Analysis of Aperture Coupled Microstrip Antenna with Circular Polarization Diversity

Wireless Pers Commun (2011) 56:301–314DOI 10.1007/s11277-009-9833-x

Analysis of Aperture Coupled Microstrip Antennawith Circular Polarization Diversity

Mohamed Elhefnawy · Widad Ismail

Published online: 9 October 2009© Springer Science+Business Media, LLC. 2009

Abstract The circular polarization diversity with the square patch microstrip antenna wasobtained by the implantation of the quadrature hybrid as a microstrip feed line. The smallsize antenna is achieved by using the aperture coupled structure. The analysis of an aperture-coupled microstrip antenna (ACMSA) based on the cavity model theory is presented in thispaper. The cavity model has been used to design an ACMSA and determine the relationshipbetween the input impedance of the ACMSA and the position of the aperture. The matlab andthe Advanced Design Software have been used for designing and simulating the ACMSA.There is a good agreement between the simulated and the experimental results.

Keywords Aperture coupled structure · Cavity model · Circular polarization diversity

1 Introduction

For indoor dynamic environments and applications like a real time tracking; the implemen-tation of the circular polarization is more suitable because it doesn’t require an alignmentbetween the transmitting and receiving antenna; but the effect of the reflection in a multipathchannel can reflect the Right Hand Circular Polarization (RHCP) wave and changes it to LeftHand Circular Polarization (LHCP) wave and vice versa [1,2]. In this case; the polarizationmismatch can degrade the signal more than 20dB [3]. Although the transmission line model(TLM) is easy to use, the cavity model has been used to analyze the aperture-coupled micro-strip antenna (ACMSA) with square patch; because the TLM is only useful for patches ofrectangular shape [4]. A circularly polarized ACMSA which excited by a symmetrical cross-slot has been previously analyzed in [5] using a cavity model. In this paper; the quadraturehybrid has been used as a feeder for obtaining circular polarization diversity with a microstripantenna [6]; but this feeding using a quadrature hybrid results in large antenna size. In order

M. Elhefnawy (B) · W. IsmailSchool of Electrical and Electronic Engineering, Universiti Sains Malaysia,14300 Nibong Tebal, Seberang Perai Selatan, Pulau Pinang, Malaysiae-mail: [email protected]

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302 M. Elhefnawy, W. Ismail

to minimize the antenna size; the microstrip antenna has been fed by a quadrature hybridthrough two orthogonal apertures; the position of these apertures has been determined basedon a cavity model theory. The cavity model theory has been started with Maxwell’s equationsthen followed by the solution of the homogeneous wave equations; finally ended up with theeigenfunction expansion for the calculation of the input impedance. Although this approachis not new; but up to our knowledge before this paper it hasn’t been used for analyzing theACMSA with square patch and fed by a quadrature hybrid.

2 The Cavity Model Theory

2.1 Resonant Frequency

The cavity model is based on treating the microstrip antennas as cavities formed by micro-strip lines as shown in Fig. 1. The region between the patch and ground plane may be treatedas a cavity bounded by electric walls above and below, and magnetic walls along the edges.The fields inside the antenna are assumed to be the fields inside of this cavity. Due to anelectrically thin substrate the fields in the interior region do not vary with z. Also inside thecavity the electric field has only a z component (Ez) and the magnetic field has Hx and Hy

components [4]. Figure 1 shows the cavity model of the ACMSA.The magnetic field H inside the cavity volume can be developed by Maxwell’s equations

[5]:

∇ × H = Je + jωεoεrE (1)

∇ × H =

∣∣∣∣∣∣∣

∧x

∧y ∧

z∂∂x

∂∂y

∂∂z

Hx Hy 0

∣∣∣∣∣∣∣

(2)

+ + + + +

h

x

z y

Aperture

Square patch

La

BoundedCavity

Microstrip feed-line

Ground plane

+ + + + + - - - - -

- - - - -

h

Fig. 1 Cavity model of the ACMSA

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Analysis of Aperture Coupled Microstrip Antenna with Circular Polarization Diversity 303

∇ × H =(∂Hy

∂x− ∂Hx

∂y

)∧z (3)

