mat eriaux magn etiques et solutions innovantes de ltrage ... · mat eriaux magn etiques et...

137
Mat´ eriaux magn´ etiques et solutions innovantes de filtrage CEM pour applications a´ eronautiques Fanny Mesmin To cite this version: Fanny Mesmin. Mat´ eriaux magn´ etiques et solutions innovantes de filtrage CEM pour ap- plications a´ eronautiques. Autre. Universit´ e Grenoble Alpes, 2012. Fran¸cais. <NNT : 2012GRENT039>. <tel-00759383v2> HAL Id: tel-00759383 https://tel.archives-ouvertes.fr/tel-00759383v2 Submitted on 6 Sep 2013 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es.

Upload: others

Post on 04-Sep-2020

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

Materiaux magnetiques et solutions innovantes de

filtrage CEM pour applications aeronautiques

Fanny Mesmin

To cite this version:

Fanny Mesmin. Materiaux magnetiques et solutions innovantes de filtrage CEM pour ap-plications aeronautiques. Autre. Universite Grenoble Alpes, 2012. Francais. <NNT :2012GRENT039>. <tel-00759383v2>

HAL Id: tel-00759383

https://tel.archives-ouvertes.fr/tel-00759383v2

Submitted on 6 Sep 2013

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

Page 2: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

THÈSEPour obtenir le grade de

DOCTEUR DE L’UNIVERSITÉ DE GRENOBLESpécialité : Génie électrique

Arrêté ministériel : 7 août 2006

Présentée par

Fanny MESMIN

Thèse dirigée par Afef Lebouc et codirigée par Hervé Chazal et Fabien Sixdenier

préparée au sein du Laboratoire de Génie Électrique de Grenoble dans l'École Doctorale Électronique, Électrotechnique,Automatique et Traitement du Signal

Matériaux magnétiques et solutions innovantes de filtrage CEM pour applications aéronautiquesThèse soutenue publiquement le 28 septembre 2012 devant le jury composé de :

Pr. Eric LABOUREProfesseur des universités de Paris SUD, Rapporteur

Pr. Nadir IDIRProfesseur des universités de Lille, L2EP, Rapporteur

Pr. Belahcène MAZARIProfesseur des universités, CESI, Président

Pr. Patrick DULARDirecteur de recherche, université de Liège, Examinateur

Dr. Afef LEBOUCDirecteur de recherche CNRS, G2Elab, Examinateur

Dr. Hervé CHAZALMaître de conférence, G2Elab, Examinateur

Dr. Fabien SIXDENIERMaître de conférence, Ampère, Examinateur

Membres invités :

Dr. Houmam MOUSSA, Hispano-Suiza

Mr. Dominique GAUTARD, TCT

Page 3: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 4: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%$&

' (% )*%+",(-*&.

' (&/ 0%*&+1/.

' 2#$34

Page 5: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 6: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$ %$& '!()*+$&

!"!#$%!"!&'( !

)&'#*+,$'%*& -.&.#/0! "

) 1*&'!2'! !' *34!$'%5( +! 06.',+! #

!" #$ %&'($)*+*,*)- .,/0)1&2$34-)*56/ !

!"!# $%&'()(*' !

!"!+ ,-. /-0)10+#)(*'. 2*'31()-. -' %4-2)0*'(51- 3- /1(..#'2- "

!7 8$49 ,/ :&'$*4/ $-1&4$6)*56/ #

!6!# ,7#8(*' 9/41. %4-2)0(51-: #

!6!+ ,- /0*;-) <<=>*?-0 $

!6!2 ,-. '*0@-. ABC %&

!; </19 64 =*,)1/ %.2 $>/0 64 9/6, 0&'(&9$4) '$34-)*56/ %%

!D!# >0*+4%@#)(51- 31 2*@/*.#') @#E'%)(51- 1'(51- %%

!D!+ B)#) 3- 47#0) %!

!D!2 $%@#02F- 3- 47%)13- %'

)) 17*%2 +! 0/ '*8*0*-%! +, $*"8*(/&' "/-&.'%9,! ,&%9,! "$

!" ?$0)/619 *4=,6/4@$4) ,$ )&(&,&3*/ %$

!"!# C(.- -' %8(3-'2- 3- G#2)-10. %$

!"!+ ,- 2F*(H 31 @#)%0(#1 @#E'%)(51- %(

!"!2 <%4-2)(*' 3- 51#)0- )*/*4*E(-. )*

!7 %A&*B :/ ,$ '&:-,*9$)*&4 C9D9)E'/F )"

!6!# $%&'()(*' 3- 4# /-0G*0@#'2- 31 &4)0- )"

!6!+ ')%0I) 3- 47#//0*2F- 9.J.)K@-: )'

!; %&49)160)*&4 :6 '&:E,/ )#

!D!# ,# G*'2)(*' *+;-2)(G -) 4-. 2*')0#(')-. )#

!D!+ C(.- -' %51#)(*'. 31 .J.)K@- )$

!D!2 L#4(3#)(*' 3- 4# @(.- -' %51#)(*'. /#0 1' 4*E(2(-4 2(021() *'

!G %&'($1$*9&4 :/9 :*==-1/4)/9 )&(&,&3*/9 *'

!M!# ,- 2*1/4#E- 3- @*3- *'

!M!+ $(.21..(*' .10 4-. )*/*4*E(-. 0-)-'1-. *$

))):*+.0%(/'%*& +, $*"8*(/&' "/-&.'%9,! %#

!"2&:-,*9$)*&4 :6 0&'(&9$4) '$34-)*56/ !!

!"!# ,-. 2#0#2)%0(.)(51-. 3-. @#)%0(#1H @#E'%)(51-. !!

!7%A&*B :6 '&:E,/ (&61 ,/ 0&'(&1)/'/4) =1-56/4)*/, !"

Page 7: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$%& '&( )#"*+,&(

!"!# $%&'()%*+#+,-* (.%/+',01% (01,2#.%*+% 3 4-56.%) 7.-8#19 - - - - - - - - - - ./

!"!8 :-56.% 5% /,'/1,+) 4#7*(+,01%) (01,2#.%*+) - - - - - - - - - - - - - - - - .0

!"#$%&%'($%)* +, -)+.&/ 0)-1)'(*$ -(2*3$%4,/ +(*' &( -)+3&%'(5

$%)* '6'$.-/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12

!;!# <',)% %* /-4&+% 51 /-4&-'+%4%*+ ='(01%*+,%. - - - - - - - - - - - - - - - 12

!;!8 <',)% %* /-4&+% 5% .# &-.#',)#+,-* )1' .% +'#>%+ 5% ?19 5% 4-5% 5,@('%*+,%. 1/

!7 8%-,&($%)* +, 9%&$:/ ;<= 0)-1&/$ - - - - - - - - - - - - - - - - - - - 13

!"#$%&%'($%)* +$ ,-(.%'($%)* /0 1)&#)'(*$ &(2*-$%30+ !

>!? =3$@)+/' +A)1$%-%'($%)* +/ &( $)1)&)2%/ - - - - - - - - - - - - - - - /4

A!B!# :-5(.,)#+,-* 5% .# +-&-.-7,% #2%/ %*+'%=%' - - - - - - - - - - - - - - - - - /4

A!B!8 C-*/+,-* -8>%/+,= - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /5

A!B!/ DE-,9 5% .F#.7-',+E4% 5F-&+,4,)#+,-* - - - - - - - - - - - - - - - - - - - - //

>!B C3',&$($' +/ &A)1$%-%'($%)* - - - - - - - - - - - - - - - - - - - - - - - - - /0

A!"!# D-*+'#,*+%) .,() #1 4#+(',#1 %+ #1 8-8,*#7% - - - - - - - - - - - - - - - - /6

A!"!8 G*+'%=%' 4,*,4#. '(#.,)#8.% - - - - - - - - - - - - - - - - - - - - - - - - - 37

>!" ;(:(0$3:%'($%)* +, 0)-1)'(*$ - - - - - - - - - - - - - - - - - - - - - - 3.

