background image





8.à$'<=$6,/$1,$75$1=<6725Ï:



:<%Ï5381.7835$&<75$1=<6725$

3U]H]Z\EyUSXQNWXSUDF\HOHPHQWXDNW\ZQHJRQDOH*\UR]XPLHü

Z\EyUSXQNWXQDMHJRFKDUDNWHU\VW\FHSUGRZRQDSL FLRZHMOXEZSROX

URG]LQ\FKDUDNWHU\VW\NQSNROHNWRURZ\FKOXEGUHQRZ\FK

-DN Z\QLND ] RSLVX ZLHONRV\JQDáRZ\FK PRGHOL WUDQ]\VWRUyZ

ELSRODUQ\FK L XQLSRODUQ\FK RSLVDQ\FK RGSRZLHGQLR Z UR]G]  RUD]

GODMHGQR]QDF]QHJRRNUHOHQLDSXQNWXSUDF\WUDQ]\VWRUDNRQLHF]QH

MHVW SRGDQLH GZyFK ZLHONRFL VSRUyG QDSL ü L SUGyZ RSLVXMF\FK

URG]LQ\ MHJR FKDUDNWHU\VW\N VWDW\F]Q\FK : SU]\SDGNX WUDQ]\VWRUD

ELSRODUQHJR ZLHONRFLDPL W\PL V QDMF] FLHM SUG NROHNWRUD

I

C

LQDSL FLH NROHNWRU  HPLWHU

U

CE

 OXE QDSL FLH ED]D   HPLWHU

U

BE



:SU]\SDGNXWUDQ]\VWRUDXQLSRODUQHJRVWRSUGGUHQX

I

D

LQDSL FLH

GUHQ(UyGáR

U

DS

OXEQDSL FLHEUDPND(UyGáR

U

GS



'REyU SXQNWX SUDF\ Z ]QDF]Q\P VWRSQLX ]DOH*\ RG SU]H]QDF]HQLD

LZDUXQNyZSUDF\XNáDGX3RGXZDJ QDOH*\Z]LüF]\QQLNL]ZL]DQH

]HVWUXNWXUXNáDGXVWDZLDQ\PLSU]HGQLPZ\PDJDQLDPLWHFKQLF]Q\PL

RUD]URG]DMHPX*\W\FKWUDQ]\VWRUyZ

3XQNWSUDF\SRZLQLHQOH*HüZREV]DU]HZNWyU\PWUDQ]\VWRU\Z\ND]XM

OLQLRZHZáDFLZRFLZ]PDFQLDMFH'ODWUDQ]\VWRUyZELSRODUQ\FKMHVWWR

REV]DU SUDF\ DNW\ZQHM SU]\ SRODU\]DFML QRUPDOQHM GOD WUDQ]\VWRUyZ

XQLSRODUQ\FKREV]DUQDV\FHQLD

8

&( PD[

X

&(

0

L

&

,

& PD[

3

& PD[

,

& PLQ

8

&( PLQ

8

'6 PD[

X

'6

0

L

'

,

' PD[

3

'PD[

,

'PLQ

8

8

8

'6

*6

7

=

b)

a)

5\V 'RSXV]F]DOQH REV]DU\ Z\ERUX SXQNWX SUDF\ Z SROX FKDUDNWHU\VW\N

Z\MFLRZ\FKD WUDQ]\VWRUDELSRODUQHJRE WUDQ]\VWRUDXQLSRODUQHJR

'OD ND*GHJR WUDQ]\VWRUD PR*QD Z\]QDF]\ü Z SROX MHJR

FKDUDNWHU\VW\NZ\MFLRZ\FKGRSXV]F]DOQ\REV]DUSUDF\SR]DNWyU\QLH

background image



SRZLQLHQ Z\FKRG]Lü FKZLORZ\ SXQNW SUDF\ Z\]QDF]RQ\ FKZLORZ\PL

ZDUWRFLDPLSUGXLQDSL FLD

-DN SRND]DQR QD U\VD REV]DU WHQ GOD WUDQ]\VWRUD ELSRODUQHJR

RJUDQLF]DMOLQLH

− 

PLQLPDOQHJR SUGX NROHNWRUD

I

C min

 SRQL*HM NWyUHJR WUDQ]\VWRU

ZFKRG]L Z VWDQ RGFL FLD  Z\VWSL ZWHG\ GX*H ]QLHNV]WDáFHQLD

QLHOLQLRZH 

− 

PDNV\PDOQHJRSUGXNROHNWRUD

I

C max

SRZ\*HMNWyUHJRSRMDZLDMVL

]QLHNV]WDáFHQLD]ZL]DQH]H]PQLHMV]DQLHPZ]PRFQLHQLDSUGRZHJR

β



SU]\GX*\FKSUGDFK

− 

PLQLPDOQHJR QDSL FLD

U

U

CE

CEsat

min

=

  ZFKRG]HQLH Z ]DNUHV

QDV\FHQLDZL*HVL ]GX*\PL]QLHNV]WDáFHQLDPLQLHOLQLRZ\PL 

− 

PDNV\PDOQHJRQDSL FLD

U

CE max

 RJUDQLF]HQLHZ\QLNDMFH]H]MDZLVND

SRZLHODQLDODZLQRZHJROXE]MDZLVND=HQHUD 

− 

PDNV\PDOQHM PRF\ VWUDW

P

C max

 Z\QLNDMFHM ] PR*OLZRFL

UR]SURV]HQLD UHGQLHM PRF\ Z\G]LHORQHM Z WUDQ]\VWRU]H

LPDNV\PDOQHMWHPSHUDWXU\VWUXNWXU\WUDQ]\VWRUD

3RGREQ\ REV]DU Z SROX FKDUDNWHU\VW\N Z\MFLRZ\FK WUDQ]\VWRUD

SRORZHJR

i

f u

D

DS

=

(

)

SU]HGVWDZLRQRQDU\VE

2JUDQLF]DMJROLQLH

− 

SDUDEROD

U

U

U

DS

GS

T

=

UR]JUDQLF]DMFD REV]DU OLQLRZ\  WULRGRZ\

RG REV]DUX QDV\FHQLD  W\ONR Z REV]DU]H QDV\FHQLD WUDQ]\VWRU

FKDUDNWHU\]XMHVL OLQLRZ\PLZáDFLZRFLDPLZ]PDFQLDMF\PL 

− 

PLQLPDOQHJRSUGXGUHQX

I

D min

SRQL*HMNWyUHJR WUDQ]\VWRU ZFKRG]L

Z VWDQ RGFL FLD  FR ZL*H VL  ] GX*\PL ]QLHNV]WDáFHQLDPL

QLHOLQLRZ\PL 

− 

PDNV\PDOQHJR SUGX GUHQX

I

D max

 SRZ\*HM NWyUHJR Z\VWSL

]QLHNV]WDáFHQLD QLHOLQLRZH VSRZRGRZDQH Uy*Q\P QDFK\OHQLHP

FKDUDNWHU\VW\N Z\MFLRZ\FK  Uy*Q NRQGXNWDQFM Z\MFLRZ

WUDQ]\VWRUD 

− 

PDNV\PDOQHJR QDSL FLD

U

DS max

  RJUDQLF]HQLH Z\QLNDMFH ]

SRZLHODQLD ODZLQRZHJR QRQLNyZ Z VáDER GRPLHV]NRZDQ\P

REV]DU]HSRGáR*D 

− 

PDNV\PDOQHM PRF\ VWUDW

P

D max

 Z\QLNDMFHM ] PR*OLZRFL

UR]SURV]HQLDUHGQLHMPRF\Z\G]LHORQHMZWUDQ]\VWRU]H

2GZ\EUDQHJRSXQNWXSUDF\WUDQ]\VWRUD]DOH*SUDZLHZV]\VWNLH

SDUDPHWU\WUDQ]\VWRUDSU]\F]\P]DOH*QRüWDMHVWQLHNLHG\EDUG]RVLOQD

1DMF] FLHM QLH MHVW PR*OLZH X]\VNDQLH GOD Z\EUDQHJR SXQNWX SUDF\

ZV]\VWNLFKSDUDPHWUyZ]PLHQQRSUGRZ\FKRRSW\PDOQ\FKZDUWRFLDFK

GOD ]DSHZQLHQLD VWDZLDQ\FK Z\PDJD SURMHNWRZ\FK WDNLFK MDN

background image



ZLHONRü Z]PRFQLHQLD LPSHGDQFMD ZHMFLRZD L Z\MFLRZD V]XP\

SDVPRSU]HQRV]HQLD]QLHNV]WDáFHQLDQLHOLQLRZHPRFZ\MFLRZDLWS1D

RJyá Z\EyU SXQNWX SUDF\ MHVW NRPSURPLVHP SRPL G]\ UR]ELH*Q\PL

Z\PDJDQLDPL NWyU\ QDMOHSLHM MHVW GRNRQDü LQG\ZLGXDOQLH GOD

SURMHNWRZDQHJRXNáDGX



67$7<&=1( , '<1$0,&=1( 35267( 52%2&=( 8.à$'Ï:

:=0$&1,$-&<&+

1D U\VD SU]HGVWDZLRQR VFKHPDW LGHRZ\ Z]PDFQLDF]D

ZNRQILJXUDFMLZVSyOQHJRHPLWHUDZNWyU\P]DVWRVRZDQRQDMSURVWV]\

]PR*OLZ\FK VSRVREyZ ]DVLODQLD WUDQ]\VWRUD SU]\ Z\NRU]\VWDQLX

MHGQHJR(UyGáD]DVLODMFHJRLUH]\VWRUyZ W]ZXNáDG]DVLODQLD]HVWDá\P

SUGHPED]\ 

a)

b)

X

&(

0

L

&

,

%

,

%4

8

&(4

8

&(4

, 5

&4 &

4

,

%

,

&4

8

&&

1

5

&

N a c h y l e n i e

8

5

&&

&

0

L

%

5

&

5

%

X

%(

c)

8

5

&&

%

8

&(

=



8

8

&(

&&

=

4

,

%4

, 5

%4 %

8

%(4

8

&&

L

%

L

&

5

%

5

&

L

J

+

8

&&

X

&(

L

E

L

F

5

%

5

&

L

J

X

FH

5\V 3URVW\ SU]\NáDG XNáDGX ]DVLODQLD WUDQ]\VWRUD ELSRODUQHJR D  VFKHPDW

LGHRZ\E VFKHPDW]PLHQQRSUGRZ\F JUDILF]QHZ\]QDF]HQLHSXQNWXSUDF\

'ODXNáDGX]U\VDSU]\RGáF]RQ\PRGZHMFLD]PLHQQRSUGRZ\P

(UyGOHi

g

PR*HP\]DSLVDüQDVW SXMFHUyZQDQLD.LUFKKRIID

U

i R

u

CC

C

C

CE

=

+

 

U

i R

u

CC

B

B

BE

=

+

 

SU]\ F]\P Z\VW SXMFH Z SRZ\*V]\FK UyZQDQLDFK ZDUWRFL FKZLORZH

SUGyZLQDSL üR]QDF]DMZDUWRFLVWDáRSUGRZHZSXQNFLHSUDF\

background image



8NáDGUyZQD  PR*HP\UR]ZL]DüJUDILF]QLHMDNWRSRND]DQR

QDU\VF

5yZQDQLH  MHVWUyZQDQLHPW]Z VWDW\F]QHMSURVWHMURERF]HMZSROX

FKDUDNWHU\VW\N  Z\MFLRZ\FK

i

f u

C

CE

=

(

)

 WUDQ]\VWRUD SU]HFKRG]FHM

SU]H] SXQNW SUDF\ I

CQ



8

&(4

 L SU]HFLQDMFHM R

i

C

 Z SXQNFLH

U

R

CC

C

RUD]R

u

CE

ZSXQNFLH

U

CC



:SXQNFLHSUDF\VSHáQLRQDMHVWUHODFMD

U

U

I

R

CC

CEQ

CQ

C

=

+

 

-H*HOL GR ZHMFLD XNáDGX ]RVWDQLH GRáF]RQH ]PLHQQRSUGRZH (UyGáR

SUGX i

g

 WR XNáDG UyZQD .LUFKKRIID    RERZL]XMH GOD

FKZLORZ\FKZDUWRFLQDSL üLSUGyZWUDQ]\VWRUD

U

i R

u

CC

C

C

CE

=

+

 

(

)

U

i

i R

u

CC

B

g

B

BE

=

+

 

SU]\ F]\P FKZLORZH ZDUWRFL QDSL ü L SUGyZ V Z\QLNLHP QDáR*HQLD

VNáDGRZ\FK ]PLHQQ\FK QDSL ü L SUGyZ QD VNáDGRZH VWDáH RNUHODMFH

SXQNWSUDF\WUDQ]\VWRUD

i

I

i

B

BQ

b

=

+

 

i

I

i

u

U

u

C

CQ

c

CE

CEQ

ce

=

+

=

+

 

1D U\VE SU]HGVWDZLRQR UyZQRZD*Q\ VFKHPDW ]PLHQQRSUGRZ\

UR]SDWU\ZDQHJR XNáDGX Z NWyU\P GOD VNáDGRZ\FK ]PLHQQ\FK

RERZL]XM]DOH*QRFL

u

i R

ce

c

C

= −

 

3RGVWDZLDMF]DOH*QRFL  GRUyZQDQLD  RWU]\PXMHP\



i

R

u

I

U

R

C

C

CE

CQ

CEQ

C

− −

+

+

1

 

5yZQDQLH    SU]HGVWDZLD W]Z G\QDPLF]Q SURVW URERF] Z SROX

FKDUDNWHU\VW\N Z\MFLRZ\FK WUDQ]\VWRUD NWyUD SU]HFKRG]L SU]H] SXQNW

SUDF\ D MHM QDFK\OHQLH

R

C

 RGSRZLDGD Z\SDGNRZHM UH]\VWDQFML Z

REZRG]LH Z\MFLRZ\P WUDQ]\VWRUD GOD VNáDGRZHM ]PLHQQHM

:UR]ZD*DQ\PSU]\SDGNXRELHSURVWHURERF]HVWDW\F]QDLG\QDPLF]QD

SRNU\ZDMVL 

background image



$E\ MHGQDN SRND]Dü Uy*QLF  SRPL G]\ VWDW\F]Q D G\QDPLF]Q SURVW

URERF] UR]ZD*P\ QLHFR LQQ\ XNáDG SU]HGVWDZLRQ\ QD U\VD

:XNáDG]LH W\P Z REZRG]LH HPLWHUD MHVW ZáF]RQD UH]\VWDQFMD

R

E

]ERF]QLNRZDQD SRMHPQRFL

C

E

 WDN GREUDQD *H GOD F] VWRWOLZRFL

V\JQDáyZ SU]HQRV]RQ\FK SU]H] Z]PDFQLDF] MHM UHDNWDQFMD MHVW

SRPLMDOQLHPDáD NRQGHQVDWRU

C

E

VWDQRZL]ZDUFLH 

a)

b)

X

&(

0

L

&

,

%1

,

%4

8

&(4

8

&(4

, 5

&4 &

4

,

%

,

&4

8

&&

1

5

&

Nachylenie

8

5

&&

&

, 5

&4 (

8

5

5

&&

&

(

+

(

)

