Design and Analysis of Compact Multiband Fractal Antenna

Abstract'This paper presents a design and analysis of a compact dual band square fractal antenna designed on FR4 substrate. The antenna resonates at 2.23 GHz and 6.48 GHz compared to conventional antenna resonating at 2.83 GHz. The designed fractal antenna shows improved impedance bandwidth compared to conventional antenna at resonating frequencies. The azimuthal radiation pattern of the antenna at 0 degree elevation angle is found to be omni directional at all the resonant frequencies. The antenna can be designed for its use in many wireless bands.

Keywords'Fractal antenna, reflection coefficient, compact, multiband


The multichannel communications are widely exploited for multimedia applications [1]-[3] with the development in wireless communication technology. For example; around 1985, we were having only Doordarshan in India with 1 or 2 channels for TV reception requiring very less antenna bandwidth whereas in 2011-12, we are entertained by at least 100 of channels through many service provider by a single antenna. Further, these services are also received at compact and handheld equipments like laptop terminals, tablet PCs, mobile or cell phone terminals. These need antennas to be small in size and multiband in nature with desiring bandwidth and gain. Some of the wireless applications are listed in Table 1. Also, the wireless local area network (WLAN) service is increased its demands for telecommunication systems [1]-[4]. Fractal antennas are reported for their applications in compact, multiband wireless communication. Benoit Mandelbrot in 1975 coined the word fractal which is called as fractus in Latin language, meaning "broken" or "fractured. 'A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole" [5], [9], [10]. A fractal often has applications in antennas for multiband wireless communication, image processing for data compression, packaging, mechanics (fracture mechanics is a widely studied subject by mechanical engineers) etc. The use of self similarity property in fractal antennas can achieve multiband characteristics whereas space filling property in these antennas can be used for miniaturization. Fractal antennas have been reported for compact, multiband and broadband applications [1], [6-7], [8], [10].

This paper presents the design and analysis of the square antenna (i.e. a conventional patch antenna) perturbed to behave as compact and multiband fractal antenna using iterative fractal technique.


Wireless Applications Frequency Band (MHz)

2G 800/900 1800/1900

3G 1800-2500

4G 2000-8000

Wireless Communication Service 2305-2320 /

2345 -2360

Satellite Digital Radio 2320-2680

Multichannel Multipoint

Distribution Service (MMDS) 2150 -2680

GPS 1570.42-1580.42

DCS ' 1800 1710-1880

PCS ' 1900 1850-1990

IMT-200 / UMTS 1885-2200

ISM Band I (Cordless Phone 1G WLAN)

ISM Band II ( Bluetooth 802.11b WLAN) 902-928


Lower LTE (long term evolution) bands

Upper LTE bands 790'960



First, a square patch of dimension, L(length) = W (width) = 23 mm has been designed on FR4 substrate material with dielectric constant ( ??r ) 4.3 and thickness (h) 1.56 mm. The size of the substrate is 625 sq. mm backed by finite ground plane of same size as shown in Fig. 1.

To design the proposed fractal antenna, a slot of dimension L = W = 13.861 mm has been generated in the square patch of dimensions, L = W = 23 mm. This slot is space filled using a gap ( 4.5 mm) coupled small square patch of dimension L = W = 9.351 mm. The designed self similar fractal antenna has been shown in Fig. 2.


Fig. 1. Design of conventional antenna.

Fig. 2. Design of first iterated fractal antenna.


The comparative reflection loss plot of square patch antenna i.e. the conventional antenna (Fig. 1) and first iteration fractal antenna (Fig. 2) has been shown in Fig. 3. It has been observed that although the size of the conventional and fractal antenna are identical, but the resonance frequency, 2.35 GHz of the first iterated fractal antenna is less than 2.83 GHz that of the conventional antenna. The reason for lowering of resonance frequency is increased length of current path on patch (L) [3] due to slot. As shown in Fig. 2, the first iterated fractal antenna has two square patches separated by a gap which resonate independently ignoring the mutual coupling between them. This fractal antenna has two resonant frequencies 2.35 GHz and 6.46 GHz, first due to outer square ring and second due to inner square ring as shown in Fig. 4. In addition to these two resonance frequencies, a spurious second resonance is observed due to outer square ring at 4.14 GHz.

As shown in Fig. 5, square patch antenna with a square slot shows maximum reflections compared to space filled first iterated square patch fractal antenna. This shows the importance of space filling geometry in fractal antenna.

The resonance frequencies of dual band first iterated fractal antenna can be found using following empirical formula [3].

f1 = c / 2 (' ??eff) * L' (1)

f2 = c / 2 (' ??eff) * L'' (2)

Where, L' = L + W2 = 36. 861 mm and L'' = '2 * W3 = 13.224 mm, are average lengths of the current paths for first & second resonance and L = 23 mm, W2 = 13.861mm & W3 = 9.351 mm. These relations may be used for designing the antenna.

