Research ArticleDesign of Ring-Focus Elliptical Beam Reflector Antenna
Jun-Mo Wu Xue Lei Dong-fang Zhou Lei Hou and Hong-wei Chen
School of Zhengzhou Information Science and Technology Institute Zhengzhou 450002 China
Correspondence should be addressed to Jun-MoWu wjmandylqqcom
Received 8 October 2015 Revised 30 December 2015 Accepted 4 January 2016
Academic Editor Herve Aubert
Copyright copy 2016 Jun-MoWu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A newmethod for the design of elliptical beam reflector antenna is presented in this paper By means of the basic principles of ring-focus antenna a circularly symmetric feed and two specially shaped reflectors are used to form an elliptical beam antenna Firstlythe design process of this ring-focus elliptical beam antenna is studied in detail Transition function is defined and used in thedesign process Then combining the needs of practical engineering a ring-focus elliptical beam reflector antenna is manufacturedand tested The gain at center frequency (12GHz) is 377 dBi with an aperture efficiency of 746 3 dB beam-width in 120593 = 0
∘ and120593 = 90
∘ plane is 26∘ and 14∘ respectively Ratio of the elliptical beam (ratio of 3 dB beam-width in 120593 = 0∘ and 120593 = 90
∘ plane) is2614 = 185 substantially equal to designed ratio 2 Simulating and testing results match well which testify the effectiveness ofthis design method
1 Introduction
In some special applications of radio engineering the spacefor antenna carrier instead of being circular has some strictconstraints For example on most occasions of vehicular andship-borne satellite communication the aperture of antennais required to be rectangular or elliptical In this situationconventional rotationally symmetric reflector antenna is nolonger suitable while elliptical aperture antenna is a goodchoice On the other hand the antenna beam is also requiredto be elliptical on some occasions For example in manysatellite scenarios the desired coverage on the ground iselliptical so elliptical beam antenna is needed [1] what ismore in vehicle satellite communication if the pattern ofvehicle antenna is elliptical when the antenna has a narrowbeam in the azimuth plane and a broad beam in the verticalplane it can track the azimuth plane and no longer trackthe vertical plane so the tracking system is largely simplified[2] All in all elliptical beam reflector antenna is being moreand more widely used in radio engineering and worthy of afurther study
Basically there are three methods for the design ofelliptical beam reflector antenna First is simply to cut theparabolic antenna into ellipse or rectangular By using thismethod the energy leakage is very large so the antenna
efficiency is low Second is to use elliptical feed in orderto get a high efficiency [3] This design method brings thedisadvantage of poor polarization performance and is hard tobe used on the occasions of requiring a polarization rotationwhat is more it is forbidden to be used on the occasionsof circular polarization Third is to use offset shaped dual-reflector antenna in order to form an elliptical beam [4ndash6] The projection of main reflector is an ellipse while theprojection of subreflector is circular (in the plane verticalto the main beam direction) The advantages of this designmethod are as follows the radiation pattern of the feed iscircularly symmetric so it is easy to design and manufac-ture and achieve good circular polarization characteristicthe antenna aperture has an equivalent taper level so itcan achieve elliptical beam with a high antenna efficiencyadditionally due to the use of offset dual-reflector structurethe high side lobe level in linear polarization and beamsquint in circular polarization can be reduced by properlydeploying the main and subreflector However offset dual-reflector structure also increases the longitudinal and lateraldimensions of the antenna not conducive to vehicular andship-borne satellite communication
In this paper we propose a new method for the designof elliptical beam reflector antenna By means of the basic
Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2016 Article ID 9615064 7 pageshttpdxdoiorg10115520169615064
2 International Journal of Antennas and Propagation
y
x
z
r
o
1 2
120579
120593s(xs ys zs)
M(xm ym zm)
Figure 1 Coordinate system of ring-focus elliptical beam antenna
principles of ring-focus antenna we use a circularly sym-metric feed and two specially shaped reflectors to forman elliptical beam antenna Firstly shaped subreflector isdesigned in order to transform the circular beam of feed intoelliptical beam then axial symmetric shaped main reflectoris designed in order to make sure that the antenna satisfiesthe law of reflection and aplanatic condition Compared tothe offset dual-reflector structure this design method canreduce the antennarsquos longitudinal height effectively makingit especially suitable for vehicular and ship-borne satellitecommunication
2 Design Process of Ring-Focus EllipticalBeam Antenna
A specially shaped subreflector is used in order to transformthe circularly symmetric beam of the feed into an ellipticalbeam then the main reflector is designed to make surethat the optical path is equal The detailed design processof this ring-focus elliptical beam reflector antenna is asfollows firstly determine the long and short axis plane ofthe main and subreflector secondly carefully design thetransition function in order to determine the entire shapedsubreflector thirdly according to the law of reflection andaplanatic condition determine the shaped main reflectorlastly verify the design as it is important to check whetherthe four constraint conditions are satisfied
21 Long and Short Axis of the Reflector The coordinateof ring-focus elliptical beam reflector antenna is shown inFigure 1 119909 119910 119911 axis constituting orthogonal Cartesian coor-dinate system and 119903 120579 120593 constituting orthogonal sphericalcoordinates 119900 is the origin point of the coordinate system119909119900119910 plane is the reference plane of aplanatic condition thephase center of feed is put at the origin point reflector 1 is themain reflector and reflector 2 is the subreflector
In the design of ring-focus elliptical beam reflectorantenna the first thing is to determine the long and shortaxis plane of the reflector In the coordinate system shown inFigure 1 120593 = 0
∘ plane is the short axis plane of the reflectorand 120593 = 90
∘ plane is the long axis plane of the reflector
o zP
120593 = 0∘ plane
120593 = 90∘ plane
120588
f1
f212057311205732
120579m1205951
1205952
a0
s1s2
Figure 2 Parameters in long and short axis plane
In these two planes the normal is still in the plane andparameters can be designed by the principles of ring-focusantenna but for arbitrary 120593 = 120593
119904plane the normal is out of
the plane and parameters should be designed using transitionfunction The parameters in 120593 = 0
∘ and 120593 = 90∘ plane are
shown in Figure 2 Point 119900 is the phase center of the feedand also one focus of the subreflector ellipse 119891
1and 119891
2are
the other focus of the ellipse in 120593 = 0∘ and 120593 = 90
∘ planerespectively At the same time they are also the focus of mainreflector The main parameters are as follows main reflectordiameter 119863
119898 subreflector diameter 119863
119904 focus of diameter
ratio 120578 and distance between vertex of the subreflector andphase center of the feed 119900119875 = 119886
0 Parameters like focal
length of the main paraboloid 119865 opening angle of mainreflector 120595 opening angle of subreflector 120579
119898 focus length
of the subreflector ellipse 2119888 long axis of the subreflectorellipse 2119886 eccentricity of the subreflector ellipse 119890 can becalculated by basic principles of ring-focus antenna In thisletter subscript 2 represents parameters in 120593 = 90
∘ planesubscript 1 represents parameters in 120593 = 0
∘ plane andsubscript without 1 or 2 represents commonparameters of thetwo planes
Firstly determine the geometric parameters of 120593 = 90∘
plane that is the long axis plane The parameters can becalculated as follows [7]
1198652= 120578 (119863
1198982minus 1198631199042)
1205952= 2 tanminus1 (
1198631198982
minus 1198631199042
4119865) = 2 tanminus1 ( 1
4120578)
1205732= tanminus1 (
1198631199042
21198860minus 1198631199042cot1205952
)
21198882= 1199001198912=
1198631199042
2 sin1205732
120579119898= sinminus1 [
1198631199042(21198860+ (11986311990422) tan (120595
22))
11986321199042
4 + (21198860+ (11986311990422) tan (120595
22))2
]
1198902=
11986311990422 sin120573
2
1198860+ 11986311990422 sin120595
0
(1)
Then the geometric parameters of 120593 = 0∘ plane that
is the short axis plane can be determined according to theaplanatic condition (all optical paths are equal) The optical
International Journal of Antennas and Propagation 3
zo P
120579
1205731
120579ma0
120588s
2c(120593)r(120579m)
120573(120593)
s(120593)s1
r(120579)
Figure 3 Parameters of arbitrary 120593 plane
path 119862119896 in 120593 = 90
∘ plane can be written as (according to thereference plane 119909119900119910)
119862119896=11986311989822
sin1205952
+ 1198860minus (1198860minus1198631198982
2
cos1205952
sin1205952
)
=1198631198982
2 tan (12059522)
(2)
In 120593 = 0∘ plane
119862119896=
1198631198981
2 tan (12059512)
1198631198981
= 1205911198631198982
(3)
where 120591 is the ratio of elliptical beam (in this letter 120591 is equalto 2) So parameters in 120593 = 0
∘ plane can be calculated asfollows
1205951= 2 tanminus1 [120591 tan
1205952
2]
1205731= tanminus1 [
2 tan (12059512) tan (120579
1198982)
tan (12059512) minus tan (120579
1198982)
]
21198881= 1199001198911= 1198860
sin1205951
sin (1205951+ 1205731)
1198901=
sin1205951
sin (1205731+ 1205951) + sin120573
1
1198631199041
2=1198860sin1205951sin1205731
sin (1205731+ 1205951)
(4)
