microstrip Fractal antenna

1. Published in IET Microwaves, Antennas & Propagation
Received on 20th May 2014
Revised on 16th July 2014
Accepted on 26th July 2014
doi: 10.1049/iet-map.2014.0326
ISSN 1751-8725
Hexagonal fractal ultra-wideband antenna using Koch
geometry with bandwidth enhancement
Shrivishal Tripathi1, Akhilesh Mohan2, Sandeep Yadav1
1
CoE-Information and Communication Technology, Indian Institute of Technology Jodhpur, Rajasthan 342 011, India
2
Electronics and Electrical Communication Department, Indian Institute of Technology Kharagpur,
West Bengal 721 302, India
E-mail: shrivishal@iitj.ac.in
Abstract: In this study, a design approach to achieve multiresonance phenomena in ultra-wideband (UWB) bandwidth using
fractal geometry is investigated. The introduction of Koch fractal geometry in monopole as well as in the ground plane of the
antenna generates additional resonances, which helps to achieve entire UWB operational bandwidth. Therefore the bandwidth
is increased up to 122%. Moreover, the fractal nature of the antenna also facilitates to obtain the stable radiation pattern. The
compact dimension 31 mm × 28 mm of the antenna exhibits nearly omnidirectional radiation pattern, with good reflection
coefficient over the entire UWB frequency range. The proposed prototype is fabricated and its measured results are in good
agreement with the simulated one. The time-domain analysis of the antenna is performed and it is found that fidelity factor is
better than 0.81, which shows good pulse preserving capability of the antenna.
1 Introduction
The ultra-wideband (UWB) antenna attracts research
communities now a days because of its many advantages
such as high data rate, low spectral density radiated power,
low power consumption, wideband operability, robustness
to fading and transmission capacity of short-duration pulses
of large bandwidth. The commercial application for UWB
technology (3.1–10.6 GHz) requires compact antenna [1].
To obtain the wideband bandwidth in a smaller area,
different methods such as variation in substrate thickness
and dielectric constant, modification in monopole and
ground plane and variation in feed gap are frequently used
[2–4]. The planar antenna is preferred because of its small
size, low cost and simple structure.
The compactness in structure as well as wideband
operational bandwidth can be achieved by using fractal
geometry in antenna design because of its self-similarity
and space filling properties [5–7]. The space filling property
of fractal geometry is used in antenna design to increase the
effective electrical path length of the antenna in a given
small area [5, 6]. Many fractal geometries like Koch
snowflake [6, 8], hexagonal shaped [5] and Sierpinski
triangle [5, 6] are used to design UWB antenna.
In this paper, a novel design approach for bandwidth
enhancement of UWB antenna is presented. In this
design, fractal Koch geometry is applied at the edges of
hexagonal monopole as well as at the ground plane. The
application of Koch geometry offers miniaturisation and
wideband phenomena in antenna design. It has been
demonstrated that measured results show good agreement
with simulated results. Time-domain analysis is also
performed to provide more insight into the behaviour of
the proposed antenna.
2 Antenna design
The proposed antenna is generated by combining the Koch
fractal and the hexagonal geometry. The recursive
procedure for generation of Koch fractal geometry is shown
in Fig. 1. The first iteration divides the initial length in
three equal parts, and Koch structure is created. This
iterative process is repeated for higher-order iteration. The
Koch fractal geometry is further applied to the edges of the
hexagonal geometry as shown in Fig. 2. Here, this
hexagonal shape works as an initiator, and Koch fractal
works as a generator in the evolution of initial antenna design.
The initial structure of the antenna without application of
fractal geometry is shown in Fig. 2a. Figs. 2b and c display
the structures of the antenna after applying first and second
iterations of the Koch geometry at the edges of monopole,
respectively. The introduction of Koch geometry in the
ground plane of antenna structure is shown in Fig. 2d. The
proposed structures (with and without Koch fractal) is
simulated using high-frequency structure simulator v.13 on
a rectangular substrate (W × L), FR4, having a dielectric
constant (εr) 4.4, loss tangent (tan δ) 0.023 and thickness
(h) 1.6 mm. The rectangular substrate is chosen as a basic
structure of the proposed antenna because of its
characteristics of wideband operability and good radiation
property [9]. The hexagonal monopole with the edges of
length R is connected to a 50 Ω microstrip line of width
(Wm) and length (Lm) for impedance matching. Ground
plane is positioned on the other side of the substrate having
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IET Microw. Antennas Propag., 2014, Vol. 8, Iss. 15, pp. 1445–1450
doi: 10.1049/iet-map.2014.0326
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2. length (Lg) and width (W ). The values of above-mentioned
parameters are same as given in Table 1.
The reflection coefficient (S11) for the various antenna
structures generated in the evolution process is shown in
Fig. 3. It is observed that addition of Koch geometry with
monopole increases the electrical path length of monopole.
