Study the Effect of Using Low-Cost Dielectric Lenses with Printed Log-Periodic Dipole Antennas for Millimeter-Wave Applications

1KACST Technology Innovation Center in Radiofrequency and Photonics for the e-Society (RFTONICS), King Saud University, Riyadh 11451, Saudi Arabia 2Electrical Engineering Department, Faculty of Engineering, Assiut University, Assiut 71515, Egypt 3Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada H3G 1M8 4Electrical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia


Introduction
Recently, the need for wideband and high-gain antennas becomes very essential for modern wireless communication systems to achieve high speed and high data rates with maximum possible coverage. Therefore, antennas having wide bandwidth, high-gain, and stable radiation patterns across the frequency band of interest are highly demanded. Moreover, those candidate antennas should exhibit compact size and low profile with ease of integration with other components on the same printed circuit board (PCB). Printed log-periodic dipole array (PLPDA) antennas are good candidates for wireless communication applications due to their huge bandwidth with good gain stability across the entire frequency range and simple geometrical architecture for ease of fabrication [1]. The design of a suitable feeding network of PLPDA is very crucial in order to have the dipole elements correctly driven with the proper desired magnitude and phase. A PLPDA antenna can be fed by different feeding techniques such as coaxial cable, microstrip line, coplanar waveguide (CPW), conductor-backed coplanar waveguide (CBCPW), and substrate integrated waveguide (SIW). The problem with coaxial cable feeding technique is the possibility of having a severe fabrication error and misalignment problem, which come from soldering coaxial cables at microwave frequencies especially at millimeter-waves frequency bands [2,3]. Several PLPDA antenna designs fed by coplanar waveguide (CPW) were proposed [4]. It has been reported that the CPW-fed PLPDA antenna designs suffer from the higher losses, serious crosstalk, and the disadvantage of lower power handling capability. Substrate integrated waveguide (SIW) has been 2 International Journal of Antennas and Propagation used as a feeding network for the PLPDA antenna [5][6][7]. According to the proposed designs, the SIW feeding network has a large size compared to the traditional printed transmission lines such as microstrip, strip lines, and CPW. Lenses have been used by many researchers in different applications. The most typical spherical lens is Luneburg lens [8]. Because of the difficulty of manufacturing such lens, it is usually replaced by spherical shells. Lenses can be classified into two main categories depending on their applications. Lenses can be used either for shaping the beam or for beam scanning. Lenses of canonical shapes, such as hyperbolical, elliptical, and hemispherical, are used for collimating the radiated energy. Parameters of these canonical lenses can be derived analytically. However, it has been shown that Luneburg lenses do not provide optimal performance in terms of complexity of construction [9].
In this paper, antenna prototype based on printed log-periodic dipole array (PLPDA) antenna at V-band millimeter-wave frequencies has been designed, simulated, and optimized using a full-wave industry-standard simulation software program. In the proposed design, the PLPDA antenna, which is called reference antenna, is designed on a single-layer substrate and fed by a simple microstrip feeding network. It has the advantage of simple structure, compact-size, low-cost, wideband and easy of integration with other circuits on the same PCB. Proposed high-gain antenna consists of the reference antenna loaded with lowcost spherical dielectric lens. In Section 2, the geometrical configuration of the proposed antenna is presented. In Section 3, both simulated and measured results are investigated and discussed. Finally, conclusions are given in

Antenna Geometry and Design
The dielectric lens is used here because it focuses the incident divergent energy in the desired direction. Spherical lenses are mostly used for beam scanning with single or multiple feeding possibilities [10]. Dielectric lenses, same as the metallic reflectors, are used for enhancing the directivity of radiation. In our case, the radiation comes from the proposed PLPDA antenna. From [11], the paraxial focus, normalized to lens radius, is given by where the refractive index = √ . It can be noticed from the above equation that the lens focus depends on the lens dielectric constant . So, it is very important to study the effect of lens dielectric constant on the antenna performance especially the antenna gain. For lens dielectric constant = 2.2, the refractive index = 1.483 and hence the paraxial rays arrive at the paraxial focus of 1.53 radii.
The top view and bottom view of the reference PLPDA antenna are shown in Figures 1(a) and 1(b), respectively. The proposed antenna prototype with a spherical dielectric lens is shown in Figure 1(c). The 3D view of the proposed antenna in CST [13] is presented in Figure 1(d). All antenna optimized parameters are listed in Table 1. The sphere has a radius and its center is located at a distance from the edge of substrate. The center of the sphere is located at a distance   from the end of the PLPDA antenna. For better mounting of the spherical lens to the antenna practically, a hole can be made inside the sphere to enter the substrate inside it. In our case, we stick two identical half spheres together with a special glue to form a full sphere. In that case we have the opportunity to install the substrate inside the sphere and then we can hold them together as one object as shown in Figure 1(e).

