J Mater Sci: Mater Electron DOI 10.1007/s10854-017-7387-3
Microstrip antenna based on knitted fabrics with biodegradable synthetic fibers Samanta M. de Holanda1 · José P. da Silva1 · Idalmir de S. Queiroz Jr.2 · Humberto D. de Andrade2 · Juan R. F. Guerra2 · José de A. P. Magno2 · Marcos S. de Aquino3 · Moisés V. de Melo3 · Neil O. L. Filho3
Received: 30 April 2017 / Accepted: 19 June 2017 © Springer Science+Business Media, LLC 2017
Abstract In this paper a microstrip antenna with substrate constituted by knitted fabrics based on biodegradable synthetic fibers is analyzed. The knitted structure used was jersey composed by polypropylene and polylactic acid from corn. The physical characteristics (yarn count, weight, thickness, dimensional stability and tensile strength) of the knitted fabrics were obtained according to technical norms. The dielectric constant and the loss tangent of the substrate were obtained using the coaxial probe method. Based on results obtained from the simulation, one prototype of the microstrip antenna with rectangular patch was manufacture and tested. The results for the return loss measured from prototype were compared with the simulations. The microstrip antenna proposed resounded below −10 dB in 2.5 GHz with bandwidth of 70 MHz (2.8%).
* Samanta M. de Holanda
[email protected] 1
Department of Electrical Engineering, Federal University of Rio Grande do Norte (UFRN), University Campus Lagoa Nova, P. O. Box 1524, Natal, Rio Grande do Norte 59078‑970, Brazil
2
Department of Environmental Sciences and Technology, Federal Rural University of the Semi-Arid Region (UFERSA), district Pres. Costa e Silva, P. O. Box 137, Mossoró, Rio Grande do Norte 59625‑900, Brazil
3
Department of Textile Engineering, Federal University of Rio Grande do Norte (UFRN), University Campus Lagoa Nova, P. O. Box 1524, Natal, Rio Grande do Norte 59078‑970, Brazil
1 Introduction Due to the increased production of mobile devices it is necessary to develop interference-free and noise-proof devices. In this context, the research antenna development has intensified in recent years, especially the ones related to microstrip antennas, since they have unique properties and a wide range of applications [1–7]. Features such as low cost, small size and adaptability to flat or curved surfaces, made this dish one of the most interesting area for scientific, medical and industrial applications. In its simplest build a microstrip antenna consists of two conducting plates (patch and ground plan) separated by a dielectric material (substrate). The substrate is the most expensive part of a microstrip antenna, due this, researches related to synthesis and characterization of dielectric materials are important [8–11]. The microstrip antenna operating in the frequency of 2.45 GHz in the industrial scientific and medical band (ISM) is more appropriate for integration to clothing due to its low profile and planar structure [12]. The textile antenna is an important component in wireless communication in smart fabrics, attracting great attention for industrial [13], military [14] and medical applications [15]. These antennas are malleable and, therefore, have great utility in applications in which rigidity of traditional antennas is considered limiting, as in military clothing use for people location using global positioning system (GPS) and the biomedical area in sensing circuits and monitoring heart rate [16]. The demand for increasingly light and flexible devices have driven research in the field of wearable technology [17–19], in which electronic components are fully embedded in their fibers. Thus, the knitted fabrics have the necessary elasticity to create adaptable and sports parts, enabling high mobility and comfort to its users. In addition, knitted
13
Vol.:(0123456789)
fabrics have simpler fabrication than flat fabrics, a superior variety of constructions and greater thermal physiological comfort due to their high porosity. The knitted fabric is composed of structures produced by interlacing yarns by using loop-forming techniques, where: the career or course is the sequence of consecutive stitches in the horizontal direction and the wale is the sequence of consecutive stitches in the vertical one, [20] as shown in Fig. 1. The length of the stitch is related to the level of porosity that the knitted fabrics present, besides defining a physical rigidity of the made structure. This length is determined by the knitted fabric manufacturing process, by its maximum limit related to the maximum stress that the yarn can withstand at the time of manufacture, that is, the smaller the stitch the greater the tension applied to the yarn. This paper aims to analyze textile substrates made of knitted fabrics based on biodegradable synthetic fibers for use in microwave devices, showing the procedures and materials used in the research. There were chosen three knitted fabrics with jersey structure with different compositions of manufactured fibers: polypropylene and soybean protein (PP + SPF), polypropylene and polylactic acid from corn (PP + PLA), and polypropylene and bamboo (PP + BAM).