Moreover, fractal monopole possesses greater perimeter
length in a smaller area as compared with other geometries
such as circle, ellipse and hexagon etc. The lower operating
frequency changes slightly with the increase in iteration of
Koch geometry. These modifications in the geometry
improve the S11 characteristics significantly in the mid as
well as high-frequency ranges of UWB spectrum. The
fractal geometry produces multiple resonances and by
combining these resonances wideband bandwidth is
achieved. The introduction of Koch geometry into the
ground plane further improves bandwidth because of
change in the electrical path length and excitation of
additional resonances. Tuning the ground plane has been
useful to increase bandwidth of the antenna elements [10–
13], this helps to achieve the operational bandwidth up to
122%. The optimised structure of the UWB antenna is
shown in Fig. 4, which has the operational bandwidth from
3 to 12.8 GHz with three resonant frequencies at 4.3, 7.2
and 10 GHz, and optimised parameters are shown in Table 1.
The surface current density distribution on the fractal
monopole and fractal ground plane at resonant frequencies is
shown in Fig. 5. At 4.3 GHz resonant frequency, the surface
current distribution is mainly concentrated at the edges of the
fractal structure of monopole and ground as can be seen from
Fig. 5a. This shows that Koch fractal affects the impedance
matching significantly at lower frequencies. Fig. 5b shows the
surface current distribution at 7.2 GHz. It is observed that the
fractal edges of the monopole and lower portion of the ground
plane have more effect on the impedance matching. At 10
GHz resonant frequency, the surface current distribution is
shown in Fig. 5c, which illustrates that the current distribution
intensity is significant at the fractal edges of the ground plane
and junction of the monopole and feed. This demonstrates that
Fig. 2 Evolution of the fractal UWB antenna with application of Koch geometry
a Antenna-0
b Antenna-1
c Antenna-2
d Antenna-3
Fig. 1 Recursive generation of Koch structure
a Iteration-0
b Iteration-1
c Iteration-2
Fig. 4 Optimised structure of the proposed fractal UWB antenna
Table 1 Optimised geometrical parameter of the proposed
UWB antenna
Parameters Dimensions, mm Parameters Dimensions, mm
L 31.0 Lm 12.0
W 28.0 Wm 3.0
R 9.0 Lg 11.1
Fig. 3 Simulated |S11| of the different antenna structures in the
evolution
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IET Microw. Antennas Propag., 2014, Vol. 8, Iss. 15, pp. 1445–1450
doi: 10.1049/iet-map.2014.0326

3. the application of the Koch structure in the ground plane has
more significant impact at higher frequencies as compared
with lower frequencies, which is also reflected in the S11
behaviour as depicted in Fig. 3. The surface current
distribution at monopole is more uniform at lower frequency as
compared with higher frequency because of the change in
nature of the current [14]. At lower frequencies, the
wavelength of the electromagnetic (EM) waves is long and
small segments of the Koch structure contribute less in the
overall radiations. However, at higher frequencies, the segment
dimensions become comparable with the wavelength, which
enhance the radiation characteristic significantly [15].
3 Frequency-domain analysis
The prototype of the proposed UWB antenna structure is
fabricated and its characteristic is investigated. The
measurement is performed by Agilent Vector Network
Analyzer E5071C. The top and bottom views of the
fabricated prototype of the proposed antenna are shown in
Fig. 6. Fig. 7 shows the simulated and measured S11 results.
The measured results show almost entire UWB bandwidth
from 3.4 to 13 GHz with multiple resonant frequencies. The
multiple resonant frequencies are observed because of the
introduction of Koch geometry in the antenna design.
However, some differences have been observed because of
the measurement environment, losses introduced by Sub
Miniature version A connectors and the fabrication tolerances.
The simulated real and imaginary impedances of the fractal
UWB antenna are shown in Fig. 8. The impedance matching
is good throughout UWB operating frequency range. It is
observed that at the resonant frequencies real input
impedance approaches to 50 Ω. The input reactance varies
between −15 and 15 Ω in the UWB range. It illustrates the
broadband nature of the proposed UWB antenna. It is
Fig. 5 Surface current distribution of the fractal UWB antenna at
a 4.3 GHz
b 7.2 GHz
c 10 GHz
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4. relevant to see that the flat response of both the real and
imaginary parts of the input impedance resulting in a
broadband bandwidth from 3 to 12.8 GHz. The variations
in the impedance over the UWB operating ranges are in
acceptable range.
