Download Short-Circuit Hand Calculation (IEC 60909) Short-Circuit Calculation (IEC 60909)...
[ [flrt-Kcrkuct flrtK`dkud`tcle(CMK 9:3:3)
0.0. 0. 0.0 0
[f [flr lrtt-Kc Kcrk rkuc uctt Ca Capm pmh` h`ek ekm m K` K`dk dkud ud`t `tcl cle e
Emtwlrg [lurkm> ["g;P 1=?=AY@, C"g0 1:.;39g@,
ζ1`rkt`e(V/_)1`rkt`e(?.=8)196.=0º ζ1`rkt`e(V/_)1`rkt`e(:.:;06)10.6?0º
Emtw Em twlr lrg g [l [lur urkm km Ca Capm pmh` h`ek ekm m
k]eP ? 0.0x(??gY)? ^P 1 10:08.:3 a℩ 1 =?=AY@ ["gP ^P 10:08.:3 a℩4 a℩496. 96.=0º =0º ^P 1(;20.=+n38;.9)a℩ J ??gY ;.8=gY ^P 1(;20.=+n38;.9)a℩ x ??gY
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^P 1(3.08+n?;.?: ) a℩ J ;.;gY
Emtwl Emt wlrg rg [lu [lurkm rkm B Brlu rlueh eh Cap Capmh` mh`ekm ekm
^P 1
∞ ;k] ;k]e C"g0
-?^0 1
∞ ;x0.0x??gY ;x0.0x??gY :.;
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-?(;20.=+n38;.9)a℩
^P 1(0:=:=0+n0829)a℩ J ??gY ;.8=gY ^P 1(0:=:=0+n0829)a℩ x ??gY
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^P 1(?=6;.80+n;9.;0)a℩ J ;.;gY X`odm 0 [flr [flrtt Kc Kcrkuct rkuct [upp [uppdy dy Em Emtwlr twlrg g Ca Capmh` pmh`ekm ekm ^ Xypm J ??gY J ;.;gY ℩) (a℩ (a _ (a℩) V (a℩ ) _ (a℩) V (a℩) ;Zf ;20.=: 38;.9: 3.08 ?;.?: ^P 0Zf 0:=:=0 0829 ?=6;.80 ;9.;0
Xr`esilramr Capmh`ekm X_-2:@
(??gY)? ]rX ¿ ^X 1½gr 1:.:2x 1=8?:.6a℩ [rX 9.?=AY@ X`odm ? Xr`es Xr`esilram ilramrr Xypck Xypck`d `d %^ `eh V V/_ /_ (Ir (Irla la CMK 9 9::29-= ::29-= ?: ?::: :: `eh @rmv` _`Kf.=) tceb (AY@) ≨:.9;: :.9;0 - 0.?= 0.?=0 - ?.= ?.=:0 - 9.;
%^
V/_
8 = 9 2
0.= ;.= 9 6.=
Irla t`odm `olvm ` 9.?=AY@ tr`esilramr wcdd f`vm V/_ r`tcl li 6.= ζ1 `rk `rkt`e t`e
V 1 `rk `rkt`e t`e(6.=) 16;.?3º _
^X 1 =8?:.6a℩46;.?3º ^X 1 (9;;.;2+n=;6;.92)a (9;;.;2+n=;6;.92)a℩ J??gY
Rctf Klrrmktcle I`ktlr gX xX 1½Vr 1
xX 1½Vr 1
VX ]rX ¿ [rX
pmr uect
=;6;.92a℩ ¿
1:.:93= 1:. :93= pmr ue uect ct
(??gY) 9.?=AY@ :.3=x0.0 :.3=ka`x
gX 1 0+:.9xX 1 0+:.9(:.:93=) 10.::;? ^Xg 1^X gX 1(9;;.;2+n=;6;.92)a℩x0.::;? ^Xg 1(9;=.;2+n=8::.99)a℩ J??g ??gY ;.8=gY ^Xg 1(9;=.;2+n=8::.99)a℩x ??gY ^Xg 1(0=.9;+n0;?.60)a℩ J ;.;gY
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Xr`esilramr Capmh`ekm X_-0@
(;.;gY)? ]rX ¿ ^X 1½gr 1:.:8x 1620.?a℩ [rX :.=AY@ Irla t`odm `olvm ` :.=AY@ tr`esilramr wcdd f`vm V/_ r`tcl li 0.= ζ1 `rk `rkt`e t`e V 1 `rk `rkt`e t`e(0.=) 1=9.;0º _ ^X 1 620.?a℩4=9.;0º ^X 1 (86;.?=;39+n2?8.66?6)a (86;.?=;39+n2?8.66?6)a℩ J;.;gY
Rctf Klrrmktcle I`ktlr gX xX 1½Vr 1
VX ¿
]rX [rX
pmr uect
1:.:;; 1:. :;;?6? ?6? pmr uect uect xX 1½Vr 1 2?8.66a℩ (;.;gY)¿ :.=AY@ :.3=ka`x :.3=x0.0 gX 1 1 10.:?8=8 0+:.9xX 0+:.9(:.:;;?6?) ^Xg 1^X gX 1(86;.?=;39+n2?8.66?6)a℩x0.:?8=8 ^Xg 1(83=.00;+n28?.9208)a℩ J;.; J;.;gY gY ??gY ^Xg 1(83=.00;+n28?.9208)a℩x ;.8=gY
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^Xg 1(?:0;;+n;:?::)a℩ J ??gY X`od X` odm m ; [f [flr lrtt Kcr Kcrku kuct ct Xr Xr`e `esi silr lram amrr Ca Capm pmh` h`ek ekm m ^Xg J ??gY J ;.;gY (a℩ ) _tg (a℩ ) Vtg (a℩) _tg (a℩ ) Vtg (a℩) ^Xg X_-2:@ 9;=.;2 =8::.99 0=.9; 0;?.60 ^Xg X_-20@ 33?.22 68;6.=; ?8.80 ?:2.=? ^Xg X_-0@ ?:0;; ;:?:: 83=.00 28?.92 ^Xg X_-?@ 9026 ?09?8 0=0.3; =;0.22 ^Xg X_-;@ 9026 ?09?8 0=0.3; =;0.22 ^Xg X_-8@ 9026 ?09?8 0=0.3; =;0.22
Emutr`d M`rtfceb _mscstlr (EM_)
;.8=gY Yp _EM_-2:@ 1 1 ∞ ; 18 1832 323. 3.9a 9a℩ ℩ J ;.;g ;.;gY Y C 8::@
