13 Liniowe zastosowania wzmacniaczy operacyjnych

background image

/,1,2:(=$67262:$1,$:=0$&1,$&=<
23(5$&<-1<&+

:352:$'=(1,(

:]PDFQLDF]H RSHUDF\MQH G]LNL VZHM XQLZHUVDOQRFL ]QDMGXM

SRZV]HFKQH ]DVWRVRZDQLH Z UHDOL]DFML Uy*QRURGQ\FK XNáDGyZ

DQDORJRZ\FK Z ZLHOX G]LHG]LQDFK HOHNWURQLNL ]ZáDV]F]D Z XNáDGDFK

VWHURZDQLD DXWRPDW\NL D WDN*H Z XNáDGDFK SRPLDURZ\FK 8NáDG\ ]H

Z]PDFQLDF]DPL RSHUDF\MQ\PL MDNR HOHPHQWDPL DNW\ZQ\PL SUDZLH

FDáNRZLFLH ]DVWSLá\ NODV\F]QH UR]ZL]DQLD WUDQ]\VWRURZH Z ]DNUHVLH

PDá\FK F]VWRWOLZRFL 1RZD JHQHUDFMD V]\ENLFK Z]PDFQLDF]\

RSHUDF\MQ\FK JáyZQLH ] SUGRZ\P VSU]*HQLHP ]ZURWQ\P

RF]VWRWOLZRFLDFK

f

T

GR*+]L

SR

U]GXNLONXW\VLF\9

µ

V

]QDF]QLH UR]V]HU]D ]DNUHV F]VWRWOLZRFL XNáDGyZ EXGRZDQ\FK

ZRSDUFLXRWHZ]PDFQLDF]H

=D SRPRF Z]PDFQLDF]\ RSHUDF\MQ\FK PR*QD UHDOL]RZDü

IXQNF\MQH RSHUDFMH OLQLRZH L QLHOLQLRZH QD V\JQDáDFK DQDORJRZ\FK

WDNLHMDNQSVXPRZDQLHFDáNRZDQLHUy*QLF]NRZDQLHSU]HVXZDQLHID]\

QDSLFLDSU]HWZDU]DQLHQDSLFLHSUGOXESUGQDSLFLHSUHF\]\MQH

SURVWRZDQLH L ZLHOH ZLHOH LQQ\FK 6]F]HJyOQ NODV XNáDGyZ

UHDOL]RZDQ Z RSDUFLX R Z]PDFQLDF]H RSHUDF\MQH V ILOWU\ DNW\ZQH

RFKDUDNWHU\VW\NDFKSDVPRZ\FK]ELHJXQDPL]HVSRORQ\PLDSU]\W\P

EH] X*\FLD LQGXNF\MQRFL 1L*HM ]RVWDQ SU]HGVWDZLRQH ]DVWRVRZDQLD

OLQLRZH Z]PDFQLDF]\ RSHUDF\MQ\FK Z XNáDGDFK Z]PDFQLDMF\FK

ZXNáDGDFK UHDOL]XMF\FK RSHUDFMH PDWHPDW\F]QH RUD] ILOWUDFK

DNW\ZQ\FK

32'67$:2:(.21),*85$&-(:=0$&1,$&=$

23(5$&<-1(*2:8.à$'$&+:=0$&1,$-&<&+

:]PDFQLDF]RGZUDFDMF\

8NáDG Z]PDFQLDF]D RGZUDFDMFHJR ID] SRND]DQR QD U\V

:XNáDG]LH W\P ]DVWRVRZDQR XMHPQH VSU]*HQLH ]ZURWQH QDSLFLRZH

UyZQROHJáH =DNáDGDMF LGHDOQ\ PRGHO Z]PDFQLDF]D RSHUDF\MQHJR

background image

UH]\VWDQFMDZHMFLRZD

R

ind

→ ∞

LGRZHMüZ]PDFQLDF]DQLHZSá\ZDM

*DGQHSUG\=DWHP

i

i

1

2

=

F]\OL

u

u

R

u

u

R

in

d

d

o

+ = − −

1

2

u

in

u

o

u

d

i

1

i

2

R

1

R

3

k

ud

+

Z

5

5\V:]PDFQLDF]RGZUDFDMF\

3RQLHZD* SRWHQFMDá ZHMFLD QLHRGZUDFDMFHJR MHVW UyZQ\

SRWHQFMDáRZLPDV\SU]H]UH]\VWRU

R

3

QLHSá\QLHSUGZLF

u

u

k

d

o

ud

=

:LGHDOQ\PSU]\SDGNXJG\

k

u

ud

d

→ ∞

,

,

0

SRWHQFMDáSXQNWX

=MHVWEOLVNLSRWHQFMDáRZLPDV\LGODWHJRSXQNWWHQQD]\ZDQ\MHVWÄPDV

SR]RUQ´ YLUWXDO JURXQG 3U]\ ]DáR*HQLX

u

d

=

0,

]H Z]RUX

PR*HP\Z\]QDF]\üZDUWRüZ]PRFQLHQLDQDSLFLRZHJRZ]PDFQLDF]D

RGZUDFDMFHJR

k

u

u

R

R

u f

o

in

0

2

1

=

= −

: FHOX X]\VNDQLD QDMPQLHMV]HJR EáGX VSRZRGRZDQHJR

QDSLFLHP QLH]UyZQRZD*HQLD SRZVWDMFHJR QD VNXWHN SU]HSá\ZX

ZHMFLRZ\FKSUGyZSRODU\]XMF\FKQDOH*\GREUDü

R

R R

3

1

2

=

||

: RJyOQ\P SU]\SDGNX UH]\VWRU\

R i R

1

2

PR*HP\ ]DVWSLü

LPSHGDQFMDPL

Z i Z

1

2

ZWHG\Z]yUSU]\MPXMHSRVWDü

k

u

u

Z

Z

uf

o

in

=

= −

2

1

: ]DOH*QRFL RG GRERUX W\FK HOHPHQWyZ PR*HP\ UHDOL]RZDü

GRZROQ WUDQVPLWDQFM L XNáDG PR*H VSHáQLDü V]HUHJ IXQNFML

SU]\QDMPQLHM MHGQD ] W\FK LPSHGDQFML PXVL ]DSHZQLü SU]HSá\Z

VNáDGRZHMVWDáHMZHMFLRZHJRSUGXSRODU\]DFML

3RQLHZD* Z]PRFQLHQLH Uy*QLFRZH Z]PDFQLDF]D RSHUDF\MQHJR

MHVWEDUG]RGX*HWRQDSLFLHUy*QLFRZH

u

d

QD]DFLVNDFKZHMFLRZ\FK

Z]PDFQLDF]DMHVWEDUG]RPDáH

background image

3U]\NáDGRZR

MH*HOL

R

k

R

k

k

ud

1

2

5

10

100

10

=

=

,

,

,

WR

k

V V

u f

0

10

= −

/

'OD QDSLFLD ZHMFLRZHJR QS

u

V

in

=

0 2

,

QDSLFLH

Z\MFLRZH

u

V

o

= −

2

D EH]SRUHGQLR QD ]DFLVNDFK ZHMFLRZ\FK

Z]PDFQLDF]DQDSLFLH

u

u

k

V

d

o

ud

= −

/

20

µ

WMUD]\PQLHM

QL*

u

in

= WHJR Z]JOGX SU]\MPXMH VL *H QD ]DFLVNDFK ZHMFLRZ\FK

Z]PDFQLDF]DRSHUDF\MQHJRZ\VWSXMHÄEH]SUGRZH]ZDUFLH´

=ZDUFLH MHVW EH]SUGRZH SRQLHZD* SUG ZHMFLRZ\ SU]H] WR ]ZDUFLH

SUDNW\F]QLHQLHSU]HSá\ZDNLHUXMFVLQLHPDOZFDáRFL]UH]\VWRUD5

GRUH]\VWRUD5

5H]\VWDQFMDZHMFLRZDXNáDGXZ\QRVL

(

)

R

u

i

u

u

u

R

R

u

u

u

k

R

k

k

R

k

k

R

in

in

in

d

in

in

o

ud

u f

ud

u f

ud

inf

/

=

=

+

=

+

=

=

+



 ≈



 ≈

1

1

1

1

0

1

0

1

1

1

1

SRQLHZD*

k

k

u f

ud

0

<<

:\NRU]\VWXMF]DVDGÄEH]SUGRZHJR]ZDUFLD´QDZHMFLX

Z]PDFQLDF]DRSHUDF\MQHJRPR*HP\EH]SRUHGQLRZ\]QDF]\ü

R

R

inf

.

=

1

=XZDJLQDEDUG]RVLOQHXMHPQHVSU]*HQLH]ZURWQHQDSLFLRZH

UH]\VWDQFMDZ\MFLRZD R

R

k

k

of

o

u f

ud

0

R

o

MHVW UH]\VWDQFM Z\MFLRZ

Z]PDFQLDF]DRSHUDF\MQHJRMHVWSRPLMDOQLHPDáDLXNáDG]DFKRZXMHVL

SUDZLHMDNLGHDOQHVWHURZDQH(UyGáRQDSLFLRZH

7U]\GHF\EHORZDSXOVDFMDJUDQLF]QDZ]PDFQLDF]D

ω

g f

MHVWUyZQD

LORUD]RZL SXOVDFML RGFLFLD

ω

T

Z]PDFQLDF]D RSHUDF\MQHJR L PRGXáX

VWDáRSUGRZHJRZ]PRFQLHQLD|

|

k

u f

0

Z]PDFQLDF]D

ω

ω

gf

T

u f

k

0

FR EH]SRUHGQLR Z\QLND ] ]DVDG\ *H SROH Z]PRFQLHQLD MHVW VWDáH L

UyZQHSXOVDFMLRGFLFLDZ]PDFQLDF]DRSHUDF\MQHJR

:]PDFQLDF]VXPXMF\

: XNáDG]LH SU]HGVWDZLRQ\P QD U\V PR*HP\ ]UHDOL]RZDü

background image

VXPRZDQLHQDSLü

k

ud

i

3

u

in3

u

in2

u

in1

u

o

i

2

i

1

i

4

Z

u

d

R

3

R

2

R

1

R

4

R

5


+

5\V:]PDFQLDF]VXPXMF\

=DNáDGDMF LGHDOQ\ PRGHO Z]PDFQLDF]D RSHUDF\MQHJR

RWU]\PXMHP\

i

i

i

i

1

2

3

4

+ + =

6WG

u

R

u

R

u

R

u

R

o

in

in

in

= −

+

+



4

1

1

2

2

3

3

3U]\GRERU]HMHGQDNRZ\FKZDUWRFLUH]\VWRUyZ

R

R

R

R

1

2

3

=

=

=

RWU]\PXMHVLZXNáDG]LHVXPRZDQLHQDSLü

(

)

u

R

R

u

u

u

o

in

in

in

= −

+

+

4

1

2

3

5H]\VWDQFMH ZHMFLRZH XNáDGX ZLG]LDQH ] ND*GHJR ] ZHMü

Z\QRV]RGSRZLHGQLR

R R R

1

2

3

,

,

.

'OD ]PLQLPDOL]RZDQLD ZSá\ZX QDSLFLD QLH]UyZQRZD*HQLD

SRZVWDMFHJR QD VNXWHN SU]HSá\ZX ZHMFLRZ\FK SUGyZ

SRODU\]XMF\FKQDOH*\GREUDü

R

R R R R

5

1

2

3

4

=

||

||

||

:]PDFQLDF]QLHRGZUDFDMF\

3RGVWDZRZ\

XNáDG

Z]PDFQLDF]D

QLHRGZUDFDMFHJR

SU]HGVWDZLRQR QD U\V : XNáDG]LH W\P ]DVWRVRZDQR XMHPQH

VSU]*HQLH ]ZURWQH QDSLFLRZH V]HUHJRZH D QLH UyZQROHJáH MDN ZH

Z]PDFQLDF]X RGZUDFDMF\P 'ODWHJR Z XNáDG]LH W\P QDOH*\ VL

VSRG]LHZDüZVWRVXQNXGRZ]PDFQLDF]DRGZUDFDMFHJREDUG]RGX*HM

UH]\VWDQFMLZHMFLRZHM

=JRGQLH]R]QDF]HQLDPLQDU\VRWU]\PXMHP\

u

k

u

k

u

u

R

R

R

o

ud

d

ud

in

o

=

=

+



1

1

2

background image

k

u d

+

R

3

R

1

R

2

u

in

i

1

i

2

u

1

u

o

u

d

u

2

5\V:]PDFQLDF]

