Compact Broadband Antenna with Vicsek Fractal Slots for WLAN and WiMAX Applications

: This paper aims to design a compact broadband antenna for wireless local area network (WLAN) and worldwide interoperability for microwave access (WIMAX) applications. The suggested antenna consists of an octagonal radiator with Vicsek fractal slots and a partial ground plane, it is printed on FR-4 dielectric substrate, and its global dimension is 50 × 50 × 1.6 mm 3 . The antenna is designed and constructed using both CST MICROWAVE STUDIO ® and CADFEKO electromagnetic solver, and in order to validate the acquired simulation results, the antenna is manufactured and tested using vector network analyzer E5071C. The measurement results show that the designed antenna attains a broadband bandwidth (S 11 < − 10 dB) from 2.48 to 6.7 GHz resonating at 3.6 and 5.3 GHz, respectively. The broadband bandwidth covers the two required bands: WiMAX at the frequencies 2.3/2.5/3.3/3.5/5/5.5 GHz and WLAN at the frequencies 3.6/2.4–2.5/4.9–5.9 GHz. In addition, the suggested antenna provides good gains of 2.78 dBi and 5.32 dBi, omnidirectional measured radiation patterns in the E-plane and the H-plane and high efﬁciencies of 88.5% and 84.6% at the resonant frequencies. A close agreement of about 90% between simulation and measurement results is noticed.