K`odm K`o dm Cap Capmh` mh`ekm ekm
??gY K`odm> ^K2: 1:.:?ga x (:.;8?+n:.00=)℩/ga ℩ J ??gY ^K2:1(9.68+n?.;)a 1(9.68+n?.;)a℩ ;.8=gY ^K2: 1(9.68+n?.;)a℩x ??gY
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^K2: 1(:.096?+n:.:=99)a℩ J; J;.; .;gY gY ;.;gY K`odm> ^K0 1:.8?ga x (:.3?2+n:.000)℩/ga ^K01(;63.;8+n89.9?) 1(;63.;8+n89.9?)a℩ a℩ J ;.;gY ??gY ^K0 1(;63.;8+n89.9?)a℩x ;.8=gY
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^K0 1(0=6;?+n0639)a℩ J??gY ??gY X`odm 8 [flr [flrt-Kc t-Kcrkuct rkuct K`od K`odms ms Capm Capmh`ek h`ekm m ^ J ??gY J ;.;gY (a℩ ) _ (a℩ ) V (a℩ ) _ (a℩) V (a℩) ^K2: 9.68 ?.; :.096? :.:=99 ^K20 ^K0 ^K? ^K; ^K8 ^K= ^K9 ^K2 ^K6 ^K3 ^K0: ^K00
3=2.9 0=6;? 0=6;? 03326 ??902 ;:0=9 06686 ?9;62 ?;286 ?;286 ?9;62 ?9;62
;?? 0639 0639 ?;3? ?2:6 ;900 ??=2 ;09: ?688 ?688 ;09: ;09:
?;.=83 ;63.;8 ;63.;8 830.;0 ==9.?: 280.9: 89;.=: 986.3: =68.:0 =68.:0 986.3: 986.3:
2.303 89.9? 89.9? =6.6; 99.9: 66.6: ==.=: 22.2: 93.3; 93.3; 22.2: 22.2:
K0? ^K0;
60:=60?
=3 9? 8;
0; 3.62.0 2=
00 :.6;.6 ::
^K08 ^K0=
=8;0 6686
?3=0 =6::
0;;.=9 ?02.9:
2?.=6 08?.9;
Altlr Alt lr Cap Capmh mh`ek `ekm m
0 ]rA? Z ^A 1 7 [rA 1 CD_ [rA pixȪ CrA (;.;gY)? 0 169;9.03a℩ x ^A01 09:gR 9.= :.62x:.386 Xfm _A `eh VA li `e `syekfrlelus altlr k`e om k`dkud`tmh wctf suiickcmet `kkur`ky usceb _A /VA r`tcl li :.0= `ppdck`odm ilr AY altlr wctf dmss tf`e 0AY@ `s pmr CMK 9:3:3. ζ1 `rk `rkt`e t`e
V 0 1 `rk `rkt`e t`e 160.893º _ :.0=
^A0 1 69;9.03a℩460.893º ^A0 1 (0?60+n6=80)a℩ (0?60+n6=80)a℩ J;.;gY
??gY ^A01(0?60+n6=80)a℩x ;.8=gY
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^A01(=?:38+n;82?38)a℩ J? J??g ?gY Y X`od X` odm m = [f [flr lrtt-Kc Kcrk rkuct uct @sye @syekf kfrl rlel elus us Ca Capm pmh` h`ek ekm m (a^℩) (a℩ ^A0 ^A? ^A; ^A8 ^A= ^A9 ^A2 ^A6 ^A3 ^A0: ^A00
_ (a℩)J ??gY V (a℩) =?:38 ;82?38 =?:38 ;82?38 ;6:82 ?=;98; 28638 833?38 =?:38 ;82?38 9??62 80=?89 9??62 80=?89 ;6:82 ?=;98; ;6:82 ?=;98; ;6:82 ?=;98; ;6:82 ?=;98;
_ (a℩ )J ;.;gVY (a℩) 0?60 6=80 0?60 6=80 3;9 9?;6 068? 0??23 0?60 6=80 0=;? 0:?0? 0=;? 0:?0? 3;9 9?;6 3;9 9?;6 3;9 9?;6 3;9 9?;6
;.;gY Duap Dl`h Capm Capmh`ekm h`ekm
Altlr dl`hs tf`t `rm lutschm tfm sklpm out kletrcoutceb sflrt-kcrkuct k`e om klaocemh cetl ` scebdm mqucv`dmet altlrs lr duapmh dl`h. Xfm ;.;gY duap0 cs `ssuamh tl om 3:% li tr`esilramr r`tmh plwmr wctf C D_ /CrA r`tcl li 9.=. 0 ]rA ? ^Duap01 CD_ [rA CrA
(;.;gY)? 0 ^Duap01 x 189=.;689a℩ 9.= (:.3x8AY@) Xfm _A `eh VA li Duap0 k`e om k`dkud`tmh usceb _ A /VA r`tcl li :.0: `ppdck`odm ilr AY altlr wctf mqu`d lr brm`tmr tf`e 0AY@ `s pmr CMK 9:3:3. `rkt`e t`e 0 168.?63º ζ1 `rk `rkt`e t`e V 1 `rk :.0 _ ^Duap0 1 89=.;6a℩468.?63º ^Duap0 1 (89.;0+n89;.:6)a℩ (89.;0+n89;.:6)a℩ J;.;gY
??gY ^Duap01(89.;0+n89;.:6)a℩x ;.8=gY
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^Duap01(066;+n066;:)a℩ J??g J??gY Y X`od X` odm m 9 [f [flr lrtt-Kc Kcrk rkuc uctt Du Duap ap0 0 Ca Capm pmh` h`ek ekm m ^ J ??gY J ;.;gY (a℩) _ (a℩) V (a℩) _ (a℩ ) V (a℩) ^Duap0 066; 066;: 89.;0 89;.:6
DY Duap Dl`h
Xl scapdciy tfm k`dkud`tcle m`kf DY duap dl`h cs `ssuamh tl om 3:% li tr`esilramr r`tmh plwmr. @ typck`d CD_ /CrA r`tcl li = om usmh ilr DY altlrs `s pmr CMK 9:3:3.
