17 szumy w ukladach elektronicznyc (2)

background image





6=80<:8.à$'$&+(/(.7521,&=1<&+



'5Ï'à$,52'=$-(6=80Ï:

 8ZDJLZVW SQH

6]XP\ V HIHNWHP  SU]\SDGNRZ\FK IOXNWXDFML HOHNWU\F]Q\FK

SRZVWDMF\FK  ZVNXWHN ]LDUQLVWHM VWUXNWXU\ HOHPHQWyZ EG( áDGXQNyZ

HOHNWU\F]Q\FK%H]áDGQ\UXFKáDGXQNyZSRZRGXMH*HFKZLORZDZDUWRü

SUGX  OXE QDSL FLD IOXNWXXMH  SU]\SDGNRZR ZRNyá UHGQLHM ZDUWRFL

&KDUDNWHULSR]LRPW\FKIOXNWXDFML]DOH*\RGURG]DMXHOHPHQWXVSRVREX

Z\NRQDQLD L ZDUXQNyZ MHJR SUDF\  :\SDGNRZ\ V]XP XNáDGX

HOHNWURQLF]QHJR MHVW Z\QLNLHP VXSHUSR]\FML SRV]F]HJyOQ\FK URG]DMyZ

V]XPyZ SRZVWDMF\FK Z ND*G\P HOHPHQFLH WHJR XNáDGX 1DMZL NV]\

SR]LRP V\JQDáX Z XNáDG]LH  Z\]QDF]DM FKDUDNWHU\VW\NL REZRGX

MHGQDN*HQDMPQLHMV]UR]Uy*QLDOQZDUWRüV\JQDáXGHWHUPLQXMHSR]LRP

V]XPyZ  6NXWNL V]XPyZ XMDZQLDM VL  Z VWRSQLX Z\MFLRZ\P  WRUX

HOHNWURQLF]QHJR QDWRPLDVW (UyGáD V]XPyZ WNZL Z  ZHMFLRZHM

QLVNRV]XPQHM F] FL XNáDGX 3RVW S Z PLQLPDOL]RZDQLX V]XPyZ

HOHPHQWyZ L XNáDGyZ HOHNWURQLF]Q\FK MHVW QLHZLHONL Z SRUyZQDQLX ]

SRVW SHP WHFKQRORJLL Z\WZDU]DQLD  HOHPHQWyZ L XNáDGyZ L MHVW

RJUDQLF]RQ\ VDP QDWXU V]XPyZ 6]XP MHVW V\JQDáHP FDáNRZLFLH

VWRFKDVW\F]Q\P-HVWRQXWZRU]RQ\]HVNáDGRZ\FKF] VWRWOLZRFLRZ\FK

R SU]\SDGNRZHM DPSOLWXG]LH L ID]LH 0R*HP\ ]PLHU]\ü ZDUWRü

VNXWHF]Q V]XPX MHGQDN*H QLH PR*HP\ SU]HZLG]LHü MHJR ZDUWRFL

FKZLORZHM  0R*OLZ\ MHVW RSLV V]XPX SRM FLDPL WHRULL

SUDZGRSRGRELHVWZD 'OD SU]HELHJyZ VWRFKDVW\F]Q\FK RNUHOD VL

JáyZQHSDUDPHWU\

ZDUWRüRF]HNLZDQ ZDUWRüUHGQL



( )

[ ]

( ) ( )

( L W

L W

7

L W S L W GW

7

7

=

→∞

+







 OLP

7









 

ZDULDQFM  NZDGUDWZDUWRFLVNXWHF]QHMVNáDGRZHM]PLHQQHM

( ) ( )

[

]

( ) ( )

[

]

( )

σ

2

2

2

2

2

1

=

=

→∞

+

E i t

i t

T

i t

i t

p i t dt

T

T

T

lim

,

/

/

 

: ]DOH*QRFLDFK  RUD]   V\PEROÄ ´R]QDF]D

XUHGQLHQLH Z F]DVLH D

( )

p i t

,

 MHVW IXQNFM J VWRFL

SUDZGRSRGRELHVWZDUR]NáDGXDPSOLWXG\SU]HELHJX

background image



2PyZLRQHZGDOV]HMF] FLURG]DMHV]XPyZ ]Z\MWNLHPV]XPX

Z\EXFKRZHJR 

PDM

QRUPDOQ\

JDXVVRZVNL 

UR]NáDG

SUDZGRSRGRELHVWZDFKZLORZHMDPSOLWXG\SU]HELHJXV]XPRZHJR

( )

p i t

i

,

exp

=



1

2

2

2

2

σ

π

σ

 

5\V LOXVWUXMH SRM FLH UR]NáDGX SUDZGRSRGRELHVWZD

DPSOLWXG\SU]HELHJXV]XPRZHJR

S ,

,

[

]

S L W

,

>



,



W

L W

5\V5R]NáDGSUDZGRSRGRELHVWZDDPSOLWXG\SU]HELHJXV]XPRZHJR

UHGQLD ZDUWRü IOXNWXDFML SUGX V]XPyZ MHVW UyZQD ]HUX =H

Z]JO GX QD PHFKDQL]P SRZVWDZDQLD V]XPyZ QDMRJyOQLHM PR*QD

SRG]LHOLü V]XP\ QD FLHSOQH UXWRZH VWUXNWXUDOQH QD]\ZDQH UyZQLH*

V]XPDPLPLJRWDQLDOXEW\SX

f

1

Z\EXFKRZHLODZLQRZH

 6]XP\FLHSOQH

6]XP FLHSOQ\ QD]\ZDQ\ UyZQLH* V]XPHP -RKQVRQD SRZVWDMH

ZVNXWHN SU]\SDGNRZ\FK GUJD FLHSOQ\FK QRQLNyZ áDGXQNX Z

SU]HZRGQLNDFK

:WHPSHUDWXU]HSRZ\*HM]HUDEH]Z]JO GQHJRHOHNWURQ\]QDMGXM

VL  Z XVWDZLF]Q\P EH]ZáDGQ\P UXFKX NWyUHJR HQHUJLD ]DOH*\ RG

WHPSHUDWXU\ = ND*G\P HOHNWURQHP SRUXV]D VL  áDGXQHN

e

=

1 59 10

19

,

& ]DWHP SRMDZLD VL  RJURPQD LORü HOHPHQWDUQ\FK

LPSXOVyZ SUGRZ\FK ]ZL]DQ\FK ] UXFKHP SRMHG\QF]\FK áDGXQNyZ

)OXNWXDFMH WHJR SUGX SRZRGXM SRZVWDZDQLH QD NRFyZNDFK

SU]HZRGQLND Uy*QLF\ SRWHQFMDáyZ R ZDUWRFL UHGQLRNZDGUDWRZHM VLá\
HOHNWURPRWRU\F]QHM  e

T

2

  OXE UyZQRZD*QHJR (UyGáD SUGX  i

T

2



RNUHORQ\FK]DOH*QRFL1\TXLVWD

u

k T R f

T

2

4

=

 D

background image



i

k T

R

f

T

2

4

1

=

 E

:SRZ\*V]\FK]DOH*QRFLDFKk MHVWVWDá%ROW]PDQD

1D U\V SU]HGVWDZLRQR VFKHPDW ]DVW SF]\ UH]\VWRUD ]

XZ]JO GQLHQLHP ]DVW SF]HJR (UyGáD V]XPRZHJR QDSL FLRZHJR OXE

SUGRZHJR

u

kTR f

T

=

4

R bezszumny

(

)

a)

b)

bezszumny

R

i

kT f

R

T

=

4

5\V6FKHPDW\]DVW SF]HUH]\VWRUDXZ]JO GQLDMFH(UyGáDV]XPyZFLHSOQ\FK

* VWRüZLGPRZDV]XPXFLHSOQHJRMHVWVWDáDD*GRF] VWRWOLZRFL





>+]@ 6]XPFLHSOQ\MHVW]DWHPÄV]XPHPELDá\P´5H]\VWDQFMD

R

]DZDUWD Z UyZQDQLX   MHVW U]HF]\ZLVW F] FL LPSHGDQFML

]HVSRORQHM HOHPHQWX : WHPSHUDWXU]H SRNRMRZHM  .  J VWRü

ZLGPRZDV]XPyZFLHSOQ\FKUH]\VWRUDN

Z\QRVL

[

]

u

f

V

Hz

T

2

18

2

16 10

∆ = ⋅

 FR R]QDF]D *H QDSL FLH V]XPyZ WHJR

UH]\VWRUDZSDPLH+]PDZDUWRü Q 9  +] 

