capitolul 1 propriet i generale ale componentelor electronice pasive

CAPITOLUL 1

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ELECTRONICE PASIVE

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Un condensator multistrat de tipul MC 3202, având valoarea de 470pF poateIL FRQVLGHUDW FD UHSUH]HQWkQGRXQLWDWH FRQVWUXFWLY GH VLQH VWWWRDUH3HGH DOWSDUWHVWUXFWXUDFRQVWUXFWLYDVLJXUGLQSXQFWGHYHGHUHHOHFWULFIXQF LDGHFDSDFLWDWHHOHFWULFIXQF LDGHDFXPXODUHGHVDUFLQHOHFWULF&DDWDUHVHSRDWHYRUELGHIDSWXOFDFHVWFRQGHQVDWRUGHWLSXO0&UHSUH]LQWRFRPSRQHQWHOHFWULFGLVFUHWGHRDUHFH VWUXFWXUD VD FRQVWUXFWLY LQFOXGH GRDU IXQF LD GH FDSDFLWDWH 'DF vQVVWUXFWXUD FRQVWUXFWLY GH VLQH VWWWRDUH LQFOXGH PDL PXOWH IXQF LL HOHFWURQLFHFRPSRQHQWD HVWH FRQVLGHUDW FD ILLQG GLQ FDWHJRULD FLUFXLWHORU LQWHJUDWH ASIC,RAM, ROM, microprocesor, etc.).

Toate componentele VXQWDOFWXLWHGLQPDWHULDOHvQWURVWUXFWXUELQHGHILQLWHIHFWHOH IL]LFH VSHFLILFH DFHVWRU PDWHULDOH vQWUHEXLQ kQGXVH SHQWUX RE LQHUHDSURSULHW LORUFDUDFWHULVWLFH ILHFUXL WLSGHFRPSRQHQW vQSDUWH&XDOWH FXYLQWH ODED]DUHDOL]ULLFRPSRQHQWHORUHOHFWURQLFHVWDXOHJLDOHIL]LFLLFDUHPDWHULDOL]DWHSULQintermediul proceselor tehnologice conduc la realizarea de componente cu diverseFRPSOH[LW LIXQF LRQDOHúLFRQVWUXFWLYHÌQWUHFRPSRQHQWHúLPDWHULDOHSHGHRSDUWHúLOHJLOHIL]LFLLSHGHDOWSDUWHH[LVWRGLUHFWOHJWXUYH]LILJXUD

Satisfac cerin H

electronice

Procese tehnologice

Componente

Materiale

Fig. 1.1$F LXQHDSURFHVXOXLWHKQRORJLFvQUHDOL]DUHDFRPSRQHQWHORU

Cap1. 3URSULHW Lgenerale ale componentelor electronice pasive

2

La fabricarea componentelor sunt necesare anumite procedee tehnologiceSURFHGHHFHDOFWXLHVFWHKQRORJLDXQXLSURGXV

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mai mic.,PSHGDQ DZHVWHGHILQLWFDILLQGUDSRUWXOGLQWUHWHQVLXQHDUúLFXUHQWXOI .

ϕjZejXRI

UZ =+== (1.1)

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. , 22

R

XtgXRZ =+= ϕ (1.2)

ÌQ IXQF LH GH WLSXO LPSHGDQ HL FDUH VH GRUHúWH V VH RE LQ UH]XOW úL WLSXOcomponentei pasive.• 'DFZ = R, LPSHGDQ DHVWHUH]LVWLY LDUFRPSRQHQWDSDVLYFDUDFWHUL]DWGHRDVHPHQHDLPSHGDQ VHQXPHúWHrezistor. Rezistorul este caracterizat de parametrulIXQGDPHQWDOUH]LVWHQ FHGHILQHúWHFRPSRQHQWD5H]LVWRUXOLGHDODUHLPSHGDQ DSXUUH]LVWLYúLGHID]DMXOGLQWUHWHQVLXQHúLFXUHQW]HUR• 'DFZ = 1/jωC, LPSHGDQ DHVWHFDSDFLWLYLDUFRPSRQHQWDSDVLYFDUDFWHUL]DWGHRDVHPHQHDLPSHGDQ VHQXPHúWHcondensator. Condensatorul este caracterizatGH SDUDPHWUXO IXQGDPHQWDO FDSDFLWDWH HOHFWULF FH GHILQHúWH FRPSRQHQWD&RQGHQVDWRUXO LGHDO DUH LPSHGDQ D SXU FDSDFLWLY úL GHID]DMXO GLQWUH WHQVLXQH úLcurent este -π$GLFFXUHQWXOHVWHGHID]DWvQDLQWHDWHQVLXQLL• 'DF Z = jωL, LPSHGDQ D HVWH LQGXFWLY LDU FRPSRQHQWD FDUDFWHUL]DW GH RDVHPHQHD LPSHGDQ VH QXPHúWH inductor . Inductorul este caracterizat deSDUDPHWUXO IXQGDPHQWDO LQGXFWDQ HOHFWULF FH GHILQHúWH FRPSRQHQWD ,QGXFWRUXOLGHDODUHLPSHGDQ DSXULQGXFWLYúLGHID]DMXOGLQWUHWHQVLXQHúLFXUHQWHVWHπ/2.

5H]XOW GHFL vQ IXQF LH GH WLSXO LPSHGDQ HL SULQFLSDOD FODVLILFDUH DFRPSRQHQWHORUSDVLYHUH]LVWRDUHFRQGHQVDWRDUHúLLQGXFWRDUH

CRPSRUWDUHDUHDODXQHLFRPSRQHQWHQXFRUHVSXQGHPRGHOXOXLLGHDOL]DWGHDFHHDVHDOFWXLHVFPRGHOHFXHOHPHQWHLGHDOHFHSRWDSUR[LPDDFHDVWFRPSRUWDUH'HRDUHFHVWUXFWXUDUHDODFRPSRQHQWHLGHWHUPLQDSDUL LDXQRUHIHFWHSDUD]LWHFDUHLQIOXHQ HD]HIHFWXOIL]LFGRULWGHFHOHPDLPXOWHRULQHOLPLWPGLQFRQVLGHUHQWHGHVLPSOLILFDUHQXPDLODHIHFWXOIL]LFGRULWLGHDOFHHDFHGHUHJXOHVWHYDODELOGRDUSHKkUWLH&DXUPDUHvQDQXPLWHFRQGL LLGHIXQF LRQDUHSHQWUXRvQ HOHJHUHPDLDPSODFRPSRUWULL XQHL DQXPLWH FRPSRQHQWH HVWH QHFHVDU V VH LQ VHDPD GH HIHFWHOHparazite, aceasta conducând la completarea schemei echivalente. În cazulrezistorului, luându-se în considerare efectul de înmagazinare a energiei electrice,UHVSHFWLYPDJQHWLFHVFKHPDHOHFWULFHFKLYDOHQWGHYLQHFDFHDGLQILJXUD

Componente úLFLUFXLWHSDVLYH Note de curs

3

R Lp

Cp

Fig. 1.26FKHPDHFKLYDOHQWDUH]LVWRUXOXL

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'H PXOWH RUL GLIHULWH XWLOL]UL LPSXQ H[LVWHQ D XQRU QRL FDWHJRULL GHFRPSRQHQWH &D XUPDUH GH UHJXO SH ED]DPDWHULDOHORU úL D OHJLORU IL]LFLL SRW ILGH]YROWDWHQRLFRPSRQHQWHFDUHSULQSURSULHW LOHORUVUVSXQGFHULQ HORUXWLOLWDUHReferitor la materialele implicate în realizarea componentelor electronice pasive,SUHSRQGHUHQWH VXQW PDWHULDOHOH GLHOHFWULFH úL FRQGXFWRDUH XUPDWH GH PDWHULDOHPDJQHWLFHúLvQPVXUPDLPLFGHPDWHULDOHVHPLFRQGXFWRDUHúLHOHFWUROL L

