High Performance Metasurface Antennas

*Haisheng Hou, Haipeng Li, Guangming Wang,Tong Cai, Xiangjun Gao and Wenlong Guo*

## **Abstract**

Recently, metasurfaces (MSs) have received tremendous attention because their electromagnetic properties can be controlled at will. Generally, metasurface with hyperbolic phase distributions, namely, focusing metasurface, can be used to design high-gain antennas. Besides, metasurface has the ability of controlling the polarization state of electromagnetic wave. In this chapter, we first propose a new ultrathin broadband reflected MS and take it into application for high-gain planar antenna. Then, we propose multilayer multifunctional transmitted MSs to simultaneously enhance the gain and transform the linear polarization to circular polarization of the patch antenna. This kind of high-gain antenna eliminates the feed-block effect of the reflected ones.

**Keywords:** focusing, metasurface, high-gain, polarization conversion, reflection, transmission

## **1. Single-layer broadband planar antenna using ultrathin high-efficiency focusing metasurfaces**

Recently, metasurfaces (MSs) have attracted growing interests of many researchers due to their planar profile, easy fabrication, and also strong beam control capacity [1–6]. For phase gradient metasurfaces (PGMS), proposed by Yu et al. [7], a wide range of applications have been found, such as anomalous beam bending [8, 9], focusing [7, 10], surface-plasmon-polariton coupling [11, 12], and polarization manipulation. With the ability of tuning the phase range covering 2*π*, metasurface can be used to improve performance of antenna. By fixing proper phase distributions on the metasurface, we can manipulate the wavefronts and the polarizations of the electromagnetic waves (EM) at will.

The focusing metasurface, which is one kind of functional metasurfaces, can focus the incident plane wave to its focal point. These characters indicate that the focusing metasurface can be applied for designing planar high-gain antenna by placing the feed sources at the focal point over the focusing metasurface [1]. Generally, there are two types of focusing metasurface, namely, reflective focusing metasurface and transmitted focusing metasurface. Based on upon two types of focusing metasurface, there are two kinds of high-gain antenna, namely, reflective metasurface high-gain antenna and transmissive metasurface high-gain antenna. Compared with the reflective metasurface antenna based on the focusing metasurface, transmissive metasurface antenna avoids the feed blockage effect,

making it more suitable for a high-gain antenna design. Besides, when designing a reflective focusing metasurface, the reflection magnitude is close to 1 (0 dB) due to grounded plane composed of PEC. Therefore, the reflection phase is the only modulated character by the focusing metasurface. However, transmitted phase and amplitude are both needed to be considered when designing a transmissive focusing metasurface. In [1], a dual-mode and dual-band flat high-gain antenna based on focusing metasurface is proposed. The reflection beam and transmission beam can be obtained. In [2], the modified I-shaped particles, which can independently manipulate the phases and amplitudes of the cross-polarization waves, have been proposed. Based on the proposed unit cell, three high-gain antennas are fabricated and tested. In [5], a novel split beam antenna using transmission-type coding metasurface is proposed, which provides a new way to design focusing metasurface. Although reflective metasurface antenna and transmissive metasurface antenna have been studied for many years, more efforts should be done to improve the performance (such as realized gain, bandwidth, polarization states, and so on) of antenna.

*ε<sup>r</sup>* = 2.65, loss tangent of 0.001, and thickness of 2 mm. For characterization, the element is simulated in commercial software CST Microwave Studio, unit cell boundary conditions are employed along *x* and *y* directions. Moreover, the element

nearly parallel to each other, leading to a large bandwidth for focusing EM

**Figure 2** shows the reflective phase of the reflection wave versus the length of parameter a. To demonstrate the ability of tuning the reflective phase at broadband, the reflective phases versus parameter a varying from 1.8 to 5 mm have been plotted from 15 to 22 GHz in **Figure 2**, respectively. Obviously, the phase tuning range is covering 2*π* at all frequencies (15–22 GHz). In additions, the eight phase shift curves

Generally, the reflected wave will always deflect to the phase delay direction

where *Φ* is the phase discontinuity at the local position on the metasurface, *θ*r/*θ*<sup>i</sup> is the reflected/incident angle, *n*r/*n*<sup>i</sup> is the reflective index of the reflected/incident medium, and *λ* is the wavelength. To clearly demonstrate the general reflection law, *d*Φ*=dx* can be denoted as 2*π*/*np*, where *n* is the number of elements arranged in order along *x* direction and *p* is the periodicity of element. In such case, the element is illuminated normally, so the *θ*<sup>i</sup> can be denoted by 0°. At the same time, the *n*<sup>i</sup> = 1 can be realized because the element is placed in free space. Consequently, the

> 2π � 2π

Then designing a focusing phase distribution on the metasurface by using the

*λ* 2π *d*Φ

*dx* (1)

*np* (2)

*n*<sup>r</sup> sin ð Þ� *θ*<sup>r</sup> *n*<sup>i</sup> sin ð Þ¼ *θ*<sup>i</sup>

*<sup>θ</sup><sup>r</sup>* <sup>¼</sup> sin �<sup>1</sup> *<sup>λ</sup>*

proposed element is the key procedure. Based on Fermat's principle, the EM

is illuminated by *x*-polarized plane wave along �*z* direction.

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

**1.2 Broadband and focusing metasurface design**

reflected angle *θ*<sup>r</sup> can be depicted in Eq. (2):

*Reflected phase shift with a (1.8–5 mm) from 15 to 22 GHz.*

according to the general reflection law as depicted in Eq. (1):

wavefronts.

**Figure 2.**

**45**

However, most reported metasurfaces suffer from a narrow bandwidth, which restrict their further applications, especially in planar antenna design. To overcome this drawback, several methods have been proposed such as using stacked phase shifting elements or aperture patches coupled to true-time delay lines. Besides, there is another way to obtain a broadband working width by using a single-layer broadband planar antenna using ultrathin high-efficiency focusing metasurfaces.

In this chapter, a single-layer broadband focusing metasurface has been proposed to enhance the gain of the antenna. Theoretically, the spherical wave emitted by a point source at the focal point can be transformed to a plane wave. Therefore, a Vivaldi antenna has been fixed at the focal point of focusing metasurface, obtaining wideband planar antennas. In this case, the directivity and gain of the point source have been improved remarkably.

## **1.1 Element design**

**Figure 1** shows the proposed element, which is used to design reflective metasurface. The element is composed of orthogonally I-shaped structures and a metal-grounded plane spaced by a dielectric isolator with a permittivity of

#### **Figure 1.**

*Structure of the element and the simulated setup: (a) top view; (b) perspective view. The parameters are listed as d = 0.3 mm, p = 6 mm, h = 2 mm, and a = 1.8–5 mm.*

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

making it more suitable for a high-gain antenna design. Besides, when designing a reflective focusing metasurface, the reflection magnitude is close to 1 (0 dB) due to grounded plane composed of PEC. Therefore, the reflection phase is the only modulated character by the focusing metasurface. However, transmitted phase and amplitude are both needed to be considered when designing a transmissive focusing metasurface. In [1], a dual-mode and dual-band flat high-gain antenna based on focusing metasurface is proposed. The reflection beam and transmission beam can be obtained. In [2], the modified I-shaped particles, which can independently manipulate the phases and amplitudes of the cross-polarization waves, have been proposed. Based on the proposed unit cell, three high-gain antennas are fabricated and tested. In [5], a novel split beam antenna using transmission-type coding metasurface is proposed, which provides a new way to design focusing metasurface. Although reflective metasurface antenna and transmissive metasurface antenna have been studied for many years, more efforts should be done to improve the performance (such as realized gain, bandwidth, polarization states, and so on)

However, most reported metasurfaces suffer from a narrow bandwidth, which restrict their further applications, especially in planar antenna design. To overcome this drawback, several methods have been proposed such as using stacked phase shifting elements or aperture patches coupled to true-time delay lines. Besides, there is another way to obtain a broadband working width by using a single-layer broadband planar antenna using ultrathin high-efficiency focusing metasurfaces. In this chapter, a single-layer broadband focusing metasurface has been proposed to enhance the gain of the antenna. Theoretically, the spherical wave emitted by a point source at the focal point can be transformed to a plane wave. Therefore, a Vivaldi antenna has been fixed at the focal point of focusing metasurface, obtaining wideband planar antennas. In this case, the directivity and gain of the

**Figure 1** shows the proposed element, which is used to design reflective metasurface. The element is composed of orthogonally I-shaped structures and a metal-grounded plane spaced by a dielectric isolator with a permittivity of

*Structure of the element and the simulated setup: (a) top view; (b) perspective view. The parameters are listed*

of antenna.

*Modern Printed-Circuit Antennas*

**1.1 Element design**

**Figure 1.**

**44**

point source have been improved remarkably.

*as d = 0.3 mm, p = 6 mm, h = 2 mm, and a = 1.8–5 mm.*

*ε<sup>r</sup>* = 2.65, loss tangent of 0.001, and thickness of 2 mm. For characterization, the element is simulated in commercial software CST Microwave Studio, unit cell boundary conditions are employed along *x* and *y* directions. Moreover, the element is illuminated by *x*-polarized plane wave along �*z* direction.

**Figure 2** shows the reflective phase of the reflection wave versus the length of parameter a. To demonstrate the ability of tuning the reflective phase at broadband, the reflective phases versus parameter a varying from 1.8 to 5 mm have been plotted from 15 to 22 GHz in **Figure 2**, respectively. Obviously, the phase tuning range is covering 2*π* at all frequencies (15–22 GHz). In additions, the eight phase shift curves nearly parallel to each other, leading to a large bandwidth for focusing EM wavefronts.

### **1.2 Broadband and focusing metasurface design**

Generally, the reflected wave will always deflect to the phase delay direction according to the general reflection law as depicted in Eq. (1):

$$n\_{\mathbf{r}}\sin\left(\theta\_{\mathbf{r}}\right) - n\_{\mathbf{i}}\sin\left(\theta\_{\mathbf{i}}\right) = \frac{\lambda}{2\pi} \frac{d\Phi}{d\mathbf{x}}\tag{1}$$

where *Φ* is the phase discontinuity at the local position on the metasurface, *θ*r/*θ*<sup>i</sup> is the reflected/incident angle, *n*r/*n*<sup>i</sup> is the reflective index of the reflected/incident medium, and *λ* is the wavelength. To clearly demonstrate the general reflection law, *d*Φ*=dx* can be denoted as 2*π*/*np*, where *n* is the number of elements arranged in order along *x* direction and *p* is the periodicity of element. In such case, the element is illuminated normally, so the *θ*<sup>i</sup> can be denoted by 0°. At the same time, the *n*<sup>i</sup> = 1 can be realized because the element is placed in free space. Consequently, the reflected angle *θ*<sup>r</sup> can be depicted in Eq. (2):

$$\theta\_r = \sin^{-1}\left(\frac{\lambda}{2\pi} \times \frac{2\pi}{np}\right) \tag{2}$$

Then designing a focusing phase distribution on the metasurface by using the proposed element is the key procedure. Based on Fermat's principle, the EM

**Figure 2.** *Reflected phase shift with a (1.8–5 mm) from 15 to 22 GHz.*

wavefront can be modified by changing the phase distribution on the metasurface. In order to focus the incident plane wave to a quasi-spherical wave, the phase Φ(*m*,*n*) imposed at location (*m*,*n*) should satisfy Eq. (3):

$$\Phi(m,n) = \frac{2\pi}{\lambda} \left( \sqrt{\left(mp\right)^2 + \left(np\right)^2 + L^2} - L \right) + \Phi\_0 \tag{3}$$

The metasurface is illuminated by a plane wave with a polarization propagating along *z* direction. To verify the focusing effect, the electrical field at both *yoz* and *xoz* planes in the center frequency 18 GHz is plotted in **Figure 5b** and **c**. It is obvious that the incident plane wave is transformed into quasi-sphere wave in the orthogonal planes. Furthermore, to verify the position of the focus point, a curve is put along *z* direction, and power field is evaluated on the curve. As **Figure 5d** shown, the energy is focused at both *xoz* and *yoz* planes. The red spot is the focus point. Normalized power field versus the distance to the metasurface is described in **Figure 5d**. Observing the normalized power field, it is drawn that the focal point is

According to the above analysis, a spherical wave, emitted by a source located at

focal point of the focusing metasurface, can be transformed into a plane wave theoretically. Therefore, a high-gain planar antenna can be realized by putting a feed antenna at the focal point of the focusing metasurface. The well-designed feed antenna is a Vivaldi antenna to offer a wide operating bandwidth. **Figure 6a** depicts

*(a) The simulated focusing MS; (b) simulated reflected electric field distribution in yoz plane at 18 GHz; (c) simulated reflected electric field distribution in xoz plane at 18 GHz; and (d) power distribution of focusing*

at *L* = 33 mm, which agrees well with the theoretical calculation.

**1.3 Broadband and high-gain planar antenna design**

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

**Figure 5.**

**47**

*wave at 18 GHz and distance to the MS.*

where *L* is the focal length, Φ<sup>0</sup> is the phase of origin point (0,0), and *p* is the periodicity of the element. **Figure 3a** depicts the conversion of an incident plane wave to a quasi-sphere wave, and **Figure 3b** depicts the conversion of a quasisphere wave to plane wave using the focusing metasurfaces.

Based on the procedure, a focusing metasurface with a size of 90 � 90 mm<sup>2</sup> , composed of 15 � 15 elements, is proposed and simulated. By theatrically calculating, a hyperbolic phase distribution is assigned on the metasurface. As shown in **Figure 4a** shows, the phase response along *x* direction is a hyperbolic phase distribution, and **Figure 4b** is a plot of the whole phase distribution on the metasurface.

In order to have an intuitionistic view of the focusing metasurface, the proposed metasurface, as shown in **Figure 5a**, is simulated in the commercial software CST.

*(a) Schematic used to describe focusing effect and (b) schematic used to describe operating mechanism of planar antenna.*

**Figure 4.**

*(a) Phase response on the cut line along x direction and (b) relative reflection phase distribution in xoy plane.*

## *High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

wavefront can be modified by changing the phase distribution on the metasurface. In order to focus the incident plane wave to a quasi-spherical wave, the phase

ð Þ *mp*

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �

<sup>2</sup> <sup>þ</sup> *<sup>L</sup>*<sup>2</sup>

� *L*

þ Φ<sup>0</sup> (3)

,

<sup>2</sup> <sup>þ</sup> ð Þ *np*

where *L* is the focal length, Φ<sup>0</sup> is the phase of origin point (0,0), and *p* is the periodicity of the element. **Figure 3a** depicts the conversion of an incident plane wave to a quasi-sphere wave, and **Figure 3b** depicts the conversion of a quasi-

Based on the procedure, a focusing metasurface with a size of 90 � 90 mm<sup>2</sup>

composed of 15 � 15 elements, is proposed and simulated. By theatrically calculating, a hyperbolic phase distribution is assigned on the metasurface. As shown in **Figure 4a** shows, the phase response along *x* direction is a hyperbolic phase distribution, and **Figure 4b** is a plot of the whole phase distribution on the metasurface. In order to have an intuitionistic view of the focusing metasurface, the proposed metasurface, as shown in **Figure 5a**, is simulated in the commercial software CST.

*(a) Schematic used to describe focusing effect and (b) schematic used to describe operating mechanism of planar*

*(a) Phase response on the cut line along x direction and (b) relative reflection phase distribution in xoy plane.*

Φ(*m*,*n*) imposed at location (*m*,*n*) should satisfy Eq. (3):

2*π λ*

sphere wave to plane wave using the focusing metasurfaces.

Φð Þ¼ *m; n*

*Modern Printed-Circuit Antennas*

**Figure 3.**

*antenna.*

**Figure 4.**

**46**

The metasurface is illuminated by a plane wave with a polarization propagating along *z* direction. To verify the focusing effect, the electrical field at both *yoz* and *xoz* planes in the center frequency 18 GHz is plotted in **Figure 5b** and **c**. It is obvious that the incident plane wave is transformed into quasi-sphere wave in the orthogonal planes. Furthermore, to verify the position of the focus point, a curve is put along *z* direction, and power field is evaluated on the curve. As **Figure 5d** shown, the energy is focused at both *xoz* and *yoz* planes. The red spot is the focus point. Normalized power field versus the distance to the metasurface is described in **Figure 5d**. Observing the normalized power field, it is drawn that the focal point is at *L* = 33 mm, which agrees well with the theoretical calculation.

## **1.3 Broadband and high-gain planar antenna design**

According to the above analysis, a spherical wave, emitted by a source located at focal point of the focusing metasurface, can be transformed into a plane wave theoretically. Therefore, a high-gain planar antenna can be realized by putting a feed antenna at the focal point of the focusing metasurface. The well-designed feed antenna is a Vivaldi antenna to offer a wide operating bandwidth. **Figure 6a** depicts

### **Figure 5.**

*(a) The simulated focusing MS; (b) simulated reflected electric field distribution in yoz plane at 18 GHz; (c) simulated reflected electric field distribution in xoz plane at 18 GHz; and (d) power distribution of focusing wave at 18 GHz and distance to the MS.*

the geometry parameters of Vivaldi antenna, and **Figure 6b** plots the reflection coefficient. It is clear to find that the designed antenna can operate from 15 to 22 GHz with the S11 lower than 10 dB, indicating that the proposed feed antenna is a good feed source for the planar antenna.

simulated. **Figures 7**–**9** plot the electrical field distributions at three representative frequencies (15, 18, and 22 GHz). As expected, the spherical wave emitted by feed antenna is transformed into nearly plane wave with the focusing metasurface in

The simulated and measured radiation patterns in *xoz* plane and *yoz* plane at 18 GHz are plotted in **Figure 12**. It is obvious that the designed planar antenna has a remarkably enhanced gain compared to without focusing metasurface. The peak gain enhancement is about 15 dB relative to the bare Vivaldi antenna both in *xoz* plane and *yoz* plane. To demonstrate the broadband performance of the high-gain planar antenna, the simulated and measured gain versus frequency is described in **Figure 13**. It can be concluded that 3-dB gain bandwidth is from 15 to 22 GHz and the measured results conform to simulation well. Due to thin thickness, polarization

*Simulated electric field distribution at 18 GHz in (a and b) yoz plane and (c and d) xoz plane, respectively, for*

*the Vivaldi antenna without (a and c) and (b and d) with the PGMS.*

To clearly show the farfield performance of the planar antenna, the 3D radiation patterns at 15, 18, and 22 GHz are shown in **Figure 10**. The gain has been remarkably enhanced in a broad bandwidth comparing with the gain of the feed antenna. And pencil-shaped radiation pattern is achieved. Thus, the broadband and high-gain planar antenna is obtained. In order to verify the simulation, a sample composed of 15 15 elements is fabricated as **Figure 11a** shown. Besides, the designed Vivaldi antenna is fabricated and put at the focal point

both *xoz* and *yoz* plane.

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

with a foam.

**Figure 8.**

**49**

To demonstrate the performance of the planar antenna, the simulated electrical field distributions with/without focusing metasurface at both *xoz* and *yoz* planes are

**Figure 6.**

*(a) Parameters of Vivaldi antenna and (b) simulated S11 of Vivaldi antenna.*

**Figure 7.**

*Simulated electric field distribution at 15 GHz in (a and b) yoz plane and (c and d) xoz plane, respectively, for the Vivaldi antenna without (a and c) and (b and d) with the PGMS.*

## *High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

the geometry parameters of Vivaldi antenna, and **Figure 6b** plots the reflection coefficient. It is clear to find that the designed antenna can operate from 15 to 22 GHz with the S11 lower than 10 dB, indicating that the proposed feed antenna is

To demonstrate the performance of the planar antenna, the simulated electrical field distributions with/without focusing metasurface at both *xoz* and *yoz* planes are

*Simulated electric field distribution at 15 GHz in (a and b) yoz plane and (c and d) xoz plane, respectively, for*

*the Vivaldi antenna without (a and c) and (b and d) with the PGMS.*

a good feed source for the planar antenna.

*Modern Printed-Circuit Antennas*

*(a) Parameters of Vivaldi antenna and (b) simulated S11 of Vivaldi antenna.*

**Figure 6.**

**Figure 7.**

**48**

simulated. **Figures 7**–**9** plot the electrical field distributions at three representative frequencies (15, 18, and 22 GHz). As expected, the spherical wave emitted by feed antenna is transformed into nearly plane wave with the focusing metasurface in both *xoz* and *yoz* plane.

