International Journal of Networks and Communications 2012, 2(2): 13-19
Input Impedance, VSWR and Return Loss of a
Conformal Microstrip Printed Antenna for
Mode Using Two Different Substrates
, Khaled Elleithy, Hassan Bajwa
Department of Computer and Electrical Engineering, University of Bridgeport, Bridgeport, CT 06604, USA
Abstract Curvature has a great effect on fringing field of a microstrip antenna and consequently fringing field affects
effective dielectric constant and then all antenna parameters. A new mathematical model for input impedance, return loss
and voltage standing wave ratio is introduced in this paper. These parameters are given for TM
mode and using two dif-
ferent substrate materials K-6098 Teflon/Glass and Epsilam-10 Ceramic-Filled Teflon materials.
Keywords Fringing Field, Curvature, Effective Dielectric Constant and Return Loss (S11), Voltage Standing Wave
Ratio (VSWR), Transverse Magnetic TM
Due to the unprinted growth in wireless applications and
increasing demand of low cost solutions for RF and
microwave communication systems, the microstrip flat
antenna, has undergone tremendous growth recently.
Though the models used in analyzing microstrip structures
have been widely accepted, the effect of curvature on di-
electric constant and antenna performance has not been
studied in detail. Low profile, low weight, low cost and its
ability of conforming to curve surfaces, conformal mi-
crostrip structures have also witnessed enormous growth in
the last few years. Applications of microstrip structures
include Unmanned Aerial Vehicle (UAV), planes, rocket,
radars and communication industry. Some advantages of
conformal antennas over the planer microstrip structure
include, easy installation (randome not needed), capability
of embedded structure within composite aerodynamic sur-
faces, better angular coverage and controlled gain, depend-
ing upon shape[3,4]. While Conformal Antenna provide
potential solution for many applications, it has some draw-
backs due to bedding. Such drawbacks include phase,
impedance, and resonance frequency errors due to the
stretching and compression of the dielectric material along
the inner and outer surfaces of conformal surface. Changes
in the dielectric constant and material thickness also affect
the performance of the antenna. Analysis tools for confor-
mal arrays are not mature and fully developed.
* Corresponding author:
firstname.lastname@example.org (Ali Elrashidi)
Published online at http://journal.sapub.org/ijnc
Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved
Dielectric materials suffer from cracking due to bending
and that will affect the performance of the conformal mi-
Conventional microstrip antenna has a metallic patch
printed on a thin, grounded dielectric substrate. Although
the patch can be of any shape, rectangular patches, as
shown in Figure 1 , are preferred due to easy calculation
Figure 1. Rectangular microstrip antenna.
Fringing fields have a great effect on the performance of
a microstrip antenna. In microstrip antennas the electric
filed in the center of the patch is zero. The radiation is due
to the fringing field between the periphery of the patch and
the ground plane. For the rectangular patch shown in the
Figure 2, there is no field variation along the width and
thickness. The amount of the fringing field is a function of
the dimensions of the patch and the height of the substrate.
Higher the substrate, the greater is the fringing field.
Due to the effect of fringing, a microstrip patch antenna
would look electrically wider compared to its physical di-
mensions. As shown in Figure 2, waves travel both in sub-
14 Ali Elrashidi et al.: Input Impedance, VSWR and Return Loss of a Conformal Microstrip Printed Antenna
for TM01 mode Using Two Different Substrates
strate and in the air. Thus an effective dielectric constant ε
is to be introduced. The effective dielectric constant ε
takes in account both the fringing and the wave propagation
in the line.
Figure 2. Electric field lines (Side View).
The expression for the effective dielectric constant is in-
troduced by A. Balanis, as shown in Equation 1.
+ 1 12
The length of the patch is extended on each end by ΔL is
a function of effective dielectric constant ε
and the width
to height ratio (W/h). ΔL can be calculated according to a
practical approximate relation for the normalized extension
of the length , as in Equation 2.
The effective length of the patch is L
and can be calcu-
lated as in Equation 3.
= L+2ΔL (3)
By using the effective dielectric constant (Equation 1)
and effective length (Equation 3), we can calculate the re-
sonance frequency of the antenna f and all the microstrip
Figure 3. Physical and effective lengths of rectangular microstrip patch.
Cylindrical-Rectangular Patch Antenna
All the previous work for a conformal rectangular micro-
strip antenna assumed that the curvature does not affect the
effective dielectric constant and the extension on the length.
The effect of curvature on the resonant frequency has been
presented previously. In this paper we present the effect
of fringing field on the performance of a conformal patch
antenna. A mathematical model that includes the effect of
curvature on fringing field and on antenna performance is
presented. The cylindrical rectangular patch is the most
famous and popular conformal antenna. The manufacturing
of this antenna is easy with respect to spherical and conical
Effect of curvature of conformal antenna on resonant
frequency been presented by Clifford M. Krowne[9,10] as:
2 a 2b
Where 2b is a length of the patch antenna, a is a radius of
the cylinder, 2θ is the angle bounded the width of the patch,
ε represents electric permittivity and µ is the magnetic per-
meability as shown in Figure 4.