'H]YROWDUHDHOHFWURQLFLLúLHOHFWURWHKQLFLLPRGHUQHHVWH vQFRQH[LXQHGLUHFW

FX GH]YROWDUHD FRPSRQHQWHORU )U SURJUDPHOH GH GH]YROWDUH FH DX DYXW ORF vQGRPHQLXO FRPSRQHQWHORU DWkW DFWLYH FkW úL SDVLYH QX DU IL IRVW SRVLELOH DFWXDOHOHSHUIRUPDQ HDOHFRPXQLFD LLORUVDXDSUHOXFUULORUGHGDWH

2 LPDJLQH JOREDO D XWLOL]ULL FRPSRQHQWHORU vQ SULQFLSDOHOH GRPHQLL GHXWLOL]DUH HVWH SUH]HQWDW vQ FHOH FH XUPHD] 2 SRQGHUH PDUH R DX GRPHQLLOHSURIHVLRQDOHDOFWXLWHGLQFRPXQLFD LLúLSUHOXFUDUHDGDWHORUDSDUDWXUDGHPVXUDUHUHJODUHúLFRPDQGHOHFWURQLFDHQHUJHWLFGHSXWHUH&HOHODOWHGRPHQLLHOHFWURQLFDGH GLYHUWLVPHQW HOHFWURQLFD FDVQLF HOHFWURQLFD DXWR DX vQ YHGHUH vQ SULPXO UkQGLPSOHPHQWDUHD vQ YLD D SDUWLFXODU (OHFWURQLFD GH GLYHUWLVPHQW FXSULQGH R JDP

ODUJ GH DSDUDWXU PDL DOHV vQ GRPHQLXO DXGLR YL]XDOXOXL 3HQWUX IDEULFDQWXO GHFRPSRQHQWHHVWHH[WUHPGHLPSRUWDQWFDSHQWUXGLIHULWHGRPHQLLDOHHOHFWURQLFLLV

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0ULPLFDUDFWHULVWLFH

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4

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9DORDUHDQRPLQDOXNúLWROHUDQ DGHIDEULFD LHWSe va nota cX; YDORDUHD SDUDPHWUXOXL IXQGDPHQWDO UH]LVWHQ FDSDFLWDWH

LQGXFWDQ DOFRPSRQHQWHORUSDVLYH9DORDUHDQRPLQDOXNUHSUH]LQWYDORDUHDFH VH GRUHúWH V VH RE LQ vQ SURFHVXO GH IDEULFD LH D FRPSRQHQWHL úL HVWH vQ

JHQHUDOPDUFDWSHFRUSXODFHVWRUDÌQPRGLGHDOSURFHVXOGHIDEULFD LHDUWUHEXLVVHGHVIúRDUHDVWIHOvQFkWVVHRE LQ FX ULJXUR]LWDWH FHHD FH VD SURLHFWDW 'DWRULW FRQGL LLORU UHDOH vQ FDUH VHGHVIúRDUSURFHVXOGHIDEULFD LHHVWHSRVLELOVDSDUDEDWHULvQWUHYDORULOHSURLHFWDWHúLYDORULOHIDEULFDWH'DFVHXUPUHúWHODXQSURGXVRE LQHUHDXQXLSDUDPHWUXX1, deexemplu capacitatea în cazul unui condensator, este posibil ca în urma procesului deIDEULFD LHSDUDPHWUXOVUH]XOWHFXYDORDUHD;PDLPXOWVDXPDLSX LQGLIHULWGHX1,FD DWDUH VH SRDWH IDFH DILUPD LD F YDORDUHD ; RE LQXW HVWH YDULDELO DOHDWRDUH9DULDELODDOHDWRDUHHVWHRPULPHFDUHvQIXQF LHGHUH]XOWDWXOXQXLH[SHULPHQWSRDWHlua valoarea dintrRPXO LPHELQHGHILQLW GH YDORUL PXO LPHD YDORULORU SRVLELle).$FHDVWYDORDUHQXSRDWHILFXQRVFXWvQDLQWHGHHIHFWXDUHDH[SHULPHQWXOXL'DFVHPVRDU DFHHDúL PULPH ; FDUDFWHULVWLF OD XQ PDUH QXPU GH DFHODúL WLS GHFRPSRQHQWH GHH[HPSOX UH]LVWHQ D vQ FD]XOXQXL ORWGHGH UH]LVWRDUHGH WLS5&* FX UH]LVWHQ D QRPLQDO GH1kΩ úL VH UHSUH]LQW SH RUGRQDW QXPUXOYDORULORUFRQ LQXWHvQ∆;VHRE LQHGHUHJXORKLVWRJUDPGLVSXVVXEIRUPGHclopot, figura 1.3.

Fig. 1.3'LVWULEX LDYDORULORUXQHLPULPLFDUDFWHULVWLFH


5

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e2

12

2

2

)x(x--

σπσ=Y(x) (1.3)

XQGH<[HVWHGHQVLWDWHDGHSUREDELOLWDWHDGLVWULEX LHLYDULDELOHLDOHDWRDUH x - valoarea variabilei aleatoare; x - valoarea medie; σ DEDWHUHD PHGLH SWUDWLF GLVWDQ D GH OD YDORDUHD PHGLH OD SXQFWXO GHinflexiune al curbei).

&XUEHOHGLVWULEX LHLQRUPDOHSUH]LQWXUPWRDUHOHSURSULHW L

- toate admit un maxim pentru x = x VF]kQG GH R SDUWH úL GH DOWD VSUH D[Dabsciselor;WRDWHFXUEHOHVXQWVLPHWULFHID GHRSDUDOHOODD[DRUGRQDWHORUGXVSULQSXQFWXOde maxim;WRDWHFXUEHOHDXIRUPGHFORSRWDYkQGFRQYH[LWDWHDvQGUHSWDWvQVXVvQDSURSLHUHDpunctului de maxim;- în punctele x-σúLx+σHOHvúLVFKLPEFRQYH[LWDWHDFXFkWσHVWHPDLPLFFXDWkWFORSRWXOHVWHPDLDVFX LWLDUFXFkWσ este mai mare cu atât clopotul este mai turtit.

Schimbarea valorii x UHYLQH OD R WUDQVODWDUH D JUDILFXOXL IXQF LHL SH D[Dabsciselor.

'DF VH LQWHJUHD] SH LQWHUYDOXO >xn , xn+1@ VH RE LQH SUREDELOLWDWHD FX FDUHPULPHDFDUDFWHULVWLFVHVLWXHD]vQLQWHUYDOXOUHVSHFWLY

dxY(x)=Px

xn

1n+

n

∫ (1.4)

3ULQ PXOWLSOLFDUHD FX QXPUXO WRWDO GH FRPSRQHQWH UH]XOW QXPUXO GHFRPSRQHQWHFXPULPHDFDUDFWHULVWLFvQLQWHUYDOXOUHVSHFWLY

1H SURSXQHP V FDOFXOP SUREDELOLWDWHD FX FDUH UHVSHFWLYD PULPH

FDUDFWHULVWLFVHDIOvQLQWHUYDOXO>x-3σ , x+3σ]:

dxY(x)=)3+x,3-xP(3+x

3-x∫

σ

σσσ (1.5)

GHXQGHFXVFKLPEDUHDGHYDULDELOσ

xx-=u UH]XOW

997,0 = due 2

1=3)<u<P(-3 2

u-3

3-

2

∫π (1.6)


6

&XDOWHFXYLQWHFRUHVSXQ]WRUXQHLGLVWULEX LLQRUPDOHDPULPLLFDUDFWHULVWLFHXQXL ORW GH FRPSRQHQWH XQ SURFHQWDM GH GLQWUH HOH DX YDORDUHD UHDO DPULPLLFDUDFWHULVWLFHvQFD]XOFRQGHQVDWRDUHORUFDSDFLWDWHDFXSULQVvQLQWHUYDOXO[ x -3σ, x+3σ].

