phase correction by dielectric slabs in sec horn ant

7/27/2019 Phase Correction by Dielectric Slabs in Sec Horn Ant

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where HT:am(z~'s the deri\, ative ofwith respect to its argument.In reg-ion 2,

Thus,

end

PROPAGATIONONSTAKTSThe fields insidewaveguidesre as-

sumed to be exponentially propagated, i.e.,where y is a propagationconstant.Following the example set by Barrow and

Chu,' and assuming this is also true insidethe horn, then for region 1,

-1 aEZlEzl ar1=--'

Substituting Ezl from ( 6 ) ,7 1 = a1 +j61

= - d p o e 1 (2)- : ; L ~ ( ~ ~ ~ E G) , (12)H r / + , , , ( ~ d p T l r )wrhere HT;$,,,(?)'s the derivative of H T / ~ , a ( 2 )withespect to its argument; CUI is theattenuation onstant n region 1; an d 81is the phase shift constant in region 1.

Similarly for region 2,y.= a?+ &

It should be observed hat both 7 1 an d 7 2vary with r .

electromagnetic horn." h o c . IRE. vol. 27, pp. 51-64:I \V. I.. Barrowan d L. J. Chu,*Theory of th eJanuary. 1939.

COKKECTIOSF THE PHASE ROKTITHA S OPTIhfLW r\MOUST OF DIELECTRICI t is convenient o define the dielectric

having he argestproduct pe as he harddielectric, and the other as the softielectric.\\'hen the ard ielec tric is used in th emiddle of t he horn (region l ) , the circularwave front of const ant phase has a smallerradius i n theharddielectricand a largerradius in the soft dielectric. If theproperamount of hard dielectric is used i n region1, i t is possible to reshape he phase frontand approximate a uniforlu phase distri bu-tion at the mout h of the horn.

Fig. 2 s h o w a drawing epresenting aphase front at the mou th of t he horn con-taining a harddielectric in region 1. Th etotal phase shift in each region is given by

phase shift in region 1 = Jo"Bldr,an d

phase shift in region 2 = JoBzdr.r2From Fig.2, it can be seen that the phase

shift will bemorenearlyuniform if theshadedportion is a minimum.Designatingthe shaded area as A s h ,

L ! C O S P Q d i 2A s h = 2 l , Jo rdrdO

If the shaded area is to be a minimum, then

Sol\-in:: for the opti mum # d :

Fo r a given horn, the length L and radiusr2 are known, but rI must be calculated fromthe relation

JoBldr = "@?dr.As an example,with & =60" an d I:!

side of the horn is 0.54 X out of phase with= - LO h, the wave reaching the aperture at thethesamewavereaching hecenter of th eaperture. This difference in phase is usuallyconsidered too largefor a n optimum horn.

Fig. 3 sho\x-s a plot of thephase con-stants @,nd 19.s the radial distance fromth eapes. $ is theplot of the magi narypart of ( 1 3 ) . Iiegion 1 is assumed to containa dielectricithelativeermittivityc,=1.22. Theareaunder he urveup toradius r.=4.O X is found grdp hic dy to be

FIE. 2-A phase front at the ap erture withtwo dielectrim in th e horn.

i 4 ) .Fig, 3-Phase constants 81an d 81 vs radial dis tanofor Q~ =bo". e,,=1.22. r r , = l . O O .

relative square units. The area under ,& asa function of r , is plotted in Fig. 4. Theradius r l r where heareaunder he wocun-e s is th e sam e, is found graphically tobe r l = 3 . 7 X. Substituting in (14) he opti-mum q4d becomes ~ d = 4 9 ' .

~ I E A S C R E DATA.A plot of the relative powerat a distance

from his horn (example above), with andXvithout the hard dielec tric inside, is showni ll Fig. 5. Both cun-es have been normalizedto the same relative magnitude: the barn-width of the main lobe at the 3-db points isreduced from 24O to 20", and it will be ob-


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1961

B U G L E : So ' < = ,.DOD l E L E t - R C i L B e

f , = 1. 2 2___._L T T E R V PIT^ P H A S E F R C N - C O R R E C T E D- P ~ . T T E R N W l i H P H 4 S E F R O h T U N C O R R E C T E D

FiK. 5-H-planeectoralornntenna.plativepower v s azimuth angle 9.Dotrrd ine =pattern~ l - i t h hase h n r co rrected; d i d line =pat t e r nw;th phase iront uncorrected.

served tha t he sidelobes areconsiderablyaltered.

COSCLLWOSSThe phase front of a wave nside a H-

plane sectoral horn can be altered b>- a di-electric nserted inside thehorn. .in opti-mum-sizeharddielectriccanbecalculatedwith a flare angle given h>.

This correction of ph ase mprov es he arfield pat ter n as x-erified by measuremen t.

31. A Q E D D U SSuclear Engrg. Dept..Agricultural and hlechanical

College of TexasCollege Station, Tes.J . P. GEKMAS

Dept. of Elec. Engrg. and Tesas Engrg.Experiment StationAgricultural ndMechanical College of

'Texas. College Station, Tex.