Introduction
With fast progress in wireless technology systems, there is a strong request for antennas with low profiles, compact dimensions, planar geometry and especially the ability to provide a large impedance bandwidth for WLAN and WiMAX applications in several bands, such as 2.4-2.5/3.6/4.9-5.9GHz and 2.3/2.5/3.3/3.5/5/5.5 GHz, respectively [1][2][3].Microstrip antennas are the best type of antennas that meet these requirements due to their low weight, easy miniaturization, portability, installation flexibility, good performance and low manufacturing costs [4,5].
In the literature, various structures of microstrip antennas are suggested to shield WLAN and WiMAX applications.Most of these antennas are slotted patch antennas fed by a coplanar waveguide (CPW) technique, such as CPW-fed monopole antennas, or a fractal antenna approach.A monopole antenna with a slot and dual ring resonator in the ground plane was proposed in [6] to achieve a triple band at 2.5, 3.7 and 4.6 GHz for WLAN and WiMAX applications.According to [7], a CPW-fed hexagonal shaped patch antenna was designed to achieve three bands i.e., 0.4, 1.2 and 1.75 GHz.These bands were obtained by inserting H-tree fractal slots in the radiating elements.Similarly, in [8], a Hilbert fractal slot was inserted in an octagonal radiator to operate in WLAN and WiMAX applications, and it offered a dual band at 2.48 and 5.68 GHz with a bandwidth of about 0.7 and 3.55 GHz, respectively.A novel CPW rectangular antenna with a cantor fractal slot was developed in [9]; it shielded two bands of about 1 and 1.7 GHz at resonant frequencies 3 and 5.1 GHz.Likewise, in [10], a compact antenna for UWB notched applications was developed; it covered a bandwidth from 3.1 to 10.6 GHz, with a rejected band from 2.4 to 2.484 GHz, for WLAN applications.
On the other hand, the defected ground structure DGS approach can be applied.A monopole antenna consisting of a rectangular ring and a fork-shaped strip with a defected ground plane was developed in [11] to generate three bands for WLAN and WiMAX applications at 2.5, 3.5 and 5.5 GHz.Thereafter in [12], a rectangular radiator with defected ground structure was suggested, offering three resonant frequencies of 2.40, 3.5 and 5.8 GHz which shield the WLAN and WiMAX bands.
References [13][14][15] additionally propose antennas for WLAN and WiMAX applications using an asymmetrical feed line.In ref. [13], a compact antenna consisting of three monopoles with different lengths and an asymmetrical feed line was suggested to achieve four bands of about 0.17, 0.16, 0.17 and 0.15 GHz for WLAN and WiMAX applications.Naik, in [14], developed an asymmetric CPW antenna with a split ring for two bands for WLAN and WiMAX at 2.46 and 3.51 GHz with bandwidths of about 0.17 and 0.15 GHz, respectively.An inverted L-shaped strip in the radiator, fed by an asymmetric CPW, was proposed in [15]; it offered a wide bandwidth of about 3.3 GHz which covers the WLAN and WiMAX bands at 5.725-5.85GHz and 3.3-3.7 GHz, respectively.
Furthermore, antennas for WLAN and WiMAX applications based on the metamaterial approach are presented in references [16][17][18].In ref. [16], a compact antenna consisted of a utilizing complementary split ring resonators (CSRRs) placed in the radiator to reject four bands for WLAN and WiMAX applications at 3.4, 4.1, 4.8 and 5.6 GHz.Ken proposed, in [17], a broadband antenna composed of two interspaced ring resonators as radiator elements printed on FR-4 substrate, and the overall size of the antenna was 60 × 90 × 1.6 mm 3 .The antenna offered two bands of about 0.7 and 1.3 GHz at 2.4 and 5.8 GHz.A CPW-fed metamaterial antenna was proposed in [18] to support WLAN and WiMAX applications at 2.4/5.5 GHz and 3.5 GHz bands, respectively.
The authors in [19] developed a MIMO antenna comprised of two spider-shaped radiators printed on FR-4 substrate sized 50 × 37 mm 2 to shield WLAN and WiMAX bands at 2.43, 3.83, 4.4 and 5.8 GHz.According to [20], a 4 × 4 MIMO antenna with dual operating bands was modelled, with four elements positioned on both sides of the dielectric material in the proposed MIMO antenna.Each element had a rectangular open-loop resonator inserted into the ground plane.The antenna had bandwidths of 0.08 GHz and 0.17 GHz at 2.46 and 3.5, respectively.WLAN (2.4-2.485GHz) and WiMAX (3.4-3.6 GHz) bandwidth requirements were met.
The design in [21] was composed of two layers, one layer comprising an E-shaped patch and the second comprising a U-slot.The proposed antenna covered the WLAN at 2.4 GHz and the WiMAX at 3.5 GHz.Altaf, in [22], designed a Y-shaped dielectric resonator antenna with size of 120 × 70 mm 2 ; it presented two bands from 2.401 GHz to 2.495 GHz and from 3.4 GHz to 3.69 GHz which shielded WLAN and WiMAX bands, respectively.In all the above analyses, it can be observed that these antennas had complex structures with large areas, or they do not cover all the bands of WLAN and WiMAX applications.This work is related to the design of a broadband octagonal microstrip patch antenna with Vicsek fractal slots for WLAN and WiMAX applications.The investigated antenna offers a broadband of 4.22 GHz from 2.48 GHz to 6.7 GHz with two resonant frequencies at 3.6 GHz and 5.3 GHz which shield both the WLAN and WiMAX bands.
The broadband characteristic is realized by using the fractal slots and partial ground plane.The designed antenna has good gains of 2.78 dBi and 5.32 dBi, an omnidirectional radiation pattern in both the E-plane and the H-plane and high efficiency of 88.5% and 84.6% at the resonant frequencies.In the first section of this paper, the antenna geometry and the design evolution procedure are described.A parametric analysis of critical dimensions is presented in Section 2. The discussion of the simulated and experimental results is elaborated upon in Section 3. The conclusion of this work is given in the last section.

Antenna Geometry
The configuration of the suggested antenna is displayed in Figure 1.It comprises an octagonal radiator loaded with the two first iterations of Vicsek fractal slot structure, and it is engraved on a 1.6-mm-thick FR-4 dielectric substrate with relative permittivity ε r = 4.4 and tan(δ) = 0.02.In addition, a partial ground plane with initial dimensions 50 × 15 mm 2 is printed on the bottom side of the substrate.The antenna geometry has a complete size of 50 × 50 × 1.6 mm 3 and a 50-Ω feed line of width 'W f ' and length 'L f ' with an inset of length 'd', and gap 'g' is used to excite the antenna.The antenna has been designed and performed using the CST MWS simulator, and the optimal dimensions of the investigated antenna are listed in Table 1.
In all the above analyses, it can be observed that these antennas had complex structures with large areas, or they do not cover all the bands of WLAN and WiMAX applications.This work is related to the design of a broadband octagonal microstrip patch antenna with Vicsek fractal slots for WLAN and WiMAX applications.The investigated antenna offers a broadband of 4.22 GHz from 2.48 GHz to 6.7 GHz with two resonant frequencies at 3.6 GHz and 5.3 GHz which shield both the WLAN and WiMAX bands.
The broadband characteristic is realized by using the fractal slots and partial ground plane.The designed antenna has good gains of 2.78 dBi and 5.32 dBi, an omnidirectional radiation pattern in both the E-plane and the H-plane and high efficiency of 88.5% and 84.6% at the resonant frequencies.In the first section of this paper, the antenna geometry and the design evolution procedure are described.A parametric analysis of critical dimensions is presented in Section 2. The discussion of the simulated and experimental results is elaborated upon in Section 3. The conclusion of this work is given in the last section.