QLHRGZUDFDMF\

6WG

u

u

k

u

R

R

R

in

o

ud

o

=

+

+

1

1

2

'OD

k

ud

→ ∞

RWU]\PXMHP\

k

u

u

R

R

R

R

R

uof

o

in

=

=

+

= +

1

2

1

2

1

1

:]PRFQLHQLH MHVW GRGDWQLH L ZLNV]H RG MHGQRFL :H

Z]PDFQLDF]X QLHRGZUDFDMF\P QLH PD SXQNWX ÄPDV\ SR]RUQHM´ L Z

SU]HFLZLHVWZLH GR Z]PDFQLDF]D RGZUDFDMFHJR Z XNáDG]LH W\P

Z\VWSXMHZHMFLRZ\V\JQDáVXPDF\MQ\]HZ]JOGXQDVWHURZDQLHREX

ZHMü 3RQLHZD* Z]PDFQLDF] QLHRGZUDFDMF\ MHVW XNáDGHP

]QDSLFLRZ\PV]HUHJRZ\PVSU]*HQLHP]ZURWQ\PWRUy*QLFD]ZURWQD

Z\QRVL

F

k

R

R

R

k

k

k

k

ud

ud

u f

ud

u f

= +

+

= +

1

1

1

1

2

0

0

: RSDUFLX R HOHPHQWDUQ WHRUL VSU]*HQLD ]ZURWQHJR PR*HP\

Z\]QDF]\ü UH]\VWDQFM ZHMFLRZ L Z\MFLRZ Z]PDFQLDF]D

QLHRGZUDFDMFHJR

R

R

k

k

ind

ud

uof

inf

=

R

R

k

k

of

o

uof

ud

=

SU]\ F]\P

R

R

ind

o

,

V RGSRZLHGQLR Uy*QLFRZ UH]\VWDQFM ZHMFLRZ

LUH]\VWDQFMZ\MFLRZZ]PDFQLDF]DRSHUDF\MQHJR

5H]\VWDQFMD

R

inf

RGSRZLDGDMFD Z\UD*HQLX MHVW EDUG]R

GX*D L PR*H E\ü SRPLQLWD QDWRPLDVW RJUDQLF]HQLHP ZHMFLRZHM

UH]\VWDQFML Z]PDFQLDF]D QLHRGZUDFDMFHJR MHVW ZHMFLRZD UH]\VWDQFMD

R

inc

GOD V\JQDáyZ ZVSyOQ\FK NWyUD QLH MHVW REMWD SWO VSU]*HQLD

background image

]ZURWQHJR 5H]\VWDQFMD R

of

MHVW WDN PDáD *H SUDNW\F]QLH XNáDG

]DFKRZXMHVLSUDZLHMDNLGHDOQHVWHURZDQH(UyGáRQDSLFLRZH

: FHOX ]PLQLPDOL]RZDQLD ZSá\ZX QDSLFLD QLH]UyZQRZD*HQLD

SRZVWDMFHJR

QD

VNXWHN

SU]HSá\ZX

ZHMFLRZ\FK

SUGyZ

SRODU\]XMF\FKQDOH*\]DSHZQLü R

R R

g

=

1

2

||

JG]LH R

g

MHVWUH]\VWDQFM

(UyGáDVWHUXMFHJR

:WyUQLNQDSLFLRZ\

3U]\MPXMFZHZ]PDFQLDF]XQLHRGZUDFDMF\P

R

1

= ∞

X]\VNXMH

VL ]JRGQLH ]H Z]RUHP Z]PRFQLHQLH QDSLFLRZH UyZQH

MHGQRFL 8NáDG SUDFXMH ZWHG\ MDNR ZWyUQLN QDSLFLRZ\ U\V

LFKDUDNWHU\]XMH VL EDUG]R GX* UH]\VWDQFM ZHMFLRZ NWyUD

ZXNáDG]LH U]HF]\ZLVW\P VWDQRZL UyZQROHJáH SRáF]HQLH ZHMFLRZHM

UH]\VWDQFML GOD V\JQDáyZ ZVSyOQ\FK L ZHMFLRZHM UH]\VWDQFML

Uy*QLFRZHM Z]PDFQLDF]D SRPQR*RQHM SU]H] Z]PRFQLHQLH SU]\

RWZDUWHM SWOL VSU]*HQLD ]ZURWQHJR

(

||

)

R

R

R k

in

inc

ind

ud

=

5H]\VWDQFMD

Z\MFLRZDMHVWSRPLMDOQLHPDáD R

R

k

of

o

ud

=

/

:DUWRüUH]\VWDQFML

R

QDOH*\ WDN GREUDü DE\ E\áD UyZQD UH]\VWDQFML ZHZQWU]QHM (UyGáD

V\JQDáX

k

ud


+

u

o

u

in

u

d

R

5\V:WyUQLNQDSLFLRZ\

7U]\GHF\EHORZDSXOVDFMDJUDQLF]QDZWyUQLNDQDSLFLRZHJRZ\QRVL

ω

ω

gf

T

=

:]PDFQLDF]Uy*QLFRZ\

1D U\V SU]HGVWDZLRQR Z]PDFQLDF] Uy*QLFRZ\ ]H

VSU]*HQLHP ]ZURWQ\P NWyU\ PR*H VáX*\ü GR RGHMPRZDQLD GZyFK

QDSLü

background image

k

ud


+

u

in1

u

in2

u

1

u

2

u

d

u

o

R

1

R

2

R

3

R

4

5\V:]PDFQLDF]Uy*QLFRZ\

GRRGHMPRZDQLDQDSLü

3U]\ ]DáR*HQLX *H ZHMFLH Z]PDFQLDF]D QLH SRELHUD SUGX

PR*HP\QDSLVDüUHODFMH

u

u

R

R

R

u

u

R

u

u

R

in

in

o

2

2

4

3

4

1

1

1

1

2

=

+

− = −

-H*HOL

k

ud

→ ∞

WR

u

u

1

2

=

L]UyZQDRWU]\PXMHP\

u

R

R

R

R

R

R

u

R

R

u

o

in

in

=

+

+



1

2

3

4

4

1

2

2

1

1

6WRVXMF

R

R

R

R

1

3

2

4

=

=

,

X]\VNXMH VL QDSLFLH Z\MFLRZH

SURSRUFMRQDOQHGRUy*QLF\QDSLüZHMFLRZ\FK

(

)

u

R

R

u

u

o

in

in

=

2

1

2

1

:FHOX]DSHZQLHQLDPLQLPDOQHJREáGXZ\QLNDMFHJR]QDSLFLD

QLH]UyZQRZD*HQLD

VSRZRGRZDQHJR

ZHMFLRZ\PL

SUGDPL

SRODU\]XMF\PLQDOH*\GREUDü

R R

R R

1

2

3

4

||

||

=

8.à$'<&$à.8-&(,5Ï)1,&=.8-&(

8NáDGFDáNXMF\

6WRVXMF NRQGHQVDWRU Z REZRG]LH VSU]*HQLD ]ZURWQHJR

Z]PDFQLDF]D RGZUDFDMFHJR MDN QD U\V RWU]\PXMHP\ XNáDG

FDáNXMF\QD]\ZDQ\SRZV]HFKQLHLQWHJUDWRUHP0LOOHUD

-H*HOL ]DVWRVXMHP\ ]DSLV RSHUDWRURZ\

Z

R

Z

sC

=

=

,

/

WR

UyZQDQLHSU]\MPXMHSRVWDü

( )

( )

U s

U

s

sR C

o

in

= −

1

background image

k

ud


+

u

in

u

o

u

d

R

1

C

i

1

i

2

5\V,QWHJUDWRU

=DOH*QRüZG]LHG]LQLHF]DVXR]QDF]D

( )

( )

u t

R C

u t dt

o

in

t

= −

1

1

0

,QWHJUDWRU ] U\V QLH XZ]JOGQLD ZDUXQNyZ SRF]WNRZ\FK

ZSURFHVLHFDáNRZDQLD

7UDQVPLWDQFMDLQWHJUDWRUDZ\]QDF]RQD]UyZQDQLDZ\QRVL

( )

( )

H s

U s

U

s

s R C

s

I

o

in

i

=

= −

= −

( )

1

1

ω

SU]\F]\P

ω

i

R C

=

1

1

D

QD]\ZDVLSXOVDFMLQWHJUDWRUD

8NáDG FDáNXMF\ NWyUHJR WUDQVPLWDQFMD RSLVDQD MHVW UyZQDQLHP

QD]\ZD VL LQWHJUDWRUHP LGHDOQ\P -DN ]D]QDF]RQR OLQL

SU]HU\ZDQ QD U\V FKDUDNWHU\VW\ND PRGXáX WUDQVPLWDQFML

LGHDOQHJR LQWHJUDWRUD MHVW SURVW R QDFK\OHQLX G%GHN Z FDá\P

]DNUHVLH F]VWRWOLZRFL D SXOVDFMD RGFLFLD FKDUDNWHU\VW\NL F]\OL

SXOVDFMDSU]\NWyUHMPRGXáWUDQVPLWDQFMLMHVWUyZQ\OXEG%MHVW

UyZQD SXOVDFML LQWHJUDWRUD

ω

i

.W SU]HVXQLFLD ID]RZHJR QDSLFLD

Z\MFLRZHJRZLQWHJUDWRU]HLGHDOQ\PZ\QRVL

π

GODND*GHMSXOVDFML

:U]HF]\ZLVW\PLQWHJUDWRU]HNRQLHF]QU]HF]MHVWXZ]JOGQLHQLH

VNRF]RQHJR Z]PRFQLHQLD L VNRF]RQHJR SDVPD Z]PDFQLDF]D

RSHUDF\MQHJR

3U]\MPXMF *H Z]PRFQLHQLH Z]PDFQLDF]D RSHUDF\MQHJR RSLVXMH

MHGQRELHJXQRZDIXQNFMD

( )

k

s

k

s

ud

g

=

+

0

1

ω

GODLQWHJUDWRUDQDU\VPR*HP\QDSLVDüUyZQDQLH

background image

( )

( )

( )

( )

[

]

U

s

U s

R

U s

U s sC

U s

U s

k

s

in

d

o

d

d

o

ud

+

= −

+

=

1

( )

( )

( )

5R]ZL]XMF EDUG]R SURVW\ XNáDG UyZQD PR*HP\

Z\]QDF]\üWUDQVPLWDQFMQDSLFLRZU]HF]\ZLVWHJRLQWHJUDWRUD

( )

( )

( )

(

)

H s

U s

U

s

k

s

k

R C

s R C

I

o

in

g

g

=

= −

+

+

+



 +

0

0

1

2

1

1

1

1

ω

ω

3RQLHZD*

k

k

0

0

1

+ ≈

RUD] VWRVXMF R]QDF]HQLH D

RWU]\PXMHP\

( )

H s

k

s

k

s

k

I

o

i

g

= −

+



+



1

1

0

0

ω

ω

/

5yZQDQLHZVND]XMH*HWUDQVPLWDQFMDU]HF]\ZLVWHJRLQWHJUDWRUD

SRVLDGDGZDELHJXQ\

p

k

p

k

i

g

T

1

0

2

0

= −

= −

=

ω

ω

ω

,

RUD]VNRF]RQZDUWRüZ]PRFQLHQLDVWDáRSUGRZHJRUyZQ

k

0

( )

H

j

dB

I

ω

k

0

1

ω

i

k

0

ω

i

ω

T

ω

ω

g

dek

dB /

20

dek

dB /

40

:]PDFQLDF]

RSHUDF\MQ\

,QWHJUDWRU

U]HF]\ZLVW\

,QWHJUDWRU

LGHDOQ\

5\V&KDUDNWHU\VW\NLPRGXáXWUDQVPLWDQFMLLQWHJUDWRUDLGHDOQHJR

LQWHJUDWRUDU]HF]\ZLVWHJRZ]PDFQLDF]DRSHUDF\MQHJR

&KDUDNWHU\VW\NPRGXáXWUDQVPLWDQFMLU]HF]\ZLVWHJRLQWHJUDWRUD

SU]HGVWDZLRQROLQLFLJáQDU\VQDNWyU\PUyZQLH*]D]QDF]RQR

FKDUDNWHU\VW\NDPSOLWXGRZZ]PDFQLDF]DRSHUDF\MQHJROLQLD

-DN ZLGDü DSURNV\PRZDQH FKDUDNWHU\VW\NL PRGXáyZ

WUDQVPLWDQFML LQWHJUDWRUyZ LGHDOQHJR L U]HF]\ZLVWHJR SRNU\ZDM VL

W\ONRZSU]HG]LDOHSXOVDFML

ω

ω ω

i

T

k

/

.