2 Materials and methods In this topic, it will be described the materials and methods used in the accomplishment of this work from the characterization stage to the preparation and testing of the textile antenna. Figure 2 summarizes the methodology used in the development of this work. The composite fibers have been selected aiming ideal parameters for use in microstrip antenna substrates, thus, all knitted fabrics have dielectric characteristics and low profile for integration of clothes. The composition and structure of knitted fabrics used can be seen in Table 1.
J Mater Sci: Mater Electron
Fig. 2 Summarized diagram of the methodology
Figure 3, captured using a Nikon SMZ18 stereoscope with ×3 approach, shows clearly the jersey knitted weft structure of the three fibers. Polypropylene (PP) is a synthetic fiber obtained by the polymerization of propylene (C3H6), which holds moisture resistance properties, high chemical inertia, light weight, resistance to abrasion and to the action of molds and bacteria, and provides excellent insulation [21]. Soybean protein fiber (SPF) is classified as artificial as protein and it is obtained from the soybean seed regeneration. This fiber has natural fibers qualities and synthetic fibers physical properties [22]. The SPF has a large accordance in mixture with cotton and other fibers, improving the properties of tissues [22]. The fiber of polylactic acid (PLA) is a biodegradable synthetic fiber obtained from plant material. In this study, PLA used was obtained from the synthesis of corn. This material exhibits good chemical and mechanical properties, being resistant to perspiration and successive washes [23]. The bamboo (BAM) is an artificial fiber regenerated from Table 1 Composition and structure of knitted fabric used
Fig. 1 Knitted fabric structure
13
Composition
Structure
Abbreviation
Polypropylene + soybean Polypropylene + corn Polypropylene + bamboo
Jersey Jersey Jersey
PP + SPF PP + PLA PP + BAM
J Mater Sci: Mater Electron
Fig. 3 Images of jersey structure of the knitted fabrics analyzed magnification ×3: a PP + SPF; b PP + PLA; c PP + BAM
cellulose obtained from the bamboo plant. This fiber has natural anti-bacterial properties, hypoallergenic functions, as well as it is very absorbent and quick-drying [24].
3 Electrical characterization The electrical permittivity is a complex magnitude that describes how the material behaves when subjected to an electric field, quantifying the facility with which it allows the passage of this field [25]. The electric permittivity can be described by the following equation:
Fig. 4 Measurement system using the method of the coaxial probe
𝜀 = 𝜀0 𝜀r = 𝜀�r − j𝜀�� r
(1) where 𝜀0 is the vacuum permittivity (8.885 × 10− 12 F/m) and 𝜀r is the relative permittivity of the material. The real part of the relative permittivity (dielectric constant), 𝜀′r , is a measure of the amount of energy stored in a material from an external electric field, and the imaginary part (loss factor), 𝜀′′r , is the amount dissipation or loss of energy of a material from an external electric field. The loss tangent (tan 𝛿) is the ratio between the two parts of 𝜀r, being expressed by:
𝜀�� tan 𝛿 = � r 𝜀r
(2)
The permittivity in the low frequency range (<1 GHz) is predominantly influenced by the ion conductividty, in the microwave range (1 GHz ≤ f ≤ 10 GHz) is mainly modified by dipolar relaxation, and the absorption peaks in the infrared region and above (f > 10 GHz) is mainly due to atomic and electronic polarizations [26]. For the electrical characterization it was used the coaxial probe method with an impedance meter Agilent model 85070E. In this method, the dielectric permittivity is measured from the return loss parameter. Thus, each sample was prepared on multiple layers of fabric forming a substrate with a height around 1.5 cm (only for the characterization phase). The probe 020 was positioned above each element,
Fig. 5 The dielectric constant by frequency of the knitted fabrics
and the measurements were performed within the ISM frequency band ranging from 0.9 at 2.5 GHz. Figure 4 illustrates the measuring system used. The data were sent to a computer connected to the impedance meter and, according to the processing, it was possible to obtain the dielectric constant values, as shown in Fig. 5, loss factor and loss tangent, that can be seen in Fig. 6. The dielectric constants showed a similar behavior without large discrepancy and with values around 1.5 in the IEEE 802.11b standard. These relatively low values of dielectric constant show the high porosity rates presented in knitted fabrics. However, the loss of surface waves can be reduced, and there is an increase of space
13
J Mater Sci: Mater Electron
4 Physical characterization
Fig. 6 The loss tangent by frequency of the knitted fabrics
waves, increasing, consequently, the bandwidth and allowing the development of antennas with high gain and efficiency [27]. In Fig. 6 it is observed a characteristic increase in loss tangent of this type of material at high frequencies, with all peaks at 1.75 GHz followed by a reduction of this parameter. Among the existing frequencies within the ISM band, the frequency of 2.45 GHz is the most widely used in wireless communication systems (Wi-Fi, Bluetooth etc.), enabling several applications for devices that operate under this condition. Values of dielectric constant, loss factor and loss tangent of the tissues analyzed for that frequency can be seen in Table 2. Considering that the ideal loss tangent is equal to zero, it is observed in Table 2 that the loss tangents from all tissues were high (2.45 GHz), even when compared with other tissues [1–4]. The PP + PLA fabric had the lowest values among the samples tested, showing a reduction of 27.5 and 57.9% at its dielectric constant and loss tangent, respectively, compared to PP + BAM, which showed the highest values. The low constant dielectric can be compensated with the increase of the height of substrate, as opposed of the loss tangent, that it is incorrigible.
