CHAPTER 3 MINKOWSKI FRACTAL ANTENNA FOR DUAL BAND WIRELESS APPLICATIONS

Transcription

1 38 CHAPTER 3 MINKOWSKI FRACTAL ANTENNA FOR DUAL BAND WIRELESS APPLICATIONS 3.1 INTRODUCTION The explosive growth in wireless broadband services demands new standards to provide high degree of mobility and enhanced data transmission (Yin and Alamouti 2006). Among the emerging standards, WiMAX or the IEEE standard is one of the most promising broadband wireless technologies nowadays. It is characterized by its high data rates, large coverage area, and flexible design. An important amendment to IEEE is the IEEE e standard which adds a capability for full mobility support to WiMAX (Hoadley and Javed 2005). An important requirement of WiMAX wireless systems is the significant increase in data throughput and link range without additional bandwidth or transmit power, with a combination of higher spectral efficiency and link reliability or diversity (Jenkins 2008). The system throughput is significantly improved with the support of multiple-inputmultiple-output (MIMO) antenna technology as well as Beamforming and Advanced Antenna Systems (AAS), which are referred to as "smart" antenna technologies (Pedersen et al 2003). Multiple-input-multiple-output (MIMO) antenna systems have been reported for wireless applications to improve the capacity of the radio communication (Naguib et al 1994, Konanur et al 2005, Sayeed and

2 39 Raghavan 2007, Zhang and Chen 2008, Chen et al 2008). This technology brings potential benefits in terms of coverage, self installation, low power consumption, frequency re-use and bandwidth efficiency. The performance aspects of MIMO system shows a significant increase in throughput using an antenna array compared to single antenna system (Guterman et al 2004). However, MIMO techniques create an additional difficulty of housing multiband antennas with low level of mutual coupling between the antenna elements (Salvekar et al 2004). Multiple antennas in a portable device require that the spacing between antennas be small and compact. With small antenna element spacing, the mutual coupling can be significant, and this is accounted for the design of MIMO antenna systems (Wennstrom 2002). Many attempts to design small and compact antennas in the past have been endeavoured through slots, shorting and folded geometries, but it was not until the introduction of fractals in antenna engineering that this could be done in a most efficient and sophisticated way (Wang and Lee 2004, Khodaei et al 2008, Gianvittorio and Rahmat Samii 2002, Gianvittorio 2003). Fractal antennas have facilitated miniaturization as they are electrically small and at the same time self-resonant radiators. Minkowski fractal geometry has received lot of attention in respect of reduction in the size of the conventional loop antenna leading to compactness and miniaturization (Cohen 1995). Tight packing of Minkowski Island loop antenna elements in the array and reduced mutual coupling was achieved without affecting the bandwidth (Gianvittorio and Rahmat Samii 2002). Recent studies have shown that the application of printed Koch curve fractal shapes in MIMO antenna design allows reduced mutual coupling between antenna elements in (MIMO) system for multiband applications besides providing miniaturization (Guterman et al 2004). However this requires PIFA configuration and the use of slot to achieve multiband behaviour.

3 40 This chapter evaluates the performance of fractal array based on Minkowski geometry for WiMAX dual band operation with MIMO application. The generation of Minkowski fractal geometry is explained in section 3.1. The structure has been used in microstrip configuration. The numerical analysis of Minkowski patch antenna is presented in section 3.3. The performance evaluation of Minkowski fractal antenna and the results are discussed in section 3.4. The Minkowski fractal based two element array for WiMAX application is presented in section 3.5. The simulated results are experimentally validated in section 3.6. A brief summary of the work proposed is presented in section MINKOWSKI FRACTAL GEOMETRY Minkowski fractals were first introduced by Hermann Minkowski in the form of representation and definition of geometries in the year 1885 (Strobl 1985, Schwermer 1991). The basic square patch geometry is compressed five smaller squares to form the Minkowski fractal geometry as shown in Figure 3.1 This is explained in terms of affine transformation here. w 1 (x,y)=(a 1 x+b 1 y+e 1, c 1 x+d 1 y+f 1 ) w 1 w 2 W w 2 (x,y)= (a 2 x+b 2 y+e 2, c 2 x+d 2 y+f 2 ) w 3 (x,y)= (a 3 x+b 3 y+e 3, c 3 x+d 3 y+f 3 ) w 4 (x,y)= (a 4 x+b 4 y+e 4, c 4 x+d 4 y+f 4 ) w 5 (x,y)= (a 5 x+b 5 y+e 5, c 5 x+d 5 y+f 5 ) w 5 Figure 3.1 Generation of Minkowski fractal geometry