>!7 ;)*0&,'%)* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 31

! !+,' 0* 1)&#)'(*$ &(2*-$%30+ 0*%30+ %*$-2,(4.+ '0, 567 ""

>!? DA%*$32:($%)* ',: E;F +/' 0)-1)'(*$' -(2*3$%4,/' - - - - - - - - 30

A!B!# HF(+#+ 5% .F#'+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 30

A!B!8 I-&-.-7,% 51 /-4&-)#*+ 4#7*(+,01% - - - - - - - - - - - - - - - - - - - - 36

A!B!/ A%''-1) +%/E*-.-7,01%) #/+1%.) &-1' .F,*+(7'#+,-* )1' <DJ - - - - - - - - 02

>!B D/ G/::), $/0@*)&)2%4,/ +/ &( -%'/ /* 9):-/ - - - - - - - - - - - - 02

A!"!# K(/-1&% 5% .F#4-'&E% &'(/1')%1' - - - - - - - - - - - - - - - - - - - - - 04

A!"!8 $%/1,+ 5% *#*-/',)+#..,)#+,-* - - - - - - - - - - - - - - - - - - - - - - - - 05

>!" D/ G/::), $/0@*)&)2%4,/ +, :/0,%$ '),' 0@(-1 $:(*'G/:'/ ',:

+/' 0(+:/' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 06

A!;!# <',*/,&% 51 5,)&-),+,= - - - - - - - - - - - - - - - - - - - - - - - - - - - 06

A!;!8 D-*+'#,*+%) )1' .% 5,4%*),-**%4%*+ - - - - - - - - - - - - - - - - - - - - 62

A!;!/ A#.,5#+,-* %+ '(#.,)#+,-* 51 5,)&-),+,= - - - - - - - - - - - - - - - - - - - 67

A!;!5 $()1.+#+) %9&(',4%*+#19 - - - - - - - - - - - - - - - - - - - - - - - - - - 64

>!7 *$32:($%)* ',: E;F /$ 0(:(0$3:%'($%)* - - - - - - - - - - - - - - - - 61

A!L!# K,4%*),-**%4%*+ 51 <DJ - - - - - - - - - - - - - - - - - - - - - - - - - 61

A!L!8 D-4&-)#*+ 4#7*(+,01% ,*+(7'( )1' <DJ - - - - - - - - - - - - - - - - - - 6/

>!H ;)*0&,'%)* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 6/

6)*1.0'%)* +$ #+,'#+1$%8+' ##

7%4.%)2,(#9%+ !$#

:**+;+ : < :/(#$($%)* /=%&#-/(*1+ +$ 1)0#.(2+ /+ &)/+ /+ .(

')0,1+ /+ #+,$0,4($%)*' !!!

Page 8: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$ %$& '! ()*$& +,,

!!"#" $ % &'()(*+"),-(+,.! ./ 0(1!"+,* 2")0"(3,4,+5 62"*+)(

76,!1 3.+' /47#0"+),* (!8 ,02"8(!*" (22).(*'"6 !

Page 9: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 10: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$ %$& '()*+$&

!" #$%&'()* &(+ +(,$--*.*-/ */ &(+ 0$-1%0/2$- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3

!4 #2+0%'(/2$- 1*5 0$%+(-/5 1* .$1* 1267+*-/2*' *-/+* 1*%8 5,5/9.*5 ! ! ! ! ! ! :

!; #2+0%'(/2$- 1*5 0$%+(-/5 1* .$1* 0$..%- *-/+* 1*%8 5,5/9.*5 ! ! ! ! ! ! ! :

!< =2'/+*5 #>? &(552@5 A0'(552B%*5C ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! D

!3 E75*(% 7'*0/+2B%* F G$+1 1H%- (I2$- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! J

!: K'(- 1% &+$L*/ MM K$N*+ O #$-/+$' ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! P

!D =2'/+* #>? Q ?$1* 0$..%- */ .$1* 1267+*-/2*' RSTT

+UPV ! ! ! ! ! ! ! ! ! "U

!J W2I*(% .(82.(' 1* &*+/%+G(/2$-5 0$-1%2/*5 (1.2552G'*5 XW$+.* YZ[":U=\ ! ""

!P #,0'*5 B(H) */ J(H) /,&2B%*5 1H%- .(/7+2(% .()-7/2B%*! ! ! ! ! ! ! ! ! ! ! "4

!"U #,0'*5 SX]\ &$%+ 1267+*-/5 /,&*5 1H*802/(/2$-5 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ";

!"" +(L*/5 1* _%8 1* .$1* 0$..%- */ 1* .$1* 1267+*-/2*' ! ! ! ! ! ! ! ! ! ! ! "3

!"4 K+$/$/,&* &+$&$57 &(+ '* #K>M ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ":

!"; K+$/$/,&* &+$&$57 &(+ ]25&(-$[M%2`( ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ":

!" $&$'$)2* G(57* 5%+ '( 1255,.7/+2* 1*5 /+(L*/ 1* _%8 ! ! ! ! ! ! ! ! ! ! ! ! ! "J

!4 $&$'$)2* G(57* 5%+ '( 1255,.7/+2* 1*5 G$G2-()*5 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "J

!; ''%5/+(/2$- 1*5 0$%+(-/5 1* =$%0(%'/ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "P

!< M0a7.( 1H7'(G$+(/2$- 1H%- +%G(- -(-$0+25/(''2- R?*/JJV ! ! ! ! ! ! ! ! ! ! ! 4U

!3 #$.&(+(25$- 1*5 &*+.7(G2'2/75 *- @$-0/2$- 1* '( @+7B%*-0* RK*+PDV ! ! ! ! ! 44

!: =+()2'2/7 1* +%G(- 1H(''2()* -(-$0+25/(''2- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4;

!D $&$'$)2* G(57* 5%+ '( @$+.* 1*5 .(/7+2(%8 .()-7/2B%*5 ! ! ! ! ! ! ! ! ! ! ! 4<

!J $&$'$)2* #K>M ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4<

!P #(5 1* +7@7+*-0* Q '*5 2-1%0/(-0*5 0$%&'7*5 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4:

!"U ?$19'* A5,5/9.*C 1% 0$.&$5(-/ .()-7/2B%* */ 1* 5$- *-I2+$--*.*-/ ! ! ! 4:

!"" M0a7.( 1% B%(1+2&b'* A0$.&$5(-/ .()-7/2B%*C ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4D

!"4 Y7c-2/2$- 1* '( 5*0/2$- (&&(+*-/* 1H%- 0$.&$5(-/ ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4D

!"; EM d #$%+G* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4P

!"< M0a7.( 1% EM d 0$.&(/2G'* (I*0 '( -$+.* YZ[":U ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;U

!"3 M0a7.( 1% EM d ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;U

!": M0a7.( 1* '( 5$%+0* 1* &*+/%+G(/2$-5 X/,&* AG$2/* -$2+*C\ ! ! ! ! ! ! ! ! ! ! ;"

!"D M0a7.( 1*5 0(&(02/75 #8 */ #, 1% c'/+* #>? ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;4

!"J M0a7.( )7-7+(' 1% 0$.&$5(-/ .()-7/2B%* %-2B%* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;;

!"P e(+2(/2$- 1% 0$*f02*-/ 1* 0$%&'()* 1* .$1* *- @$-0/2$- 1* 8 ! ! ! ! ! ! ! ! ;<

!4U e(+2(/2$- 1% 0$*f02*-/ 1* 0$%&'()* 1* .$1* *- @$-0/2$- 1* g"4 ! ! ! ! ! ! ! ;3

!4" #$.&(+(25$- *-/+* '* '$)202*' 02+0%2/ */ 'H70+2/%+* .(/+202*''* ! ! ! ! ! ! ! ! ! ;:

!44 -_%*-0* 1% 0$%&'()* 1* .$1* 5%+ '( /*-52$- 1* .$1* 0$..%- ! ! ! ! ! ! ! ;D

!4; -_%*-0* 1% 0$%&'()* 1* .$1* 5%+ '( /*-52$- 1* .$1* 1267+*-/2*' ! ! ! ! ! ;D

Page 11: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$% &%' ()*+,%'