Table 2 Electrical characteristic of the knitted fabric at a frequency of 2.45 GHz Knitted fabric
𝜀′r
𝜀′′r
tan δ
PP + SPF PP + PLA PP + BAM
1.7581 1.4060 1.9383
0.3728 0.1341 0.4390
0.2120 0.0954 0.2265
13
In order to better understand the influence of knitted fabrics composition in the electrical parameters, and aiming the viability and applications of these textile antennas, they were performed titration assays, grammage, dimensional stability and tensile strength. The obtained textile properties were made in accordance with the technical standards, following the ISO 139. The standards of textile characterization are designed to determine the quality of the yarn and its best application for some knitted fabrics. The yarn count and weight assays were realized according to ISO 2060 and ASTM D 3776 norm. The samples of yarn were weighed on an analytical balance Shimadzu AUY-220, and once the mass values measured, it was possible to calculate the yarn count according to the International System Units (SI), which uses the direct system TEX, which represents the quantity in grams of 1000 m of yarn. The weight is the mass per unit area of the fabric, being a very useful date to control the material quality. In order to perform the weight test was used a circular cutter fabric MESDAN 175B of 100 cm2. The knitted fabrics thickness measures were performed with a digital caliper PowerFix model Z22855. The results of these tests can be seen in Table 3. The PP + BAM showed higher weight and thickness among the analyzed samples. As all polypropylene-based fabrics have the same structure, it is possible to relate the fact of this knitted fabric has the highest dielectric constant, among other factors, its composition and cover factor (that was directly related with the size of the stitch). The PP + SPF presented yarn count and weight around 25.0 and 19.4%, respectively, less than PP + BAM, implying in a slighter knitted fabric. The dimensional stability is related to the resistance to dimensional changes of the tissue when subjected to controlled environmental conditions. The dimensional stability tests were performed according to ISO 6330 and ISO 105 C6, using a Washtester MATHIS. After this process, the samples were dried in an oven Nova Ética 220 W at 37 °C (+/−2 °C) for about 4 h. Then, the samples were fixed on a flat surface, and their measures towards the wale and course were obtained. The dimensions measured after the washing process were compared with the initial sample Table 3 Physical characteristics of the knitted fabric Knitted fabric
Yarn count (TEX)
Weight (g/m²)
Thickness (mm)
PP + SPF PP + PLA PP + BAM
15.37 18.83 20.50
258.57 299.90 320.80
0.62 0.70 0.70
J Mater Sci: Mater Electron
Fig. 7 Dimensional stability of knitted fabrics used
sizes, establishing a percentage relation of variation in the dimensions of the knitted fabrics tested, which can be seen in Fig. 7. The PP + PLA showed the best stability in both directions, and PP + SPF is the second most stable in general. For the application to antennas, the more stable is the fabric, the better it is, because the contraction or expansion of the fibers directly affect the antennas geometry and mechanical properties, which are fundamental conditions to conserve the projected operating characteristics. The tensile strength is the relation between tensile force applied to the sample and the elongation suffered by it. The measurement of tensile strength was performed according to ASTM D5034-95 (2009). The tests were performed with the dynamometer Tensolab Auto 3000 MESDAN, and the results of the tensile strength in direction of wale and of curse can be seen in Fig. 8a, b respectively. The difference of first decline between PP + SPF (105.2%, 345.48 N) and PP + PLA (106.0%, 379.54 N), in Fig. 8a was not as significant as compared to PP + BAM (123, 2%, 418.52 N), that showed greater elongation and strength, which may be associated to greater rigidity than the bamboo fiber when combined with PP. In Fig. 8b the PP + SPF (96.8%, 295.5 N) had the lowest values compared to PP + PLA (121.6%, 398.28 N) and PP + BAM (146%, 437 N), which, again, obtained the highest values of stretching and strength for the first decline. It is possible to notice that the deformation in the direction of the wale, in all cases, was smaller than in the direction of the course. This occurs due to the formation of pressure points (nodes) that generate a force opposing the traction applied to the fabric in the direction of the wale. In the direction of the course, the influence of these points is minor, and for this reason, the elongation is usually greater. These data are important for the implementation and application of the
Fig. 8 Tensile strength in direction of the: a wale; b curse
knitted fabric in microstrip antennas, which must be constructed and positioned considering the locations where the antenna undergoes the least possible deformation and, if it is tensioned, resist to the maximum before the rupture.
