Design and realization of microstrip filters with new defected ground structure (DGS)

Abstract

In this paper, various microstrip filters, such as bandpass (narrow/wideband) filters, dual band bandpass filter and lowpass filters, are designed with new metal strips loaded defected ground structure (DGS). In this proposed DGS, metal strips are introduced in connecting slot of dumbbell shaped DGS (DB-DGS). This new DGS is an improved version of conventional (dumbbell-shaped) DGS with enhanced characteristics of filters. With this new metal strip loaded DB-DGS, a bandpass (narrow-band/wide-band) filters, dual-band bandpass filter and lowpass filters, are designed with improved characteristics. The entire proposed filters are designed and fabricated with the same substrate area using 50 Ω, λg/4 microstrip line which is very compact to conventional microstrip filters. For validation of proposed designs, all fabricated filters are measured in Rohde and Schwarz Vector Network Analyzer 1127.8500 and also compared with circuit simulated results. All the simulations are carried out in HFSS V10 and ADS2006A.

Full text

Full Length Article
Design and realization of microstrip filters with new defected ground
structure (DGS)
Arjun Kumar
⇑
, M.V. Kartikeyan
Department of Electronics and Communication Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India
article info
Article history:
Received 28 June 2016
Revised 3 October 2016
Accepted 26 October 2016
Available online xxxx
Keywords:
Metal strip DB-DGS
Microstrip filters and conventional DGS
abstract
In this paper, various microstrip filters, such as bandpass (narrow/wideband) filters, dual band bandpass
filter and lowpass filters, are designed with new metal strips loaded defected ground structure (DGS). In
this proposed DGS, metal strips are introduced in connecting slot of dumbbell shaped DGS (DB-DGS). This
new DGS is an improved version of conventional (dumbbell-shaped) DGS with enhanced characteristics
of filters. With this new metal strip loaded DB-DGS, a bandpass (narrow-band/wide-band) filters, dual-
band bandpass filter and lowpass filters, are designed with improved characteristics. The entire proposed
filters are designed and fabricated with the same substrate area using 50 O,k
g
/4 microstrip line which is
very compact to conventional microstrip filters. For validation of proposed designs, all fabricated filters
are measured in Rohde and Schwarz Vector Network Analyzer 1127.8500 and also compared with circuit
simulated results. All the simulations are carried out in HFSS V10 and ADS2006A.
Ó2016 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC
BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
A defected ground structure (DGS) is a very popular methodol-
ogy for reducing the size of microwave components in recent
years. Still, a continuous research is going on this methodology
for improving the properties of microwave/millimeter wave com-
ponents. The concept of DGS is originated from photonic band
gap structures (PBG) in the optical field [1]. The DGS is realized
by etching simple shape in the ground plane of microstrip line
[2]. The etched pattern disturbs the current path in the ground
plane which changes the performance of microstrip line. The DGS
has two main characteristics: one is slow-wave effect and another
one is bandstop characteristics [3]. These characteristics can be
modified by changing the dimensions and shapes of DGS. In this
paper, microstrip bandpass filters (narrow band/wide band),
dual-band bandpass and low pass filters are proposed with new
metal loaded DGS. This new metal loaded DGS is compared with
the other conventional DGS and this new proposed DGS shows
the better performance characteristics among all the conventional
DGS [1–10]. On the basis of the performance of proposed DGS,
bandpass, dual-band and low pass filters are designed, fabricated
and tested with the same substrate area (20 mm 19.5 mm) or
(0.0065k
g
0.0064k
g
).
2. Comparison of various dumbbell-shaped DGS with metal
loaded DGS
Fig. 1 shows design configurations of various DB-DGSs with
metal loaded DB-DGS. In this new DB-DGS, two metal strips are
added in the connecting slot of the square dumbbell shaped DGS
as shown in Fig. 1(e).
These strips provide better effective parallel capacitance com-
pared to other conventional DB-DGS which improves the sharp-
ness of the filters response [6–10].