))-./ 012345 6776859: ;3 <2:85 59 =19>:?19 ;5 26 :59@?19 63 A1895@ ;3 ,')$ - - BC

))-.D 012345 6776859: ;3 <2:85 59 =19>:?19 ;5 26 :59@?19 63 A1895@ ;3 ,')$

EµriFGHHHI - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - BC

))-.J K147686?@19 ;5@ 758=18469>5@ ;5 26 :17121L?5 M?@7691N'3?O6 6P5> 25 >6@ ;5

8Q=Q859>5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /H

))-.R K147686?@19 ;5@ 758=18469>5@ ;5 26 :17121L?5 6P5> 59:85=58 6P5> 25 >6@ ;5

8Q=Q859>5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /S

)))-S 068?6:?19 ;5 26 7584Q6A?2?:Q 59 =19>:?19 ;5 26 =8QT359>5 - - - - - - - - - - - //

)))-. )9U359>5 ;5 26 71268?@6:?19 @38 25@ >138A5@ ;5 7584Q6A?2?:Q 8526:?P5 59 =19>N

:?19 ;5 26 =8QT359>5 V µr F 768:?5 8Q5225W µi F 768:?5 ?46L?96?85 - - - - - - - /D

)))-B '>XQ46 ;3 419:6L5 ;5 Y86AX6Z6869 5: 62- ;69@ [Y'H.\ - - - - - - - - - - - - /J

)))-/ K?8>3?: QT3?P6259: ;5 2]?9;3>:69>5 - - - - - - - - - - - - - - - - - - - - - - - - /R

)))-D ,578Q@59:6:?19 ;]39 L^86:538 - - - - - - - - - - - - - - - - - - - - - - - - - - /C

)))-J _1;`25 ;]39 >19;59@6:538 - - - - - - - - - - - - - - - - - - - - - - - - - - - - DS

)))-R K147686?@19 ;5@ 45@385@ 5: ;3 41;`25 7138 K 5: K^ - - - - - - - - - - - - DS

)))-G _5@385@ ;]?47Q;69>5 ;5 2]?9;3>:69>5 5: ;3 >19;59@6:538 - - - - - - - - - - - D.

)))-C '>XQ46 ;3 41;`25 L^86:538N>676>?:Q ;5 2]?9;3>:69>5 @13@ a+K' - - - - - - DB

)))-SHK147686?@19 59:85 25 41;`25 L^86:538N>676>?:Q 5: 26 45@385 - - - - - - - - - DB

)))-SS_1;`25 L^86:538N>676>?:Q ;5@ ;53 ?9;3>:69>5@ - - - - - - - - - - - - - - - - DD

)))-S.K147686?@19 59:85 25 41;`25 L^86:538N>676>?:Q 5: 26 45@385 @38 39 >1471N

@69: 8Q52 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - DD

)))-SBK19:138 ;]"47`85 @38 26 :17121L?5 6P5> 59:85=58 - - - - - - - - - - - - - - - - DJ

)))-S/K^>25 #EMI b SHH 4MO - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - DR

)))-SD'>XQ46 ;3 <2:85 K%_ 6P5> >1471@69:@ >676>?:?=@ 5: ?9;3>:?=@ ?;Q63 - - - - DG

)))-SJ'>XQ46 ;3 <2:85 K%_ 6P5> >1471@69:@ 8Q52@ - - - - - - - - - - - - - - - - - DG

)))-SR)9U359>5 ;5 26 78?@5 59 >147:5 ;5 26 =8QT359>5 @38 25 41;`25 - - - - - - - - - DC

)0-S !17121L?5 6P5> 59:85=58 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - J.

)0-. 0Q8?<>6:?19 ;5 2]Q>8?:385 46:8?>?5225 - - - - - - - - - - - - - - - - - - - - - - - J.

)0-B %@76>5 ;5@ @123:?19@ 7138 26 >19;?:?19 LQ14Q:8?T35 21L?T35 ;5@ ;?64`:85@ - JB

)0-/ %@76>5 ;5@ @123:?19@ 7138 26 >19;?:?19 ;5 A1A?96L5 @38 395 @5325 >13>X5

7138 cF BH @7?85@ ;5 <2 ;]39 ;?64`:85 ;5 S-J 44 - - - - - - - - - - - - - - - J/

)0-D %@76>5 ;5@ @123:?19@ 7138 26 >19;?:?19 ;5 :86P6?2 ;69@ 26 O195 2?9Q6?85 ;3 :185 J/

)0-J %P123:?19 ;3 @?4725 5 ;5 c52;58 5: _56; E25 @?4725 5 18?L?962 5@: 59 71?9:?22QI JJ

)0-R '>XQ46 ;5 78?9>?75 ;5 2]62L18?:X45 LQ9Q:?T35 - - - - - - - - - - - - - - - - - JG

)0-G #1A?96L5 ;]39 :185 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - JC

)0-C '>XQ46 5 72?>6:?= ;5 26 2?4?:6:?19 59 X63:538 - - - - - - - - - - - - - - - - - RH

)0-SH012345 6776859: ;3 >1471@69: 39?T35 - - - - - - - - - - - - - - - - - - - - - RS

)0-SS'>XQ46 ;3 d:185 ?478QL9Qe - - - - - - - - - - - - - - - - - - - - - - - - - - - RS

)0-S.d:185 ?478QL9QW ;Q>137QW 85=184Qe - - - - - - - - - - - - - - - - - - - - - - - R.

)0-SBd:185 ?478QL9Q f ;54?Ng64A5 e - - - - - - - - - - - - - - - - - - - - - - - - - R.

)0-S/K147686?@19 ;5@ 758=18469>5@ ;3 781:1:^75 <962 6P5> 25 >1471@69: ;5

8Q=Q859>5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - RB

)0-SDYX1:1 ;3 >1471@69: 46L9Q:?T35 39?T35 6P5> 59:85=58 - - - - - - - - - - - - R/

Page 12: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$ %$& '()*+$& ,-

(./012345676-839 :;8 -45<:69=;8 ;9>7; ?; 7<8@?>6> :; ?A35>-4-86>-39 ;> ?; =34B

53869> C96? / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / DE

./0 F7-9=-5; :; >7698G3746>;@7 5?6967 / / / / / / / / / / / / / / / / / / / / / / / DH

./I (9:@=>69=;8 G;77->; -9><J7<;8 :698 ?; F2" K!?-0IL / / / / / / / / / / / / / / / DM

./N &=O<46 :; 57-9=-5; :@ =3453869> @9-P@; 8@7 F2" QR2 S J6@=O; ;> R% S

:73->;T / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / DM

./U 2V=?;8 :AOV8><7<8-8 8>6>-P@;8 :; ?A6??-6J; 9693=7-8>6??-9 Fe73.5Cu1Nb3Si13.5B9

KF;7MDL / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / H0

./E 23@7W;8 :A6-469>6>-39 657X8 7;=@-> 53@7 :-Y;78;8 Y6?;@78 :; ?6 =39>76-9>; :;

>76=>-39 σ KZ[M1L / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / H0

./1 F?69 :; ?A;4537>;B5-X=; 53@7 ?6 :<=3@5; :;8 7@W698 / / / / / / / / / / / / / / HI

./D $,;45?; :; :<=3@5; 567 <?;=>73B<738-39 / / / / / / / / / / / / / / / / / / / / HN

./H #; G3@7 :; 7;=@-> / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / HU

./M #; W?3= =O6@\69> W3W-9< / / / / / / / / / / / / / / / / / / / / / / / / / / / / / HE

./0] R39>6J; -98>7@4;9>< :@ G3@7 :; 7;=@-> / / / / / / / / / / / / / / / / / / / / / H1

./00 !??@7; :@ =V=?; :; 7;=@-> / / / / / / / / / / / / / / / / / / / / / / / / / / / / / HD

./0I 2345676-839 :;8 =V=?;8 :AOV8><7<8-8 8>6>-P@;8 53@7 ?;8 :;@, 7;=@->8/ / / / / / HH

./0N !55?-=6>-39 :A@9 =O645 >7698Y;78; 8@7 @9 93V6@ >37-P@; / / / / / / / / / / / HM

./0U %-8538->-G :A655?-=6>-39 :@ =O645 / / / / / / / / / / / / / / / / / / / / / / / / HM

./0E 2676=><7-8>-P@;8 46J9<>-P@;8 :A6??-6J;8 G;77346J9<>-P@;8 K23@MH^23@MU^."M0L M]