+

1

5 5

&

(

Nachylenie

c)

L

%

L

&

5

%

5

&

L

J

+

8

&&

X

&(

5

(

&

(

L

E

L

F

5

%

5

&

L

J

X

FH

5\V8NáDG]DVLODQLDWUDQ]\VWRUDELSRODUQHJR]GZyMQLNLHP 5 &

(

(

__

ZREZRG]LH

HPLWHUDD VFKHPDWLGHRZ\E VFKHPDW]PLHQQRSUGRZ\F VWDW\F]QDLG\QDPLF]QD

SURVWDSUDF\ZSROXFKDUDNWHU\VW\NZ\MFLRZ\FK

: W\P SU]\SDGNX UyZQDQLH .LUFKKRIID GOD REZRGX NROHNWRUD SU]\

RGáF]RQ\P]PLHQQRSUGRZ\P(UyGOHi

g

RSLVXMH]DOH*QRü

(

)

U

i R

R

u

CC

C

C

E

CE

=

+

+

 

SU]\F]\P

i

C



u

CE

VZDUWRFLDPLVWDáRSUGRZ\PLRNUHODMF\PLSXQNW

SUDF\

5yZQDQLH    RSLVXMH VWDW\F]Q SURVW URERF] SU]HFKRG]F SU]H]

SXQNWSUDF\ I

CQ

 U

CEQ

LSU]HFLQDMFHMR

i

C

ZSXQNFLH

(

)

U

R

R

CC

C

E

+

RUD]R

u

CE

ZSXQNFLH

U

CC

 U\VF 

'OD VNáDGRZ\FK ]PLHQQ\FK UH]\VWDQFMD

R

E

 MHVW ]ZDUWD ]DWHP

]PLHQQRSUGRZ\ VFKHPDW XNáDGX  U\VE  MHVW LGHQW\F]Q\ MDN

ZSRSU]HGQLR UR]ZD*DQ\P SU]\NáDG]LH =DWHP G\QDPLF]Q SURVW

URERF]RSLVXMHZW\PSU]\SDGNXUyZQLH*UyZQDQLH  -DNSRND]DQR

QD U\VF RELH SURVWH URERF]H SU]HFKRG] SU]H] SXQNW SUDF\

background image



RZVSyáU] GQ\FK I

CQ

 L U

CEQ

 SU]\ F]\P LFK QDFK\OHQLD Z\QRV]

RGSRZLHGQLRVWDW\F]QHM

(

)

+

R

R

C

E

]DG\QDPLF]QHM

R

C



-DNRRVWDWQLSU]\NáDGUR]ZD*\P\XNáDGZ]PDFQLDMF\ZNWyU\P

REFL*HQLH GRáF]RQH MHVW GR REZRGX NROHNWRURZHJR WUDQ]\VWRUD ]D

SRUHGQLFWZHPWUDQVIRUPDWRUDVSU] JDMFHJR U\V 

a)

4

nachylenie

b)

8

8

&(4

&&

=

2

8

&&

X

&(

L

&

Prosta statyczna

nachylenie

Prosta dynamiczna

 5

/

,

&4

+

8

&&

X

L

5

5

/

5

S 5

/

/

=

2

S  1

X

/

5\V:]PDFQLDF]]HVSU] *HQLHPWUDQVIRUPDWRURZ\PD VFKHPDWLGHRZ\

E SURVWHURERF]HVWDW\F]QDLG\QDPLF]QDZXNáDG]LH

-H*HOLUH]\VWDQFMDX]ZRMHQLDSLHUZRWQHJRWUDQVIRUPDWRUDMHVWSRPLMDOQLH

PDáDWRVWDW\F]QDSURVWDURERF]DSU]HFKRG]LSLRQRZRSU]H]SXQNWSUDF\

Q

 SU]HFLQDMF R

u

CE

 Z SXQNFLH U

U

CEQ

CC

=

 '\QDPLF]QD SURVWD

URERF]D SU]HFKRG]L SU]H] SXQNW SUDF\  D MHM QDFK\OHQLH

R

L

'

RGSRZLDGDSU]HWUDQVIRUPRZDQHMUH]\VWDQFMLREFL*HQLD R

p R

L

L

'

=

2

SU]\

F]\P pMHVWSU]HNáDGQLWUDQVIRUPDWRUD

8VWDOHQLH Z\EUDQHJR SXQNWX SUDF\ L ]DSHZQLHQLH MHJR VWDáRFL

SU]\]PLDQDFKF]\QQLNyZ]HZQ WU]Q\FKWDNLFKMDN]PLDQ\WHPSHUDWXU\

QDSL ü]DVLODMF\FKF]\Z\PLDQLHHOHPHQWyZZ\PDJD]DSURMHNWRZDQLD

RGSRZLHGQLHJR XNáDGX ]DVLODQLD L VWDELOL]DFML SXQNWyZ SUDF\

WUDQ]\VWRUyZZSURMHNWRZDQ\PXNáDG]LH



=$6,/$1,(

,

67$%,/,=$&-$

381.7Ï:

35$&<

75$1=<6725Ï::8.à$'$&+'<6.5(71<&+

 8NáDG\]DVLODQLDWUDQ]\VWRUyZELSRODUQ\FK

'R DQDOL]\ VWDáRSUGRZ\FK ZDUXQNyZ SUDF\ Z REV]DU]H

DNW\ZQ\PZ\NRU]\VWDP\RPyZLRQ\ZUR]G]PRGHO(EHUVD0ROOD

U\V

background image



B

,

&

C

E

,

(

α

1 (

,

,

%

8

%(

B

,

&

C

E

,

(

α

1 (

,

,

%

8

%(

,

&0

B

,

&

C

E

,

(

β

1 %

,

,

%

8

%(

(

)

,

,

&(

1

&

0

0

1

=

+

β

5\V0RGHOVWDáRSUGRZ\WUDQ]\VWRUDELSRODUQHJR

=JRGQLH]UR]Sá\ZHPSUGyZZWUDQ]\VWRU]HRWU]\PXMHP\

I

I

I

E

N

E

C

=

+

α

0

 

I

I

I

E

N

B

CE

=

+

β

0

 

(

)

I

I

CE

N

C

0

0

1

=

+

β

 

I

0

SUG]HURZ\NROHNWRUDZNRQILJXUDFML2%

=DWHP R]QDF]DMF

β

β

N

=

0

SUGNROHNWRUD

I

C

Z\QRVL

(

)

I

I

I

C

B

C

=

+

+

β

β

0

0

0

1

 

7HUPLF]QD ]DOH*QRü NRQFHQWUDFML VDPRLVWQ\FK QRQLNyZ SUGX

UXFKOLZRFL QRQLNyZ SUGX ZVSyáF]\QQLND G\IX]ML F]DVX *\FLD

QRQLNyZRUD]SRWHQFMDáX)HUPLHJRSRZRGXM*HSDUDPHWU\WUDQ]\VWRUD

]DOH*RGWHPSHUDWXU\

0R*QDSU]\Mü*HWHUPLF]QH]PLDQ\SUGXNROHNWRUDZL*VL JáyZQLH

]H ]PLDQDPL WU]HFK ZLHONRFL

I

0



U

BE

 L

β

0

 NWyUH ]DOH* RG

WHPSHUDWXU\ L NWyUH Z VSRVyE MDZQ\ GHWHUPLQXM ZLHONRü SUGX

NROHNWRUDZXNáDG]LH]DVLODQLDWUDQ]\VWRUD

(

)

I

f U

I

C

BE

C

=

,

,

β

0

0



 

3UG

I

0

 WUDQ]\VWRUyZ NU]HPRZ\FK MHVW EDUG]R PDá\  Z WHPSHUDWXU]H



°

& U] GX Q$  L Z SU]\EOL*HQLX SRGZDMD VL  SU]\ Z]URFLH

WHPSHUDWXU\RND*GH

°

&ZRWRF]HQLXWHPSHUDWXU\

°

&

1DSL FLH

U

BE

 Z\QRVL RN 9 Z WHPSHUDWXU]H 

°

& L PDOHMH ]H

Z]URVWHPWHPSHUDWXU\RNP9

°

&

:VSyáF]\QQLN

β

0

 URQLH ]H Z]URVWHP WHPSHUDWXU\ L Z RSDUFLX

RHPSLU\F]QH ]DOH*QRFL PR*QD VWZLHUG]Lü OLQLRZ\ SU]\URVW

β

0

]V]\ENRFL

°

&

background image



7HUPLF]QH ]PLDQ\ Z\V]F]HJyOQLRQ\FK SDUDPHWUyZ WUDQ]\VWRUD

PRJE\üRSLVDQHSU]\EOL*RQ\PL]DOH*QRFLDPLDQDOLW\F]Q\PL

( )

( )

I

T

I

C

C

C

T

C

0

0

8

25

2

$

$

 

( )

( )

U

T

U

C

T

V

C

BE

BE

25

0 0022

$

$

,

 

( )

( )

β

β

0

0

25

1

80

T

C

T

C

⋅ +





$

$

 

=PLDQ\

β

0



U

BE



I

0

PRJZ\QLNDüQLHW\ONR]H]PLDQ\WHPSHUDWXU\

DOH UyZQLH* ] UR]U]XWX SURGXNF\MQHJR SDUDPHWUyZ 6]F]HJyOQLH GX *\

UR]U]XWSURGXNF\MQ\PR*HSRVLDGDüZVSyáF]\QQLN

β

0

1SZNDWDORJDFK

G\VNUHWQH WUDQ]\VWRU\ WHJR VDPHJR W\SX V QDMF] FLHM G]LHORQH QD

JUXS\]DOH*QLHRGZLHONRFLZ]PRFQLHQLDSUGRZHJR

β

0

]HZ]JO GX

QDEDUG]RGX*\UR]U]XWWHFKQRORJLF]Q\WHJRSDUDPHWUX]DZLHUDMF\VL

QDZHWZJUDQLFDFK

3U]\URVW SUGX NROHNWRUD Z\ZRáDQ\ SU]\URVWDPL SRV]F]HJyOQ\FK

ZLHONRFL

β

0



U

BE



I

0

 PR*HP\ Z\]QDF]\ü Z SRVWDFL Uy*QLF]NL

]XSHáQHMSUGX

I

C

RNUHORQHJRZ]RUHP 

dI

I

d

I

U

dU

I

I

dI

C

C

C

BE

BE

C

C

C

+

+

∂ β

β

0

0

0

0

 

3RFKRGQH F]VWNRZH Z UyZQDQLX    V IXQNFMDPL XNáDGRZ\PL

REZRGyZ ]DVLODQLD WUDQ]\VWRUyZ L RNUHOD VL  MH PLDQHP

ZVSyáF]\QQLNyZVWDELOL]DFMLSUGXNROHNWRUDZQDVW SXMF\VSRVyE

S

I

I

I

I

I

C

C

C

C

=

0

0



 

S

I

U

I

U

U

C

BE

C

BE

=

 

S

I

I

C

C

β

∂ β

=

0

0

∆β

 

=DWHPUyZQDQLH  PR*HP\]DSLVDüZSRVWDFL

∆β

I

S

I

S

U

S

C

I

C

U

BE

+

+

0

0

β

 

'OD WUDQ]\VWRUyZ NU]HPRZ\FK F] VWR SRPLMD VL  ZVSyáF]\QQLN

VWDELOL]DFML

S

I

]HZ]JO GXQDEDUG]RPDáZDUWRüSUGX]HURZHJR

I

0

WUDQ]\VWRUDLSRPLMDOQZDUWRüVNáDGQLND

6 ,

,

&





background image



8NáDG]DVLODQLDWUDQ]\VWRUDMHVWW\POHSV]\LPPQLHMV]H]DSHZQLD

ZVSyáF]\QQLNLVWDELOL]DFMLSUGXNROHNWRUDZWHG\ERZLHPQDZHWGX*H

]PLDQ\

I

0



U

BE



∆β

0

  RGSRZLDGDMFH GX*\P ]PLDQRP

WHPSHUDWXU\ Z\ZRáXMQLHZLHONLSU]\URVWSUGXNROHNWRUD

-HGQ\P ] QDMSURVWV]\FK XNáDGyZ ]DVLODQLD WUDQ]\VWRUD MHVW

UR]ZD*DQ\ ZF]HQLHM XNáDG ]DVLODQLD VWDá\P SUGHP ED]\ NWyUHJR

VFKHPDWLGHRZ\SRZWyU]RQRQDU\V

,

&

,

(

β

0

,

%

,

%

8

%(

,

&( 0

8

&&

5

&

5

%

8

&&

8

&(

5

&

5

%

,

%

,

&

8

&(

5\V8NáDG]DVLODQLDVWDá\PSUGHPED]\LMHJRPRGHOGODVNáDGRZHMVWDáHM

=HVFKHPDWXQDU\VRWU]\PXMHP\

,

8

8

5

8

5

FRQVW

8

8

%

&&

%(

%

&&

%

&&

%(

=

>>

GOD

 

=]DOH*QRFL  Z\QLNDQD]ZDXNáDGX

:\NRU]\VWXMF ]DOH*QRFL     RUD] UyZQDQLH .LUFKKRIID GOD

REZRGX NROHNWRURZHJR XNáDGX ] U\V RWU]\PXMHP\ ZVSyáU]  GQH

SXQNWXSUDF\WUDQ]\VWRUD

(

)

I

U

U

R

I

U

R

U

U

I R

C

CC

BE

B

C

CC

B

CE

CC

C

C

=

+

+

=

β

β

β

0

0

0

0

1

 

: XNáDG]LH W\P QLH PD *DGQ\FK PR*OLZRFL RSW\PDOL]DFML

ZDUWRFLHOHPHQWyZXNáDGXSRODU\]DFMLJG\*GOD]DGDQHJRSXQNWXSUDF\

I

C



U

CE

 L QDSL FLD ]DVLODQLD

U

CC

 Z\QLNDM MHGQR]QDF]QLH RNUHORQH

ZDUWRFL HOHPHQWyZ

R

B



R

C

 NWyUH V NRQVHNZHQFM UyZQD

RNUHODMF\FKSXQNWSUDF\

:DUWRFL ZVSyáF]\QQLNyZ VWDELOL]DFML Z W\P XNáDG]LH V GX*H ]DWHP

SXQNWSUDF\MHVWVLOQLHX]DOH*QLRQ\RGSDUDPHWUyZWUDQ]\VWRUD

/HSV]H ZáDVQRFL VWDELOL]DF\MQH SRVLDGD XNáDG ]DVLODQLD VWDá\P

SUGHPHPLWHUD U\V 

background image



,

&

,

(

α

0

,

(

,

%

8

%(

,

&0

8

&&

5

&

5

(

8

&&

8

&(

5

&

5

(

,

%

,

&

8

&(

,

(

8

((

C

E

B

8

((

5\V8NáDG]DVLODQLDVWDá\PSUGHPHPLWHUDLMHJRPRGHOGODVNáDGRZHMVWDáHM

=HVFKHPDWXSU]HGVWDZLRQHJRQDU\VRWU]\PXMHP\

I

U

U

R

U

R

const

U

U

E

EE

BE

E

EE

E

EE

BE

=

>>

(

)

GOD

 