22 Design of Subreflector Once the long and short axis planeof the reflector are carefully designed the next problem is howto determine the parameters in arbitrary 120593 plane The basicidea is to define a transition function that is a parameterchanges with 120593 from 120593 = 0
∘ plane to 120593 = 90∘ plane
Parameters120573 119903 and 119904 can be chosen as transition function Inthis letter distance between the edge of the subreflector and 119911-axis in120593 plane 119904(120593) is chosen as shown in Figure 3 Transitionfunction should have the following two characteristics
(1) Satisfy the boundary conditions that is to say in 120593 =
0∘ and 120593 = 90
∘ plane 119904(120593) should be equal to 1199041and 119904
2
respectively
119904 (0) = 1199041=1198631199041
2
119904 (120587
2) = 1199042=1198631199042
2
(5)
(2) 119904(120593) should change slowly in120593 = 0∘ and120593 = 90
∘ planein order to make sure that the normal of the subreflector inthese two planes is still in the corresponding plane that is(119889119904(120593)119889120593)|
120593=0∘
90∘ = 0
All transition functions should satisfy the above twoconditions A common choice is polynomial function suchas 119904(120593) = 119860 + 119861120593 + 119862120593
2
+ 1198631205933 According to the above two
conditions the following can be derived
119904 (0) = 119860 = 1199041
119904 (120587
2) = 119860 + 119861 sdot
120587
2+ 119862 sdot (
120587
2)
2
+ 119863 sdot (120587
2)
3
= 1199042
119889119904 (120593)
119889120593
100381610038161003816100381610038161003816100381610038161003816120593=0
= 119861 = 0
119889119904 (120593)
119889120593
100381610038161003816100381610038161003816100381610038161003816120593=1205872
= 119861 + 2119862 sdot120587
2+ 3119863 sdot (
120587
2)
2
= 0
(6)
Then 119904(120593) is designed According to the authorrsquos design expe-rience a better choice of transition function is trigonometricfunction such as
119904 (120593) =1198631199041
2+1
2(1198631199042minus 1198631199041) sin2120593 (7)
This transition function satisfies the above two conditionsand is used in this paper
Other parameters can be calculated using the geometricalrelationship shown in Figure 3
119903 (120579119898) =
119904 (120593)
sin 120579119898
1198860minus
119904 (120593)
tan120595 (120593)= 2119888 (120593) cos120573 (120593)
1198860+
119904 (120593)
sin120595 (120593)= 119903 (120579
119898)
+ (119903 (120579119898) cos 120579
119898minus 2119888 (120593) cos120573 (120593))
(8)
4 International Journal of Antennas and Propagation
Then
120595 (120593) = 2 tanminus1 (cot120579119898
2minus
21198860
119904 (120593))
120573 (120593) = tanminus1 (119904 (120593) tan120595 (120593)
1198860tan120595 (120593) minus 119904 (120593)
)
2119888 (120593) =119904 (120593)
sin120573 (120593)
119890 (120593) =2119888 (120593) sin120595 (120593)
1198860sin120595 (120593) + 119904 (120593)
119903 (120579) = 1198860
1 minus 119890 (120593) cos120573 (120593)1 minus 119890 (120593) cos (120573 (120593) minus 120579)
119909119904= 119903 (120579) sin 120579 cos120593
119910119904= 119903 (120579) sin 120579 sin120593
119911119904= 119903 (120579) cos 120579
(9)
where (119909119904 119910119904 119911119904) is the coordinate of arbitrary point on sub
reflector
23 Design of Main Reflector The coordinate of main reflec-tor can be calculated by the law of reflection and aplanaticcondition Suppose the point on main reflector correspond-ing to (119909
119904 119910119904 119911119904) on subreflector is (119909
119898 119910119898 119911119898) the distance
between (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is119889119898 and the unit vector
of (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is points tomain reflector
= 119890119903(120579)
minus 2 [ 119890ns sdot 119890119903(120579)
] 119890ns (10)
where 119890ns is the unit vector of normal on subreflector 119890119903(120579)
is the unit vector of 119903(120579) and 119903(120579) is the norm of vector 119903(120579)Corresponding point on the main reflector can be calculatedas
= 119898119909119909+ 119898119910119910+ 119898119911119911
119909119898= 119909119904+ 119889119898119898119909
119910119898= 119910119904+ 119889119898119898119910
119911119898= 119911119904+ 119889119898119898119911
(11)
In it
119898119909=
1
119903 (120579)[119909119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119909]
119898119910=
1
119903 (120579)[119910119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119910]
119898119911=
1
119903 (120579)[119911119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119911]
119889119898=119862119896minus 119903 (120579) + 119911
119904
1 minus 119898119911
(12)
where 119862119896is constant of equivalent optical path
Suppose the derivatives of vector 119903(120579) with respect to 120579and 120593 are as follows
119903120579=120597 119903 (120579)
120597120579=120597119909119904
120597120579119909+120597119910119904
120597120579119910+120597119911119904
120597120579119911
119903120593=120597 119903 (120579)
120597120593=120597119909119904
120597120593119909+120597119910119904
120597120593119910+120597119911119904
120597120593119911
(13)
Then
119890ns = ns119909119909+ ns119910119910+ ns119911119911=
119903120579times 119903120593
10038161003816100381610038161003816119903120579times 119903120593
10038161003816100381610038161003816
(14)
24 Verify the Design The main and subreflector can bedesigned by the formulas given above At last it is importantto verify the design that is whether the following fourconstraint conditions are satisfied
(1) The opening angle of subreflector edge point to phasecenter in arbitrary 120593 plane is equal to 120579
119898 in order to make
sure that the radiation level of subreflector is equal(2) The vertex of subreflector is the public point of
all subreflector curves otherwise the subreflector has nosolution
(3) The curves of main and subreflector in 120593 = 0∘ and
120593 = 90∘ plane are conventional ring-focus structure the ratio
of main reflector dimension is equal to the ratio of ellipticalbeam
(4) For subreflector point (119909119904 119910119904 119911119904) in 120593 = 0∘ sim90∘ space
corresponding main reflector point (119909119898 119910119898 119911119898) should also
be designed in the space of 120593 = 0∘ sim90∘ otherwise thesolution of main reflector is not unique
The previous three constraint conditions are easy tosatisfy but the fourth constraint condition should be carefullytreated A good transition function can reduce the number ofmain reflector points out of 120593 = 0∘ sim90∘ space
3 Modeling of Ring-Focus EllipticalBeam Antenna
This ring-focus elliptical beam antenna is simulated by CSTMicrowave Studio It should be noted that none of the existingfull wave analysis tools (such as FEKO or HFSS or CST)can achieve the modeling of this antenna for the reason ofcomplicated modeling Both the main and subreflector areirregular shapes that is their Cartesian coordinates (119909 119910 119911)change continuously by 120579 and 120593 and it is impossible toexpress 119909 119910 119911 by 120579 and 120593 in an analytical expression Apossible way to overcome this problem is to use NURBSmodeling
Nonuniform rational basis spline (NURBS) is a math-ematical model commonly used in computer graphics forgenerating and representing curves and surfaces NURBScurves and surfaces are generalizations of both B-splines andBezier curves and surfaces the primary difference being theweighting of the control points which makes NURBS curvesrational By using a two-dimensional grid of control pointsNURBS surfaces including planar patches and sections ofspheres can be created
International Journal of Antennas and Propagation 5
0 100 200 300 400 500
0200
400600
xy
minus360minus340minus320minus300
zminus280minus260minus240minus220minus200
Figure 4 Designed model given by Matlab
The modeling procedures done in this paper are asfollows firstly by using numerical simulation software (suchas Matlab) calculate the discrete Cartesian coordinates ofthe main and subreflector (changed by 120579 and 120593) secondlyimport the discrete Cartesian coordinates into professional3Dmodeling software (such as 3D StudioMax) and use themas the control points of NURBS surface in order to build theNURBSmodel of themain and subreflector lastly import the3Dmodel into full wave analysis tools (such as CST) in orderto finish the simulation
For the purpose of verifying the effectiveness of NURBSmodeling we simulate a ring-focus antenna for whichmodeled by CST andNURBS respectivelyThe parameters ofthis ring-focus antenna are as followsmain reflector diameter119863119898= 1000mm subreflector diameter 119863
119904= 100mm focus
to diameter ratio 120578 = 04 opening angle of subreflector120579119898
= 55∘ with a minus17 dB taper level Combining the given
parameters and the conventional ring-focus design formulaswe can finish the ring-focus antenna design The antennasmodeled by CST and NURBS are called antennas A and Bhere for simplification The designed model given by Matlabis shown in Figure 4 Using the discrete points calculated byMatlab as the control points the NURBS surface includingplanar patches and sections of spheres can be created whichis shown in Figure 5 The gains of antennas A and B are405 dBi and 404 dBi with an aperture efficiency of 711and 694 respectively The simulating radiation pattern in120593 = 90
∘ plane is shown in Figure 6 The simulating radiationpattern in 120593 = 0
∘ and another arbitrary 120593 plane is similar forthe reason of the symmetrical characteristic of a ring-focusantenna so it is not presented here for simplification It can beseen that the simulating radiation pattern of antennas A andB coincide with each other especially their copolarizationwhich declares that NURBS model method has little effect tothe performance of a reflector antenna
4 Testing Results
