BSTJ 50: 4. April 1971: Maximum Power Transmission Between Two Reflector Antennas in the Fresnel Zone. (Chu, T.S.)

6 MB·English

‘Two Reflector Antennas in
the Fresnel Zone

by T. 8, CHU
(trnvmet rnived Armt HH)

Pocer transfer between to eipsoial reflector antennes wth oom
sion focal points nd ral-mae feed has been investigated. Aas
A esrvdatyeyunnciie jo! prtins, the Bape pattern aj open
fend circular weavenuide crete by the TEs mote, the mime Cr
Inissiom eaefieinn! betoron reteetor apertures % found to be within
1 perce of th wat comptes for Wansascn beeen fe srniae
fawertices with opbinwn Rlowisalion denribed by the generalised
rotate sphere! jenetion. Monasrioin tone betecen te reflector
rena se fepur se computed for vores vetves of
the puraneter iB]. The minis teanswiion owe
btaned nen compromie beeen ice! spltosar and pee tore downs
imision efcency

The vioe of th inconnenieace of building dierent eliuoial rfor
fora for aiferent antenna apaengs te seh we peer
rransfor, we axamine the feasibly af wting © defocused ehipenid fo
siwlte elipoide of aifeext foral irgtts. The deviation of the
Getare phase sitbubion of « dejocused elipaoid from a required
plerisl phase fomt wagpronuately piven ty en explect expres
A eimpbe expe do the treason ons ro smd! pee a
‘ito ahaa {ura gine mazinana pose deviation

‘Milner waves hase ever fen nein Togelaal cao trans:
son ayeveue Because urn clei, However, ileal ase
fon ever start sje (eas Ise “han T kev owt be atari? 3p
Iilineler wave systems, Tor sail, De Pistarephenel diseibation
in Inge cts preeonad log Ry Roars Te vor igh Urnwaeon
1408 yun nats sxeueon mreMTeML FoMNNAL, APE 12

flvieney may leave e ange margin for sn attenuation Uo insure igh
Salinity. Heve the onmemniring ata wveriving ancengae my be
‘shin the Braerel zone of rat other.

‘Mesirnum power transfer between two apertures in the Frrnel
gon tees place shen the ld ction appears 8 ce lowes! t=
{or tolls of confocal open rsonstor:"* Two ellipsoidal restore
‘vith common fore! pints maar provice the requved apertare plese
slibacon Tie is epherie! ‘ave ‘Tont wit Die eener of eat
fe located a Uy enter ofthe ater sjertue. The optimum ampli
fue tistencioz prolate spheroidal fonetien fo> a relangulsr
perture or n geurcalies prolate splstaidal funesion for w ereular
Sperlars 8 Takeebita’ bes shown (hat erases ted zaosienMhuninagion,
‘hich fs vaynclrsealy icenten) tg the generulizod prolate spheroidal
function, souy give a tramason efleiency betwen bv cireular ap
fuses altel se pond ae tat unr george! pelatesperuil r=
ination. Towever the truneatedgousna distsbution ony looks simple
in terme of nathersatess manipiltion hala st prea! realization
hppeare sot ary essior than taat of poate specoldal funtions, Fur=
Thevmare, ifs lens or wileto i ured vo produce the spberial phase
frant, she ised spil-oves mus. be ter into acount. The maxima,
power eranefer btwn the feeds of (vu relector antennas wi be ob
tained aa « eorapromine between Seed cpil-over Ines and apertae tans
Iris efctouy. This pooeocare ie eilar to ontinziag the gun of
puvaholoida! antnns. The aperture blucking eMart ean be mae very
Tht iy asin the periscope tzpe structure” which vrsally eliminates
Ue ford eupperte, This paper mi prevent the ealnlated rests of
Fresnel zone trunsiichan between tay ellysoidal estar entemnus
tri dalemosde fea. Th ven of che meouvenierey uf Inilng dier-
Fvellipsaial sectors fon aiferone anton spaings, we wil al ex-
nine the fevslity of asing a dafoeaveeligeek® to sinalate cli
‘eich of itera fal lena

Nealoetng the intazetionetwecn the anceznae ond exeuming thet
the tangential cumpenents of the elie sid magnetic lds are re=
Teted by the few space impedance ay oxch poiat of Ube twe apertures
fh ary thereto of the reeiva o ltont od pear beteve. RU
‘sparvure" nj any’ aparation cam be show to he

+ Not mo he camfamed with tacetiiow Uetwoon twa entennas which inludes
slave of he Fou
nse, wine mie aaxrER 1400

where BE and BS a2" tangential enmpanents of the aperture Geld ise
sibulioow when ay ane ty ore landing tespelively Using tae
‘noc angle Presi apprasinacion, the ditasee Ze may be sppran=
roslea y

