Chapter 2 : Fundamental parameters of antennas

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Myrtle Douglas
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1 Chap : Fundamnal paams of annnas Fom adiaion an adiaion innsiy Bamwidh Diciviy nnna fficincy Gain olaizaion Fom Cicui viwpoin Inpu Impdanc 1

2 Chap : opics nnna ffciv lngh and ffciv aa Fiis ansmission quaion ada ang quaion nnna mpau

3 Dfiniion of adiaion an Onc h lcomagnic M ngy lavs h annna h adiaion pan lls us how h ngy popagas away fom h annna. Dfiniion : Mahmaical funcion o a gaphical psnaion of h adiaion popis of an annna as a funcion of spac coodinas 3

4 4 adiaion an xampl

5 adiaion an 1 Can b classifid as: Isoopic dicional and omnidicional Isoopic: Hypohical annna having qual adiaion in all dicions Dicional: having h popy of ansmiing o civing M ngy mo ffcivly in som dicions han ohs Omnidicional: having an ssnially nondicional pan in a givn plan and a dicional pan in any ohogonal plan 5

6 adiaion an incipal pans o plans: -plan : h plan conaining h lcic fild vco and h dicion of maximum adiaion H-plan : h plan conaining h magnic fild vco and h dicion of maximum adiaion 6

7 adiaion an 3 θ H φ Omnidicional 7

8 Fild gions Fa fild gion Faunhof zon D 1 aciv na fild gion D=lags annna dimnsion adiaing na fild gion Fsnl zon 8

9 aciv Na Fild gion gion suounding h annna whin h aciv fild pdominas Fo D : D Fo Dsmall annna : 3 D max[ 0.6 ] ngula fild disibuion dpnds on disanc fom annna 9

10 adiaing Na Fild gion gion bwn aciv na-fild and fafild gions Fsnl zon Fo D D : D max[3 ] D Fo Dsmall annna :3 max[ D ] adiaion filds pdomina bu angula fild disibuion sill dpnds on disanc fom annna 10

11 Fa Fild gion gion wh angula fild disibuion is ssnially indpndn of h disanc fom annna Faunhof zon Fo Fo D D D : small annna : 3 D max[3 ] 11

12 Chang of annna ampliud pan shap 1

13 Sphical coodina and Solid ngl : Sadian Masu of solid angl: 1 sadian = solid angl wih is vx a h cn of a sph of adius ha is subndd by a sufac of aa d sindd d; d sindd solid angl 13 Quiz: Wha s h solid angl subndd by a sph?

14 adiaion ow Dnsiy oyning vco = ow dnsiy W H W : insananous oyning vco [W/m ] :insananous lcic fild Innsiy [V/m] H :insananous magnic fild Innsiy [/m] oal pow: W ds W nda ˆ S :insananous oal pow [W] nˆ : uni vco nomal o h sufac S da :infinisimal aa of h closd sufac[m ] 14

15 15 adiaion ow Dnsiy Fo im-hamonic M filds oyning vco im avag oyning vco avag pow dnsiy o adiaion dnsiy ] [ ; j z y x z y x ] [ ; j z y x z y x H H ] [ 1 ] [ 1 * j H H H W filds psn pak valus appas bcaus 1 ] [ 1 ] ; [ * H H W av av z y x z y x W

16 ad adiaion ow Dnsiy 3 vag pow adiad pow av ad S W * W av ds Wav nda ˆ [ H ] ds xampl.1: h avag pow dnsiy is givn by sin W ˆ ˆ av W 0 [W / m ] h oal adiad pow bcoms S av nda ˆ S sin ˆ ˆ 0 sindd S 0 [W] 16

17 adiaion ow Dnsiy 4 Fo an isoopic annna ad 0 0 S W 0 ds [ W ˆ ] ˆ 0 sindd 4 W0 [W] h pow dnsiy is hn givn by W 0 ad ˆ 4 ˆW0 [W / m ] 17

18 adiaion Innsiy Dfiniion : h pow adiad fom an annna p uni solid angl U W ad U oal pow can b givn by W ad : adiaion innsiy [W/uni solid angl] : adiaion dnsiy [W/m ] ad Ud 0 0 U sindd 18

19 19 adiaion Innsiy adiaion innsiy is lad o h fa-zon lcic fild of annna ] [ 1 ] [ o o U in f spac 377 h mdium :ininsic impdanc of h annna - zon lcic- fild componns of :fa h annna - zon lcic- fild innsiy of :fa η jk o

20 ad adiaion Innsiy 3 xampl.: h adiaion innsiy is givn by ad U W 0 0 U ad U sindd sin 0 sin h oal adiad pow bcoms Fo an isoopic annna dd [W] 0d U 0 d 4U U 0 ad 4

