VHF COMMUNICATIONS 3190

Angel Vilaseca, HB 9 SL V

Microwave Lens Antennas

In order that directivity may be enhancedIn the THz range 01 frequencies, I.e. Ilghtl,two properties are u88d most frequently.These are rsflectlon, aa from the sur1ace of amirror, and refraction, as In a refractor tele­scope lena. The basic differences In the twopropertlea are shown clearly In figure 1. In themicrowave range, by far the most commonconcentration technlquBa use the properties01 reflection, but there Is no reason whyrefraction cannot be used just In the 88memanner as It Is In optics.

1.SOME BASIC OPTICS

The phenomenon that Is usually associatedwith the property of refraction is caused by thedispersal of electromagnetic waves throughmedia possess ing differing densities and mere­fore at different speeds , In vacuum, the speedof an EM-wave is 300 )( 106 m/s and throughair It is almost same. In other dielectrics, suchas optical glass. the speed of light Is very muchsmaller than through air and vacuum and thesame applies to dielectrics such as plastics ,ceramics, wru etc. All materials have their owncharacteristic relative permittivitles whIch directlyaffects the speed of light passing through them.Tabla 1 gives a few examples at the relallvapermittivilies E, of a law common materials :

- -=

\-:==---~-""=--,,.....o::: _

FIg. 1: Concerrtllltion through ",nec:tlon In 8 mirrorandthrough refraction In , lena

Air 1Polystyrene foam 1

PTFE (Teflon) 2Wax 2.2Glass 2 - 5Ceramic 4.4Crystal 4.5Mica 8

Table 1: Relative permittivity of Bome materiel,

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Fig . 2.: Every electro magnetic take!' the path havingthe ehortest transit time

When a wave passes irorn point A to poinl BIhrough two mediums having di"erlng retracnveindexes (fig. 2), itwill always lake the path whichgives it Ihe shortest transit lime. " then, Ihepropagation time through medium 2 is smallerthan that through medium 1 (fig. 2a). the pathlenglh through Ihe medium 2 is minimized. Thiscould be lhe case il one medium 1 were air andIhe oiher medium were, say, glass. It, on theother hand. medium (1) were glass and medium(2) were air, as in (fig. 2b) , then the EM-wavewould be propagated largely through air as itwould then be faster.

II is analogous with a situat ion where one wanted10 go from a point A to a point B in the shortestpossible time, and thai medium t is solid groundand medium 2 Is water . As one can (normally)walk taster than one can swim, Ihen the routeshown in (fig. 2a) would be Iraversed . II thepositions of ground and water were transposed,route 2b would be the natural course to follow.

It could be asked at Ihis slage: why then can"optical lenses be made from wax or ceramic?The answer Is. Ihat these two materials areImpervious 10 light. i.e, lhey have high lossesal this wavelength. But what goes for lighl wave­lenglhs does not necessarily apply to otherwavelengths . Both way. and ceramic are excellentfor wavelengths corresponding to 10 GHz. Un­Iortunately. these two materials are not very goodto work wnh and would be very unpracticable as

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materials for an amateur lens. A better materialis polystyrene loam which is very easy to workwith and exhibits very low losses. As "sods law"would have it, however, this material has arelative permittivity (e.) very close to that 01 airsince it is very largely composed 01 air. This rulesit out for 10 GHz work since a small diameterpolystyrene lens would have no influence on themicrowaves passing through it. The transit limehas not been appreciably altered.

2.METAL-PLATE LENSES

There Is a practical means for radio amateurs tofabricate microwave lenses . This makes useof the "metal-plate lens". This is made from thismetal plates, cut to a predetermined torrn. andthen placed in parallel juxtaposition at a constantdistance !rom each other. The lens shown in("g. 3) is a possible configuration and Is knownas the planar-concave lens because the virtualoutline surface 01 the combined metal plates isplane on Ihe rear side and concave on Ihe Irontside as in (fig. 4).