Combining the needs of practical engineering we manufac-ture and test a ring-focus elliptical beam reflector antenna
Figure 5 Designed model given by NURBS
Cross-CST modelCo-NURBS model Cross-NURBS modelCo-CST model
minus5
0
5
10
15
20
25
30
35
40
45
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 6 Simulating radiation pattern of antennas A and B in 120593 =
90∘ plane
Table 1 Main parameters of the elliptical beam antenna
1198631198982
(mm) 1198631199042
(mm) 1198631198981
(mm) 1198631199041
(mm) 120578 120591
1000 100 500 806 04 21205732
(∘) 1205952
(∘) 1205731
(∘) 1205951
(∘) 1198860
(mm) 119862119896
(mm)809 64 1226 347 324 800
as shown in Figure 7This ring-focus elliptical beam reflectorantenna has an aperture of 1times05m and the center frequencyis 12GHz in order to receiveKu-band satellite signalThe feedof this antenna is a RHCP corrugated conical horn antennawith a minus10 dB beam-width of 80∘ so the copolarization of thisantenna is still RHCP after the reflection of two reflectorsThe main parameters of this antenna in 120593 = 90
∘ plane (thelong axis plane) are inherited from the ring-focus antenna inSection 3 Combining the ratio of elliptical beam 120591 = 2 andthe formulas given above we can finish the antenna designThe main parameters of this antenna are shown in Table 1
Its simulating and testing radiation pattern in 120593 = 0∘
120593 = 45∘ and 120593 = 90
∘ plane is shown in Figures 8 9and 10 respectively The gain at center frequency is 377 dBiwith an aperture efficiency of 746 The peak side lobe level
6 International Journal of Antennas and Propagation
Figure 7 Photograph of ring-focus elliptical beam antenna
Cross-simulatingCotesting Cross-testingCosimulating
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane
Cross-simulatingCotesting Cross-testingCosimulating
05
10152025303540
Gai
n (d
Bi)
2 4 6minus2
minus15minus10minus5
minus20minus4 0minus6
120579 (deg)
Figure 9 Simulating and testing radiation pattern in 120593 = 45∘ plane
(PSLL) in 120593 = 90∘ plane is minus103 dB relatively high when it
compares with the minus14 dB minimum requirement in satellitecommunicationThis shortcoming may bring interference insignal reception and transmission especiallywhen the system
Cross-simulatingCotesting Cross-testingCosimulating
minus10
minus5
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
minus4 minus2 0 2 4 6minus6120579 (deg)
Figure 10 Simulating and testing radiation pattern in120593 = 90∘ plane
0
1
2
3
4
5VS
WR
Feed-testReflector_test
11 12 13 14 15 1610Frequency (GHz)
Figure 11 Test VSWR of the feed and reflector
has a relatively low GT Further works need to be done inorder to decrease the PSLL The cross-polarization level canbe decreased by properly designing the axis ratio of the feedThe 3 dB beam-width in 120593 = 0
∘ 120593 = 45∘ and 120593 = 90
∘ planeis 26∘ 17∘ and 14
∘ respectively Ratio of elliptical beam(ratio of 3 dB beam-width in 120593 = 0
∘ and 120593 = 90∘ plane) is
2614 = 185 substantially equal to the designed ratio 2The VSWR of the antenna is shown in Figure 11 The curve offeed test and reflector test is almost coincident which declaresthat the reflector has little effect to the VSWR of the feedSimulating and testing results match well which testify theeffectiveness of this design method
The advantages of this design method are as followscompared to the first design method the aperture efficiencyis improved effectively for the reason of equivalent taper levelwhich means less energy leakage compared to the seconddesign method polarization rotation and circular polariza-tion are improved with the use of axial symmetric feed and
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
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DistributedSensor Networks
International Journal of
2 International Journal of Antennas and Propagation
y
x
z
r
o
1 2
120579
120593s(xs ys zs)
M(xm ym zm)
Figure 1 Coordinate system of ring-focus elliptical beam antenna
principles of ring-focus antenna we use a circularly sym-metric feed and two specially shaped reflectors to forman elliptical beam antenna Firstly shaped subreflector isdesigned in order to transform the circular beam of feed intoelliptical beam then axial symmetric shaped main reflectoris designed in order to make sure that the antenna satisfiesthe law of reflection and aplanatic condition Compared tothe offset dual-reflector structure this design method canreduce the antennarsquos longitudinal height effectively makingit especially suitable for vehicular and ship-borne satellitecommunication
2 Design Process of Ring-Focus EllipticalBeam Antenna
A specially shaped subreflector is used in order to transformthe circularly symmetric beam of the feed into an ellipticalbeam then the main reflector is designed to make surethat the optical path is equal The detailed design processof this ring-focus elliptical beam reflector antenna is asfollows firstly determine the long and short axis plane ofthe main and subreflector secondly carefully design thetransition function in order to determine the entire shapedsubreflector thirdly according to the law of reflection andaplanatic condition determine the shaped main reflectorlastly verify the design as it is important to check whetherthe four constraint conditions are satisfied
21 Long and Short Axis of the Reflector The coordinateof ring-focus elliptical beam reflector antenna is shown inFigure 1 119909 119910 119911 axis constituting orthogonal Cartesian coor-dinate system and 119903 120579 120593 constituting orthogonal sphericalcoordinates 119900 is the origin point of the coordinate system119909119900119910 plane is the reference plane of aplanatic condition thephase center of feed is put at the origin point reflector 1 is themain reflector and reflector 2 is the subreflector
In the design of ring-focus elliptical beam reflectorantenna the first thing is to determine the long and shortaxis plane of the reflector In the coordinate system shown inFigure 1 120593 = 0
∘ plane is the short axis plane of the reflectorand 120593 = 90
∘ plane is the long axis plane of the reflector
o zP
120593 = 0∘ plane
120593 = 90∘ plane
120588
f1
f212057311205732
120579m1205951
1205952
a0
s1s2
Figure 2 Parameters in long and short axis plane
In these two planes the normal is still in the plane andparameters can be designed by the principles of ring-focusantenna but for arbitrary 120593 = 120593
119904plane the normal is out of
the plane and parameters should be designed using transitionfunction The parameters in 120593 = 0
∘ and 120593 = 90∘ plane are
shown in Figure 2 Point 119900 is the phase center of the feedand also one focus of the subreflector ellipse 119891
1and 119891
2are
the other focus of the ellipse in 120593 = 0∘ and 120593 = 90
∘ planerespectively At the same time they are also the focus of mainreflector The main parameters are as follows main reflectordiameter 119863
119898 subreflector diameter 119863
119904 focus of diameter
ratio 120578 and distance between vertex of the subreflector andphase center of the feed 119900119875 = 119886
0 Parameters like focal
length of the main paraboloid 119865 opening angle of mainreflector 120595 opening angle of subreflector 120579
119898 focus length
of the subreflector ellipse 2119888 long axis of the subreflectorellipse 2119886 eccentricity of the subreflector ellipse 119890 can becalculated by basic principles of ring-focus antenna In thisletter subscript 2 represents parameters in 120593 = 90
∘ planesubscript 1 represents parameters in 120593 = 0
∘ plane andsubscript without 1 or 2 represents commonparameters of thetwo planes
Firstly determine the geometric parameters of 120593 = 90∘
plane that is the long axis plane The parameters can becalculated as follows [7]
1198652= 120578 (119863
1198982minus 1198631199042)
1205952= 2 tanminus1 (
1198631198982
minus 1198631199042
4119865) = 2 tanminus1 ( 1
4120578)
1205732= tanminus1 (
1198631199042
21198860minus 1198631199042cot1205952
)
21198882= 1199001198912=
1198631199042
2 sin1205732
120579119898= sinminus1 [
1198631199042(21198860+ (11986311990422) tan (120595
22))
11986321199042
4 + (21198860+ (11986311990422) tan (120595
22))2
]
1198902=
11986311990422 sin120573
2
1198860+ 11986311990422 sin120595
0
(1)
Then the geometric parameters of 120593 = 0∘ plane that
is the short axis plane can be determined according to theaplanatic condition (all optical paths are equal) The optical
International Journal of Antennas and Propagation 3
zo P
120579
1205731
120579ma0
120588s
2c(120593)r(120579m)
120573(120593)
s(120593)s1
r(120579)
Figure 3 Parameters of arbitrary 120593 plane
path 119862119896 in 120593 = 90
∘ plane can be written as (according to thereference plane 119909119900119910)
119862119896=11986311989822
sin1205952
+ 1198860minus (1198860minus1198631198982
2
cos1205952
sin1205952
)
=1198631198982
2 tan (12059522)
(2)
In 120593 = 0∘ plane
119862119896=
1198631198981
2 tan (12059512)
1198631198981
= 1205911198631198982
(3)
where 120591 is the ratio of elliptical beam (in this letter 120591 is equalto 2) So parameters in 120593 = 0
∘ plane can be calculated asfollows
1205951= 2 tanminus1 [120591 tan
1205952
2]
1205731= tanminus1 [
2 tan (12059512) tan (120579
1198982)
tan (12059512) minus tan (120579
1198982)
]
21198881= 1199001198911= 1198860
sin1205951
sin (1205951+ 1205731)
1198901=
sin1205951
sin (1205731+ 1205951) + sin120573
1
1198631199041
2=1198860sin1205951sin1205731
sin (1205731+ 1205951)
(4)
22 Design of Subreflector Once the long and short axis planeof the reflector are carefully designed the next problem is howto determine the parameters in arbitrary 120593 plane The basicidea is to define a transition function that is a parameterchanges with 120593 from 120593 = 0
∘ plane to 120593 = 90∘ plane
