6th International Conference on Electrical and Computer Engineering ICECE 2010, 18-20 December 2010, Dhaka, Bangladesh

Design of an X band Aperture Matched Horn Antenna by Optimization of Back-lobe and Cross-Polarization Level Sajid Muhaimin Choudhury*, Md. Gaffar, Mohammad Asif Zaman and Md. Abdul Matin† Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology Dhaka, Bangladesh * [email protected] † [email protected] Abstract— In this paper, an aperture matched horn antenna is designed for operation in the microwave X band region. A conical horn is designed first, and the effect of additional aperture matching structure is studied to find the optimum dimension of the structure. The study is performed through computer simulation by Finite Element Method. Finally, the performance of the designed horn antenna for band operation is simulated. The obtained structure through simulation provides optimum performance in terms of backlobe level and cross polarization level. Keywords— Aperture Polarization, Back Lobe

Matched

Horn

Antenna,

Cross

I. INTRODUCTION Horn antenna acts as an intermediate device for transition of electromagnetic wave propagating in a transmission line into the free space for propagation [1]. An efficient feed horn must have a nearly symmetric E and H plane pattern and a low value of S11 parameter in its operating region. A corrugated horn is perhaps most popular for the application as reflector antenna feed owing to its high aperture efficiency [2]-[3]. The corrugated structure reduces edge diffraction by spatially designed surface with corrugation placed in the interior horn walls. The operating wavelength of such horn antenna is dependent on the length and depth of corrugation. Implementing a corrugated structure with high precision is a complex process. Due to the high complexity of the structure of a corrugated horn, a simple structure was proposed by Burnside and Chuang [4]. A curved surface is added to the aperture of the horn that forms a smooth matching section between the horn aperture and free-space, and hence, termed as “Aperture Matched Horn”. A further modification to the aperture matched structure was proposed by Heedy and Burnside [5] by adding curved throat section to the Aperture Matched Horn. An appropriately designed aperture-matched horn provides superior E-plane patterns, input impedance, and frequency characteristics compared to conventional horns [4], uniform patterns across a wide beamwidth with low backlobes, low VSWR, a wide frequency response, and constant phase centre [5]. For certain applications, particularly for compact range feed antennas, aperture matched horns can be very useful. Due to the addition of aperture matching structure, the size and weight of the aperture-matched horn are increased over those of a conventional horn. The simplicity of modification

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ensures the minimal cost for modification of a conventional horn antenna. Burnside and Chuang [4] proposed arbitrary smooth convex shapes as matching sections of the horn, in such a way so that they form a smooth junction, i.e. the tangent of the matching section is parallel to the flare of the horn. Elliptic shapes were used for simplicity in numerical analysis. To use horn antennas as feed of reflector antennas, the backlobe level of it should be minimum in order to minimize the overall antenna temperature [6]. In this paper, the effect of changing the structure of the aperture matching section on the backlobe and cross polarization levels of the horn antenna is studied. Based on simulation results, an optimum aperture matched horn antenna is designed.

Fig. 1 General Structure of a aperture matched horn antenna

II. DESIGN METHOD The structure of an aperture matched horn is shown in Fig. 1. The structure is composed of a conical horn having an aperture matching section attached to it. Elliptical aperture matching structure proposed by Burnside and Chuang [4] is used. A cross-sectional view of the structure is shown in Fig. 2. The aperture matching part can be thought to be as formed by rotating an ellipse with tilted rotational axis, the axis being aligned to the flare of the conical horn. The radius of the waveguide and the flare is Awg and Ahorn respectively.

550

Awg

Cross Polarization Exp, can be readily obtained from Equation (4) after computing the effect of aperture matching section on the Eθ and Eφ components. The cross polarization becomes a function of both θ and φ. Fig. 3 shows typical copular and cross polar directivity pattern of an aperture matched horn. Co-polar directivity

Lhorn

0 -20 -40 -60

Lwg

-80

The length of the waveguide and horn is lwg and lhorn. The two radii of the ellipse forming the aperture matching section is ae and be. The studied horn is designed for X band operation. The horn operates in microwave 8.00-12.00 GHz band. In order to study the effect of adding aperture matching section, a Xband conical horn is designed first. The cutoff frequency of a circular waveguide is given by [8],

p11′ c 2π a ε r

0

50

100

150

100

150

-60 -80 -150

-100

-50

0

50

Fig. 3 Copolar and Cross Polar directivity of a normal conical horn (blue) and aperture matched horn (red)

Backlobe level -20

(1)

where a = radius of the waveguide,

-25

p11′ = 1.841 for TE11

mode, fc = cut off frequency of the waveguide. For X band, fc = 8 GHz, and a = 0.011m suffices the design. The dimensions of the flare of the horn are chosen for a Gain of 20dB. From the relationship chart given by King [9], Awg = 4.2 λ and Lwg=6 λ can be obtained. For centre frequency of X band λ=0.03 m. The horn is excited in TE 11 Mode. The radiated far field for this mode for a conical horn is given by, [9]