Bem UE te = Ry =, e

a e
ee

lee che coordinate system is hstrated in Fig. 1. Then the near

Tiel poster avai “orm ls heroes

pote Ulver epee!
PP welf mead imcash
a - ten [HEH], an
R= Roo, i] ay

le, 1 elisa ellen nt cot fre oi,
14) ra wen SvoTESE MBCHOTEAE SOUUNAL, AFT 1871

1 ie aperuze cisributions ane ereulrly syrametrig, equation (8)
con be reduced to

LEE etowe nen a vir ae
{finoveralfineve cp ®

where p (haya) for twe eiveiar apertures o° radii ay and ga
Ohne notes that Die Usnemnting snd weeiving apertures may hae
Hifecent rad, while the optima FTaminction funetion Is dents!
for fve two enarmizes, Wha boll end Biz are seal, Ue Sehwarte
principle gives the following wdicion forthe rnimization of equne
tion (6)

Qlnovin [Biwi saroviw ee ©

“The eubectpt of has boon Amped beenuso eyuntion (i) is satisiod
by both fi H. Tae abowsHndegeal equetion ns heer thoroughly
fveaignied by 1. Slepina® and gi?) — Birh/e i designsted a
fenerilized prose spheroidal fanetion, The opimam transmission
oeTiiens taken from Sleian's wrk is given in Table | Zor reference.
“Siw a simple way of eppmoaitotely reiing the opsinus apart
distsbution appears be the iCamsinntion of a elpeoid eestor by
fs cuulennce fe. Inthe vvinily of ch efector, se west fea will
fallow the yeomoitieal ootits 187s whieh are poked towara the neat
focal int ae shown in Fig 1, sod thus the require sperieal pine
font wil be oteated in the spertara. An experimest on dale
fpertares, one fo two wavelengths in diate, showed the mowsuced
patting to be cently symmetric ara emontaly is agreement with
Zhe Haplane pastero of wn epenvend eicalar waveguide excited by
TE tie i.

TPE sone] ng
~ Gat)

wire ue the ceunfreon aoe narod in avons. Stage
Usa ea every ely elem araelh
beso in ic eit ser he sera ator nae fo
the rae esa frm te ee thereto wuz om
Cy th sacs hat pct Tin the pete dsbaton
ipl tote cd pater
dened sos wont cassia co

He

oo

where ar/2h = tao wr fi the fowl length uf the rter, The
forcbination of equations (71 ana (8) cam be usad 20 drvenmine the
‘value of for any enrtsponding illumination taper as plottec in Pig
2 Sulaliuling equion (8b into equstion (5), umereal integration
sll gre che stanewiesion eorficins Lecce tio elipwoidel elector

mde foale. Phe eamputed dala Inve been
ploties in Fig. 9 for 1) = 0.5 ana various values of the parameter
‘The masizum cbicisney using dual-anede Zec2 as exeacing spillover
tie bean totlsted in aby for oman with be uphimay ee
ney using samplitude illumination of peneralized peuate eheroidel
neon,

"The agneesisat between he second and thine enuanne in ‘Tbe Jie
inn excelent. The insensitiity of the tesnamision eoeficion: ta
‘saul digercones in ilkguination ie not muzprsing in view of the ea
Honsey property of equction (Si, Zable I dees net show the maxiauma
seiezey wh du ial for p= 2 al 10, bore “0 hem
snstical model in equicon (7) for Une dual-mode putters hue not een
‘emerientally verified fo Ce steurterenee ofthe wvesuice outside
{Ee range 4 = 6, Humor, ae amlel coors the anne teoatege
range a deel ie Vanes Co senithesice ruven guia
tistricntion ure unwarranted, As far ce maximum power teats be-
‘vcen Seo aperture is enews, my apertucedstbutien. wil
sumbles the grazralized prolate epbereida! fanetoa may aekievs peas
tally the optimum trapemaston eicczey. As n example of talerable
ldsezepacey, the shiloh fed hasinatio foment taper

jai mains rasan ve foe = 85
‘wth the roresponding generalized yrola-e spheroWal faneion

‘Tamue I~ Pownn ‘Desvarmn Hemierescy oF Two
(Cueran Aruarmns
1412 rus anaa avszese emevomest soumean, Am

Jn Fig 4, One notes thatthe over-al sinilsity i efficent to sebieve
‘rasemission elicits Gflerng by er'y 03 percent wll the age
Nyinwriena der by sone uhan a dB.