./01 &-4@?6>-39 :@ 8V8>X4; :A655?-=6>-39 :@ =O645 >7698Y;78; S 1]]

2 83@8

'?@, I% Q0_U 6@ Y@ :;8 8V4<>7-;8T / / / / / / / / / / / / / / / / / / / / / / / M0

./0D FO3>3 :;8 =6:7;8 9693=7-8>6??-8<8 :698 ?; :-8538->-G :A655?-=6>-39 :@ =O645 / MI

./0H %-8538->-G :; =676=><7-86>-39 :;8 =6:7;8 9693=7-8>6??-8<8 / / / / / / / / / / / / MN

./0M 2V=?; :AOV8><7<8-8 :;8 =6:7;8 7;=@-> 83@8 =O645 >7698Y;78; / / / / / / / / / / MN

./I] FO3>3 :@ 439>6J; :; =676=><7-86>-39 `@,4<>7-P@; S W68 =O645 / / / / / / / MU

./I0 (9`@;9=; :@ =O645 >7698Y;78; 8@7 ?; =V=?; :AOV8><7<8-8 / / / / / / / / / / / / ME

./II .@; :; =3@5; 8=O<46>-P@; :; ?A-9:@=>69=; :698 ?; F2" / / / / / / / / / / / M1

./IN %<C9->-39 :;8 39:;8 -9=-:;9>;8 ;> 7<`<=O-;8 / / / / / / / / / / / / / / / / / / 000

./IU &V8>X4; =34538< :; ?6 83@7=; :; 5;7>@7W6>-398 ;> :@ +&(# / / / / / / / / / 00I

./IE &V8>X4; 7<:@-> :; ?6 83@7=; :; 5;7>@7W6>-398 ;> :@ +&(# / / / / / / / / / / / 00I

Page 13: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 14: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"!#$%!"!&'(

!"#$%& '()* +,-*+, +& .)*"& %/& 012#&3 '& 4& #%*# *4)5*/,& -!44& 6(%/ +&# 7&"#!//)5&#

+& 819 :!4*-# ; 0")<)*66&" /!/ #0!7 &0 !%=6*&" 6& 4!/+& &>0,"*&%"? @)*# 6& 6)=!")0!*"&

ABC6)= -& /(&#0 7)# D) 4)*# 76%0E0 +&# 01,#)"+# <&/)/0 +&# $%)0"& -!*/# +% 4!/+& &0

0!%'!%"# $%&6$%(%/ 7!%" 0()*+&" $%)/+ 0) 4)/*7 4)"-1& 7)# F)% 4!*/# 4!")6&4&/0 GH? I6

&#0 +!/- 0&47# +& "&4&"-*&" 0!%0&# 6&# 7&"#!//&# $%& '()* -E0!J,&# 7&/+)/0 -&# )//,&# &0

$%(!/0 .)*0 +& -&00& 012#& %/& =&66& )<&/0%"&?

8"&4*2"&4&/03 '& 0*&/# K "&4&"-*&" 0!%# 6&# 4&4="&# +& 4!/ '%"J +& 012#&? L!%0 +()=!"+3

4&"-* K C"*- MNOPQC &0 R)+*" I9IQ3 ")77!"0&%"# +& -&00& 012#&3 7!%" 6&%" 6&-0%"& 4*/%S

0*&%#& +% 4)/%#-"*03 6&# "&4)"$%&# +& 6&%"# ")77!"0# &0 6&# $%&#0*!/# 6& '!%" +& 6) #!%0&/)/-&

$%* -!/#0*0%&"!/0 #)/# +!%0& 6) 6*5/& +*"&-0"*-& +& 6) #%*0& +& -&# 0")<)%>? @&"-* K 8)0"*-T

9P MQ3 4&4="& +% '%"J3 7!%" #!/ */0,"U0 7!%" -& 0")<)*6 &0 -&# $%&#0*!/# 7&"0*/&/0&#?

@&"-* &/V/ K N&6)1-2/& @MWMQI 7!%" )<!*" 7",#*+, -& '%"J )<&- 0)6&/0?

M% -!%"# +& -&# 0"!*# )//,&# +& +!-0!")03 '()* &% 6) -1)/-& +(U0"& &/-)+", 7)" +&# 7&"#!//&#

&>-&70*!//&66&# 0)/0 #%" 6& 76)/ #-*&/0*V$%& $%& 1%4)*/? X& "&4&"-*& M.&. CNOP:3 4)

+*"&-0"*-& +& 012#&3 7!%" 4()<!*" #%*<*& 0!%0 )% 6!/5 +& 6) 012#& &0 +!//, 6(!77!"0%/*0, +&

0")<)*66&" #%" %/ #%'&0 7)##*!//)/0? @&"-* K Y&"<, :YMWM 3 -!S&/-)+")/0 +& -&00& 012#&3

7!%" #) <*#*!/ 7")54)0*$%& +% 7"!'&0 &0 7!%" #&# -!/#&*6#? @&"-* K Z)=*&/ [I\9CRICQ3

-!S&/-)+")/0 +& -&00& 012#&3 7!%" #) ",)-0*<*0, &0 #!/ )*+& #%" 6) 4!+,6*#)0*!/? P/ 5")/+

4&"-* K 9!4*/*$%& AMPLMQ93 +& 6) #!-*,0, L:L3 7!%" #&# -!/#&*6# &0 6(*/0,"U0 $%(*6 )

7!"0, K #&# 0")<)%>? C/V/3 4&"-* K 6) #!-*,0, Y*#7)/!S[%*])3 "&7",#&/0,& 7)" R*-!6)# AMS

WC 7%*# Y!%4)4 @OP[[M3 7!%" 4()<!*" 7&"4*# +& 0")<)*66&" #%" -& #%'&0 *//!<)/0 &0

7!%" 6&%"# */0,"U0# #%" 6&# $%&#0*!/# "&6)0*<&# K 6(*/+%#0"*)6*#)0*!/ +& -&00& 0&-1/!6!5*&?

X& 0*&/# K "&4&"-*&" 7)"0*-%6*2"&4&/03 [,=)#0*&/ Z PQ^ &0 :6)%+& NQPR3 #)/# $%* 6&

-1)7*0"& _ +& -& 4)/%#-"*0 /()%")*0 ')4)*# &>*#0,? @&"-* )%##* K 6(&/#&4=6& +% 6)=!")0!*"& ;

6&# ILM3 6&# 7&"4)/&/0#3 6&# #0)5*)*"&#3 6&# 4)#0&"# &0 6&# +!-0!")/0#? 9%")/0 -&# 0"!*# )//,&#3

'()* "&/-!/0", +&# 7&"#!//&# &>-&70*!//&66&# &0 .!"4*+)=6&#? X& "&4&"-*& [J6<*&3 @*"&*66& &0

Q!#*0) 7!%" 6&%" 5&/0*66&##&? @&"-* K `6*#& 7!%" #!/ #!%"*"& &0 7!%" )<!*" )##%", 6) 6!5*#S

0*$%& 7!%" 6&# +,76)-&4&/0#? &# =)"=*&#S5*"6# 7!%" /!0"& <*-0!*"& G P/ 5")/+ 4&"-* K 0!%0

6& #&"<*-& */.!3 :!"*/&3 X%6*&/3 a*/-&/03 Y&"<, &0 81*6*77&3 7!%" 6&%" )*+& K 6) ",#!6%0*!/

+&# 7"!=624&# "&/-!/0",# )<&- +&# 6!5*-*&6# &>!0*$%&# G 8!%" 6&# +*b,"&/0# )#7&-0# +& -&00&

Page 15: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!" #$%$&'!$%$()*

)+,*$- ./0! 1'+0(21 0"$' 345*!$5&* 3$&*6(($* 7$ 76%0!($* *'!$()!895$* "0&!1*: ;$ &$%$&'!$

)65)$* '$* 3$&*6(($* 365& 4$5& 0!7$: <( 30&)!'54!$& %$&'! = >4!"!$& ?<>@@#>A 365& 0"6!&

30&)021 *$* '6((0!**0('$* 7$* %0)1&!05 $) 4$5&* &$'5!)*:

B$* )&6!* 0((1$* 7$ )+,*$ (/05&0!$() 30* 1)1 4$* %C%$* $) *D&$%$() %6!(* E$44$* *0(*

40 3&1*$('$ 7$ %$* '644,25$* $) 0%!* 75 40E6&0)6!&$: F$&'! = ;54!$( 365& *6( 0!7$ *5& 4$*

462!'!$4* $) 365& *6( *65)!$(: F$&'! = F!'G0H4 365& 4$* 3I)!**$&!$* $) 4$* *6!&1$*: F$&'! =

F0)+!$5 365& *0 '5&!6*!)1 *'!$()!895$ 95! %/0 3$&%!* 7$ )&65"$& 7$* *645)!6(*: F$&'! = J!