To clearly show the farfield performance of the planar antenna, the 3D radiation patterns at 15, 18, and 22 GHz are shown in **Figure 10**. The gain has been remarkably enhanced in a broad bandwidth comparing with the gain of the feed antenna. And pencil-shaped radiation pattern is achieved. Thus, the broadband and high-gain planar antenna is obtained. In order to verify the simulation, a sample composed of 15 15 elements is fabricated as **Figure 11a** shown. Besides, the designed Vivaldi antenna is fabricated and put at the focal point with a foam.

The simulated and measured radiation patterns in *xoz* plane and *yoz* plane at 18 GHz are plotted in **Figure 12**. It is obvious that the designed planar antenna has a remarkably enhanced gain compared to without focusing metasurface. The peak gain enhancement is about 15 dB relative to the bare Vivaldi antenna both in *xoz* plane and *yoz* plane. To demonstrate the broadband performance of the high-gain planar antenna, the simulated and measured gain versus frequency is described in **Figure 13**. It can be concluded that 3-dB gain bandwidth is from 15 to 22 GHz and the measured results conform to simulation well. Due to thin thickness, polarization

**Figure 8.**

*Simulated electric field distribution at 18 GHz in (a and b) yoz plane and (c and d) xoz plane, respectively, for the Vivaldi antenna without (a and c) and (b and d) with the PGMS.*

insensitivity, and broad bandwidth, the proposed broadband high-gain planar antenna opens up a new route for the applications of the metasurface in microwave

*The photographs of (a) metasurfaces top view and (b) planar high-gain antenna.*

*Simulated and measured farfield radiation pattern at 18 GHz (a) xoz plane and (b) yoz plane.*

*Simulated and measured realized gain with/without PGMS from 15 to 22 GHz.*

band.

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

**Figure 11.**

**Figure 12.**

**Figure 13.**

**51**

**Figure 9.**

*Simulated electric field distribution at 22 GHz in (a and b) yoz plane and (c and d) xoz plane, respectively, for the Vivaldi antenna without (a and c) and (b and d) with the PGMS.*

**Figure 10.**

*(a) Simulated model for planar antenna and 3D radiation pattern for (b) 15 GHz; (c) 18 GHz; and (d) 22 GHz.*

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

insensitivity, and broad bandwidth, the proposed broadband high-gain planar antenna opens up a new route for the applications of the metasurface in microwave band.

**Figure 11.** *The photographs of (a) metasurfaces top view and (b) planar high-gain antenna.*

**Figure 12.** *Simulated and measured farfield radiation pattern at 18 GHz (a) xoz plane and (b) yoz plane.*

**Figure 13.** *Simulated and measured realized gain with/without PGMS from 15 to 22 GHz.*

**Figure 9.**

*Modern Printed-Circuit Antennas*

**Figure 10.**

*(d) 22 GHz.*

**50**

*Simulated electric field distribution at 22 GHz in (a and b) yoz plane and (c and d) xoz plane, respectively, for*

*(a) Simulated model for planar antenna and 3D radiation pattern for (b) 15 GHz; (c) 18 GHz; and*

*the Vivaldi antenna without (a and c) and (b and d) with the PGMS.*

## **2. Highly efficient multifunctional metasurface for high-gain lens antenna application**

With the development of the metasurface, it is a trend to design multifunctional devices to satisfy increasing requests of communication system in microwave region. Due to the ability of solving some key challenges like susceptibility to multipath, atmospheric absorptions, and reflections, circularly polarized antennas play an important role in wireless and satellite communication. At the same time, high-gain antenna plays an essential role in achieving long-distance wireless communication.

Owing to the function of linear-to-circular polarization conversion [13–17], metasurface opens up a novel route to realize the circular polarization. Therefore, it is interesting to design a circular antenna with high gain using metasurface. Generally, there are two categories of metasurface—transmitting type and reflecting type—according to the format of the metasurface. Compared with reflecting type, transmitting type allows reducing feed blockage effect when designing high-gain antenna. Therefore, it is more suitable for high-gain antenna. And it will be more novel to design a circularly polarized high-gain antenna engineered to realize linearto-circular polarization conversion and EM waves focusing by transmitting metasurface.

## **2.1 Theoretical analysis of transmitted linear-to-circular polarization conversion**

Assuming that the EM wave propagates through an arbitrary transmitted metasurface placed on *xoz* plane (*z* = 0), for simplicity, we only consider normal incidence illumination. Therefore, it can be assumed that an incident wave propagates along �*z* direction. Then the incident wave's electric field can be described as

$$
\overrightarrow{E}\_i = \left(\hat{\mathbf{x}} E\_\mathbf{x} + \hat{\mathbf{y}} E\_\mathbf{y}\right) \tag{4}
$$

can be transformed to transmitted wave of a right-handed circular polarized

to +*x* direction. Thus the vertical and horizontal components of *E* are set as

¼ 1 ffiffi 2 p

Therefore, the vertical and horizontal components of the transmitted electric

<sup>¼</sup> *<sup>T</sup>* <sup>1</sup> ffiffi 2 p

To get the circular polarization, the amplitudes of *E* for vertical and horizontal components are ideally equal, and the phase of *E* for vertical and horizontal com-

(*Tyx*) = 0, and Arg(*Txx*) � Arg(*Tyy*) = �90° should be satisfied. At the same time, Arg(*Tij*) represents the phase of *j*-polarized incident wave into *i*-polarized transmission wave. And Mag(*Tij*) represents the amplitude of *j*-polarized incident wave

> *<sup>T</sup>* <sup>¼</sup> �*<sup>j</sup>* <sup>0</sup> 0 1 � �*<sup>e</sup>*

1 1 � �*<sup>e</sup>*

*<sup>x</sup>* þ ^*yE*<sup>0</sup> *y* � � <sup>¼</sup> <sup>1</sup>

where *φ* is the phase obtained from the metasurface. Thereinto, the transmitted

ffiffi 2

�*j<sup>φ</sup>* <sup>¼</sup> <sup>1</sup> ffiffi 2 <sup>p</sup> �*<sup>j</sup>* 1 � �*<sup>e</sup>*

p ð Þ �*jx*^ þ ^*y e*

�*jkze*

*The proposed two schematic models of LTC polarized for different incident electric fields at (a) θ = 135°; (b)*

1 1 � �*<sup>e</sup>*

> 1 1 � �*<sup>e</sup>*

� � ¼ �90°. Therefore, Mag(*Txx*) = Mag(*Tyy*) = 1, Mag(*Txy*) = Mag

�*jkz* (9)

�*jkz* (10)

*x*

�*j<sup>φ</sup>* (11)

�*jkze*

�*jkze*

�*j<sup>φ</sup>* (12)

�*j<sup>φ</sup>* (13)

� � <sup>¼</sup> Mag *<sup>E</sup>*<sup>0</sup>

*y* � � and

*Ex Ey* � �

> *E* 0 *x E* 0 *y*

ponents experiences the distinct 90° phase shift, namely, Mag *E*<sup>0</sup>

into *i*-polarized transmission wave. In this case, the *T* matrix is

!

As depicted in **Figure 14**, there are two typical cases of realizing linear-to-

Take the case of *θ* = 45° as an example; the metasurface is illuminated with a linear polarization incident wave with the incident electric field *E*, titled 45° relative

(RHCP) or a left-handed circular polarized (LHCP).

circular polarized conversion.

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

field *E* can be denoted as

*y*

electric fields can be calculated as

*E* 0 *x E* 0 *y*

!

*Et* ⇀ <sup>¼</sup> *<sup>T</sup>* <sup>1</sup> ffiffi 2 p

¼ *xE*^ <sup>0</sup>

*θ = 45° relative to +x direction (θ is the angle between E and +x axis).*

Arg *E*<sup>0</sup> *x* � � � Arg *<sup>E</sup>*<sup>0</sup>

**Figure 14.**

**53**

$$
\begin{pmatrix} E\_{\chi} \\ E\_{\chi} \end{pmatrix} = \begin{pmatrix} \cos \theta \\ \sin \theta \end{pmatrix} e^{-jkx} \tag{5}
$$

where *k* is the wave number, *θ* is the angle along *x* axis, and complexes *Ex* and *Ey* represent the *x*-polarized and *y*-polarized states, respectively. The transmitted electric field through the metasurface can be described as [18]

$$
\vec{E}\_t = \left(\hat{\mathbf{x}}E\_\mathbf{x}' + \hat{\mathbf{y}}E\_\mathbf{y}'\right) \tag{6}
$$

$$
\begin{pmatrix} E\_\mathbf{x}' \\ E\_\mathbf{y}' \end{pmatrix} = T \begin{pmatrix} E\_\mathbf{x} \\ E\_\mathbf{y} \end{pmatrix} \tag{7}
$$

Furthermore, the complex amplitudes of the incident and transmitted fields can be connected by the *T* matrix (transmission matrix) [19]:

$$T = \begin{pmatrix} T\_{\text{xx}} T\_{\text{xy}} \\ T\_{\text{yx}} T\_{\text{yy}} \end{pmatrix} \tag{8}$$

where *Tij* represents the transmission coefficient of *j*-polarized incident wave and *i*-polarized transmission wave. Thus, the incident wave of linear polarization **2. Highly efficient multifunctional metasurface for high-gain lens**

devices to satisfy increasing requests of communication system in microwave region. Due to the ability of solving some key challenges like susceptibility to multipath, atmospheric absorptions, and reflections, circularly polarized antennas play an important role in wireless and satellite communication. At the same time, high-gain antenna plays an essential role in achieving long-distance wireless

Owing to the function of linear-to-circular polarization conversion [13–17], metasurface opens up a novel route to realize the circular polarization. Therefore, it is interesting to design a circular antenna with high gain using metasurface. Generally, there are two categories of metasurface—transmitting type and reflecting type—according to the format of the metasurface. Compared with reflecting type, transmitting type allows reducing feed blockage effect when designing high-gain antenna. Therefore, it is more suitable for high-gain antenna. And it will be more novel to design a circularly polarized high-gain antenna engineered to realize linear-

to-circular polarization conversion and EM waves focusing by transmitting

**2.1 Theoretical analysis of transmitted linear-to-circular polarization**

*Ei* ⇀

*Ex Ey* � �

> *Et* ⇀

> > *E*0 *x E*0 *y*

!

¼ *xE*^ <sup>0</sup>

tric field through the metasurface can be described as [18]

be connected by the *T* matrix (transmission matrix) [19]:

Assuming that the EM wave propagates through an arbitrary transmitted metasurface placed on *xoz* plane (*z* = 0), for simplicity, we only consider normal incidence illumination. Therefore, it can be assumed that an incident wave propagates along �*z* direction. Then the incident wave's electric field can be

¼ *xE*^ *<sup>x</sup>* þ ^*yEy*

<sup>¼</sup> cos *<sup>θ</sup>* sin *θ* � �

where *k* is the wave number, *θ* is the angle along *x* axis, and complexes *Ex* and *Ey* represent the *x*-polarized and *y*-polarized states, respectively. The transmitted elec-

> *<sup>x</sup>* þ ^*yE*<sup>0</sup> *y*

> > *Ex Ey* � �

� �

¼ *T*

Furthermore, the complex amplitudes of the incident and transmitted fields can

*<sup>T</sup>* <sup>¼</sup> *TxxTxy TyxTyy* � �

where *Tij* represents the transmission coefficient of *j*-polarized incident wave and *i*-polarized transmission wave. Thus, the incident wave of linear polarization

*e*

� � (4)

�*jkz* (5)

(6)

(7)

(8)

With the development of the metasurface, it is a trend to design multifunctional

**antenna application**

*Modern Printed-Circuit Antennas*

communication.

metasurface.

described as

**52**

**conversion**

can be transformed to transmitted wave of a right-handed circular polarized (RHCP) or a left-handed circular polarized (LHCP).

As depicted in **Figure 14**, there are two typical cases of realizing linear-tocircular polarized conversion.

Take the case of *θ* = 45° as an example; the metasurface is illuminated with a linear polarization incident wave with the incident electric field *E*, titled 45° relative to +*x* direction. Thus the vertical and horizontal components of *E* are set as

$$
\begin{pmatrix} E\_{\mathbf{x}} \\ E\_{\mathbf{y}} \end{pmatrix} = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ 1 \end{pmatrix} e^{-jkx} \tag{9}
$$

Therefore, the vertical and horizontal components of the transmitted electric field *E* can be denoted as

$$
\begin{pmatrix} E\_x' \\ E\_y' \end{pmatrix} = T \frac{1}{\sqrt{2}} \begin{pmatrix} \mathbf{1} \\ \mathbf{1} \end{pmatrix} e^{-jkx} \tag{10}
$$

To get the circular polarization, the amplitudes of *E* for vertical and horizontal components are ideally equal, and the phase of *E* for vertical and horizontal components experiences the distinct 90° phase shift, namely, Mag *E*<sup>0</sup> *x* � � <sup>¼</sup> Mag *<sup>E</sup>*<sup>0</sup> *y* � � and Arg *E*<sup>0</sup> *x* � � � Arg *<sup>E</sup>*<sup>0</sup> *y* � � ¼ �90°. Therefore, Mag(*Txx*) = Mag(*Tyy*) = 1, Mag(*Txy*) = Mag (*Tyx*) = 0, and Arg(*Txx*) � Arg(*Tyy*) = �90° should be satisfied. At the same time, Arg(*Tij*) represents the phase of *j*-polarized incident wave into *i*-polarized transmission wave. And Mag(*Tij*) represents the amplitude of *j*-polarized incident wave into *i*-polarized transmission wave. In this case, the *T* matrix is

$$T = \begin{pmatrix} -j & \mathbf{0} \\ \mathbf{0} & \mathbf{1} \end{pmatrix} e^{-j\varphi} \tag{11}$$

where *φ* is the phase obtained from the metasurface. Thereinto, the transmitted electric fields can be calculated as

$$
\begin{pmatrix} E\_{\ \chi}' \\ E\_{\ \chi}' \end{pmatrix} = T \frac{\mathbf{1}}{\sqrt{2}} \begin{pmatrix} \mathbf{1} \\ \mathbf{1} \end{pmatrix} e^{-jkx} e^{-j\rho} = \frac{\mathbf{1}}{\sqrt{2}} \begin{pmatrix} -j \\ \mathbf{1} \end{pmatrix} e^{-jkx} e^{-j\rho} \tag{12}
$$

$$
\overrightarrow{E}\_t = \left(\hat{\varkappa}E\_\varkappa' + \hat{\jmath}E\_\jmath'\right) = \frac{1}{\sqrt{2}}(-j\hat{\varkappa} + \hat{\jmath})e^{-jkx}e^{-j\varphi} \tag{13}
$$

**Figure 14.**

*The proposed two schematic models of LTC polarized for different incident electric fields at (a) θ = 135°; (b) θ = 45° relative to +x direction (θ is the angle between E and +x axis).*

From Eq. (13), it can be concluded that a RHCP wave is obtained in this case as shown in **Figure 14b**.

In the other case of *θ* = 135° as shown in **Figure 14a**, the transmitted electric field can be calculated as

$$
\begin{pmatrix} E'\_{\mathbf{x}} \\ E'\_{\mathbf{y}} \end{pmatrix} = T \frac{\mathbf{1}}{\sqrt{2}} \begin{pmatrix} -\mathbf{1} \\ \mathbf{1} \end{pmatrix} e^{-jkx} e^{-j\varphi} = \frac{\mathbf{1}}{\sqrt{2}} \begin{pmatrix} j \\ \mathbf{1} \end{pmatrix} e^{-jkx} e^{-j\varphi} \tag{14}
$$

$$
\vec{E}\_t = \left(\hat{\mathbf{x}}E\_x' + \hat{\mathbf{y}}E\_y'\right) = \frac{\mathbf{1}}{\sqrt{2}}(j\hat{\mathbf{x}} + \hat{\mathbf{y}})e^{-jkx}e^{-j\varphi} \tag{15}
$$

Therefore, a LHCP wave will be obtained.

### **2.2 Design of the unit cell**

Based on above theoretical analysis, it is necessary to design a unit cell with the ability of controlling *x*/*y*-polarized waves independently. The proposed unit cell, demonstrated in **Figure 15**, is composed of four metallic layers and three intermediate dielectric layers. Each metallic layer contains a same rectangular metal, which is employed to control the transmission phases and amplitudes of *x*/*y*-polarized EM waves. The dielectric layer has a substrate with the permittivity of *ε<sup>r</sup>* = 4.3, loss tangent of 0.001, and thickness of *h* = 1 mm. The detailed parameters are denoted by *h* = 1 mm, *p* = 4.1 mm (periodicity of the unit cell), and *ay*/*ax* (1–3.8 mm).

To verify the polarization-independent property for *x*/*y*-polarized EM waves, the unit cell is illuminated by a plane wave propagating along �*z* direction as shown in **Figure 15b**. Open boundary conditions and unit cell boundary conditions are applied in the *z* direction and *x*/*y* direction, respectively.

To demonstrate the ability of independently manipulating different polarized waves, the 2D map of phase shifts and amplitudes versus *ax* and *ay* is depicted in **Figures 16** and **17**. The phases and amplitudes of *Txx* is plotted in **Figure 16**. As *ax* and *ay* vary from 1 to 3.8 mm, the phase of *Txx* shown as **Figure 16a** nearly keeps a constant, indicating that the parameter *ay* has no influence on the phase of *Txx*, while the parameter *ax* has an obvious influence on the phase of *Txx*. As shown in **Figure 16b**, varying the parameter *ay*, the amplitude of *Txx* keeps a constant, indicating that *ay* has no influence on the amplitude of *Txx*. Therefore, it is can be drawn that *Txx* can be controlled by varying the parameter *ax* independently.

Moreover, **Figure 17** shows the phase and amplitude of *Tyy* when the unit cell is illuminated by *y*-polarized wave when varying *ax* and *ay* from 1 to 3.8 mm. As *ax* and *ay* vary from 1 to 3.8 mm, the phase of *Tyy* shown as **Figure 17a** nearly keeps a constant, indicating that the parameter *ax* has no influence on the phase of *Tyy*, while the parameter *ay* has an obvious influence on the phase of *Tyy*. As shown in **Figure 17b**, varying the parameter *ax*, the amplitude of *Tyy* keeps a constant, indicating that *ax* has no influence on the amplitude of *Tyy*. Therefore, it is can be drawn

Based on above analysis, it is concluded that the proposed unit cell has the ability

where *φ* is the phase discontinuity as the local position on the metasurface, *θ*t(*θ*i) is the refracted (incident) angle of the EM waves, *n*t(*n*i) is the refractive index of the transmissive (incident) medium, and *λ* is the wavelength. To simplify the analysis, *dφ*/*dx* can be denoted as 2*π*/*np*, where *n* is the number of the unit cell arranged along *x* direction and *p* is the periodicity of the unit cell. In the design, the unit cell is normally illuminated by EM wave in the free space; thus *θ*<sup>i</sup> and *n*<sup>t</sup> are denoted by 0° and 1, respectively. Thus the refraction angle *θ*<sup>t</sup> can be depicted in

*λ* 2π *dφ*

*dx* (16)

As we all know, the refracted wave will always deflect to the phase delay direction according to the general refraction law [3] as described in Eq. (16):

*n*<sup>t</sup> sin ð Þ� *θ*<sup>t</sup> *n*<sup>i</sup> sin ð Þ¼ *θ*<sup>i</sup>

that *Tyy* can be controlled by varying the parameter *ay* independently.

of controlling *x*/*y*-polarized wave independently.

Eq. (17):

**55**

**Figure 17.**

**Figure 16.**

*Phases and amplitudes of Tyy of the unit cell.*

*Phases and amplitudes of Txx of the unit cell.*

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

**Figure 15.** *Structure of the unit cell and simulated setup (a) top view and (b) perspective view.*

From Eq. (13), it can be concluded that a RHCP wave is obtained in this case as

In the other case of *θ* = 135° as shown in **Figure 14a**, the transmitted electric field

¼ 1 ffiffi 2 p ð Þ *jx*^ þ ^*y e*

Based on above theoretical analysis, it is necessary to design a unit cell with the ability of controlling *x*/*y*-polarized waves independently. The proposed unit cell, demonstrated in **Figure 15**, is composed of four metallic layers and three intermediate dielectric layers. Each metallic layer contains a same rectangular metal, which is employed to control the transmission phases and amplitudes of *x*/*y*-polarized EM waves. The dielectric layer has a substrate with the permittivity of *ε<sup>r</sup>* = 4.3, loss tangent of 0.001, and thickness of *h* = 1 mm. The detailed parameters are denoted by *h* = 1 mm, *p* = 4.1 mm (periodicity of the unit cell), and *ay*/*ax* (1–3.8 mm). To verify the polarization-independent property for *x*/*y*-polarized EM waves, the unit cell is illuminated by a plane wave propagating along �*z* direction as shown in **Figure 15b**. Open boundary conditions and unit cell boundary conditions are

To demonstrate the ability of independently manipulating different polarized waves, the 2D map of phase shifts and amplitudes versus *ax* and *ay* is depicted in **Figures 16** and **17**. The phases and amplitudes of *Txx* is plotted in **Figure 16**. As *ax* and *ay* vary from 1 to 3.8 mm, the phase of *Txx* shown as **Figure 16a** nearly keeps a constant, indicating that the parameter *ay* has no influence on the phase of *Txx*, while the parameter *ax* has an obvious influence on the phase of *Txx*. As shown in **Figure 16b**, varying the parameter *ay*, the amplitude of *Txx* keeps a constant, indicating that *ay* has no influence on the amplitude of *Txx*. Therefore, it is can be drawn that *Txx* can be controlled by varying the parameter *ax* independently.

