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Submitted on 19 Oct 2012
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Circuit générique de commandes rapprochées pourl’électronique de puissance
The Van Nguyen
To cite this version:The Van Nguyen. Circuit générique de commandes rapprochées pour l’électronique de puissance.Energie électrique. Université de Grenoble, 2012. Français. tel-00743576
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4AC !57;;7 >D? !ED AE 2AA E DD BDD >?
&ADAE2AAEDDBDD77777777777777777777777777777777777777777 1DP
4AC!57;B7>D?%EBEDEDDAEDDBDD>?D
EDEDDAEDDBDD7 77777777777777777777777777777777777777777777777777 1DF
4AC!57;D7AADAEDAEDD7 77777777777777777777777777777777777777777777 1DG
4AC!57;J7FDBAEAAEADBDDBAEDAEEAAC7
77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 1JA
4AC!57;P7EAA777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 1JA
4AC!57;F7ACABB2E! .1! .;! .D7 77777777777777777777777777777777777777 1J1
4AC!57;G7#DEDBAEDAEBDDC7 7777777777777777777777777777777777777777 1J:
4AC!57BA7!DCAEBDAC777777777777777777777777777777777777777777777777777777777777777777777 1J:
A
-AAA
FACEA
1
F%2%6$
( BAA E CA ADB E
A7 #* DABA B D 4D DA D BD DA E CA
BDB BA ED B*DAD BD EA B D EDA
6BDCDADAEDBEA7#E*CA6AC
EAADEDABEAE*BAE
AD7 D CA A AD B BABBBDA
>BAAD-DDBBB?EDDDCAEADB7#EDBBABA
CDEE'A DE D ECDEE
AAEDEDEMCDEAO7#BDABABEDE#.
BEDADEEDABBD7"DAE
D MCD EAO DDB E DE E BAB A >J
BEDDADAB6DC?BDC
AC7$AAABDDEEDBADABDAB'EBADDA
CDB BDDEEMCOEBEADD B'DADADDBBBE
A BB D AED E A DADB DD
EDA B E A DDBBB7 !B CDB DABA A
DED D- DBADA BADA 'BB A A >BAAD-? DDBBB
>ABD?7!BEDDCAB'BEA
D AB BB7 F ABADA DA E EA B S E
AED-AE'BAEAD7
+ ABADA B'AEED E A E'ADC BD
ACDABAEDAEE'BAEAD7(DBABADAE
BBB BDA CDD DE*AEAD-EDD-AD
DBAD6ATDEAEB-AAEADABA7$B'ADC
EB'BAEBDABAADEDABDBCAEBD
BCAD-AEDEBDDED
EABEADEEAACDBAC7
# B A DA E A E B - E
B'EBDBDAEBDDEEAEADCABBAB
FACEA
:
DABA E%9F4+7" DBBEAA B DDAAE D DEA22A
E A E A E AD DA E A U E U
D70DAEEABACDADB'DEB'DEBCAE
DE D DA E E A DAA B'BA E
B'ACDA BAEAD7 + DD B BAAE D E BA-
D AD EAA A DBA E
DECAADBADAEDBE'DBADADA7
/DBE-ADADBBBBBCAEDE
D D E' DD E'ABA D E'B
E*DACABBDC D D EDA E DD7 +BB D V ED BD
AEADAEDEACDBCAAB
BD A T D E BBB BDA7 " EA B AA E
A E BB BCA A E DDB DEA
D DDDC -7 (D DBAEDA -ADB
A E BD E DE7 ( A E BCA E
DEA22AB'ACDABA-BDAEDA7
( AA DA A DBA E BD BCA E DE
DED B DA :7#BB2A BA ADBA A
DEAEA6DCA9"D
944 D A B'DDA E BD BAA E BCA BDA E DE
D D E DD E'ABA7 ( BD -AD-
B'ADAEBA7#6DACDBEAEBD
AB AADA E AA A22A E EAA E D
DABA B DA E B*A E*- =B EDA E BD
DAEDAEADDEAAEDE7
4EAE'ACDAEBDBCAEDEDEDB
E-A DA B EA DA D BD DA E BD ED E
AEAACAEDEDBEABCAE
A E B'CA7 #BA2A A E BBB BDA DE
D BA A E AD A E E UACU B
EA B B EA DBADA BA2DA7 (D A E EA
FACEA
;
E E- DA E BD A BD A E' AC
BCA#%9FDA>:A5?BDE-ABDAEDD
E'ABABDD BAA AABA70DBADA-ADBE
EAACDEABDDBAE7
A
B
CAAACACFAFAAFACAAEEAEA
D
/FBF" C$% $22!.!2.!!$H6!%
F9%%$!&+
AEEEBEBFEFEEFEBEEDDED............................ 5
F=:=F%2%..................................................................................................................... 7
F='=*%%62<>@<$AB2%>2CC$!!%D ........ 7
F................................................................................................................................... 7
#DDAABACADA ................................................................... 8
DDAA ............................................................................................................... 9
F=E=2% $2.%<>2.!!$ .......................................... 12
DAEBBDDEB=B.......................................... 12
#DAE%9F4+................................................................................................ 14
$DBE'DEADB .................................................................................. 17
#ABDEAEDA
DABABDCA>#+%? ............................................................................................ 17
!DEBDAEBDCABBBDEDAEDA .................... 19
!DEBDAEBDCABBBCADAEB'A ............. 20
E!DBDADB'DDD............................................................... 20
EE!DBDBAAEDE2AA ................................................ 21
"AE'AECABBCDAB'DB@+E'D2BAEDC
................................................................................................................................................................ 22
A/AAAEAE'DEADB .......................................................... 23
F=F=$2D$2!!2% $2 ..................................................................... 24
ABCAEAAEDED .......................................................... 24
A#DEA .................................................................................................. 24
A#DED ................................................................................................. 25
AAEDBACDBBDADEDE.................................... 27
ADEACDBEADDE-AD............................... 28
AEDBACDBABDACDBDA.................................................... 28
CAAACACFAFAAFACAAEEAEA
J
AEE$BADABDDBADA-D2DBADAD
DC ............................................................................................................................... 28
ADEACDBEADD6ADD
E'ABA........................................................................................................................................... 34
A#DDAEAEDE'CAEDE ...................... 37
A+BAEAAEDEAC .................................................................. 38
F=G=/!.0"0!62% $2!$..%*!.%
D%2.!!$ ............................................................................................. 41
1%6$.* ....................................................................................................................... 43
CAAACACFAFAAFACAAEEAEA
P
F=:= F%2%
('AEADBDDADTEBABB
BCA E B'BA E AD7 /D A DA DBB
DBA DA AADB B DA E AD CABB AB
%9F4+ D DE D7/DA DBB BD
A E -2A DD DA A DBB EAA B
DDAAEDDEA22AEAEAEADDAE
AUEUD7#BDEADDDBB'ADEACDB
EDE7/DEDBBDEB'DEB'DEAAE
DE DA E E A7 # EA D D
BA E B'ACDA ED B'BA E AD A B'ACDA E
EAEADB'ACDAEAAEDED7
0ADABADB*DDBEB'BAEAAEDEAC
B DBADA ABB AA E B'BA E AD7 +
DDDEBA-DADEAAA
DBAEDECA ADBADA EDB
E'DBADADA7
F='= *%%6 2 <> @<$ AB2 % >2 CC
$!!%D
(%9F4+ B DA E D CABB AB B DA B B
ABA ABA ED B A E AD DAB
A D AB DAB DE BD B* E E
DDAADADABADDB7(D4AC!71>D?B
B BD A E %9F4+ K1L7 ( %9F4+ D A
BEEDACABBWEDDEAEA-ABEDA
BD BB2A DA B %9F4+ D AEAAB D7 (D
CAAACACFAFAAFACAAEEAEA
F
E%9F4+ A2EA A E- CA
E6DDE7(DCAECABBE
2AABDCADBDDAE'DDBBE-CA-67
ν
>D? >?
4AC!717>D?&DABA>?FAE%9F4+7
$$!!6 !$
(D4AC!7:BDEBDDDAABAE%9F4+E
EAACAEE'DA
2 +DBDEBD AE BDCABB AA BD AEAB5 FX
5BDDB'DABDEEDAB7
&CAA > BADA? DE BD AE BDCABB A BD AE
AB 5 FY5 E'AA DB B M DDB O
D BD ABDA E' D A E AD E'AA7 (D A
EAEDADAEEAEB'ED7
(DAEDA25/FDAB7(DDBEDEDBDDBCABADA
DBBDB'DA>!71?K:L7
canalcanalthGScanal VVVVCI ).2
1.(0 −−=
>!71?
9Z
CAAACACFAFAAFACAAEEAEA
G
2
2 00
...