A11 J1 (υθ ) sin φ H y (2)(kr ) r sin θ A Eφ = 1/ 2 11 υ J1′(υθ ) cos φ H y (2)(kr ) r sin θ 1/ 2

-30

-35

-40

0.6

0.8

1

1.2

Cross Polarization level at θ = 0

-20

(3) -25

angle of the horn. Adding the aperture matching section slightly modifies the effective aperture radius of the horn antenna and also reduces the edge diffraction. The co-polar and cross-polar electric field components can be calculated from Ludwig’s third definition of cross polarization [10]. If the co-polar electric field is written by Ecp and cross-polar electric field component is written by Exp then,

-30

cos φ ⎤ ⎡ Eθ ⎤ ⎢ ⎥ . − sin φ ⎥⎦ ⎣ Eφ ⎦

0.4

(2)

where Hy(2) is the Hankel function of second kind, J1 is the ′ / α 0 , α 0 = aperture Bessel function of first kind. υ = p11

⎡ Ecp ⎤ ⎡ sin φ ⎢E ⎥ = ⎢ ⎣ xp ⎦ ⎣ cos φ

-50

-40

Fig. 2 Cross Sectional View of the Aperture Matched Horn antenna showing different dimensional parameters.

Eθ =

-100

Cross-polar directivity

Awg

fc =

-150

(4)

be=0.33λ be=0.67λ

-35

be=λ be=1.33λ

-40

0.4

0.6

0.8 ae

1

1.2

Fig. 4 Backlobe level and Cross Polarization level at θ = 0 by varying ae and be for the aperture matched horn antenna. Copolar and Cross Polar directivity ae varied along horizontal axis

551

ae 2 − be 2 e= ae 2

Backlobe level 1.2

tells that the value of cross polarization is low when the value of eccentricity is low. This can be explained through Geometric Theory of Diffraction [12] proposed by Russo et al. The low eccentricity ensures a flat aperture marching surface at the flare of the horn, thus reducing the tangential Eφ component, thereby reducing cross polarization level

1

be

0.8 0.6

obtained by Equation (4). The Back lobe level is low when be is greater compared to ae. The flat surface of aperture matching section produces sharper edge, which increases the backlobe level. In order to design an optimum horn antenna, the value of ae and be should be chosen so that the backlobe and cross polarization levels remain low. The values were determined to be ae = 0.8 and be = 0.3.

0.4 0.2 0

(5)

0

0.2

0.4

0.6 0.8 ae

1

1.2

Cross Polarization level at θ = 0

IV. PERFORMANCE ANALYSIS OF DESIGNED HORN The designed horn was simulated using both Finite Difference Time Domain (FDTD) and Finite Element Method (FEM) in order to ensure the designed optimum performance. The radiation pattern, S11 parameter and cross polarization level and backlobe levels at different frequencies are simulated to analyse the antenna performance.

1.2 -26 1 -28

be

0.8 0.6

-30

0.4 -32

0.2 0

0

0.2

0.4

0.6 0.8 ae

1

1.2

Fig. 5 Contour plots showing Backlobe level and Cross Polarization level at θ = 0 by varying ae and be

III. OPTIMIZATION The radius of curvature of the aperture matching sections should be at least λ / 4 [11]. The dimensions of the aperturematching section were varied, and the total structure of the horn antenna was simulated using Finite Element Method. The simulation was performed at the centre frequency of the X band, 10 GHz. The addition of aperture matching section results in reduction of backlobe of the antenna but also causes the cross polarization level of the antenna to increase. Fig. 3 shows the co-polar and cross-polar directivity of a normal conical horn and an aperture matched horn antenna (ae =2cm be = 1cm). So to reduce the back lobe using a aperture matched horn antenna, the cross polarization is increased. For an optimum performance there must be some trade-off between backlobe level and cross polarization level. Fig. 4 shows simulation results of an aperture matched horn by varying the radii of the parabola that is obtained by taking a cross section of the aperture matching part. ae and be are normalized with respect to the operating wave length of the antenna. By interpolation, the contour plots of Fig. 5 are obtained. From the contour plots it can be seen that the cross polarization level is low when the value of be is less compared to ae . The eccentricity of an ellipse, defined by,

A. Backlobe Level By frequency sweep, the backlobe levels of the designed antenna at various frequencies were observed. The simulation results are shown in Fig. 6. The backlobe level at the desired X band frequency range was found to be substantially low, the peak value of backlobe at X band was found to be below 25dB. At other frequency bands, the backlobe levels were substantially higher. B. Cross Polarization Fig. 7. Shows the cross polarization level of the antenna at different frequencies. The cross polarization level at the designed X band range was also found to be low. At the designed X band, the maximum cross polarization level was found to be below -32dB.

