Introduction
Transmitting and receiving signals with the same polarization in portable communication devices that apply linear polarization for size reduction is difficult. The problem worsens when the antenna is used to operate at multiple bands. Circular polarization (CP) antennas are currently used in modern communication systems to avoid many serious problems, such as mismatch polarization and multipath interferences [Reference Abed, Singh and Islam1]. Researchers have used many techniques to generate CP radiation; these methods include using two orthogonal modes with a 90° time–phase difference between them to excite the antenna [Reference Abed, Singh and Islam1]; rotating the radiator [Reference Ge, Sim, Su, Lu and Ku2] or the slot [Reference Wangwang, Yang, Long, Zhou and Yan3] with respect to the diagonal of the patch to create a required phase shift to generate CP radiation; using the termination circuit of a capacitor or inductor serial/parallel tank to produce CP of two types (LHCP and RHCP) [Reference Zhou and Cheung4]; and using special structures in designing antennas to generate CP radiation characteristics, such as the Amer fractal slot [Reference Abed, Singh and Islam5] and the Fibonacci spiral structure [Reference Chetna Sharma and Vishwakarma6].
This study aims to investigate the CP characteristics of the Q-slot antenna by three methods, studying the distribution of surface current, the phase difference between left and right polarization at some resonant frequencies and the measured values of the axial ratio bandwidth (ARBW).
CP technique
This study investigates the CP technique used in the slot antenna reported in [Reference Abed and Singh7]. The method is presented in Fig. 1 [Reference Abed and Singh7]. The proposed slot antenna uses the ground-slotted technique, where a Q-shaped slot is cut in the ground plate, which comprises a strip line that is provided different width and length dimensions to excite the antenna through a step impedance strip line to generate many resonant frequencies. These frequencies are collected together to have multi-operating bands that cover Wireless Fidelity (Wi-Fi) and Worldwide Interoperability for Microwave Access (WiMAX) requirements.
Fig. 1. The Q-slot antenna. (a) Geometry of the Q-Slot antenna. (b) The impedance bandwidth of the Q-Slot antenna [Reference Abed and Singh7].
A new technique is used to generate CP radiation by cutting normal arms (E 1 and E 2) in an elliptical upper strip feeding line F 3 to generate the modes (TM 010 and TM 001), the mode TM 001 produces far-field in Y-direction E y while the other mode produces far-field in X-direction E x, which are needed to have CP characteristics. With a simulation of surface current distribution, the function of each part of the proposed antenna structure can be examined. Both electric fields (E y and E x) are linearly polarized in Y and X directions [Reference Stutzman and Thiele8].
$$E_y\, = \,c\,\displaystyle{{{\rm sin}\,({\rm (}\pi /E_1{\rm )}{y}^{\prime})} \over {k^2\,(1-j/Q_t)\,-\,{(k_y)}^2}},$$
$$E_x\, = \,c\,\displaystyle{{{\rm sin}\,({\rm (}\pi /E_2{\rm )}{z}^{\prime})} \over {k^2\,(1-j/Q_t)-{(k_z)}^2}},$$
$$k_y = \displaystyle{\pi \over {E_1}},\,k_x = \displaystyle{\pi \over {E_2}}$$where Q t = 1/tanδ is the quality factor, and c is the speed of the light in free space. k y and k x are the propagation constants in Y and X directions. If the feed point is selected to be at (y′, X′) along the major axis of the elliptical strip feeding line F 3, the arms E 1 and E 2 can be represented as
$$\displaystyle{{{\rm \;} {y}^{\prime}} \over {E_1}} = \displaystyle{{{X}^{\prime}} \over {E_2}}.$$At the broad side of the electric fields E y and E x can be formed
$$\displaystyle{{E_y} \over {E_x}}\,\approx \,\displaystyle{{k\,(1-j/2Q_t)\,-\,(k_y)} \over {k\,(1-j/2Q_t)\,-\,(k_x)}},$$when the numerator and denominator in equation (5) are equals and out of phase 900, the CP can be achieved and that can happen when
$$E_y\,-\,E_x\, = \,k_x\,-\,k_y\; = \,0,$$k x and k y are equal in amplitude and out of phase by 900 . The dual resonant frequencies f 1, f 2 of the modes TM 010 and TM 001 selected by the arms E 1 and E 2.
$$f_1\, = \,\displaystyle{{\,f_0} \over {\sqrt {1 + 1/Q_t}}}, $$
$$f_2\, = \,f_0\sqrt {1 + \displaystyle{1 \over {Q_t}}}, $$where f 0 is the center frequency of the bandwidth (f 2 − f 1), tanδ equals to 4.3 for substrate FR-4. According to equations (7) and (8), f 1 = 4.8 GHz while f 2 = 6.1 GHz.
