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International Journal of Networks and Communications 2012, 2(2): 13-19

DOI: 10.5923/j.ijnc.20120202.03

Input Impedance, VSWR and Return Loss of a

Conformal Microstrip Printed Antenna for

TM

01

Mode Using Two Different Substrates

Ali Elrashidi

*

, 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

01

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

01

Mode

1. Introduction

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[1], 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[2]. 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[5]. 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[6].

* Corresponding author:

aelrashi@bridgeport.edu (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-

crostrip antenna.

2. Background

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 [7], are preferred due to easy calculation

and modeling.

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-

L

W

ɛ

r

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

reff

is to be introduced. The effective dielectric constant ε

reff

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[7], as shown in Equation 1.

1

2

rr

reff

11 h

+ 1 12

22 w

εε

ε

−

+−

= +

(1)

The length of the patch is extended on each end by ΔL is

a function of effective dielectric constant ε

reff

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 [8], as in Equation 2.

( )

( )

reff

reff

w

0.3 0.264

h

0.412

w

h

0.258 0.8

h

L

ε+ +

∆

=

ε− +

(2)

The effective length of the patch is L

eff

and can be calcu-

lated as in Equation 3.

L

eff

= 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

antenna parameters.

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[9]. 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

antennas.

Effect of curvature of conformal antenna on resonant

frequency been presented by Clifford M. Krowne[9,10] as:

[ ]

22

mn

r

1m n

f

2 a 2b

2

= +

θ

µε

（ ）

(4)

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[9].

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[11]. Kwai et al. [12]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

10

and TM

01

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

θ

and E

φ

as a functions of

Hankel function of the second kind H

p

(2)

. The input imped-

ance and Q factors are also calculated under the same con-

ditions.

y

x

L

ε

r

R

z

W

ΔL

L

ΔL

h

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[13].

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

match peculiarity.

Nickolai Zhelev introduced a design of a small conformal

microstrip GPS patch antenna[14]. 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 [15]. Also, the effect of curvature on the perfor-

mance of a microstrip antenna as a function of temperature

for TM

01

and TM

10

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

in

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-

low:

1

2

2

2

+

2

2

+

2

= (5)

By solving this Equation, the electric field at the surface

can be expressed in terms of various modes of the cavity

as[15]:

(

,

)

=

(, )

(6)

where A

nm

is the amplitude coefficients corresponding to the

field modes. By applying boundary conditions, homogene-

ous wave Equation and normalized conditions for

nm

ψ

, we

can get an expression for

nm

ψ

as shown below:

1.

nm

ψ

vanishes at the both edges for the length L:

zz

0

zz

ψψ

∂∂

∂∂

L

(7)

2.

nm

ψ

vanishes at the both edges for the width W:

=

1

=

=

1

= 0 (8)

3.

nm

ψ

should satisfy the homogeneous wave Equation :

(

1

2

2

2

+

2

2

+

2

)

= 0 (9)

4.

nm

ψ

should satisfy the normalized condition:

=

1

=

1

=

=0

= 1 (10)

Hence, the solution of

nm

ψ

will take the form shown

below:

(

,

)

=

2

1

cos(

2

1

(

1

)

) cos(

) (11)

with

=

1 = 0

2 0

The coefficient A

mn

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

nm

ψ

,

one obtains:

=

2

2

(12)

Now, let the coaxial feed as a rectangular current source

with equivalent cross-sectional area

z

SS

centered at

00

,)

, so, the current density will satisfy the Equation

below:

=

0

×

0

2

0

+

2

0

2

0

+

2

0

(13)

Use of Equation (31) in (30) gives:

=

2

2

2

1

cos

2

1

0

cos

0

(

2

0

)(

2

1

0

)

(14)

So, to get the input impedance, one can substitute in the

following Equation:

in

in

0

v

Z

(15)

where

in

v

is the RF voltage at the feed point and de-

fined as:

=

(

0

,

0

)

× (16)

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

following Equation:

=

1

2

2

2

1

cos

2

2

1

0

cos

2

0

16 Ali Elrashidi et al.: Input Impedance, VSWR and Return Loss of a Conformal Microstrip Printed Antenna

for TM01 mode Using Two Different Substrates

× (

2

0

)(

2

1

0

) (17)

4. Voltage Standing Wave Ratio and

Return Loss

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

i

and reflected voltage wave ampli-

tude V

r

, and by using the definition of a voltage reflection

coefficient at the input terminals of the antenna Γ, as shown

below:

input 0

input 0

zz

r

zz

(18)

where, Z

0

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,

1

r

1

VSWR

VSWR

(19)

Consequently,

r

r

VSWR

(20)

The characteristic can be calculated as in [14],

0

c

L

Z

(21)

where : L is the inductance of the antenna, and C is the

capacitance and can be calculated as follow:

n

2

2

l

w

ah

a

π

π

C=

(22)

n

l

22

ahw

a

ππ

l=

(23)

Hence, we can get the characteristic impedance as shown

below:

0n

1

l

2

ah

a

π

Z=

(24)

The return loss s

11

is related through the following Equa-

tion:

r

11

i

v

log log

v

VSWR

s= =

VSWR

(25)

5. Results

For the range of 2-5 GHz, the dominant modes are TM

01

and TM

10

for h<<W which is the case. In this paper we

concentrate on TM

01

. 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

01

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

curved antenna.

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

01

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

curved antenna.

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

curvature.

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.

6. Conclusions

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

01

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-

tively.

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