0 ]rA ? ^Duap?1 CD_ [rA CrA 0 (:.8gY)? 120.000a℩ ^Duap?1 x = (:.3x:.=AY@) Xfm _A `eh VA li Duap? Duap? k`e om k`dk k`dkud`tm ud`tmh h usceb usceb _A /VA r`tcl li :.8? `ppdck`odm ilr DY altlr `s pmr CMK 9:3:3. ζ1 `rk `rkt`e t`e
V 0 1 `rk `rkt`e t`e 192.?06º _ :.8?
^Duap? 1 20.000a℩492.?0 20 .000a℩492.?06º 6º ^Duap? 1 (?2.=;9+n9=.=9;)a (?2.=;9+n9=.=9;)a℩ J:.8gY ;.;gY ^Duap?1(?2.=9;+n9=.=9;)a℩x :.8?gY
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^Duap?1(02::+n8:86)a℩ J;. J;.;gY ;gY ??gY ^Duap?1(02::+n8:86)a℩ ;.8=gY
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^Duap?1(930?2+n098=62)a℩ J? J??g ?gY Y X`od X` odm m 2 [f [flr lrtt-Kc Kcrk rkuct uct DY Du Duap ap Ca Capm pmh` h`ek ekm m ^ J ??gY J ;.;gY (a℩) _ (a℩) V (a℩) _ (a℩ ) V (a℩) ^Duap? 930?2 098=62 02:: 8:86 ^Duap; ^Duap8 ^Duap=
;8=98 ;8=98 ;8=98
6??3= 6??3= 6??3=
6=: 6=: 6=:
?:?8 ?:?8 ?:?8
0.0. 0. 0.? ?
[f [flr lrtt-Kc Kcrk rkuc uctt K K`d `dku kud` d`tc tcle le `t AY [R [RB_ B_-: -:? ?( (Hm Hmvc vckm km Hu Huty ty) )
Ic Icbur burm m 0 Cap Capmh` mh`ekm ekm H Hc`b c`br`a r`a J ; ;.;g .;gY Y [ldvceb [ldv ceb Z`rtc`d Z`rtc`d Capmh Capmh`ekm `ekm `t or` or`ekf ekf ^s
^s 1^Xg X_-2:@ +^k2:+
^P x ^k20+^Xg X_-20@ +^Duap0 ^P +^k20+^Xg X_-2 X_-20@ 0@+^Duap0
^s1(? 1(?8.8 8.8;+n ;+n0== 0==.;= .;=)) a℩
0.0.?. 0.0 .?.0 0 [ld [ldvce vceb b Cec Cectc` tc`dd [fl [flrt-K rt-Kcrk crkuct uct Kur Kurrme rmett
Z`rtc` Z`r tc`dd [flrt [flrt-Kc -Kcrku rkuct ct Kurr Kurrme mett `t or` or`ekf ekf ^s
C"g 1
Or`ekf ^s
0.0x;.;gY k]e 1 10;.;?9g@4-60.:9º ;(?8.8;+n0==.;=)a℩ ∞ ;^ ;^0 ∞ ;(?8.8;+n0==.;=)a℩
^ rmhuktcle smm `olvm
Z`rtc`d ^ J ;.;gY ℩) (a℩ (a ?8.8;+n0==.;=
Z`rtc`d C‑ gJ;.;gY (g@) 0;.;;4-60.:9º
A0 A? A; A8 A= A9 A2 A6 A3 A0: A00 D]AZ? D]AZ; D]AZ8 D]AZ=
^a0+^k0 ^a?+^k? ^a;+^k; ^a8+^k8 ^a=+^k= ^a9+^k9 ^a2+^k2 ^a6+^k6 ^a3+^k3 ^a0:+^k0: ^a00+^k00 ^Duap?+^tg +^k0? ^Duap;+^tg +^k0; ^Duap8+^tg +^k08 ^Duap=+^tg +^k0=
092:.88+n6=62.?9 092:.88+n6=62.?9 08?9.3=+n9?39.80 ?;32.33+n0?;8=.?: ?:??.2:+n69?3.88 033=.?9+n0:?92.?0 ?06:.99+n0:?63.80 0=03.9=+n9;:2.=0 0=03.9=+n9;:2.=0 0=68.=8+n9;0=.?6 0=68.=8+n9;0=.?6 ?036.26+ 26+n8230.=9
:.?;3=4-23º :.?;3=4-23º :.;?894-22 :.09994-23 :.?;9=4-22 :.?::84-23 :.033;4-26 :.;?;:4-29 :.;?;:4-29 :.;?034-29 :.;?034-29 :.;32=4 =4--9=
0?::.92+ 92+n?99;.=9
:.202;4 ;4--99
00;=.86+ 86+n?9?6.0;
:.2;?:4 :4--99
0?03.=?+ =?+n?936.03
:.2:264-99
Xltt`d Cect Xl ctc` c`dd [ [fl flrt rt--Kcrk crkuct `t A AY Y[ [R RB_ B_-: -:? ?