�*j<sup>φ</sup>* <sup>¼</sup> <sup>1</sup> ffiffi 2 p

*j* 1 � � *e* �*jkze*

�*jkze*

�*j<sup>φ</sup>* (14)

�*j<sup>φ</sup>* (15)

shown in **Figure 14b**.

*Modern Printed-Circuit Antennas*

can be calculated as

**2.2 Design of the unit cell**

**Figure 15.**

**54**

*E*0 *x E*0 *y*

!

*Et* ⇀

Therefore, a LHCP wave will be obtained.

<sup>¼</sup> *<sup>T</sup>* <sup>1</sup> ffiffi 2 <sup>p</sup> �<sup>1</sup> 1 � � *e* �*jkze*

¼ *xE*^ <sup>0</sup>

applied in the *z* direction and *x*/*y* direction, respectively.

*Structure of the unit cell and simulated setup (a) top view and (b) perspective view.*

*<sup>x</sup>* þ ^*yE*<sup>0</sup> *y*

� �

**Figure 16.** *Phases and amplitudes of Txx of the unit cell.*

**Figure 17.** *Phases and amplitudes of Tyy of the unit cell.*

Moreover, **Figure 17** shows the phase and amplitude of *Tyy* when the unit cell is illuminated by *y*-polarized wave when varying *ax* and *ay* from 1 to 3.8 mm. As *ax* and *ay* vary from 1 to 3.8 mm, the phase of *Tyy* shown as **Figure 17a** nearly keeps a constant, indicating that the parameter *ax* has no influence on the phase of *Tyy*, while the parameter *ay* has an obvious influence on the phase of *Tyy*. As shown in **Figure 17b**, varying the parameter *ax*, the amplitude of *Tyy* keeps a constant, indicating that *ax* has no influence on the amplitude of *Tyy*. Therefore, it is can be drawn that *Tyy* can be controlled by varying the parameter *ay* independently.

Based on above analysis, it is concluded that the proposed unit cell has the ability of controlling *x*/*y*-polarized wave independently.

As we all know, the refracted wave will always deflect to the phase delay direction according to the general refraction law [3] as described in Eq. (16):

$$n\_{\rm t} \sin \left(\theta\_{\rm t}\right) - n\_{\rm i} \sin \left(\theta\_{\rm i}\right) = \frac{\lambda}{2\pi} \frac{d\rho}{d\mathbf{x}} \tag{16}$$

where *φ* is the phase discontinuity as the local position on the metasurface, *θ*t(*θ*i) is the refracted (incident) angle of the EM waves, *n*t(*n*i) is the refractive index of the transmissive (incident) medium, and *λ* is the wavelength. To simplify the analysis, *dφ*/*dx* can be denoted as 2*π*/*np*, where *n* is the number of the unit cell arranged along *x* direction and *p* is the periodicity of the unit cell. In the design, the unit cell is normally illuminated by EM wave in the free space; thus *θ*<sup>i</sup> and *n*<sup>t</sup> are denoted by 0° and 1, respectively. Thus the refraction angle *θ*<sup>t</sup> can be depicted in Eq. (17):

$$\theta\_t = \sin^{-1}\left(\frac{\lambda}{2\pi} \times \frac{2\pi}{np}\right) \tag{17}$$

In order to efficiently convert the incident plane wave into a quasi-spherical wave, the phase *φ*(*m*, *n*) at unit cell location (*m*, *n*) should be carefully optimized,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �

<sup>2</sup> <sup>þ</sup> *<sup>L</sup>*<sup>2</sup>

� *L*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r� � � *<sup>L</sup>*

<sup>2</sup> <sup>þ</sup> *<sup>L</sup>*<sup>2</sup>

<sup>2</sup> <sup>þ</sup> *<sup>L</sup>*<sup>2</sup>

� � (20)

� � (19)

<sup>2</sup> <sup>þ</sup> ð Þ *np*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r� � � *<sup>L</sup>*

<sup>2</sup> <sup>þ</sup> ð Þ *np*

<sup>00</sup>≈ � 90° should be satisfied for *x*/*y*-polarized incident

ð Þ *mp*

ð Þ *mp*

þ *φ*ð Þ 0*;* 0 (18)

*mn*≈ � 90°

<sup>2</sup> <sup>þ</sup> ð Þ *np*

where *p* is periodicity of unit cell and *L* is the focal length and *m* and *n* are the

In order to realize the LTC conversion, the transmitted phase for *x*-polarized incident wave should have a phase difference of 90° with the *y*-polarized incident

should be satisfied, and a RHCP wave can be obtained. For *x*-polarized incident

ð Þ *mp*

unit cell positions along *x* and *y* directions, respectively. Moreover, *φ*(0, 0) represents the phase at the origin unit cell (*m* = 0, *n* = 0). It is easy to convert the incident plane wave into quasi-spherical wave using the above metasurface. Moreover, we concentrate on designing a linear-to-circular polarization conversion

metasurface according to the theory and unique feature described in the

wave through each unit cell. In this chapter, we design a LTC conversion metasurface according to **Figure 14b**. Namely, *Arg T*ð Þ *xx mn* � *Arg Tyy* � �

*λ*

<sup>00</sup> <sup>¼</sup> <sup>2</sup>*<sup>π</sup> λ*

For *y*-polarized incident wave, the phase distribution can be denoted as

To achieve *Arg T*ð Þ *xx mn* � *Arg Tyy* � �*mn*<sup>≈</sup> � 90° simply, the phase difference

Based on above analysis, the multifunctional transmission metasurface is composed of 15 � 15 unit cells. The working frequency and focal length are *f* = 15 GHz and *L* = 30 mm, respectively. A patch antenna, operating from 14.5 to 15.3 GHz, is placed on the focal point to be a feed source. By insertion of *p* = 4.1 mm, *λ* = 20 mm,

q

yielding the following phase distribution:

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

*φ*ð Þ¼ *m; n*

wave, the phase distribution can be denoted as

*Arg T*ð Þ *xx mn* � *Arg T*ð Þ *xx* <sup>00</sup> <sup>¼</sup> <sup>2</sup>*<sup>π</sup>*

*mn* � *Arg Tyy* � �

*Absolute phase distributions for (a) x polarization and (b) y polarization.*

preceding section.

*Arg Tyy* � �

*Arg T*ð Þ *xx* <sup>00</sup> � *Arg Tyy* � �

**Figure 19.**

**57**

waves at origin point *φ*(0, 0).

2*π λ*

To verify the performance of manipulating the *x*/*y*-polarized wave independently, one-dimensional metasurface with inverse linear phase gradient along *x* direction for *x*/*y*-polarized wave has been proposed in **Figure 17**. The proposed supercell is composed of six unit cells with the parameters demonstrated in **Table 1**. Phase gradients are assigned to +60° to �60° for *x*/*y*-polarized incident plane wave, respectively. *Φ<sup>x</sup>* and *Φ<sup>y</sup>* in **Table 1** represent the phase response for *x*/*y*-polarized incident waves.

4 � 16 supercells are fixed as **Figure 18a** has shown. The supercell is perpendicularly illuminated by plane wave along *z* direction in CST Microwave Studio. And open (add space) boundary condition is set along all directions.

Based on Eq. (17), the refracted angles for *x*/*y*-polarized incident wave can be calculated as 54.4°. And the refracted wave will deflect to �*x*/+*x* direction, respectively. The 3D farfields are calculated as shown in **Figure 18a**. Beam 2 and beam 1 are calculated under *x*/*y*-polarized plane wave illumination, respectively. To clearly show the refracted angles for *x*/*y*-polarized waves, the normalized farfield patterns in polar are depicted in **Figure 18b**. The simulated refracted angles are in good accordance with theoretic ones calculated by Eq. (17). Therefore, a conclusion can be drawn that the phases of *x*/*y*-polarized incident waves can be manipulated by *ax* and *ay*, respectively.

## **2.3 Design of multifunctional transmission PGMS**

Based on above unique property, it is easy to design a hyperbolic phase distribution on the multifunctional metasurface, which has the ability of polarization conversion and gain enhancement.


#### **Table 1.**

*The sizes and absolute phase shifts of the six distributed unit cells.*

**Figure 18.**

*(a) The supercells; (b) the designed one-dimensional phase gradient metasurface; and (c) the farfield results.*

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

*<sup>θ</sup>*<sup>t</sup> <sup>¼</sup> sin �<sup>1</sup> *<sup>λ</sup>*

incident waves.

*Modern Printed-Circuit Antennas*

**Table 1.**

**Figure 18.**

**56**

2π � 2π *np* 

To verify the performance of manipulating the *x*/*y*-polarized wave independently, one-dimensional metasurface with inverse linear phase gradient along *x* direction for *x*/*y*-polarized wave has been proposed in **Figure 17**. The proposed supercell is composed of six unit cells with the parameters demonstrated in **Table 1**. Phase gradients are assigned to +60° to �60° for *x*/*y*-polarized incident plane wave, respectively. *Φ<sup>x</sup>* and *Φ<sup>y</sup>* in **Table 1** represent the phase response for *x*/*y*-polarized

4 � 16 supercells are fixed as **Figure 18a** has shown. The supercell is perpendicularly illuminated by plane wave along *z* direction in CST Microwave Studio. And

Based on Eq. (17), the refracted angles for *x*/*y*-polarized incident wave can be calculated as 54.4°. And the refracted wave will deflect to �*x*/+*x* direction, respectively. The 3D farfields are calculated as shown in **Figure 18a**. Beam 2 and beam 1 are calculated under *x*/*y*-polarized plane wave illumination, respectively. To clearly show the refracted angles for *x*/*y*-polarized waves, the normalized farfield patterns in polar are depicted in **Figure 18b**. The simulated refracted angles are in good accordance with theoretic ones calculated by Eq. (17). Therefore, a conclusion can be drawn that the phases of *x*/*y*-polarized incident waves can be manipulated by *ax* and *ay*, respectively.

Based on above unique property, it is easy to design a hyperbolic phase distribution on the multifunctional metasurface, which has the ability of polarization

**Index** *n* **1 2 345 6** *ax* (mm) 3.8 3.75 3.64 3.52 3.1 2.53 *ay* (mm) 2.53 3.1 3.52 3.64 3.75 3.8 *Φ<sup>x</sup>* (deg) �704.3 �644.3 �584.3 �524.3 �464.3 �404.3 *Φ<sup>y</sup>* (deg) �404.3 �464.3 �524.3 �584.3 �644.3 �704.3

*(a) The supercells; (b) the designed one-dimensional phase gradient metasurface; and (c) the farfield results.*

open (add space) boundary condition is set along all directions.

**2.3 Design of multifunctional transmission PGMS**

*The sizes and absolute phase shifts of the six distributed unit cells.*

conversion and gain enhancement.

(17)

In order to efficiently convert the incident plane wave into a quasi-spherical wave, the phase *φ*(*m*, *n*) at unit cell location (*m*, *n*) should be carefully optimized, yielding the following phase distribution:

$$\rho(m,n) = \frac{2\pi}{\lambda} \left( \sqrt{\left(mp\right)^2 + \left(np\right)^2 + L^2} - L \right) + \rho(\mathbf{0}, \mathbf{0}) \tag{18}$$

where *p* is periodicity of unit cell and *L* is the focal length and *m* and *n* are the unit cell positions along *x* and *y* directions, respectively. Moreover, *φ*(0, 0) represents the phase at the origin unit cell (*m* = 0, *n* = 0). It is easy to convert the incident plane wave into quasi-spherical wave using the above metasurface. Moreover, we concentrate on designing a linear-to-circular polarization conversion metasurface according to the theory and unique feature described in the preceding section.

In order to realize the LTC conversion, the transmitted phase for *x*-polarized incident wave should have a phase difference of 90° with the *y*-polarized incident wave through each unit cell. In this chapter, we design a LTC conversion metasurface according to **Figure 14b**. Namely, *Arg T*ð Þ *xx mn* � *Arg Tyy* � � *mn*≈ � 90° should be satisfied, and a RHCP wave can be obtained. For *x*-polarized incident wave, the phase distribution can be denoted as

$$\operatorname{Arg}(T\_{\infty})\_{mn} - \operatorname{Arg}(T\_{\infty})\_{00} = \frac{2\pi}{\lambda} \left( \sqrt{\left( \left( mp \right)^2 + \left( np \right)^2 + L^2} \right)} - L \right) \tag{19}$$

For *y*-polarized incident wave, the phase distribution can be denoted as

$$\operatorname{Arg}\left(T\_{\mathcal{\mathcal{Y}}}\right)\_{\min} - \operatorname{Arg}\left(T\_{\mathcal{\mathcal{Y}}}\right)\_{00} = \frac{2\pi}{\lambda} \left(\sqrt{\left(\left(mp\right)^2 + \left(np\right)^2 + L^2\right)} - L\right) \tag{20}$$

To achieve *Arg T*ð Þ *xx mn* � *Arg Tyy* � �*mn*<sup>≈</sup> � 90° simply, the phase difference *Arg T*ð Þ *xx* <sup>00</sup> � *Arg Tyy* � � <sup>00</sup>≈ � 90° should be satisfied for *x*/*y*-polarized incident waves at origin point *φ*(0, 0).

Based on above analysis, the multifunctional transmission metasurface is composed of 15 � 15 unit cells. The working frequency and focal length are *f* = 15 GHz and *L* = 30 mm, respectively. A patch antenna, operating from 14.5 to 15.3 GHz, is placed on the focal point to be a feed source. By insertion of *p* = 4.1 mm, *λ* = 20 mm,

**Figure 19.** *Absolute phase distributions for (a) x polarization and (b) y polarization.*

*L* = 30 mm, and *Arg*(*Txx*)00 = 704.3° into Eqs. (19) and (20), the phase distribution for the *x*/*y* polarization waves is calculated as **Figure 19**. Finally, the proposed multifunctional transmission metasurface is depicted in **Figure 20a**.

obvious that the pencil-beam 3D radiation pattern is obtained and realized gain has

Furthermore, the near-field electric field distributions in *xoz* and *yoz* planes have been depicted in **Figure 22**. The incident wave has been converted into near-plane wave through the proposed metasurface. The simulated result is in line with our

Lastly, a sample is fabricated and measured in a microwave anechoic chamber as

shown in **Figure 23**. And simulated and measured 2D radiation patterns of lens antenna are plotted in **Figure 24**. As shown in **Figure 24**, the co-polarization and cross-polarization of simulation and measurement are plotted in two orthogonal planes. And the simulated results are in good accordance with the measured ones. Compared with patch antenna, the radiation patterns of proposed multifunctional antenna are more directional. The measured peak gain of patch antenna and proposed multifunctional antenna is about 5.9 and 16.9 dB at 15 GHz, respectively. And the realized gain has been enhanced with 11 dB at 15 GHz, and calculated aperture efficiency is about 41.2%. Comparing co-polarization with cross-polarization at

*θ* = 0°, we find that the isolation is better than 17 dB.

*Electric field distributions in (a) xoz and (b) yoz plane at 15 GHz.*

*The photographs of (a) PGMS top view and (b) lens antenna.*

been enhanced remarkably.

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

expectation.

**Figure 22.**

**Figure 23.**

**59**

To verify the proposed multifunctional transmission metasurface's function of focusing EM wave at *L* = 30 mm, the metasurface is simulated in CST. As shown in **Figure 20a**, the metasurface is normally illuminated by a plane wave with *θ* = 45° along the *x* axis, and a curve is put along *z* axis to evaluate power field on curve to calculate the focal point. Besides, a power flow monitor is set at 15 GHz. It is obvious that the plane wave is focused to a pink focal spot and the maximum power field is at *L* = 30 mm.

## **2.4 High-gain lens antenna design**

A designed patch antenna, operating at 15 GHz, is put at the focal point of the multifunctional metasurface. As **Figure 20** has shown, the polarization of EM wave emitted by the feed source antenna has an angle of *θ* = 45° along the *x* axis. To clearly show the function of proposed lens antenna, simulated 3D radiation pattern at 15 GHz and measured S11 of the lens antenna are plotted in **Figure 21**. It is

#### **Figure 20.**

*(a) The multifunctional transmission PGMS and simulated conditions and (b) power field distribution in xoz and yoz planes and power field distribution along z axis.*

**Figure 21.** *The simulated 3D radiation pattern and measured S11 of lens antenna.*

## *High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

*L* = 30 mm, and *Arg*(*Txx*)00 = 704.3° into Eqs. (19) and (20), the phase distribution for the *x*/*y* polarization waves is calculated as **Figure 19**. Finally, the proposed

To verify the proposed multifunctional transmission metasurface's function of focusing EM wave at *L* = 30 mm, the metasurface is simulated in CST. As shown in **Figure 20a**, the metasurface is normally illuminated by a plane wave with *θ* = 45° along the *x* axis, and a curve is put along *z* axis to evaluate power field on curve to calculate the focal point. Besides, a power flow monitor is set at 15 GHz. It is obvious that the plane wave is focused to a pink focal spot and the maximum power

A designed patch antenna, operating at 15 GHz, is put at the focal point of the multifunctional metasurface. As **Figure 20** has shown, the polarization of EM wave emitted by the feed source antenna has an angle of *θ* = 45° along the *x* axis. To clearly show the function of proposed lens antenna, simulated 3D radiation pattern at 15 GHz and measured S11 of the lens antenna are plotted in **Figure 21**. It is

*(a) The multifunctional transmission PGMS and simulated conditions and (b) power field distribution in xoz*

multifunctional transmission metasurface is depicted in **Figure 20a**.

field is at *L* = 30 mm.

*Modern Printed-Circuit Antennas*

**Figure 20.**

**Figure 21.**

**58**

**2.4 High-gain lens antenna design**

*and yoz planes and power field distribution along z axis.*

*The simulated 3D radiation pattern and measured S11 of lens antenna.*

obvious that the pencil-beam 3D radiation pattern is obtained and realized gain has been enhanced remarkably.

Furthermore, the near-field electric field distributions in *xoz* and *yoz* planes have been depicted in **Figure 22**. The incident wave has been converted into near-plane wave through the proposed metasurface. The simulated result is in line with our expectation.

Lastly, a sample is fabricated and measured in a microwave anechoic chamber as shown in **Figure 23**. And simulated and measured 2D radiation patterns of lens antenna are plotted in **Figure 24**. As shown in **Figure 24**, the co-polarization and cross-polarization of simulation and measurement are plotted in two orthogonal planes. And the simulated results are in good accordance with the measured ones. Compared with patch antenna, the radiation patterns of proposed multifunctional antenna are more directional. The measured peak gain of patch antenna and proposed multifunctional antenna is about 5.9 and 16.9 dB at 15 GHz, respectively. And the realized gain has been enhanced with 11 dB at 15 GHz, and calculated aperture efficiency is about 41.2%. Comparing co-polarization with cross-polarization at *θ* = 0°, we find that the isolation is better than 17 dB.