Investigation of CP
The CP characteristics of the Q-slot antenna will be investigated carefully by three methods; studying the distribution of surface current, the phase difference between left and right polarization at some resonant frequencies and the measured values of the ARBW.
Surface current distribution
The current distribution of the resonant frequencies is simulated by the software (CST), as shown in Fig. 2. The maximum current is concentrated at the narrow edge of the slot in the ground plane for all resonant frequencies due to the main intensity of the surface current at the left edge of the oval strip F 3, which is near the narrow edge of the slot, while the current distribution on the radiation plate (F 1, F 2, and F 3) depends on the resonant frequency. At a low resonant frequency 2.5 GHz (Fig. 2(a)), the current is mainly concentrated along the strips F 1 and f 2; the summation of the lengths f 1l and f 2l is equal to 22 mm, which is approximately a quarter of the wavelength for the resonant frequency of 2.5 GHz. At 3.5 GHz, most of the current is on the feed strips F 1, f 2, and the lower part of F 3. This condition means that the 1st and 2nd operating bands are affected significantly by the dimensions of the lower and middle feed lines f 1 and f 2. At the upper operating band 4.7–6.8 GHz (Figs 2(b) and 2(c)), the intensity of the surface current along the feeding line increases, especially at the resonant frequency 5.8 GHz, compared with that at the low operating bands because the summation of lengths f 1l, f 2l, and the circumference of F 3 is equal to 61 mm, which matches the wavelength of the frequency 5.8 GHz. The current is concentrated on the ground plane at the narrow edge of the slot S e and near the slot Q w, as shown in Figs 2(b) and 2(c) (at resonant frequencies 5 and 5.8 GHz, respectively). This finding means that the upper band is affected by the dimensions of the slot Q w and the width of the slot Se, which is directly affected by the location of the elliptical shape Q e.
Fig. 2. Surface current distribution. (a) At 2.5 and 3.5 GHz. (b) At 5 GHz. (c) At 5.8 GHz.
Three nulls are observed in the current distribution at the resonant frequency 5 GHz (Fig. 2(b)). Meanwhile, four nulls are observed at 5.8 GHz. Figures 2(b) and 2(c) present the surface current distributions at 5 and 5.8 GHz along F 3, which explain the aim of using perpendicular arms E 1 and E 2 in an elliptical shape F 3. The surface current along the arms E 1 and E 2 have two components that seem normal to each other, especially at resonant frequencies 5 and 5.8 GHz. These normal components generate normal components of the field, which are necessary in radiating CP. At lower resonant frequencies of 2.5 and 3.5 GHz (Fig. 2(a)), the surface current either does not exist along the arms E 1 and E 2 or exists with low intensity, which means that the proposed antenna has CP at the upper band only.
Left- and right-hand polarization
The left- and right-hand polarization patterns on the E-Plane (when 
$\islant 20%{\emptyset} = 90^{\rm o}$) are illustrated in Fig. 3 at the resonant frequencies of 2.5, 3.5, 5, and 5.8 GHz. The phase difference between the left- and right-hand polarization patterns is 170o at 2.5 GHz (Fig. 3(a)) and reduces to 70o at 3.5 GHz (Fig. 3(b)). Thus, no CP radiation exists at resonant frequencies 2.5 and 3.5 GHz, this study matched with the surface current distribution shown in Fig. 2(a).
Fig. 3. Left (black curves) and right-hand (red curves) polarization patterns in E-Plane. (a) At 2.5 GHz. (b) At 3.5 GHz. (c) At 5 GHz. (d) At 5.8 GHz.
The left and right polarization at 5 and 5.8 GHz are almost perpendicular to each other as shown in Figs 3(c) and 3(d), this result agrees with the current distribution along the arms E 1 and E 2as it is shown in Figs 2(b) and 2(c) where two normal components of the surface current observed produce CP at the upper operating band. In another meaning, the values of ARBW are <3 dB during the upper band only. The left- and right-hand radiation at all resonant frequencies had asymmetrical shapes because the Q-slot in ground plate is asymmetrical, which causes different paths of the surface current when changing the phase of excited signal.