SiO
rSiOn e
µL
ZC
εε=
>!7:?
o CBDCEDDB(BCEDDB7
o EBDABAEEDC7
o #-BDDAE'-EECABB7
o rSiO2ε BDEABABDAEB'-E7
o 0ε BDFBEEEEBEBEB
o 2SiOe B'FEBBB
(D-AEDEEDAEDBDBAAEDBAEAEB'DA
E5 F 25I5DDB79DB BEAEDDB7(
DDEDBCAEDDAED7
2 &CAD>8DA?BDEDDBED8EA
EDB'DA>!7;?
20
20 .).(2 canalthGScanal VCVV
CI =−=
>!7;?
4AC!7:7#DDAADAE%9F4+7
/$$ ?!!
(DE%9F4+DEDDADDA B
BBBD4AC!7;>D?
CAAACACFAFAAFACAAEEAEA
1A
2 # F1 BD DDA BD CABB BD "[[ > A BD
DBBADA E BD ?7 # DDA EA D BD D
DBA-7
2 ># F: [ # F;? B DDA BDA E CABB2 ED BD
CA7# F:BDDDAEABAEA-DB# F;EBDCA
EEBABDBEDABBDADBDAECABB7
2 ># /1[# /:?DAEE-DAB*A-B*DDADB7# /1
DDA EABA # /: DA ACAADA B BD A
EDA2CABBDCEBDA7
2 #/FBDDDAEDA2BBDADBDAEEDA7
#DDADDADB6CABEBBDA
E%9F4+ED D 8 DA B BD 4AC !7; >?7 ( DDAED
EBBADAEEEABDBAD-BEE
%9F4+ >5/F 5 F?7 (D DDA CABB2EDA # / BADA BB
E BD DDA %9F A2E E ν 7 +BB AADB
DBEB'%ABBEDBDDAE%9F4+7/DBDA
BDCEBDCABBDABDDA# F# /7
ν
4AC !7;7 >D? 5 E %9F4+ D E DDA DDA >? FD
BAADBE%9F4+EDBD8DA7
D BD'DEDD-DDAA2E BEE
EBDBEBB2AEADA
CAAACACFAFAAFACAAEEAEA
11
2 #!FFI# F[# /2BDDDAE'7
2 #9FFI# /[#/F2BDDDAEA7
2 #&FFI# /2BDDDAE%ABB7
#DBEADDBEBDAEDA2B
BD4AC!7B>D?7
0DDDADE%9F4+BDDCDBDAR A
BD CABB DA BD A E BD CABB E 8 DB EA >1A5D
-B? A2D DA B%9F4+7 # DD AEADA
AD BD A E BD DE D B%9F4+7 (D DC
DBEADAEBDAR FBDDCADADA
BDAEBDCABBE8'DBDD%ABBBDE-AR /BDDC
AED BBDD%ABB BDEADA DA BD AE BD
CABB'BDDBADB7(D4AC!7B>?E-BEBDR A
EBDAEBDCABB7
CAAACACFAFAAFACAAEEAEA
1:
>D? >?
4AC!7B7/EB%9F4+!&4;DA>5/F%$HBAA5!/I1J$?>D?B
DDAABE>?BDDAEDCDADCBDCABB7
F=E= 2% $2.%<>2.!!$
/!$%2! !.%$% $2%J
+CDBBBDABDDEB=BE'A
EAD6 BA BD4AC !7D K;L7 !BAADBE
DE BAC DA E D B ACDB E DE C D B AA
BCA 4 $ >4ABE2CDDB D $D? D -B DE
D A D E'D B'CA BD DA E'DA E
AEAE B'A DD ABDACDBDA
DBADAAB'CABDDE7
R F R /
CAAACACFAFAAFACAAEEAEA
1;
4AC!7D7FDADB*ABAE*A
EADDEDBK;L7
B%9F4+EADBDDADADBDDEA
DBAD A AA BD A CDA BB
B' BD CABB BD 7 # DE A E EA BD
DA E'CA D B'CA EA 6 A B D E BD
DA D DA E DC DA BD DDA E' E
DA BD A B DC B'7 $ B*D DD
BBDAEADEB'CABDDBD
AEDDADE B*-EECABB7(AAEDEA
EAEABBDCABBBAE>BD?A6
B-EDDAEAEADDAEBDBBABDE
DA AB BD B D E ED B A BD
BD 4AC !7J7 /D EAA B'DBADA B ACDB E DE
BACEA6BDE%9F4+MACAEOCDDABD
BDADAEB*BEECABBDDBBEBDBABAB
DBBABAABAED7
/DBDDAADDBBDDBBDDEE%9F4+EAD
B A B A E B'A7 + DABA BD BDDA
D BDBB EDA AB B D EDA ADB B ACDB E
DE AEDB B D B DD E ACDB E DE
D2ABBDDAEDAEDEAD\+A
DBBB'DEB'DEAAEDEEDA7
CAAACACFAFAAFACAAEEAEA
1B
4AC!7J7DAMBNAEOMACAEOE'DE'EB7
% $%!2<>
$A E EAA B D D BD DA E%9F4+EAD
ECDBBACD-EDEAEBDBBBD
E DA A B* BD E BA2A KBL7 BD
BDEABDAEDABBD4AC
!7PAABDBBBEDADDABAEDDDA
DA7
0I
VddCGSV
GRGI
D
DSI
DI
4AC!7P7FDE'DA7
(D DA AEDBA BD E%9F4+ ED
DABBBD4AC!7F>D?
2 D1BDCBDAEBDCABB'BDAEAB5
BDEBDCABBDCABD# F# /7(AAEDE
EADAEEDBDA5/FBD!/FDCD7
2 D:BBEDEBDAEBDCABBDDABDAEABB
DEDA2)7(DAEEDADAA5EE
CAAACACFAFAAFACAAEEAEA
1D
DABC!/FX!ABDEAEEBA/EA7(DA
!/FAAADBBDAC!AAEADED7
0AB%9F4+EABBAD!ADAEDBD8DA
BD A CABB2 D D D DB B
BDD%ABBABDDDAE'E%9F4+BAAADD
EB'DCDAEBDDDACABB2EDA# /KDL7
2 D ; BD A E EDA E) BB EAA ED E-
ADBBED BA B D ED BD 8DA
ED1EDBE-AABEDBD8AED
:7
2 D B 0 A BD A EDA2 D AA E E) D DA D
DB B'D DD DA 5/FI&/F7!A BD A E BD CABB A
DC ' DDBD-ADB A AAB
EDDB7/DABDAEDA2DADDBAADBDEAAA
E&/F7 (D A ADB D- E BD CABB EAA DAA B AD E
BDADAE BD E A B*DDDE DA BA2A
A%9F4+! .7
FABDEAEEBA/ABDAEDEKBLKJL
BE'EEDADBEAABBD4AC!7F>?7
(DEEBDEAE!AB'ACAEDABDEEDAA
DADBCDEBE!AA '!A[!7#AD)ADE5 FAD2
EBEBDDBEBDDB'DBBBMO7RDEBDEBD
EAE'A)''DBBEDADAEBDAECABB'A
ABDDBDAEEADE5 F'BDDBEBDD70ABDDE
E BD EAE A B DEEDA A !A BD DA
AEDBDEBDEAEAEDB'22EAEADEBDA5/FA
E-ADBB7
(DDAB'E%9F4+DAE6D'BD
DAEDB'EA7(E'EBDAABB
EDBD4AC!7F>D?DBEBDAEDEEBDCABBE5 FD-A57
CAAACACFAFAAFACAAEEAEA
1J
thV
maxGSV
maxGIGSV
DSV
GI
DSI
tri tfu tru tfi
Qrr
Qrr
minGI
PoffPon
Vdd
DSVDSIDI
0IVdd
0I
maxGSV
t
t
t
t
t
GSV
tri tfutrr
1trr 2trr
thV
1tfu 2tfuDSonV
rrI
rrI
Pcond
)1( )2( )3( )4(
4AC!7F7>D?#DABDB*E%9F4+>?#DA
BDDBEBDEAE7
CAAACACFAFAAFACAAEEAEA
1P
$B!2D% $2%. $
% .% !$2%2!.!% $%1%
% .$1% $6@<D
ED B DA BD B* AB D E Z B
DBDAD-EB'ADBBDE
EDAADADEDA BD4AC!7F
>D?7FAEBEBDEAE/BDCBEE
DABDRBEDABDB'
E %9F4+ DBB D B DA >!7B? >!7D? A2EED BBB BD
EEDC
).2
.0..().(.)(.0
VddQrrtfutri
IVddfPPdttItVfP onQrronDS
tfutri
DSonM ++=+== +
>!7B?
)2
.0..().(.)(.0
tfitruIVddfEdttItVfP offDS
tfitru
DSoffM
+=== +
>!7D?
