Reflector Antennas. Contents

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1 Rlctr Antnnas Mtivatin: - incras th aprtur ara and, thrr, incras dirctivity - cllimat nrgy in n dirctin - rduc th siz th antnna systm - us th rlctr (and subrlctr) r bam shaping Cntnts 1. Intrductin. Crnr rlctrs 3. Parablic rlctrs 4. Systms with subrlctrs 5. Aprtur blckag 1

2 1. Intrductin Gmtrical cniguratins sm rlctr systms a) Plan rlctr b) Crnr rlctr Exampl: Micrstrip antnna n larg grund plan Exampl: Sctr-illuminating bas-statin antnna c) Parablic rlctr d) Subrlctr systm Exampl: Satllit dish Exampl: On-bard satllit antnna (subrlctr might b shapd)

3 . Crnr rlctrs Prspctiv viw crnr rlctr and wir-grid mdl. Typical rang dimnsin: l l D a Imag thry can b usd i na = p a = 9 a = 6 a = 45 a = 3 3

4 3 Exampl: Lt a = 9 and (, ) th pattrn th radiating lmnt s z. y 4 1 -jkr + jks cs Y + jks cs Y + jks cs Y + jks cs Y Er é ù ê ú ë û cs Y = aˆ aˆ = sin cs (,, ) = (, ) x 1 cs Y = aˆ aˆ = sin sin cs Y =-aˆ aˆ =-sin cs 3 x y x r r cs Y 4 =-aˆy aˆr =-sin sin Er (,, ) = [ cs( kssin cs) -cs( kssin sin ) ] (, ) p AF(, ) = [ cs( ks cs )-cs( ks sin )] r AF(, ) -jkr r r 4

5 Similarly: With X = kssin cs, Y = kssin sin a a a æ Xöé æxö æ Yöù = 6 : AF(, ) = 4j sin cs cs 3 - ç è ø ê ç ç ë è ø è øúû é æ X ö æy öù = 45 : AF(, ) = cs( X ) cs( Y ) cs cs + - ê çè ø èç ø ë úû é æ 3 ö æy = 3 : AF(, ) = ö cs( X )- cs X cs ê ç çè ø èç ø ë æx ö æ 3 öù - cs( Y) + cs cs Y ú ç ú è ø ç è øú û 5

6 Othr crnr rlctrs Exampl: -3 amplitud/db MM (Fk) Ray tchniu Ray tracing mdl ID Incidnt Diractd RD Rlctd Diractd RRD Rlctd Rlctd Diractd dgrs Cmparisn btwn ray tracing tchniu and numrical cd (Mthd Mmnts) 6

7 3. Parablic rlctrs Th parablic surac is mst cmmnly usd as a rlctr. Exampls: Satllit TV Cmmunicatin links Radar Tsting Radi astrnmy 7

8 Gmtry: OP + PO = ( = cnstant) =cal distanc OP + PQ = OP = r ', PQ = r 'cs ' r'(1 + cs ') = r æ ' ö = = 1+ cs ' ç çè ø ' sc, ' /d rati: Subtndd angl: ( ) 1 = ct d 4 1 æö d 1 1 ç - - èø d = tan = tan d æö ç d 16 èø 8

9 Radiatd ild Lt G ( ', ') b th gain pattrn th d, thn th ild incidnt n th rlctr is: -jkr ' i E ( r', ', ') = ac ˆi 1 G( ', ') r ' Pt m whr C1 = and Pt is th ttal radiatd pwr p Th rlctd ild is: -jkr ' r E ( r', ', ') = aˆ rc1 G( ', ') dl r ' aˆx sin ' cs '(1 -cs ') - aˆy(sin ' cs ' + cs ') whr aˆ r = 1- sin 'sin ' At th plan passing thrugh th cal pint: - jkr '(1+ cs ') E ( r', ', ') = aˆc G ( ', ') = aˆ E + aˆ E r ' ap r 1 x ax y ay 9

10 Th radiatd ild th rlctr systm can b writtn as: -jkr jk Es = (1 -cs ) (-Eax cs -Eay sin ) r òò -jkr S jk( x ' sin cs + y ' sin sin ) jk E = (1 -cs ) (- E sin + E cs ) s ax ay r òò S jk( x ' sin cs + y ' sin sin ) dx' dy' dx' dy' Nt: Th backward radiatin th d is nglctd hr. 1