Axial ratio bandwidth
Figure 4 presents the measured values of the ARBW for different types of cutting in the upper feed line F 3. The AR values for circular cutting (red curve) and without cutting (blue curve) are considerably greater than the AR value required for CP generation (<3 dB). Nearly no current distribution is present along the perpendicular arms E 1 and E 2 at 2.5 and 3.5 GHz. In using an open-end mouth slot with perpendicular arms E 1 and E 2 in F 3, the AR values decrease for the frequency spectrum 2–7 GHz, especially at the 3rd operating band. ARBW is <3 dB at 4.8–5.93 GHz (black curve in Fig. 4), which is approximately 52% of the 3rd band of 4.7–6.8 GHz. The ARBW values shown in Fig. 4 match the above studies about the surface current distribution in Fig. 2 and the LHP–RHP represented in Fig. 3.
Fig. 4. Measured AR for different types of cuts in strip line F3.
Radiation fields
The Q-slot is almost similar to the elliptical slot. Therefore, its radiation pattern will be likened to the radiating antenna for the elliptical slot. According to the previous study, the complementary antenna for the elliptical slot is the elliptical loop. As it is shown in Fig. 5. In rectangular coordinates, the ellipse can be presented by the following parameters
$$X\, = \,a\,\cos \,u ,\,Y\, = \,b\,{\rm sin}\,u,\,-\pi \, \le \,u\, \le \pi, $$where a, b are the minor and major axes of the ellipse. In terms of rectangular coordinates, the x component of the Hertzian vector potential at point P can be written as [Reference Stutzman and Thiele8]
$$A_x\, = \,\displaystyle{{e^{-i\beta R}} \over {i4\pi Rw\epsilon}} \,\mathop \int \limits_{u = -\pi} ^{u = \pi} I_o\,e^{[ik\,(x\,{\rm cos}\,{\islant20% \emptyset} \,{\rm sin}\,\theta \, + \,y\,{\rm sin}\,\theta \,{\rm sin}\, {\islant20% \emptyset} )]}\,dx,$$where I o is the current in ds (an element length) = 2π/ λ.
Fig. 5. The Q-slot and the complimentary. (a) Q-slot. (b) The complementary.
By substituting equation (9) in equation (10)
$$A_x\, = \,\displaystyle{{-I_o\,ae^{-i\beta R}} \over {i4\pi Rw\epsilon}} \,\mathop \int \limits_{-\pi} ^\pi e^{[ik\,(a\,{\rm cos}\,u\,{\rm cos}\, {\islant20% \emptyset} \,{\rm sin}\,\theta \, + \,b\,{\rm sin}\,u\,{\rm sin}\,\theta {\rm \;} \,{\rm sin}\,{\islant20% \emptyset} )]}\,\sin \,u\,du.$$Let
$$\gamma \, = \,{\rm ta}{\rm n}^{-1}\left( {\displaystyle{b \over a}\,\tan \,{\islant20% \emptyset}} \right)\,{\rm and}\,\delta \, = \,ka\,\sin \,\theta \,\sqrt {({\rm co}{\rm s}^2\, {\islant20% \emptyset} \, + \,{(b/a)}^2} \,\sin \, {\islant20% \emptyset} ^2).$$Equation (10) reduced to
$$A_x\, = \,\displaystyle{{-I_o\; ae^{-i\beta R}} \over {i4\pi Rw\epsilon}} \,\mathop \int \limits_{-\pi} ^\pi e^{[{\rm i}\delta \,{\rm (cos\;} \,u-\gamma {\rm )}]}\,\sin \,u\,du.$$The term e [iδ (cos u−γ)] can be expended by Fourier series with Bessel function and equation (13) simplified to
$$A_x\, = \,\displaystyle{{-I_o{\rm \;} ae^{-i\beta R}} \over {2Rw\epsilon}} \,J_1\,(\delta )\,{\rm sin}\,{\rm (}\gamma {\rm )}{\rm.} $$By the same method the Y component can be driven
$$A_y\, = \,\displaystyle{{-I_o\; ae^{-i\beta R}} \over {2Rw\epsilon}} {\rm \;} \,J_1\,(\delta )\,{\rm cos}\,{\rm (}\gamma {\rm )}{\rm.} $$In spherical coordinates
$$A_\theta \, = \,A_x\,\cos \,\theta \,{\rm cos}\, {\islant20% \emptyset} \, + \,A_y\,\cos \,\theta \,\sin \, {\islant20% \emptyset}, $$
$$A_{\islant20% \emptyset} \, = \,-A_x\,\sin \, {\islant20% \emptyset} \, + \,A_y\,{\rm cos}\, {\islant20% \emptyset}. $$After substituting the spherical components become
$$A_\theta \, = \,0.$$The electric field component can be driven by applying the following vector relationship
$$A_{\islant20% \emptyset} \, = \,\displaystyle{{I_o\; ae^{-i\beta R}} \over {2Rw\epsilon}} \,J_1\,(\delta )\,\sqrt {({\rm si}{\rm n}^2\gamma + {(b/a)}^2{\rm co}{\rm s}^2\gamma {\rm \;}} ).$$ That means there is no θ component for the Hertizan vector, or the current in the elliptical loop has only 
$ {\islant20% \emptyset} $ component i.e. the radiation is outside the loop.
