The Behavior of CPW-Fed Sierpinski Curve Fractal Antenna

Brazilian Microwave and Optoelectronics Society-SBMO received 20 Feb 2018; for review 08 Mar 2018; accepted 22 June 2018 Brazilian Society of Electromagnetism-SBMag © 2018 SBMO/SBMag ISSN 2179-1074 Abstract— In this paper, the behavior of Coplanar Waveguide (CPW) fed SIERPINSKI curve fractal antenna is studied. The results show that there is a relationship between the iteration number and the resonance frequencies. With increase in the number of iteration the resonance frequency decreases with a constant ratio. The use of fractal structures to design antennas makes them more miniaturized. The simulated results obtained from CADFEKO a Method of Moments (MoM) model based Solver and measurement using Vector Network Analyzer Anritsu MS2026C are in good agreement.


I. INTRODUCTION
With the multiplication and the miniaturization of telecommunication systems and their integration in restricted environments like tablets, smartphones, laptops and other embedded systems.The design of miniaturized antennas with multi-band and broadband behavior becomes a necessity.
Miniaturization techniques are based on geometric manipulation (using fractal geometries, the use of bend forms, varying distance between feeder and short plate, PIFA shape [1]- [5]) or material manipulation (Loading with a high-dielectric material, lumped elements, conductors, capacitors, short plate [6] ), or the combination of two or more techniques [7].Also several works have appeared in the literature in which the size of the microstrip patch antenna has been reduced by introducing various types of slots in the microstrip patch antenna [8]- [12].
In this paper, we will study the behavior of a CPW-Fed SIERPINSKI Curve fractal antenna designed initially based on the modification of a rectangular patch antenna.The modification of rectangular geometry to the first iteration of SIERPINSKI curve fractal structure, while keeping the same area, allows having a lower resonance frequency.The use of higher iterations allows reducing the resonance frequency with a constant ratio of 0.71 similar or better than for some other works [13]- [17].The results are obtained using CADFEKO a MoM Based solver and are validated with measurement using Vector Network Analyzer ANRITSU MS2026C.The construction of SIERPINSKI Curve structure is made from a lozenge and applying the following steps: 1-We rotate the diamond at an angle of /2 around its center, 2-We add to the result four copies of a lozenge with 2 as a factor of reduction.
3-We bring together the 5 elements.4-Between the iteration i and i + 1, 5 copies are generated with 2 as a factor of reduction.The HAUSDORFF dimension of the SIERPINSKI Curve is given by the equation ( 1) [18]:

A. CPW-Fed rectangular patch antenna
Based on Transmission Lines Method [19], the dimensions of a CPW-fed rectangular patch antenna operating in the frequency f r =2.5GHz printed on a FR-4 substrate with dielectric constant ε r =4.4,thickness h=1.6mm are: W p =36.22mm, L p =28.01mm, W f =2.95mm (Figure 2). Figure 5 (red line) shows the S 11 parameter versus frequencies.The Simulated S 11 shows that with increase in the number of iteration the resonance frequency decreases and the bandwidth decreases (Figure 5).Table I summarizes the different resonance frequencies, bandwidths, maximum gains at the resonance frequencies, and the range of gains in the bandwidths.We note that despite the decrease in resonance frequencies, the antenna loses its ultra-wideband behavior and its gain decreases.We also note that the ratio of resonance frequencies between iteration i+1 and i is constant (Formula 2).This result is considered similar or better than for some other works, table II summarizes this comparison.
Figure 6 shows the radiation patterns for the CPW-fed Rectangular patch and the 3 iterations of SIERPINSKI Curve fractal antennas at their resonance frequencies.We observe that the gain pattern is omnidirectional and stable.
The behavior of the resonance frequencies when we change the iteration number has been tested for the antennas with other dimensions (W s =18.25mm and L s =13.76mm).Figure 7 shows the variation of S 11 parameters versus iterations numbers.We confirm that the formula 2 is respected even if we change the antennas dimensions.measurements were performed with ANRITSU MS2026C Vector Network Analyzer.Figure 9 shows the comparison between S 11 simulated and measured.We note that there is an agreement between the simulated and measured results even if there are some differences that are due to the manufacturing process.

III. CONCLUSION
The behavior of CPW-Fed SIERPINSKI Curve fractal antenna was studied.Both simulation and measurement results prove that there is a relationship between the iteration number and the first resonance frequency.In fact, with increase in the number of iteration the resonance frequency decreases with a constant ratio of 0.71, but the maximum gain and the bandwidth decreases.
The use of fractal geometries is one of the best solutions to design braodband and multiband antennas.
Also, it is one of the techniques used for the antenna miniaturization.Indeed, to reduce the CPW-fed rectangular patch antenna resonance frequency, we need to increase its dimensions or increase the relative permittivity of its substrate.But, by the modification of its geometry using SIERPINSKI Curve Fractal structure we can design an antenna with smaller resonance frequencies when the iteration number increases.Also, we can predict the resonance frequency while the reduction ration of the first resonance frequency is similar.

Figure 1 -
Figure 1-c shows the first four iterations of the SIERPINSKI Curve fractal structure.

Fig. 2 .
Fig.2.The geometry of rectangular patch antenna fed by CPWB.Modifying the rectangular geometry using the SIERPINSKI Curve Fractal structureTo reduce the resonance frequency of a rectangular patch antenna, it is necessary to increase the size of the antenna or increase the permittivity of the substrate[19].To reduce this frequency without changing the size of the antenna or changing the permittivity of the substrate, several techniques are introduced among which the addition of slots or the use of fractal geometry structures.The previous rectangular patch antenna fed by CPW (Figure2) will be modified based on the first iteration of the SIERPINSKI Curve structure to keep the surface of the radiating element almost equal to the surface of the rectangular patch as shown in figure3.After that, three iterations are studied (Figure4).

Fig. 5 .
Fig.5.The simulated S 11 parameter of the CPW-Fed rectangular patch and the 3 first iterations of the SIERPINSKI Curve fractal antennas

Fig. 6 .
Fig.6.Radiation pattern for the CPW-fed Rectangular patch and the 3 iterations of SIERPINSKI Curve fractal antennas at their resonance frequencies.

Fig. 7 .Figure 8
Fig.7.The simulated S 11 parameter of the CPW-Fed rectangular patch and the 3 first iterations of the SIERPINSKI Curve Fractal antennas (Ws=18.25mmand Ls=13.76)C. Realization and measurements Figure 8 shows the manufactured CPW-Fed rectangular patch and the three first iterations of the SIERPINSKI Curve fractal antennas.The antennas are printed on a FR-4 substrate with dielectric constant ε r =4.4,thickness h=1.6mm, with W s =36.22mm and L s =28.01mm.The S 11 parameters

TABLE II .
COMPARISON WITH SOME OTHER WORKS