Engineering, 2010, 2, 197-200
doi:10.4236/eng.2010.23028 lished Online March 2010 (http://www.SciRP.org/journal/eng/) Pub
An Improved Parameters Extraction Method for
Dumbbell-Shaped Defected Ground Structure
Yuchun Guo1,2, Qing Wang3
1National Laboratory of Information Control Technology for Communication System, Jiaxing, China
2JiangNan Electronic Communication Institute, Jiaxing, China
3National Key Laboratory of Antenna and Microwave Technology, Xidian University, Xi’an, China
Received October 4, 2009; revised November 2, 2009; accepted November 13, 2009
Abstract
The paper presents an improved equivalent circuit parameters extraction method for the dumbbell-shaped
defected ground structure (DGS). The new extraction parameters equations are obtained in closed-form ex-
pressions, which contain S11 and S21. The DGS unit with center frequency of 5 GHz is designed and fabri-
cated on a TLX substrate with thickness of 1 mm and dielectric constant of 2.55. The circuit simulated re-
sults are in good agreement with the measured results. This parameters extraction method can be widely used
for the design and analysis of DGS .
Keywords: Defected Ground Structure, Equivalent Circuit, Parameters Extraction Method,
Dumbbell-Shaped DGS
1. Introduction
In the late 1990s, defected ground structure (DGS) was
firstly proposed by Korean scholar J. I. Park et al. [1]. It
is based on the idea of photonic band-gap structure, and
applied to the design of planar circuits. DGS is an etched
periodic or non-periodic cascaded configuration defect
in ground of a planar transmission line [2] (e.g microstrip,
coplanar and conductor backed coplanar wave guide),
which disturbs the shield current distribution in the
ground plane. This disturbance will change characteris-
tics of a transmission line such as the line capacitance
and inductance to obtain the slow-wave effect and
band-stop property [3-6]. DGS has been used for the
control of an active microstrip antenna [7], improved
efficiency of powers [8], performance enhancement of
filters [9-10], and dividers [11].
There are two main methods for the design and analy-
sis of DGS [2]. The commercially EM software is the
main simulate software to design and analyze DGS,
which is relatively slow and does not give any physical
insight of the operating principle of DGS. On the con-
trary, the equivalent circuit method can quickly give the
frequency responses of DGS by exacting equivalent cir-
cuit parameters. In general, DGS can be equivalent by
three types of equivalent circuits [2,12-14]: 1) LC and
LCR equivalent circuits, 2)

shaped equivalent cir-
cuit, 3) quasi-static equivalent circuit. The LC and LCR
equivalent circuit are simple and most widely used [2].
however, the LCR equivalent circuit model can not pro-
vide the exact response curve, which should be in line
with the measured or simulated results [1,15,16].
In this paper, based on the LCR equivalent circuits，an
improved parameters extraction method is proposed,
which uses the S11 and S21 information and can give bet-
ter frequency responses of defected ground structure. To
show the validity of the method, a dumbbell-shaped DGS
unit was fabricated on a TLX substrate with 1mm thick-
ness and 2.55 dielectric constant, and the measured re-
sults are in good agreement with the simulated results.
2. Parameters Extraction Method
The dumbbell-Shaped DGS [1] is composed of two
ab

rectangular defected areas,
g
l gaps and a
narrow connecting slot wide etched areas in backside
metallic ground plane, as shown in Figure 1(a). DGS
unit can be modeled by a parallel R, L, and C resonant
circuit connected to transmission liens at its both
sides ,as shown in Figure 1(b).
The equivalent circuit parameters L, C, R of dumb-
bell-shaped DGS unit can be given by [1]:

Y. C. Guo ET AL. 198
b
a
g
l
W
（a）
0
Z
g
V
0
Z
L
R
C
（b）
Figure 1. Dumbbell-shaped DGS unit and its equivalent
circuit.
)(2 2
c
2
00



Z Cc (1)
C
L2
0
1

 (2)
1
1
2
)(
1
2
))(( 2
0
2
11
0
11















L
CZ
S
Z
SR




(3)
where, 0

is the angular resonance frequency, c

is
the 3-dB cutoff angular frequency, and is the char-
acteristic impedance of the microstrip line,
0
Z



11
S is
the input reflection coefficient of the equivalent circuit
network.
In Equation (3), the parameter is obtained by the
magnitude of
R


