A Circularly Polarized Rectangular Patch Antenna on a ... - IJMOT

INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY VOL. 3, NO. 4, SEPTEMBER 2008

A Circularly Polarized Rectangular Patch Antenna on a Cylindrical Surface Reena Pant*, Pradyot Kala1, S. S. Pattnaik2 and R. C. Saraswat3 *Department of Electronics & Instrumentation Engineering, M J P Rohilkhand University, Bareilly-INDIA. Email: [email protected] 1 Department of Electronics & Communication Engineering, A. A. I. Deemed University, Allahabad-INDIA Email: [email protected] 2 Department of Electronics & Communication Engineering, NITTTR, Chandigarh-INDIA. Email: [email protected] 3 Department of Electronics & Communication Engineering, S.G.S.I.T.S., Indore-INDIA. Email: [email protected]

Abstract: The aperture method is used to examine the effect of (i) aspect ratio and curvature on polarization, and (ii) curvature on the radiation pattern for thin substrate cylindrical rectangular microstrip antenna. Numerical computations of the Eθ and Eφ for different modes for different cylinder radii and aspect ratios have been carried out. At aspect ratio 1.038, the phase difference within the operating bandwidth is found to range from about 85.40 to 88.10. The optimal center operating frequency is 2196.5 MHz and the 3 dB bandwidth is found to be 27.7 MHz. Optimal aspect ratio decreases with an increase in the radius, and approaches a limiting value for a radius greater than about 35 cm. The half power bandwidth is almost constant with curvature radius. For a curvature radius of few wavelengths the pattern looks almost like a planar case, except for the radiation near 90o. Index Terms Patch antenna, Cylindricalrectangular patch, Circular polarization, aspect ratio, curvature effect

I. INTRODUCTION The need for small, portable antennas for mobile communications has recently spurred the study of microstrip antennas (MSA). MSA are quite flexible and have been used as conformal antennas on arbitrary curved surfaces. The characteristics of conformal MSA can be expected to differ from those of planer models. Some work has been devoted to the analysis of microstrip patch antenna mounted on cylindrical surface. This structure was first proposed by

Krowne [1]. Using a cavity model, he observed that resonant frequency changes with surface curvature. Wu et al [2], calculated the radiation patterns using cavity model in conjunction with the method of images, but this method is not applicable when the ground plane is not flat. In the paper by Fonseca and Giarola [3], the radiation from the wraparound cylindrical microstrip element was computed from a magnetic wall cavity model. In the paper by Ashkenazy et al. [4], the radiation from the wraparound and the rectangular patches was computed by assuming an electric surface current distribution on microstrip patch antenna. The paper shows an analysis of microstrip antennas on cylindrical substrates for a given current distribution on the patches. Dahele et al. [5] investigated the effect of curvature on the characteristics of rectangular patch antenna theoretically and experimentally. They found that for TM01 mode, the resonant frequency is not affected by curvature. However, as curvature increases the pattern broadens, the resonant resistance decreases, and bandwidth increases. Luk et al. [6], considered the case when the substrate thickness is much smaller than the wavelength and the radius of curvature. Based on the cavity model, they found that the resonant frequencies and electric field under the patch were not affected by curvature. However, the patterns, Q factors, and input impedances are affected. Habashy et al. [7] calculated the input impedance and radiated field from the cylindrical-rectangular and the wraparound

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elements excited by a probe using moment method. Wong and Ke [8] investigated the curvature effect on aspect ratio and circular polarization conditions for cylindrical-rectangular microstrip patch antennas. Kashiwa et al. [9] calculated the rectangular microstrip patch antennas mounted on the curved surface wave analyzed using curvilinear FD-TD method. In this work, the aperture method is used to analyze a circularly polarized rectangular microstrip patch antenna, mounted on a cylindrical structure. Section II of this paper describes the theoretical approach, based on the common assumption that the cylinder is infinite in the axial direction and that the patch is infinitesimally thin. Once the electric field vector generated by the different slots is found, the characteristics of the antenna, such as axial ratio, phase difference, and radiation patterns can be calculated.

II. FORMULATION

In order to calculate the far-zone fields, we model the probe feed to be a ρ directed unit amplitude current ribbon. In this case the electric fields under the curved patch have only Eρ component, which is independent of ρ and is given by [5]  mπ (φ − φ1 ) cos nπ x  E ρ = jωµ o ∑ C mn cos  m ,n  2ψ   L 

(1) The analysis begins by considering the radiation from the elemental area which is a part of some arbitrary aperture bounded by the curve S. Here the elemental area being analyzed are basically fringing slots and excited by electric fields at the slots. It is convenient to use electric field vector F .