Comparison of ObservedTropospheric Refraction withValues Computed from theSurface Refractivity*

Summory-Radarlevation-angler-rors observed in the Tularosa Basin f NewMexico are compared with values predictedfrom the surface valuef the ra dio ref ractiveindex.Although hismethod of predictionis not particularly efficacious un de r th e con-

* Received by th e PG.W, March 24. 1961.

ditions of thisxperiment,ncouragingagreementneverthelesswa sobtainedbe -tween redicted nd bserved: )meanvalue of elevation angle error, b) variationof elevation angle error with N,, nd e), thedegree of reduction n heuncertainty ofprediction gained over the us e of a single-standard atmosphere.

INTKODCCI.IOS.i recent artic-le by =\nderson, Beyers and

I- upon the urfacevalue of the efractive indes, did not ap -preciably mpro\-e he prediction over hatobtain ed from a fixed standard arnlos phere.Th e purpose of this note is to show the rela-tive agreement between the abol-e rneawre-mentsandan ndependentmethod of pre-dicting the elevation-angle error i n terms ofthe surface l-alue f the refrac tive index.

~ < E F l < A C ' I I O STHEORYThe angular bending of a radio ra>'m;iybe well represented by [2], 3 ]

I 2T = - l . ,ot edn , !1)

where n is the refrac tive index and e is theapparentelevation angle. Eq. ( 1 ) maybeevaluated for the ota!bending of aradioray passing completelyhroughhet-mosphere b>. integration h?- parts to o btain

= s,. 0- 6 cot e,wt e,-S,,,, R , . % 7 = ~ . 10-6d(cot e!, (2,

where ~ V = ( n - 1 ) 1 O 6 and the subscript s in-dicate. a value at the ear th's su rfac e.

The second term of ( 2 ) contributes. atmost, only a few per cent of t he tot al for allS , 2 l O 0 [ 3 ] , where 8, is the apparent eleva-tion angle a t the earth's surface. This is animpo rtan t and well-known result at opticalfrequencies. I t has also been shown t o holda t radio frequencies [ 3 ] , 4] sufficiently high( > Z O O kIc\ as o be negligiblyaffected bythe onospheres. Fo r large in i t ia l l e i~at ionafzgles, he b e n d i n g 0.f a radio ia? p a s s i n g rom-pletely t lzmuglz t k e atmosphere is efectir ,elyi a d e p e n d e n t of tlzt Etertiral ~ ~ f ~ a c t i w - i m i r xstrurture afzd m a y be determined j r o n l thei z i t i a l e a l ue s o f t h t r r f r a r t i z i n d e x nn d elera-ti077 atrgle. Eq . ( 2 may be \witten as

71 I7 = - n cot 8dn b:Ys+ a , (3)

where a an d 6 are constants to be determinedempiricall>.. S ot e ha t for ah = 3 3 , T is

identical o he elevation angle error e bu tdiffers systematically for targ ets within theearth's atmosphere. Even so, e may be wellrepresented as a linear unction of ~3'~ [1].

The elevation-angle error has een evalu-atedbynumerical ntegration for a argenumber of refractive-index prohles. 'l'heaeprohles were chosen to represe nt the rangeof profiles likely to be encoun tered a t an ylocation or climate [ + I . The values of e an d'\,? were tabulated. These data. comprisingsome 77 profiles, thenserved todeterminei f e could i n fact be represented as a linearfunction of S,. T h i s was done by deriving aleas t-squares regression line of e upon X , .'Thus dete rminat ions of th e slo pe b and theintercept c i n ( 3 ) [modified for e ] wereob-tained i n addition to a determination of th escatter of the indix-idual values of e aboutth e regression line. This astvalue. calledthe standard error of estimate ( S E ) , llowsa quantitativemeasure of how well varia-tions i n e are accounted for by variations ofiV,-. For example, i f all of the variations of ecould be attributed to :X7&, then SE(cj=O or.conversely, i f none of the -ariation n ecould be attr ibut ed to LV.~,hen SE(e)=s(ej.the standard derivation oi e , and nothing isgained by the use of LY~.-4 measure of rhe practical usefulness ofthi? approach is the ratio [SE(e!/s(e)]=P,.(This is the s ame basic. measu re of improve -ment used i n both eferences [ l ] an d [4] . )P, s no greater than 0 . 1 for radio rays pass-ing completely hrough heatmosphere a t&>3" . P, ecomes largeras: 1 the aytraversesas limited height nterv al of theatmosphere A h : or, 2 ) 8, becomes stnaller.For example, P , is less than 0 .5 if ah25k M and & > l o , or i f Alz>.3 k>I an d 8,>3"

The .\nderaon. Beyers and Rainey ex-periment \vas conducted a t &-Ic an dAh-1.7 kM where P , would be expected tobe about 0.9, and thus constitutes a severetest of t h i s approach o efraction correc-tions.

D l .

COMP.4RISOfi OF hIEASLKED A N DPREDICTEDLEvxrIox-.L\SGLI

phase correction by dielectric slabs in sec horn ant

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