0

< <

-HGQDNSXOVDFMDV\JQDáX

background image

QDZHMFLXLQWHJUDWRUDPXVLE\üPQLHMV]DQL*

ω

T

SRQLHZD*GOD

ω ω

=

T

Z\VWSXM

MX*

GX*H

Uy*QLFH

SRPLG]\

FKDUDNWHU\VW\NDPL

F]VWRWOLZRFLRZ\PL

LQWHJUDWRUD

LGHDOQHJR

L

U]HF]\ZLVWHJR

ZDPSOLWXG]LHG%RUD]ZID]LH

π

8NáDGUy*QLF]NXMF\

1DMSURVWV]\ VSRVyE UHDOL]DFML XNáDGX Uy*QLF]NXMFHJR DQJ

GLIIHUHQWLDWRU ]H Z]PDFQLDF]HP RSHUDF\MQ\P SU]HGVWDZLRQR QD

U\V

k

ud


+

u

in

i

1

R

2

u

d

u

o

i

2

C

5\V8NáDGUy*QLF]NXMF\

3U]\MPXMF Z W\P XNáDG]LH

Z

sC Z

R

1

2

2

1

=

=

/

,

RWU]\PXMHP\

ZG]LHG]LQLHRSHUDWRURZHM

( )

( )

U s

R C s U

s

o

in

= −

2

:G]LHG]LQLHF]DVXRGSRZLDGDWR]DOH*QRFL

( )

( )

u t

R C

du t

dt

o

in

= −

2

7UDQVPLWDQFMD QDSLFLRZD LGHDOQHJR XNáDGX Uy*QLF]NXMFHJR

Z\]QDF]RQD]]DOH*QRFLZ\QRVL

( )

( )

( )

H

s

U s

U

s

s R C

s

D

o

in

d

=

= −

= −

2

ω

:LHONRü

ω

d

R C

=

1

2

/

QD]\ZD VL SXOVDFM XNáDGX Uy*QLF]NXMFHJR

7UDQVPLWDQFMD PD SRMHG\QF]H ]HUR Z ]HU]H 1D U\V

SU]HGVWDZLRQROLQLSU]HU\ZDQFKDUDNWHU\VW\NPRGXáXWUDQVPLWDQFML

LGHDOQHJR XNáDGX Uy*QLF]NXMHJR 1DFK\OHQLH FKDUDNWHU\VW\NL Z\QRVL

G%GHNDPRGXáWUDQVPLWDQFMLMHVWUyZQ\OXEG%GODSXOVDFML

ω

d

.W SU]HVXQLFLD ID]RZHJR QDSLFLD Z\MFLRZHJR Z LGHDOQ\P

XNáDG]LH Uy*QLF]NXMF\P Z\QRVL

π

GOD ND*GHM SXOVDFML

:SU]\SDGNX U]HF]\ZLVWHJR XNáDGX Uy*QLF]NXMFHJR JG\ Z]PDFQLDF]

RSHUDF\MQ\PDVNRF]RQHZ]PRFQLHQLHLVNRF]RQHSROHZ]PRFQLHQLD

PR*HP\ SU]HSURZDG]Lü UR]ZD*DQLD DQDORJLF]QH GR W\FK MDNLH

SU]HSURZDG]RQR

GOD

LQWHJUDWRUD

7UDQVPLWDQFM

QDSLFLRZ

background image

U]HF]\ZLVWHJRXNáDGXUy*QLF]NXMFHJRRSLVXMH]DOH*QRü

( )

( )

( )

(

)

(

)

H

s

U s

U

s

s

s

s

k

k

D

o

in

d

g

g

d

g

d

=

= −

+

+

+

+

/

ω

ω

ω

ω ω

ω ω

α

2

0

0

1

&KDUDNWHU\VW\N PRGXáX WUDQVPLWDQFML U]HF]\ZLVWHJR XNáDGX

Uy*QLF]NXMFHJR RGSRZLDGDMF ]DOH*QRFL SU]HGVWDZLRQR

OLQL FLJá QD U\V ZUD] ] FKDUDNWHU\VW\N DPSOLWXGRZ

Z]PDFQLDF]DRSHUDF\MQHJROLQLD

( )

H

j

dB

D

ω

k

0

a

N

J

ω

ω

α

ω

g

ω

G

ω

T

ω ω

G 7

ω

dek

dB /

20

dek

dB /

20

+

:]PDFQLDF]

RSHUDF\MQ\

5]HF]\ZLVW\ XNáDG

Uy*QLF]NXMF\

,GHDOQ\ XNáDG

Uy*QLF]NXMF\

5\V&KDUDNWHU\VW\NLPRGXáXWUDQVPLWDQFMLLGHDOQHJRXNáDGX

Uy*QLF]NXMFHJRU]HF]\ZLVWHJRXNáDGXUy*QLF]NXMFHJR

Z]PDFQLDF]DRSHUDF\MQHJR

$SURNV\PRZDQHFKDUDNWHU\VW\NLPRGXáyZWUDQVPLWDQFMLXNáDGyZ

Uy*QLF]NXMF\FK LGHDOQHJR L U]HF]\ZLVWHJR SRNU\ZDM VL Z ]DNUHVLH

SXOVDFML

ω

ω ω

ω

<

=

d

T

g

k

R C

0

2

),/75<$.7<:1(

.ODV\ILNDFMDILOWUyZDNW\ZQ\FKLPHWRG\LFKUHDOL]DFML

5R]SDWU\ZDQH Z QLQLHMV]\P UR]G]LDOH ILOWU\ DNW\ZQH VWDQRZL

JUXS OLQLRZ\FK XNáDGyZ VWDFMRQDUQ\FK UHDOL]RZDQ\FK Z RSDUFLX

REORNRZH XNáDG\ DNW\ZQH MDNLPL PRJ E\ü VFDORQH Z]PDFQLDF]H

RSHUDF\MQH *\UDWRU\ OXE ]HVSRá\ RGSRZLHGQLR SRáF]RQ\FK

WUDQ]\VWRUyZRUD]SRGXNáDGX]áR*RQHJR]SRMHPQRFLUH]\VWDQFMLOXE

DNW\ZQ\FK HOHPHQWyZ WUDQVNRQGXNWDQF\MQ\FK -H*HOL GR UHDOL]DFML

ILOWUyZDNW\ZQ\FKZ\NRU]\VWXMHVLUH]\VWDQFMHWRWDNLHILOWU\QD]\ZD

VL ILOWUDPL DNW\ZQ\PL 5& )LOWU\ UHDOL]RZDQH W\ONR ] HOHPHQWyZ

background image

DNW\ZQ\FK L SRMHPQRFL QD]\ZD VL ILOWUDPL DNW\ZQ\PL & )LOWU\ WH

UHDOL]XMHVLZSRVWDFLVFDORQ\FKXNáDGyZ026L]DOH*QLHRGURG]DMX

SUDF\]V\JQDáHPFLJá\PF]\WH*SUyENRZDQ\PG]LHOLVLMHQDILOWU\

DNW\ZQH

&SU]HáF]DQHDQJVZLWFKHGFDSDFLWRU

SUDFXMFHZF]DVLHFLJá\PDQJFRQWLQRXVWLPHILOWHUV

=DOHW\ ILOWUyZ DNW\ZQ\FK Z SRUyZQDQLX ] SDV\ZQ\PL ILOWUDPL

5/&VV]F]HJyOQLHZ\UD(QLHZLGRF]QH Z ]DNUHVLH PDá\FK L UHGQLFK

F]VWRWOLZRFL GR RN N+] JG\* XQLND VL Z W\P SU]\SDGNX

VWRVRZDQLD NáRSRWOLZ\FK Z X*\FLX FHZHN LQGXNF\MQ\FK R GX*\FK

LQGXNF\MQRFLDFK=DGDQLHPILOWUXDNW\ZQHJRMHVW]UHDOL]RZDQLH]DGDQHM

WUDQVPLWDQFML Z SRVWDFL Z\PLHUQHM IXQNFML +V ]PLHQQHM ]HVSRORQHM

s

j

= +

σ

ω

DSURNV\PXMFHM]DGDQHFKDUDNWHU\VW\NLILOWUX

( )

( )

( )

H s

U s

U

s

a s

a

b s

b

a

b

s z

s

p

o

in

m

m

n

n

m

n

i

i

j

j

=

=

+ +

+ +

=

...

...

(

)

(

)

0

0

Π

Π

JG]LH

a b

i

j

,

U]HF]\ZLVWHZVSROF]\QQLNLZLHORPLDQyZ

z

i

, p

j

]HUDLELHJXQ\IXQNFML H s

( )

GODi

m

=

0 1 2

, , ,.....,

M Q

3DV\ZQHREZRG\5&QLHSR]ZDODMQDX]\VNDQLHGRZROQHJRUR]NáDGX

]HULELHJXQyZWUDQVPLWDQFMLZOHZHMSyáSáDV]F]\(QLH]PLHQQHM sMDN

WRPDPLHMVFHZSU]\SDGNXSDV\ZQ\FKREZRGyZ/&

:ILOWU]HDNW\ZQ\P]HZ]PDFQLDF]HPRSHUDF\MQ\PNRU]\VWDMF

]ZáDFLZRFLVSU]*HQLD]ZURWQHJRPR*QDWDNPRG\ILNRZDüSRáR*HQLD

]HU L ELHJXQyZ IXQNFML WUDQVPLWDQFML DE\ RWU]\PDü Z\PDJDQ\ LFK

UR]NáDG GOD ]DSHZQLHQLD *GDQHM FKDUDNWHU\VW\NL ILOWUX 3RáR*HQLH

ELHJXQyZIXQNFMLWUDQVPLWDQFMLZOHZHMSyáSáDV]F]\(QLH]PLHQQHMVWM

]DSHZQLHQLH XMHPQ\FK ZDUWRFL LFK U]HF]\ZLVW\FK F]FL JZDUDQWXMH

VWDELOQSUDFILOWUX-H*HOLELHJXQ\WUDQVPLWDQFMLILOWUXOH*QDRVL j

ω

WR ILOWU VWDMH VL XNáDGHP QLHVWDELOQ\P :\PDJDQLD VWDZLDQH ILOWURP

ZL*VLQDMF]FLHM]UHDOL]DFM]DGDQHMFKDUDNWHU\VW\NLPRGXáXLID]\

WUDQVPLWDQFML H s

( )

GOD s j

=

ω

( )

( )

( )

[

]

H s

H

j

=

ω

ϕ

ω

exp

JG]LH

( )

H

ω

FKDUDNWHU\VW\NDPRGXáX

( )

ϕ ω

FKDUDNWHU\VW\NDID]\

'RNRQXMFSRG]LDáXILOWUyZ]DZ]JOGXQDSDVPRF]VWRWOLZRFL

SU]HQRV]RQ\FK V\JQDáyZ PR*HP\ Z\Uy*QLü ILOWU\ GROQR

LJyUQRSU]HSXVWRZH

ILOWU\

URGNRZRSU]HSXVWRZH

ILOWU\

background image

URGNRZR]DSRURZH ILOWU\ ZV]HFKSU]HSXVWRZH R VWDáHM ZDUWRFL

PRGXáXLID]LHEGFHMIXQNFMF]VWRWOLZRFLLLQQH&KDUDNWHU\VW\NL

F]VWRWOLZRFLRZHZ\PLHQLRQ\FKURG]DMyZILOWUyZPRJE\üGRZROQLH

NV]WDáWRZDQH Z ]DOH*QRFL RG VSRVREX LFK ]HVWURMHQLD 1DMF]FLHM V

VWRVRZDQHW\SRZHFKDUDNWHU\VW\NLPDNV\PDOQLHSáDVND%XWWHUZRUWKD

UyZQRPLHUQLH IDOLVWD &]HE\V]HZD PDNV\PDOQLH OLQLRZHM ID]\

7KRPVRQD HOLSW\F]QD &DXHUD DSHULRG\F]QD NU\W\F]QD LWS

:áDFLZRFL W\FK FKDUDNWHU\VW\N PRJ E\ü SU]HGVWDZLRQH ]DUyZQR

SU]H] ZDUWRFL ZVSyáF]\QQLNyZ ZLHORPLDQyZ IXQNFML Z\PLHUQHM

H s

( )

MDNL]DSRPRFUR]NáDGX]HULELHJXQyZIXQNFMLWUDQVPLWDQFMLQD

SáDV]F]\(QLH ]PLHQQHM ]HVSRORQHM &]FLHM MHGQDN ZáDFLZRFL WH

UHSUH]HQWRZDQH V SU]H] ZDUWRFL FKDUDNWHU\VW\F]Q\FK SXOVDFML

ELHJXQyZ IXQNFML WUDQVPLWDQFML L LFK GREURFL 3R GRNRQDQLX Z\ERUX

RGSRZLHGQLHM FKDUDNWHU\VW\NL F]VWRWOLZRFLRZHM Z ]DOH*QRFL RG

Z\PDJDQHJR URG]DMX L ZáDFLZRFL ILOWUX NROHMQ\P ]DGDQLHP MHVW

Z\EyU RSW\PDOQHM UHDOL]DFML WUDQVPLWDQFML ILOWUX F]\OL Z\EyU VWUXNWXU\

XNáDGX .RFRZ\P HWDSHP SURMHNWRZDQLD ILOWUX MHVW Z\]QDF]HQLH

ZDUWRFLHOHPHQWyZSU]\MWHMVWUXNWXU\LLFKRSW\PDOL]DFMDSRGNWHP

Uy*Q\FK Z\PDJD :\PDJDQLD WH VSURZDG]DM VL QDMF]FLHM GR

PLQLPDOL]DFML ZUD*OLZRFL PRGXáX WUDQVPLWDQFML QD UR]U]XW\ ZDUWRFL

HOHPHQWyZ]PLDQ\WHPSHUDWXU\F]DVXLWS

:FLJXNLONXG]LHVLFLROHWQLHJRUR]ZRMXWHRULLILOWUyZDNW\ZQ\FK

]DSURSRQRZDQR EDUG]R ZLHOH PHWRG SURMHNWRZDQLD L UHDOL]DFML W\FK

XNáDGyZ]NWyU\FKNLOND]QDOD]áRV]HURNLH]DVWRVRZDQLH

:LNV]Rü ]QDQ\FK REHFQLH VSRVREyZ UHDOL]DFML DNW\ZQ\FK

ILOWUyZRSLHUDVLQDMHGQHM]GZyFKRJyOQ\FKPHWRG

NDVNDGRZHM

ZLHORSWORZHJRVSU]*HQLD]ZURWQHJR

5HDOL]DFMD PHWRG NDVNDGRZ SROHJD QD UR]NáDG]LH

GHNRPSR]\FML WUDQVPLWDQFML Z\VRNLHJR VWRSQLD QD VWUXNWXU\

RWUDQVPLWDQFML GUXJLHJR VWRSQLD L HZHQWXDOQLH MHGQ WUDQVPLWDQFM

SLHUZV]HJR VWRSQLD )XQNFMD WUDQVPLWDQFML H s

( )