$$E_{\islant20% \emptyset} \, = \,w^2\mu \varepsilon A_{\islant20% \emptyset} \, + \,\nabla \,(\nabla \cdot A_\emptyset ),$$
$$E_{\islant20% \emptyset} \, = \,\displaystyle{{I_ok\; ae^{-i\beta R}} \over {2R}}\,J_1\,(\delta )\,\sqrt {({\rm si}{\rm n}^2\gamma + {(b/a)}^2{\rm co}{\rm s}^2\gamma {\rm \;}} ).$$The first-order Bessel function can be equal to
$${\rm \;\;\;} J_1\,(x)\, = \,\displaystyle{1 \over 2}\,x.$$The normalized field for elliptical loop
$$F_{\islant20% \emptyset} \, = \,\delta \,\sqrt {({\rm si}{\rm n}^2\,\gamma \, + \,{(b/a)}^2\,{\rm co}{\rm s}^2\gamma {\rm \;}} ).$$From equation (23), the radiation pattern for elliptical loop which is complementary of the elliptical slot depends on the size (values of a and b) and the pattern is non-uniform, for the small elliptical slot (a ≈ b), the normalized field will be
$$F_{\islant20% \emptyset} \, = \,kb\,{\rm sin}\,{\rm (}\theta {\rm )}{\rm.} $$ Therefore, the radiation pattern for a small elliptical slot depends on 
$\emptyset $ and seems to be circular. But the desired Q-slot antenna is asymmetrical, so the radiation pattern will be asymmetrical also. However, for the small slot, it was demonstrated that the radiation pattern is independent of the shape, and it is almost circular. Consequently, the radiation pattern of the small elliptical slot in the H-plane is independent of the angle 
$(\emptyset )$ and therefore, it is omnidirectional. But all radiation patterns in H-plane represented in Fig. 6 are not omnidirectional due to the asymmetrical slots used in the proposed antenna, that is a narrow slot on the left side and a wide slot on the right side as shown in Fig. 1, which caused asymmetrical current distribution.
Fig. 6. The simulated and measured radiation fields in E and H-plane.
Conclusion
Clearly, the CP technique used in the Q-slot antenna is new, where in normal arms (E 1 and E 2) in an elliptical upper strip feeding line have been cut to generate CP characteristics with wide ARBW in small size and low profile. Therefore, this technique overcame the limits of generating CP with wide ARBW. Notably, the driven formula for normalized field shows that the radiation pattern for the small slot is independent of the slot shape.
Acknowledgement
The authors would like to thank Al-Rafidain University College, Baghdad, Iraq for supporting this research.
Amer T. Abed received a degree in Electrical Engineering from College of Engineering, University of Baghdad, 1984. He did his master in Communication Engineering from University of TENAGA, Malaysia and his Ph.D. from UKM, Malaysia. He has wide experience in designing the RF circuit and antennas. Dr. Abed has published 25 papers in ISI journals and two books about antenna design. He has reviewed more than 30 articles in IET and IEEE journals. Currently, he is a lecturer in Communication Engineering Department, Al-M'mamon University College, Baghdad-Iraq.
Mandeep S.J. Singh received his B.Eng. (with honors) and Ph.D. degrees in electrical and electronic engineering from the University of Notrhumbria, UK, and Universiti Sains Malaysia, in 1998 and 2006, respectively. From 2006 up to June 2009, he was attached at Universiti Sains Malaysia as a Lecturer. Currently, he is attached to the Universiti Kebangsaan Malaysia as a Professor. Dr. Singh has published 190 papers in ISI journals. He has reviewed more than 200 articles in impact factors journal.
Aqeel M. Jawad received his B.Sc. in Computer and Communication Eng. from Al-Rafidain University College, Iraq in 2009, his M.Sc. in Electrical Eng. Universiti Tenaga National (UNITEN), Malaysia, 2014. He is currently pursuing the Ph.D. degree with the Department of Electrical, Electronics and Systems Engineering, Faculty of Engineering and Built Environments, Universiti Kebangsaan Malaysia. He is currently with the Department of Computer and Communication Engineering, as a Lecturer in Al-Rafidain University College, Baghdad-Iraq and head of the communication laboratory.
