SYMMETRCA COMPONENTS Syl oponn llow ph un of volg n un o pl y h p ln yl oponn Con h ph ln oponn wh Engy Convon o 4 o o wh o, 4 o, 6 o
Engy Convon SYMMETRCA COMPONENTS Dfn h opo wh o Th o of pho : pov ph un : ngv ph un (pov un (ngv un zo un 4 o o o 4 o o o
Engy Convon SYMMETRCA COMPONENTS Con h ph unln un,, h yl oponn of h un h x fo of h un n of yl oponn h yl oponn n of h h ph un A > * A A wh A
SYMMETRCA COMPONENTS Con h ph unln un,, h yl oponn n of h h ph un ( ( ( Zo un un on-h of h u of h ph un n h ph y wh ungoun nul, h zo un un n x (KC f nul goun, zo-un un flow wn nul n goun Engy Convon
Engy Convon SYMMETRCA COMPONENTS Con h ph unln volg,, h yl oponn of h un h x fo of h un n of yl oponn h yl oponn n of h h ph un A > * A A wh A
Th Ph Tnfoon Tnfoon u o oupl vl wh -vyng offn n f ll vl o oon fn f Tnfoon o oupl ph vl [f ][T ][f ] [ T] wh Th yl nfoon ppll o y- vo o nnnou un o
SYMMETRCA COMPONENTS Con h ph unln un,, h yl oponn n of h h ph un ( Th ph oplx pow n of yl oponn S φ T * (A T (A * n A T A, A T A * S φ ( T ( * * * * ol unln pow n on fo h u of h yl oponn pow Engy Convon ( (
Sun pn of Y-onn o Con h ph ln lo wh lf n uul ln (Fg..4 PSA-S Z Z Zn Z Zn Z Zn Z Z Z Z Z Z n n n Z Zn Z Zn Z Z n Z A Z Z Z Z Z Z n n n Z Z Zn Z Zn Z Zn Z Z Z Z Z Z n n n
Sun pn of Y-onn o Con h ph ln lo wh lf n uul ln n h ov fgu volg uon: Z u nfoon: A Z A Z, wh Z A - Z A Z n of h ov fgu Z Z Z Z n A Z Z Z pn of nonzo pp n pnpl gonl fo ln lo, h un pn npnn un of h ph un pou volg op of h ph un only Z
Pk Tnfoon Pk nfoon o oupl h-ph un no woph vl (gno noon [f ][T ( ][f ] gno noon, / lonhp wn n un, pov -x long wh gn fl wnng x pov -x long wh nnl volg f f nnl volg l gn fl y 9 g (gnng [ ] n - n - n o o o ( T [ ] n - o n - o -n o ( T
Pk Tnfoon Pk nfoon (oo noon [f ][T ( ][f ] oo noon, - / [ T ] ( o n o n o n lonhp wn n un, pov -x long wh gn fl wnng x pov -x long wh ngv of h nnl volg f f (nu volg oong -x f fo -x
Pk Tnfoon Pk nfoon o oupl ph vl [f ][T ( ][f ] gno noon, / lonhp wn n un, -x long wh nnl volg -x long wh h gn fl -x f fo -x [ ] n n n o o o ( T [ ] n o n o -n o ( T
Tnfoon Bwn n Sng fo pov un vo, h on ow n nll, h ov x n fo n of l p n gny p ( * ( ( * * R - ( - ( R( ( - - - - [ ] [ ][ ] T
Tnfoon Bwn n Bln h-ph un n of Ung h nfoon, o Sl un p vo ( 4 o(, o(, o φ φ φ o( n( o( φ φ φ { } φ φ φ φ ~ n( o( ( h pho uny whh, ~ φ wh
Tnfoon Bwn n Sl un p vo ( φ lly fo ln h-ph un, n ohogonl n hy hv h pk vlu h ph un pk 9 o h of n h uln un o oun-lokw p of fo nl poon of φ o h ph x
Tnfoon Bwn o y fn f Nw ong x wh ony x oponn p vo fo o n n o ( ( ( ( h ov uon pl ong ony oponn kw y ngl ynhonou ong f w... ony f ( o( φ ( un n ynhonou f onn lonhp wn yn. f n pk vlu pho of ph un ~ ( ~ yn. f un n pk vlu pho un of ph un h ( ( ( n( φ (
Tnfoon Bwn n Full nfoon fo ony f o y ong f full nfoon fo o n n o n x noon, [ ] n of ognl un [ ] [ ] [ T ][ ] [ T ][ T ][ ] [ T Tol nnnou pow no h ph u n y f P v v v v v ( v no on on un, oul ln o unln ][ ]
Po 4- Coplx un n nfoon Tnfo h nnnou h-ph un o p vo n pov n ngv-un n h pl on Th un of h fo o( o(-/ o(/ Ung h followng nfoon x [ ] n - n - n o o o ( T
Po 4- Coplx un n nfoon Show h wo ong p vo n oponn oponng o nuol n oplx ph un un h un oponn n ony f f ong f - f f 5 f
Sun Cun Sp o Sun p vo Bln h-ph un n of Sun un p vo Ruln gp f fo ln ph un, F ong p vo whh h nuol pl uon oun h gp wh p of ( 4 o(, o(, o ( * ( ( N N F o 4 n n ( *
Rlon Bwn Sp o An Ph Quny Cun p vo n ph un un p vo pk vlu of ph un lon wn un p vo n ph xpon Bln un un p vo ( ( o ( ( *
Tnfoon o S R Con h ph ln R non ln wh lf n uul ln ] ][ [ ] ][ [ ] [ ] [ p R R Wh g g g S v v v [ ] g g R v v v g ] [ g g g g g g g g g [R ] g gg g g gg g g gg g g gg g gg g g gg g g gg g g gg g gg ] [
Tnfoon o S R Con h ph ln ln wh lf n uul ln n Fg. 5.7 volg uon: Δ[ ] [R ][ ]p [ ][ ] u nfoon: [T (] - Δ [R ] [T (] - [ ] [ ] p [T (] - [ ] [T (] [T (] - Δ [T (] [R ] [T (] - [ ] [T (] [ ] p ( [T (] - [ ] Δ [R ] [ ] [ ] p[ ] [T (] [ ] [ ] p [T (] - [R ][T (] [R ] [T (] -, [ ] [T (] [ ] [T (] - R n n of Fg. 5.7 R pn of nonzo pp n pnpl gonl
Tnfoon o S R Tnfo fo o uvln u p volg p volg v v v ( ( ( ( ( ( ( (
Sp o n Tnfoon A gp f u o un ( F (N n / ( o(, F n ou - ph wnng x p vo noon Ruln gp f y un flowng no ll h wnng wh N F o (, n ( ( ( ( { } ( N N N N N F F F F n n 4 4 n n n 4 4 4 o o o o
Po. 4- Tnfoon Gvn on-ln g of h-ph y hown low, kh h npuoupu lon wn h oponn gno pn y n uvln volg ou E hn ou nun g n h-w y, no zo un oponn. zo-un u o