Arashpreet Kaur and Amanpreet Kaur
Department of Electronics and Communication Engineering,
Thapar University, Patiala, India 147004
Corresponding author:
sohi_arsh@ymail.com, Ph:
7889253068
Abstract : In this manuscript, a two-port semi-circular patch
antenna with Koch curve fractals is presented as a suitable candidate
for portable UWB communication systems. The proposed fractal array is
engraved on a 1.57 mm thick FR-4 substrate with an overall array size of
30.5 × 47 × 1.64 mm3. The upper substrate layer
consists of two microstrip-line fed semi-circular patches combined with
two Koch curve fractals (optimized up to 2nd order of
iteration) separated by a distance of λ/2. To mitigate the effect of
mutual coupling between the radiating elements, the lower substrate
layer consists of a reduced ground plane with a funnel-shaped decoupling
structure. To achieve a high degree of isolation
(S21/S12 ≤ -16.8 dB) between the ports
of the proposed array, two rectangular and L-shaped slots (mirror images
of each other) are etched from the upper surface of the reduced ground.
The design and simulation of the proposed antenna array is implemented
in CST MWS’18. The optimized fractal array covers the simulated
frequency band from 4.395-10.184 GHz with a fractional bandwidth of 79.4
% (at a center frequency of 5.789 GHz) and provides a peak radiation
efficiency of 88.8% (at 6.2 GHz frequency). The antenna diversity
performance is analyzed in terms of envelope correlation coefficient
(ECC ≤ 0.0021), diversity gain (DG ≥ 9.989), mean effective gain (MEG ≥
-3.7 dB), channel capacity loss (CCL ≤ 0.4 bits/s/Hz) and total active
reflection coefficient (TARC ≤ -10 dB). The experimentally measured
S-parameter results show a good match with the simulated ones.
Keywords : Koch curve fractal; multiple-input multiple-output
(MIMO); defected ground structure (DGS); ultra-wideband (UWB).
INTRODUCTION
Over the past few years, the advancement in ultra-wideband (UWB) radio
technology has played a significant role in the wireless
telecommunication industry to fulfill the escalating needs of large
bandwidth with high speed of data transfer at a low cost and low energy
consumption [1]. In 2002, the Federal Communication Commission (FCC)
has allocated the usage of unlicensed radio spectrum from 3.1-10.6 GHz
(with a fractional bandwidth of 109.5% at 6.85 GHz center frequency)
for commercial UWB applications [2]. Apart from the admirable
properties of UWB technology, conventional UWB radio systems suffer from
the problem of co-channel fading and interference due to multipath wave
propagation from the transmitter to the receiver end. To curb the
adverse effects of multipath fading, the UWB devices are designed with
multiple-input multiple-output (MIMO) wireless technology which
multiplies the capacity of radio channel using multiple antennas at
transmitter and receiver. Equation (1) shows the linear relationship
between the capacity and signal to noise ratio (SNR) of the MIMO antenna
system.
\(C=B\left[\log_{2}\det\left(I_{\text{Nr}}+\frac{E_{t}}{\sigma_{n}^{2}+N_{t}}\right)\text{H.}H^{H}\right]\)(1)
where B, INr, Et,
σn2, Nt, H and
HH is the channel bandwidth, identity matrix, total
input power, noise power, number of transmitter antennas, channel matrix
and the hermitian transpose of the channel matrix respectively [3].
The integration of UWB-MIMO technologies has become an essential part of
modern wireless systems to achieve a high data rate (about 1Gbps),
superior radio link reliability, broad communication range and little
interference in a rich multipath environment [4]. The physical size
constraints of the portable and handheld gadgets pose a challenge to the
antenna designers to develop small-sized and low-profile MIMO antennas.
To meet these specifications, microstrip patch antenna (MPA) is a
suitable choice due to its innate benefits of light-weight, simplicity,
less cost, mechanically robust and planar/non-planar surface conformity
[5]. For modeling compact user equipment, the inter-element spacing
in the MIMO configuration is reduced which in turn degrades the array
performance due to increased mutual coupling and alters the radiation
pattern of actively radiating elements. Therefore, it is favored to
incorporate fractal geometries in MPAs to achieve the desired
compactness and multiband/wideband operation in a given restricted area
due to its inherent self-similar, self-affine and space-filling
characteristics [6]. Also, the combination of defected ground
structure (DGS) approach with fractal MIMO antennas helps in achieving
the desired size reduction, improved operational bandwidth and reduced
mutual coupling between the actively radiating patches [7].