In conventional DB-DGS, the effective capacitance could be
improved by adjusting the dimensions of the connecting slot
between the dumbbells i.e. connecting slot length (d) and slot
gap (g). However, these dimensions cannot be adjusted beyond
the limitations of the overall dimensions and hence, limits the
scope of the use of this DGS configuration. All the design configu-
rations of DB-DGS are etched out with a line width of 3.4 mm and
line length of 19.5 mm.
The dielectric constant (
e
r
) of the substrate Neltec is 3.38 with
the loss tangent (tand) of 0.0025. The conductor thickness is
0.07 mm and substrate height is 1.524 mm. The dimensions of var-
ious DB-DGS structures are given in Table 1.
http://dx.doi.org/10.1016/j.jestch.2016.10.015
2215-0986/Ó2016 Karabuk University. Publishing services by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
⇑
Corresponding author.
E-mail addresses: akdec.iitr@gmail.com (A. Kumar), kartik@ieee.org
(M.V. Kartikeyan).
Peer review under responsibility of Karabuk University.
Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx
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Please cite this article in press as: A. Kumar, M.V. Kartikeyan, Design and realization of microstrip filters with new defected ground structure (DGS), Eng.
Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.10.015

2.1. Frequency characterstics of various DB-DGS in compared to new
DB-DGS
The characteristics of some simulated DB-DGS design
configurations have been shown in Fig. 2. All DB-DGS design
configurations have been simulated using EM simulator HFSS
V10. The 3 dB cutoff is kept same for all the DB-DGS geometries
at 4 GHz. From the Fig. 2, it is clearly seen that the sharpness
and selectivity of metal loaded DGS is more than the other
conventional DB-DGS geometries. The sharpness factor (S.F.) or
roll off factor has been calculated using the expression given
below [8,9]:
Sharpness Factor ðS:F:Þ¼f
c
f
o
ð1Þ
Selecti
v
ity ðnÞ¼
a
ðminÞ
a
ðmaxÞ
f
s
f
c
ð2Þ
where
a
(min),
a
(max), are the 20-dB and 3-dB attenuation respec-
tively, whereas f
s
,f
c
, and f
o
are the stop frequency at 20-dB attenu-
ation, 3-dB cut-off and resonant frequency in GHz. The unit of
selectivity (n) is dB/GHz.
The L-C equivalent circuit model of all DB-DGS configurations is
shown in Fig. 3.
C
p
¼5f
c
p
f
2
o
f
2
c
hi
pF ð3Þ
L
p
¼250
C
p
ð
p
f
o
Þ
2
nH ð4Þ
Fig. 1. Various DB-DGS pattern: (a) triangular head (b) square head (c) circular head (d) hexagonal head (e) Proposed square head loaded with metal strips [1–6].
Table 1
Dimensions of various DB-DGSs.
Dimensions (in mm) Circular Hexagonal Triangular Square Metal Loaded
a – – 4 3.2 3.5
g 0.8 1 1.1 0.3 1
d1212121111
r 0.3 3.1 – – –
r
0
0.3 3.1 – – –
k – – – – 0.2
m – – – – 1.2
t – – – – 2.2
s – – – – 3.2
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Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.10.015

In the Table 2, the performances of various DB-DGS configura-
tions are tabulated on the basis of simulated results in Fig. 2. From
the Table 2, it is clearly observed that the selectivity (n) and sharp-
ness of the proposed metal strip loaded DGS microstrip bandstop
filters is better than the other conventional DB-DGS.
The effective capacitance is increased and the inductance is
decreased by inserting the metal strip in connecting slot of pro-
posed DB-DGS. So this improvement in capacitance and inductance
of proposed DB-DGS is responsible for high selectivity and sharp-
ness of filter.
3. Parametric analysis of proposed DB-DGS
In this section, the effect of various dimensions of proposed DB-
DGS on its frequency characteristics have been studied in terms of
cut-off and resonant frequency. The critical parameters such as
cut-off and resonant frequencies of proposed DB-DGS have been
studied with respect to the variation in the dimensions. The main
dimensions of proposed DB-DGS are ‘a’, ‘g’ and ‘s’, which effect the
cut-off and resonant frequencies in significant manner. By control-
ling these dimensions, the desired cut-off and resonant frequencies
can be achieved for various applications. The effect of various
dimensions of proposed DB-DGS on the frequency characteristics
have been shown in Figs. 4–6. The parametric analysis is also stud-
ied in terms of effective inductance and effective capacitance.