It is nevertheless a spherical lens since the frontface is (almost) a spheroid. Actually , this is anover-simplification as it must be an exact hyper­boloid in order that it can focus the incomingEM-wave 10 a single point. The difference be­tween the two forms is very small when lhediameter of the lens is large in terms of a wav&­length. The lens is easier to make if the surfaceis spherical and il made large enough . it will focusIhe EM-wave to a point. That is, parallel rays froman extremely distant point source will be con­verted Into a point source and also the reverse istrue, a point source at the local point will be con­verted to parallel rays of energy.

As may be further seen in figure 3. every platehas its own individual form and size from that of itsneighbour. If all plates were identical, lhen theresull would be a planar-coneave cylindricallens (figs. 5 and 6). In this case, the Iront surfaceof the lens IS a segment of a cylinder and the

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fRaNl VIEIJ

Fig.3: Threeviews 01 a spherical m9lal-plate lens

IIlJ:] I IIlUll lh lckn~ ss

( ~S 'O'l':'!1 1 as~CIlilr. I Cd ) stre rgtnper llli ts)

Fig. 4: Form of lin elemenUlI metal plate. The focusof radius Is not n9C8'Ulllrily coincident withlens focus point.

locus is a line parallel to the line that joins allcurve centre points .

The lenses shown in figs. 5 and 6 are not equiv­alent: their insertion loss Is dependent upon thepolarizat ion 01 the Incident wave - it is at aminimum when the polarization is parallel 10theplates.

These metal-plate lenses are known as aeealara­tlon lenses and represent a basic differenceto the classical oielectnc lens 01 the stamp­collector's magnifying glass which delays Iheincident light waves. When the waves are dis­tributed between the metal elements of a platelens. they are actually accelerated. 01 course, thisexplanation is necessarily simpl\fied in orderto make the comprehension a little easier as itis known. from the theory 01 relativity . that nothIngtravels faster lhan the speed of light.

Following this reasoning, it can be seen that platelenses have a reversed effect upon waves thanthaI of the dielectric lenses . This means that aconcave plate lens has a converging effect and aconvex plate lens has a diverging effect. In fig. 7.the lens types are shown together lor purposes01 contrast.

front viQIJ

lateral vi~

=::=e:::::: ..

Obl i queview

ro t v iew

---lateral VltHJ

FIg.5: Threeviews of a planar-concave, cylindricalmetal-plate,venlcally-polarUed lens.

Fig. 6: Threeviews of a plenar-ecneave, cylindricalmetal-plate, horizontally-polarized lens.

181

6 )

COI'CclVt' l~ns : divergent lens

COI'Cd'<'e I ens =convergent lens

CC(\VilX lens = collleraenl hIlS

IXlIlveJ lens = dlYElrgenl lens

VHF COMMUNICATIONS 3190

Fig. 7:Above :dlelec1rlc lenee,(Mdelay~en8·).

Centnl : metal-plBte lenll(~.ooelera'ion-Ien.·)_

Below: opt ical centres,F =' Focus length

ffi = I) 'T!CAL IH Ii..J.

A wave which is dislribuled Irom Ihe locus pointIn a ball-shaped wave. becomes a planar wavewhen il has encounlered a spherical con cavemetal-plate lens (fig. 7e). That would be thecase lor transmission of a wave. II. on 'he otherhand . a planar wave is intercepted by this lens.it Is translormed into a spherical wave andconcentraled at the local point 01 the lens . Thisis the case lor Ihe reception of a wave.

It will be noticed 'hat the lens effect is independentupon direction Irom which the wave arrives - seeflgure 7e: in both lelt-hand diagrams the samelens Is depicted. one with the waves arriving lromthe concave sIde and the olher w~h the wavescom ing from the convex side . The points at whichIhe waves are concentrated - the locus - isalways at the same distance Irorn Ihe optical

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centre. The optical centre is an important pointbecause the focal length Is measured trom here.