/D IDEULFD LD GH FRPSRQHQWH VH vQFHDUF FD SULQ SURFHVXO WHKQRORJLFvPSUúWLHUHD GHFL LPSOLFLW DEDWHUHD YDORULL FDUDFWHULVWLFH V ILH FkW PDL PLFÌPSUúWLHUHDvQMXUXOYDORULLQRPLQDOHWUHEXLHVILHDVWIHOvQFkWILHFDUHFRPSRQHQWvQIXQF LXQHVSRDWILYkQGXWDVWIHOvQFkWVQXH[LVWHUHEXWXUL

'LQFDX]DQHQXPUD LORUIDFWRULFHSRWVLQWHUYLQvQSURFHVXOWHKQRORJLFvQPDUHHLSRWILJUXSD LvQWUHLFDWHJRULLFDUDFWHULVWLFLGHPDWHULDOSUHFL]LDSURFHVXOXLWHKQRORJLF IDFWRUXO XPDQ YDORDUHD UHDO UH]XOWDW VH VLWXHD] vQ MXUXO YDORULLQRPLQDOH&XFkWDSURSLHUHDGLQWUHFHOHGRXYDORULQRPLQDOúLUHDOHVWHPDLPDUHFXDWkWWROHUDQ DYDORULLUHDOHFRPSDUDWLYFXYDORDUHDQRPLQDOHVWHPDLPLF

7ROHUDQ D UHSUH]LQW DEDWHUHD PD[LP D YDORULL UHDOH ID GH YDORDUHDQRPLQDO SH FDUH R SRDWH SUH]HQWD R PULPH FDUDFWHULVWLF GLQWU-un lot deFRPSRQHQWHÌQFD]XOXQXLORWGHGHUH]LVWRDUHFXYDORDUHDQRPLQDOGH1kΩúLWROHUDQ D GH ± vQVHDPQ SUDFWLF F PULPHD FDUDFWHULVWLF D UH]LVWRUXOXLUH]LVWHQ DVDVHYDDIODvQLQWHUYDOXO>Ω, 1100Ω].

7ROHUDQ D GH IDEULFD LH HVWH vQ XOWLP LQVWDQ R GHFL]LH D SURLHFWDQWXOXL GHcomponente. În afara celor expuse anterior, un factor important în stabilireaWROHUDQ HLPLQLPHvODUHVWDELOLWDWHDFRPSRQHQWHLFHYDILSUH]HQWDWXOWHULRUúLPDLGHWDOLDW OD ILHFDUH WLS GH FRPSRQHQW 6WDELOLWDWHD FRPSRQHQWHL H[SULP DEDWHULOHLUHYHUVLELOH DOH FRPSRQHQWHL GDWRULW GLYHUúLORU IDFWRUL HOHFWULFL VDX neelectrici. ÎnIXQF LH GH DFHDVWD WROHUDQ D PLQLP D FRPSRQHQWHL HVWH SX LQ PDL PLF GHFkWVWDELOLWDWHD 'H H[HPSOX UH]LVWRDUHOH FX SHOLFXO GH FDUERQ DX VWDELOLWDWH GH±3%...±7ROHUDQ DPLQLPHVWHGH±7ROHUDQ DGHIDEULFD LHILLQGvQIRQGvQXOWLP LQVWDQ UH]XOWDWXOPVXUWRULLFRQIRUPGHFL]LHLSURLHFWDQWXOXLVDUSXWHDRE LQHvQDFHVWFD]úLRWROHUDQ GH± 1%, ±HWF&XFkWWROHUDQ DFRPSRQHQWHLVFDGHSUH XOFUHúWHDHFL vQDFHVWFD]VDURE LQHRFUHúWHUH LQDGHFYDW DSUH XOXLSHQWUX F YDORDUHD UH]LVWHQ HL GDWRULW LQVWDELOLW LL VH PRGLILF GXS XWLOL]DUHDDFHVWHLDvQWUXQFLUFXLWúLPDLDOHVvQWLPSFX± 10% ... ±GHFLWUHEXLHUHDOL]DWDFHDVW FRUHODUH D WROHUDQ HL PLQLPH FX VWDELOLWDWHD FRPSRQHQWHL SHQWUX F DOWIHOSUH XOFRPSRQHQWHLFUHúWHIURMXVWLILFDUHWHKQLF

0DWHPDWLFWROHUDQ DHVWHUHSUH]HQWDWGHH[SUHVLD

N

N

X

XX |-|max=t r± (1.7)

sau de expresia

[%] 100|-|

max=tN

Nr

X

XX± (1.8)


7

Acest mod de determinare este valabil pentru WROHUDQ VLPHWULF DGLFDEDWHUHDSR]LWLYHVWHHJDOFXFHDQHJDWLY6XQWvQVFD]XULFkQGFHOHGRXGLIHUÌQDFHVWVHQVYRPGHILQLRWROHUDQ SR]LWLYQRWDWt+úLXQDQHJDWLYt-

N

NM

X

XXt

−=+ (1.9)

N

Nm

X

XXt

−=− (1.10)

unde XM, respectiv Xm UHSUH]LQW YDORDUHD PD[LP UHVSHFWLY PLQLP Dparametrului fundamental.

'H H[HPSOX VXQW FRQGHQVDWRDUH FH DX WROHUDQ H GH IRUPD -20%+80%. Pe acestea le vom numi ca având WROHUDQ QHVLPHWULF.

(VWHHYLGHQWFWROHUDQ DVLPHWULFSRDWHILGHWHUPLQDWúLFXUHOD LD

N

mN

N

NM

X

XX

X

XXt

−±=

−±= (1.11)

$úDFXPVDSUHFL]DWDEDWHUHDYDORULLUHDOHID GHYDORDUHDQRPLQDOHVWHXQDWULEXW DO IDEULFD LHL FRPSRQHQWHORU HOHFWURQLFH úL FD DWDUH FX FkW PD[LPXPXOGLIHUHQ HL HVWH PDL PLF FX DWkW IDEULFD LD FRPSRQHQWHL VH ED]HD] SH XQ XWLODMWHKQRORJLFPDL EXQ UHJODMXO SURFHVXOXL WHKQRORJLF HVWH FRUHVSXQ]WRUPDWHULDOHOHXWLOL]DWHvQIDEULFD LHSUH]LQWFDUDFWHULVWLFLPDLEXQHÌQJHQHUDOWRDWHDFHVWHDVSHFWHconduc la scumpirea componentei.

