I Rakotomalala
email: imbolatiana.rakotomalala@lcis.grenoble-inp.fr

P Lemaitre-Auger
email: pierre.lemaitre-auger@lcis.grenoble-inp.fr

S Tedjini
email: smail.tedjini@lcis.grenoble-inp.fr

UHF Near-Field Wireless RFID Power Transfer Through Two Distant Rectangular Waveguides

Keywords: near-field, relay antenna, RFID, rectangular waveguide, wireless power transfer

Feasibility of a wireless power transfer (WPT) system for supplying power to a metallically closed volume is demonstrated. The solution proposed is based on a metallic rectangular waveguide. After optimization, simulated transmission coefficient is -1dB, corresponding to power transmission efficiency of 80%. This near-field WPT system is a good candidate for several specific RFID UHF applications where the measuring volume is mobile with respect to the base station.

I. INTRODUCTION

Passive radiofrequency identification (RFID) is a well know technique nowadays. It has become progressively popular in automatic identification data collection systems. It allows wireless transfer and the collect of information about goods and products, animals, people [START_REF] Finkenzeller | RFID Handbook[END_REF]. Usually, an RFID system is composed of RFID readers and RFID tags. The latter are attached to every object to be identified, and transmits a unique identification code, and the RFID reader reads and writes the identification codes stored by the RFID tag [START_REF]En ultra et super hautes fréquences UHF-SHF Théorie et mise en oeuvre[END_REF]. The operating frequency ranges cover from Low Frequency (LF) to Ultra High Frequency (UHF) bands, depending on the purpose of the system, and the communication ranges, and according standards of legislation the maximum effective isotropic radiated power (EIRP) is limited to 35 dBm [3] for the European region.

Naturally, for such cases of use to work, a complete RFID system has to be located inside the closed volume [START_REF] Michael | RF passive repeater for metal container[END_REF] . Or at least antennas must be located inside the closed volume and be connected with coaxial cables to an external RFID reader located outside of it [START_REF] Kodukula | Method and system for reading objects having radio frequency identification (RFID) tags inside enclosures[END_REF]. In both cases, the system can be made mobile with the use of batteries, but it will require to be connected to an external power source from time to time. And an RFID reader is required per closed volume.

In some situations, it would be interesting to have mobile and at the same time completely passive mobile closed volumes, eliminating all environmental problems created by batteries [6][7] . To do this, a system includes a local RFID reader with several antennas installed inside the enclosure. The system establishes communication between a local RFID reader and a central station with protocols such as Bluetooth or Zigbee there are several patents related to that idea. Three of them present the details of a system for tracking and monitoring an inventory within one or several confined metallic enclosure [START_REF] Kodukula | Method and system for reading objects having radio frequency identification (RFID) tags inside enclosures[END_REF], [START_REF] Sabesan | Passive UHF RFID interrogation system using wireless RFID repeater nodes[END_REF]- [START_REF] Denise | System and method for monitoring and tracking invetories[END_REF]. However, in this system, only information is transmitted through the confined metallic enclosure, the power required by the RFID reader is contained inside the enclosure.

In addition to the previous requirement, sharing the same RFID reader for several mobile closed volumes would be a great economical advantage. An example of a scenario could be several work shop trolleys containing tools used in an aeronautic industry, aero spatial industry or a nuclear plant. A single RFID reader could be placed on a fixed station and to realize the inventory of the tools inside a trolley, an operator would simply have to punch the trolley next to the fixed station. This requires the need of a wireless power transmission of the interrogating RFID signal and the retro diffused responses of the tags inside the trolley.

In this work, we propose and study such a wireless power transfer (WPT) system. It is composed of two separate rectangular waveguides. The WPT system is equivalent to a waveguide discontinuity, namely, an open one which is describe in [START_REF] Guglielmi | Rigorous Multimode Network Numerical Representation of Inductive Step[END_REF]- [START_REF] Marcuvitz | Waveguide Handebook[END_REF]. These study analyze the behavior of an open-ended discontinuity of a rectangular waveguide as a radiating element from a computational point of view, without taking into account possible applications.

In Section II, the whole structure and the optimization of the design of the WPT system is presented with numerical simulations. In Section III, experimental results are presented to validate the concept

II. SYSTEM DESIGN

A. Waveguide antenna design

The whole system consists in a mobile metallic cabinet and a fixed station. The later contains the RFID reader connected to the WPT system. The former contains all tag items and at least one inner antenna connected to the WPT system, as it is shown in Fig. 1. The WPT system is two rectangular waveguides connected to a coaxial cable on one side and open in air on the other side. The separation between the two openings and proper alignment can easily be assured by an appropriate mechanical system. The solution uses such waveguides, as depicted in Fig. 2. The WPT system is equivalent to a waveguide discontinuity, namely, an open one. Therefore, when the electromagnetic field impinges on the termination of the transmitting waveguide, part of the associated power is coupled to the second waveguide, while a second part is reflected, and a third part is radiated in free space.

There is a standard rectangular waveguide which covers the concerned frequency band: the European Telecommunication Institute (ETSI) frequency band, 866 to 868 MHz. It is the WR1150 waveguide, with a broad wall width, W, of 291.1 mm, a height, H, of 146.05 mm, and a cutoff frequency at 513 MHz. These dimensions are still very large, especially when it is necessary to use more than one WPT system, depending on the number of inner antennas. It is necessary to resize the waveguides, not only to get less bulky solution, but also a lighter solution. So, according to [START_REF] Pozar | Microwave Engineering Fourth Edition[END_REF], it is possible to estimate the dimensions of the waveguide especially the broad wall width:

ܹ = ଶ (1)
where c is the speed of light, and ݂ is the cutoff frequency.

With the W obtain as a starting point for one waveguide. Numerical optimization is done to minimize the reflected and radiated power losses by considering the two waveguides with Ansys HFSS. A cutoff frequency less than 860 MHz was found. W equal to 174.8 mm, H equal to 40 mm, and a length, L, of 305 mm, as presented in Fig. 2, gave the best results. Both transmitting and receiving waveguides are well impedance-matched with the feeding circuit and the load impedance, respectively. A reflection loss of -19 dB, and a minimal insertion loss of 1.02 dB are achieved at 868MHz, when they are face-toface and separated by an air gap of 2 cm. Results show that the system operates from 864 MHz to 870 MHz, as shown in Fig. 3, which is compatible with the ETSI UHF RFID band.