4 41 Iterated function systems (IFS) represent an extremely versatile method for conveniently generating a wide variety of useful fractal structures (Michael Barnsley 1993). These iterated function systems are based on the application of a series of affine transformations, w, defined by x a b x e w y c d y f (3.1) or, equivalently, by w( x, y) ( ax by e, cx dy f ) (3.2) where a, b, c, d, e, and f are real numbers. In affine transformation, w, is represented by six parameters a c b e d f (3.3) such that a, b, c, and d control rotation and scaling, while e and f control linear translation. Let w 1, w 2,..., w N be a set of affine linear transformations, and A be the initial geometry, then a new geometry is produced by applying the set of transformations to the original geometry A, and is represented as N W ( A) w ( A) (3.4) n1 n where W is known as the Hutchinson operator (Peitgen 1992). The IFS coefficient values to generate Minkowski fractal geometry as shown in Figure 3.7 are tabulated in Table 3.1. The successive fractal

5 42 geometry can be obtained by repeatedly applying the previous geometry. The fractal similarity dimension of this geometry is given by log5 D (3.5) log3 This implies that there are five copies of squares are generated in successive iteration having dimension scaled down to one third. Table 3.1 IFS Transformation coefficients for the Minkowski fractal geometry w i a i b i c i d i e i f i w 1 1/3 0 1/ w 2 1/3 0 1/3 0 1/6 0 w 3 1/3 0 1/ /6 w 4 1/3 0 1/3 0 1/6 1/6 w 5 1/3 0 1/3 0 1/3 1/3 The iterative procedure is continued to get the successive stages of Minkowski fractal patch antenna is shown in Figure 3.2. The starting geometry of the Minkowski fractal antenna is the initiator square patch, and the successive iterations of fractal antenna is obtained by replacing each of the four straight sides of the starting structure with the generator with indentation as shown in the Figure 3.2. The indentation width S, can vary from 0 to 1.

6 43 Figure 3.2 Generation of Minkowski fractal patch antenna (a) Initiator patch (b) First iterated Minkowski fractal patch (c) Second iterated Minkowski fractal patch (d) Third iterated Minkowski fractal patch 3.3 SBTD ANALYSIS OF MINKOWSKI FRACTAL ANTENNA The governing equations for a coaxial fed Minkowski fractal antenna shown in Figure 3.2 are the following updated equations as explained in Chapter X X y K 1/2 H, m 1/2, n 1/2 k 1/2 H, m 1/2, n 1/2 ai. k E, m 1 2, n i 1, m 1 2, n 1 2 z i3 t z 1 z ai. k E, mi1, n ai. k E, mi1, n y i3 y (3.6) i3 2 y y z K 1/2 H 1 2, m, n 1/2 k 1/2 H 1 2, m, n 1/2 ai. k E i 1, m 1 2, n 1 2, m, n 1 2 x i3 t x 1 x ai. k E 1 2, m, n i 1 ai. k E 1 2, m, n i 1 z i3 z (3.7) i3