Antenna Geometry
The configuration of the suggested antenna is displayed in Figure 1.It comprises an octagonal radiator loaded with the two first iterations of Vicsek fractal slot structure, and it is engraved on a 1.6-mm-thick FR-4 dielectric substrate with relative permittivity εr = 4.4 and tan(δ) = 0.02.In addition, a partial ground plane with initial dimensions 50 × 15 mm 2 is printed on the bottom side of the substrate.The antenna geometry has a complete size of 50 × 50 × 1.6 mm 3 and a 50-Ω feed line of width 'Wf' and length 'Lf' with an inset of length 'd', and gap 'g 'is used to excite the antenna.The antenna has been designed and performed using the CST MWS simulator, and the optimal dimensions of the investigated antenna are listed in Table 1.

Design Evolution Procedure
Figure 2 presents the evolutionary stages of the investigated antenna.The antenna evolution process starts with a rectangular microstrip antenna excited by a feed line.Thereafter, four triangular parts are cut in the four angles of the rectangular radiator in order to make an octagonal radiator.Subsequently, the octagonal patch is loaded with the first and the second iterations of Vicsek fractal slots to achieve the final geometry.

Design Evolution Procedure
Figure 2 presents the evolutionary stages of the investigated antenna.The antenna evolution process starts with a rectangular microstrip antenna excited by a feed line.Thereafter, four triangular parts are cut in the four angles of the rectangular radiator in order to make an octagonal radiator.Subsequently, the octagonal patch is loaded with the first and the second iterations of Vicsek fractal slots to achieve the final geometry.The first step in the design of the suggested antenna is displayed in Figure 2a.A rectangular microstrip antenna of length Lp and width Wp was taken as a reference antenna (simple microstrip patch).The dimensions of the rectangular radiator were determined using the theory of transmission lines using the following Equations ( 1)-( 4) [23]: The width of a microstrip antenna can be calculated by: where c and εr are the speed of light (3 × 10 8 m/s) and relative permittivity of the medium, respectively, and fr represents the resonant frequency at which the antenna is designed.
The effective dielectric constant of the substrate is yielded by [23]: where h is the substrate thickness.Finally, the length of the rectangular radiator is given by [24]: The first step in the design of the suggested antenna is displayed in Figure 2a.A rectangular microstrip antenna of length L p and width W p was taken as a reference antenna (simple microstrip patch).The dimensions of the rectangular radiator were determined using the theory of transmission lines using the following Equations ( 1)-( 4) [23]: The width of a microstrip antenna can be calculated by: where c and ε r are the speed of light (3 × 10 8 m/s) and relative permittivity of the medium, respectively, and f r represents the resonant frequency at which the antenna is designed.
The effective dielectric constant of the substrate is yielded by [23]: where h is the substrate thickness.Finally, the length of the rectangular radiator is given by [24]: In Equation (3), ∆L corresponds to the increase in length of the antenna due to fringing effects and is given by [23]: The corresponding simulated S 11 of the different steps of the design process of the investigated antenna is depicted in Figure 3.The simple microstrip patch antenna generates one resonant frequency at 7.4 GHz, and it provides a bandwidth of 1.5 GHz.The truncated patch antenna structure is obtained by cutting four triangular shapes in the four angles of the radiating element to obtain an octagonal patch antenna as depicted in Figure 2b.It is noticed from Figure 4 that the truncated patch antenna provides a broadband of 3.91 GHz from 2.29 to 6.2 GHz with one resonant frequency at 3.8 GHz.
fringing effects and is given by [23]: The corresponding simulated S11 of the different steps of the design process of the investigated antenna is depicted in Figure 3.The simple microstrip patch antenna generates one resonant frequency at 7.4 GHz, and it provides a bandwidth of 1.5 GHz.The truncated patch antenna structure is obtained by cutting four triangular shapes in the four angles of the radiating element to obtain an octagonal patch antenna as depicted in Figure 2b.It is noticed from Figure 4 that the truncated patch antenna provides a broadband of 3.91 GHz from 2.29 to 6.2 GHz with one resonant frequency at 3.8 GHz.The corresponding simulated S11 of the different steps of the design process of the investigated antenna is depicted in Figure 3.The simple microstrip patch antenna generates one resonant frequency at 7.4 GHz, and it provides a bandwidth of 1.5 GHz.The truncated patch antenna structure is obtained by cutting four triangular shapes in the four angles of the radiating element to obtain an octagonal patch antenna as depicted in Figure 2b.It is noticed from Figure 4 that the truncated patch antenna provides a broadband of 3.91 GHz from 2.29 to 6.2 GHz with one resonant frequency at 3.8 GHz.In the third step, the first iteration of Vicsek fractal slots is incorporated in the radiating element (slotted patch) as presented in Figure 2c.
The construction of Vicsek fractal slots is based on square rotated by π/4 and decomposed into nine squares.The four corner squares and the middle square are kept, while the remaining squares are eliminated, as illustrated in the Vicsek fractal [24] with: The Hausdorff dimension of the Vicsek fractal is presented by Equation (5) [24]: The slotted patch antenna presents a broadband of 4.3 GHz from 2.3 to 6.6 GHz with two resonant frequencies at 3.55 and 5.3 GHz with reflection coefficients −42 dB and −40 dB, respectively.Finally, the geometry of the suggested antenna is obtained by introducing the second iteration of Vicsek fractal slots on the octagonal patch antenna, as shown in Figure 2d.The suggested antenna achieves a broadband of 4.35 GHz from 2.3 to 6.65 GHz with good impedance matching at resonant frequencies 3.6 and 5.2 GHz.