From the S-parameters, the power transfer efficiency, K, can be computed the following way [START_REF] Wang | A Novel Coupling Factor Independent Highly Efficient Resonant Based Wireless Power Transfer[END_REF]:

ߟ = ೃೣ ౬ = |ௌ మభ | మ ൫ଵି|௰ ೃೣ | మ ൯ |ଵିௌ మమ ௰ ೃೣ | మ (ଵି|௰ ೣ | మ ) (2)
where ܲ ோ௫ is the power delivered to the receiving port and ܲ ௩ is the available power from the excitation port, ߁ ோ௫ and ߁ ்௫ are the reflection coefficients at the receiving and excitation ports respectively. They are expressed as [START_REF] Pozar | Microwave Engineering Fourth Edition[END_REF]:

߁ ்௫ = S ଵଵ + ௌ భమ ௌ మభ ௰ ೃೣ ଵିௌ మమ ௰ ೃೣ ߁ ோ௫ = S ଶଶ + ௌ భమ ௌ మభ ௰ ೣ ଵିௌ భభ ௰ ೣ
The power transfer efficiency is higher than 80% over all the band, the maximum value is 85%.

C. Tolerance estimation

The tolerances of the system were evaluated in order to validate the feasibility of a real implementation. For that, the frequency was fixed to 868MHz, and the parameter S 21 was simulated while one side of the WPT system was displaced. along z, y, and x axis.

The threshold limit was fixed to -3dB where half of injected power should be received by the second waveguide. As depicted in Fig. 4 a tolerance of 2.8 cm is obtained along the x-axis while more than 5 cm is obtained for y and z axes. Measured and simulated S-parameters of the WPT system are presented in Fig. 6. The agreement between simulation and measurements is fair, and validates the feasibility of this solution. The power transfer efficiency is also presented in Fig. 7. Best results of 85% are obtained at 2.45 GHz. A tolerance study was also done, but since this structure does not operate at the desired frequency, we arbitrarily evaluated the tolerance at 2.45 GHz as depicted in Fig. The results can be observed in Fig. 8. Regarding the longitudinal distance between the receiving and transmitting parts of the WPT system, a stable an optimal distance is found between 0 cm to 1 cm air gap. For smaller gaps or bigger ones, insertion loss increases. This is caused by mismatch of the whole structure. For an arbitrary value of 3 dB of the S 21 , a tolerance of 2.5 cm is obtained along the z-axis. Concerning height (along the x-axis) or lateral (along the y-axis) misalignments, at 3 dB , tolerances of 2 cm and 2.5 cm were respectively obtained.

IV. CONCLUSION This paper demonstrated the feasibility of WPT system for UHF applications for RFID applications. The solution is based on metallic waveguides placed face to face. A power tranfert efficiency of 80% and acceptable tolerances to misalignement were obtained. The proposed solution has very satisfactory performance in terms of efficiency, it is robust and well adapted for transmitting power between two seperated elements of an RFID system.

Fig. 1 .

 1 Fig. 1. Reading RFID tag with WPT systemB. Waveguide DesignWaveguide are commonly used in a variety of application in the microwave frequency band, especially in the range of centimeter and millimeter waves, mostly because they are relatively low loss and have a large power-handling capability. The solution uses such waveguides, as depicted in Fig.2. The WPT system is equivalent to a waveguide discontinuity, namely, an open one. Therefore, when the electromagnetic field impinges on the termination of the transmitting waveguide, part of the associated power is coupled to the second waveguide, while a second part is reflected, and a third part is radiated in free space.There is a standard rectangular waveguide which covers the concerned frequency band: the European Telecommunication Institute (ETSI) frequency band, 866 to 868 MHz. It is the WR1150 waveguide, with a broad wall width, W, of 291.1 mm, a height, H, of 146.05 mm, and a cutoff frequency at 513 MHz. These dimensions are still very large, especially when it is necessary to use more than one WPT system, depending on the number of inner antennas. It is necessary to resize the waveguides, not only to get less bulky solution, but also a lighter solution. So, according to[START_REF] Pozar | Microwave Engineering Fourth Edition[END_REF], it is possible to estimate the dimensions of the waveguide especially the broad wall width:

Fig. 2

 2 Fig. 2 Design of the straight waveguide WPT system

Fig. 3

 3 Fig. 3 Performances of waveguide system: (a) S-parameters, (b) PTE

Fig. 4 S21Fig. 5 Fig. 6

 456 Fig.4S21 variation at 868 MHz. Along the x, y and z-axis III. EXPERIMENTAL VALIDATION In order to validate the efficiency of the proposed solution, measurements were made. But because of available components in our laboratory, a standard rectangular waveguide, WR430, was used instead of the optimized one. It worth mentioning here that the waveguide band is out of the target one in UHF RFID but measurements of the Sparameters can still be done, as well as the calculation of the power transfer efficiency. The response of the WR430 waveguide was simulated so it can be compared to the measurements. The dimensions and the photography of the WR430-based-system are shown in Fig.5.

Fig. 7

 7 Fig. 7 PTE of the rectangular waveguide WR 430

8

 8

Fig. 8

 8 Fig. 8 S21 variation at 2.45 GHz. Along the x, y and z-axis


Imbolatiana Rakotomalala
email: imbolatiana.rakotomalala@lcis.grenoble-inp.fr

Pierre Lemaitre Auger
email: pierre.lemaitre-auger@lcis.grenoble-inp.fr

Transmission Lines to Enhance the Reading of UHF RFID Tags on Small Metallic Objects

Keywords: Passive enhancement structure, CBCPW transmission line, Miniature RFID tag, Near-field UHF RFID

This paper presents an antenna-like passive structure that allows to read miniaturized UHF RFID tags attached to small metallic objects. The solution is realized by combing far-field Wireless Power Transfer (WPT) with a Conductor-Baked Coplanar Waveguide (CBCPW) transmission line. Low cost proof-of-concept prototypes were realized on a FR4 substrate. Measurements are in good agreement with simulations. A maximum read range of 2.20 m can be achieved for the far-field operation.

I. INTRODUCTION

Nowadays, automatic identification data collection systems have become very useful and popular in many applications. Thanks to the advantages of large amount of stored data, fast reading speed, and no need of human intervention to read the data, Radio Frequency Identification (RFID) has been widely adopted [START_REF] Finkenzeller | RFID Handbook[END_REF] The management of small precious assets with RFID technologies is an interesting challenge, especially when those assets are small metallic items. Recently, Ultra-High Frequency (UHF) near-field RFID technology received a lot of attention due to the promising opportunities in item-level RFID applications such as sensitive products tracking, pharmaceutical, logistics, transport and medical products [START_REF] For | Industry solutions[END_REF]. Moreover, near-field systems allow a considerable size reduction of tags compare to those used in far-field systems, expending the range of applications of RFID to extremely small items [START_REF] Shen | A Yagi -Uda Antenna With Load and Additional Reflector for Near-Field UHF RFID[END_REF].