It can be seen In fig . 7e thal the optical centrelies on the optical axis - namely in the middle01 surfaces of Ihe two lenses. assuming thelenses are symmelrica\ (bi-concave or bl-con­vex). With an unsymmetrical lens (plane concaveor plane convex). however. the optical centrelies on the optical axis near the lens but theexact location must be determined experimen­tally.

II the local point is measured from the opticalcentre and not from the surface of Ihe lens , thenit will be found 10be equal on both sides of thelens . The Ihree lenses depleted in fig. 79 havethe same local length and can therelore be con­sidered 10be equivalent.

VHF COMMUNICATIONS 3190

FIg.a:Enhancing the directivityof samail hom by using alen$. The divergent beamfrom the horn Is focussedby a suitably platl8d lens.

<,

PLRNE WRVEFRONT

LENS FOCA prj INT

F'HMS:: LE.lS

The same occurs, incidently , with the concaveparaboloid only the waves do not pass throughthe lens but are reflected Irom it.

As possible applications for microwave platelenses, the following are offered : -

• Increase Ihe direc1ivity. and theretors thegain, of a small antenna e.g. a hom, withoutmuch of an increase in its overall dimensions(fig. 8).

• Optimizing the illumination of any givenparabolic reflector and radiator which wouldotherwise be Incompatible with each other(lig. 9). This should be of interest to radioamateurs as they often use surplus feed hornsand/or parabolic reflectors .A plate lens is mucheasier 10 fabricate than a cassegraln sub-re­lIeclor to serve the same purpose.

divergent

opti malI I luu nat ionof peraoot e

Flg.9 1I:Optimizing the illumination 01 B parabolicrellector by the use DI a horn lena.

3.DIMENSIONING A METAL-PLATELENS

A lens is characterised by the following dimen­sions:

1) The tocallength2) The diameter (aperture)3) The insertion loss

opt imalI ll uminat ionof pareto Ie

Fig. 9 b:Optlmlzlng the lIlumlnlltlon of a parabolicreflector by convergln!ilthe radiation by~n. of the lena In order to mInimizeaITav radlaUon.

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a) !ens as a radomef\

calion 01 amateur nom- parabolic antennas ISsomewhat dlff lcull (5) as the parabolic elementalsegments must be Quite accurate.

FIg. 10: Three methods 01 Improving the dlrecllvltyof 8 horn antenna:8) lens lorms a radomeb) parabolic horn (hoghom)c) "flyswaner" antenna

3.1. The Insertion Loss

This depends upon Ihree parameters:

a) The angle between the wave 's polar ization inIhe E-plane and the metal plates. The insertionloss is at a minimum when the E-plane liesparallel to the plates.

b) The thickness of the lens

c) The materials used in the construction.

The insertion loss IS one of the reasons whythis type of lens linds Iitlle use In commercialpractice. In order to increase the direclivity andthe gain of horn antennas. there are severalpossibilities which may be considered. The lenscould be located In front 01 the horn (fig. lOa)with a consequent increase in the insertion loss .Alternatively. a hog -horn antenna could be used(fig. 10b) . This is a combination of a horn anda parabolic reflector which IS often emp loyedlor terrestrial radio links. The lIyswaner antenna(fig. 10c) is also In common use .

Another important point concerns both the hornand the reflector (planar or parabolic); they areInherently broad -banded whereas the charac ­teristics 01 lenses are essentially Irequencydependent Since radio amateurs are usuallyinterested in small frequency ranges . thiS polntis of little consequence. In acdnion, the labn-

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(t)

3.2 . The Lens Aperture

Ttns ISthe same dimension as for the cornbmanon01 both feed horn and lens. and it IS that (orslightly larger) oltha horn aperture.

A good method IS 10 comb ine the lens with Ihehorn as shown in fig. •Oa. The local point must lieon the phase centre of the horn - the latte rbeing approximately in the (virtual) apex of thepyramid. In Ihis case. the spherical wave willbe retracrso by the tens into a plane wave withthe focus point being at an infinite distance ­its centre being that of the phase centre 01 thehorn.

