Design of a New Multiband Planar Fractal Antenna Array for Wireless Power Transmission Taoufik BENYETHO*, Larbi EL ABDELLAOUI LMEET, FST of Settat Hassan 1st University Settat, Morocco *
[email protected]
Jamal ZBITOU, Hamid BENNIS LMEET, FPK / FST of Settat Hassan 1st University Settat, Morocco
Abdelwahed TRIBAK
Mohamed LATRACH
Microwave Team INPT Rabat, Morocco
Microwave Group ESEO Angers, France
Abstract—This paper presents a new multiband planar antenna array based on fractal geometry. This structure is validated in ISM band at 2.4 GHz and 5.8 GHz which makes it suitable for wireless power transmission applications. The return loss at the validated bands is around -18 dB. The radiation pattern shows wide aperture angles characteristics of 75° with a gain of 8 dBi at both bands. The antenna is designed on an FR4 substrate with 120 x 63 mm² as dimensions, 4.4 as relative permittivity, 1.6 mm as height and 0.025 as loss tangent. Keywords- Wireless Power Transmission; Fractal Antenna; ISM Band; Rectenna.
I.
INTRODUCTION
Since the confirmation of James Clerck Maxwell theory by Heinrich Hertz experiences in 1886 [1], in which he proved that the electric and magnetic fields spread through the air as waves, the antennas have not stopped evolving what has boosted the wireless applications development. The antennas known several advances [2-5] before the invention of microstrip antenna in 1972 [6], since this date the mobile applications were born. This kind of antennas presents a lot of advantages like simple fabrication and feeding, ability to be incorporated with integrated circuits and low cost production [7]. Also they could be used easily in arrays. But they have some disadvantages like low gain, narrow bandwidth and large size. Research is always ongoing to resolve these drawbacks and several progresses are done until this day. The low gain disadvantage could be increased by using antenna arrays concept [8]. The narrow bandwidth and large size problems are resolved by changing the substrate and then the characteristics [9] like the height, relative permittivity and loss tangent or by changing the antenna geometry. A Technique that proved its ability to shrink antennas size is the fractal geometry used in this work [10]. A mobile application that benefited from antennas evolution is the Wireless Power Transmission. It's the transfer of electrical energy from a source to a load without using wires. Such technology is already operated in a lot of fields
like RFID applications [11] and low power feed equipments. But some experiences showed that it's possible to use wireless power transmission for systems that need a lot of energy like SHARP (Stationary High Altitude Relay Platform) the microwave powered aircraft [12]. Other project under study that show how wireless power transmission can improve the electricity production trough the renewable energy (Solar in this case) is the construction of solar stations with great photovoltaic panels in space which will produce electricity that would be sent directly to Earth by microwaves to replace towers and power lines. The first steps in wireless power transmission were done by Nicola Tesla when he proved that the electricity travel wirelessly through the space [13], but the true beginning of this technology came with the invention of the high-power microwave tube at Raytheon Company in 1950's [14] and the Rectenna circuit [15]. This last circuit is the key element for an efficient wireless power transmission system. The rectenna is a rectifier plus antenna circuit. The antenna collect the electromagnetic energy and the rectifier convert it to a DC current. The fig. 1 shows block schema of a rectenna system.
