S r f J
î \ * 1 h p 1 \ 1 I h V f 7 f # f J I i / ' / i
6 » | ■—1 — J 4 K p
i j
I SB
m
d)
IJÎ1 u
F(GHz]
Fig. 7. The measured values of complex transmission and reflection coefficients of the measuring tools (1) and the sample under test (2), and calculated self values of complex coefficients (3): (a) - reflection coefficient in case of vertical polarization; (b) - transmission coefficient in case of vertical polarization; (c) - reflection coefficient in case of horizontal polarization; (d) -transmission coefficient in case of horizontal polarization.
Fig. 8 (a - d) presents the calculated values of the sample calculations show, that in the band gap frequency area the effective permittivity and permeability, obtained separately sample effective permittivity and permeability values are for cases of vertical and horizontal field polarization. Both negative, what is a metamaterial unconditional property.
a)
c)
b)
— A
/
\
V \ /
V
d)
Li 1.525 1.55 1.573 14
F [GHz]
Fig. 8. Calculated values of measured metamaterial sample effective permittivity and permeability: (a) - permittivity in case of vertically-polarized wave propagation along the metamaterial surface; (6) - permeability in case of vertically-polarized wave propagation along the metamaterial surface; (b) - permittivity in case of horizontally-polarized wave propagation along the metamaterial surface; (r) - permeability in case of horizontally-polarized wave propagation along the metamaterial surface.
Conclusion
The paper presents the methodology of metamaterial effective permittivity and permeability values determination, which is based on measuring of complex reflection and transmission coefficients of the structures. The mathematical equations to calculate the parameters are provided. Several measuring tools constructions, which are necessary for parameter determination, and which can be used during the metamaterial sample investigations in case of different field polarizations. A practical measurement of S-parameters of a dual frequency mushroom-type metamaterial are made and its effective permittivity and permeability values are determined. The obtained experimental results have good correlation with the result of simulation.
References
1. Caloz Ch., Itoh T. Electromagnetic metamaterials: transmission line theory and microwave applications (the engineering approach), New Jersey, John Wiley & Sons Inc., 2006. 352 p.
2. Engheta N., Ziolkowsky R. W. Metamaterials - physics and engineering exploration, Danvers, John Wiley & Sons Inc., 2006. 414 p.
3. Kim H., Seo C. Inverse Class-F Power Amplifi er
Using the Metamaterial Structure on the Harmonic Control Circuit, Microwave and Optical Technology Letters. 2008. Vol. 50. No 2, pp. 2881-2884.
4. Awasthi S., Biswas A., Akhtar M. J. Compact Bandstop Filt er Using Triangular Metamaterial Mushroom Resonators, Asia-Pacifi c Microwave Conference Proceedings (APMC) 2012, pp. 217-219.
5. Morata M., Gil I., Fernandez-Garcia R. Parametric Design of Stop Band Pass Filter Based on RF Metamaterials in LTCC Technology, Progress in Electromagnetics Research Symposium Proceedings. 2012. No 8, pp. 813-817.
6. Boyko S. N., Veselago V. G., Vinogradov V. G., Vinogradov Y. A. Antenny. 2012. No 12, pp. 32-41. (In Russian)
7. Kukharenko A.S., Yelizarov A.A. Analysis of metamaterial physical features and constituted frequency-selective devices . T-Comm. 2015. Vol 9. No.5, pp. 36-41. (in Russian).
8. Boyko S. N., Yelizarov A. A., Zakirova E. A., Kukharenko A. S. APEP-2014. Saratov. 2014. Vol. 1, pp.218225. (In Russian)
9. Conrood J. Methods for characterizing the dielectric constant of microwave PCB laminates, Microwave Journal. 2011. Vol. 54. No 5, pp.132-144.
10. Resso M., Begley S. Maximizing Data Rates of PCB
Structures by Understanding Dielectric Properties. www. home.agilent.com.
11. Sievenpiper D., Zhang L., Broas R. J., Alexopolous N. G., Yablonovitch E. High-impedance electromagnetic surfaces with a forbidden frequency band, IEEE Trans. MTT. 1999. Vol. 47. No 11, pp. 2059-2074.
12. Lee J., Yoo M., Lim S. A study of ultra-thin single layer frequency selective surface microwave absorbers with three different bandwidth using double resonance, IEEE Trans. AP. 2015. Vol. 63. No 1. pp. 221-230.
13. Chen X., Grzegorcezyk T. M., Wu. B., Pacheco J. Jr. and Kong J. A. Robust method to retrieve the constitutive effective parameters of metamaterials, Physical review. July 2004. E 70, 016608.