**Figure 22.**

*Electric field distributions in (a) xoz and (b) yoz plane at 15 GHz.*

**Figure 23.** *The photographs of (a) PGMS top view and (b) lens antenna.*

Moreover, the simulated and measured axial ratios (AR)(*θ* = 0°) are plotted in **Figure 25**. The simulated and measured realized gain of lens antenna and patch antenna is described in **Figure 25**. All the simulated and measured results are in good accordance. It is obvious that the gain enhancement is about 11 dB at 15 GHz. Besides, the axial ratio bandwidth for AR < 3 dB ranges from 14.5 to 15.3 GHz with the fractional bandwidth 5.3%. And we find that the 1-dB gain bandwidth is 5.3%

In this chapter, we have reviewed our recent efforts in utilizing metasurface to

The authors would like to express their gratitude to anonymous reviewers for their helpful comments and China North Electronic Engineering Research Institute for the fabrication. This work was supported by the National Natural Science

Haisheng Hou, Haipeng Li\*, Guangming Wang\*, Tong Cai, Xiangjun Gao

Microwave Laboratory, Air Force Engineering University, Xi'an, China

\*Address all correspondence to: s\_lihaipeng@sina.cn and wgming01@sina.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

(14.5–15.3 GHz), which agrees well with the axial ratio bandwidth.

enhance the performance of the conventional antenna. For the reflected metasurface, we propose a new broadband, single-layered reflected focusing metasurface, and take it into application for high-gain planar antenna. The metasurface exhibits good focusing phenomenon from 15 to 22 GHz. Both simulation and measured results show that the peak gain of planar antenna has been averagely enhanced by 16 and 1 dB gain bandwidth which is from 15 to 22 GHz, while for the transmitted metasurface, a novel multifunctional metasurface combining linear-to-circular polarization conversion and EM waves focusing has been proposed and applied to designed a high-gain lens antenna. A RHCP lens antenna is simulated and measured. The measured results show that the lens antenna can convert LP waves into RHCP waves at 15 GHz. The 3-dB axial ratio bandwidth is 5.3%. Realized gain at 15 GHz is 16.9 dB, corresponding to aperture efficiency of 41.2%. These above metasurface antennas not only open up a new route for the applications of focusing metasurfaces in microwave band but also afford an

alternative for high-performance antennas.

Foundation of China (Grant Nos. 61372034).

provided the original work is properly cited.

**Acknowledgements**

**Author details**

and Wenlong Guo

**61**

**Conclusions**

*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

**Figure 24.** *2D radiation patterns at 15 GHz. (a) xoy plane and (b) yoz plane.*

**Figure 25.** *Simulated and measured realized gain for patch antenna and lens antenna and axial ratio.*

## *High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

Moreover, the simulated and measured axial ratios (AR)(*θ* = 0°) are plotted in **Figure 25**. The simulated and measured realized gain of lens antenna and patch antenna is described in **Figure 25**. All the simulated and measured results are in good accordance. It is obvious that the gain enhancement is about 11 dB at 15 GHz. Besides, the axial ratio bandwidth for AR < 3 dB ranges from 14.5 to 15.3 GHz with the fractional bandwidth 5.3%. And we find that the 1-dB gain bandwidth is 5.3% (14.5–15.3 GHz), which agrees well with the axial ratio bandwidth.

## **Conclusions**

In this chapter, we have reviewed our recent efforts in utilizing metasurface to enhance the performance of the conventional antenna. For the reflected metasurface, we propose a new broadband, single-layered reflected focusing metasurface, and take it into application for high-gain planar antenna. The metasurface exhibits good focusing phenomenon from 15 to 22 GHz. Both simulation and measured results show that the peak gain of planar antenna has been averagely enhanced by 16 and 1 dB gain bandwidth which is from 15 to 22 GHz, while for the transmitted metasurface, a novel multifunctional metasurface combining linear-to-circular polarization conversion and EM waves focusing has been proposed and applied to designed a high-gain lens antenna. A RHCP lens antenna is simulated and measured. The measured results show that the lens antenna can convert LP waves into RHCP waves at 15 GHz. The 3-dB axial ratio bandwidth is 5.3%. Realized gain at 15 GHz is 16.9 dB, corresponding to aperture efficiency of 41.2%. These above metasurface antennas not only open up a new route for the applications of focusing metasurfaces in microwave band but also afford an alternative for high-performance antennas.

## **Acknowledgements**

The authors would like to express their gratitude to anonymous reviewers for their helpful comments and China North Electronic Engineering Research Institute for the fabrication. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61372034).

## **Author details**

**Figure 24.**

*Modern Printed-Circuit Antennas*

**Figure 25.**

**60**

*2D radiation patterns at 15 GHz. (a) xoy plane and (b) yoz plane.*

*Simulated and measured realized gain for patch antenna and lens antenna and axial ratio.*

Haisheng Hou, Haipeng Li\*, Guangming Wang\*, Tong Cai, Xiangjun Gao and Wenlong Guo Microwave Laboratory, Air Force Engineering University, Xi'an, China

\*Address all correspondence to: s\_lihaipeng@sina.cn and wgming01@sina.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

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[2] Li HP, Wang GM, Cai T, Liang JG, Gao XJ. Phase- and amplitude-control metasurfaces for antenna main-lobe and sidelobe manipulations. IEEE Transactions on Antennas and Propagation. 2018;**66**(10):5121-5129

[3] Biswas SR, Gutierrez CE, Nemilentsau A, Lee IH, Oh SH, Avouris P, et al. Tunable graphene metasurface reflectarray for cloaking, illusion, and focusing. Physical Review Applied. 2018;**9**(3):034021

[4] Liang JJ, Huang GL, Zhao JN, Gao ZJ, Yuan T. Wideband phase-gradient metasurface antenna with focused beams. IEEE Access. 2019;**7**:20767-20772

[5] Katare KK, Chandravanshi S, Biswas A, Akhtar MJ. Realization of split beam antenna using transmission-type coding metasurface and planar lens. IEEE Transactions on Antennas and Propagation. 2019;**67**(4):2074-2084

[6] Yang WC, Gu LZ, Che WQ, Meng Q, Xue Q, Wan C. A novel steerable dual-beam metasurface antenna based on controllable feeding mechanism. IEEE Transactions on Antennas and Propagation. 2019;**67**(2): 784-793

[7] Yu NF, Genevet P, Kats MA, Aieta F, Tetienne J-P, Capasso F, et al. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science. 2011;**334**:333-337

[8] Wong AMH, Eleftheriades GV. Perfect anomalous reflection with a bipartite Huygens' metasurface. Physical Review X. 2018;**8**(1):011036 [9] Xu WK, Zhang M, Ning JY, Wang W, Yang TZ. Anomalous refraction control of mode-converted elastic wave using compact notch-structured metasurface. Material Research Express. 2019;**6**(6): 065802

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*High Performance Metasurface Antennas DOI: http://dx.doi.org/10.5772/intechopen.88395*

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[17] Ratni B, de Lustrac A, Plau GP, Burokur SN. Electronic control of linear-to-circular polarization conversion using a reconfigurable metasurface. Applied Physics Letters.

[18] Wang W, Guo ZY, Ran LL, Sun YX,

[19] Menzel C, Rockstuhl C, Lederer F. Advanced Jones calculus for the

classification of periodic metamaterials. Physical Review A. 2010;**82**:053811

Shen F, Li Y, et al. Polarizationindependent characteristics of the metasurfaces with the symmetrical axis's orientation angle of 45° or 135°. Journal of Optics. 2016;**18**:035007

[16] Khan MI, Khalid Z, Tahir FA. Linear and circular-polarization conversion in X-band using anisotropic metasurface.

**17**(8):1459-1463

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[10] Asadpor L, Sharifi G, Rezvani M. Design of a high-gain wideband antenna using double-layer metasurface. Microwave and Optical Technology Letters. 2019;**61**(4):1001-1010

[11] Ling YH, Huang LR, Hong W, Liu TJ, Jing L, Liu WB, et al. Polarization-switchable and wavelength-controllable multifunctional metasurface for focusing and surface-plasmon-polariton wave excitation. Optics Express. 2017;**25**(24): 29812-29821

[12] Meng YY, Ma H, Li YF, Feng MD, Wang JF, Li ZQ, et al. Spoof surface plasmon polaritons excitation and wavefront control by Pancharatnam-Berry phase manipulating metasurface. Journal of Physics D: Applied Physics. 2018;**51**(21):215302

[13] Lin BQ, Guo JX, Chu P, Huo WJ, Xing Z, Huang BG, et al. Multiple-band linear-polarization conversion and circular polarization in reflection mode using a symmetric anisotropic metasurface. Physical Review Applied. 2018;**9**:024038

[14] Jia YT, Liu Y, Zhang WB, Wang J, Wang YZ, Gong SX, et al. Ultrawideband metasurface with linear-tocircular polarization conversion of an electromagnetic wave. Optical Materials Express. 2018;**8**(3):597-604

[15] Zheng Q, Guo CJ, Ding J. Wideband metasurface-based reflective polarization converter for linear-tolinear and linear-to-circular polarization conversion. IEEE Antennas and

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Wireless Propagation Letters. 2018; **17**(8):1459-1463

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3706-3711

[1] Li HP, Wang GM, Gao XJ, Liang JG, Hou HS. Novel metasurface for dualmode and dual flat high-gain antenna application. IEEE Transactions on Antennas and Propagation. 2018;**66**(7):

*Modern Printed-Circuit Antennas*

[9] Xu WK, Zhang M, Ning JY, Wang W, Yang TZ. Anomalous refraction control of mode-converted

Material Research Express. 2019;**6**(6):

[10] Asadpor L, Sharifi G, Rezvani M. Design of a high-gain wideband antenna

using double-layer metasurface. Microwave and Optical Technology Letters. 2019;**61**(4):1001-1010

[11] Ling YH, Huang LR, Hong W, Liu TJ, Jing L, Liu WB, et al. Polarization-switchable and wavelength-controllable multi-

surface-plasmon-polariton wave excitation. Optics Express. 2017;**25**(24):

functional metasurface for focusing and

[12] Meng YY, Ma H, Li YF, Feng MD, Wang JF, Li ZQ, et al. Spoof surface plasmon polaritons excitation and wavefront control by Pancharatnam-Berry phase manipulating metasurface. Journal of Physics D: Applied Physics.

[13] Lin BQ, Guo JX, Chu P, Huo WJ, Xing Z, Huang BG, et al. Multiple-band linear-polarization conversion and circular polarization in reflection mode

metasurface. Physical Review Applied.

[14] Jia YT, Liu Y, Zhang WB, Wang J, Wang YZ, Gong SX, et al. Ultrawideband metasurface with linear-tocircular polarization conversion of an electromagnetic wave. Optical Materials

[15] Zheng Q, Guo CJ, Ding J. Wideband

using a symmetric anisotropic

Express. 2018;**8**(3):597-604

metasurface-based reflective polarization converter for linear-tolinear and linear-to-circular polarization

conversion. IEEE Antennas and

elastic wave using compact notch-structured metasurface.

065802

29812-29821

2018;**51**(21):215302

2018;**9**:024038

[2] Li HP, Wang GM, Cai T, Liang JG, Gao XJ. Phase- and amplitude-control metasurfaces for antenna main-lobe and

sidelobe manipulations. IEEE Transactions on Antennas and Propagation. 2018;**66**(10):5121-5129

[3] Biswas SR, Gutierrez CE, Nemilentsau A, Lee IH, Oh SH, Avouris P, et al. Tunable graphene metasurface reflectarray for cloaking, illusion, and focusing. Physical Review

Applied. 2018;**9**(3):034021

[5] Katare KK, Chandravanshi S,

[6] Yang WC, Gu LZ, Che WQ, Meng Q, Xue Q, Wan C. A novel steerable dual-beam metasurface antenna based on controllable feeding mechanism. IEEE Transactions on Antennas and Propagation. 2019;**67**(2):

784-793

**62**

[4] Liang JJ, Huang GL, Zhao JN, Gao ZJ, Yuan T. Wideband phase-gradient metasurface antenna with focused beams. IEEE Access. 2019;**7**:20767-20772

Biswas A, Akhtar MJ. Realization of split beam antenna using transmission-type coding metasurface and planar lens. IEEE Transactions on Antennas and Propagation. 2019;**67**(4):2074-2084

[7] Yu NF, Genevet P, Kats MA, Aieta F, Tetienne J-P, Capasso F, et al. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science. 2011;**334**:333-337

[8] Wong AMH, Eleftheriades GV. Perfect anomalous reflection with a bipartite Huygens' metasurface. Physical Review X. 2018;**8**(1):011036 [16] Khan MI, Khalid Z, Tahir FA. Linear and circular-polarization conversion in X-band using anisotropic metasurface. Scientific Reports. 2019;**9**:4552

[17] Ratni B, de Lustrac A, Plau GP, Burokur SN. Electronic control of linear-to-circular polarization conversion using a reconfigurable metasurface. Applied Physics Letters. 2017;**111**(21):214101

[18] Wang W, Guo ZY, Ran LL, Sun YX, Shen F, Li Y, et al. Polarizationindependent characteristics of the metasurfaces with the symmetrical axis's orientation angle of 45° or 135°. Journal of Optics. 2016;**18**:035007

[19] Menzel C, Rockstuhl C, Lederer F. Advanced Jones calculus for the classification of periodic metamaterials. Physical Review A. 2010;**82**:053811

**Chapter 4**

**Abstract**

Fractal Antennas for Wireless

*Amer T. Abed, Mahmood J. Abu-AlShaer and Aqeel M. Jawad*

When the length of the antenna is less than a quarter of the wavelength of the operating frequency, good radiation properties are difficult to obtain. However, size limitations can be overcome in this case using a fractal geometry antenna. The shape is repeated in a limited size such that the total length of the antenna is increased to match, for example, half of the wavelength of the corresponding desired frequency. Many fractal geometries, e.g., the tree, Koch, Minkowski, and Hilbert fractals, are available. This chapter describes the details of designing, simulations, and experimental measurements of fractal antennas. Based on dimensional geometry in terms of desired frequency bands, the characteristics of each iteration are studied carefully to improve the process of designing the antennas. In depth, the surface current distribution is investigated and analyzed to enhance the circular polarization radiation and axial ratio bandwidth (ARBW). Both, simulation and experimental, results are discussed and compared. Two types of fractal antennas are proposed. The first proposed fractal antenna has a new structure configured via a five-stage process. The second proposed fractal antenna has a low profile, wherein the configuration of

Fractal means broken or irregularly fragmented and refers to a family of complex shapes that possess an inherent self-similarity in their geometrical structures. Good radiation properties are difficult to obtain when the length of the antenna is less than a quarter of the wavelength for the operating frequency. However, size limitations can be overcome in this case using a fractal geometry antenna. The shape is repeated in a limited size such that the total length of the antenna is increased to match, for example, half of the wavelength of the corresponding desired frequency. Many fractal geometries, such as tree, Koch, Minkowski, and Hilbert fractals, are used in designing antennas [1]. But through using a fractal geometry antenna, where the shape is repeated in a limited size, in a way that increases the total length of the antenna to match, for example, half of the wavelength of the corresponding desired frequency, the size limitations can be overcome in this case. Many fractal geometries such as the tree, Koch, Minkowski, and Hilbert fractals are used in

There are many geometries used in designing fractal antennas such as: Fractal slot [2], Giuseppe Peano Fractal Geometries [3], Fractal loop [4], Fractal Cantor [5],

Communications

the antenna was based on three iterations.

**1. Introduction**

designing this type of antenna.

**65**

**Keywords:** fractal antenna, compact size, circular polarization

## **Chapter 4**

## Fractal Antennas for Wireless Communications

*Amer T. Abed, Mahmood J. Abu-AlShaer and Aqeel M. Jawad*

## **Abstract**

When the length of the antenna is less than a quarter of the wavelength of the operating frequency, good radiation properties are difficult to obtain. However, size limitations can be overcome in this case using a fractal geometry antenna. The shape is repeated in a limited size such that the total length of the antenna is increased to match, for example, half of the wavelength of the corresponding desired frequency. Many fractal geometries, e.g., the tree, Koch, Minkowski, and Hilbert fractals, are available. This chapter describes the details of designing, simulations, and experimental measurements of fractal antennas. Based on dimensional geometry in terms of desired frequency bands, the characteristics of each iteration are studied carefully to improve the process of designing the antennas. In depth, the surface current distribution is investigated and analyzed to enhance the circular polarization radiation and axial ratio bandwidth (ARBW). Both, simulation and experimental, results are discussed and compared. Two types of fractal antennas are proposed. The first proposed fractal antenna has a new structure configured via a five-stage process. The second proposed fractal antenna has a low profile, wherein the configuration of the antenna was based on three iterations.

**Keywords:** fractal antenna, compact size, circular polarization

## **1. Introduction**

Fractal means broken or irregularly fragmented and refers to a family of complex shapes that possess an inherent self-similarity in their geometrical structures. Good radiation properties are difficult to obtain when the length of the antenna is less than a quarter of the wavelength for the operating frequency. However, size limitations can be overcome in this case using a fractal geometry antenna. The shape is repeated in a limited size such that the total length of the antenna is increased to match, for example, half of the wavelength of the corresponding desired frequency. Many fractal geometries, such as tree, Koch, Minkowski, and Hilbert fractals, are used in designing antennas [1]. But through using a fractal geometry antenna, where the shape is repeated in a limited size, in a way that increases the total length of the antenna to match, for example, half of the wavelength of the corresponding desired frequency, the size limitations can be overcome in this case. Many fractal geometries such as the tree, Koch, Minkowski, and Hilbert fractals are used in designing this type of antenna.

There are many geometries used in designing fractal antennas such as: Fractal slot [2], Giuseppe Peano Fractal Geometries [3], Fractal loop [4], Fractal Cantor [5], Minkowski Fractal [6], Koch Fractal [7], H-Fractal [8], Sierpinski gasket arrangement [9], Fern Fractal leaf [10], Mandelbrot Fractal antenna [11], Amer fractal slot [12], Sunflower Fractal [13], Flame Fractal [14] and Butterfly Structure [15].

## **2. Compact fractal antenna**

One of the most widely used structures in fractal antennas is Sierpinski gasket [16]; it consists of equilateral triangles. There are two ways to build this structure, either by the decomposition method or by a multiple copy method. In this research, the second method is used in designing the fractal antenna; **Figure 1** represents this method.

At the first iteration, the structure made two copies of the same triangle in the 0th iteration, one of them located on its side while the other located above them. In the second iteration the same process is repeated, but with all first iteration structure. So the dimensions of the next iteration increased by factor 3 compared with the dimensions of the previous iteration. The above transformation of the triangle to generate any order of iterations can be represented by the mathematical formula [16]:

$$
\mathcal{W} \begin{bmatrix} \mathbf{x} \\ \mathbf{y} \end{bmatrix} = \begin{bmatrix} r\cos\theta & -s\cos\mathcal{Q} \\ r\sin\theta & s\sin\mathcal{Q} \end{bmatrix} \begin{bmatrix} \mathbf{x} \\ \mathbf{y} \end{bmatrix} + \begin{bmatrix} \mathbf{x}\_0 \\ \mathbf{y}\_0 \end{bmatrix} \tag{1}
$$

where *r* and *s* are the scale factor, *θ* and ∅ are the rotation angles, and *x*<sup>0</sup> and *y*<sup>0</sup> are the amounts of translation. If the factors *r*, *s* are either reductions or magnifications, the transformation process is called self-affine, while, if *r* = *s* and *θ* = ∅, the transformation is called self-similar.

The structure of the proposed antenna is new; the initiator is a square patch as shown in **Figure 2a**; the two arms of the patch are equal and unity, i.e., *x* = *y* = 1. In 0th iteration, four symmetrical slots are cut in the square patch as shown in **Figure 2b**. The modified patch (**Figure 2c**) is configured by cutting increasable slips to change the dimensions of the arms at the corners in a way to configure asymmetrical corner dimensions:

$$W\begin{bmatrix}\boldsymbol{\chi} \\ \boldsymbol{\chi}\end{bmatrix} = \begin{bmatrix} r\cos\theta & -s\cos\mathcal{Q} \\ r\sin\theta & s\sin\mathcal{Q} \end{bmatrix} \begin{bmatrix} \boldsymbol{\chi} \\ \boldsymbol{\chi} \end{bmatrix} + \begin{bmatrix} \boldsymbol{\chi}\_0 \\ \boldsymbol{\chi}\_0 \end{bmatrix} \tag{2}$$

The upper arm in **Figure 2c** has total length 0.43*x* + 0.3*y* + 0.1*x* + 0.16*y* + 0.33*x*

Firstly, different electrical lengths of the arms generate many resonant frequen-

Secondly, different lengths of both sides of each corner, for example, the lengths of the two sides of the right-upper corner, are 0.35*y* and 0.33*x*; this difference in lengths is useful to generate two orthogonal modes with phase shift 90° which are

0.39 = 1.48*x*. The lower arm length is 0.41*x* + 0.24*y* + 0.22*y* + 0.1*x* + 0.35*x* = 1.32*x*. The right arm length is 0.37*y* + 0.2*x* + 0.1*y* + 0.18*x* + 0.35*y* = 1.2*x*. So, each arm in the square patch (**Figure 2a**) has unity length (*x* = *y*), while the lengths of the arms in the modified patch expand to 1.32*x*, 1.4*x*, and 1.2*x*. This expedition gives two

=1.32*x*, where *x* = *y*. The left arm's length is 0.45*y* + 0.28*x* + 0.1*y* + 0.26 +

*Configuration of fractal antenna. (a) Initiator patch. (b) 0th iteration. (c) Modified patch.*

additional properties in designing the fractal antenna.