3.1. Effect of dimension ‘a’
In Fig. 4,S
21
parameter is plotted with variation of dimension
‘a’. The other dimensions ‘g’ = 1.5 mm and ‘s’ = 0.3 mm are kept
fixed. From the Fig. 4, it is clearly observed that as dimension ‘a’
increases the 3-dB cut-off and resonant frequency shifts toward
lower frequency side but in this case, 3-dB cut-off is more signifi-
cantly changed as compared to resonant frequency. This 3-dB cut-
off frequency changed significantly due to large current path.
As the dimension ‘a’ is varied, the current flow path is also var-
ied; which implies that the effective inductance will change more
dominantly as compared to effective capacitance [15,180].
3.2. Effect of dimension ‘g’
In this subsection, the effect of dimension ‘g’ on frequency char-
acteristics has been plotted in Fig. 5. The dimension ‘g’ is slot gap of
the square head connecting slot. As the slot gap ‘g’ is increased, the
resonant frequency shifts toward higher frequency. It means that if
the slot gap is less; the fringing field coupling capacitance will be
more.
As the slot gap minimizes, the coupling of electric field will be
better due to fringing effect. From the Fig. 5, it is clear, the 3-dB
cut-off is almost same, but only resonant frequency varies signifi-
cantly as the slot gap ‘g’ is varied. This resonant frequency depends
on effective capacitance. So by adjusting the slot gap dimension ‘g’,
the desired resonant frequency can be achieved.
Fig. 2. Simulated S-parameters of various DB-DGS pattern.
Fig. 3. The L-C equivalent circuits for DB-DGS [11].
Table 2
Comparative performance of microstrip bandstop filter with DGSs.
Parameters Circular Hexagonal Triangular Square Metal Loaded
f
o
(GHz) 6 5.7 5.6 5.4 4.91
S.F. 0.66 0.7 0.71 0.74 0.81
C
p
(pF) 0.318 0.386 0.414 0.484 0.785
L
p
(nH) 2.214 2.021 1.953 2.1 1.339
f
s
(GHz) 5.7 5.5 5.4 5.3 4.8
n(dB/GHz) 10 11.3 12.1 13 21.3
Fig. 4. Simulated S-parameters with variation of dimension ‘a’ proposed DB-DGS.
A. Kumar, M.V. Kartikeyan / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx 3
Please cite this article in press as: A. Kumar, M.V. Kartikeyan, Design and realization of microstrip filters with new defected ground structure (DGS), Eng.
Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.10.015

3.3. Effect of dimension ‘s’
The effect of dimension ‘s’ on the frequency characteristics is
shown in Fig. 6. As the dimension ‘s’ is increased, the resonant fre-
quency is shifted toward the lower frequency. The shift in the fre-
quency to lower side is due to reduction in gap between the metal
strips of connecting slot. If the gap between metal strips of the con-
necting slot is less, the coupling will be better due to fringing field.
In this case, 3-dB cut-off frequency varies little bit but the resonant
frequency significantly changes with the variation of dimension ‘s’.
4. Design and realization of banpass filters with narrow and
wide bandwidth
In this section, narrow band, wide band and dual-band micro-
strip bandpass filters are designed with new metal strip DGS for
wireless applications. All the bandpass filters are designed using
50 O,k
g
/4 microstrip line. The size of these bandpass filters are
kept fixed which is 20 mm 19.5 mm (0.0065k
g
0.0064k
g
). The
dielectric constant (
e
r
) of substrate = 3.38, height of substrate (h)
= 1.524 mm, thickness of conductor (t) = 0.07 mm and loss tangent
(tand) = 0.0025 are used in all design configurations. The design
configurations of all bandpass filters have been explained with fab-
rication and measurement results in the subsection ‘A’, ‘B’ and ‘C’:
4.1. Narrow band microstrip bandpass filter (NBMBF)
The specifications for designing narrow band bandpass filter are
the center- frequency (f
o
) = 5.4 GHz, bandwidth (BW)300 MHz,
10-dB attenuation bandwidth 900 MHz, insertion loss in pass
band <1.0 dB and 20-dB attenuation in stopband. These specifica-
tions are suitable for WLAN applications.
