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].

(1)$$E_y\, = \,c\,\displaystyle{{{\rm sin}\,({\rm (}\pi /E_1{\rm )}{y}^{\prime})} \over {k^2\,(1-j/Q_t)\,-\,{(k_y)}^2}},$$

(2)$$E_x\, = \,c\,\displaystyle{{{\rm sin}\,({\rm (}\pi /E_2{\rm )}{z}^{\prime})} \over {k^2\,(1-j/Q_t)-{(k_z)}^2}},$$

(3)$$k_y = \displaystyle{\pi \over {E_1}},\,k_x = \displaystyle{\pi \over {E_2}}$$

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

(4)$$\displaystyle{{{\rm \;} {y}^{\prime}} \over {E_1}} = \displaystyle{{{X}^{\prime}} \over {E_2}}.$$

At the broad side of the electric fields E _y and E _x can be formed

(5)$$\displaystyle{{E_y} \over {E_x}}\,\approx \,\displaystyle{{k\,(1-j/2Q_t)\,-\,(k_y)} \over {k\,(1-j/2Q_t)\,-\,(k_x)}},$$

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

(6)$$E_y\,-\,E_x\, = \,k_x\,-\,k_y\; = \,0,$$

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.        

(7)$$f_1\, = \,\displaystyle{{\,f_0} \over {\sqrt {1 + 1/Q_t}}}, $$

(8)$$f_2\, = \,f_0\sqrt {1 + \displaystyle{1 \over {Q_t}}}, $$

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 170^o at 2.5 GHz (Fig. 3(a)) and reduces to 70^o 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

(9)$$X\, = \,a\,\cos \,u ,\,Y\, = \,b\,{\rm sin}\,u,\,-\pi \, \le \,u\, \le \pi, $$

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]

(10)$$A_x\, = \,\displaystyle{{e^{-i\beta R}} \over {i4\pi Rw\epsilon}} \,\mathop \int \limits_{u = -\pi} ^{u = \pi} I_o\,e^{[ik\,(x\,{\rm cos}\,{\islant20% \emptyset} \,{\rm sin}\,\theta \, + \,y\,{\rm sin}\,\theta \,{\rm sin}\, {\islant20% \emptyset} )]}\,dx,$$

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)

(11)$$A_x\, = \,\displaystyle{{-I_o\,ae^{-i\beta R}} \over {i4\pi Rw\epsilon}} \,\mathop \int \limits_{-\pi} ^\pi e^{[ik\,(a\,{\rm cos}\,u\,{\rm cos}\, {\islant20% \emptyset} \,{\rm sin}\,\theta \, + \,b\,{\rm sin}\,u\,{\rm sin}\,\theta {\rm \;} \,{\rm sin}\,{\islant20% \emptyset} )]}\,\sin \,u\,du.$$

Let

(12)$$\gamma \, = \,{\rm ta}{\rm n}^{-1}\left( {\displaystyle{b \over a}\,\tan \,{\islant20% \emptyset}} \right)\,{\rm and}\,\delta \, = \,ka\,\sin \,\theta \,\sqrt {({\rm co}{\rm s}^2\, {\islant20% \emptyset} \, + \,{(b/a)}^2} \,\sin \, {\islant20% \emptyset} ^2).$$

Equation (10) reduced to

(13)$$A_x\, = \,\displaystyle{{-I_o\; ae^{-i\beta R}} \over {i4\pi Rw\epsilon}} \,\mathop \int \limits_{-\pi} ^\pi e^{[{\rm i}\delta \,{\rm (cos\;} \,u-\gamma {\rm )}]}\,\sin \,u\,du.$$

The term e ^{[iδ (cos u−γ)]} can be expended by Fourier series with Bessel function and equation (13) simplified to

(14)$$A_x\, = \,\displaystyle{{-I_o{\rm \;} ae^{-i\beta R}} \over {2Rw\epsilon}} \,J_1\,(\delta )\,{\rm sin}\,{\rm (}\gamma {\rm )}{\rm.} $$

By the same method the Y component can be driven

(15)$$A_y\, = \,\displaystyle{{-I_o\; ae^{-i\beta R}} \over {2Rw\epsilon}} {\rm \;} \,J_1\,(\delta )\,{\rm cos}\,{\rm (}\gamma {\rm )}{\rm.} $$

In spherical coordinates

(16)$$A_\theta \, = \,A_x\,\cos \,\theta \,{\rm cos}\, {\islant20% \emptyset} \, + \,A_y\,\cos \,\theta \,\sin \, {\islant20% \emptyset}, $$

(17)$$A_{\islant20% \emptyset} \, = \,-A_x\,\sin \, {\islant20% \emptyset} \, + \,A_y\,{\rm cos}\, {\islant20% \emptyset}. $$

After substituting the spherical components become

(18)$$A_\theta \, = \,0.$$

The electric field component can be driven by applying the following vector relationship

(19)$$A_{\islant20% \emptyset} \, = \,\displaystyle{{I_o\; ae^{-i\beta R}} \over {2Rw\epsilon}} \,J_1\,(\delta )\,\sqrt {({\rm si}{\rm n}^2\gamma + {(b/a)}^2{\rm co}{\rm s}^2\gamma {\rm \;}} ).$$

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.

(20)$$E_{\islant20% \emptyset} \, = \,w^2\mu \varepsilon A_{\islant20% \emptyset} \, + \,\nabla \,(\nabla \cdot A_\emptyset ),$$

(21)$$E_{\islant20% \emptyset} \, = \,\displaystyle{{I_ok\; ae^{-i\beta R}} \over {2R}}\,J_1\,(\delta )\,\sqrt {({\rm si}{\rm n}^2\gamma + {(b/a)}^2{\rm co}{\rm s}^2\gamma {\rm \;}} ).$$

The first-order Bessel function can be equal to

(22)$${\rm \;\;\;} J_1\,(x)\, = \,\displaystyle{1 \over 2}\,x.$$

The normalized field for elliptical loop

(23)$$F_{\islant20% \emptyset} \, = \,\delta \,\sqrt {({\rm si}{\rm n}^2\,\gamma \, + \,{(b/a)}^2\,{\rm co}{\rm s}^2\gamma {\rm \;}} ).$$

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

(24)$$F_{\islant20% \emptyset} \, = \,kb\,{\rm sin}\,{\rm (}\theta {\rm )}{\rm.} $$

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.