In many existing applications of the near-field UHF RFID, the reader is directly attached to the antenna that generates a strong enough and well distributed magnetic field to ensure the best reading rate in the interrogation area. The tagged objects (TOs) are placed optimally in the interrogation area. As the communication is performed in a near field region, hence, the reading distance is in the order of few centimeters [START_REF] Qing | A Broadband UHF Near-Field RFID Antenna[END_REF]- [START_REF] Wu | Large-area RFID reader antenna for smart shelf at UHF[END_REF]. However, these types of solutions are not practical for an operation in the far field, since the free space loss will weaken the field generate by the antenna in near-field.

In this work, we propose and study the performance of an antenna-like structure capable of reading several miniaturized UHF RFID tags mounted on small metallic objects. The proposed solution is fully passive, low cost and can produce strong and uniform magnetic field in the region near to the antenna, even for a far field operation. It is a CBCPW transmission line [START_REF] Medeiros | RFID smart shelf with confined detection volume at UHF[END_REF], and it can easily be inserted in foam supports which also comprise the space for the positioning of the TOs. That way, the relative placement of the TOs to the antenna-like structure is ensured. The proposed solution is tolerant to the angular orientation of the objects within their place.

This paper is organized as follows. In section II, the characteristics of the considered solution is presented, the theoretical model and analysis are discussed. In section III, experimental validation of the proposed solution is presented.

II. GENERAL CONFIGURATION

The Fig. 1 shows the schematic diagram of the studied configuration. The solution is composed of a CBCPW transmission line terminated by a matching load, i.e. 50 Ohm in the present case. This line is connected to the RFID reader either directly by a coaxial cable, either through a relay antenna system [START_REF] Rakotomalala | UHF Near-Field Wireless Power Transfer , Application To RFID System[END_REF] if the reader is not located in the same space as the tags to be read. With this configuration TOs are arranged optimally with respect to CBCPW line, i.e. the axes of the TOs is parallel to the transmission line plane and perpendicular to the direction of the transmission line. Fig. 2 shows the geometry of the CBCPW. It consists of three coplanar metal strips of finite width, ݓ and ݃ for the center and side strips, respectively. The distance between two neighborin strips is denoted by "s. For this study the structural parameters and the material constants are so chosen that the structure supports only the CPW mode and the Microstrip-Like mode below 1 GHz. The overall dimensions of the CBCPW line are 200 x 20 mm. A 1.6 mm FR4 substrate is used. The central line width "w" is 1.8 mm, and the side strips width "g" is while the distance between two neighborin strips "s" is 1.5 mm so that a ~50Ω impedance line is obtained [START_REF] Pozar | Microwave Engineering Fourth Edition[END_REF]. In its immediate surroundings, it creates and uniform magnetic field strong enough to awake the RFID chip. To detect tags, it is necessary that the power received at the terminals of the tag antenna, ܲ ் , is higher than the minimum power needed to activate the chip, ܲ ௧ [START_REF] Daiki | Contribution au développement d ' antennes lecteurs champ proche pour les systèmes RFID UHF passifs To cite this versionௗ: HAL Idௗ: tel-01179964 Contribution au développement d ' antennes lecteur champ proche pour les systèmes RFID UHF passifs[END_REF]. For near field UHF RFID system, this power is:

ܲ ் ൌ ܲ ோௗ ܥߩ ே ߬ (1)
where ܲ ௗ is the power emitted by the RFID reader, ȡ is the impedance matching coefficient between the reader and its antenna, ܥ ே the coupling coefficient between the CBCPW line and the RFID tag, and ߬ is the impedance matching coefficient between the tag chip and its antenna.

However, when the tag is located in the far field region, the coupling coefficient is different and can be written as:

ܥ ி ൌ ܩ ௧௫ ܮ ௧ ܩ ௫  (2)
where ܩ ௧௫ is the gain of the transmitting reader antenna, ܮ ௧ is the propagation path loss, ܩ ௫ is the gain of the receiving relay antenna, and  is the polarization mismatch loss between the reader antenna and relay antenna. In free space, the path loss is given by well known Friis equation:

ܮ ௧ ൌ ሺ ఒ ସగௗ ሻ; ሺ͵ሻ
where d is the distance between the reader antenna and relay antenna.

Combining (1), (2), and (3), we can obtain the total power received ܲ ்்௧ , at the terminals of the tag antenna for the configuration depicted in Fig. 1 (b) as :

ܲ ்்௧ ൌ ܲ ோௗ ܥߩ ே ܩ߬ ௧௫ ܩ ௫  ሺ ఒ ସగௗ ሻ; (4)
In the present case, considering that the TO are small enough not to disturb the magnetic field created by the CBCPW line, the coupling coefficient ܥ ே depends on the frequency of operation, the distance between the central line and the tag, the missalignement between the tags and the line Hence, according to [3][12],the magnitude of the magnetic field normal to the surface of the tag (referred to as ȁܪ ௭ ȁ ) should be greater than the threshold value ܪ ௧ which is about -30 dBA/m for the Dash XXS by Xeraf, a passive UHF Class 1 Gen 2 tag [START_REF]Dash XXS[END_REF]. It is equipped with the Alien Higgs-3 chip that has a typical sensitivity, ܲ ௧ , of -17dBm.

Full wave simulations were done using Ansys HFSS and the simulated magnetic fields are evaluate at 868MHz. The top view and the side view of the simulated magnetic field distribution at are shown in Fig. 3. Top view is 1mm above the transmission line while the side view is at the center of it. The simulated values of the magnetic field at several observing height (1 to 20 mm) over the transmission line and y = 0 for an input power of 15.24 dBm at the entrance of the transmission line is shown in Fig. 5.

When the observing height is below 10 mm, strong values of ȁܪ ௭ ȁ greater to െʹͲ ݉Ȁܣܤ݀ are achieved within the tag's antenna area for all x positions. At the height of 15 mm, the limit value of Ȃ ͵Ͳ ݉Ȁܣܤ݀ is reached. Theses first simulated results show that a single transmission line is very well adapted to detect a miniature metallic object with a tag height below 15 mm. This configuration is thus suitable for applications where the user wants to track TO that can be placed at a fixed location. Precise position can indeed easily be obtained with preformed foams.