 6]XP\UXWRZH

6]XP\UXWRZHQD]\ZDQHWH*V]XPDPL6FKRWWN\¶HJR]ZL]DQH

V]DZV]H]SU]HSá\ZHPVNáDGRZHMVWDáHMSUGXSU]H]EDULHU SRWHQFMDáX

6]XP\ WH SRZVWDM Z ]áF]RZ\FK SU]\U]GDFK SyáSU]HZRGQLNRZ\FK

ZVNXWHNIOXNWXDFMLG\IX]ML JáyZQLHQRQLNyZPQLHMV]RFLRZ\FK F]\OL

QLHUHJXODUQHJR SU]HFKRG]HQLD QRQLNyZ SU]H] EDULHU\ SRWHQFMDáX

DFLOHMSU]H]REV]DU\áDGXQNXSU]HVWU]HQQHJRQDVW\NXREV]DUyZSQ

SyáSU]HZRGQLND 3RGREQ\ HIHNW Z\ZRáXMH SU]HMFLH QRQLNyZ SU]H]

VWUHI\JUDQLF]QHPHWDOSyáSU]HZRGQLN EDULHU\6FKRWWN\¶HJR OXEPHWDO

L]RODWRU

3UGSá\QF\SU]H]]áF]H]DZLHUDGZLHVNáDGRZH]NWyU\FKMHGQD

Z\ZRáDQD MHVW SU]H] QRQLNL PQLHMV]RFLRZH JHQHURZDQH FLHSOQLH

ZZDUVWZLH]DSRURZHMQDWRPLDVWGUXJDVNáDGRZD RGJU\ZDMFDJáyZQ

URO  SU]\ SRODU\]DFML Z NLHUXQNX SU]HZRG]HQLD  UHSUH]HQWXMH G\IX]M

QRQLNyZ ZL NV]RFLRZ\FK SU]H] EDULHU  SRWHQFMDáX QD ]áF]X

REQL*RQ QD VNXWHN GRSURZDG]HQLD GR ]áF]D ]HZQ WU]QHJR QDSL FLD

background image



SRODU\]XMFHJR

2ELH VNáDGRZH SUGX Z\ZRáXM  SHáQ\ V]XP UXWRZ\ L FKRü

NLHUXQNLLFKSU]HSá\ZXVUy*QHWRMHGQDNUHGQLRNZDGUDWRZHZDUWRFL

V]XPyZSU]H]QLHZ\WZRU]RQ\FKGRGDMVL 

0R*QD Z\ND]Dü *H MH*HOL SUG 

( )

i t

 ]áR*RQ\ MHVW ] VHULL

SU]\SDGNRZ\FK QLH]DOH*Q\FK LPSXOVyZ R UHGQLHM ZDUWRFL I

Q

  WR

UHGQLRNZDGUDWRZDZDUWRüV]XPyZUXWRZ\FKZ\QRVL

[ ]

i

q I

f A

s

Q

2

2

2

=

 

JG]LH

q

áDGXQHNHOHNWURQX 



& 

I

Q

VNáDGRZDVWDáDSUGX>$@

f

V]HURNRüSDVPD>+]@

=UyZQDQLD  Z\QLND*HUHGQLRNZDGUDWRZDZDUWRüSUGX

V]XPyZ UXWRZ\FK MHVW ZSURVW SURSRUFMRQDOQD GR V]HURNRFL SDVPD

f

F] VWRWOLZRFLSRPLDUX

:\QLND VWG *H J VWRü ZLGPRZD PRF\ JHQHUDWRUD SUGRZHJR

V]XPyZ

i

f

q I

s

Q

2

2

=

  MHVW VWDáD Z IXQNFML F] VWRWOLZRFL F]\OL V]XP

WHJR W\SX MHVW V]XPHP ELDá\P  6WDáD J VWRü ZLGPRZD Z\VW SXMH Z

SU]HG]LDOH F] VWRWOLZRFL ]QDF]QLH PQLHMV]\FK RG 

1

τ

 F]\OL RG

F] VWRWOLZRFL Z\QLNDMFHM ] F]DVX SU]HORWX QRQLNyZ 

τ

 SU]H]

ZDUVWZ  ]XER*RQ ]áF]D VWDQRZLF MHG\QH PLHMVFH RGG]LDá\ZDQLD

SROD]HZQ WU]QHJRQDQRQLNLDNW\ZQH

 6]XP\VWUXNWXUDOQH V]XP\

f

1

OXEV]XP\PLJRWDQLD

7HUPLQHP W\P RNUHOD VL  VNáDGRZ V]XPyZ GRPLQXMF Z

]DNUHVLH PDá\FK F] VWRWOLZRFL R J VWRFL ZLGPRZHM PRF\
SURSRUFMRQDOQHM GR 1 f

b

 ]Z\NOH 

b

1

  VWG LFK QD]ZD  6]XP WHQ

Z\VW SXMH ]DUyZQR Z SU]\U]GDFK SyáSU]HZRGQLNRZ\FK MDN WH* L Z

HOHPHQWDFK ELHUQ\FK 3RZVWDZDQLH V]XPX

f

1

 PR*QD SU]\SLVDü Z

GHF\GXMF\P VWRSQLX HIHNWRP SRZLHU]FKQLRZ\P D JáyZQLH SURFHVRP

SXáDSNRZDQLDVZRERGQ\FKQRQLNyZ]ZL]DQ\FK]SRZROQ\PLVWDQDPL

SRZLHU]FKQLRZ\PL  3HZLHQ ZNáDG Z V]XP\

f

1

 GDM FHQWUD

JHQHUDF\MQR  UHNRPELQDF\MQH ]QDMGXMFH VL  Z REV]DU]H ]XER*RQ\P

SyáSU]HZRGQLND  : HOHPHQWDFK HOHNWURQLF]Q\FK V]XP

f

1

 PR*H

Z\VW SRZDüMHG\QLHZZDUXQNDFKLFKSRODU\]DFML

background image



UHGQLRNZDGUDWRZ  ZDUWRü SUGX V]XPyZ

f

1

 Z SDPLH

f

RNUHOD]DOH*QRü

i

K

I

f

f

f

Q

a

b

2

1

=

 

JG]LH

I

Q

VNáDGRZDVWDáDSUGX

K

1

VWDáDGODGDQHJRSU]\U]GXSyáSU]HZRGQLNRZHJR PR*HE\üUy*QD

QDZHWGODWUDQ]\VWRUyZWHJRVDPHJRW\SX 

a

VWDáDZSU]HG]LDOHGR

b

VWDáDUyZQDSUDZLHMHGQRFL

 * VWRü ZLGPRZ V]XPyZ I SU]HGVWDZLRQR QD U\V

&KRFLD* J VWRü ZLGPRZD PRF\ V]XPyZ I MHVW QDMZL NV]D SU]\

PDá\FKF] VWRWOLZRFLDFKWRMHGQDNZSU]\U]GDFKZ\ND]XMF\FKGX*\

SR]LRPW\FKV]XPyZPRJRQHE\üGRPLQXMF\PVNáDGQLNLHPV]XPyZ

ZSDVPLHRGPDá\FKF] VWRWOLZRFLD*GR]DNUHVX0+]

skala log

skala log

i

f

f

2

1

f

f

5\V* VWRüZLGPRZD

V]XPyZ I

 6]XP\Z\EXFKRZH

7HQ W\S QLVNRF] VWRWOLZRFLRZ\FK V]XPyZ PD V]F]HJyOQH

]QDF]HQLH Z XNáDGDFK VFDORQ\FK  JáyZQLH ZH Z]PDFQLDF]DFK

RSHUDF\MQ\FK DOHZ\VW SXMHUyZQLH*ZXNáDGDFKG\VNUHWQ\FK

t

Amplituda szumów

f

s k a l a

log

f

c

1

f

i

f

w

2

b)

a)

