antenna test & measurement society (atms india-16) study of...

Study of Vicsek and Koch inspired fractals as EBG

structures on mutual coupling of planar multiband

antenna array

Shravan Kaundinya

Department of Electronics and Communication

APS College of Engineering

Bangalore, India

[email protected]

Karthikeya G.S

Antenna Architects Lab

Dayananda Sagar College of Engineering

Bangalore, India

[email protected]

Abstract—The effect of fractals, in the form of an

Electromagnetic Bandgap (EBG) grid, on the mutual coupling of

an antenna array is explored. The zeroth, first, and second

iterations of Vicsek and Koch inspired fractals are employed in

this paper. These fractals in the form of 2×1, 4×1, 2×2, and 4×2

EBG grids are laid between the two elements of a 1×2 antenna

array. The antenna element of the 1×2 array has been designed

on an FR4 Epoxy substrate of dimensions 50×50×1.6 mm3 and

possesses a quad band resonance capable of supporting WLAN at

3.6 and 5.2 GHz. We observed minimal change in mutual

coupling for the 3.69 GHz band for all iterations of both fractals

in the form of all EBG grids. However for the 5.16 GHz band, we

observed an improvement in mutual coupling by nearly 2dB for

the Koch inspired fractal in the form of a 4×2 EBG grid with

column separation of 10mm.

Keywords—Mutual Coupling; Vicsek fractal; Koch inspired

fractal; EBG; antenna array

I. INTRODUCTION

Antenna arrays are widely used for two major reasons: increase in overall gain and beam steering ability [1]. Some of the factors which affect the performance of the array are the shape and total number of elements, geometrical configuration (including separation between each element), and the inputs to each element [2]. Several unique concepts have been employed for designing novel antenna arrays. Reconfigurable arrays using PIN diodes for MIMO systems [3], MEMS-switched parasitic antenna array [4], arrays using SIW technology [5, 6], and metamaterial structures for increasing gain of the array [7] have been explored.

Mutual coupling is an important parameter in arrays as it affects the overall radiation pattern, efficiency and also the impedances of the elements. The common methods used to control the amount of mutual coupling are the physical separation, relative orientation, and radiation pattern of each individual element in the array [1].

The concept of Electromagnetic Bandgap (EBG) structures have been explored extensively for the reduction of mutual coupling in an array [8-12]. In [8], EBG structure in the form of connected I-shape and a defected ground structure (DGS) in

the form of rectangular loop are employed in a 1×2 array of patch antennas resonating at 5.8 GHz. When both DGS and EBG structures were inserted, they observed a 22dB reduction in mutual coupling. EBG structures in the form of meandered geometry have been explored in [9] and [10]; they achieved a measured mutual coupling reduction of 4dB and 19.18dB respectively, at the resonating frequencies. A 2×5 EBG grid consisting of squares connected to each other using meandered lines were explored in [11] and they observed a reduction of coupling by 17dB. In [12], EBG structures in the form of rectangular patches with rectangular slots are used to suppress mutual coupling and they reported a reduction of 13dB and 30dB at 2.4 and 5.2GHz.

Another method to reduce mutual coupling is the use of defected ground structure (DGS). In [13], U-shaped DGS and resonator were used and they observed the coupling suppressed by 15.7 and 8dB at 2.45 and 4.5GHz respectively. A dumbbell shaped DGS was employed in [14] and they reported a maximum coupling reduction of 5dB. Metamaterial spiral resonator structure was used in [15] and it resulted in mutual coupling reduction of 5.5dB at 4.5GHz. In [16], various patch configurations like concave and hexagonal rectangular patches were studied to reduce the mutual coupling and return loss.

In this paper, we explore the effects of the combination of EBG structures and fractals on mutual coupling. The zeroth, first and second iterations of Vicsek and Koch inspired fractals are utilized as EBG structures in the form of grids between the elements in a 1×2 antenna array. This combination of EBG structures and fractals has not been employed to study the effect on mutual coupling in an antenna array. The single element as well as the various arrays is capable of supporting WLAN at 3.6 and 5.2 GHz.

II. PRELIMINARY ANTENNA ARRAY DESIGN AND ANALYSIS

A. Single Element Design

The individual element of the array was designed on a 50×50×1.6 mm

3 FR4 Epoxy substrate. The antenna consists of

a 10×3 mm2 feed line and a 30×30 mm

2 slotted patch; a ground

plane is also present on the bottom surface of the substrate of

Antenna Test & Measurement Society (ATMS India-16)

01-03 Feb, 2016 1 Goa, India

TABLE I. Dimensions of the single element design

Label L1 L2 L3 L4 L5 L6 L7 L8 L9 L10

Length (mm)

5 29 8 10 3 50 50 9 30 30

dimensions 50×50 mm

2. The dimensions of the slots are

mentioned in Table 1 and the entire element is shown in Figure 1. All the slots have a thickness of 1mm and they are also 1mm away from the patch edges. The return loss and radiation pattern graphs are shown in Figure 2 and 3 respectively. The antenna resonance consists of a quad band at 3.69, 4.29, 4.65, and 5.16 GHz. The bandwidths at 3.69 and 5.16 GHz are 92.7 and 200.5 MHz and hence capable of supporting WLAN at 3.6 and 5.2 GHz.

