UNIFORM PLANE WAVES (PROPAGATION IN FREE SPACE)
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- Candice Wilkins
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1 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 7//0 UNIFORM PLAN WAVS (PROPAGATION IN FR SPAC) Saing wih pin fm f Mawll quain f im vaing fild in f pac: B D 0 0 L a ˆ Thn a a ˆ ˆ And a a ˆ ˆ Cllcing ul Gd mind f lgaphi quain! T bain h wav quain, diffnia h fi w.. and h cnd w.. and aanging g: f wav quain On dimninal O ving diffniain g: f wav quain On dimninal And a gnal luin i givn b: v f v f, Fm which h vlci f wav ppagain ma b dducd (b ubiuing f in h wav quain, pfming h indicad diff )
2 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; v m c TM wav: Tanv lcmagnic wav impli i ppndicula and bh ling in a anv plan (a plan nmal h dicin f ppagain) Unifm Plan Wav UPW: and fild hav cnan magniud and pha in h anv plan. (Cnan pha and ampliud). F inuidal wav:,,, al k c v p c c v p k c k ad pha hif p uni im ad pha hif p uni dianc m cnan pha impli k cnan d d k cnan 0 d d d v p c(in f pac) d k Th wav numb in f pac i dfind a: k ad c m Th wavnumb i a pp f a wav, i paial fqunc, ha i ppinal h cipcal f h wavlngh. I i al h magniud f h wav vc ( b n la). Th wavnumb ha dimnin f cipcal lngh, i SI uni i m -. Simpl h numb f wavlngh p π uni f dianc. Al h wav lngh i givn b: D. Na Abu-Zaid Pag 7//0
3 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; c f m dianc v phapaial h which b π hif Mawll quain and h wav quain ma b win in fqunc dmain wih h hlp f h anfmain; j B j D j 0 0 3D WAV QUATIONS (FR SPAC) Taking h cul f h fi quain, naml j Uing h idni F F F Subiuing j Uing h f Mawll quain j j j Wih k k Vc lmhl quain (Wav qain f ) k v p Simila appach ma b fllwd bain h wav quain f h magnic fild ad m D. Na Abu-Zaid Pag 3 7//0
4 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; k Vclmhlquain (Wav qainf ) RLATION BTWN AND F h pviu aumpin aˆ, h wav quain duc : d k d Wih h fqunc dmain luin givn b: jk jk 0 Bu fm Mawll quain j d j d Subiuing h luin jk jk d 0 j d Diffniaing and lving f Idnifing f b jk 0 jk jk 0 And h ininic impdanc f f pac i O 0 jk D. Na Abu-Zaid Pag 4 7//0
5 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Wh I can b hwn ha: aˆ n aˆ â : uni vc in h dicin f ppagain. n â : uni vc in h dicin f. â : uni vc in h dicin f. aˆ n O aˆ aˆ n D. Na Abu-Zaid Pag 5 7//0
6 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; j0.07..: L A 40 aˆ ˆ 30 a m f a unifm plan wav avling in f pac. Find: P,,3, 3n ) h igin PROPAGATION IN DILCTRICS Auming a impl dilcic, h wav quain i win a: k (Wav qainf ) Wh k i h wav numb. D. Na Abu-Zaid Pag 6 7//0
7 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; k Allwing h pmiivi b a cmpl cnan ( b plaind la), impli ha h wav numb ma b cmpl and i i calld h cmpl ppagain cnan. Th ppagain cnan f an lcmagnic wav i a mau f h chang undgn b h ampliud f h wav a i ppaga in a givn dicin. Th ppagain cnan ilf mau chang p m bu i hwi dimninl. Th quani maud, uch a vlag lcic fild inni, i pd a a inuidal pha. Th pha f h inuid vai wih dianc which ul in h ppagain cnan bing a cmpl numb, h imagina pa bing caud b h pha chang. F a On dimninal pblm Dfin S, h luin i givn b d d aˆ k, h wav quain duc jk j jk j j Tanfing im dmain, and cniding nl h fwad pa:, c jk Dfin h cmpl pmiivi (dipl cillain and cnducin lcn and hl) a: j j j D. Na Abu-Zaid Pag 7 7//0
8 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 8 7//0 j j j k Wih R R jk Im Im jk Clal fm h im dmain pin f,, h pha vlci i givn b: m v p And h wav lngh i (dianc quid chang h pha b ) : m And h magnic fild aciad wih h fwad ppagaing pa i: (can b fund hugh h u f Mawll quain) Wih h ininic impdanc bing a cmpl quani, givn b: j j j j j j jk
9 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 9 7//0 Sinc c, c, Thn lad b. And u ma d h am f h backwad wav. Ll mdium (Pfc dilcic) 0 0 R R jk Im Im jk m c v p m f c 0 & j j