Parameters120573 119903 and 119904 can be chosen as transition function Inthis letter distance between the edge of the subreflector and 119911-axis in120593 plane 119904(120593) is chosen as shown in Figure 3 Transitionfunction should have the following two characteristics
(1) Satisfy the boundary conditions that is to say in 120593 =
0∘ and 120593 = 90
∘ plane 119904(120593) should be equal to 1199041and 119904
2
respectively
119904 (0) = 1199041=1198631199041
2
119904 (120587
2) = 1199042=1198631199042
2
(5)
(2) 119904(120593) should change slowly in120593 = 0∘ and120593 = 90
∘ planein order to make sure that the normal of the subreflector inthese two planes is still in the corresponding plane that is(119889119904(120593)119889120593)|
120593=0∘
90∘ = 0
All transition functions should satisfy the above twoconditions A common choice is polynomial function suchas 119904(120593) = 119860 + 119861120593 + 119862120593
2
+ 1198631205933 According to the above two
conditions the following can be derived
119904 (0) = 119860 = 1199041
119904 (120587
2) = 119860 + 119861 sdot
120587
2+ 119862 sdot (
120587
2)
2
+ 119863 sdot (120587
2)
3
= 1199042
119889119904 (120593)
119889120593
100381610038161003816100381610038161003816100381610038161003816120593=0
= 119861 = 0
119889119904 (120593)
119889120593
100381610038161003816100381610038161003816100381610038161003816120593=1205872
= 119861 + 2119862 sdot120587
2+ 3119863 sdot (
120587
2)
2
= 0
(6)
Then 119904(120593) is designed According to the authorrsquos design expe-rience a better choice of transition function is trigonometricfunction such as
119904 (120593) =1198631199041
2+1
2(1198631199042minus 1198631199041) sin2120593 (7)
This transition function satisfies the above two conditionsand is used in this paper
Other parameters can be calculated using the geometricalrelationship shown in Figure 3
119903 (120579119898) =
119904 (120593)
sin 120579119898
1198860minus
119904 (120593)
tan120595 (120593)= 2119888 (120593) cos120573 (120593)
1198860+
119904 (120593)
sin120595 (120593)= 119903 (120579
119898)
+ (119903 (120579119898) cos 120579
119898minus 2119888 (120593) cos120573 (120593))
(8)
4 International Journal of Antennas and Propagation
Then
120595 (120593) = 2 tanminus1 (cot120579119898
2minus
21198860
119904 (120593))
120573 (120593) = tanminus1 (119904 (120593) tan120595 (120593)
1198860tan120595 (120593) minus 119904 (120593)
)
2119888 (120593) =119904 (120593)
sin120573 (120593)
119890 (120593) =2119888 (120593) sin120595 (120593)
1198860sin120595 (120593) + 119904 (120593)
119903 (120579) = 1198860
1 minus 119890 (120593) cos120573 (120593)1 minus 119890 (120593) cos (120573 (120593) minus 120579)
119909119904= 119903 (120579) sin 120579 cos120593
119910119904= 119903 (120579) sin 120579 sin120593
119911119904= 119903 (120579) cos 120579
(9)
where (119909119904 119910119904 119911119904) is the coordinate of arbitrary point on sub
reflector
23 Design of Main Reflector The coordinate of main reflec-tor can be calculated by the law of reflection and aplanaticcondition Suppose the point on main reflector correspond-ing to (119909
119904 119910119904 119911119904) on subreflector is (119909
119898 119910119898 119911119898) the distance
between (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is119889119898 and the unit vector
of (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is points tomain reflector
= 119890119903(120579)
minus 2 [ 119890ns sdot 119890119903(120579)
] 119890ns (10)
where 119890ns is the unit vector of normal on subreflector 119890119903(120579)
is the unit vector of 119903(120579) and 119903(120579) is the norm of vector 119903(120579)Corresponding point on the main reflector can be calculatedas
= 119898119909119909+ 119898119910119910+ 119898119911119911
119909119898= 119909119904+ 119889119898119898119909
119910119898= 119910119904+ 119889119898119898119910
119911119898= 119911119904+ 119889119898119898119911
(11)
In it
119898119909=
1
119903 (120579)[119909119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119909]
119898119910=
1
119903 (120579)[119910119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119910]
119898119911=
1
119903 (120579)[119911119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119911]
119889119898=119862119896minus 119903 (120579) + 119911
119904
1 minus 119898119911
(12)
where 119862119896is constant of equivalent optical path
Suppose the derivatives of vector 119903(120579) with respect to 120579and 120593 are as follows
119903120579=120597 119903 (120579)
120597120579=120597119909119904
120597120579119909+120597119910119904
120597120579119910+120597119911119904
120597120579119911
119903120593=120597 119903 (120579)
120597120593=120597119909119904
120597120593119909+120597119910119904
120597120593119910+120597119911119904
120597120593119911
(13)
Then
119890ns = ns119909119909+ ns119910119910+ ns119911119911=
119903120579times 119903120593
10038161003816100381610038161003816119903120579times 119903120593
10038161003816100381610038161003816
(14)
24 Verify the Design The main and subreflector can bedesigned by the formulas given above At last it is importantto verify the design that is whether the following fourconstraint conditions are satisfied
(1) The opening angle of subreflector edge point to phasecenter in arbitrary 120593 plane is equal to 120579
119898 in order to make
sure that the radiation level of subreflector is equal(2) The vertex of subreflector is the public point of
all subreflector curves otherwise the subreflector has nosolution
(3) The curves of main and subreflector in 120593 = 0∘ and
120593 = 90∘ plane are conventional ring-focus structure the ratio
of main reflector dimension is equal to the ratio of ellipticalbeam
(4) For subreflector point (119909119904 119910119904 119911119904) in 120593 = 0∘ sim90∘ space
corresponding main reflector point (119909119898 119910119898 119911119898) should also
be designed in the space of 120593 = 0∘ sim90∘ otherwise thesolution of main reflector is not unique
The previous three constraint conditions are easy tosatisfy but the fourth constraint condition should be carefullytreated A good transition function can reduce the number ofmain reflector points out of 120593 = 0∘ sim90∘ space
3 Modeling of Ring-Focus EllipticalBeam Antenna
This ring-focus elliptical beam antenna is simulated by CSTMicrowave Studio It should be noted that none of the existingfull wave analysis tools (such as FEKO or HFSS or CST)can achieve the modeling of this antenna for the reason ofcomplicated modeling Both the main and subreflector areirregular shapes that is their Cartesian coordinates (119909 119910 119911)change continuously by 120579 and 120593 and it is impossible toexpress 119909 119910 119911 by 120579 and 120593 in an analytical expression Apossible way to overcome this problem is to use NURBSmodeling
Nonuniform rational basis spline (NURBS) is a math-ematical model commonly used in computer graphics forgenerating and representing curves and surfaces NURBScurves and surfaces are generalizations of both B-splines andBezier curves and surfaces the primary difference being theweighting of the control points which makes NURBS curvesrational By using a two-dimensional grid of control pointsNURBS surfaces including planar patches and sections ofspheres can be created
International Journal of Antennas and Propagation 5
0 100 200 300 400 500
0200
400600
xy
minus360minus340minus320minus300
zminus280minus260minus240minus220minus200
Figure 4 Designed model given by Matlab
The modeling procedures done in this paper are asfollows firstly by using numerical simulation software (suchas Matlab) calculate the discrete Cartesian coordinates ofthe main and subreflector (changed by 120579 and 120593) secondlyimport the discrete Cartesian coordinates into professional3Dmodeling software (such as 3D StudioMax) and use themas the control points of NURBS surface in order to build theNURBSmodel of themain and subreflector lastly import the3Dmodel into full wave analysis tools (such as CST) in orderto finish the simulation
For the purpose of verifying the effectiveness of NURBSmodeling we simulate a ring-focus antenna for whichmodeled by CST andNURBS respectivelyThe parameters ofthis ring-focus antenna are as followsmain reflector diameter119863119898= 1000mm subreflector diameter 119863
119904= 100mm focus
to diameter ratio 120578 = 04 opening angle of subreflector120579119898
= 55∘ with a minus17 dB taper level Combining the given
parameters and the conventional ring-focus design formulaswe can finish the ring-focus antenna design The antennasmodeled by CST and NURBS are called antennas A and Bhere for simplification The designed model given by Matlabis shown in Figure 4 Using the discrete points calculated byMatlab as the control points the NURBS surface includingplanar patches and sections of spheres can be created whichis shown in Figure 5 The gains of antennas A and B are405 dBi and 404 dBi with an aperture efficiency of 711and 694 respectively The simulating radiation pattern in120593 = 90
∘ plane is shown in Figure 6 The simulating radiationpattern in 120593 = 0
∘ and another arbitrary 120593 plane is similar forthe reason of the symmetrical characteristic of a ring-focusantenna so it is not presented here for simplification It can beseen that the simulating radiation pattern of antennas A andB coincide with each other especially their copolarizationwhich declares that NURBS model method has little effect tothe performance of a reflector antenna
4 Testing Results
Combining the needs of practical engineering we manufac-ture and test a ring-focus elliptical beam reflector antenna
Figure 5 Designed model given by NURBS
Cross-CST modelCo-NURBS model Cross-NURBS modelCo-CST model
minus5
0
5
10
15
20
25
30
35
40
45
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 6 Simulating radiation pattern of antennas A and B in 120593 =
90∘ plane
Table 1 Main parameters of the elliptical beam antenna