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

**Figure 2.**

**67**

cies which can be integrated to have wide operating bands.

**Figure 1.** *Multiple copy approach of Sierpinski gasket arrangement.*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

Minkowski Fractal [6], Koch Fractal [7], H-Fractal [8], Sierpinski gasket arrangement [9], Fern Fractal leaf [10], Mandelbrot Fractal antenna [11], Amer fractal slot [12], Sunflower Fractal [13], Flame Fractal [14] and Butterfly Structure [15].

One of the most widely used structures in fractal antennas is Sierpinski gasket [16]; it consists of equilateral triangles. There are two ways to build this structure, either by the decomposition method or by a multiple copy method. In this research, the second method is used in designing the fractal antenna; **Figure 1** represents this

At the first iteration, the structure made two copies of the same triangle in the 0th iteration, one of them located on its side while the other located above them. In the second iteration the same process is repeated, but with all first iteration structure. So the dimensions of the next iteration increased by factor 3 compared with the dimensions of the previous iteration. The above transformation of the triangle to generate any order of iterations can be represented by the mathematical

> <sup>¼</sup> *r cos<sup>θ</sup>* �*s cos* <sup>∅</sup> *r sinθ s sin* ∅ � � *x*

0th iteration, four symmetrical slots are cut in the square patch as shown in **Figure 2b**. The modified patch (**Figure 2c**) is configured by cutting increasable slips to change the dimensions of the arms at the corners in a way to configure

> <sup>¼</sup> *r cos<sup>θ</sup>* �*s cos* <sup>∅</sup> *r sinθ s sin* ∅ � � *x*

where *r* and *s* are the scale factor, *θ* and ∅ are the rotation angles, and *x*<sup>0</sup> and *y*<sup>0</sup> are the amounts of translation. If the factors *r*, *s* are either reductions or magnifications, the transformation process is called self-affine, while, if *r* = *s* and *θ* = ∅, the

The structure of the proposed antenna is new; the initiator is a square patch as shown in **Figure 2a**; the two arms of the patch are equal and unity, i.e., *x* = *y* = 1. In

*y*

*y*

þ

*x*0 *y*0

" #

" #

þ

*x*0 *y*0

(1)

(2)

" #

" #

**2. Compact fractal antenna**

*Modern Printed-Circuit Antennas*

*W x y*

transformation is called self-similar.

asymmetrical corner dimensions:

*W x y*

*Multiple copy approach of Sierpinski gasket arrangement.*

" #

" #

method.

formula [16]:

**Figure 1.**

**66**

**Figure 2.** *Configuration of fractal antenna. (a) Initiator patch. (b) 0th iteration. (c) Modified patch.*

The upper arm in **Figure 2c** has total length 0.43*x* + 0.3*y* + 0.1*x* + 0.16*y* + 0.33*x* =1.32*x*, where *x* = *y*. The left arm's length is 0.45*y* + 0.28*x* + 0.1*y* + 0.26 + 0.39 = 1.48*x*. The lower arm length is 0.41*x* + 0.24*y* + 0.22*y* + 0.1*x* + 0.35*x* = 1.32*x*. The right arm length is 0.37*y* + 0.2*x* + 0.1*y* + 0.18*x* + 0.35*y* = 1.2*x*. So, each arm in the square patch (**Figure 2a**) has unity length (*x* = *y*), while the lengths of the arms in the modified patch expand to 1.32*x*, 1.4*x*, and 1.2*x*. This expedition gives two additional properties in designing the fractal antenna.

Firstly, different electrical lengths of the arms generate many resonant frequencies which can be integrated to have wide operating bands.

Secondly, different lengths of both sides of each corner, for example, the lengths of the two sides of the right-upper corner, are 0.35*y* and 0.33*x*; this difference in lengths is useful to generate two orthogonal modes with phase shift 90° which are

very important requirements to create circularly polarized radiation. The modified patches will be arranged in a cascade arrangement to increase the total electrical length of the antenna to generate resonant frequencies have wave lengths ≫ of the physical length of the antenna. **Figure 4** represents the arrangement of the cascade modified patch (two symmetrical structures). According to Eq. (1), the affine transformations will be:

$$W\_2 \begin{bmatrix} \varkappa \\ \varkappa \end{bmatrix} = \begin{bmatrix} \mathbf{0.25} & \mathbf{0.25} \\ \mathbf{0} & \mathbf{0} \end{bmatrix} \begin{bmatrix} \varkappa \\ \varkappa \end{bmatrix} + \begin{bmatrix} \mathbf{0} \\ \mathbf{6.375} \end{bmatrix} \tag{3}$$

If the *x*-axis is the bottom of the left modified patch and *y*-axis passes through the center of the left modified patch in **Figure 3**, *W*<sup>1</sup> configures by adding a half size of the modified patch in **Figure 3** to both structures (left and right sides). The dotted yellow line in **Figure 3** is on the *y*-axis and passes through all centers (black points) of the transformation structures (*W*1,*W*<sup>2</sup> and *W*3), so the scale factors are (*r* = *s* = 0.5), the rotation angles are *θ* ¼ ∅ ¼ 0, and the translation factors are (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 4*:*25 ):

$$
\begin{bmatrix} \mathcal{W}\_1 \\ \mathcal{Y} \end{bmatrix} = \begin{bmatrix} \mathbf{0.5} & \mathbf{0.5} \\ \mathbf{0} & \mathbf{0} \end{bmatrix} \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{y} \end{bmatrix} + \begin{bmatrix} \mathbf{0} \\ \mathbf{4.25} \end{bmatrix} \tag{4}
$$

*W*<sup>2</sup> *x y*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

> *W*<sup>3</sup> *x y*

" #

(*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 7*:*4375):

*Process of fractal antenna configuration.*

**Figure 4.**

switching the inputs.

**69**

" #

<sup>¼</sup> <sup>0</sup>*:*25 0*:*<sup>25</sup> 0 0 � � *<sup>x</sup>*

<sup>¼</sup> <sup>0</sup>*:*125 0*:*<sup>125</sup> 0 0 � � *<sup>x</sup>*

*y*

*y*

þ

" #

And for *W*3, the scale factors are (*r* = *s* = 0.1250) and the translation factors are

The antenna had dual operating bands that meet the specifications of the Wi-Fi and WiMAX applications. The structure of the antenna was carefully studied and analyzed so as to achieve a diversity of circular polarization (RHCP and LHCP) by

The proposed antenna consisted of two symmetrical fractal structures as shown in **Figure 4**. The radiated plate is etched on a FR-4 substrate with εr = 4.3, tan δ = 0.027, and compact size of 18 � <sup>18</sup> � 0.8 mm3, while the dimensions of the ground plate are 18 mm � 14.5 mm. **Figure 4** shows the initiator; it is a square patch with dimensions of (*Lo*= *Wo* = 8.5 mm). The square patch is modified by cutting equal slots (0.1*Lo* = 0.1*Wo*) in the middle of each arm and then modifying the dimensions of the arms at the corners by cutting increasable slips to change the dimensions of the arms at the corners in a way to configure asymmetrical corners, so the dimensions of each corner are not matching the others to generate different resonant frequencies that collected together to have wide impedance bandwidth. This

þ

0

0

<sup>6</sup>*:*<sup>375</sup> " # (5)

<sup>7</sup>*:*<sup>4375</sup> " # (6)

" #

While *W*<sup>2</sup> is done by adding quarter size of the modified patch, the scale factors are (*r* = *s* = 0.25), there are no rotation angles, and the translation factors are (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 6*:*375):

**Figure 3.** *Fractal dual-input antenna.*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

very important requirements to create circularly polarized radiation. The modified patches will be arranged in a cascade arrangement to increase the total electrical length of the antenna to generate resonant frequencies have wave lengths ≫ of the physical length of the antenna. **Figure 4** represents the arrangement of the cascade modified patch (two symmetrical structures). According to Eq. (1), the affine

*y*

*y*

While *W*<sup>2</sup> is done by adding quarter size of the modified patch, the scale factors

þ

0 4*:*25

" #

" #

If the *x*-axis is the bottom of the left modified patch and *y*-axis passes through the center of the left modified patch in **Figure 3**, *W*<sup>1</sup> configures by adding a half size of the modified patch in **Figure 3** to both structures (left and right sides). The dotted yellow line in **Figure 3** is on the *y*-axis and passes through all centers (black points) of the transformation structures (*W*1,*W*<sup>2</sup> and *W*3), so the scale factors are (*r* = *s* = 0.5), the rotation angles are *θ* ¼ ∅ ¼ 0, and the translation factors are

þ

0 6*:*375

(3)

(4)

" #

" #

<sup>¼</sup> <sup>0</sup>*:*25 0*:*<sup>25</sup> 0 0 � � *x*

<sup>¼</sup> <sup>0</sup>*:*5 0*:*<sup>5</sup> 0 0 � � *x*

are (*r* = *s* = 0.25), there are no rotation angles, and the translation factors are

transformations will be:

*Modern Printed-Circuit Antennas*

(*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 4*:*25 ):

(*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 6*:*375):

**Figure 3.**

**68**

*Fractal dual-input antenna.*

*W*<sup>2</sup> *x y*

> *W*<sup>1</sup> *x y*

" #

" #

**Figure 4.** *Process of fractal antenna configuration.*

$$W\_2 \begin{bmatrix} \mathbf{x} \\ \mathbf{y} \end{bmatrix} = \begin{bmatrix} \mathbf{0}.25 & \mathbf{0}.25 \\ \mathbf{0} & \mathbf{0} \end{bmatrix} \begin{bmatrix} \mathbf{x} \\ \mathbf{y} \end{bmatrix} + \begin{bmatrix} \mathbf{0} \\ \mathbf{6.375} \end{bmatrix} \tag{5}$$

And for *W*3, the scale factors are (*r* = *s* = 0.1250) and the translation factors are (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 7*:*4375):

$$
\begin{bmatrix} \mathbf{w} \\ \mathbf{y} \end{bmatrix} = \begin{bmatrix} \mathbf{0.125} & \mathbf{0.125} \\ \mathbf{0} & \mathbf{0} \end{bmatrix} \begin{bmatrix} \mathbf{x} \\ \mathbf{y} \end{bmatrix} + \begin{bmatrix} \mathbf{0} \\ \mathbf{7.4375} \end{bmatrix} \tag{6}
$$

The antenna had dual operating bands that meet the specifications of the Wi-Fi and WiMAX applications. The structure of the antenna was carefully studied and analyzed so as to achieve a diversity of circular polarization (RHCP and LHCP) by switching the inputs.

The proposed antenna consisted of two symmetrical fractal structures as shown in **Figure 4**. The radiated plate is etched on a FR-4 substrate with εr = 4.3, tan δ = 0.027, and compact size of 18 � <sup>18</sup> � 0.8 mm3, while the dimensions of the ground plate are 18 mm � 14.5 mm. **Figure 4** shows the initiator; it is a square patch with dimensions of (*Lo*= *Wo* = 8.5 mm). The square patch is modified by cutting equal slots (0.1*Lo* = 0.1*Wo*) in the middle of each arm and then modifying the dimensions of the arms at the corners by cutting increasable slips to change the dimensions of the arms at the corners in a way to configure asymmetrical corners, so the dimensions of each corner are not matching the others to generate different resonant frequencies that collected together to have wide impedance bandwidth. This

modified square patch looks like the logo of Microsoft Office; it is the basic structure for the construction of the proposed antenna. All dimensions are illustrated in **Table 1**.

**Figure 4** shows that antenna 0 (0th iteration) is made through the integration of two square patches. The first iteration consists of dual modified square patches, while the second iteration is made by adding a half size of the modified patch to the first iteration. The same procedure is to be applied to the third iteration, except for the fact that the additional modified patch has quarter size of the original one and antenna 4 (the fourth iteration) is configured by adding <sup>1</sup> <sup>8</sup> of the size of the original modified square patch to antenna 3. In this way, the modified patches are arranged in cascade arrangement so as to increase the total electrical length of the antenna of the same size. **Figure 4** represents the arrangement of the cascade modified patch (two symmetrical structures). According to Eq. (1), *W*<sup>1</sup> configures by adding a half size of the modified patch in **Figure 4** to both structures (left and right sides). The dotted yellow line in **Figure 5** is in the Y-axis and passes through all centers (black points) of the transformation structures (*W*1,*W*<sup>2</sup> and *W*3) which are calculated previously.

From Eq. (4), for the transformed function *W*1, the scale factors are *r* =*s* = 0.5, the rotation angles *θ* ¼ ∅ ¼ 0, and the translation factors (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 4*:*25). Eq. (5) represents the values of scale factor (*r* = *s* = 0.25), the values of the rotation angle (0), and values of scale factor (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 6*:*375) for the transformed structure *W*2. According to Eq. (6), the values of scale factor (*r* = *s* = 0.125), values of the rotation angle are (0), and values of scale factor are (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 7*:*4375) for the transformed structure *W*<sup>3</sup> .

So, antenna 1 (first iteration) is formed by the integration of two modified patch antennas—each is fed by symmetrical strip lines *F*<sup>1</sup> and *F*2—the second iteration is made by adding half size of the modified patch to antenna 1 to configure antenna 2. The same procedure is applied in the third iteration except for the fact that the additional modified patch has quarter size of the original one (see **Figure 5**). Antenna 4 (fourth iteration) is configured by adding <sup>1</sup> <sup>8</sup> of the size of the original modified patch to antenna 3.

(antenna 1), the resonant frequency is shifted to 3.3 GHz, and the second band

*fr* <sup>≈</sup> *<sup>c</sup>* 2 *L* ffiffiffiffi *εr*

of the square patch (**Figure 2a**) is 34 mm, and it is well known that different dimensions create different resonant frequencies. If the perimeter of the square patch is denoted by P0, the perimeter of the modified patch is P1, and the perimeter

> *<sup>P</sup>*<sup>3</sup> <sup>¼</sup> <sup>1</sup> 4

The perimeter of the cascade modified patches *PCi* at each iteration can be

The term (2L) in Eq. (7) represents the half perimeter of the square patch, so

*fr* <sup>≈</sup> <sup>2</sup>*<sup>C</sup> P* ffiffiffiffiffiffiffiffi

*<sup>P</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup> 8

*PCi*�<sup>1</sup> þ *PCi*�<sup>1</sup> *i* ¼ 1, 2, 3 and 4 (9)

<sup>∈</sup> *ef* <sup>p</sup> (10)

*<sup>P</sup>*<sup>4</sup> <sup>¼</sup> <sup>1</sup> 2

*PCi* <sup>¼</sup> <sup>1</sup> 2

The perimeter of the modified patch (**Figure 2c**) is 42 mm, while the perimeter

p (7)

*P*1 (8)

disappeared (the black curve):

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

*The translation processes [17].*

of the first iteration is P2, so:

Eq. (7) can be rewritten as:

calculated as:

**71**

**Figure 5.**

## **2.1 Resonant frequencies**

The resonant frequency for the square patch antenna (the initiator) can be calculated by empirical Eq. (7), which is almost equal to ≈ 8*:*6 GHz. Since antenna 0 (0th iteration) is configured by the integration of twin square patches, there are two resonant frequencies, for one patch 8.5 GHz and for twin patch 4.3 GHz, which is matched with the notched resonant frequencies 4.5 GHz and 8.97 GHz observed in **Figure 6** (the dotted curve). By modifying the square patches in the first iteration


**Table 1.**

*Dimensions for the dual-input fractal antenna (mm).*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

modified square patch looks like the logo of Microsoft Office; it is the basic structure for the construction of the proposed antenna. All dimensions are illustrated in

antenna 4 (the fourth iteration) is configured by adding <sup>1</sup>

Antenna 4 (fourth iteration) is configured by adding <sup>1</sup>

**Figure 4** shows that antenna 0 (0th iteration) is made through the integration of two square patches. The first iteration consists of dual modified square patches, while the second iteration is made by adding a half size of the modified patch to the first iteration. The same procedure is to be applied to the third iteration, except for the fact that the additional modified patch has quarter size of the original one and

modified square patch to antenna 3. In this way, the modified patches are arranged in cascade arrangement so as to increase the total electrical length of the antenna of the same size. **Figure 4** represents the arrangement of the cascade modified patch (two symmetrical structures). According to Eq. (1), *W*<sup>1</sup> configures by adding a half size of the modified patch in **Figure 4** to both structures (left and right sides). The dotted yellow line in **Figure 5** is in the Y-axis and passes through all centers (black points) of the transformation structures (*W*1,*W*<sup>2</sup> and *W*3) which are calculated

From Eq. (4), for the transformed function *W*1, the scale factors are *r* =*s* = 0.5,

So, antenna 1 (first iteration) is formed by the integration of two modified patch antennas—each is fed by symmetrical strip lines *F*<sup>1</sup> and *F*2—the second iteration is made by adding half size of the modified patch to antenna 1 to configure antenna 2. The same procedure is applied in the third iteration except for the fact that the additional modified patch has quarter size of the original one (see **Figure 5**).

The resonant frequency for the square patch antenna (the initiator) can be calculated by empirical Eq. (7), which is almost equal to ≈ 8*:*6 GHz. Since antenna 0 (0th iteration) is configured by the integration of twin square patches, there are two resonant frequencies, for one patch 8.5 GHz and for twin patch 4.3 GHz, which is matched with the notched resonant frequencies 4.5 GHz and 8.97 GHz observed in **Figure 6** (the dotted curve). By modifying the square patches in the first iteration

**Para mm Para mm Para mm Para mm Para mm Para mm W** 18 **Fw1** 1 **L1** 4.25 **W4** 2.9 **S6** 1.76 **D**1 0.7 **L** 18 **Fl2** 2 **W2** 3.9 **L4** 1.1 **S7** 1.5 **D**2 0.7 **S1** 2.9 **Fw2** 1 **L2** 3.5 **S3** 2.4 **S8** 1 **D**3 0.7 **S2** 2.9 **h** 0.8 **W3** 3.1 **S4** 1 **S9** 1.7 **D**4 0.7

**Fl1** 2 **W1** 4.3 **L3** 3.25 **S5** 2.1 **S10** 1.45

*Dimensions for the dual-input fractal antenna (mm).*

the rotation angles *θ* ¼ ∅ ¼ 0, and the translation factors (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 4*:*25). Eq. (5) represents the values of scale factor (*r* = *s* = 0.25), the values of the rotation angle (0), and values of scale factor (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 6*:*375) for the transformed structure *W*2. According to Eq. (6), the values of scale factor (*r* = *s* = 0.125), values of the rotation angle are (0), and values of scale factor are (*x*<sup>0</sup> ¼ 0, *y*<sup>0</sup> ¼ 7*:*4375) for

<sup>8</sup> of the size of the original

<sup>8</sup> of the size of the original

**Table 1**.

*Modern Printed-Circuit Antennas*

previously.

the transformed structure *W*<sup>3</sup> .

modified patch to antenna 3.

**2.1 Resonant frequencies**

**Table 1.**

**70**

**Figure 5.** *The translation processes [17].*

(antenna 1), the resonant frequency is shifted to 3.3 GHz, and the second band disappeared (the black curve):

$$f\_r \approx \frac{c}{2L\sqrt{\epsilon\_r}}\tag{7}$$

The perimeter of the modified patch (**Figure 2c**) is 42 mm, while the perimeter of the square patch (**Figure 2a**) is 34 mm, and it is well known that different dimensions create different resonant frequencies. If the perimeter of the square patch is denoted by P0, the perimeter of the modified patch is P1, and the perimeter of the first iteration is P2, so:

$$P4 = \frac{1}{2}P3 = \frac{1}{4}P2 = \frac{1}{8}P1\tag{8}$$

The perimeter of the cascade modified patches *PCi* at each iteration can be calculated as:

$$PC\_i = \frac{1}{2}PC\_{i-1} + PC\_{i-1} \; i = 1, 2, 3 \text{ and } 4 \tag{9}$$

The term (2L) in Eq. (7) represents the half perimeter of the square patch, so Eq. (7) can be rewritten as:

$$f\_r \approx \frac{2C}{P\sqrt{\Xi\_{\epsilon f}}} \tag{10}$$

But, the perimeter of modified Patch the perimeter of square Patch <sup>¼</sup> <sup>42</sup> <sup>34</sup> ¼ 1*:*23 Eq. (10) will be:

$$f\_i \approx \frac{2C}{1.23P\_i\sqrt{\Xi\_{cf}}}\tag{11}$$

**2.2 Effect of the ground size**

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

operating band.

