Miniaturization of a Patch Antenna with Dispersive Double Negative

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Miniaturization of a Patch Antenna with Dispersive Double Negative
Miniaturization of a Patch Antenna with Dispersive
Double Negative Medium Substrates
M.-F. Wu, F.-Y. Meng, Q. Wu
Harbin Institute of Technology, Harbin, Heilongjiang, China
J. Wu
China Research Institute of Radiowave Propagation, Xinxiang, Henan, China
L.-W. Li
National University of Singapore, Kent Ridge 119260, Singapore
Abstract- In this letter, a potential application of practically
resonators [3]. Because the hybrid materials were utilized to
dispersive double negative medium substrates on the dimensions
support forward and backward waves, the phase shift gained by
miniaturization of patch antennas is explored. By using the
waves propagating in double positive medium could be
transmission line theory, it is shown that the use of such a
compensated by waves in double negative medium. Another
practically dispersive double negative material could not offer
potential application of the above “phase compensator” is
such a broadband characteristic as a hypothetical non-dispersion
antenna miniaturization and bandwidth enhancement. By
double negative medium, but it can indeed greatly miniaturize
theoretical analysis, several groups have found that the size of
the dimensions of the patch antenna.
patch antennas can be significantly reduced by multi-pair
dielectric substrates, and the dimensions of patch antennas
could be no longer proportional to the working wavelength but
I.
INTRODUCTION
approximately to the ratio of the dimensions of the dielectric
Double negative material represents a new kind of artificial
blocks [4-6]. Although the research results can be promising
dielectric media which are usually synthesized using periodic
for patch antenna miniaturization, more details of research
structures and exhibit negative refractive index characteristics
works are still necessary because the inherent dispersion of
(resulted
double negative medium may greatly affect it [7],which has
from
simultaneous
negative
permittivity
and
permeability). Such a material has been also referred to as
been experimentally verified by Tretyakov [8].
several other names such as left-handed material (LHM),
In this paper, we will consider a patch antenna partially
metamaterials, and backward wave material (BWM). The basic
loaded by traditional double positive medium (DPS) substrates,
concept of such a double negative medium was introduced by
perfect non-dispersive double negative medium (DNG)
Veselago in 1968, who concluded that a theoretical medium
substrates,
with simultaneous negative permittivity and permeability could
respectively. We will investigate the possibility of patch
support backward wave propagation and exhibit negative
antenna miniaturization with practically dispersive DNG
refractive index by theory [1]. Experimentally the first effective
materials. The problem is analytically modeled by the
double negative medium was synthesized by Smith et al. in
transmission line model in Section II. The practical double
microwave regime [2]. There are a few potential applications,
negative medium is synthesized based on the traditional SRRs,
and this paper will consider one of them. Recently, Enghata has
and its permittivity and permeability are then retrieved in
shown that a pair of double positive medium and double
Section III. Patch antennas partially loaded by three substrates
negative medium blocks could be used to build small
are demonstrated and the results are compared in Section IV.
0-7803-9433-X/05/$20.00 ©2005 IEEE
and
practically
dispersive
DNG
substrates,
APMC2005 Proceedings
Lastly conclusions can be obtained in Section V.
range. Overlaying these two frequency regions, both the
permittivity and permeability are simultaneously negative, and
thus the index of refraction may have a negative real value
II.
THE EQUIVALENT TRANSMISSION LINE MODEL
over a passband region. By manipulating the two structures,
In this section, we will derive the expressions for the input
the effective permittivity and permeability can be changed
admittance the patch antenna partially loaded by double
separately, giving us the capability to control the position of
negative medium. The illustration of the under considered
the double negative regime.
antenna and its equivalent transmission line (TL) model is
The illustration of the DNG material unit cell is shown in
shown in Fig. 1. The substrate consists of a pair of DPS and
Fig. 2. The DNG material unit cell is made of dielectric
DNG blocks, and the DNG blocks consist of 40 × 2 DNG
material with relative permittivity constant of 2.2. And then a
unit cells. In the TL model, the G denotes the radiation
PEC split ring resonator and a PEC thin rod is embedded in it,
admittance of the patch edges, and C means the edge
whose geometric parameters are marked in Fig. 2. To obtain
capacitance to model the patch end-effect extension. LR and LL
the effective constitutive parameters, the CST Microwave
represent the lengths of patch loaded by DPS and DNG,
Studio is used to retrieve the S parameters of the DNG material
respectively, and they sum to be the patch length L. YR and YL
unit cell. Then we can extract the effective constitutive
respectively represent the characteristic admittance of the
parameters from S parameters by the methods demonstrated in
equivalent right-handed TL and left-handed TL. Consequently,
literature [10][11].
the input admittance Yin can be stated as following expressions
[9]
The effective permittivity and permeability of the DNG unit
cell are retrieved and their variations are demonstrated in Fig.
