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JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING
AND SCIENCE, VOL. 11, NO. 2, JUN. 2011 JKIEES 2011-11-2-08
DOI : 10.5515/JKIEES.2011.11.2.122
122
Network Modeling and Circuit Characteristics of Aperture-Coupled
Vertically Mounted Strip Antenna
Jeong Phill Kim
Abstract
A general analysis of an aperture-coupled vertically mounted
strip antenna is presented to examine its circuit characteristics.
Based on the present analysis, an equivalent circuit model is
developed, and an analytic or semi-analytic evaluation of the
related circuit element values is described. The effects of
structure parameters on the antenna characteristics were studied
with the developed equivalent circuit, and the design curves were
obtained. To check the validity of the proposed analysis and design
theory, two C-band antennas (5.0 GHz and 4.5 GHz) were designed and
fabricated. Their computed characteristics, derived from the
proposed network analysis, were compared with the measurement and
simulation results. The error of the current model in predicting
the operating center frequency was less than 0.50 %. In addition,
the observed bandwidth was found to be comparable to the
conventional microstrip antennas. All the results fully validated
the efficiency and accuracy of the proposed analysis and network
model.
Key words : VerticaLly Mounted Strip Antenna, Coupling
Structure, Equivalent Circuit, Microstripline, Aperture.
Manuscript received March 14, 2011 ; revised May 16, 2011. (ID
No. 20110314-010J)School of Electronic and Electrical Engineering,
Chung-Ang University, Seoul, Korea.Corresponding Author : Jeong
Phill Kim (e-mail : [email protected])
. IntroductionThere has been increasing demand for microwave
and
millimeter-wave antenna configurations with efficient coupling
and novel feed structures for better perform-ance, easier
fabrication, and design freedom. Aperture- coupling [1] and
vertically mounted (VM) strip trans-mission line [2] are examples
of two such configura-tions. Recently, an aperture-coupled VM
slotline and aper-ture-coupled VM strip transmission line have been
stud-ied for feed of the tapered slot antenna [3] and new coupling
structure [4], respectively. In the former, the related coupling
can be analyzed from the assumed aperture electric field and the
related Greens functions. On the contrary, the coupling in the
latter has been for-mulated with a strip current density and the
related Greens functions, which are different to those of the
former. Based on these studies, aperture-coupled VM strip cir-cuits
or antennas are expected to provide alternative or complementary
solutions to the conventional approaches as well offering the
advantages associated with aper-ture-coupling.
An aperture-coupled vertically mounted strip antenna (ACVMSA) is
shown in Fig. 1(a). Compared to a con-ventional dipole or patch, it
is expected to yield a com-parable or somewhat broader bandwidth
with an elabo-rate design [5]. However the design was based on
the
equivalent circuit, developed with the help of a full- wave
numerical simulator [6].
Forming radiators on one or both sides of the VM substrate may
also provide additional design flexibility. In addition, multiple
sub-array plates can easily be plug-ged in and pulled out for
overall array integration and maintenance (Fig. 1(b)).
In this paper, a general analysis of ACVMSA is pre-sented to
examine its circuit characteristics including in-put impedance and
bandwidth. For this, an equivalent cir-cuit model is developed
using analytic and semi-analytic approaches to calculate the
related circuit element va-lues. Especially, the analytic
evaluation of radiation loss and the fringing field effect at the
end of the VM strip antenna are included. A parametric study was
performed and the design curves were obtained. For the validation
check of the proposed theory and the equivalent circuit developed,
two C-band ACVMSAs were designed and their characteristics were
compared with the measured and numerical simulation results. Some
comparisons were also made between the characteristics of ACVMSA
and conventional microstrip antenna.