In Ihe configuration shown In f ig. 11. the lensserves also as a radome - the space betweenthe lens elements being filled by a materialhaving a low relative permll1lvity E, and low loss.such as polystyrene foam . Thrs keeps Il1eweather from the horn and Ihe wave -guide corn­ponents - a most useful characteristic. It willbe remembered 1l1al polystyrene toam does notchange the characteristics of the lens .

where.

A = tree-space wavelengthd = distance between plates

n = V,- (~)'2d

3.3, The Focal Length

By the he lp 01a lil11e mathernaucs, Ihe local lengthcan be determined. As wl1h every lens. thefocal length ot Ihe rnetat -p'ate lens depenosupon :

a) The refractive indexb) The curve radius of both trent and rear lens

surface

The refractive Index n IS calculated acco rding/0 torrnula (t)

lyswa erc)LJ ) hoghor n

Now that the refract ive index of the lens is known ,the focal length can be calculated using formula(4) :

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1 1(n - 1) . (R1 + R2 ) (4)

(2)

(3)

Rg . ,, : A physical combination of hom and lena

II can be seen from the formula , that the refractiveindex n for microwave plate lenses (i.e. ac­celeration lens) are always smaller than unity.Dielectr ic lenses . on the other hand. alwayspossess refractive indexes which are greaterthan one.

Further intereslJng relationships are as follows:

where,

£., = Permittivity of a vacuum= 8.859 x 10-.2 Farads per metre

e -= Absolule permittivity of the med ium inQuestion

e, = Relative permll1lvity (as in table 1)

Furthermore :

n = clvo

where.

c = velocity 01 light in a vacuum (300 x 106 rn/s)

"0 = velocity of light In the refractive medium inQuestion

Table 2 gives examples of refractive indexes01 rnetal-plats lenses for three frequenciescorresponding 10the 3 em amateur band and tivediffering spacings d between two plates.

where .

I = focal lengthn = refract ive indexR, and R2 = CUNe radii of the front or rear sur­

laces of the lens . A convex surfaceis expressed by A > 0, a concavesurface by A < 0

The fact that the surlaces are described withcurved radii means that they are spheroidswhereas a perfect lens would have hyperboloidsurfaces. According 10(1). Ihey could be providedwith one spherical and one hyperbolic surface. Inany case. Ihe spheroid represents an approxi·mallon which is sufficiently accurate where theradius is no1 too small. Sphero id lenses arBeasier both to calculate and 10fabricate.

Turning again to formula (4) : Assuming that oneof the lens surfaces is lIal, R2 would representan infinite radius , Formula (4) may be simplifiedas/ollows:

1 n - 1

f A1

there/ore

Rlf ""

n - I

therefore

R1=l(n-l) (5)

Frequency 10.0 GHz 10.25 GHz 10.5GHz

d = 18 mm n -= 0.55 n =0.58 n =0.61d =19 mm n = 0.61 n = 0 .64 n =0.66d = 20mm n = 0.66 n = 0.68 n =0 .70d = 23mm n = 0.75 n = 0.77 n = 0.78d =25mm n = 0.80 n = 0.81 n = 0.82

TBble2

II it Is assumed, on the olher hand, thaI bothsurfaces are identical and having Ihe sameradius. as lor example , in a bt-concavs lens,formula (4) may be simplified as follows :

Rl

2(n - 1)

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In order to rnanutactura lenses 10 predeterminedcharactenstics. it is recommended to assumea plate spacing of between 19 mm and 25 mm forlhe :3 cm band. This entails refract ive indexesof between 0.61 and 0.80. For the other micro­wave bands, the spacings can be calculatedfrom formula (1). As it maybe seen.me refractionof the lens is inversely proportional to the spacingof the plates. For a given focal length, a relativelylarge lens radius will have to be given in orderthat its construction is rendered easier. It mustalways be remembered. however, Ihat the re­fractive index must be held within the givenboundaries.

therefore,

Rl =2f(n-l) (6)

h)Fig. 1J: Three methods of achIevIng directivIty by

means of a lens

Fig. 12: Hom dimensions for calculation In 8K8mple

l 35 mrn

4.EXAMPLES

lally, as shown in fig. 6. The matal plates arerectangular in form for ease 01 manufacture ­easier than those of figs 3 or 5 for example ,

It is possible to Increase lhe direc1ivity (gain) ineilher the horizontal plane or the vertical plane byusing cylindrical lenses . as in figs, 13& or 13b.The directivity may be increased in both planes byIhe use 01a spherical lens as in flg , 13c.

