8×8 Near-Field Focused Circularly Polarized Cylindrical DRA Array for RFID Applications

─ The design of an 8×8 near-field focused circularly polarized dielectric resonator antenna (DRA) array for fixed RFID reader applications at 5.8 GHz is presented. The proposed antenna array consists of 64-element of cylindrical dielectric resonator antennas (CDRA) with two orthogonal feeding probes located inside the CDRA element. A single element CDRA with supporting arms is used as a building block of the array provided good impedance matching and circular polarization at 5.8 GHz. The perforation technique is used for the supporting arms to reduce the manufacturing complexities in the CDRA mounting over the ground plane. The sequential feeding technique is applied to improve the gain and circular polarization bandwidth of the single element and the array. The characteristics of the near-field focused array are introduced compared to that of the uniformly phased array. The finite integral technique and the finite element method are used to compute the array performance. Index Terms ─ CDRA, fixed reader antenna, RFID, sequential feeding.


I. INTRODUCTION
RFID systems have been applied in many applications for their advantages over other automatic identification systems [1]. Practically, the RFID reader has a read zone that can sometimes be difficult to control due to multipath effects or reflections of the RF signal. Problems that may arise with conventional RFID readers include:1) the reader may detect tags that are not in the reader coverage area, and 2) the tags may be located adjacent to the reader antenna thus blocking its field. Spatial isolation of an RFID tag may be difficult if the interrogation range of the RFID readers is not easily controlled or adjusted to a lower power setting. This can lead to errors in customer purchases or errors in verification that an item is in a specific physical location (e.g., baggage on a specific cart) [2,3]. The RFID reader antenna is an important component in RFID systems and it has been designed with circularly polarized (CP) operation. CP for the reader antenna in transmission is preferred because the tag antenna (which is linearly polarized) will receive enough power from the transmitter irrespective of its orientation. A CP antenna with a low profile, small size, lightweight, high gain, and high front-to-back ratio is required in a portable RFID reader [4][5][6]. The other type of RFID reader is the fixed reader. Generally, fixed-reader antennas are complex microstrip patch arrays with high gain, and a relatively narrow beam and low side lobe level [7][8][9].
Using antenna arrays for a fixed RFID reader will result in long read range. The far-field region is determined according to the dimensions of the array (L×L) and the operating frequency by (2L 2 /λ). In some applications, tags may be located in the near-field region of the fixed reader antenna array not in their far-field region as is usually the case in a standard communication system. Therefore, a reader antenna array exhibiting a near-field (NF) focused radiation, which is able to maximize the field amplitude in a size-limited spot within the antenna near-field region, while not affecting the field strength far from the antenna (far-field region), is needed. Recently, NFfocusing has attracted major interest due to its potential applications in near-field sensing and imaging microscopy [10][11]. NF-focusing is used in RFID to increase the field incident on the tags at allowed effective isotropic radiated power (EIRP) [12][13][14]. In [15], a circular half-wavelength dipole array is used to study the effect of changing the focusing distance on the power in the Fresnel region. In this paper, an 8×8 NF-focused cylindrical DRA phased array with supporting arms for fixed RFID reader at 5.8 GHz is proposed. The NF-focused CDRA array is designed to maximize the radiated power density in a limited size spot in the near field of the RFID reader. The performance parameters of the NFfocused array are compared with that of uniform phased array. The array consists of 64 sequentially fed CDRA elements with two supporting arms mounted on a square ground plane. Each CDRA element is fed via two orthogonal probes located at two orthogonal points from the CDRA center. The finite integration technique (FIT) [16] is used to optimize and analyze the antenna array performance parameters such as reflection coefficient, radiation pattern and antenna gain. The finite element method (FEM) [17] is used to validate the results. The novelty of this work is the using of the CDRA elements in the