(AEDE6DBBDB'DA>!7J?
trr
QrrIrr
.2= >!7J?
(EAE'%9F4+DBBDB'DA>!7P?E
2 &/FBDADB'DDDE%9F4+>Ω ?7
2 α DBA7
α..20 DSoncond RIP = >!7P?
+DDBDA>!7B?>!7D?EABEDAE
B'AABDBEDAABBAB
EEDCE79E DABDAE DEADE
E5/F]EE!/F]EB ADAAECEDA
BDCA D E D ' E EA AD B DDA B
AEDDDAEDBAA7D-BDADA AD B
AA E DE D E DDA E E A D B
EAAEBA2AB BD4AC!7GKPL7/DD BDE
EABDEDBDDDA#16DBBDBDB>!7F?7
CAAACACFAFAAFACAAEEAEA
1F
4AC!7G7DAED-DDAEE7
dt
dVCI DS
C 11 = >!7F?
E -AC DEAA ADCA ACDB E
DEDAAEDBADADDBECBBDAEBDDAE
DC BDCABBE%9F4+KFL BD4AC !71A BBEBA2A BD
DABDE%9F4+
2 0ABAAAADBDCDAEBDCABB'BDAEAB
57
2 0E-AABAACDED)ABDADEDE
EDADAE'ABDABDCA7
2 0DABA>A6E'ADCDBBDE?D
DAA=B7
2 0 ABA ADB B D E DC DAE BD A E BD
CABBADADB7
CAAACACFAFAAFACAAEEAEA
1G
GI
GSV
DSI
DSV
1 2 3 4
thV
maxGSV
4AC!71A7FACDBEDEAEDBBDE%9F4+7
+ABEAABDD)AEBDBBA
B EA E EA BD AD B'D DD E A7 #BB2A EE
E'DEBDBCAEDE'DDEADEAEBDCABB
ED BD EA7 B BD A E CABB CDE A BD AD
ADEDBDDAADDBBDDBBEDABB'ADEADE
AEBDCABBBDDED7
F .$2$!%2$6!$2B$ 2% $%
" D B DAE%9F4+ ' C^ BD DC
EDC E DDA E' A DBA BD CABB BD
B'7 / DA B AD E A E CABB ED B D E DA
EADBDAEDA70BDDBADEDBB
EDAD-ADA BDAEADEEEDE%9F4+
EDBDDADB'DA>!7G?KGL
Giss
m
DSthG
mDS
RC
g
IVV
gdt
di
.
.2.
−−≅
>!7G?
$
2 5 BDADBABDCABB7
2 CBDDEDAEEEBDEB'A7
2 & ADADBDCABB7
CAAACACFAFAAFACAAEEAEA
:A
+ A BD A E DC E BD A EDA2 ED BD
DABBDBBDB'DA>!71A?KGL
GGD
MillerGDS
RC
VV
dt
dV
.
−= >!71A?
m
DSthMiller g
IVV +=
>!711?
$AADDADABDAEDAEEA
BEDADA6DCBDAEBDCABB7!B-ADAE
AAEDEAE'DEDADABADEBDAE
BDCABBAEBDAEDADAK1ALK11L7
F .$2$!%2$6!6 !$2D.
E !DBDADB'DDD
DB BD AD B'D DD E A E AD
EEDEBDE-2ABBAABBDEDCEBD
8BAAEA6ADDABBDAEBDCE
B DAEAD DBA A BAD B'DDD
E DB D8 AD7 (D AD B'D DD &/F9" E'%9F4+ DA
D-ADABDAD:7JEBDAEBDDC5.&K1:L
6.2. BRDSon VR α= >!71:?
+ BD AD B'D DD EE CDB E BD A E BD CABB7
DBB%9F4+DABBDA5 FEDBDA
E AB 5 BD AD B'D DD E) D BD A E DE E DV
BA B B'DBB AE BD E BD 4AC !7117 !B E
DA E'DC BD A E BD CABB ED BD D E EA DA E
AAAADAEABEEAEDBDAE
BD CABB EA 6 AA BD AE BDDCE B'-EE CABB KDL >AJA
1AA5B%9F4+?7!BDABDAEBDCABBADD2
EEBAADAE'AAEEDABBDEB'-EECABB7$AAB
A BD EAAADB BD ADABA BA B'-EECABB
EAAEDEECABBA1A51D5B%9F4+7
CAAACACFAFAAFACAAEEAEA
:1
GSV
DSR
DSonR
thV maxGSVV15≡
4AC!7117+BAEBDADB'DDDBDAEBDCABBK1:L7
EE !DBDBAAEDE2AA
"EADEBABDAECABBBD
EDBDDDAEEABDADB'DDDEEEA
B EA DA BD ' D ADB DE B
%9F4+DADBDE2AADADB6CDED
EED7+DE2AABDAEDA2DABA
CDED D BD A B'DDD CAADB B%9F4+ DDABBD
EDBDCADAB BD4AC !71:7/DEE A B
D DB E EDA EE E BD A CABB2 5 F E BD
AEDA25/FBB'DA>!71;?
20 ).(2 thGScc VV
CI −=−
>!71;?
/DA BD4AC!71:ABB BE-DEAD
5 F1E1A55 F:E1D57+CAADBABDEEABA
5/F > B AD &/F? E E- D DEA B E CA 2AA B
D!#2#1DBDAB!#2#:
CAAACACFAFAAFACAAEEAEA
::
VVGS 101 =1ccI −
VVGS 152 =2ccI −
2DSonV1DSonV
4AC!71:7#DDAADAEB'! .7
$AA A DE B %9F4+ D A E CABB AD B
EDBDDEEAEABEEABDDAD
EADAEDCDDEEDAD7
E!!2D!%266$0HD$1%KCC2D$%-
12$6
+AB'ADEBDAEBDCABBEDBDDEB'
E%9F4+ A E 8 DA AD B BA2A7 #ED D
A6EDAACDBEDECDA>2D5CDB?BBDCE'D
DBBDAEBDDEDAB'EEAB
E'D D E CDDA B'D2BAEDC D A E D
-BAA2E7
+ B B' DBA A CDA BD CABB BD E
%9F4+ ABDDE'AAED BD8 νN E ABDDDA
E*E-DAEBDE%9F4+E'E
E'AA B BD 4AC !71;7 9 DBB MD2
BAEDCOMD2DDCOK1;L7(DDDADDA# /'-ABEDD7+
BDE*AACAEA2A2AABE-DA
[BDBAAEBDDDA# />ABD4AC!7;?DCBDDEBDDDA
#/F7DBDADAEAEDA*AEABE
DADAEDCDADEBDDDAECABBACBDB
CAAACACFAFAAFACAAEEAEA
:;
E5]E A7 ( AB E A E BD CABB DA DDD) B'D2BAEDC
AEDDAAE BD8E AE BDE%9F4+
DA6DBA 215 2:5DAE*AEDADBA
A E BD CABB E 2D5 CDDA B'D2BAEDC D 8
AD A E AD EA7 # E DE
DABADADBEDBEDEED
BD4AC!7JZABDEDADAEABDAABAE7
ν
4AC!71;75E%9F4+DE'DBADAA5 FCDA@
E'D2BAEDC7
A C%2!?!2D% $2%. $
" E'DDB BD DE E %9F4+ EA D B
BDAEAAEDEE=B BDEAAAE'ACDBE
DE E BD CABB ADB D B'ADA E DAA B
AE%9F4+7+BABBAB
BADAMODEB%9F4+
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K:FL 7 (+4&$"# b+E A DBADA E AA E DE E'! . E
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K:GL 7 dDD F7 ,DDD 7 CDA 7 %AAD %7 FDD DE d7 4ED b+AA
A A8BA2D /#2/# c A 0,A 'CEA )))A (A
)EA5CEA+A#,,;%A)5A,;AF1GGFB7:71:DD@1:J1B7:7
K;AL &C CACDC(ADCDE$7,DCb$BA2EDC2DEACAA
NAE A DC /#2/# c A 01#1A )))A )A 4A A CFA )*A
2))3:A1A7:PAJ@:P1:7
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NADDcA)A'CEA)))A'EFA(A)EAA
CFA)*+A0116%A')AA"16:AA;B71711B@1:AB717
K;:L 97/BDCb#ADBADAATE'AAACBD
A/#]/#c0AA34A:A1A7
K;;L b"% FA !BDE :_ FACB 9 /#]/# #7c /DD %DD N
FBA7
K;BL bN%9F4+/AC'%DDB7c!DADB&AA5B71PDE1;17
K;DL "7 &C DE 372#7 #A bNDE A 4BB !CDE D/A N FBAc
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K;JL &7%!95$b!CDAE B'DBADAE BD DE DE' AE
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K;PL #7 eB DE "7 FDQ b$ #2+A FBA N D /A
%BABB ! AC .D N FB Ac A B( /A 'CEA
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CAAACACFAFAAFACAAEEAEA
BD
K;FL 37 37 D8QNQAe7 (7" DEH7 e b$(N2# D/A/AC0AC.D
#DDA%BABB%9F4+!cA(A)EACFA7AEA+A
0118%A)7A0118%A)59)))A:ACCE:AAJB7:71@D7
K;GL b!&:1;;;2DAECEA7c!DADB&AA7
KBAL (D8B.DBCb/AC$E$BADA AE4,ACFE%9F4+ D/A#AA7c
$BADA"-D!7
KB1L !DADB&AA$BADA"$"2GDAbD2!BDE D/AAE
BDCEBDA7c7
KB:L %7 37_DE7 37_Ab/AACACAEN%9F4+DE ! .DACBDC
AC$F!#c A'5ABEA A(A)EA)+A ))AEEA 1GG:7
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KB;L F7 F DE 37 #7 #BD b/B D DA- AEA EAc A
)ECEA+A#,,-%AF%+A<A7FCC1GGB7F;;@F;JB7:7
KBBL b(11J12RDEE,AC2FAE%9F4+/A7c(ADBC7
KBDL b,!BAFA$,ACBBAEC4EA7c!AB7
KBJL b%#;;FF;,2.AEC D/A!#7c4DBAE7
KBPL b$/%D:;A!BDE,DB2.AEC/ANA!CDE,AC2FAEFB7c$DBC/A7
KBFL b(#1FP1_AE!&DC"&F+"F+%E.4BDQDEF+!##BB7c(AD
BC7
KBGL +7(D$7#A7$7%DE474DE+7FDDb$ADB$D
!#BB D $BADA !BDE #c )))A BCCA A (A
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KDAL "7,DA d7 eE DE,7 $QDCA b4A2(B /AE2#BDE _%# #E
.DQ22.DQ % /Ac )))A BCCA A FA 'EC B7 BB 7 B 7
1:JF@1:PJ$C7:AAF7
KD1L e7 Db9EBADADDBADADDAc
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/FBFF" E%0%.%%62$% $2$..%*H1$!2$!C% $2D .!%
F9%%$!&+
AEEE !DDEDEFEDBEBFEB"EECBEFEBBE
F#D.......................................................................................................................................... 46
FF=:=F%2% ................................................................................................................. 48
FF='=E%0%.%%62$% $2$..%*H1$!2$!C% $
2D .!%*$C.......................................................................................... 48
#AAEDED..................................................................................... 48
FDEAA......................................................................................................... 48