9DORULOH QRPLQDOH DOFWXLHVF XQ úLU GH YDORUL RE LQXW SULQ FRQFDWHQDUHDDOWXUDUHDXQXL úLUGHGHFDGH ÌQ FDGUXO ILHFUHL GHFDGH VH DOHJH DFHODúL QXPU GHYDORULQRPLQDOHFHOHGHDFHODúLUDQJDYkQGDFHOHDúLFLIUHVHPQLILFDWLYH

'HWHUPLQDUHDYDORULORUQRPLQDOHDUHvQYHGHUHXUPWRDUHOHFULWHULL

D 3HQWUX GRX YDORUL QRPLQDOH FRQVHFXWLYH XN1 úL XN2, cu XN1 < XN2

DSDU LQkQGDFHOHLDúLVHULLGHYDORULSUH]LQWDFHHDúLWROHUDQ HVWHQHFHVDUVH[LVWHUHOD LD

t)-(1Xt)+(1X 2N1N ≥ (1.12)FHHDFHDVLJXUFDODXQQXPUPDUHGHFRPSRQHQWHFXYDORDUHDQRPLQDOXN1 sauXN2 GLVWULEX LD YDORULL UHDOH FDUH SHQWUX XQ QXPU UHGXV GH FRPSRQHQWH HVWH RGLVWULEX LHGLVFUHWGHYDORULSRDWHVGHYLQRGLVWULEX LHFRQWLQXDYDORULL UHDOH&RQGL LD SUHFL]HD] F GLVWULEX LLOH GH YDORUL UHDOH DOH FHORU GRX YDORULQRPLQDOHWUHEXLHV VH LQWHUVHFWH]HVSUH]LQWHXQGRPHQLXFRPXQGHYDORULYH]Lfigura 1.4.

E 7ROHUDQ DILHFUHLVHULLGHYDORUL WUHEXLHV ILH LQGHSHQGHQWGHYDORDUHDQRPLQDO&RQGL LLOHPHQ LRQDWHSRWILVDWLVIFXWHvQFD]XOvQFDUHYDORULOHQRPLQDOHDOFWXLHVFRSURJUHVLHJHRPHWULFFXUD LDUSULPXOWHUPHQILLQGYDORDUHDQRPLQDOX0.

002

00 .....................,, XrXrrXX n (1.13)


8

XN1 XN2(1-t) XN1(1+t) XN2

Fig. 1.46XSUDSXQHUHDGRPHQLXOXLGHYDORULSHQWUXGRXYDORULnominale consecutive.

'DFVHFRQVLGHURGHFDGDOFWXLWGLQQYDORULQRPLQDOHvQUHOD LDtermenul rnX0 HVWH SULPXO FDUH DSDU LQH GHFDGHL LPHGLDW XUPWRDUH &RQVLGHUkQGvalorile nominale X0úLrX0úLSXQkQGFRQGL LDUH]XOWODOLPLW

, t)-(1r=t)+(1 00 XX

t-1

t+1=r (1.14)

5HOD LD RIHU OHJWXUD GLQWUH UD LD SURJUHVLHL úL WROHUDQ ILLQGHFKLYDOHQWFX

1r+

1r-=t (1.15)

5D LDUSRDWHILSUHFL]DWGHQXPUXOGHYDORULH[LVWHQWHLQWURGHFDG LQkQGVHDPDFUDSRUWXODGRLWHUPHQLGHDFHODúLUDQJDSDU LQkQGDGRXGHFDGHVXFFHVLYHHVWH &RQVLGHUkQG SULPLL WHUPHQL D GRX GHFDGH VXFFHVLYH GLQ SURJUHVLDJHRPHWULFUH]XOW

, 10=r

0

0n

X

X

n 10=r (1.16) 5HOD LD SUHFL]HD] UD LD XQHL VHULL IXQF LH GH QXPUXO YDORULORUQRPLQDOHFRQ LQXWHGHRGHFDGÌQDFWXDOXOVWDGLXGHGH]YROWDUHDOHOHFWURQLFLLQXP UXOQDGHYHQLWIRDUWHPDUHXQHRULFkWHYDVXWHHOGHSLQ]kQGGHWHKQRORJLDFXFDUHVHUHDOL]HD] FRPSRQHQWHOHGH UHJODMXO SURFHVXOXL WHKQRORJLF GH FDOLWDWHD SURFHVXOXL WHKQRORJLF vQ XOWLP

LQVWDQ În tabelul 1.1 sunt prezentate caracteristicile seriilor de valori nominale

GHWHUPLQDWH FRQIRUP UHOD LLORU DQWHULRDUH ÌQ DQH[D $ VXQW WUHFXWH YDORULOHnominale pentru câteva serii.


9

Tabelul 1.1 Caracteristicile seriilor de valoriNXPUXOGHYDORULQRPLQDOHQFRQ LQXWHGHRGHFDG

RD LD VHULHL r

TROHUDQ Dt[%]

Denumirea seriei

6 1,5 ±20 E612 1,2 ±10 E1224 1,1 ±5 E2448 1,05 ±2,5 (±2) E4896 1,025 ±1,25 (±1) E96192 1,012 ±0,5 E192384 1,006 ±0,25 E384

Structura valorilor nominale dintrR GHFDG DSDU LQkQG GLIHULWHOor serii deYDORUL LQGLF IDSWXO F vQWRWGHDXQD GHFDGD VHULHL VXSHULRDUH LQFOXGH YDORULOHQRPLQDOH DOH GHFDGHL VHULHL LQIHULRDUH'UHSW XUPDUH HVWH DGPLV FD R FRPSRQHQWHOHFWURQLF GH R DQXPH YDORDUH QRPLQDO DSDU LQkQG XQHL VHULL LQIHULRDUH V ILHvQORFXLW FX R FRPSRQHQW GH DFHHDúL YDORDUH QRPLQDO GDU DSDU LQkQG XQHL VHULLVXSHULRDUHGHYDORULQXúLLQYHUV

'LQ FHOH SUH]HQWDWH VH SRDWH UHPDUFD IDSWXO F vQWUH WROHUDQ D W FHFDUDFWHUL]HD]RVHULHGHYDORULQRPLQDOHúLQXPUXOGHYDORULQRPLQDOHFRQ LQXWHGHRGHFDGH[LVWROHJWXUVWUkQV&XFkWGRXYDORULQRPLQDOHVXFFHVLYHDSDU LQkQGDFHOHDúLVHULLGHYDORULVXQWPDLDSURSLDWHFXDWkWWROHUDQ DVHULHLHVWHPDLPLFD&Durmare întrXQLQWHUYDOFHDFRSHUYDORULFRGHFDGGHH[1KΩ - 10KΩ sau 1Ω -10Ω SHQWUX UH]LVWRDUH SHPVXU FH QXPUXO GHYDORUL QRPLQDOH FUHúWH WROHUDQ DFRPSRQHQWHORUWUHEXLHVVFDG

3ULYLQGYDORDUHDQRPLQDO DPULPLL FDUDFWHULVWLFH D XQHL FRPSRQHQWH HVWHH[WUHP GH LPSRUWDQW V VH UH LQ IDSWXO F HD HVWH DWLQV GH XQ QXPU UHGXV GHH[HPSODUH &D XUPDUH XQ FLUFXLW WUHEXLH GH UHJXO V ILH DVWIHO FRQVLGHUDW vQFkWFRPSRQHQWHOHOXLVSRDWDYHDYDORDUHDUHDOUVSkQGLWvQMXUXOXQHLDQXPHYDORULQRPLQDOHIUFDSULQDFHDVWDFLUFXLWXOVVHGHIHFWH]HVDXVILHDIHFWD LSDUDPHWULLacestuia.