11 Exampl: 11

12 Crss plarizatin Crss plarizatin is n th majr prrmanc critria in rlctr antnna dsign. Its main surcs ar - Nn-idal pattrn th d hrn - Diractin at th dgs th d hrn - Inducd currnts n th rlctr - Diractin at th rlctr dgs Th irst tw itms ar addrssd by th dvlpmnt multi-mdal hrns and crrugatd hrns. Nt that crss plarizatin vanishs in th principal plans and appars t b maximum in th diagnal plans. Multi-mdal hrns ar basd n th principl xciting crtain highr-rdr mds which straightn ut th aprtur ild. Exampl: Th hrizntal cmpnnts th lctric dipl ar cmpnsatd by ths th magntic dipl, thus rsulting in a vrtically plarizd aprtur ild. 1

13 Arthur C. Ludwig, Th Dinitin Crss Plarizatin, IEEE Trans. Antnnas Prpagat., Vl. 1, pp , Jan Ludwig s dinitin 3 is widly accptd as th crrct mthd t masur crss plarizatin. Exampl: Micrstrip patch antnna (spctral-dmain analysis) Principal plan pattrns 45-dgr c-plar E-ild 45-dgr crss-plar E-ild 13

14 Ludwig III Assum that th antnna systm (hrn at rigin) radiats a ild having Ex and Ey. Assum that th dsird plarizatin is th y-dirctin. E = E cs -E x E = E sin + E y sin cs E = E cs = E sin x x C-plarizd ild: rcivd by mving th masuring hrn axis but kping th allignmnt with th y axis Crss-plarizd ild: ild prpndicular t c-plarizd ild Lt E(, ) = E(, ) aˆ + E(, ) aˆ On th z axis, E can b writtn in x and y cmpnnts: (crss-plarizd ild) (c-plarizd ild) c-plarizd ild = ( )(sin + cs ) = ( ) c-pl. rintatin: crss-pl. rintatin: aˆ = aˆ sin + aˆ aˆ = aˆ cs -aˆ cs sin E E (, ) = ()sin (, ) = ()cs Cnditin r zr crss plarizatin in all dirctins! Fr rlctr antnnas: Idally, th rlctd ild has n crss-plar cmpnnt i th E- and H-plan pattrns th d ar idntical. Maximum crss plarizatin ccurs in th diagnal plans. 14

15 Dirctivity and aprtur icincy Lt thn G ì G ( ') circular symmtric ' 9 ( ', ') = ï í ï ' > 9 ïî ì ü æpd ö æ ö æ' ö D = ïct G ( ') tan d' ï ç í ý è l ø çè øò è çø ï î ïþ Sinc D 4 p Ara 4 p ædö æ dö = = p p l l ç = è ø è ç l ø max In gnral: ap = s t px b r æ ö æ ö ' ap = ct G ( ') tan ç d' è øò çè ø Aprtur icincy 1. 1(1- s)=prcntag pwr lss du t nrgy rm d spilling past th rlctr.. 1(1- t)=prcntag pwr lss du t nnunirm amplitud distributin vr rlctr. 3. 1(1- p)=prcntag pwr lss du t phas variatins vr th rlctr surac. 4. 1(1- x)=prcntag pwr lss du t crss-plarizd ilds vr aprtur plan. 5. 1(1- b)=prcntag pwr lss du t blckag (d, struts, subrlctr, tc). 6. 1(1- r)=prcntag pwr lss du t randm rrrs vr rlctr surac. 15

16 Cmprmis btwn spillvr and tapr icincis é êë cs n ( ') aprtur distributinù úû Spillvr icincy s = ò p ò G G ( ')sin ' d' ( ')sin ' d' Tapr icincy t æ ö = ct ç çè ø ò ò G G æ ' ö ( ')tan ç d' çè ø ( ')sin ' d' 16

17 Aprtur, spillvr and tapr icincis as a unctin th d s angular aprtur 17

18 Apprximatins r aprtur icincy ì n n G cs ( ') ' p/ n Lt G ( ') = ï í and G = ( n + 1) ï p/ < ' p ïî whr ap( n = ) = 4 sin + ln cs ct ê ú { ( ) é ( ) ù } ( ) ê ú ap( n = 4) = 4 sin + ln cs ct ê ú { 4( ) é ( ) ù } ( ) ê ú ì ( ) [ 1 cs 3 ( )] ( 6) 14 ln cs 1 ü - ap n sin = = ï é ù ï í + + ct ï ê ú 3 ï ïî ë 4 ï1- cs ( ) ( ) ( 8) 18 é n ln cs ù ap = = - - ï 4 ê ú n û ë ë û û ( ) ( ) ï ý ì [ 1 cs 3 ( )] 1 ü - ï æ ö í - sin ( ) ï ý ct ç ë û 3 çè ø ïî ïþ d ( ) -1-1 d = tan = tan ( ) d d 16 Nt: I G ¹ ( n+ 1), thn th intgratin n p. 15 must b usd. 1 ïþ 18