Figure 1. Bock diagram of a rectenna circuit [16]
The antenna will harvest the RF energy and the schottkey diode will rectify this energy. The low pass filter will let pass the fundamental frequency and rejects the high order harmonics generated by the nonlinear Schottky diode. The capacitor after the diode acts as a DC pass filter that will
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protects the load from HF harmonics. The load is the element that will receive the rectified energy. In order to have an efficient rectenna system, the antenna must presents good characteristics. A good return loss to avoid reflected energy, a big gain and wide radiation pattern to maximize RF collected energy. The rectenna conversion efficiency (η) is defined by (1) [17] : 𝜂𝜂 =
𝑃𝑃𝐷𝐷𝐷𝐷
PDC is the output power and PLOSS is the loss power. Since the rectenna output is a DC power, the output power could be defined as follow: 𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 2
(2)
𝑅𝑅𝐿𝐿
Vout is the output voltage of the rectifier and RL is the load resistance. When only conduction losses of the diode are considered and all the other losses are neglected. The conversion efficiency can be determined by (3)[17] : 𝜂𝜂 =
1
(3)
𝑉𝑉 𝑑𝑑 2𝑉𝑉 𝑜𝑜𝑜𝑜𝑜𝑜
1+
Vd is the voltage drop across the conducting diode. II.
PLANAR FRACTAL ANTENNA THEORY
A. Planar Antenna Theory The patch antennas are planar radiating elements made by etching a printed circuit. They could be rectangular, circular, slit, or more elaborate forms. They are mounted on the top of a dielectric substrate surface with a conductive plane (ground plane) on the other side. The theory of microstrip antennas is well explained in [18]. The resonant frequency of an antenna is related to its length, a method which help to calculate the antenna length for a wished frequency is described below [19] : Define the width W of the antenna related to the relative permittivity of the substrate by (4): 𝑊𝑊 =
𝜆𝜆 0 2
2
�1+𝜀𝜀
𝜆𝜆0 =
𝑐𝑐
(4)
𝑟𝑟
(5)
𝑓𝑓𝑟𝑟
Where 𝜆𝜆0 is wavelength, c the velocity of light, 𝜀𝜀𝑟𝑟 the relative permittivity of the substrate and 𝑓𝑓𝑟𝑟 the wished frequency. Calculate the effective dielectric constant𝜀𝜀𝑒𝑒𝑒𝑒𝑒𝑒 by using (6): 𝜀𝜀𝑒𝑒𝑒𝑒𝑒𝑒 =
𝜀𝜀 𝑟𝑟 + 1 2
+
𝜀𝜀 𝑟𝑟 − 1 2
�1 +
Find the effective length 𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒 of the antenna using (7): 𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒 =
12ℎ −0.5 𝑊𝑊
�
(6)
𝑐𝑐
2𝑓𝑓𝑟𝑟 �𝜀𝜀 𝑒𝑒𝑒𝑒𝑒𝑒
(7)
Finally, identify the length of the antenna defined by (8): (8)
𝐿𝐿 = 𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒 − 2𝑑𝑑𝑑𝑑
(1)
𝑃𝑃𝐷𝐷𝐷𝐷 +𝑃𝑃 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜 =
h is the height of the substrate.
Where
𝑑𝑑𝑑𝑑 = 0.412 ℎ
𝑊𝑊
�𝜀𝜀 𝑒𝑒𝑒𝑒𝑒𝑒 + 0.3�� ℎ + 0.264� 𝑊𝑊
�𝜀𝜀 𝑒𝑒𝑒𝑒𝑒𝑒 − 0.258�� ℎ + 0.8�
(9)
B. Fractal Antenna Theory The Fractal term was first used by Benoit Mandelbrot a French mathematician on his book "les objets fractals" [20]. it's Latin word derived from "fractus" which means "broken". Effectively, a fractal is a geometric object "infinitely fragmented" whose details are similar at any chosen level. This characteristic of self -similarity gives fractal antennas the aspects of multiband or reduced size. When apply a fractal technique to a structure, this one presents the same shape at different scales, which gives the antenna multiband aspect, because as mentioned before the resonant frequency of an antenna is related to its length. The fractal dimension D is the number that calculate the irregularity degree and fragmentation of a geometric assembly or a natural object. It's defined by [20]: 𝐷𝐷 =
ln (𝑁𝑁𝑁𝑁𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) ln (
1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
)
(10)
The "Number of self similar pieces" mean the multiple pieces identical to the original shape when applying a fractal aspect from one step (or iteration) to another. The "magnification factor" signify the scaling value between an iteration and the next one when applying a fractal technique. To understand this well, the fractal geometry aspect applied to the antenna of this paper is explained. The fractal antenna used in this work is based on Koch curve invented in 1904 by the Swedish mathematician Helge Von Koch [21]. The fig. 2 illustrates the Koch curve in the iterations 0 to 4. The creation of this structure starts with a line of specific length. The first iteration consist to delete the middle segment equal to the 1/3 length of the original segment and replace it by two segments with the same length as the removed one, but these two segments construct a 60° angle s shown in fig. 2. Know there is four segments with a 1/3 length of the original. Applying the same aspect to these segments, the second iteration is reached, with 16 segments and each segment measures 1/9 length compared to the first original segment.