PR*H E\ü

SU]HGVWDZLRQD Z SRVWDFL LORF]\QX Z\PLHUQ\FK IXQNFML U]HF]\ZLVW\FK

VWRSQLDQLHZLNV]HJRQL*GZD

( )

( )

( )

( )

( )

( )

H s

N s

D s

H s

N s

M s

k

k

k

k

k

=

=

=

JG]LHVWRSLH

( )

N s

k

VWRSLH

( )

M s

k

1D XZDJ ]DVáXJXMH IDNW *H ]ELyU ]HU L ELHJXQyZ WUDQVPLWDQFML

H s

k

( )

WZRU]F\FK NDVNDGRZ UHDOL]DFM ILOWUX DNW\ZQHJR MHVW

LGHQW\F]Q\]H]ELRUHP]HULELHJXQyZUHDOL]RZDQHMIXQNFML H s

( )

background image

3URFHGXUDV\QWH]\ILOWUyZSU]\PHWRG]LHNDVNDGRZHMMHVWSURVWD

RSLHUD VL ERZLHP QD UHDOL]DFML L]RORZDQ\FK VHNFML GUXJLHJR U]GX

6WDELOQRü ILOWUX NDVNDGRZHJR MHVW RNUHORQD VWDELOQRFL VHNFML

:RGUy*QLHQLX RG PHWRG\ NDVNDGRZHM PHWRGD ZLHORSWORZHJR

VSU]*HQLD ]ZURWQHJR SROHJD QD REMFLX EORNyZ GUXJLHJR U]GX

HZHQWXDOQLH SLHUZV]HJR MHGQ OXE ZLNV] OLF]E SWOL QLHORNDOQHJR

VSU]*HQLD ]ZURWQHJR : ]ELRU]H ]HU L ELHJXQyZ EORNyZ DNW\ZQ\FK

Z\VWSXMF\FK Z VWUXNWXU]H ILOWUX ] ZLHORSWORZ\P VSU]*HQLHP

]ZURWQ\P ]QDMGXM VL WDNLH ]HUD L ELHJXQ\ NWyUH QLH V ]HUDPL

LELHJXQDPL UHDOL]RZDQHM IXQNFML WUDQVPLWDQFML H s

( )

LQDF]HM QL* SU]\

UHDOL]DFML NDVNDGRZHM 7D PHWRGD UHDOL]DFML ILOWUyZ MHVW WUXGQLHMV]D

XPR*OLZLD MHGQDN Z SRUyZQDQLX ] PHWRG NDVNDGRZ X]\VNDQLH

FKDUDNWHU\VW\N

F]VWRWOLZRFLRZ\FK

ILOWUyZ

R

PQLHMV]\FK

ZUD*OLZRFLDFKQD]PLDQ\SDUDPHWUyZILOWUX

3URFHGXUD V\QWH]\ ILOWUyZ ] ZLHORSWORZ\P VSU]*HQLHP

]ZURWQ\PMHVWRSDUWDQDV\PXODFMLEH]VWUDWQ\FKILOWUyZ/&SUDFXMF\FK

PLG]\ GZRPD UH]\VWDQFMDPL OXE Z\NRU]\VWDQLX PHWRG ]PLHQQ\FK

VWDQX : WHM EDUG]R ]Uy*QLFRZDQHM JUXSLH ILOWUyZ DNW\ZQ\FK QD

V]F]HJyOQH Z\Uy*QLHQLH ]H Z]JOGX QD V]HURNLH ]DVWRVRZDQLD

SUDNW\F]QH]DVáXJXM

ILOWU\DNW\ZQH]]DVWRVRZDQLHPVWUXNWXU\)/))ROORZWKH/HDGHU

)HHGEDFNRUD]W\SXÄ/HDS)URJ´

ILOWU\DNW\ZQH]EH]SRUHGQLV\PXODFMDLQGXNF\MQRFL

ZSURWRW\SRZ\FKILOWUDFK5/&

ILOWU\DNW\ZQHUHDOL]RZDQHQD]DVDG]LH]PLHQQ\FKVWDQX

=HZ]JOGXQDRJUDQLF]RQREMWRüSRGUF]QLNDSU]HGVWDZLP\

W\ONRNLONDPHWRGUHDOL]DFMLILOWUyZDNW\ZQ\FK

UHDOL]DFMDNDVNRGRZD]VHNFMDPLELNZDGUDWRZ\PL

EH]SRUHGQLDV\PXODFMDLQGXNF\MQRFLZILOWUDFK/&

ILOWU\UHDOL]RZDQHQD]DVDG]LH]PLHQQ\FKVWDQX

ILOWU\&SU]HáF]DQH

ILOWU\&SUDFXMFHZF]DVLHFLJá\P

)LOWU\ELNZDGUDWRZH

6HNFMDELNZDGUDWRZDPD]D]DGDQLH]UHDOL]RZDüWUDQVPLWDQFM

( )

( )

H s

a s

a s

a

s

b s

b

N

s

s

b s

b

k

k

=

+

+

+

+

=

+

+

2

2

1

0

2

1

0

2

1

0

SU]\F]\P

N

s

k

( )

MHVWZLHORPLDQHPVWRSQLDGUXJLHJROXEQL*V]HJR

3U]\ SURMHNWRZDQLX VHNFML ELNZDGUDWRZ\FK QD RJyá NRU]\VWD VL

background image

]SRVWDFL ]QRUPDOL]RZDQ\FK WUDQVPLWDQFML

H s

k

( )

1RUPDOL]DFML

SRGOHJDM UyZQLH* ZDUWRFL HOHPHQWyZ SDV\ZQ\FK 5& VHNFML

=QRUPDOL]RZDQDIXQNFMD

H s

k

( )

PDSRVWDü

( )

( )

(

)(

)

H s

N

s

s

Q

s

N

s

s p

s

p

k

k

k

( )

=

+

+

=

2

0

0

2

1

2

ω

ω

JG]LH

p p

1

2

,

VELHJXQDPLWUDQVPLWDQFML

( )

H s

k

'ODGREURFLQ

>

1 2

/

ELHJXQ\V]HVSRORQH

p

Q

j

Q

Q

j

p

p

,

= −

±

− =

±

ω

ω

σ

ω

&]FLU]HF]\ZLVWHLXURMRQHELHJXQyZRNUHORQHV]DOH*QRFLDPL

σ

ω

p

Q

= −

D

ω

ω

p

Q

=

E

3RPLG]\SXOVDFM

ω

LGREURFLQ DF]FLU]HF]\ZLVWLXURMRQ

ELHJXQDLVWQLHMQDVWSXMFH]DOH*QRFL

ω

σ

ω

=

+

p

p

Q

p

p

p

p

=

+

=

σ

ω

σ

ω

σ

2

2

0

2

2

&]DVHP]DPLDVWGREURFLQ GHILQLXMHVLZVSyáF]\QQLNWáXPLHQLD

ξ =

1

2 Q

'ODGX*\FKZDUWRFLQ SXOVDFMDELHJXQD

ω

0

QD]\ZDQDQLHNLHG\

SXOVDFMFKDUDNWHU\VW\F]QILOWUXMHVWSUDZLHUyZQDF]FLXURMRQHM

ELHJXQD]JRGQLH]]DOH*QRFLE

ω

ω

p

=SRUyZQDQLDPLDQRZQLNyZZ\UD*HLRWU]\PXMHVL

s

b s

b

s

Q

2

1

0

2

0

0

+

+ = +

+

ω

ω

:SRGREQ\VSRVyERWU]\PXMHVL]DOH*QRFL

Q

b

b

b

=

=

0

1

0

0

/

oraz

ω

:]DOH*QRFLRGSRVWDFLZLHORPLDQXOLF]QLND

N

s

k

( )

PR*QD

RWU]\PDüILOWU\Uy*Q\FKW\SyZ

background image

DILOWUGROQRSU]HSXVWRZ\DQJORZSDVVILOWHU

H

H

s

Q

s

LP

=

+

+

0

0

2

2

0

0

2

ω

ω

ω

0RGXáWUDQVPLWDQFMLSU]\MPXMHZDUWRüPDNV\PDOQGODSXOVDFMLUyZQHM

F]FLXURMRQHMELHJXQDZ]yUMHGQDNGOD GX*\FK Q

p

,

ω

ω

0

LZ WDNLP SU]\SDGNX PDNV\PDOQD ZDUWRü PRGXáX WUDQVPLWDQFML

Z\VWSXMH SUDZLH SU]\ SXOVDFML ELHJXQD U\V D :\VNRNL

FKDUDNWHU\VW\NL DPSOLWXGRZHM V W\P ZLNV]H LP ZLNV]D MHVW GREURü
ILOWUX 'OD GREURFL Q

=

1

2

/

RWU]\PXMHP\ W]Z FKDUDNWHU\VW\N

PDNV\PDOQLHSáDVNLZW\PSU]\SDGNXJyUQDWU]\GHF\EHORZDSXOVDFMD

JUDQLF]QDMHVWUyZQDSXOVDFMLELHJXQD
EILOWUJyUQRSU]HSXVWRZ\DQJKLJKSDVVILOWHU

( )

H

s

H

s

s

Q

s

HP

=

+

+

0

2

0

0

2

ω

ω

-DN

SRND]DQR

QD

U\VE

UyZQLH*

GOD

ILOWUX

JyUQRSU]HSXVWRZHJR PR*QD Z\Uy*QLü FKDUDNWHU\VW\N PDNV\PDOQLH
SáDVNGODQ

=

1

2

/

FILOWUURGNRZRSU]HSXVWRZ\DQJEDQGSDVVILOWHU

( )

H

s

H

s

s

Q

s

BP

=

+

+

0

0

2

0

0

2

ω

ω

ω

:SU]\SDGNXILOWUyZURGNRZRSU]HSXVWRZ\FKSU]HZD*QLHQ

>>

1

LW\P

VDP\P F]ü XURMRQD ELHJXQD MHVW UyZQD SXOVDFML ELHJXQD EGFHM

MHGQRF]HQLHSXOVDFMURGNRZILOWUX

3RQLHZD* GREURü ILOWUX MHVW UyZQD GREURFL ELHJXQD WR

WU]\GHF\EHORZHSDVPRILOWUXMHVWUyZQH

B

f

dB

dB

gH

gL

dB

p

3

3

3

2

2

=

=

=

=

ω

ω

ω

π

σ

-DNSRND]DQRQDU\VFFKDUDNWHU\VW\NDPRGXáXWUDQVPLWDQFMLPD

DV\PSWRW\F]QHQDFK\OHQLDG%GHNLG%GHN
GILOWUURGNRZR]DSRURZ\DQJEDQGUHMHFWILOWHU

( )

H

s

H

s

Q

s

s

Q

s

BP

z

z

z

=

+

+

+

+

0

2

2

2

0

0

2

ω

ω

ω

ω

background image

[ ]

H

H

dB

LP

0

a)

d )

b)

log

ω

log

ω

log

ω

0

[ ]

H

H

dB

HP

0

[ ]

H

H

dB

BR

0

ω

0

0

Q

Q

0

Q

Q

2

1

>

Q

1

Q

2

dek

dB /

20

dek

dB /

20

+

Q

Q

Z

<

Q

Q

Z

>

Q

Z

= ∞

ω

Z

c)

log

ω

3dB

Q

[ ]

H

H

dB

BP

0

ω

0

Q

Q

2

1

>

Q

2

Q

1

dek

dB /

20

dek

dB /

20

+

Q

Q

2

1

>

Q

2

Q

1

2

/

2

=

Q

ω

0

gL

ω

gH

ω

2

/

2

=

Q

5\V&KDUDNWHU\VW\NLDPSOLWXGRZHILOWUyZELNZDGUDWRZ\FK

DGROQRSU]HSXVWRZHJREURGNRZRSU]HSXVWRZHJR

FJyUQRSU]HSXVWRZHJRGURGNRZR]DSRURZHJR

'OD

Q

Q

z

>

RWU]\PXMHP\ILOWUURGNRZR]DSRURZ\]DGOD

Q

z

= ∞

ILOWU

HOLSW\F]Q\RFKDUDNWHU\VW\FHDPSOLWXGRZHMSU]HGVWDZLRQHMQDU\VG

RWUDQVPLWDQFML

( )

H

s

H

s

s

s

Q

BR

z

z

=

+

+

+

0

2

0

2

2

2

2

0

2

0

1

1

ω
ω

ω

ω

ω

HILOWUZV]HFKSU]HSXVWRZ\XNáDGRSy(QLDMF\3DGH¶JRGUXJLHJRU]GX

DQJDOOSDVVILOWHU

( )

H

s

H

s

Q

s

s

Q

s

AP

z

=

+

+

+

0

2

0

0

2

2

0

0

2

ω

ω

ω

ω

&KDUDNWHU\VW\NID]RZWHJRILOWUXRNUHOD]DOH*QRü

background image

( )

Φ

$3

DUF WJ

4

ω

ω

ω

ω
ω

= −

:ILOWUDFKDNW\ZQ\FKZVSyáF]\QQLNLIXQNFMLWUDQVPLWDQFML]DOH*

RG ZDUWRFL HOHPHQWyZ SDV\ZQ\FK RUD] RG Z]PRFQLHQLD HOHPHQWX

DNW\ZQHJR ,VWRWQ\P SDUDPHWUHP ILOWUX MHVW MHJR ZUD*OLZRü DQJ

VHQVLWLYLW\ 'HILQLXMH VL ZUD*OLZRü Q RUD]

ω

0

QD ]PLDQ\ ZDUWRFL

HOHPHQWyZSDV\ZQ\FKLZ]PRFQLHHOHPHQWyZDNW\ZQ\FKWZRU]F\FK

ILOWUZDUWRFLWHRJyOQLHR]QDF]RQRWXMDNR

x

i

S

x

Q

Q

x

S

x

x

i

n

x

Q

i

i

x

i

i

i

i

=

=

=


ω

∂ ω

ω

;

, , ...

