## An Improved Compact & Multiband Fractal Antenna Using the Koch Curve Geometry

**Manas Ranjan Jena**^{1,}, **B.B. Mangaraj**^{1}, **Rajiv Pathak**^{2}

^{1}Deparment of ELTCE, VSSUT, Burla, Odisha, India

^{2}BIT, Durg, Chhatisgadh, India

### Abstract

In this paper, we have achieved an compact & multiband fractal antenna using a Koch curve geometry. The simulation of the proposed antenna is done by CST Microwave Studio EM simulation software. The proposed Koch curve fractal antenna proves that it is capable to create multiband frequencies. The proposed fractal antenna is designed on FR-4 substrate with ℇr= 4.4. The antenna is fed with the probe feed method. We got two resonant frequencies like 32.84GHz & 34.28GHz which shows multiband characteristics. Simulated results shows that the return loss is better than 15 dB, the VSWR is less than 1.3, the directivity is greater than 6dBi & the gain is more than 6dB in each band. So this fractal antenna can be suitable for the radio astronomy & space research applications.

### At a glance: Figures

**Keywords:** fractal antenna, koch curve, CST, IFS, self similarity, self filling, multiband

*Wireless and Mobile Technologies*, 2014 2 (1),
pp 1-6.

DOI: 10.12691/wmt-2-1-1

Received March 26, 2014; Revised May 30, 2014; Accepted June 02, 2014

**Copyright**© 2014 Science and Education Publishing. All Rights Reserved.

### Cite this article:

- Jena, Manas Ranjan, B.B. Mangaraj, and Rajiv Pathak. "An Improved Compact & Multiband Fractal Antenna Using the Koch Curve Geometry."
*Wireless and Mobile Technologies*2.1 (2014): 1-6.

- Jena, M. R. , Mangaraj, B. , & Pathak, R. (2014). An Improved Compact & Multiband Fractal Antenna Using the Koch Curve Geometry.
*Wireless and Mobile Technologies*,*2*(1), 1-6.

- Jena, Manas Ranjan, B.B. Mangaraj, and Rajiv Pathak. "An Improved Compact & Multiband Fractal Antenna Using the Koch Curve Geometry."
*Wireless and Mobile Technologies*2, no. 1 (2014): 1-6.

Import into BibTeX | Import into EndNote | Import into RefMan | Import into RefWorks |

### 1. Introduction

Now-a-days there is a need for more compact and portable communication systems. We know that antenna is an integral part of all the communication systems. So there is a demand for small antennas for portable communication systems ^{[1]}.

It is well known that the antenna dimension is a function of its operating wavelength (λ). i.e if the antenna size is less than the operating wavelength (λ), the antenna becomes inefficient as its characteristics like radiation resistance, directivity, gain & bandwidth are diminished ^{[2]}. Fractal geometry is a very good solution for this problem due to its two major characteristics like self similarity & space filling. so fractal geometry has become an important approach for designing multiband antennas ^{[3, 4]}.

A fractal is a rough or fragmented that can be sub-divided into parts, each of which is a reduced copy of whole. Therefore the basic property of a fractal shape is self similarity and structure at all scales ^{[5]}.

The goal of this paper is to design and characterize a fractal antenna with Koch curve geometry as it has the potential to provide multiband solution ^{[6]}.

A koch curve is a famous fractal objects in mathematics ^{[7]}. These are low profile antennas with better return loss, VSWR, directivity and gain. So Koch curve can be made operative at multiple frequency bands and hence are multi-functional ^{[8, 9]}.

### 2. Antenna Design

**Design Equations:**

Here we have designed a 3 GHz antenna using the following parameters.

Substrate: FR4 (ε_{r}= 4.4, h=1.6 mm).

This proposed fractal antenna is an iterative model to a normal square patch as shown in Figure 2a with a generator of the shape shown in the following Figure 1.

**Fig**

**ure**

**1**

**.**proposed generator

Figure 2a shows a normal wire square patch antenna in which the length of each side is 6 mm. Iteration 1 is produced by replacing each straight wire with the proposed generator shape as shown in figure 2b. Iteration 2 is produced from iteration 1 by using IFS (Iterated Function System) as shown in figure 2c ^{[10, 11]}.

**Figure**

**2.**Different iteration stages of the proposed Koch curve fractal antenna. Here One stage is generated by applying the affine transformation to the previous one

### 3. Simulation Setup & Results

CST Microwave Studio electromagnetic simulator software is used for design & simulation. Antenna is fed with probe feed. Results like Reflection coefficient (return loss), VSWR (voltage standing wave ratio), Variation of Impedance Z (real & Imaginary part), 2D radiation patterns, 3D radiation patterns are simulated ^{[12, 13]}. Simulation results of iteration 1, iteration 2 & iteration 3 are summerised in Table 1, Table 2 & Table 3 respectively.