:
Yin = Yr + YR
Yin1 = YL
Yin1 + jYR tan( β R LR )
YR + jYin1 tan( β R LR )
Yr + jYL tan( β L LL )
YL + jYr tan( β L LL )
Yr = G + jω C
W
YR =
h
W
YL =
h
ε DPS
µ DPS
ε DNG
µ DNG
(1)
(2)
(3)
3. Fig. 3(a) illustrates the real part (marked with cross) and the
image part (marked with diamond) of the effective relative
permittivity, and the Fig. 3(b) illustrates the real part (marked
with cross) and the image part (marked with diamond) of the
effective relative permeability. Then we combine the real part
of the effective relative permittivity (marked with cross) and
(4a)
the real part of the effective relative permeability (marked
with diamond) in Fig. 3(c) for convenience. So we can obtain
that the real part of the effective permittivity equals to the real
(4b)
part of the effective permeability, which is about -0.9 at 7.7
GHz.
β R = ω ε DPS µ DPS
(5a)
β L = ω ε DNG µ DNG .
(5b)
IV. NUMERICAL RESULTS AND DISCUSSION
By employing the transmission line model, for validation
purpose we firstly reproduce the known results for antenna
miniaturization with non-dispersive DNG substrate. Then a
III. THE DNG SYNTHESIS AND PARAMETERS RETRIEVE
practically dispersive behavior of the DNG materials
The DNG material unit cell employs split ring resonators
synthesized in Section III is embedded into the model, and we
and thin wires described here. Thin wire structures can
can check whether the dimensions of the patch antenna can be
produce an effective negative permittivity below the effective
miniaturized by a practical DNG substrate. Assume that the
plasma frequency and split ring resonators can result in an
DPS block has the relative permittivity and permeability of εr
effective negative permeability over a particular frequency
= 1 and µr = 1, and also that the DNG blocks as filled with
three different materials for comparisons: (a) the normal
514860303.
material with εr = 1 µr = 1, (b) the perfectly non-dispersive
DNG medium with εr=-1 µr=-1, (c) the practically dispersive
DNG medium with εr = εr (ω) and µr = µr (ω) described in
REFERENCES
[1]
V. G. Veselago, “The electrodynamics of substances with simultaneously
Section III. We choose 7.7 GHz as the patch antenna working
negative values of µ and ε,” Sov. Phys. Usp., vol. 10, no. 4, pp.509–514,
frequency for convenience, because of the dispersive DNG
Jan.–Feb. 1968.
medium with εr = µr = 0.9 at 7.7 GHz.
[2]
Set the electrical length of the patch antenna as 0.2λ0, which
is slightly smaller than the 0.5λ0 limitation. And the
a negative index of refraction,” Science, vol. 292, pp. 77-79, April 2001.
[3]
parameters are chosen as follows: L = W = 8 mm, LL = 10 L
N. Engheta, “An idea for thin subwavelength cavity resonators using
metamaterials with negative permittivity and permeability,” IEEE
/19 and LR = 9 L /19 because of LL/LR = µr(DPS)/µr(DNG). Fig. 4
shows the calculated reflection coefficient for the patch loaded
R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of
Antennas and Wireless Propagation Letters, vol. 1, pp. 10-13, 2002.