0

0

0

1 2

RUD]ZUD*OLZRü]HULELHJXQyZ

S

x

z

z

x

S

x

p

p

x

i

n

x

z

i

i

x

p

i

i

i

i

=

=

=

;

, ,.....,

:UD*OLZRüILOWUXMHVWLVWRWQ\PNU\WHULXPMDNRFLILOWUXLSRZLQQD

E\üPLQLPDOL]RZDQD

(OHPHQWDPLDNW\ZQ\PLVWRVRZDQ\PLZVHNFMDFKGUXJLHJRU]GX

ILOWUXNDVNDGRZHJRVQDMF]FLHMZ]PDFQLDF]HRSHUDF\MQHZXNáDGDFK

RGZUDFDMF\FK OXE QLHRGZUDFDMF\FK ]H VSU]*HQLHP ]ZURWQ\P

GRGDWQLP OXE XMHPQ\P 6HNFMD ILOWUX PR*H WH* ]DZLHUDü XNáDG NLONX

Z]PDFQLDF]\ RSHUDF\MQ\FK ] PLHV]DQ\P VSU]*HQLHP ]ZURWQ\P

8NáDG\ ] MHGQ\P Z]PDFQLDF]HP ]DSHZQLDM QD RJyá PDá GREURü

Q

10

L V EDUG]LHM ZUD*OLZH QL* XNáDG\ ] NLONRPD HOHPHQWDPL

DNW\ZQ\PL Z NWyU\FK Q

>

10

=DVWRVRZDQLH XMHPQHJR VSU]*HQLD

]ZURWQHJR ZH Z]PDFQLDF]X G]LDáD VWDELOL]XMFR QD SDUDPHWU\ ILOWUX

'X*DUH]\VWDQFMDZHMFLRZDLPDáDUH]\VWDQFMDZ\MFLRZDZ]PDFQLDF]D

]DSHZQLDM RGSRZLHGQL VHSDUDFM SRV]F]HJyOQ\FK VHNFML ILOWUX

NDVNDGRZHJR LXPR*OLZLDM QLH]DOH*QH ]HVWUDMDQLH W\FK VHNFML EH]

Z]DMHPQHJRRGG]LDá\ZDQLD

: PRQRJUDILDFK SRZLFRQ\FK WHPDW\FH ILOWUyZ DNW\ZQ\FK

PR*QD]QDOH(üREV]HUQ\SU]HJOGPHWRGV\QWH]\VHNFMLELNZDGUDWRZ\FK

L Uy*Q\FK VSRVREyZ LFK UHDOL]DFML 7\WXáHP SU]\NáDGX SU]HGVWDZLP\

SRZV]HFKQLH ]QDQ\ XNáDG ]DSURSRQRZDQ\ Z URNX SU]H]

6DOOHQ.H\¶DNWyU\Z]DOH*QRFLRGNRQILJXUDFMLHOHPHQWyZVSU]*HQLD

]ZURWQHJR PR*H UHDOL]RZDü ZV]\VWNLH W\S\ ILOWUyZ ELNZDGUDWRZ\FK

>@

background image

+

u

in

R

1

u

o

R

2

C

1

C

2

R

a

R

b

5\V'ROQRSU]HSXVWRZ\

ILOWU6DOOHQ.H\¶D

1D U\V SU]HGVWDZLRQR ILOWU GROQRSU]HSXVWRZ\ Z NWyU\P

]DVWRVRZDQRZ]PDFQLDF]QLHRGZUDFDMF\

6WRVXMFQSQDSLFLRZHSUDZR.LUFKKRIIDZXNáDG]LHPR*QD

Z\]QDF]\üMHJRWUDQVPLWDQFM

( )

( )

H

s

U s

U

s

k

R R C C

s

R C

R C

k

R C

s

R R C C

LP

o

in

u

u

( )

=

=

+

+

+ −



 +

1

2

1

2

2

1

1

2

1

2

2

1

2

1

2

1

1

1

1

JG]LH

k

R

R

u

b

a

= +

/

D

3RUyZQXMFZ\UD*HQLH]MHJR]QRUPDOL]RZDQSRVWDFL

RWU]\PXMHP\

ω

0

1

2

1

2

1

=

R R C C

Q

R R C C

R C

R C

k

R C

u

=

+

+ −



H

k

u

0

=

1DMPQLHMV]H ZUD*OLZRFL GROQRSU]HSXVWRZHJR ILOWUX 6DOOHQ.H\¶D

RWU]\PXMHVLZSU]\SDGNXJG\Z]PDFQLDF]RZ]PRFQLHQLX

k

u

]RVWDQLH

SU]HNV]WDáFRQ\ZHZWyUQLNQDSLFLRZ\

k

u

=

1

:W\PSU]\SDGNX GOD

R

R

R

1

2

=

=

C

Q

C

Q

1

0

2

0

2

1

2

=

=

ω

ω

oraz

]DZUD*OLZRFLGREURFLQ LSXOVDFML

ω

0

VUyZQH

S

S

S

S

R

Q

C

Q

R

C

=

= ±

=

= −

0

1 2

1 2

0

0

;

/ ;

/

ω

ω

=DVWSXMF QD U\V UH]\VWDQFMH SRMHPQRFLDPL ]D

SRMHPQRFLUH]\VWDQFMDPLRWU]\PXMHVLJyUQRSU]HSXVWRZ\ILOWU6DOOHQ

background image

.H\¶DSU]HGVWDZLRQ\QDU\V

+

C

1

C

2

R

b

5

D

u

o

R

2

R

1

u

in

5\V*yUQRSU]HSXVWRZ\ILOWU

ELNZDGUDWRZ\6DOOHQ.H\¶D

7UDQVPLWDQFMDWHJRXNáDGXMHVWRNUHORQD]DOH*QRFL

( )

( )

H

s

U s

U

s

k s

s

R C

R C

k

R C

s

R R C C

HP

o

in

u

u

( )

=

=

+

+

+ −



 +

2

2

2

1

2

2

1

1

1

2

1

2

1

1

1

1

SU]\ F]\P

k

u

RNUHORQH MHVW ]DOH*QRFL D 3U]\MPXMF

SRGREQLHMDNSRSU]HGQLR

k

C

C

u

=

=

1

1

2

;

RWU]\PXMHVL

Q =

1

2

oraz

R

R

C R R

1

2

0

1

2

1

ω =

1D U\V SU]HGVWDZLRQR MHGQ ] PR*OLZ\FK NRQILJXUDFML

URGNRZRSU]HSXVWRZHJRILOWUX6DOOHQ.H\¶D

+

u

in

R

a

R

b

u

o

R

2

R

1

C

1

C

2

R

3

5\VURGNRZRSU]HSXVWRZ\

ILOWUELNZDGUDWRZ\6DOOHQ.H\¶D

1DSRGVWDZLHUyZQDRF]NRZ\FKXNáDGXPR*HP\Z\]QDF]\ü

WUDQVPLWDQFM

background image

H

s

U

s

U

s

k

R C

s

s

R C

R C

R C

k

R C

s

R

R

R R R C C

BP

o

in

u

u

( )

( )

( )

=

=

=

+

+

+

+ −



 +

+

3RUyZQXMFZ\UD*HQLH]MHJR]QRUPDOL]RZDQSRVWDFL

RWU]\PXMHP\

ω

0

1

2

1

2

3

1

2

=

+

R

R

R R R C C

Q

R

R

R R R C C

R C

R C

R C

k

R C

u

=

+

+

+

+ −



H

k

R C

R C

R C

R C

k

R C

u

u

0

1

1

1

1

3

2

3

1

2

2

1

1

1

1

=

+

+

+ −



)LOWU\ ]DZLHUDMFH Z]PDFQLDF]H QLHRGZUDFDMFH RG]QDF]DM VL

GX*\PLZUD*OLZRFLDPLZSU]\SDGNXJG\VUHDOL]RZDQHGX*HGREURFL

-HVW WR Z\QLNLHP VWRVRZDQLD Z XNáDG]LH GRGDWQLHJR VSU]*HQLD

]ZURWQHJR

)LOWU\DNW\ZQHR]PQLHMV]RQHMZUD*OLZRFLDSU]\W\PRGX*HM

GREURFLPRJE\ü]UHDOL]RZDQHSU]\X*\FLXZ]PDFQLDF]\RSHUDF\MQ\FK

RGZUDFDMF\FKID]


+

R

2

R

1

C

1

C

2

u

in

u

o

5\VURGNRZRSU]HSXVWRZ\

ILOWU6DOOHQ.H\¶D

3U]\NáDGHP WDNLHJR UR]ZL]DQLD MHVW ILOWU SU]HGVWDZLRQ\ QD U\V

>@

background image

( )

( )

H

s

U s

U

s

R C

s

s

R C

R C

s

R R C C

BP

o

in

( )

=

=

+

+



 +

1

1

1

1

1

1

2

2

1

2

2

1

2

1

2

'OD

C

C

C

1

2

=

=

RWU]\PXMHVL

Q

R

R

C R R

=

=

1

2

1

2

1

0

1

2

,

ω

]DGOD

ω ω

=

=

,

H

Q

:áDFLZRFL ILOWUX ] U\V V SRGREQH GR ZáDFLZRFL ILOWUX

GROQRSU]HSXVWRZHJR]ZWyUQLNLHPQDSLFLRZ\PLMHJRZUD*OLZRFLV

QLHZLHONLH

)LOWU\DNW\ZQHUHDOL]RZDQHPHWRG]PLHQQ\FKVWDQX

5HDOL]DFMDILOWUyZDNW\ZQ\FKPHWRG]PLHQQ\FKVWDQX SROHJD QD

]DVWRVRZDQLXHOHPHQWDUQ\FKLQWHJUDWRUyZ]NWyU\FKND*G\XPR*OLZLD

G]LHOHQLH WUDQVIRUPDW\ V\JQDáX SU]H] RSHUDWRU s 1D U\V

SU]HGVWDZLRQR VFKHPDW EORNRZ\ VHNFML ELNZDGUDWRZHM R GRZROQHM

WUDQVPLWDQFML]EXGRZDQHMZRSDUFLXRGZDLQWHJUDWRU\

U

s

in

( )

H

0

U s

0

( )

b

0

b

1

a

1

1

s

1

s

a

2

a

0

5\V6FKHPDWEORNRZ\VHNFMLELNZDGUDWRZHM]GZRPDLQWHJUDWRUDPL

7UDQVPLWDQFMD XNáDGX ] U\V MHVW RNUHORQD ]DOH*QRFL

)LOWU\ UHDOL]RZDQH PHWRG ]PLHQQ\FK VWDQX XPR*OLZLDM

MHGQRF]HVQH

X]\VNDQLH

WUDQVPLWDQFML

GROQR

JyUQR

LURGNRZRSU]HSXVWRZ\FK D SU]H] VXPRZDQLH V\JQDáyZ ] Z\MFLD

GROQR L JyUQR SU]HSXVWRZHJR MHVW UyZQLH* PR*OLZH X]\VNDQLH

WUDQVPLWDQFMLURGNRZR]DSRURZHM )LOWU\ WH FKDUDNWHU\]XM VL PDá\PL

ZUD*OLZRFLDPLLGX*GREURFLVLJDMFDZDUWRFLQ

=

100

background image

1D U\V SU]HGVWDZLRQR XQLZHUVDOQ\ ILOWU ]UHDOL]RZDQ\

PHWRG]PLHQQ\FKVWDQXQD]\ZDQ\ILOWUHP.+1WZyUFDPLILOWUXE\OL

.HOYLQ+XHOVPDQL1HZFRPE>@


+

+


+

U

in

R

R

1

=

R

R

4

=

R

R

3

=

(

)