=]DOH*QRFL  Z\QLNDQD]ZDXNáDGX

8Z]JO GQLDMF

I

I

I

C

E

C

=

+

+

β

β

0

0

0

1

 

]UyZQD  L  RWU]\PXMHP\

I

U

U

R

I

U

U

R

U

R

C

EE

BE

E

C

EE

BE

E

EE

E

=

+

+

β

β

0

0

0

1



 

:SRGREQ\VSRVyEPR*QDREOLF]\üQDSL FLH

U

CE

U

U

I R

U

I R

CC

EE

C

C

CE

E

E

+

=

+

+

 

=UyZQD    RWU]\PXMHP\

(

)

U

U

U

I

R

R

I R

U

U

I

R

R

CE

CC

EE

C

C

E

C

E

CC

EE

C

C

E

=

+

+

+



 +

+

+

+

β

β

β

β

0

0

0

0

0

1

1

 

-HVW WR UyZQDQLH VWDW\F]QHM SURVWHM SUDF\ Z SROX FKDUDNWHU\VW\N

Z\MFLRZ\FK WUDQ]\VWRUD 5yZQDQLD       RNUHODM

ZVSyáU] GQHSXQNWXSUDF\LPR*QD]QLFKMHGQR]QDF]QLHZ\]QDF]\ü

R

C

L

R

E

 SU]\ ]DGDQ\FK

U

CC



U

EE

 :V]\VWNLH ZVSyáF]\QQLNL VWDELOL]DFML

6 6 6

,

8





β

  NWyUH PR*QD Z\]QDF]\ü ] UyZQDQLD    REOLF]DMF

SRFKRGQHF]VWNRZHNROHMQRZ]JO GHP

I

0



U

BE

L

β

0

PDMPQLHMV]H

background image



ZDUWRFL QL* Z SU]\SDGNX XNáDGX ]D VWDá\P SUGHP ED]\ 6WDELOL]DFMD

SXQNWXSUDF\MHVWW\POHSV]DLP

5

(

MHVWZL NV]H

8NáDG ]DVLODQLD ]H VSU] *HQLHP NROHNWRURZ\P ]RVWDá

SU]HGVWDZLRQ\ QD U\V 6SU] *HQLH ]ZURWQH QDSL FLRZH UHDOL]RZDQH

SU]H]UH]\VWRU

R

F

VWDELOL]XMH]PLDQ\QDSL FLD

U

CE

-H*HOL]PDOHMHSUG

NROHNWRUD

I

C

 WR ]PDOHMH VSDGHN QDSL FLD QD UH]\VWRU]H

R

C

 UyZQ\

(

)

I

I

R

C

B

C

+

 Z]URQLH QDSL FLH

U

CE

 ]DWHP Z]URQLH QDSL FLH QD

UH]\VWRU]H

R

F

I R

U

U

B

F

CE

BE

=

 Z]URQLH SUG ED]\

I

B

 Z]URQLH

SUGNROHNWRUD

I

C

FR]ZURWQLHVSRZRGXMH]ZL NV]HQLHVSDGNXQDSL FLD

QD UH]\VWRU]H

R

C

 F]\OL ]PQLHMV]HQLH QDSL FLD

U

CE

 1D W\P SROHJD

VWDELOL]XMFD UROD VSU] *HQLD ]ZURWQHJR : UH]XOWDFLH

U

CE

 Z]URQLH

PQLHM QL* Z XNáDG]LH EH] VSU] *HQLD 6SU] *HQLH ]ZURWQH MHVW W\P

VLOQLHMV]H L VWDELOL]DFMD SXQNWX SUDF\ OHSV]D LP ZDUWR ü

R

F

 MHVW

PQLHMV]D

,

&

β

0

,

%

,

%

8

%(

,

&( 0

=

8

&&

5

&

5

)

8

&&

8

&(

5

&

5

)

,

%

,

&

8

&(

C

E

B

(

)

=

+

β

0

0

1

,

&

5\V8NáDG]HVSU] *HQLHPNROHNWRURZ\PLMHJRPRGHOGODVNáDGRZHMVWDáHM

'ODXNáDGX]U\VRWU]\PXMHP\

(

)

R

I

I

I

R I

U

U

C

B

B

CE

F

B

BE

CC

β

0

0

+

+

+

+

=

 

(

)

I

I

I

B

C

C

=

+

β

β

0

0

0

1

 

6WG

(

)

(

)(

)

(

)

I

U

U

I

R

R

R

R

C

CC

BE

C

C

F

F

C

=

+

+

+

+

+

β

β

β

0

0

0

0

1

1

 

(

)

U

I

I

R

U

CE

C

B

C

CC

+

+

=

 

.RU]\VWDMF ] ]DOH*QRFL    L    RWU]\PXMHP\ UyZQDQLH

VWDW\F]QHMSURVWHMREFL*HQLDZSROXFKDUDNWHU\VW\NZ\MFLRZ\FK

background image



(

)

U

I

I

R

U

CE

C

C

C

CC

+

+

+



=

β

β

0

0

0

1

 

=DOH*QRFL    L    RNUHODM ZVSyáU] GQH SXQNWX SUDF\

WUDQ]\VWRUD

,QQ\ VSRVyE Z\NRU]\VWDQLD XMHPQHJR VSU] *HQLD ]ZURWQHJR GR

VWDELOL]DFML SXQNWX SUDF\ SU]HGVWDZLRQR QD U\V Z XNáDG]LH

SRWHQFMRPHWU\F]Q\P ]H VSU] *HQLHP HPLWHURZ\P -HVW WR SRGVWDZRZ\

VSRVyE ]DVLODQLD WUDQ]\VWRUD Z XNáDGDFK G\VNUHWQ\FK ]DZLHUDM F\FK

MHGQR(UyGáRQDSL FLD]DVLODMFHJR

8

&&

5

&

5

(

,

%

,

&

8

&(

,

(

5



5



5

5 5

%

=





__

tw. Thevenina

8

8

5

5 5

8

5

5

%%

&&

&&

%

=

+

=









8

&&

5

&

5

(

,

%

,

&

8

&(

,

(

5

%

8

%(

8

%%

a)

b)

5\V 3RWHQFMRPHWU\F]Q\ XNáDG ]D VSU] *HQLHP HPLWHURZ\P  D  L MHJR

UyZQRZD*Q\XNáDG]]DVW SF]\P(UyGáHP7KHYHQLQD E

.RU]\VWDMF ] ]DVDG\ 7KHYHQLQD XNáDG WHQ PR*HP\ SU]HNV]WDáFLü Z

UyZQRZD*Q\ XNáDG ]H VSU] *HQLHP HPLWHURZ\P L ] GZRPD (UyGáDPL

]DVLODQLD U\VE 

6SU] *HQLH ]ZURWQH SUGRZH UHDOL]RZDQH SU]H]

R

E

 VWDELOL]XMH

]PLDQ\ SUGX

I

E

 -H*HOL ]PDOHMH SUG HPLWHUD

I

E

 WR ]PDOHMH VSDGHN

QDSL FLDQDUH]\VWRU]H

R

E

]DWHPZ]URQLHQDSL FLH

U

BE

Z]URQLHSUG

ED]\

I

B

FR]ZURWQLHVSRZRGXMHZ]URVWSUGXHPLWHUD

I

E

:UH]XOWDFLH

SUGHPLWHUD

I

E

]PDOHMHPQLHMQL*ZXNáDG]LHEH]VSU] *HQLD]ZURWQHJR

'ODXNáDGX]U\VEPR*HP\]DSLVDüUyZQDQLD

(

)

U

I R

U

I R

I

I

I

I

I

I

BB

B

B

BE

E

E

C

B

C

E

B

C

=

+

+

=

+

+

=

+




β

β

0

0

0

1

 

]NWyU\FKPR*HP\Z\]QDF]\üSUGNROHNWRUD

(

)

(

)(

)

(

)

I

U

U

I

R

R

R

R

C

BB

BE

C

B

E

B

E

=

+

+

+

+

+

β

β

β

0

0

0

0

1

1



 

background image



:\NRU]\VWXMF UyZQDQLD    RUD] UyZQDQLH .LUFKKRIID GOD REZRGX

NROHNWRURZHJR

U

I R

U

I R

CC

C

C

CE

E

E

=

+

+

 

RWU]\PXMHP\

U

U

I R

I

R

R

CE

CC

C

E

C

C

E

=

+

+



 −

+

+



0

0

0

0

0

1

1

β

β

β

β

 

-HVW WR UyZQDQLH VWDW\F]QHM SURVWHM REFL*HQLD Z SROX Z\MFLRZ\FK

FKDUDNWHU\VW\N

( )

I U

C

CE



.RU]\VWDMF]]DOH*QRFL  L  áDWZRPR*QDZ\ND]Dü *H

VWDELOL]DFMDSRSUDZLDVL JG\VWRVXQHN

R

R

B

E

0

JG\VWDELOL]RZDQ\

MHVW SUG HPLWHUD -HGQDN JG\ ZDUWRü

R

E

 MHVW ]E\W GX*D WR QDSL FLH

]DVLODQLD PXVL E\ü GX*H RUD] SRJDUV]D VL  VWDELOL]DFMD QDSL FLD

U

CE

DOERSU]\W\PVDP\PVWRSQLXVWDELOL]DFMLQDSL FLD

U

CE

UH]\VWDQFMD

R

C

PXVLE\üPDáD VWUDW\Z]PRFQLHQLD 

3U]\MPXMF

I

0

0

=



β

β

0

0

1

+ ≈

L

U

const

CC

=

PR*HP\QDSLVDü

(

)

U

U

I

R

R

CE

CC

C

C

E

=

+

 

(

)

=

+

U

R

R

I

CE

C

E

C

 

%H]SLHF]QLHMMHVW]DPLHQLüUyZQDQLH  QDQLHUyZQR ü

(

)

+

U

R

R

I

CE

C

E

C

 

R

R

U

I

C

E

CE

C

+

≤ ∆

 

=E\W PDáD ZDUWRü UH]\VWDQFML

R

B

 RJUDQLF]D Z]PRFQLHQLH GOD

VNáDGRZHM]PLHQQHM]HZ]JO GXQDVLOQHWáXPLHQLHZHMFLDWUDQ]\VWRUD

:Sá\Z UH]\VWDQFML

R

E

 QD SDUDPHWU\ URERF]H Z]PDFQLDF]D

Z]PRFQLHQLH QDSL FLRZH L LPSHGDQFM  ZHMFLRZ  GOD VNáDGRZHM

]PLHQQHM PR*QD ]QDF]QLH ]PQLHMV]\ü SRSU]H] ]DVWRVRZDQLH

NRQGHQVDWRUD EORNXMFHJR 7DN ZL F SU]\ Z\ERU]H ZDUWRFL

R

E



R

B

QDOH*\ VL  NLHURZDü NRPSURPLVHP SRPL G]\ ZDUXQNDPL VWDELOL]DFML

SUGX

I

C

 QDSL FLD

U

CE

 ZLHONRFL QDSL FLD ]DVLODMFHJR

U

CC

LZ]PRFQLHQLHPXNáDGX

1DMOHSV]H ZáDVQRFL VWDELOL]DF\MQH PD XNáDG ] GZRPD (UyGáDPL

]DVLODQLD  Z W\P XNáDG ]H VWDá\P SUGHP HPLWHUD  0RF SRELHUDQD ]H

(UyGHá ]DVLODQLD Z W\P SU]\SDGNX MHVW ] UHJXá\ PQLHMV]D QL *

background image



ZSU]\SDGNX XNáDGX ] MHGQ\P (UyGáHP 1DWRPLDVW ZDG MHVW

NRQLHF]QRüVWRVRZDQLDGZyFK(UyGHá]DVLODQLD

=DGDZDODMFH HIHNW\ GDMH ]DVWRVRZDQLH XNáDGX ]H VSU] *HQLHP

HPLWHURZ\PNROHNWRURZ\PL]RE\GZRPDQDUD]-HGQDN *HZXNáDG]LH

]H VSU] *HQLHP NROHNWRURZ\P VWDELOL]DFMD ]DOH*\ RG UH]\VWDQFML

R

C



]DWHP XNáDG WHQ MHVW WUXGQLHMV]\ GR UHDOL]DFML =H Z]JO  GyZ

VWDELOL]DF\MQ\FKQDMJRUV]HZáDVQRFLPDXNáDG]HVWDá\PSUGHPED]\

8NáDG ]DVLODQLD VWDá\P SUGHP HPLWHUD FKDUDNWHU\]XMF\ VL

QDMNRU]\VWQLHMV]\PL ZáDFLZRFLDPL VWDELOL]DF\MQ\PL QDMáDWZLHM MHVW

]UHDOL]RZDüZSRVWDFL(UyGáDSUGXVWDáHJRZREZRG]LHHPLWHUD

3U]\NáDG UHDOL]DFML SURVWHJR (UyGáD VWDáRSUGRZHJR Z WHFKQLFH

HOHPHQWyZ G\VNUHWQ\FK L MHJR VFKHPDW ]DVW SF]\ SU]HGVWDZLRQR QD

U\V

5

(

,

,

2

&

=

,

(

8

((

C

8

'

8

=

8

%(

5



5

(

,

,

2

&

=

,

(

8

((

J

HF

J

HE

5

(

,

H

E

α



,

H

J

FE

B'

,

F

8

FE

U

EE



U

R

b)

c)

a)

5\V'UyGáRSUGXVWDáHJRD ]GLRG=HQHUDE ]X]LHPLRQED]

F ]PLHQQRSUGRZ\VFKHPDW]DVW SF]\(UyGáD

:\NRU]\VWXMF SUDZR .LUFKKRIID Z XNáDG]LH QD U\VD PR *HP\

Z\]QDF]\üSUGZ\MFLRZ\(UyGáD

I

I

I

U

U

U

R

U

R

O

C

E

Z

D

BE

E

Z

E

=

=

+

α

0

 

: XNáDG]LH Z\VW SXMH Z]DMHPQD NRPSHQVDFMD QDSL FLD

U

BE

 ]

QDSL FLHP

U

D

 GLRG\ ' ZáF]RQHM V]HUHJRZR ] GLRG =HQHUD Z W\P

UyZQLH*WHPSHUDWXURZ\FK]PLDQW\FKQDSL ü

: XNáDG]LH QD U\VE ] X]LHPLRQ ED] GOD SUGX VWDáHJR SUG

(UyGáDZ\QRVL

I

I

I

U

U

R

U

U

R

O

C

E

EE

BE

E

EE

BE

E

=

=

=

+

α

β

β

0

0

0

1

 

5y*QLF]NRZD UH]\VWDQFMD Z\MFLRZD (UyGáD Z\]QDF]RQD Z RSDUFLX R

PDáRV\JQDáRZ\VFKHPDW]DVW SF]\QDU\VFZ\QRVL

r

U

I

g

g

g

o

cb

c

cb

ec

ec

+

'

'

1

1

 

background image



3U]HGVWDZLRQH (UyGáR SUGRZH SRVLDGD GX* UH]\VWDQFM  Z\MFLRZ

NWyUHM SU]\EOL*RQD ZDUWRü MHVW WDND MDN WUDQ]\VWRUD Z NRQILJXUDFML

]X]LHPLRQED]