Parametric Analysis of the Suggested Antenna
The broadband characteristics of the suggested antenna are achieved with the help of parametric study.This study is used to obtain the optimal values of the antenna dimensions and the best performance by modifying one parameter and fixing the other parameters.

The Feed Line Length L f and Width W f Variation Effects
The effect of the microstrip feed line length L f on the suggested antenna performance is studied by changing the L f from 13 to 15 mm and the feed line width from 2.6 mm to 3.5 mm. Figure 5 illustrates the variation of S 11 versus frequency for various lengths and widths of the feed line, L f and W f .It can be noticed from the figure that by increasing the length of the feed line, the bandwidth increases from 3.8 GHz to 4.35 GHz.The simulations confirm that to obtain good impedance matching and the desired broadband, the optimal values for the length and width of the feed line are L f = 15 mm and W f = 3.5 mm.Frequency (GHz) Figure 5. Parametric studies for the variation in the feed line length Lf and width Wf.

The Ground Plane Length Lg Variation Effects
Similar to Lf and Wf, Lg is also varied, as depicted in Figure 6.By changing the length Lg from 13 to 16 mm, the bandwidth increases from 1.5 GHz to 4.35 GHz.Moreover, it is seen that the optimal value of the length of the ground plane is Lg = 15 mm, for which the suggested antenna achieves the desired broadband with good impedance matching.

The Ground Plane Length L g Variation Effects
Similar to L f and W f , L g is also varied, as depicted in Figure 6.By changing the length L g from 13 to 16 mm, the bandwidth increases from 1.5 GHz to 4.35 GHz.Moreover, it is seen that the optimal value of the length of the ground plane is L g = 15 mm, for which the suggested antenna achieves the desired broadband with good impedance matching.
Similar to Lf and Wf, Lg is also varied, as depicted in Figure 6.By changing the length Lg from 13 to 16 mm, the bandwidth increases from 1.5 GHz to 4.35 GHz.Moreover, it is seen that the optimal value of the length of the ground plane is Lg = 15 mm, for which the suggested antenna achieves the desired broadband with good impedance matching.