7 44 t 2 z z y K 1 E, m, n 1 2 k E, m, n 1 2 ai. k 1 2 H 1/2 i, m, n 1/2, m, n 1/2 x i x 1 x ai. k1 2 H, m1/2 i, n1/2 ai. k 1 2 H, m1/2 i, n1/2 y i3 y (3.8) i3 where the coefficient {a i }, a i Q i x S 1/ 2 x x dx (3.9) A Gaussian pulse of t T 2 f ( t) A.exp. is used as excitation field Antenna Structure Discretization Figure 3.3 shows the top view and cross section of the second iterated Minkowski fractal antenna. Figure 3.3 Top view and the cross section of the second iterated Minkowski microstrip fractal patch antenna

8 Boundary Conditions (i) on the ground plane Since the entire antenna lay on the ground plane, a perfect electric conductor boundary condition is chosen on the ground plane of the antenna, as the entire antenna lies on the ground plane. That is E x =E y =0, and Ez exists in the substrate (ii) on the metallized antenna, it is assumed that E x =E y =0 for k=3 where k is the representation of the cell for the metal antenna and E z exists in the free space above the antenna (iii) on the feed line conductor, the respective cells have E x =E y =0 and E z exists in the substrate around the conductor Results and Discussion A Minkowski fractal antenna having a dimension of 28.6mm 28.6mm and the dielectric substrate having ε r =4.4 and thickness 1.6mm is chosen for analysis. This antenna is analysed using SBTD technique with mesh specification of Yee cells. The cell size x = y =0.286mm, z =0.2mm is chosen to accommodate the single element antenna structure conveniently. The time step selected is 0.88 ps to ensure courant stability condition. The coding for SBTD is developed in MATLAB. The reflected voltage of the Minkowski fractal antenna at the input port is presented in Figure 3.4.

9 46 Figure 3.4 Reflected Voltage at the input port of the antenna The simulated input characteristic of the antenna are obtained using Empire 3D EM simulator. To validate the analysis of the Minkowski fractal antenna, the antenna is fabricated as shown in Figure 3.5 and the measurements are made using vector network analyzer. Figure 3.5 Prototype of the second iteration Minkowski fractal antenna

10 47 Figure 3.6 shows the comparison of SBTD with the FDTD, simulated and measured return loss. The results shows the resonance behaviour of the second iterated Minkowski fractal antenna operating at 1.8GHz and it shows good agreement with the measured results. Figure 3.6 Return loss (S 11 ) of the Second iteration Minkowski antenna The SBTD technique used smaller number of meshes for the computation to get the same accuracy. The measured result shows a small degree of variation from the simulated and the numerical results. This is due to the mesh truncation at the edges of the fractal antenna during the EM simulation. The performance of SBTD technique is also compared with FDTD method in respect of CPU time and memory requirement. SBTD technique still gives good performance with coarse mesh having accurate result. Compared to conventional FDTD method, the SBTD technique reduces by a factor of 3.5 and 1.3 of the computer memory and computation speed respectively.

11 PERFORMANCE EVALUATION OF MINKOWSKI FRACTAL ANTENNA Preamble In order to study the effectiveness of miniaturization in Minkowski fractal antenna, the antenna at different stages of fractal iterations are studied through simulation software ADS 2002C. Then the influence of parameter such as indentation of the Minkowski fractal antenna on the frequency response is studied in order to make it suitable for dual band operation Influence of Minkowski Fractal Iteration Figure 3.7 shows the first three stages of Minkowski fractal antenna. These structures are simulated, fabricated and tested. The antenna has been fabricated at different stages of fractal iterations and the measured results are compared with that of simulated values. Figure 3.8 shows the prototype of Minkowski fractal patch antenna at different stages of fractal iteration. Figure 3.7 First three stages of Minkowski fractal antenna

12 49 Figure 3.8 Prototype of Minkowski microstrip fractal antenna in different iteration Figure 3.9 presents the return loss of simple microstrip antenna (K0) resonating at 2.41GHz 0-5 Return loss (db) Simulated Measured Frequency (GHz) Figure 3.9 Comparison of simulated and measured return loss of simple microstrip patch (K0) antenna

