78/3 EISCAT TECHNICAL NOTES. THE EFFECT OF ICE ON AN ANTENNA REFLECTOR T. Hagfors. KIRUNA Sweden
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1 78/3 EISCAT TECHNICAL NOTES THE EFFECT OF ICE ON AN ANTENNA REFLECTOR T. Hagfors KIRUNA Sweden
2 EISCAT TECHNICAL Na TE No. 3 JANUARY 1978 THE EFFECT OF ICE ON AN ANTENNA REFLECTOR T. Hagfors Summary. The effect of an ice 1a ye r on an antenna reflector i s assess e e by eva1uating the phase deviation caused by an ice layer on a plane metallic ref1ector. The ice is treated as a slightly 1assy dielectric. The calculations are made for an arbitrary angle of incidence and for both principal linear polarization The resu1ts are presented in terms of curves of the phase of the ref1ections coefficients versus angle of incidence.
3 EISCAT SCIENTIFIC ASSOCIATION S KIRUNA 1. SWEDEN re U " HOPrl E_ l l"' «I fllvl IJ7llooI(lEOFVSIl.S THE EFFECT OF l CE ON AN ANTENNA REFLECTOR The presenee of ice on a n antenna reflector modifies the antenna performance in two ways. The phase of the reflected wa ve wi l l deviate f rom the desired value ; the reflection coefficient will be l e s s tha n unity if t here is appreci able loss i n the l a y e r. The f ormer of t hese t wo effects is generally the more important since ice can often be t reated as a sliqhtly lossy d i e l e c t r i c. To assess the effect we c omp ute the p lane metallic reflector covered by dielectric as s hown in Figure l. reflection coefficient of a a un iform a l o s s y z 8 8 n =1 'r (ice) 1 n(l-i Kl 2 refleclor y Figure l. Lossy dielectr ic s lab on gerfect metallic reflector. Above t he die l e c tri c s l ab we represent the field by F =A Ox - i k O(y -si n8- z c os8 ) - iko(ysine+zc os 8 ) e +Be (1 ) where A, B s ign i fy the e lectr ic f ield norma l t o o lane of i ncidence the mag netic field in t he x- d i r e c t i o n when the nolarization is o rthogonal.
4 2 - EISCAT SCIENTIFIC ASSOCIATION $ 98'01 KIRUNA t. SWEDEN TlLEI'HOI'rIE_I\f740 H l U OlonSK s In the dielectric medium we have - i k O n (1- i K) ry - s i.ne v- ec o s a " ) = C -e - i k On (l-ik) (ys1n8 l +zcos8 ') + O e (2 ) I n med i um 2 the f ields must vanish. Whe n A,B, C a nd D s ignify incidenc e a nd when A, B,C p lane of i nc i de nc e. E fie lds, E i s norm a l to the plane of and D s iqni fy B f iel ds, E l i e s i n the Since the y-variat ion must be ident ical in media (O) and ( l) we must have : n (1- ik)sin8 ' = sin S (3) We now p ut : 8 ' = Lo (4 ) and obtain : (sin 81Cosha. + i c o s 81S i nh a ) n (1-i K) = sins (5 ) Th e two conditions must be satisfied : A. (6 ) whic h means t hat (7 ) "The argument et i s propor t ional to K to firs t o rder.
5 3 - EISCAT SCIENTIFIC ASSOCIATION S KIRUNA 1, SWEDEN n UI'ttONl_' m'*3 n u x 17M QfOfYSII S ( 8) To fir s t order i n K we recqver Snell 's law : s ine l sine l = n (9 ) I n the followi ng boundary value cansideration t he y -variation can be ignored : Case l E 1 plane of incidence -, E = E x e x ( 10) In medium l we must have Ex = O at z = O. This g ive s : c = - D. (ll) At z = d continuity of Ex gives : i k On (l- i K) zc o s S ' C (e -ik On ( 1- i K) zcos8' ) - e = ikozcos8 A'e when z = d. ( 12) Co n t i nu i t y of H gives : ikon( 1-iK)zCOS 8 ' C(n(1-iK)COSe') (e -ik On (l-i K) z c o s S' + e ) ikozcos8 = cosa (Ae - i kozc os 8 Be ) whe n z = d. ( 13) S imp l ified system of equations for B and A: -l A' "O + B ' " O - CI " l - l "l ) - l T -l A " fl O - B'" C S( " l + " l ) O ( 1 4 )
6 4 - EISCAT SCIENTIFIC ASS OCIATION S 9I1 01 KIRUNA 1. SWEDEN TlUfOttOHl_'''. nux"'" OIOf'YII( I s = cose T = n(! - ik)cos6 1 - nccos8 l _ i K ) c o s e l From which we derive : G ikodg+ - i k Od G_ e + B G+e A ikodg_ - i k Od G+ G+e + G e = = Rl (15) where ( to first o rde r in K ) G+ = In 2 -sin 2 e + cose - Case 2 E I l plane of incidence - 2 Le n I n 2 -S i n 2 e ( 16) + + B = B e x x (1 7) I n med ium l we must ha v e E y = O at z = O. This means t hat o r C = D. ab x O at O äz = z = ( 18) ( 1 9 ) The two boundary c onditions at z = dbecome : ( 20) = Or : ( 21 )
7 5 - EISCAT SCIENTIFIC ASSOCIATION S 98' 01 KIRUNA t, SWEOEN TEU I'tlO"l( 0IMI0/ HU.Xl75t QEOFYI It S where G+ and G K we have : were defined above and where to first order in - i Kn 2 ( ZCOs e :+ (22) Nume ric a l e xample : For a n ice- layer K is negligible and n 2 3.0, passibly slightly larger. Computations we r e made of Rl and R 1 I for several combinations of layer thickness and angles of i ncidence. Same r e s ul t s are s hown i n F igure 2.
8 . -i 0.10 '" "c -90 o 0.08 u O 0 06 u c -60 O." "u < O -3 O 002.c o. ' O Ang le of incidence Figure 2. Phase o f r e f l e c t i o n coefficient of R (degrees ) plotted a gainst a ngle of i ncidence (deqre e s). = '" " 90 c." " - O U c 120 "u -<, 5 O O.c o. '" I 1 8 O Angle of i nc i de nc e l Figure 28. Phase o f reflection coe f f i c i e nt of Ry agains t angl e o f incidence ( degr e e s ) (degrees) plotte d
9 o occ.-<.-< 90 o..:-l ". m = O.OB 006 O U " H " "' -o.co Angle of inc i de n c e Fig ure 2C. Phase "error" of the phase difference between R n and Rl. I plotted against angle o f i nc i de nc e (degrees). l '- - _.
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