5\V D  7\SRZ\ RVF\ORJUDP V]XPyZ Z\EXFKRZ\FK E  J VWRü ZLGPRZD

V]XPyZZ\EXFKRZ\FK

background image



0HFKDQL]PLFKSRZVWDZDQLDQLHMHVWZSHáQLZ\MDQLRQ\DOHZL*HVL

RQ]REHFQRFL]DQLHF]\V]F]HZSRVWDFLMRQyZFL *NLFKPHWDOL

1D]ZD ÄV]XP Z\EXFKRZ\´ Z\ZRG]L VL  VWG *H REVHUZRZDQ\ QD

RVF\ORVNRSLHSU]HELHJV]XPRZ\PDNV]WDáWQLHVWDFMRQDUQ\FK IOXNWXDFML

W\SXLPSXOVRZHJRSRMDZLDMF\FKVL FRSHZLHQF]DV

&] VWRWOLZRüLPSXOVyZV]XPXZ\EXFKRZHJRPLHFLVL Z

SDPLHF] VWRWOLZRFLDNXVW\F]Q\FKDMHJRJ VWRüZLGPRZDPR*HE\ü

RSLVDQD]DOH*QRFL

i

K

I

f

f

f

w

Q

c

c

2

2

2

1

=

+



 

JG]LH

K

2

VWDáDFKDUDNWHU\VW\F]QDGODGDQHJRSU]\U]GX

I

Q

VNáDGRZDVWDáDSUGXSRODU\]DFML

c

VWDáDZJUDQLFDFKGR

f

c

F] VWRWOLZRü FKDUDNWHU\VW\F]QD ]DOH*QD RG PHFKDQL]PX

SRZVWDZDQLDV]XPyZ

 6]XP\ODZLQRZH

3RZVWDZDQLH V]XPyZ ODZLQRZ\FK ZL*H VL  ] SU]HFKRG]HQLHP

QRQLNyZSU]H]]áF]DSQVSRODU\]RZDQH]DSRURZR:W\PSU]\SDGNX

]DSRURZHQDSL FLHSRODU\]DFMLPXVLE\üMHGQDNQDW\OHGX*HDE\ SROH

HOHNWU\F]QH Z ZDUVWZLH ]DSRURZHM  ]DSHZQLDáR QRQLNRP SU]\

]GHU]HQLX HQHUJL  Z\VWDUF]DMF  GOD ODZLQRZHJR XZROQLHQLD SDU\

HOHNWURQG]LXUD.D*GH]GHU]HQLHZ\WZDU]DLPSXOVSUGRZ\q /

τ

SU]\

F]\P

τ

 MHVW UHGQLP F]DVHP SRPL G]\ ]GHU]HQLDPL 6]XP ]MDZLVND

ODZLQRZHJRPR*HE\üRSLVDQ\]DSRPRFPRGHOX+LQHVDSU]\SRPRF\

NWyUHJRRNUHODVL J VWRüZLGPRZWDNLHJRV]XPX

(

)

i

q I

f

z

2

2

2

2

=

π τ

 

I

R]QDF]DUHGQLZDUWRüSUGX]áF]DVSRODU\]RZDQHJR]DSRURZR

3U]\MPXMHVL *HUR]NáDGZDUWRFLFKZLORZ\FKSU]HELHJyZV]XPX

ODZLQRZHJRMHVWQRUPDOQ\

background image





6=802:(02'(/(35=<5='Ï:3Ïà35=(:2'1,

.2:<&+

'LRGDSyáSU]HZRGQLNRZD

6]XPRZ\ VFKHPDW ]DVW SF]\ GLRG\ SyáSU]HZRGQLNRZHM MHVW

SRND]DQ\QDU\V

T

K

=

0

i

2

U

6

X

V



T

K

=

0

U

N7

T,

G

'

=

i

D

U

G

5\V6]XPRZ\VFKHPDW]DVW SF]\

GLRG\SyáSU]HZRGQLNRZHM

3U]\ SRODU\]DFML Z NLHUXQNX SU]HZRG]HQLD PDáRV\JQDáRZ\

VFKHPDW ]DVW SF]\ GLRG\ ]DZLHUD UH]\VWDQFM  Uy*QLF]NRZ 

r

d

 L

UH]\VWDQFM  V]HUHJRZ 

r

S

 3RQLHZD*

U

6

 MHVW UH]\VWDQFM IL]\F]Q

GODWHJRQDOH*\GRáF]\üGRQLHM(UyGáRQDSL FLRZHV]XPyZWHUPLF]Q\FK

5yZQROHJOH GR 

r

d

  QDOH*\ GRáF]\ü (UyGáR SUGRZH UHSUH]HQWXMFH

V]XP\UXWRZHLV]XP\

f

1



u

k T r

f

s

s

2

4

=

 

i

q I

f

K

I

f

f

D

D

a

2

2

=

+

 

5H]\VWDQFMH

r

S

L

r

d

ZVFKHPDFLH]DVW SF]\PVEH]V]XPQH

 7UDQ]\VWRUELSRODUQ\

6]XPRZ\ PRGHO WUDQ]\VWRUD ELSRODUQHJR Z MHJR DNW\ZQ\P

REV]DU]H SUDF\ WZRU]\ VL  Z WHQ VSRVyE *H GR VFKHPDWX ]DVW SF]HJR

K\EU\G

π

  GRáF]DP\ V\PEROLF]QH (UyGáD V]XPyZ UHSUH]HQWXMFH

RGSRZLHGQLHSURFHV\IL]\F]QHJHQHUXMFHV]XP\ U\V 

6]XP\ FLHSOQH Z WUDQ]\VWRUDFK V Z\WZDU]DQH SU]H] IL]\F]QH

UH]\VWDQFMHUR]SURV]RQHREV]DUyZHPLWHUDED]\LNROHNWRUD3UDNW\F]QLH

XZ]JO GQLDVL MHG\QLHV]XP\FLHSOQHREV]DUXED]\

r

bb'

u

k T r

f

b

bb

2

4

=

'

 

background image



r

b e

'

U

b e

'

g U

m

b e

'

&

MF

r

ce

B

'

C

i

c

2

i

b

2

u

b

2

r

bb'

E

B

&

H

5\V6]XPRZ\PRGHOWUDQ]\VWRUDELSRODUQHJR

1RQLNLSUGXZVWU]\NLZDQHSU]H]HPLWHUGRED]\JG]LHVWDM VL

QRQLNDPL PQLHMV]RFLRZ\PL G\IXQGXM Z NLHUXQNX ]áF]D

NROHNWRURZHJRJG]LHVSU]\VSLHV]DQHSU]H]SROHHOHNWU\F]QHZDUVWZ\

]XER*RQHMZNLHUXQNXNROHNWRUD1LHUHJXODUQHSU]HFKRG]HQLHQR QLNyZ

SU]H] REV]DU áDGXQNX SU]HVWU]HQQHJR  ]áF]D NROHNWRURZHJR GDMH Z

HIHNFLHV]XPUXWRZ\

i

q I

f

c

C

2

2

=

 

3RZVWDZDQLH V]XPX UXWRZHJR i

b

2

 ]ZL]DQH MHVW ] SU]HSá\ZHP

SRV]F]HJyOQ\FK VNáDGRZ\FK SUGX ED]\ : ]áF]X ED]D  HPLWHU

SRZVWDMH UyZQLH* V]XP

f

1

 RUD] V]XP Z\EXFKRZ\ FR ZL*H VL

JáyZQLH]H]MDZLVNDPLSRZLHU]FKQLRZ\PLL]H]MDZLVNLHPUHNRPELQDFML

ZREM WRFLED]\:\SDGNRZ\V]XPUHSUH]HQWRZDQ\MHVWSU]H]SU GRZH

(UyGáRV]XPyZ

i

q I

f

K

I

f

f

K

I

f

f

f

b

B

B

a

B

c

c

2

1

2

2

2

1

=

+

+

+



szum rutowy szum 1 / f szum wybuchowy



 

:\SDGNRZ J VWRü V]XPyZ  i

b

2

 RNUHORQ QD SRGVWDZLH

UyZQDQLD  SU]HGVWDZLRQRQDU\V

f

skala log

f

a

i

f

b

2

skala log

2qI

B

K

I

f

B

a

1

5\V* VWRüZLGPRZD

V]XPyZSUGXED]\

background image



 7UDQ]\VWRUXQLSRODUQ\-)(7

:G]LDáDQLXWUDQ]\VWRUyZXQLSRODUQ\FKELHU]HXG]LDáW\ONRMHGHQ

URG]DM QRQLNyZ VWG PQLHMV]D UROD ]MDZLVN ]ZL]DQ\FK ]

