IOP PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 20 (2009) 015201 (7pp)
doi:10.1088/0957-0233/20/1/015201
Exploiting a patch antenna for strain
measurements
U Tata1, H Huang1,3 , R L Carter2 and J C Chiao2
1
Department of Mechanical and Aerospace Engineering, University of Texas at Arlington,
500 W First Street, WH211, Arlington, TX 76019, USA
2
Department of Electrical Engineering, University of Texas at Arlington, 416 Yates Street, NH538,
Arlington, TX 76019, USA
E-mail: huang@uta.edu
Received 21 August 2008, in final form 30 September 2008
Published 12 November 2008
Online at stacks.iop.org/MST/20/015201
Abstract
The feasibility of applying patch antennas for strain measurement is investigated. The
resonance frequency of a patch antenna is determined by the size of its metallic patch. An
applied strain changes the dimensions of the metallic patch, resulting in a shift in the antenna
resonant frequency. Therefore, the applied strains can be measured from the changes in
antenna resonant frequency. A dual-frequency patch antenna was designed and fabricated
using conventional photolithography techniques. The application of the patch antenna for
strain measurement was evaluated by bonding the patch antenna to an aluminum cantilever
beam and applying loads at the free end of the cantilever beam. The shifts of the return loss S11
curves under loads were correlated to the strains experienced by the patch antenna. The strain
sensitivity of the antenna obtained from experimental measurements agreed well with the
analytical prediction.
Keywords: strain sensor, patch antenna, flexible substrate, passive wireless sensor
(Some figures in this article are in colour only in the electronic version)
strain sensors in order to obtain a distributed assessment
of the structural condition, thin-film strain gauges are not
favorable for SHM systems because of the complexity and
weight penalty associated with the wiring of these strain
gauges. Optical fiber-based strain sensors, on the other hand,
are an attractive choice of sensor for SHM systems due to their
compact size, light weight, remote accessibility, multiplexing
capability and immunity to electromagnetic interferences
(Bhatia et al 1995, Liu et al 2007, Murphy et al 1993,
Murphy and Poland 1997, Song and Hotate 2007, Wang et al
1996). Even though many optical fiber strain sensors
have been implemented for various SHM applications, the
inherent shortcomings of optical fiber sensors, e.g. expensive
interrogation equipment, limited strain range and fragility, etc,
have not been resolved.
Recently, wireless strain sensors are becoming more
and more popular for SHM systems (Hou and Lynch 2006,
Kiremidjian et al 2004, Kurata et al 2005, Nagayama
et al 2007).
These sensors, equipped with embedded
microprocessors and wireless communication capabilities,
1. Introduction
Structural health monitoring (SHM) is a technology critical
for the safety assurance of mechanical, aerospace and civil
structures (Liu et al 2006, Rao 1996, Spencer et al 2004).
By performing autonomous inspection of structures using
embedded sensors, a SHM system can provide advanced
warnings that prevent catastrophic structural failures. Strain is
one of the most important mechanical parameters acquired by
SHM systems. By monitoring strain changes in load-bearing
structures, the factors that could potentially cause structural
failures such as excessive loading, vibration, foundation
damages, crack development and environmental aging, etc
can be detected.
Various strain sensors have been developed in the past.
A detailed review of different strain sensing mechanisms can
be found in the literature (Sun 2006). The most commonly
used strain sensor is the piezoresistive thin-film strain gauge.
However, since SHM systems usually require a network of
3
Author to whom correspondence should be addressed.
0957-0233/09/015201+07$30.00
1
© 2009 IOP Publishing Ltd Printed in the UK
U Tata et al
Meas. Sci. Technol. 20 (2009) 015201
εr, the substrate thickness h and the electrical width of the
patch we , i.e.,
εr − 1
εr + 1
εre =
+ √
.
(2)
2
2 (1 + 10h/we )
The line extension Loc is calculated from the effective
dielectric constant εre, the substrate thickness h and the electric
width we ,
(εre + 0.3)(we / h + 0.264)
.