[4]
J. S. Petko and D. H. Werner, “Theoretical Formulation for an
with different substrates. Results show that: (a) when the patch
Electrically Small Microstrip Patch Antenna Loaded with Negative
antenna loaded entirely by the substrate with εr = 1 and µr = 1,
Index Materials,” Proceedings of the 2005 IEEE Antennas and
the antenna cannot radiate beyond 7.7 GHz (solid line),
Propagation Society International Symposium and USNC/URSI National
because its electrical length is only 0.2λ0 and much shorter
Radio Science Meeting, Washington DC, July 3-8, 2005.
than the half-a-wavelength limitation; (b) when half of the
[5]
W. Xu, L.-W. Li, H.-Y. Yao, T.-S. Yeo and Q. Wu, “Left-handed material
patch antenna loaded by the perfect non-dispersive DNG
effects on wave’s modes and resonant frequencies: field waveguide
substrate with εr = -1 and µr = -1, it can work over a broadband
structures
(marked with circle); and (c) when it comes to the practically
Electromagnetic Waves and Applications, vol. 19, no. 15, pp. 2033-2047,
dispersive DNG medium, although it cannot offer such
broadband performance as the hypothetical non-dispersive
and
substrate-loaded
patch
antennas,”
Journal
of
October, 2005.
[6]
S.F. Mahmoud, “New miniaturized annular ring patch resonator partially
DNG substrate, it indeed works at 7.7 GHz (dash line) and the
loaded by a metamaterial ring with negative permeability and
theoretical prediction appears to be validated.
permittivity,” IEEE Antennas and Wireless Propagation Letters, vol. 3,
pp. 19-22, 2004.
[7]
V.
CONCLUSION
M.E. Ermutlu and S. Tretyakov, “Patch antennas partially loaded with a
dispersive backward-wave material,” Proceedings of the 2005 IEEE
By employing the substrate partially filled with double
Antennas and Propagation Society International Symposium and
negative medium, the dimensions of the patch antenna could be
USNC/URSI National Radio Science Meeting, Washington DC, July 3-8,
significantly miniaturized, and the calculated results for the
2005.
patch length 0.2λ0 show that although the use of a practically
[8]
Pekka Ikonen, Stanislav Maslovski, Constantin Simovski, and Sergei
dispersive double negative medium could not support such
Tretyakov, “On Artificial Magneto-Dielectric Loading for Improving the
broadband performance as a hypothetical non-dispersion
Impedance Bandwidth Properties of Microstrip Antennas,” unpublished.
double negative medium, but it proves the approach is
perspective and important for the miniaturization of patch
antenna.
[9]
R. Garg, P. Bhartia, I. Bahl and A. Ittipiboon, Microstrip Antenna Design
Handbook. Norwood, MA: Artech House, 2001, sec.5.2, 5.3.
[10] R. W. Ziolkowski, “Design, fabrication, and testing of double negative
metamaterials,” IEEE Transactions on Antennas and Propagation, vol.
51, no. 7, pp. 1516-1529, July 2003.
ACKNOWLEDGMENT
[11] B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk and J. A Kong,
This work was supported by the Natural Science Foundation
“A Study of Using Metamaterials as Antenna Substrate to Enhanced
of China under Grant 60571026, and the grant from National
Gain,” Progress In Electromagnetics Research, vol. 51, pp. 295-328,
Key Laboratory of Electromagnetic Environment under Grant
2005.
1
real (µr)
imag (µr)
0.5
0
-0.5
Yin G
C
LR
LL
YR
YL
-1
7
7.5
f/GHz
8
8.5
(b)
C G
4
Yin1
3
Fig. 1. Schematic illustration of the patch antenna configuration and its
2
equivalent transmission line model.
1
0
-1
-2
-3
-4
7.5
7.6
7.7
7.8
real (εr)
real (µr)
7.9
8
(c)
Fig. 3. The retrieval results of effective permittivity and permeability. (a)
Retrieval results of the effective permittivity. (b) Retrieval results of the
Fig. 2. Schematic illustration of the DNG unit cell geometry, a = 3.2 mm, b =
effective permeability. (c) Combination of real parts of effective permittivity
0.25 mm, c = 2.62 mm, d = 0.25 mm, e = 0.3 mm, f = 0.46 mm, g = 3.0 mm,
and permeability.
and h=0.25 mm.
0
-5
20
-10
10
-15
-20
0
-25
-20
7
εr=-1
µr=-1
εr=1
µr=1
εr=εr(ω) µr=µr(ω)
-30
-10
7.5
f/GHz
(a)
8
real (εr)
imag(εr)
8.5
-35
7
7.5
f/GHz
8
8.5
Fig. 4. Calculated reflection coefficient for the patch loaded with different
substrates.

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