UHNRPELQDFMD]DWHPPQLHMV]DURODV]XPyZUXWRZ\FK=WHJRSRZRGX

GRPLQXMV]XP\FLHSOQHRUD]V]XP\

f

1



6]XPRZ\ VFKHPDW ]DVW SF]\ WUDQ]\VWRUD  -)(7 MHVW SRND]DQ\ QD

U\V

C

gs

U

gs

g U

m

gs

C

gd

r

ds

D

i

d

2

i

g

2

S

G

C

gb

5\V6]XPRZ\PRGHOWUDQ]\VWRUD-)(7

=SUGHPXSá\ZQRFLEUDPNL]ZL]DQ\MHVWV]XPUXWRZ\

i

q I

f

g

G

2

2

=

 

6]XP WHQ PD SUDNW\F]QH ]QDF]HQLH W\ONR Z SU]\SDGNX JG\

UH]\VWDQFMD(UyGáDVWHUXMFHJRMHVWGX*D

*HQHUDWRU  i

d

2

  UHSUH]HQWXMH V]XP\ WHUPLF]QH SU]HZRG]FHJR

NDQDáX RUD] V]XP\

f

1

 NWyUH SRZVWDM JáyZQLH Z Z\QLNX SHZQ\FK

]MDZLVNSRZLHU]FKQLRZ\FKRUD]ZVNXWHNIOXNWXDFMLáDGXQNXZFHQWUDFK

JHQHUDF\MQRUHNRPELQDF\MQ\FKZDUVWZ\]XER*RQHM

i

k T

g

f

K

I

f

f

d

m

D

2

1

2

4

2

3

=





+

szum termiczny szum 1 / f



 

 7UDQ]\VWRUXQLSRODUQ\026)(7

6]XPRZ\VFKHPDW]DVW SF]\WUDQ]\VWRUD026)(7PR*HE\üWDNL

VDPMDNWUDQ]\VWRUD-)(7SU]\LORFLRZ\FKPRG\ILNDFMDFKJHQHUDWRUyZ

V]XPRZ\FK  6]XP\ FLHSOQH Z WUDQ]\VWRUDFK 026)(7 V  UyZQLH*

]ZL]DQH ] NRQGXNWDQFM SU]HZRG]FHJR NDQDáX 6]XP\

f

1

 V

]GHWHUPLQRZDQH JáyZQLH SU]H] ]MDZLVND SRZLHU]FKQLRZH NWyUH

VWDQRZL UyZQRF]HQLH SRGVWDZ  G]LDáDQLD W\FK SU]\U]GyZ

7UDQ]\VWRU\026PDMOHSV]HZáDFLZRFLV]XPRZHZ]DNUHVLHZF]

background image



QL*WUDQ]\VWRU\-)(7FKRFLD*PDM]QDF]QLHZ\*V]\SR]LRPV]XPyZ

Z]DNUHVLHPDá\FKF] VWRWOLZRFL* VWRüZLGPRZDV]XPyZFLHSOQ\FK

SU]HZRG]FHJR NDQDáX WUDQ]\VWRUD  026)(7  PR*H E\ü RNUHORQD

]DOH*QRFL

S

obszar liniowy

obszar nasycenia

IT

=







4 k T

R

4 k T

2

3

g

FET

m

 

JG]LH

R

FET

  MHVW HNZLZDOHQWQ UH]\VWDQFM SU]HZRG]FHJR WUDQ]\VWRUD

ZREV]DU]HOLQLRZ\P

g

m

  PDáRV\JQDáRZD WUDQVNRQGXNWDQFMD WUDQ]\VWRUD Z REV]DU]H

QDV\FHQLD
'ODWHPSHUDWXU\.

8

3

1 1 10

20

k T

=

,

V A sec

⋅ ⋅

* VWRü ZLGPRZD V]XPyZ  VWUXNWXUDOQ\FK I  ]DUyZQR GOD REV]DUX

OLQLRZHJRMDNLQDV\FHQLDZ\QRVL

S

K K I

C

L f

If

f

D

x

=

2

0

2

'

 

SU]\F]\P

K

f

ZVSyáF]\QQLNV]XPyZPLJRWDQLDW\SRZR K

V F

f

= ⋅

3 10

24

2



I

D

SUGGUHQXZVSRF]\QNRZ\PSXQNFLHSUDF\WUDQ]\VWRUD

C

ox

SRMHPQRüEUDPNDNDQDáQDMHGQRVWN SRZLHU]FKQL

K'

SDUDPHWUWUDQVNRQGXNWDQFML

L



:

GáXJRüLV]HURNRüNDQDáX



6802:$1,('5Ï'(à6=802:<&+

=DVW SF]H (UyGáD V]XPyZ ]DZLHUDM ZLHON OLF]E  VNáDGRZ\FK

VLQXVRLGDOQ\FK R Uy*Q\FK F] VWRWOLZRFLDFK  RUD] SU]\SDGNRZHM

DPSOLWXG]LH L ID]LH *G\ SRáF]\P\ V]HUHJRZR GZD QLH]DOH*QH (UyGáD

V]XPyZ U\V WRPRFZ\MFLRZDMHVWVXPQLHVNRUHORZDQ\FKPRF\

Z\MFLRZ\FKRGSRV]F]HJyOQ\FKVNáDGRZ\FKFRSR]ZDODQDZ\UD *HQLH

Z\SDGNRZHMZDUWRFLUHGQLRNZDGUDWRZHMQDSL FLDV]XPyZMDNRVXP\

UHGQLFK NZDGUDWyZ QDSL ü NROHMQ\FK VNáDGRZ\FK 3RZ\*V]H

VWZLHUG]HQLH MHVW ZD*QH UyZQLH* GOD SUGRZ\FK (UyGHá V]XPyZ

SRáF]RQ\FKUyZQROHJOH

background image



R

2

u

1

2

R

1

u

2

2

u

T

2

5\V6XPRZDQLHQLH]DOH*Q\FK(UyGHá

V]XPRZ\FK

5R]ZD*P\ SU]\NáDGRZR WHUPLF]QH QDSL FLH V]XPyZ UH]\VWRUyZ

1

R

L

2

R

SRáF]RQ\FKV]HUHJRZRMDNQDU\V

u

k T R

f

1

2

1

4

=

 

u

k T R

f

2

2

2

4

=

 

UHGQLRNZDGUDWRZD ZDUWRü QDSL FLD V]XPyZ R FKZLORZHM ZDUWRFL

]DVW SF]HM

( )

( )

( )

u t

u t

u t

T

=

+

1

2

 

Z\QRVL

( )

( ) ( )

[

]

( )

( )

( ) ( )

0

2

2

1

2

2

2

1

2

2

1

2

t

u

t

u

t

u

t

u

t

u

t

u

t

u

T

+

+

=

+

=

3RQLHZD* V]XP\ SRFKRG] ] Uy*Q\FK UH]\VWRUyZ V RQH ]DWHP
QLHVNRUHORZDQHLUHGQLDZDUWRü

( ) ( )

u t u t

1

2

PXVLE\üUyZQD]HUX

=DWHP

u

u

u

T

2

1

2

2

2

=

+

 

3RGVWDZLDMF  L  GR  RWU]\PXMHP\

(

)

u

k T R

R

f

T

2

1

2

4

=

+

 

: SU]\SDGNX JG\ F] ü V]XPyZ Z REX (UyGáDFK SRFKRG]L RG

SURFHVyZ IL]\F]Q\FK ]ZL]DQ\FK ]H VRE WR Z\SDGNRZD

UHGQLRNZDGUDWRZDZDUWRüQDSL FLDV]XPyZF] FLRZRVNRUHORZDQ\FK

Z\QRVL

u

u

u

C u u

T

r

2

1

2

2

2

1

2

2

=

+

+

 

JG]LH

C

r

R]QDF]D ZVSyáF]\QQLN NRUHODFML L PR*H SU]\ELHUDü ZDUWRü ]

SU]HG]LDáX

[

]