. Antenna Geometry and Equivalent Circuit As shown in Fig. 1(a),
the ACVMSA consists of a
microstrip feed line, an aperture on the ground plane,
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(a) ACVMSA
(b) Hybrid phased array
Fig. 1. Configuration.
and a VM strip on the dielectric substrate just above the ground
plane. The terms Lv and Wv denote the length and width of the strip
radiator, respectively, while Sv is the gap spacing between the VM
strip and the ground plane, and La and Wa are, respectively, the
length and width of the coupling aperture. Wm and Lm are the width
of the microstrip feed line and the length of the open stub
introduced for impedance matching, respectively. The substrate
thickness and dielectric constant of the feed substrate are,
respectively, denoted by hm and rm, and for the VM substrate they
are hv and rv, res-pectively.
A VM stripline is a transmission line whose signal line is
vertically mounted, and for this reason the cou-pling between the
VM stripline and the aperture can be modeled in a similar manner to
a conventional micro-stripline and aperture [4], [7]. The
equivalent circuit of ACVMSA can therefore be represented as shown
in Fig. 2(a). In this model, the parameters Z0v and v are the
characteristic impedance and phase constant of the VM
(a) Model for ACVMSA
(b) Model for calculating the characteristics of VMS
(c) Model for calculating the characteristics of VMSA
Fig. 2. Equivalent circuits.
stripline, Ya is the aperture admittance at its center, and Z0m
and m are the characteristic impedance and phase constant of the
microstrip feed line, respectively. The turns ratios of the upper
and the lower ideal trans-formers are represented by nv and nm,
respectively. Gr is the equivalent radiation conductance and Lv is
the ef-fective extended line length accounting for the radiation
and fringing field effect at the ends of the VM strip.
Contrary to our previous study [5], where the equiv-alent
circuit values were obtained by invoking numerical simulation [6],
analytic or semi-analytic (only a numeri-
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AND SCIENCE, VOL. 11, NO. 2, JUN. 2011
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cal integration is involved) approaches are used in this paper
for a simple and efficient calculation of equivalent circuit
values. The circuit values nm, nv, and Ya can be calculated by the
method described previously [4], [7]. The remaining work is to
calculate Z0v, v, Lv, and Gr. Because a VM stripline can be
regarded as half of the odd-mode coplanar strip (CPS) line,
Z0v=Z0cps/2 and v=cps hold. Even though analytic and numerical
me-thods have been applied to calculate Z0cps and cps [8], most
studies focus on the narrow strip. For developing the equivalent
circuit of ACVMSA, finding methods of analytic or semi-analytic
calculation that can handle the wide strip is highly desirable.
The Cohn's method based on the transverse-resonance technique
[9] is adopted in this study with two modifi-cations: in
longitudinal direction, a strip resonator with perfect magnetic
conductor (PMC) walls was considered instead of an aperture
resonator with perfect electric conductor (PEC) walls, and in the
transverse direction, the structure is open, not enclosed. Fig.
2(b) shows the VM strip resonator with PMC walls for calculating
Z0v and v. It is well known that X, the reactance at x=0 be-comes
zero at the resonant frequency f0. After finding L to satisfy X=0,
the guide wavelength can be found as g =2L, and v is therefore
given as
(1)
For a simple but accurate calculation of X, it is highly
desirable to choose a closed-form function capable of closely
approximating the current density of the CPS line. In this paper,
only an x-component current density ( ),( yxJxJ x=
),( yxJxJ x= ) is considered as
(2)with
cos (3)
sgn (4)
where a=Sv and b=Sv+Wv. The choice of A(x) and B(y) are known to
yield good modeling results [7], [4]. The signum function sgn(y) is
introduced to represent an odd-mode distribution of current
density. Because a VM strip is formed on a dielectric substrate, L
for the reso-nance is smaller than half the wavelength in the free
space. Therefore, only the evanescent mode is suppor-ted, and Z is
expressed as
(5)where P and Iv0 are, respectively, the complex power
and root-mean-square value of the current flow at x=0.
Considering the relation between VM strip and the odd-mode CPS
lines, P=(1/2) Pcps holds.
