capitolul 1 - cetti · 2011. 1. 6. · componente œlflufxlwhsdvlyh note de curs 3 tabelul 1.3&...

23
CAPITOLUL 1 35235,(7,*(1(5$/($/(&20321(17(/25 ELECTRONICE PASIVE 1.6.1 TUDQVPLVLDFOGXULL &RPSRQHQWHOHHOHFWURQLFHOXFUHD]FXGLVLSDLH GH SXWHUH $FHDVWD vQVHDPQ FRSDUWHDHQHUJLHLHOHFWULFHWUDQVIHUDWHFRPSRQHQWHLHVWHWUDQVIRUPDW vQFOGXU 6ROLFLWDUHD WHUPLF PD[LP DGPLV SHQWUX R FRPSRQHQW XQHRUL QXPLW œL vQFUFDUHDWHUPLFPD[LPHVWHGHSHQGHQWGHXUPWRDUHOHPULPL FDQWLWDWHDGHFOGXU4SURGXVGHHQHUJLDHOHFWULFFHLV-a transferat; WHPSHUDWXUDPD[LP T M ODFDUHHVWHDGPLVVDMXQJFRPSRQHQWDvQWLPSXO IXQFLRQULL WHPSHUDWXUDDPELDQW7 a ; WUDQVPLVLDFOGXULLGHODFRPSRQHQWvQPHGLXDPELDQW &DQWLWDWHDGHFOGXU4SURGXVGHHQHUJLDHOHFWULFWUDQVIHUDWFRPSRQHQWHL HVWH vQ UHJLP VWDLRQDU vQ HFKLOLEUX FX FDQWLWDWHD GH FOGXU WUDQVPLV PHGLXOXL DPELDQW1LYHOXOGHHFKLOLEUXHVWHVWDELOLWGHWHPSHUDWXU $FHDVWD QX SRDWH GHSœL WHPSHUDWXUDPD[LPDGPLVLELOFDDWDUHFOGXUDSURGXVHOHFWULFvQWURFRPSRQHQW HVWHSDULDOvQPDJD]LQDWœLSDULDOFHGDWPHGLXOXLDPELDQW 7UDQVPLVLDFOGXULLFWUHPHGLXODPELDQWVHIDFHSULQFRQGXFLHFRQYHFLHœL UDGLDLH 8OWLPHOHWUHLIRUPHD]PHFDQLVPHOHGHVFXUJHUHGHHYDFXDUHDFOGXULL)U HYDFXDUHDFOGXULLGLQWURFRPSRQHQW DFHDVWDVDUGLVWUXJHGXS un anumit timp ca urmare a VXSUDFUHœWHULL WHPSHUDWXULL GH IXQFLRQDUH œL GHSœLUHD WHPSHUDWXULL maxime. $FXPXODUHDGHFOGXU &RUHVSXQ]WRU SUHOXULL FOGXULL DFXPXOULL DFHVWHLD VH œWLH GLQ IL]LF FDUH HVWH H[SUHVLD FOGXULL FH VH SRDWH vQPDJD]LQD vQWUXQ FRUS GH PDV P œL FOGXUD VSHFLILFFDWXQFLFkQGHVWHvQFO]LWGHODWHPSHUDWXUD7 a la temperatura T CM, : T mc ) T - mc(T = mcdT = Q a = CM a T T CM a (1.54) T C = Q t h a (1.55) unde C th PF HVWH FDSDFLWDWHD WHUPLF D FRUSXOXL LDU T= T CM - T a HVWH YDULDLD temperaturii, ( VXSUDFUHœWHUHDWHPSHUDWXULLFRPSRQHQWHL ÌQ XUPWRUXO WDEHO VH SUH]LQW FkWHYD YDORUL DOH FOGXULL VSHFLILFH SHQWUX FkWHYDPDWHULDOHIRORVLWHvQHOHFWURQLF

Upload: others

Post on 26-Jan-2021

2 views

Category:

Documents


0 download

TRANSCRIPT

  • CAPITOLUL 1

    35235,(7��,��*(1(5$/(�$/(�&20321(17(/25ELECTRONICE PASIVE

    1.6.1 TUDQVPLVLD�F�OGXULL

    &RPSRQHQWHOH�HOHFWURQLFH�OXFUHD]��FX�GLVLSD LH�GH�SXWHUH��$FHDVWD� vQVHDPQ�F��R�SDUWH�D�HQHUJLHL�HOHFWULFH�WUDQVIHUDWH�FRPSRQHQWHL�HVWH�WUDQVIRUPDW��vQ�F�OGXU��

    6ROLFLWDUHD� WHUPLF�� PD[LP�� DGPLV�� SHQWUX� R� FRPSRQHQW��� XQHRUL� QXPLW�� úLvQF�UFDUHD�WHUPLF��PD[LP���HVWH�GHSHQGHQW��GH�XUP�WRDUHOH�P�ULPL�

    ��FDQWLWDWHD�GH�F�OGXU��4�SURGXV��GH�HQHUJLD�HOHFWULF��FH�L�V-a transferat;��WHPSHUDWXUD�PD[LP��TM�OD�FDUH�HVWH�DGPLV�V��DMXQJ��FRPSRQHQWD�vQ�WLPSXO

    IXQF LRQ�ULL���WHPSHUDWXUD�DPELDQW��7a;��WUDQVPLVLD�F�OGXULL�GH�OD�FRPSRQHQW��vQ�PHGLX�DPELDQW�&DQWLWDWHD�GH�F�OGXU��4�SURGXV��GH�HQHUJLD�HOHFWULF��WUDQVIHUDW��FRPSRQHQWHL

    HVWH� vQ� UHJLP� VWD LRQDU� vQ� HFKLOLEUX� FX� FDQWLWDWHD� GH� F�OGXU�� WUDQVPLV�� PHGLXOXLDPELDQW��1LYHOXO�GH�HFKLOLEUX�HVWH�VWDELOLW�GH�WHPSHUDWXU���$FHDVWD�QX�SRDWH�GHS�úLWHPSHUDWXUD�PD[LP��DGPLVLELO���FD�DWDUH�F�OGXUD�SURGXV��HOHFWULF�vQWU�R�FRPSRQHQW�HVWH�SDU LDO�vQPDJD]LQDW��úL�SDU LDO�FHGDW��PHGLXOXL�DPELDQW�

    7UDQVPLVLD�F�OGXULL��F�WUH�PHGLXO�DPELDQW�VH�IDFH�SULQ�FRQGXF LH��FRQYHF LH�úLUDGLD LH�

    8OWLPHOH�WUHL�IRUPHD]��PHFDQLVPHOH�GH�VFXUJHUH��GH�HYDFXDUH�D�F�OGXULL��)�U�HYDFXDUHD�F�OGXULL�GLQWU�R�FRPSRQHQW��DFHDVWD�V�DU�GLVWUXJH�GXS��un anumit timp caurmare a VXSUDFUHúWHULL� WHPSHUDWXULL� GH� IXQF LRQDUH� úL� GHS�úLUHD� WHPSHUDWXULLmaxime.

    $FXPXODUHD�GH�F�OGXU��&RUHVSXQ]�WRU� SUHOX�ULL� F�OGXULL�� DFXPXO�ULL� DFHVWHLD�� VH� úWLH� GLQ� IL]LF�� FDUH

    HVWH� H[SUHVLD� F�OGXULL� FH� VH� SRDWH� vQPDJD]LQD� vQWU�XQ� FRUS� GH�PDV�� P� úL� F�OGXUDVSHFLILF��F��DWXQFL�FkQG�HVWH�vQF�O]LW�GH�OD�WHPSHUDWXUD�7a la temperatura TCM, :

    Tmc)T-mc(T=mcdT=Q a ∆=∫ CMaT

    T

    CM

    a

    (1.54)

    TC=Q t ∆ha (1.55)unde Cth �PF� HVWH� FDSDFLWDWHD� WHUPLF�� D� FRUSXOXL�� LDU�∆T= TCM - Ta� HVWH� YDULD LDtemperaturii, (VXSUDFUHúWHUHD�WHPSHUDWXULL�FRPSRQHQWHL��

    ÌQ� XUP�WRUXO� WDEHO� VH� SUH]LQW�� FkWHYD� YDORUL� DOH� F�OGXULL� VSHFLILFH�� SHQWUXFkWHYD�PDWHULDOH�IRORVLWH�vQ�HOHFWURQLF��

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    2

    Tabelul 1.2�&�OGXUD�VSHFLILF��SHQWUX�FkWHYD�PDWHULDOHMaterial c [ J/g×K ]

    g/cm32EVHUYD LL������

    aluminiu 0,896 argint 0,129 cupru 0,383 staniu 0,226 grafit 0,841�DOXPLQ���Al2O3 ) 0,92 suport pt. componente�QLWUXU��GH�DOXPLQLX�AlN 3,30 suport pt. componente��VWLFO������������������ 0,69-0,93 suport pt. componente��FHUDPLF� 0,42-0,65 suport pt. componente siliciu 0,234 suport��JOD]XU� 0,6-0,8 SURWHF LHcimenturi 0,87-1,04 SURWHF LH

    &DQWLWDWHD� GH� F�OGXU�� DFXPXODW�� GH� FRUSXO� XQHL� FRPSRQHQWH� HVWH� GLUHFWSURSRU LRQDO�� FX� PDVD� DFHVWHLD� úL� FX� F�OGXUD� VSHFLILF�� D� PDWHULDOHORU� XWLOL]DWH� ODrealizarea ei; depinde de temperatura mediului ambiant.