552

Backlobe Level for Designed Horn 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50

0

5

10 Frequency f (GHz)

15

Fig. 6 Backlobe levels of designed Aperture Matched Horn

20

Cross Polarization Level for Designed Horn

Radiation Pattern of Designed Horn

10

20

0

10

Copolarization Pattern Cross polarization Pattern

0 -10

-10 -20

-20 -30

-30

-40 -40

-50 -50

-60

-60 -70 0

5

10 Frequency f (GHz)

15

20

-80

Fig. 7 Cross Polarization Level of designed Aperture Matched Horn

-90

-150

-100

-50

0

50

100

150

θ (Degrees)

C. S11 Parameter For the designed horn, the S11 parameters varied as a function of frequency is shown in Fig. 8. The value of S11 parameter was found to be below -27dB or 0.04467 at the operating frequency band. The voltage standing wave ratio is related to S11 parameter by [7],

VSWR =

1 + S11 1 − S11

.

(6)

The maximum VSWR in the designed frequency band is found to be 1.0935. For feed antennas used in satellite ground stations, the VSWR should be below 1.3 [2], and the designed antenna successfully meets this criteria. For VSWR=1.3, the corresponding value of S11 is approximately -17.69dB, and the antenna can successfully be operated as a feed horn up to frequency range of 15GHz.

Fig. 9 Radiation Pattern of the Designed Aperture Matched Horn

V. CONCLUSIONS This paper studies the design approach of an aperture matched horn antenna. The design mainly enhances a predesigned conical horn antenna, and by adding an aperture matching section. There is a significant improvement in the performance of the designed horn antenna over conventional conical horn. The designed antenna can be readily constructed to be used for feed horn of reflector antennas. REFERENCES [1] [2] [3]

[4] [5] [6] [7] [8] [9]

Fig. 8 S11 parameter as a function of frequency

D. Radiation Pattern Radiation Pattern of the designed horn at center frequency of X band is shown in Fig. 9. The back lobe level of the antenna is below -27dB at this band, and cross polarization level is below -37dB. The main lobe follows a smooth shape up to θ=45°. In this range, the horn will illuminate a subreflector with taper and the illumination of the horn can be modelled with the qillumination function [13] proposed by Zaman et al.

[10] [11] [12] [13]

553

John L. Volakis, Trevor S. Bird and Allan W. Love, Antenna Engineering Handbook, Chapter 14: Horn Antennas, 4th edition, McGraw-Hill, 2007. Constantine A. Balanis, Antenna Theory Analysis and Design, John Wiley & Sons, 2005 M. A. Matin, M. A. Zaman, S. M. Choudhury, M. Gaffar, "Analysis of a conical corrugated horn operating in the K-band with low crosspolarization and high aperture efficiency, and observing its radiation patterns," Antennas and Propagation Society International Symposium, 2009 W. Burnside, C. Chuang, "An aperture-matched horn design," IEEE Trans. Antennas and Propagation, vol. 30, no.4, pp. 790- 796, Jul 1982 D. Heedy, W. Burnside, "An aperture-matched compact range feed horn design," IEEE Trans. Antennas and Propagation, vol. 33, no. 11, pp. 1249- 1255, Nov 1985 Jacob W. M. Baars, The Paraboloidal Reflector Antenna in Radio Astronomy and Communication:Theory and Practice, Springer, 2007 David M. Pozar, Microwave Engineering, 3rd Edition, John Wiley & Sons, Inc. M. Narasimhan, B. Rao, "Radiation from conical horns with large flare angles," IEEE Trans. Antennas and Propagation, vol.19, no.5, pp. 678- 681, Sep 1971 A. P. King, “The Radiation Characteristics of Conical Horn Antennas”, Proceedings of The I.R.E., pp 249-251, 1950. A. Ludwig, “The definition of cross polarization”, IEEE Transaction on Antennas and Propagation, vol.21, no.1, pp. 116-119, Jan 1973 John D. Kraus, Ronald J. Marhefka, Antennas for All Applications, 3rd edition, McGraw-Hill 2002. P. M. Russo, R. C. Rudduck, and L. Peters, Jr., “A method for computing E-plane patterns of horn antennas,” IEEE Trans. Antennas Propagat., vol. AP-13, no. 2, pp. 219-224, Mar. 1965. M. A. Zaman, S. M. Choudhury, M. Gaffar, M. A. Matin, “Modeling the illumination function of a Cassegrain reflector for a corrugated horn feed and calculation of far field pattern”, Loughborough Antennas & Propagation Conference, LAPC, pp. 101-104, Nov 2009