− +

1 1

;



background image





&$à.2:,7<  6=80  =$67 3&=<  2'1,(6,21<  '2

:(-&,$:=0$&1,$&=$

 =DVW SF]H(UyGáDV]XPyZRGQLHVLRQHGRZHMFLD

Z]PDFQLDF]D

'ODGRZROQHJRF]ZyUQLNDLVWQLHMHXQLZHUVDOQ\VFKHPDW]DVW SF]\

V]XPyZSU]HGVWDZLRQ\QDU\V

i

i

2

u

i

2

5

J

6LHü

EH]V]XPQD

5

J

6LHü

] V]XPDPL

5\V=DVW SF]H(UyGáDV]XPyZRGQLHVLRQHGRZHMFLDF]ZyUQLND

0R*QDZ\ND]DüNRQLHF]QRüX*\FLDGZyFK(UyGHá]DVW SF]\FKQD

ZHMFLX Z]PDFQLDF]D  SUGRZHJR L QDSL FLRZHJR NWyUH UHSUH]HQWXM

VRE ZV]\VWNLH PR*OLZH ZNáDG\ V]XPRZH SRFKRG]FH RG HOHPHQWyZ

F]ZyUQLNDDQDOL]XMF]DFKRZDQLHVL XNáDGXGODJUDQLF]Q\FKZDUWRFL
UH]\VWDQFML R

g

 *G\  R

g

=

0

 (UyGáR i

i

2

 QD U\V MHVW ]ZDUWH L GOD

UHSUH]HQWDFML V]XPyZ QD Z\MFLX XNáDGX QDOH*\ ]DVWRVRZDü (UyGáR
QDSL FLRZH u

i

2



3RGREQLH JG\ R

g

= ∞

 (UyGáR QDSL FLRZH u

i

2

  QLH Z\WZDU]D

V]XPyZ QD Z\MFLX XNáDGX L GOD LFK UHSUH]HQWDFML QD ZHMFLX QDOH*\
]DVWRVRZDüSUGRZH(UyGáRV]XPyZi

i

2



 =DVW SF]H(UyGáDV]XPyZWUDQ]\VWRUDELSRODUQHJR

=DVW SF]H (UyGáD V]XPyZ QD ZHMFLX WUDQ]\VWRUD ELSRODUQHJR

PR*HP\ Z\]QDF]\ü QD SRGVWDZLH MHJR V]XPRZHJR VFKHPDWX

]DVW SF]HJR SU]HGVWDZLRQHJR QD U\VD 6]XP\ REZRGX

Z\MFLRZHJR V DQDOL]RZDQH SU]\ ]ZDUW\P REFL*HQLX L SRPLQL FLX

SRMHPQRFL

jc

C



8NáDG]DVW SF]\]U\VEUHSUH]HQWXMHV]XP\WUDQ]\VWRUD Z

SRVWDFLUyZQRZD*Q\FKJHQHUDWRUyZV]XPyZQDZHMFLXGDMFWHVDPH

V]XP\ QD Z\MFLX SU]\ GRZROQHM LPSHGDQFML (UyGáD VWHUXMFHJR

=ZLHUDMF ZHMFLD REX XNáDGyZ ]DVW SF]\FK U\V  Z\]QDF]\P\

background image



ZDUWRü]DVW SF]HJR(UyGáDQDSL FLRZHJRV]XPyZ u

i

2



r

b e

'

U

b e

'

g U

m

b e

'

&

H

r

ce

i

c

2

i

b

2

X

EE

2

U

EE

L

R

r

b e

'

U

b e

'

g U

m

b e

'

&

H

r

ce

L

L

2

X

L

2

U

EE

L

R

a)

b)

5\V D  6]XPRZ\ VFKHPDW ]DVW SF]\ WUDQ]\VWRUD ELSRODUQHJR E  XNáDG

UyZQRZD*Q\]]DVW SF]\PL(UyGáDPLV]XPRZ\PLQD]DFLVNDFKZHMFLRZ\FK

3U]\MPXMHP\ *H SRV]F]HJyOQH (UyGáD V]XPyZ V ]H VRE

QLHVNRUHORZDQH RUD] SRPLMDP\ LFK ]QDNL SRQLHZD * V WR V\JQDá\

VWRFKDVW\F]QH=DNáDGDMF

r

r

bb

b e

<<

'

RWU]\PXMHP\

g u

i

g u

m

bb

c

m

i

+ =

 

VWG

u u

i

g

i

bb

c

m

=

+

 

RUD]

u

u

i

g

i

bb

c

m

2

2

2

2

=

+

 

3RGVWDZLDMF]DOH*QRFL  L  GRUyZQDQLD 

RWU]\PXMHP\

u

k T r

f

q I

f

g

i

bb

C

m

2

2

4

2

=

+

 

3RQLHZD* g

I

q I

k T

m

C

T

C

=

=

ϕ

WR]UyZQDQLD  RWU]\PXMHP\

u

f

k T r

g

i

bb

m

2

4

1

2

=

+



 

* VWRüZLGPRZ]DVW SF]HJR(UyGáDSUGRZHJRV]XPyZ i

f

i

2

Z\]QDF]D VL  SU]\ UR]ZDUFLX ZHMü REX XNáDGyZ ]DVW SF]\FK

background image



U\V 3RUyZQXMF]HVRESUG\Z\MFLRZHRWU]\PXMHP\

( )

( )

β

ω

β

ω

j

i

i

j

i

i

c

b

= +

 

VWG

( )

i

i

i

j

i

b

c

= +

β ω

 

=DNáDGDMF *H (UyGáD V]XPyZ 

i

b

 RUD] 

i

c

 V QLHVNRUHORZDQH

RWU]\PXMHP\

( )

i

i

i

j

i

b

c

2

2

2

2

= +

β ω

 

JG]LH

( )

β ω

β

ω

ω

β

j

j

=

+

0

1

 

3RGVWDZLDMF]DOH*QRFL  L  GRUyZQDQLD 

RWU]\PXMHP\

( )

i

f

q I

K

I

f

I

j

i

B

B

a

C

2

1

2

2

=

+

+

'

β ω

 

JG]LH

K

K

q

1

1

2

'

=

 

'ODXSURV]F]HQLDSRPLQL WRV]XP\Z\EXFKRZH

8Z]JO GQLDMF QD ZHMFLX UH]\VWDQFM  (UyGáD VWHUXMFHJR L ]ZL]DQH ]

QLV]XP\WHUPLF]QHOLF]E ]DVW SF]\FK(UyGHáV]XPRZ\FKQDZHMFLX

Z]PDFQLDF]D ]UHGXNRZDQR GR WU]HFK G]L NL ]DVWRVRZDQLX (UyGHá

i

u

i

i

2

2

oraz

 U\VD SU]\F]\PWUDQ]\VWRU7PR*HE\üXZD*DQ\]D

EH]V]XPQ\

L

L

2

X

L

2

a)

X

J

2

5

J

7

5

/W

X

L1

2

b)

5

J

7

5

/W

5\V D  =DVW SF]H (UyGáD V]XPRZH RGQLHVLRQH GR ZHMFLD Z]PDFQLDF]D E

FDáNRZLWH]DVW SF]H(UyGáRV]XPRZHQDZHMFLXZ]PDFQLDF]D

background image



-DNSRND]DQRQDU\VE]DVW SF]H(UyGáRV]XPyZQDZHMFLX

u

iN

2

UHSUH]HQWXMHVXPDU\F]Q\ZSá\ZZV]\VWNLFKWU]HFK (UyGHáV]XPyZ

Z PLHMVFX Z NWyU\P XPLHV]F]RQH MHVW (UyGáR V\JQDáX ']L NL WHPX

RNUHOHQLHVWRVXQNX

N

S

 V\JQDáV]XP MHVWEDUG]RXáDWZLRQH

=DNáDGDMF *H VNáDGRZH (UyGáD V]XPyZ V QLHVNRUHORZDQH

RWU]\PXMHP\

u

u

u

i R

iN

g

i

i

g

=

+ +

 

u

u

u

i R

iN

g

i

i

g

2

2

2

2

2

=

+

+

 

:\NRU]\VWXMFUyZQDQLD    RUD]  RWU]\PXMHP\

( )

u

f

k T R

k T r

g

R

q I

I

j

iN

g

bb

m

g

B

C

2

2

2

4

4

1

2

2

=

+

+



 +

+

β ω

 

5yZQDQLH  MHVWVáXV]QHSU]\PDá\FKZDUWR FLDFK

r

bb



 =DVW SF]H(UyGáDV]XPyZWUDQ]\VWRUyZSRORZ\FK

=DVW SF]H (UyGáD V]XPyZ QD ZHMFLX WUDQ]\VWRUD SRORZHJR

Z\]QDF]\P\ Z SRGREQ\ VSRVyE MDN WR XF]\QLRQR GOD WUDQ]\VWRUD

ELSRODUQHJR  1D U\VD SU]HGVWDZLRQR V]XPRZ\  VFKHPDW

]DVW SF]\ WUDQ]\VWRUD -)(7 D QD U\VXQNX E MHJR UyZQRZD *Q\

XNáDG]]DVW SF]\PL(UyGáDPLV]XPRZ\PLQD]DFLVNDFKZHMFLRZ\FK

$QDOL]D ]RVWDQLH SU]HSURZDG]RQD SU]\ ]ZDUW\P Z\M FLX

LSRPLQL FLX SRMHPQRFL  C

gd

 3U]\ ]ZDUW\P ZHMFLX REX XNáDGyZ

SRUyZQXMFSUG\

L

R

RWU]\PXMHP\

i

g u

d

m i

=

 