ÌQSURLHFWDUHDFLUFXLWHORUvQXOWLPXOWLPSVHLPSXQHFRQGL LDFDFLUFXLWXOVILHDVWIHO FRQFHSXW vQFkW ILHFUHL FRPSRQHQWH V L VH SHUPLW GRPHQLXO PD[LP GHYDULD LHDGPLVGHFDOFXOXOFLUFXLWXOXL3ULQDFHDVWDVHRE LQHRULXQUDQGDPHQWULGLFDWDO IDEULFD LHL GHRDUHFH úL OD FRPSRQHQWH D FURUPULPH FDUDFWHULVWLF VH VLWXHD]GHSDUWHGHYDORDUHDQRPLQDOPHGLHQXVHDMXQJHODGHIHFWDUHvQIXQF LRQDUHRULRUDWGHGHIHFWDUHUHGXVvQFD]XOvQFDUHFRPSRQHQWHOHODIDEULFD LDFLUFXLWXOXLVXQWDOHVHFXWROHUDQ DPDLPLFGHFkWFHDDGPLVGHFDOFXOXOGHvPSUúWLHUH$FHVWSURFHGHXGHRSWLPL]DUHDSOLFDWvQSURLHFWDUHDFLUFXLWHORUSRDUWGHQXPLUHDGHcentrarea circuitului ( Device centering).

Domeniul temperaturilor de utilizare, [θm, θM ] UHSUH]LQW LQWHUYDOXO GHYDORULGHWHPSHUDWXUθm úLθM vQFDUHFRPSRQHQWDSRDWHIXQF LRQD$FHVWLQWHUYDOHVWHVDXWUHEXLHSUHFL]DWGHIDEULFDQWXOGHFRPSRQHQWHúLHVWHVSHFLILFILHFUXLWLSGHFRPSRQHQWDvQSDUWH(VWHSHUIHFWSRVLELOFDGRXFRPSRQHQWHVSUH]LQWHDFHOHDúL


10

FDUDFWHULVWLFLHOHFWULFHúLPHFDQLFHGDUVSUH]LQWH LQWHUYDOGLIHULWDO WHPSHUDWXULORUvQFDUHILHFDUHSRDWHIXQF LRQD'HSúLUHDOLPLWHORUGRPHQLXOXLGHWHUPLQPRGLILFULLUHYHUVLELOH vQPDWHULDOHOH GLQ FDUH HVWH DOFWXLW FRPSRQHQWD úL DUH GUHSW XUPDUHmodificarea QHSHUPLVDSDUDPHWULORUDFHVWHLDúLFKLDUGHIHFWDUHDVD

'DWRULWDGHSHQGHQ HLGHWHPSHUDWXUDSURSULHW LORUGHPDWHULDODWkWDFHORUHOHFWULFHFkWúLFHORUneelectrice, componentele în interiorul intervalului admis, de laRWHPSHUDWXUODDOWDYRUSUH]HQWDYDORULFHGLIHUvQWURPVXUPDLPDUHVDXPDLPLF ÌQ FD]XO XQXL FRQGHQVDWRU PDWHULDOXO DUPWXULORU úLVDX GLHOHFWULFXO GLQWUHDUPWXULODYDULD LLGHWHPSHUDWXUvúLPRGLILFDWkWJHRPHWULDFkWúLFDUDFWHULVWLFLOHelectrice.

7HPSHUDWXUD PLQLP θm úL WHPSHUDWXUD PD[LP θM sunt prezentate deSURGXFWRUvQFDWDORDJHSULQLQWHUPHGLXOFDWHJRULHLFOLPDWLFHFDUHHVWHGHIRUPDN1,N2, N3. N1 este θm , N2 este θM , iar N3HVWHQXPUXOGH]LOHSHQWUXFDUHSURGXFWRUXOUHDOL]HD]YHULILFULOHFOLPDWLFHDOHFRPSRQHQWHL vQDQXPLWHFRQGL LL VSHFLILFDWHGHQRUPHLQWHUQD LRQDOH

$YkQGvQYHGHUHFRQGL LLOHUHDOHvQFDUHIXQF LRQHD]FLUFXLWXOSURLHFWDQWXOYDWUHEXL V DOHDJ FRPSRQHQWHOH DVWIHO vQFkW vQ WLPSXO IXQF LRQULL WHPSHUDWXUDcorpului componentei θcVQXGHSúHDVFSHθm , respectiv θM ,

θc∈[θm , θM] , (1.17)9DULD LDYDORULLFRPSRQHQWHLFXWHPSHUDWXUD

9DORDUHD XQHL FRPSRQHQWH SDVLYH VH PRGLILF PDL PXOW VDX PDL SX LQ vQIXQF LHGHWHPSHUDWXU

3HQWUX D SXWHD VWDELOL IHOXO vQ FDUH FLUFXLWXO HOHFWURQLF IXQF LRQHD] vQWU-unDQXPH LQWHUYDO GH WHPSHUDWXU HVWH QHFHVDU V VH FXQRDVF FX FkW VH PRGLILFYDORDUHDFRPSRQHQWHLSDVLYHFRPSDUDWLY FXYDORDUHD UHDO GH ODR WHPSHUDWXU GHUHIHULQ FRQVLGHUDW°C sau 25 &QXPLWúLWHPSHUDWXUDFDPHUHL0RGDOLW LOHSULQFDUHSURLHFWDQ LLGHFLUFXLWHSRWFXQRDúWHYDORDUHDUHDOIXQF LHGHWHPSHUDWXUpresupun utilizarea datelor de catalog. Acest aspect poate fi precizat în trei moduri.a) 5HSUH]HQWDUHJUDILFIRORVLWvQJHQHUDOSHQWUXFRPSRQHQWHFXYDULD LHPDUHDvalorii cu temperatura sau QHOLQLDU

X

θm θM θ Fig. 1.59DULD LDFXWHPSHUDWXUDDSDUDPHWUXOXLIXQGDPHQWDO


11

E 7ROHUDQ H GDWRUDWH YDULD LHL FX WHPSHUDWXUD D YDORULL FRPSRQHQWHL OD

WHPSHUDWXUD PLQLP θm úL WHPSHUDWXUD PD[LP θM IDW GH YDORDUHDFRPSRQHQWHLODWHPSHUDWXUDGHUHIHULQ θ0.

( ) ( )( )0

01 θ

θθX

XXt m −= (1.18)

( ) ( )( )0

02 θ

θθX

XXt M −

= (1.19)

F&RHILFLHQWXOGHYDULD LHFXWHPSHUDWXUDαθFDUHHVWHGHILQLWGHUHOD LD

θαθ d

dX1=

X (1.20)

Felul în cDUH R FRPSRQHQW vúL PRGLILF YDORDUHD OD FUHúWHUHD WHPSHUDWXULLGHWHUPLQVHPQXOFRHILFLHQWXOXLWHUPLF'DFOHJHDGHYDULD LHFXWHPSHUDWXUDHVWHOLQLDUFRHILFLHQWXOWHUPLFVHSRDWHH[SULPDSULQUHOD LD

X

X

1=

20 θαθ ∆

∆ (1.21)

θθθθθ

20

20

-=

)X(-)X(=X unde

∆∆

$FHDVWDYDORDUHGDWGHDSUR[LPHD]YDORDUHDH[DFWFXDWkWPDLELQHFXFkWLQWHUYDOXOGHWHPSHUDWXUHVWHPDLPLF'HPHQ LRQDWFGXSUHOD LDRYDULD LH OLQLDU D PULPLL ; FX WHPSHUDWXUD QX FRQGXFH OD XQ FRHILFLHQW GHWHPSHUDWXUFRQVWDQWúLUHFLSURF

&RHILFLHQ LLGHWHPSHUDWXUGD L vQUHOD LLOHúLVXQWDSUR[LPDWLYHJDOL GDF YDULD LLOH FX WHPSHUDWXUD VXQW PLFL 'RDU vQ FD]XO XQRU FRHILFLHQ L GHWHPSHUDWXU PLFL VDX GRPHQLL GH WHPSHUDWXU PLFL XQGH YDULD LD OXL ; HVWHQHVHPQLILFDWLYFHOHGRXUHOD LLúLGDXYDORULVHQVLELOHJDOH

3HQWUX R YDULD LH OLQLDU FX WHPSHUDWXUD FRQVLGHUkQG ∆θ = 1°& UH]XOWFRHILFLHQWXOGHYDULD LHFXWHPSHUDWXUDαθFDUHUHSUH]LQWGHIDSWWROHUDQ DGDWRULWYDULD LHLWHPSHUDWXULLFX°&6HGvQppm/°C = 10 -6/°C.