R

Q

R

2

2

1

=

C

C

1

0

ω

C

1

0

ω

C

U

oLP

U

oHP

U

oBP

LP

BP

HP

5\V8QLZHUVDOQ\ILOWU.+1

=DNáDGDMF *H Z]PDFQLDF]H RSHUDF\MQH V LGHDOQH RUD] VWRVXMF

PHWRGVXSHUSR]\FML]JRGQLH]R]QDF]HQLDPLQDU\VRWU]\PXMHP\

U

R

R

R

U

R

R

R

U

R

R

R

U

R

R

R

U

s C

C

U

s

U

s

U

in

oBP

oHP

oLP

oLP

oBP

oBP

oHP

2

1

2

1

1

2

3

3

4

4

3

4

0

0

0

2

2

1

+

+

+

=

+

+

+

= −

= − 



=







ω

ω

ω

8Z]JOGQLDMF SRGDQH QD VFKHPDFLH ]DOH*QRFL PLG]\

UH]\VWDQFMDPL

(

)

R

R

R

R

R

Q

R

1

3

2

2

1

=

=

=

,

,

RWU]\PXMHP\

( )

( )

( )

( )

( )

( )

+

V

8

V

8 V

V

+

V

V

8

V

8 V

V

+

V

/3

R/3

LQ

%3

R%3

LQ

+3

=

= − 



= − 



=

=

ω

ω

ω

( )

( )

=

=

+

+

ω

ω

ω

V

8

V

8 V

4

4

V

4

V

R+3

LQ

SU]\F]\P

Q

R

R

= +

1

2

2

1

/

-DNPR*QD]DXZD*\üSXOVDFMD

ω

0

LGREURü Q ]DOH*RGZDUWRFL

Uy*Q\FK HOHPHQWyZ FR XPR*OLZLD QLH]DOH*Q\ GREyU REX W\FK

SDUDPHWUyZ 'RGDWNRZ ]DOHW ILOWUyZ UHDOL]RZDQ\FK PHWRG

]PLHQQ\FK VWDQX MHVW LFK PDá\ EáG G\QDPLF]Q\ Z\QLNDMF\

background image

]RJUDQLF]H F]VWRWOLZRFLRZ\FK LQWHJUDWRUyZ SRQLHZD* ]DNUHV

SRSUDZQHJR FDáNRZDQLD VLJD SXOVDFML R ZDUWRFL EOLVNLHM

ω

T

Z]PDFQLDF]DRSHUDF\MQHJR

)LOWU\DNW\ZQH]DQDORJDPLLQGXNF\MQRFL

5HDOL]DFM EH]LQGXNF\MQ\FK ILOWUyZ Q WHJR U]GX PR*QD

GRNRQDü SRSU]H] ]DVWSLHQLH HOHPHQWyZ LQGXNF\MQ\FK Z SDV\ZQ\FK

ILOWUDFK /& VSHFMDOQ\PL F]ZyUQLNDPL DNW\ZQ\PL XPR*OLZLDMF\PL

RGSRZLHGQL WUDQVIRUPDFM LPSHGDQFML -HGQ\P ] WDNLFK F]ZyUQLNyZ

MHVW *\UDWRU NWyU\ Z LGHDOQ\P SU]\SDGNX MHVW RSLVDQ\ QDVWSXMF

PDFLHU]DGPLWDQF\MQ

[ ]

y

g

g

m

m

=



0

0

SU]\F]\P

g

m

MHVWNRQGXNWDQFM*\UDFML

-H*HOLF]ZyUQLNRSLVDQ\PDFLHU]REFL*\VLQDZ\MFLX

SRMHPQRFL&WRMHJRLPSHGDQFMDZHMFLRZDZ\QRVL

Z

Y

s C

g

s L

in

in

m

z

=

=

=

1

2

SU]\F]\P

/

&

J

]

P

=

Z

in

C

g

m

g

m

g

m

C

a)

b)

c)

g

m

g

m

11

:

L

C

g

z

m

=

2

L

L

C

g

i

z

m

=

=

2

5\V6\PXODFMHGRNRQ\ZDQH]DSRPRFLGHDOQ\FK*\UDWRUyZDLQGXNF\MQRFL

X]LHPLRQHMELQGXNF\MQRFLQLHX]LHPLRQHMFLGHDOQHJRWUDQVIRUPDWRUD

8NáDG WDNL V\PXOXMH EH]VWUDWQ LQGXNF\MQRü X]LHPLRQ QD ]DFLVNDFK

ZHMFLRZ\FK :\NRU]\VWDQLH GZyFK *\UDWRUyZ SR]ZDOD QD V\PXODFM

LQGXNF\MQRFL QLHX]LHPLRQHM W\SX IORDWLQJ OXE LGHDOQHJR

WUDQVIRUPDWRUDU\V

-HGQ]ZLHOXPR*OLZ\FKVSRVREyZUHDOL]DFML*\UDWRUD]DSRPRF

Z]PDFQLDF]\ WUDQVNRQGXNWDQF\MQ\FK RPyZLRQ\FK Z UR]G]

SU]HGVWDZLRQRQDU\V

background image

:FHOXZ\MDQLHQLD]DVDG\G]LDáDQLDXNáDGX]U\VPDFLHU]

UR]NáDGDVLQDVXPGZyFKPDFLHU]\

[ ]

y

g

g

m

m

= 


 + −



0

0

0

0

0

0

U

1

U

2

I

1

I

2

g

m

g

m

+

g

m

+

g

m

5\V5HDOL]DFMD*\UDWRUD]DSRPRF

GZyFKZ]PDFQLDF]\27$

.D*GD ]H VNáDGRZ\FK PDFLHU]\ UHSUH]HQWXMH LGHDOQH (UyGáR

SUGRZH VWHURZDQH QDSLFLHP SU]\ F]\P SLHUZV]H (UyGáR WUDQVPLWXMH

V\JQDá ] Z\MFLD QD ZHMFLH EH] RGZUDFDQLD ID]\ ]D GUXJLH (UyGáR

WUDQVPLWXMHV\JQDá]ZHMFLDQDZ\MFLH]RGZUDFDQLHPID]\6\PXODFMD

LQGXNF\MQRFL]DSRPRF*\UDWRUyZGDMHPR*OLZRüX]\VNDQLD GX*\FK

ZDUWRFL LQGXNF\MQRFL

L

z

R GX*HM GREURFL VLJDMFHM NLONXVHW

ZV]HURNLP SDPLH F]VWRWOLZRFL FR SR]ZDOD QD UHDOL]DFM XNáDGyZ

VHOHNW\ZQ\FK R GX*HM GREURFL L PDáHM ZUD*OLZRFL )LOWU\ DNW\ZQH

]*\UDWRUDPL SU]\ ]DáR*HQLX *H *\UDWRU\ V LGHDOQH PDM ZV]\VWNLH

FKDUDNWHU\VW\NL WUDQVPLV\MQH L ZUD*OLZRFLRZH LGHQW\F]QH ] LFK

SURWRW\SDPL/&

)LOWU\&SU]HáF]DQH

8ZDJLZVWSQH

:NRFXODWVLHGHPG]LHVLW\FK]RVWDáDZSURZDG]RQDQRZDNODVD

DQDORJRZ\FKXNáDGyZPRQROLW\F]Q\FK]SU]HáF]DQ\PLSRMHPQRFLDPL

QD]\ZDQD UyZQLH* &SU]HáF]DQH OXE 6& DQJ VZLWFKHG FDSDFLWRU

:QLQLHMV]\P UR]G]LDOH ]RVWDQLH SU]HGVWDZLRQD MHG\QLH RJyOQD

NRQFHSFMD UHDOL]DFML L DQDOL]\ SU]\NáDGRZ\FK UR]ZL]D XNáDGyZ 6&

.RQFHSFMD V\PXODFML UH]\VWDQFML PR*H E\ü SRGVWDZ SURVWHM PHWRG\

SURMHNWRZDQLD XNáDGyZ 6& SROHJDMFHM QD W\P *H Z NODV\F]Q\FK

XNáDGDFK DNW\ZQ\FK 5& SRV]F]HJyOQH UH]\VWRU\ ]DVWSXMH VL

RGSRZLHGQLPL SRGXNáDGDPL 6& 3RF]WNRZR WHFKQLND 6& ]QDOD]áD

background image

]DVWRVRZDQLHGRUHDOL]DFMLILOWUyZERZLHPILOWU\6&FKDUDNWHU\]XMVL

GZLHPDEDUG]RLVWRWQ\PLFHFKDPL

ZVSyáF]\QQLNL WUDQVPLWDQFML QDSLFLRZHM OXE SUGRZHM ILOWUX QLH

]DOH*RGZDUWRFLEH]Z]JOGQ\FKSRMHPQRFLDOHRGLFKVWRVXQNyZ

WU]\GHF\EHORZD F]VWRWOLZRü JUDQLF]QD ILOWUX OXE F]VWRWOLZRü

URGNRZD SDVPD SU]HSXVWRZHJR MHVW ZSURVW SURSRUFMRQDOQD GR

F]VWRWOLZRFL ]HJDUD ]H ZVSyáF]\QQLNLHP SURSRUFMRQDOQRFL

]DOH*Q\PRGVWRVXQNXSRMHPQRFL

:\PLHQLRQH ZáDFLZRFL SR]ZDODM QD GX* GRNáDGQRü

Z\NRQDQLDILOWUXQLHPR*OLZGRX]\VNDQLDZ*DGQHMLQQHMWHFKQRORJLL

PRQROLW\F]QHM)LOWU\6&PRJE\üUyZQLH*DXWRPDW\F]QLHSU]HVWUDMDQH

SRSU]H] ]PLDQ F]VWRWOLZRFL ]HJDUD .RQGHQVDWRU\ Z\NRQDQH

ZWHFKQRORJLL 026 PDM ZáDFLZRFL EOLVNLH LGHDOQ\P W]Q PDáH

ZVSyáF]\QQLNL WHPSHUDWXURZH U]GX SSP

R

& OXE PQLHMV]H RUD]

EDUG]R PDáH ZVSyáF]\QQLNL VWUDWQRFL : VWDQGDUGRZHM WHFKQRORJLL

026 ZDUWRü EH]Z]JOGQD SRMHPQRFL PR*H E\ü Z\NRQDQD

]GRNáDGQRFLGROHF]*GDQ\VWRVXQHNSRMHPQRFLPR*HE\ü

X]\VNDQ\ ] GRNáDGQRFL

δ

.OXF]H Z\NRU]\VW\ZDQH GR

SU]HáF]DQLD NRQGHQVDWRUyZ UHDOL]XMH VL QDMF]FLHM Z SRVWDFL

SRMHG\QF]\FKWUDQ]\VWRUyZOXESDUWUDQ]\VWRUyZ

b)

0

0

1

2

nMOS

pMOS

+

c)

2

1

S

d )

3

1

2

e)

S

1

S

2

1

2

3

a)

0

1

2

5\V.OXF]HMHGQRSR]\F\MQHDSU]\Z\NRU]\VWDQLXWUDQ]\VWRUDQ026ESU]\

Z\NRU]\VWDQLXSDU\WUDQ]\VWRUyZ&026FV\PERONOXF]D.OXF]HGZXSR]\F\MQH

GV\PERONOXF]DHNOXF]]áR*RQ\]GZyFKNOXF]\MHGQRSR]\F\MQ\FK

1D U\V SU]HGVWDZLRQR UHDOL]DFM NOXF]\ MHGQRSR]\F\MQ\FK

SU]\ X*\FLX WUDQ]\VWRUD Q026 OXE SDU\ WUDQ]\VWRUyZ &026 RUD]

SRGDQR]DVDGRWU]\P\ZDQLDNOXF]DGZXSR]\F\MQHJR]GZyFKNOXF]\

MHGQRSR]\F\MQ\FK

:XNáDG]LH 6& NOXF]H PRJ E\ü SU]HáF]DQH Z GZX OXE ZLFHM

ID]DFKMHGQDNQDMF]FLHMVWRVRZDQHV]HJDU\GZXID]RZH]HZ]JOGX

QDáDWZLHMV]UHDOL]DFMXNáDGRZ

1D U\V SU]HGVWDZLRQR SU]HELHJL F]DVRZH ]HJDUD

background image

GZXID]RZHJR ] UyZQ\PL RGVWSDPL ID]RZ\PL 'OD OHSV]HM VHSDUDFML

SRPLG]\ SRV]F]HJyOQ\PL ID]DPL Z SU]HELHJDFK VWHUXMF\FK

ZSURZDG]D VL VWUHI\ PDUWZH U\VE 3RV]F]HJyOQH ID]\ ]HJDUD

GZXID]RZHJRR]QDF]RQR

φ

e

ID]DSDU]\VWDDQJHYHQ

φ

o

ID]DQLHSDU]\VWDDQJRGG

a )

b)

φ

H

T

T

'

T

x

T

T

'

T

x

φ

φ

H

φ

5\V3U]HELHJLF]DVRZH]HJDUDGZXID]RZHJRDEH]VWUHIPDUWZ\FKE]H

VWUHIDPLPDUWZ\PL

.OXF]HVWHURZDQHID]

φ

e

V]ZLHUDQHZFKZLODFKSDU]\VW\FK]D

NOXF]HVWHURZDQHID]