(3)
Loc = 0.412h
(εre − 0.258)(we / h + 0.813)
Assuming the antenna is subjected to a tensile strain εL
along its electrical length direction, the patch width and the
substrate thickness will change due to Poisson’s effect, i.e.,
w
Metallic
patch
h
E
L
Dielectric
substrate
Substrate
Figure 1. Passive patch antenna.
have the potential to reduce the installation and maintenance
costs of distributed sensor networks. Many of these wireless
sensors require batteries to be operational. Therefore, their life
spans are limited by battery life. Passive wireless sensors are
attractive alternatives because they do not require any power
supply (Butler et al 2002, Chuang et al 2005, Gattiker et al
2008, Gu et al 2005, Harpster et al 2002, Jia et al 2006,
Matsuzaki et al 2005, Nomura et al 2006, Pohl and Seifert
1996, Reindl et al 1996, Tan et al 2008). These passive
wireless sensors usually consist of a sensing unit and a data
transmitting unit. The electromagnetic (EM) impedance of
the sensing unit varies with the physical measurand. When it
is connected to an antenna, the EM impedance change of the
sensing unit shifts the resonant frequency of the antenna. This
frequency shift is then remotely interrogated using inductive
coupling. Because the sensing unit is not integrated with the
antenna, these passive wireless sensors are usually quite large
in size.
In this paper, we demonstrated that a patch antenna itself
can serve as the sensing unit for strain measurement. With
integrated sensing and data transmitting capability, the size
of the antenna sensor can be reduced significantly. The
relationship between the applied strain and the resonant
frequency of the patch antenna is first derived. The design,
fabrication and evaluation of a dual-frequency patch antenna
for strain measurement are then discussed. The agreement
between the simulated and measured strain sensitivities proved
the feasibility of applying patch antennas for strain sensing.
we = (1 − υp εL )we0
h = (1 − υs εL )h0 .
(4)
If Poisson’s ratios of the metallic patch and the substrate
material υ p and υ s are the same, the ratio we /h remains to be
a constant as the tensile strain εL changes. As a result, εre in
equation (2) is independent of εL, and Loc in equation (3)
is proportional to the substrate thickness h. Therefore, the
resonant frequency in equation (1) can be expressed as
1
c
C1
fres = √
,
(5)
=
2 εre Le + 2Loc
Le + C2 h
+0.3)(we / h+0.264)
where C1 = 2√cεre and C2 = 0.812 (ε(εre re−0.258)(w
. The
e / h+0.813)
strain-induced elongation, therefore, will shift the antenna
resonant frequency. At an unloaded state, the antenna
frequency fres0 is calculated from the antenna length Le0 and
substrate thickness h0, i.e.,
C1
fres0 =
.
(6)
Le0 + C2 h0
Under a strain εL, the antenna frequency shifts to
C1
fres (εL ) =
.
(7)
Le0 (1 + εL ) + C2 h0 (1 − υεL )
Combining equations (6) and (7), we can establish the
relationship between the strain εL and the frequency shift fres,
i.e.,
L0 + υs C2 h0 fr
fres
εL = −
=C
,
(8)
L0 + C2 h0 fr
fres
where fres = fres − fres0. Analyzing the constant C indicates
that the strain sensitivity of antenna is determined by the
dielectric constant of the substrate material for an antenna
operating at a specific frequency.
For a positive strain εL, the antenna resonant frequency
will shift to a lower frequency because of the elongation of its
electrical length. A strain applied along the antenna’s electrical
width direction, however, will increase the antenna resonant
frequency due to Poisson’s effect. Therefore, fres is more
sensitive to strains applied along the electrical length direction
than those applied along the electrical width direction. If the
antenna is fed with an electric field polarized parallel to its
geometric length direction, the electrical length Le is the same
as the geometric length L of the antenna. Rotating the electric
field polarization by 90◦ , however, will switch the electrical
length to the antenna’s geometric width w. By feeding the
antenna with two orthogonal electric fields, an antenna that is
sensitive to strains along both directions of the antenna patch
can be achieved.
2. Principle of operation
The patch antenna, as shown in figure 1, consists of a
layer of dielectric substrate, a rectangular patch printed on one
side of the substrate and a ground plane coated on the other
side of the substrate. The rectangular patch and the ground
plane, both made of conductive metals, form an EM resonant
cavity that radiates at a specific resonant frequency. Based on
the transmission line model (Bhartia et al 1991), the resonant
frequency of a rectangular patch antenna is calculated as
1
c
,
fres = √
2 εre Le + 2Loc
and
(1)
where c is the velocity of light. The electrical length Le of the
antenna is defined as the dimension of the metallic patch along
the direction of the radiation mode. The effective dielectric
constant εre is related to the dielectric constant of the substrate
2
U Tata et al
Meas. Sci. Technol. 20 (2009) 015201
y
Microstrip
line
x=L/2
5.33
2.0
(x0,w/2)
(x0, y0)
4.0
y=w/2
(L/2, y0)
o
0.8
1.0
x
(a )
Unit: mm
(b )
Figure 2. Antenna feeding: (a) 50 impedance matching, (b) microstrip line feeding.
where the calculation of antenna impedance Riny is given by
Balanis (2005). Similarly, only the TM01 mode can be excited
if the antenna is fed at a point along x = L/2. The feeding
position y0 for TM01 excitation is again calculated from the
antenna impedance Rinx, i.e.,
50
w
−1
y0 = cos
.