5 Project and simulation The antenna projected was a microstrip antenna with rectangular patch and fed by an impedance line, as presented in Fig. 9. It was developed an algorithm in Fortran language to implement the model of transmission line to calculate the dimensions of microstrip antennas [28]. Impedance matching techniques were applied to improve antenna gain and return loss. Thus, the dimensions of inset feed were calculated using Eqs. 8 and 9 presented by Ramesh and Yip [29], and Matin and Sayeed [30], respectively, and approximated considering the manually construction in the patch, as shown in Fig. 10. The project values and dimensions can be seen in Table 4.
13
J Mater Sci: Mater Electron
Fig. 9 Dimensions of a microstrip antenna with rectangular patch (standards antennas): a front view; b side view
Fig. 10 Dimensions of a microstrip antenna with inset feed in rectangular patch
y0 = 104 (0.001699𝜀7r + 0.13761𝜀6r − 6.1783𝜀5r )L 2
+ 93.187𝜀4r − 682.69𝜀3r + 2561.9𝜀2r − 4043𝜀r + 6697
(3)
yw = √
c 4.65 × 10−12 fr 2𝜀ref
With these sizes, the antennas were designed and simulated in the software Ansys HFSS® (High frequency structural simulator), enabling the visualization parameters of the return loss, radiation pattern and current density, as shown in Figs. 11, 12 and 13, respectively. The antennas were projected to operate on resonance frequency (fr) of 2.45 GHz, with substrate thickness of three knitted fabric layers, to ensure the isolation among the conductive parts (aiming the implementation of the antenna), to keep the flexibility and to reduce the dimensions of the patch. The antennas resounded below −10 dB and can be considered broadband (BW > 2%), but only PP + PLA was within the proposed central frequency. The closest resonance frequency to the design was the PP + PLA one with 2.45 GHz, return loss of −16.76 dB and bandwidth of 8.32%, followed by PP + SPF, which resounded in 2.51 GHz with −25.13 dB and 10.85% of bandwidth, implying in greater efficiency and directivity of these antennas. The PP + BAM has resonance in 2.61 GHz with −25.98 dB and bandwidth of 8.97%. For this reason, the radiation patterns were plotted in 2D to the antennas with substrate of PP + PLA, as shown in Fig. 12a, and substrate of PP + BAM as seen in Fig. 12b. It is possible note that the antenna substrate composed by PP + PLA presented the maximum gain around 2.17 dB, i.e., considerably lager that PP + BAM, which had maximum gain of 0.65 dB. This difference in the total gain can be related to loss tangent of the material, with PP + PLA lower than the PP + BAM one. Figure 13 shows the surface current density of the patch antenna for PP + PLA substrate. The current density indicates the presence of moving charges on conductor, more intense around the edges due to feathering effect caused by the dielectric constant of the material. In the transmission line, the current density is more concentrated due to its narrow width. The PP + PLA substrate showed better performance compared to the others and it was chosen for manufacturing the prototype.