φ

o

V]ZLHUDQHZFKZLODFKQLHSDU]\VW\FK

8NáDG\ &SU]HáF]DQH QDOH* GR NODV\ XNáDGyZ ] V\JQDáHP

SUyENRZDQ\P :DUWRü V\JQDáX QDOH*\ GR ]ELRUX FLJáHJR OHF] MHVW

REVHUZRZDQD Z G\VNUHWQ\FK PRPHQWDFK F]DVX 8NáDG\ G\VNUHWQH

RSLVXMH VL Z G]LHG]LQLH F]DVX UyZQDQLDPL Uy*QLFRZ\PL 'R

UR]ZL]\ZDQLDW\FKUyZQDV]F]HJyOQLHSU]\GDWQDMHVWWUDQVIRUPDWD

Ζ

SR]ZDODMFD QD VSURZDG]HQLH UyZQD Uy*QLFRZ\FK GR UyZQD

DOJHEUDLF]Q\FKZG]LHG]LQLH]PLHQQHM]HVSRORQHM z

1D U\V SU]HGVWDZLRQR QDMSURVWV]H VWUXNWXU\ 6&

]DZLHUDMFHSRMHGQHMSRMHPQRFLLGZDNOXF]HGRV\PXODFMLUH]\VWDQFML

V]HUHJRZHMLUyZQROHJáHM>@

: XNáDG]LH ] U\VD SRGF]DV ID]\ e NRQGHQVDWRU MHVW

áDGRZDQ\ GR QDSLFLD

u nT

u nT

u nT

k

(

)

(

)

(

)

=

1

2

QDWRPLDVW SRGF]DV

ID]\o NRQGHQVDWRUMHVW]ZLHUDQ\LFDáNRZLFLHUR]áDGRZ\ZDQ\

a)

1

2

b)

1

2

C

C

i

1

i

2

e

o

e

o

u

1

u

2

u

1

u

2

5\V6WUXNWXU\6&V\PXOXMFHUH]\VWDQFMDV]HUHJRZ]GZRPDNOXF]DPLE

UyZQROHJá]GZRPDNOXF]DPL

background image

:F]DVLH MHGQHJR RNUHVX ]HJDURZHJR T

'

SU]HSá\ZD ]DWHP áDGXQHN

q

C u nT

u nT

=

[ (

)

(

)]

1

2

àDGXQHNWHQSU]HSá\ZDRVWU\PLLPSXOVDPLQD

SRF]WNX RNUHVyZ ]HJDURZ\FK 0R*HP\ ]DWHP ]GHILQLRZDü UHGQL

ZDUWRü SUGX MDNR VWRVXQHN SU]HSá\ZDMFHJR áDGXQNX

q

Z F]DVLH

ND*GHJRRNUHVX]HJDURZHJR T

'

GRWHJRRNUHVX

( )

( )

[

]

( )

I

I

C

T

u n T

u n T

C

T

u

n T

sr

sr

k

1

2

1

2

= −

=

=

'

'

=JRGQLH]UyZQDQLHPSU]HáF]DQDSRMHPQRü]DFKRZXMHVLMDN

UH]\VWDQFMDRZDUWRFL

R

T

C

k

=

'

/

UHGQLDZDUWRüSUGXSU]HSá\ZDMFHJRPLG]\]DFLVNDPLLZ

XNáDG]LH]U\VEOLF]RQD]DRNUHV T

'

Z\QRVL

(

)

[

]

I

I

C

T

u

n

T

sr

sr

k

1

2

1

= −

=

'

:DUWRüV\PXORZDQHMUH]\VWDQFMLMHVWWDNDVDPDMDNSRSU]HGQLR

R

T

C

k

=

'

/

3U]\NáDG\UHDOL]DFMLLQWHJUDWRUyZLILOWUyZ6&

1D

U\V

SU]HGVWDZLRQR

QDMSURVWV]\

XNáDG

5&

MHGQRELHJXQRZ\ILOWU5&RUD]V\PXOXMFJRVWUXNWXU6&ZNWyUHM

UH]\VWDQFMD

R

k

MHVW V\PXORZDQD ]D SRPRF SU]HáF]DQHJR

NRQGHQVDWRUDV]HUHJRZHJR

8NáDG ] U\VE VWDQRZL ]DUD]HP SU]\NáDG NLHG\ ]DFLVNL

VWUXNWXU\ 6& V\PXORZDQHM UH]\VWDQFML QLH V GRáF]DQH GR SXQNWyZ

RPDá\FK LPSHGDQFMDFK : XNáDG]LH W\P UHGQLD ZDUWRü SUGX

i

k

]DOH*\RGSU]\URVWXáDGXQNX

q

QDNRQGHQVDWRU]H

C

a

( )

(

)

[

]

q

u n T

u

n

T C

a

=

2

2

1

[

]

u

2

1

2

C

C

a

o

e

b)

1

u

u

2

1

u

R

k

i

k

1

2

a)

C

a

5\V-HGQRELHJXQRZ\ILOWU5&DLV\PXOXMFDJRVWUXNWXUD6&E

: ID]LH e áDGXQHN RGSá\ZDMF\ ] NRQGHQVDWRUD

C

a

MHVW UyZQ\

background image

áDGXQNRZLGRSá\ZDMFHPXGRUR]áDGRZDQHJRZID]LH o NRQGHQVDWRUD

&

(

)

[

]

( )

[

]

( )

( )

[

]

C u

n

T

u nT

C u nT

u nT

a

=

=UyZQDQLDRWU]\PXMHP\

( )

(

)

[

]

( )

(

)

[

]

[

]

u n T

u

n

T

C

C

C

u nT

u

n

T

a

2

2

1

2

1

1

=

+

3RGVWDZLDMFGRRWU]\PXMHP\

( )

(

)

[

]

[

]

q

u nT

u

n

T

C C

C

C

a

a

=

+

8UHGQLDMF Z\UD*HQLH ]D RNUHV T

'

RWU]\PXMHP\ ZDUWRü

V\PXORZDQHMUH]\VWDQFML

R

T

C

C

k

a

=

+



'

5H]\VWDQFMD

R

k

MHVW]DOH*QDRGREXSRMHPQRFL

C

a

L

C

:SU]\SDGNXJG\

C

a

!!

C

WRZ\UD*HQLHXSUDV]F]DVLGR

SRVWDFL R

T

C

k

'

/

,GHQW\F]QH ]DOH*QRFL RWU]\PXMHP\ Z SU]\SDGNX JG\

R

k

MHVW

PRGHORZDQD ]D SRPRF SU]HáF]DQHJR NRQGHQVDWRUD UyZQROHJáHJR

3U]H] DQDORJL GR XNáDGX 5& PR*HP\ RNUHOLü VWDá F]DVRZ GOD

V\PXORZDQHMVWUXNWXU\6&

τ

SC

k

a

a

a

R C

T

C

C

T

C

C

=

=

+



 ≈

'

'

6WDáD

τ

SC

]DOH*\RGF]VWRWOLZRFL]HJDUDRUD]RGVWRVXQNXSRMHPQRFL

=DVWRVRZDQLH ]HJDUD NZDUFRZHJR SR]ZDOD QD X]\VNDQLH GRNáDGQHM

LXVWDELOL]RZDQHM ZDUWRFL F]VWRWOLZRFL ]D VWRVXQHN SRMHPQRFL

C

C

a

/

PR*H ]DZLHUDü VL Z JUDQLFDFK

=DWHP VWDáD

F]DVRZD5&PR*HE\ü]UHDOL]RZDQD]GX*GRNáDGQRFL'RGDWNRZ

]DOHWWHFKQLNL6&MHVW]QDF]QDPLQLDWXU\]DFMDXNáDGyZUHDOL]RZDQ\FK

WWHFKQLN1DU\VSU]HGVWDZLRQRSURVW\LQWHJUDWRU&SU]Há F]DQH

NWyU\ QLHFR ]PRG\ILNRZDQ\ Z FHOX HOLPLQDFML ZSá\ZX SRMHPQR FL

SDVR*\WQLF]\FKVWDQRZLSRGVWDZRZ\EORNZ\NRU]\VW\ZDQ\ZV\QWH]LH

ILOWUyZ6&

: XNáDG]LH SRND]DQ\P QD U\VE UH]\VWRU

R

MHVW

V\PXORZDQ\ ]D SRPRF UyZQROHJáHM VWUXNWXU\ 6& : XNáDG]LH W\P
ZFKZLOL

(

)

t

n

T

= −

'

NRQGHQVDWRU

C

1

MHVW GRáF]RQ\ GR QDSLFLD

u

i

]DWHP]JURPDG]RQ\QDQLPáDGXQHNZ\QRVL

(

)

[

]

C u n

T

i

1

1

'

:GUXJLHM

SRáRZLHSyáRNUHVX (

)

'

n

T

1

QDVWSXMHSU]HáF]DQLHNRQGHQVDWRUD

C

1

GR

background image

ZHMFLD Z]PDFQLDF]D L SU]HODQLH ] QLHJR F]FL áDGXQNX GR

NRQGHQVDWRUD

C

2


+


+

u

i

u

o

u

i

u

o

a)

b)

R

1

C

2

C

2

C

1

5\V,QWHJUDWRU\DUHDOL]DFMD5&EUHDOL]DFMD6&

:FKZLOLt nT

=

'

VSHáQLRQHMHVWUyZQDQLHáDGXQNRZH

( )

(

)

[

]

(

)

[

]

C u n T

C u

n

T

C u

n

T

o

o

i

2

2

1

1

1

'

'

'

=

3RGRNRQDQLXWUDQVIRUPDFML

Ζ

Z\UD*HQLDRWU]\PXMHP\

( )

( )

C U

z

z

C U

z

z

C U

z

i

2

0

1

2

0

1

1

=

( )

7UDQVPLWDQFMDZ\]QDF]RQD]UyZQDQLDPDSRVWDü

( )

( )

( )

H z

U

z

U z

C

C

z

z

i

=

= −

0

1

2

1

1

1

2PyZLRQ\ LQWHJUDWRU SRVLDGD ZDG MDN MHVW ZUD*OLZRü QD

SRMHPQRFLSDVR*\WQLF]HZ\VWSXMFHPLG]\Uy*Q\PLZ]áDPLXNáDGX

D PDV :FHOX Z\HOLPLQRZDQLD WHM ZDG\ VWRVXMH VL EDUG]LHM

UR]EXGRZDQH ]ZLNV] LORFL NOXF]\ XNáDG\ V\PXOXMFH UH]\VWDQFM

LQWHJUDWRUD *HQHUDOQ ]DVDG MDN QDOH*\ VL NLHURZDü SU]\

SURMHNWRZDQLX XNáDGyZ 6& MHVW SU]HáF]DQLH RE\GZX RNáDGHN

NRQGHQVDWRUyZ PLG]\ SXQNWDPL R PDáHM UH]\VWDQFML QS (UyGáHP

QDSLFLRZ\P PDV L PDV SR]RUQ SU]\ F]\P WD VDPD RNáDGND QLH

PR*HE\üSU]HáF]DQDPLG]\(UyGáHPQDSLFLRZ\PDPDVSR]RUQ

,QWHJUDWRU6&QLHZUD*OLZ\QDSRMHPQRFLSDVR*\WQLF]HPR*HE\ü

XNáDGHP RGZUDFDMF\P DOER QLHRGZUDFDMF\P ]DOH*QLH RG VWHURZDQLD

NOXF]\ LQWHJUDWRUD ID] SDU]\VW OXE QLHSDU]\VW 8NáDG\ WDNLH

SU]HGVWDZLRQRQDU\V

0R*OLZRüV\PXODFMLUH]\VWDQFMLSR]ZDODQDUHDOL]DFMZXNáDGDFK6&

RPyZLRQ\FK ZF]HQLHM ILOWUyZ 5& D Z\NRU]\VWXMF LQWHJUDWRU\ 6&

PR*QDEXGRZDüILOWU\W\SX]PLHQQHMVWDQXRUD]LQQHDQDORJLHGRILOWUyZ

FLJá\FK ,VWQLHMH UyZQLH* PR*OLZRü WZRU]HQLD QRZ\FK VWUXNWXU L

NRQILJXUDFMLQLH]QDQ\FKZXNáDGDFKFLJá\FK

3U]\NáDGRZRQDU\VSU]HGVWDZLRQRNROHMQHHWDS\WZRU]HQLDILOWUX

ELNZDGUDWRZHJR ] GZRPD LQWHJUDWRUDPL SRF] ZV]\ RG VFKHPDWX

EORNRZHJRSRSU]H]XNáDGDNW\ZQ\5&GRUHDOL]DFML6&

background image


+

u

i

a )

e

o

e

o

C

1

C

2

u

o


+

u

i

b)

e

o

o

e

C

1

C

2

u

o

5\V,QWHJUDWRU\6&

QLHZUD*OLZHQDSRMHPQRFL

SDVR*\WQLF]HDRGZUDFDMF\

EQLHRGZUDFMF\


+


+

C

K

6

2

=

( )

u t

i

( )

u t

o

R

K

1

0

0

=

ω

/

C

K

5

1

0

=

/

ω

C

A

=

1

C

B

=

1

R

3

0

1

=

/

ω

R

2

0

1

=

/

ω

C

Q

4

1

=

/

b)