However, for objects having rotational symmetry, the angular orientation can't usually be controlled, resulting in an uncertainty on the tag's height. In the latter case, the magnetic field is also evaluated for all angular positions of the TO (0 to 360°) at 868 MHz. In this simulation a small metallic tool (a 7 mm socket, diameter of 11.2 mm) is used. As expected, a maximum value of 16 dBA/m is observed at 0° while a minimum value -28 dBA/m is observed at 180° as depicted in Fig. 6. Hence, we can consider that the maximum diameter of a symmetrical tool should be 15 mm in order to be detected by the structure 8 shows the test environment used to evaluate the far field reading performance of the solution. The relay antenna with gain of 1 dBi, is placed 30 cm away from the reader antenna, measurement is done with Tagformance Voyantic platform [START_REF]Tagformance pro[END_REF]. A 7 mm sockets is used for the measurement, where the tags is attached directly on the surface of the metallic tool. We evaluate the read range of the tag, for 3 different orientation, and as depicted in Fig. 9 maximum read range is observed at 0° (2.20 m), while the minimal read range is observed at 180° (1.22 m), as expected where the magnetic field distributions are less intense. An antenna-like structure, a CBCPW line, for the reading of small metallic tagged objects is presented with UHF RFID readers. A low cost prototype of the solution was fabricated on FR4 and tested. Results demonstrate a read range of 2.20 m can be achieved in the best case while 1.22 m for the worst case. More results will be presented at the conference.

REF ERENCES

Fig. 1 .

 1 Fig. 1. Schematic representation of the antenna-like structure: (a) direct connection; (b) with WPT for far field operation.

Fig. 2

 2 Fig. 2 Top view of the CBCPW line configuration.

Fig. 3 .

 3 Fig. 3. Simulated distribution of ȁܪ ௭ ȁ at the time t = 0. (a) At an a height of 1mm above the transmission line. (b) Side view centered on the transmission line (y = 0). Some minimum values can be seen in Fig. 3. This is naturally caused by the traveling nature of the electromagnetic field in the transmission line. The length between two zeros is: 100 mm, which correspond to ~ ߣ Ȁʹ at f = 868 MHz, εeff is indeed equal to 3.031 in the transmission line. In Fig 4, Hz is computed along the length of transmission line, at the center of it, and for different time. It can be seen that the maximum value of Hz is almost constant all along the transmission line length.

Fig. 4 .

 4 Fig. 4. Simulated ȁܪ ௭ ȁ value of the proposed line for different period

Fig. 5 .

 5 Fig. 5. Simulated ȁ ȁ value with different observing height.

Fig. 6 .

 6 Fig. 6. Simulated ȁܪ ௭ ȁ value in vicinity of cylindrical metallic tool III. EXPERIMENTAL VALIDATION In order to validate the solution, a prototype of the proposed CBCPW line has been fabricated. The reflection coefficient of the antenna-like structure is measured and compared to the simulated one. It shows a broadband behavior, which is from 800 to 1000 MHz (with ȁܵ ଵଵ ȁ < -10).

Fig. 7 .

 7 Fig. 7. Simulated and measured reflection coefficient of the line Fig.8shows the test environment used to evaluate the far field reading performance of the solution. The relay antenna with gain of 1 dBi, is placed 30 cm away from the reader antenna, measurement is done with Tagformance Voyantic platform[START_REF]Tagformance pro[END_REF]. A 7 mm sockets is used for the measurement, where the tags is attached directly on the surface of the metallic tool.

Fig. 8 .

 8 Fig. 8. Measurement experiment setup.

Fig. 9 .

 9 Fig. 9. Measured read range of TO°4 for different orientation IV. CONCLUSION


Fateh Benmahmoud
email: fateh.benmahmoud@lcis.grenoble-inp.fr

Pierre Lemaitre-Auger
email: pierre.lemaitre-auger@lcis.grenoble-inp.fr

Smail Tedjini
email: smail.tedjini@lcis.grenoble-inp.fr

Abanob Abdelnour
email: abanob.assaad-amin.abdelnour@lcis.grenoble-inp.fr

Fully Metallic Crooked Wire Antenna for UHF RFID Tags

Keywords: Crooked wire antenna, Radio Frequency Identification (RFID), RFID chip

In this paper, a 3 dimensions (3D) fully metallic antenna for an RFID tag is presented. It is a crooked wire monopole antenna. Close to the frequencies of the European UHF RFID band, it exhibits an input impedance that is the conjugate of the one of the Monza R6 chip. The latter with the proposed antenna presents a reading range of 11.87 meters and occupies a volume of 23 mm x 23.4 mm x 23.8 mm. This 3D tag structure could be useful for applications in metallic environments or applications in very severe environments where nonmetallic materials are useless such as in some aerospatiale applications. With a simple meander antenna, the proposed antenna, the reading range is approximately 6m.

I. INTRODUCTION

With the development of microelectronics technology, the usage of embedded systems that include wireless communication units is rapidly increasing rises in both civil and industrial domains. In these domains, Radio Frequency Identification (RFID) is one of the most popular wireless techniques. Its usage varies from simple identification to more advanced applications such as sensing and localization. New developments of RFID chip has to be accompanied with a parallel step towards novel antennas that are more efficient, more compact, and less expensive. Traditionally, RFID tags employ planar antennas realized on Printed Circuit Board (PCB). This includes a wide type of designs like dipoles, meander dipoles, bowtie antennas [START_REF] Lin | A looped-bowtie RFID tag antenna design for metallic objects[END_REF], [START_REF] Braaten | A compact meanderline UHF RFID tag antenna loaded with elements found in right/left-handed coplanar waveguide structures[END_REF]. These antennas present good performances and does not usually require a very complex fabrication process. On the other hand, obtaining good performances with smaller topologies becomes a challenge because the antenna efficiency decreases with its size reduction. Moreover, antenna substrates (dielectrics and ceramics in most cases) does not always behave well in some extremely severe environments. Also, a degradation of the antenna efficiency is caused by the lossy nature of these materials.

An alternative to such antennas on PCB could be a fully metallic antenna, like a wire one. It has a very high radiation efficiency because dielectric and ohmic losses are eliminated (almost totally in the second case). However, obtaining antennas that present a specific impedance value at a given frequency is a complicated subject for antennas whose size is much smaller than Ȝ. In the present work, this difficulty is solved by using an optimization tool based on multi-objective genetic algorithms. The goal is to design a fully metallic wire antenna that fulfills the requirements of small size and high efficiency at the frequency of the European RFID band: 866 to 868 MHz.