The Vicsek Slot Length Variation Effects
The parametric study in this section looks into the effect of the length of the Vicsek fractal slot on the impedance bandwidth and on the resonant frequencies.Figure 7 depicts the variation of S 11 when the length a of the Vicsek fractal slot is changed and all other dimensions remain constant.It can be claimed from the figure that the parameter a has no effect on the suggested antenna's impedance bandwidth but it does change the position of the resonant frequencies.The range of this parameter (a) is between 0.7 and 1.6 mm.Additionally, the value a = 1.3 mm is found to provide satisfactory impedance matching in the 3.6 and 5.8 GHz frequencies corresponding to the WLAN and WiMAX bands.

The Vicsek Slot Length Variation Effects
The parametric study in this section looks into the effect of the length of the Vicsek fractal slot on the impedance bandwidth and on the resonant frequencies.Figure 7 depicts the variation of S11 when the length a of the Vicsek fractal slot is changed and all other dimensions remain constant.It can be claimed from the figure that the parameter a has no effect on the suggested antenna's impedance bandwidth but it does change the position of the resonant frequencies.The range of this parameter (a) is between 0.7 and 1.6 mm.Additionally, the value a = 1.3 mm is found to provide satisfactory impedance matching in the 3.6 and 5.8 GHz frequencies corresponding to the WLAN and WiMAX bands.

Results and Discussion
The simulation of the suggested antenna was carried out in both CST MICROWAVE STUDIO ® , which is based on finite integration technology (FIT), and the CADFEKO simulator, which uses the method of moments (MoM).The antenna was excited by a waveguide port, and the boundary box had an area of 200 mm × 200 mm × 200 mm, as shown in Figure 8, while the number of mesh cells was 374,088.To prove that the

