A New Compact Dual-band Antenna Based on Sierpinski Curve Slotted Ground Plane and Current Distribution Analysis

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Introduction
Modern wireless applications make the dual band antennas have the vital role of the other types of antennas in many academic and commercial researches. Regarding the slotted antennas, the design of dual-band antenna structure can take three main ways [1]. The first one is to achieve a dual-band resonance frequency depending on two resonators to radiate an electromagnetic wave at two different operating frequencies [2][3]; each of these resonant frequencies of the designed antenna is attributed by each resonator, which has different shape and size. The larger structure will excite the lower resonant frequency and vice versa. The second way includes the excitation another mode by added a reactive load to the structure of a wideband antenna to create a resonance at a second band [4] while the third way denote to splitting the broadband resonance by inserting a notch frequency band [5] to generate a dual bands behavior. A slotted antenna, which has been fed by a microstrip, feed line [6] represents a good example to satisfy the methods mentioned above. It is considered an attractive one because of its simple structure and easy of fabrication. In these types of antennas, slots can take any shape to achieve the purpose of dual band response such as the Euclidean form or fractal shapes as will be explained briefly. Fractal geometries possess two unique properties; space-filling and self-similarity. These properties have essential contributions to find solutions for antennas and electronic in the course of the last three decades. Also, fractals give another era of optimized design tools, initially utilized effectively in antennas but applicable in a general manner [7]. In this respect, the successful application of various fractal geometries to design compact dual-band slot antenna design has been intensively reported in the literature [8][9][10][11][12][13][14]. In this paper, an attractive approach to generate a dual-band response from a multi-band antenna has been introduced. The idea of this method is based on changing the path of the electric current from a particular region in the structure of multiband antenna by using the current distribution analysis to reject an undesired band from the multi-band response. Figure 1 shows the geometry of the proposed multi-band antenna, which is supposed to be, printed on a compact FR-4 substrate having a relative dielectric constant of 4.4 with dimensions (35.28 × 35.28 × 1.6) mm3. Figure 1(b) represents the front view of the structure which shows the slotted ground plane, the ground plane in the form of a square ring having external dimensions of (Wex × Lex), and internal dimensions of (Win × Lin). A Sierpinski curve 704 fractal shape of the first iteration has been employed to the four corners of a small square having dimensions of (Wsq × Wsq) at the middle area inside the ring of the ground plane, each one of them having dimensions equal to the half dimensions of the small square. The proposed multi-band antenna fed by a simple (50) Ω microstrip feed line having dimensions of (Wfl × Lfl) as shown in Figure 1(c).

Figure 1: The modeled triple-band antenna structure
The generation process of the Sierpinski curve fractal geometry up to the second iteration is shown in Figure 2 [15]. The square shape in Figure 2(a) represents the starting pattern for this type of fractal. While the generator, which represents the first iteration, is shown in Figure  2(b). The construction of the generator considers four small squares each one of them having dimensions of about half the dimensions of the original one in the previous iteration, has been rotated by (45) degrees and has been placed at each corner of the original square. Then the generator would repeat itself at each corner of a square as a second iteration but with dimensions equal to half the dimensions of the previous iteration and so on. Table 1

The Proposed Antenna Design
The current distributions on the surface of the proposed antenna at different frequencies have to be examined, and thoroughly testing relevant antenna parameters have to be checked. Consequently, it has been found that both of the lengths of the internal slot (2×Lin) with the width of it (Win) represent the active parameters on the lower resonance frequency of the designed antenna. In terms of an effective length: (1) Then the lower resonance frequency can be calculated as:

Performance Evaluation of the Proposed Antenna
Modeling and the performance evaluation of the proposed antennas have been carried out using two EM simulators; the CST Microwave Studio [16], and the High-Frequency Structure Simulation HFSS [17] to verify the results. Figure  3 shows the simulated input reflection coefficient S11 of the modeled antenna. Referring to the CST response and for a swept frequency range from (1-10) GHz, there are three resonating bands. The first band extends from (2.32-2.62) GHz with a center frequency of 2.44 GHz at S11 of -17.12 dB. The second band extends from (4.58-4.96) GHz with a center frequency of 4.77 GHz at S11 of -22.83 dB. The third band extends from (6.42-7.10) GHz with a center frequency of 6.72 GHz at S11 of -25.28 dB. As described in Equation (1), the current is concentrated around the lower width (Win) of the slot and both of the slot lengths (Lin) as shown in Figure 4(a) and (b). Figure 4 demonstrates the distribution of the current on the surface of the triple band antenna at 2.32 GHz and 2.44 GHz respectively. While the center frequency of the second band in Figure 4(c), the current is concentrated at the internal four corners especially the upper two corners. The structure of the Sierpinski curve shows the current concentration at the center frequency of the third band in Figure  4(d).

The Dual-Band Antenna Structure and Performance Evaluation
Since the second band covers the range of frequency extending from (4.58-4.96) GHz and as known there are no applications in this range of frequency. Accordingly, an approach has been studied to remove the middle un-used band from the resonance of Figure  3. This approach is based on current distribution analysis, as the second band depends on the current concentrated at both internal upper corners of the slotted ground plane of the triple-band antenna as shown in Figure 4(c). The current distribution analysis has been found to be an attractive approach in the dual-band and multiband planar antenna design [18]. Then by adding two small squares with dimensions of (4.7×4.7) mm2 to these corners as demonstrated in Figure 5 to control the path of the current, it has been found that the current will change its path resulting to two resonating bands only. As a result of the above modification of the structure of the triple band antenna, the resulting antenna shows a dual band response in the frequency range from (1-10) GHz in Figure 6. The lower resonating band extends from (2.28-2.6) GHz with a center frequency of 2.42 GHz at S11 of -26.5 dB, and the second resonating band from (5-5.58) GHz with a center frequency of 5.24 GHz at S11 of -28.17 dB.   Figure 7(b), the current is focused at the internal two lower corners and around the two squares that have been added to the two inner upper corners. The structure of the Sierpinski curve supports the current concentration at the center frequency of the two resonating bands.  Figure 8 shows the simulated far-field radiation patterns for the total electric field in the x-y plane, the x-z plane, and the y-z plane at the center frequency of the obtained two bands in this antenna. Figure 8  The 3D radiation patterns for the total electric field of the resulted dual band antenna are shown in Figure 9. Figure 9(a) shows the 3D radiation pattern corresponding to 2.42 GHz. The results imply that maximum electric field (Emax) equal to 17.04 dBV/m. Figure 9 (b) shows the 3D radiation pattern corresponding to 5.24 GHz, which recorded that maximum electric field (Emax) equal to 16.98 dBV/m. While the values of the peak gain at the two bands are shown as in Figure 10. Throughout the lower resonant band, the peak gain is shown to be as large as 2.27 dBi as demonstrated in Figure 10(a). The upper band gain response is depicted in Figure 10(b). The maximum copolarization gain of is shown to be of about 2.16 dBi. Furthermore, the peak gain of the resulted antenna is almost unchanged throughout the two resonant bands as illustrated in Figure 10.

Conclusion
A compact slotted ground plane dual -band antenna fed by a simple microstrip feed line has been designed by controlling the path of electric current on the surface of the multi-band antenna. The idea of current distribution analysis proves its capability on rejecting any undesired band from the resonance of any multi-band antenna by modifying its structure to change the path of current away from the regions that responsible on the resonance at the undesired band. The first iteration Sierpinski curve fractal geometry that has been employed to the slotted ground plane of the proposed and the resulted antennas also supports the resonance of these antennas. The resulted antenna offers two resonating bands with acceptable radiation pattern and gain. The lower resonating band ranges from (2.28-2.6) GHz with a center frequency of 2.42 GHz at S11 of -26.5 dB, and the upper resonating band from (5-5.58) GHz with a center frequency of 5.24 GHz at S11 of -28.17 dB. The characteristics of the designed antenna make it suitable for Bluetooth, ISM, RFID, WLAN, 2.5/5.5 WiMax, and WiFi operations.