The cylindrical lens of fig . 13a is now consideredfor the first example as this Is easier 10 fabricatethan Ihe spherical lens. In the horizontal plane,the lobe is not concentrated and therefore thegain will be lower lhan with a sphe rical lens, butstili higher than that wrth the hom alone. Inpractical transmit operation, this may be advanta­geous as alilhe other stations will be on or overthe horizon thus making the operational align­ment of the antenna less critical. In this arrange­ment. the valuable microwave energy, which wasuselessly radiated into the ground or into thesky, is now concentrated onto the horizon .

The required focal length must now be deter­mined. The phase centre oi the horn can bedetermined in a dimensional draw ing: It is ap­proximately 170 mm away from the aperture .Since the lens will be a lew centimetres thick,and the focallenglh is measured from the opticalfocal point. which lies somewhere inside Ihelens and on lhe opncal axis , 30 mm must beadded to the 170 mm : a lens of 200 mm locallength Is required.

56 mm

In order to increase Ihe gain of any given hornantenna, a match ing plate lens is 10 be con­structed. The:3 em horn antenna has an apertureof 78 mm x 56 mm and a length of 135 mm(fig , 12),

As usual, the horn should be operated in thehodzontal plane . For lhe minimum insertio nloss. the plates of the lens are mounted horizon-

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hor naper ture

1

4hornaper lure

FIg. 14: Lens made with 20 mm thick expandedpo Ivstyrene

The lens is made from rectangular plates otaluminium kitchen foil which is about the thinnestmetal fol/ available. The thinner the plates. theless the obstruction they offer to the passage 01the microwaves so that the insertion loss is mini ­mized. For mechanical slabllization, the spacesbetween the toi ls are lilled with polystyrenenaat-msutatmq sheets and glued together. ThISmaterial is easily obtainable in thicknesses 0120 mm. does not refract microwaves and haslittle attenuation . The adhesive at 10 GHz .however. can be very lossy and so as linle asposs ible should be used - just enough to keepthe assembly in one piece. A glue which doesnOl dissolve polystyrene loam shou ld. 01course.be used .

From formula (1) . a refract ive index of 0.690can be obtained at 10.368 GHz for this lens.

The radius of the concave surface of the lensis from formula (5). 62 mm.

The plate widths are:

Nos 1 and 7: 58 mmNos , 2 and 6: 22 mmNos . 3 and 5: 10 mmNo.4: 7 mm

The length of the metal plates should be 120 mmor more ,

Six polystyrene sheets of dimension 65 mm x120 mm x 20 mm are now requ ired .

Fig. 15: Lens made with 18 mm thick expllnoocspolystyrene

Figure 14 shows the lens . Only the bold hori­zontal lines of the draWing represent the metalfoil plates.

lithe curve radius appears to be somewhat small .the 18 mm thic k polystyrene sheeting should betried: the refractive index at 10.36B GHz thenbecomes 0.595 and the radius 81 mm The platewidths then become:

Nos . 1 and 7: 31 mmNos . 2 and 6: 19 mmNos . 3 and 5: 12 mmNo.4: 10mm

The six oolystyrans sheets are dimensioned3S mm x 110 mm x 18 mm. This lens is shownin fig. 15 and with the small plate spac ings.the lens refracts more strongly so that the radiusis mcreaseo and lhe lens becomes thinner.