3U]HGVWDZLRQ\ XNáDG (UyGáD SUGRZHJR MHVW GREU\P SU]\NáDGHP

ZVND]XMF\PQDPR*OLZRüZ\NRU]\VWDQLDHOHPHQWyZQLHOLQLRZ\FKGR

NRPSHQVDFML ZSá\ZX WHPSHUDWXURZ\FK ]PLDQ Z\EUDQ\FK SDUDPHWUyZ

WUDQ]\VWRUD

/LQLRZH REZRG\ ]DVLODQLD WM REZRG\ ]DZLHUDM FH Z\áF]QLH OLQLRZH

UH]\VWRU\]DSHZQLDMVWDáRüSXQNWXSUDF\U] GXNLONXNLONXQDVWX

SU]\]PLDQDFKWHPSHUDWXU\ZSU]HG]LDOH

°

&

: XNáDGDFK Z\PDJDMF\FK ]QDF]QLH ZL NV]HM VWDáRFL SUGX  U] GX

 VWRVXMH VL  REZRG\ ]DVLODQLD ] HOHPHQWDPL QLHOLQLRZ\PL

3U]\NáDGHP XNáDGyZ R WDN GX*\FK Z\PDJDQLDFK VWDáRFL SUGX Z

VSRF]\QNRZ\P SXQNFLH SUDF\ PRJ E\ü (UyGáD SUGRZH ]DVLODMFH

VWRSQLH Z]PDFQLDF]D R VSU] *HQLDFK JDOZDQLF]Q\FK  QS ZH

Z]PDFQLDF]X RSHUDF\MQ\P  SUGRZH (UyGáD UHIHUHQF\MQH LWS

:QLHOLQLRZ\FK REZRGDFK ]DVLODQLD Z\NRU]\VWXMH VL   RJyOQ ]DVDG

NRPSHQVDFML ]PLDQ SDUDPHWUyZ VWDELOL]RZDQHJR HOHPHQWX ]PLDQDPL

SDUDPHWUyZLQQHJRHOHPHQWXREDUG]RSRGREQ\FKZáD FLZRFLDFK

1D U\V SU]HGVWDZLRQR XNáDG ] SRWHQFMRPHWU\F]Q\P

]DVLODQLHPED]\LVSU] *HQLHPHPLWHURZ\PRUD]]NRPSHQVDFM]PLDQ

QDSL FLD

U

BE



5

(

,

&

,

,

,

(

&

&

=

+

β

β







8

((

8

'

8

%(

5



8

'

5



5

&

,



,



1

n

Q8

'

+

8

&&

,

%

5\V 8NáDG ]DVLODQLD ] GLRGRZ

NRPSHQVDFM]PLDQQDSL FLD8

%(

=DNáDGDMF*HSUGED]\MHVWSRPLMDOQLHPDá\ZSRUyZQDQLXGRSU GX

G]LHOQLND

I

I

1

2

 RUD] SU]\MPXMF

I

I

E

C

 ]H VFKHPDWX QD U\V

RWU]\PXMHP\

nU

I R

U

I R

U

I R

I

U

nU

R

R

D

BE

E

E

BE

C

E

CC

D

+

=

+

+

=

+




2

2

2

1

2

 

=XNáDGXUyZQD  PR*HP\Z\]QDF]\ü

I

C

background image



(

)

(

)

I

R U

nU R

R

R U

R R

R

C

CC

D

BE

E

=

+

+

+

2

1

1

2

1

2

 

:DUXQHNSHáQHMNRPSHQVDFML]PLDQQDSL FLD

U

BE

PR*HP\Z\]QDF]\ü]

SU]\UyZQDQLDGR]HUDSRFKRGQHM

dI

dT

C

=

0

F]\OL

(

)

nR

dU

dT

R

R

dU

dT

D

BE

1

1

2

0

+

=

 

-H*HOL GLRGD L WUDQ]\VWRU V Z\NRQDQH Z SRGREQ\P SURFHVLH

WHFKQRORJLF]Q\P  GLRGD ]UHDOL]RZDQD MDNR WUDQ]\VWRU Z SRá F]HQLX

GLRGRZ\P LSUDFXMZWHMVDPHMWHPSHUDWXU]HWR

dU

dT

dU

dT

D

BE

 

LZDUXQHNSHáQHMNRPSHQVDFMLPDSRVWDü

(

)

nR

R

R

1

1

2

0

+

=

F]\OL

R

R

n

2

1

1

= −

 

1DMF] FLHMVWRVXMHVL GZLHGLRG\

n

=

2

LZyZF]DV

R

R

1

2

=



5R]ZD*DQ\ ZF]HQLHM XNáDG (UyGáD SUGX VWDáHJR QD U\VD MHVW

XNáDGHPVWDELOL]DFML]MHGQGLRG

n

=

1

L

R

2

0

=



 8NáDG\]DVLODQLDWUDQ]\VWRUyZXQLSRODUQ\FK

7UDQ]\VWRU 026)(7 ] NDQDáHP ]XER*DQ\P PR*H SUDFRZDü

]DUyZQR ]H Z]ERJDFDQLHP MDN L ]H ]XER*DQLHP -HGQDN*H SUDFD ]H

Z]ERJDFDQLHP RGE\ZD VL  GOD PDáHJR SU]HG]LDáX ZDUWRFL QDSL FLD

EUDPND  (UyGáR

U

GS

 'ODWHJR SRGVWDZRZ\P ]DNUHVHP SUDF\ W\FK

WUDQ]\VWRUyZ MHVW SUDFD ]H ]XER*DQLHP 7UDQ]\VWRU\ WH ] NDQDáHP Q

SUDFXMZREV]DU]HQDV\FHQLDSU]\XMHPQ\FKZDUWRFLDFKQDSL FLD

U

GS

L

GRGDWQLFK ZDUWRFLDFK

U

DS

 QDWRPLDVW ] NDQDáHP S JG\ SRODUQRü

ZVSRPQLDQ\FKQDSL üMHVW]PLHQLRQDWMJG\QDSL FLH

U

GS

MHVWGRGDWQLH

D

U

DS

MHVWXMHPQH2WU]\PDQLHQDSL üRSRGDQHMSRODUQRFLXPR*OLZLD

XNáDG]GZRPD(UyGáDPL]DVLODQLD U\V 

3UGEUDPNL

I

G

WUDQ]\VWRUyZ026)(7MHVWU] GXSLNRDPSHUyZLMHJR

ZSá\Z Z REZRG]LH SRODU\]DFML PR*QD SRPLQü 3U]\ WDNLP ]DáR*HQLX

XNáDG]U\VDRSLVXM]DOH*QRFL

(

)

U

U

I R

U

U

I

R

R

GS

GG

D

S

DD

DS

D

D

S

= −

=

+

+

 

background image



+

8

''

5

'

5

6

,

'

8

'6

>



,

,

6

'

=

8

**

,

*

=



5

*

8

*6

<



8

*6

8

''

5

'

5

6

,

'

8

'6

<



,

,

6

'

=

+

8

**

,

*

=



5

*

8

*6

>



8

*6

b)

a)

5\V 8NáDG ] GZRPD (UyGáDPL ]DVLODQLD WUDQ]\VWRUD 026 ] NDQDáHP

]XER*DQ\PD W\SXQE W\SXS

1DWRPLDVW XNáDG ] U\VE ]JRGQLH ] ]DVWU]DáNRZDQ\PL NLHUXQNDPL

SUGyZLQDSL üRSLVXMDUyZQDQLD

(

)

U

U

I R

U

U

I

R

R

GS

GG

D

S

DD

DS

D

D

S

=

+

= −

+

+

 

1DOH*\]D]QDF]\ü*HZREXXNáDGDFKQDU\V]D]QDF]RQRIL]\F]QH

NLHUXQNLSU]HSá\ZXSUGyZGUHQX

I

D



: REX XNáDGDFK ]DVWRVRZDQR Z REZRG]LH (UyGáD UH]\VWRU

R

S

VWDELOL]XMF\  SRGREQLH MDN UH]\VWRU

R

E

 Z REZRG]LH HPLWHUD  SXQNW

SUDF\WUDQ]\VWRUDRZVSyáU] GQ\FK I

DQ

U

DSQ

3UREOHPVWDáRFLSXQNWX

SUDF\ZL*HVL ]UR]U]XWHPWHFKQRORJLF]Q\PZDUWRFLQDSL FLDRGFL FLD

U

P

 L SUGX QDV\FHQLD

I

DSS

  GOD WUDQ]\VWRUyZ ] NDQDáHP ]XER*DQ\P

QDSL FLD SURJRZHJR

U

T

 L ZVSyáF]\QQLND

K W L

'

  GOD WUDQ]\VWRUyZ

]NDQDáHPZ]ERJDFDQ\P  RUD] ZSá\ZHP WHPSHUDWXU\ QD WH SDUDPHWU\

7HUPLF]QD]DOH*QRüUXFKOLZRFLQRQLNyZSUGXZNDQDOHRUD]QDSL ü

U

P

L

U

T

VJáyZQ\PF]\QQLNLHPWHPSHUDWXURZ\FK]PLDQSUGXGUHQX

,VWQLHMH MHGQDN WDND ZDUWRü SUGX GUHQX SU]\ NWyUHM ZSá\Z\ WH

NRPSHQVXM VL  3UG WHQ QRVL QD]Z  SUGX DXWRNRPSHQVDFML :DG

SU]HGVWDZLRQ\FK QD U\V XNáDGyZ SRODU\]DFML WUDQ]\VWRUD MHVW

NRQLHF]QRü ]DVWRVRZDQLD GZyFK (UyGHá ]DVLODQLD L WR RGPLHQQHM

SRODUQRFL

:DG\ WHM SR]EDZLRQ\ MHVW XNáDG ]DVLODQLD ] DXWRPDW\F]Q SRODU\]DFM

EUDPNL]UHDOL]RZDQ\ZRSDUFLXRXNáDG]U\VZNWyU\P

U

GG

=

0



%UDPND MHVW QDGDO SRODU\]RZDQD VSDGNLHP QDSL FLD QD UH]\VWRU]H

R

S



:WHG\XNáDG]U\VDQD]\ZDP\XNáDGHP]DVLODQLD]DXWRPDW\F]Q\P

PLQXVHP

U

I R

GS

D

S

= −

 

background image



D]U\VEXNáDGHP]DVLODQLD]DXWRPDW\F]Q\PSOXVHP

U

I R

GS

D

S

=

 

-HGQR (UyGáR ]DVLODQLD MHVW WDN*H Z\NRU]\VW\ZDQH Z XNáDG]LH

SRWHQFMRPHWU\F]Q\PSU]HGVWDZLRQ\PQDU\V

+

8

''

5

'

5

6

,

'

8

'6

>



,

,

6

'

=

5



8

*6

8

''

5

'

5

6

,

'

8

'6

<



,

,

6

'

=

5

*

8

*6

b)

a)

5



5\V 3RWHQFMRPHWU\F]Q\ XNáDG ]DVLODQLD WUDQ]\VWRUD 026)(7 ] NDQDáHP

]XER*DQ\PD W\SXQE W\SXS

8NáDG]U\VDRSLVXMUyZQDQLD

(

)

U

R

R

R

U

I R

U

U

I

R

R

GS

DD

D

S

DD

DS

D

D

S

=

+

=

+

+




2

1

2

 

QDWRPLDVWXNáDG]U\VE

(

)

U

R

R

R

U

I R

U

U

I

R

R

GS

DD

D

S

DD

DS

D

D

S

= −

+

+

= −

+

+




2

1

2

 

8NáDG\WHGDMZL NV]VZRERG GRERUXSXQNWXSUDF\

7UDQ]\VWRU\]áF]RZH-)(7 NWyUHSUDFXM]D]XER*DQLHP PRJ

E\ü]DVLODQHSU]H]RPyZLRQHXNáDG\WUDQ]\VWRU-)(7]NDQDáHPW\SXQ

SU]H] XNáDG\ ] U\VD D D WUDQ]\VWRU ] NDQDáHP W\SX S SU]H]

XNáDG\]U\VEE

7UDQ]\VWRU\026]NDQDáHPZ]ERJDFDQ\PZREV]DU]HQDV\FHQLD

Z\PDJDMQDSL ü

U

GS

L

U

DS

RMHGQDNRZ\FK]QDNDFK]NDQDáHPW\SXQ

GRGDWQLFK]NDQDáHPSXMHPQ\FK3RGW\PZ]JO GHPVRQHSRGREQH

GRWUDQ]\VWRUyZELSRODUQ\FK7UDQ]\VWRU]NDQDáHPZ]ERJDFDQ\PW\SX

QPR*HE\ü]DVLODQ\SU]H]XNáDG]U\VDZNWyU\PZPLHMVFH(UyGáD

]DVLODQLD 

U

GG

 ]DVWRVXMHP\ (UyGáR 

+

U

GG

 RUD] SU]H] XNáDG

]U\VD 5H]\VWDQFMH Z REX XNáDGDFK PXV] E\ü WDN GREUDQH DE\

QDSL FLH EUDPND  (UyGáR E\áR GRGDWQLH $QDORJLF]QLH WUDQ]\VWRU

]NDQDáHP Z]ERJDFDQ\P W\SX S PR*H E\ü ]DVLODQ\ SU]H] XNáDG ]

background image



U\VE Z NWyU\P Z PLHMVFH (UyGáD ]DVLODQLD 

+

U

GG

 ]DVWRVXMHP\

(UyGáR 

U

GG

 RUD] SU]H] XNáDG ] U\VE 5H]\VWDQFMH Z REX

XNáDGDFK PXV] E\ü WDN GREUDQH DE\ QDSL FLH EUDPND  (UyGáR E\áR

XMHPQH



=$6,/$1,(

,

67$%,/,=$&-$

381.7Ï:

35$&<

75$1=<6725Ï::8.à$'$&+6&$/21<&+

 2JyOQDFKDUDNWHU\VW\NDREZRGyZ]DVLODQLDZXNáDGDFK

VFDORQ\FK

7HFKQRORJLD PRQROLW\F]QD VWZDU]D LGHDOQH ZDUXQNL GOD

Z\HNVSRQRZDQLD Z XNáDG]LH NRU]\VWQ\FK ZáDFLZRFL HOHPHQWyZ

Z\WZDU]DQ\FK QD Sá\WFH SyáSU]HZRGQLND Z W\P VDP\P SURFHVLH

WHFKQRORJLF]Q\P 1DOH*\ WX SU]HGH ZV]\VWNLP Z\PLHQLü GX*H

SRGRELHVWZR WUDQ]\VWRUyZ ]EOL*RQ WHPSHUDWXU  ]áF] ZVSyáELH*QH

]PLDQ\ SDUDPHWUyZ WUDQ]\VWRUyZ RUD] UH]\VWDQFML SU]\ ]PLDQDFK

WHPSHUDWXU\RWRF]HQLD

:XNáDGDFKPRQROLW\F]Q\FKZ\VW SXMWH*LQQHRJUDQLF]HQLDQL*

Z XNáDGDFK G\VNUHWQ\FK : WHFKQRORJLL NáDGyZ ELSRODUQ\FK ]DNUHV

ZDUWRFL UH]\VWDQFML MHVW RJUDQLF]RQ\ GR NLONXG]LHVL FLX N

  N

 