Results and Discussion
The simulation of the suggested antenna was carried out in both CST MICROWAVE STUDIO ® , which is based on finite integration technology (FIT), and the CADFEKO simulator, which uses the method of moments (MoM).The antenna was excited by a waveguide port, and the boundary box had an area of 200 mm × 200 mm × 200 mm, as shown in Figure 8, while the number of mesh cells was 374,088.To prove that the simulation results are accurate, the suggested broadband antenna was manufactured as depicted in Figure 9.The reflection coefficient S 11 was measured using vector network analyzer E5071C.The variation of the reflection coefficient S 11 of the suggested broadband antenna is illustrated in Figure 10.It is noticed from the measured results that the antenna presents a broadband of 4.22 GHz from 2.48 GHz to 6.7 GHz with two resonant frequencies at 3.6 and 5.3 GHz with reflection coefficients −41.3 dB and −57.2 dB, respectively.The designed antenna provides a broadband which covers the WiMAX bands at frequencies 2.3/2.5/3.3/3.5/5/5.5 GHz and the WLAN at frequencies 3.6/2.4-2.5/4.9-5.9GHz.
The simulated surface current distribution of the suggested broadband antenna results acquired by CST MICROWAVE STUDIO ® at resonant frequencies 3.6 and 5.3 GHz is depicted in Figure 11.It is seen from the figure that the current distribution is concentrated at the inset microstrip feed line, the ground plane and the extremity of the octagonal radiator at 3.6 GHz.Similarly, in the 5.3 GHz frequency, the high current surface is concentrated at the inset feed line, the ground plane.The simulated surface current distribution of the suggested broadband antenna results acquired by CST MICROWAVE STUDIO ® at resonant frequencies 3.6 and 5.3 GHz is depicted in Figure 11.It is seen from the figure that the current distribution is concentrated at the inset microstrip feed line, the ground plane and the extremity of the octagonal radiator at 3.6 GHz.Similarly, in the 5.3 GHz frequency, the high current surface is concentrated at the inset feed line, the ground plane.The measurements of radiation pattern and peak gain of the proposed antenna were made in an anechoic chamber, as shown in Figure 12.In addition, Figure 13 illustrates the measured radiation pattern together with the simulated results acquired by CST MICROWAVE STUDIO ® and the CADFEKO simulator at resonant frequencies 3.6 and 5.3 GHz.It can be claimed from the figure that the suggested antenna presents a good radiation pattern performance since it achieves an omnidirectional pattern in the H-plane and in the E-plane.The measurements of radiation pattern and peak gain of the proposed antenna were made in an anechoic chamber, as shown in Figure 12.In addition, Figure 13 illustrates the measured radiation pattern together with the simulated results acquired by CST MI-CROWAVE STUDIO ® and the CADFEKO simulator at resonant frequencies 3.6 and 5.3 GHz.It can be claimed from the figure that the suggested antenna presents a good radiation pattern performance since it achieves an omnidirectional pattern in the H-plane and in the E-plane.
The measured peak gain and simulated peak gain obtained by CST MICROWAVE STUDIO ® and CADFEKO software are illustrated in Figure 14 and the simulated radiation efficiency acquired by CST MWS is depicted in Figure 15.From the figures, it can be revealed that the suggested antenna presents good performance in terms of peak gain and radiation efficiency.The antenna offers considerable gains and radiation efficiencies: 2.78/5.32dBi and 88.5/84.6% at the operating frequencies 3.6/5.3GHz, respectively.
The measurements of radiation pattern and peak gain of the proposed antenna were made in an anechoic chamber, as shown in Figure 12.In addition, Figure 13 illustrates the measured radiation pattern together with the simulated results acquired by CST MICROWAVE STUDIO ® and the CADFEKO simulator at resonant frequencies 3.6 and 5.3 GHz.It can be claimed from the figure that the suggested antenna presents a good radiation pattern performance since it achieves an omnidirectional pattern in the H-plane and in the E-plane.The measured peak gain and simulated peak gain obtained by CST MICROWAVE STUDIO ® and CADFEKO software are illustrated in Figure 14 and the simulated radiation efficiency acquired by CST MWS is depicted in Figure 15.From the figures, it can be revealed that the suggested antenna presents good performance in terms of peak gain and radiation efficiency.The antenna offers considerable gains and radiation efficiencies: 2.78/5.32dBi and 88.5/84.6% at the operating frequencies 3.6/5.3GHz, respectively.The measured peak gain and simulated peak gain obtained by CST MICROWAVE STUDIO ® and CADFEKO software are illustrated in Figure 14 and the simulated radiation efficiency acquired by CST MWS is depicted in Figure 15.From the figures, it can be revealed that the suggested antenna presents good performance in terms of peak gain and radiation efficiency.The antenna offers considerable gains and radiation efficiencies: 2.78/5.32dBi and 88.5/84.6% at the operating frequencies 3.6/5.3GHz, respectively.The simulation results obtained by the CADFEKO and CST solvers, as well as the measurement results, are collected and summarized in Table 2.The impedance bandwidth is 4.15 GHz with two operating frequencies 3.5 and 5.1 GHz for CADFEKO, and the impedance bandwidth is about 4.35 GHz with two resonant frequencies at 3.6 and 5.2 GHz for CST.The measured impedance bandwidth is 4.22 GHz, with two operating frequencies at 3.6 and 5.3 GHz.In addition, when evaluating gain values, the CST result is 2.75 and 5.37 dBi at 3.6 and 5.2 GHz, respectively.In addition, the CADFEKO result is 2.63 and 5.26 dB at 3.5 and 5.1 GHz, respectively, and the measured gain value was around 2.78 and 5.32 dBi at 3.6 and 5.3 GHz.As a result, for the impedance bandwidth, resonant frequencies and gain comparison, the CST produced results that were closer to the measured results.The CST based on the FIT approach produced a better outcome for broadband antennas, as predicted by the literature [25].The simulation results obtained by the CADFEKO and CST solvers, as well as the measurement results, are collected and summarized in Table 2.The impedance bandwidth is 4.15 GHz with two operating frequencies 3.5 and 5.1 GHz for CADFEKO, and the impedance bandwidth is about 4.35 GHz with two resonant frequencies at 3.6 and 5.2 GHz for CST.The measured impedance bandwidth is 4.22 GHz, with two operating frequencies at 3.6 and 5.3 GHz.In addition, when evaluating gain values, the CST result is 2.75 and 5.37 dBi at 3.6 and 5.2 GHz, respectively.In addition, the CADFEKO result is 2.63 and 5.26 dBi at 3.5 and 5.1 GHz, respectively, and the measured gain value was around 2.78 and 5.32 dBi at 3.6 and 5.3 GHz.As a result, for the impedance bandwidth, resonant frequencies and gain comparison, the CST produced results that were closer to the measured results.The CST based on the FIT approach produced a better outcome for broadband antennas, as predicted by the literature [25].Table 3 compares the proposed broadband antenna for WLAN and WIMAX applications to various antennas previously reported in the literature.The antenna presented in [17,22] did not shift all the resonant frequencies of WLAN and WiMAX applications and had a large size.The antenna proposed in [18] provided a low gain compared to our designed antenna.In ref. [19], the antenna had a large size and narrow impedance bandwidth.In ref. [20], the antenna had a simple structure; moreover, it did not cover all the required bands of WLAN and WiMAX and it provided a lower gain compared to our antenna.In ref. [21], the antenna had a complex structure printed in Taconic RF-35, it achieved a broadband, and it did not cover all the bands of WLAN and WiMAX.The suggested broadband antenna has various advantages over previously reported antennas [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] in terms of size, impedance bandwidth and gain, as shown by the comparison.