(12)
π
Rinx
3. Antenna design
In order to feed the patch antenna with two orthogonal electric
fields, a dual-frequency patch antenna was designed. For a
dual-frequency antenna, the radiation mode with its polarized
electric fields parallel to the geometric length direction of
the metallic patch is denoted as the TM10 mode while the
radiation mode whose electric fields are along the geometric
width direction of the metallic patch is designated as the TM01
mode. For a chosen substrate thickness h and a relative
dielectric constant εr, the dimensions of the antenna patch
are calculated from the resonant frequencies corresponding to
these two radiation modes. Denoting the resonant frequency
for the TM10 mode as f10, the geometric length of the antenna
patch can be calculated from equation (1) as
L=
c
√ − 2Loc .
2f10 εre
Feeding the patch antenna at (x0, y0) excites both radiation
modes and matches the impedances of the patch antenna at the
two resonant frequencies f10 and f01 (Chen and Wong 1996). In
order to facilitate mechanical testing of the patch antenna, the
patch antenna was designed to be fed using a microstrip line,
as shown in figure 2(b). The microstrip line joins the metallic
patch at (0, y0), which means only the impedance of the patch
antenna for the TM01 mode is matched. The length and the
width of the microstrip line were tuned to achieve optimum
return losses at the two resonant frequencies. The final design
of the dual-frequency patch antenna is shown in figure 2(b).
(9)
Similarly, the geometric width of the antenna patch is
calculated from the resonant frequency f01 of the TM01 mode,
i.e.,
c
w=
(10)
√ − 2woc ,
2f01 εre
4. Antenna fabrication
The patch antennas were fabricated on a flexible polyimide
film (Kapton HN) using semiconductor fabrication processes,
as illustrated in figure 3. A Kapton film was chosen because
its dielectric constant is not very sensitive to temperature
changes (Hammoud et al 1992). First, a 50 μm thick Kapton
film was cut into 4 × 4 square strips. They were cleaned
in ultrasonic acetone bath for a few minutes. Following
cleaning, a layer of hexamethyldisiliazane (HMDS) was spincoated on the Kapton strips at a speed of 2000 rpm for 30 s.
Positive photoresist S1813 was then spin-coated using the
same speed and time, producing a film thickness of 1.5 μm
(figure 3(a)). After baking the Kapton strips on a hotplate
at 100 ◦ C for 1 min, the antenna pattern was transferred
from a dark field mask to the photoresist by exposing the
photoresist to UV light of 25 mW cm−2 intensity for 15 s.
A photoresist developer MF319 was used to develop the
antenna patch (figure 3(b)). The developing time was set
to be 30 s. After developing, the Kapton strips were rinsed
with DI water and dried using dry nitrogen air. A copper film
of 1 μm thickness was then deposited on the Kapton strips
using thermal evaporation (figure 3(c)). The final fabrication
where the line extension w oc is calculated from equation (3)
by replacing w with L. For a 50 μm thick polyimide substrate
with a relative permittivity of 3.4, a dual-frequency patch
antenna operating at f10 = 15 GHz and f01 = 20 GHz will
result in a metallic patch with a length of 5.33 mm and a width
of 4 mm.
The patch antenna can be fed using either a contact or a
non-contact technique. Since this paper is focused on proving
the feasibility of the patch antenna for strain sensing, the
contact technique was adopted. In order to excite the two
orthogonal radiation modes simultaneously, the patch antenna
has to be fed at a proper position. For the coordinated system
given in figure 2(a), only the TM10 mode will be excited if the
patch antenna is fed at any point along y = w/2. The optimum
position of the feeding point x0 is determined by impedance
matching, i.e.,
50
L
−1
x0 = cos
,
(11)
π
Riny
3
U Tata et al
Meas. Sci. Technol. 20 (2009) 015201
Photoresist
Kapton
(a)
Kapton
(b )
Kapton
(d )
Copper
Kapton
(c )
Figure 3. Fabrication steps of the patch antenna.
to the antenna sensor through an SMA connector. The signal
reflected by the antenna sensor was routed back to the receiver
of the network analyzer from which the antenna radiation
parameters, i.e. the S11 parameters, can be determined. Weight
was added at the free end of the cantilever beam in increments
of 5 lb (1 lb 0.45 kg).
In order to stretch the antenna along its width direction,
the patch was oriented with its microstrip line perpendicular
to the length direction of the cantilever beam (see figure 5(b)).