First presented in 1997 by E. Altshuler [START_REF] Altshuler | Wire-antenna designs using genetic algorithms[END_REF], crooked wire topology has shown its great potential in solving very challenging tasks. Since then, it was used to design, wideband antennas [START_REF] Altshuler | An Ultrawide-Band Impedance-Loaded Genetic Antenna[END_REF], electrically small antenna [START_REF] Choo | Design of electrically small wire antennas using a Pareto genetic algorithm[END_REF], [START_REF] Benmahmoud | Design of electrically small 3D wire antennas for UHF RFID applications using genetic algorithm[END_REF] and to optimize antennas radiation pattern and gain [START_REF] Lohn | Automated synthesis of a lunar satellite antenna system[END_REF]- [START_REF] Ghosh | Non-dominated rank based sorting genetic algorithms[END_REF].

In this work, an antenna having the conjugate value of the Monza R6 chip input impedance optimized using CST Microwave Studio in conjunction with Matlab. A proof of concept prototype is realized and measured. In section II, the antenna design is presented and discussed. In Section III, simulation and experimental results obtained with a prototype are presented, compared, and discussed.

II. TAG DESIGN

The topology used in this work is based on a fixed number of straight segments oriented arbitrarily in space. Each straight segment is characterized by three variables: the length, li, the azimuth angle, iji, and the elevation angle, și. The values of these variables describe the size and orientation of each segment in space. Elevation angles are restricted to [0 -ʌ/2] while azimuth angles are not restricted: [0 -2ʌ]. The minimum length of a segment is limited to 2.5 mm to avoid fabrication complexities. The maximum length is 0.1Ȝ to avoid priorly bulky structures, Ȝ is wavelength at the frequency 867 MHz, which is equivalent to 35 mm. The radius of all segments is fixed to 0.65 mm.

The implemented optimization algorithm starts by generating N arbitrary individuals. After evaluating the fitness functions of each individuals based on the results of electromagnetic simulations, a selection process using the non-dominated sorting method [START_REF] Hallam | Handling Diversity in Evolutionary Multiobjective Optimistion[END_REF] and the crowding distance criterion [11] is realized to choose the best individuals. The later will survive to form the next generation after the mating and mutation processes.

A geometrical filter is also implemented with the optimization algorithm to avoid topologies considered unrealizable or incorrect. This includes topologies with intersecting segments, ground plane penetration, and topologies with very sharp angles (less than 25°). Fig. 1 shows an example of a 3D crooked wire antenna that has four segments. It is also important to mention that the optimization is elaborated over a ground plane considered infinite for simplification reasons. This makes this type of antennas suitable in metallic environments. Every iteration, individuals' electromagnetic properties are simulated, and with it, the fitness functions of each individual is calculated. In this work, three fitness functions are used: the maximal size of the antenna, the real part of the input impedance of the antenna and its imaginary part. It concerns the antenna size and its input impedance. Table 1 resumes the implemented fitness functions.

The fitness functions mentioned in Table 1 are calculated in the frequency range 840-880 MHz with a sampling of 1 MHz. The average of the 31 samples is calculated to produce the values of f2 and f3. The first fitness function produces the minimization of the antenna size while the second and third fitness functions forces the antenna impedance to the conjugate value of the input impedance of the RFID chip. The non-dominated sorting method minimizes all three functions simultaneously.

After almost 150 generations with a population of 512 individuals, the optimization tool halted since it reached a point where no significant amelioration between two generations is observed. A topology with the best fitness values among the last generation is chosen. The topology is first re-simulated in a more accurate environment that includes the RFID chip MONZA R6 [12] package and a finite ground plane of a size of 100 mm x 100 mm. The simulated input impedance of the designed tag antenna shows a real part very close to 10 and an imaginary part of +j133 close to 867 MHz. The impedance of the MONZA R6 chip is 10 -j126@867 MHz.

III. PROTOTYPE AND EXPERIMENTAL CHARACTERIZATION

A prototype of the chosen solution was realized as illustrated in Fig. 2(b). The fabrication of the antenna was hand-made assisted with a 3D printed polymer model to reduce fabrication errors. A copper wire of a radius 0.65 mm is employed, bending was done manually. The antenna occupies a total volume of Ȝ/15 × Ȝ/14.8 × Ȝ/14.56 where Ȝ is the wavelength at the frequency 866MHz. The RFID chip is connected to the antenna on one end and to the ground plane on the other end. The tag is measured in an anechoic chamber, as illustrated in Fig. 3(a)with the Voyantic UHF RFID system. The simulated and measured reading range of the fabricated prototype is shown in Fig. 3(b). it can be seen, the measured values have the same behavior as the one simulated but with a shift towards lower frequencies. This can be explained by the fact that the fabricated prototype is slightly longer than it should be because of the hand-made fabrication process. The additional length is the accumulation of the wire length in the bents areas which makes the current path longer than expected. The fabricated tag presents a maximal reading range of 11.87 m at the central frequency of the European UHF RFID band: 867 MHz while it is 11.3 m at 880 MHz for simulation. It's important to mention that the MONZA R6 RFID chip can perform the auto-tuning. This feature gives to the chip the ability to adjust its capacitive impedance part to assure the best adaptation impedance with load (antenna). It worth nothing that the tag also response in the American RFID UHF band, 902 to 928 MHz. The measured reading range at 915 MHz is 2.6 m.

IV. CONCLUSION

In this paper, a 3D RFID tag based on a crooked wire antenna is optimized, realized, and measured. The tag shows good performances in terms of adaptation and efficiency at the desired frequencies. Further results will be presented at the conference.

Fig. 1 .

 1 Fig. 1. 3D structure of a crooked wire antenna with four segments.

Fig. 2 .

 2 Fig. 2. Selected design. (a) Simulated real and imaginary input impedance. (b) The fabricated 3D crooked wire RFID tag.

Fig. 3 .

 3 Fig. 3. Tag characterization. (a) Measurements environment. (b) Measured and simulated reading range.


Fateh Benmahmoud
email: fateh.benmahmoud@lcis.grenoble-inp.fr

Pierre Lemaitre-Auger
email: pierre.lemaitre-auger@lcis.grenoble-inp.fr

Smail Tedjini
email: smail.tedjini@lcis.grenoble-inp.fr

Wideband Circularly Polarized 3D Wire Antenna for Wi-MAX Applications

Keywords: Axial ratio (AR), circular polarization (CP), Wideband Antennas, Wi-Max

In this paper, a crooked wire antenna is optimized to be functional in both the WLAN and the Wi-Max bands (2.4-2.48 and 3.3-3.7 GHz). The antenna presents a right-hand circular polarization (RHCP) with a 3 dB axial ratio (AR) bandwidth of 3.28 to 4.11 GHz. For the WLAN band (2.4-2.48 GHz), the polarization was linear. The antenna is fabricated using 3D printing techniques and occupy a total volume of 33.8 mm × 30.4 mm × 37.4 mm. The simulated and measured farfield results show good agreement with a radiation pattern that assures a near hemispherical coverage toward the upper hemisphere and a measured maximum gain value of approximately 6 dB. The radiation pattern of the antenna assures a near hemispherical coverage toward the upper hemisphere.