What should be done now if the radius stillappears to be too small ? The plates cannot bearranged \.0 be any tighter because the minimumrecommended refractive index of 0.6 has alreadybeen reached .

The lens can be made wilh a larger radius 11 ilis bi-concave in construction. II both surfaceshave the same radius. the previously calculatedradius from formula (6) must merely be multipliedby two: that resu lts. Using 20 rnrn polystyrene, In124 mm and the plate width then becomes

187

\

3 4

hor n I

7

VHF COMMUN ICATIONS 3190

400 Inm0:] - - - - - - - - - - -----'=

FIg. 17: A 400 mm focal length lensFig. 16: BI-ilOncaV8metal-plate Ions:

Redll '" 124 mm. Plate spacing -= 20 mm

Nos. 1 and 7: 40.5 mmNos. 2 and 6: 23.5 mmNos. 3 and 5: 13 mmNo.4: 9 mm

The lens is depic1ed in fig. 16,

II 18 mm polystyrene is used. the radius 01bothconcave surfaces becomes 162 mm.

Should even Ihis rastus be too small. a largerIocal lenqth will have to be accepted in order ihatil can be enlarged. For example 400 mm. Usingtorrnuta (6). lor refractive index 01 0.690. aradius lor both lens surfaces of 248 mm Is ob­tained (20 mm polystyrene sheeling). This lensis shown in fig. 17 where it can be seen thal theaperture 01 the lens has been doubled. Thisinfluences all microwaves emanating Irom thehorn (or into il ). This lens is rather thick.

II a small focal lenglh together with a Ihln lens isrequired . a multl·lens system can be adopted asshown in fig. 18. The total local lenglh I is cal­culated according to lormula (7) from the locallenglhs 01the individual lenses. 11.12....ln:

lit = lltl + 1/12 + llt3 + ". llln (7)

If it is desired that the radiation is beamed In bothplanes and the gain is then maximized. A bi­concave spherical lens as shown in fig. 13c canbe used. The melal plates must then have a

188

FIg. 18: VorlouBlen, combinations

spacing of 20 rnrn, a loeallength 01200 mm andhave a form as depicted in fig. 19. This is thebi-concave-spherical version of the bi-concavecylindrical lens as shown in fig. 1G.

When commissioning this combination 01 leedhorn and lens, only the distance between the hornaperture and lens needs to be adjusted. Thenighest gain Is achieved when 'he focal pointof the lens is coincident with the phase centre01the horn .

For 24 GHz, 10 mm thick polystyrene sheetscan be used as distance spacers between Ihealuminium plates. In this case. the refractiveindex would amount to approximately 0.78 (It IS

frequency dependenll).

Alter these many theoretical considerations, Ihave resolved to commence the construction andtesting of a metal-plate lens. logether with otherlocal amateurs. without delay. The results will bepublished as soon as lhey become available . Ihope that many readers will lind the inspirationto bUild and experiment with this torrn of antenna !

VHF COMMUNICATIONS 3190

-;,TRIP ~ Fig. 19:A spherical convergentmetal-plate lens (SC8le2 : 1)

7

RRD IUS 109 , ii1

.~ TR IPS 2 Ail[! .;

R:';DlUS 124 mm

STRIPS 3 riND 5

5.REFERENCES

(1) Kildal, Jakobsen, Rao:Meniscus-Iens-corrected oorrugated horn :a compact leed for a Cassegrain antenna.lEE Proceedings, Vol. 131, PI H, No.6,December 1984. pages 390·394

(2) Clarricoals, Saha: Radialion patterns of alens-corrected conical scalar horn .Electron . Lett .. 1969.5, PP.592 - 593

(3) The Handbook of Antenna DesignVol. 1, 1982, ISBN 0-906048-82-6

(4) Reference Data for Radio EngineersHoward W. Sams & Co. Inc . 1981,ISBN 0-672-21218-8

(5) Reilhofer, J., DL 6 MH:Praxis der Mikrowellen·AntennenISBN 3-9801367-0-1Verlag UKW·BEAICHTE, 1987

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