An SMA connector was mounted on the edge of the cantilever
with its pin touching the end of the microstrip line. A solder
ball was placed at the end of the SMA tip to ensure a sound
electrical connection between the SMA tip and the antenna
microstrip line. In order to stretch the antenna along its length
direction, however, the antenna has to be oriented with its
microstrip line parallel to the length direction of the cantilever
beam (see figure 5(c)). The only feasible way to feed the patch
antenna was then to vertically hold the SMA connector and
press the tip of the SMA connector onto the end of the antenna
microstrip line.
Kapton
Metallic
patch
1 mm
Figure 4. Fabricated patch antenna.
involved soaking the Kapton strips in pure acetone for 3 h to
remove the developed photoresist and lift off the metal on top
(figure 3(d)). Since we will bond the antenna to a metallic
structure, no ground plane was fabricated on the substrate.
The fabricated patch antenna is shown in figure 4.
5. Mechanical testing of the patch antenna
Mechanical testing of the patch antenna for strain measurement
was carried out using a cantilever beam, as shown in
figure 5(a). The antenna sensor was bonded on an aluminum
cantilever beam using a conventional strain gauge adhesive.
The microwave signal supplied by a network analyzer was fed
6. Results and discussions
The design of the dual-frequency antenna was verified using
a commercial EM simulation tool, Sonnet Pro ver. 11.5. The
SMA
connector
((a)
a)
To network
analyzer
ε
Patch
antenna
Cantilever
beam
((b)
b)
Patch antenna
SMA
connector
ε
Weights
((c)
c)
Patch antenna
Figure 5. Experimental setup for strain measurement: (a) loading of the cantilever beam, (b) width-direction elongation and
(c) length-direction elongation.
4
U Tata et al
Meas. Sci. Technol. 20 (2009) 015201
simulated results. The measured patch antenna displayed two
resonant frequencies in its S11 curve. The length-direction
resonant frequency f10 was measured at 17.2 GHz while
the width-direction resonant frequency f01 was measured at
20.5 GHz. The 2 GHz discrepancy between the designed
frequency and the measured frequency for the TM10 mode
was probably due to the additional capacitance introduced by
the SMA connector.
The patch antenna was tested by applying strains along
its geometric width direction first. The load was increased in
increments of 5 lb until a total load of 30 lb. Based on the
stress calculation of a cantilever beam under bending, a load of
5 lb will lead to a strain of 0.084% at the antenna position. The
network analyzer was set to acquire 1600 points from 16 GHz
to 21.5 GHz. An overview of the measured S11 curves under
different strain levels is shown in figure 7(a). Zooming in the
regions near the f01 and f10 frequencies (see figures 7(b) and
(c)) demonstrated the parallel shifts of these two frequencies.
The f10 frequencies shifted to the right as the strains increased
while the f01 frequencies shifted to the left. This is consistent
with the analytical prediction. The percentages of frequency
shifts for these two resonant frequencies, both calculated and
measured, were plotted with respect to the applied strains, as
shown in figure 8. Excellent linearity was achieved for both
Freq. (GHz)
14
15
16
17
18
19
20
21
0
Return Loss (dB)
-5
f10
-10
-15
-20
f10
f01
Simulated
Measured
-25
Figure 6. Comparison of the simulated and measured antenna S11
curves.
simulated S11 curve of the dual-frequency antenna is shown
in figure 6. The two resonant frequencies were found to be
f10 = 14.9 GHz and f01 = 19.6 GHz. The return loss at f01 is
higher than that at f10 because of better impedance matching
for the TM01 mode. The S11 parameters of the patch antenna
under zero loading were measured and compared with the
Freq. (GHz)
17
17.5
18
18.5
19
19.5
20
20.5
21
-6
-8
-10
S11 (dB)
-12
-14
0% strain
f01
-16
0.08% strain
-18
0.17% strain
-20
0.25% strain
0.34% strain
-22
-24
0.42% strain
f10
((a)
a)
0.50% strain
-26
Freq. (GHz)
Freq. (GHz)
17.51
17.52
-15
19.83 19.86 19.89 19.92 19.95 19.98
-8.7
0.0%
0.42%
-16
0.08%
0.17%
-8.9
0.17%
0.25%
0.34%
-15.5
S11 (DB)
S
DB)
19.8
17.55
0.08%
-15.75
-16.5
17.54
0.0%
-15.25
-16.25
17.53
S11 (dB)
S1
d
17.5
εw
-9.1
εw
0.25%
0.34%
0.42%
-9.3
-9.5
-16.75
-17
(b )
-9.7
(c )
Figure 7. Shifts of S11 curves under width-direction strains: (a) overview, (b) shifts of f10 frequency-enlarged view and (c) shifts of the f01
frequency-enlarged view.