phased array for wide bandwidth, no metallic loss (high radiation efficiency), and high gain (wide coverage area for RFID reader). The paper is organized as follows. In Section II, numerical results for a circularly polarized CDRA with supporting arms as a building block for the RFID reader antenna array are investigated. Near field focused CDRA array for fixed RFID reader consists of 64 CDRA elements is designed at 5.8 GHz. Section III concludes the results. Figure 1 shows the geometry of a single cylindrical dielectric resonator antenna with two feed probes excitation. The CDRA with dielectric constant ε r of 10.2 is used [18]. It has a radius 'a' of 5.9 mm and a height 'H d ' of 8.3mm. The CDRA is designed to operate around 5.8 GHz. Two coaxial probes are located off the center by distance d f of 5.1 mm. Each probe has radius of 0.25 mm and height h f of 3.9 mm. The two probes are parallel and located at similar positions on two orthogonal diameters and the feeding is arranged such that the two probes have a phase difference of 90 o . Because of the fabrication complexity of CDRA over ground plane, four supporting arms having rectangular shape are connected with the CDRA. In [19], perforated structure was proposed to overcome the mounting problems of the CDRA over the ground plane and save more manual effort in the alignment of the CDRA with the feeding structure especially for arrays. The technique of perforating a dielectric sheet eliminates the need to position and bond individual CDRA elements in the array. Perforations create different effective dielectric permittivity and make the fabrication of CDRA arrays feasible. The perforations result in lowering the effective dielectric constant for the region between the CDRA elements. The CDRA element is made from one piece of dielectric material; with a perforated bonding dielectric rods and completely eliminating all the rest of the dielectric material. The dielectric rods have low dielectric constant and thin enough to avoid guiding waves around the design frequency of the element itself. The effective dielectric constant, ε reff , of the perforated material can be calculated from [19] ( ) ( )

III. NUMERICAL RESULTS
where R p is the radius of the air holes, and S p is the center to center separation distance of the holes. The holes forming the perforation are only one line centered along the axis of the ribbon forming the supporting arm. Thus, the supporting arms are used to reduce the fabrication complexity while keeping the same radiation characteristic as arm free element [19,20].
The dimensions of the supporting arms are width W p = 4 mm and thickness H p = 1 mm. The supporting arms are perforated by incorporating air holes in the arms. The air holes have equal radii, R p = 1.2 mm and center to center separation S p =3R p . The CDRA elements with supporting arms are mounted on square ground plane with edge length 'G' of 35.15 mm. Figure 2 shows the simulated reflection, S 11 , at the two ports of the feeding pins of the single CDRA element with perforated supporting arms against the frequency. The two ports produced the same performance due to their position similarity. Good impedance matching is obtained with impedance bandwidth extending from 5.62 GHz to 6.12 GHz for S 11 < -10 dB.
The simulated radiation pattern components, left hand polarization, E L , and right hand polarization, E R , of the single CDRA element at 5.8 GHz in x-z plane and y-z plane are shown in Fig. 3. Asymmetrical radiation pattern is obtained with high cross-polarization level due to the coupling effect between the excitation orthogonal probes, as well as the asymmetrical positioning of the feeds with respect to the two planes. Good agreement is obtained between the results calculated by FEM and FIT techniques.
The main polarization (E L ) is within -10 dB level in a beam of about 100° width centered at the 0° direction. The cross polarization (E R ) level is more than -10 dB relative to the main polarization (E L ) within the circular polarization beam (100°). These results indicate good performance of this dielectric resonator antenna for RFID reader application.
The axial ratio at the normal axis, φ= θ=0 o , versus frequency is shown in Fig. 4a. The antenna provides circular polarization with minimum value of 1.9 dB at 5.8 GHz with a relatively wide axial a. x-z plane ratio bandwidth (AR< 3dB) of the order of 40.74%. The antenna gain at the normal axis over the operating band is shown in Fig. 4b. The gain at the normal axis is 7.15 dB at 5.8 GHz and nearly constant within 0.5 dB over the RFID frequency band (5.65-5.95 GHz).