365& *0 *36()0(1!)1 $) *6( 7K(0%!*%$: F$&'! = L(76 365& *6( 'M)1 E6( "!"0(): F$&'! =

NK4"0!(- F6&20(- F0($4- L()+6(K 365& )65* 4$* %6%$()* *K%30* 30**1* *5& 40 340)$O6&%$:

<(8( 5( 2&0(7 %$&'! = B+&!*)63+$- %6( '6PE5&$05- 365& 4$* 714!&$*- 4$* &0(76*- 4$* *6!&1$*

$) 4$ *65)!$(:

;/0!%$&0!* 05**! &$%$&'!$& 4$* 0%!* 95! %/6() $()$(75 &076)$& 3$(70() )&6!* 0(* *5& %0

)+,*$: ;$ )!$(* = &$%$&'!$& %0 O0%!44$ $) %0 E$44$PO0%!44$ 365& %/0"6!& $('65&021 $) *65)$(5

75&0() )65)$* '$* 0((1$* 7/1)57$*: Q( 2&0(7 %$&'! = %0 2&0(7P%,&$ 365& C)&$ "$(5 0**!*)$&

= %0 *65)$(0('$: <(8(- .$ &$%$&'!$ )65) 30&)!'54!,&$%$() F!'G0H4 365& *6( *65)!$( *0(*

O0!44$:

Page 16: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&'"($! )*!*#+,-

!"#!$%&'!() *+ ,!-./(#0 %- *+ ,!+*(/1 %- *&10-$2(- -./ +! 3-0/$- %- /#!/-. *-. +//-0/(#0. 4

%+0. /#!/-. *-. %(.3(5*(0-. *(1-. +! 210(- 1*-3/$(,!- -/ +! .-0. *+$2- *+ 5'6.(,!- +55*(,!1-

-/ *-. .3(-03-. %- *&(0210(-!$) *-. -7#$/. .#0/ 5#$/1. .!$ *&#5/(8(.+/(#0 %- *+ 5$#%!3/(#0)

*- /$+0.5#$/ -/ *+ 3#09-$.(#0 %- *&10-$2(- 1*-3/$(,!-: ;&+81*(#$+/(#0 %-. $-0%-8-0/. %-.

%(.5#.(/(<. -/ 3-**- %- *+ ,!+*(/1 %- *&10-$2(- 1*-3/$(,!-) 8=8- .( 3- 0- .#0/ 5+. *-. .-!*.

5#(0/. %&+//-0/(#0.) .&+91$-0/ <#$/-8-0/ 3#!5*1-. +!> +.5-3/. .#3(+!>?13#0#8(,!-. 4 +!3!0

%(.5#.(/(< 0- 5-!/ 13'+55-$ +!> 3#0/$+(0/-. -09($#00-8-0/+*-. -/ %#(/ 5#!9#($ .&(0/12$-$

%+0. !0- *#2(,!- 13#0#8(,!- %&!0 8+$3'1 (0%!./$(-* 8#0%(+*: ;-. -7#$/. %- 3#03-5/(#0 .!$

3'+3!0 %-. #$2+0-. %-. .6./@8-. %&10-$2(- %#(9-0/ %#03 8-0-$ A %-. 5$#%!(/. (00#9+0/.)

+B0 %- *(8(/-$ *- 3#C/ %-. %(.5#.(/(<. /#!"#!$. 5*!. 5-$<#$8+0/.:

;&(0%!./$(- +1$#0+!/(,!-) %+0. *- 3+%$- %- *&+9(#0 5*!. 1*-3/$(,!-) 8-/ -0 D!9$- *-

$-85*+3-8-0/ %&+3/(#00-!$. 50-!8+/(,!-. #! '6%$+!*(,!-. 5+$ %-. +3/(#00-!$. 1*-3/$#?

813+0(,!-.: E-*+ 5-$8-/ %- $1%!($- *- 0#8F$- %- $1.-+!> %- %(./$(F!/(#0 5$1.-0/. %+0.

*&+9(#0) %- <+3(*(/-$ *+ 8+(0/-0+03- -/ %&+81*(#$-$ *- $-0%-8-0/: ;- F!/ B0+* -./ %- $1%!($-

*+ 8+..- -/ %&+81*(#$-$ *&-G3+3(/1 10-$21/(,!- 2*#F+*- %&!0 +9(#0 5#!$ $1%!($- .+ 3#0.#8?

8+/(#0 -0 3+$F!$+0/: H+0. 3- 3#0/->/-) *- $1.-+! %- %(./$(F!/(#0 1*-3/$(,!- -./ $-5-0.1

5#!$ *+ 5$#3'+(0- 2101$+/(#0 %&+9(#0: ;- $1.-+! 1*-3/$(,!- -8F+$,!1 /$+%(/(#00-* -./ !0 $1?

.-+! /$(5'+.1 +*/-$0+/(< IIJ K #! LMN K A <$1,!-03- 9+$(+F*- #! A ONN PQ: ;-. +3/(#00-!$.

1*-3/$#813+0(,!-. %-9-0+0/ 5*!. 0#8F$-!>) *&(%1- 5$(03(5+*-) 5#!$ *&19#*!/(#0 %! $1.-+!

1*-3/$(,!- -8F+$,!1) 3#0.(./- A 8!/!+*(.-$ *-. $-%$-..-!$. ,!( .#0/ '+F(/!-**-8-0/ 5*+31.

-0 /=/- %- 3'+,!- +3/(#00-!$: ;&#F"-3/(< -./ %- $1%!($- *- 0#8F$- -/ *+ 8+..- %-. 3#09-$?

/(..-!$.: ;-. /$+9+!> %- 3- 818#($- %- /'@.- .&(0.3$(9-0/ %#03 %+0. *+ *#2(,!- %- $1%!3/(#0

%- *+ 8+..- %-. 3#09-$/(..-!$. /#!/ -0 .&+..!$+0/ %! $-.5-3/ %-. 3$(/@$-. %- 5-$/!$F+/(#0.

ERS TE#85+/(F(*(/1 R*-3/$#S+201/(,!-U: R0 -7-/) *-. 0#$8-. ERS 1/+0/ %- 5*!. -0 5*!.

3#0/$+(20+0/-.) -0 5+$/(3!*(-$ %+0. *-. %#8+(0-. .-0.(F*-. /-* ,!- *&+1$#0+!/(,!-) *-. B*/$-.

ERS .#0/ %#03 %- 5*!. -0 5*!. 0#8F$-!>: H+0. 3-. B*/$-.) *-. 3#85#.+0/. 8+201/(,!-.

#33!5-0/ 5*!. %- JN V %- *+ 5*+3- -/ .!$/#!/ %- *+ 8+..-: ;&#F"-3/(< %- 3-//- /'@.- -./ %-

<+($- 18-$2-$ %-. .#*!/(#0. (00#9+0/-.) -0 %#/+0/ *-. B*/$-. ERS 5+..(<. %&!0 3#85#.+0/

8+201/(,!- !0(,!- 5#!$ *-. 5-$/!$F+/(#0. %- 8#%- 3#0%!(/-. +B0 %- $1%!($- *-!$ 8+..-:

;- 5$-8(-$ 3'+5(/$- %- 3- 818#($- %- /'@.- 5$1.-0/- *- 3#0/->/- %- *&1/!%- -/ *+ 5$#F*1?

8+/(,!- %! 3#85#.+0/ 8+201/(,!- !0(,!-: ;- 3+'(-$ %-. 3'+$2-. ,!( -./ 5$1.-0/1 B>- *-.

Page 17: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&'(#)%" *+"+$,-.