6WG

u

i

g

i

d

m

2

2

2

=

 

3RGVWDZLDMF  GR  RWU]\PXMHP\

u

f

k T

g

K

I

g f

i

m

D

m

2

1

2

2

4

2

3

1

=

+

 

background image



8

JV

J 8

P

JV

&

JV

U

GV

L

G

2

L

J

2

L

R

8

JV

J 8

P

JV

&

JV

U

GV

L

L

2

X

L

2

L

R

a)

b)

'

6

*

5\VD 6]XPRZ\VFKHPDW]DVW SF]\WUDQ]\VWRUD-)(7E XNáDGUyZQRZD*Q\]

]DVW SF]\PL(UyGáDPLV]XPRZ\PLQDZHMFLX

1D U\V SU]HGVWDZLRQR ]DOH*QRü J VWRFL ZLGPRZHM

QDSL FLD V]XPyZ ]DVW SF]HJR (UyGáD ZHMFLRZHJR  u

f

i

2

  Z IXQNFML

F] VWRWOLZRFL

f

1

 I

10

5

10

6

10

7

10

8

+]

10

4

10

3

10

2

10

10

18

10

17

10

16

10

15

10

14

9 +]

2

X

I

L

2

5\V* VWRüZLGPRZDQDSL FLDV]XPyZ]DVW SF]HJR(UyGáDZHMFLRZHJR

X

I

L



GODWUDQ]\VWRUD-)(7

: SU]HFLZLHVWZLH GR WUDQ]\VWRUD ELSRODUQHJR ]DVW SF]\

JHQHUDWRUQDSL FLRZ\V]XPyZWUDQ]\VWRUD-)(7RGQLHVLRQ\GRZHM FLD

XNáDGX ]DZLHUD VNáDGRZ V]XPX PLJRWDQLD 

f

1

 UR]FLJDMF VL  Z

QLHW\SRZ\VSRVyED*GR]DNUHVXF] VWRWOLZRFLU] GX0+]

6]XP\ PLJRWDQLD PDM V]F]HJyOQH ]QDF]HQLH Z WUDQ]\VWRUDFK

026)(7NWyUHZL*VL ]HQHUJHW\F]Q\PLVWDQDPLSRZLHU]FKQLRZ\PL

QD JUDQLF\  6L  6L2



 : WUDQ]\VWRUDFK  026 GOD F] VWRWOLZRFL

PQLHMV]\FK RG  GR  N+] V]XP\ PLJRWDQLD V ZL NV]H RG V]XPyZ

WHUPLF]Q\FK QDMF] FLHM QLH]DOH*QLH RG SUGyZ SRODU\]XMF\FK

LJHRPHWULLWUDQ]\VWRUyZ

: ZL NV]RFL SU]\SDGNyZ DPSOLWXGD ]DVW SF]HJR (UyGáD

QDSL FLRZHJRV]XPyZWUDQ]\VWRUD026MHVWRGZURWQLHSURSRUFMRQDOQD

background image



GR MHJR DNW\ZQHM SRZLHU]FKQL EUDPNL *G\ SRZLHU]FKQLD EUDPNL MHVW

GX*D ZL NV]Rü GHIHNWyZ SRZLHU]FKQLRZ\FK L ]ZL]DQ\FK ] QLPL

HQHUJHW\F]Q\FK VWDQyZ SRZLHU]FKQLRZ\FK ]QDMGXMH VL  SRG EUDPN

SRZRGXMFRJyOQH]PQLHMV]HQLHV]XPyZ

* VWRü ZLGPRZD ]DVW SF]HJR (UyGáD V]XPyZ RGQLHVLRQHJR GR

ZHMFLDWUDQ]\VWRUD026PR*HE\üRSLVDQD]DOH*QRFL

u

f

k T

g

K

W L C

f

i

m

f

x

2

0

4

2

3

1

=



 +

 

* VWRü ZLGPRZ ]DVW SF]HJR (UyGáD SUGRZHJR V]XPyZ

Z\]QDF]DP\SU]\UR]ZDUFLXZHMüREXXNáDGyZ]DVW SF]\FK U\V 

3RUyZQXMF VNXWHF]QH ZDUWRFL Z\MFLRZ\FK SUGyZ V]XPyZ

i

o

 REX

XNáDGyZRWU]\PXMHP\

i

g

j

C

i

g

j

C

i

i

m

gs

g

m

gs

d

ω

ω

=

+

 

6WG

i

i

j

C

g

i

i

g

gs

m

d

=

+

ω

 

3RQLHZD*  i

g

  RUD] 

i

d

 V QLH]DOH*QH  WR ] UyZQDQLD 

RWU]\PXMHP\

i

i

C

g

i

i

g

gs

m

d

2

2

2

2

2

2

= +

ω

 

3RGVWDZLDMF]DOH*QRFL  L  GR  RWU]\PXMHP\

i

f

q I

C

g

k T

g

K

I

f

i

G

gs

m

m

D

2

2

2

2

1

2

2

4

2

3

=

+



 +



ω

 

:UyZQDQLX  ZLHONRü

K

g

C

i

m

gs

=

ω

  

R]QDF]D Z]PRFQLHQLH  SUGRZH 6WG V]XP\ JHQHURZDQH QD Z\MFLX
SU]HQRV]RQHVQDZHMFLH]HZVSyáF]\QQLNLHP1

2

K

i



: ]DNUHVLH PDá\FK F] VWRWOLZRFL ]DVW SF]H (UyGáR SUGRZH V]XPyZ

MHVWGHWHUPLQRZDQHSU]H]SUGXSá\ZQRFLEUDPNL

I

G

NWyU\MHVWEDUG]R

PDá\

I

G

 



 $   : WUDQ]\VWRUDFK SRORZ\FK  026)(7 VNáDGRZD

V]XPyZ GHWHUPLQRZDQD SU]H] SUG XSá\ZQRFL EUDPNL  2q I

G

 MHVW

background image



SRPLMDOQLHPDáD :SU]\SDGNX(UyGáDVWHUXMFHJRRGX*HMLPSHGDQFML

JG\ ZRJyOQ\P ELODQVLH FDáNRZLWHJR ]DVW SF]HJR V]XPX ZHMFLRZHJR

GRPLQXMF URO  RGJU\ZD (UyGáR SUGRZH WUDQ]\VWRU\  -)(7

]DSHZQLDM PQLHMV]\ SR]LRP V]XPyZ QD Z\MFLX QL* WUDQ]\VWRU\

ELSRODUQH 3URSRUFMH WH PRJ E\ü F]DVDPL RGZUyFRQH QD NRU]\ü

WUDQ]\VWRUyZ ELSRODUQ\FK Z SU]\SDGNX  (UyGáD VWHUXMFHJR R PDáHM

LPSHGDQFML JG\ Z ELODQVLH  ]DVW SF]HJR V]XPX ZHMFLRZHJR

GRPLQXMFURO RGJU\ZD(UyGáRQDSL FLRZH']LHMHVL WDNGODWHJR*H

GOD GDQHJR SUGX SRODU\]DFML WUDQ]\VWRU\ ELSRODUQH PDM ZL NV]

