Research Article Design of Ring-Focus Elliptical Beam ... · 2. Design Process of Ring-Focus...

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)


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


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


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)


Figure 8 Simulating and testing radiation pattern in 120593 = 0∘ plane


05

10152025303540

Gai

n (d

Bi)

2 4 6minus2

minus15minus10minus5

minus20minus4 0minus6

120579 (deg)


(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


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


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


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



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


zo P

120579

1205731

120579ma0

120588s

2c(120593)r(120579m)

120573(120593)

s(120593)s1

r(120579)


path 119862119896 in 120593 = 90


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)



1205951= 2 tanminus1 [120591 tan

1205952

2]


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)





0∘ and 120593 = 90


2

respectively

119904 (0) = 1199041=1198631199041

2

119904 (120587

2) = 1199042=1198631199042

2

(5)



120593=0∘

90∘ = 0


2



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)


119904 (120593) =1198631199041

2+1

2(1198631199042minus 1198631199041) sin2120593 (7)



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)


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


119909119904= 119903 (120579) sin 120579 cos120593

119910119904= 119903 (120579) sin 120579 sin120593

119911119904= 119903 (120579) cos 120579

(9)


reflector



119898 119910119898 119911119898) the distance

between (119909119904 119910119904 119911119904) and (119909


of (119909119904 119910119904 119911119904) and (119909


= 119890119903(120579)

minus 2 [ 119890ns sdot 119890119903(120579)

] 119890ns (10)



= 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)



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)

















0 100 200 300 400 500

0200

400600

xy






119904= 100mm focus






4 Testing Results




minus5

0

5

10

15

20

25

30

35

40

45

Gai

n (d

Bi)



90∘ plane


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




120593 = 45∘ and 120593 = 90





0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)




05

10152025303540

Gai

n (d

Bi)

2 4 6minus2



120579 (deg)





minus10

minus5

0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)



0

1

2

3

4

5VS

WR


11 12 13 14 15 1610Frequency (GHz)



∘ 120593 = 45∘ and 120593 = 90



∘ and 120593 = 90∘ plane) is





5 Conclusion




References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










zo P

120579

1205731

120579ma0

120588s

2c(120593)r(120579m)

120573(120593)

s(120593)s1

r(120579)


path 119862119896 in 120593 = 90


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)



1205951= 2 tanminus1 [120591 tan

1205952

2]


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)





0∘ and 120593 = 90


2

respectively

119904 (0) = 1199041=1198631199041

2

119904 (120587

2) = 1199042=1198631199042

2

(5)



120593=0∘

90∘ = 0


2



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)


119904 (120593) =1198631199041

2+1

2(1198631199042minus 1198631199041) sin2120593 (7)



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)


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


119909119904= 119903 (120579) sin 120579 cos120593

119910119904= 119903 (120579) sin 120579 sin120593

119911119904= 119903 (120579) cos 120579

(9)


reflector



119898 119910119898 119911119898) the distance

between (119909119904 119910119904 119911119904) and (119909


of (119909119904 119910119904 119911119904) and (119909


= 119890119903(120579)

minus 2 [ 119890ns sdot 119890119903(120579)

] 119890ns (10)



= 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)



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)

















0 100 200 300 400 500

0200

400600

xy






119904= 100mm focus






4 Testing Results




minus5

0

5

10

15

20

25

30

35

40

45

Gai

n (d

Bi)



90∘ plane


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




120593 = 45∘ and 120593 = 90





0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)




05

10152025303540

Gai

n (d

Bi)

2 4 6minus2



120579 (deg)





minus10

minus5

0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)



0

1

2

3

4

5VS

WR


11 12 13 14 15 1610Frequency (GHz)



∘ 120593 = 45∘ and 120593 = 90



∘ and 120593 = 90∘ plane) is





5 Conclusion




References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





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


119909119904= 119903 (120579) sin 120579 cos120593

119910119904= 119903 (120579) sin 120579 sin120593

119911119904= 119903 (120579) cos 120579

(9)


reflector



119898 119910119898 119911119898) the distance

between (119909119904 119910119904 119911119904) and (119909


of (119909119904 119910119904 119911119904) and (119909


= 119890119903(120579)

minus 2 [ 119890ns sdot 119890119903(120579)

] 119890ns (10)



= 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)



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)

















0 100 200 300 400 500

0200

400600

xy






119904= 100mm focus






4 Testing Results




minus5

0

5

10

15

20

25

30

35

40

45

Gai

n (d

Bi)



90∘ plane


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




120593 = 45∘ and 120593 = 90





0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)




05

10152025303540

Gai

n (d

Bi)

2 4 6minus2



120579 (deg)





minus10

minus5

0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)



0

1

2

3

4

5VS

WR


11 12 13 14 15 1610Frequency (GHz)



∘ 120593 = 45∘ and 120593 = 90



∘ and 120593 = 90∘ plane) is





5 Conclusion




References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500

0200

400600

xy






119904= 100mm focus






4 Testing Results




minus5

0

5

10

15

20

25

30

35

40

45

Gai

n (d

Bi)



90∘ plane


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




120593 = 45∘ and 120593 = 90





0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)




05

10152025303540

Gai

n (d

Bi)

2 4 6minus2



120579 (deg)





minus10

minus5

0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)



0

1

2

3

4

5VS

WR


11 12 13 14 15 1610Frequency (GHz)



∘ 120593 = 45∘ and 120593 = 90



∘ and 120593 = 90∘ plane) is





5 Conclusion




References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)




05

10152025303540

Gai

n (d

Bi)

2 4 6minus2



120579 (deg)





minus10

minus5

0

5

10

15

20

25

30

35

40

Gai

n (d

Bi)



0

1

2

3

4

5VS

WR


11 12 13 14 15 1610Frequency (GHz)



∘ 120593 = 45∘ and 120593 = 90



∘ and 120593 = 90∘ plane) is





5 Conclusion




References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusion




References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Design of Ring-Focus Elliptical Beam ... · 2. Design Process of Ring-Focus...

Documents

Transcript of Research Article Design of Ring-Focus Elliptical Beam ... · 2. Design Process of Ring-Focus...