**Figure 7.**

**Figure 8.**

**73**

*The effect of ground plate size on reflection coefficient.*

*The effect of ground plate size on the gain and the radiation efficiency [17].*

**Figure 7** shows the effect of ground size on the impedance bandwidth of the proposed fractal antenna. Given that modifying the ground dimensions can change the antenna impedance and the matching factor between the antenna and the excitation port, the dimensions of the ground plate can be modified to select the

When the dimensions of the ground plate are set to 18 mm 10 mm, the lower

operating band shifts to 3 GHz and the upper operating band disappears as

Let <sup>2</sup>*C*ffiffiffiffiffiffi <sup>∈</sup>*ef* <sup>p</sup> <sup>¼</sup> *<sup>k</sup>*, and Eq. (11) will be:

$$f\_i \approx \frac{k}{1.23 \text{PC}\_i} \tag{12}$$

According to Eq. (12), the resonant frequency of the modified patch (the first iteration) is 3.2 GHz. While the resonant frequencies for first iteration, which are presented in **Figure 6** (the black curve), are 3.3 and 7.1 GHz. However, these resonant frequencies are not useful for Wi-Fi and WiMAX applications. For second iteration, the resonant frequency calculated by Eq. (12) is 5.2 GHz and the lower resonant frequency is 2.6 GHz, which matched the lower resonant frequency shown in **Figure 6** (the blue curve). In this way, the resonant frequencies that are calculated using Eq. (12) approximately matched the values of the resonant frequencies, as presented in **Figure 6**.

Certain dual operating bands of 2.5–2.6 GHz and 5–6 GHz in the third iteration (antenna 3) are observed in the return loss curve (the red curve; **Figure 6**). The proposed antenna (fourth iteration) has a lower operating band of 2.4–2.6 GHz around resonant frequency 2.5 GHz and an upper operating band of 4.9–6 GHz around resonant frequency 5.1 GHz as shown in **Figure 6** (the dashed curve). These operating bands meet the specifications of Wi-Fi and WiMAX applications. So, the required operating bands are achieved by using novel fractal geometry at the fourth iteration in the same size of the 0th iteration.

**Figure 6.** *Simulated return loss values for all antennas (S*<sup>11</sup> ¼ *S*22*) [17].*

## **2.2 Effect of the ground size**

But, the perimeter of modified Patch

*Modern Printed-Circuit Antennas*

Eq. (10) will be:

as presented in **Figure 6**.

**Figure 6.**

**72**

Let <sup>2</sup>*C*ffiffiffiffiffiffi ∈*ef*

the perimeter of square Patch <sup>¼</sup> <sup>42</sup>

p ¼ *k*, and Eq. (11) will be:

iteration in the same size of the 0th iteration.

*Simulated return loss values for all antennas (S*<sup>11</sup> ¼ *S*22*) [17].*

<sup>34</sup> ¼ 1*:*23

*fi* <sup>≈</sup> <sup>2</sup>*<sup>C</sup>* 1*:*23*Pi*

> *fi* <sup>≈</sup> *<sup>k</sup>* 1*:*23*PCi*

According to Eq. (12), the resonant frequency of the modified patch (the first iteration) is 3.2 GHz. While the resonant frequencies for first iteration, which are presented in **Figure 6** (the black curve), are 3.3 and 7.1 GHz. However, these resonant frequencies are not useful for Wi-Fi and WiMAX applications. For second iteration, the resonant frequency calculated by Eq. (12) is 5.2 GHz and the lower resonant frequency is 2.6 GHz, which matched the lower resonant frequency shown in **Figure 6** (the blue curve). In this way, the resonant frequencies that are calculated using Eq. (12) approximately matched the values of the resonant frequencies,

Certain dual operating bands of 2.5–2.6 GHz and 5–6 GHz in the third iteration (antenna 3) are observed in the return loss curve (the red curve; **Figure 6**). The proposed antenna (fourth iteration) has a lower operating band of 2.4–2.6 GHz around resonant frequency 2.5 GHz and an upper operating band of 4.9–6 GHz around resonant frequency 5.1 GHz as shown in **Figure 6** (the dashed curve). These operating bands meet the specifications of Wi-Fi and WiMAX applications. So, the required operating bands are achieved by using novel fractal geometry at the fourth

ffiffiffiffiffiffiffiffi ∈ *ef*

p (11)

(12)

**Figure 7** shows the effect of ground size on the impedance bandwidth of the proposed fractal antenna. Given that modifying the ground dimensions can change the antenna impedance and the matching factor between the antenna and the excitation port, the dimensions of the ground plate can be modified to select the operating band.

When the dimensions of the ground plate are set to 18 mm 10 mm, the lower operating band shifts to 3 GHz and the upper operating band disappears as

**Figure 7.** *The effect of ground plate size on reflection coefficient.*

**Figure 8.** *The effect of ground plate size on the gain and the radiation efficiency [17].*


indicated by the dotted curve in **Figure 7**. The dashed curve in **Figure 7** represents the value of return losses when the dimensions of the ground plate are 18 mm 18 mm, the lower band shifts to 2.3 GHz, while the upper band covers the 4.4–5.6 GHz frequency range. These bands are not suitable for Wi-Fi, WiMAX, and ISM applications. The solid curve in **Figure 7** indicates that the ground plate has optimum dimensions of 18 mm 14.5 mm and that the dual notched bands meet the purpose

**Figure 8** presents the effect of ground size on the radiation efficiency (black curves) and gain (blue curves) of the proposed antenna. As shown in **Figure 8**, a fully grounded antenna (18 mm 18 mm) has a low radiation efficiency (blue dotted curve) and gain (black dotted curve), especially at the lower operating band. The values of simulated gain and radiation efficiency are improved by reducing the size of the ground plate to 18 mm 10 mm as indicated by the dashed curves in **Figure 8**. The gain increases to 0–1.5 dB at the lower operating band and to 1.5–2.5 dB at the upper operating band. Meanwhile, the radiation efficiency increases to 70–90% when the ground size is set to 18 mm 14.5 mm as indicated by the black solid curve in **Figure 8**. Therefore, the optimum dimensions of the ground are 18

**Table 2** illustrates some important radiation properties for each iteration, such

**Figure 9** shows the simulated surface current at the resonant frequency of 2.45 GHz for phase references of 0°, 90°, 180°, and 270°. When the first input for phase references at 0° and 180° is excited, most of the surface current direction on the feed strip line is along the +Y before circulating counter clockwise, as shown in

as impedance bandwidth, efficiency, gain, and ARBW.

**2.3 Surface current and circular polarization**

of designing the fractal antenna.

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

mm 14.5 mm.

**Figure 9a**.

**Figure 10.**

**75**

*Simulated axial ratio for all iterations [17].*

**Table 2.**

*The radiation properties for all iterations of the dual-input fractal antenna.*

#### **Figure 9.**

*Surface currents at 2.45 GHz for both inputs. (a) First input at 0° and 180° phase references. (b) First input at 90° and 270° phase references. (c) Second input at 0° and 180° phase references. (d) Second input at 90° and 270° phase references [17].*

**74**

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

**Iteration 1st BW**

**Table 2.**

**Figure 9.**

**74**

*270° phase references [17].*

**(2.4–2.6)**

*Modern Printed-Circuit Antennas*

**2nd BW (5–6)**

**Efficiency %**

**ARBW (GHz)**

0th (4–4.5) (8.1–9.4) 40 — 12 to 0 The resonant frequencies are out of the

1st (3.1–3.6) — 40–55 0.1 8 to 0 2nd band disappeared, ARBW around

3rd (2.5–2.6) (5–6) 55–68 0.2 1.5 to 1.6 Does not cover all frequencies at the

*Surface currents at 2.45 GHz for both inputs. (a) First input at 0° and 180° phase references. (b) First input at 90° and 270° phase references. (c) Second input at 0° and 180° phase references. (d) Second input at 90° and*

2nd (2.6–2.7) (5.4–6.4) 50–60 0.07 2 to 1 Does not cover all required

4th (2.4–2.6) (4.9–6) 65–85 0.1, 0.3 0–2.4 Optimum

*The radiation properties for all iterations of the dual-input fractal antenna.*

**Gain (dB) State**

required, LP

3.4 GHz

frequencies, ARBW around 5 GHz

1st band, ARBW around 3.5 GHz

indicated by the dotted curve in **Figure 7**. The dashed curve in **Figure 7** represents the value of return losses when the dimensions of the ground plate are 18 mm 18 mm, the lower band shifts to 2.3 GHz, while the upper band covers the 4.4–5.6 GHz frequency range. These bands are not suitable for Wi-Fi, WiMAX, and ISM applications. The solid curve in **Figure 7** indicates that the ground plate has optimum dimensions of 18 mm 14.5 mm and that the dual notched bands meet the purpose of designing the fractal antenna.

**Figure 8** presents the effect of ground size on the radiation efficiency (black curves) and gain (blue curves) of the proposed antenna. As shown in **Figure 8**, a fully grounded antenna (18 mm 18 mm) has a low radiation efficiency (blue dotted curve) and gain (black dotted curve), especially at the lower operating band. The values of simulated gain and radiation efficiency are improved by reducing the size of the ground plate to 18 mm 10 mm as indicated by the dashed curves in **Figure 8**. The gain increases to 0–1.5 dB at the lower operating band and to 1.5–2.5 dB at the upper operating band. Meanwhile, the radiation efficiency increases to 70–90% when the ground size is set to 18 mm 14.5 mm as indicated by the black solid curve in **Figure 8**. Therefore, the optimum dimensions of the ground are 18 mm 14.5 mm.

**Table 2** illustrates some important radiation properties for each iteration, such as impedance bandwidth, efficiency, gain, and ARBW.

### **2.3 Surface current and circular polarization**

**Figure 9** shows the simulated surface current at the resonant frequency of 2.45 GHz for phase references of 0°, 90°, 180°, and 270°. When the first input for phase references at 0° and 180° is excited, most of the surface current direction on the feed strip line is along the +Y before circulating counter clockwise, as shown in **Figure 9a**.

**Figure 10.** *Simulated axial ratio for all iterations [17].*

For phase references at 90° and 270°, the surface current flows towards the Y direction along the strip feeding line and then circulates clockwise, as shown in **Figure 9b**. Contrary to that, when the second input is excited, the surface current direction on the feed strip line and the circulating direction of the current changed, as shown in **Figure 9c** and **d**. RHCP and LHCP can be achieved by switching the two inputs. The signals of LHCP and RHCP can be received simultaneously. Thus,

**Figure 10** presents the AR values for all iterations. The AR values at the 0th iteration are too high, especially at the lower operating band as indicated by the dashed black curve. These values have changed during the configuration of the proposed antenna as shown in **Figure 10**. The ARBW of 0.09 GHz, which is approximately 66% of that of the lower operating band, is indicated by the solid black curve. Meanwhile, the ARBW of 0.35 GHz is approximately 30% of that of the upper operating band. The ARBW values in **Figure 10** match those that have been

**Figure 11** shows the left and right polarizations at the frequencies of 2.5, 3.5, 5, and 5.8 GHz. The phase differences between the radiation patterns at 3.5 GHz and 5 GHz are 170° and 15°, respectively, whereas the LHCP and RHCP patterns at 2.5 GHz and 5.8 GHz shift by 88° (almost perpendicular to each other). Therefore, the antenna demonstrates circular polarization around the frequencies of 2.5 and 5.8 GHz. The antenna structure has zigzag edges that are configured by the arrangement of modified patches and creates lengthy paths for the surface current. At some frequencies, such as 2.5 and 5.8 GHz, the components of the surface currents are perpendicular to each other, thereby exciting orthogonal electric fields that, in turn, result in circular polarization [18]. The AR values in **Figure 10** and the current distribution in **Figure 9** match each other. The circular polarization is improved by the special design and arrangements of the modified structure during the antenna configuration, and the orthogonal components are generated at the resonant

reported in previous circular polarization studies as shown in **Figure 10**.

the proposed antenna has a dual circular polarization.

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

frequencies of 2.5 and 5.8 GHz.

**Figure 13.**

**77**

*The simulated and measured S-parameters for the proposed antenna [17].*

**Figure 11.** *Left (black curves) and right (red curves) polarization at 2.5, 3.5, 5, and 5.8 GHz [17].*

**Figure 12.** *The prototypes for all iterations [17].*

### *Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

For phase references at 90° and 270°, the surface current flows towards the Y direction along the strip feeding line and then circulates clockwise, as shown in **Figure 9b**. Contrary to that, when the second input is excited, the surface current direction on the feed strip line and the circulating direction of the current changed, as shown in **Figure 9c** and **d**. RHCP and LHCP can be achieved by switching the two inputs. The signals of LHCP and RHCP can be received simultaneously. Thus, the proposed antenna has a dual circular polarization.

**Figure 10** presents the AR values for all iterations. The AR values at the 0th iteration are too high, especially at the lower operating band as indicated by the dashed black curve. These values have changed during the configuration of the proposed antenna as shown in **Figure 10**. The ARBW of 0.09 GHz, which is approximately 66% of that of the lower operating band, is indicated by the solid black curve. Meanwhile, the ARBW of 0.35 GHz is approximately 30% of that of the upper operating band. The ARBW values in **Figure 10** match those that have been reported in previous circular polarization studies as shown in **Figure 10**.

**Figure 11** shows the left and right polarizations at the frequencies of 2.5, 3.5, 5, and 5.8 GHz. The phase differences between the radiation patterns at 3.5 GHz and 5 GHz are 170° and 15°, respectively, whereas the LHCP and RHCP patterns at 2.5 GHz and 5.8 GHz shift by 88° (almost perpendicular to each other). Therefore, the antenna demonstrates circular polarization around the frequencies of 2.5 and 5.8 GHz. The antenna structure has zigzag edges that are configured by the arrangement of modified patches and creates lengthy paths for the surface current. At some frequencies, such as 2.5 and 5.8 GHz, the components of the surface currents are perpendicular to each other, thereby exciting orthogonal electric fields that, in turn, result in circular polarization [18]. The AR values in **Figure 10** and the current distribution in **Figure 9** match each other. The circular polarization is improved by the special design and arrangements of the modified structure during the antenna configuration, and the orthogonal components are generated at the resonant frequencies of 2.5 and 5.8 GHz.

**Figure 13.** *The simulated and measured S-parameters for the proposed antenna [17].*

**Figure 11.**

*Modern Printed-Circuit Antennas*

**Figure 12.**

**76**

*The prototypes for all iterations [17].*

*Left (black curves) and right (red curves) polarization at 2.5, 3.5, 5, and 5.8 GHz [17].*

## **2.4 Measurements and results**

The five iterations are fabricated as shown in **Figure 12**. The compact size of the proposed fractal antenna is clear in this figure. The physical dimensions of the 0th iteration are the same of that for the fourth iteration, while the electrical length of the fourth iteration is much greater than the 0th iteration.

in the prototype. The impedance bandwidth of the first input (the red dotted curve)

The measured reflection coefficient for the second input *S*<sup>22</sup> is represented in **Figure 13** by the dashed curve. The measured impedance bandwidth expanded to the frequency band of 2.38–2.6 GHz and 4.9–6.1 GHz with low values of the reflection coefficient. Since the antenna is not MIMO antenna, the mutual coupling between the dual inputs *S*<sup>12</sup> and *S*<sup>21</sup> is not important in these measurements.

**Figure 14** presents the simulated and measured radiation patterns on the E and H planes. The red or black solid curves represent the simulated data, while the red or black dashed curves represent the experimental results. The measured and sim-

The measured radiation patterns on the H plane (the red dashed curve) at all resonant frequencies are almost omnidirectional. The E and H planes measured at 2.5 and 5.8 GHz when phi = 90 are perpendicular to each other, which matches the CP characteristics and the results of previous theoretical works on CP generation as shown in **Figures 11** and **12**. Meanwhile, the radiation pattern at the lower resonant frequency of 2.5 GHz is almost omnidirectional because the length of the surface current path is approximately half the wavelength of this frequency. Therefore, no side lobes are observed in its radiation pattern. As the frequency increases, the surface current path becomes greater than the wavelength of this frequency, thereby producing many side lobes at their radiation patterns. The radiation pattern is almost omnidirectional at resonant frequencies lower than 2.5 GHz because the length of the surface current path is approximately half the wavelength of this frequency. Therefore, side lobes are not observed in its radiation pattern. As the frequency increases, the surface current path becomes greater than the wavelength of this frequency, causing many side lobes at their radiation

The proposed fractal antenna displays an ARBW of 2.48–2.55 and 5.6–5.9 GHz, which is lesser than 3 dB as shown in **Figure 15** (the blue squared points) which is about 35% of the first operating band 2.4–2.6 GHz and about 30% of the second band 5–6 GHz. The values of the measured gain (the black circular points) vary

expanded to the range of 2.4–2.63 GHz and 4.8–6.4 GHz.

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

patterns.

**Figure 15.**

**79**

*The measured gain, efficiency, and AR [17].*

ulated radiation curves in **Figure 14** show an acceptable agreement.

**Figure 13** illustrates the simulated and measured reflection coefficients of the proposed fractal antenna. Generally, good matching is observed between simulated data (the solid curve) and the measured data (dashed and red dotted curves). However, several resonant frequencies in the experimental results are shifted unlike those in the simulated curve. Shifting occurs due to the impurity of materials used

**Figure 14.** *Simulated and measured radiation patterns in E&H planes [17].*

## *Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

**2.4 Measurements and results**

*Modern Printed-Circuit Antennas*

**Figure 14.**

**78**

*Simulated and measured radiation patterns in E&H planes [17].*

The five iterations are fabricated as shown in **Figure 12**. The compact size of the proposed fractal antenna is clear in this figure. The physical dimensions of the 0th iteration are the same of that for the fourth iteration, while the electrical length of

**Figure 13** illustrates the simulated and measured reflection coefficients of the proposed fractal antenna. Generally, good matching is observed between simulated data (the solid curve) and the measured data (dashed and red dotted curves). However, several resonant frequencies in the experimental results are shifted unlike those in the simulated curve. Shifting occurs due to the impurity of materials used

the fourth iteration is much greater than the 0th iteration.

in the prototype. The impedance bandwidth of the first input (the red dotted curve) expanded to the range of 2.4–2.63 GHz and 4.8–6.4 GHz.

The measured reflection coefficient for the second input *S*<sup>22</sup> is represented in **Figure 13** by the dashed curve. The measured impedance bandwidth expanded to the frequency band of 2.38–2.6 GHz and 4.9–6.1 GHz with low values of the reflection coefficient. Since the antenna is not MIMO antenna, the mutual coupling between the dual inputs *S*<sup>12</sup> and *S*<sup>21</sup> is not important in these measurements.

**Figure 14** presents the simulated and measured radiation patterns on the E and H planes. The red or black solid curves represent the simulated data, while the red or black dashed curves represent the experimental results. The measured and simulated radiation curves in **Figure 14** show an acceptable agreement.

The measured radiation patterns on the H plane (the red dashed curve) at all resonant frequencies are almost omnidirectional. The E and H planes measured at 2.5 and 5.8 GHz when phi = 90 are perpendicular to each other, which matches the CP characteristics and the results of previous theoretical works on CP generation as shown in **Figures 11** and **12**. Meanwhile, the radiation pattern at the lower resonant frequency of 2.5 GHz is almost omnidirectional because the length of the surface current path is approximately half the wavelength of this frequency. Therefore, no side lobes are observed in its radiation pattern. As the frequency increases, the surface current path becomes greater than the wavelength of this frequency, thereby producing many side lobes at their radiation patterns. The radiation pattern is almost omnidirectional at resonant frequencies lower than 2.5 GHz because the length of the surface current path is approximately half the wavelength of this frequency. Therefore, side lobes are not observed in its radiation pattern. As the frequency increases, the surface current path becomes greater than the wavelength of this frequency, causing many side lobes at their radiation patterns.

The proposed fractal antenna displays an ARBW of 2.48–2.55 and 5.6–5.9 GHz, which is lesser than 3 dB as shown in **Figure 15** (the blue squared points) which is about 35% of the first operating band 2.4–2.6 GHz and about 30% of the second band 5–6 GHz. The values of the measured gain (the black circular points) vary

**Figure 15.** *The measured gain, efficiency, and AR [17].*

between 0 dB at 2.5 GHz and 2.7 dB at 5.8 GHz. Meanwhile, the maximum efficiency (the red triangle points) is �0.7 dB (85%) at 5 GHz.

## **3. Meandered ring fractal antenna**

The universal serial bus (USB) dongles are used in many portable communication devices such as laptops and pads in order to transmit and receive the data with a high bit rate. Since USB dongles are used with portable devices, the desired antenna must solve serious challenges such as the size, multiband, and the stability of radiation characteristics during the notched bands (gain and efficiency).