14. Numman A. B. and Sharawi M. S. Extraction of material parameters for metamaterials using a full-wave simulator, IEEE AP Magasine. 2013. Vol. 55. No 5, pp. 202-211.
15. Smith D. R., Schultz S., Markos P., Soukoulis C. M. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients, Phisical review. 2002. B 65, 195104.
16. Smith D. R., Vier D. C., Koschny Th., Soukoulis C. M. Electromagnetic parameter retrieval from inhomogeneous metamaterials, Phisical review. 2005. E 71, 036617.
17. Narayanan P. M. Microstrip transmission line method for broadband permittivity measurement of dielectric substrates. IEEE Trans. AP. 2014. Vol. 62. No 11, pp. 2784-2790.
18. Mulenga C. B., Flint J. A., Vaja R., Chauraya A. Measurement techniques for polar electromagnetic band gap structures using an air spaced microstrip line, Laughborough antenna and propagation conference. 2008. pp. 341-344.
19. Nefedov E. I. UHF Devices and antennas (Ustroystva SVCH y antenny), Moscow. Academia. 2009. 384 с. (In Russian)
20. Heeebel M. Vector network analysis basics (Osnovy vectornogo analisa tsepey), Moscow. ME. 2009. 500 p. (In Russian).
21. MI 3411-2013. Novosybirsk. FGUP "SNIIM". 2013. 54 p. (In Russian).
22. Kukharenko A. S. Youth and future of aviation and astronautics conference. Moscow. MAI. 2014, pp. 296 -298. (In Russian).
23. Yelizarov A. A., Kukharenko A. S. 25-th International Crimea conference UHF Technique and telecommunication technologies. Sevastopol, 2015. Vol. 1. pp. 586-587. (In Russian)
24. Yelizarov A. A., Kukharenko A. S. Collection of the thesis of the conference «UHF electronics problems. Innovative decisions.» Moscow. Media Publisher, 2015. pp. 45-48. (In Russian)
ОБОСНОВАНИЕ ОПТИЧЕСКИХ МЕТОДОВ КОНТРОЛЯ НЕФТЯНЫХ ЗАГРЯЗНЕНИЙ ВОДНОЙ ПОВЕРХНОСТИ
Мельников Г.С.-
Старший научный сотрудник, АО «Государственный оптический институт им. С.И. Вавилова»
Самков В.М.-
Ведущий научный сотрудник, АО «Государственный оптический институт им. С.И. Вавилова JUSTIFICATION OPTICAL METHODS FOR MONITORING OF OIL POLLUTION OF THE WATER SURFACE Melnikov G.S., senior researcher, JSC « State Optical Institute . SI Vavilov « Samkov VM, leading researcher, JSC « State Optical Institute . SI Vavilov « АННОТАЦИЯ
Многолетние исследования по наблюдению загрязнений морской и речной поверхностей позволили авторам разработать методики, алгоритмы и требования к комплексированной системе (ГОИ) наблюдения и экологического мониторинга лёгких и тяжелых фракций нефтепродуктов на водной поверхности [1,2]
ABSTRACT
Long-term studies to monitor pollution of sea and river surfaces allowed the authors to develop techniques, algorithms and requirements for the construction of all-weather vsesutochnoy complexed security surveillance and environmental monitoring [1,2] Ключевые слова: система, разливы нефти, нефтепродукты, водная поверхность. Key words: system, oil spills, petroleum products, water areas.
Постановка проблемы.
Проблема контроля загрязнения водных акваторий нефтепродуктами остро стоит не только для экологических служб, но, в первую очередь, и для самих нефтедобывающих предприятий, т.к. она связана напрямую с проблемой рентабельности производства.
Одновременное измерение в ИК диапазонах 7,5-14 мкм и 2,0-5, 6 мкм обеспечит контрастное выделение разлива нефти (за счет сглаживания флуктуаций волнения моря и за счет локального изменения линейного градиента температур в верхних скин-слоях воды) и нефтяного разлива сопутствующих и обусловленных тепломассобменам
между средами « вода-атмосфера « и « нефть-атмосфера». Известная из многолетних наблюдений зависимость перепада температур в поверхностном скин-слое морей и океанов от разности температур воды и воздуха [1-4] обеспечит достоверность решения задачи обнаружения нефтяных разливов в неблагоприятных условиях, даже в условиях смены знака градиента температуры, обусловленного сменой направлением тепломассопереноса. На основании чего можно обосновать следующую систему контроля:
Система предназначена для
1. Охраны объектов в дневных, ночных и сложных ус-