DEDABD>A21?........................................................... 52
9DAEDBDDEEA>12:?.................................................. 54
DEDAB'>:2;?............................................................. 57
B9DAEDBDDEBDC>;2B? ........................................................ 58
$DB ................................................................................................................................. 60
$DDCABBEBDBBBCAEBDDE
D ............................................................................................................................................ 60
&CBDAEADEAEDEEDBDE
A .................................................................................................................................... 61
FEDEEAAEAEBDE
DE............................................................................................................................................. 64
E#A-EBDAE'DBADA[+BD#%9FA-E
AEABEEAECC1C:................................................................................ 64
EE/AAEDDE'ABAA-EDA
ED#%9F ................................................................................................................................ 64
AEBACD-EDEBD#%9F
AD ............................................................................................................................................. 67
B!DEBDDBDDDAAEEAEC ....................... 69
5DBAEDA-ADB ................................................................................................... 71
DAEAAAB ...................................................................... 71
/AAAEAAEDE ................................... 72
E#A-EEAEC........................................................................................ 72
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
BP
EE#ADDADAEDDE'ABAD
A-EDAED#%9F ....................................................................................... 72
EEE5AADAEEAA .................................................................... 75
&BD-AD-............................................................................................. 77
$DBEEAAEDED ...................................... 84
E.ABDCA................................................................................................... 84
EE#DDADA-ADB............................................................................ 86
B#DDAEBDBBBCAEDEDDBD
ABB ................................................................................................................... 88
FF=E=/!.0!.%D6$%22% $2.................................... 90
!CDAED#%9F................................................................................................ 91
&DBADAEDDE'ABAD>BAA
AADABDBDFA? ............................................................................................ 91
!CDAEDDEDAEDDDAE
B'AEAD ..................................................................................................................... 91
FF=F=%!% ................................................................................................................... 93
1%6$.* ....................................................................................................................... 95
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
BF
FF=:= F%2%
(ADADDADDBBEAAEDED
E DA CABB AB -AD D EAA B A DA E'DA
DEADBDADEBDCABBEEA7ADBAB'DEB'D
E E DE D A E E A
DDADDBBBAAEEDE-AD7/DDA
DBB BB BCA E DE D D BD A
T E* DD E'ABA D 7 +BB D V ED BD
AEADAEDECAADBDAB
BDAT'DDADEBAAEBA-AD7(AA
E A E BB BCA D EA7 " DBB DA DDB BD
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FF='= E%0 %.%%6 2 $ % $2 $..%* H 1$! 2
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2 0BDDDADEDB1:"1":E1
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E'ABA7
2 0 DD E'ABA E D DD E- A
D B ACDB B'CAE DE B'AEAD
6 D B'ABDA CDBDA B AA E DE B
AAEAD7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
BG
2 $ EDA E DD A FN BD DA E'A BD
EDC E BD DDA E CABB E B'A AADB B E B'DBADA
E'ABBBDDE'ABA7
2 0ADECABB& ADEBB2EN&E6ABA
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4AC!!717FDEBDBBBCAEDED7
$ E B'A FN DA DA A B 'AB
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C^BDA79DACDBAA
6ACDAEB'AEADDEDAEADBA
EDEEADD7AEAABA
EDAE-EAEC626BD
4AC !!71 # ACDA E DBA A FN D
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BD A E'DDBD 5CA BD DB DB E BD E A EA E
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ABDDBDB 12 fZBRZ VV + BA2AEAEAWABDAD-
EAAABDDB 21 fZBRZ VV +− BA2AEADADD7/DB
DDB'AFN7(DDAADDEDABBBAE
AA E DE D7 " EDAB B AA E A
CDBDAABEAEDAABAEAADA
BD DE E CABB7 0 EA DA E DA D D BD AB
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DA
ACDAEE-EAECDAEB'AEADDEAD
BDE*"22"7
Vp
t
tSw
4AC!!7:74E*EAEEDAEDDE*ABA
DEB*AFN7
SwI
21 fZBRZ VV +−
12 fZBRZ VV +
4AC!!7;7#DDAAAEDBEB'AFN7
!B D ED B MEAE CO ABA DABA BD
A7 + DBA B EAE EA C A E AB A
AAD5DEEADB'ECDEABBA
AEBDDCAD5EADB'E'DDBDK:L7
( A DE E BB DA B ABA E A
AACDADBADADAEDDDABD6DBAE
BD 6 E7 #BB2A E DC EDC A BD DDA
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
D1
E' E B'A E AD D E B E DCADA
EDCADADADEDDE*ABA7
$AA BAD-EABAACDADBABDCABBEDA
EEEADEBDAE*DBADAEB*EB#%9FDAAEAB
E*DDBDEEAE70ABDDCECABBBDBEAECA
DBDAAEABCABBEDAEAD7
(E'EABAAEACD-EDAEEAE
B'AEADABBBD4AC!!7BE
2 5 5 A B A D ADA D EDA E
DD7/DDE'E'ABDE
EADEDD7(DEDDAEη
Vp
Vs=η >!!71?
2 5CABDAD-EBDEAECA7
2 0BDABDADEBDCABB& BBECABB
E%9F4+7
2 5 FBDABDCABBBDE%9F4+7
2 ! BDEBDCABBE%9F4+7
2 α BDBA7
(DE AE BB BCAE DE D
-BAEDABEDBDAAD7 !B DE'DEED
BDEADB'DAEDABBDADE
AAEBDCABBAD
21 ZZ VVVsUt −+= >!!7:?
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
D:
Vp
1ZV
2BRZV
2fZV−
2ZV
UtSGV
GI
t
E+
E−
1BRZV
1fZV−t
t
t
t
0t 1t 2t 3t 4t
1V
2V
211 . BRZfZ VVEV −−=η
212 . fZBRZ VVEV ++−= η
4AC!!7B7(E'ECDBDBADAAEEEDC7
/*$!2% $%H$C @(-:D
!AADB B DA E AD %9F4+ B*D B
DDBA7(AEDAABDADAEDDEDBD
DEDABDBD4AC!!7D7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
D;
4AC!!7D7DEDABD7
ED BD D E DA BD E DA E AD B
DA 1 ": DE EA 6 B D E =
ADAE DDABDAE BD[+AD B%9F1 B'B
ADAEDDE'ABAAB"%9F":*BDD7(DA
1":EAEDEB'EEBDA
DE A EE E DA DC A BD DC E BD
DDAE'E%9F4+EADDE7/DAABA
E A AA E DB [+ D ADA E DD BD A D
EDADE E.η+ 7$AA BDEAECC:DEDCAE'DDBD
DEABDEAECC1BDAEA7
(DA0EDE6EEAEB'DA>!!7;?