Figure 1 .
Figure 1.The suggested antenna structure with notations: (a) top view and (b) back view.

Figure 1 .
Figure 1.The suggested antenna structure with notations: (a) top view and (b) back view.

Figure 3 .
Figure 3.The iterations of the Vicsek fractal structure.

Figure 4 .
Figure 4. Simulated S11 of the different evolutionary stages of the suggested antenna.

Figure 3 .
Figure 3.The iterations of the Vicsek fractal structure.

Figure 3 .
Figure 3.The iterations of the Vicsek fractal structure.

Figure 4 .
Figure 4. Simulated S11 of the different evolutionary stages of the suggested antenna.

Figure 4 .
Figure 4. Simulated S 11 of the different evolutionary stages of the suggested antenna.

Figure 5 .
Figure 5. Parametric studies for the variation in the feed line length L f and width W f .

Figure 6 .
Figure 6.Parametric studies for the variation in the ground plane length Lg.

Figure 6 .
Figure 6.Parametric studies for the variation in the ground plane length L g .

Figure 7 .
Figure 7. Parametric studies for the variation in the Vicsek fractal slot length a.

Figure 7 .
Figure 7. Parametric studies for the variation in the Vicsek fractal slot length a.

15 Figure 8 .
Figure 8. Boundary box of the proposed antenna.

Figure 9 .
Figure 9. Manufactured prototype of the proposed antenna.

Figure 9 .
Figure 9. Manufactured prototype of the proposed antenna.

Figure 9 .
Figure 9. Manufactured prototype of the proposed antenna.

Figure 10 . 15 Figure 10 .
Figure 10.Measured and simulated S-parameters of the suggested antenna.

Figure 11 .
Figure 11.The simulated surface current distribution of the suggested broadband antenna at (a) 3.6 and (b) 5.3 GHz.

Figure 11 .
Figure 11.The simulated surface current distribution of the suggested broadband antenna at (a) 3.6 and (b) 5.3 GHz.

Figure 12 .
Figure 12.The measurement setup of radiation pattern and gain in an anechoic chamber.Figure 12.The measurement setup of radiation pattern and gain in an anechoic chamber.

Figure 12 .Figure 13 .
Figure 12.The measurement setup of radiation pattern and gain in an anechoic chamber.Figure 12.The measurement setup of radiation pattern and gain in an anechoic chamber.

Figure 14 . 15 Figure 14 .
Figure 14.Simulated and measured peak gain of the suggested antenna versus frequency.

Figure 15 .
Figure 15.Simulated radiation efficiency of the suggested antenna.

Figure 15 .
Figure 15.Simulated radiation efficiency of the suggested antenna.

Table 1 .
Dimensions of the suggested antenna.

Table 1 .
Dimensions of the suggested antenna.

Table 2 .
Summary of simulation and measurement results of the suggested antenna.

Table 2 .
Summary of simulation and measurement results of the suggested antenna.

Table 3 .
Comparison of the suggested antenna performances with other antennas in the literature.