13 50 The first iteration of the fractal patch resonates at 2.2GHz and hence it provides 12 % miniaturization as shown in Figure The second iteration of the fractal patch further lowers the resonance to 16 % as shown in Figure For this fractal, it is seen that the second iteration of the fractal actually has a lower resonant frequency than the first iteration. This is because the current does not follow the straight path, but rather ease around the edges of the patch increased electrical length and hence the miniaturization of antenna. Figure 3.12 shows the return loss of third iterated Minkowski fractal antenna. Table 3.3 shows the resonant frequencies at first and second iteration and the frequency reduction factor. As iteration increases, there exists a shift in resonance frequency towards lower value. This is due to the increase in the electrical dimension of the Minkowski fractal antenna. Figure 3.10 Comparison of simulated and measured return loss of first iteration Minkowski fractal (K1) antenna

14 51 Figure 3.11 Comparison of simulated and measured return loss of second iteration Minkowski fractal (K2) antenna Figure 3.12 Comparison of return loss of Minkowski microstrip fractal antenna at different stages of iteration

15 52 Table 3.2 Resonant frequencies and scale factor between adjacent bands in Minkowski fractal antenna n f n (GHz) S 11 (db) f n /f n Figure 3.13 shows the radiation patterns of the Minkowski fractal patch antenna at different stages and first iterated Minkowski antenna in the parallel and perpendicular plane respectively. The antenna shows bidirectional radiation in horizontal plane and uniform radiation in the direction perpendicular to the plane of antenna. There is a slight reduction in the measured value at null direction which may be due to the cable loss during the measurement. Figure 3.13 Radiation patterns of Square patch antenna (KO), First iterated Minkowski fractal patch (K1) and Second iterated Minkowski fractal patch (K2)

16 Significance of Indentation Width The slots between fractal segments have indentation having a width S V and S H along x and y directions as shown in Figure The influence of indentation width is studied so that the Minkowski fractal antenna can be customized for the required specifications. Figure 3.14 Minkowski fractal antenna showing Indentation widths The effect of varying the input indentation is shown in the plot of the input characteristics of the antenna shown in Figures 3.15 and Three indentation sizes for the first iteration of the antenna have been simulated. It can be seen that the indentations miniaturize the patch and that an increase in the indentation, increases the amount of miniaturization. The patches have a dimension of 28.6 mm by 28.6 mm and are printed on a 1.6mm-thick FR4 substrate which has a dielectric constant of 4.4. The square patch is resonant at 2.41 GHz and the perimeter is mm, which is 2λ at the resonant frequency. The patch that uses the first iteration of Minkowski fractal antenna indented by 5.4 mm is resonant at 2.1 GHz. The perimeter of this patch has increased to mm, which is 3.385λ at this frequency. The patch that uses 6.2 mm for the indentation width is resonant at 1.95 GHz and the perimeter is mm which is 4.25λ. It can be seen that the effect of increasing the

17 54 indentation has diminishing returns, in the sense that the miniaturization tapers off as the indentation is increased sv=5.4mm sv=4.8mm sv=3.7mm Resonant frequency (GHz) Iteration n Figure 3.15 Resonant frequency of a first iterated Minkowski fractal patch for varying indentation widths, S V and S H Sh=9.7 Sh=8.7 Sh=7.8 Sh=6.5 Resonant frequency (GHz) Iteration n Figure 3.16 Resonant frequency of a first iterated Minkowski fractal patch for varying indentation widths, S V and S H