UH]\VWRU\ ED]RZH  D SRQDGWR UR]U]XW\ ZDUWRFL UH]\VWDQFML V GX*H

± :WHFKQRORJLLXQLSRODUQHMSUDZLHZRJyOHQLHVWRVXMHVL

UH]\VWRUyZ SU]\ F]\P V RQH ]DVW SRZDQH (UyGáDPL SUGRZ\PL OXE

XNáDGDPL ÄOXVWHU SUGRZ\FK´ Z REZRGDFK SRODU\]DFML SUGHP VWDá\P

RUD] V VWRVRZDQH MDNR REFL*HQLD G\QDPLF]QH GOD VNáDGRZ\FK

]PLHQQ\FK

1LH PD PR*OLZRFL UHDOL]DFML NRQGHQVDWRUyZ R SRMHPQRFL

SU]HNUDF]DMFHM NLONDG]LHVLW S) GODWHJR XNáDG\ ZLHORVWRSQLRZH V

]UHJXá\ XNáDGDPL R VSU] *HQLDFK JDOZDQLF]Q\FK EH] NRQGHQVDWRUyZ

VHSDUXMF\FK L RGVSU] JDMF\FK : XNáDGDFK W\FK V]F]HJyOQHJR

]QDF]HQLDQDELHUDVWDáRüSXQNWyZSUDF\WUDQ]\VWRUyZJG\*LFK]PLDQ\

V Z]PDFQLDQH Z NROHMQ\FK VWRSQLDFK =H Z]JO GX QD EH]SRUHGQLH

VSU] *HQLDF] VWR]DFKRG]L SRWU]HED VWRVRZDQLD XNáDGyZ SU]HVXZDQLD

SR]LRPX QDSL FLD 6WDELOL]DFM  SXQNWyZ SUDF\ ]DSHZQLD VL  SU]H]

SRZV]HFKQH VWRVRZDQLH NRPSHQVDFML QLHOLQLRZHM NWyUD MHVW ]QDF]QLH

XáDWZLRQD G]L NL ]EOL*RQHM WHPSHUDWXU]H WUDQ]\VWRUyZ L GX*HPX

SRGRELHVWZXLFKFKDUDNWHU\VW\N

: PRQROLW\F]QHM WHFKQRORJLL ELSRODUQHM  ] Z\MWNLHP W]Z

NRPSOHPHQWDUQHM WHFKQRORJLL ELSRODUQHM ] L]RODFM WOHQNRZ

FKDUDNWHU\VW\NLLSDUDPHWU\WUDQ]\VWRUyZSQSVJRUV]H QS

β

0

10

=

background image



QL* WUDQ]\VWRUyZ QSQ  QS

β

0

40

200

=

 GODWHJR RJUDQLF]D VL  LFK

VWRVRZDQLH

:XNáDGDFKPRQROLW\F]Q\FKSUDNW\F]QLHQLHPDPR*OLZRFLZ\NRQDQLD

HOHPHQWyZLQGXNF\MQ\FK

=H ZV]\VWNLPL HOHPHQWDPL XNáDGX VFDORQHJR ]ZL]DQH V ELHUQH

LF]\QQH HOHPHQW\ SDVR*\WQLF]H VNG NRQLHF]QRü VWRVRZDQLD

HOHPHQWyZ R ZDUWRFLDFK W\SRZ\FK D QLH PLQLPDOQ\FK

LPDNV\PDOQ\FK

 3RGVWDZRZHEORNLZXNáDGDFK]DVLODQLDLVWDELOL]DFMLSXQNWyZ

SUDF\WUDQ]\VWRUyZELSRODUQ\FK

 'UyGáDVWDáRSUGRZHOXVWUDSUGRZH

1D U\V SU]HGVWDZLRQR W\SRZ\ VSRVyE ]DVLODQLD WUDQ]\VWRUD

7



VWRVRZDQ\ZELSRODUQ\FKXNáDGDFKVFDORQ\FK

,

&

5

5

&

,

&

+

8

&&

,

%

,

%

,

5

8

%(

2

T

1

T

5\V 3U]\NáDG ]DVLODQLD WUDQ]\VWRUD

ZELSRODUQ\FKXNáDGDFKVFDORQ\FK

7UDQ]\VWRU 7



 FKRFLD* SUDFXMH Z SRáF]HQLX GLRGRZ\P WR MHVW QDGDO

HOHPHQWHP DNW\ZQ\P SRQLHZD* ]QDMGXMH VL  QD JUDQLF\ REV]DUX

DNW\ZQHJR

U

CB

=

0



7UDQ]\VWRU\7



L7



SUDFXMSU]\W\PVDP\PQDSL FLX

U

BE

PDMWDNLH

VDPHSUG\ED]

I

I

I

B

B

B

1

2

=

=

DW\PVDP\PUyZQLH*WDNLHVDPHSUG\

NROHNWRUyZ

I

I

I

C

C

C

1

2

=

=



'ODXNáDGX]U\VPR*QD]DSLVDü]DOH*QRFL

U

I R

U

I

I

I

I

I

CC

R

BE

R

C

B

C

B

=

+

=

+

=

+

1

2

2

 

5R]ZL]XMFXNáDGUyZQD  ]HZ]JO GXQD

,

&

RWU]\PXMHP\

I

U

U

R

I

U

U

R

I

C

CC

BE

B

CC

BE

C

=

=

2

2

0

β

 

-H*HOL

U

U

CC

BE

>>



β

0

2

>>

WRZ]yU  XSUDV]F]DVL GRSRVWDFL

background image



I

U

R

C

CC

 

=DWHPZVSyáU] GQHSXQNWXSUDF\WUDQ]\VWRUD7



RNUHODM]DOH*QRFL

I

I

U

R

U

U

I R

U

R

R

C

C

CC

CE

CC

C

C

CC

C

2

2

2

1

=

=






 

3RQLHZD* WHPSHUDWXURZH ]PLDQ\ UH]\VWDQFML

R

C

 L

R

 Z XNáDG]LH

VFDORQ\P PRJ E\ü ZVSyáELH*QH  WHPSHUDWXURZ\ ZVSyáF]\QQLN

VWRVXQNX

R

R

C

MHVWEDUG]RPDá\ ]DWHPSXQNWSUDF\WUDQ]\VWRUD7



QLH

]DOH*\ RG ]PLDQ WHPSHUDWXU\ D MHG\QLH RG Uy*QLF\ SDUDPHWUyZ

WUDQ]\VWRUyZ7



L7





7HQ SURVW\ VSRVyE Z\PXV]DQLD SUGX MHGQHJR WUDQ]\VWRUD SU]H]

GUXJL VWDQRZL SRGVWDZ  UHDOL]DFML (UyGHá VWDáRSUGRZ\FK Z XNáDGDFK

VFDORQ\FK

6FKHPDW LGHRZ\ QDMSURVWV]HJR D SU]\ W\P SRGVWDZRZHJR (UyGáD

VWDáRSUGRZHJR]WUDQ]\VWRUDPLELSRODUQ\PLSU]HGVWDZLRQRQDU\V

,

,

2

&

=



,

&

,

%

,

%

,

5()

8

%(

2

T

1

T

8

&( 

5\V 3RGVWDZRZH (UyGáR

VWDáRSUGRZHOXVWURSUGRZH

=DNáDGDMF MDN SRSU]HGQLR LGHQW\F]QRü WUDQ]\VWRUyZ RUD] SRPLMDMF

ZSá\ZQDSL FLD

U

CE 2

WUDQ]\VWRUD7



QDMHJRSUGNROHNWRUDZREV]DU]H

DNW\ZQ\PPR*HP\QDSLVDü

I

I

I

I

I

I

I

I

C

B

B

C

B

O

C

REF

1

1

2

1

1

0

2

2

+

+

=

+

=

+

=

β

 

VWGRWU]\PXMHP\

I

I

I

O

REF

C

=

+

=

1 2

0

1

β

 D

-H*HOL

β

0

1

>>

WR

I

I

O

REF

 E

3UG Z\MFLRZ\ (UyGáD

I

O

 MHVW UyZQ\ Z SU]\EOL*HQLX SUGRZL

RGQLHVLHQLD

I

REF

 Z\PXV]RQHPX SU]H] (UyGáR RGQLHVLHQLD  DQJ

background image



UHIHUHQFH FXUUHQW  7HQ URG]DM (UyGáD VWDáRSUGRZHJR QRVL QD]Z

]ZLHUFLDGáDSUGRZHJROXEOXVWUDSUGRZHJR DQJFXUUHQWPLUURU 

:Sá\Z QDSL FLD

U

CE 2

 QD SUG (UyGáD RNUHOLP\ QD SRGVWDZLH

FKDUDNWHU\VW\NLZ\MFLRZHMWUDQ]\VWRUD7



 U\V

0

X

&(2

8

&(2

(

)

, 8

&

&(

2

2

(

)

, 8

&

&(

2

2

0

=

L

&2

8

$

QDSL FLH (DUO\HJR

U]HF]\ZLVWD UH]\VWDQFMD

(UyGáD SUGX

QLHVNRF]RQD UH]\VWDQFMD

(UyGáD SUGX

$

%

5\V:Sá\ZQDSL FLD

8

&(

QDSUG(UyGáD

3U]\ ]PLDQLH QDSL FLD

U

CE 2

 ]PLHQLD VL  SUG NROHNWRUD

I

2

 ZVNXWHN

]MDZLVNDPRGXODFMLV]HURNRFLED]\

I

I

U

U

U

C

S

BE

T

CE

A

2

2

1

=



 −



exp

ϕ

 

.RU]\VWDMF]SURSRUFMLPR*HP\QDSLVDü

(

)

(

)

I

U

U

U

I

U

U

C

CE

A

CE

C

CE

A

2

2

2

2

2

0

+

=

=

 

&]\OL

(

)

(

)

I

I

U

I

U

U

U

O

C

CE

C

CE

CE

A

=

=

=

+



2

2

2

2

2

0 1

 

=HZ]JO GXQDUy*QHQDSL FLD

U

CE

WUDQ]\VWRUyZUyZQLH*SUG\

LFK NROHNWRUyZ QLH V MHGQDNRZH 

I

I

C

C

1

2

 =DNáDGDMF UyZQRü

SUGyZSU]\]HURZ\PQDSL FLX

U

CE

VWRVXQHNW\FKSUGyZZ\QRVL

I

I

U

U

U

U

U

U

C

C

CE

A

CE

A

CE

A

2

1

2

1

2

1

1

1

=

+

+

≈ +

 

5y*QLF]NRZDUH]\VWDQFMDZ\MFLRZD(UyGáDZ\QRVL

(

)

(

)

r

u

i

U

U

I

U

U

I

U

r

o

CE

C

A

CE

C

CE

A

C

CE

ec

=

=

+

2

2

2

2

2

2

2

 

background image



: OXVWU]H SUGRZ\P LVWQLHMH PR*OLZRü Z\PXV]HQLD Z GUXJLP

WUDQ]\VWRU]HSUGXUy*QHJRRGSUGXRGQLHVLHQLD=DOHWDWDMHVWEDUG]R

ZD*QD ]H Z]JO GyZ SUDNW\F]Q\FK -H*HOL SRZLHU]FKQLD ]áF] HPLWHU 

ED]D WUDQ]\VWRUyZ 7



 L 7



 Z XNáDG]LH ] U\V V Uy*QH L Z\QRV]

RGSRZLHGQLR

S

1

L

S

2

WRVWRVXQHNSUGyZNROHNWRUyZW\FKWUDQ]\VWRUyZ

MHVWUyZQ\VWRVXQNRZLSRZLHU]FKQLLFK]áF]HPLWHURZ\FK

=DWHP

I

I

S

S

C

C

1

2

1

2

=

 

3RQLHZD*

I

I

I

I

I

I

I

C

REF

B

B

REF

C

C

1

1

2

1

0

2

0

=

=

β

β



 

WRSRSRGVWDZLHQLX  GR  RWU]\PXMHP\

I

I

I

S S

S S

O

C

REF

=

=

+ +

2

2

1

2

1

0

1

1

β

 

-H*HOL

S

S

1

2

=

 WR Z]yU    SU]\MPXMH SRVWDü    QDWRPLDVW JG\

β

0

2

1

1

>> +

S S

WR

I

I

S

S

O

REF

2

1

 

:\UD*HQLH

S S

S S

S

S

2

1

2

1

0

2

1

1

1

+ +

β

 QD]\ZD VL  Z]PRFQLHQLHP OXVWUD

SUGRZHJR

1DU\VSU]HGVWDZLRQR]HVSyáOXVWHUSUGRZ\FKZNWyU\PWHQ

VDP SUG RGQLHVLHQLD Z\PXV]D MHGQRF]HQLH ]JRGQLH ] ]DOH*QRFL

 XVWDORQHSUG\Z\MFLRZHZZLHOXWUDQ]\VWRUDFK

,

&

1,

%

,

%

,

5()

T

1

T

2

T

3

T

T

N

,

1

,

2

,

3

,

1

5\V=HVSyáOXVWHU

SUGRZ\FK

=Dáy*P\ GOD XSURV]F]HQLD UR]ZD*D *H ZV]\VWNLH WUDQ]\VWRU\ V

MHGQDNRZH PDMW VDPSRZLHU]FKQL ]áF]DHPLWHURZHJR 

:WHG\]JRGQLH]HVFKHPDWHPRWU]\PXMHP\

background image



(

)

I

I

N

I

REF

C

B

=

+

+

1

 

6WG

I

I

I

I

I

N

N

O

REF

1

2

0

1

1

= =

=

=

=

+

+



β

 

'OD GX*\FK ZDUWRFL

β

0

 L QLH]E\W GX*HM OLF]E\

N

 ZV]\VWNLH SUG\

Z\MFLRZH V Z SU]\EOL*HQLX UyZQH

I

REF

 =Uy*QLFRZDQLH W\FK SUGyZ

RWU]\PXMHP\SU]\Uy*Q\FKSRZLHU]FKQLDFK]áF]HPLWHURZ\FK

: SU]\SDGNX ]DVWRVRZDQLD WUDQ]\VWRUyZ SQS R PDáHM ZDUWRFL

β

0

β

0

10

 DOER SU]\ SRáF]HQLX UD]HP ]E\W GX*HM LORFL ED]

WUDQ]\VWRUyZUHDOL]XMF\FK]HVSyáOXVWHUSUGRZ\FKSRMDZLDMVL FRUD]

ZL NV]H Uy*QLFH SRPL G]\ SUGHP RGQLHVLHQLD

I

REF

 D SUGHP

Z\MFLRZ\P

1D U\V SU]HGVWDZLRQR ]PRG\ILNRZDQ\ XNáDG (UyGáD

VWDáRSUGRZHJR  OXVWUD SUGRZHJR R ]PQLHMV]RQ\P ZSá\ZLH SUGyZ

ED]

,

,

2

&

=



,

&

,

%

,

%

,

5()

8

%(

2

T

1

T

,

( 3

,

%3

T

3

5\V 'UyGáR VWDáRSUGRZH 

OXVWUR SUGRZH R ]PQLHMV]RQ\P

ZSá\ZLHSUGyZED]

