Miniaturised microstrip bandpass filters based on moore fratal geometry

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Miniaturised microstrip bandpass filters based on
Moore fractal geometry
Y.S. Mezaal, J.K. Ali & H.T. Eyyuboglu
To cite this article: Y.S. Mezaal, J.K. Ali & H.T. Eyyuboglu (2015) Miniaturised microstrip
bandpass filters based on Moore fractal geometry, International Journal of Electronics, 102:8,
1306-1319, DOI: 10.1080/00207217.2014.971351
To link to this article: http://dx.doi.org/10.1080/00207217.2014.971351
Accepted online: 30 Sep 2014.Published
online: 28 Oct 2014.
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Miniaturised microstrip bandpass filters based on Moore fractal
geometry
Y.S. Mezaala,b
*, J.K. Alib
and H.T. Eyyuboglua
a
Department of Electronic and Communication Engineering, Cankaya University, Ankara, Turkey;
b
Microwave Research Group, Department of Electrical Engineering, University of Technology,
Baghdad, Iraq
(Received 25 January 2014; accepted 5 July 2014)
This paper presents new microstrip bandpass filter design topologies that consist of
dual edge-coupled resonators constructed in the form of Moore fractal geometries of
second and third iteration levels. The space-filling property for proposed fractal filters
has found to produce reduced size shapes in accordance with sequential iteration
levels. These filters have been prepared for ISM band applications at a centre
frequency of 2.4 GHz using a substrate with a dielectric coefficient of 10.8, dielectric
thickness of 1.27 mm and metallisation thickness of 35 µm. The output responses of
each fractal bandpass filter have been determined by a full-wave-based electromagnetic
simulator Sonnet software package. Simulated and experimental results are approxi-
mately compatible with each other. These responses clarify that these fractal filters
have good transmission and return loss characteristics with blocked higher harmonics
in out-of-band regions.
Keywords: narrowband microstrip bandpass filter; Moore fractal geometry; filter
miniaturisation; higher harmonics suppression
1. Introduction
Microstrip bandpass filters (BPFs) have been extensively adopted in variety of microwave
circuits because of their outstanding properties of flexible manufacturing, low mass, small
sizes and so on. Compact microstrip resonators and filters are essential for the next
generation of wireless communication systems, because with the quick expansions of
modern communication systems, more miniaturised filters with excellent performances
are still requested (Hong & Lancaster, 2001).
Benoit Mandelbrot defined and expanded fractals for the first time as a method of
assorting structures whose dimensions were not complete numbers and had irregular
fragments. He pointed out that many fractals existed in nature could accurately simulate
some irregularly shaped objects or spatially inhomogeneous natural phenomena which are
impossible to be constructed by Euclidean geometry, like mountains, trees or blood
vessels. In mathematics, fractal is a type of complicated geometric structure that typically
has the property of self-similarity, so that a small portion of it can be seen as a reduced
scale copy of the whole (Mandelbrot, 1983).
Many fractal geometries like Sierpinski carpet, Koch curve, Cantor and Hilbert
geometries have been widely adopted in the fabrication of microwave antennas and filters.
These fractal structures have dual essential properties, space filling and self-similarity. A
*Corresponding author: Email: yakeen_sbah@yahoo.com
International Journal of Electronics, 2015
Vol. 102, No. 8, 1306–1319, http://dx.doi.org/10.1080/00207217.2014.971351
© 2014 Taylor & Francis
Downloadedby[IndianInstituteofTechnology-Kharagpur]at04:2508October2015