( )

U s

I

( )

U

s

O

ω

0

ω

0

s Q

/

1

s

1

s

K s

2

K

s

1

0

ω

K

0

0

/

ω

a)

C

2


+


+

u

i

e

o

o

e

C

1

C

5

C

6

e

e

o

o

C

3

C

4

e

o

e

C

A

=

1

C

B

=

1

u

o

c)

5\V5HDOL]DFMDILOWUX6&RGREURFL

4

>

DVFKHPDWEORNRZ\EXNáDG

DNW\ZQ\5&FUHDOL]DFMD6&

background image

)LOWU\DNW\ZQH&SUDFXMFHZF]DVLHFLJá\P

)LOWU\ DNW\ZQH & UHDOL]RZDQH V Z WHFKQRORJLL PRQROLW\F]QHM

W\ONR]HOHPHQWyZDNW\ZQ\FKLSRMHPQRFLLVQD]\ZDQH ILOWUDPLR

G]LDáDQLXFLJá\PDQJFRQWLQRXVWLPHILOWHUV1DMEDUG]LHMUR]ZLQLWL

XVWDELOL]RZDQJUXSILOWUyZRG]LDáDQLXFLJá\PVILOWU\W\SX

G

C

m

OXE 27$

& NWyUH QLH]DOH*QLH RG VSRVREX LFK V\QWH]\ ED]XM QD

SRGVWDZRZ\P HOHPHQFLH DNW\ZQ\P MDNLP MHVW WUDQVNRQGXNWRU OXE

Z]PDFQLDF]WUDQVNRQGXNWDQF\MQ\27$,VWQLHMHUyZQLH*JUXSDILOWUyZ

W\SX026)(7&ZNWyU\FKIXQNFMUH]\VWDQFMLG\QDPLF]QHMVSHáQLD

WUDQ]\VWRU026)(73R]\FMDILOWUyZVFDORQ\FKRG]LDáDQLXFL Já\PMHVW

MX*PRFQRXJUXQWRZDQDZG]LHG]LQLHSU]HWZDU]DQLDV\JQDáyZLLVWQLHM

WDNLH ]DVWRVRZDQLD Z NWyU\FK X*\FLH WHJR W\SX ILOWUyZ MHVW MHG\QLH

X]DVDGQLRQH =DNUHV Z\NRU]\VW\ZDQ\FK F]VWRWOLZRFL ZDKD VL

ZJUDQLFDFK RG NLONX +] GR G]LHVLWHN 0+] SU]\ ]DNUHVLH

G\QDPLF]Q\PU]GX

G%)LOWU\RG]LDáDQLXFLJá\PQDMF]FLHM

VX*\ZDQHGREXGRZ\ILOWUyZDQW\DOLDVLQJRZ\FKZDSOLNDFMDFKDXGLR

79 L +'79 Z XNáDGDFK RGF]\WX L ]DSLVX G\VNRZHJR Z V\VWHPDFK

NRPXQLNDFMLEH]SU]HZRGRZHMGREXGRZ\RGELRUQLNyZ$0L)0RUD]

ZLHOXLQQ\FK*áyZQ\PL]DOHWDPLILOWUyZRG]LDáDQLXFL Já\PVGX*D

V]\ENRüG]LDáDQLDPDá\SREyUPRF\ZV]F]HJyOQRFLZSRUyZQDQLX

GR ILOWUyZ F\IURZ\FK RUD] EUDN HIHNWyZ ]ZL ]DQ\FK ]H ]MDZLVNDPL

W\SX ÄFORFN IHHGWKURXJK´ Z\VWSXMF\PL Z ILOWUDFK UHDOL]RZDQ\FK

ZWHFKQLFH ] SU]HáF]DQ\PL SRMHPQRFLDPL 3U]\ Z\NRU]\VWDQLX WHJR

W\SXILOWUyZGRNRQXMHVLSU]HWZDU]DQLDV\JQDáXRSRVWDFLDQDORJRZHM

XQLNDMF SUREOHPyZ ]ZL]DQ\FK ] SUyENRZDQLHP OXE SU]HáF]DQLHP

V\JQDáX -HGQDN PLPR ZLHOX ]QDF]F\FK ]DOHW UHDOL]DFMD ILOWUyZ

RG]LDáDQLXFLJá\PSU]HGVWDZLDUyZQLH*ZLHOHSRZD*Q\FKSUREOHPyZ

,FK ]DNUHV G\QDPLF]Q\ MHVW RJUDQLF]RQ\ SU]\ F]\P RJUDQLF]HQLH WR

Z\QLND JáyZQLH ]PR*OLZRFL SU]HQLNDQLD V\JQDáyZ F\IURZ\FK ]

F]FLF\IURZHMXPLHV]F]RQHMUD]HP]XNáDGHPDQDORJRZ\PZMHGQ\P

XNáDG]LH VFDORQ\P RUD] LVWQLHQLD SU]HVáXFKyZ SU]H] OLQLH ]DVLODM FH

'UXJLP SRZD*Q\P SUREOHPHP V ]QDF]QH UR]U]XW\ SDUDPHWUyZ ILOWUX

VFDORQHJR Z\QLNDMFH ] WROHUDQFML SURGXFHQWD ]PLDQ WHPSHUDWXU\

SURFHVyZ VWDU]HQLD L LQQ\FK .RQLHF]QH MHVW LPSOHPHQWRZDQLH

VSHFMDOQ\FK VWUXNWXU XNáDGRZ\FK VáX*F\FK GR VWURMHQLD ILOWUX

DQDORJRZHJR 6WURMHQLH ILOWUX RGE\ZD VL QD ]DVDG]LH ]PLDQ

SDUDPHWUyZSUDF\LQWHJUDWRUyZVWDQRZLF\FKSRGVWDZRZHEORNLILOWUX

6WURMHQLDGRNRQXMHVL]PLHQLDMFQDSLFLDSUG\SRODU\]XMFHOXELFK

UR]Sá\Z\ FR Z NRQVHNZHQFML SRZRGXMH SU]HVXQLFLD SXQNWyZ SUDF\

SRV]F]HJyOQ\FKWUDQ]\VWRUyZZFKRG]F\FKZVNáDGXNáDGX

:\NRU]\VWXMF HOHPHQW\ WUDQVNRQGXNWDQF\MQH L SRMHPQRFL

background image

PR*QD]EXGRZDüLQWHJUDWRU\OXE *\UDWRU\NWyUHVWDQRZLSRGVWDZRZH

EORNL IXQNFMRQDOQH GOD Uy*Q\FK PHWRG V\QWH]\ ILOWUyZ 1D U\V

SU]HGVWDZLRQR LQWHJUDWRU\

G

C

m

] NRPSOHPHQWDUQ\P Z\MFLHP

SUGRZ\P 6SRW\ND VL UyZQLH* LQWHJUDWRU\ ] SRMHG\QF]\P Z\MFLHP

SUGRZ\P

+

+

+

+

+

U

i

+

U

i

U

i

U

i

U

o

+

U

o

U

o

+

U

o

C

2C

2C

I

o

I

o

I

o

I

o

G

m

G

m

a)

U

i

+

U

i

U

o

+

U

o

C

C

U

c

b)

U

c

+

+

5\V,QWHJUDWRU\D*

P

&E026)(7&

'OD REX XNáDGyZ ] U\VD WUDQVPLWDQFMD LQWHJUDWRUD Z\UD *D

VLZ]RUHP

( )

H s

G

s C

s

m

=

= ω

0

JG]LH

ω

0

=

G

C

m

R]QDF]D SXOVDFM GOD NWyUHM

Z]PRFQLHQLHPDZDUWRüMHGQRVWNRZ8NáDGZNWyU\PND*GHZ\MFLH

SRVLDGD LQG\ZLGXDOQ SRMHPQRü SR]ZDOD QD RJUDQLF]HQLH ZSá\ZX

SRMHPQRFL SDVR*\WQLF]\FK SRPLG]\ SRGáR*HP D RNáDGNDPL

NRQGHQVDWRUD

7UDQVNRQGXNWRU EGF\ VWHURZDQ\P QDSLFLRZR (UyGáHP

SUGRZ\PSRZLQLHQSRVLDGDüFKDUDNWHU\VW\NLPR*OLZLHMDNQDMEDUG]LHM

OLQLRZH GOD FDáHJR UR]ZD*DQHJR ]DNUHVX QDSLü ZHMFLRZ\FK VWDá

ZDUWRü

g

m

Z FDá\P ]DNUHVLH F]VWRWOLZRFL L DPSOLWXG V\JQDáX

ZHMFLRZHJR RUD] SRVLDGDü PR*OLZRü VWURMHQLD 1DMSURVWV]H ZHUVMH

LQWHJUDWRUyZ VWRVRZDQH F]VWR Z DSOLNDFMDFK Z\PDJDMF\FK EDUG]R

GX*\FK SUGNRFL G]LDáDQLD VNáDGDM VL ] SURVW\FK WUDQVNRQGXNWRUyZ

MHGQRVWRSQLRZ\FK -HGQDN Z]PRFQLHQLH VWDáRSUGRZH RUD] OLQLRZRü

WDNLFKXNáDGyZVQLHZLHONLH7RZDU]\V]UyZQLH*WDNLPUR]ZL]DQLRP

VWRVXQNRZR GX*H ZDUWRFL SRMHPQRFL SDVR*\WQLF]\FK FR XWUXGQLD

VWURMHQLH=QDF]QLHF]FLHMVWRVXMHVLOLQHDU\]RZDQHVWUXNWXU\ED]XMFH

QDXNáDG]LHZ]PDFQLDF]DUy*QLFRZHJR

,QWHJUDWRU 026)(7

& U\VE ED]XMH QD SRGVWDZRZHM

background image

VWUXNWXU]H LQWHJUDWRUD Z NWyUHM Z PLHMVFH UH]\VWRUyZ XPLHV]F]RQH

]RVWDá\ WUDQ]\VWRU\ 026 SUDFXMFH Z ]DNUHVLH WULRGRZ\P 6WDQRZL

RQH VWHURZDQH QDSLFLHP EUDPNL UH]\VWDQFMH FR XPR*OLZLD ]PLDQ

VWDáHMF]DVRZHMLQWHJUDWRUDD]DWHPSDUDPHWUyZILOWUX

1DU\VSU]HGVWDZLRQRSU]\NáDGUHDOL]DFMLILOWUXHOLSW\F]QHJR

WU]HFLHJR U]GX VWDQRZLFHJR DNW\ZQ LPSOHPHQWDFM 27$

&

SDV\ZQHJR ILOWUX GUDELQNRZHJR /& WU]HFLHJR U]GX 1LHX]LHPLRQD

LQGXNF\MQRü

L

1

Z ILOWU]H SURWRW\SRZ\P MHVW V\PXORZDQD Z ILOWU]H

27$

&GZRPD*\UDWRUDPLREFL*RQ\PLSRMHPQRFLDPL

C

L

SU]\F]\P

ND*G\ ] *\UDWRUyZ ]UHDOL]RZDQ\ MHVW Z RSDUFLX R GZD XNáDG\ 27$

U\V

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

i

o

+

i

o

G

m

G

m

G

m

G

m

G

m

G

m

G

m

G

m

u

o

C

3

C

3

C

2

C

2

C

L

C

L

C

1

C

1

b)

u

in

I

in

R

1

C

1

C

2

C

3

L

1

R

2

u

1

a)

5\V)LOWUHOLSW\F]Q\JRU]GXDSURWRW\S/&EDNW\ZQDLPSOHPHQWDFMD

27$&


Wyszukiwarka

Podobne podstrony:
13 Liniowe zastosowania wzmacniacz (2)
E 4 - Zastosowanie wzmacniaczy operacyjnych w ukladach liniowych, Elektronika
Elektronika - Zastosowanie wzmacniaczy operacyjnych - układy liniowe, Politechnika Opolska, sprawozd
Elektronika- Zastosowanie wzmacniaczy operacyjnych w układach liniowych, LABORATORIUM Z ELEKTRONIKI
E 4 - Zastosowanie wzmacniaczy operacyjnych w układach liniowych, Wykonali:
podstawowe zastosowania wzmacniaczy operacyjnych
Zastosowanie wzmacniaczy operacyjnych
Zastosowanie wzmacniacza operacyjnego Wzmacniacz odwracający i nieodwracajacy
Elektronika- ZASTOSOWANIE WZMACNIACZY OPERACYJNYCH - FILTRY AKTYWNE.DOC, LABORATORIUM Z ELEKTRONIKI
Badanie elektronicznych filtrów aktywnych z zastosowaniem wzmacniaczy operacyjnych
09 - Nieliniowe zastosowania wzmacniaczy operacyjnych, studia, Nowy folder, Nowy folder
cw 3?danie układów z zastosowaniem wzmacniaczy operacyjnych
podstawowe zastosowania wzmacniaczy operacyjnych
PE LAB 6 Zastosowanie wzmacniacza operacyjnego
podstawowe zastosowania wzmacniaczy operacyjnych
Lab 12 (Zastosowanie wzmacniaczy operacyjnych, cz 2 )
cw 3 Badanie układów z zastosowaniem wzmacniaczy operacyjnych

więcej podobnych podstron