In past, researchers have reported many fractal geometries such as
Sierpinski gasket [8], Pythagorean tree [9], Hilbert curve
[10], Minkowski [11], etc. for designing MIMO antennas with the
ultimate goal to achieve miniaturization and multiband/wideband
frequency response. All the previously designed fractal MIMO antennas
[8-11] had larger dimensions, less port-to-port isolation and were
employed for multiband wireless systems. Based on the literature review,
the primary objective of this article is to design, simulate and
experimentally test a miniaturized fractal MPA array for high bandwidth
and good diversity performance to support high data rate portable UWB
systems. In this article, a Koch curve fractal (up to
2nd order of iteration) semi-circular antenna array
with the DGS technique is proposed. The proposed fractal array is
designed on a commercially available FR-4 substrate with relative
permittivity (εr), loss tangent (tan δ) and height
(ht) of 4.4, 0.024 and 1.57 mm respectively. The
designing and simulation of the proposed fractal array is carried out in
time domain solver of computer simulation tool microwave studio version
18 (CST MWS V’18) software with open boundary conditions. The proposed
fractal MPA array covers the simulated frequency band from 4.395-10.184
GHz (79.4 % fractional bandwidth) with a peak return loss of -54.5 dB
(at 9.4 GHz frequency) and isolation ≤ -16.8 dB. To justify the
performance of the proposed fractal array for practical applications, it
is fabricated (using photolithography process) and experimentally tested
for S-parameters (S11, S22,
S21, S12) using a vector network
analyzer (VNA). The diversity performance parameters are computed using
simulated and measured S-parameters which are found to lie within their
acceptable limits.
ANTENNA GEOMETRY AND PARAMETRIC ANALYSIS
Figure 1 (a, b) shows the geometry of a dual-port semi-circular MPA
array with Koch curve fractals and a minimized ground plane with DGS for
MIMO implementation in UWB radio systems. The proposed fractal array is
modeled on a low-cost FR-4 substrate (εr = 4.4, tan δ =
0.024 and ht = 1.57 mm) with the overall array
dimensions of 30.5 × 47 mm2. As shown in Figure 1(a),
the upper FR-4 substrate layer consists of two semi-circular radiating
patches (copper), each joined with Koch curve fractal (up to
2nd order of iteration) on its upper edge. The
separation distance between the fractal radiators is kept as λ/2 (21.2
mm). The optimized parametric values of the proposed fractal array are
mentioned in Table 1. The semi-circular patches are designed for high
resonating frequency where the radius of each semi-circle is calculated
by Equation (2,3).
\(r=\ \frac{92\times 10^{9}}{f_{r}\sqrt{\varepsilon_{\text{eff}}}}\)(2)
\(\varepsilon_{\text{eff}}\approx\frac{\varepsilon_{r}+1}{2}\) (3)
where r, fr εr and εeffis the radius of the semi-circle, resonating frequency (GHz), the
relative permittivity of the FR-4 substrate and effective dielectric
constant of FR-4 substrate respectively [12].
The proposed MSA array is fed using two microstrip transmission lines
with 50 Ω characteristic impedance (Zo). To realize the
desirable matching performance between the radiating patch and
microstrip line, the feedline width (b) is chosen according to the
Equation (4,5) [5].
\(Z_{O}=\ \frac{120\pi}{\sqrt{\varepsilon_{\text{eff}}}\ \left[\frac{b}{h_{t}}+1.393+0.667ln\left(\frac{b}{h_{t}}+1.444\right)\right]}\), for \(\frac{b}{h_{t}}>1\) (4)\(\varepsilon_{\text{eff}}=\ \frac{\left(\varepsilon_{r}+1\right)}{2}+\ \frac{\left(\varepsilon_{r}-1\right)}{2}\left(1+\frac{12h_{t}}{b}\right)^{-1/2}\)(5)
A stub is added at the bottom of the feedline to achieve a wideband
response with an improved impedance matching characteristic. The length
of the stub is calculated using Equation 6 [4].