Figure 2. Koch curve iterations from 0 to 4
The "Number of self similar pieces" in this case is 4, because in each iteration the number of copies is multiplied by 4. The "magnification factor" is 1/3 because each new segment have the 1/3 length of the previous. The Koch curve fractal dimension is :
III.
𝐷𝐷 =
ln (4)
ln (
1 ) 1/3
= 1.26
(11)
THE ANTENNA DESIGN
A. One Element Antenna Design The aim of this work is to design an antenna that presents a good performance in the ISM bands at 2.4 and 5.8 GHz, to reach this objective, we inspired from [22] based on Koch fractal shape in its 3rd iteration. The fig. 3 shows the designed antenna over an FR4 substrate with relative permittivity of 4.4, height of 1.6 mm, loss tangent of 0.025 and 10*38 mm² as dimensions calculated using the equations described in [19]. The feeding line of the antenna has a 14 mm length and a 2.2 mm width, these parameters are obtained by using CST Microwave Studio [23] optimization tool. The table I gives the one element antenna dimensions details. TABLE I. Parameter a b c d e f g h
ANTENNA DIMENSIONS Length (mm) 10 38 14 2.2 22 5.8 24 14
Figure 3. The front face (a) and back face (b) of fractal antenna
The fig. 4 illustrates the return loss of the one element antenna. The structure is validated in two bands defined from (2.13 - 2.5) GHz and (5.65 - 6.2) GHz with a -18 dB return loss, which enclose the ISM bands at 2.4 and 5.8 GHz defined from (2.4 - 2.5) GHz and (5.525 - 5.875) GHz.
Figure 4. One element antenna return loss
The radiation pattern of the antenna presents a directive propagation through the x-axis but with wide aperture angles of 90° and a gain of 2.4 dBi at 2.4 GHz. At 5.8 GHz the propagation is slightly oriented through the x-axis with an angle aperture of 55° and 2.7 dBi as a gain. The fig. 5 describes the radiation pattern of the antenna at 2.4 and 5.8 GHz. The fig. 6 shows the current surface distribution at 2.4 GHz and 5.8 GHz. The current distribution is more concentrated at part near to the feed line at the low band while its equally concentrated through the antenna surface in the upper band.
(a)
Figure 6. Antenna current distribution at 2.4 GHz (a) and 5.8 GHz (b)
Z0 is the characteristic impedance of the line and ZL the load impedance, β the electric length defined by (13):
𝜆𝜆
β=
2π λ
When 𝑥𝑥 = then (12) become (14) : 4
𝜆𝜆
𝑍𝑍𝑖𝑖𝑖𝑖 � � = 4
𝑍𝑍02 𝑍𝑍𝐿𝐿
(13)
(14)
It's possible to control the input impedance by controlling the characteristic impedance. (b) Figure 5. Antenna radiation pattern at 2.4 GHz (a) and 5.8 GHz (b)
B. Antenna Array Design An array antenna aspect was applied to the previous antenna in order to improve its gain and radiation pattern. The antenna array is constructed by four element antennas fed with the parallel line method. This technique is based on quarter length transformation in order to preserve constant antenna array input impedance (50 ohm in our case).