10 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; & 0 and a in pha D. Na Abu-Zaid Pag 0 7//0
11 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Bu n h h hand, Cmpaing h w quain Al fm h cnd quain (L Dilcic) j j j J j j j D. Na Abu-Zaid Pag 7//0
12 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; J J c d j j J c and J d a 90 u f im pha, and w idnif h maial a having lag l mall l dpnding n h magniud f h l angn dfind b: L angn an i h angl b which J d lad h al cun dni J Gd Dilcic Appimain Small l jk j j j D. Na Abu-Zaid Pag 7//0
13 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; j Th abv w ac pin ma b appimad uing h binmial panin nc n n n n! R Rjk Im Imjk..., 8 j Wh Cmpl Pmiivi? L mchanim ccu in dilcic vn in h abnc f f lcn 0, hi i du ain f h dipl align wih applid im vaing fild du h n hif f h lcn clud wih pc h piiv nuclu. A high fqunci h plaiain P f h maial i u f im pha wih applid fild. Thi l mchanim i mdld b a cmpl pmiivi, a hwn pviul, vn wih cnducivi j S, again fm Amp law j j j ng ag mchanim J And h l angn hwn ali i: Langn an d Lmchanim, ma b ad a dilcic cnducivi D. Na Abu-Zaid Pag 3 7//0
14 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; vn if h cnducivi i nn 0 bu qui mall, ill w ma wi Amp law a: S, w ma wi Cnduc l mchanim J c j ng ag mchanim J d Cnducand dilcicl mchanim ffciv And h l angn i dfind a: cnducivi j j Dilcic L mchanim, mab ad a ( dilcic cnducivi ) j j Langn an j ffciv pmiivi ng ag mchanim J d Dph f pnain (Skin Dph) Cnid a fwad avling wav in a l dilcic;, c A, h wav i anuad b a fac f: Th quani i calld h kin dph, dph f pnain Of i maimum ampliud D. Na Abu-Zaid Pag 4 7//0
15 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Illuain f kin dph D. Na Abu-Zaid Pag 5 7//0
16 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; POYNTING S TORM (POWR TORM) D J Lf d bh id wih. hn uing h idni And wih m vc manipulain, n can bain (Fllw bk) J D B Diffnial fm f hpning Thm Ingaing v a vlum v ncld b a ufac dv Jdv D dv B v v v Upn uing h divgnc hm f LS d Jdv D dv Talpw flwing in vlum v v v v B dv Jdv D dv d v v v B dv Talpw flwing u f vlum d D. Na Abu-Zaid Pag 6 7//0
17 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Illuain f pw balanc f M fild And h inananu Pning vc S ( inananu pw dni) i dfind a: W S m F UPW wih,, aˆ Thn S,, aˆ, aˆ, aˆ S aˆ ) Pfc Dilcic (fwad pa nl):, c, c D. Na Abu-Zaid Pag 7 7//0
18 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 8 7//0 S c, ) L Dilcic: c, c, S c c, Th avag pw dni (im avagd Pning vc) i (f im hamnic ca): T T d T d T c c S S c T d T S S Th abv pin i ail valuad uing pha b dfining * R S Ding i f l dilcic (Sinuidal wav) * R j j j S c S
19 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; ampl.5: A fqunci f, 00, and 3000M, h dilcic cnan f ic mad fm pu wa ha valu 0f 4.5, 3.45, and 3., pcivl, whil h l angn i 0., 0.035, and , al pcivl. If a UPW wih ampliud f =0 i ppagaing hugh h ic, fin h im avag pw =0 and =0m f ach fqunc. Sluin: f S S T fill h. Gd cnduc Appimain (Skin ffc) jk j j ighl j j Th abv w ac pin ma b appimad uing h binmial panin nc n n n n! f..., D. Na Abu-Zaid Pag 9 7//0
20 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; j Cnid a fwad avling wav;, A J 45 c f, c f f, c f, h wav i anuad b a fac f: f 0.37 Of i maimum ampliud f Which i h kin dph again, dph f pnain. 7 F cpp S m, cpp f f cpp mm 0 G mm Af a fw kin dph wihin h cnduc, all fild a alm. v p D. Na Abu-Zaid Pag 0 7//0
21 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; If Thn j j 45 f, c f 45 lag b 45, c D. Na Abu-Zaid Pag 7//0
22 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 7//0
23 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Aacking h pw pblm (in gd cnduc); L 0 UPW b, c 45 J, c, c J c * aˆ S R 4 Th al avag pw (l) cing h cnduc ufac a 0 ; P L S S d b L ddaˆ bl bl J 4 4 Wha ul wuld b baind f h pw l, if i i aumd ha h al cun i diibud unifml in n kin dph. T calcula h al cun cing h ufac a 0, wi in pha fm: S J J j aˆ D. Na Abu-Zaid Pag 3 7//0