fractal shape can be packed in a restricted area as the iteration level raises and takes up the
same area in any case of considered iteration. This is because of space-filling property. By
self-similarity, a piece of the fractal curve constantly has the same shape as that of whole
structure (Kim et al., 2006; Mandelbrot, 1983). The researches on fractal geometries are
lightly more focused on compact antenna as compared to filters. The space-filling
property can be used to produce miniaturised microwave filters and antennas, while the
property of self-similarity may be utilised to design broadband and multiband antennas
(Ali, 2008; Kim et al., 2006).
In this context, one of the pioneer research work in the prediction of the use of fractal
geometry in filter design is that of Yordanov et al. (1991). Their predictions are based on
their investigation of Cantor fractal geometry. Since then, research work in this field has
shown a dramatic increase. In this respect, various fractal geometries have been applied to
design compact single-band and dual-band microstrip BPFs (Ahmed, 2012; Alqaisy, Ali,
Chakrabarty, & Hock, 2013; Barra, 2004; Chen & Lin, 2011; Chen, Weng, Jiao, & Zhang,
2007; Crnojevic-Bengin, Radonic, & Jokanovic, 2006; Feng, Ming, & Hui, 2012; Ghatak,
Pal, & Sarkar, 2013; Li et al., 2012; Liu, Chien, Lu, Chen, & Lin, 2007; Liu et al., 2012;
Mezaal, 2009; Mezaal, Eyyuboglu, & Ali, 2013a, 2013b).
Miniaturised high temperature superconductivity microstrip BPFs have been applied
for mobile wireless applications (Barra, 2004). The contribution of Barra (2004) has been
concentrated on Minkowiski and Hilbert fractal geometries. Sierpinski fractal geometry
has been employed in the design of a complimentary split ring BPF (Crnojevic-Bengin
et al., 2006). This filter has been achieved to decrease the resonant frequency of the
structure with more enhanced frequency selectivity (Crnojevic-Bengin et al., 2006).
Hilbert fractal geometry has been harnessed as a defected ground structure in the design
of a microstrip lowpass filter for L-band communication application (Chen et al., 2007).
Typical and simplified cross-coupled spiral resonators with Hilbert configuration were
introduced by Liu et al. (2007) for a huge coupling factor with comparison between each
other. Narrow band dual resonator microstrip BPFs based on Hilbert fractal curves have
been proposed for wireless application as in Mezaal (2009) within ISM band at funda-
mental frequency of 2.4 GHz. A modern narrow band BPF based on Hilbert-zz fractal
curve has been reported in Mezaal et al. (2013a). This filter has more compactness as
compared with the traditional Hilbert filter; besides, it exhibits satisfactory return loss and
transmission responses as well as higher harmonics suppression. Furthermore, compact
microstrip BPFs have been implemented with their ground planes being defected based on
Koch fractal geometries (Feng et al., 2012; Li et al., 2012).
Fractal geometries have also been adopted to design compact dual-band BPFs using a
variety of techniques as recently reported in the literature (Ahmed, 2012; Chen & Lin,
2011; Ghatak et al., 2013; Liu et al., 2012; Mezaal et al., 2013b). In some techniques, the
fractal geometry constitutes the whole microstrip filter structure producing the two
resonant bands (Ahmed, 2012; Chen & Lin, 2011; Ghatak et al., 2013; Mezaal et al.,
2013b). However, the dual-band resonant response has been reported to be produced
using two fractal structures; each contributes to excite one of the resonant bands (Liu
et al., 2012). In other techniques, the dual-band resonant response has been produced
using a hybrid structure composed of two substructures: one is fractal and the other is
non-fractal (Alqaisy et al., 2013).
In this paper, new microstrip BPF designs, based on second and third iterations of
Moore space-filling curve (SFC), have been presented as miniaturised filters. The intro-
duced filters have narrow band frequency responses, high selectivity and blocked harmo-
nics in out-of-band regions.
International Journal of Electronics 1307

2. Moore fractal structures
First of all, Moore is a continuous fractal SFC which differs from Hilbert curve. Precisely,
it is the loop version of the Hilbert curve, and it has a special recursive procedure as
compared with Hilbert fractal curve in such manner to cause the endpoints of Moore curve
coincide. In Figure 1a and b, Hilbert and Moore SFCs are outlined, respectively, the
second, the third and the fourth iterations have been presented in Figure 1 for these fractal
curves (Ali, 2009; Sagan, 1994).
Because Moore SFC is a loop version as compared to Hilbert geometry of the same
iteration level, the whole number of line segments forming the circumference of Moore
fractal curve is equivalent to that of Hilbert plus one. The total sum of all line segments
for Hilbert fractal curve is determined by (Ali, 2009; Barra, 2004):
Sn ¼ ð2n
þ 1ÞL (1)
So, the corresponding total perimeter length of Moore SFC of the same iteration level,
n, will be (Ali, 2009):
Sn ¼ ð2n
þ 1Þ þ
1
2n
À 1

L (2)
From these equations, it is clear that SFCs are long in terms of physical total curve
length but miniaturised in terms of area in which the curve can be included. The total
perimeter with a fractal form are electrically long, but it can be compacted in a very small
surface area and hence the possibility to obtain a smaller packaging using this technique
(Ali, 2009; Barra, 2004; Mezaal et al., 2013a).
n = 3
(b)
n = 4n = 2
n = 3
(a)
n = 4n = 2
L
Figure 1. (a) Hilbert fractal curves and (b) Moore fractal curves.
1308 Y.S. Mezaal et al.