(4)
Table 4 Calculated dimensions of microstrip antenna with rectangular patch for a frequency of 2.45 GHz Knitted fabric
PP + SPF PP + BAM PP + PLA (Standard) PP + PLA (Inset_feed_4 mm)
13
Patch
Transmission line
Subtract
Inset feed
W (mm)
L (mm)
W0 (mm)
L0 (mm)
Ls (mm)
Ws (mm)
h (mm)
y0 (mm)
yW (mm)
52.0996 50.4768 55.7817 55.7817
44.8893 42.6683 49.6965 49.6965
6.6299 7.0572 8.5373 8.5373
23.4885 22.4770 26.1216 26.1216
104.1992 100.9535 111.5634 111.5634
93.9541 89.9080 104.4864 104.4864
1.8600 2.1000 2.1000 2.1000
– – – 11.0000
– – – 4.0000
J Mater Sci: Mater Electron
Fig. 11 The return loss by frequency simulated for standard antennas
6 Implementation and tests The antenna prototype was constructed using manual techniques. In this study, the selected knitted fabric was cut into three rectangles with the dimensions of the substrate calculated with 1 cm of border to ease the manufacturing process. The three knitted fabric samples were overlapped and, subsequently, their borders were sewn to ensure stability between the substrate layers. The patch and the ground plane were obtained from a copper sheet with a conductivity of 5.8 × 107 S/m and 0.05 mm of thickness. This conductive material was chosen
because of its low resistivity, aiming to investigate in a more specific way the losses caused by the textile substrate, besides being widely used in the manufacture of microstrip antennas and to allow certain conformity and adaptability to curved surfaces. Figure 14a, b show the antenna without (Standard) and with the inset feed (Inset_feed_4 mm), respectively. Next, the structure was fed with a gold-plated copper female SMA-KE connector, with impedance of 50 Ω and a 0–6 GHz operating range. The antenna was tested using a Rohde & Schwarz Spectrum Analyzer model FSH6 with integrated ARV function. The results for standard antenna constructed were not satisfactory. To improve the antenna performance, the inset feed technique was implemented using the parameters shown in the Table 4. With this test, it was possible to obtain the results for reflection coefficient shown in the graphics of the reflection Fig. 15. The Standard antenna did not resonate below −10 dB in the design frequency range and it had the first frequency mode indication at 2.71 GHz (−8.20 dB). The inductive reactance for this antenna was 18.4 Ω and the resistance 50% below the characteristic impedance (50 Ω), showing the need to implement impedance matching techniques. The insertion of the slots approached the input impedance value of the characteristic impedance, doing the Inset_feed_4 mm antenna resonate around 2.50 GHz (−22.04 dB), maintaining the bandwidth over 2%, which is the property expected for this type of antenna.
Fig. 12 Radiation pattern 2D for substrate of a PP + PLA and b PP + BAM
13
J Mater Sci: Mater Electron
8 Conclusions
Fig. 13 Current density for PP + PLA substrate
Using the Smith charts, the input impedance obtained for the antenna Inset_feed_4 mm was Zin = 54.3 − j66.6 Ω resonating in 2.5667 GHz. For the structure with inset feed, the loss reflection decreased when compared to the standard antenna 25.4 + j18.4 Ω at 2.7000 GHz.
In this work, it can be concluded that the knitted fabric substrates based on synthetic fibers offered high dimensional stability (with maximum variation of 5%), thin thickness (below 0.8 mm), lightness (weight < 330 g/m²) and tensile strength around 400 N. Also, the knitted fabrics presented low dielectric constant (ε�r < 2) and relatively high loss tangent (tan δ > 0.09). However, their use in microstrip antennas to operate in ISM frequency is viable. The antennas designed resonate below −10 dB and they have a broadband over 2%. The proper nature of the knitted fabric made possible the confection of different configurations of antenna. In addition, the radiation properties of this type of substrates agree with the radiation pattern of the classic microstrip antennas made of non-textile material. Thus, it was found that knitted fabrics have the electrical and physical features necessary to create adaptable textile antennas, enabling high mobility and comfort to its users.
7 Data analyses The comparison among the return loss of the measured and simulated antennas are presented in Fig. 16. The antenna prototype that presented better performance was the Inset_feed_4 mm, for which the measured value for reflection coefficient and bandwidth presented a variation of +79.54 and −3.74%, respectively, when compared with simulated values. The decrease of the bandwidth can be attributed to the formation of a frequency filter originated due to the presence of the capacitive effect generated by the insertion of the inset feed. Fig. 14 Textile antenna constructed: a standard and b Inset_feed_4 mm
13
Fig. 15 Return loss by frequency for textile antennas measure
J Mater Sci: Mater Electron
Fig. 16 Comparison of return loss by frequency to textile antennas: a standard and b Inset_feed_4 mm Acknowledgements The authors thank those responsible for laboratories LAPCOM, in the Department of Electrical Engineering, and LABCTEX in the Department of Textile Engineering, Federal University of Rio Grande do Norte (UFRN) and the Federal Rural University of the Semi-Arid (UFERSA). The authors also thank Mr. Anibal de S. Mascarenhas Filho for the English version of this paper.