**3.1. Simulated Results of Iteration 0**

**Figure**

**3**

**.**a. Variation of simulated reflection coefficient(S11)with frequency

**Figure**

**3**

**.**b. Variation of VSWR with frequency

**Figure**

**3**

**.**c. 3D Radiation pattern (Directivity) at Fr=32.37 GHz

**Figure**

**3**

**.**D. 3D Radiation pattern (Gain) at Fr=32.37 GHz

**3.2. Simulated Results of Iteration 1**

**Figure**

**4**

**.**a. Variation of simulated reflection coefficient (S11) with frequency

**Figure**

**4**

**.**b. Variation of VSWR with frequency

**Figure**

**4**

**.**c: 3D Radiation pattern (Directivity) at Fr=32.73 GHz

**Figure**

**4**

**.**d. 3D Radiation pattern (Gain) at Fr=32.73 GHz

**3.3. Simulated Results of Iteration 2**

**Figure**

**5**

**.**a. Variation of simulated reflection coefficient (S11) with frequency

**Figure**

**5**

**.**b: Variation of VSWR with frequency

**Figure**

**5**

**.**c. 3D Radiation pattern(Directivity) at Fr=32.84 GHz

**Figure**

**5**

**.**d. 3D Radiation pattern(Gain) at Fr=32.84 GHz

**Figure**

**5**

**.**e. 3D Radiation pattern(Directivity) at Fr=34.28 GHz

**Figure**

**5**

**.**F. 3D Radiation pattern (Gain) at Fr=34.28 GHz

**BW Calculation**

1. For 0^{th} iteration

fc=32.37 GHz, f_{L}=31.67GHz & f_{H}=33.83GHz

So BW=100%=6.67%

2. For 1^{st} iteration

fc=32.73 GHz, f_{L} =32.21GHz & f_{H} =33.19GHz

So BW=100%=2.99%

3. For 2^{nd} iteration

For 1^{st} band

fc=32.84GHz, f_{L}=30.91GHz & f_{H}=33.41GHz So BW=100%=7.61%

For 2^{nd} band

fc=34.28GHz, f_{L}=33.92GHz & f_{H}=34.94GHz So BW=100%=2.97%

### 4. Conclusion

A fractal antenna with Koch curve geometry is designed & characterized. The simulated results show that return loss is more than -15 dB, VSWR is less than 1.3, directivity is more than 6dBi, gain is more than 6dB. This antenna not only improve return loss, VSWR, directivity & gain, but also can Provide a compact size of radiating patch. Gain is enhanced with multiple iterations. Bandwidth enhancements for multiple iterations is compared. Antenna size is reduced by using fractal shapes with multiple iterations. After these comparisons, it is clear that the proposed fractal antenna is superior than the conventional rectangular patch antenna. It follows the multiband characteristics which enables to use a single antenna instead of many. So the proposed antenna is suitable for the radio astronomy & space research applications.

### Acknowledgement

The authors sincerely thank to the Vice Chancellor & the H.O.D of EL & TCE Dept. VSSUT, BURLA for constant encouragement and support. Authors are thankful to all the staff of EL & TCE Dept. VSSUT, BURLA for their support directly or indirectly.

### References

[1] | Balanis, Constantine, “Antenna theory-Analysis and Design”, John Wiley & Sons Ltd, Reprinted 2008. | ||

In article | |||

[2] | B. B. Mandelbrot, “The Fractal Geometry of Nature” San Francisco, CA: Freeman, 1983. | ||

In article | |||

[3] | N. Cohen, “Fractal Antenna Application In Wireless Telecommunications” Proceedings of Electronics Industries Forum of New England, 1997, pp. 43-49. | ||

In article | CrossRef | ||

[4] | R.M. Crownover, “Introduction to Fractals and Chaos, Boston”, MA Jones & Bartlett, 1995. | ||

In article | |||

[5] | D. H. Werner, P. L. Werner, and K. H. Church, “Genetically engineered multi-band fractal antennas,” Electron. Lett., vol. 37, no. 19, pp. 1150-1151, Sep. 2001. | ||

In article | CrossRef | ||

[6] | B. Manimegalai, S. Raju, & V. Abhaikumar, “A multi fractal cantor antenna for multiband wireless applications,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 359-362, 2009. | ||

In article | CrossRef | ||

[7] | D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antennas Propag. Mag., vol. 45, no. 1, pp. 38-57, Feb. 2003. | ||

In article | CrossRef | ||

[8] | K. J. Vinoy, “Fractal Shaped Antenna Elements for Wide and Multi-Band Wireless Applications” Thesis, Pennsylvania, Aug. 2002. | ||

In article | |||

[9] | Best S.R. “The Effectiveness of Space Filling Fractal Geometry in Lowering Resonant Frequency”, Antennas & Propagation Letters, Vol. 1, (2002), 112-115. | ||

In article | CrossRef | ||

[10] | X. Yang, J. Chiochetti, D. Papadopoulos, and L. Susman, “Fractal antenna elements and arrays,” Appl. Microw. Wireless, vol. 5, no. 11, pp. 34-46, May 1999. | ||

In article | |||

[11] | Puente, C., Romeu, J., and Cardama, A. (2000). “The Koch Monopo le: A Small Fractal Antenna”. IEEE Transactions On Antennas And Propagation 48 (11). | ||

In article | |||

[12] | Best, S.R. (2002). “On the resonant properties of the Koch fractal and other wire monopole antennas”. IEEE Antennas and Wireless Propagation Letters. 1 (1). | ||

In article | CrossRef | ||

[13] | Vinoy, K. J., Abraham, J.K., and Varadan, V.K. (2003). “Fractal dimension & frequency response of fractal shaped antennas”. IEEE Antennas &Propagation Society International Symposium. 22-27 June. Volume 4, 222-225. | ||

In article | |||