3UG\HPLWHUDLED]\WUDQ]\VWRUD7



Z\QRV]

I

I

I

I

I

I

E

B

B

C

C

O

3

1

2

1

2

0

0

2

=

+

=

+

=

β

β

 

(

)

I

I

I

B

E

O

3

3

0

0

0

1

2

1

=

+

=

+

β

β β

 

3R]VXPRZDQLXSUGyZZZ (OHNROHNWRUDWUDQ]\VWRUD7



RWU]\PXMHP\

(

)

I

I

I

REF

C

O

+

=

1

0

0

2

1

0

β β

 

6WG

background image



(

)

I

I

O

REF

=

+

+

1

2

1

0

0

β β



 

1DZHWGODPDá\FKZDUWRFL

β

0

ZDUXQHN

(

)

β β

0

0

1

2

+ >>

MHVWVSHáQLRQ\

DW\PVDP\PSUGZ\MFLRZ\

I

O

QLHZLHOHUy*QLVL RGSUGXRGQLHVLHQLD

I

REF



3RGREQHZáDFLZRFLGRRSLVDQ\FKZ\*HMSRVLDGD(UyGáRSUGRZH

OXVWURSUGRZH:LOVRQD U\V ZNWyU\PUHODFM SRPL G]\SUGHP

Z\MFLRZ\P

I

O

DSUGHPRGQLHVLHQLD

I

REF

RSLVXMHLGHQW\F]QD]DOH*QRü

MDN  

,

2

,

5()

8

%(

2

T

T

3

1

T

U

R

8

%(

5\V /XVWUR SUGRZH

:LOVRQD

=H Z]JO GX QD NDVNRGRZH SRáF]HQLH WUDQ]\VWRUyZ 7



 L 7



 OXVWUR

SUGRZH :LOVRQD SRVLDGD ]QDF]QLH ZL NV] G\QDPLF]Q UH]\VWDQFM

Z\MFLRZQL*XNáDG\]SRMHG\QF]\PLWUDQ]\VWRUDPL

5H]\VWDQFMDWDZ\QRVL

r

U

I

o

A

O

β

0

2

 

3RQDGWR OXVWUR SUGRZH :LOVRQD FKDUDNWHU\]XMH VL  OHSV]\PL

ZáDFLZRFLDPL

F] VWRWOLZRFLRZ\PL

V]HURNRSDVPRZ\PL 

ZSRUyZQDQLXGRLQQ\FKOXVWHUSUGRZ\FK

2JyOQPHWRG]DSHZQLDMF]ZL NV]HQLHUH]\VWDQFMLZ\MFLRZHM

(UyGáD VWDáRSUGRZHJR  OXVWUD SUGRZHJR MHVW EXGRZDQLH XNáDGyZ

NDVNRGRZ\FK

3RGVWDZRZ\ XNáDG NDVNRGRZHJR OXVWUD SUGRZHJR SU]HGVWDZLRQR QD

U\V

7UDQ]\VWRU 7



 SUDFXMH SRGREQLH MDN WUDQ]\VWRU 7



 SU]\ QDSL FLX

U

CB

=

0

 '\QDPLF]QD UH]\VWDQFMD Z\MFLRZD WHJR WUDQ]\VWRUD UyZQD

r

U

I

U

I

ce

A

C

A

O

4

4

=

 ZQRVL XMHPQH VSU] *HQLH ]ZURWQH SUGRZH

V]HUHJRZH Z REZRG]LH HPLWHUD WUDQ]\VWRUD 7



 SRZRGXMF ]QDF]QH

]ZL NV]HQLHZ\SDGNRZHMG\QDPLF]QHMUH]\VWDQFMLZ\MFLRZHMXNáDGXGR

ZDUWRFL

background image



r

U

I

o

A

O

β

0



 

,

2

,

5()

8

%(

4

T

T

2

3

T

U

R

8

%(

1

T

5\V .DVNRGRZH (UyGáR

VWDáRSUGRZHOXVWURSUGRZH

']L NL WDN GX*HM ZDUWRFL G\QDPLF]QHM UH]\VWDQFML Z\MFLRZHM

SUGZ\MFLRZ\(UyGáDQLHXOHJD]PLDQLHSRGZSá\ZHP]PLHQLDMFHJR

VL QDSL FLDQDZ\MFLX

 6WDáRSUGRZH(UyGáDRGQLHVLHQLD

2PyZLRQH Z SRSU]HGQLP UR]G]LDOH (UyGáD VWDáRSUGRZH

QD]\ZDQH UyZQRF]HQLH OXVWUDPL SUGRZ\PL UR]ZD*DQR JáyZQLH SRG

NWHP GRNáDGQRFL ] MDN Z\PXV]DQ\ MHVW SUG Z\MFLRZ\

I

O

 SU]H]

SUG RGQLHVLHQLD

I

REF

 1LH ]DMPRZDQR VL  QDWRPLDVW Z MDNL VSRVyE

Z\WZRU]\ü SUG RGQLHVLHQLD R PDáHM ZUD*OLZRFL QD ]PLDQ\ QDSL FLD

]DVLODMFHJRLWHPSHUDWXU\

: SU]\SDGNX UHDOL]DFML VWDáRSUGRZ\FK (UyGHá RGQLHVLHQLD

SRGVWDZRZ VSUDZ MHVW VWDELOL]DFMD QDSL FLRZD WDN DE\ Z\MFLRZH

SUG\ RGQLHVLHQLD E\á\ QLH]DOH*QH RG QDSL ü ]DVLODMF\FK 1D U\V

SU]HGVWDZLRQR SURVWH SU]\NáDG\ WDNLFK (UyGHá Z NWyU\FK Z\VW SXMH

MHGQDNVáDED]DOH*QRüSUGXZ\MFLRZHJRRGQDSL FLD]DVLODMFHJR

,

2

,



8

%(

8

%(

3

T

2

T

5



5



8

%(

T

1

a)

,

2

,



8

%(

2

T

5



5



T

1

b)

8

%(

+

8

&&

+

8

&&

5\V'UyGáD VWDáRSUGRZH

QLH]DOH*QHRGQDSL FLD]DVLODQLD

=DQLHGEXMFSUGED]\WUDQ]\VWRUD7



GODREXXNáDGyZPR*QDQDSLVDü

background image



I

U

R

R

I

I

O

BE

T

S

=

2

2

1

ϕ

ln

 

3RQLHZD*SUG

I

1

]DOH*\RGQDSL FLD

U

CC

I

U

U

R

CC

BE

1

1

2

=

 

]DWHP SUG (UyGáD SRUHGQLR MHVW ORJDU\WPLF]Q IXQNFM QDSL FLD

]DVLODQLD

1D SRGVWDZLH ]DOH*QRFL       PR*HP\ Z\]QDF]\ü

ZUD*OLZRü

I

O

SUGXQD]PLDQ\QDSL FLD

U

CC

S

U

I

I

U

I R

U

I

CC

O

O

CC

T

O

CC

O

=





 =

ϕ

2

 

:DG XNáDGyZ ] U\V MHVW VLOQD ]DOH*QRü QDSL FLD

U

BE

 RG

WHPSHUDWXU\

'OD RFHQ\ ZUD*OLZRFL (UyGáD QD ]PLDQ\ WHPSHUDWXU\ GHILQLXMH VL

WHPSHUDWXURZ\ZVSyáF]\QQLNZ]JO GQHM]PLDQ\SUGX(UyGáD

( )

TW I

I

I

T

T

T

I

I

T

T

S

O

O

O

O

O

T

I

O

=

=





 =

1

1

1



 

:VSyáF]\QQLN

TW

Z\UD*DVL ZMHGQRVWNDFK





°

&OXEZSSP

°

&

$QDOL]RZDQ\ XNáDG FKDUDNWHU\]XMH VL  GRü GX* ZUD*OLZRFL

I

O

 QD

]PLDQ\

U

CC

 Z\QRV]F RN  RUD] GX*\P ZVSyáF]\QQLNLHP

( )

TW I

O

NWyU\PR*QDRV]DFRZDüRNSSP

°

&

/HSV]\P UR]ZL]DQLHP MHVW (UyGáR VWDáRSUGRZH SU]HGVWDZLRQH QD

U\VQD]\ZDQH(UyGáHP:LGODUD

,

2

,

&

,

%

,

%

5



8

%(

2

T

1

T

8

%( 

,



+

8

&&

5



5\V 6WDáRSUGRZH (UyGáR

:LGODUD

6WRVXMFSUDZR.LUFKKRIIDRWU]\PXMHP\

background image



U

U

I R

I

I

I

I

I R

BE

BE

O

T

C

ES

T

O

ES

O

1

2

2

1

1

2

2

0

=

=

ϕ

ϕ

ln

ln

 

-H*HOLWUDQ]\VWRU\VMHGQDNRZHWR

I

I

ES

ES

1

2

=

LZWHG\

I

R

I

I

O

T

C

O

= ϕ

2

1

ln

 

=DNáDGDMF I

I

I

B

B

C

1

2

1

,

<<

 RUD]

U

U

BE

CC

1

<<

 PR*HP\ Z\]QDF]\ü

SU]\EOL*RQZDUWRüSUGXNROHNWRUD

I

C1

I

I

U

U

R

U

R

C

CC

BE

CC

1

1

1

1

1

≈ =

 

3RGVWDZLDMF  GR  RWU]\PXMHP\

I

R

U

I R

O

T

CC

O

≈ ϕ

2

1

ln

 

-DNZ\QLND]UyZQDQLD  VSDGHNQDSL FLD

I R

O

2

MHVWUyZQ\Uy*QLF\

U

U

BE

BE

1

2

 FR R]QDF]D *H QDZHW SU]\ VWRVRZDQLX QLH]E\W GX*\FK

ZDUWRFL

R

2

SUG

I

O

PR*HE\üPDá\-HVWWRZáDFLZRü(UyGáD:LGODUD

Z\NRU]\VW\ZDQD]DZV]HJG\Z\PDJDQ\MHVWPDá\SUG(UyGáD
3UG (UyGáD

I

O

 MHVW ORJDU\WPLF]Q IXQNFM QDSL FLD ]DVLODQLD U

CC

UyZ  D MHJR ZUD*OLZRü QD ]PLDQ\ WHPSHUDWXURZH MHVW PQLHMV]D

QL*ZXNáDG]LH]U\V

1D U\V SU]HGVWDZLRQR VWDáRSUGRZH (UyGáR RGQLHVLHQLD ]

VDPRF]\QQSRODU\]DFMQDSL FLHP

8

%(

ZNWyU\PSUG\Z\MFLRZHV

FDáNRZLFLHQLH]DOH*QHRGQDSL FLD]DVLODMFHJR DQJVHOIELDVLQJ

8

%(

UHIHUHQFH >@

,

2

,

&

5



,



+

8

&&

5



3

T

,

2

5



2

T

4

T

5

T

6

T

1

T

'



'



'



'



'



a)

,



,

&

3

,

5

,

,

&

7

2







=

ϕ

OQ

,

,

&



=

b)



5\V6WDáRSUGRZH(UyGáRRGQLHVLHQLD]VDPRF]\QQSRODU\]DFMQDSL FLHP

8

%(



D VFKHPDWEORNRZ\E FKDUDNWHU\VW\NDSU]HMFLRZD

background image



8NáDG PD GZD Z\MFLD MHGQR W\SX HPLV\MQHJR Z NWyU\P SUG (UyGáD

Z\Sá\ZD RG GRGDWQLHJR ELHJXQD QDSL FLD ]DVLODQLD RUD] GUXJLH W\SX

DEVRUEF\MQHJR Z NWyU\P SUG (UyGáD ZSá\ZD GR PDV\ XNáDGX  DQJ

FXUUHQWVRXUFHVLQN 

7UDQ]\VWRU\7



7



WZRU]XNáDGMDNQDU\VE]DWHPSUGNROHNWRUD

I

C1

GDQ\MHVWZ]RUHP  /XVWURSUGRZH]áR*RQH]WUDQ]\VWRUyZ7





7



Z\PXV]DUyZQRüSUGyZ

I

I

C1

1

=

5R]ZL]DQLHPREXUyZQDMDN

WR SU]HGVWDZLRQR JUDILF]QLH QD U\VE MHVW SXQNW 3 OXE SXQNW

]QDMGXMF\ VL  Z SRF]WNX XNáDGX ZVSyáU] GQ\FK  F]\OL

I

I

C1

1

0

= =



$E\ Z\HOLPLQRZDü PR*OLZRü XVWDOHQLD VL  QLHSR*GDQHJR SXQNWX

SUDF\ SU]\

I

C1

0

=

 XNáDG SRVLDGD VSHFMDOQH ]DEH]SLHF]HQLH ] GLRGDPL

'



'



  WUDQ]\VWRU\ Z SRáF]HQLX GLRGRZ\P  NWyUHJR ]DGDQLHP MHVW

VSRZRGRZDQLH SU]HSá\ZX SUGX SU]H] UH]\VWRU 5



 ZyZF]DV JG\

I

C1

0

=

 = FKZLO JG\ RVLJQL W\ ]RVWDQLH ZáDFLZ\ SXQNW SUDF\ 3

GLRGD'



VSRODU\]RZDQDMHVW]DSRURZRLXNáDG]DEH]SLHF]DMF\]RVWDMH

RGáF]RQ\RGUHV]W\XNáDGX

 'UyGáDQDSL FLDRGQLHVLHQLD

'UyGáD QDSL FLD RGQLHVLHQLD  DQJ YROWDJH UHIHUHQFHV  SRZLQQ\

SRVLDGDüPDáUH]\VWDQFM Z\MFLRZRUD]SRZLQQ\E\üQLHZUD*OLZHQD

]PLDQ\ QDSL FLD ]DVLODQLD L WHPSHUDWXU\ : SU]\SDGNX UHDOL]DFML W\FK

(UyGHá JáyZQ\P ]DGDQLHP MHVW VWDELOL]DFMD WHPSHUDWXURZD .RV]WHP

UH]\JQDFML ] EDUG]R PDáHM UH]\VWDQFML Z\MFLRZHM Z\PDJD VL  DE\

WHPSHUDWXURZ\ ZVSyáF]\QQLN QDSL FLD RGQLHVLHQLD

(

)

TW U

REF

 E\á

PQLHMV]\QL*SSP

°

&

3URVWHSU]\NáDG\(UyGHáQDSL FLRZ\FKSU]HGVWDZLRQHQDU\V

LOXVWUXMMHG\QLHPHWRG\XVWDODQLDQDSL FLDZ\MFLRZHJRR]PQLHMV]RQHM

ZUD*OLZRFL QD ]PLDQ\ QDSL FLD ]DVLODQLD EH] VWDELOL]DFML

WHPSHUDWXURZHM

1DSL FLH QD Z\MFLX RUD] G\QDPLF]QD UH]\VWDQFMD Z\MFLRZD XNáDGX ]

U\VDZ\QRV]

U

U

U

REF

Z

BE

=

+

 

r

U

I

U

I

r

I

o

Z

BE

z

T

=

+

= +

ϕ

 