    CRQGXF LD�F�OGXULL�HVWH�GHSHQGHQW��GH�WLSXO�PDWHULDOXOXL��(D�SRDWH�DYHD�ORFQXPDL� vQ� FD]XO� H[LVWHQ HL� XQXL� JUDGLHQW� GH� WHPSHUDWXU��� &DQWLWDWHD� GH� F�OGXU�WUDQVPLV��vQ�XQLWDWHD�GH�WLPS��dQ /GW��SULQ���FRQGXF LH�VH�SRDWH�DSUR[LPD�SULQ�

    thcththc

    R

    TP

    ∆=∆= Tl

    A=

    dt

    dQ λ (1.56)

    unde: - λth�HVWH�FRQGXFWLYLWDWHD�WHUPLF��D�PDWHULDOXOXL���������$��O�GLPHQVLXQLOH�PDWHULDOXOXL�RPRJHQ�GH�VHF LXQH�$�úL�OXQJLPH�O� - ∆T=T1-T2�GLIHUHQ D�GH�WHPSHUDWXU��GLQWUH�VHF LXQLOH�FRUSXOXL�DIODWH�OD�R�GLVWDQ �l (vezi fig. 1.6 ).

    ,A

    lR

    ththc λ

    = HVWH�UH]LVWHQ D�WHUPLF��GH�FRQGXF LH�

    )LJ������&RQGXF LD�F�OGXULL�

    &RQGXFWLYLWDWHD� WHUPLF�� HVWH� R� SURSULHWDWH� GH�PDWHULDO�� ILLQG� UHODWLY�PDUH� ODPDWHULDOHOH�FRQGXFWRDUH�HOHFWULF�FRPSDUDWLY�FX�FHOH�L]RODWRDUH��ÌQ�WDEHOXO�XUP�WRU�VHSUH]LQW��FkWHYD�YDORUL�SHQWUX�λth.

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    3

    Tabelul 1.3�&RQGXFWLYLWDWHD�WHUPLF�Materialul ]

    mK

    W[ ]

    msK

    J[ sauthλ

    argint 410 cupru 380 aluminiu 210���QLWUXU��GH�DOXPLQLX��AlN) 170���DOXPLQ���Al2O3) 25

    ���VWLFO��������������� 0,8 aer uscat 20 °C 0,0257

    60 °C 0,0285���DS� 20 °C 0,60

    60 °C 0,65ulei mineral 0,12

    &RQYHF LD� F�OGXULL� HVWH�PHFDQLVPXO� GH� FHGDUH� D� F�OGXULL� SULQ� WUDQVIHUXO� GHHQHUJLH�PROHFXOHORU� XQXL� IOXLG� �DHU�� DS��� XOHL�� FDUH� LQWU�� vQ� FRQWDFW� FX� UHVSHFWLYXOcorp.

    &DQWLWDWHD�GH�F�OGXU��FHGDW��GH�XQ�FRUS�SULQ�FRQYHF LH�� vQ�XQLWDWHD�GH� WLPS�are expresia:

    ( )thcv

    accvcvthcvR

    TTDTTAP

    dt

    dQ ∆=∆=−== α (1.57)

    unde: αcv�HVWH�FRHILFLHQWXO�GH�FRQYHF LH�Acv� HVWH� VXSUDID D� GH� FRQYHF LH�� ILLQG� HJDO�� FX� VXSUDID D� WRWDO�� ODWHUDO�� D

    componentei care vine în contact cu fluidul;Tc, respectiv Ta este temperatura corpului componentei, respectiv temperatura

    mediului ambiant (a fluidului);D=αcvAcv��HVWH�IDFWRUXO�GH�GLVLSDUH�WHUPLF��Rthcv= ��'�HVWH�UH]LVWHQ D�WHUPLF��GH�FRQYHF LH�&RHILFLHQWXO�GH�FRQYHF LH�αcv depinde puternic de tipul fluidului, fiind mult

    PDL�PDUH�SHQWUX�OLFKLGH�ID ��GH�JD]H��'HSLQGH�GH�DVHPHQHD�GH�YLWH]D�GH�FXUJHUH�DIOXLGXOXL��GH�SR]L LD�FRPSRQHQWHL�ID ��GH�GLUHF LD�GH�FXUJHUH�

    Predominant în mediul ambiant al componentelor este aerul, caz în care αcvGHSLQGH�úL�GH�XPLGLWDWH��SUHVLXQH�

    Componentele sunt amplasate pe circuite imprimate. Coeficientul αcv depindeGH�SR]L LD�FLUFXLWXOXL�LPSULPDW�

    5HOD LL�GH�FDOFXO�SHQWUX�FRHILFLHQWXO�GH�FRQYHF LH��vQ�IXQF LH�GH�GLVSXQHUHD�vQVSD LX�D�FRPSRQHQWHL�VXQW�GDWH�vQ�ILJXUD������

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    4

    Fig. 1.7�&RHILFLHQWXO�GH�FRQYHF LH�vQ�IXQF LH�GH�SR]L LD�PRGXOXOXL�HOHFWURQLF��� SODF� GH FLUFXLW LPSULPDW �VXSRUW�� �� FRPSRQHQW� �FRUS FDOG�

    'LQ�ILJXUD�����UH]XOW��F��SR]L LD�YHUWLFDO��HVWH�PXOW�PDL�DYDQWDMRDV��DYkQG�vQYHGHUH�GLVLSDUHD�GH�F�OGXU��GH�OD�FRPSRQHQWH�OD�PHGLXO�DPELDQW�

    5DGLD LD� HOHFWURPDJQHWLF��� 2ULFH� FRUS� vQF�O]LW� HVWH� VXUV�� GH� UDGLD LLHOHFWURPDJQHWLFH�FX�OXQJLPL�GH�XQG��FXSULQVH�vQ�LQWHUYDOXO������������������µm.

    &DQWLWDWHD� GH� F�OGXU�� FHGDW�� vQ� XQLWDWHD� GH� WLPS� �SXWHUHD�� GH� XQ� FRUS� SULQUDGLD LH�HVWH�GDW��GH�OHJHD�Stefan-Boltzmann:

    )T-T(A=Pdt

    dQ 4a

    4crσε rthr= (1.61)

    unde: - εr�HVWH�JUDGXO�GH�UDGLD LH�D�VXSUDIH HL� ��εr=1 pentru corpul negru, εr = 0,8SHQWUX�XQ�FRUS�FHQXúLX�

    - Km

    W 105,67= 42

    8-σ este constanta Stefan-Boltzmann;

    - Ar�HVWH�DULD�GH�UDGLD LH��- Tc�úL�7a�VXQW�WHPSHUDWXUD�FRUSXOXL��UHVSHFWLY�WHPSHUDWXUD�DPELDQW ��'DF�� VH� IDFH�XQ�FDOFXO� VH�REVHUY�� F�� QXPDL�GDF�� WHPSHUDWXUD�FRUSXOXL� HVWH

    ULGLFDW���∼1000 &���FDQWLWDWHD�GH�F�OGXU��UDGLDW��GHYLQH�FRPSDUDELO��FX�FDQWLWDWHDGH�F�OGXU��FHGDW��SULQ�FRQYHF LH��&XP�FRPSRQHQWHOH�HOHFWURQLFH�OXFUHD]��PXOW�VXE1000 &�VH�SRDWH�FRQVLGHUD�FD�QHJOLMDELO��HYDFXDUHD�GH�F�OGXU��SULQ�UDGLD LH�vQ�FD]XOFRPSRQHQWHORU� SDVLYH�� (VWH� GH� UHPDUFDW� IDSWXO� F ��� VSUH� GHRVHELUH� GH� FRQYHF LH�FHGDUHD�F�OGXULL�SULQ�UDGLD LH�SRDWH�DYHD�ORF�úL�vQ�YLG��ÌQ�WDEHOXO�XUP�WRU�VXQW�GDWH��RULHQWDWLY��FkWHYD�YDORUL�SHQWUX�JUDGXO�GH�UDGLD LH�D�VXSUDIH HL�

    ( ) [ ]KmWTcv 24/1 /5,2 ∆⋅=α (1.58)

    ( ) [ ]KmWTcv 24/1 /3,1 ∆⋅=α (1.59)

    ( ) [ ]KmWTcv 24/1 /2,4 ∆⋅=α (1.60)

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    5

    Tabelul 1.4�*UDGXO�GH��UDGLD LH�

    Material εrAl lustruit 0,039

    Cu lustruit 0,03

    Ag lustruit 0,02

    Fe ruginit 0,61 ... 0,85

    Cu negru oxidat 0,78

    Zn oxidat 0,23

    /D� SUH]HQWDUHD� VHJPHQWXOXL� WHUPLF� SH� OkQJ�� HQHUJLD� WHUPLF�� úL� SXWHUHDWHUPLF���DX�IRVW� LQWURGXVH�QR LXQL�GH�WLSXO�FDSDFLWDWH� WHUPLF��� UHVSHFWLY�UH]LVWHQ DWHUPLF��� 3OHFkQGX�VH� GH� OD� WHRULD� FLUFXLWHORU� HOHFWULFH� HVWH� SRVLELO� FD�� SULQWU�ROHJ�WXU�� DGHFYDW��� PRGXOHORU� WHUPLFH� V�� OL� VH� SXQ�� vQ� FRUHVSRQGHQ �� VFKHPHHFKLYDOHQWH�VLPLODUH�FLUFXLWHORU�HOHFWULFH��ÌQ�DFHVW�VHQV�vQWUH�GRPHQLXO�WHUPLF�úL�FHOHOHFWULF�SRW�IL�VWDELOLWH�FRUHVSRQGHQ HOH�SUH]HQWDWH�vQ�WDEHOXO�����

    Tabelul 1.5�&RUHVSRQGHQ D�PHGLX�WHUPLF�±�PHGLX�HOHFWULF�Mediul termic Mediul electric

    0�ULPHD�IL]LF� Simbol Unitate deP�VXU�

    0�ULPHD�IL]LF� Simbol Unitate deP�VXU�

    *UDGLHQW�GH�WHPSHUDWXU� T [K] SRWHQ LDO�HOHFWULF V [V]'LIHUHQ D�GH�WHPSHUDWXU� ∆T [K] Tensiune U [V]Putere P [W] Curent I [A]5H]LVWHQ D�WHUPLF� Rth [K/W] 5H]LVWHQ ��HOHFWULF� R [Ω]&DSDFLWDWH�WHUPLF� Cth

    K

    J;

    K

    S*W CDSDFLWDWH�HOHFWULF� C [F]

    (QHUJLH�WHUPLF� Q [J] EQHUJLH�HOHFWULF� E [J])RORVLQG� HFKLYDOHQ HOH� SUHFL]DWH�� XQXL� PRGul termic i se poate stabili o

    VFKHP��HFKLYDOHQW��VLPLODU��FX�FHD�D�XQXL�FLUFXLW�HOHFWULF��&DOFXOXO�VFKHPHL�SRDWH�ILHIHFWXDW� VLPLODU�RULF�UXL�FLUFXLW�HOHFWULF�XWLOL]kQG�FXQRúWLQ HOH�GLQ� WHRULD� FLUFXLWHORUelectrice.

    ������%LODQ XO�HQHUJHWLF�úL�YDULD LD� temperaturii corpului componentelorvQ�IXQF LH�GH�SXWHUHD�GLVLSDW�

    %LODQ XO� HQHUJHWLF� YD� DYHD� vQ� YHGHUH� FHOH� H[SXVH� DQWHULRU��(QHUJLD� HOHFWULF�WUDQVIRUPDW�� vQ� F�OGXUD� 4� HVWH� SDU LDO� DFXPXODW�� �Wa� GH� FRUSXO� FRPSRQHQWHL� úLSDU LDO�HYDFXDW��Wev�F�WUH�PHGLXO�DPELDQW�

    Q=Wa+Wev (1.62)

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    6

    (YDFXDUHD� F�OGXULL� VH� IDFH� SULQ� FHOH� WUHL� PHWRGH� SUH]HQWDWH�� FRQGXF LH�FRQYHF LH�úL�UDGLD LH�

    Q=Wa+Wc+Wcv+Wr (1.63)unde:

    Wc��F�OGXU��HYDFXDW��SULQ�FRQGXF LD�WHUPLF��D�WHUPLQDOHORU�Wcv��F�OGXU��HYDFXDW��SULQ�FRQYHF LH�Wr��F�OGXU��HYDFXDW��SULQ�UDGLD LH�

    %LODQ XO�HQHUJHWLF�vQ�FD]XO�XQHL�FRPSRQHQWH�SRDWH�IL�UHSUH]HQWDW�GH�ILJXUD����

    Fig. 1.8�%LODQ XO�HQHUJHWLF�DO�XQHL�FRPSRQHQWH�disipative.

    ÌQFHUF�P� V�� VFULHP� � HFXD LD� FDUH� V�� H[SULPH� ELODQ XO� HQHUJHWLF� QHJOLMkQGHYDFXDUHD�GH�F�OGXU��SULQ�FRQGXF LH�úL�UDGLD LH�SH�ED]D�XUP�WRDUHORU�SUHVXSXQHUL�

    �� WHPSHUDWXUD� OD� FDUH� IXQF LRQHD]�� FRPSRQHQWD� H� UHODWLY� MRDV�� DVWIHO� vQFkWF�OGXUD�UDGLDW��SRDWH�IL�QHJOLMDW��

    �� LQkQG� VHDPD� GH� GLPHQVLXQLOH� FRPSRQHQWHORU�� VHF LXQHD� SULQ� FDUH� FXUJHF�OGXUD� GH� FRQGXF LH� SULQ� WHUPLQDOH� HVWH� PLF�� úL� DFHDVWD� SRDWH� IL� QHJOLMDW���DSUR[LPD LH�FDUH�QX�vQWRWGHDXQD�HVWH�YDODELO��úL�YD�IL�SUH]HQWDW��vQ�SDUDJUDIXO�������

    ÌQ�DFHVW�FD]�UHOD LD���������GHYLQH�Q=Wa+Wcv (1.64)

    ( ) ( )∫∫ −+−=t

    aath

    tdtTTDTTCuidt

    00

    (1.65)

    'HULYkQG�UHOD LD�DQWHULRDU��vQ�UDSRUW�FX�WLPSXO�úL�SUHVXSXQkQG�F��WHPSHUDWXUD

    DPELDQW��HVWH�FXDVLVWD LRQDU��

    = 0

    dt

    dTa ��UH]XOW�

    ( )ath TTDdt

    dTCui −+= (1.66)

    $YkQG�vQ�YHGHUH�F��D=1/Rth��VH�RE LQH�

    ( )aththth TTdt

    dTRCuiR −+= (1.67)

    0�ULPHD�CthRth=τth�VH�QXPHúWH�FRQVWDQWD�WHUPLF��GH�WLPS��ÌQORFXLQG�VH�RE LQHHFXD LD�

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    7

    )(T-+dt

    dT=uiRt athh Tτ (1.68)

    ÌQ�FHOH�FH�XUPHD]��YRP�DQDOL]D�VWDUHD�VWD LRQDU��vQ�FDUH�FRPSRQHQWD�QX�úLPDL�P�UHúWH�WHPSHUDWXUD��FDQWLWDWHD�GH�F�OGXU��SUHOXDW��FH�VH�vQPDJD]LQHD]��HVWHQXO���GHFi�WRDW��F�OGXUD�HVWH�HYDFXDW��F�WUH�PHGLXO�DPELDQW���3UHVXSXQHP�F��TCMHVWH�WHPSHUDWXUD�OD�FDUH�DMXQJH�FRUSXO�FD�XUPDUH�D�GLVLS�ULL�SXWHULL�P=u×i. Din�������UH]XOW��

    athcM TD

    P +=TP+R=T a (1.69)

    'HFL��R�FRPSRQHQW��FDUH�GLVLS��SXWHUHD�3��vQ�UHJLP�VWD LRQDU�DUH�WHPSHUDWXUDFRUSXOXL�GHSHQGHQW��GH�WHPSHUDWXUD�PHGLXOXL�DPELDQW��SXWHUHD�GLVLSDW��úLUH]LVWHQ D�WHUPLF���UHVSHFWLY�FRHILFLHQWXO�GH�GLVLSDUH�

    5H]XOW�� GLQ� UHOD LD� ������� VXSUDWHPSHUDWXUD� FRPSRQHQWHL� IDW�� GH� PHGLXOambiant,

    thaCM PRD

    PTT ==− (1.70)

    3H�GH�DOW��SDUWH�HFXD LD�>����@�HVWH�GH�IRUPD�

    Z=X(t)+dt

    dX(t)0thτ (1.71)

    FHHD�FH�UHSUH]LQW��R�HFXD LH�GLIHUHQ LDO��GH�RUGLQXO�,�

    6ROX LD�HFXD LHL�HVWH��

    )tX(+)e-)](1tX(-)[X(=X(t) 0tt-

    -0

    0

    thτ∞ (1.72)

    LQkQG� VHDPD� F�� OD� W �� WHPSHUDWXUD� LQL LDO�� D� FRUSXOXL� HVWH� 7a, iar când t→∞temperatura corpului este TCM��VH�SRDWH�VFULH�VROX LD�SHQWUX�HFXD LD��������

    T+)e-)(1T-T(=T(t) att-

    -a

    0

    thCM τ (1.73)

    ([SUHVLD� � ������� DSUR[LPHD]�� FUHúWHUea în timp a temperaturii corpului înFD]XO�vQ�FDUH�vQ�HO�VH�GLVLS��SXWHUHD�3�

    1H� SURSXQHP� V�� G�P� R� LQWHUSUHWDUH� SHQWUX� τth�� 3HQWUX� DFHDVWD� V�� FDOFXO�P

    YLWH]D� LQL LDO�� GH� FUHúWHUH� D� WHPSHUDWXULL��th

    CMt τ

    1)T-T(=

    dt

    dTa

    =t 0

    deci

    0dt

    dTT-T

    = a

    tt

    CMth

    =

    τ ��'HRDUHFH�GHULYDWD�DUH�VHPQLILFD LD�XQHL�WDQJHQWH�UH]XOW��F��τth este

    ODWXUD�SDUDOHO��FX�D[D�WLPSXOXL�vQ�WULXQJKLXO�IRUPDW�GH�WDQJHQWD�vQ�RULJLQH�OD�JUDILF�verticala t=t0��úL�RUL]RQWDOD�T=TCM��VDX�FXP�VH�PDL�QXPHúWH��VXEWDQJHQWD�vQ�RULJLQH

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    8

    OD�JUDILF��$FHDVW�� LQWHUSUHWDUH�QH�SHUPLWH� V��REVHUY�P�F��SHQWUX�XQ� WLPS� t>t0+3τthUH]XOW��7�t>t0+3τth) ≅ TCM��DGLF��vQWU�XQ�WLPS�GH�WUHL�RUL�PDL�PDUH�GHFkW�τth se poateFRQVLGHUD�F��WHPSHUDWXUD�FRPSRQHQWHL�DMXQJH�vQ�UHJLP�VWD LRQDU�

    5HOD LD� ������� DSUR[LPHD]�� HYROX LD� WHPSHUDWXULL� FRUSXOXL� FRPSRQHQWHL� ODvQF�O]LUHD�DFHVWHLD��'HFL��GDF��vQFHSkQG�FX�XQ�DQXPLW�PRPHQW�t0��FRPSRQHQWD�GLVLS�SXWHUHD� 3� FRQVWDQW�� vQ� WLPS�� WHPSHUDWXUD� FRPSRQHQWHL� YD� FUHúWH� H[SRQHQ LDO�începând de la temperatura mediului ambiant Ta��úL�DMXQJkQG�GXS����τth la valoareaPD[LP��GH�UHJLP�VWD LRQDU�TCM, vezi figura 1.9.

    3URFHGkQG� vQ� PRG� DVHP�Q�WRU� VH� SRDWH� GHWHUPLQD� HYROX LD� WHPSHUDWXULLFRUSXOXL�FRPSRQHQWHL�OD�U�FLUH��'HFL�SUHVXSXQHP�F��R�FRPSRQHQW��GLVLS��R�YUHPHvQGHOXQJDW�� � SXWHUHD� FRQVWDQW�� 3� úL� OD� XQ�PRPHQW� GDW� t0 aceasta devine zero. ÎnDFHVW�FD]�UHOD LD���������GHYLQH�

    Wa+ Wev=0 (1.74)

    ( ) ( )∫ =−+−t

    aath dtTTDTTC0

    0 (1.75)

    t0

    P

    Pd

    TC

    t0

    TCM

    Ta

    t

    t

    3τth

    Fig. 1.9�(YROX LD�WHPSHUDWXULL�FRUSXOXL�FRPSRQHQWHL�OD�vQF�O]LUH�

    6H�RE LQH�HFXD LD�

    ( ) 0=−+ ath TTdt

    dTτ (1.76)

    FDUH�DUH�VROX LD�GH�IRUPD�

    ( ) ( ) ( )[ ] ( )∞+∞−=−

    −TeTtTtT th

    tt

    τ0

    0 (1.77)

    $YkQG�vQ�YHGHUH�F���7�t0)=TCM�úL�7�∞)=Ta��VH�RE LQH�

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    9

    ( ) [ ] att

    aCM TeTTtT th +−=

    −−

    τ0

    (1.78)&RQVWDQWD�WHUPLF��GH�WLPS�HVWH�DFHHDúL�FD�úL�vQ�FD]XO�DQWHULRU��'H�DVHPHQHD

    UH]XOW��F��7�W�!t0+3τth) ≅ Ta.'HFL� OD� U�FLUH�� DGLF�� DWXQFL� FkQG� SXWHUHD� GLVLSDW�� GH� FRPSRQHQW�� GHYLQH

    ]HUR��WHPSHUDWXUD�FRUSXOXL�FRPSRQHQWHL�VFDGH�H[SRQHQ LDO�GH�OD� WHPSHUDWXUD�TCMGH�UHJLP�VWD LRQDU�DMXQJkQG�OD�WHPSHUDWXUD�PHGLXOXL�DPELDQW�GXS���τth, vezi figura1.10.

    &X�DMXWRUXO�UHOD LHL��������VDX��������VH�SRDWH�GHWHUPLQD�FRHILFLHQWXO�GHFRQYHF LH�αCV.

    CVCV

    ththththth

    A

    C

    D

    CRC

    ατ === (1.79)

    CVth

    thCV

    A

    C

    τα = (1.80)

    P

    TcM

    Tc t0

    t0

    t

    t 3τth

    Pd

    Ta

    Fig. 1.10�(YROX LD�WHPSHUDWXULL�FRUSXOXL�FRPSRQHQWHL�OD�U�FLUH�

    'HWHUPLQkQGX�VH� FRQVWDQWD� WHUPLF�� GH� WLPS� SULQ�P�VXUDUHD� WLPSXOXL� GXS�care se ajunge la TCM�� FXQRVFkQG� FDSDFLWDWHD� WHUPLF�� Cth PF� úL� GHWHUPLQkQGVXSUDID D�GH�FRQYHF LH��VH�SRDWH�GHWHUPLQD�FRHILFLHQWXO�GH�FRQYHF LH�

    1.6.3 Determinarea temperaturii maxime a corpului componentei înIXQF LH�GH�SXWHUHD�GLVLSDW�

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    10

    ÌQ� SURLHFWDUHD� WHUPLF�� D� FLUFXLWHORU� HOHFWURQLFH� GHWHUPLQDUHD� WHPSHUDWXULLPD[LPH� D� FRUSXOXL� FRPSRQHQWHORU� HVWH� IRDUWH� LPSRUWDQW��� GHRDUHFH� DFHDVWD� QXWUHEXLH� V�� GHS�úHDVF�� vQ� WLPSXO� IXQF LRQ�ULL� FRPSRQHQWHORU� WHPSHUDWXUD� ORUPD[LP��GH�XWLOL]DUH�

    &X� DMXWRUXO� UHOD LLORU� ������� úL� ������� VH� SRDWH� GHWHUPLQD� FX� DSUR[LPD LHtemperatura corpului componentelor pasive pentru diverse forme ale puterii disipateGH� FRPSRQHQW��� 3XWHUHD� GLVLSDW��� DYkQG� vQ� YHGHUH� FLUFXLWHOH� HOHFWULFH� XWLOL]DWH� vQHOHFWURQLF�� DUH� R� PDUH� YDULHWDWH� GH� IRUPH�� ÌQ� OXFUDUHD� GH� ID �� YRU� IL� DQDOL]DWH�FD]XULOH� FHOH�PDL� IUHFYHQWH� vQ� SUDFWLF��� úL� DQXPH� SXWHUH� GLVLSDW�� FRQVWDQW�� úL� VXEIRUP��GH�LPSXOVXUL�D��3XWHUH�GLVLSDW��FRQVWDQW���6H�FRQVLGHU��SXWHUHD�GLVLSDW��GH�FRPSRQHQW��FD�ILLQGDSUR[LPDWLY�FRQVWDQW��vQ�WLPS��LDU�GXUDWD�GH�IXQF LRQDUH�HVWH�vQGHOXQJDW���PXOW�PDLPDUH�GHFkW�FRQVWDQWD�WHUPLF��GH�WLPS�D�FRPSRQHQWHL��ÌQ�DFHVW�FD]�VH�SRDWH�FRQVLGHUDF�� GXS�� UHJLPXO� WUDQ]LWRULX� FDUH� DSDUH� OD� DOLPHQWDUHD� FLUFXLWXOXL�� FRPSRQHQWDIXQF LRQHD]��vQ�UHJLP�WHUPLF�VWD LRQDU�

    $YkQG�vQ�YHGHUH�F��WHPSHUDWXUD�RULF�UXL�PHGLX�DPELDQW�HVWH�YDULDELO���OXkQGvalori în intervalul, Ta∈[Tam, TaM@�� UH]XOW�� FRQIRUP� UHOD LHL� �������� WHPSHUDWXUDPD[LP��D�FRUSXOXL�FRPSRQHQWHL�

    aMdthaMd

    cM TPRTD

    PT +=+= (1.81)

    CD� DWDUH�� R� FRPSRQHQW�� VLWXDW�� vQWU�XQ� PHGLX� DPELDQW� FX� WHPSHUDWXUD� FHpoate atinge valoarea TaM� vQ� FD]XO� vQ� FDUH� GLVLS�� R� SXWHUH� FH� GHWHUPLQ�VXSUDvQF�O]LUHD�RthPd��YD�DWLQJH�R�WHPSHUDWXU��D�FDSVXOHL��FDUFDVHL���HJDO��FX�VXPDGLQWUH�WHPSHUDWXUD�DPELDQW��úL�supratemperatura componentei.b) Regim de impulsuri��6H�YRU�FRQVLGHUD�GRX��VLWXD LL�

    b1- regim de impulsuri singulare;b2- regim de impulsuri periodice.

    b1) Regim de impulsuri singulare��3ULQ�UHJLP�GH�LPSXOV�VLQJXODU�VH�YD�vQ HOHJH�RSXWHUH� GLVLSDW�� GH� FRPSRQHQW�� VXE� IRUPD�GH� LPSXOV�� FX�R�GXUDW�� SH� FDUH� R�YRPnota cu ti�úL�FX�R�GXUDW��GH�UHSHWL LH�D�LPSXOVXOXL�DOHDWRDUH��úL�PXOW�PDL�PDUH�GHFkWti���YH]L�ILJXUD������úL��������ÌQ�IXQF LH�GH�P�ULPLOH�Wi úL�τth�VH�GLVWLQJ�GRX��VLWXD LL�

    b11) Regim de impuls singular cu durata impulsului ti mult mai maredecât 3τth,

    ti>>3τth (1.82) $YkQG� vQ� YHGHUH� UHOD LLOH� ������� úL� ������� vQ� DFHVW� FD]� WHPSHUDWXUD� FRUSXOuiFRPSRQHQWHL�SRDWH�IL�DSUR[LPDW��F��YD�IL�GH�IRUPD�SUH]HQWDW��vQ�ILJXUD������

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    11

    t

    t

    ti

    Pd

    Pi

    Tc

    TcM

    Ta

    3τth 3τth

    Fig. 1.11 Temperatura corpului componentei în regim de impuls singular cu ti >> 3τth.

    5H]XOW�� F�� DFHVW� FD]�� GHYLQH� HFKLYDOHQW� FX� D�� GLQ� SXQFW� GH� YHGHre alGHWHUPLQ�ULL�WHPSHUDWXULL�PD[LPH�D�FRPSRQHQWHL�

    aMi

    cM TD

    PT += (1.83)

    b12) Regim de impuls singular cu durata impulsului ti�PXOW�PDL�PLF�� GHFkWFRQVWDQWD�WHUPLF��GH�WLPS,

    ti

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    12

    7HPSHUDWXUD�PD[LP��D�FRPSRQHQWHL�vQ�DFHVW�FD]��FRQIRUP�UHOD LHL��������va fi,

    T+)e-)(1T-T(=T(t) att--

    acM0

    τ (1.85)

    ����������$YkQG�vQ�YHGHUH�UHOD LD���������UH]XOW��F��

    th

    i

    tt

    e thi

    ττ −≅

    −1 (1.86)

    T+)e-)(1T-T(=T(t) att--

    acM0

    thτ (1.87)

    $YkQG�vQ�YHGHUH�UHOD LD���������UH]XOW���

    T+T at

    Mth

    iicMi D

    = (1.88)

    &RQIRUP�UHOD LLORU��������úL��������WHPSHUDWXUD�PD[LP��D�FRPSRQHQWHL�vQ�UHJLP�GHimpuls singular cu ti > 3 τth (1.89)În acest caz temperatura componentei va fi de forma din figura 1.14.

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    13

    t ti

    Pd

    Pi

    Tc

    TcM

    Ta

    3τth 3τ th

    tp

    t

    Fig. 1.14 Temperatura corpului componentei în regim de impulsuri periodicecu ti; tp>> τth.

    &D� úL� vn cazul b11�� DYkQG� vQ� YHGHUH� WHPSHUDWXUD� PD[LP�� D� FRUSXOXLFRPSRQHQWHL��DFHDVW��VLWXD LH�GHYLQH�HFKLYDOHQW��FX�FD]XO�a��GHFL�úL�vQ�DFHVW�FD]�

    T+T aMi

    cMi D

    P= (1.90)

    b22�� 5HJLP� GH� LPSXOVXUL� SHULRGLFH� FX� SHULRDGD� PDL� PLF�� GHFkW� FRQVWDQWDWHUPLF��GH�WLPS�

    tp

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    14

    8WLOL]kQG� UHOD LLOH� ������� úL� ������� úL� XQ� SURJUDP� PDWHPDWLF� VH� SRDWHGHWHUPLQD�FX�GHVWXO��DFXUDWH H�HYROX LD�WHPSHUDWXULL�FRPSRQHQWHL�vQ�DFHVW�FD]�

    )RUPD� WHPSHUDWXULL� GLQ� ILJXUD� ����� VH� H[SOLF�� vQ� IHOXO� XUP�WRU�� &UHúWHUHDWHPSHUDWXULL� HVWH� PDL� UDSLG�� GHFkW� GHVFUHúWHUHD�� 'HFL� GXS�� � SULPXO� LPSXOV�temperatura nu ajunge la temperatura mediului ambiant, fiind mai mare, deci apareo VXSUDWHPSHUDWXU���'XS�� FHO�GH�DO�GRLOHD� LPSXOV� vQF��R� VXSUDWHPSHUDWXU�� úL�DúDPDL�GHSDUWH��$FHDVW��VXSUDWHPSHUDWXU�� VFDGH� vQ� WLPS��GHYHQLQG�IRDUWH�PLF��GXS�XQ� DQXPLW� QXP�U� GH� LPSXOVXUL�� FkQG� SRDWH� IL� QHJOLMDW�� úL� VH� SRDWH� FRQVLGHUD� F�WHPSHUDWXUD�HVWH�DSUR[LPDWLY�HJDO��FX�TCMi.

    6H� YD� FRQVLGHUD� F�� GXS�� XQ� QXP�U� RDUHFDUH� GH� LPSXOVXUL�� WHPSHUDWXUDcomponentei are o valoare oarecare Ti. În acest caz se poate scrie,

    ( ) ik TtT = (1.92)

    ( ) ( ) sit

    icMk TTeTTtT thi

    =+

    −−=

    +τ11 (1.93)

    ( ) ( ) iat

    ask TTeTTtT thi

    =+−=−

    2 (1.94)Din aceste rHOD LL��UH]XOW��

    th

    p

    th

    p

    th

    i

    th

    i

    t

    tt

    a

    t

    cM

    s

    e

    eeTeT

    T

    τ

    τττ

    −−−

    −+

    =

    1

    1

    (1.95)

    $YkQG�vQ�YHGHUH�F��ti/τth

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    15

    ( ) ( )p

    iacMas t

    tTTTT −=− (1.100)

    sau ( ) ap

    iacMs Tt

    tTTT +−= (1.101)

    Raportul ti/tp� VH� QXPHúWH� FRHILFLHQW� VDX� IDFWRU� GH� XPSOHUH� DO� VHPQDOXOXLGUHSWXQJKLXODU�SHULRGLF�úL�VH�QRWHD]��FX�γ.