06 06.2 .20g 0g@ @44-26 26
0.0. 0. 0.?. ?.? ? [l [ldv dvce ceb b Zm Zm`g `g [fl [flrt rt-K -Kcrk crkuc uctt Kurr Kurrme mett
Z`rtc`d pm`g sflrt-kcrkuct kurrmet `t or`ekf ^s
Amtflh O g-i`ktlr wcdd om usmh ce k`dkud`tceb tfm pm`g kurrmet. cp 10.0=g ?C"g 7
g10.:?+:.36m-;_/V
@s ametclemh ce CMK9:3:3 ci `dd or`ekf _/V rma`ces sa`ddmr tf`e :.; lr ci `dd or`ekf V/_ rma`ces fcbfmr tf`e ;.;; tfme ct cs elt emkmss`ry tl usm 0.0=. Out scekm, _/V or`ekf le duap0, ?, ; & 8 mxkmmhmh :.; ` audtcpdck`tcle i`ktlr li 0.0= wcdd om usmh tl `kkluet ilr ce`kkur`ky k`usmh oy emtwlrg rmhuktcle. g10.:?+:.36m-;(?8.8;/0==.;=) 10.9;08 cp 10.0=xg ?C"g 10. 0.0= 0=x x0. 0.9; 9;08 08 ?(0;.;;g@)1;=.;9g@
[ldvceb `syekfrlelus a`kfcem r`tmh kurrmet C rA J;.;gY Or`ekf A01
09:gR ;x;.;gYx:.62x:.386 ∞ ;x;.;gYx:.62x:.386
1;;.38@
:.8=AY@ 1983.=0@ ;x8::Y ∞ ;x8::Y :.8? 1983.=0@x 16?.99 16? .99@ @ J;.;gY J;.;gY ;.;
Or`ekf D]AZ?1
Or`ekf ^s A0 A? A; A8 A= A9 A2 A6 A3 A0: A00 D]AZ? D]AZ; D]AZ8 D]AZ= Xlt`d J AY [RB_-:? 0.0. 0. 0.? ?.;
Cp J;.;gY (g@) ;=.;9 :.90:8 :.90:8 :.6::9 :.8?82 :.=266 :.=0:2 :.8362 :.26=6 :.26=6 :.22=9
CrA J:.8gY (@) -
CrA J; J;.; .;gY gY (@ (@)) ;;.3= ;;.38 89.82 ?;.90 ;;.38 ?6.;6 ?6.;6 89.82 89.82 89.82
:.22=9 :.6038 0.86=9 0.=;;= 0.8983 82.6?
983.=; 0?33.:2 0?33.:2 0?33.:2 -
89.82 6?.99 09=.;; 09=.;; 09=.;; 33;.?=
[ld ldvc vce eb [f [flr lrtt-K Kcrk crkuc uctt Or Orm m`g `gce ceb b kur urrm rme et J;. ;.; ;gY us usce ceb b AY KO tace
CoA 1½qC"gA ilr @syekfrlelus A`kfcem CoP 1C"gP
ilr Emtwlrg
Xlt`d orm`gceb kurrmet cs tfm sua li p`rtc`d orm`gceb kurrmet li m`kf or`ekf Co1CoA+CoP. [kfemchmrr FYV0? kcrkuct orm`gmr wctf acecaua lpmeceb tcam li 8:as [kfemchm pdus f`di kykdm tcam rmd`y `s pmr CMK9??20-0:: wcdd om usmh le ;.;gY. Kcrkuct orm`gmr acecaua lpmeceb tcam cs 8:as+0/(?x=:fz) 8:as+0/(?x=:fz)1=:as 1=:as
[ldv [l dvce ceb b p` p`rtc rtc`d `d or orm` m`gc gceb eb ku kurrm rrmet et `t or or`e `ekf kf ^s
@s pmr CMK 9:3:3 stm`hy st`tm, orm`gceb kurrmet `eh cectc`d sflrt-kcrkuct kurrmet kurrm et i`r iirla rla b bmemr` memr`tlr tlr `r `rm m Cg1Co1C‑ g. Xfmrmilrm, CoP1C‑ gP gP10;.;;g@
[ldvceb [ldvc eb p`rtc p`rtc`d `d orm` orm`gceb gceb kurrm kurrmet et `t O Or`ekf r`ekf A0
]sceb mqu`tcle tace li :.:=smk ilr AY KO ½-I`ktlr ½1:.20+:.=0m-:.;C"rA /CrA
tace 1:.:=smk
½1:.20+:.=0m-:.;(:.?;3=g@) //;;.3=@ 1:.2208 Ci eltfceb cs hmicectm gelwe tfme usm ZrA /p1:.:= `s pmr CMK CMK 9:3:3 q1:.23+:.0?Ce
ZrA p
tace1:.:=smk
q1:.23+:.0?Ce:.:= 1:.8;:= Xfmrmilrm, CoA01½qC"gA 1:.2208x:.8;:=x:.?;3=g@1:.:23=g@ 0.0. 0. 0.?. ?.8 8
[l [ldv dvce ceb bp p`rt `rtc` c`dd h hk kk kla lapl plem emet et chk J;.;gY
[ldv [l dvce ceb b hk kl klap aple leme mett `t or or`e `ekf kf ^s
chk 1 ?C"gm-?
it_/V
ϊ
hk klaplemet
chk 1 ?*0;.;;g@*m-?
(=:fz)(:.:=s)(?8.8;/0==.;=)
ϊ
10.=3g@
[ldv [l dvce ceb b hk kl klap aple leme mett `t or or`e `ekf kf A0
chk 1 ?C"gm-?
it_/V
ϊ
hk klaplemet
chk 1 ?*:. ?*:.?; ?;3= 3=g@ g@*m *m-?
(=:fz)(:.:=s)(092:.88/6=62.?9)
ϊ
Or`ekf
1:.:0=3g@
^s A0 A? A; A8
Co J;.;gY (g@) 0;.;? :.:23= :.:23= :.0:23 :.:==;
Chk J;.;gY (g@) 0.=3;2 :.:0=3 :.:0=3 :.:0;: :.:000
A= A9
:.:269 :.:99=
:.::68 :.:0;;
A2 A6 A3 A0: A00 D]AZ? D]AZ; D]AZ8 D]AZ= Xlt`d J AY [RB_-:?