21 Bamwidh Bamwidh is h angula spaaion bwn wo idnical poins on opposi si of h pan maximum Half-pow bamwidh HBW: in a plan conaining h dicion of h maximum of a bam h angl bwn h wo dicions in which h adiaion innsiy is on-half valu of h bam Fis-Null bamwidh FNBW: angula spaaion bwn h fis nulls of h pan 1

22 Bamwidh

23 Bamwidh 3 xampl.3: h nomalizd adiaion innsiy of an annna is psnd by U U cos h 0 0 cos 0.5 cos h cos Sinc h pan is symmic wih spc o h maximum HBW = θ h = π/ h h angl θ h a which h funcion qual o half of is maximum can b found by Likwis FNBW = θ n = π sinc U n 0 n cos 0 1 3

24 Diciviy aio of adiaion innsiy in a givn dicion fom h annna o h avag adiaion innsiy D U U 4U 0 ad dimnsion - lss No ha h avag adiaion innsiy quals o h adiaion innsiy of an isoopic souc. 4

25 Sinc D D max ad 4 4 ' ' ' Diciviy U ' ' d' U U ' ' d' U max U ' ' d' 4 Ω is calld bam solid angl and is dfind as solid angl hough which all h pow of h annna would flow if is adiaion innsiy w consan and qual o U max fo all angls wihin Ω D max : maximum diciviy ' U ' ' U max d' ad U max 5

26 Diciviy 3 If h dicion is no spcifid i implis h diciviy of maximum adiaion innsiy maximum diciviy xpssd as D max D 0 U U max 0 4 U max ad dimnsion - lss 6

27 Diciviy 4 7 xampl.4: h adial componn of h adiad pow dnsiy of an infinisimal lina dipol is givn by sin W ˆ ˆ av W 0 [W/m ] wh 0 is h pak valu of h pow dnsiy. h adiaion innsiy is givn by U W 0 sin h maximum adiaion is dicd along θ = π/ and U max = 0. h oal adiad pow is givn by 8 ad Ud 0 sin sindd hus 4U max 3 D0 and D D0 sin 1.5sin ad

28 nnna fficincy h ovall annna fficincy ak ino h following s: flcions bcaus of h mismach bwn h ansmission lin and h annna Conducion and dilcic s 0 cd c 0 cd cd 1 : oal fficincy : flcion mismach fficincy :annna adiaion fficincy d : conducion dilcic fficincis : volag flcion cofficin a h inpu minal c d 8

29 Gain I aks ino accoun h fficincy of h annna as wll as is dicional popis. Diciviy only masus dicional popis. in in G U 4 in : ow inpu o annna; 1 o ad : Ohmic and dilcic pow 9 Gain : aio of adiaion innsiy in a givn dicion o h avag adiaion innsiy ha would b obaind if all h pow inpu o h annna w adiad isoopically

30 Gain Using cd ad = cd in and U G 4 cd cd D ad laiv gain: aio of pow gain in a givn dicion o h pow gain of a fnc annna in h sam dicion. h pow inpu mus b h sam fo boh annnas. If h fnc annna is a lss isoopic souc hn G 4 in U lss isoopic souc 30

31 31 Gain 3 bsolu gain aks ino accoun impdanc mismach s a h inpu minals in addiion o s wihin annna D U U U G cd ad in o abs

32 3 olaizaion opy of an M wav dscibing h im vaying dicion and laiv magniud of h lcic fild. h figu acd as a funcion of im by h ip of h lcic fild and h sns in which is acd as obsvd along dicion of popagaion. Wav popagaing in z dicion ẑ j y L im dpndnc x y z; xˆ x z; yˆ z; x z x y z yo z; z; xo j y xo yo j jkz x jkz wh cos cos y xo yo kz x y kz 0

33 olaizaion. Lina olaizaion i xo 0 o o ii an yo 0 0 wh n y n 1 yo x xo δ γ dmin polaizaion sa xampl ẑ xo yo 33

34 B. Cicula olaizaion olaizaion 3 i xo yo and o 1 an 1 / 1 n ; CW/C ii y x 1 n ; CCW/LC wh n No ha h sns of oaion is obsvd along h dicion of popagaion.