ZDUWRüWUDQVNRQGXNWDQFML

g

m





:3à<:  635= )(1,$  =:5271(*2  1$  3$5$0(75<

6=802:(:=0$&1,$&=$

6WRVRZDQLH GZyFK ]DVW SF]\FK (UyGHá V]XPRZ\FK QD ]DFLVNDFK

ZHMFLRZ\FK WUDQ]\VWRUD SU]\ XPRZQ\P XF]\QLHQLX UHV]W\ VFKHPDWX

EH]V]XPQHM MHVW V]F]HJyOQLH SU]\GDWQH SU]\ UR]ZD*DQLX ZSá\ZX

VSU] *HQLD]ZURWQHJRQDZáDFLZRFLV]XPRZHZ]PDFQLDF]D

1D U\VD SU]HGVWDZLRQR VFKHPDW EORNRZ\ Z]PDFQLDF]D ]H

VSU] *HQLHP ]ZURWQ\P  QDSL FLRZ\P  V]HUHJRZ\P Z NWyU\P

]DVWRVRZDQRXQLODWHUDOQ\LGHDOQ\F]ZyUQLNVSU] *HQLD]ZURWQHJR

=DVW SF]H JHQHUDWRU\ V]XPyZ u

ik

2

 RUD] i

ik

2

 UHSUH]HQWXM V]XP\

F]ZyUQLND Z]PDFQLDMFHJR N ]D  u

i

2

 RUD] i

i

2

 U\VE  V

]DVW SF]\PL JHQHUDWRUDPL V]XPyZ Z]PDFQLDF]D ]H VSU] *HQLHP
]ZURWQ\P :DUWRü u

i

2

 PR*HP\ Z\]QDF]\ü ]ZLHUDMF ZHMFLD REX

XNáDGyZQDU\V

L

LN

2

X

LN

2

8

R

N

8

LQ

β

8

R

a)

L

L

2

X

L

2

8

R

N

8

LQ

β

8

R

b)

5\V D  6FKHPDW EORNRZ\ Z]PDFQLDF]D ] LGHDOQ\P VSU] *HQLHP ]ZURWQ\P

QDSL FLRZ\PV]HUHJRZ\P ] XZ]JO GQLHQLHP V]XPyZ  E  XNáDG ] ]DVW SF]\PL

(UyGáDPLV]XPyZ

3RQLHZD* UH]\VWDQFMD Z\MFLRZD F]ZyUQLND VSU] *HQLD ]ZURWQHJR MHVW

UyZQD]HUXZL F

background image



u

u

i

ik

2

2

=

 

:DUWRü  i

i

2

 Z\]QDF]DP\ SU]\ UR]ZDUW\FK ZHMFLDFK REX

XNáDGyZ 3U]\ UR]ZDUW\P ZHMFLX XNáDGX U\VE  V\JQDá ]ZURWQ\

QLHRGG]LDá\ZDQDZHMFLHZ]PDFQLDF]D]DWHPGODUyZQRFLV]XPyZQD

Z\MFLXRWU]\PXMHP\

i

i

i

ik

2

2

=



 

=UyZQRFL  L  Z\QLND*HQDZHMFLXREXXNáDGyZEH]

VSU] *HQLD]ZURWQHJRMDNUyZQLH*]HVSU] *HQLHP]ZURWQ\PVWRVXQHN

V\JQDáX GR V]XPX 

S N

  SR]RVWDMH EH] ]PLDQ\  : XNáDG]LH ]H

VSU] *HQLHP ]ZURWQ\P  Z\VWSL ]PQLHMV]HQLH Z]PRFQLHQLD  ]DUyZQR

GOD V\JQDáX X*\WHF]QHJR MDN L GOD V]XPX  ]DWHP VWRVXQHN V\JQDáX GR

V]XPXQDZ\MFLXZ]PDFQLDF]DSR]RVWDQLHWDNLVDPMDNZXNáDG]LHEH]

VSU] *HQLD]ZURWQHJR

1D U\VD SRGDQR SUDNW\F]Q\ VSRVyE UHDOL]DFML XMHPQHJR

VSU] *HQLD ]ZURWQHJR QDSL FLRZHJRV]HUHJRZHJR 6\JQDá ]ZURWQ\

RWU]\P\ZDQ\ MHVW ] G]LHOQLND UH]\VWDQF\MQHJR

R

R

E

F

,

 SU]\ F]\P GOD

FHOyZ DQDOL]\ ZáDFLZRFL V]XPRZ\FK XNáDGX Z V]HUHJ ] ND*G

UH]\VWDQFM ZáF]RQR (UyGáR QDSL FLRZH UHSUH]HQWXMFH MHJR V]XP\

WHUPLF]QH

u

k T R

f

u

k T R

f

e

E

f

F

2

2

4

4

=

=

 

X

LN

2

N

a)

5

)

5

(

X

H

2

X

I

2

L

LN

2

X

L

2

N

b)

5

)

5

(

L

L

2

5\VD Z]PDFQLDF]D]XMHPQ\PVSU] *HQLHP]ZURWQ\PQDSL FLRZ\P

V]HUHJRZ\P XZ]JO GQLDMF\(UyGáDV]XPyZ E XNáDG]]DVW SF]\PL(UyGáDPL

V]XPyZ

=DVW SF]H JHQHUDWRU\ V]XPyZ  u

i

ik

ik

2

2

,

  UHSUH]HQWXM V]XP\

Z]PDFQLDF]DEH]VSU] *HQLD]ZURWQHJR

: XNáDG]LH SRND]DQ\P QD U\VE ]DVW SF]H (UyGáD V]XPyZ

u

i

2

 RUD] i

i

2

 UHSUH]HQWXM FDáNRZLW\ ]DVW SF]\ V]XP ZHMFLRZ\

background image



Z]PDFQLDF]D]XMHPQ\PVSU] *HQLHP]ZURWQ\P'RZ\]QDF]HQLD u

i

2

]ZLHUDP\ ZHMFLD REX XNáDGyZ  ] U\V L SRUyZQXMHP\ V]XP\

Z\MFLRZH=Dáy*P\SU]\W\P*H UH]\VWDQFMD Z\MFLRZD Z]PDFQLDF]D

R

R

o

F

<<



u

u

i R

R

R

R

u

R

R

R

u

i

ik

ik

F

F

E

e

E

F

E

f

=

+

+

+

+

+

 

SU]\F]\P

R

R

R

F

E

=

||

=DNáDGDMF*HSRV]F]HJyOQHVNáDGRZHV]XPyZVQLH]DOH*QHRUD]

Z\NRU]\VWXMF]DOH*QRü  RWU]\PXMHP\

u

u

i R

k T R f

i

ik

ik

2

2

2

2

4

=

+

+

 

$QDOL]XMFVWDQUR]ZDUFLDREZRGyZZHMFLRZ\FKREXXNáDGyZ]

U\VRWU]\PXMHP\

i

i

i

ik

2

2

=

 

=UyZQDQLD  Z\QLND*H]ZL NV]DVL UHGQLRNZDGUDWRZD

ZDUWRü QDSL FLD V]XPyZ  ]DVW SF]HJR (UyGáD QDSL FLRZHJR ]DWHP

]ZL NV]\VL VWRVXQHNV\JQDáXGRV]XPX

S N

QDZHMFLXXNáDGX]H

VSU] *HQLHP]ZURWQ\P:WDNLPVDP\PVWRSQLXZ]URQLHWHQVWRVXQHN

QD Z\MFLX XNáDGX  3RGREQH UR]ZD*DQLD PR*HP\ SU]HSURZDG]Lü GOD

Z]PDFQLDF]D]XMHPQ\PVSU] *HQLHP]ZURWQ\PLQQHJRW\SX

2JyOQLH PR*QD VWZLHUG]Lü *H ZH Z]PDFQLDF]X ] XMHPQ\P

VSU] *HQLHP]ZURWQ\PVWRVXQHNV\JQDáXGRV]XPX

S N

QDZHMFLX

XNáDGXMHVWZL NV]\QL*ZXNáDG]LHEH]VSU] *HQLD]ZURWQHJRZVNXWHN

SHZQHM GRGDWNRZHM SRUFML V]XPX FLHSOQHJR JHQHURZDQHJR

ZHOHPHQWDFKVSU] *HQLD]ZURWQHJR



3$5$0(75<6=802:(8.à$'Ï:(/(.7521,&=1<&+



1DMF] FLHM VWRVRZDQ\P SDUDPHWUHP RSLVXMF\P ZáDFLZRFL

V]XPRZH HOHPHQWX DNW\ZQHJR  OXE XNáDGX HOHNWURQLF]QHJR MHVW

ZVSyáF]\QQLN V]XPyZ ) DQJ QRLVH IDFWRU  -HVW RQ GHILQLRZDQ\ MDNR

VWRVXQHNFDáNRZLWHMPRF\V]XPyZQDZ\MFLXXNáDGXZSDPLH

f

GR

PRF\ V]XPyZ QD Z\MFLX SRFKRG]F\FK ] V]XPyZ WHUPLF]Q\FK

UH]\VWDQFML(UyGáDV\JQDáX

F

P

k T

f k

oN

ps

=

1

 