21. BRZfZ VVEUt −−=η >!!7;?
(*BAEBDABDCABBBD5 FAEEEA
DB'DA>!!7B?7+BBDCDBADBDEDCEBD[+
BDDDAE'E%9F4+7
)(.)( tIRUttV GGGS −= >!!7B?
FABDEEB*ABAA@1ADCDEBDABDCABBBD
5 FDADDBD-ADB6DBBDB'DA>!!7D?7
211max . BRZfZGS VVEVUtV −−=== η >!!7D?
9 D CDDA B AD E A D-ADB BD CABB E
DA E AD BD E E B'ABA E A >12A? EA 6 CDB
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DB
A BD D E E DC E BD DDA E' E DA E
AD7FAEAABDAEDCDDDA
DABAADEADDEAEABCABBE
DEAD7
.$%.2$$.*$!2%2%@:-'D
$ B*AD : DE D 6 DBA A AB B D
ADAEDDDDAEB*EDEB*EB7(AE
DE=ADAEDDEDDABBBD4AC!!7J
>D?7+B*CAEDCADAEDDAAAED
E* E B*DE DD7 # B D B BA BD ABDA D
EDAEAABDEBDCEB*AFN7!BABDBAD
BDDBE%9F:EDB AAAD B%9F17 !BDBE-
%9F1:DEDAE'ABDEDCADAB
D BD EAE A E %9F : D E A D ADA B
ADACEEAEADBBB
BA7 9 EA D D E BA ED BDBB BD
EDCADADBBEDDDBA7+AEBDEEBDD>:2
1? E DDAA E DD BD EDCADA E DD
DABB B7" B BA DCA AD CDDA BD
EDCADABEDDDABAEDE7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DD
E+
1_PdsONR 2_PdsONR
LmI
Lm
Rp
>D? >?
4AC!!7J7>D?ADEDAAE5 FEEDCADADABBDB
>?FDBAADBABAA7
(D4AC!!7J>?BDBAADBABAAEDBDD
E BA( B'AEDDCADE DD& BDADE
B'B ADA E DD &E9"f1 &E9"f: A B
ADB'DDDE%9F4+1:7+BEBDDEDA
BDEB'EB'ABAEAAA[+EDB
>12A?BDEDB'AEDDCADDDADDBADB!(>1?
B B'DA >!!7J? BD 4AC !!7P @ BD DA E ABAADA DA
B' B'AED DCAD DA DB EDC D E E
D
Lm
ttEtI Lm
)01.()1(
−= >!!7J?
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DJ
LmI
t
0t 1t 2t 3t 4t
Vp
t
E+
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2I∆
≈ ≈ ≈ ≈
≈ ≈
)3(tVp
)1(tVp
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EDD>α DAB?7
+BDDEBAEBB'ABAEA'DB7
(D ABDA E D D ADA AEA A CDA D ADA E
DDADBBDB'DA>!!7P?A2E
)).(1()1( 2_1_ RpRRtItVp PdsONPdsONLm ++−= >!!7P?
RpRR
Lm
PdsONPdsON ++=
2_1_
τ >!!7F?
# A CDA D ADA E DD EE E AADB
E'DEBDAE*DBADAEBDEEB*ABAEDEE*D
DEDBE B'AEDDCADE DDE AD B'D
DDEDA1:7+ABACDAEBD
DB Vp.η− DDD)DEDAEDD7
DADEDEEBDCABB! ADABDBAD
B'DDDE%9F1E:AADA7/DABDDE
τ EBDDEEDCADADBBADBBDB'DA>!!7F?
D8CDEBDEDB'AEDDCADEAAAE
EDBDDEBAEAAADB 1I∆ 7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DP
/ = EDA E DD DAD B* BD A 5
CBACDB B*DA E DABB A B BDC E BD EAE C C17 ( D D
EDAEDDEAEEAEC17(DA5 F>?EBDDB
5 FD-DBDDABDE)AEDEA
ASE BDADEBBENABB2A7/DD BDEAE
CC:BCBDAEA7
B AE DV AB D BD A
DBDEAEC1AABAADAE*DDBD7FAA
ADBACEEEABEBDEAEBDEADADEBD
CABBEDADDABBBD4AC!!7F6DBDEDCEBD
DDAE'E%9F4+7DABDA5 FD-ABABD
A 5.&C1 B*AD E*AAADBADA E BD D E BA D DA D
E'DDBD EAE A D EDC DABB E BD CABB 'D
DADAB*DA>!!7G?AD7
12 BRZfZGS VVsVV <−− >!!7G?
ED D BD DC E BD DDA E' E%9F4+E AD
DABBEAABCAEADBAAEBDCABB>BEAE
CBDADEBDCABB& ?DAADBDADEBB2EN&E'ABD7
+BDAEBDCABBEAABCEDD7
ZV
ZI
fZVBRZV
4AC!!7F7#DDAAE*EAECDDBD7
/*$!2% $%HD%0@'-ED
(D 4AC !!7G B A E D ED BD D E DA
B'EDAEAD7AAADBEDEB*EB
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DF
#%9F7(DA:"1DBEADEAB1"1
B7/ =ADAE DD B D AB DA E [+AD B
%9F : A AD B'B ADA E DD A AD B "%9F ":
'BDD7/DAABAEACDA@+DADAE
DD7 9 D B* ABA D E CDB BB E
B'ABA AA ABA ED BD D E DA BD ED B
E'DDDA AEAB DBA CDDA BDEDCADAE
DDCADBA7DBDEAECC1BDAA
ACAE'DDBDDEABDEAECC:BDAEA7
4AC!!7G7DEDAB'7
(DA0BDABDCABBBDDBBA
21. fZBRZ VVEUt ++−= η >!!71A?
)(.)( tIRUttV GGGS += >!!711?
(DAEBDCABBEAAAEEACDADE*
D E CABB CDA A BD EDC A B*AA E BDA E BD
DDA E' E %9F4+ E AD7 ( BD D E EDC AA BD
A5 FDADDBAADBACDADBBDB'DA>!!71:?7
212min . fZBRZGS VVEVUtV ++−=== η >!!71:?
B .$%.2$$.*$!21%$6@E-FD
(D4AC!!71A>D?ABBBAEDBDDEBDCE%9F4+
EAD7(DDADAEDDABEDBD6EAA
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
DG
BB ED BD D E DA B' EA E7 !B
ED B CDAED B'AEDDCADE DD7# D AB
AD B%9F1D BDDBED B AA B%9F:E-%9F4+
DADEEAEDBDD>:21?7#DDA
AE DE BA D AEA BA E BD
DEBAADBAEDB'DDD>12:?DDBAADB
BD4AC!!71A>?7
E+
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LmI
Lm
Rp
>D? >?
4AC!!71A7>D?FEDEDAAE5 FEEDCADADABBDB
>?FDBAADBABAA7
ED BD D E E DA B* B D ED
B'AEDDCAD*AEACDAB'EB'ABAEA
CDA@+EDB>;2:?DDBD;6DBDB'DA
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C^BDEDCADADBB>ABD4AC!!7P?7
Lm
ttEItItI LmLm
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−−∆−= >!!71;?
+AAADDDD)DADAEDDD
DB6DBBDB'DA>!!71B?
)).(3()3( 2_1_ RpRRtItVp PdsONPdsONLm ++= >!!71B?
/D BD D EDAA D BDC E%9F4+ E AD B D ED
B'AED DCAD EAA DB DB A E D
DEτ CDBBBEDBDDEEA>:21?BDEAAABDA
EDDB 2I∆ 7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
JA
EDDBDAEBDCABBDCDABDEAECC1E
BDADAEA7#*BDEAECC:A6BDABDAEDEBD
EDCEBDCABB7BDABDDAE*DDBDAADB
DB BD A D AD E BD CABB E DA E AD
EDBDEAAED>!!71D?