24 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; and I S J d I b J 0 0 J j J b dd b c 4 j Auming hi cun i diibud unifml wih cun dni J unifm hugh h c cins b hn I J J unifm c S 4 Thn h al inananu pw diipad in vlum f n kin dph hickn i: P L in b v L J unifm J dv c 4 J bl c 4 And h im avag pw l wihin hi vlum i; J P P d bl L L in 4 T Thi i acl h am fmula baind bf. Cncluin: Th avag pw l in a cnduc wih kin ffc ma b calculad auming ha h al cun i diibud unifml in n kin dph. O, h ianc f widh b and lngh L f an infinil hick lab wih kin ffc i h am a h ianc f a cangula lab f widh b, lngh L, and hickn wihu kin ffc. ddd I S D. Na Abu-Zaid Pag 4 7//0
25 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Wih Skin ffc Wihu Skin ffc L b L b L R dc S L R ac b a F a cicula c-cin wi wih adiu L L R S a, and a high fqunci M fn, h ufac kin ianc i dfind a h al pa f h ininic impdanc f a gd cnduc. Thu f R inc j j 45 D. Na Abu-Zaid Pag 5 7//0
26 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; WAV POLARIZATION Plaiain i dfind a Th lcu ha h ip f h fild ac a im vai f a fid pin in pac. O, h im-vaing bhavi f a a givn pin in pac. Cnid a wav ppagaing in h ngaiv -dicin, aˆ Ε, aˆ, Aum ach cmpnn hav a inuidal im dpndnc, and Sinc c j R, hn ach cmpnn mab win a a al pa f m cmpl quani (cmpl pha); j, R ˆ wih ˆ jk jk j Cmpl pha j, R ˆ wih ˆ jk jk j Cmpl pha S, h im dmain pnain i baind a; D. Na Abu-Zaid Pag 6 7//0
27 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; c k j k, R j k, R c k Th ca a b cnidd. Ca: Lina plaiain n wihn 0,,,... ampl: Find h plaiain (lina, cicula, llipical) and n f ain f h unifm plan wav wh lcic fild i givn b Sluin:, ˆa 0c k ˆa 5c k Tak 0 0, ˆa 0c ˆa 5c And inc c c 0, ˆa 0c ˆa 5c 0, 0 c 5 c 5c 0, an 5c 5 c 0c an 5 an D. Na Abu-Zaid Pag 7 7//0
28 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Linal plaid wih an angl f an N ha, 0 and 0. S, fm h bginning w ma a ha h plaiain i lina, bu wih wha angl? Ca: Cicula plaiain n 0,,,... n n f CW RCP f CCW LCP If h dicin f ppagain i in h piiv -dicin, hn h pha f CW and CCW mu b vd. ampl: Find h plaiain (lina, cicula, llipical) and n f ain f h unifm plan wav wh lcic fild i givn b 5, ˆa 0c k ˆa 0c k Sluin: Tak 0 0, ˆa 0c ˆa 0c 5 0, ˆa 0c ˆa 5 And inc c in 0in 0, 0 c 0 in 00 c 0, an in 0in 0c 00 0 an an D. Na Abu-Zaid Pag 8 7//0
29 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 9 7//0 Sinc h wav i ppagaing in ngaiv -dicin, hi i a RCP cicula plaiain CW plaiain. N ha: 0, 5, 0 and S, fm h bginning w ma a ha h plaiain i CW cicula. Ca3: llipical plaiain 0,,,... f CCW LP 0 f CW RP 0 O f CCW LP f CW RP n n n n 0 0
30 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 30 7//0 Th cuv acd i a ild llip. c c OB OA OB OA AR min ai maj ai Aial ai And h il angl w.. h -ai i c an ampl: Find h plaiain (lina, cicula, llipical), n f ain, aial ai AR, and h il angl f h unifm plan wav wh lcic fild i givn b 0.5 c ˆ 0c ˆ, k k a a Sluin: Tak 0
31 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; D. Na Abu-Zaid Pag 3 7//0 5 c ˆ 0c ˆ 0, a a And inc in c in 5 ˆ 0c ˆ, 0 a a 0.5 an an 0c 5 in an 0, in 5 c 0 0, Thi i an llipical plaiain wih 5 c c 0 c c OB OA 5 0 min ai maj ai ai Aial OB OA AR And h il angl i c an c an
32 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Sinc h wav i ppagaing in ngaiv -dicin, hi i a R llipical plaiain CW llipical plaiain. N ha:,, 0 and 0 0. S, fm h bginning w ma a ha h plaiain i CW llipical. Fm Wikipdia, h f ncclpdia D. Na Abu-Zaid Pag 3 7//0
33 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; T LCTROMAGNTIC SPCTRUM wh:c = 99,79,458 m/ i h pd f ligh in vacuum and h = (33) 0 34 J = (0) 0 5 V i Planck cnan. [5] Fm Wikipdia, h f ncclpdia D. Na Abu-Zaid Pag 33 7//0
34 D. Na Abu-Zaid; Lcu n in lcmagnic h ; Rfncd ngining lcmagnic b a, 8 h diin 0; Fm Micwav ngining b David M. Pa, 005 D. Na Abu-Zaid Pag 34 7//0
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