I. INTRODUCTION

Nowadays, the internet of things (IoT) gets high attention for both research and industrial communities. As a part of the internet of the future, IoT will constitute billions of intelligent autonomous communicating devices. Among several communicating protocols for an IoT device such as ZigBee or Wi-Fi, Wi-Max is considered as one of the most efficient option when the communication distance is long and/or the needed data rate is high. Considering that lots of IoT devices are dedicated to operate in an harsh environment, physical phenomenon such as polarization mismatch, multi-path interferences, and the Faraday Effect have a significant impact on the reliability of the IoT system [START_REF] Counselman | Multipath-rejecting GPS antennas[END_REF]. In such situations, circularly polarized (CP) antennas are considered more efficient and a better choice comparing to linearly polarized (LP) ones.

As one the most interesting IoT applications, designing WLAN/Wi-Max antennas with a low profile will permit easier integration of these antennas. It is also a vital element when an embedded system is targeted where a lightweight of the IoT device is recommended. This is generally related to lowering the power consumption or controlling the device center of mass. However, reaching high performances in while employing a planar design could be a complex task to accomplish, especially when severe constraints are imposed. One of probable solutions is the employment of a threedimensional structures. Indeed, thanks to the third dimension, 3D-antennas exhibit better performance than 2Dones of the same size when properly designed [START_REF] Best | A Discussion on the Significance of Geometry in Determining the Resonant Behavior of Fractal and Other Non-Euclidean Wire Antennas[END_REF]. It also gives a higher degree of freedom of the geometrical shape of the antenna, which makes it a promising and suitable solution for problems that present very conflicting requirements. Among many three dimensional antennas design, G. Hornby and J. Lohn presented in [START_REF] Lohn | Human-competitive evolved antennas[END_REF]- [START_REF] Lohn | Automated synthesis of a lunar satellite antenna system[END_REF] a threedimensional wire antenna topology that has high performances in term of gain, space coverage, and polarization. It consists of six straight connected segments oriented arbitrary in space and operates above a ground plane. The use of a fully metallic wire antenna offers high radiation efficiency. Regarding the flexibility of this design and reliability of the measured results in the cited works, we envisioned to employ this topology.

IoT communication protocol defers from an application to another. In this work, we have chosen the WLAN (2.4-2.48 GHz) and Wi-Max band (3.3-3.7 GHz). The designed antenna covers the both WLAN and Wi-Max frequency bands and offers a CP for the Wi-Max band. One of the challenges is to maintain a proper matching with a 50 source. To design this 3D antenna, the use of computational optimization technique is mandatory because of the complex configurations. In the present case, a multi-objective genetic algorithm is employed. It is developed using MATLAB in conjunction with the electromagnetic simulator "Computer Simulation Technology Micro Wave Studio" (CST MWS).

This antenna could be used in many IoT applications and devices, such as IoT scenarios that involve drones or Unmanned ground and aerial vehicles. (UGV & UAV). The topology used in this work is a multi-segment wire monopole antenna. It consists of a fixed number of straight segments oriented randomly in space. The implemented multi-objective genetic approach starts by generating a number N of individuals (vectors) that describe the antenna geometrical shape defined by the following parameters: di, the length of each segment, i and i, the azimuth and elevation angles respectively. The former and the later define the orientation of the segment in space. Figure 1 shows the parametrization of the active 3D antenna.

II. ANTENNA DESIGN AND RESULTS

A. Design Technique

Besides the genetic-based optimization tool, a geometrical filter was developed and included in the optimization process in order to avoid wrong or unfeasible geometrical shapes, more specifically shapes with segments that go below the ground plane (z = 0) or with intersecting segments. It also excludes geometrical shapes with very sharp angles to respect fabrication constraints. Also, all structures that have a volume higher than 0.3 × 0.3 × 0.3 are excluded to limit the search inside acceptable volume of the final structure.

The implemented genetic algorithm employs the concepts of non-dominated sorting [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: NSGA-II[END_REF] which allows the use of multiple fitness functions without the need of weighted factors rather than a single one. Also, the crowding distance criterion [START_REF] Fortin | Revisiting the NSGA-II crowding-distance computation[END_REF] is implemented in order to conserve diversity in each generation and to avoid the convergence to very similar solutions. Table 1 resumes the fitness functions used.

In Table . 1, f r1 and fr2 represent the frequency intervals (2.4-2.483) GHz and (3.3-3.7) GHz respectively. The axial ratio criterion was applied only on the Wi-Max frequency band. A frequency step of 10 MHz is chosen to evaluate the fitness functions fi while 100 MHz is fixed for f2.

The optimization tool evaluates all the individuals of a generation and selects the best according to the fitness functions and the crowding distance criterion. Those elements are transferred to the next generation. During transfer, cross-over and mutation are applied to the population with rates of 70% and 10% respectively. The number of individuals per generation is fixed to 120.

The optimization tool is halted when no significant amelioration is recorded in any of three fitness functions. In the present study, it happened at the 637 th generation. Among the population of the last generation, one individual that shows good performances in term of adaptation (S11) and axial ratio is chosen. The structure is simulated another time in more realistic conditions, including the SMA connector and a limited ground plane. This can't be done during the optimization process because of the time that it would requires. Performances are not so different than the ones obtained previously.

B. Fabrication of a Prototype

The chosen structure was fabricated. For that, we used a 3D-printer, the 3ntr A4v3, to fabricate a model of the antenna using a polymer adapted to Fused Deposition Modeling (FDM) 3D printing technique [START_REF] Masood | Advances in Fused Deposition Modeling[END_REF]. The printed structure was fixed to a SMA connector, and finally, we applied a thin layer of metallization on the external surface of the printed structure using conductive silver ink. The radius of the wire structure is 0.65 mm, and it has a total length of 1.89 (237 mm). The antenna fit into a box of 0.27 × 0.24 × 0.29 which is equal to 33.8 mm × 30.4 mm × 37.4 mm. Fig. 2 shows the final fabricated prototype.

III. EXPERIMENTAL VALIDATION

The fabricated prototype was tested to evaluate its reflection coefficient, S11, its radiation pattern, and its polarization axial ratio. The measurements were done in an anechoic chamber using a vector network analyzer and two identical horn antennas, one as the emitting antenna and the second one for the calibration of the setup.