The proposed BPFs based on dual edge-coupled Moore fractal resonators are shown in
Figures 2 and 3, respectively. From these figures, the external side length, L at iteration,
n = 2, 3, taking into account the strip width w and the gap between strips g, can be
calculated from (Ali, 2009):
L ¼ 2n
ðw þ gÞ À g (3)
3. Filter design and performance evaluation
The layout of the proposed microstrip BPF is essentially based on that presented in Hsieh
and Chang (2003) and later reported in Chang and Hsieh (2004). A filter structure
composed of two open-loop ring resonators with asymmetric tapping feed lines has
been proposed in an attempt to produce a compact BPF with high selectivity. What is
new here is to present a new filter design with more miniaturisation and high selectivity
by applying fractal geometry on the two open-loop resonators. Moore fractal geometry
has been chosen for this purpose because it possesses considerable space-filling property
besides the symmetrical open loop structure at any iteration level. The procedural steps of
Moore fractal BPF designs using electromagnetic modelling and simulation have been
represented in the flowchart depicted in Figure 4.
By the way, dual edge-coupled resonators based on second iteration Moore fractal
curve have been firstly designed at a frequency of 2.4 GHz as shown in Figure 2. It has
been assumed that these filter structures being etched using RT/duroid substrate with a
relative dielectric constant of 10.8, substrate thickness of 1.27 mm and metallisation
thickness of 35 µm by using the standard mask etching technique. The resulting filter
dimensions have been found to be 12.9 × 6.1 mm2
with w = 0.4 mm, g = 1.5 mm,
g
d
w
y
L
q
x
Figure 2. The modelled layout of second iteration Moore fractal BPF.
g
d
y
L
q
x
w
Figure 3. The modelled layout of third iteration Moore fractal BPF.

Start
Set the design frequency (2.4
GHz) and substrate parameters
{h = 1.27 mm and εr = 10.8 and
metallisation thickness = 35 µm}
Design the 50 ohm I/O feeds at f0
Choose fractal iteration
Modelling the single microstrip resonator using Sonnet simulator
Parameters optimisation and dimension scaling (w, g and L)
Check resonance at f0
Modelling the double-resonator bandpass filter
Tuning of inter-resonators spacing and I/O port position
Resonance at f0 with
reasonable performance
Final design
Yes
No
Yes
No
End
Figure 4. Flowchart for Moore BPF designs.

q = 0.5 mm, x = 1.3 mm and y = 1.5 mm. The coupling spacing between the two
resonators (d) is of 0.7 mm while I/O feeder lengths are 1.75 mm.
The previous steps have been repeated, but now with a microstrip resonator based on
the third iteration Moore fractal geometry, designed at the same frequency and using a
substrate with the same specifications. Figure 3 shows the topology of this dual-resonator
microstrip BPF. This filter has overall dimensions of 9.68 × 4.64 mm2
with
w = 0.405 mm, g = 0.2 mm, q = 0.45 mm, x = 0.2 mm, y = 0.2 and d = 0.4 mm. The
50 ohm I/O feeder lengths are 1.1 mm.
Filter shapes, outlined in Figures 2 and 3, have been modelled and analysed using a
full-wave-based EM simulator from Sonnet Software Inc. (2007). The corresponding
simulated responses of return loss, S11, and transmission, S21, for these filters are
shown in Figures 5 and 6, respectively. It is clear that the resulting BPFs based on
second and third iteration Moore fractal geometries offer a quasi-elliptic transmission
response with transmission zeros that are rather symmetrically located around the design
frequency near the passband edges. It is apparent from these graphs that the performance
response does not back up harmonics that conventionally accompany the BPF
performance.
In this context, some modifications in the filter structure can lead to induce these
harmonics to produce multiband bandpass response. However, this issue is out of the scope
of this study to produce miniaturised BPF. Moreover, the higher harmonics levels realised by
the third iteration fractal based filter are less than those of the filter based on the second
iteration. This difference in the out-of-band levels (the upper stopbands) is primarily attributed
to the positions of the tapping positions and the spacing between the two resonators of the two
filter structures. This supports the findings reported by Chang and Hsieh (2004) and Hsieh and
Chang (2003), since these factors affect the couplings between the two resonators. The
respective in-band fractional bandwidths for second and third iteration Moore BPFs are of
5% and 3.75% which are theoretically within narrow band ranges.
Table 1 shows the modelled Moore filter dimensions as designed for 2.4 GHz
applications and important result parameters of BPF responses. These parameters include
dimensions of proposed filters insertion loss, return loss and bandwidth.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Frequency (GHz)
–80
–70
–60
–50
–40
–30
–20
–10
0
S21andS11(dB)
S21
S11
Figure 5. The return loss and transmission responses of second iteration Moore BPF designed for
2.4 GHz.