B. 1×2 antenna array design

The elemental design described in the previous section is arranged in the form a 1×2 array on a 100×50×1.6 mm

3 FR4

Epoxy substrate, as shown in Figure 4. Parametric analysis is performed on the separation of the two elements for optimum configuration. With a median line perpendicular to the 100mm side of the array as reference, the elements are symmetrically

moved away from each other and Figure 5 shows the S12 curves for separation distances from 2mm to 38mm.

For a separation of 2mm, the 5.16GHz band possesses maximum return loss value. However for the next two separations of 8mm and 14mm, the return loss value reduces and is lowest for the latter. As the separation increases, the return loss values too gradually increase for the 5.16GHz band. However for the 3.69GHz, the S11 values do not vary much when the separation increases as compared to the 5.16GHz band. For the case of S12 values, as the separation increases the mutual coupling decreases for both the above mentioned frequency bands. In the final array design, the separation between the edges of each element’s slotted patch is 0.57λ. The S-parameters and radiation pattern graphs of the array with separation distance of 30mm are shown in Figure 6 and 7 respectively. This final array design with 0.57λ separation is the base for further mutual coupling study.

Fig. 1. Diagram of the single element design

Fig. 2. Return loss graph of the single element design

(a) (b)

Fig. 3. Radiation patterns of single element design for (a) 3.69 GHz at ϕ=0o

and 90o, (b) 5.16 GHz at ϕ=0o and 90o

Fig. 4. Diagram of 1×2 antenna array

Fig. 5. Graph of S12 curves for separation distances from 2mm to 38mm

Fig. 6. Graph of S-parameters for separation distance of 30mm

(a) (b)

Fig. 7. Radiation patterns of 1×2 antenna array for (a) 3.69 GHz at ϕ=0o and

90o, (b) 5.16 GHz at ϕ=0o and 90o


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III. EFFECT OF EBG FRACTALS ON MUTUAL COUPLING

The zeroth iteration for both Vicsek and Koch inspired fractals consist of a square of side 9mm. Considering the limitations of fabrication in mind, the least dimension possible is 1mm, which is for the 2

nd iteration of both fractals. Scaling

up the dimensions, we get a square of side 9mm for the zeroth iteration. The first iteration of Vicsek fractal is formed by dividing the 9mm sided square into 9 equal squares of side 3mm and then removing the squares at the four corners, thereby obtaining a shape of a “plus” sign. This procedure is repeated to all squares of side 3mm in the “plus” sign, except the square at the center and hence arriving at the second iteration. The Koch inspired fractal is obtained by applying the standard procedure for forming a Koch fractal on each side of the 9mm square. An equilateral triangle of side 3mm is subtracted from each side of the 9mm square to arrive at the first iteration and subsequently an equilateral triangle of side 1mm is subtracted from the two sides of the 3mm equilateral triangle to arrive at the second iteration.

A. 2×1 EBG fractal grid design and analysis

The zeroth, first and second iterations of both fractals are arranged in a 2×1 grid which is placed equally from both elements of the array. The distance between the two elements in the grid is 3mm and the distance between the outer edge of the grid element and the 100mm side of the array is 14.5mm. Figure 8 shows the diagrams of arrays consisting of all iterations in the form of 2×1 grid. Figure 9 and 10 shows the S12 graphs for Vicsek and Koch inspired fractals respectively.

From the graph for the Vicsek fractal, we observe that for the 3.69 GHz band, there is no distinguishable change in mutual coupling for the different iterations. For the 5.16 GHz band, we can observe a slight reduction in mutual coupling for the second iteration. For the Koch inspired fractal, we observe that there is no prominent change in mutual coupling for the 3.69 GHz band. However for the 5.16 GHz band, we notice that the zeroth iteration results in least mutual coupling when compared to the next two iterations of Koch inspired fractal.

B. 4×1 EBG fractal grid design and analysis

The zeroth, first and second iterations of both fractals are arranged in a 4×1 grid which is placed equally from both elements of the array and is an extension of the 2×1 grid. The distance between each element in the grid is 3mm and the elements closer to the 100mm side of the array are 2.5mm from it. Figure 11 and 12 shows the S12 graphs for Vicsek and Koch inspired fractals respectively.