The fig. 7 illustrates the quarter length transformation line. To have 50 ohm input impedance in the input line with a load impedance of 100 ohm, the transmission line must have a λ and width equivalent to its characteristic length of 4 impedance equal to : 𝑍𝑍0 = �𝑍𝑍𝑖𝑖𝑖𝑖 𝑍𝑍𝐿𝐿 = √50 ∗ 100 = 70.7 𝑜𝑜ℎ𝑚𝑚
Equation (12) defines the input impedance Zin for line transmission from a distance x to the load [18]: 𝑍𝑍𝑖𝑖𝑖𝑖 (𝑥𝑥) = 𝑍𝑍0 �
𝑍𝑍𝐿𝐿 +𝑗𝑗 𝑍𝑍0 tan (𝛽𝛽𝛽𝛽 ) 𝑍𝑍0 +𝑗𝑗 𝑍𝑍𝐿𝐿 tan (𝛽𝛽𝛽𝛽 )
�
(12) Figure 7. Quarter length transformation line
(15)
The antenna width is defined by analytic method [18] or by using calculation tools by inquire the resonant frequency and the substrate parameters. In this case we used CST Microwave Calculation tool. The resulted width is 1.55 mm. The fig. 8 shown the four elements antenna array. The dimensions are 120 x 63 mm² and the distance between elements antenna equal to 35 mm. Normally in an antenna array design, the distance between elements should be more than the half wavelength of lower resonant frequency [18] which is 60 mm in our case at 2.4 GHz. The topology of this antenna array permits to reduce this distance without affecting antenna performances. The optimal distance was reached by using the CST Microwave Studio optimization tool.
Figure 9. Antenna array return loss
The antenna array radiation pattern presents wide aperture angles of 75° at 2.4 GHz and 5.8 GHz. The propagation is through the z-axis as illustrates the fig. 10 and the gain is 8 dBi in both bands.
(a)
(a)
(b) Figure 8. The fractal antenna array front face (a) and back face (b)
The table II gives the antenna array dimensions details. TABLE II. Parameter i j k l m n o
ANTENNA ARRAY DIMENSIONS Length (mm) 3 29.2 1.55 3 14 24 38.5
This antenna is matched in two wide bands, the first is (2 2.8) GHz and the second is (5.35 - 5.93) GHz with -18 dB return loss in both bands as shown in fig. 9, which covert widely the ISM band at 2.4 GHz and 5.8 GHz.
(b) Figure 10. Antenna array radiation pattern at 2.4 GHz (a) and 5.8 GHz (b)
The fig. 11 describes the surface current distribution over the antenna surface at 2.4 GHz and 5.8 GHz. Like the one element antenna the current at 2.4 GHz is distributed near to the feed line and equally concentrated on antenna surface at 5.8 GHz.
REFERENCES [1] [2]
[3] [4] [5]
[6] (a)
[7] [8] [9] [10] [11]
[12] (b) Figure 11. Antenna array current distribution at 2.4 GHz (a) and 5.8 GHz (b)
[13] [14]
CONCLUSION A new planar multiband fractal antenna array was presented. The structure presents a good performances at bands (2 - 2.8) GHz and (5.35 - 5.93) GHz with -18 dB return loss in ISM band wished frequencies at 2.4 and 5.8 GHz. The radiation pattern is approximately the same in both bands with a wide aperture angles of 75° and a gain of 8 dBi. These characteristics makes this antenna suitable for wireless power transmission application which need a rectenna circuit composed by an antenna with a good gain and wide aperture angle to collect the maximum RF energy and a Schottkey diode that presents good specifications. The structure is low cost, simple to fabricate and easy to associate with integrated circuits.
[15] [16] [17] [18] [19] [20]
ACKNOWLEDGMENT We have to thank Mr. Mohamed Latrach Professor in ESEO, engineering institute in Angers, France, for allowing us to use all the equipments and software available in his laboratory.