21 BRZGSfZ VVVVs <−− >!!71D?
/DEAA BDEAECC: AEDBCAEBDADA
ADDEAADEBDEAEAAE BDCABB BD
AAAEDAE'DDBD7
( E AA E BD CABB ED B'D B AABDA BA
ED B'DDD BD DDAE'E%9F4+EADEDCD B
AAEBDCABBADBDADBB2EN&EBDAEBDCABBEAADB
DBAE7(BEDADBD7
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% $2$..%*
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DEEBDADECABBDBDDEEDCE
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DE E* ACDA BAA A ADC E'AC
DD E'ABA EA ABAA K;L ABA
DDE'ABADDDBAA#.KBLDAEDA
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
J1
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DA!5E7
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BDBAAD-7"DB*DAE*DEBDEDB
DAAA7
2 ( DE= EDAE DD EEAECA
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2 #EDACDBEDEDBDCCD
E D BA D BA2A 'D D BD DDA E DD
DADEABDADEDDE'ABAABAA
BDBAA7D>4AC!7:B?7
2 +BB ABA DBADA ABDA ACDB E DE
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CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
J:
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Vp
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maxGSV GSV
1BRZV
E+
t
Vp
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2BRZV
minGSV
maxGSVGSV
1BRZV
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4AC!!7117FACDBEDEABDADAD-7
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AADBE BD AE BDCABBED BDEDA BD
B'7EDB'DDDBADEAEBDCABBBAADBDA
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D BD A E'DDBD E BD EAE C C: 5.&C:7 / DA D
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BD AE'DDBDE BDEAEC:5.&C: DB DB7(D AE BDCABBD
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5 FD-Y5.&C1 2min BRZGS VV > BD AE BD CABB DDAD-ED D7"
DEA5 FD-CDEDADADAEEDBDDE
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DE2AADEEDDDEEDBDA!7
0 D D AD BD AABA E BAA BD A A-
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CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
J;
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D
2 8 BD E E ED BDBB BD A E BD CABB DA D DB
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t
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1w
2w
3w
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maxGSV
4AC!!71:7&CBDAEAD-EAECABB7
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CABB DA D DB D-ADB DD BD A E B'ABA7 + EAAD BD E E
B'ABAEN1N:N;DBADEAEBDCABBED
BDDEDAAEDB'DDD7#ADBADA6
AB BD CA E B'CA D E DC DADB Z AB DA E
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B*?! 2! $.! 2 2 !% 2 %.% 2 $
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( D E A EAA E AA E DE
E-DA
E #A-EBDAE'DBADA[+BD#%9FA-
EAEABEEAECC1C:
(D A DA E A A D- A- E BD DB 6 6 E BD
A$#DBDAEDDED#%9FEAEAB
EEAECC1C:D-2AADBAD-EAEBDCABB
ED B D E A7 + A E DBADA A A E
AD-ADB AADBE BD CABB EA E D E DDAη
EAAEEAECAABDAE'DBADA+C^
E-DAA2EADADDBDB
21max . BRZfZGS VVEV −−=η >!!71J?
21min . fZBRZGS VVEV ++−= η >!!71P?
EE /AA E DD E'ABA A- E
DAED#%9F
( DD E'ABA D E'D ABDA CDBDA
D ACDBEDE BDD B DAEADA
D6D6ABE7!BEADAAAD
DDDAEAEBAEAED ADDE BDCABBE
DAEAD7 !B DA 6ABA DC B'BBE A B
ADABEDA>DEDDAADA?7!BEAAABDA
BAADBADABEDA7
(D A E DD E'ABA DDB BB E'
DDEAD BA B DD E ED B
EAEDBDBD!!717
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
JD
DDBDAEDDE'ABA
2 A
2 &DEDDA
2 EAAg+g>5gE?
2 AD
2 "ADE'ABDA
2 DEA
DBD!!717DDABDAEDDE'ABA7
DA B DD BA A2E DBA DA B EA
>Ag?+g5gEABEAEBDAEB'ABADBDEE
BB2ADBADDDE'ABA7(D4AC!!71;BDE'E
CA D E D ED B'AED DCAD A E D
BAα 7 ED B'ABA AA [+ DBA ED B UU BD
EA E B- DA E' DB UE.U DA .D- AA7 ( ABA
'DBBDBDABDDEUBAUDEBA
B BEAAEBDEEDCADADBB7( B-
DCA D ED B D A EE E D BADA DA E BD
EEDC AB DEAA 'D 8 A BD DEEDCADA
DBBADBC7FAABACDA@+DBAED
DA CDB UU A B B-7 #BB2A D E EDCA
BBDADDBDDAABAAABDEAEB-DA
DAE'DBE.BBDB.ACDA7+AED
BA E-DB.D-.A EA B BD4AC !!71;
EDBDE 5.0<α 5.0=α 5.0>α 7"EDBDE 5.0=α DBD
ABB ABADA E D A D B A E BD EA E B- B A
AD7 $A E D D B D A E DD E'ABA B
EAEB-.A.D-EADEDBDEAEB-D-ADBED
A DB DB7 /'Z B EA >Ag? +g A DDA BD DABB
DEAABEDABDDABBEDDE'ABA7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
JJ
Vp
E−
dB
E+
maxB
Vp
E−
dB
E+
t t
maxB
Vp
E−
dB
E+
t
maxB
α
minB
minB
α
minBα
5.0<α
5.0=α
5.0>α
4AC!!71;7(DE'EEDEDB'AEDDCADAE
DBA7
(DADEBDAAAA BDABA2AEDA
DA CDE DABA D-AA B'AED DCAD AAA
B'AED E A E DD7 0 A B D A AA
ABEADBDB>!!71F?E
2 ""EADADADEDA7
2 .D-BDEAEB-B*AEAD-ADBDEAABED>BD?7
2 $DBDAED>h?7
noyauAB
tENp
.max
.= >!!71F?
4ADB A BD DB E B'AED DCAD E
DDDBDB>!!71G?D$(ABDE'AEDEDA
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
JP
2* NpALm L= >!!71G?
!B D E A DB E B'AED DCAD E
DD E'ABA B AD B'D DD E %9F 1 : D
DDADBDBEBDADADAEDDDE
ED BD D E BA BD D E EDCADA DBB7 !B D
DBADADDABBAAEBDCABBED
BDEDAAB'DDDB'DB7#BDADADA
E DDDEE BDDE BAED BDDEDAA B'D
DDE%9F4+EADDBBDBDBAD
).( 2_1_max RpRRIVp PdsONPdsONLm ++−= >!!7:A?
"DBAEADADADBBDEAA>!!7G?*22EA
12 . BRZfZGS VVpVV <−− η
(DADADAEDDDEEBDDEBAEDBD
DEDAAB'DBE%9F4+EADDBB
).( 2_1_min RpRRIVp PdsONPdsONLm ++= >!!7:1?
#AEADADADBBDEAA>!!71D?'22EA
21. BRZGSfZ VVVVp <−−η >!!7::?
/DBE-DBD maxLI minLI EAA
EDBDBBAA*22EABEAEB-.D-.AD-ADB
DBDBBDDE'ABAADDABBEDBDC
EABDBCDEAB7
Lm
ttEII LmLm
)01.(minmax
−== >!!7:;?
!%2! .! %!!!6$A2% $2.%!1$!