The aim of this study is to design a fractal ring antenna with a compact size and low profile, configured by three iterations, which covered the frequency range that meets the specification of the upper operating band for Wi-Fi and WIMAX applications and has high efficiency and stable radiation properties.

### **3.1 Antenna design**

In this study, the proposed antenna with a compact size of 24 � <sup>9</sup> � 0.8 mm<sup>3</sup> was configured by a three-step process. The radiator of reference antenna (**Figure 16**) is a square patch with dimensions *x* = *y* =9 mm and is separated from the ground by a gap of 0.3 mm. According to empirical Eq. (7), the dimension of the square patch will be equal to 36 mm for the resonant frequency ( *fr* = 5 GHz) and substrate FR-4 with *ε<sup>r</sup>* ¼ 4*:*3. To miniaturize the dimension of the antenna, let *X* ¼ *<sup>Y</sup>* <sup>¼</sup> <sup>1</sup> <sup>4</sup> � 36 mm ¼ 9 mm. The ground plate features a rectangular shape with dimensions of 9.7 � 9 mm<sup>2</sup> . The radiator and ground are printed on the same side of commercial substrate (FR-4) with *εr*= 4.3, tan *δ* = 0.027, and thickness = 0.8 mm. **Figure 16** shows the first iteration in the design of antenna with square slot cuts in the radiator plate to configure the square ring with arm width equal to 0.1�. In the second iteration, the square ring is modified as a meandered ring to increase its electrical length to generate more resonant frequencies, which are collected to obtain a notched operating band of 4.4–6.7 GHz which is shown in **Figure 16** (the solid curve). All dimensions of the meandered ring are denoted as a function of *x*, which corresponds to the dimension of the square ring in the first iteration, as indicated in **Figure 16**. The length of the square ring in the first iteration equals 4x.

Length of the upper arm ¼ 0*:*5X þ 0*:*3X þ 0*:*1X þ 0*:*12X þ 0*:*34X ¼ 1*:*36X (13)

Length of left arm ¼ 0*:*34X þ 0*:*17X þ 0*:*1X þ 0*:*22X þ 0*:*38X ¼ 1*:*21X (14)

for all antennas are almost equal at frequencies < 4.7 GHz. Thereafter, the values

**Figure 18** shows that negative imaginary values (capacitance) are observed in the curves of imaginary part impedance for all antennas at frequencies < 4.4 GHz. In the frequency band of 4.4–6 GHz, the values of the imaginary part are closer to zero (red line), that is, only real-part impedances for the three antennas are resistant. This property provides stable matching factor that leads to stable gain and

**Table 3** illustrates some important radiation properties for each iteration, such as impedance bandwidth, efficiency, gain, and ARBW. It is clear that most of the required specifications that can be achieved at the second iteration are due to improving the values of radiation properties during the progress of antenna

configuration, especially the impedance bandwidth, efficiency, gain, and an ARBW

of real-part impedance for the second iteration are closer to the input impedance of excitation port (50 ohms red line), especially in the frequency

range of 5.1–6.4 GHz.

**Figure 16.**

as shown in **Table 3**.

**81**

efficiency in the operating band.

*The process of configuring the meandered ring antenna [19].*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

Length of bottom arm ¼ 0*:*4X þ 0*:*13X þ 0*:*1X þ 0*:*17X þ 0*:*47X ¼ 1*:*27X (15)

Length of right arm ¼ 0*:*44X þ 0*:*1X þ 0*:*1X þ 0*:*13X þ 0*:*52X ¼ 1*:*29X (16)

Thus, the total length of meandered ring equals 5.13X. The length of meandered ring increases by a factor of 1.28 compared with the length of the square ring of the same size in the first iteration. Of course, the increase in length of the four arms leads to increase in the length of the surface current paths and thus generates new resonant frequencies which collected together to give a wide impedance bandwidth, and this is clear in **Figure 17** (the solid curve) where the operating band increased when the ring becomes meandered at the second iteration.

**Figure 17** depicts the real (black curves) and imaginary (blue curves) parts of the impedance values for the three antennas. The values of real-part impedance

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

between 0 dB at 2.5 GHz and 2.7 dB at 5.8 GHz. Meanwhile, the maximum effi-

The universal serial bus (USB) dongles are used in many portable communication devices such as laptops and pads in order to transmit and receive the data with a high bit rate. Since USB dongles are used with portable devices, the desired antenna must solve serious challenges such as the size, multiband, and the stability

The aim of this study is to design a fractal ring antenna with a compact size and low profile, configured by three iterations, which covered the frequency range that meets the specification of the upper operating band for Wi-Fi and WIMAX appli-

In this study, the proposed antenna with a compact size of 24 � <sup>9</sup> � 0.8 mm<sup>3</sup>

(**Figure 16**) is a square patch with dimensions *x* = *y* =9 mm and is separated from the ground by a gap of 0.3 mm. According to empirical Eq. (7), the dimension of the square patch will be equal to 36 mm for the resonant frequency ( *fr* = 5 GHz) and substrate FR-4 with *ε<sup>r</sup>* ¼ 4*:*3. To miniaturize the dimension of the antenna, let *X* ¼

<sup>4</sup> � 36 mm ¼ 9 mm. The ground plate features a rectangular shape with

commercial substrate (FR-4) with *εr*= 4.3, tan *δ* = 0.027, and thickness = 0.8 mm. **Figure 16** shows the first iteration in the design of antenna with square slot cuts in the radiator plate to configure the square ring with arm width equal to 0.1�. In the second iteration, the square ring is modified as a meandered ring to increase its electrical length to generate more resonant frequencies, which are collected to obtain a notched operating band of 4.4–6.7 GHz which is shown in **Figure 16** (the solid curve). All dimensions of the meandered ring are denoted as a function of *x*, which corresponds to the dimension of the square ring in the first iteration, as indicated in **Figure 16**. The length of the square ring in the first iteration equals 4x.

Length of the upper arm ¼ 0*:*5X þ 0*:*3X þ 0*:*1X þ 0*:*12X þ 0*:*34X ¼ 1*:*36X (13)

Length of left arm ¼ 0*:*34X þ 0*:*17X þ 0*:*1X þ 0*:*22X þ 0*:*38X ¼ 1*:*21X (14)

Length of bottom arm ¼ 0*:*4X þ 0*:*13X þ 0*:*1X þ 0*:*17X þ 0*:*47X ¼ 1*:*27X (15)

Length of right arm ¼ 0*:*44X þ 0*:*1X þ 0*:*1X þ 0*:*13X þ 0*:*52X ¼ 1*:*29X (16)

when the ring becomes meandered at the second iteration.

Thus, the total length of meandered ring equals 5.13X. The length of meandered ring increases by a factor of 1.28 compared with the length of the square ring of the same size in the first iteration. Of course, the increase in length of the four arms leads to increase in the length of the surface current paths and thus generates new resonant frequencies which collected together to give a wide impedance bandwidth, and this is clear in **Figure 17** (the solid curve) where the operating band increased

**Figure 17** depicts the real (black curves) and imaginary (blue curves) parts of the impedance values for the three antennas. The values of real-part impedance

. The radiator and ground are printed on the same side of

was configured by a three-step process. The radiator of reference antenna

of radiation characteristics during the notched bands (gain and efficiency).

cations and has high efficiency and stable radiation properties.

ciency (the red triangle points) is �0.7 dB (85%) at 5 GHz.

**3. Meandered ring fractal antenna**

*Modern Printed-Circuit Antennas*

**3.1 Antenna design**

dimensions of 9.7 � 9 mm<sup>2</sup>

*<sup>Y</sup>* <sup>¼</sup> <sup>1</sup>

**80**

#### **Figure 16.**

*The process of configuring the meandered ring antenna [19].*

for all antennas are almost equal at frequencies < 4.7 GHz. Thereafter, the values of real-part impedance for the second iteration are closer to the input impedance of excitation port (50 ohms red line), especially in the frequency range of 5.1–6.4 GHz.

**Figure 18** shows that negative imaginary values (capacitance) are observed in the curves of imaginary part impedance for all antennas at frequencies < 4.4 GHz. In the frequency band of 4.4–6 GHz, the values of the imaginary part are closer to zero (red line), that is, only real-part impedances for the three antennas are resistant. This property provides stable matching factor that leads to stable gain and efficiency in the operating band.

**Table 3** illustrates some important radiation properties for each iteration, such as impedance bandwidth, efficiency, gain, and ARBW. It is clear that most of the required specifications that can be achieved at the second iteration are due to improving the values of radiation properties during the progress of antenna configuration, especially the impedance bandwidth, efficiency, gain, and an ARBW as shown in **Table 3**.

**3.2 Current distribution**

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

**3.3 Circular polarization**

becomes 90° and 270°.

**Figure 19.**

**83**

*The surface current at 5 GHz for all iterations [19].*

The maximum distribution currents at 5 GHz for the 0th iteration are mainly concentrated close to the feeding point on the patch and ground plates, as shown in **Figure 19**. In the first iteration, the currents are distributed in the additional area, especially on the square ring, which leads to the generation of new resonant frequency. The operating band is expanded compared with that at 0th iteration. The distribution of the surface current on ground plate is the same in all iterations because there is no change in surface current path at the ground plate during the

**Figure 19** (second iteration) shows that the surface current has two paths. The first path begins from the feeding point F and then passes through the right arm to point A, which has a total length equal to 1.79X = 16 mm, which is approximately

The total length of the other path, which is almost perpendicular to the first and begins from feeding point F and then passes through the bottom arm to point B, is equal to 1.87X = 17 mm, which is approximately one-fourth of the wavelength for the resonant frequency at 5 GHz. Thus, two equal components of surface current

The length of the first surface current path from feeding point F to point A is 16 mm, which is almost equal to the length of the second surface current path from the feeding point to point B. These normal components are approximately ¼ of the wavelength for 5 GHz generated CP, as shown in **Figure 20**, which represents surface current distributions for phases at 0°, 90°, 180°, and 270° at 5 GHz resonant frequency. Surface current circulates clockwise along the upper and lower right quarters and counterclockwise along the lower left quarter for 0° and 180° phases. **Figure 20** shows the circulation direction of surface current when the phase

progress of antenna configuration compared with the radiator plane.

one-fourth of the wavelength for the resonant frequency at 5 GHz.

normal to each other provide circular polarization radiation at 5 GHz.

**Figure 17.** *The simulated reflection coefficient for the 0th iteration, first iteration, and the second iteration [19].*

**Figure 18.** *The impedance values of the three iterations [19].*


**Table 3.**

*The radiation properties for all iterations of the meandered ring fractal antenna.*

## **3.2 Current distribution**

The maximum distribution currents at 5 GHz for the 0th iteration are mainly concentrated close to the feeding point on the patch and ground plates, as shown in **Figure 19**. In the first iteration, the currents are distributed in the additional area, especially on the square ring, which leads to the generation of new resonant frequency. The operating band is expanded compared with that at 0th iteration. The distribution of the surface current on ground plate is the same in all iterations because there is no change in surface current path at the ground plate during the progress of antenna configuration compared with the radiator plane.

**Figure 19** (second iteration) shows that the surface current has two paths. The first path begins from the feeding point F and then passes through the right arm to point A, which has a total length equal to 1.79X = 16 mm, which is approximately one-fourth of the wavelength for the resonant frequency at 5 GHz.

The total length of the other path, which is almost perpendicular to the first and begins from feeding point F and then passes through the bottom arm to point B, is equal to 1.87X = 17 mm, which is approximately one-fourth of the wavelength for the resonant frequency at 5 GHz. Thus, two equal components of surface current normal to each other provide circular polarization radiation at 5 GHz.

## **3.3 Circular polarization**

**Figure 17.**

*Modern Printed-Circuit Antennas*

**Figure 18.**

**Table 3.**

**82**

**Iteration BW**

**(GHz)**

*The impedance values of the three iterations [19].*

**Efficiency (%)**

**ARBW (GHz)**

0th (5.2–6) 50–65 — 12 to 0 10 Low efficiency, low

1st (4.7–6) 60–75 — 1–3 14 Does not have stable

2nd (4.4–6.7) 85–90 0.083 2.2–2.4 20 Optimum

*The radiation properties for all iterations of the meandered ring fractal antenna.*

**Gain (dB)** **Lower S1, 1 (dB)**

**State**

gain, and LP

value of gain, LP

*The simulated reflection coefficient for the 0th iteration, first iteration, and the second iteration [19].*

The length of the first surface current path from feeding point F to point A is 16 mm, which is almost equal to the length of the second surface current path from the feeding point to point B. These normal components are approximately ¼ of the wavelength for 5 GHz generated CP, as shown in **Figure 20**, which represents surface current distributions for phases at 0°, 90°, 180°, and 270° at 5 GHz resonant frequency. Surface current circulates clockwise along the upper and lower right quarters and counterclockwise along the lower left quarter for 0° and 180° phases. **Figure 20** shows the circulation direction of surface current when the phase becomes 90° and 270°.

**Figure 19.** *The surface current at 5 GHz for all iterations [19].*

**Figure 20.** *Surface current for sequential phases (0°, 90°, 180°, and 270°) at 5 GHz [19].*

**Figure 21** depicts the left and right polarizing radiation in E-plane at 5 and 5.8 GHz, which show that the phase differences at 5 and 5.8 GHz is approximately 86° and 180°, thereby indicating that CP is radiated at 5 GHz only. This study matches the surface current distribution, which indicates that a circular polarization radiation at 5 GHz is generated by dual orthogonal components of electrical field created by the surface currents that flow along the perpendicular arms of the meandered ring at the feed point, as shown in **Figure 20**.

bandwidth of 4.4–6.7 GHz, and the resonant frequency shifted to 5 GHz compared with 5.8 GHz for the simulated value as shown in **Figure 23**. That takes place due to impurities of some of the materials that are used in prototypes and due to the

*Simulated left (black curves) and right (red curves) polarization in E-plane at 5 and 5.8 GHz [19].*

**Figure 24** shows a distinguishing agreement between simulated (solid) and measured (dashed) patterns. Radiation patterns in the H-plane (black curves) for the proposed antenna are almost omnidirectional at 5 and 5.8 GHz. **Figure 24b** shows that the radiation pattern at 5.8 GHz is similar to that at 5 GHz, but the former is more directional. At E-plane (when phi = 0), the radiation patterns looked like number 8 where two major lobes observed shifted by an angle of 180° as shown in **Figure 24a** (the red curves), while at 5.8 GHz, the radiation pattern in E-plane

**Figure 25** depicts the measured values of the gain, efficiency, and an axial ratio. At frequency bands of 5–6 GHz, gain values are almost constant 2.3–2.4 dB, and efficiency reaches 0.45 dB (90%), whereas axial ratio bandwidth measures 83

soldering.

**85**

**Figure 22.**

**Figure 21.**

had dual asymmetrical major lobes.

*The prototypes of all fractal antenna iterations [19].*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

## **3.4 Measurements and results**

**Figure 22** represents the photographs of the all iteration prototypes; it is clear that the size of the proposed antenna is compact that can be used for portable communication devices.

The measured impedance bandwidth for the proposed antenna compresses to the frequency band of 4.8–6.7 GHz compared with the simulated impedance

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

**Figure 21.** *Simulated left (black curves) and right (red curves) polarization in E-plane at 5 and 5.8 GHz [19].*

**Figure 22.** *The prototypes of all fractal antenna iterations [19].*

bandwidth of 4.4–6.7 GHz, and the resonant frequency shifted to 5 GHz compared with 5.8 GHz for the simulated value as shown in **Figure 23**. That takes place due to impurities of some of the materials that are used in prototypes and due to the soldering.

**Figure 24** shows a distinguishing agreement between simulated (solid) and measured (dashed) patterns. Radiation patterns in the H-plane (black curves) for the proposed antenna are almost omnidirectional at 5 and 5.8 GHz. **Figure 24b** shows that the radiation pattern at 5.8 GHz is similar to that at 5 GHz, but the former is more directional. At E-plane (when phi = 0), the radiation patterns looked like number 8 where two major lobes observed shifted by an angle of 180° as shown in **Figure 24a** (the red curves), while at 5.8 GHz, the radiation pattern in E-plane had dual asymmetrical major lobes.

**Figure 25** depicts the measured values of the gain, efficiency, and an axial ratio. At frequency bands of 5–6 GHz, gain values are almost constant 2.3–2.4 dB, and efficiency reaches 0.45 dB (90%), whereas axial ratio bandwidth measures 83

**Figure 21** depicts the left and right polarizing radiation in E-plane at 5 and 5.8 GHz, which show that the phase differences at 5 and 5.8 GHz is approximately 86° and 180°, thereby indicating that CP is radiated at 5 GHz only. This study matches the surface current distribution, which indicates that a circular polarization radiation at 5 GHz is generated by dual orthogonal components of electrical field created by the surface currents that flow along the perpendicular arms of the meandered

**Figure 22** represents the photographs of the all iteration prototypes; it is clear that the size of the proposed antenna is compact that can be used for portable

The measured impedance bandwidth for the proposed antenna compresses to

the frequency band of 4.8–6.7 GHz compared with the simulated impedance

ring at the feed point, as shown in **Figure 20**.

*Surface current for sequential phases (0°, 90°, 180°, and 270°) at 5 GHz [19].*

**3.4 Measurements and results**

*Modern Printed-Circuit Antennas*

communication devices.

**84**

**Figure 20.**

**Figure 23.** *Measured (dashed) and simulated (solid) S*1,1 *for the proposed antenna [19].*

**4. Conclusion**

**Figure 25.**

communication devices.

**87**

orthogonal components of electrical field.

*Measured gain, efficiency, and AR for the antenna [19].*

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

Fractal geometry is another type of micro strip antenna used in designing antennas. Two fractal antennas, namely, dual-input fractal antenna and meandered ring antenna, were investigated. All antennas are fabricated on commercial and cheap FR-4 substrate. The proposed fractal antennas are CP radiated by generating

The prototype of the dual-input fractal antenna has a compact size, which is approximately 9 and 16% of the Q-slot [20] and crescent slot [21] antenna size, respectively. The measured operating bands for the first input of the fractal antenna are 2.38–2.62 GHz and 5–6 GHz, whereas those for the second input of the fractal antenna are 2.4–2.65 and 4.8–6.2 GHz. The prototype of the dual-input fractal antenna displays an ARBW of 2.48–2.55 and 5.6–5.9 GHz, which is approximately 35% of the first operating band 2.4–2.6 GHz and approximately 30% of the second band 5–6 GHz. The values of the measured gain vary between 0 dBi at 2.5 GHz and

2.7 dBi at 5.8 GHz. The maximum efficiency is 0.7 dB (85%) at 5 GHz.

The fourth investigated antenna in this study is the meandered ring fractal antenna with compact size, which is approximately 9% of that of the Q-slot antenna, 10% of the crescent slot antenna size, and 66% of dual-input fractal antenna size. However, the meandered ring antenna only covers the upper bandwidth of 5–6 GHz used for Wi-Fi and WiMAX applications. The proposed antenna in this study has a small size, low profile, high measured efficiency (90%), stable gain (2.3–2.4) dBi, and CP radiation with an ARBW of 0.083 GHz, which is approximately 6% of the measured operating band at 4.8–6.2 GHz. Thus, the meandered ring monopole antenna is suitable for the requirements of portable

**Table 4** shows that the previous fractal antennas have circular polarization radiation, such as those reported in [3], which is the Giuseppe Peano fractal antenna that covered the frequency band of 1.5–4 GHz and ARBW of 0.2 GHz,

**Figure 24.** *Simulated (solid) and measured (dashed) radiation pattern. (a) At 5 GHz. (b) At 5.8 GHz [19].*

MHz (approximately 8.3% of operating band) around a resonant frequency of 5 GHz.

Although the meandered ring fractal antenna has impedance bandwidth that covers only the upper band required for Wi-Fi, WiMAX, and ISM applications, it has stable radiation properties especially the gain and the efficiency. Furthermore, the meandered ring antenna has high efficiency (90%), highly compact size, and omnidirectional radiation pattern in H-plane that can be used for portable Wi-Fi and WiMAX devices.

**Figure 25.** *Measured gain, efficiency, and AR for the antenna [19].*

## **4. Conclusion**

Fractal geometry is another type of micro strip antenna used in designing antennas. Two fractal antennas, namely, dual-input fractal antenna and meandered ring antenna, were investigated. All antennas are fabricated on commercial and cheap FR-4 substrate. The proposed fractal antennas are CP radiated by generating orthogonal components of electrical field.