Fig. 7 shows the design configuration of narrow band bandpass
filter along with fabricated components using proposed DB-DGS.
The dimension of proposed filter is shown in Fig. 7. In this design
configuration two U-shaped slots are introduced in the strip of
microstrip line in alternate fashion [12].
These two slots in conducting strip add capacitance in series
with inductance and in turn parallel to the capacitance of L-C res-
onator of proposed DB-DGS [13–15]. The L-C equivalent circuit of
this proposed design is shown in Fig. 8. This type of prototype cir-
cuit model will provide the narrow band effect. This circuit model
has two resonant frequency characteristics with resonance and
anti-resonance. There are two resonant circuits in Fig. 8, one is ser-
ies resonant and second one is parallel resonant. For these resonant
circuits, the circuit parameters can be calculated using the follow-
ing equations [13]:
For series resonant circuit
C
k
¼C
o
f
2
h
f
2
o
1
"# ð1Þ
L
k
¼1
4
p
2
f
2
o
C
k
ð2Þ
f
o
¼1
2
p
ffiffiffiffiffiffiffiffiffiffi
L
k
C
k
pð3Þ
For parallel resonant circuit
C
k
¼C
o
f
2
o
f
2
l
1
"# ð4Þ
Fig. 5. Simulated S-parameters with variation of dimension ‘g’ proposed DB-DGS.
Fig. 6. Simulated S-parameters with variation of dimension ‘s’ proposed DB-DGS.
Fig. 7. Design configuration for narrow band bandpass filter with fabricated design
(top view and bottom view).
4A. Kumar, M.V. Kartikeyan / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx
Please cite this article in press as: A. Kumar, M.V. Kartikeyan, Design and realization of microstrip filters with new defected ground structure (DGS), Eng.
Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.10.015

L
k
¼1
4
p
2
f
2
l
C
k
ð5Þ
f
l
¼1
2
p
ffiffiffiffiffiffiffiffiffiffi
L
k
C
k
pð6Þ
Here f
o
,f
h
and f
l
are the resonant, anti-resonant frequencies.
C
p
and C
o
can be determined using the same modeling method
as presented in [13,14]. The extracted values of circuit parameters
are: L
k
= 8.03nH, C
k
= 0.118pF, C
p
= 0.659pF and C
o
= 0.365pF. If the
number of slots increases in the conducting strip, it will increase
the series capacitance which will make the response narrower.
The effect of increased slots has not been shown here. This pro-
posed filter has been tested after fabrication. The measured results
of proposed narrow band bandpass filter are shown in Fig. 9. These
measured result are compared with circuit simulated and HFSS
simulated results. The measured results are in good agreement
with simulated results. In Fig. 9, it can be clearly seen that the cen-
ter frequency is 5.4 GHz, 3-dB upper and lower cut-off frequencies
are 5.5 GHz and 5.2 GHz, respectively, bandwidth (BW) is
300 MHz, insertion loss in passband is 0.6 dB and 10-dB attenua-
tion bandwidth is 1 GHz. It can be observed that the measured val-
ues are in good agreement with simulated results.
4.2. Wide band microstrip bandpass filter (WBMBF)
In Fig. 10, a wide band microstrip band pass filter is shown. The
design specifications are chosen like center frequency (f
o
) is 4 GHz,
3-dB upper and lower cut-off frequencies are 6.4 GHz and 1.4 GHz,
respectively, bandwidth (BW) is 5 GHz, insertion loss in pass-
band ’0.5 dB and 10-dB attenuation bandwidth is 6.3 GHz. The
dimensions are shown in Fig. 10. This filter is also designed using
50
X
,k
g
/4 microstrip line. In this bandpass filter a new metal
loaded DBDGS array is used with U-slot in conducting strip. This
DB-DGS array gives a wide stopband because it suppresses the
other frequency bands [1,14–17]. U-slot in the conducting strip
gives a series capacitance due to fringe field coupling. This U-slot
will also produce inductance effect in parallel with line capaci-
tance. This whole combinations of L-C circuit model behave as a
wide band bandpass filter. The L-C circuit model for this proposed
filter is shown in Fig. 11. The values of circuit parameters as shown
in Fig. 11, can be determined as in case of narrow-band bandpass
filter in subsection ‘A’.