:.:99? :.:0:0 :.0:2= :.:0:; :.0:2= :.:0:; :.0:2? :.::66 :.0:2? :.::66 :.08?0 :.:::8 :.?9?0 :.:::6 :.?99; :.::00 :.?=3; :.:::6 0=.?? 0.2?; ? ? Co `sya1∞(Co +chk ) `k `eh hk klaplemet 1∞W(0=.??)?+(0.2?;)?Q10=.;?g@
0.0. 0. 0.?. ?.= = [l [ldv dvce ceb b [f [flr lrtt-Kc Kcrk rkuc uctt Or Orm` m`gc gceb eb ku kurr rrme mett J; J;.; .;gY gY us usce ceb b AY Iusm tace
Iusm acecaua lpmeceb tcam cs `ssuamh tl om f`di kykdm 0/(?x=:fz) 10:as [ldv [l dvce ceb b p` p`rtc rtc`d `d or orm` m`gc gceb eb ku kurrm rrmet et `t or or`e `ekf kf ^s
@s pmr CMK 9:3:3 stm`hy st`tm, orm`gceb kurrmet `eh cectc`d sflrt-kcrkuct kurrmet kurrm et i`r iirla rla b bmemr` memr`tlr tlr `r `rm m Cg1Co1C‑ g. Xfmrmilrm, CoP1C‑ gP gP10;.;;g@ [ldvceb [ldvc eb p`rtc p`rtc`d `d orm` orm`gceb gceb kurrm kurrmet et `t O Or`ekf r`ekf A0
]sceb mqu`tcle tace li :.:?smk ilr AY Iusm ½-I`ktlr ½1:.68+:.?9m-:.?9C"rA /CrA
tace 1:.:?smk
½1:.68+:.?9m-:.?9(:.?;3=g@)/;;.3=@ 1:.660= Ci eltfceb cs hmicectm gelwe tfme usm ZrA /p1:.:= `s pmr CMK CMK 9:3:3 q10.:;+:.0?Ce
ZrA p
tace1:.:?smk
q10.:;+:.0 q10.: ;+:.0?Ce:. ?Ce:.:= := 1:.92 1:.92:= := Xfmrmilrm, C oA0
1½qC" 1:.660=x:.92:=x:.?;3=g@1:.0809g@ gA
0.0. 0. 0.?. ?.9 9
[l [ldv dvce ceb b p` p`rt rtc` c`dd h hk kk kla lapl plem emet et chk J;.;gY
[ldv [l dvce ceb b hk kl klap aple leme mett `t or or`e `ekf kf ^s
chk 1 ?C"gm-?
it_/V
ϊ
hk klaplemet
chk 1 ?*0;.;;g@*m-?
(=:fz)(:.:0s)(?8.8;/0==.;=)
ϊ
100.=g@
[ldv [l dvce ceb b hk kl klap aple leme mett `t or or`e `ekf kf A0
chk 1 ?C"gm-?
it_/V
ϊ
hk klaplemet
chk 1 ?*:. ?*:.?; ?;3= 3=g@ g@*m *m-?
(=:fz)(:.:0s)(092:.88/6=62.?9)
ϊ
1:.06;6g@
Co `sya1Co sya+chk1∞W(0;.;;g@)?+(0.=3g@)?Q10;.8;g@ Or`ekf ^s A0 A? A; A A8 = A9 A2 A6 A3 A0: A00 D]AZ? D]AZ; D]AZ8 D]AZ= Xlt`d J AY [RB_-:?
Co J;.;gY (g@) 0;.;? :.080= :.080= :.03?:
Chk J;.;gY (g@) 00.833 :.06;6 :.06;6 :.??=?
: : :..: 03 ;6 38 33 :..0 0? 96 :: 0 :.0068; :.0=;6 :.0026? :.0886 :.03002 :.?08; :.03002 :.?08; :.03:= :.?:93 :.03:= :.?:93 :.?8;2= :.0;?3 :.8888 :.?890 :.8=?9 :.?998 :.8;30 :.?803 09.9?:? 08.80 laplemet emet Co `sya1∞(Co?+chk?) `k `eh hk kklapl ? ? 1∞W(09.9?) +(08.80) Q1?0.33g@
0.0.?.2 0.0.? .2 [mdm [mdmktmh ktmh [ [flrtflrt-Kcrku Kcrkuct ct _`t _`tceb ceb li Y YKO KO `eh [ [wctk wctkfbm` fbm`r r ilr ;.;gY
]sceb [kfemchmr FYV0? Y`kuua Kcrkuct Orm`gmr> _`tmh Orm`gceb K`p`kcty1 ?=g@ ras sya _`tmh A`gceb K`p`kcty 1 9;g@
_`tmh @syaamtrck`d @syaamtrck`d Orm`gceb K` K`p`kcty p`kcty li FY FYV0? V0? Kcrkuct Orm`gmr acecaua lpmeceb tcam cs 8:as+0/(?x=:fz)1=:as wctf st`eh st`eh`rh `rh tca tcam m kles klest`et t`et (ψ) li 8=as
%
(
1 0::
)
ψ
(
1 0::
) 8=as
1 ;?.3?%
chk 1%hkxC`k 1%hkx∞?xCo sya 1;?.3?%x∞
[email protected]@ Co `sya 1
?
Co sya +(Chk )? 1 ((?=g@)? +(00.98g@)? )1?2.=6g@
Ouso`r [flrt-Kcrkuct _`tceb ([kfemchmr ZCV 0?) _`tmh sflrt tcam wctfst`eh kurrmet cs ?=g@ _`tmh pm`g wctfst`eh kurrmet cs 9;g@
0.0.?.6 0.0.? .6 [mdm [mdmktmh ktmh [flrt [flrt-Kcrk -Kcrkuct uct _`tce _`tceb bl lii A AY YI Iusm usm
]sceb [kfemchmr Kurrmet Dcactceb Iusm>
_`tmh Orm`gceb K`p`kcty1 =:g@ ras sya V/_ tmst r`tcl cs k`dkud`tmh o`smh le 09%plwmr i`ktlr tmst Ace. lpmeceb tcam cs `ssuamh tl om f`di-kykdm 0/(?x=:fz)1 0/(?x=:fz)10:as 0:as Zlwmr i`ktlr tmst li 09%1klsζ ζ16:.23 V/_1X`eζ1X`e6:.2319.093
1
1=:g@ 0+?m
0.0. 0. 0.; ;
0+? -
/
8ϊx=:fzx:.:0s 9.093
19=.9?g@
[t [tm` m`hy hy [t [t`t `tm m[ [fl flrt rt-K -Kcrk crkuc uctt K Kur urrm rmet et `t A AY Y[ [RB RB__-:? :?