An 8×8 RFID reader antenna array with supporting arms is shown in Fig. 5. The area of the array is L×L= 28.13 × 28.13 cm 2 (5.44 λ×5.44 λ where λ is the free-space wavelength at 5.8 GHz). The distance G between the elements is 35.16 mm (0.68λ) to reduce the mutual coupling between the elements. The sequential feeding technique is applied to the CDRA elements in order to improve the circular polarization bandwidth (axial ratio bandwidth) and gain of the antenna array [21]. For each sub-array forming (2×2) elements, the elements in one diagonal are 90 o out of phase and rotated -90 o in orientation relative to the elements in the other diagonal (see Fig. 5b). This sequential feeding mechanism produces two fields with equal magnitude and out of phase by 90 o which results in improving the circular polarization bandwidth of the array.
The antenna array aperture is placed in the (x, y) plane and (x i , y i ) are the position coordinates of the i th element. The phase of the feeding currents has been adjusted to maximize the radiated field at a distance z = R o = 40 cm (The assumed boundary for the far field is 2L 2 /λ = 306.11 cm) from the antenna aperture. For the NF-focused phased array, the phase shift for the i th element can be calculated from, (2) The beamwidth between 3-dB points in the focal plane is defined as the array spot size. The spot size area radius, W, of a NF-focused planar array depends on the interelement distance, array size and geometry [22] (3) In this case, W= 6.52 cm (1.26 λ o ). The Poynting vector is equal to the cross product of electric field, Ē, by the complex conjugate of the magnetic field, Ĥ. The magnitude of its real part is the active power density while the magnitude of its imaginary part is the reactive power density [23].
Adding the phase shift to the array elements results in focusing both the active and reactive power density at the focal plane (the plane includes the focus point). The ratio between the active power density and the reactive power density is very large (about 256). Thus, only the active radiated power density will be taken into account and is given by The equivalent plane wave power density p is defined from the E-field or the H-field as follows [21] where η o =377Ω. The normalized power density distribution in the x-y plane for the uniformly phased array compared to that of the NF-focused array is used to introduce the effect of focusing as shown in Fig. 6. The power density of the NFfocused antenna array decreases rapidly from the focal point than that of the uniformly phased array. The -3dB contour curve of the NF-focused array exhibits a diameter of about 8 cm. Contour plots of the normalized power density in the x-z plane is plotted in Fig. 7. Figure 8 shows the variations of the power density along the z-axis from the antenna aperture of the NF-focused array. The 3-dB focused depth of the array is 31.2 cm along the array axis.
Using a rectangular to spherical coordinate transformation, the three components of the electric field E x , E y , and E z are transformed to their spherical counterpart E r , E θ , and E φ . For NF-focused array, the radial component of the electric field E r is very small and can be ignored in the near field region [24]. Thus, only the components E θ and E φ are used to calculate the axial ratio. The AR in the area of 20 × 20 cm 2 of the transverse plane at focal point 40 cm away from the NF array aperture is shown in Fig. 9. The NF-focused array exhibits focused circular polarization in area around the focal point less than that for the uniformly phased array. The variations of the normalized power density along x-axis and y-axis for the uniformly phased array and NF-focused array are shown Fig. 10. The side lobe level, SLL, in the 32 × 32 cm 2 area around the focal point is less than -13.5 dB while -5.82 dB for the uniformly phased array. Approximately the same field distributions in the far-field region for the uniformly phased array are obtained in the near field region for the NF-focused array due to the phase correction of each element in the array.
b. NF-focused array Fig. 6. A 3-D plot of the simulated normalized power density of the 8×8 CDRA at z=R o =40 cm.

IV. CONCLUSION
The performance of the proposed NF-focused CDRA array compared with the uniformly phased CDRA array has been presented. The NF-focused CDRA array is maximizing the radiated power at a limited size spot of radius 6.5 cm in the focal plane at 40 cm from the array aperture with a 3-dB focus depth of 31.2 cm along the axis normal to the array aperture. The NF-focused array produces a far-field like pattern in the near-field at the focal plane. Thus, the near field focused array will improve the performance of the reader antenna for the RFID application, and consequently improve the detectability of the tagged objects in the near field.