C b Appl lcomancs Nos S 3b Insuco: Pof. Val Loman Dpamn of lccal an Compu nnn Unvs of Calfona San Do
Rflcon an Tansmsson. Nomal ncnc T R T R Fs fn h manc fls:
3 Rflcon an Tansmsson T R T R T R T R R T Soluon: hn If. hn If. T R T R Spcal cas:
4 Rflcon an Tansmsson 3. Oblqu ncnc A. Ppncula polaaon -pol. sn sn sn T T R R sn sn sn sn sn sn T R
Rflcon an Tansmsson 4 n o an an R n o an T sn sn Phas machn: R an sn T sn sn sn sn sn sn sn sn Snll s law of flcon sn sn sn sn Snll s law of facon 5
6 T R T R T R Soluon: Z Z Z Z R Z Z Z T Z Rflcon an Tansmsson 5 Ths fomulas a v smla o hos n ansmsson lns!
7 Rflcon an Tansmsson 6. Oblqu ncnc B. Paalll polaaon -pol. sn sn sn T R sn sn T R Rsul:
Rflcon an Tansmsson 7 L Z R Z Z Z Z T Z Z Z Bws anl No flcon A. Fo -polaaon Bws anl If B R R Toal ansmsson B sn sn B sn Snll s law 8
Rflcon an Tansmsson 8 Soluon: sn B. Fo -polaaon B ± B If R Bws anl Fo R unlss! no oal ansmsson Toal ansmsson sn B ± sn B ± f 9
Rflcon an Tansmsson 9 Ccal anl Toal flcon: Snll s law of facon sn sn sn sn sn sn sn sn π c - sn - c sn f < Ccal anl I ss onl f
Rflcon an Tansmsson Whn : R T c T T sn sn sn * R S S S c c c av av av All ncn pow s flc bac! Whn os h pow n mum com fom???
Rflcon an Tansmsson Wha happns whn? > c T sn Whn sn > > c sn > T sn sn ± sn sn Anuaon consan: sn α v p < v sn Phas vloc: p Non-unfom plan wav Applcaon: Opcal fb
Rflcon an Tansmsson Tansmsson no a lf-han mum: 3
Rflcon an Tansmsson 3 Phas machn: sn sn Ponn vco: T S sn Pn s pfc lns a plan-wav pcu 4
5 Plan Wavs n Unaal Ma Opcal as Fo a unaal mum: B D < > nav unaal : posv unaal : Cons a plan wav:
6 Plan Wavs n Unaal Ma
7 Plan Wavs n Unaal Ma 3 Fo non-val soluons: ] [ Two possbl soluons:. D B Ona wav. pmv wh a hos n an soopc mum wav bhavs h sam as Ths
8 4 Plan Wavs n Unaal Ma 4. Dspson laon D B D
Plan Wavs n Unaal Ma 5 D B Obsvaon: Thus s no ppncula o. As a sul h Ponn vco s no n h con of. aona wav Spcal Cass:. If h wav popaas ppncula o h opcal as : Fo ona wavs Fo aona wavs o o 9
Plan Wavs n Unaal Ma 6 Phas vloc: o p po v v Bfnnc A h fon: Af passn houh h slab: o o o Lnal pola
cculal pola Plan Wavs n Unaal Ma 7 o o ± ± ± 3 If π π 4 If o o o o o o o λ λ λ λ λ λ λ π λ π λ π π π Qua-wav pla
Plan Wavs n Unaal Ma 8. Polao σ ~ as : o h opcal paalll Fo aona wavs as : ppncula o h opcal Fo ona wavs σ σ σ o aona wavs wll b anua. s anua houh passs Smlal σ σ
3 Plan Wavs n Goopc Ma Fo a oopc mum: Cons a plan wav: W fn
4 Plan Wavs n Goopc Ma Fo non-val soluons: 4 4 Dfn : sn Rw: 4 C B A 4 4 sn sn C B A
5 Plan Wavs n Goopc Ma 3 Two soluons: A AC B B 4 ± sn sn sn sn sn ẑ Spcal cass:
6 ± ± ± ± 4 - han cculal pola wav lf a p v Plan Wavs n Goopc Ma 4
Plan Wavs n Goopc Ma 5 b Cons h - han cculal pola wav v p Lnal pola RCP LCP 7
8 Faaa oaon Plan Wavs n Goopc Ma 6 A : co / / / / lnal pola wav wh an anl a Sll F
9 π p v a b 4 4 Plan Wavs n Goopc Ma 7 llpcall pola.
Plan Wavs n Chal Ma Consuv laons: χ - chal paam Mawll s quaons: 3
Plan Wavs n Chal Ma Assum : D B χ χ χ χ χ χ χ χ Soluons: ± ± χ ± 3
Plan Wavs n Chal Ma 3 LCP: v p χ RCP: v p χ Obsvaon: Faaa oaon bfnnc cpocal oopc mum. 3