In the Vicsek fractal graph, there is no distinguishable change in coupling for the 3.69 GHz. For the 5.16 GHz band, mutual coupling degrades slightly as the iterations are performed from zeroth to the second. In the Koch inspired fractal graph, the 3.69 GHz band shows no prominent change in coupling. However, for the 5.16 GHz band the coupling improves slightly as the iterations are performed.

Fig. 8. Diagrams of 2×1 array with EBG grid for (a) Zeroth iteration, (b) Vicsek first iteration, (c) Vicsek second iteration, (d)

Koch inspired first iteration, and (e) Koch inspired second iteration

Fig. 9. Graph of S12 curves for 2×1 EBG Vicsek fractal for all iterations

Fig. 10. Graph of S12 curves for 2×1 EBG Koch inspired fractal for all

iterations


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C. 2×2 EBG fractal grid design and analysis

The iterations of both fractals are arranged in a 2×2 grid between the elements of the array. The horizontal distance between the columns of elements is 2mm and the vertical distance between the rows of elements is 3mm. The upper and bottom two elements are each 14.5mm from the 100mm side of the array. The distance between the columns closest to the respective array elements is 5mm. Figure 13 shows the diagrams of arrays consisting of all iterations in the form of 2×2 grid.

For the Vicsek fractal iteration, the coupling for 3.69 GHz does not vary much but for the 5.16 GHz, the coupling degrades as the iterations are performed. For the Koch inspired fractal iteration, the coupling for both 3.69 GHz and 5.16 GHz varies minimally and does not greatly affect the performance of the array.

D. 4×2 EBG fractal grid design and analysis

The iterations of both fractals are arranged in a 4×2 grid and a parametric analysis is performed on the separation between the two columns of the EBG grid. The two outer elements of the columns in the EBG grid are 2.5mm from the 100mm side of the array and the vertical distance between each element within each column is 3mm. Parametric analysis is performed on the separation of the two columns by symmetrically moving each column away from the central median reference line of the array.

The above mentioned parametric analysis is performed on all three iterations for both fractals to observe the effect on mutual coupling. Figure 18 shows the diagrams of arrays consisting of all iterations in the form of a 4×2 grid with separation of 10mm between each column in the EBG grid.



iterations


with separation of 2mm


iterations with separation of 2mm

Fig. 13. Diagrams of 2×2 array with EBG grid for (a) Zeroth iteration, (b) Vicsek first iteration, (c) Vicsek second iteration, (d)

Koch inspired first iteration, and (e) Koch inspired second iteration


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Figure 14 shows the mutual coupling for zeroth, first and second iterations for Vicsek fractal with separation of 2mm between the columns of the EBG grid. There is minimal change in coupling at 3.69 GHz; however for the 5.16 GHz, we observe there is degradation in coupling for the first and second iterations when compared to the zeroth iteration. Figure 15 shows the coupling for the iterations for Koch inspired fractal with the same separation between the columns. The effect on coupling for both frequency bands is similar to that of the Vicsek fractal.

Figure 16 shows the S12 curves for the iterations of Vicsek fractal with separation of 6mm between the columns of the EBG grid. For the 3.69 GHz band, there is no distinguishable change in coupling between the iterations. However for the 5.16 GHz band, we observe degradation in coupling of nearly 2.6dB between the zeroth and first iteration. Figure 17 shows

S12 curves for the iterations of Koch inspired fractal with separation of 6mm between the columns. Similar to the Vicsek fractal, there is a very slight change in coupling for the 3.16 GHz band and a degradation of nearly 1.7dB between the zeroth and first iteration.

Figure 19 shows the coupling characteristics for the iterations of Vicsek fractal with separation of 10mm between the columns of the EBG grid. We can see that the mutual coupling for both frequency bands vary minimally for all three iterations. Figure 20 shows the coupling for the iterations of Koch inspired fractal with separation of 10mm between the columns. Similar to the previous variations, there is very little change for the 3.69 GHz band. However, there is improvement of almost 2dB in mutual coupling for the 5.16 GHz band, between the zeroth and second iterations.





Fig. 18. Diagrams of 4×2 array with EBG grid of separation 10mm for (a) Zeroth iteration, (b) Vicsek first iteration, (c) Vicsek

second iteration, (d) Koch inspired first iteration, and (e) Koch inspired second iteration






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Figure 21 shows the radiation patterns for 4×2 EBG Vicsek fractal, with column separation of 10mm in the grid, at 3.69 GHz for ϕ=0

o and 90

o. Figure 22 shows the patterns for the

same geometry at 5.16 GHz for ϕ=0o and 90

o. Figure 23 and 24

shows the radiation patterns for 4×2 EBG Koch inspired fractal, with same column separation and same ϕ, at 3.69 and 5.16 GHz respectively.