An essential problem in the miniaturisation of passive resonators and filters comes
from the fact that resonating structures must have certain size relative to the guided
wavelength, λg, which is calculated, at the design frequency, by Barra (2004), Hong
and Lancaster (2001) and Waterhouse (2003):
λg ¼
c
f
ffiffiffiffi
εe
p ; (4)
where
εe ¼
εr þ 1
2
; (5)
where εe represents the effective dielectric coefficient and c is the speed of light. From these
equations, the effective dielectric constant εe ¼ 5:4 and guided wavelength λg ¼ 53:79 mm
have been determined at frequency f ¼ 2:4 GHz. Based on these calculations, the overall
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Frequency (GHz)
–70
–60
–50
–40
–30
–20
–10
0
S21andS11(dB)
S11 S21
Figure 6. The return loss and transmission responses of third iteration Moore BPF designed for
2.4 GHz.
Table 1. Summary of the dimensions and simulation results of Moore BPFs.
Parameter Second iteration Third iteration
Side length (L), mm 6.1 4.64
Occupied area, mm2
78.69 44.9152
Return loss, S11 (dB) −23.9 −20.5
Insertion loss (dB) −0.1 −0.155
Bandwidth (MHz) 120 90

dimensions in terms of λg are found to be of ð0:24 λg Â 0:11 λgÞ and ð0:18 λg Â 0:086 λgÞ for
second and third iteration Moore BPFs, respectively.
The size reduction percentage of third iteration Moore BPF with respect to the second
iteration one is about 43%.
It is worth to mention that these filters can be designed for other operating frequen-
cies according to the given system requirements by using dimensions scaling as indi-
cated in design procedure of Figure 4 using suitable w and g values that control the side
length, L, of fractal resonators according to Equation (3). For instance, resonance at
1.7 GHz design frequency has been obtained by choosing w = 0.5 mm and g = 0.3 mm
that produce L = 6.1 mm for third iteration Moore BPF under the same substrate
specifications.
Depending on the given specifications, the filter bandwidth could be adjusted under
same iteration level and design frequency. This is achieved by varying the w/g ratio in
such a manner to change L slightly (not quite different) using suitable scaling. For
example, 40 MHz bandwidth has been acquired via the EM simulator by choosing
w = 0.5 mm and g = 1.3 mm which results in L = 5.9 mm for second iteration Moore
BPF under same frequency, 2.4 GHz and substrate specifications.
The design frequency and bandwidth adjustments in this study have been also adopted
for fractal resonators reported in Barra (2004). The edge spacing between the two
resonators, d, as shown in Figure 2 and input/output feeder positions can be completely
tuned to minimise insertion loss and maximise return loss in order to optimise frequency
response of the filter as far as possible (Mezaal, 2009; Swanson, 2007).
The proposed fractal filters have remarkable lower insertion loss and greater return
loss values as compared with Minkowski-like and Hilbert fractal BPFs reported in Ali
(2008) and Mezaal (2009), respectively, under similar design frequency and substrate
specifications. Moreover, our two pole fractal BPFs are more compact than dual-mode
Minkowski and Koch-like pre-fractal BPFs reported in Ali (2008) and Mahdi and Aziz
(2011), respectively, designed at the same resonant frequency and using a substrate with
the same specifications. However, it is expected that, more size reduction can be gained
for the ﬁlter structure corresponding to the fourth iteration of the prescribed fractal
generation process, if there are no practical limitations.
In order to get insight into the nature of current distributions of the proposed filters,
simulation results for the surface current density at two different frequencies of operation,
2.4 GHz (the centre frequency) and 2.7 GHz (in the reject band region), are depicted in
Figures 7 and 8, respectively. In these current distribution graphs, the maximum current
density magnitude indicates the highest coupling effect while the minimum magnitude
indicates the lowest one. As it can be seen, the current distributions at 2.4 and 2.7 GHz are
quite different and they are scaling themselves as second and third iteration Moore fractal
geometries. The maximum surface current densities can be observed at the design
frequency, which is straightforward from the fact that low losses are present and the
desired resonant frequency is within higher excitation condition. On the contrary, the
lowest current densities can be noticed at 2.7 GHz in the stopband region. In this case,
weakest coupling can be seen, which is given by the fact that Moore BPFs are not being
excited and, therefore, provide a strong rejection in an otherwise passband structure.
On the other hand, the highest current densities are quite concentrated in only one
resonator of each Moore BPFs based on second and third iterations at both frequencies.
This might explain the suppression of higher harmonics in out-of-band regions.