‘Next ne lum aut attention (othe spillover Tos of x feed. LF te =
thctor fe laminated oy twenty eymcetrie fend paver FCG,
then the cretion af the eassey dmerogled oy the rolevior wil be

ere is Ube hal angle eubtended by the relent dhe focus ar
the heck lobes have bio neplated. Substituting equation (7) sen
fusion (8), we compute the loal spillover lose in desibls from
S130 logs 11 | an skew in Fig 3. Tae poceence of v0 feeds in the
totem neon fr the Evlat tv Tis sen thatthe pillnver los i
Sr uportans as the pom trunser los erveen two refeetor aperbies
{h ctceroining thw toa, transuieian Joa ebween Uso ovostor act
feanns The rincmun: tral ura lose bec fs wil always
be preabr tin the power tnafer lee betwoes the reflector apertare,
fd ulways oorute at ea iluaination taper stronger thn Cat for tbe
fuaxinom wanemigeion beiwrsn sn aaerizes, Avr ight decease 3
ftansaigeioy lose die to devin of the aperture dsibulion from
‘hye generelized prolate ephereii) faseion will ertkin'y be swamped
by the feu power toes, Pgnee 8 indiatee chat sb ilination
taper cerrspuncing #0 he enssium power transfer deeeuses as the
pvametr pvroate, bs the distance beteza two rlloeorsinceaees
omend the far zone condition p =O, 2 optima: Muanivaion taper

ig, 2-Rellina ume fod pete arse sad ap
FnEsSrt ZOSE PORTER TRANSTRS, iis

EUR NE t ee e

@

will uporonel: 1 dL which masimiaes the Prauno‘er gain of « pere~
Dole antenn? One retes that 12-1 peruse taper arse bo
Wall ow patie taper, slowing 6 2-€B space attention fel for
(5 4/0 ratio, Wha {1 deseases restr values lw ep eovr lowe
curve will bo ested fo the righ! Deesue of inercasng space atteite
tion taeor, hea the suiitnom of sw ou wil Iw alen nivel tn he
Fight ond upd, Longe {7D ratio whisk requis wary for pater

fesse sigReant Ines due 20 apertateleking wiih aw bees
elt ia the alee en gulaions

a the preceding setton ine have shown thas ellipeidal retetons
are new Zor maxima power lansier beara te reetonanienons
inthe #reamel regier. "The -eqyiee “eeu lel «of the ellipaoidal ro-
144 ry aca sxeiman emoyomeat sounaty APR

Fi. -Conyarom hater exmuanaprt tans

flctors aro determines bythe dicenee betwee: Une star and ie
dese (72 ti, Tris abvioaay incon senien: to build dierent elip~
boil zeviors tne diferent enkeuns epacizgs; hawecer, appraxnnale
jing poole af differen: focal rts I” a delacucd epi ean be
fn atiretive possibilty in sume praetial stucions, The neeesry
tisphcnen ofthe foe tlons the aye 30 bo fet deerme. Then
rel cule the appron tiie phase deviscon between the weve
Font reteetol om a defocssel cian and sho spericn) was fut
inthe aperare ut n quired ellipsoidal reactor. An upper hound of
tie tronsrision fe wl Be wllained for 8 given maxi phase
‘heviation
"The ection of at elipsid ean be writen a

[eR

=! 38 r-Vi-g ou
2-8 e] ®
whore fend are te twa foe bogs, Now let us oonsidar another
‘Alpe wih eorresponding feel enaths ae RY

a

eae ee ae SS Se
[mRESSTL zoe row ams wis

‘These sw lini acne a the ip = 0. We wil imps the wn:
‘ition thi che to ellipsoid also coiolde ab the ei p = a se shown
in Fig, 5. Taking te fine: three eras of ae Linonal expansion of
Whe sears sao fs gusto: TO) and (111, We obtain an expression
fur the required dione silane

03

in which the approximations f 2 2 and fA have boom used Sud~
sunting esquet tn C12) te epariess 00) ane (1, she appneximate
Aviation besmven the vv eligi heewnes|

Froote reflected from tbo elses shun mt Pig & Sino these
clipes er le droutpncubahs, fe relation ton @°2 = oy 2E ie
fnprosinately vais. ‘Then one ariver at the following expression

yl
nape?

feiya-n

ay

‘De las actor in eapatn (14) yey Dene Bra iy whem 2
> RL. ThisTuclor snorouches unily whi R > >, in, soprninaling
sallipsuid in eons praholnd Th suai wi the Draee
ft eqanton (14) fs tle pace aviation’ uly ee Fa peal ed

i, SCacmry of dolore lin
1418 came auth aremme seOMSIOML FoEREAL, AIL 102

Aeteeures paraboloid fez w dese spherical wave font for Fresnel
number (@'/AR) of tity, wn has been plot ix Fig 6 for vasious
alts 0° (72 vetio, The maxizictn lar devitios te four Ua he To-

seh] os

-16)] on

optim ellipsoid for sinizaining tie phase deviation of equacon (4)
fan be fond bi equatiog

Tig, foAvcuny yy divjasae betmeea x desu stolid ea an
ae TR cee “ecw