7ROHUDQ H GDWRUDWH GLIHUL LORU IDFWRUL tj (umiditate, depozitare, solicitareWHUPLF VROLFLWDUH PHFDQLF vPEWUkQLUH HWF VH GHILQHVF FD UDSRUWXO SURFHQWXDOvQWUH YDULD LD PULPLL VXE DF LXQHD IDFWRUXOXL M úL YDORDUHD HL vQDLQWH GH DF LXQHDfactorului j

0

0j max=

X

XXt

j −± (1.22)

Xj HVWH YDORDUHD GXS DF LRQDUHD IDFWRUXOXL MX0 HVWH YDORDUHD vQDLQWHD DF LXQLLfactorului j.

'XS SURFHVXO GH IDEULFD LH DEDWHUHD YDORULL XQHL FRPSRQHQWH SDVLYH HVWHFDUDFWHUL]DW GH WROHUDQ D GH IDEULFD LH GDU úL GH DOWH DEDWHUL UHYHUVLELOH GDWRUDWHWHPSHUDWXULLWHQVLXQLLHWFÌQWLPSXOXWLOL]ULLYDORDUHDFRPSRQHQWHLSRDWHVXIHULR


12

VHULH GHPRGLILFUL LUHYHUVLELOH GDWRULW GLYHUúLORU IDFWRUL HOHFWULFL úLneelectrici laFDUH HVWH VXSXV vQ IXQF LH GH FRQGL LLOH UHDOH GH XWLOL]DUH OLSLUHD FRQWDFWDUHDGHSR]LWDUHD IDFWRUL FOLPDWLFL VROLFLWDUH WHUPLF YLEUD LLPHFDQLFH úRFXUL WHUPLFHHOHFWULFH PHFDQLFH HWF ÌQ IXQF LH GH WLSXO FRPSRQHQWHL UH]LVWRU FRQGHQVDWRULQGXFWRU H[LVW QRUPH LQWHUQD LRQDOH FDUH SUHFL]HD] FRQGL LLOH GHWDOLDWH OD FDUHWUHEXLH VXSXV ILHFDUH FRPSRQHQW SHQWUX D YHULILFD PRGLILFDUHD YDORULL DVXSUDGLYHUúLORU IDFWRUL PRGLILFUL FH VXQW SUH]HQWDWH GH SURGXFWRUL vQ FDWDORDJH 'HRELFHL YDORDUHD PD[LP D DEDWHULL PD[LP GH tj UHSUH]LQW VWDELOLWDWHDFRPSRQHQWHL 8QHRUL vQV SULQ VWDELOLWDWH SRDWH IL vQWkOQLW vQ OLWHUDWXU úL VXPDWXWXURU PRGLILFULORU 'HFL SURLHFWDQWXO GH FLUFXLWH HOHFWURQLFH vQ IXQF LH GHFRQGL LLOHUHDOHvQFDUHYDIXQF LRQDFLUFXLWXOYDWUHEXLVDLEvQYHGHUHWRDWHDFHVWHPRGLILFULSHQWUXDRE LQHVWDELOLWDWHDSDUDPHWULORUFLUFXLWHORUHOHFWURQLFHDWkWGXS

SURFHVXOGHIDEULFD LHGDUPDLDOHVvQWLPS 7ROHUDQ D JOREDO tg UHSUH]LQW DEDWHUHD PD[LP D YDORULL UHDOH DFRPSRQHQWHL IDW GH YDORDUHDQRPLQDO FDUH SRDWH V DSDU vQ WLPSXO IXQF LRQULLFRPSRQHQWHLvQWUXQFLUFXLWHOHFWULFDYkQGvQYHGHUHFRQGL LLOHUHDOHGHIXQF LRQDUH

3HQWUXGHWHUPLQDUHDWROHUDQ HLJOREDOHtgYRPDSOLFDGHILQL LDWROHUDQ HL

N

mN

N

NMg X

XX

X

XXt

−=

−= (1.23)

unde XMUHSUH]LQWYDORDUHDPD[LPXmYDORDUHDPLQLP

XM = XN (1+t)(1+tθ)(1+t1)…(1+tj) (1.24)Xm = XN (1-t)(1-tθ)(1-t1)…(1-tj) XM = XN (1+t+tθ+Σtj+ttθ+tt1+ttj+…) (1.25)

$YkQGvQYHGHUHFWWθúLtj sunt mult mai mici decât 1, se poate aproxima:XM ≅ XN (1+t+tθ+Σtj) (1.26)

5H]XOWtg = t+tθ+Σtj . (1.27)

7ROHUDQ D GH IDEULFD LH W úL WROHUDQ HOH tj VXQW SUH]HQWDWH GH SURGXFWRU vQFDWDORJ7ROHUDQ DGDWRUDWWHPSHUDWXULLWθWUHEXLHvQVGHWHUPLQDWvQIXQF LHGHαT.

2ULFHFRPSRQHQWIXQF LRQHD]vQWUXQPHGLXDPELDQWFXWHPSHUDWXUDθa,θa∈[θam, θaM], (1.28)

unde θamHVWHWHPSHUDWXUDPLQLPDPHGLXOXLúLθaMHVWHWHPSHUDWXUDPD[LPÌQWLPSXOIXQF LRQULLWHPSHUDWXUDFRPSRQHQWHLθc,

θc∈[θcm, θcM], (1.29)unde θcmHVWHWHPSHUDWXUDPLQLPDFRUSXOXLFRPSRQHQWHLúLθcM HVWHFHDPD[LP θcm= θam

θcM=θaM + ∆θ (1.30)unde ∆θ este VXSUDWHPSHUDWXUDGDWRUDWGLVLSULLGHSXWHUHGHFWUHFRPSRQHQW


13

ÌQ IXQF LHGHFRHILFLHQWXO GHYDULD LHFX WHPSHUDWXUDVHSRDWHGHWHUPLQDFXH[DFWLWDWH WROHUDQ DGDWRUDW WHPSHUDWXULL UH]XOWkQG R DQXPLW DEDWHUHSR]LWLY úLDOWDQHJDWLY

'HH[HPSOXGDFαT >UH]XOWtθ+= αθ (θcM-θ0) (1.31)tθ-= αθ (θcm-θ0) (1.32)

$YkQG vQ YHGHUH FD]XO FHO PDL GHIDYRUDELO DEDWHUHD PD[LP WROHUDQ DGDWRUDWWHPSHUDWXULLLQGLIHUHQWGHVHPQXOOXLαθVHSRDWHGHWHUPLQDFXUHOD LD

tθ=±αθ∆θM , (1.33)∆θM = maxim θcM-θ0, θ0-θcm (1.34)