Xfm acecaua stm`hy st`tm sflrt-kcrkuct kurrmet wcdd om usmh ilr rmd`y kllrhce`tcle purplsms. Ce tfcs rmplrt, tfm slurkm emtwlrg cs tfm ledy kletrcoutlrs li stm`hy st`tm sflrt-kcrkuct kurrmet. Cg 1C"g ilr emtwlrg
Cg 1C"g 1
0.0. 0. 0.8 8
kace]e 0.:x;.;gY 1 10?.0?g@4-60.:9º ∞ ;^ ;^0 ∞ ;(?8.8;+n0==.;=)a℩ ;(?8.8;+n0==.;=)a℩
[f [flr lrtt-Kc Kcrk rkuc uctt K` K`dk dkud ud`t `tcl cle e `t AY [ [RB RB__-:0 :0 ( (Hm Hmvc vckm km H Hut uty) y)
Ic Icbur burm m ? Cap Capmh` mh`ekm ekm Hc` Hc`br` br`a a J ??gY ??gY
Capmh`ekm _mhuktcle K`dkud`tcle 0 0 0 0 0 + + + 1 ^A (^K0+^A0) (^K? +^A?) (^K;+^A;) (^K8 +^A8) +
0 0 0 0 + + + (^K= +^A=) (^K9+^A9) (^K2 +^A2) (^K6+^A6)
+
0 0 0 + + (^K3 +^A3) (^K0:+^A0:) (^K00 +^A00)
+
0 ^K0? +^Xg X_-0@+^Duap?
+
0 ^K0; +^Xg X_-?@ +^Duap;
+
0 ^K08 +^Xg X_-;@ +^Duap8
+
0 ^K0=+^Xg X_-8@ +^Duap=
^A 1 ( 8698.8?6+n08380.92)a℩
^D 1^K2: +^Xg X_-2:@+^A ^D 1(==:9.980+n?:;88.9;9)a℩ ^P 1(;20.839+n38;.=33)a℩ ^D]AZ01^K20+^Xg X_-20@ +^Duap0 ^D]AZ01(;6;;.8:8+n?2=3:.663)a℩ 0.0.8. 0.0 .8.0 0 [ld [ldvce vceb b Cec Cectc` tc`dd [fl [flrt-K rt-Kcrk crkuct uct Kur Kurrme rmett
Z`rtc`d [flrt-Kcrkuct Kurrmet `t or`ekf slurkm ^P
C"g 1
0.0x??gY k]e 1 10;.22g@4-96.=0º ;(;20.839+n38;.=33)a℩ ∞ ;^ ;^0 ∞ ;(;20.839+n38;.=33)a℩
Or`ekf
^ rmhuktcle
^P ^D]AZ0 ^D
smm `olvm smm `olvm smm `olvm
Z`rtc`d ^ J ??gY Z`rtc`d C‑ gJ??gY (a℩ ) (g@) ;20.839+n38;.=33 0;.224-96.=0º ;6;;.8:8+n?2=3:.3 :.=:094-6?.:3º ==:9.980+n?:;88.9 :.99?34-28.69º
Xlt` Xl t`dd CCec ectc tc`d `d [f [flr lrtt-Kc Kcrk rkuc uctt ` `tt AY [RB RB__-:0 :0 0.0. 0. 0.8. 8.? ?
08 08.3 .3?4 ?4-9 -93. 3.?8 ?8
[l [ldv dvce ceb b Zm Zm`g `g [f [flr lrtt-Kc Kcrk rkuc uctt Ku Kurrm rrmet et
Z`rtc`d Z`rtc `d pm`g sflrt sflrt-kcrku -kcrkuct ct kurrme kurrmett `t or`ekf ^P
Amtflh O g-i`ktlr wcdd om usmh ce k`dkud`tceb tfm pm`g kurrmet. cp 10.0=g ?C"g 7
g10.:?+:.36m-;_/V
@s ametclemh ce CMK9:3:3 ci `dd or`ekf _/V rma`ces sa`ddmr tf`e :.; lr ci `dd or`ekf V/_ rma`ces fcbfmr tf`e ;.;; tfme ct cs elt emkmss`ry tl usm 0.0=. Out scekm, _/V or`ekf le ^ P mxkmmhmh :.; ` audtcpdck`tcle i`ktlr li 0.0= wcdd om usmh tl `kkluet ilr ce`kkur`ky k`usmh oy emtwlrg rmhuktcle.
g10.:?+:.36m-;(;20.839/38;.=33) 10.;?:6 cp 10.0=xg ?C"g 10. 0.0= 0=x x0. 0.;? ;?:6 :6 ?(0;.22g@)1?3.=6g@
[ldvceb `syekfrlelus a`kfcem r`tmh kurrmet C rA J??gY Xlt`d `syekfrlelus r`tmh kurrmet irla AY [RB_-:? cs 33;.?=@ ?? 19;;;. 19; ;;.22@ 22@ J?? J??gY gY ;.8= ;.9AY@ Or`ekf ^D]AZ0 1 138.82@ ∞ ;x??gY ;x??gY
Or`e Or `ekf kf ^D 133;.?=@x
Or`ekf ^P ^D]AZ0 ^D Xlt`d J AY [RB_-:0 0.0. 0. 0.8 8.;
Cp J??gY (g@) ;=.;9 0.;9 0.=2 ;?.=?