    Deci în DFHVW� FD]� WHPSHUDWXUD� � PD[LP�� � D� FRUSXOXL� FRPSRQHQWHL� SRDWH� ILDSUR[LPDW��GH�UHOD LD�

    ( ) aMiaMaMcMcMi TDP

    TTTT +=+−= γγ (1.102)

    &RQIRUP�UHOD LLORU��������±����������supratemperatura, respectiv temperaturaPD[LP��D�FRUSXOXL�FRPSRQHQWHL�HVWH�PDL�PLF��vQ�UHJLP�GH�LPSXOVXUL�SHULRGLFH�FXti

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    16

    FRPSRQHQWHL�HVWH�HJDO��FX�FHD�PD[LP���θM�úL�vQ�FRQIRUPLWDWH�FX�UHOD LD����������YDfi,

    ( )aMA DP θθθ −= (1.105)$YkQG�vQ�YHGHUH�úL�UHOD LD����������UH]XOW��

    ( )( )NM

    aMNA PP θθ

    θθθ −

    −= (1.106)

    Reprezentând grafic pe PAθ� vQ� IXQF LH� GH�θa�� UH]XOW�� DúD� ]LVD� GLDJUDP�� GHGLVLSD LH�D�FRPSRQHQWHL�

    PAθ

    PN

    θm θN θM θaFig. 1.16�'LDJUDPD�GH�GLVLSD LH���

    &RQIRUP� UHOD LHL� �������� úL� ILJXULL� ������ UH]XOW�� F�� SXWHUHD� WHUPLF��PD[LP�DGPLVLELO��SRDWH�IL�PDL�PDUH�GHFkW�SXWHUHD�QRPLQDO��GDF��WHPSHUDWXUD�PHGLXOXL�HVWHPDL� PLF�� GHFkW� FHD� QRPLQDO�� úL� HVWH� PDL� PLF�� GHFkW� SXWHUHD� QRPLQDO�� GDF�WHPSHUDWXUD�PHGLXOXL� HVWH�PDL�PDUH� GHFkW� FHD� QRPLQDO��� GHYLQH� HJDO�� FX� ]HUR� ODWHPSHUDWXUD�PHGLXOXL�HJDO��FX�WHPSHUDWXUD�PD[LP��GH�XWLOL]DUH�D�FRPSRQHQWHL�

    'LQ�PRWLYH�GH�VLPSOLILFDUH��SH�GH�R�SDUWH��GDU�úL�GLQ�PRWLYH�SUDFWLFH��SH�GHDOW��SDUWH��DYkQG�vQ�YHGHUH�F��WHPSHUDWXUD�PD[LP��D�PHGLXOXL�HVWH�SUHGRPLQDQW�GH30°C…..70°C, diagrama de disipare pentru majoritatea componentelor pasive,SUH]HQWDW��GH�SURGXF�WRUL�vQ�FDWDORDJH�HVWH�GH�IRUPD�FHOHL�GLQ�ILJXUD������

    θm

    PN

    PAθ

    θN θM θa

    Fig. 1.17�'LDJUDPD�GH�GLVLSD LH���

    ÌQ� �DFHVW�FD]�SXWHUHD� WHUPLF��PD[LP�DGPLVLELO�� HVWH�HJDO�� FX�FHD�QRPLQDO��pentru θa∈[θm, θN@�úL�HVWH�PDL�PLF��GHFkW�FHD�QRPLQDO��SHQWUX�θa∈[θN, θM].

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    17

    $FHVW� PRG� GH� FDUDFWHUL]DUH� ILLQG� SUHGRPLQDQW�� vQ� OXFUDUHD� GH� ID ��� vQFRQWLQXDUH�YD�IL�XWLOL]DW��QXPDL�DFHDVW��YDULDQW��

    &D� úL� vQ� SDUDJUDIXO� SUHFHGHQW�� YRP� GHWHUPLQD� SXWHUHD� WHUPLF�� PDximDGPLVLELO��SHQWUX�DFHOHDúL�FD]XUL��QRWDWH�LGHQWLF�úL�SHQWUX�θa∈[θam, θaM].a) 3XWHUH�GLVLSDW��vQ�WLPS�FRQVWDQW��

    $YkQG�vQ�YHGHUH�FHOH�H[SXVH�DQWHULRU��UH]XOW��

    PAθ = PN��GDF��θaM∈[θm, θN] (1.107)

    ( )aMMNM

    aMMNA DPP θθθθ

    θθθ −=−

    −= ��GDF��θa∈[θN, θM]. (1.108)

    Cazurile b11- regim de impuls singular cu ti>3τth�úL�b21 – regim de impulsuriperiodice cu ti; tp> 3τth��GHYLQ�HFKLYDOHQWH�FX�D��GHFL�úL�SHQWUX�DFHVWH�VLWXD LL�3Aθ va fiGHWHUPLQDW��FX�UHOD LLOH���������úL���������

    b12 Regim de impuls singular cu durata impulsului ti�PXOW�PDL�PLF��GHFkWFRQVWDQWD�WHUPLF��GH�WLPS�τth.

    3XQkQG�FRQGL LD�FD�WHPSHUDWXUD�PD[LP��D�FRPSRQHQWHL�vQ�UHJLP�GH�LPSXOV�V�GHYLQ��HJDO��FX�WHPSHUDWXUD�PD[LP��GH�XWLOL]DUH��UH]XOW��GLQ�UHOD LD��������

    th

    iiaMM

    t

    D

    P

    τθθ =− (1.109)

    ( )i

    th

    NM

    aMMN

    i

    thaMMi t

    Pt

    DPτ

    θθθθτθθ

    −−=−= (1.110)

    $YkQG� vQ�YHGHUH�úL� UHOD LLOH� ��������� ��������� UH]XOW�� SXWHUHD� WHUPLF��PD[LPDGPLVLELO��vQ�UHJLP�GH�LPSXOV�VLQJXODU�FX�ti

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    18

    γθN

    iAP

    P = ��GDF��θaM ∈[θm, θN] (1.115)

    γθθθθ

    θ1

    NM

    aMMNiA PP −

    −= ���GDF��θaM ∈[θN, θM] (1.116)

    Deci în regim de impulsuri periodice dreptunghiulare cu perioada mult maiPLF��GHFkW�FRQVWDQWD�WHUPLF���SXWHUHD�WHUPLF��PD[LP�DGPLVLELO��HVWH�GH���γ ori maiPDUH�ID ��GH�FHD�GH�UHJLP�SHUPDQHQW��SXWkQG�IL�PDL�PDUH�GHFkW�SXWHUHD�QRPLQDO��

    ������'HWHUPLQDUHD�SXWHULL�QRPLQDOH�vQ�IXQF LH�GH�SXWHUHD�GLVLSDW�

    6H�FRQVLGHU��R�FRPSRQHQW��SDVLY��FDUH�vQ�WLPSXO�IXQF LRQ�ULL�GLVLS��SXWHUHDPd� úL� IXQF LRQHD]�� vQWU�XQ� PHGLX� DPELDQW� FX� WHPSHUDWXUD� θa ∈[θam, θaM]. PutereaQRPLQDO�� UH]XOW�� GLQ� UHOD LLOH� GH� GHWHUPLQDUH� D� SXWHULL� WHUPLFH�PD[LPH� DGPLVLELOH�SDUDJUDIXO� ��������� SXQkQG� FRQGL LD� FD� Pd≤PAθ�� DVWIHO� vQFkW� V�� QX� VH� GHS�úHDVF�WHPSHUDWXUD�PD[LP��GH�XWLOL]DUH�D�FRPSRQHQWHL��6H�YRU�DQDOL]D�DFHOHDúL�VLWXD LL�FD�úLvQ�SDUDJUDIHOH��������úL�������

    Pentru cazurile, a - regim permanent, b11 – regim de impuls singular cuti>>3τth�úL�b21 – regim de impuls singular cu tp>>3τth��DYkQG�vQ�YHGHUH�UHOD LLOH��������úL����������UH]XOW��

    dN PP ≥ , GDF��θaM ∈[θm, θN] (1.117)

    aMM

    NMdN PP θθ

    θθ−−≥ , GDF��θaM ∈[θN, θM] (1.118)

    b21) Regim de impuls singular cu ti

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    19

    QX� úL� VXILFLHQWH�� ÌQ� IXQF LH� GH� WLSXO� FRPSRQHQWHL� VH� YD�GHWHUPLQD�SXWHUHD�PD[LP�DGPLVLELO��OD�FDUH�SRDWH�IL�VROLFLWDW��FRPSRQHQWD�

    ������7UDQVPLVLD�F�OGXULL�SULQ�WHUPLQDOH

    $úD� FXP� V�D� SUHFL]DW�� R� FRPSRQHQW�� HOHFWULF�� FH� GLVLS�� SXWHUH� GDWRULW�DFXPXO�ULL� GH� F�OGXU�� SRDWH� DWLQJH� R� YDORDUH� FH� GHS�úHúWH� XQHRUL� FX� PXOWWHPSHUDWXUD�DPELDQW���GDU�FDUH�SHQWUX�R�IXQF LRQDUH�QRUPDO��WUHEXLH�V��ILH�FHO�PXOWHJDO��FX�WHPSHUDWXUD�PD[LP��TM�UHVSHFWLY��ILHF�UHL�FRPSRQHQWH�vQ�SDUWH��ÌQ�DFHODúLWLPS� vQWU�XQ� UHJLP� WHUPLF� VWD LRQDU� SXWHUHD� HOHFWULF�� GLVLSDW�� vQ� FRPSRQHQWH� HVWHHJDO��FX�SXWHUHD�WHUPLF��HYDFXDW����FRPSRQHQWD�ILLQG�vQWU�XQ�HFKLOLEUX�WHUPLF�

    'H� FHOH� PDL� PXOWH� RUL� VH� FRQVLGHU�� GUHSW� FDOH� GH� WUDQVPLVLH� D� F�OGXULLFRQYHF LD��UHVSHFWLY�FHOHODOWH�F�L��FRQGXF LD�úL�UDGLD LD�ILLQG�QHJOLMDWH��7RWXúL�SHQWUXR�DQDOL]��PDL�H[DFW��HVWH�XWLO�V�� VH� LQ�� VHDPD�úL�GH�SRVLELOLWDWHD�GH�HYDFXDUH�SULQFRQGXF LH��UDGLD LD�ILLQG�vQ�PRG�RELúQXLW�PDL�UHGXV��

    6H� GHWHUPLQ�� vQ� FRQWLQXDUH� IHOXO� vQ� FDUH� DUH� ORF� WUDQVPLVLD� F�OGXULL� SULQterminalele componentelor. În plus în cadrul componentelor de tip SMD (SurfaceMounted 'HYLFHV���FRQGXF LD�WHUPLF��MRDF��XQ�URO�LPSRUWDQW�OD�HYDFXDUHD�F�OGXULL�FHVH� GLVLS�� vQ� FRPSRQHQW��� &RPSRQHQWHOH� GH� WLS� 60'� VH� FRQWDFWHD]�� GLUHFW� SHsubstratul ce constituie modulul electronic.

    Analiza se face pentru un terminal de lungime l, de arie A D�VHF LXQLL�úL�FX�XQSHULPHWUX� DO� VHF LXQLL� GH� YDORDUH� S�� 7HUPLQDOXO�� ILLQG� OD� XQ� FDS�W� VROLGDU� FXFRPSRQHQWD� FH� GLVLS�� SXWHUH�� YD� DYHD� WHPSHUDWXUD� HJDO�� FX� WHPSHUDWXUDFRPSRQHQWHL��7RW�RGDW��WHUPLQDOXO�SULPHúWH�OD�FDS�WXO�GLQVSUH�FRPSRQHQW��R�SXWHUHP0�FDUH�SH�P�VXU��FH�VH�WUDYHUVHD]��WHUPLQDOXO�FHGHD]��SULQ�VXSUDID D�GH�FRQWDFW�FXmediul ambiant putere mediului ambiant aflat la temperatura θa�� 3XWHUHD� HYDFXDW�SULQ�S�U LOH�ODWHUDOH�HVWH�GHWHUPLQDW��GH�FRHILFLHQWXO�úL�DULD�GH�FRQYHF LH�SUHFXP�úL�GHsupratemperatura terminalului.

    P0 P1 P2

    l

    x d x

    0 x

    dp

    Fig. 1.18 Transmisia temperaturii prin terminal.

    /D�VWDELOLUHD�YDULD LHL�GH�WHPSHUDWXU��θ de-a lungul terminalului, deoareceGLPHQVLXQHD�DFHDVWD�HVWH�PXOW�PDL�PDUH�FRPSDUDWLY�FX�FHD�UDGLDO��VH�SRDWH

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    20

    FRQVLGHUD��vQWU�R�DQXPLW��VHF LXQH�D�WHUPLQDOXOXL��F��WHPSHUDWXUD�HVWH�FRQVWDQW��'HFL�SXWHUHD�VH�SURSDJ��GH�D�OXQJXO�FRRUGRQDWHL�D[LDOH�SH�GLUHF LD�D[HL�Ox.

    %LODQ XO�WHUPLF�DO�XQXL�HOHPHQW�GH�OXQJLPH�dx�DIODW�OD�GLVWDQ D�x deFRPSRQHQWD�HOHFWURQLF��VH�H[SULP��SULQ�UHOD LD

    P1=P2+dP (1.123)

    $GLF���SXWHUHD�P1�FH�S�WUXQGH�SULQ�VHF LXQHD�GH�LQWUDUH�DIODW��OD�GLVWDQ D�x�HVWH�HJDO�cu suma dintre puterea G3�FDUH�VH�HOLPLQ��SULQ�FRQYHF LH�SH�SRU LXQHD�GH�OXQJLPH�dxúL�SXWHUHD�P2�FH�S�WUXQGH�SULQ�VHF LXQHD�DIODW��OD�GLVWDQ D�dx�ID ��GH�VHF LXQHD�LQWU�ULL�

    Deoarece P1 este puterea ce se transmite de a lungul terminalului prinFRQGXF LH�úL�VH�SRDWH�VFULH��Y��������

    xAP

    ∂∂−= θλ1 (1.124)

    3H�GH�DOW��SDUWH��YDULD LD�WHPSHUDWXULL�vQ�WHUPLQDO�GH�D�OXQJXO�HOHPHQWXOXL�GH

    lungime dx este: dxx∂

    ∂+ θθ

    iar puterea P2 este

    ∂∂+

    ∂∂−= dx

    xxAP

    θθλ2 (1.125)

    dxx

    Ax

    AP2

    2

    2∂∂−

    ∂∂−= θλθλ (1.126)

    ÌQ� FHHD� FH� SULYHúWH� SXWHUHD� G3� FH� VH� HOLPLQ�� SULQ� FRQYHF LH�� GDF�� VH� LQH�VHDPD�GH��������UH]XOW��

    ( )apdxdP θθα −= 1 (1.127)&X�UHOD LLOH�SUHFL]DWH�ELODQ XO�WHUPLF�GHYLQH�

    ( )apx

    A θθαθλ −=∂∂

    12

    2(1.128)

    &X�QRWD LLOH�

    A

    p

    λαβ 12 = (1.129)

    úL ( ) a, θθ +=x (1.130)unde Θ�UHSUH]LQW��VXSUDWHPSHUDWXUD�FRUSXOXL��UHOD LD���������GHYLQH

    Θ=∂

    Θ∂ 22

    x (1.131)

    &HHD�FH�UHSUH]LQW��H[SUHVLD�XQHL�HFXD LL�GLIHUHQ LDOH�GH�RUGLQ���6ROX LD�HL�HVWH�

    xx eCeC ββ −+=Θ 21 (1.132)

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    21

    Constantele C1�úL�C2�VH�SRW�GHWHUPLQD� LQkQG�VHDPD�GH�YDORDUHD�WHPSHUDWXULLOD�H[WUHPLW� LOH�WHUPLQDOXOXL��x=0, x=l).'DF��x=0Supratemperatura 00 Θ=Θ =x

    ùL�� 210 CC +=Θ (1.133)În cazul în care x=l

    Supratemperatura llx Θ=Θ =Iar al

    lll eCeC θθ

    ββ −=+=Θ −21 (1.134)Deoarece θl�HVWH�QHFXQRVFXW���SHQWUX�GHWHUPLQDUHD�HL�VH�DUH�vQ�YHGHUH�IDSWXO

    F��SXWHUHD�FH�VH�WUDQVPLWH�SULQ�WHUPLQDOXO�FRPSRQHQWHL�HVWH�FHGDW��SULQ�FRQYHF LHvQ�ILQDO�PHGLXOXL�DPELDQW�DGLF��

    llx

    Ax

    A Θ=∂∂−

    =2α

    θλ (1.135)

    unde α2�HVWH�FRHILFLHQWXO�GH�FRQYHF LH�OD�FDS�WXO�WHUPLQDOXOXL��LQkQG�VHDPD�GH����������úL����������UHOD ia (1.135) devine