The photographs of fabricated filter prototypes based on the second and third iteration
Moore fractal geometries are shown in Figures 9 and 10, respectively. The responses of
these prototypes have been measured using HP8720C vector network analyser.
Figures 11 and 12 show measured and simulated out-of-band S21 responses of second
and third iteration fractal filters respectively, while measured and simulated return loss
S11 responses for same filters are show in Figures 13 and 14, respectively. In the
measured and simulated results, only one pole appears in the passband in spite of the
filters are of second order. This is because the results are displayed through a wide swept
frequency range, and the passband only occupies a small portion of the displayed
frequency range. If the results are displayed through a narrow swept frequency range,
more details throughout the passband, including the two poles, will start to appear. The
measured return loss values are 15.5 dB and 17 dB for second and third iteration Moore
fractal BPFs, respectively, while the measured insertion loss values are better than 1 dB
78
72
65
59
52
46
39
33
26
20
13
6.5
0.0
25
23
21
17
15
12
10
8.3
6.2
4.2
2.1
0.0
(a)
(b)
Figure 7. Simulated current density distributions of the second iteration Moore microstrip BPF (a)
at 2.4 GHz and (b) at 2.7 GHz.

for both fractal filters. Accordingly, the simulated and experimental results are slightly
different. This difference might be attributed to tolerances in the substrate specifications
and in fabrication, where the spacing between the two resonators and the tapping feed line
positions have considerable effect on the overall coupling required to produce the filter
response. However, these results are in good agreement.
(a)
(b)
51
47
43
38
34
30
26
21
17
13
8.5
4.3
0.0
22
20
18
16
15
13
11
7.3
9.2
5.5
3.7
1.8
0.0
Figure 8. Simulated current density distributions of the third iteration Moore microstrip BPF (a) at
2.4 GHz and (b) at 2.7 GHZ.
Figure 9. Photograph of fabricated second iteration Moore fractal BPF.

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Frequency (GHz)
–80
–70
–60
–50
–40
–30
–20
–10
0
S21(dB)
Simulated S21
Measured S21
Figure 11. Simulated and measured out-of-band S21 responses of the proposed filter based on
second iteration Moore curve geometry.
Figure 10. Photograph of fabricated third iteration Moore fractal BPF.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Frequency (GHz)
–70
–60
–50
–40
–30
–20
–10
0
S21(dB)
Simulated S21
Measured S21
Figure 12. Simulated and measured out-of-band S21 responses of the proposed filter based on
third iteration Moore curve geometry.

4. Conclusion
New narrowband microstrip BPF designs for use in modern wireless communication
systems have been presented in this paper. The proposed filter structures have been
composed of dual edge-coupled resonators based on second and third iteration Moore
fractal geometries. These filter designs have small sizes, low insertion losses and high
performances, which are very interesting features required for modern wireless
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Frequency (GHz)
–25
–20
–15
–10
–5
0
S11(dB)
Measured S11
Simulated S11
Figure 13. Simulated and measured S11 responses of the proposed filter based on second iteration
Moore curve geometry.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Frequency (GHz)
–25
–20
–15
–10
–5
0
S11(dB)
Measured S11
Simulated S11
Figure 14. Simulated and measured S11 responses of the proposed filter based on third iteration
Moore curve geometry.

applications. Also, it has been observed that fractal-based filters have no trend to back up
consecutive harmonics in out-of-band responses. Simulated and experimental results for
proposed filter have been found to be in good agreement.
Funding
This work was supported by the Scientific and Technological Research Council of Turkey
(TUBITAK) for PhD Research Fellowship of Foreign Citizens Program under Fund Reference
[B.14.2.TBT.0.06.01.03-215.01-24962].
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fractal filters and reflectors. IEE 7th international conference on antenna and propagation,
ICAP 91, York (pp. 698–700). IET.

Miniaturised microstrip bandpass filters based on moore fratal geometry

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