CrA J;.;gY (@) 33;.?= -
CrA J??gY (@) 38.82 9;;;.22 -
[ld ldvc vce eb [f [flr lrtt-K Kcrk crkuc uctt Or Orm m`g `gce ceb b kur urrm rme et J?? ??gY gY
CoA 1½qC"gA ilr @syekfrlelus A`kfcem CoP 1C"gP
ilr Emtwlrg
Xlt`d orm`gceb kurrmet cs tfm sua li p`rtc`d orm`gceb kurrmet li m`kf or`ekf Co1CoA+CoP. [kfemchmrr FYV?8 kcrkuct orm`gmr wctf acecaua lpmeceb tcam li 8:as [kfemchm pdus f`di kykdm tcam rmd`y `s pmr CMK9??20-0:: wcdd om usmh le ??gY. Kcrkuct orm`gmr orm`gmr acecaua lpmeceb tcam cs 8:as 8:as+0/(?x=:fz) +0/(?x=:fz)1=:as 1=:as
[ldv [l dvce ceb b p` p`rtc rtc`d `d or orm` m`gc gceb eb ku kurrm rrmet et `t or or`e `ekf kf ^P
@s pmr CMK 9:3:3 stm`hy st`tm, orm`gceb kurrmet `eh cectc`d sflrt-kcrkuct kurrmet kurrm et i`r iirla rla b bmemr` memr`tlr tlr `r `rm m Cg1Co1C‑ g. Xfmrmilrm, CoP1C‑ gP gP10;.22g@
[ldvce [ld vceb b p`r p`rtc` tc`dd orm orm`gc `gceb eb kur kurrme rmett `t Or` Or`ekf ekf ^D]AZ0
]sceb mqu`tcle tace li :.:=smk ilr AY KO ½-I`ktlr ½1:.20+:.=0m-:.;C"rA /CrA
tace 1:.:=smk
½1:.20+:.=0m-:.;(:.=:09g@) //38.82@ 1:.60;2 Ci eltfceb cs hmicectm gelwe tfme usm ZrA /p1:.:= `s pmr CMK CMK 9:3:3 q1:.23+:.0?Ce
ZrA p
tace1:.:=smk
q1:.23+:.0?Ce:.:= 1:.8;:= Xfmrmilrm, CoA01½qC"gA 1:.60;2x:.8;:=x:.=:09g@1:.02=2g@ 0.0. 0. 0.8. 8.8 8
[l [ldv dvce ceb bp p`rt `rtc` c`dd h hk kk kla lapl plem emet et chk J??gY
[ldv [l dvce ceb b hk kl klap aple leme mett `t or or`e `ekf kf ^P
chk 1 ?C"gm-?
it_/V
ϊ
hk klaplemet
chk 1 ?*0;.26g@*m-?
(=:fz)(:.:=s)(;20.83/38;.9)
ϊ
Or`ekf
Co J??gY (g@) Chk J??gY (g@) 0;.26 :.:8:? :.02=2 :.:233 :.;8;2 :.:0;; 08.;: :.0;;= ? ? Co `sya1∞(Co +chk ) `k `eh hk klaplemet 1∞W(08.;:)?+(:.0;;=)?Q108.;g@
^P ^D]AZ0 ^D Xlt`d J AY [RB_-:0
%
1 0::
1:.:8:?g@
(
) ψ
chk 1%hkxC`k 1%hkx∞?xCo sya 1
1∞
+ (
)
0.0.8.= 0.0.8 .= [mdm [mdmktmh ktmh [ [flrtflrt-Kcrku Kcrkuct ct _`t _`tceb ceb li Y YKO KO `eh [ [wctk wctkfbm` fbm`r r ilr ??gY
]sceb [kfemchmr FYV?8 Y`kuua Kcrkuct Orm`gmr> _`tmh Orm`gceb K`p`kcty1 09g@ ras sya
_`tmh A`gceb K`p`kcty 1 8:g@
_`tmh @syaamtrck`d @syaamtrck`d Orm Orm`gceb `gceb K`p`kcty li F FYV?8 YV?8 Kcrkuct Kcrkuct Orm`gmr acecaua lpmeceb tcam cs 8:as+0/(?x=:fz)1=:as wctf st`eh st`eh`rh `rh tca tcam m kles klest`et t`et (ψ) li 8=as
%
1 0::
(
)
ψ
1 0::
(
) 8=as
1 ;?.3?%
chk 1%hkxC`k 1%hkx∞?xCo sya 1;?.3?%x∞
[email protected]=g@ Co `sya 1
?
Co sya +(Chk )? 1 ((09g@)? +(2.8=g@)?)102.9=g@
Ouso`r [flrt-Kcrkuct _`tceb ([kfemchmr ZCV ?8) _`tmh sflrt tcam wctfst`eh kurrmet cs 09g@ _`tmh pm`g wctfst`eh kurrmet cs 8:g@
0.0. 0. 0.= =
[t [tm` m`hy hy [t [t`t `tm m[ [fl flrt rt-K -Kcrk crkuc uctt K Kur urrm rmet et `t A AY Y[ [RB RB__-:0 :0
Xfm acecaua stm`hy st`tm sflrt-kcrkuct kurrmet wcdd om usmh ilr rmd`y kllrhce`tcle purplsms. Ce tfcs rmplrt, tfm slurkm emtwlrg cs tfm ledy kletrcoutlrs li stm`hy st`tm sflrt-kcrkuct kurrmet. Cg 1C"g ilr emtwlrg Cg 1C"g 1
kace]e 0.:x??gY 10?.=?g@4-96.=0º 1 ;^0 ;(;20.839+n38;.=33)a℩ ∞ ;^ ∞ ;(;20.839+n38;.=33)a℩
0.0. 0. 0.9 9
]e ]esy syaa aamt mtrck rck`d `d [f [flr lrtt-Kc Kcrk rkuc uctt `t AY [R [RB_ B_-: -:0 0
Icburm Icb urm ; Ca Capmh pmh`ek `ekm m Hc` Hc`br` br`a a `t ??gY o`s o`sm m ^A 1 ( 8698.8?6+n08380.92)a℩ ^D]AZ01(;6;;.8:8+n?2=3:.663)a℩ ^P 1(;20.839+n38;.=33)a℩ ^X 1^Xg X_-2:@ +^K2:1(98?.??+n=8:?.39)a℩
Xlt`d plsctcvm, emb`tcvm `eh zmrl smqumek smqumekm m capmh`ekms ^0 1^?1
0 0
0 ^X +^A
0
+^ +^ P D]AZ0
1 (;;0.2=+n62=.;9)a℩
^: 1^P 1(0:=:=0+n0829)a℩ zmrl smqumekm brlueh caph`ekm 0.0.9. 0.0 .9.0 0 [ce [cebdm bdm Dcem tl B Brlu rlueh eh I I`ud `udtt ([D ([DB) B)
;k]e ∞ ;k]
C" 1
^0 +^? +^:
g0
1
∞ ;x0.0x??gY ;x0.0x??gY ?(;;0.2=+n62=.;9)a℩+(0:=:=0+n0829)a℩
1:.;
[email protected]=º 0.0. 0. 0.9. 9.? ? Dc Dcem em ttl l Dc Dcem em I I`u `udt dt ( (DD DD) )
C"g? 1
k]e 0.0x??gY 1 10?.3;g@ ^0 +^? ?(;;0.2=+n62=.;9)a℩
0.0.9. 0.0 .9.; ; Hlu Hluodm odm Dce Dcem m tl B Brlue rlueh h I`u I`udt dt (H (HDB) DB)
C"g?MD? 1 1
-nk]e (^: -`^? ) ^0^?+ ^0^:+^?^:
-n0.0x??gYW(0:=.:=0+n0.829)℩-(040?:)x(:.;;02=+n:.62=;9)℩Q (998=?.:3+n06=82=.9)℩
10;g@4-0=3.80 k]e ( ∟ )
C"g?MD?1
^0 ^? + ^0 ^: +^? ^: n0.0x??gYW(0:=.:=0+n0.829)℩-(04?8:)x(:.;;02=+n:.62=;9)℩Q 1 (998=?.:3+n06=82=.9)℩ 10;g@4?:.3?