References 1. S. Subramaniam, S. Dhar, K. Patra, et al., Antennas and Propagation Society International Symposium (APSURSI), 2014 IEEE, 309–310 (2014) 2. R.E. Iglesias, I.G. Gallego, L.I. Sanchez et al., IEEE Trans. Antennas Propag. 62, 3873–3878 (2013)
3. N.A. Elias, N.A. Samsuri, M.K.A. Rahim, et al., 2012 IEEE Asia-Pacific Conference on Applied Electromagnetics, 132–136, (2012) 4. S.J. Boyes, P.J. Soh, Y. Huang, et al., On-body performance of dual-band textile antennas. IET Microwav. Antennas Propag. 6, 1696–1703 (2012) 5. J. Lilja, P. Salonen, T. Kaija et al., IEEE Trans. Antennas Propag. 60, 4130–4140 (2012) 6. G. Wu et al., J. Mater. Sci. 27(6), 5592–5599 (2016) 7. H. Wu, G. Wu, L. Wang, Powder Technol. 269, 443–451 (2015) 8. G. Wu et al., J. Mater. Sci. 28(9), 6544–6551 (2017) 9. G. Wu et al., J. Mater. Sci. 28(1), 576–581 (2017) 10. G. Wu et al., J. Alloys Compd. 652, 346–350 (2015) 11. G. Wu et al., Mater. Lett. 144, 157–160 (2015) 12. C. Hertleer, A.V. Laere, H. Rogier, et al., Text. Res. J. 80, 177– 183 (2010) 13. J. Virkki, T. Björninen, S. Merilampi, et al., Text. Res. J. 85, 294–301, (2015) 14. E.G. Lim, Z. Wang, J.C. Wang, M. Leach, R. Zhou, C.U. Lei, K.L. Man. Eng. Lett. 22, 2–8 (2014) 15. C. Hertleer, A. Tronquo, H. Rogier, et al., Text. Res. J. 78, 651– 658 (2008) 16. C. Lin, K. Ito, Electronics 3, 398–408 (2014) 17. A. Tsolis, W.G. Whittow, A.A. Alexandridis, et al., Electronics 3, 314–338 (2014) 18. M. Tokarska, J. Mater. Sci. 27(7), 7335–7341 (2016) 19. T. Dias, (ed.) Electronic Textiles: Smart Fabrics and Wearable Technology. (Woodhead Publishing, Cambridge, 2015), p. 156 20. M. Stoppa, A. Chiolerio, in Performance Testing of Textiles: Methods, Technology and Applications, ed. by L. Wang, (Woodhead Publishing, Cambridge, 2016), p. 262 21. N. Yaman et al., Appl. Surf. Sci. 255(15), 6764–6770 (2009) 22. T. Rijavec, Ž. Zupin, Soybean protein fibres (SPF), recent trends for enhancing the diversity and quality of soybean products, ed. by D. Krezhova (InTech, Rijeka, 2011), http://cdn.intechopen.com/pdfs/22617/InTech-Soybean_protein_fibres_spf_.pdf. Acessed 30 Jun 2016 23. N. Reddy, Y. Yiqi, Innovative Biofibers from Renewable Resources (Springer, Heidelberg, 2015), pp. 377–385 24. Y.L. Yu, X.A. Huang, W.J. Yu, J. Appl. Polym. Sci. 131(12), 1–8 (2014) 25. D.M. Pozar, Microwave Engineering. 4th edn, (Wiley, New Jersey, 2012), p. 756 26. L.F. Chen et al., Microwave Electronics: Measurement and Materials Characterization (Wiley, Bognor Regis, 2004), p. 552 27. B. Gupta, S. Sankaralingam, S. Dhar IEEE Conference Publications: Microwave symposium (MMS), 2010 Mediterranean. 251–267 (2010) 28. C.A. Balanis, Antennas Theory: Analisys and Design. 3th edn. (Wiley, New Jersey, 2005). p. 1073 29. M. Ramesh, K.B. Yip, Design inset-feed microstrip patch antennas. (Microwaves & RF, Paramus, 2003), http://mwrf.com/components/design-inset-fed-microstrip-patch-antennas. Accessed 28 Jun 2016 30. M.A. Matin, A.I. Sayeed, WSEAS Trans. Commun. 9, 63–72 (2010)
13