∇ × (∇ × H) =

∣∣∣∣∣∣∣∣

∧x

∧y ∧

z∂∂x

∂∂y

∂∂z

0 0(∂Hy∂x − ∂Hx

∂y

)

∣∣∣∣∣∣∣∣

(4)

∇ × (∇ × H) =(

∂2Hy

∂x∂y− ∂2Hx

∂y2

)

∧x +

(

∂2Hx

∂x∂y− ∂2Hy

∂x2

)

∧y (5)

∇ × (Je + jωεoεrE) = (

jωεJmx + ω2μεHx) ∧

x + (

jωεJmy + ω2μεHy) ∧

y (6)

K = ω√με (7)

where K is the propagation constant inside the cavity. Equations (8) and (9) are obtained bysubstituting the right hand side of Eq. (5) into the left hand side of Eq. (6);

∂2Hy

∂x∂y− ∂2Hx

∂y2 − K2Hx = jωεJmx (8)

∂2Hx

∂x∂y− ∂2Hy

∂x2 − K2Hy = jωεJmy (9)

In order to solve Eq. (8), the cavity model assumes that the tangential magnetic field iszero, so that Jmx equals to zero.

∂2Hy

∂x∂y− ∂2Hx

∂y2 − K2Hx = 0 (10)

Letting the Eigen functions of the homogeneous wave Eq. (10) be �mn and Kmn be theeigenvalue of K. The value of Kmn can be obtained from Eq. (11) as indicated in “AppendixA”.

K2mn = K2

m + K2n (11)

The resonance frequency of (m, n) mode can be obtained by Eq. (12);

fmn = cKmn

2π√εr

(12)

where c is the speed of light, εr is the relative dielectric constant.

2.2 Magnetic field component in x direction

The solutions of Eq. (8) can be expressed in the following eigenfunction expansion form [5];

Hx =∑

mn

βx,mnψx,mn (13)

where βx,mn is the mode coefficients and given by (see “Appendix B”)

βx,mn = jωε

(K2mn − K2)K2

n

Wa∫

0

La∫

0

Jmx.ψ∗x,mndxdy (14)

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La

Y1

l

x

X1

Jmx

Wa

Aperture

Square patch

Microstrip feed line

y

Fig. 2 Position of the aperture which parallel to x axis

the propagation constant (K) in Eq. (14) is replaced by the effective propagation constant(Keff ) because the losses of the cavity are included [7,8].

K2eff = ω2μεo

(

εr

(

1 − j

Q

))

(15)

where Q is the quality factor. It is assumed that the electric field distribution in the aperturewhich parallel to x axis (Eay) is in the form of a single piece-wise sinusoidal mode [9]; thedistance from the square patch edge to the center of the aperture and parallel to the aperturelength (La) is defined as X1; Y1 is the distance from the square patch edge to the center ofthe aperture and parallel to the aperture width (Wa) as shown in Fig. 2.

Eay = Vox

Wa

sin[

Ka

(La2 − (X1 − x)

)]

sin(

KaLa2

) X1 − La

2≤ x ≤ X1 (16)

Eay = Vox

Wa

sin[

Ka

(La2 − (x − X1)

)]

sin(

KaLa2

) X1 ≤ x ≤ X1 + La

2(17)

Vox is the voltage at the middle of the aperture parallel to the x axis. Ka is the wave numberof the aperture [10]. The magnetic current in the aperture parallel to x axis given by [5,8]:

Max = −2Eay (18)

The corresponding current density Jmx is given by:

Jmx = −2Eay

h(19)

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Fig. 3 Position of the aperturewhich parallel to y axis

l

X2

Aperture

Square patch Y2

Microstripfeed line Jmy

x

y

By substituting for Jmx from Eq. (19) into Eq. (14) the modes coefficients βx,mn aredetermined; then the magnetic field Hx in the cavity is given by:

Hx =∑

mn

Amnβx,mnKn cos(Kmx) sin(Kny) (20)

2.3 Magnetic field component in y direction

The eigenfunction expansion for the magnetic field component in y direction Hy has beenused for solving Eq. (9) [5];

Hy =∑

mn

βy,mnψy,mn (21)

Figure 3 shows the aperture which parallel to y axis; the electric field distribution in axis(Eax) can be determined using the following equations:

Eax = Voy

Wa

sin[

Ka

(La2 − (Y2 − y)

)]

sin(

KaLa2

) Y2 − La

2≤ y ≤ Y2 (22)

Eax = Voy

Wa

sin[

Ka

(La2 − (y − Y2)

)]

sin(

KaLa2

) Y2 ≤ y ≤ Y2 + La

2(23)

where Voy is the voltage at the middle of the aperture parallel to the y axis. The correspondingcurrent density Jmy is given by:

Jmy = −2Eax

h(24)

The modes coefficients βy,mn are obtained by;

βy,mn = jωε

(K2mn − K2)K2

m

La∫

0

Wa∫

0

Jmy.ψ∗y,mndxdy (25)

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The magnetic field Hy in the cavity is given by:

Hy =∑

mn

Amnβy,mnKm sin(Kmx) cos(Kny) (26)

2.4 Input Impedance

If the aperture is parallel to x direction; the admittance of the patch can be obtained by thefollowing equation [5,11]:

Yx,ant =∫ ∫ ∫

VHxJ∗

mxdV

|Ezh|2 (27)

where V is the volume occupied by the source within which the magnetic currents exist. Theelectric field Ez inside the cavity is determined based on Eqs. (1) and (3) as the following:

Ez = 1

jωε

(∂Hy

∂x− ∂Hx

∂y

)

(28)

But the admittance of the patch in case of the aperture is parallel to y direction can beobtained from Eq. (29):

Yy,ant =∫ ∫ ∫

VHyJ∗

mydV

|Ezh|2 (29)

The admittance value of the aperture Yap can be obtained from the transmission line modelof the aperture by considering the aperture as two short circuited slot lines [7].

Yap = −2j

Zcacot

(

KaLa

2

)

(30)

where Zca, La are, respectively, the characteristic impedance, the length of the aperture. Theinput impedance of the ACMSA is given by:

Zin = n2

Yx,ant + Yap+ n2

Yy,ant + Yap(31)

The open microstrip stub line (Los) is used for forcing the imaginary part of the inputimpedance to be zero, Los is obtained by;

Los = 1

KFcot−1

(imaginary(Zin)

2ZF

)

(32)

The input impedance of the ACMSA with the open microstrip stub line is given by;

Zin_stub = n12

Yx,ant + Yap+ n12

Yy,ant + Yap− 2jZF cot(KFLos) (33)

ZF and KF, are, respectively, the characteristic impedance and the wave number of themicrostrip feed line; n1 is the transformation ratio which describes the coupling between themicrostrip feed line and the patch [5,10].

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3 Circular Polarization Diversity with ACMSA

The electric field component in x direction (Ex) is generated by putting an aperture parallel toy axis; also the electric field component in y direction (Ey) is obtained by putting an apertureparallel to x axis as shown in Fig. 4. The circular polarization diversity requires the phaseshift between Ex and Ey to be ±90

◦. By using the quadrature hybrid as a feeder for the square

patch microstrip antenna the circular polarization diversity can be achieved. When the right

Fig. 4 Circular polarizationdiversity with ACMSA

x

y

Square patch

Jmy

Jmx

Ey

Ex

z

LHCP

RHCP Quadrature hybrid

Fig. 5 Geometry of the proposed ACMSA

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port of the hybrid is selected; Ex will lead Ey by 90◦

and the Right Hand Circular PolarizationRHCP is generated as indicated in Eq. (34) [11];

ERHCP = Ex cos(ωt − Koz)∧x + Ey cos(ωt − Koz − 90)

∧y (34)

where Ko is the propagation constant in free space. If the left port of the hybrid is selected; Ex

will lag Ey by 90◦

and the Left Hand Circular Polarization LHCP is generated as given by;

ELHCP = Ex cos(ωt − Koz − 90)∧x + Ey cos(ωt − Koz)

∧y (35)

4 Results

The geometry of the proposed ACMSA with a circular polarization diversity at resonantfrequency 2.437 GHZ is shown in Fig. 5, the square patch is printed on Rogers’s substrate(patch substrate) with a thickness h = 0.85 mm, a loss tangent = 0.0021 and a dielectric

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035-40

-20

0

20

40

60

80

X1 (m)

Inpu

t im

peda

nce

(Ohm

s)

Input impedance imaginary part of the ACMSA .