IV. CONCLUSION

The effect of EBG fractals on the mutual coupling of a 1×2 antenna array has been observed. The Vicsek and Koch inspired fractals were chosen and arranged in the form of EBG grids between the array elements. The antenna element of the array and all the subsequent explored arrays are capable of supporting WLAN at 3.6 GHz and 5.2 GHz. There was minimal change observed in the mutual coupling for 3.69 GHz band for all iterations of both fractals in the form of all EBG grids. It was observed that for the 5.16 GHz band, there was an

improvement in mutual coupling by nearly 2dB for the Koch inspired fractal in the form of a 4×2 EBG grid with column separation of 10mm.

REFERENCES

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John Wiley & Sons, 2012.

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[3] Piazza, Daniele, Nicholas J. Kirsch, Antonio Forenza, Robert W. Heath Jr, and Kapil R. Dandekar. "Design and evaluation of a reconfigurable antenna array for MIMO systems." Antennas and Propagation, IEEE Transactions on 56, no. 3 (2008): 869-881.

[4] Petit, Laurent, Laurent Dussopt, and Jean-Marc Laheurte. "MEMS-switched parasitic-antenna array for radiation pattern diversity." Antennas and Propagation, IEEE Transactions on 54, no. 9 (2006): 2624-2631.

[5] Lin, Song, Songnan Yang, Aly E. Fathy, and Adel Elsherbini. "Development of a novel UWB vivaldi antenna array using SIW technology." Progress In Electromagnetics Research 90 (2009): 369-384.

[6] Chen, Xiao-Ping, Ke Wu, Liang Han, and Fanfan He. "Low-cost high gain planar antenna array for 60-GHz band applications." Antennas and Propagation, IEEE Transactions on 58, no. 6 (2010): 2126-2129.

[7] Li, Bin, Bian Wu, and Chang-Hong Liang. "Study on high gain circular waveguide array antenna with metamaterial structure." Progress In Electromagnetics Research 60 (2006): 207-219.

[8] Abdalla, Mahmoud, Ahmed M. Abdelreheem, Mohamed H. Abdegellel, and Asem M. Ali. "Surface wave and mutual coupling reduction between two element array MIMO antenna." In Antennas and Propagation Society International Symposium (APSURSI), 2013 IEEE, pp. 178-179. IEEE, 2013.

[9] Trinh-Van, Son, and Keum Cheol Hwang. "Meandered UC-EBG structure for a reduction of the mutual coupling in a patch antenna array." IEICE Electronics Express 9, no. 22 (2012): 1748-1755.

[10] Islam, Mohammad Tariqul, and Md Shahidul Alam. "Design of high impedance electromagnetic surfaces for mutual coupling reduction in patch antenna array."Materials 6, no. 1 (2013): 143-155.

[11] Islam, Mohammad Tariqul, and Md Shahidul Alam. "Compact EBG structure for alleviating mutual coupling between patch antenna array elements." Progress In Electromagnetics Research 137 (2013): 425-438.

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[13] Ghosh, Chandan Kumar, Bappaditya Mandal, and Susanta Kumar Parui. "Mutual Coupling Reduction of a Dual-Frequency Microstrip Antenna Array by Using U-Shaped DGS and Inverted U-Shaped Microstrip Resonator." Progress In Electromagnetics Research C 48 (2014): 61-68.

[14] Zulkifli, Fitri Yuli, Eko Tjipto Rahardjo, and Djoko Hartanto. "Mutual coupling reduction using dumbbell defected ground structure for multiband microstrip antenna array." Progress In Electromagnetics Research Letters 13 (2010): 29-40.

[15] Kondori, Hamideh, Mohammad Ali Mansouri-Birjandi, and Saeed Tavakoli. "Reducing mutual coupling in microstrip array antenna using metamaterial spiral resonator." IJCSI International Journal of Computer Science Issues 9, no. 3 (2012): 51-56.

[16] Farahbakhsh, Ali, Shahram Mohanna, Saeed Tavakoli, and Mahmood Oukati Sadegh. "New patch configurations to reduce the mutual coupling in microstrip array antenna." In Antennas & Propagation Conference, 2009. LAPC 2009. Loughborough, pp. 469-472. IEEE, 2009.

Fig. 21. Radiation Patterns for 4×2 EBG Vicsek fractal, with separation of

10mm, at 3.69 GHz for ϕ=0o and 90o respectively

Fig. 22. Radiation Patterns for 4×2 EBG Vicsek fractal, with separation of

10mm, at 5.16 GHz for ϕ=0o and 90o respectively

Fig. 23. Radiation Patterns for 4×2 EBG Koch inspired fractal, with

separation of 10mm, at 3.69 GHz for ϕ=0o and 90o respectively

Fig. 24. Radiation Patterns for 4×2 EBG Koch inspired fractal, with

separation of 10mm, at 5.16 GHz for ϕ=0o and 90o respectively


01-03 Feb, 2016 6 Goa, India

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