The values of these circuit parameters are: L
k
= 2.1667nH,
C
k
= 0.342 pF, C
p
= 0.620 pF, L
p
= 4.186nH, and C
o
= 0.1.199pF. The
fabricated bandpass filter is measured in Vector Network Analyzer.
Fig. 12 shows the measured result along with HFSS simulated and
circuit simulated results. The simulated and circuit simulated
results are similar but the measured results differ a little bit. The
difference in results is due to fabrication error.
4.3. Dual-band microstrip bandpass filter (DBMBF)
In this section, a dual band bandpass filter is designed. Fig. 13
shows the design configuration of proposed dual band bandpass
Fig. 8. L-C equivalent circuit model for proposed narrow band bandpass filter [13].
Fig. 9. S-parameter results of narrow band bandpass filter with proposed DB-DGS.
Fig. 10. Design configuration for wide band bandpass filter with fabricated design
(top view and bottom view).
Fig. 11. L-C equivalent circuit model for proposed wide band bandpass filter [13–
16].
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filter with same new metal strip DB-DGS topology. In this proposed
design, two via is used for getting dual band properties
In this proposed dual band bandpass filter, a slot is introduced
in the conducting strip with the two via with different dimensions
as 1.2 mm and 1 mm respectively [18]. This slot adds the series
capacitance due to fringing field convergence or coupling. This ser-
ies capacitance behaves like a high pass filter for particular fre-
quency that characteristics applied to design bandpass filter. The
proposed DB-DGS gives one pole low pass characteristics [7].So
the combination of low-pass and high-pass will give the bandpass
characteristics. That is why series capacitance is included in series
with the line. The two via which make the microstrip line shorted
with ground which will give two inductances in parallel with
capacitances. The L-C equivalent circuit model for this proposed
dual band bandpass filter is shown in Fig. 14.
The extracted values of equivalent circuit parameters are:
L
1
= 2.2575 nH, C
1
= 2.61039 pF, L
2
= 1.9276 nH, C
2
= 0.06294 pF,
L
3
= 1.0487 nH, C
3
= 0.62237 pF, L
4
= 2.4869 nH, C
4
= 1.71129 pF,
L
5
= 1.2085 nH, C
5
= 0.45255 pF and C
o
= 0.6024 pF. In this pro-
posed dual-band band filter, the center frequencies are 4.2 GHz
and 7.7 GHz. The bandwidths of this dual band are 400 MHz and
500 MHz. The other design specifications such as dielectric con-
stant, loss tangent, height of substrate and thickness of conductors
are same as in Fig. 1. This proposed design is fabricated and the lay-
out of fabricated design is also shown in Fig. 13.
After the fabrication, the fabricated design is measured in VNA.
The simulated, circuit simulated and measured results are shown
in Fig. 15. The resonant frequencies are almost same in all the sim-
ulated and measured results. It is clearly observed in the Fig. 15,
the insertion loss is more in measurement as compared HFSS sim-
ulated and circuit simulated results. Insertion loss is 0.7 dB in both
the passband but in measurement it is 0.9 dB. This additional loss
is due to attenuation in VNA cable. This additional loss is very less.
The measured and simulated results are almost good in agreement.
5. Design and realization of low pass filter
In Fig. 16, a microstrip low pass filter is shown. This low pass fil-
ter is also designed using 50 O,k
g
/4 microstrip line. In this design
configuration the specifications are dielectric constant (
e
r
) = 3.38,
height of substrate (h) = 1.524 mm, thickness of conductor (t)
= 0.07 mm and loss tangent (tand) = 0.0025. The design goals for
designing this low pass filter are 3-dB cutoff frequency = 6.6 GHz,
insertion loss in passband 0.5-dB, 20-dB attenuation from
7.4 GHz to 10 GHz. The proposed DB-DGS is used in the ground
plane of 50 Omicrostrip line. The size of filter is
Fig. 12. S-parameter results of wide band bandpass filter with proposed DB-DGS.