/.$0%$1,"(.2 ,##."&'.2 &. "%#$. (%1/%2,"#3 45+#'&. 6)6-)%*$,/7)8'. 8') .2# 0,)#. 1%"#$.

8'. /-'2).'$2 (%1/%2,"#2 %"# +#+ $+,-)2+2 &,"2 (.##. %/#)8'.3 9,"2 -. &.':);1. (7,/)#$.<

,=" &. (%1/$."&$. -.'$ 0%"(#)%"".1."# .# -.'$ ,#%'# /%'$ "%#$. +#'&.< "%'2 ,>%"2 $+,-)2+

'". +#'&. (%1/,$,#)>. &.2 &)?+$."#.2 #%/%-%*).2 &. (%1/%2,"#23 @%'$ (.-,< "%'2 ,>%"2

&+#.$1)"+ -.2 (%"#$,)"#.2 /7A2)8'.2 .# *+%1+#$)8'.2 2'$ (7,8'. (%1/%2,"# .# &+=") '"

($)#;$. &. /.$0%$1,"(.3 B.##. +#'&. "%'2 , /.$1)2 &. (%"(-'$. 2'$ -.2 0,(#.'$2 0,>%$)2,"#

-.2 /.$0%$1,"(.2 &' (%1/%2,"# '")8'. .# &%"( &. $+&')$. "%#$. +#'&. C &.': #%/%-%*).23

D%$#2 &.2 /$%6-+1,#)8'.2 .:/%2+.2 &,"2 (.2 &.': (7,/)#$.2 .# ,A,"# ()6-+ -.2 #%/%-%*).2

C +#'&).$< "%'2 ,>%"2 &+>.-%//+ '" %'#)- &. 1%&+-)2,#)%" 0$+8'."#).--. &' (%1/%2,"# 1,E

*"+#)8'. '")8'.3 F /,$#)$ &5'". 1%&+-)2,#)%" G2A2#;1.H "%'2 ,>%"2 /' /$."&$. ." (%1/#.

-5.">)$%"".1."# &' (%1/%2,"# 1,*"+#)8'. IJ+2.,' K#,6)-)2,#.'$ &5!1/+&,"(. &. 4)*".

IJK!4L< K%'$(. &. /.$#'$6,#)%"2< B,/,()#+2L3 M". 1%&+-)2,#)%" /-'2 =". &.2 /$%/$)+#+2

1,*"+#)8'.2 &' (%1/%2,"# .2# +*,-.1."# &+#,)--+.3 N" .?.#< C -5,)&. &5'" 1%&;-. *A$,#.'$E

(,/,()#+< "%'2 ,>%"2 /' /$+&)$. -.2 /.$0%$1,"(.2 &' =-#$. (%1/-.# &,"2 2%" .">)$%"".1."#3

O$P(. C -, 1%&+-)2,#)%" *A$,#.'$E(,/,()#+< "%'2 ,>%"2 /' 2+/,$.$ -.2 /,$,1;#$.2 *+%E

1+#$)8'.2 .# -.2 *$,"&.'$2 /7A2)8'.23 B.##. ,//$%(7. "%'2 , /.$1)2 &. 1.##$. ." /-,(.

'" /$%*$,11. &5%/#)1)2,#)%" &' >%-'1. %(('/+ /,$ -. (%1/%2,"# (%"#$,)"# /,$ (.2 /.$E

0%$1,"(.23 @,$ ,)--.'$2< "%#$. 1%&+-)2,#)%" +#,"# 0,()-.1."# )1/-+1."#,6-.< "%'2 ,>%"2 /'

/$."&$. ." (%1/#. -.2 (%"#$,)"#.2 )"&'2#$).--.2 )"&)2/."2,6-.2 C -, 0,6$)(,#)%" &' (%1/%E

2,"#3 B.##. +#'&. "%'2 , /.$1)2 &. $+,-)2.$ '" (%1/%2,"# 1,*"+#)8'. '")8'. /-'2 (%1/,(#

.# /-'2 /.$0%$1,"# 8'. -. (%1/%2,"# .:)2#,"#3

9,"2 -. &.$").$ (7,/)#$.< "%'2 /$+2."#.$%"2 '" $,/)&. +#,# &. -5,$# &.2 (%1/%2,"#2 1,E

*"+#)8'.2 /,22)02 )"#+*$+2 2'$ @BQ3 F' >' &.2 ,>,"#,*.2 &.2 ,--),*.2 ","%($)2#,--)"2< "%'2

'#)-)2%"2 -.2 (%"(-'2)%"2 &.2 (7,/)#$.2 /$+(+&."#2< ,=" &. &)1."2)%"".$ .# &. (%"(.>%)$

'" (%1/%2,"# '")8'. 6,2+ 2'$ -.2 1R1.2 0,(#.'$2 8'. -. /$+(+&."# 1,)2 )"#+*$+ &,"2 '"

@BQ I@$)"#.& Q%,$& B)$(')#L3 B. (%1/2,"# , /%'$ 6'# &. &+1%"#$.$ -, 0,)2,6)-)#+ &. (.##.

)"#+*$,#)%" ." '#)-)2,"# &.2 ,--),*.2 ","%($)2#,--)"23 B. (7,/)#$. /$+2."#. ,-%$2 -.2 >.$$%'2

#.(7"%-%*)8'.2 ,':8'.-2 "%'2 ,>%"2 +#+ (%"0$%"#+2 .# -.2 2%-'#)%"2 8'. "%'2 ,>%"2 /$%/%2+

/%'$ -.2 $+2%'&$.3

B.2 #$,>,': 0,>%$)2."# -5+1.$*."(. &. &)2/%2)#)02 &. =-#$,*. /-'2 (%1/,(# ." #.$1.

&. (%1/%2,"#2 1,*"+#)8'.23 4, /$)2. ." (%1/#. &' (%1/%$#.1."# 0$+8'."#).- /.$1.# &.

&)1."2)%"".$ -.2 (%1/%2,"#2 ,' /-'2 /$;2 &. -.'$ /.$0%$1,"(. $+.--.3 4.2 /.$2/.(#)>.2

%?.$#.2 /,$ (.2 #$,>,': 2%"# &%"( )1/%$#,"#.2 .# /$%/%2."# &. $./."2.$ -, (%"(./#)%" .#

-, 1)2. ." S'>$. &.2 )"&'(#,"(.2 &. =-#$,*. ." '#)-)2,"# -.2 ,--),*.2 ","%($)2#,--)"2 /%'$

-5)"#+*$,#)%" 2'$ @BQ3

Page 18: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&' (

!"#$%#$ $# !&'$(#)*+ ,$ -./#0,$

!""#$%&

!" #$ %&'($)*+*,*)- .,/0)1&2$34-)*56/

! " # $%&'()(*' +

!"!# $%& '%()*(#+),-.& /-.0*,)%& %. 12%/)(-.,3*% 0% '*,&&+./% ! ! ! ! ! ! ! ! ! ! 4

!"!#5, 6-0% /-77*. %) 7-0% 0,81(%.),%2 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4

!"!#5,, 9-),-.& &*( 2%& :2)(%& ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;

!" #$%& '( )*+$,%( $-.*%$/0,1/( ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

!<!+ $=+>,-. ?'2*& 12%/)(,3*%@ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! A

!<!# $% '(-B%) CC5D-E%( ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! F

!<!/ $%& .-(7%& GH6 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "I

!2 3(.& /% 4,'0.( 567 $8(9 /% &(/' 9*+:*&$%0 +$;%-0,1/( ! ! ! ! !!

!J!+ D(-#217+),3*% 0* /-7'-&+.) 7+K.1),3*% *.,3*% ! ! ! ! ! ! ! ! ! ! ! ! ! ! ""

!J!# H)+) 0% 2=+() ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "L

!J!#5, M-*( 0=N-(,O-. 0%& #(%>%)& ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "L

!J!#5,, $% /-7'-&+.) P,&'+.-5C*,O+ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "4

!J!/ Q17+(/N% 0% 2=1)*0% ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ";

!"#$!