1DSL FLH

U

BE

 QD WUDQ]\VWRU]H 7



 Z SRáF]HQLX GLRGRZ\P R XMHPQ\P

ZVSyáF]\QQLNXWHPSHUDWXURZ\PF] FLRZRNRPSHQVXMHWHPSHUDWXURZH

]PLDQ\QDSL FLD

U

Z

RGRGDWQLPZVSyáF]\QQLNXWHPSHUDWXURZ\P

background image



+

8

&&

1

T

'=

a)

8

5()

1

T

2

T

N

T

8

5()

+

8

&&

+

8

&&

8

5()

1

T

,



,



,

%

5



5



8

%(

,

,

,

b)

c)

5\V 3URVWH SU]\NáDG\ (UyGHá QDSL FLRZ\FK D  ] GLRG =HQHUD E  R QDSL FLX

Z\MFLRZ\P

18

%(

F PQR*QLN

8

%(

'UyGáRQDSL FLRZHQDU\VESRVLDGDQDSL FLHZ\MFLRZH

U

NU

REF

BE

=

 

RUD]G\QDPLF]QUH]\VWDQFM Z\MFLRZ

r

N

U

I

N

I

o

BE

T

=

=

ϕ

 

:DG WHJR XNáDGX MHVW EDUG]R GX*D ZDUWRü WHPSHUDWXURZHJR

ZVSyáF]\QQLNDQDSL FLDZ\MFLRZHJR

U

T

N

U

T

N mV

C

REF

BE

=

≈ −

2

$

 

5\VFSU]HGVWDZLDDOWHUQDW\ZQHUR]ZL]DQLHQD]\ZDQHPQR*QLNLHP

U

BE

 Z NWyU\P SU]\ SRPLQL FLX SUGX ED]\ Z VWRVXQNX GR SUGX

G]LHOQLND

I

I

1

2

RWU]\PXMHP\

U

R

R

R

U

BE

REF

=

+

2

1

2

6WG

U

R

R

U

REF

BE

= +



1

1

2

 

'\QDPLF]QDUH]\VWDQFMDZ\MFLRZD(UyGáDZ\QRVL

r

R

R

R

g R

o

m

=

+

+

1

0

1

2

2

β

 

1DU\VSU]HGVWDZLRQR(UyGáRQDSL FLDRGQLHVLHQLD]WHPSHUDWXURZ

NRPSHQVDFMQDSL ü

U

Z

L

U

BE

>@

background image



'

=

1

T

3

T

8

5()

+

8

&&

5



8

%(

,

2

T

8

%(

8

=

8

%(

5



5\V 'UyGáR QDSL FLD

RGQLHVLHQLD ] WHPSHUDWXURZ

NRPSHQVDFMQDSL ü

8

=

L

8

%(

1DSL FLHZ\MFLRZH(UyGáDZ\QRVL

(

)

(

)

U

U

U

U

R

R

R

R U

R

R U

R

R

REF

BE

Z

BE

Z

BE

=

+

+

=

+

+

3

2

2

1

2

2

1

2

1

2

 

=DQLHGEXMF ZSá\Z WHPSHUDWXURZHJR ZVSyáF]\QQLND VWRVXQNX

UH]\VWRUyZ

R R

1

2

 QD QDSL FLH Z\MFLRZH ZDUXQHN NRPSHQVDFML

RWU]\PXMHVL SU]\UyZQXMFGR]HUDSRFKRGQ

dU

dT

REF

F]\OL

dU

dT

R

R

R

dU

dT

R

R

R

R

dU

dT

REF

Z

BE

=

+

+

+

=

2

1

2

1

2

1

2

2

0

 

=UyZQDQLD  RWU]\PXMHP\ZDUXQHNNRPSHQVDFML

R

R

dU

dT

dU

dT

Z

BE

1

2

2

= +

 

=DNáDGDMFW\SRZHZDUWRFL

dU

dT

mV

C

Z

= +

3

$

RUD]

dU

dT

mV

C

BE

= −

2

$

RWU]\PXMHP\

R

R

1

5

0 5

/

,

=



U

U

REF

Z

=

3

 

:WHFKQLFHXNáDGyZPRQROLW\F]Q\FKEDUG]RF] VWRZ\NRU]\VWXMH

VL  RJyOQ ]DVDG  UHDOL]DFML (UyGáD QDSL FLD RGQLHVLHQLD SROHJDMF QD

NRPSHQVDFML XMHPQHJR WHPSHUDWXURZHJR ZVSyáF]\QQLND QDSL  FLD

U

BE

background image



SU]H] GRGDWQL ZVSyáF]\QQLN QDSL FLD

ϕ

T

 =DVDG  W  ]LOXVWURZDQR

VFKHPDWHPEORNRZ\PQDU\V>@

T

8

8

.

5()

%(

7

=

+

ϕ

8

%(

8

%(

,

.

7

ϕ

.

ϕ

7

ϕ

7

*HQHUDWRU

+

5\V2JyOQD]DVDGDUHDOL]DFML(UyGáDQDSL FLDRGQLHVLHQLDW\SXEDQGJDS

1DSL FLHRGQLHVLHQLD

8

5()

MHVWUyZQH

8

8

.

5()

%(

7

=

+

ϕ

 

:DUXQHNNRPSHQVDFMLRWU]\PXMHVL JG\

G8

G7

G8

G7

.

G

G7

5()

%(

7

=

+

=

ϕ



 

= UyZQDQLD   PR*HP\ Z\]QDF]\ü Z\PDJDQ ZLHONRü

QLH]DOH*QHJRRGWHPSHUDWXU\ZVSyáF]\QQLND.

.

8

7

7

%(

7

=

ϕ

 

8Z]JO GQLDMFW\SRZHZDUWRFL

G8

G7

P9 &

%(

= −



$

RUD]

ϕ

7

7

P9 &

= +

 



$

RWU]\PXMHP\

.

=

RUD]

8

5()

=

9

3RQLHZD* ZDUWRü QDSL FLD RGQLHVLHQLD MHVW ]EOL*RQD GR ZDUWRFL

QDSL FLDEDULHU\SRWHQFMDáXNU]HPXGODWHJRXNáDG\UHDOL]RZDQHZJWHM

]DVDG\ V QD]\ZDQH XNáDGDPL ] EDULHU SRWHQFMDáX  DQJ EDQG  JDS

UHIHUHQFHFLUFXLWV 

1D U\V SU]HGVWDZLRQR SU]\NáDGRZH UR]ZL ]DQLH (UyGáD

QDSL FLDRGQLHVLHQLDW\SXEDQGJDS

7UDQ]\VWRU\ 7



 L 7



 WZRU] VWDáRSUGRZH (UyGáR :LGODUD 6SDGHN

QDSL FLDQDUH]\VWDQFML

R

3

SU]\SRPLQL FLXSUGyZED]Z\QRVL

I R

U

U

I

I

C

BE

BE

T

C

C

2

3

1

2

1

2

=

=

ϕ

ln

 

background image



,

&

8



2

T

5



5



8

%(

+

8

&&

5



8

%( 

1

T

,

&

3

T

8

5()

,

5\V

3U]\NáDGRZD

UHDOL]DFMD (UyGáD RGQLHVLHQLD

W\SXEDQGJDS

:\]QDF]DMF ] UyZQDQLD    SUG

I

2

 SU]\

β

0

1

>>

 PR*HP\

Z\]QDF]\üQDSL FLHQDUH]\VWDQFML

R

2

U

I R

R

R

I

I

C

T

C

C

2

2

2

2

3

1

2

=

=

ϕ

ln

 

1DSL FLHRGQLHVLHQLDMHVWUyZQH

U

U

U

U

R

R

I

I

REF

BE

BE

T

C

C

=

+

=

+

2

3

3

2

3

1

2

ϕ

ln



 

3RUyZQXMF  L  RWU]\PXMHP\

K

R

R

I

I

C

C

=

2

3

1

2

ln

 

6WRVXQHNSUGyZ

I

I

C

C

1

2

MHVWQLH]DOH*Q\RGWHPSHUDWXU\

$E\ X]\VNDü SHáQ NRPSHQVDFM  WHPSHUDWXURZ QDSL FLD

U

REF

 WR

GRELHUDMF QS  GOD 7 . 

I

I

C

C

1

2

10

=

 PXVLP\ ]DSHZQLü

R R

2

3

10 2

=

,



 3RGVWDZRZHEORNLZXNáDGDFK]DVLODQLDLVWDELOL]DFMLSXQNWyZ

SUDF\WUDQ]\VWRUyZXQLSRODUQ\FK

 'UyGáDVWDáRSUGRZHOXVWUDSUGRZH

8NáDG\(UyGHáVWDáRSUGRZ\FKOXVWHUSUGRZ\FKUHDOL]RZDQHV

Z WHFKQRORJLL 026 QD EDUG]R SRGREQ\FK ]DVDGDFK MDN Z WHFKQRORJLL

ELSRODUQHM

background image



1D U\V SU]HGVWDZLRQR SURVWH (UyGáR VWDáRSUGRZH  OXVWUR

SUGRZH ] WUDQ]\VWRUDPL 026)(7 ] NDQDáHP Z]ERJDFDQ\P W\SX Q

VWDQRZLFHRGSRZLHGQLNXNáDGX]U\V

,

,

2

'

=



,

'

,

5()

8

*6

8

'6

2

M

1

M

5\V 3URVWH OXVWUR

SUGRZH

-H*HOLWUDQ]\VWRU\0



0



SUDFXMZREV]DU]HQDV\FHQLDWR

(

) (

)

(

) (

)

I

K W L U

U

U

I

K W L U

U

U

D

N

GS

T

DS

D

N

GS

T

DS

1

1

1

2

1

2

2

2

2

2

1

1

=

+

=

+

'

'

λ

λ

 

3RQLHZD*REDWUDQ]\VWRU\SUDFXMSU]\W\PVDP\PQDSL FLX SRGáR*H 

(UyGáR

U

BS

GODWHJRPDMWHVDPHQDSL FLDSURJRZH

U

U

U

T

T

T

1

2

=

=



=DWHPQDSRGVWDZLHUyZQD  RWU]\PXMHP\

(

) (

)

(

) (

)

I

I

I

I

K W L

U

K W L

U

O

REF

D

D

N

DS

N

DS

=

=

+
+

2

1

2

2

1

1

1

1

'

'

λ
λ

 

3U]\ SRPLQL FLX HIHNWX PRGXODFML GáXJRFL NDQDáX VWRVXQHN SUGyZ

I

I

O

REF

]DOH*\W\ONRRGUR]PLDUyZWUDQ]\VWRUyZ

(

)

(

)

I

I

W L

W L

O

REF

=

2

1

 

'\QDPLF]QDUH]\VWDQFMDZ\MFLRZD(UyGáDZ\QRVL

r

U

I

I

I

r

o

DS

D

D

O

ds

=

=

=

=

2

2

2

2

1

1

λ

λ

 

$E\ WUDQ]\VWRU 0



 SUDFRZDá ]DZV]H Z REV]DU]H QDV\FHQLD PXVL E\ü

VSHáQLRQ\ZDUXQHN

U

U

U

U

GS

T

DS

>

=

2

min

 

,

1

,

5()

2

M

M

,

2

3

M

,

1

N

M

5\V=HVSyá OXVWHU

SUGRZ\FK

background image



1DU\VSU]HGVWDZLRQR]HVSyáOXVWHUSUGRZ\FKZNWyU\PWHQ

VDP SUG ZHMFLRZ\ OXVWUD

I

REF

 Z\PXV]D MHGQRF]HQLH 1 SUGyZ

Z\MFLRZ\FK]JRGQLH]UHODFM  

1D U\V SU]HGVWDZLRQR VFKHPDW\ OXVWHU SUGRZ\FK :LOVRQD

NWyUH ] XZDJL QD NDVNRGRZH SRáF]HQLH GZyFK WUDQ]\VWRUyZ Z

REZRG]LH Z\MFLRZ\P FKDUDNWHU\]XM VL  GX*R ZL NV] UH]\VWDQFM

Z\MFLRZQL*UH]\VWDQFMDSURVWHJROXVWUD

,

5()

2

M

1

M

3

M

8

*6

,

2

,

5()

2

M

1

M

3

M

,

2

4

M

a)

b)

5\V/XVWUD:LOVRQD D ]PRG\ILNRZDQH E

: XNáDG]LH ]PRG\ILNRZDQ\P QD U\VE G]L NL GRGDQLX

WUDQ]\VWRUD0



ZREXJDá ]LDFKWUDQ]\VWRU\SUDFXMSU]\WDNLFKVDP\FK

QDSL FLDFK

U

DS

  FR PD LVWRWQH ]QDF]HQLH GOD VSHáQLHQLD UHODFML

I

I

REF

O

=



=SRUyGZLHOXUy*Q\FKUR]ZL]DXNáDGRZ\FKOXVWHUSUGRZ\FKOXVWUD

:LOVRQD

Z\Uy*QLDM

VL 

NRU]\VWQLHMV]\PL

ZáDFLZRFLDPL

F] VWRWOLZRFLRZ\PL V]HURNRSDVPRZ\PL 

: ZLHOX ]DVWRVRZDQLDFK Z\PDJD VL  EDUG]R GX*HM UH]\VWDQFML

G\QDPLF]QHM(UyGáDSUGXZV]HURNLP]DNUHVLH]PLDQQDSL FLD(UyGáD

2SLVDQH UR]ZL]DQLD XNáDGRZH (UyGHá SUGRZ\FK Z WHFKQRORJLL

ELSRODUQHM PRJ PLHü UyZQLH* ]DVWRVRZDQLH GR UHDOL]DFML (UyGHá

SUGRZ\FKZWHFKQRORJLL&026

1D U\V SU]HGVWDZLRQR VFKHPDW LGHRZ\ NDVNRGRZHJR OXVWUD

SUGRZHJRVWDQRZLFHRGSRZLHGQLNELSRODUQHJRXNáDGX]U\V

=DNáDGDMF*HWUDQ]\VWRU\0



0



VLGHQW\F]QH]HVFKHPDWXQD

U\VDRWU]\PXMHP\

U

U

U

U

U

U

DS

GS

GS

GS

GS

GS I

I

I

D

REF

O

1

2

2

1

2

=

=

=




=

=

 

U

U

DS

GS

1

=

 

:DUXQNLHPSUDF\WUDQ]\VWRUyZ0



L0



ZREV]DU]HQDV\FHQLDMHVWDE\

VSHáQLRQHE\á\QLHUyZQRFL

background image



U

U

U

U

U

U

DS

GS

T

O

GS

T

2

2

2

 

,

5()

2

M

,

2

a)

3

M

4

M

1

M

8

*6

8

*6 2

8

*61

8

'6 2

8

'61

8

2

b)

8

*6

8

2

,

2

2

8

8

*6

7

(

)