Fig. 13. Design configuration for dual-band bandpass filter with fabricated design
(top view and bottom view).
Fig. 14. L-C equivalent circuit model for proposed dual-band bandpass filter.
Fig. 15. S-parameter results of dual-band bandpass filter with proposed DB-DGS.
6A. Kumar, M.V. Kartikeyan / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx
Please cite this article in press as: A. Kumar, M.V. Kartikeyan, Design and realization of microstrip filters with new defected ground structure (DGS), Eng.
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20 mm 19.5 mm. The dimensions of this proposed filter is shown
in Fig. 16 with fabrication. In this low pass filter, there is no use of
stub or hi-lo impedance. Various DB-DGS low pass filter is reported
[11,19] but in this low pass filter metal strip is inserted in the con-
necting slot of DB-DGS which gives the high sharpness as well as
high selectivity. The DB-DGS array suppressed the higher order
mode of frequency due to this high rejection is achieved in stop-
band [17]. The L-C equivalent circuit model of this proposed low
pass filter is shown in Fig. 17.
There three resonator circuits each for three DGS. Extreme left
and extreme right DGS are symmetrical so due to this the values
of these resonators are same. Only center DGS is different in
dimension so the values of circuit parameters are more as compare
to small DGS resonators. The mathematical derivations for calcu-
lating extracted parameters are described in [1]. After the fabrica-
tion, the filter is measured in terms of S- parameter. The simulated,
circuit simulated and measured results are shown in Fig. 18.
It is clearly observed that 3-dB cut-off frequency is same in both
simulation and in measurement. In measurement insertion loss in
passband is 0.7 dB which is quite comparable with insertion loss in
simulated results. So the measured results are good in agreement.
5.1. Comparison of recently reported work
Here, in this section, recently reported works have been com-
pared with the proposed work, shown in Table 3.
In the Table 3, it is clearly observed that the proposed design
has the lesser size as compare to other recently reported work.
6. Conclusions
All type filters are investigated with new metal loaded DB -DGS
which shows the high selectivity and high sharpness factor. All the
filters designed on a same substrate with same area
20 mm 19.5 mm 390 mm
2
. No stubs, hi-lo impedance are used
in the designing of bandpass and low pass filter designing. In this
paper, all filters are designed using metal loaded DB-DGS. All filters
show measured and simulated results in good agreement. So far no
detailed work is reported for designing all filters such bandpass fil-
ters with narrow/wide band, dual band and low pass filter by using
same design configuration with same area.
References
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[2] Arjun. Kumar, M.V. Kartikeyan, Microstrip filter with defected ground
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Fig. 16. Design configuration for low pass filter with fabricated design (top view
and bottom view).
Fig. 17. L-C equivalent circuit model for proposed low-pass filter [1].
Fig. 18. Design configuration for low pass filter with S-parameters results of low
pass filter with new DB-DGS fabricated design (top view and bottom view).
Table 3
Comparison of recently reported work with proposed work.
Ref. Effective size of filter (k
g
k
g
) IL (dB)
[20] 0.06k
g
0.05k
g
1dB
[21] 0.106k
g
0.05k
g
0.3 dB
[22] 0.17k
g
0.15k
g
1.49 dB
[23] 1.1k
g
0.4k
g
1.5 dB
[24] 0.37k
g
0.182k
g
0.32 dB
[25] 0.489k
g
0.278k
g
0.5 dB
In this work 0.0065k
g
0.0064k
g
<1dB (in all the filter type)
A. Kumar, M.V. Kartikeyan / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx 7
Please cite this article in press as: A. Kumar, M.V. Kartikeyan, Design and realization of microstrip filters with new defected ground structure (DGS), Eng.
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8A. Kumar, M.V. Kartikeyan / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx
Please cite this article in press as: A. Kumar, M.V. Kartikeyan, Design and realization of microstrip filters with new defected ground structure (DGS), Eng.
Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.10.015