The prototype of the dual-input fractal antenna has a compact size, which is approximately 9 and 16% of the Q-slot [20] and crescent slot [21] antenna size, respectively. The measured operating bands for the first input of the fractal antenna are 2.38–2.62 GHz and 5–6 GHz, whereas those for the second input of the fractal antenna are 2.4–2.65 and 4.8–6.2 GHz. The prototype of the dual-input fractal antenna displays an ARBW of 2.48–2.55 and 5.6–5.9 GHz, which is approximately 35% of the first operating band 2.4–2.6 GHz and approximately 30% of the second band 5–6 GHz. The values of the measured gain vary between 0 dBi at 2.5 GHz and 2.7 dBi at 5.8 GHz. The maximum efficiency is 0.7 dB (85%) at 5 GHz.

The fourth investigated antenna in this study is the meandered ring fractal antenna with compact size, which is approximately 9% of that of the Q-slot antenna, 10% of the crescent slot antenna size, and 66% of dual-input fractal antenna size. However, the meandered ring antenna only covers the upper bandwidth of 5–6 GHz used for Wi-Fi and WiMAX applications. The proposed antenna in this study has a small size, low profile, high measured efficiency (90%), stable gain (2.3–2.4) dBi, and CP radiation with an ARBW of 0.083 GHz, which is approximately 6% of the measured operating band at 4.8–6.2 GHz. Thus, the meandered ring monopole antenna is suitable for the requirements of portable communication devices.

**Table 4** shows that the previous fractal antennas have circular polarization radiation, such as those reported in [3], which is the Giuseppe Peano fractal antenna that covered the frequency band of 1.5–4 GHz and ARBW of 0.2 GHz,

MHz (approximately 8.3% of operating band) around a resonant frequency of

*Simulated (solid) and measured (dashed) radiation pattern. (a) At 5 GHz. (b) At 5.8 GHz [19].*

*Measured (dashed) and simulated (solid) S*1,1 *for the proposed antenna [19].*

Although the meandered ring fractal antenna has impedance bandwidth that covers only the upper band required for Wi-Fi, WiMAX, and ISM applications, it has stable radiation properties especially the gain and the efficiency. Furthermore, the meandered ring antenna has high efficiency (90%), highly compact size, and omnidirectional radiation pattern in H-plane that can be used for portable Wi-Fi

5 GHz.

**86**

**Figure 24.**

**Figure 23.**

*Modern Printed-Circuit Antennas*

and WiMAX devices.


ARBW in a compact size, especially the dual fractal antenna, which has CP radiation

Fifthly, the highly compact size and omnidirectional radiation patterns in H-plane, especially the meandered ring antenna, facilitated the possibility

Sixthly, aside from being low profile and easy to fabricate and the use of commercial FR-4 substrate in addition to existing features, these antennas can be

\*, Mahmood J. Abu-AlShaer<sup>2</sup> and Aqeel M. Jawad<sup>2</sup>

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 Communication Engineering Department, Al-Mamun University College,

2 Al-Rafidain University College, Filastin, Baghdad, Iraq

\*Address all correspondence to: amer.t.abed@ieee.org

provided the original work is properly cited.

during the first and third bands, can avoid many serious problems, such as

mismatched polarization and multipath interferences.

*Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

adopted for the purpose for which they are designed.

communication devices.

**Author details**

Amer T. Abed<sup>1</sup>

Baghdad, Iraq

**89**

of using the proposed antennas for mobile Wi-Fi and WiMAX

#### **Table 4.**

*Comparisons between proposed fractal antennas and previous related works.*

and the fractal antenna proposed in [6] whose size is approximately twice as that of the proposed fractal antenna is used in this study. The antenna has an ARBW of 0.06, 0.09, and 0.3 GHz at the three operating bands, but it does not cover all of the required frequencies, especially at the band of 5–6 GHz.

The meandered line fractal antenna is CP with an ARBW of 0.6 GHz reported in [22]. This meandered line antenna only covered the first band. The size of this antenna is very large and its efficiency has not been mentioned in the report. Modified Koch curve is used in designing the antenna based on Fibonacci sequence reported by [23]. The antenna is miniaturised to 54 � 36 � 1.5 mm and covered the frequency band (2.7–10.3) GHz with an ARBW of approximately 1.1 GHz around resonant frequency 6 GHz. The antenna does not cover the lower band (2.4–2.6) GHz, its CP radiation around 6 GHz, uses unbalanced feeding coaxial, and no gain values.

Therefore, the two proposed fractal antennas in the current study (dual fractal and meandered ring antennas) have specific characteristics better than the previous related antennas in **Table 4**. They are the best when possibly applied for Wi-Fi, WiMAX, and ISM communication purposes for the following reasons:

Firstly, the dual-input fractal antenna has dual operating bands for Wi-Fi (IEEE 802.11b,g,n) and WiMAX (IEEE 802.16e), Wi-Fi (IEEE802.11y), Wi-Fi (IEEE 802.11a,h,j,n), and WiMAX (IEEE 802.16d). The meandered ring fractal only covers the upper band (5–6) GHz.

Secondly, acceptable and greater values of gain for both antennas than the specified gain for fractal antennas in **Table 4** compared with their compact size.

Thirdly, the two types of fractal antennas are highly efficient (>80%Þ, which matched the specific efficiency in **Table 4**. Despite the small size of the proposed antennas compared with many of the previous fractal antennas in **Table 4**, the manufactured antennas in the present study are characterized by superior and stable efficiency, thereby making them suitable for Wi-Fi and WiMAX applications.

Fourthly, the circular radiation properties at some operating bands for both proposed fractal antennas, that overcome the limits of generation CP with wide

## *Fractal Antennas for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.90332*

ARBW in a compact size, especially the dual fractal antenna, which has CP radiation during the first and third bands, can avoid many serious problems, such as mismatched polarization and multipath interferences.

Fifthly, the highly compact size and omnidirectional radiation patterns in H-plane, especially the meandered ring antenna, facilitated the possibility of using the proposed antennas for mobile Wi-Fi and WiMAX communication devices.

Sixthly, aside from being low profile and easy to fabricate and the use of commercial FR-4 substrate in addition to existing features, these antennas can be adopted for the purpose for which they are designed.

## **Author details**

and the fractal antenna proposed in [6] whose size is approximately twice as that of the proposed fractal antenna is used in this study. The antenna has an ARBW of 0.06, 0.09, and 0.3 GHz at the three operating bands, but it does not cover all

The meandered line fractal antenna is CP with an ARBW of 0.6 GHz reported in

Therefore, the two proposed fractal antennas in the current study (dual fractal and meandered ring antennas) have specific characteristics better than the previous related antennas in **Table 4**. They are the best when possibly applied for Wi-Fi,

Firstly, the dual-input fractal antenna has dual operating bands for Wi-Fi (IEEE

802.11b,g,n) and WiMAX (IEEE 802.16e), Wi-Fi (IEEE802.11y), Wi-Fi (IEEE 802.11a,h,j,n), and WiMAX (IEEE 802.16d). The meandered ring fractal only

Secondly, acceptable and greater values of gain for both antennas than the specified gain for fractal antennas in **Table 4** compared with their compact size. Thirdly, the two types of fractal antennas are highly efficient (>80%Þ, which matched the specific efficiency in **Table 4**. Despite the small size of the proposed antennas compared with many of the previous fractal antennas in **Table 4**, the manufactured antennas in the present study are characterized by superior and stable efficiency, thereby making them suitable for Wi-Fi and WiMAX

Fourthly, the circular radiation properties at some operating bands for both proposed fractal antennas, that overcome the limits of generation CP with wide

WiMAX, and ISM communication purposes for the following reasons:

[22]. This meandered line antenna only covered the first band. The size of this antenna is very large and its efficiency has not been mentioned in the report. Modified Koch curve is used in designing the antenna based on Fibonacci sequence reported by [23]. The antenna is miniaturised to 54 � 36 � 1.5 mm and covered the frequency band (2.7–10.3) GHz with an ARBW of approximately 1.1 GHz around resonant frequency 6 GHz. The antenna does not cover the lower band (2.4–2.6) GHz, its CP radiation around 6 GHz, uses unbalanced feeding coaxial, and no gain

of the required frequencies, especially at the band of 5–6 GHz.

values.

applications.

**88**

covers the upper band (5–6) GHz.

**Ant. BW (GHz) Gain**

*Modern Printed-Circuit Antennas*

(3.37–3.45) (5.6–5.9)

(2.4–2.6) (4.7–6.5)

[6] (2.32–2.52)

Fractal antenna

Meander ring

**Table 4.**

**(dB)**

0.5 to –6 0.06,

0–2.4 0.07, 0.3

(4.8–6.2) 2.3–2.4 0.083 24 � 9 �

*Comparisons between proposed fractal antennas and previous related works.*

[3] (1.5–2.7) 3–4 0.2 60 � 60

[23] (2.7–10.3) — 1.1 54 � 36

[24] (3.4–3.6) 6 0.1 40 � 40

[22] (2.2–2.6) 1.8t–4.6 0.6 100 �

**ARBW (GHz)**

> 0.09, 0.3

**Size (mm)**

� 10

50 � 50 � 3.2

� 1.5

� 1

100 � 13

18 � 18 � 0.8

0.8

**Effie. (%)**

**Weak points**

40–80 Does not cover all required bands, low efficiency at lower frequency, used air gap

— Used RT/duroid substrate, does not cover all frequencies in the upper band

85–95 No values of gain, missed 2.5 GHz band

91 Missed 2.4 GHz and 5 GHz bands

— Covered only 2.4 GHz band, large, no efficiency values

85–90 Missed 2.4 GHz and 3.5 GHz bands

70–85 Missed 3.5 GHz band

Amer T. Abed<sup>1</sup> \*, Mahmood J. Abu-AlShaer<sup>2</sup> and Aqeel M. Jawad<sup>2</sup>

1 Communication Engineering Department, Al-Mamun University College, Baghdad, Iraq

2 Al-Rafidain University College, Filastin, Baghdad, Iraq

\*Address all correspondence to: amer.t.abed@ieee.org

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

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[2] Chen W-L, Wang G-M, Zhang C-X. Bandwidth enhancement of a microstrip-line-fed printed wide-slot antenna with a fractal-shaped slot. IEEE Transactions on Antennas and Propagation. 2009;**57**:2176-2179

[3] Oraizi H, Hedayati S. Miniaturization of microstrip antennas by the novel application of the Giuseppe Peano fractal geometries. IEEE Transactions on Antennas and Propagation. 2012;**60**: 3559-3567

[4] Chaimool S, Chokchai C, Akkaraekthalin P. Multiband loaded fractal loop monopole antenna for USB dongle applications. Electronics Letters. 2012;**48**:1446-1447

[5] Srivatsun G, Subha Rani S. Compact multiband planar fractal cantor antenna for wireless applications: An approach. International Journal of Antennas and Propagation. 2012;**2012**

[6] Reddy V, Sarma N. Triband circularly polarized Koch fractal boundary microstrip antenna. IEEE Antennas and Wireless Propagation Letters. 2014;**13**:1057-1060

[7] Tripathi S, Mohan A, Yadav S. Hexagonal fractal ultra-wideband antenna using Koch geometry with bandwidth enhancement. IET Microwaves, Antennas & Propagation. 2014;**8**:1445-1450

[8] Weng W-C, Hung C-L. An H-fractal antenna for multiband applications. IEEE Antennas and Wireless Propagation Letters. 2014;**13**:1705-1708

[9] Dhar S, Patra K, Ghatak R, Gupta B, Poddar DR. A dielectric resonatorloaded minkowski fractal-shaped slot loop heptaband antenna. IEEE Transactions on Antennas and Propagation. 2015;**63**:1521-1529

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Transactions on Internet & Information

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[21] Abed AT, Singh MSJ, Islam MT, Khaleel AD. Dual crescent-shaped slot antenna fed by circular polarisation into

Microwaves, Antennas & Propagation.

[22] Luo K, Chen B, Ding W-P. Meander line coupled cavity-backed slot antenna for broadband circular polarization. IEEE Antennas and Wireless

Propagation Letters. 2015;**14**:1215-1218

[23] Chetna Sharma SM, Vishwakarma DK. Miniaturization of spiral antenna based on fibonacci sequence using modified Koch curve. IEEE Antennas and Wireless Propagation Letters. 2017;

[24] Cai T, Wang G-M, Zhang X-F, Shi J-P. Low-profile compact circularlypolarized antenna based on fractal metasurface and fractal resonator. IEEE Antennas and Wireless Propagation

Letters. 2015;**14**:1072-1076

dual orthogonal strip lines. IET

WiMAX communications. KSII

technique in Q-slot antenna.

[10] Li D, Mao J-F. Coplanar waveguidefed Koch-like sided Sierpinski hexagonal carpet multifractal monopole antenna. IET Microwaves, Antennas & Propagation. 2014;**8**:358-366

[11] Yogesh Kumar Choukiker SKB. Wideband frequency reconfigurable Koch snowflake fractal antenna. IET Microwaves, Antennas & Propagation. 2017;**11**:203-208

[12] Abed AT, Singh MS, Islam MT. Amer fractal slot antenna with quad operating bands high efficiency for wireless communications. In: 2016 IEEE 3rd International Symposium on Telecommunication Technologies (ISTT). 2016. pp. 6-8

[13] Abed AT. Novel sunflower MIMO fractal antenna with low mutual coupling and dual wide operating bands. International Journal of Microwave and Wireless Technologies. 2020

[14] Abed AT. A new fractal antenna flame structure with impedance ration 10.6: 1 high efficiency for UWB applications. Al-Ma'mon College Journal. 2017:215-231

[15] Abed AT. A novel coplanar antenna butterfly structure for portable communication devices, a compact antenna with multioperating bands. IEEE Antenna and Propagation Magazine. 2020

[16] Werner DH, Haupt RL, Werner PL. Fractal antenna engineering: The theory and design of fractal antenna arrays. IEEE Antennas and Propagation Magazine. 1999;**41**:37-58

[17] Amer MSJS, Abed T, Islam MT. Compact fractal antenna circularly

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polarised radiation for Wi-Fi and WiMAX communications. IET Microwaves, Antennas & Propagation. 2018;**12**:2218-2224

**References**

3559-3567

[1] Werner DH, Gangul S. An overview of fractal antenna engineering research. loaded minkowski fractal-shaped slot loop heptaband antenna. IEEE Transactions on Antennas and Propagation. 2015;**63**:1521-1529

[10] Li D, Mao J-F. Coplanar waveguidefed Koch-like sided Sierpinski hexagonal carpet multifractal monopole antenna.

IET Microwaves, Antennas & Propagation. 2014;**8**:358-366

2017;**11**:203-208

[11] Yogesh Kumar Choukiker SKB. Wideband frequency reconfigurable Koch snowflake fractal antenna. IET Microwaves, Antennas & Propagation.

[12] Abed AT, Singh MS, Islam MT. Amer fractal slot antenna with quad operating bands high efficiency for wireless communications. In: 2016 IEEE

3rd International Symposium on Telecommunication Technologies

Wireless Technologies. 2020

[13] Abed AT. Novel sunflower MIMO fractal antenna with low mutual

coupling and dual wide operating bands. International Journal of Microwave and

[14] Abed AT. A new fractal antenna flame structure with impedance ration 10.6: 1 high efficiency for UWB applications. Al-Ma'mon College

[15] Abed AT. A novel coplanar antenna

[16] Werner DH, Haupt RL, Werner PL. Fractal antenna engineering: The theory and design of fractal antenna arrays. IEEE Antennas and Propagation

[17] Amer MSJS, Abed T, Islam MT. Compact fractal antenna circularly

butterfly structure for portable communication devices, a compact antenna with multioperating bands. IEEE Antenna and Propagation

(ISTT). 2016. pp. 6-8

Journal. 2017:215-231

Magazine. 2020

Magazine. 1999;**41**:37-58

[2] Chen W-L, Wang G-M, Zhang C-X.

[3] Oraizi H, Hedayati S. Miniaturization of microstrip antennas by the novel application of the Giuseppe Peano fractal geometries. IEEE Transactions on Antennas and Propagation. 2012;**60**:

microstrip-line-fed printed wide-slot antenna with a fractal-shaped slot. IEEE

IEEE Anlennas and Propagation Magazine. 2003;**45**:38-57

*Modern Printed-Circuit Antennas*

Bandwidth enhancement of a

Transactions on Antennas and Propagation. 2009;**57**:2176-2179

[4] Chaimool S, Chokchai C,

2012;**48**:1446-1447

Propagation. 2012;**2012**

[6] Reddy V, Sarma N. Triband circularly polarized Koch fractal boundary microstrip antenna. IEEE Antennas and Wireless Propagation

Letters. 2014;**13**:1057-1060

2014;**8**:1445-1450

**90**

[7] Tripathi S, Mohan A, Yadav S. Hexagonal fractal ultra-wideband antenna using Koch geometry with bandwidth enhancement. IET

Microwaves, Antennas & Propagation.

[8] Weng W-C, Hung C-L. An H-fractal antenna for multiband applications. IEEE Antennas and Wireless

Propagation Letters. 2014;**13**:1705-1708

[9] Dhar S, Patra K, Ghatak R, Gupta B, Poddar DR. A dielectric resonator-

Akkaraekthalin P. Multiband loaded fractal loop monopole antenna for USB dongle applications. Electronics Letters.

[5] Srivatsun G, Subha Rani S. Compact multiband planar fractal cantor antenna for wireless applications: An approach. International Journal of Antennas and

[18] Abed AT, Singh MSJ, Jawad AM. Investigation of circular polarization technique in Q-slot antenna. International Journal of Microwave and Wireless Technologies. 2020;**12**:176-182

[19] Abed AT, Singh MS, Islam MT. Compact-size fractal antenna with stable radiation properties for Wi-Fi and WiMAX communications. KSII Transactions on Internet & Information Systems. 2018;**12**

[20] Abed A, Singh M. Slot antenna single layer fed by step impedance strip line for Wi-Fi and Wi-Max applications. Electronics Letters. 2016;**52**:1196-1198

[21] Abed AT, Singh MSJ, Islam MT, Khaleel AD. Dual crescent-shaped slot antenna fed by circular polarisation into dual orthogonal strip lines. IET Microwaves, Antennas & Propagation. 2017;**11**:2129-2133

[22] Luo K, Chen B, Ding W-P. Meander line coupled cavity-backed slot antenna for broadband circular polarization. IEEE Antennas and Wireless Propagation Letters. 2015;**14**:1215-1218

[23] Chetna Sharma SM, Vishwakarma DK. Miniaturization of spiral antenna based on fibonacci sequence using modified Koch curve. IEEE Antennas and Wireless Propagation Letters. 2017; **16**:932-935

[24] Cai T, Wang G-M, Zhang X-F, Shi J-P. Low-profile compact circularlypolarized antenna based on fractal metasurface and fractal resonator. IEEE Antennas and Wireless Propagation Letters. 2015;**14**:1072-1076

**Chapter 5**

**Abstract**

beams.

**93**

**1. Introduction**

Radiation Pattern Synthesis of

Planar Arrays Using Parasitic

Active Elements

feeding network, array pattern synthesis

known to be very complex and expensive.

Patches Fed by a Small Number of

*Jafar Ramadhan Mohammed and Karam Mudhafar Younus*

In this chapter, several planar array designs based on the use of a small number

of the active elements located at the center of the planar array surrounded by another number of the uniformly distributed parasitic elements are investigated. The parasitic elements are used to modify the radiation pattern of the central active elements. The overall radiation pattern of the resulting planar array with a small number of active elements is found to be comparable to that of the fully active array

elements with a smaller sidelobe level (SLL) at the cost of a relatively wider beamwidth and lower directivity. Nevertheless, the uses of only a small number of the active elements provide a very simple feeding network that reduces the cost and the complexity of the array. Simulation results which have been computed using computer simulation technology-microwave studio (CST-MWS) show that the sidelobe level of the designed array pattern with parasitic elements is considerably better than that of the similar fully active array elements. The proposed array can be effectively and efficiently used in the applications that require wider antenna

**Keywords:** planar arrays, parasitic elements, driven elements, mutual coupling,

By properly controlling the design parameters of the antenna arrays, it is possible to generate the desired radiation characteristics such as higher directivity and lower sidelobe level. The most design parameters that have been given an increased attention for many practical applications are the amplitude and the phase excitations of the individual elements [1–3] in addition to the element's spacing [4, 5]. However, the practical implementation of the feeding networks in such arrays is

Recently, the feeding networks were made very easy and practically efficient by controlling only a certain number of the active elements rather than all of the array elements [6, 7]. Other methods used a number of parasitic elements illuminated by a single active element to simplify the complexity issue of the feeding network.

## **Chapter 5**