Fig. 3. Comparative reflection loss plot of conventional and fractal antenna.

Fig. 4. Comparative reflection loss plot of conventional and fractal antenna showing dual band characteristics.

Fig. 5. Comparative reflection loss plot of square slotted and space filled fractal antenna.

Fig. 6. Comparative real impedance plot of the antennas.

Fig. 7. Comparative impedance plot of the conventional antenna.

Fig. 8. Comparative impedance plot of the fractal antenna.

The comparative impedance characteristics of these antennas are shown in Fig. 6, 7 and 8 to depict multiband characteristics of the fractal antenna. It is seen that impedance bandwidth of the fractal antenna is increased compared to the conventional antenna (Fig. 6). These antennas are resonant where the impedance of the excitation (50 ??) and the antenna found a good matching. As seen in Fig. 7 and 8, near the resonance the reactance exhibited by the antenna is minimum reducing the stored reactive power.

Radiation Patterns: The realized gain radiation patterns of the conventional and fractal antenna at resonating frequencies have been simulated and are shown in azimuth and elevation plane in Fig. 9, 10 and 11. The similar radiation pattern has been obtained in fractal antenna at both the resonant frequencies. In azimuth plane at theta 0 degree, the conventional antenna as well as fractal antenna exhibits an omnidirectional radiation pattern at all resonant frequencies. At 90 degree elevation a conventional antenna exhibits two major lobes. These lobes get fractured in fractal antenna at 2.35 GHz and 6.46 GHz compared to a conventional antenna. In elevation plane, it is seen that the beam width gets reduced in fractal antenna at 2.35 GHz and 6.46 GHz compared to conventional antenna at 2.83 GHz. The maximum realized gain of 7 dB at 2.83 GHz in conventional antenna at 0 degree elevation in azimuth plane is noted whereas it is 6.798 dB and 8 dB at 2.23 GHz and 6.48 GHz respectively in fractal antenna.

Fig. 9. Realized gain pattern at phi = 0 and 90 degree and theta = 0 and 90 degree for conventional antenna at 2.83 GHz.

Fig. 10. Realized gain pattern at phi = 0 and 90 degree and theta = 0 and 90 degree for fractal antenna at 2.35 GHz.

Fig. 11. Realized gain pattern at phi = 0 and 90 degree and theta = 0 and 90 degree for fractal antenna at 6.46 GHz.


The square fractal patch antenna shows multiband behavior due to self similar properties in antenna compared to its conventional counterparts. The space filling properties in the antenna make the antenna compact and minimize the reflection loss. The antenna can be useful for wireless applications in varying frequency bands.


I am thankful to Prof. R. B. Dhumale (Guide), Dr. S. D. Lokhande (Co-guide), Dr. A. D. Jadhav (PG Head PG Program) and Principal, SCOE Pune for their valuable Guidance.


[1] J. Kim, C. Yang, T. Yun, and C. Jung, 'Multimode Multiband (VHF / UHF /L / 802.11 a/b) Antennas for Broadcasting and Telecommunication Services', IEEE Antennas and Wireless Propagation Letters, Vol. 10, 2011.

[2] Cheng-Hung Kang, Sung-Jung Wu, and Jenn-Hwan Tarng, 'A Novel Folded UWB Antenna for Wireless Body Area Network', IEEE Transactions on Antennas and Propagation, Vol. 60, No. 2, February 2012.

[3] Homayoon Oraizi and Shahram Hedayati, 'Circularly Polarized Multiband Microstrip Antenna Using the Square and Giuseppe Peano Fractals', IEEE Transactions On Antennas and Propogation, Vol. 60, No. 7, July 2012.

[4] A. Goldsmith, 'Wireless Communications', Chapter1- Overview of Wireless Communications, Cambridge University Press.

[5] Balanis, Antenna Theory and Analysis, John Wiley publications.

[6] Hattan F. Abutarboush et al., 'A Reconfigurable Wideband and Multiband Antenna Using Dual-Patch Elements for Compact Wireless Devices', IEEE Antennas and Wireless Propagation Letters, Vol. 8, 2009.

[7] Leonardo Lizzi, Federico Viani, Edoardo Zeni, and Andrea Massa, 'A DVBH /GSM/UMTS Planar Antenna for Multimode Wireless Devices' , IEEE Transactions on Antennas and Propagation, Vol. 60, No. 1, January 2012.

[8] Fong Chen et al.,'Bowtie-Feed Broadband Monopole Antenna for Laptop Applications', IEEE Antennas and Wireless Propagation Letters, Vol. 10, 2011.

[9] B. B. Mandelbrot, The Fractal Geometry of Nature, New York: W.H. Freeman, (1983).

[10] D. H. Werner, Raj Mitra, Frontiers in Electromagnetics, IEEE Press Series on Microwave Technology and RF.

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