Fig. 9 shows the measured radiation pattern of the proposed
antenna at 4.3, 7.2 and 10 GHz in both E-plane (xz-plane) and
H-plane (yz-plane). According to the figures, H-plane pattern
is nearly omnidirectional, whereas E-plane pattern is
bi-directional. The cross-polarisation component in the
E-plane as well as in the H-plane inevitably increases with
the increase in resonant frequency. It is observed that the
radiation pattern at higher resonant frequency shows small
deviations as compared with lower resonant frequency
because of the reflection at edges from the fractal antenna
structure and the change in the nature of the current from
standing wave pattern at lower frequencies to a travelling
wave pattern at higher frequencies [14]. The surface current
distribution intensity at the fractal edges of the Koch
geometry is significant at low and high resonant
frequencies. The fractal curves and bends cause for the
change in the current path, which supports to enhance the
radiation characteristics of the antenna [16]. This helps to
improve the antenna gain. Fig. 10 shows the gain of the
proposed antenna on xy-plane (θ = 90°, j = 0°). It shows
that the gain varies between 6 and 4 dBi in the UWB
frequency range. At higher frequencies above 6 GHz, gain
of the antenna increases steadily.
4 Time-domain analysis
The frequency-domain characteristic of antennas which
processes short pulses of large bandwidth becomes
cumbersome. In such cases, time-domain characteristic
provides a better understanding of antenna performance.
The proposed antenna is analysed using fidelity factor. It
determines the level of distortion introduced by the antenna
to its input signal. The fidelity factor is defined as
r = max
t
S(t)R(t − t) dt
S2(t) dt R2(t) dt
⎧
⎪⎨
⎪⎩
⎫
⎪⎬
⎪⎭
(1)
where t is delay, S(t) is the source pulse and R(t) is the
received pulse. The cross-correlation is performed on the
two signals, and maximum is calculated. The time-domain
characteristics of the proposed antenna is analysed using
computer simulation technology default Gaussian
modulated pulse, with a spectrum range 3.1–10.6 GHz. This
pulse satisfies the Federal Communications Commission
indoor and outdoor power masks [17]. The input signal is
Fig. 6 Fabricated prototype of the antenna
a Top view
b Bottom view
Fig. 8 Simulated real and imaginary impedance of the proposed
antennaFig. 7 Measured and simulated |S11| of the proposed antenna
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IET Microw. Antennas Propag., 2014, Vol. 8, Iss. 15, pp. 1445–1450
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5. given to the antenna and the received pulse is obtained by
means of a virtual probe as suggested in [18]. Fidelity
factor is calculated for elevation and azimuthal plane. The
probe is defined at a distance of 400 mm for every 10° from
0 to 90°. The chosen distance is large enough to
accomplish the far-field criteria, nearly four times the
wavelength of the lower UWB operating frequency. The
value of fidelity factor >0.7 can be considered for well
matching of radiated pulse with source pulse [19, 20].
Table 2 shows the fidelity factor variation in the range of
0.81 to 0.92. The results show that the proposed antenna
structure does not distort the incident pulse significantly,
which makes it a suitable choice for UWB application.
5 Conclusion
The Koch fractal structure has been studied for designing
novel UWB antenna and its properties are investigated. The
Koch fractal is applied in the monopole as well as in the
ground plane, which excites additional resonances and leads to
bandwidth improvement up to 122%. The proposed structure
has the compact dimensions of 31 mm × 28 mm × 1.6 mm.
The measured results are in good agreement with the
simulated one. The radiation pattern of the antenna shows
omnidirectional behaviour in H-plane and bi-directional
behaviour in E-plane. The time-domain analysis parameter,
fidelity factor >0.8 shows the good pulse preserving
Fig. 9 Measured radiation pattern with co-polarisation (_ ) and cross-polarisation (‐‐‐) at
a 4.3 GHz
b 7.2 GHz
c 10 GHz
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6. capability of the antenna. This design approach provides a
solution for wideband compact antenna with good antenna
characteristics. The miniaturisation of structure makes it an
appropriate choice for its applications in wireless devices,
body area network etc.
6 References
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Fig. 10 Measured gain of the proposed antenna against frequency
Table 2 Fidelity factor of the proposed antenna
Probe positions
(x–z-plane)
Fidelity
factor
Probe positions
(x − y-plane)
Fidelity
factor
θ = 0°, j = 0° 0.8918 j = 0°, θ = 90° 0.8165
θ = 10°, j = 0° 0.8916 j = 10°, θ = 90° 0.8279
θ = 20°, j = 0° 0.8914 j = 20°, θ = 90° 0.8313
θ = 30°, j = 0° 0.8778 j = 30°, θ = 90° 0.8537
θ = 40°, j = 0° 0.8644 j = 40°, θ = 90° 0.8524
θ = 50°, j = 0° 0.8544 j = 50°, θ = 90° 0.8638
θ = 60°, j = 0° 0.8487 j = 60°, θ = 90° 0.8819
θ = 70°, j = 0° 0.8427 j = 70°, θ = 90° 0.8996
θ = 80°, j = 0° 0.8373 j = 80°, θ = 90° 0.9119
θ = 90°, j = 0° 0.8371 j = 90°, θ = 90° 0.9183
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IET Microw. Antennas Propag., 2014, Vol. 8, Iss. 15, pp. 1445–1450
doi: 10.1049/iet-map.2014.0326