ε M e − jkr F= ds 4π ∫s r1 1

(2)

where

The geometry of the cylindricalrectangular microstrip antenna is shown in Fig. 1-2. The dimension of the straight edge is L and that of the curved edge is W [=2(R+h)ψ] where R is the radius of the cylindrical and 2ψ the angle subtended by the curved edge. The thickness of the substrate is h and the permittivity is εr. The region between the patch and the cylindrical surface is considered as a cavity bounded by electric walls on the top and bottom and by magnetic walls on the sides.

M = n Χ E

(3)

ρ

where M is the magnetic surface current densities and n is the unit vector normal to the elemental area.

Z’

Feed Point X

Y

Reference line

θ

Z

Y’

α ψ

W L

R

R

Fig 1: A cylindrical-rectangular patch

Fig. 2: Cross sectional view of the patch

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Again, if only the far field is of interest, then

F=

ε e − jkr M e jkr cos ϕ ds ∫ 4π r s

aα Fα 10 =

'

(4)

∫ {e

ε e − jk r Eρ10 . 4π r

− jkR sin θ sin φ

s

where, ϕ is the angle between origin to far field line and elemental area to far field line, and r’ and r1 are distances of elemental area and the point where the potential is computed from origin respectively.

{a

y

aα Fα 10 = a x .0 + a y Fy10 + a z Fz10

Fy10 =

(10)

ε e − jkr E ρ 10 4π r

 Re − j k R sin θ sin φ .  j k sin θ cos φ x ' . ∫s  j k R [sineθ sin φ cos α ' +cos θ e 

  sin α ' dα ' dx '  sin α ' ]  

(11)

(6)

where

Fy10 =

)

y ' = R cos α ' − 1

ε e− jk r Eρ10 Re− jkR sin θ sin φ . 4π r

 kh  sin  sin θ cosφ  2 .  kh   2 sin θ cosφ 

and

z ' = R sin α '

θU

substituting the above values in (6)

(

(9)

Which may be further simplified as

ar' = a x x ' + a y y ' + a z z '

(

'

Which can be rewritten in Cartesian coordinate as

a r = a x sin θ cos φ + a y sin θ sin φ

In case of TM10 mode, only curved slots will radiate, hence the elemental area vector may be defined by

'

}

Where

(5)

'

R sin α ' + a z R cosα ' dα 'dx '

The direction of the radial position vectors are given in terms of the reference Cartesian coordinates as

+ a z cos θ

}

.e jk sin θ cos φ x .e jkR[sin θ sin φ cos α +cos θ sin α ] .

)

ar' = a x x ' + a y R cosα ' − 1 + a z R sin α '

∫e θ

[

jkR sin θ sin φ cos α ' + cos θ sin α '

(12)

] sin α 'dα '

L

(7) Similarly

So

Fz10 =

r ' cos ϕ = x ' sin θ cos φ

(

)

+ R cos α ' − 1 sin θ sin φ + R sin α ' cos θ Substituting the above values in (4)

(8)

ε e − jk r Eρ10 Re− jkR sin θ sin φ . 4π r  kh  sin  sin θ cosφ  2 . kh    2 sin θ cosφ 

θU

∫e θ

[

jkR sin θ sin φ cos α ' + cos θ sin α '

L

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(13)

] cosα 'dα '

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where θ L and θ U are the left most and right most inclination angle of the elements from the reference line which contribute on radiation. Total far field radiation for two curved slots spaced at distance L apart may be written as (14)

  kL Fz10T = 2 Fz10 cos sin θ cos φ    2

(15)

The spherical components of electric field vector generated by curved and straight slots can be obtained by rectangular components, using the following relationships

and

Similarly considering axial (straight) slots as radiating aperture, the electric field vector in TM01 mode may be derived with some approximations (that width of the fringing slot is very small and subtend a small angle on cylinder center)

ε − jkr − jkR sin θ sin φ .e .h.e . 4π r

 kL  sin  sin θ cos φ  2 .   kL  2 sin θ cos φ  e jkR [cosψ . sin θ . sin φ + sin ψ . cos θ ]

Fθ = (Fx cos φ + Fy sin φ )cos θ − Fz sin θ

(19)

and

Fφ = − Fx sin φ + Fy cos φ

(20)

In XY plane, θ = π / 2

Fθ = − Fz

For slot 1,

Fx 01 _ 1 =

(18)

cos(kR sin ψ . cos θ )

  kL = 2 Fy10 cos sin θ cos φ    2

Fy10T

  kL sin  sin θ cos φ   2 Fx10T kL    2 sin θ cos φ    jkR cos ψ . sin θ . sin φ − jkR sin θ sin φ .e .e .