11
S. In fact, it can also be found from
Equation (4), which is derived from the


21
Svariable.
In general, ))((11

SR is not equal to))((11

SR .
2
2
0
2
2
21
21
2
21
2
21
0
21
1
4
)(1
)(
)(1
)(
2
))((


















L
CZ
S
S
S
S
Z
SR







(4)
where,



21
S is the forward transmission coefficient
of the equivalent circuit network.
Although the resistance R is the function of frequency,
it is expected that R is independent frequency. Consider-
ing the main characteristics of DGS is single pole
low-pass, the loss resistance is determined by:
11
R
011 0
11
11 0
2(
1()

ZS
RS
)


(5)
where，0

is the resonance frequency of DGS.
If the parameter is obtained by the magnitude of
, then the parameter is given by:
R
21
S21 R
21 0
21 0
21 0
1(
2()
)

S RZ
S


(6)
The resistance obtained by Equation (5) is typi-
cally different from the resistance obtained by
Equation (6). In most literature, the resistance R in Fig-
ure 1. is obtained by Equation (5), that is . This ap-
proach can guarantee the accuracy of , however,
have a large error at the center frequent point. If
and are used to extract the parameter R, the fre-
quency responses can be better. The parameter value
is given by:
11
R
21
R
11
S
11
R
21
S
11
S
R
21
S
11 21
2

RR R (7)
On the basis of the above principle, steps of the im-
proved LCR equivalent circuit parameters extraction
method for DGS are given as follows:
1) The resonant frequency 0

, the cut-off frequency
c

and the terminal impedance 0
Z
are obtained by
frequency response curves;
2) Calculate the equivalent capacitance C and equiva-
lent inductance L by Equations (1) and (2);
3) Calculate and by Equations (5) and (6);
11
R21 R
4) The value of parameter R in equivalent circuit is
obtained by Equation (7).
3. Results and Discussions
To show the validity of the method, the dumbbell-shaped
DGS were designed at a fundamental resonant frequency
of 5
0

fGHz and fabricated on a TLX substrate with a
thickness = 1 mm, transmission line width W= 2.82
mm, and relative dielectric constant
h
55.2
r

. The
configuration parameters of DGS is a = 3 mm, b = 5 mm,

Y. C. Guo ET AL. 199
g = 1 mm, l = 11 mm, respectively, as shown in Figure 2.
From the measured data, we have the scattering parame-
ter values, )( 011

S= –1.147 dB, )( 021

S= –25.624 dB.
According to the equivalent circuit parameter extraction
steps in section II, the LCR equivalent circuit parameters
are L = 3.969uH, C = 0.2553pF, R = 1259.67

(=
608.647 , =1810.69), respectively.
11
R
21
R
The measured results and equivalent circuit simulation
results using the equivalent circuit parameters are shown
in Figure 3. It can be seen that the equivalent circuit
Figure 2. Fabricated DGS unit at resonance frequency 5GHz.
012345678910
-30
-25
-20
-15
-10
-5
0
R=1259.67
R21=1810.69
R11=608.647
S11-Measured
S11(dB)
Frequency(GHz)
(a)
012345678910
-35
-30
-25
-20
-15
-10
-5
0
R=1259.67
R21=1810.69
R11=608.647
S21-Measured
S21(dB)
Frequency(GHz)
(b)
Figure 3. Measured and equivalent circuit simulated S-pa-
rameters for various R. (a) S11 parameter; (b) S21 parameter.
Table 1. Ealaulation equivalent circuit frequency responses
and error for various resistance at center frequency.
S11/dB S21/dB
Resis-
tance Circuit
model MeasuredError Circuit model Measured Error
R –0.664 0.483 –22.668 2.394
R11 –1.146 0.001 –18.155 6.907
R21 –0.467
–1.147
0.680 –25.273
–25.062
–0.211
simulation results show excellent agreement with meas-
ured results; they have the same resonance frequency.
Table 1 gives the S-parameters results of that compari-
son at the center frequency. When the resistance
takes , the accuracy of can be ensured, but
have nearly 7dB error and if the resistance takes,
the accuracy of can be ensured, but have 0.68
dB error. Calculated the S-parameters by the proposed
method, the errors of S-parameter can be smaller.
11
R11 S
21
S21 R
21
S11 S
Measured results show that the improved LCR
equivalent circuit parameter extraction method is effec-
tive, it can be used for DGS quick simulation and ensures
higher accuracy.
4. Conclusions
The equivalent circuit has been widely applied to simu-
late the frequency responses of DGS by exacting equiva-
lent circuit parameters. In this paper, an improved equi-
valent circuit parameters extraction method for dumb-
bell-shaped DGS is proposed. Compared with the con-
venient methods，the proposed method can give the more
accurate frequency response curves, it can be widely
used in the design and analysis of DGS.
5. Acknowledgment
The author is grateful to the reviewers for their profes-
sional comments and valuable suggestion in this paper.
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