! "#$%&'(! &)'(*+,&' -$ )*'&*) +! *.%$'&/&-&'0 1-!"'(*2$3)0'&4,! 5 1267 8! "$9

+!9 %!(',(/$'&*)9 +! .*+! "*)+,&': !) 0-!"'(*)&4,! +! %,&99$)"!: !9' %(&)"&%$-!.!)'

$/*(+07 ;<) +! (0+,&(! "!9 %!(',(/$'&*)9: -!9 +&=0(!)'9 '>%!9 +! <-'($3! 4,& %!,?!)'

@'(! ,'&-&909 9!(*)' %(09!)'097

A$)9 ,)! 9!"*)+! %$('&!: )*,9 )*,9 &)'0(!99!(*)9 B -C$?&*) D%-,9 0-!"'(&4,!E7 8!9 &)F

'0(@'9 +! "!''! 0?*-,'&*) +$)9 -! +*.$&)! $0(*)$,'&4,! 9!(*)' !G%-&4,09 !' %!(.!''(*)'

+! "*)'!G',$-&9!( -! %(*H!' IJJFK*L!( M *)'(*-: B -C&)'0(&!,( +,4,!- "!9 '($?$,G 9*)'

+0?!-*%%097 1)<): +$)9 "! "$+(! !G&3!$)' 4,C!9' -C$0(*)$,'&4,!: -C&)'0(@' +!9 )*(.!9

12 !' +! -!,( +0<)&'&*) 9!(*)' +&9",'097

A$)9 -$ '(*&9&N.! %$('&!: -! "$#&!( +!9 "#$(3!9 +, "*.%*9$)' .$3)0'&4,! +, <-'(! 12

9!($ %(09!)'07 8$ %(*/-0.$'&4,! +, "*.%*9$)' .$3)0'&4,! ,)&4,! 9!($ !G%*90! !' %-,F

9&!,(9 '*%*-*3&!9 +! "*.%*9$)'9: &99,!9 +! /(!?!'9 !' +! %,/-&"$'&*)9: 9!(*)' %(09!)'0!9

!' +0'$&--0!97

Page 19: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$%&'%& &% #()&*%+,- .& /01%2.&

!" #$ %&'($)*+*,*)- .,/0)1&2$34-)*56/

!"!# $%&'()(*'

! "#$%!&'(')'&* *)+"&,#$!-.*&'/0+1 %)02 2#03+.& .#$$*+ %!, 2#. !",#.4$+ 5671 +2&

)8!%&'&09+ 980. 9'2%#2'&':1 980. !%%!,+') #0 980. 242&;$+ < :#."&'#..+, 9!.2 2#. +.3',#..+=

$+.& *)+"&,#$!-.*&'/0+ 9+ :!>#. 2!&'2:!'2!.&+ +& 2!.2 %,#90',+ )0'=$?$+ 9+2 %+,&0,(!&'#.2

*)+"&,#$!-.*&'/0+2 '.&#)*,!()+2 %#0, &#0& "+ /0' 2+ &,#03+ 9!.2 "+& +.3',#..+$+.&@ +

"#."+%& +2& !%%!,0 9!.2 )+2 !..*+2 ABCD )#,2 90 9*3+)#%%+$+.& 9+2 ,!9'#"#$$0.'"!&'#.2@

! $0)&'%)'"!&'#. 9+2 !%%!,+')2 *)+"&,'/0+2 %,#3#/0!'& 9+2 %+,&0,(!&'#.2 9+ ,*"+%&'#. 9+

%)02 +. %)02 -?.!.&+2 EF!0DG15H!DD"15H!DD(15#"BB17!,DIJ@ K0L#0,98H0'1 )+2 9'2%#2'&':2

*)+"&,'/0+2 +& *)+"&,#.'/0+2 2#.& 9+ %)02 +. %)02 M

N .#$(,+0O +& 3!,'*2 M 90 %!"+$!P+, +. $*9+"'.+ !0O "',"0'&2 '$%,'$*2 +. *)+"&,#.'/0+

+. %!22!.& %!, )8'.2&,0$+.&!&'#. 9+2 %')+2 < "#$(02&'()+2 +. *)+"&,#"H'$'+@

N "#$%)+O+2 M %#0, .+ "'&+, /0+ )8*3#)0&'#. 9+2 %+,:#,$!."+2 9+2 "#$%#2!.&2 9+ "#$=

$0&!&'#.1 )8*$+,-+."+ 9+ )8QRST UQ.20)!&+9 R!&+ S'%#)!, T,!.2'2&#,V +& )! 9'W02'#.

90 7XYZ6T U7+&!) XO'9+ Y')'"#. Z'+)9 6W+"& T,!.2'2&#,V@

N 2&,!&*-'/0+2 M )8!3'#. #0 )+ 3*H'"0)+ [%)02 *)+"&,'/0+\@

5+&&+ $0)&'%)'"!&'#. "#.&,'(0+ < !0-$+.&+, )+2 .'3+!0O 9+ %#))0&'#. *)+"&,#$!-.*&'/0+

+& +.-+.9,+ 9+2 %,#();$+2 9+ ]!(')'&* +& 9+ 2^,+&* 9+ :#."&'#..+$+.& 9+2 9'2%#2'&':2@ 5+2

9+,.';,+2 !..*+21 .#02 !3#.2 30 !%%!,!_&,+ 0. !O+ $!L+0, 9+ ,+"H+,"H+ 20, "+&&+ &H*$!=

&'/0+ 9!.2 )+2 9#$!'.+2 9+2 &,!.2%#,&2 E`#(AA1S+)AA1 !(ADJ@

K %!,&', 9+ )! 9*].'&'#. 9+ )! 5671 .#02 %#03#.2 9*&+,$'.+, &,#'2 *)*$+.&2 '$%#,=

&!.&2 M

N ! 2#0,"+ 9+ %+,&0,(!&'#.2 /0' 2+ "!,!"&*,'2+ %!, 2! %0'22!."+1 2! 90,*+1 2#. 2%+"&,+

9+ :,*/0+."+ +& )+2 "H!$%2 /08+))+ -*.;,+@ 6))+ %+0& ?&,+ E5#2DDJ M

A@ a!&0,+))+ U)! :#09,+1 )+ (,0'& -!)!"&'/0+1 )8+W+& 9+2 ,!4#.2 '#.'2!.&21 )+2 '$%0)=

2'#.2 *)+"&,#$!-.*&'/0+21 +&"@V

C@ K,&']"'+))+ '.&+.&'#..+))+ U#.9+2 b'Z'1 2'-.!) ,!9!,1 +&"@V

I@ K,&']"'+))+ .#.='.&+.&'#..+))+ U,!4#..+$+.& 9+2 .*#.21 "#0,!.&2 9+ :0'&+ 9+2

!%%!,+')2 *)+"&,#$*.!-+,21 +&"@V

N + 242&;$+ %+,&0,(*1 !0&,+$+.& !%%+)* [)! 3'"&'$+\@

N +2 "#0%)!-+2 /0' "#,,+2%#.9+.& < 0. &,!.2:+,& 98*.+,-'+ +.&,+ )! 2#0,"+ +& )! 3'"&'$+

UZ'-@ Q@AV@ Q)2 %+03+.& ?&,+ ")!22*2 +. 9+0O "!&*-#,'+2 M

A@ 5#0%)!-+2 %!, ,!4#..+$+.& M 2' )! 2#0,"+ +& )! 3'"&'$+ 2#.& *)#'-.*+2 +& 2!.2

)'!'2#. -!)3!.'/0+1 )! %+,&0,(!&'#. +2& %,#%!-*+ %!, 0.+ #.9+ *)+"&,#$!-.*&'/0+

"#$%#2*+ 980. "H!$% $!-.*&'/0+ H1 -*.*,* %!, 0. "#0,!.& *)+"&,'/0+ 3!,'!()+1

+& 980. "H!$% *)+"&,'/0+ E1 -*.*,* %!, )+2 9'W*,+."+2 9+ %#&+.&'+)2 3!,'!()+2@

C@ 5#0%)!-+2 %!, "#.90"&'#. M 2' )! 2#0,"+ +& )! 3'"&'$+ 2#.& 3#'2'.+2 !3+" #0

2!.2 )'!'2#. -!)3!.'/0+1 )+ "#0%)!-+ +2& 9'& %,#"H+ +& ') %+0& ?&,+ 9+ .!&0,+

"!%!"'&'3+1 '.90"&'3+ #0 ,*2'2&'3+@ +2 %H*.#$;.+2 %+,&0,(!&+0,2 2#.& 9!.2 "+

"!2 )+2 3!,'!&'#.2 ,!%'9+2 9+ "#0,!.& #0 9+ &+.2'#. U9'c9&1 93c9&V@ 5+ &4%+ 9+

%+,&0,(!&'#. +2& !%%+)* %+,&0,(!&'#.2 "#.90'&+2 +& +))+2 2+ %,#%!-+.& )+ )#.- 9+2