[21] [22]
[23]
F. W. Van Name,"Modern Physics", Prentice-Hall, p. 30, 1962. J. S.Belrose, "Fessenden and Marconi: Their Differing Technologies and Transatlantic Experiments During the First Decade of this Century, International Conference on 100 Years of Radio", pp. 5–7, September 1995. H. Yagi and S. Uda,"On the feasibility of power transmission by electric waves", in Proc. 3rd Pan-Pacific Sci. Congr., vol. 2, Tokyo, Japan, pp. 1305–1313, 1926. D. Olver, "Microwave horns and feeds", USA: IET, ISBN 0-85296-8094, pp. 2–4, 1994. J. Spradley, "A Volumetric Electrically Scanned Two-Dimensional Microwave Antenna Array", IRE National Convention Record, Part I Antennas and Propagation Microwaves, New York: The Institute of Radio Engineers, pp. 204-212, 1958. J. Howell, "Microstrip Antennas", IEEE International Symposium on Antennas and Propagation, Williamsburg Virginia, pp. 177-180, 1972. R. Bancroft, "Microstrip and Printed Antenna Design", Noble Publishing, chapter 2-3, 2004. L.E. Frenzel, "Welcome to antennas", Electronic Design, 2008. Y. T. Lo, D. Solomon, W. F. Richards, "Theory and Experiment on Microstrip Antennas", IEEE Transactions on Antennas and Propagation, AP-27, pp. 137-149, 1979. D.H. Werner, "Fractal Antennas", antenneX Online magazine, Issue No. 81, January 2004. S. V. Georgakopoulos and O. Jonah, "Optimized wireless power transfer to RFID sensors via magnetic resonance", IEEE International Symposium on Antennas and Propagation, Spokane, Washington, USA, pp. 1421 - 1424, 3-8 July 2011. J. Schlesak, A. Alden and T. Ohno, “A microwave powered high altitude platform,” in IEEE MTT-S Int. Microwave Symp. Dig., pp. 283-286, 1988. M. Cheney Book, “Tesla Man Out of Time”, Englewood Cliffs, NJ: Prentice-Hall, 1981. W. C. Brown, "The history of power transmission by radio waves", IEEE Transactions on Microwave Theory Techniques, 32, pp 12301242, 1984. W. C. Brown, “Performance characteristics of the thin-film, etched circuit rectenna,” in IEEE MTT-S Inc. Microwave Symp. Dig., pp. 365 367, 1984. J. Zbitou, M. Latrach and S. Toutain, “Hybrid Rectenna and Monolithic Integrated Zero-Bias Microwave Rectifier”, IEEE Trans. Microwave Theory Tech., vol. 54, no. 1, pp. 147–152, January 2006. T. Yoo and K. Chang, "Theoretical and experimental development of 10 and 35 GHz rectennas", IEEE Transactions on Microwave Theory Techniques, 40(6), pp. 1259-1266, 1992. C. A. Balanis, "Antenna theory: Analysis and Design", J. Wiley & Sons (Ed). New York, 2005. C. A. Balanis, "Advanced Engineering Electromagnetics", J. Wiley & Sons (Ed). New York, 1989. B. B. Mandelbrot, "Fractals: Form, Chance and Dimension, les objets fractals : forme hasard et dimension", Nouvelle bibliothèque scientifiques, French edition, January 1, 1975. H. V. Koch, "Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planes", Acta Mathematica, 30(1), pp. 145-174, 1904. A. Jamil, M. Z. Yusoff, N. Yahya and M. A. Zakariya, "A Compact Multiband Hybrid Meander- Koch Fractal Antenna for WLAN USB Dongle", 2011 IEEE Conference on Open Systems (ICOS2011), September, Langkawi, Malaysia, pp. 25 - 28, 2011. CST Microwave Studio, https://www.cst.com/Products/CSTMWS.