The expression of complex power in the spectral do-main in
consideration of the symmetry of the integrand becomes
(6)
with kx=v=/L. The expression of EJxxG~ (kx,ky), the
spec-tral-domain Greens function of Ex for Jx, can be found with
the spectral-domain immittance approach [10], and given as
(7)where Ztm and Zte are the input wave impedances for the TMz-
and TEz-modes, respectively [4]. Even though B(y) in (4) is known
to closely approximate the distribution of the current on the CPS
line, unfortunately its Fourier transform is not available in a
closed form. To circum-vent this problem, the function in (4) is
represented by a linear combination of the entire basis functions,
whose Fourier transforms are available in closed formulas. Weighted
Chebyshev polynomials are good candidates for this purpose, and the
resulting expression of B~ (ky) was described previously [4]. Now
P, which is given as a one-dimensional integral, can be evaluated
numerically without difficulty, and v can be determined as
previously described.
From another point of view, because the VM strip resonator with
PMC walls can be modeled by two quar-ter-wavelength open stubs,
which are connected in series as shown in Fig. 2(b), Z can also be
expressed as
cot (8)Now the characteristic impedance Z0v can be deter-
mined in terms of the reactance slope parameter, Xsp, as
with
(9)In order to calculate Lv and Gr, the PMC walls
should be removed as shown in Fig. 2(c). )/( 20vv
invin IPZ = ,
the input impedance of the VM strip antenna (VMSA) at the x=0
plane, can be calculated in a similar way as before. The difference
is the two-dimensional represen-tation, and the resulting
expression becomes
(10)
where ),(~
yx kkJ ))(~)(~( yx kBkA= is the two-dimensional Fourier
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transform of the current density function. Now the in-tegral
(10) can be performed in the polar domain (k and ) with the
following transformations, kx=k cos, and ky=k sin. Related
numerical integration tips were de-scribed previously [11]. Because
of the open space, vinZ becomes a complex value with a nonzero real
part as
vin
vin
vin jXRZ += , where
vinR and vinX reflect the radiation
loss and near-field stored energy, respectively. The half- wave
resonant length L0 is determined from 0=
vinX =0 at the
frequency of interest. Since L0 becomes smaller than g/ 2
because of the effect of the fringing field, the follow-ing
extended line length Lv0 can be introduced:
(11)
However, there is a need for slight compensation be-
cause of the y-component current flow around the open ends,
which is different to the assumption. Due to this kind of
phenomena, the path length of the current flow becomes slightly
larger. This effect can be taken into account by numerical
analysis, such as the method of moments or the finite-difference
time-domain method. By comparing the data from the present theory
and the nu-merical eigen-mode analysis [6], the following
compen-sation was found to be appropriate:
(12) Last, the equivalent radiation conductance Gr can be
found from the calculated vinR by the well-known trans-
mission-line analysis as
.
(13)
The input impedance and operating bandwidth can be calculated by
a network analysis of the developed equiv-alent circuit. The
fractional bandwidth (FBW) of the an-tenna for the given reference
voltage standing-wave ra-tio (S) can be estimated from its quality
factor (Q) as [12]
(14)
Even though many parameters affect the value of Q, such as
radiation loss from VMSA and the aperture, and surface-wave,
conductor, and dielectric losses, the radia-tion term of VMSA (Qr)
is found to be dominant, that is, QQr. From the developed
equivalent circuit, Qr can be calculated as
(15)
. Design and Results
To validate the present theory, two C-band ACVMSAs were
designed, one is Design A ( f0=5.0 GHz and FBW =1.7 %), and the
other is Design B ( f0=4.5 GHz and FBW =3.0 %). At first,
equivalent circuit values were calcu-lated as a function of Wv for
different Sv at f0=5.0 GHz and 4.5 GHz, and the derived design
curves of Gr and Lv are shown in Fig. 3. It is found that both
increase with Wv and Sv. From the obtained Gr, the corresponding
fractional bandwidth was calculated, and is displayed in Fig. 4.
Because of the structural difference between ACVMSA and
aperture-coupled microstrip patch antenna (ACMPA), it is debatable
whether a direct comparison of their characteristics should be
made. Nevertheless, it is observed that FBW of 0.57.5 % with
Sv=0.52.0 mm and Wv=2.08.0 mm is comparable to that of ACMPA. It is
expected that broader bandwidth can be
(a) Gr
(b) Lv
Fig. 3. Equivalent circuit values of VMSA.