ε .e − jkr .h. = 2. 4π r

(21)

and

Fφ = − Fx sin φ + Fy cos φ (16)

(22)

Similarly, in ZY plane φ = π / 2

Fθ = Fy cos θ − Fz sin θ

(23)

and

and for slot 2

Fx 01 _ 2 =

Fφ = − Fx

ε − jkr − jkR sin θ sin φ .e .h.e . 4π r

 kL  sin  sin θ cos φ  2 .   kL  2 sin θ cos φ  e jkR [cosψ . sin θ . sin φ − sin ψ . cos θ ]

(24)

Using the above equations, one may calculate Eθ and Eφ for TM10 and TM 01 modes.

(17)

Therefore the total electric field vector in TM01 mode can be expressed as

For circular polarization excitation, the feed position is selected to be on the diagonal line, and the operating frequency is also chosen to be between f01 and f10, the two lowest resonant frequencies of the cylindrical-rectangular patch where the dimensions 2(R+h)ψ and L are approximately the same. The radiation field

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Eθ = Eθ 1 + Eθ 2

(25)

110 100

Phase Difference (Degree)

from the patch can be obtained by superposing the radiation from four equivalent slots along its edges (two straight and two curved) and located at a height h above the ground plane. Thus the total far zone electric fields are then given by

90 80 70 60

Eφ = Eφ 1 + Eφ 2

(26)

50

2185 2185 Wong & Ke 2195 2195 Wong & Ke 2205 2205 Wong & Ke

40

In order to produce circularly polarized radiation the two conditions need to be satisfied are

30 20 10

∠ E θ − ∠ E φ = ±90 o

Aspect Ratio

(27)

0 1.01 1.015 1.02 1.025 1.03 1.035 1.04 1.045 1.05

Fig. 3: Variation of the phase difference ∠Eθ - ∠Eφ with the aspect ratio for different frequencies, f = . 2185, 2195, and 2205 MHz.

and

Eθ = Eφ

(28) 8

III. RESULTS AND DISCUSSION

Fig. 4 compares the axial ratio vs frequency graph obtained by aperture theory with that from modal-expansion theory. It is observed that for the given patch dimensions the optimal center operating frequency is 2196.5 MHz and the 3 dB bandwidth is found to be 27.7 MHz which is very near to the results of Wong and Ke [8].

Axial Ratio [dB]

Numerical computations of the Eθ and Eφ for different modes for different cylinder radii and aspect ratios have been carried out. Initially the results from formulations are compared with those from [8], for a cylindrical-rectangular microstrip antenna. The phase difference vs aspect ratio is shown in Fig. 3, it is found that at aspect ratio a = 1.038, the phase difference within the operating bandwidth are found to range from about 85.40 to 88.10 and a good match is observed. Asymmetrical nature of the graph is also observed, which is probably due to the curvature effect.

6

4

2

Aperture Theory Wong & Ke

0 2170

2190 2210 Frequency [MHz]

2230

Fig. 4: Variation of axial ratio with operating frequency.

Fig. 5 shows the dependence of the optimal aspect ratio on the curvature radius R. it is observed that it decreases with an increase in the radius R, and approaches a limiting value of a = 1.037 for a radius greater than about 35 cm. The calculated results are compared with results of Wong and Ke [8] and the agreement is very good.

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The variation of center operating frequency varies with curvature radius and found that it increases with an increase in the radius, R, as shown in Fig. 6. Its limiting value is about 2201.7 MHz for R > 40 cm and a very good match is observed [8].

1.05

Aspect Ratio

1.04

1.03

Aperture theory Wong & Ke

1.02

R (cm )

1.01 5

10

15

20

25

30

35

40

45

50

It is also observed (Fig. 7) that the half power bandwidth is almost constant with curvature radius (27.7 MHz for R= 5 cm and 28.3 MHz for planar surface). The variation is nearly 0.6 MHz and basically due to change in effective width (curved) with curvature.

Fig. 5: Variation of optimal aspect ratio with curvature radius. 0 0

10

20

30

40

50

60

70

80

90

-3 2225

2215

2205

2195

2185

-9 -12 -15 -18 -21 -24

Radius [ in cm ]

2175 0

10

20

30

Relative power [dB]

Resonant Frequency [MHz]

-6

E(theta) R= 5 cm E(theta) R= 5 cm Luk et al E(theta) plane surface E(theta) plane surface Luk et al E(phi) R=5 E(phi) R=5 Luk et al E(phi) plane surface

40

50

Fig. 6: Variation of resonant frequency with aperture radius

-27 -30

E(phi) plane surface Luk et al

Angle (degree)

Fig. 8: Radiation pattern in XY plane [E(theta)] and YZ plane[E(phi)] for TM10 mode with patch parameters of [6].