Figurer 4. Geometry of cylindrical-rectangular patch antenna.
Joseph A. et al, presented an approach to the analysis of
microstrip antennas on cylindrical surface. In this approach,
the field in terms of surface current is calculated, while
considering dielectric layer around the cylindrical body. The
assumption is only valid if radiation is smaller than stored
energy. Kwai et al. gave a brief analysis of a thin
cylindrical-rectangular microstrip patch antenna which in-
cludes resonant frequencies, radiation patterns, input im-
pedances and Q factors. The effect of curvature on the cha-
racteristics of TM
modes is also presented in
Kwai et al. paper. The authors first obtained the electric
field under the curved patch using the cavity model and
then calculated the far field by considering the equivalent
magnetic current radiating in the presence of cylindrical
surface. The cavity model, used for the analysis is only va-
lid for a very thin dielectric. Also, for much small thickness
than a wavelength and the radius of curvature, only TM
modes are assumed to exist. In order to calculate the radia-
tion patterns of cylindrical-rectangular patch antenna. The
authors introduced the exact Green’s function approach.
Using Equation (4), they obtained expressions for the far
zone electric field components E
as a functions of
Hankel function of the second kind H
. The input imped-
ance and Q factors are also calculated under the same con-
International Journal of Networks and Communications 2012, 2(2): 13-19 15
Based on cavity model, microstrip conformal antenna on
a projectile for GPS (Global Positioning System) device is
designed and implemented by using perturbation theory is
introduced by Sun L., Zhu J., Zhang H. and Peng X.
The designed antenna is emulated and analyzed by IE3D
software. The emulated results showed that the antenna
could provide excellent circular hemisphere beam, better
wide-angle circular polarization and better impedance
Nickolai Zhelev introduced a design of a small conformal
microstrip GPS patch antenna. A cavity model and
transmission line model are used to find the initial dimen-
sions of the antenna and then electromagnetic simulation of
the antenna model using software called FEKO is applied.
The antenna is experimentally tested and the author com-
pared the result with the software results. It was founded
that the resonance frequency of the conformal antenna is
shifted toward higher frequencies compared to the flat one.
The effect of curvature on a fringing field and on the re-
sonance frequency of the microstrip printed antenna is stu-
died in . Also, the effect of curvature on the perfor-
mance of a microstrip antenna as a function of temperature
is introduced in [16, 17].
3. Input Impedance
The input impedance is defined as “the impedance pre-
sented by an antenna at its terminals” or “the ratio of the
voltage current at a pair of terminals” or “the ratio of the
appropriate components of the electric to magnetic fields at
a point”. The input impedance is a function of the feeding
position as we will see in the next few lines.
To get an expression of input impedance Z
for the cy-
lindrical microstrip antenna, we need to get the electric field
at the surface of the patch. In this case, we can get the wave
equation as a function of excitation current density J as fol-
By solving this Equation, the electric field at the surface
can be expressed in terms of various modes of the cavity
is the amplitude coefficients corresponding to the
field modes. By applying boundary conditions, homogene-
ous wave Equation and normalized conditions for
can get an expression for
as shown below:
vanishes at the both edges for the length L:
vanishes at the both edges for the width W:
= 0 (8)
should satisfy the homogeneous wave Equation :
= 0 (9)
should satisfy the normalized condition:
= 1 (10)
Hence, the solution of
will take the form shown
1 = 0
The coefficient A
is determined by the excitation cur-
rent. For this, substitute Equation (11) into Equation (5) and
multiply both sides of (5) by
, and integrate over area
of the patch. Making use of orthonormal properties of
Now, let the coaxial feed as a rectangular current source
with equivalent cross-sectional area
, so, the current density will satisfy the Equation
Use of Equation (31) in (30) gives:
So, to get the input impedance, one can substitute in the
is the RF voltage at the feed point and de-
By using Equations (6), (11), (14), (16) and substitute in
(15), we can obtain the input impedance for a rectangular
microstrip antenna conformal in a cylindrical body as in the
16 Ali Elrashidi et al.: Input Impedance, VSWR and Return Loss of a Conformal Microstrip Printed Antenna
for TM01 mode Using Two Different Substrates
4. Voltage Standing Wave Ratio and
Voltage Standing Wave Ration VSWR is defined as the
ration of the maximum to minimum voltage of the antenna.
The reflection coefficient ρ define as a ration between inci-
dent wave amplitude V
and reflected voltage wave ampli-
, and by using the definition of a voltage reflection
coefficient at the input terminals of the antenna Γ, as shown
is the characteristic impedance of the antenna.
If the Equation is solved for the reflection coefficient, it is
found that, where the reflection coefficient ρ is the absolute
vale of the magnitude of Γ,
The characteristic can be calculated as in ,
where : L is the inductance of the antenna, and C is the
capacitance and can be calculated as follow:
Hence, we can get the characteristic impedance as shown
The return loss s
is related through the following Equa-
For the range of 2-5 GHz, the dominant modes are TM
for h<<W which is the case. In this paper we
concentrate on TM
. Also, for the antenna operates at the
ranges 2.12 and 4.25 GHz for two different substrates we
can use the following dimensions; the original length is 20
mm, the width is 23 mm and for different lossy substrate we
can get the effect of curvature on the effective dielectric
constant and the resonance frequency.