Parametric Studies
For understanding the role of spherical dielectric lens in increasing the antenna gain, intensive parametric studies have been carried out. This is to investigate the effect of spherical lens parameters such as the lens dielectric constant , radius R L , and location from the edge of substrate D L on the antenna gain. Figure 2(a) shows the effect of varying the spherical dielectric lens radius R L from 5 mm to 25 mm. It can be seen that the lens radius strongly affects the antenna gain and by increasing the lens radius, the antenna gain increases by a big value. However, after increasing the lens radius to more than 20 mm, the antenna gain starts decreasing. For example, the antenna gain increases from 11.5 dBi for R L = 5 mm to 25.9 dBi for R L = 20 mm at 60 GHz. The gain starts decreasing to 19.5 dBi for R L = 25 mm at 60 GHz. The effect of varying the spherical dielectric lens location from the substrate edge D L on the antenna gain has been studied and presented in Figure 2(b). From results, it can be noticed that the parameter D L also has a great effect on the antenna gain. By increasing parameter D L from 25 mm to 30 mm, the antenna gain increases from 20.8 dBi to 25.7 dBi at 60 GHz. However, by increasing the parameter D L to more than 30 mm, the antenna gain starts decreasing.
Finally, the parametric study on the lens dielectric constant is carried out and introduced in Figure 2(c). In case of = 1, which means there is no lens, the antenna gain was 12.1 dBi at 60 GHz. By increasing the dielectric constant of the spherical lens from = 1 to = 2, the gain of the antenna starts increasing too much. However, by increasing the dielectric constant to more than = 3, the antenna gain decreases.
After performing the above parametric studies, optimized lens parameters can be determined based on achieving the best antenna gain. The optimized lens parameters are found: = 20 mm, = 28 mm, and = 2.2.

Results
The measured and simulated return losses of the proposed PLPDA antenna prototype with a full spherical dielectric lens are presented in Figure 3. The antenna exhibits good impedance matching characteristics across the measured range. The gain comparison between the proposed antenna prototype and the reference antenna is shown in Figure 4. The antenna with a full spherical lens achieves higher gain compared to the reference antenna (prototype without lens). The gain of the proposed antenna prototype is about 14.5 dBi larger than that of the reference antenna. A good agreement between the measured and simulated curves is achieved.
The measured and simulated copolarization and crosspolarization radiation patterns in H-plane at different frequencies are shown in Figure 5. It can be seen from results that the directive behavior of proposed antenna prototype after adding a full spherical dielectric lens is clearly noticed. It is worthy to mention that installing the spherical lens not only improves the antenna gain but also enhances greatly the other radiation characteristics such as side lobe level (SLL), front-to-back (FTB) ratio, half power beam width (HPBW), and cross-polarization level (XPL).
A performance comparison among the proposed antenna prototypes with reference antenna at 60 GHz in terms of gain, total efficiency, FTB ratio, side lobe suppressions, HPBW, and XPL in both E-and H-planes is presented in Table 2.    For further understanding of the role of dielectric lens in increasing the antenna gain, the near-field distributions are calculated at different frequencies. The electric field distributions inside the spherical lens are shown in Figure 6. As shown, electric fields pass through the lens and thus the circular waves are flattened. In this case, the cylindrical waves are converted into quasiplane waves on the opposite side of the lens with a noticeable increase in the antenna gain in terms of highly directive radiation.
A comparison of performance among the reported millimeter-wave works in the literature has been done in detail and summarized in Table 3. It can be noticed that the International Journal of Antennas and Propagation 7 proposed PLPDA antenna with spherical dielectric lenses is the best candidate to be used in many applications at millimeter-waves especially at V-band frequency range.

Conclusion
The design of high-gain printed log-periodic dipole array (PLPDA) antenna prototype operating at V-band millimeterwave frequency range has been presented. The proposed antenna is fabricated using cheap PCB technology which makes it easy for integration with other circuits. For achieving high-gain, a low-cost spherical dielectric lens was installed. Radiation patterns and antenna gains of the proposed antenna prototype were studied and presented. Both measured and simulated results verify several advantages such as high-gain, stable radiation pattern, good SLLs in both E-and H-planes, high FTB ratio, and excellent cross-polarization levels. A detailed comparison of performance with previously reported work has been presented. The proposed antenna can be among the best candidates to be used in many V-band applications.