1198631198982
(mm) 1198631199042
(mm) 1198631198981
(mm) 1198631199041
(mm) 120578 120591
1000 100 500 806 04 21205732
(∘) 1205952
(∘) 1205731
(∘) 1205951
(∘) 1198860
(mm) 119862119896
(mm)809 64 1226 347 324 800
as shown in Figure 7This ring-focus elliptical beam reflectorantenna has an aperture of 1times05m and the center frequencyis 12GHz in order to receiveKu-band satellite signalThe feedof this antenna is a RHCP corrugated conical horn antennawith a minus10 dB beam-width of 80∘ so the copolarization of thisantenna is still RHCP after the reflection of two reflectorsThe main parameters of this antenna in 120593 = 90
∘ plane (thelong axis plane) are inherited from the ring-focus antenna inSection 3 Combining the ratio of elliptical beam 120591 = 2 andthe formulas given above we can finish the antenna designThe main parameters of this antenna are shown in Table 1
Its simulating and testing radiation pattern in 120593 = 0∘
120593 = 45∘ and 120593 = 90
∘ plane is shown in Figures 8 9and 10 respectively The gain at center frequency is 377 dBiwith an aperture efficiency of 746 The peak side lobe level
6 International Journal of Antennas and Propagation
Figure 7 Photograph of ring-focus elliptical beam antenna
Cross-simulatingCotesting Cross-testingCosimulating
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane
Cross-simulatingCotesting Cross-testingCosimulating
05
10152025303540
Gai
n (d
Bi)
2 4 6minus2
minus15minus10minus5
minus20minus4 0minus6
120579 (deg)
Figure 9 Simulating and testing radiation pattern in 120593 = 45∘ plane
(PSLL) in 120593 = 90∘ plane is minus103 dB relatively high when it
compares with the minus14 dB minimum requirement in satellitecommunicationThis shortcoming may bring interference insignal reception and transmission especiallywhen the system
Cross-simulatingCotesting Cross-testingCosimulating
minus10
minus5
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
minus4 minus2 0 2 4 6minus6120579 (deg)
Figure 10 Simulating and testing radiation pattern in120593 = 90∘ plane
0
1
2
3
4
5VS
WR
Feed-testReflector_test
11 12 13 14 15 1610Frequency (GHz)
Figure 11 Test VSWR of the feed and reflector
has a relatively low GT Further works need to be done inorder to decrease the PSLL The cross-polarization level canbe decreased by properly designing the axis ratio of the feedThe 3 dB beam-width in 120593 = 0
∘ 120593 = 45∘ and 120593 = 90
∘ planeis 26∘ 17∘ and 14
∘ respectively Ratio of elliptical beam(ratio of 3 dB beam-width in 120593 = 0
∘ and 120593 = 90∘ plane) is
2614 = 185 substantially equal to the designed ratio 2The VSWR of the antenna is shown in Figure 11 The curve offeed test and reflector test is almost coincident which declaresthat the reflector has little effect to the VSWR of the feedSimulating and testing results match well which testify theeffectiveness of this design method
The advantages of this design method are as followscompared to the first design method the aperture efficiencyis improved effectively for the reason of equivalent taper levelwhich means less energy leakage compared to the seconddesign method polarization rotation and circular polariza-tion are improved with the use of axial symmetric feed and
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
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DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 3
zo P
120579
1205731
120579ma0
120588s
2c(120593)r(120579m)
120573(120593)
s(120593)s1
r(120579)
Figure 3 Parameters of arbitrary 120593 plane
path 119862119896 in 120593 = 90
∘ plane can be written as (according to thereference plane 119909119900119910)
119862119896=11986311989822
sin1205952
+ 1198860minus (1198860minus1198631198982
2
cos1205952
sin1205952
)
=1198631198982
2 tan (12059522)
(2)
In 120593 = 0∘ plane
119862119896=
1198631198981
2 tan (12059512)
1198631198981
= 1205911198631198982
(3)
where 120591 is the ratio of elliptical beam (in this letter 120591 is equalto 2) So parameters in 120593 = 0
∘ plane can be calculated asfollows
1205951= 2 tanminus1 [120591 tan
1205952
2]
1205731= tanminus1 [
2 tan (12059512) tan (120579
1198982)
tan (12059512) minus tan (120579
1198982)
]
21198881= 1199001198911= 1198860
sin1205951
sin (1205951+ 1205731)
1198901=
sin1205951
sin (1205731+ 1205951) + sin120573
1
1198631199041
2=1198860sin1205951sin1205731
sin (1205731+ 1205951)
(4)
22 Design of Subreflector Once the long and short axis planeof the reflector are carefully designed the next problem is howto determine the parameters in arbitrary 120593 plane The basicidea is to define a transition function that is a parameterchanges with 120593 from 120593 = 0
∘ plane to 120593 = 90∘ plane
Parameters120573 119903 and 119904 can be chosen as transition function Inthis letter distance between the edge of the subreflector and 119911-axis in120593 plane 119904(120593) is chosen as shown in Figure 3 Transitionfunction should have the following two characteristics
(1) Satisfy the boundary conditions that is to say in 120593 =
0∘ and 120593 = 90
∘ plane 119904(120593) should be equal to 1199041and 119904
2
respectively
119904 (0) = 1199041=1198631199041
2
119904 (120587
2) = 1199042=1198631199042
2
(5)
(2) 119904(120593) should change slowly in120593 = 0∘ and120593 = 90
∘ planein order to make sure that the normal of the subreflector inthese two planes is still in the corresponding plane that is(119889119904(120593)119889120593)|
120593=0∘
90∘ = 0
All transition functions should satisfy the above twoconditions A common choice is polynomial function suchas 119904(120593) = 119860 + 119861120593 + 119862120593
2
+ 1198631205933 According to the above two
conditions the following can be derived
119904 (0) = 119860 = 1199041
119904 (120587
2) = 119860 + 119861 sdot
120587
2+ 119862 sdot (
120587
2)
2
+ 119863 sdot (120587
2)
3
= 1199042
119889119904 (120593)
119889120593
100381610038161003816100381610038161003816100381610038161003816120593=0
= 119861 = 0
119889119904 (120593)
119889120593
100381610038161003816100381610038161003816100381610038161003816120593=1205872
= 119861 + 2119862 sdot120587
2+ 3119863 sdot (
120587
2)
2
= 0
(6)
Then 119904(120593) is designed According to the authorrsquos design expe-rience a better choice of transition function is trigonometricfunction such as
119904 (120593) =1198631199041
2+1
2(1198631199042minus 1198631199041) sin2120593 (7)
This transition function satisfies the above two conditionsand is used in this paper
Other parameters can be calculated using the geometricalrelationship shown in Figure 3
119903 (120579119898) =
119904 (120593)
sin 120579119898
1198860minus
119904 (120593)
tan120595 (120593)= 2119888 (120593) cos120573 (120593)
1198860+
119904 (120593)
sin120595 (120593)= 119903 (120579
119898)
+ (119903 (120579119898) cos 120579
119898minus 2119888 (120593) cos120573 (120593))
(8)
4 International Journal of Antennas and Propagation
Then
120595 (120593) = 2 tanminus1 (cot120579119898
2minus
21198860
119904 (120593))
120573 (120593) = tanminus1 (119904 (120593) tan120595 (120593)
1198860tan120595 (120593) minus 119904 (120593)
)
2119888 (120593) =119904 (120593)
sin120573 (120593)
119890 (120593) =2119888 (120593) sin120595 (120593)
1198860sin120595 (120593) + 119904 (120593)
119903 (120579) = 1198860
1 minus 119890 (120593) cos120573 (120593)1 minus 119890 (120593) cos (120573 (120593) minus 120579)
119909119904= 119903 (120579) sin 120579 cos120593
119910119904= 119903 (120579) sin 120579 sin120593
119911119904= 119903 (120579) cos 120579
(9)
where (119909119904 119910119904 119911119904) is the coordinate of arbitrary point on sub
reflector
23 Design of Main Reflector The coordinate of main reflec-tor can be calculated by the law of reflection and aplanaticcondition Suppose the point on main reflector correspond-ing to (119909
119904 119910119904 119911119904) on subreflector is (119909
119898 119910119898 119911119898) the distance
between (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is119889119898 and the unit vector
of (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is points tomain reflector
= 119890119903(120579)
minus 2 [ 119890ns sdot 119890119903(120579)
] 119890ns (10)
where 119890ns is the unit vector of normal on subreflector 119890119903(120579)
is the unit vector of 119903(120579) and 119903(120579) is the norm of vector 119903(120579)Corresponding point on the main reflector can be calculatedas
= 119898119909119909+ 119898119910119910+ 119898119911119911
119909119898= 119909119904+ 119889119898119898119909
119910119898= 119910119904+ 119889119898119898119910
119911119898= 119911119904+ 119889119898119898119911
(11)
In it
119898119909=
1
119903 (120579)[119909119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119909]
119898119910=
1
119903 (120579)[119910119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119910]
119898119911=
1
119903 (120579)[119911119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119911]
119889119898=119862119896minus 119903 (120579) + 119911
119904
1 minus 119898119911
(12)
where 119862119896is constant of equivalent optical path
Suppose the derivatives of vector 119903(120579) with respect to 120579and 120593 are as follows
119903120579=120597 119903 (120579)
120597120579=120597119909119904
120597120579119909+120597119910119904
120597120579119910+120597119911119904
120597120579119911
119903120593=120597 119903 (120579)
120597120593=120597119909119904
120597120593119909+120597119910119904
120597120593119910+120597119911119904
120597120593119911
(13)
Then
119890ns = ns119909119909+ ns119910119910+ ns119911119911=
119903120579times 119903120593
10038161003816100381610038161003816119903120579times 119903120593
10038161003816100381610038161003816
(14)
24 Verify the Design The main and subreflector can bedesigned by the formulas given above At last it is importantto verify the design that is whether the following fourconstraint conditions are satisfied