    ( )llll eCeCeCeC ββββλβα −− +−=− 21221 (1.136)

    úL� vPSUHXQ�� FX� UHOD LD� �������� IRUPHD]�� XQ� VLVWHP� GH� GRX�� HFXD LL� FX� GRX�necunoscute C1�úL�C2�FDUH�UH]ROYDW�OH�VWDELOHúWH�H[SUHVLLOH�

    ( )lllll

    eeee

    e

    Cββββ

    β

    λβα

    λβα

    −−

    −++

    Θ=2

    2

    01

    1

    (1.137)

    úL

    ( )lllll

    eeee

    e

    Cββββ

    β

    λβαλβα

    −− −++

    +

    Θ=2

    2

    02

    1

    (1.138)

    FD�XUPDUH�VROX LD�HFXD LHL�GLIHUHQ LDOH���������YD�DYHD�VROX LD�( ) ( )

    ( )lllllxlx

    eeee

    ee

    ββββ

    ββ

    λβα

    λβα

    λβα

    −−

    −−−

    −++

    ++

    −Θ=Θ

    2

    22

    0

    11

    (1.139)

    'DF�� VH� DX� vQ� YHGHUH� H[SUHVLLOH� IXQF LLORU� KLSHUEROLFH� úL� VH� LQH� VHDPD� GHUHOD LD����������UHOD LD���������GHYLQH�

  • Cap1. 3URSULHW� L�generale ale componentelor electronice pasive

    22

    ( ) ( )

    lshlch

    lxshlxch

    βλβαβ

    βλβαβ

    2

    2

    0+

    −−−Θ=Θ (1.140)

    úL� vnlocuind în (1.135) se poate calcula temperatura θl a terminalului la oGLVWDQ ��O�GH�OD�ORFXO�IL[�ULL�VDOH�vQ�FRPSRQHQW��

    lshlch βλβαβ 2

    01

    +Θ=Θ (1.141)

    • 3XWHUHD�WUDQVPLV��SULQ�WHUPLQDO�úL�FHGDW��DSRL�PHGLXOXL�vQFRQMXU�WRU�HVWH�HJDO��FXSXWHUHD�SULPLW��GH�WHUPLQDO�OD�FRQWDFWDUHD�VD�GH�FRPSRQHQW���[ ����&D�DWDUH�GDF�vQ�UHOD LD���������VH� LQH�VHDPD�GH�UHOD LD���������úL�VH�SXQH�FRQGL LD�[ ��UH]XOW�

    lth

    lthAP

    βλβα

    λβαβ

    λβ2

    2

    001+

    +Θ= (1.142)

    5HOD LD���������HVWH�H[WUHP�GH�XWLO��HD�SHUPL kQG�FDOFXOXO�SXWHULL�FH�SRDWH�GDWRULW�FRQGXF LHL�V��ILH�HYDFXDW���SULQ�WHUPLQDOXO�FRPSRQHQWHL�

    Exemplu:� �6��VH�DQDOL]H]H�SXWHUHD�WUDQVPLV��SULQ� WHUPLQDOXO�FRPSRQHQWHL�5&*������ vQF�UFDW� ODSXWHUHD�QRPLQDO��� WHPSHUDWXUD�DPELDQW�� ILLQG�WHPSHUDWXUD�QRPLQDO���7HUPLQDOXO�FRPSRQHQWHL�DUHOXQJLPHD�GH���FP��GLDPHWUXO�GH�����PP��ILLQG�FRQIHF LRQDW�GLQ�FXSUX��&RHILFLHQWXO�GH�FRQYHF LH�αeste 8W/m2K

    Se dau Se cere 6H�FDOFXOHD]�PN=0,5WθN=70°CθM=130°CD=0,8mmα1=8W/m2KλCu=380W/mK

    P0=? $�VHF LXQHD�WHUPLQDOXOXLA=πD2/4=0,5⋅10-6m2S�SHULPHWUXO�VHF LXQLLp=πD=2,5⋅10-3mβ2=α1p/λCuA ≅ 102

    βCu≅10 [m-1]βCul=0,3

    Deoarece βl ≅ 0,1, thβl ≅ βl, iar coeficientul α2� GH� FRQYHF LH� DSUR[LPDWLY� GH� DFHODúL� RUGLQ� GHP�ULPH�FX�α1��UHOD LD���������VH�UHGXFH�OD

    02

    0 θλβ lAP =&X�YDORULOH�FXQRVFXWH�UH]XOW�

    P0 ≅ 80mW.&X�DOWH�FXYLQWH�vQ�FRQGL LLOH�FRQVWUXFWLYH�SUHFL]DWH�GH�SUREOHP���SULQ�WHUPLQDO�GLQ�SXWHUHD

    GLVLSDW��GH�FRPSRQHQW��VH�HYDFXHD]����P:��LDU�SULQ�FHOH�GRX��WHUPLQDOH�VH�HYDFXHD]��vQ�MXU�GH160mW.

    6�� SUHVXSXQHP� PDWHULDOXO� WHUPLQDOHORU� FD� ILLQG�� nu cupru, ci fier acesta avândFRQGXFWLYLWDWHD� WHUPLF�� FHYD�PDL� VF�]XW��λFe=50W/mK. Reluând calculele puterea ce poate fiHYDFXDW��SULQ�FHOH�GRX��WHUPLQDOH�HVWH�≅ 125 mW. Ca urmare prin simpla înlocuire a terminalelor

  • Componente úL�FLUFXLWH�SDVLYH Note de curs

    23

    GLQ�FXSUX�FX�WHUPLQDOH�GLQ�ILHU��GLQ�SXWHUHD�GLVLSDW��SULQ�FRQGXF LH�VH�HYDFXHD]��GRDU�����mW înloc de 160 P:��'LIHUHQ D�GH����P:�IDFH�FD�vQ�WLPS�HQHUJLD�DFXPXODW��V��GHWHUPLQH�FUHúWHUHDtemperaturii componentei.

    ÌQ� SULYLQ D� WHPSHUDWXULL� WHUPLQDOXOXL� OD� FDS�WXO� FRQWDFW�ULL� VDOH� OD� VWUXFWXUD� deLQWHUFRQHFWDUH�FX�R�EXQ��DSUR[LPDUH�VH�SRDWH�SUHVXSXQH�F��HD�HVWH�GDW��GH�H[SUHVLD�

    lchl β1

    0Θ≅Θ (1.143)

    &D�DWDUH�vQ�GLVFX LH�SRW�LQWHUYHQL�GRX��VLWXD LL�1) βl >13ULPXO�FD]�LQWHUYLQH�GH�RELFHL�OD�WHUPLQDOHOH�H[WUHP�GH�VFXUWH�FX�R�OXQJLPH�GH�SkQ��OD���FP�

    ÌQ�DFHVWH�FRQGL LL�VH�SRDWH�FRQVLGHUD�chβl ≈����FHHD�FH�UHYLQH�OD�D�VSXQH�F�� WHUPLQDOXO�SUH]LQW�� ODFDS�WXO� V�X� DFHHDúL� WHPSHUDWXU�� FX� WHPSHUDWXUD� FRPSRQHQWHL��$FHVW� IDSW� VXJHUHD]�� F�� vQ� WLPSXOIXQF LRQ�ULL�� ORFXO�XQGH�VH�FRQWDFWHD]��FRPSRQHQWD�vQ�FLUFXLW�VH�vQF�O]HúWH�DSUR[LPDWLY� OD�DFHHDúLWHPSHUDWXU�� FX� WHPSHUDWXUD� FDSVXOHL�� 3HQWUX� FRPSRQHQWHOH� FH� IXQF LRQHD]�� vQWU�XQ� UHJLP� GHWHPSHUDWXU��ULGLFDW��V�DU�SXWHD�FD�DFHVWD�V��LQIOXHQ H]H�QHJDWLY�FRQWDFWXO�FRPSRQHQWHL�vQ�FLUFXLW�

    În cazul al doilea ceea ce corespunde terminalelor mai lungi eβl>>e-βl iar temperatura θlGDW��GH�UHOD LD���������GHYLQH�

    ll e

    βθθ −≅ 02�6H�REVHUY��R�GHSHQGHQ ��H[SRQHQ LDO��D� WHPSHUDWXULL�θl�HD� ILLQG�FX�DWkW�PDL�PLF��FX�FkW� O�HVWHmai mare.

    De aspeFWHOH�SUH]HQWDWH�SH�VFXUW�VH� LQH�VHDPD�OD�FRQVWUXLUHD�PRGXOHORU�HOHFWURQLFH�FkQGVH�XUP�UHúWH�DVLJXUDUHD�XQXL�UHJLP�WHUPLF�DGHFYDW