<!% .$
(DAE'DDBA2EBACDBEAAE
DED7+DBABEBDDEDCEEDCEBDCABBE
DAEADABDDAEDCQEDBDEAECC1A
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
JF
EAEAEDBDDEDABDDDA
E DC D Q ED BD EAE C C: A CDB EA EA
ED BD D E DA B'7 # DC 6 DBB
EQEBABAEA'DBDADAEDD7#
EA M E BD EAEO D D AD E AA E BD CABB B
D E E EDC BD CABB A EA EAA
ABBDADADEBDCABB7(D4AC!!71B>D?ABBB
EBDDABDEDAEADWRBDDAE
DC EQ ED BD EAE C C1 A DA BDA EA ED
B'DBADAEB'ABA[+DADAEDDW 1V∆ BDE
AEBDCABBDEDE7
E+
GI
1V∆ 2V∆2V∆
Qrr Qrr QrrmaxLmI−
VpGSV
1Vp2Vp DT DT
)(a )(b )(c
4AC!!71B7&EAEEAE7
>D?FDDDAB>?CDBDEEQDCE
DC>?ADEEQDCEDC
"AEABACDBEDEB%9F
:BAB"%9F":DD BDAEBDDEBA7ED
B"%9F": B%9F:B DEAB%9F1
DDBEDAADBBDAD-E%9F:7/DABA2A
B B D DCAD AB DB D EDA ' B A D CDA
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
JG
>4AC !!71B? E BD DB maxLmI− A D ED EDC BD DDA E BD CABB7 (D
EAECC:ADADDBDEADDBDEAECC1AEADAD
EDCQDADED8EAAEDAA
E BD A7 + D E- A D 6
ED D B E BD DC Q D EQDC AD D
ABDADAEEDE*DEBDA"EBDEAEC17
/ DA A B AD BC BD ADA A B
B'EEQDCEDCEDBDEAEDBAAABDEAEBD
CABBAAD7#AABBDBD4AC!!71B>?DEB/
CDBDDAEQBDCRDB'EADA7
/AABDEDBD4AC!!71B>?ZB/A
EEQDC7/BDDAEDCREQBBDCEBDEAE
C C1 ' BB2A A BD A E BD CABB B EDA 'A B BD
ADADAEDDBDDCADABDBDADAAD
BDEAEAAE%9F:AB%9F17#'DABDDEBADA
BDACDADADAEDDBADEDDBB
DA BD E BD A E BD AD E B'B ADA B BD E
ADBDEAEAAE:BBDEADBDAD
B'DDDE17#5:ABCDE51DBDD
EBAADBADB'DDDE%9F1:7(DEAEBD
CABBEDBE-EAD 2V∆ AAAD 1V∆ 79
B D DA B A- E EAE C C1 C: B A22A E
B*DDBD DA CDB E B DDAA E EA AD7
%DB E D DAB ED B EDA E
AAABAE*DDABBBDADEBDBA
E B*AADA E D7 D -B E EAE FQ DDBD
DA6DDDCED-DABA7
B F .$2$ .$!$$$!2!2%2!L
#AE DAD B'AD E BD D E A BD
DDAAEEAECDADEADAE'DDBDD
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PA
EABAAD-DAABBAEAA
EDED7
#D B'AD E BD D BD DDAA E EAE C B
EAECDDAE'DDBD'D7J5EADB'C
BB AAE D CDA *22EA BD AE'DDBDEAA
DE BD D DC7 $ DA B EAE C DD A
E'DDBDD2EED7J5EADB'DDBDBBAA
EDAABDAE'DDBDDCEDCDBDD7
$ E D E A BA2A DC AA A E BD
D7"DDAEABDAEDBBCAABFABDABCAABE
ABDA :/ ;/ D E EA B DDAA BA B
A E D BA E A2E
AA B'AD E BD D B DDAA E BD EAEC 1;5 E BD
EAECD7157(ADEEDCEEAEDAABB2ADA
A E'DDBD DA BD D DAD A D EAA BD
DA B DCE BD DDAA7( BDE ABDA
4AC!!71DADBAD7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
P1
AE'DE>5?
#DE'DE>$?
$CDAEAE'DDBD
$CDAEDEA
AE'DE >5?
#DE'DE>$?
/AAAEAE'DDBD
$CDAEDEA
>D? >?
4AC!!71D7!DEBDDBDDDAAEEAEC>BDE
ABDADBBCAABFABD?7
>D?/AEC1;5>?/AECD7157
$2$%A. $
/!$%2H .
"DABABBEDEDDE
%9F4+E BABE BDEDD A7(D4AC !!71J
B D BA E AA E AD E DE B DD E
DABAEDBDBD!!7:7
4AC!!71J7FDEDAEAAEDED7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
P:
DDEAAEAD
%9F4+ !&4;DABAA51J$
RC1DA#
/AE/ .dBAA5;$
4EEDC BAQ,8
& DAΩ
( JAAE,
# ::AE4BAA5
5EE :AA5
DBD!!7:7DDEAAEAD7
!% %.%22% $2
E #A-EEAEC
/D B DA ! D DDB B A BD DE D
B BACDBEDEADB B%9F4+EDA6E ABDA
D E DB ADB E [1D52D57 / DA ED A DBAEDA
-ADBDBBEAABAAEDEDABACDBE
DE7"AA-BEEAAAC1EAE
C 1J5 C: EAE C J5 B A E ABA D EDA E
DDE>[::52::5?7( AEDEDBBDD
B DA >!!7D? >!!71:? AA BD E A EA EEAE
CE[15
)(156122. 21max VVVEV BRZfZGS =−−=−−=η
)(511622. 21min VVVEV fZBRZGS −=++−=++−= η
EE #ADDADAEDDE'ABAD
A-EDAED#%9F
A DBAEDA E A E AA E DE
DABA BDA iEDB#G]J];@;+DDED4-E
DD E'ABA KDL7 0 A B D A AA
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
P;
DBB B E A D BD B >!!71F?7 ( UU AA B
EAA DB D-ADB E*ABA E DAA A
E'DBDDCBDEDCEBDCABBEDAEA
ADB'DBADA+AA1D5BEAA7(DDBEU.D-U
AAA7:DBDEDA7$ADAB'DDEAE
DDAEDDD.DDAEBDA;+DE4-E'A
A7B7 " E A B E A E B ADA "
EDA"EDD
8.610*4.4*25.0
10*500*15
.max
.6
9
=== −
−
noyauAB
tENp >!!7:B?
"DAAEAEPBADABAEEDA
EE11AAEDEDDAE'A17DP7
(DDBEB'AEDDCADEDDAA1AA
E,DBDB>!!71G?DBDDBE$(E:APA,EDB7
0ABDDE'ABAVDBA AB ADEB
DDADAE'AEAADD7"DBE'AEAADA
-ADB D E E'AED DA E D BA
ADB7/DA'AEAABBDCDCA
A D E BD DA BDA7 # A EDABB ED BD
KJL7 (D 4AC !!71P B AED AE 2AA E
DDE'ABAD BEE'AED7+DD
BE'AEAADA D AEAA BEBDCEDAE
DDDBADAB'ABBD4AC!!71FD
2 &BDADEB'BADA7
2 (B'AEDDCAD7
2 η BDEBDC7
2 &BDADEB'BEDA7
2 (B'AEDEA7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PB
10 100 1 103× 1 10
4× 1 105× 1 10
6× 1 107× 1 10
8×0.01
0.1
1
10
100
1 103×
1 104×
Fréquence (Hz)
Imp
éd
an
ce (
mo
du
le e
n O
hm
)
Z0mod
Z0°mod
Zccmod
Z°ccmod
f
4AC!!71P7!EDAE2AAEDDE'ABA7
57.1=η Ωm113Ωm57 nH404
µH107
4AC!!71F7#AAADBEBDDADCAEDD
E'ABAE-B7
('AEDDCADE1APE,EADEAADBDB7
" A DBB B D D-ADB AADB ED B'AED
DCAD BEA DE'DBADAE*ABAE ADADAE
DD7+DBEDEDDADAE'
DBADA E 1B5 DA A ::5 D EDA E DD7 "
EABDD-ADBAADBEDB'AEDDCADB
EB'DBADAEABAEA7"BD-6ZBDED
B'AEDDCADAAADBA8DDE'DBAABA7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PD
)(065.010*107
10*500*14)01.(6
9
max ALm
ttEI Lm ==−= −
−
)(065.010*107
10*500*14)01.(6
9
min ALm
ttEI Lm −=−=−−= −
−
+ A B DAE B DABA BC5":1AJ$
>&E9":Ω ?B"%9F"1":BC5:1AJ$>&E9"DΩ ?B%9F1:7
(DBD!!7;BDDEDBAAEDE7
DDEAAEDE
1: C5":1AJ$&/F9"DΩ
"1": C5":1AJ$&/F9":Ω
C1 .CHDD2#1JC1J5DAA_
C: .CHDD2#J5:CJ7:5DAA_
&C 1AΩ
&E DD Ωk
DBD!!7;7DDEAAEDE7
EEE 5AADAEEAA
" D D BD DDAA E EAE C C1 C: B'DAE E D
.1DAD$ E B'$CAB BCA A E D BD DDAA E
A E AD7 (D 4AC !!71G BD 4AC !!7:A A B
DDAAEEAECC15.& 1J5C:5.& J7:5 D 8 B
EEBDDADEAB7"DBDEAECC1D
AE'DDBDE'A1J5EAEAEA7P5DEABD
EAECC:DAE'DDBDEJ7:5AEAEA7P57
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PJ
AE'DE
#DE'DE
AE'DE
#DE'DE
>D? >?
4AC!!71G7#DDAADAEBDEAECC11J5
>D?AE'DE@#DE'DE>?CB*D-EDA7
AE'DE
#DE'DE
AE'DE
#DE'DE
>D? >?
4AC!!7:A7#DDAADAEBDEAECC:J7:5
>D?AE'DE@#DE'DE>?CB*D-EDA7
"EDBB
)(1.152.67.022. 21max VVVEV BRZfZGS =−−=−−=η
)(3.57.01622. 21min VVVEV fZBRZGS −=++−=++−= η
(DADADAEDDDEEBDDEBAEDBD
DEDAAB'DDDE%9F4+EADADBB
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PP
)(65.0)057.055(*065.0).( 2_1_max VRpRRIVp PdsONPdsONLm −=++−=++−= >!!7:D?
#ADADADBBDEAA>!!7G?