(1) The opening angle of subreflector edge point to phasecenter in arbitrary 120593 plane is equal to 120579
119898 in order to make
sure that the radiation level of subreflector is equal(2) The vertex of subreflector is the public point of
all subreflector curves otherwise the subreflector has nosolution
(3) The curves of main and subreflector in 120593 = 0∘ and
120593 = 90∘ plane are conventional ring-focus structure the ratio
of main reflector dimension is equal to the ratio of ellipticalbeam
(4) For subreflector point (119909119904 119910119904 119911119904) in 120593 = 0∘ sim90∘ space
corresponding main reflector point (119909119898 119910119898 119911119898) should also
be designed in the space of 120593 = 0∘ sim90∘ otherwise thesolution of main reflector is not unique
The previous three constraint conditions are easy tosatisfy but the fourth constraint condition should be carefullytreated A good transition function can reduce the number ofmain reflector points out of 120593 = 0∘ sim90∘ space
3 Modeling of Ring-Focus EllipticalBeam Antenna
This ring-focus elliptical beam antenna is simulated by CSTMicrowave Studio It should be noted that none of the existingfull wave analysis tools (such as FEKO or HFSS or CST)can achieve the modeling of this antenna for the reason ofcomplicated modeling Both the main and subreflector areirregular shapes that is their Cartesian coordinates (119909 119910 119911)change continuously by 120579 and 120593 and it is impossible toexpress 119909 119910 119911 by 120579 and 120593 in an analytical expression Apossible way to overcome this problem is to use NURBSmodeling
Nonuniform rational basis spline (NURBS) is a math-ematical model commonly used in computer graphics forgenerating and representing curves and surfaces NURBScurves and surfaces are generalizations of both B-splines andBezier curves and surfaces the primary difference being theweighting of the control points which makes NURBS curvesrational By using a two-dimensional grid of control pointsNURBS surfaces including planar patches and sections ofspheres can be created
International Journal of Antennas and Propagation 5
0 100 200 300 400 500
0200
400600
xy
minus360minus340minus320minus300
zminus280minus260minus240minus220minus200
Figure 4 Designed model given by Matlab
The modeling procedures done in this paper are asfollows firstly by using numerical simulation software (suchas Matlab) calculate the discrete Cartesian coordinates ofthe main and subreflector (changed by 120579 and 120593) secondlyimport the discrete Cartesian coordinates into professional3Dmodeling software (such as 3D StudioMax) and use themas the control points of NURBS surface in order to build theNURBSmodel of themain and subreflector lastly import the3Dmodel into full wave analysis tools (such as CST) in orderto finish the simulation
For the purpose of verifying the effectiveness of NURBSmodeling we simulate a ring-focus antenna for whichmodeled by CST andNURBS respectivelyThe parameters ofthis ring-focus antenna are as followsmain reflector diameter119863119898= 1000mm subreflector diameter 119863
119904= 100mm focus
to diameter ratio 120578 = 04 opening angle of subreflector120579119898
= 55∘ with a minus17 dB taper level Combining the given
parameters and the conventional ring-focus design formulaswe can finish the ring-focus antenna design The antennasmodeled by CST and NURBS are called antennas A and Bhere for simplification The designed model given by Matlabis shown in Figure 4 Using the discrete points calculated byMatlab as the control points the NURBS surface includingplanar patches and sections of spheres can be created whichis shown in Figure 5 The gains of antennas A and B are405 dBi and 404 dBi with an aperture efficiency of 711and 694 respectively The simulating radiation pattern in120593 = 90
∘ plane is shown in Figure 6 The simulating radiationpattern in 120593 = 0
∘ and another arbitrary 120593 plane is similar forthe reason of the symmetrical characteristic of a ring-focusantenna so it is not presented here for simplification It can beseen that the simulating radiation pattern of antennas A andB coincide with each other especially their copolarizationwhich declares that NURBS model method has little effect tothe performance of a reflector antenna
4 Testing Results
Combining the needs of practical engineering we manufac-ture and test a ring-focus elliptical beam reflector antenna
Figure 5 Designed model given by NURBS
Cross-CST modelCo-NURBS model Cross-NURBS modelCo-CST model
minus5
0
5
10
15
20
25
30
35
40
45
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 6 Simulating radiation pattern of antennas A and B in 120593 =
90∘ plane
Table 1 Main parameters of the elliptical beam antenna
1198631198982
(mm) 1198631199042
(mm) 1198631198981
(mm) 1198631199041
(mm) 120578 120591
1000 100 500 806 04 21205732
(∘) 1205952
(∘) 1205731
(∘) 1205951
(∘) 1198860
(mm) 119862119896
(mm)809 64 1226 347 324 800
as shown in Figure 7This ring-focus elliptical beam reflectorantenna has an aperture of 1times05m and the center frequencyis 12GHz in order to receiveKu-band satellite signalThe feedof this antenna is a RHCP corrugated conical horn antennawith a minus10 dB beam-width of 80∘ so the copolarization of thisantenna is still RHCP after the reflection of two reflectorsThe main parameters of this antenna in 120593 = 90
∘ plane (thelong axis plane) are inherited from the ring-focus antenna inSection 3 Combining the ratio of elliptical beam 120591 = 2 andthe formulas given above we can finish the antenna designThe main parameters of this antenna are shown in Table 1
Its simulating and testing radiation pattern in 120593 = 0∘
120593 = 45∘ and 120593 = 90
∘ plane is shown in Figures 8 9and 10 respectively The gain at center frequency is 377 dBiwith an aperture efficiency of 746 The peak side lobe level
6 International Journal of Antennas and Propagation
Figure 7 Photograph of ring-focus elliptical beam antenna
Cross-simulatingCotesting Cross-testingCosimulating
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane
Cross-simulatingCotesting Cross-testingCosimulating
05
10152025303540
Gai
n (d
Bi)
2 4 6minus2
minus15minus10minus5
minus20minus4 0minus6
120579 (deg)
Figure 9 Simulating and testing radiation pattern in 120593 = 45∘ plane
(PSLL) in 120593 = 90∘ plane is minus103 dB relatively high when it
compares with the minus14 dB minimum requirement in satellitecommunicationThis shortcoming may bring interference insignal reception and transmission especiallywhen the system
Cross-simulatingCotesting Cross-testingCosimulating
minus10
minus5
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
minus4 minus2 0 2 4 6minus6120579 (deg)
Figure 10 Simulating and testing radiation pattern in120593 = 90∘ plane
0
1
2
3
4
5VS
WR
Feed-testReflector_test
11 12 13 14 15 1610Frequency (GHz)
Figure 11 Test VSWR of the feed and reflector
has a relatively low GT Further works need to be done inorder to decrease the PSLL The cross-polarization level canbe decreased by properly designing the axis ratio of the feedThe 3 dB beam-width in 120593 = 0
∘ 120593 = 45∘ and 120593 = 90
∘ planeis 26∘ 17∘ and 14
∘ respectively Ratio of elliptical beam(ratio of 3 dB beam-width in 120593 = 0
∘ and 120593 = 90∘ plane) is
2614 = 185 substantially equal to the designed ratio 2The VSWR of the antenna is shown in Figure 11 The curve offeed test and reflector test is almost coincident which declaresthat the reflector has little effect to the VSWR of the feedSimulating and testing results match well which testify theeffectiveness of this design method
The advantages of this design method are as followscompared to the first design method the aperture efficiencyis improved effectively for the reason of equivalent taper levelwhich means less energy leakage compared to the seconddesign method polarization rotation and circular polariza-tion are improved with the use of axial symmetric feed and
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
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International Journal of
4 International Journal of Antennas and Propagation
Then
120595 (120593) = 2 tanminus1 (cot120579119898
2minus
21198860
119904 (120593))
120573 (120593) = tanminus1 (119904 (120593) tan120595 (120593)
1198860tan120595 (120593) minus 119904 (120593)
)
2119888 (120593) =119904 (120593)
sin120573 (120593)
119890 (120593) =2119888 (120593) sin120595 (120593)
1198860sin120595 (120593) + 119904 (120593)
119903 (120579) = 1198860
1 minus 119890 (120593) cos120573 (120593)1 minus 119890 (120593) cos (120573 (120593) minus 120579)
119909119904= 119903 (120579) sin 120579 cos120593
119910119904= 119903 (120579) sin 120579 sin120593
119911119904= 119903 (120579) cos 120579
(9)
where (119909119904 119910119904 119911119904) is the coordinate of arbitrary point on sub
reflector
23 Design of Main Reflector The coordinate of main reflec-tor can be calculated by the law of reflection and aplanaticcondition Suppose the point on main reflector correspond-ing to (119909
119904 119910119904 119911119904) on subreflector is (119909
119898 119910119898 119911119898) the distance
between (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is119889119898 and the unit vector
of (119909119904 119910119904 119911119904) and (119909
119898 119910119898 119911119898) is points tomain reflector
= 119890119903(120579)
minus 2 [ 119890ns sdot 119890119903(120579)
] 119890ns (10)
where 119890ns is the unit vector of normal on subreflector 119890119903(120579)
is the unit vector of 119903(120579) and 119903(120579) is the norm of vector 119903(120579)Corresponding point on the main reflector can be calculatedas
= 119898119909119909+ 119898119910119910+ 119898119911119911
119909119898= 119909119904+ 119889119898119898119909