19 Exampl: d = 1 m, /d =.5, runcy =3 GHz, G ( ') = 6cs ' 1 ( ) Aprtur icincy: -1 d? n = tan ( ) =, G ( ') = ( n + 1)cs ' Ys 1 - d 16 { ( ) ( )} ( ) 4 sin ln cs ct ap = + é ù =.75 (75%) ê ú ë û Dirctivity: l æpd ö æp 1ö = m =.1m ; D = = db 9 = ap 3 1 l çè ø èç.1 ø Spillvr icincy: s ò m cs ' sin ' d' = ò cs ' sin ' d' - cs ' 3 = = = p/ p/ 1 3 ò -cs m+ 1 m + 1 ' cs ' sin ' d' - cs ' Tapr icincy: t ap.75 = = =.784 s

20 Exampl (cnt d) Aprtur phas dviatin: assum m= /8 D D D D æ m ö = 1 - ç çè ø æ ( p /8) ö = 1 - = db ç çè ø D = db-.697 db» 48 db

21 Exampl: A parablic rlctr has a diamtr 1 m and an angl =. Th dirctivity at th prating runcy 5 GHz is db. Th d pattrn is givn by 1 G cs ' G ' / lswhr Find th tapr and spillvr icincy, assuming n thr lsss. 3 Slutin: æ pd ö D = ; m 1mm ç l l = = = = çè ø ap = =.799 ap æ p 1m ö ç.1m çè ø s t G G ò cs ' sin ' d' - cs ' 11 = = = ò cs ' sin ' d' - cs ' 11 ap.799 = = = s

22 4. Systms with subrlctrs (Cassgrain systms) Mtivatin: plac th d at a cnvnint lcatin rduc spillvr and minr lb radiatin btain an uivalnt cal lngth gratr than th physical cal lngth bamshaping by shaping th subrlctr scanning by mving th subrlctr

23 Hyprblic subrlctr Hyprbla x a y - = 1 b Eccntricity: æb ö = 1+ ç > 1 çèa ø Ectiv cal lngth rlctr systm = m 3

24 Ellipsidal subrlctr y b a x=a x x a y + = 1 b Eccntricity: æb ö = 1- ç < 1 çèa ø Ectiv cal lngth rlctr systm 1 + = 1 - m d Nt: Fr bth hyprblic and llipsidal subrlctrs, nly n th tw cal pints will rsult in >. m 4

25 Rlctr systms Cassgrain Grgrian 5

26 d p 5. Aprtur blckag ds ' d a d s Minimum blckag ccurs whn th diamtr th subrlctr, ds, which blcks th radiatin rm th parablid, uals th diamtr th shadw ds cast n th parablid rm th d. ds = d ' Th diamtr th subrlctr is ds = 4 a ' Lt th nulls th main bam ccur at th dgs th subrlctr, thn l a = bd ' whr b is th rati th ctiv aprtur t th blcking aprtur dp -d dp b = = -1 d d Frm abv d d d d d d ' 4 a s = = s = a = d s l bd d s = l b Subrlctr diamtr r minimum blckag 6

27 Exampl: d = 1 m, /d =.5, runcy =3 GHz, % blckag wrt t n subrlctr Find th ptimum diamtr th subrlctr Slutin: = 5m, l = m =.1m d dp 1 =. b = - 1 = - 1 = 4 d d. p d s l.1m 5m = = =.5m b 4 Us st dual-rlctr systms t rduc blckag includ plarizatin-dpndnt suracs mirrr d 7

. This is made to keep the kinetic energy at outlet a minimum.

. This is made to keep the kinetic energy at outlet a minimum. Runnr Francis Turbin Th shap th blads a Francis runnr is cmplx. Th xact shap dpnds n its spciic spd. It is bvius rm th quatin spciic spd (Eq.5.8) that highr spciic spd mans lwr had. This rquirs that th