Input impedance real part of the ACMSA.

Fig. 6 Input impedance of the ACMSA without Los

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

-40

-20

0

20

40

60

X1 (m)

Inpu

t im

peda

nce

(Ohm

s)

Input impedance imaginary part of the ACMSA.

Input impedance real part of the ACMSA.

Fig. 7 Input impedance of the ACMSA with Los

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constant εr = 3.38; from Eq. (11) and ADS optimization the length of the square patch is31.599 mm. The quadrature hybrid is printed on the Roger’s substrate (feed substrate) whichhas the same parameters likes the patch substrate. The ground plane exists in between thepatch substrate and the feed substrate. There are two apertures with the same dimension areprinted on the ground plane; one aperture is parallel to x axis and the other aperture is parallelto y axis. The length and the width of the aperture are 16 and 1.7 mm, respectively.

Figure 6 shows the input impedance of the ACMSA without the implementation of theopen microstrip stub line (Los); in this case the input impedance imaginary part of theACMSA equals to 42.86 . The length of the open microstrip stub line is determined basedon Eq. (32) in order to force the input impedance imaginary part of the ACMSA to be zero.Figure 7 shows the input impedance of the ACMSA with Los equals to 12.7 mm. Equation(33) indicates that the input impedance of the ACMSA is a function of the aperture dimen-sions, the square patch length, the substrate parameters, Los, and the position of the aperture.

1400 1600 1800 2000 2200 2400 2600 2800 3000-60

-50

-40

-30

-20

-10

0

Frequency (MHZ)

Mag

. [dB

]

Simulated S11

Measured S11

Fig. 8 Return loss versus frequency when the right port of the quadrature hybrid is selected

Fig. 9 Measured powerradiation pattern when the rightport of the quadrature hybrid isselected at 2.437 GHZ

Right Port

0°

15°

30°

45°

60°75°90°105°

120°

135°

150°

165°

±180°

-165°

-150°

-135°

-120°-105° -90° -75°

-60°

-45°

-30°

-15°

-40-30-20-100

RHCPLHCP

123


This paper emphasizes on the relation between the input impedance of the ACMSA and theposition of the aperture; this relationship gives us the ability to change the position of theaperture in order to minimize the size of the ACMSA without loss of the input and the outputmatching of the microstrip antenna.

The value of Y1 and X2 is the same; this value has been selected so that the quadraturehybrid could be placed at a further distance into the square patch; this helps to minimize theACMSA dimensions. Figure 7 shows the input impedance of the ACMSA as a function ofX1 when the value of Y1 and X2 equals to 26.548 mm. The input impedance real and theimaginary parts of the ACMSA are close to 50, zero respectively; when X1 equals to 5.688mm. Y2 equals to 5.688 mm by symmetry.

The above results for X1, X2, Y1, Y2 have been obtained using the matlab simulation;then these results have been optimized using ADS as shown in Fig. 5.

If the right port of the quadrature hybrid is selected the return loss versus frequency andthe measured power radiation pattern of the ACMSA are shown in Figs. 8 and 9 respectively;but if the left port of the quadrature hybrid is selected the return loss versus frequency and the

1400 1600 1800 2000 2200 2400 2600 2800 3000-50

-40

-30

-20

-10

0

Frequency (MHZ)

Mag

. [dB

]

Simulated S22

Measured S22

Fig. 10 Return loss versus frequency when the left port of the quadrature hybrid is selected

Fig. 11 Measured powerradiation pattern when the leftport of the quadrature hybrid isselected at 2.437 GHZ

Left Port

0°

15°

30°

45°

60°75°90°105°

120°

135°

150°

165°

±180°

-165°

-150°

-135°

-120°-105° -90° -75°

-60°

-45°

-30°

-15°

-40-30-20-100

LHCPRHCP

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Fig. 12 Fabricated patchsubstrate

Fig. 13 Fabricated feed substrate

measured power radiation pattern of the ACMSA are shown in Figs. 10 and 11, respectively.Figures 12 and 13 shows the fabricated patch substrate and feed substrate of the ACMSA,respectively.