\(v=\frac{c}{2f_{r}\sqrt{\varepsilon_{\text{eff}}}}\) (6)
The recursive procedure followed to reach the 2ndorder of iteration of the Koch curve fractal is shown in Figure 1 (c).
To construct the Koch curve fractal, initially, a straight line of
length ‘l’ is considered (0th order of iteration). The
length ‘l’ is further cut into three equal segments (each of length
‘l/3’) where the central segment is replaced by the two other segments
of an equilateral triangle (each with length ‘l/3’) resulting in the
1st order of iteration. This process is iterated
recursively to form the higher order of iterations. The self-similar
repetitions of the proposed Koch curve fractal can be generated by
iterated function system (IFS) approach, defined by generalized matrix
Equation (7) using the set of affine linear transformations ‘W’.
\(W\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}=\par
\begin{bmatrix}a&b\\
c&d\\
\end{bmatrix}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}+\par
\begin{bmatrix}e\\
f\\
\end{bmatrix}\) (7)
where the variables ‘a’, ‘b’, ‘c’ and ‘d’ deals with rotation (θ) and
scaling (s) operations and variables ‘e’ and ‘f’ deals with
translations.
Using a=cos θ/s, b = -sin θ/s, c = sin θ/s and d = cos θ/s where s = 1/3
and θ = 60˚ for two segments of equilateral triangle (one in clockwise,
other in anticlockwise direction), the required IFS transformation for
Koch curve fractal is calculated by Equations (8-11) [13].
\(W_{1}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}=\par
\begin{bmatrix}1/3&0\\
0&1/3\\
\end{bmatrix}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}+\par
\begin{bmatrix}0\\
0\\
\end{bmatrix}\) for θ = 0˚ (8)
\(W_{2}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}=\par
\begin{bmatrix}1/6&-\sqrt{3}/6\\
\sqrt{3}/6&1/6\\
\end{bmatrix}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}+\par
\begin{bmatrix}1/3\\
0\\
\end{bmatrix}\) for θ = 60˚ (9)
\(W_{3}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}=\par
\begin{bmatrix}1/6&\sqrt{3}/6\\
-\sqrt{3}/6&1/6\\
\end{bmatrix}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}+\par
\begin{bmatrix}1/2\\
\sqrt{3}/6\\
\end{bmatrix}\) for θ = -60˚ (10)
\(W_{4}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}=\par
\begin{bmatrix}1/3&0\\
0&1/3\\
\end{bmatrix}\par
\begin{bmatrix}x\\
y\\
\end{bmatrix}+\par
\begin{bmatrix}2/3\\
0\\
\end{bmatrix}\) for θ = 0˚ (11)
The self-similarity dimension (D) of the proposed Koch curve fractal is
calculated using Equation 12 [6]. In the proposed fractal
configuration, four new non-overlapping copies (N) are generated with
the scaling factor (s) of 1/3, resulting in a fractal dimension (D) of
1.262.
\(D=\frac{\log{(N)}}{\log{(1/s)}}\) (12)
As shown in Figure 1 (b), the lower FR-4 substrate layer consists of a
reduced ground with DGS. A funnel-shaped decoupling structure extends
vertically (at an angle 90˚) from the reduced ground plane. It obstructs
the steady flow of current between the two radiating patches and hence
minimizes the effect of cross-coupling. To further improve the isolation
performance, two rectangular (each with dimensions 5 × 2.5) and L-shaped
(11.6 × 0.5) slots, each with a length of λg/2 (where
λg is the guided wavelength), is etched from the upper
edge of the reduced ground. Figure 2 and Figure 4 show the geometrical
variations in the patch and ground plane configuration of the proposed
fractal array respectively for designing the final optimized geometry.
The corresponding improvement in impedance bandwidth
(S11/S22) and isolation
(S21/S12) performance for variations in
patch and ground plane geometries is depicted in Figure 3 and Figure 5
respectively.