Exemplu 6H FRQVLGHU XQ UH]LVWRU FX SHOLFXO GH FDUERQ FX WROHUDQ D W ±5%, coeficientul deYDULD LH FX WHPSHUDWXUDαθ= - 500ppm/°& FH IXQF LRQHD] vQWUXQ PHGLX FXθa∈ [ -20, 80 ]°C.3XWHUHD GLVLSDW HVWH IRDUWH PLF QHJOLMkQGXVH supratemperatura. θ0= 20°& 6 VH GHWHUPLQHWROHUDQ DJOREDORezolvare:tg = t + tθtθ=± αθ∆θM

tθ = ± ( 500 ⋅10-6 ⋅60) = ± 3%tg = ± 8%

'HWHUPLQDUHD WROHUDQ HORU SDUDPHWULORU FLUFXLWHORU HOHFWURQLFH vQ

IXQF LHGHWROHUDQ HOHFRPSRQHQWHORUSDVLYH

6HFRQVLGHUXQSDUDPHWUX\DOXQXLFLUFXLWHOHFWURQLFFDUHGHSLQGHGHYDORULOHcomponentelor pasive, pe care le vom nota cu X1, X2…Xn. Parametrului y alFLUFXLWXOXL L VH SRDWH SXQH vQ OHJWXU R IXQF LH IX1, X2...Xn FH VWDELOHúWHFRUHVSRQGHQ D vQWUH FRPSRQHQWHOH FLUFXLWXOXL úL UHVSHFWLYXO SDUDPHWUX \ IX1,X2...Xn &RPSRQHQWHOH SUH]LQW FRUHVSXQ]WRU WROHUDQ HOH t1, t2…tn 7ROHUDQ DSDUDPHWUXOXL\QRWDWFXty se poate determina în mai multe moduri.D$SOLFDUHDGHILQL LHLWROHUDQ HL

N

NMy

y

yyt

−=+ (1.35)

N

Nmy

y

yyt

−=− (1.36)

unde yM, respectiv ymHVWHYDORDUHDPD[LPUHVSHFWLYPLQLPDSDUDPHWUXOXL\yN

HVWHYDORDUHDQRPLQDO

Exemplu 6H FRQVLGHU GRX UH]LVWRDUH FX UH]LVWHQ QRPLQDO R1, respectiv R2 úL WROHUDQ HOHFRUHVSXQ]WRDUH± t1, respectiv ± t26VHGHWHUPLQHWROHUDQ DtsDUH]LVWHQ HLHFKLYDOHQWHRE LQXWHSULQFRQHFWDUHDvQVHULHDFHORUGRXUH]LVWRDUHRezolvare:

5H]LVWHQ DRs a grupului serie,Rs=R1+R2.


14

( ) ( )21

2211

21

212211 11

RR

tRtR

RR

RRtRtRts +

+=+

−−+++=+

( ) ( )21

2211

21

212211 11

RR

tRtR

RR

RRtRtRts +

+−=+

−−−+−=−

21

2211

RR

tRtRts +

+±=

b) Calculul " Taylor"y = f (X1, X2...Xn).Valorile X1, X2...Xn VXQW LQGHSHQGHQWH 'DF IXQF LD I HVWH GH n ori

GHULYDELOVHSRDWHGH]YROWDvQVHULHTaylor,

( ) ( )

( ) ( ) ( ).......

!2!2

....

22

2222

21

2211

222

111

+−

+−

+−+

++−+−+=

===

==

iNiiNiiNi

iNiiNi

XX

N

XX

N

XXnnNn

XXN

XXNN

X

fXX

X

fXX

X

fXX

X

fXX

X

fXXfy

∂

∂

∂

∂∂∂

∂∂

∂∂

(1.37)

$YkQGvQYHGHUHFDEDWHULOHGHIRUPDXi-XiN sunt mult mai mici decât unu, seSRWUH LQHQXPDLWHUPHQLLGHUDQJXOvQWkLUH]XOWkQG

( )iNi XXi i

iNiNX

fXXfy

=∑ −=−

∂∂

(1.38)

∑−

=∆

i iN

iNi

iN

iN

N X

XX

X

f

f

X

f

y

∂∂

(1.39)

∑ ∑==∆

i iiii

iN

iN

Ntht

X

f

f

X

f

y

∂∂

(1.40)

hiILLQGQXPL LFRHILFLHQ LGHSRQGHUH

iNi XXiN

iNi

X

f

f

Xh

=∂∂

=

3HQWUXWROHUDQ HVLPHWULFHGHIRUPD±tiWROHUDQ DSDUDPHWUXOXL\GHYLQH∑±=i

iiy tht (1.41)

Exemplu. 6H FRQVLGHU GRX UH]LVWRDUH FXYDORULOHQRPLQDOHR1, respectiv R2 úL WROHUDQ HOH± t1,respectiv ± t2 6 VH GHWHUPLQH WROHUDQ D tp D UH]LVWRUXOXL HFKLYDOHQW FRQHFWULL vQ SDUDOHO Drezistoarelor R1úLR2.

Rezolvare:


15

5H]LVWHQ DRpHFKLYDOHQWJUXSXOXLSDUDOHOHVWH .21

21

RR

RRRp +

=

&RQIRUPUHOD LHLWROHUDQ Dtp a lui Rp va fi,( )2211 ththt p +±=

( ) ( )( )2

21

21212

21

211

1

11

RR

RRRRR

RR

RRR

R

R

R

Rh p

p +−++

==∂∂

21

21 RR

Rh

+=

21

1

2

22 RR

R

R

R

R

Rh p

p +==

∂∂

21

2112

RR

tRtRt p +

+±=

c) Calculul probabilistic.Un circuit esteRDOFWXLUHGHFRPSRQHQWHHOHFWURQLFHLQWHUFRQHFWDWHvQWUHHOH

vQ YHGHUHD UHDOL]ULL XQHL DQXPLWH IXQF LL HOHFWURQLFH DPSOLILFDUH GH VHPQDOJHQHUDUHGHVHPQDOHWF)XQF LDRE LQXWvQXUPDLQWHUFRQHFWULLHVWHGHSHQGHQWGHHOHPHQWHOH VFKHPHL DUH SURSULHW L vQ VWUkQV OHJWXU FX FDUDFWHULVWLFLOHFRPSRQHQWHORU FH R DOFWXLHVF &XP YDORULOH DFHVWRUD UHSUH]LQW SHQWUX ILHFDUHFRPSRQHQWvQSDUWHRYDULDELODOHDWRDUHGDFVHDXvQYHGHUHRSHUD LLOHFXYDULDELOHDOHDWRDUHVHSRDWHFRQFOX]LRQDFúLIXQF LDHOHFWURQLFDFLUFXLWXOXLUHDOL]DWHVWHWRWRYDULDELODOHDWRDUHúLGHFLVHVXSXQHSURSULHW LORUDFHVWRUD

ÌQDFHVWFD]UHOD LDSRDWHILSXVVXEIRUPD

x

x=

y

y

i

ii

n

1=

∆∑

∆h

iN

(1.42)

7UHFkQGGHODDEDWHULOHUHODWLYHODDEDWHULOHPHGLLS WUDWLFHUH]XOW

)(3=)(3 x2

i2

n

1=y

2iσσ h

i∑ (1.43)

unde σxúLσyVXQWDEDWHULOHPHGLLSWUDWLFHDOHSDUDPHWULORUxiúL\Deoarece în intervalul [ x -3σ , x +3σ@VHDIOGLQYDORULOHSHFDUHOH

SRDWH OXD YDULDELOD DOHDWRDUH [ VH SRDWH FRQVLGHUD F σ HVWH SUDFWLF WROHUDQ D W5HOD LDVHWUDQVFULHVXEIRUPDHFXD LHLWROHUDQ HORU

thti

x22

i

n

1=

2y i= ∑ (1.44)

7ROHUDQ HOHWiILLQGVLPHWULFHUH]XOWWROHUDQ DSDUDPHWUXOXL\ty,

∑±=i

ii thty 22 (1.45)