5 Conclusion

Circular polarization diversity can be generated by coupling the quadrature hybrid to thesquare patch through two apertures. The input impedance of the ACMSA is a function of theaperture dimensions, the square patch length, the substrate parameters, Los, and the positionof the aperture. The aperture coupled structure minimized the size of the microstrip antennawhich feeded by the quadrature hybrid. The analysis of the ACMSA using a cavity model iscomparable with a full-wave analysis and the experimental results.

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Appendix A

∂2ψy,mn

∂x∂y− ∂2ψx,mn

∂y2 − K2mnψx,mn = 0 (36)

ψx,mn = AmnKn cos(Kmx) sin(Kn y) (37)

ψy,mn = −AmnKm cos(Kn y) sin(Kmx) (38)

where the value of Amn depends on the cavity resonant modes [4]; for a non radiating cavity

Km = mπ

l, Kn = nπ

l(39)

∂ψy,mn

∂x= −AmnK2

m cos(Kny) cos(Kmx) (40)

∂2ψy,mn

∂x∂y= AmnK2

mKn sin(Kny) cos(Kmx) (41)

∂ψx,mn

∂y= AmnK2

n cos(Kmx) cos(Kny) (42)

∂2ψx,mn

∂y2 = −AmnK3n cos(Kmx) sin(Kny) (43)

AmnK2mKn sin(Kny) cos(Kmx)+ AmnK3

n sin(Kny) cos(Kmx)

= K2mnAmnKn sin(Kny) cos(Kmx) (44)

K2mn = K2

m + K2n (45)

Appendix B

∂2Hy

∂x∂y=

∑

mn

βy,mn∂2ψy,mn

∂x∂y(46)

∂2Hx

∂y2 =∑

mn

βx,mn∂2ψx,mn

∂y2 (47)

By substituting from Eqs. (46) and (47) into Eq. (8) the following Equation is obtained:

∑

mn

βy,mn∂2ψy,mn

∂x∂y−

∑

mn

βx,mn∂2ψx,mn

∂y2 − K2∑

mn

βx,mnψx,mn = jωεJmx (48)

∂2ψx,mn

∂x∂y− ∂2ψx,mn

∂y2 = K2mnψx,mn (49)

∑

mn

βy,mn =∑

mn

βx,mn (50)

By substituting from Eqs. (49) and (50) into Eq. (48), the Eq. (51) is obtained [12]:∑

mn

βx,mnK2mnψx,mn −

∑

mn

βx,mnK2ψx,mn = jωεJmx (51)

∑

mn

βx,mn(K2mn − K2)

l∫

0

l∫

0

ψx,mn.ψ∗x,mndxdy = jωε

Wa∫

0

La∫

0

Jmx.ψ∗x,mndxdy (52)

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where ψ∗x,mn is the complex conjugate of ψx,mn

l∫

0

l∫

0

ψx,mn.ψ∗x,mndxdy = K2

n (53)

Acknowledgments We would like to express our thanks to Mr. Mohamadariff Othman and Mr. Abdul LatipAbdul Hamid for their help.

References

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Author Biographies

Mohamed Elhefnawy received the Bachelor’s degree in Electricalengineering from the Tanta University, Egypt, in 1999 and the Mas-ter degree in Electronics and Communications engineering from ArabAcademy for Science and Technology, Egypt, in 2005. From 2002 to2006 he worked with the Telecom Egypt Company as Telecom engi-neer. He is now a Research Assistant pursuing the PhD degree inthe School of Electrical & Electronic Engineering at USM University,Malaysia. His research interests include wireless systems, electromag-netic waves and antennas, RF system, digital signal processing andmodulation techniques.

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http://dx.doi.org/10.1109/22.808966


Widad Ismail received BEng (Hons) in Electronics and Communica-tions Engineering, University of Huddersfield, United Kingdom, July1999 and PhD in Electrical and Electronics Engineering, University ofBirmingham, United Kingdom, January 2004. From 2004 to presentshe is a senior lecturer at School of Electrical and Electronics Engineer-ing, University Sains Malaysia. Her research interests include ActiveIntegrated Antennas (AIA), RF systems, Wireless systems; MicrowaveEngineering, Signal Processing (Noise Measurements).

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Analysis of Aperture Coupled Microstrip Antenna with Circular Polarization Diversity

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