5
U Tata et al
Meas. Sci. Technol. 20 (2009) 015201
(b )
(a)
0.16
0.14
0
-0.2
Freq. Shift (%)
-0.1
0.08
y = 0.28x
R2 = 1.00
y = 0.18x
R2 = 0.99
0.04
0.02
0.00
0
0.4
0.5
-0.3
-0.4
Analytical
-0.4
Measured
Strain along width direction (%)
-0.5
0.3
0.4
y = -0.98x
-0.98x
R2 = 1.00
-0.3
-0.5
0.2
0.3
y = -0.81x
-0.81x
R2 = 1.00
-0.2
0.5
0.1
0.2
-0.1
0.10
0.06
0.1
0.0
Linear (Analytical)
Linear (Measured)
0.12
Freq. shift (%)
Strain along width direction (%)
Analytical
Measured
Linear (Analytical)
Linear (Measured)
Figure 8. Comparison of analytical and measured strain sensitivities: (a) f10 frequency and (b) f01 frequency.
(a )
(b )
Frequency (GHz)
17.4
17.6
17.8
18
Strains along length direction (%)
18.2
0
-10
0.1
0.2
0.3
0.4
0.5
0
-14
-16
-0.1
εL
Freq. shift (%)
Return Loss (dB)
-12
-18
-20
0.0%
-22
0.1%
-24
-26
-28
0.2%
-0.2
-0.3
-0.4
Analytical
Measured
-0.5
Linear (Analytical)
0.3%
0.4%
y = -0.97x
R2 = 0.98
y = -0.98x
R2 = 1.00
Linear (Measured)
0.5%
-0.6
-30
Figure 9. (a) Shifts of f10 frequency under length-direction strains and (b) comparison of analytical and measured strain sensitivities.
the calculated and measured data. The slopes of the fit lines
represent the strain sensitivity of the respective frequency. For
the f01 frequency, the analytical model predicted a slope of
0.98, which means a 1% strain would shift the f01 frequency
by 0.98%. The slope of the measured data is 0.81, slightly
lower than that of the calculated data. This is probably due to
the shear lag introduced by the bonding layer and the Kapton
substrate. Expressing the frequency shifts in absolute value,
the strain sensitivity of the f10 frequency was estimated to be
16.4 kHz microstrain−1. Assuming the network analyzer can
achieve a 10 Hz frequency resolution, the strain resolution of
the antenna sensor is estimated to be 6.1 × 10−4 microstrains.
The sensitivity of the f01 frequency to the width-direction
strains is much smaller. With a slope of 0.18, the strain
sensitivity in absolute value is 3.3 kHz microstrain−1, onefifth of the strain sensitivity of the f10 frequency.
When the antenna was strained along its length direction,
only the f10 frequency can be observed at the network analyzer
due to vertical feeding. Therefore, the network analyzer was
set to acquire 400 data points from 17.4 GHz to 18.1 GHz.
Because the bending of the cantilever beam causes the antenna
to slide away from the SMA connector, the antenna had to
be mounted close to the fixed end of the cantilever beam.
Applying a load of 5 lb at the free end of the cantilever
beam will produce a strain of 0.1% at the antenna position.
The parallel shifts of the S11 curve under various strains are
shown in figure 9(a). Again, we achieved excellent linearity
between the shifts of the f10 frequency and the length-direction
strains (see figure 9(b)). Moreover, the slope of the measured
data matched very well with the theoretical predictions. The
sensitivity of the f10 frequency with respect to the lengthdirection strain, around 17.2 kHz microstrain−1, is slightly
higher than that of the f01 frequency when the antenna was
under width-direction elongation.
7. Conclusions
This paper presented the analysis, design, fabrication and
validation of a patch antenna for strain measurement. Both the
theoretical analysis and the experiment results demonstrated
that the resonant frequency of the patch antenna is sensitive
to strains applied along the direction of its corresponding
radiation mode. Since the antenna resonant frequency can
be remotely interrogated using field coupling or antenna
6
U Tata et al
Meas. Sci. Technol. 20 (2009) 015201
backscattering, patch antennas have great potential to serve
as passive wireless strain sensor. The development of a
wireless radar system that can interrogate the antenna resonant
frequency remotely is under way and will be a subject of
another paper.
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Acknowledgments
This project is supported by the Air Force Office of Scientific
Research under contract no. FA9550-07-1-0465. The support
and encouragement of program manager, Dr Victor Giurgiutiu,
is greatly appreciated.
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