1 FITNESS FUNCTIONS Expression f1 |S11| (@ fr1) f2 | S11| (@ fr2) f3 Axial Ratio (@ fr2)
Ground plane Antenna Fig. 3(a) shows the comparison between the simulation results using CST MWS and the measurements. We can notice that the measured reflection coefficient values of the fabricated prototype are close to the simulated results. As it was estimated, the fabricated prototype covers the frequency band (2.42-2.64) and (2.8-4.45) GHz with a reflection coefficient below -10 dB. This comprises the WLAN (2.4-2.483 GHz) and Wi-Max bands (3.3-3.7 GHz). A slightly degraded input reflection coefficient value is measured in the frequency 2.4-2.42 GHz with values between -8.7 and -10 dB. However, these values remain acceptable for most modern reception systems. The primary cause of this degradation is generally due to the geometrical fabrication errors and uncertainty related to experimental conditions. The AR at the zenith is compared in Figure 3 The simulated maximum gain is close to 7 dB in the Wi-Max band. The measured gain was slightly lower with a value of approximately 5 dB. The difference, 2 dB, falls within the tolerances of the setup used. But more probably, it is also caused by the lower conductivity of the coating ink that affects the current flow on the radiating element leading to ohmic losses. The value of the realized gain remains high even when the adaptation is worst (above 4.5 GHz). This is explained by a high directivity near these frequencies. When the adaptation of the antenna moves away from 50 Ω, the antenna's directivity increases.

IV. CONCLUSION

The design of a small size 3D-segmented monopole antenna is presented. It is double-band, circularly polarized It was realized and tested. It has a tridimensional geometry formed by ten straight segments arbitrary distributed in space. It is light, thus it makes it suitable for aerospatiale and drones' applications involved in IoT scenarios. Future works will focus on the test of alternative fabrication techniques.

Fig. 1

 1 Fig. 1 Parametrization of the 3D antenna

Fig. 2

 2 Fig. 2 Fabricated prototype.

Fig. 3

 3 Fig. 3 Comparison between simulated and measured results. (a) Input reflection coefficient, S11. (b) Axial ratio at the zenith.

  TABLE

  Fig.3(a) shows the comparison between the simulation results using CST MWS and the measurements. We can notice that the measured reflection coefficient values of the fabricated prototype are close to the simulated results. As it was estimated, the fabricated prototype covers the frequency band (2.42-2.64) and (2.8-4.45) GHz with a reflection coefficient below -10 dB. This comprises the WLAN (2.4-2.483 GHz) and Wi-Max bands (3.3-3.7 GHz). A slightly degraded input reflection coefficient value is measured in the frequency 2.4-2.42 GHz with values between -8.7 and -10 dB. However, these values remain acceptable for most modern reception systems. The primary cause of this degradation is generally due to the geometrical fabrication errors and uncertainty related to experimental conditions. The AR at the zenith is compared in Figure3(b). The simulated AR bandwidth for 3 dB is 830 MHz (3.28-4.11 GHz), and the measured one is 690 MHz (3.41-4.1 GHz).

Fig. 4 (Fig. 4

 44 Fig. 4(a) shows the measurements environment. In Fig. 4(b), the simulated and measured maximum gain in the xz plane are illustrated. The measured xz and yz radiation patterns are very similar.


Fateh Benmahmoud

Pierre Lemaitre-Auger

Smail Tedjini

Design of Electrically Small 3D Wire Antennas for UHF RFID applications Using Genetic Algorithm

Keywords: RFID, Electrically small antennas, genetic algorithms (GA), wire antennas, UHF-tag, optimization

In this work, we discuss the design of electrically small antennas for UHF RFID tags. We implemented a genetic algorithm to design crooked-wire antennas that occupy a relatively compact size as small as 0.08λ, while exhibiting high efficiency and an acceptable radiation resistance value suitable for matching RFID chips.

Introduction

Rising interest and huge growth of the radio-frequency identification (RFID) technology happened in the last decade and similar to the evolution of several technologies, RFID devices tends to be more and more miniature, which implies the necessity of using very compact RFID tags that must exhibit high performance. Since RFID chips are very small, the miniaturization of an RFID tag means the miniaturization its antenna. This requires a long optimization process that rapidly becomes a complex task if someone employs usual design techniques [START_REF] Gianvittorio | Fractal antennas: a novel antenna miniaturization technique, and applications[END_REF][START_REF] Skrivervik | PCS antenna design: the challenge of miniaturization[END_REF]. An antenna is said electrically small if its geometrical dimensions are much smaller than the wavelength of the radiated electromagnetic field [START_REF] Chu | Physical Limitations of Omni -Directional Antennas[END_REF]. In a more explicit way, Wheeler [START_REF] Wheeler | Fundamental Limits of Small Antennas[END_REF] defined an electrically small antenna as the antenna that satisfies the relation:

1

(1). k = 2π/λ, λ is the wavelength and a the radius of sphere circumscribing the antenna. In the present study we consider that a is the radius of the sphere that enclose the radiated part of antenna without the ground plane (Fig. 1).

Since the downsizing of an antenna affects significantly its performances such the radiation efficiency and the radiation resistance, a trade-off between these factors is required. The majority of the achieved works in the miniaturization of 3D wire antennas target the VHF band, and focus on the gain and bandwidth of the antenna [START_REF] Altshuler | Electrically small self-resonant wire antennas optimized using a genetic algorithm[END_REF][START_REF] Hornby | Automated Antenna Design with Evolutionary Algorithms[END_REF][START_REF] Altshuler | Wire-antenna designs using genetic algorithms[END_REF][START_REF] Choo | Design of electrically small wire antennas using a pareto genetic algorithm[END_REF].

In most cases, the obtained results were very encouraging and lead to achieve the targeted objectives.

In the same time, several numerical optimization techniques like genetic algorithm (GA) or particle swarm optimization (PSO) has proven their usefulness in the design of antennas in complex environments [START_REF] Robinson | Particle Swarm Optimization in Electromagnetics[END_REF][START_REF] Rahmat-Samii | Electromagnetic optimization by genetic algorithms[END_REF][START_REF] Siragusa | Control of the Sensitivity of CRLH Interdigital Microstrip Balanced Structures Using a Co-Design Genetic Algorithm Approach[END_REF]. In this work, we report on the use of a (GA) in the optimization of the design of electrically small 3D wire antennas for UHF-RFID application. We especially focus on, antenna size and radiation efficiency.