2

8

8

*6

7

0 0 REV]DU OLQLRZ\

1

2



0 0 REV]DU QDV\FHQLD

1

2



0 REV]DU

QDV\FHQLD

0 REV]DU

OLQLRZ\

1

2

5\V .DVNRGRZH OXVWUR SUGRZH D  VFKHPDW LGHRZ\ E  FKDUDNWHU\VW\ND

SUGRZRQDSL FLRZD

:W\P]DNUHVLHQDSL üZ\MFLRZ\FKSUG(UyGáDMHVWVWDá\'DOV]H

]PQLHMV]DQLHQDSL FLD

U

O

SRZRGXMH]PQLHMV]HQLHQDSL FLD

U

DS 2

JG\*

QDSL FLH

U

DS1

 MHVW XVWDORQH SU]H] NRáR QDSL ü

2

2

1

U

U

U

GS

GS

DS

=

LWUDQ]\VWRU 0



 SUDFXMH GDOHM Z REV]DU]H QDV\FHQLD 7UDQ]\VWRU 0



]DF]\QDSUDFRZDüZREV]DU]HOLQLRZ\PDSUGZ\MFLRZ\

I

O

PDOHMH

FR MHVW VSRZRGRZDQH ]PQLHMV]DQLHP VL  QDSL FLD

U

DS 2

 : PRPHQFLH

JG\ ZDUWRü QDSL FLD

U

O

 ]PQLHMV]\ VL  SRQL*HM

(

)

U

U

GS

T

 RED

WUDQ]\VWRU\SUDFXMZREV]DU]HOLQLRZ\P U\VE 

'\QDPLF]QUH]\VWDQFM Z\MFLRZOXVWUDNDVNRGRZHJRPR*HP\

Z\]QDF]\üQDSRGVWDZLHMHJRPDáRV\JQDáRZHJRVFKHPDWX]DVW  SF]HJR

LMHJRNROHMQ\FKSU]HNV]WDáFHSU]HGVWDZLRQ\FKQDU\V>@

5H]\VWDQFMDWDZ\QRVL

(

)

[

]

(

)

(

)

r

U

I

U

r U

g

g

U

g

r

r

g r

r

g r

o

gs

ds

gs

m

ds

gs

ds

ds

ds

m

ds

ds

m

ds

=

=

+

+

=

+

+

+

2

2

2

2

1

2

1

1

2

2

1

2

2

1

1

1

 

:VWRVXQNXGRSRGVWDZRZHJROXVWUDSUGRZHJR]U\VUH]\VWDQFMD

Z\MFLRZDOXVWUDNDVNRGRZHJRZ]URVáD

(

)

1

2

1

+

g r

m

ds

UD]\

3RQLHZD* SRWHQFMDá GUHQX WUDQ]\VWRUD 0



 PR*H VL  QLH]QDF]QLH

]PLHQLDü WR ]PLDQD WD SRZRGXMH ]PLDQ  QDSL FLD (UyGáR  SRGáR*H Z

WUDQ]\VWRU]H0



]DWHPZWUDQ]\VWRU]HW\PZ\VWSLHIHNWSRGáR*D

background image



J

GV3

J 8

P

JV

3

3

J

GV4

J 8

P

JV

4

4

8

JV3

8

JV2

8

JV4

8

JV1

J 8

P

JV

2

2

J

GV2

J 8

P

JV

1

1

J

GV1

8

,

8

JV2

8

JV1

J 8

P

JV

2

2

J

GV2

J 8

P

JV

1

1

J

GV1

8

,

J

P3

J

GV3

J

GV4

J

P4

J 8

P

JV

2

2

J

GV2

J 8

GV

JV

1

2

8

,

J

GV1

(

)

J

J 8

P

GV

JV

2

1

2

+

8

JV2

5\V 0DáRV\JQDáRZ\ VFKHPDW ]DVW SF]\ OXVWUD NDVNRGRZHJR L MHJR NROHMQH

SU]HNV]WDáFHQLD

1D U\V SU]HGVWDZLRQR NRFRZ SRVWDü SU]HNV]WDáFRQHJR

VFKHPDWX ]DVW SF]HJR ] U\V Z NWyU\P XZ]JO GQLRQR VNáDGRZ

]PLHQQQDSL FLD(UyGáRSRGáR*H

U

bs2

WUDQ]\VWRUD0





J 8

PE

EV

2

2

J

GV2

8

,

J 8

P

JV

2

2

8

EV2

J

GV1

8

JV2

%2

5\V0DáRV\JQDáRZ\VFKHPDW

]DVW SF]\OXVWUDNDVNRGRZHJR

XZ]JO GQLDMF\HIHNWSRGáR*D

WUDQ]\VWRUD0



'\QDPLF]QD UH]\VWDQFMD Z\MFLRZD OXVWUD SU]\ XZ]JO GQLHQLX HIHNWX

SRGáR*DWUDQ]\VWRUD

(

)

[

]

r

r

r

g

g

r

o

ds

ds

m

mb

ds

=

+

+

+

1

2

2

2

1

1

 

MHVW QLHFR ZL NV]D QL* WD NWyU Z\]QDF]RQR SU]\ SRPLQL FLX HIHNWX

SRGáR*D

.DVNRGRZH OXVWUR SUGRZH ] WUDQ]\VWRUDPL 026)(7 ]DSHZQLD

]QDF]QLH ZL NV] G\QDPLF]Q UH]\VWDQFM  Z\MFLRZ QL* MHJR

RGSRZLHGQLN ] WUDQ]\VWRUDPL ELSRODUQ\PL :DG  NDVNRGRZHJR OXVWUD

SUGRZHJR]U\VMHVWVWRVXQNRZRGX*HQDSL FLHQDZHMFLXOXVWUD

UyZQH

2U

GS

 RUD] VWRVXQNRZR GX*D ZDUWRü PLQLPDOQHJR QDSL FLD

Z\MFLRZHJRNWyUDQLHPR*H E\ü PQLHMV]D QL*

U

U

U

O

GS

T

min

2

  MDN

background image



Z\MDQLRQR ZF]HQLHM SU]\ GDOV]\P REQL*DQLX QDSL FLD QD Z\MFLX

WUDQ]\VWRU 0



 ZFKRG]L Z REV]DU OLQLRZ\ L SUG Z\MFLRZ\ PDOHMH 

2JUDQLF]D WR ]QDF]QLH PR*OLZRü Z\NRU]\VWDQLD W\FK OXVWHU ZH

ZVSyáF]HVQ\FK DQDORJRZ\FK XNáDGDFK VFDORQ\FK &026 SUDFXM F\FK

SU]\QLVNLFKQDSL FLDFK]DVLODMF\FK

1D U\V SU]HGVWDZLRQR VFKHPDW LGHRZ\ QLVNRQDSL  FLRZHJR

OXVWUDSUGRZHJR DQJKLJKVZLQJFXUUHQWPLUURU NWyUHZSRUyZQDQLX

GRNDVNRGRZHJROXVWUD]U\VSRVLDGDPQLHMV]HQDSL  FLHZHMFLRZH

LZL NV]\]DNUHVQDSL FLDZ\MFLRZHJR>@

,

5()

2

M

,

2

3

M

4

M

1

M

8

*6

8

*6 2

8

*61

8

'62

8

'61

8

2

8

**

5\V 1LVNRQDSL FLRZH

OXVWUR SUGRZH W\SX ÄKLJK

VZLQJ´

=Dáy*P\GODXSURV]F]HQLDUR]ZD*D*HZV]\VWNLHWUDQ]\VWRU\0



 0



 PDM WH VDPH UR]PLDU\ L WH VDPH QDSL FLD

U

GS

 1DSL FLH

U

GG

SRODU\]XMFH EUDPNL WUDQ]\VWRUyZ 0



 L 0



 QDOH*\ WDN GREUDü DE\

ZV]\VWNLHWUDQ]\VWRU\SUDFRZDá\ZREV]DUDFKQDV\FHQLD

=DWHP

U

U

U

U

U

U

U

U

DS

GS

T

GG

DS

GS

GS

T

1

1

2

min

min

=

+

=

 

$E\WUDQ]\VWRU0



SUDFRZDáZREV]DU]HQDV\FHQLDSRWHQFMDáMHJRGUHQX

QLHPR*HE\üQL*V]\RG

U

U

GG

T

W]Q

8

8

*'

7



<



6WG QDSL FLH Z\MFLRZH

U

O

 QLH PR*H REQL*\ü VL  SRQL*HM SHZQHM

PLQLPDOQHMZDUWRFL

U

U

U

U

U

O

GG

T

GS

T

min

=

2

2

 

3RUyZQXMF ]DOH*QRFL    L    ZLG]LP\ *H QDSL FLH

U

O min

OXVWUD SUGRZHJR W\SX ÄKLJK VZLQJ´ MHVW PQLHMV]H R ZDUWRü QDSL FLD

SURJRZHJR

U

T

 RG QDSL FLD

U

O min

 Z NRQZHQFMRQDOQ\P OXVWU]H

NDVNRGRZ\P]U\VD

%LRUF SRG XZDJ  *H QDSL FLH SURJRZH

8

7

 ]DZLHUD VL  Z JUDQLFDFK

±9 PD WR LVWRWQH ]QDF]HQLH SU]\ UHDOL]DFML QLVNRQDSL  FLRZ\FK

DQDORJRZ\FKXNáDGyZ&026

background image



5yZQLH* QDSL FLH ZHMFLRZH OXVWUD W\SX ÄKLJK VZLQJ´ MHVW PQLHMV]H

LZ\QRVL

U

GS

 ZNODV\F]Q\POXVWU]HNDVNRGRZ\P

2U

GS



 'UyGáDQDSL FLRZH

%DUG]RF] VWRSXQNW\SUDF\WUDQ]\VWRUyZZXQLSRODUQ\PXNáDG]LH

VFDORQ\P XVWDODQH V ]D SRPRF (UyGHá QDSL FLRZ\FK GRáF]RQ\FK GR

EUDPHNW\FKWUDQ]\VWRUyZ

:]DNUHVLH]PLHQQRSUGRZ\P EUDPNL W\FK WUDQ]\VWRUyZ ]ZDUWH V GR

PDV\ 'UyGáD QDSL FLRZH R WDNLP SU]H]QDF]HQLX PRJ SRVLDGDü GRü

GX*H UH]\VWDQFMH ZHZQ WU]QH SRQLHZD* REFL*RQH V EDUG]R GX*\PL

LPSHGDQFMDPL ZHMFLRZ\PL WUDQ]\VWRUyZ 026)(7 D SU]H] WR PRJ

E\üUHDOL]RZDQHZQDMSURVWV]HMSRVWDFLQSG]LHOQLNyZQDSL  FLRZ\FK

6]F]HJyOQ\P URG]DMHP (UyGHá QDSL FLRZ\FK V XNáDG\

SU]HVXZDQLD QDSL FLD VWDáHJR NWyUH V VWRVRZDQH Z REZRGDFK

VSU] JDMF\FK GZyFK NROHMQ\FK VWRSQL XNáDGX VFDORQHJR RUD] QD

Z\MFLX RVWDWQLHJR VWRSQLD Z FHOX ]DSHZQLHQLD ]HURZHJR QDSL  FLD

Z\MFLRZHJR SU]\ ]HURZ\P QDSL FLX ZHMFLRZ\P 3RQLHZD* XNáDG\

SU]HVXZDQLDQDSL FLD]QDMGXMVL ZJáyZQ\PWRU]HWUDQVPLVMLV\JQDáX

GODWHJR QLH SRZLQQ\ ZQRVLü WáXPLHQLD V\JQDáX X *\WHF]QHJR REFL*Dü

VWRSQLD SRSU]HGQLHJR RUD] SRZLQQ\ JZDUDQWRZDü VWHURZDQLH

QDSL FLRZHVWRSQLDQDVW SQHJR

'UyGáD QDSL FLRZH R PDáHM ZUD*OLZRFL QDSL FLD QD ]PLDQ\

WHPSHUDWXU\LQDSL FLD]DVLODQLDQD]\ZDVL (UyGáDPLRGQLHVLHQLD'UyGáD

QDSL FLRZH V Z ]QDF]QLH ZL NV]\P VWRSQLX ZUD*OLZH QD ]PLDQ\

WHPSHUDWXU\ QL* QD ]PLDQ\ QDSL FLD ]DVLODQLD  RGZURWQLH QL* Z

SU]\SDGNX(UyGHáSUGRZ\FK 

1D U\V SU]HGVWDZLRQR SU]\NáDG\ UHDOL]DFML G]LHOQLNyZ

QDSL FLRZ\FK Z WHFKQRORJLL 1026 L &026 ]EXGRZDQ\FK

]WUDQ]\VWRUyZ026)(7ZSRáF]HQLXGLRGRZ\P

3RQLHZD* SU]H] G]LHOQLN WUDQ]\VWRURZ\ SU]HSá\ZD WHQ VDP SU G

GUHQX

I

D

  SU]\ SRPLMDOQLH PDá\FK SUGDFK REFL*H  ]DWHP QDSL FLH

U

DSi

LWHJRWUDQ]\VWRUDZG]LHOQLNXMHVWUyZQH

(

)

U

I

K W L

U

DSi

D

i

T

=

+

'

 

1DSL FLHQDMW\PZ\MFLXG]LHOQLNDZ\QRVL

U

U

U

j

DSi

SS

i

j

=

=

1

GOD M   

 N 



 

background image



SU]\F]\PNMHVWZRJyOQ\PSU]\SDGNXOLF]EWUDQ]\VWRUyZWZRU]F\FK

G]LHOQLN]DVLODQ\QDSL FLHPU

U

DD

SS

+

F]\OL

U

U

U

DD

SS

DSi

i

k

+

=

=

1

 

2

M

,

'

1

M

8

'62

8

'61

8



3

M

8

'6 

8



+

8

''

a)

2

M

,

'

1

M

8

'6 2

8

'61

8



3

M

8

'6 

8



+

8

''

b)

8

'6 

8

66

8



M

4

5\V']LHOQLNLQDSL FLRZH]EXGRZDQH]WUDQ]\VWRUyZ026)(7ZSRáF]HQLX

GLRGRZ\PD ZWHFKQRORJLL1026E ZWHFKQRORJLL&026

1DU\VSU]HGVWDZLRQRSURVWHSU]\NáDG\XNáDGyZSU]HVXZDQLD

QDSL FLDVWDáHJR

,

'

2

M

1

M

8

*6

a)

b)

,

'

X

2

X

,

8

*6

2

M

8

*6

,

X

,

X

2

8

66

+

8

''

5\V 8NáDG\ SU]HVXZDQLD QDSL FLD VWDáHJR D  ]H (UyGáHP VWDáRSUGRZ\P E

ZWyUQLNRZ\

: XNáDG]LH QD U\VD SR]LRP QDSL FLD Z\MFLRZHJR

u

O

 MHVW

SU]HVXQL W\Z]JO GHPSR]LRPXQDSL FLDZHMFLRZHJR

u

I

RVWDáZDUWRü

2U

GS

NWyU\SU]\LGHQW\F]Q\FKWUDQ]\VWRUDFK0



0



Z\QRVL

background image



u

u

U

I

K W L

U

O

I

GS

D

T

− = −

= −



2

2

'

 

:XNáDG]LHQDU\VESU]HVXQL FLHWRZ\QRVL

U

GS



,QQH W\SRZH UR]ZL]DQLD VWRVRZDQH Z REZRGDFK ]DVLODQLD

XNáDGyZ VFDORQ\FK V SU]\WDF]DQH Z GDOV]\FK UR]G]LDáDFK SU]\

RPDZLDQLXNRQNUHWQ\FKUR]ZL]DXNáDGRZ\FK