35 35

36 36 olaizaion 4 / 4 / sin / cos ; cos ; x o x o y x o x kz kz z kz z xampl: C ẑ

37 olaizaion 5 C. llipic olaizaion wav is llipically polaizd if i is no linaly o ciculaly polaizd. Lina and cicula polaizaion a spcial cass of llipic polaizaion. o hav llipic polaizaion: 1. Fild mus hav wo ohogonal lina componns.. h wo componns can b of h sam o diffn magniud. 37

38 38 olaizaion 6 yo xo x y n n FO wh CCW/L 0; CW/ 0; iiif C. llipic olaizaion yo xo x y n 01...ND wh CCW/L ; 1 n CW/ ; 1 n iif

39 olaizaion 7 xial aio 1 an 1 Majo xis Mino xis xo xo yo yo ; 1 cos 39

40 olaizaion Loss Faco LF lcic fild of incoming wav w ˆ wi lcic fild of civing annna ˆ wh ˆ w ˆ : polaizaion vco a : uni vco of h wav a a a ˆw ˆa LF ˆ ˆ w dimnsionlss a cos p 40

41 LF xampl LC wav: δ=-π/φ x =0φ y =-π/ 41 x ˆ o x o j x jkz j y o y ; y ˆ j / xˆ jyˆ wh ˆ w If h annna is also LC xˆ jyˆ LF If h annna is C ˆ o jkz xˆ a ˆ xˆ xˆ jyˆ LF a jyˆ xˆ jyˆ * ˆ w jyˆ xˆ jyˆ o jkz jkz ˆ 1 0 db 0 w o jkz

42 Gnao nnna minal a b Inpu Impdanc Impdanc psnd by h annna a is minal ansmiing cas Z jx [ ] Z V g g I g ohmic : adiaion sisanc : Loss sisanc ohmicdilcic g jx g a pak valus d V g I g Z g Z 4 Maximum pow dlivd o h annna occus whn conjuga machd: g X X g

43 43 Inpu Impdanc 8 1 g g ad g g V I V I 8 1 g g V I ad g g g g g V I Whn conjuga machd: NO: adiad ow ow o ha ow in g

44 Inpu Impdanc 3 ow supplid by gnao whn conjuga machd: 1 V * 1 g s [ Vg I g ] Vg 1 g s 1 in ad s ad cd in * V g 4 V g 4 g g in annna adiaion fficincy If 0 0 ad in cd 1 44

45 45 civing nnna a pak valus 8 1 I V V I V I X X und conjuga machd condiion civing cas Impdanc psnd by h annna a is minal jx Z jx Z 8 1 sca V I ow dlivd o load ow scad o -adiad

46 46 civing nnna c V I V 4 ] [ 1 * 8 1 V I c 1 c sca 1 sca c ow supplid by gnao whn conjuga machd: capud/collcd pow sca ow los o ha

47 nnna quivaln a Usd o dscib h pow capuing chaacisics of an annna whn a wav impings on i ffciv aa apu in dicion ow availabl a minals of civing annna Incidn pow flux dnsiy fom dicion W i I W i [m ] W i : pow dlivd o load :pow dnsiy of incidn wav 47

48 48 nnna quivaln a i X X W V 8 i s W V i i m W V W V Und conjuga machd condiion: o h scad o - adiad pow dnsiy is qual which whn muliplid by incidn pow :scaing aa o pow dlivd o load pow dnsiy is qual which whn muliplid by h incidn : ffciv aa s Maximum ffciv aa

49 nnna quivaln a 3 Und conjuga machd condiion: V 8W i s c V 4W i V 8W i c s c : aa which whn muliplid by h incidn pow dnsiy is qual o pow dlivd o load :Capud aa which whn muliplid by incidn pow dnsiy is qual o h oal pow capud by annna 49

50 nnna quivaln a 4 50 xampl.5: a unifom plan wav is incidn upon vy sho dipol whos adiaion sisanc is =80πl/λ. ssum ha = 0 h maximum ffciv aa ducs o V m 8W i Sinc h dipol is vy sho h inducd cun can b assumd o b consan and of unifom phas. h inducd volag is V l Fo a unifom plan wav h incidn pow dnsiy is givn by W i l 3 hus m / 80 l / 8

51 Vco ffciv Lngh Vco ffciv lngh o high is a quaniy usd o dmin h volag inducd on h opn-cicui minals of an annna whn a wav impings on i. I is a fa-fild quaniy. ˆ l ˆ l [m] a Z l V oc i l V i :incidn lcic fild V oc b V : opn - cicui volag a ˆ ˆ kiin j 4 jk l 51 xampl.6 : h lcic fild of a sho dipol is givn by jk ˆ kiinl a j sin l ˆ l sin 8

52 ffciv aa & Diciviy If annna #1 w isoopic is adiad pow dnsiy a a disanc would b W0 4 wh is h oal adiad pow. Bcaus of h diciviy h acual pow dnsiy bcoms D W W0D 4 h pow collcd by h annna would b o W D D

53 ffciv aa & Diciviy If annna # is usd as a ansmi 1 as a civ and h mdium is lina passiv and isoopic on obains D 4 Fom 1 and D D Incasing h diciviy of an annna incass is ffciv aa: D0 D0 m If annna #1 is isoopic m m D m 0 53