[ in MHz ]

50

40

30

Bandwidth

20

10

Aperture theory Wong & Ke Radius [ in cm ]

0 0

10

20

30

40

50

Fig. 7: Variation of beamwidth with aperture radius

Figs. 8 and 9 show the radiation patterns in two orthogonal planes i.e., XY-plane and YZplane of cylindrical-rectangular antenna as a function of curvature radius for both TM10 and TM01 modes. It is observed that for a curvature radius of few wavelength the pattern looks almost like a planar case, except for the radiation near 90o. The analytical results presented here differ slightly for Eφ in TM10 and TM01 modes but good agreement is observed over a wide range of angles (which is greater than half power beamwidth) to those reported earlier [6]. The

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disagreement in the deep shadow region is due to the surface waves, which is ignored in our simplified approximate calculation.

0 -5

-10

-15

-20

-25

Related Power in dB

0 20

40

60

REFERENCES 1.

C. M. Krowne, "Cylindrical-rectangular microstrip antenna," IEEE Trans. Antennas Propagat., vol. Ap31, pp. 194-199, January 1983.

2.

K. Y. Wu and J. F. Kaufman, "Radiation pattern computations for "Cylindrical-rectangular microstrip antenna," IEEE Antennas Propagat. Soc. Int. Symp. Dig., pp. 39-42, 1983.

3.

S. B. Fonseca and A. J. Giarola, "Analysis of microstrip wraparound antennas using dyadic Green's functions," IEEE Trans. Antennas Propagat., vol. Ap31, pp. 248-253, 1983.

4.

J. Ashkenazy, S. Shtrikman, and D. Treves, "Electric surface current model for the analysis of microstrip antennas on cylindrical bodies," IEEE Trans. Antennas Propagat., vol. Ap-48, pp. 295-300, March 1985.

5.

J. S. Dahele, R. J. Mitchell, K. M. Luk, and K. F. Lee, "Effect of curvature on characteristics of rectangular patch antenna," Electron. Lett., vol. 23, pp. 748-749, July 1987.

6.

K. M. Luk, K. F. Lee, and J. S. Dahele, "Analysis of cylindrical-rectangular microstrip patch antenna," IEEE Trans. Antennas Propagat., vol. Ap-38, pp. 143147, February 1989

7.

T. M. Habashy, S. M. Ali, and J. A. Kong, "Input impedance and radiation pattern of cylindricalrectangular and wraparound microstrip antennas," IEEE Trans. Antennas Propagat., vol. Ap-38, pp. 722731, May 1990.

8.

K. L. Wong and S. Y. Ke, "Cylindrical-rectangular microstrip antenna for circular polarization," IEEE Trans. Antennas Propagat., vol. Ap-41, pp. 246-249, February 1993.

9.

T. Kashiwa, T. Onishi, and I. Fokai, "Analysis of microstrip antennas on a curved surface using a conformal grids FD-TD method," IEEE Trans. Antennas Propagat., vol. Ap-42, pp. 423-427, March 1994.

80

E(theta) R= 5 cm E(theta) R= 5 cm Luk et al E(theta) plane surface E(theta) plane surface Luk et al E(phi) R=5 E(phi) R=5 Luk et al E(phi) plane surface E(phi) plane surface Luk et al E(theta) R=40 cm E(phi) R=40cm Angle in Degree

-30

Fig. 9: Radiation pattern in XY plane [E(theta)] and YZ plane[E(phi)] for TM 01 mode with patch parameters of [6].

IV. CONCLUSION In this paper, the aperture method is used to examine (i) effect of aspect ratio and curvature on polarization, and (ii) the effect of curvature on the radiation pattern for cylindrical rectangular microstrip antenna. The basic assumption is that the substrate thickness is much smaller than the radius of curvature and wavelength so that the field under the patch and the ground plane are flat. The analytical results presented here show that the calculations agree reasonably in the useful range (upto -10 db) [6]. From the above results, it can be said that the curved patch studied here with R > 40 cm can be treated as a planar patch. That is, the effect of curvature on the circular polarization characteristics of this curved patch can be neglected for R > 40 cm. Finally, the proposed method is less computational and gives good physical insight of the problem.

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