Two different substrate materials K-6098 Teflon/Glass
and Epsilam-10 Ceramic-Filled Teflon are used for verify-
ing the new model. The dielectric constants for the used
materials are 2.5 and 10 respectively with a tangent loss
0.002 and 0.004 respectively.
5.1. K-6098 Teflon/Glass Substrate
Figure 5 shows the effect of curvature on resonance fre-
quency for a TM
mode. The frequency range of resonance
frequency due to changing in curvature is from 4.25 to
4.27 GHz for a radius of curvature from 6 mm to flat an-
tenna. So, the frequency is shifted by 20 MHz due to
changing in curvature.
Figure 5. Resonance frequency as a function of curvature for flat and
The mathematical for input impedance, real and imagi-
nary parts for a different radius of curvatures are shown in
Figures 6 and 7. The peak value of the real part of input
impedance is almost 270 Ω at frequency 4.688 GHz which
gives a zero value for the imaginary part of input impedance
as shown in Figure 7 at 20 mm radius of curvature. The
value 4. 287 GHz represents a resonance frequency for the
antenna at 20 mm radius of curvature.
Figure 6. Real part of the input impedance as a function of frequency for
different radius of curvatures.
International Journal of Networks and Communications 2012, 2(2): 13-19 17
Figure 7. Imaginary part of the input impedance as a function of
frequency for different radius of curvatures.
Figure 8. VSWR versus frequency for different radius of curvatures.
VSWR is given in Figure 8. It is noted that, the value of
VSWR is almost 1.95 at frequency 4.287 GHz which is
very efficient in manufacturing process. It should be be-
tween 1 and 2 for radius of curvature 20 mm. The minimum
VSWR we can get, the better performance we can obtain as
shown clearly from the definition of VSWR.
Figure 9. Return loss (S11) as a function of frequency for different
radius of curvatures.
Return loss (S11) is illustrated in Figure 9. We obtain a
very low return loss, -7.6 dB, at frequency 4.278 GHz for
radius of curvature 20 mm.
5.2. Epsilam-10 Ceramic-Filled Teflon
Figure 10 shows the effect of curvature on resonance
frequency for a TM
mode. The frequency range of reson-
ance frequency due to changing in curvature is from 2.11 to
2.117 GHz for a radius of curvature from 6 mm to flat an-
tenna. So, the frequency is shifted by 7 MHz due to chang-
ing in curvature.
Figure 10. Resonance frequency as a function of curvature for flat and
Input impedance, real and imaginary parts for a different
radius of curvatures are shown in Figures 11 and 12. The
peak value of the real part of input impedance is almost 200
Ω at frequency 2.125 GHz which gives a zero value for the
imaginary part of input impedance as shown in Figure 12 at
20 mm radius of curvature. The value 2.125 GHz represents
a resonance frequency for the antenna at 20 mm radius of
Figure 11. Real part of the input impedance as a function of frequency
for different radius of curvatures.
VSWR is given in Figure 13. It is noted that, the value of
VSWR is almost 1.4 at frequency 2.125 GHz which is very
efficient in manufacturing process. It should be between 1
and 2 for radius of curvature 20 mm.
Return loss (S11) is illustrated in Figure 14. We obtain a
very low return loss, -12 dB, at frequency 2.125 GHz for
radius of curvature 20 mm.
18 Ali Elrashidi et al.: Input Impedance, VSWR and Return Loss of a Conformal Microstrip Printed Antenna
for TM01 mode Using Two Different Substrates
Figure 12. Imaginary part of the input impedance as a function of
frequency for different radius of curvatures.
Figure 13. VSWR versus frequency for different radius of curvatures.
Figure 14. Return loss (S11) as a function of frequency for different
radius of curvatures.
The effect of curvature on the input impedance, return
loss and voltage standing wave ratio of conformal micro-
strip antenna on cylindrical bodies for TM
mode is studied
in this paper. Curvature affects the fringing field and fring-
ing field affects the antenna parameters. The Equations for
real and imaginary parts of input impedance, return loss,
VSWR and electric and magnetic fields as functions of
curvature and effective dielectric constant are derived.
By using these derived equations, we introduced the re-
sults for different dielectric conformal substrates. For the
two dielectric substrates, the decreasing in frequency due to
increasing in the curvature is the trend for all materials and
increasing the radiation pattern for electric and magnetic
fields due to increasing in curvature is easily noticed.
We conclude that, increasing the curvature leads to in-
creasing the effective dielectric constant, hence, resonance
frequency is increased. So, all parameters are shifted toward
increasing the frequency with increasing curvature. The
shift in frequency is 20 MHz and 7 MHz for K-6098 Tef-
lon/Glass and Epsilam-10 Ceramic-Filled Teflon respec-
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