119910119898= 119910119904+ 119889119898119898119910
119911119898= 119911119904+ 119889119898119898119911
(11)
In it
119898119909=
1
119903 (120579)[119909119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119909]
119898119910=
1
119903 (120579)[119910119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119910]
119898119911=
1
119903 (120579)[119911119904minus 2 (ns
119909119909119904+ ns119910119910119904+ ns119911119911119904) ns119911]
119889119898=119862119896minus 119903 (120579) + 119911
119904
1 minus 119898119911
(12)
where 119862119896is constant of equivalent optical path
Suppose the derivatives of vector 119903(120579) with respect to 120579and 120593 are as follows
119903120579=120597 119903 (120579)
120597120579=120597119909119904
120597120579119909+120597119910119904
120597120579119910+120597119911119904
120597120579119911
119903120593=120597 119903 (120579)
120597120593=120597119909119904
120597120593119909+120597119910119904
120597120593119910+120597119911119904
120597120593119911
(13)
Then
119890ns = ns119909119909+ ns119910119910+ ns119911119911=
119903120579times 119903120593
10038161003816100381610038161003816119903120579times 119903120593
10038161003816100381610038161003816
(14)
24 Verify the Design The main and subreflector can bedesigned by the formulas given above At last it is importantto verify the design that is whether the following fourconstraint conditions are satisfied
(1) The opening angle of subreflector edge point to phasecenter in arbitrary 120593 plane is equal to 120579
119898 in order to make
sure that the radiation level of subreflector is equal(2) The vertex of subreflector is the public point of
all subreflector curves otherwise the subreflector has nosolution
(3) The curves of main and subreflector in 120593 = 0∘ and
120593 = 90∘ plane are conventional ring-focus structure the ratio
of main reflector dimension is equal to the ratio of ellipticalbeam
(4) For subreflector point (119909119904 119910119904 119911119904) in 120593 = 0∘ sim90∘ space
corresponding main reflector point (119909119898 119910119898 119911119898) should also
be designed in the space of 120593 = 0∘ sim90∘ otherwise thesolution of main reflector is not unique
The previous three constraint conditions are easy tosatisfy but the fourth constraint condition should be carefullytreated A good transition function can reduce the number ofmain reflector points out of 120593 = 0∘ sim90∘ space
3 Modeling of Ring-Focus EllipticalBeam Antenna
This ring-focus elliptical beam antenna is simulated by CSTMicrowave Studio It should be noted that none of the existingfull wave analysis tools (such as FEKO or HFSS or CST)can achieve the modeling of this antenna for the reason ofcomplicated modeling Both the main and subreflector areirregular shapes that is their Cartesian coordinates (119909 119910 119911)change continuously by 120579 and 120593 and it is impossible toexpress 119909 119910 119911 by 120579 and 120593 in an analytical expression Apossible way to overcome this problem is to use NURBSmodeling
Nonuniform rational basis spline (NURBS) is a math-ematical model commonly used in computer graphics forgenerating and representing curves and surfaces NURBScurves and surfaces are generalizations of both B-splines andBezier curves and surfaces the primary difference being theweighting of the control points which makes NURBS curvesrational By using a two-dimensional grid of control pointsNURBS surfaces including planar patches and sections ofspheres can be created
International Journal of Antennas and Propagation 5
0 100 200 300 400 500
0200
400600
xy
minus360minus340minus320minus300
zminus280minus260minus240minus220minus200
Figure 4 Designed model given by Matlab
The modeling procedures done in this paper are asfollows firstly by using numerical simulation software (suchas Matlab) calculate the discrete Cartesian coordinates ofthe main and subreflector (changed by 120579 and 120593) secondlyimport the discrete Cartesian coordinates into professional3Dmodeling software (such as 3D StudioMax) and use themas the control points of NURBS surface in order to build theNURBSmodel of themain and subreflector lastly import the3Dmodel into full wave analysis tools (such as CST) in orderto finish the simulation
For the purpose of verifying the effectiveness of NURBSmodeling we simulate a ring-focus antenna for whichmodeled by CST andNURBS respectivelyThe parameters ofthis ring-focus antenna are as followsmain reflector diameter119863119898= 1000mm subreflector diameter 119863
119904= 100mm focus
to diameter ratio 120578 = 04 opening angle of subreflector120579119898
= 55∘ with a minus17 dB taper level Combining the given
parameters and the conventional ring-focus design formulaswe can finish the ring-focus antenna design The antennasmodeled by CST and NURBS are called antennas A and Bhere for simplification The designed model given by Matlabis shown in Figure 4 Using the discrete points calculated byMatlab as the control points the NURBS surface includingplanar patches and sections of spheres can be created whichis shown in Figure 5 The gains of antennas A and B are405 dBi and 404 dBi with an aperture efficiency of 711and 694 respectively The simulating radiation pattern in120593 = 90
∘ plane is shown in Figure 6 The simulating radiationpattern in 120593 = 0
∘ and another arbitrary 120593 plane is similar forthe reason of the symmetrical characteristic of a ring-focusantenna so it is not presented here for simplification It can beseen that the simulating radiation pattern of antennas A andB coincide with each other especially their copolarizationwhich declares that NURBS model method has little effect tothe performance of a reflector antenna
4 Testing Results
Combining the needs of practical engineering we manufac-ture and test a ring-focus elliptical beam reflector antenna
Figure 5 Designed model given by NURBS
Cross-CST modelCo-NURBS model Cross-NURBS modelCo-CST model
minus5
0
5
10
15
20
25
30
35
40
45
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 6 Simulating radiation pattern of antennas A and B in 120593 =
90∘ plane
Table 1 Main parameters of the elliptical beam antenna
1198631198982
(mm) 1198631199042
(mm) 1198631198981
(mm) 1198631199041
(mm) 120578 120591
1000 100 500 806 04 21205732
(∘) 1205952
(∘) 1205731
(∘) 1205951
(∘) 1198860
(mm) 119862119896
(mm)809 64 1226 347 324 800
as shown in Figure 7This ring-focus elliptical beam reflectorantenna has an aperture of 1times05m and the center frequencyis 12GHz in order to receiveKu-band satellite signalThe feedof this antenna is a RHCP corrugated conical horn antennawith a minus10 dB beam-width of 80∘ so the copolarization of thisantenna is still RHCP after the reflection of two reflectorsThe main parameters of this antenna in 120593 = 90
∘ plane (thelong axis plane) are inherited from the ring-focus antenna inSection 3 Combining the ratio of elliptical beam 120591 = 2 andthe formulas given above we can finish the antenna designThe main parameters of this antenna are shown in Table 1
Its simulating and testing radiation pattern in 120593 = 0∘
120593 = 45∘ and 120593 = 90
∘ plane is shown in Figures 8 9and 10 respectively The gain at center frequency is 377 dBiwith an aperture efficiency of 746 The peak side lobe level
6 International Journal of Antennas and Propagation
Figure 7 Photograph of ring-focus elliptical beam antenna
Cross-simulatingCotesting Cross-testingCosimulating
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane
Cross-simulatingCotesting Cross-testingCosimulating
05
10152025303540
Gai
n (d
Bi)
2 4 6minus2
minus15minus10minus5
minus20minus4 0minus6
120579 (deg)
Figure 9 Simulating and testing radiation pattern in 120593 = 45∘ plane
(PSLL) in 120593 = 90∘ plane is minus103 dB relatively high when it
compares with the minus14 dB minimum requirement in satellitecommunicationThis shortcoming may bring interference insignal reception and transmission especiallywhen the system
Cross-simulatingCotesting Cross-testingCosimulating
minus10
minus5
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
minus4 minus2 0 2 4 6minus6120579 (deg)
Figure 10 Simulating and testing radiation pattern in120593 = 90∘ plane
0
1
2
3
4
5VS
WR
Feed-testReflector_test
11 12 13 14 15 1610Frequency (GHz)
Figure 11 Test VSWR of the feed and reflector
has a relatively low GT Further works need to be done inorder to decrease the PSLL The cross-polarization level canbe decreased by properly designing the axis ratio of the feedThe 3 dB beam-width in 120593 = 0
∘ 120593 = 45∘ and 120593 = 90
∘ planeis 26∘ 17∘ and 14
∘ respectively Ratio of elliptical beam(ratio of 3 dB beam-width in 120593 = 0
∘ and 120593 = 90∘ plane) is
2614 = 185 substantially equal to the designed ratio 2The VSWR of the antenna is shown in Figure 11 The curve offeed test and reflector test is almost coincident which declaresthat the reflector has little effect to the VSWR of the feedSimulating and testing results match well which testify theeffectiveness of this design method
The advantages of this design method are as followscompared to the first design method the aperture efficiencyis improved effectively for the reason of equivalent taper levelwhich means less energy leakage compared to the seconddesign method polarization rotation and circular polariza-tion are improved with the use of axial symmetric feed and
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 5
0 100 200 300 400 500
0200
400600
xy
minus360minus340minus320minus300
zminus280minus260minus240minus220minus200
Figure 4 Designed model given by Matlab
The modeling procedures done in this paper are asfollows firstly by using numerical simulation software (suchas Matlab) calculate the discrete Cartesian coordinates ofthe main and subreflector (changed by 120579 and 120593) secondlyimport the discrete Cartesian coordinates into professional3Dmodeling software (such as 3D StudioMax) and use themas the control points of NURBS surface in order to build theNURBSmodel of themain and subreflector lastly import the3Dmodel into full wave analysis tools (such as CST) in orderto finish the simulation