16)57.1*65.0(7.015
12
<−−−⇔
<−− BRZfZGS VVsVV
(DADADAEDDDEEBDDEBAEDBD
DEDAAB'DBE%9F4+EADEDBB
)(65.0).( 2_1_max VRpRRIVp PdsONPdsONLm =++= >!!7:J?
#ADADADBBDEAA>!!71D?
2.63.57.057.1*65.0
21
<−−⇔
<−− BRZGSfZ VVVVs >!!7:P?
" E -B E EAA B AA E
DED7"DBAEACDBEDE>[1D52D5?
BDCABBE%9F4+EADAEAABEAECBDAE
B'DBADADAABDDE'ABABDED#%9F7(
DD AA E DD BD DB E B'AED DCAD D
EAADADA BEAAEAAEDE7(DA
AAAEDBDBDBBDDBA7(DAE
DA D DDB B BD -AD- ABAD B AA E
DEV7
B!$!A. $A
(D4AC !!7:1 B'ADCE AAA T A E B AA E
DED BAAEAD7$AEBAABDE2AA
DEBDDAB%9FB"%9FEDB6DEBEBD
DEDDAEABACD-EDE
E E- D7" D E ABA B AA BCA CDDB 4 $
CBACD-EDEBACBDAEDEB*EB
#%9F A E DDA E B'ABADA E' AA DDBCA
CB7/DAE2BABAE'
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PF
D DDBAA B ACD- AE BD DEBACDE4 $
E'DDDBDABA2A7
4AC!!7:17!DCEAAEDEEAD
(D4AC!!7::BE'EEA BDADEDAE
DD5 B AEEAEC5C1 5C: BD A BD CABB BD
E%9F4+5 F DAA B D E BD CABB ! 7 (D 4AC !!7:: >D? B
E'E AE E DA BD 4AC !!7:: >? BD 4AC !!7:: >?
EDABBBDEE'E%9F4+EAD7
+CDEDBD4AC!!7::>?B'ABDABAE
AAAE[::5DBADEDAEDDBDEAECC:5.&
J7:5ADDBDDEABDEAECC1BDAEA7#BDB
EDABBDAEBDCABBDCBDEBDCABB
DC DAE 'D A A AB DA A E DC BD
DDAE'E%9F4+7(DEDCAABDAEBDCABB
DADDBD-ADB6DBDDB'DA>!!7D?7AA
BBD-AD-7"EAABDAD-ADBCABB
EDEADE'A1D715BDDBDBBEDBD
DA!!7:7;77AAA7
F BD4AC !!7:: >? BD4AC !!7:; >?D DA8 BDDE
DA BD E%9F4+70 E;AA D AEA B
ACDBEDEB:B":7"BEAEDBDDA
!!7:7:7EEDB%9F:DBBDDEBA'
DABDA5ADBAAEBDCABBE%9F4+B
DD
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
PG
DDCADABDEDAEDD79BD4AC
!!7:;>?BDADABEDDAE7(DDCAD
DDD)DEDAEEDCBDCABB6ABEEQ
BDDCADAQEDBDEAECC1ED B'DBADAEB'ABA7(D
EAEBDCABB 2V∆ EDADBBAA:57A
EADBBEAABDDCADABDADABDEAE
CC1B B BD4AC !!7:; >?DAA B E
BD EAE AA E %9F: EA A
CDA AD D EDA E DD7 ( B AA BD
DE BA A BD ACDA D EDA DA D
DDBADB'DDDE1:7+ABDAEBD
CABB DA D EDC D B D E A E BD EAEC1 D BD AD BB2
EN7"DAABDAAEDEADEEAEC
DE BD ADBB2EN7D -B B DE AA ABED BD
ADBB2ENAEBDCABBE1156DBBA
)(19610*56
113
µARd
VI GS
Rd ===
+CDEDBD4AC!!71G>?ABEEBDDDAA
EBDEAECC1DAE115D-EEAEBD
D E A E'A B E$ A CBACDB ED B D E A
DDBDADBB2EN7
"DDABD4AC!!7:;>D?BDZAB'DE
DA BD DDA7/D DE B'ABAE ADADA 'DB BD
DEBA7/=EDAEDDB
DEEBDEAECC1DAADABEED
ABEDCBDDDAEBDCABBEAAEEDCB
ADDADAE'DB 1V∆ E'AB57
/A DAD BD D E BDC E%9F4+ ABA E A
CDAE2::5DBADEDAEDDBBD4AC
!!7:: >?7/ DA BD EAECC15.& 1J5 CA E'DDBD DEA BD
EAE C C: 5.& J7:5 BDA EA7 (D A E BD CABB EAA '
DAEACDAA6DBBDB'DA>!!71:?7!BDD
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
FA
CDAEDBDCABBEDCBDDDAE'E%9F4+DAABB
ADBBDADCABBABCCDA7
)(3.57.0162221min VVVEV fZBRZGS −=++−=++−=
"DDA AEAE;AAED BBB
DED B D BD DA BD EA A2E
D B E D DCAD A ' B'DDA E DC
QEDBDEAECC:EDDAD BDDA B'7
(D A E BD CABB E'A 15 D E D DCAD ABD D
EDA E DD7 +A ED BD D E BDC E %9F4+ E
AD BD AE BDCABBDADBCDA BB2AD
ED DB DB BD A E'DDBD E BD EAE C C: 5.& J7:57 +BB
EAADBDBDEBDDEBDCEDBDEDCADBAA
E BD CABB AD BD AD BB2EN E BD 6 DA ED BD D E
DAA B'DDDE%9F4+EAD7#' BDEAECC:AE
BAA BD EDCE BD CABB7"DAA D B DE A
EBABDDBDADBB2EN&EBDAEBDCABB
E2B5
)(7110*56
43
µARd
VI GS
Rd =−==
+ D BD DDAA DA E BD C C: BD 4AC !!7:A >?
ABDEAAA:E$AABEDBDEAEC
A E 2B5 7 # D E A E D CBACDB ED BA
DDBDADBB2EN7
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
F1
5 F>D5]EA?5C1>D5]EA?
! >A7D$]EA?
5C:>D5]EA?
5 >1A5]EA?
>D?
5 F>D5]EA?5C1>D5]EA?
! >A7D$]EA?
5C:>D5]EA?
>?
! >A7D$]EA?
5C:>D5]EA?
5 >D5]EA?5 F>D5]EA?
5C1>D5]EA?
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
F:
>?
! >A7D$]EA?
5 F>D5]EA?
5C1>D5]EA?
5C:>D5]EA?
5 >1A5]EA?
4AC!!7::74E'EEAAEBDCABB7
>D?EDAE>?4E%9F4+>?9E%9F4+7
5 >D5]EA?
5 F>D5]EA?
! >1AA$]EA?
! >1AA$]EA?!!
&
5 F5
&
5 >D5]EA?5 F>D5]EA?
! >1AA$]EA?
! >1AA$]EA?
1V∆2V∆
>D? >?
&EAEBDACDA
4AC!!7:;7CBDDEDABDE%9F4+
>D?FD>?E;AA7
(BD-AD-A2EDEDBDDBA
B AA E A E BD BB BCA E DE D7 "
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
F;
DACDBEDEEBDCABBD AAAADBE[1D715
DADADAEBDDAEAEACDAE2D7;5
DA E'DB BD DA B'7 (D A E BD CABB
DAA115EDB'DDDAA2B5B'DBE'Z
B'D2BAEDCD BDA-A7(BD
4AC !!7:B B ACD- E DA E %9F4+ AB DBAE B
AEEA7FBDDABDE
ABBDADADEBDAEBDCABBBBED-AEDDDAE
BDCABBDADDEEBDEAEEAD7+B'AED
EADEDAEDDE'ABAACDBCDE
DAB'AEDDDAEDBAAEBDCABBE%9F4+7
>D?
5/F>DA5]EA?
5 F>D5]EA?
!/F>1$]EA?
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
FB
>?
4AC!!7:B7FACDBEDAE%9F4+
>D?#DABD>?#DAB'7
$B!2!.!22% $2$..%*
E .ABDCA
F BD4AC !!7:DEDABB BD DAAEAD D B
EABEDBAAEDE7
EP
CMOSP
TP
1ZP
2ZP
RGP
RdP
4AC!!7:D7.ABDCA7
(ABDEAD6-ADB'DA>!!7:F?
5 F>D5]EA?!/F>1$]EA?
5/F>DA5]EA?
CAAA.4EEAEAFAECACFACAADCAFACCAF"EA
FD
RdRGZZTCMOSE PPPPPPP +++++= 21 >!!7:F?
comstatiqueLmdynamiqueCMOS PPPPP +++= >!!7:G?
/
2 EP BDDADBEAAEDE7
2 CMOSP BBEBBAD
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