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AND SCIENCE, VOL. 11, NO. 2, JUN. 2011
126
Fig. 4. Bandwidth characteristics of VMSA.
obtained using various methods, such as placing another strip on
the other side of VM substrate and various types of parasitic
loading including a slot on the VM strip. Bandwidth-enhancing
techniques for ACVMSA are open to researchers interested in the
subject.
Based on the design curves in Fig. 4, Wv=4.00 mm and Sv=1.00 mm
were chosen for Design A, and Wv=6 mm and Sv=1.5 mm for Design B.
The remaining struc-ture parameters were determined with the help
of opti-mization based on circuit simulation, and the results are
displayed in Table 1. The related circuit values, except for v,
were found to be nearly constant as a function of frequency, as
shown in Table 2. In contrast, v nearly became a linear function of
frequency, and it became 117.19 and 102.89 (rad/m) at f0=5.0 GHz
(Design A) and 4.5 GHz (Design B), respectively. Using these
cir-
Table 1. Structure parameters for Designs A and B.
ParameterValue
Design A(5 GHz)
Design B(4.5 GHz)
Lv (mm) 21.60 23.80
Wv (mm) 4.00 6.00
Sv (mm) 1.00 1.50
La (mm) 8.60 12.00
Lm (mm) 7.50 9.40
hv, hm (mils) 31
rv, rm 2.2Wa (mm) 0.50
Wm (mm) 2.42
Table 2. Equivalent circuit values for Designs A and B.
ParameterValue
Design A(5 GHz)
Design B(4.5 GHz)
nv 0.4053 0.4121
nf 0.7333 0.8185
Z0v (Ohm) 84.67 86.48
Gr (mmho) 0.24 0.42
Lv (mm) 2.23 2.93
Fig. 5. Characteristics of S11.
Fig. 6. Fabricated antenna (Design A).
cuit values, the characteristics of the reflection co-efficient
were computed and are shown in Fig. 5. For comparison, the designed
antennas were fabricated (only the antenna for Design A is shown in
Fig. 6) and their characteristics were measured. As shown in the
figure, good agreement was observed with an error of 0.50 % and
0.44 % for Designs A and B, respectively, in pre-
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dicting the operating center frequency. The measured FBWs were
1.97 % and 3.23 % for Designs A and B, respectively, which are very
close to the design values.
. ConclusionsThe general theory of ACVMSA was presented for
studying the circuit characteristics. An equivalent circuit
model was developed, and the related circuit element values were
calculated both in an analytical and a semi- analytical manner. For
the efficient design of the anten-na, the design curves were also
presented. For the vali-dation check of the present analysis and
the design theo-ry, two C-band ACVMSAs were designed based on the
obtained design curves, and were optimally tuned with the circuit
analysis. The computed reflection coefficients were compared with
the measured and simulation re-sults, and reasonable agreements
were observed with an error of less than 0.5 % in predicting the
operating cen-ter frequency. The measured FBWs were 1.97 % and 3.23
% for Designs A and B, respectively, which are very close to the
design values. All the results show the validity of the design
theory and the usefulness of the proposed equivalent circuit model.
Future work will fo-cus on studying the radiation characteristics
of ACV-MSA such as beamwidth, directivity, and front-to-back
ratio.
This work was supported by the National Research Foundation of
Korea (NRF) grant funded by the Korea government (MEST) (No.
2011-0000159).
References
[1] D. M. Pozar, "A microstrip antenna aperture-coupled to a
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Jeong Phill Kimreceived the B.S. degree from Seoul Na-tional
University, Seoul, Korea in 1988, his M.S. and Ph.D. degrees from
POS-TECH, Pohang, Korea in 1990 and 1998, respectively, all in
electronic engineering. From 1990 to 2001, he had worked for LG
Innotek (LIG Nex1). From 2001, he has been with the School of
Electronic
Engineering, Chung-Ang University as an associate professor. His
research interests include the design of microwave circuits and
antenna, wireless communication and radar systems, espe-cially in
the random noise radar system.
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