18 55 Table 3.3 shows the fractal dimension and the perimeter at resonance for various indentation width and the generating iterations. Table 3.3 Minkowski fractal antenna fractal dimension and respective indentation width scaling factor Indentation width scaling factor Fractal iterations n Fractal dimension (λ) Perimeter at resonance (λ) CUSTOMIZATION OF MINKOWSKI FRACTAL ANTENNA FOR DUAL BAND WIRELESS APPLICATION The demand for miniaturized dual band antenna and compact array for WiMAX MIMO antenna system have necessitated the design of Minkowski fractal antenna array. Single Input Single Output (SISO) and multiple input multiple output (MIMO) antennas using Minkowski fractal patch is designed by customizing the values of the Iterative Function Coefficients (IFS) coefficients. The optimized IFS coefficients of the first

19 56 iteration Minkowski fractal antenna to meet the frequency of resonance for dual band applications are shown in Table 3.4. Table 3.4 IFS transformation coefficients for the optimized Minkowski fractal geometry w i a i b i c i d i e i f i w w w w w Figures 3.17 and 3.18 show the layout and the prototype of proposed optimized Minkowski fractal antenna and its suitability for dual band operation. Microstrip line is used to feed the antenna in order to have easier integration with the subsequent RF systems and circuitry. The input characteristic is measured and the results are compared with that of simulated value as shown in Figure Figure 3.17 Layout of first iterated Minkowski microstrip fractal patch antenna

20 57 Figure 3.18 Prototype of the Minkowski antenna Return loss (db) Simulated SBTD Measured Frequency (GHz) Figure 3.19 Return loss of optimized Minkowski fractal antenna It is seen from the investigation on Minkowski fractal antenna, the non uniform change in IFS coefficients has significant change in the resonant frequency has resulted in dual band operation. Larger the indentation widths S H and S V, lower the resonant frequency and hence further miniaturization of square patch antenna. Proper selection of these values has resulted required resonance.

21 58 configuration. Figure 3.20 shows the two element Minkowski fractal antenna Figure 3.20 Three dimensional view of 2 element Minkowski microstrip fractal array The array antenna is analysed using SBTD method and its resonance behaviour is obtained. The array antenna is fabricated and tested in an anechoic chamber. The photograph of two elements Minkowski array is presented in Figure Figure 3.21 Prototype of 2 element Minkowski microstrip fractal array

22 59 The return loss obtained using SBTD method, simulated results obtained using Empire software and the measured results obtained in an anechoic chamber are shown in Figure 3.22, and they are all in agreement with each other. The antenna is matched (S 11 < -10dB) at the WiMAX frequencies 2.5 GHz and 5.8 GHz respectively. The coupling coefficient S 21 at 2.5GHz and 5.8GHz frequencies obtained are -20db and -24db respectively, showing less coupling between the fractal patches. This is presented in Figure It is observed that the proposed Minkowski fractal array provides dual band operation at WiMAX frequencies 2.5 GHz and 5.8 GHz due to the resonant behaviour of the fractal elements. This in turn has resulted in reduced mutual coupling. 0-5 Return loss (db) Simulated SBTD Measured Frequency (GHz) Figure 3.22 Return loss of the Minkowski microstrip fractal array at both the input ports 1 and 2

23 60 Figure 3.23 Coupling coefficients between the elements of Minkowski microstrip fractal array The radiation pattern at 2.5GHz and 5.8GHz frequency are plotted in Figure GHz 5.8GHz Figure 3.24 Radiation pattern of Minkowski microstrip fractal antenna array in H and E plane for 2.5GHz and 5.8GHz

24 61 In the lower frequency band, the antenna exhibits max gain of 8.84db and in the high frequency band, the antenna demonstrates max gain of 7.39db which is acceptable for WiMAX application. 3.6 SUMMARY A Minkowski fractal geometry based microstrip patch antenna is investigated for miniaturization. The influence of fractal indentation width is also studied. A compact two element Minkowski fractal antenna array is customized for Multiple-Input Multiple-Output (MIMO) supported WiMAX dual band application which shows reduced mutual coupling. The experimental results are validated using SBTD based numerical results and the simulated results obtained using ADS and Empire XCcel simulator.