C"gM?M 1
∞ ;k] ;k]e ^?
^0 ^? + ^0 ^: +^? ^:
1
∞ ;x0.0x??gYW(:.;;02=+n:.62=;9)℩Q (998=?.:3+n06=82=.9)℩
1:.0330g@4-0.:8º
0.0. 0. 0.2 2
]e ]esy syaa aamt mtrck rck`d `d [f [flr lrtt-Kc Kcrk rkuc uctt `t AY [R [RB_ B_-: -:? ?
Icburm Icbu rm 8 Capm Capmh`ek h`ekm m Hc`b Hc`br`a r`a `t ;.;gY o`sm ^A 1 ( 003.9;+n;92.88)a℩ ^D]AZ01(38.?2+n926.=0)a℩ ^P 1(3.0;9+n?;.?:=)a℩ ^X 1^Xg X_-2:@ +^K2:1(0=.23+n0;?.62)a℩ Xlt`d plsctcvm, emb`tcvm `eh zmrl smqumek smqumekm m capmh`ekms ^D]AZ0 +^ ^A ^^P+^ X P D]AZ0 ^0 1^?1 1(??.82+n0:3.23)a℩ ^P ^D]AZ0 ^A + +^X ^P +^D]AZ0 ^: 1^Xg X_-2:@ +;_EM_-2:@ 10=.9?=+n0;?.60+(;x8323.9)a℩ 1(083=8+n0;?.6)a℩ zmrl smqumekm brlueh caph`ekm
0.0.2. 0.0 .2.0 0 [ce [cebdm bdm Dcem tl B Brlu rlueh eh I I`ud `udtt ([D ([DB) B)
C"g01 1
;k]e ∞ ;k] ^0 +^? +^:
∞ ;x0.0x;.;gY ;x0.0x;.;gY ?(??.82+n0:3.23)a℩+(083=8+n0;?.6)a℩
1:.8g@4-0.;=º 0.0. 0. 0.2. 2.? ?
C"g? 1
0.0. 0. 0.2. 2.; ;
Dc Dcem em tl Dcem Dcem I` I`ud udtt ( (DD DD) )
k]e 0.0x;.;gY 1 109.?g@ ^0 +^? ?(??.82+n0:3.23)a℩ Hl Hluo uodm dm Dcem Dcem tl Br Brlu lueh eh I` I`ud udtt ( (HD HDB) B)
C"g?MD? 1
-nk]e (^: -`^? ) ^0^?+ ^0^:+^?^:
1
-n0.0x;.;gYW(08.3=+n:.0;;)℩-(040?:)x(:.:??=+n:.0:36)℩Q (9;0.;?+n;?38.=)℩
109.?3g@4-096.= k]e ( ∟ )
C"g?MD;1
^0 ^? + ^0 ^: +^? ^: n0.0x;.;gYW(08.3=+n:.0;;)℩-(04?8:)x(:.:??=+n:.0:36)℩Q 1 (9;0.;?+n;?38.=)℩ 109.:3g@4-26
C"gM?M 1
;k]e ^? ∞ ;k]
^0 ^? + ^0 ^: +^? ^:
1
∞ ;x0.0x;.;gYW(:.:??=+n:.0:36)℩Q (9;0.;?+n;?38.=)℩
1:.?0:g@4-:.2?º
0.0. 0. 0.6 6
CM CMK K [f [flr lrtt-Kc Kcrk rkuc uctt [u [uaa aa`r `ry y _m _mpl plrt rt
X`odm 6 [wct [wctkfbm` kfbm`rr Alam Alamet`ry et`ry Huty Ous [flrt-Kcrkuct Kurrmet (g@) CH gY cp
[ [uaa` uaa`ry ry _mp _mplrt lrt (CMK) (CMK) Hmvckm Klekduscle K`p`kcty (g@) cp
AY-[RB_-:0 AY-[RB_-:?
8: 9;
?? ;.;
;?.=? 82.6?
@kkmpt`odm @kkmpt`odm
X`odm X`o dm 3 Hm Hmvck vckm m Alam Alamet` et`ry ry Huty Huty [uaa [uaa`ry `ry _ _mpl mplrt rt ((CMK CMK)) Hmvckm CH YKO YKO Iusm
gY ?? ;.; ;.;
[flrt-Kcrkuct Kurrmet (g@) Co sya Co `sya cp 08.; 08.; ;?.= 0=.? 0=.; 82.6 09.9 ?0.33 82.6
Hmvckm K`p`kcty (g@) Co sya Co `sya cp 09 02.2 8: ?= ?2.9 9; =: 9=.9 -
Klekduscle @kkmpt`odm @kkmpt`odm @kkmpt`odm
X`odm 0: [tm` [tm`hy hy [t`tm [t`tm [ [flrt flrt-Kcr -Kcrkuct kuct Kurrmet Kurrmet (C (CMK) MK) Ous gY Cg (g@) AY-[RB_-:0 ?? 0?.=? AY-[RB_-:? ;.; 0?.0? X`odm 00 [flr [flrt-Kc t-Kcrkuc rkuctt [ [uaa` uaa`ry ry _ _mplrt mplrt (CMK) (CMK) O AuYs-[RB_-:0 AY-[RB_-:?
g ?Y ? ;.;
[ (g@) :.D;H39 :.8
H 0;DB (g@) 09.:3
D ;8 Zf 0D?.(3g;@) 0 .3`?sm (g@) 09.? 06.20