For the purpose of verifying the effectiveness of NURBSmodeling we simulate a ring-focus antenna for whichmodeled by CST andNURBS respectivelyThe parameters ofthis ring-focus antenna are as followsmain reflector diameter119863119898= 1000mm subreflector diameter 119863
119904= 100mm focus
to diameter ratio 120578 = 04 opening angle of subreflector120579119898
= 55∘ with a minus17 dB taper level Combining the given
parameters and the conventional ring-focus design formulaswe can finish the ring-focus antenna design The antennasmodeled by CST and NURBS are called antennas A and Bhere for simplification The designed model given by Matlabis shown in Figure 4 Using the discrete points calculated byMatlab as the control points the NURBS surface includingplanar patches and sections of spheres can be created whichis shown in Figure 5 The gains of antennas A and B are405 dBi and 404 dBi with an aperture efficiency of 711and 694 respectively The simulating radiation pattern in120593 = 90
∘ plane is shown in Figure 6 The simulating radiationpattern in 120593 = 0
∘ and another arbitrary 120593 plane is similar forthe reason of the symmetrical characteristic of a ring-focusantenna so it is not presented here for simplification It can beseen that the simulating radiation pattern of antennas A andB coincide with each other especially their copolarizationwhich declares that NURBS model method has little effect tothe performance of a reflector antenna
4 Testing Results
Combining the needs of practical engineering we manufac-ture and test a ring-focus elliptical beam reflector antenna
Figure 5 Designed model given by NURBS
Cross-CST modelCo-NURBS model Cross-NURBS modelCo-CST model
minus5
0
5
10
15
20
25
30
35
40
45
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 6 Simulating radiation pattern of antennas A and B in 120593 =
90∘ plane
Table 1 Main parameters of the elliptical beam antenna
1198631198982
(mm) 1198631199042
(mm) 1198631198981
(mm) 1198631199041
(mm) 120578 120591
1000 100 500 806 04 21205732
(∘) 1205952
(∘) 1205731
(∘) 1205951
(∘) 1198860
(mm) 119862119896
(mm)809 64 1226 347 324 800
as shown in Figure 7This ring-focus elliptical beam reflectorantenna has an aperture of 1times05m and the center frequencyis 12GHz in order to receiveKu-band satellite signalThe feedof this antenna is a RHCP corrugated conical horn antennawith a minus10 dB beam-width of 80∘ so the copolarization of thisantenna is still RHCP after the reflection of two reflectorsThe main parameters of this antenna in 120593 = 90
∘ plane (thelong axis plane) are inherited from the ring-focus antenna inSection 3 Combining the ratio of elliptical beam 120591 = 2 andthe formulas given above we can finish the antenna designThe main parameters of this antenna are shown in Table 1
Its simulating and testing radiation pattern in 120593 = 0∘
120593 = 45∘ and 120593 = 90
∘ plane is shown in Figures 8 9and 10 respectively The gain at center frequency is 377 dBiwith an aperture efficiency of 746 The peak side lobe level
6 International Journal of Antennas and Propagation
Figure 7 Photograph of ring-focus elliptical beam antenna
Cross-simulatingCotesting Cross-testingCosimulating
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane
Cross-simulatingCotesting Cross-testingCosimulating
05
10152025303540
Gai
n (d
Bi)
2 4 6minus2
minus15minus10minus5
minus20minus4 0minus6
120579 (deg)
Figure 9 Simulating and testing radiation pattern in 120593 = 45∘ plane
(PSLL) in 120593 = 90∘ plane is minus103 dB relatively high when it
compares with the minus14 dB minimum requirement in satellitecommunicationThis shortcoming may bring interference insignal reception and transmission especiallywhen the system
Cross-simulatingCotesting Cross-testingCosimulating
minus10
minus5
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
minus4 minus2 0 2 4 6minus6120579 (deg)
Figure 10 Simulating and testing radiation pattern in120593 = 90∘ plane
0
1
2
3
4
5VS
WR
Feed-testReflector_test
11 12 13 14 15 1610Frequency (GHz)
Figure 11 Test VSWR of the feed and reflector
has a relatively low GT Further works need to be done inorder to decrease the PSLL The cross-polarization level canbe decreased by properly designing the axis ratio of the feedThe 3 dB beam-width in 120593 = 0
∘ 120593 = 45∘ and 120593 = 90
∘ planeis 26∘ 17∘ and 14
∘ respectively Ratio of elliptical beam(ratio of 3 dB beam-width in 120593 = 0
∘ and 120593 = 90∘ plane) is
2614 = 185 substantially equal to the designed ratio 2The VSWR of the antenna is shown in Figure 11 The curve offeed test and reflector test is almost coincident which declaresthat the reflector has little effect to the VSWR of the feedSimulating and testing results match well which testify theeffectiveness of this design method
The advantages of this design method are as followscompared to the first design method the aperture efficiencyis improved effectively for the reason of equivalent taper levelwhich means less energy leakage compared to the seconddesign method polarization rotation and circular polariza-tion are improved with the use of axial symmetric feed and
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 International Journal of Antennas and Propagation
Figure 7 Photograph of ring-focus elliptical beam antenna
Cross-simulatingCotesting Cross-testingCosimulating
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
2 4 6minus2minus4 0minus6120579 (deg)
Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane
Cross-simulatingCotesting Cross-testingCosimulating
05
10152025303540
Gai
n (d
Bi)
2 4 6minus2
minus15minus10minus5
minus20minus4 0minus6
120579 (deg)
Figure 9 Simulating and testing radiation pattern in 120593 = 45∘ plane
(PSLL) in 120593 = 90∘ plane is minus103 dB relatively high when it
compares with the minus14 dB minimum requirement in satellitecommunicationThis shortcoming may bring interference insignal reception and transmission especiallywhen the system
Cross-simulatingCotesting Cross-testingCosimulating
minus10
minus5
0
5
10
15
20
25
30
35
40
Gai
n (d
Bi)
minus4 minus2 0 2 4 6minus6120579 (deg)
Figure 10 Simulating and testing radiation pattern in120593 = 90∘ plane
0
1
2
3
4
5VS
WR
Feed-testReflector_test
11 12 13 14 15 1610Frequency (GHz)
Figure 11 Test VSWR of the feed and reflector
has a relatively low GT Further works need to be done inorder to decrease the PSLL The cross-polarization level canbe decreased by properly designing the axis ratio of the feedThe 3 dB beam-width in 120593 = 0
∘ 120593 = 45∘ and 120593 = 90
∘ planeis 26∘ 17∘ and 14
∘ respectively Ratio of elliptical beam(ratio of 3 dB beam-width in 120593 = 0
∘ and 120593 = 90∘ plane) is
2614 = 185 substantially equal to the designed ratio 2The VSWR of the antenna is shown in Figure 11 The curve offeed test and reflector test is almost coincident which declaresthat the reflector has little effect to the VSWR of the feedSimulating and testing results match well which testify theeffectiveness of this design method
The advantages of this design method are as followscompared to the first design method the aperture efficiencyis improved effectively for the reason of equivalent taper levelwhich means less energy leakage compared to the seconddesign method polarization rotation and circular polariza-tion are improved with the use of axial symmetric feed and
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 7
reflector compared to the third method offset dual-reflectorstructure is replaced by symmetric dual-reflector structurethe antennarsquos longitudinal height is reduced effectively whichmakes it especially suitable for vehicular and ship-bornesatellite communication
5 Conclusion
A new method for the design of elliptical beam reflectorantenna is presented in this paper In order to testify theeffectiveness of this design method we manufacture andtest a ring-focus elliptical beam antenna By the use of axialsymmetric structure this antenna can reduce the antennarsquoslongitudinal height effectively and form an elliptical beamwith a high efficiency It can be a good candidate of manypractical engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] N Adatia B KWatson and S Ghosh ldquoDual polarized ellipticalbeam antenna for satellite applicationrdquo in Proceedings of theInternational SymposiumDigest Antennas and Propagation vol2 pp 488ndash491 IEEE Press Piscataway NJ USA 1981
[2] A C Densmore and V Jamnejad ldquoSatellite-tracking K- andKa-band mobile vehicle antenna systemrdquo IEEE Transactions onVehicular Technology vol 42 no 4 pp 502ndash513 1993
[3] E Lier Y Rahmat-Samii and S R Rengarajan ldquoApplication ofrectangular and elliptical dielcore feed horns to elliptical reflec-tor antennasrdquo IEEE Transactions on Antennas and Propagationvol 39 no 11 pp 1592ndash1597 1991
[4] H-H Viskum and H Wolf ldquoA dual offset shaped reflector forelliptical beamsrdquo in Proceedings of the 8th IET InternationalConference on Antennas and Propagation vol 1 pp 565ndash569IET Edinburgh UK March-April 1993
[5] KAoki SMakino TKatagi andKKagoshima ldquoDesignmethodfor an offset dual-shaped reflector antenna with high efficiencyand an elliptical beamrdquo IEE Proceedings H Microwaves Anten-nas and Propagation vol 140 no 2 pp 121ndash128 1993
[6] K Aoki S Makino T Katagi and K Kagoshima ldquoDesignmethod for offset shaped dual-reflector antenna with an ellip-tical aperture of low cross-polarisation characteristicsrdquo IEEProceedingsMicrowaves Antennas and Propagation vol 146 pp60ndash64 1999
[7] C-L Lin Antenna Engineering Handbook Publishing House ofElectronic Industry Beijing China 2002 (Chinese)
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of