54 ffciv aa & Diciviy3 54 Fo xampl if annna # is a sho dipol whos ffciv aa is 3λ /8π and diciviy is 1.5 on obains m 3 m D and m D0 m D0 4 In gnal maximum ffciv aa of any annna is lad o is maximum diciviy by m If h conduciondilcic polaizaion and mismach: 4 D 0 m D0 cd 4 1 ˆ w ˆ a

55 55 Fiis ansmission quaion h Fiis ansmission quaion las h pow civd o h pow ansmid bwn wo annnas spaad by a disanc > D /λ. 4 4 D G W 4 D ˆ ˆ 4 4 D D W D ow dnsiy a disanc fom h ansmiing annna: ˆ cd D G ˆ cd D G h ffciv aa of h civing annna: h amoun of pow collcd by h civing annna:

56 56 Fiis ansmission quaion ˆ ˆ cd cd D D ˆ ˆ 4 D D h aio of h civd o h inpu pow: o G G Fo flcion and polaizaion-machd annnas alignd fo maximum dicional adiaion and cpion:

57 ada Coss Scion ada coss scion o cho aa σ of a ag is dfind as h aa incping ha amoun of pow which whn scad isoopically poducs a h civ a dnsiy which is qual o ha scad by h acual ag. lim4 W lim4 lim4 H s s s i i Wi H : ada coss scion [m : obsvaion disanc fom ag[m] W i W s :incidn scad pow dnsiy [W/m ] i s :incidn scad lcic fild [V/m] i s H H :incidn scad magnic fild [/m] ] 57

58 58

59 ada ang quaion h ada ang quaion las h pow dlivd o h civ load o h pow ansmid by an annna af i has bn scad by a ag wih a ada coss scion of σ. h amoun of capud pow a Incidn wav h ag wih h disanc 1 fom 1 ag h ansmiing annna: ansmiing annna ˆ G D cd civing annna ˆw ˆ G D cd Scad wav c W G 4 h scad pow dnsiy: 1 4 D W s 4 c 4 1 D 1 59

60 60 ada ang quaion D D W s D D W s 1 ˆ ˆ w cd cd s D D W h amoun of pow dlivd o h load: G G hus Wih polaizaion : Fo flcion and polaizaion-machd annnas alignd fo maximum dicional adiaion and cpion:

61 Bighnss mpau ngy adiad by an objc can b psnd by an quivaln mpau known as Bighnss mpau B K. wh ε : missiviy dimnsionlss 0 ε 1 m : molcula physical mpau K Γθφ : flcion cofficin of h sufac fo h polaizaion of wav xampl Gound 300 K B 1 m m 61

62 nnna mpau ngy adiad by vaious soucs appas a annna minal as annna mpau givn by wh 0 0 B 0 0 G sindd G sindd : annna mpau ffciv nois mpau of h annna adiaion sisanc ; K Gθφ : gain pow pan of h annna 6

63 Nois ow ssuming no s o oh conibuions bwn annna & civ nois pow ansfd o civ: wh : annna nois pow W k : Bolzmann s consan J/K : annna mpau K f : bandwidh Hz k f 63

64 Sysm Nois ow Modl ssum annna & ansmission lin a mainaind a cain mpau and ansmission lin is y hn h modl blow can b usd o includ all conibuions. 64

65 65 nnna mpau ffciv annna mpau a civ minals: wh a a : annna mpau a civ minals K : annna nois mpau a annna minals K : annna mpau a annna minals du o physical mpau K 1 1 α : anuaion consan of ansmission lin Np/m : hmal fficincy of annna dimnsionlss l : lngh of ansmission lin m l l 1 l 0 0 : physical mpau of ansmission lin K

66 Sysm Nois ow nois pow ansfd o civ: k a f If h s hmal nois in civ: wh k f s : sysm nois pow W s a k f a : annna nois mpau a civ minals : civ nois mpau a civ minals s = a + : ffciv sysm nois mpau a civ minals s 66

67 x.16 ffciv annna mp = 150 K. nnna is mainaind a 300 K and has hmal fficincy 99%. I is conncd o a civ hough 10-m wavguid = 0.13 db/m mp = 300 K Find ffciv annna mpau a civ minals Np/m db/m/ l a 150 l K l l

What is an Antenna? Not an antenna + - Now this is an antenna. Time varying charges cause radiation but NOT everything that radiates is an antenna!

What is an Antenna? Not an antenna + - Now this is an antenna. Time varying charges cause radiation but NOT everything that radiates is an antenna! Wha is an Annna? Tim vaying chags caus adiaion bu NOT vyhing ha adias is an annna! No an annna + - Now his is an annna Wha is an Annna? An annna is a dvic ha fficinly ansiions bwn ansmission lin o guidd