JG]LH k

ps

MHVWVNXWHF]Q\PZ]PRFQLHQLHPPRF\

background image



3R SRG]LHOHQLX OLF]QLND L PLDQRZQLND Z\UD*HQLD    SU]H] PRF
G\VSRQRZDQV\JQDáX P

E

R

s dysp

g

g

=

2

4

RWU]\PXMHP\

F

P

k T

f

k

P

P

S

N

S

N

s dysp

ps

s dysp

oN

in

in

o

o

=

=

 

:SRZ\*V]HM]DOH*QRFL

S

N

in

in

RUD]

S

N

o

o

VVWRVXQNLHPV\JQDáXGR

V]XPyZRGSRZLHGQLRQDZHMFLXLQDZ\MFLXF]ZyUQLND U\V 

6 1

R

R



6

1

LQ

LQ



5\V0RFV\JQDáXLV]XPXQD

ZHMFLXLZ\MFLXF]ZyUQLND

:VSyáF]\QQLN V]XPyZ MHVW ZL NV]\ RG MHGQRFL  L MHVW PLDU

SRJRUV]HQLD VL  VWRVXQNX V\JQDáX  GR V]XPX VSRZRGRZDQHJR SU]H]

V]XP\Z]PDFQLDF]D

: F]ZyUQLNX SU]HGVWDZLRQ\P QD U\V ZHMFLRZD PRF

V]XPyZ

N

in

SRFKRG]LRGUH]\VWDQFML(UyGáDVWHUXMFHJR]DZ\MFLRZD

PRF V]XPyZ

N

o

  UHSUH]HQWXMH ZV]\VWNLH (UyGáD V]XPyZ F]ZyUQLND

ZUD] ] PRF V]XPyZ UH]\VWDQFML (UyGáD VWHUXMFHJR SU]HQLHVLRQ QD

Z\MFLHXNáDGX

:VSyáF]\QQLN V]XPyZ PR*H E\ü WDN*H Z\UD*RQ\ ]D SRPRF

ZLHONRFL  u

i

2

 RUD] i

i

2

 WM UHGQLRNZDGUDWRZ\FK ZDUWRFL QDSL FLD

LSUGX ]DVW SF]\FK (UyGHá V]XPRZ\FK  QD ZHMFLX F]ZyUQLND *G\

ZV]\VWNLH(UyGáDV]XPyZVSU]HQLHVLRQHGRREZRGXZHMFLRZHJRWR

ZVSyáF]\QQLNV]XPyZPR*HE\üRNUHORQ\ MDNR VWRVXQHN FDáNRZLWHJR

UHGQLRNZDGUDWRZHJR  ]DVW SF]HJR V]XPX QD ZHMFLX GR

UHGQLRNZDGUDWRZHMZDUWRFLV]XPyZWHUPLF]Q\FK(UyGáDV\JQDáX

:\NRU]\VWXMF]DOH*QRFL  L  RWU]\PXMHP\

F

u

u

u

u

i R

u

u

k T R

f

i

k T

R

f

iN

gT

gT

i

i

g

gT

i

g

i

g

=

=

+

+

= +

+

2

2

2

2

2

2

2

2

2

1

4

4

1

  

JG]LH

u

gT

2

 UHGQLRNZDGUDWRZD ZDUWRü QDSL FLD V]XPyZ WHUPLF]Q\FK

UH]\VWDQFML R

g

(UyGáDVWHUXMFHJR

0LQLPDOQD ZDUWRü ZVSyáF]\QQLND V]XPyZ  )  Z\VW SXMH GOD

RSW\PDOQHMUH]\VWDQFMLJHQHUDWRUD

R

g opt

2EOLF]DMFSRFKRGQ dF dR

g

background image



]UyZQDQLD  RWU]\PXMHP\

R

u

i

g opt

i

i

2

2

2

=

 

3RGVWDZLDMF

R

g opt

GRUyZQDQLD  RUD]SU]\MPXMF

I +]

RWU]\PXMHP\PLQLPDOQZDUWRüZVSyáF]\QQLNDV]XPyZ)

PLQ

F

u i

k T

i

i

min

= +

1

2

2

2



 

1DMPQLHMV]\ ZVSyáF]\QQLN V]XPyZ  Z\VW SXMH GOD LPSHGDQFML

(UyGáDNWyUDMHVW]Z\NOHUy*QDRGLPSHGDQFMLZHMFLRZHM VSU] *RQHM 

DZL FSU]\QLHGRSDVRZDQLXHQHUJHW\F]Q\PQDZHMFLXXNáDGX=WHJR

Z]JO GX SURMHNWRZDQLH PDáRV\JQDáRZHJR Z]PDFQLDF]D Z\PDJD

SHZQHJR NRPSURPLVX SRPL G]\ MHJR ZáDFLZRFLDPL V]XPRZ\PL D

Z]PDFQLDMF\PL

3U]\DQDOL]LHZ]PDFQLDF]\RPDá\PSR]LRPLHV]XPyZGHILQLXMH

VL ]DVW SF]UH]\VWDQFM V]XPyZL]DVW SF]WHPSHUDWXU V]XPyZ

=DVW SF]DUH]\VWDQFMDV]XPyZ5

Q

MHVWWRWDNDZDUWRüUH]\VWDQFML

GOD NWyUHM V]XP FLHSOQ\ MHVW UyZQ\ FR GR ZLHONRFL ]DVW SF]HPX

ZHMFLRZHPX V]XPRZL Z]PDFQLDF]D 3RUyZQXMF V]XP FLHSOQ\ ]

V]XPDPLZ]PDFQLDF]D U\V RWU]\PXMHP\

4

2

2

2

2

k T R

f

u

u

i R

n

iN

i

i

g

∆ =

=

+



 

6WG

f

T

k

R

i

u

R

g

i

i

n

4

2

2

2

+

=

 

=DVW SF]DUH]\VWDQFMDV]XPyZQLHMHVW]ZL]DQDDQL]UH]\VWDQFM

ZHMFLRZZ]PDFQLDF]DDQLWH*]UH]\VWDQFM(UyGáDV\JQDáX

=DVW SF] WHPSHUDWXU V]XPyZ

T

n

 QD]\ZDP\ WDN ZDUWRü

WHPSHUDWXU\UH]\VWDQFML(UyGáDSU]\NWyUHMUH]\VWDQFMDWDJHQHURZDáDE\

V]XP FLHSOQ\ R ZDUWRFL UyZQHM ]DVW SF]HPX ZHMFLRZHPX V]XPRZL

Z]PDFQLDF]D

3RUyZQXMFREDV]XP\ SRUZ]yU RWU]\PXMHP\



4

2

2

2

2

k T R

f

u

u

i R

n

n

iN

i

i

g

∆ =

=

+

 

6WG]DVW SF]DWHPSHUDWXUDV]XPyZ

T =

u

i R

k R f

n

i

i

g

g

2

2

2

4

+

 

background image



-H*HOL V]XP\ Z]PDFQLDF]D ]RVWDQ RNUHORQH Z WHPSHUDWXU]H

T

]Z\NOH. WR

(

)

T

T

F

n

=

1

 


Wyszukiwarka

Podobne podstrony:
17 Szumy w ukladach elektronicznych
Szumy i zaklocenia w ukladach elektronicznych, ˙wiczenie nr 19
Szumy w układach fizycznych
test 1 - 2010, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroenergetycznych
Zasady układania elektrod, WSEiT, fizjoterapia, fizykoterapia
Laborka obwody 3 fazowe, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroenergetyc
Filtry przeciwzakloceniowe 01, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroene
17', LABORATORIUM METROLOGII ELEKTRYCZNEJ I ELEKTRONICZNEJ
kusiak druk, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroenergetycznych
Egzamin - sciagi, 17. Zjawisko indukcji elektromagnetycznej, 17
17 WYZNACZANIE KRZYWEJ ELEKTROKAPILARNEJ DLA RTĘCI
Ćw. nr 17 - Badanie instalacji elektrycznej, Ćw. nr 17 - Badanie instalacji elektrycznej
Badanie wytrzymałości powietrza napięciem przemiennymP Hz przy różnych układach elektrod v3
test nr 2 - do wydruku, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroenergetycz
Badanie wytrzymałości powietrza napięciem przemiennymP Hz przy różnych układach elektrod protokół
Filtr Przeciwzakłóceniowy, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroenerget
zakł przewodzone moje, Elektrotechnika-materiały do szkoły, Zakłócenia w układach elektroenergetyczn
wytrzymałość powietrza w układach elektrod walców współosiowych i równoległych

więcej podobnych podstron