In this investigation, in section 2, we use a multi-objective GA implemented on Matlab in conjunction with CST Microwave Studio (CST MWS) to search for resonant 3D wire structure that occupy the smallest volume, have high efficiency near the frequency 868 MHz, and present an acceptable radiation resistance. In section 3, we investigate two topologies of crooked-wire antennas, and discuss their performances. We also use the technique described in [START_REF] Best | A discussion on the quality factor of impedance matched electrically small wire antennas[END_REF] to increase the radiation resistance and achieve required matching.

Approach

The crooked wire antenna optimized in this work with the help GA consists in a determined number of wires connected in series in free space. Each antenna have a radius R=0.8 mm and a linear length between 0.2λ and 0.4λ. We consider that the structure is enclosed inside a sphere of radius a, that circumscribes the whole antenna, over an infinite ground plane as it is shown in Figure 1. The values of the elevation angles are fixed between 0° and 180° with only 32 allowed values (at every 5.80°), except the first wire angle which is limited to [0° -90°] with 16 allowed values (at every 5.80°). The azimuth angles are between 0° and 360° with also 32 allowed values (at every 11.25°). Wires lengths between 0.02λ and 0.04λ for the 10 wires antenna and 0.03λ to 0.06λ for the 7 wires antenna, with 32 allowed values in both cases.

Based on this parameterization, we code the 7 wires antenna with 21 genes and the 10 wires antenna with 30 genes.

The implemented GA is based on that proposed in [START_REF] Rahmat-Samii | Electromagnetic optimization by genetic algorithms[END_REF] where the best half of every generation is selected for the production of the next generation. The GA starts by selecting randomly a population of N chromosomes (i.e. N antennas) and evaluate the performances of each one. In the present study, different population sizes were used because a too small population size could lead to poor solutions while a large population size increases the time needed to find a solution [START_REF] Pelikan | Bayesian optimization algorithm, population sizing, and time to convergence[END_REF][START_REF] Koumousis | A saw-tooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance[END_REF][START_REF] Yu | Population sizing for entropy-based model building in discrete estimation of distribution algorithms[END_REF]. We used the technique based on the bias measure suggested by Grefenstette in [START_REF] Bäck | Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms[END_REF] to test the initial population diversity over the entire search space. This limits the population size effect. We also added a geometrical filter to eliminate impossible configurations: intersections of wires, crossing the ground plane or very close parallel wires. All these elements are incorporated during the execution of GA as constraints to ensure a good reliability of the results.

In addition to the integrated constraint of diversity, we tried to reduce the probability of local minima convergence by making sure that the geometrically rejected chromosomes are replaced, at every iteration, by new ones randomly created and geometrically correct. This way of doing increases the performances of the GA and enhances diversity [START_REF] Diaz-Gomez | Initial Population for Genetic Algorithms: A Metric Approach[END_REF].

The present work is a multi-objective problem. Three costs functions were defined to achieve the desired goal:

Table 1. The cost functions with weights.

Cost function Weight Cost1

( )

0.8 Cost2 1 - 0.1 Cost3 - 0.1
where k = 2π/λ is the wave number, η is the radiation efficiency, R rad is the radiation resistance and is a reference to evaluate the radiation resistance. It is fixed here to 14 Ω which is close to real part of the impedance of an RFID chip. Antenna size is calculated using Matlab while the radiation efficiency and the radiation resistance computed through numerical simulation with CST microwave studio. After simulation, a figure of merit calculated by the sum of the three costs with an appropriate weighing to predict the fitness of the simulated antenna (see Table 1).

Results

Processing of the GA for the 7 wires antenna took 45 iterations with an initial population of 32 chromosomes. For the 10 wires antenna with an initial population of 40 chromosomes 21 iterations were done. For both configurations, highly random shape were selected for the 3D antennas. The obtained antennas have a very small size compared to quarter-wave monopole, with a significant size reduction of 68% and 71% for the 7 wires antenna and the 10 wires antenna respectively; their total lengths are 0.243λ and 0.285λ, with a value of ka equal to 0.224 and 0.220.

The radiation efficiencies of the 7 wires and 10 wires antenna are 91.47% and 96.0% respectively. Those results are good ones, especially when considering the size reduction. Both antennas have a near hemispherical coverage with a gain of 6.24 dBi for the 7 wires antenna and 5.63 dBi for the 10 wires antenna as shown in Fig. 3a and Fig. 3b. The radiation resistance of the optimized antennas are very small: 5.41 Ω and 4.47 Ω respectively. The use of a matching technique is necessary to guarantee the functionality of the antennas. Among several matching techniques of wire antennas, we used the impedance adaptation technique described by S.Best in [START_REF] Best | A discussion on the quality factor of impedance matched electrically small wire antennas[END_REF] to increase the radiation resistance and improve the impedance matching. This technique consists in using a parallel matching stub placed near the input of the antenna as it is shown in figure 4. The usual way to design a stub consists of calculating its length and its location from the antenna feeding. This method leads to large size of stub and increase the occupied volume of the antenna. To overcome this problem we try to find a small stub that increase the radiation resistance to a reasonable value, which is done after several simulations. With that technique, the radiation resistance of the antenna increased significantly, good matching with several UHF RFID chips is now possible. It worth mentioning that radiation efficiencies after matching was reduced to 85.61% and 95% which remains a satisfactory value, while the gain remains almost the same, its also important to mention that the size of the matched antennas was slightly larger. Numerical values obtained are summarized in Table 2.

Conclusion

We have shown that using GA small size wire antennas for RFID applications can be obtained with GA. The designed antennas have a good performance except for the radiation resistance. This is significantly improved with the use of a matching stub that increases the radiation resistance. There for, obtained antennas can be matched with RFID chips. They are very good candidate for UHF RFID tags for which size is an important matter. More results will be presented at the conference.

Figure 1 .

 1 Figure 1. Shematic representation of a crooked wire antenna having 7 wires. Two different topologies of antennas are studied: 7 wires and 10 wires. Each wire is defined by three parameters: elevation angle θ, azimuth angle φ and its length d.

Figure 2 .

 2 Figure 2. Designs of the obtained antennas: a) 7 wires antenna. b) 10 wires antenna.

Figure 3a .

 3a Figure 3a. Three-dimensional simulated radiation pattern of the obtained genetic antennas at f = 868 MHz: 7 wires antenna

Figure 4 .

 4 Figure 4. Designs of the obtained antennas with its matching stub: a) 7 wires antenna. b) 10 wires antenna.

Table 2 .

 2 Impedances efficiencies and gain after impedance matching at f = 868 MHz.

		7 wires	10 wires
	Impedance (Ω)	13.9+j126.24	24+j220.63
	Rad. Efficiency (%)	85.61	95
	Gain (dBi)	6.19	5.6