$FHVWHUHOD LLVHUYHVFDQDOL]HLLQJLQHUXOXLODSURLHFWDUHDFLUFXLWHORU,QJLQHUXOWUHEXLHV DOHDJSHED]DH[SHULHQ HLDQXPLWH WROHUDQ HSHQWUXFRPSRQHQWHDVWIHO


16

vQFkW SDUDPHWUXO GH LHúLUH \ V ILH PHQ LQXW vQ OLPLWHOH VSHFLILFDWH &DOFXOXOFRHILFLHQ LORUGHSRQGHUHDMXWODGHWHUPLQDUHDFRPSRQHQWHLDFUHLDEDWHUHDUHPDUHLQIOXHQ DVXSUD IXQF LRQULL FLUFXLWXOXL GHFL D FUHL WROHUDQ HVWH ELQH V ILHPHQ LQXWVF]XW

'HWHUPLQDUHD FRHILFLHQWXOXL GH YDULD LH FX WHPSHUDWXUD DO

SDUDPHWULORU FLUFXLWHORU HOHFWURQLFH vQ IXQF LH GH FRHILFLHQ LL GH YDULD LH FXtemperatura ai componentelor pasive.

6HFRQVLGHUXQFLUFXLWHOHFWURQLFFDUDFWHUL]DWGHXQSDUDPHWUXy ce depindede valorile componentelor, pe care le vom nota cu X1, X2…Xn. Componentele auFRHILFLHQ LL GD YDULD LH FX WHPSHUDWXUD α1, α2...αn FRUHVSXQ]WRU 1RWkQG FX αy,FRHILFLHQWXOGHYDULD LHFX WHPSHUDWXUD DOSDUDPHWUXOXL\ úL FXQRVFkQGGHSHQGHQ Dlui y de valorile componentelor, y = f(X1, X2…Xn), se propune determinarea lui αy.

&RQIRUPUHOD LHLGHGHILQL LH

θα

d

dy

yy

1= (1.46)

0ULPLOHX1,X2…XnVXQWLQGHSHQGHQWH3DUDPHWUXO\GHSLQGHGHWHPSHUDWXUSULQLQWHUPHGLXOPULPLORUXi5H]XOW

+++=

θ∂∂

θ∂∂

θ∂∂α

d

dX

X

f

d

dX

X

f

d

dX

X

f

fn

ny ...

1 2

2

1

1 (1.47)

∑ ∑= =

==n

i

n

i

i

ii

ii

iy

d

dX

XX

f

f

X

d

dX

X

f

f1 1

11

θ∂∂

θ∂∂α (1.48)

ii

i hX

f

f

X=

∂∂

FRHILFLHQ LGHSRQGHUH

ii

i d

dX

Xα

θ=

1 (1.50)

5H]XOW

∑=

=n

iiiy h

1αα (1.51)

&X DMXWRUXO UHOD LHL VH SRDWH GHWHUPLQD FRHILFLHQWXO GH YDULD LH FXWHPSHUDWXUDDOSDUDPHWULORUFLUFXLWHORUHOHFWURQLFH'HDVHPHQHDUHOD LDHVWHIRDUWHXWLOSHQWUXVWDELOL]DUHD WHUPLFDSDUDPHWULORUXWLOL]kQGFRPSRQHQWHSDVLYHDVWIHOîncât αyVILH]HURVDXFkWPDLPLFSRVLELO

Exemplu. 6H FRQVLGHU XQ FLUFXLW RVFLODQW VHULH FX IUHFYHQ D GH UH]RQDQ LC

f r π2

1= 6 VH

GHWHUPLQH UHOD LD FDUH WUHEXLH V H[LVWH vQWUH FRHILFLHQ LL GH YDULD LH FX WHPSHUDWXUDαL, αC ai


17

LQGXFWRUXOXLúLFRQGHQVDWRUXOXLDVWIHOvQFkWFRHILFLHQWXOGHYDULD LHFXWHPSHUDWXUDDOIUHFYHQ HLGHUH]RQDQ VILH]HURRezolvare: 6H QRWHD] FXαfr FRHILFLHQWXO GH YDULD LH FH WHPSHUDWXUD DO IUHFYHQ HL GH UH]RQDQ &RQIRUPUHOD LHLαfr este,

αfr= h1α1+h2α2

2

1

2

1

2

12

f

Lh

r1 −=−==

LLCLCL

L

f r

ππ

∂∂

2

12 −==

C

f

f

Ch r

r ∂∂

( ) 02

1 =+−= CLfr ααα

5H]XOWαL=-αC'HFLSHQWUXRVWDELOLWDWH WHUPLFFkWPDLEXQD IUHFYHQ HLGH UH]RQDQ LQGXFWRUXOúLFRQGHQVDWRUXOWUHEXLHVDLEFRHILFLHQ LLGHYDULD LHFXWHPSHUDWXUDHJDOLGDUGHVHPQopus.

'HWHUPLQDUHDWROHUDQ HLJOREDOHDSDUDPHWULORUFLUFXLWHORUHOHFWURQLFH

vQIXQF LHGHDEDWHUHDFRPSRQHQWHORUSDVLYH

&RQVLGHUkQGFDúLvQFD]XULOHDQWHULRDUHXQFLUFXLWHOHFWURQLFFDU acterizat deparametrul y = f(X1, X2…Xn úL FXQRVFkQG X1, X2…Xn, t1…tn, α1…αn, trebuieGHWHUPLQDWWROHUDQ DJOREDODEDWHUHDPD[LPtgy a parametrului y.

6HXWLOL]HD]RUHOD LHDVHPQWRDUHFXtgy = ±ty±αy ∆θM (1.52)

Exemplu.6HFRQVLGHUXQRVFLODWRUFXSXQWH:LHQFXIUHFYHQ DGHRVFLOD LHRC2

1f 0 π

= 6 VH

GHWHUPLQHWROHUDQ DJOREDODOXLf0úWLLQGF5 1KΩ, tR = ±1%, αR = -100ppm/°C, C = 1nF, tC = ±1%, αC = ±30ppm/°C, θ0 = 20°C, temperatura componentelor θC vQ WLPSXO IXQF LRQULL LDvalori în intervalul [-20,80]°C.Rezolvare.

( )Mffgf tt θα ∆+±=000

( )CRf ththt 210+±=

11

2

12

2

20

01 −=−==

RCCR

R

f

f

Rh

ππ

∂∂

Prin simetrie,1h2 −=

( ) %2%110

±=+±=ft

( ) ./10 130...70/10 30/10 100 666

0CCCf

$$$ −−− =±=α

CCM$$ 602020 ,2080max =+−=∆θ

%78,2%60 10 130%2 6

0±=⋅±±= −

gft

2EVHUYD LL• 3HQWUX FDOFXOXO WROHUDQ HL ty VH YRU FRQVLGHUD úL WROHUDQ HOH GDWRUDWH GLYHUúLORUIDFWRULDYkQGvQYHGHUHFRQGL LLOHUHDOHvQFDUHIXQF LRQHD]FLUFXLWXO

• &XQRVFkQGWROHUDQ DJOREDODSDUDPHWUXOXL\úLSXQkQGFRQGL LD


18

Myygy Ttt ∆+≥ α (1.53)

se pot determina parametrii componentelor pasive ce pot fi utilitate în acel circuit,DVWIHOvQFkWVVHRE LQDEDWHUHDGRULWDSDUDPHWULORUFLUFXLWHORUHOHFWULFH

capitolul 1 propriet i generale ale componentelor electronice pasive

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