Page 20: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %&'($)*+*,*)- .,/0)1&2$34-)*56/

!"#$%& '% ()*&&+,!% %- '% -.+,&/*&&*0, '% &*1,+)2 0) '+,& $%& !0,')!-%).& '%

$*+*&0,& +)2 .3&%+)24 &0).!%& '53,%.1*% 0) !6+.1%& 789:;<= >+ 8?@ !0,')*-% +

'0,,3 $*%) A '% ,0/#.%)&%& 3-)'%& 7>+#B;490#BB4@)&;C4D%-;E< %, 3$%!-.0,*F)%

'% ()*&&+,!%=

!"#$% G=B H 80)($+1% (+. .+I0,,%/%,- %- (+. !0,')!-*0,

>%& (%.-).#+-*0,& &0,- 3/*&%& '+,& ),% 1+//% '% J.3F)%,!%& */(0.-+,-% %- $%& 3-)'%&

&% '*K*&%,- %, '%)2 !+-310.*%&4 8?@ !0,')*-% %- 8?@ .+I0,,3%= >% !6%/*, '% (.0(+1+-*0,

(%)- L-.% /+-3.*%$ 0) ,0, MN*1= G=BO= >% '0/+*,% J.3F)%,-*%$ !0)K%.- (+. $+ 8?@ !0,')*-%

&53-%,' '% F)%$F)%& PQR A S; @QR= T)U'%$A4 $% (63,0/V,% '% (.0(+1+-*0, '+,& $5+*. %&-

,0, ,31$*1%+#$%=

!"!# $%& '%()*(#+),-.& /-.0*,)%& %. 12%/)(-.,3*% 0% '*,&&+./%

!"!#$% &'() *'++,- ). +'() (%/01)-.%)2

W+,& $% !+'.% '% !%--% -6V&%4 ,0)& ,0)& $*/*-%.0,& A $53-)'% '% $+ 8?@ !0,')*-% %,

3$%!-.0,*F)% '% ()*&&+,!%= >53$%!-.0,*F)% '% ()*&&+,!%4 +)&&* +((%$3% -,/0)1&4*56/ 7/ 0&'8

'6)$)*&44 + /0*,& '% ; +,&= T) !0).& '% !%& +,,3%&4 $+ -+*$$%4 $% (0*'& %- $% !0X- '%&

!0,K%.-*&&%).& ,50,- J+*- F)% '*/*,)%.4 %, 1.+,'% (+.-*% 1."!% +)2 (.01.V& J+*-& '+,& $%

'0/+*,% '%& &%/*U!0,')!-%).& M@YZN?[4 G\][O4 +)1/%,-+,- +*,&* $+ J.3F)%,!% '% '3U

!0)(+1% '%& !0,K%.-*&&%).& &-+-*F)%&= 8%--% (.01.%&&*0, + +((0.-3 '% 1.+,'%& +/3$*0.+-*0,&

'+,& $% !0,-.^$% '% $+ -%,&*0,4 ') !0).+,- %- ') !0)($% '%& +!-*0,,%).& 3$%!-.*F)%& 7TW; <=

>%& (%.-%& %- $% #.)*- +!0)&-*F)% 0,- 3-3 +)&&* !0,&*'3.+#$%/%,- .3')*-&= _3+,/0*,&4 !%$+

+ %,1%,'.3 ), !%.-+*, ,0/#.% '% (.0#$V/%& '% 8?@ 7TW; < %, .+*&0, '% J0.-%& K+.*+-*0,&

'% -%,&*0, %- '% !0).+,- M'K`'-4 '*`'-O 13,3.3%& (+. $%& *,-%..)(-%).&= W% ($)&4 !%& -%,&*0,&

%- !0).+,-& &0,- +!6%/*,3& a)&F)5A $5+!-*0,,%). (+. '%& !"#$%& '% ()*&&+,!% F)* (+.-*!*(%,-

+)2 (%.-).#+-*0,& .+I0,,3%& K*+ $%& #0)!$%& '% /+&&% %- +)2 (%.-).#+-*0,& !0,')*-%& +)

-.+K%.& '%& $*+*&0,& !+(+!*-*K%& +K%! $+ /+&&% 7>+#B;4b*,;:4YNT;c<=

>%& (%.-).#+-*0,& !0,')*-%& (%)K%,- L-.% &3(+.3%& %, '%)2 !+-310.*%&=

>%& (%.-).#+-*0,& '% /0'% '*d3.%,-*%$ M@WO e >% !0).+,- @W &% (.0(+1% &). $5), '%&

!0,')!-%).&4 -.+K%.&% $+ K*!-*/% %, $+ (0$$)+,-4 %- .%K*%,- &). $5+)-.% !0,')!-%). %, &%,&

*,K%.&%= 8%& (%.-).#+-*0,& !0..%&(0,'%,- A '%& !0).+,-& %, 6+)-%& J.3F)%,!%& '% J+*#$%&

+/($*-)'%& +)2F)%$& &5+a0)-%,- ),% !0/(0&+,-% #+&&% J.3F)%,!% '% J0.-% +/($*-)'%=

>%& (%.-).#+-*0,& '% /0'% !0//), M@8O e >+ -%,&*0, '% /0'% !0//), M@8O %&- $+

/0I%,,% '%& -%,&*0,& %,-.% $%& !0,')!-%).& '% (6+&%& %- ), !0,')!-%). '% .3J3.%,!% e $+

Page 21: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$%&'%& &% #()&*%+,- .& /01%2.&

!"#$% !"# $ %&'()*+,&-. /01 (-)'+.,1 /0 2-/0 /&34'0.,&0* 0.,'0 /0)5 161,7201

,0''0" 801 (-)'+.,1 /+.1 (0 2-/0 10 9'-9+:0., /+.1 ,-)1 *01 (-./)(,0)'1 /0 9;+10 0, 10

'0<-)(*0., 9+' *0 (&'()&, /0 ,0''0 =&+ *01 (+9+(&,41 9+'+1&,01" %01 &294/+.(01 (+9+(&,&=01 9+>

'+1&,01 1-., /&1,'&<)401 /+.1 *0 161,720" 801 (;02&.1 .0 1-., /-.( 9+1 (-..)1 9'4(&1420.,"

%01 90',)'<+,&-.1 (-''019-./0., ? /01 (-)'+.,1 /0 @+&<*01 +29*&,)/01 0. ;+),01 @'4A)0.(01"

B+' +&**0)'1C 0**01 -., ).0 (-.,'&<),&-. 2+D0)'0 +) '+6-..020., 4*0(,'-2+:.4,&A)0 /+.1

*01 161,7201 EB+)FGH"

8+ 9'4/-2&.+.(0 /I). ,690 /0 90',)'<+,&-. JK%LKMN 1)' *I+),'0 0, *01 :+2201 /0

@'4A)0.(01 1)' *01A)0**01 &*1 1I4,+<*&110.,C /490./0., :'+./020., /0 *I+99*&(+,&-."

!"#$% !"O $ %&'()*+,&-. /01 (-)'+.,1 /0 2-/0 (-22). 0.,'0 /0)5 161,7201

!"!#$%% &'(%')* *+, -.* /-(,.*

PQ. /0 *&2&,0' *01 90',)'<+,&-.1 (-./)&,01C *+ 1-*),&-. *+ 9*)1 1-)=0., ),&*&140 01, *0

Q*,'+:0" !* 05&1,0 9*)1&0)'1 ,6901 /0 Q*,'01 R

$ 801 Q*,'01 9+11&@1 1-., *+ ,0(;.&A)0 *+ 9*)1 ),&*&140" !*1 10 (+'+(,4'&10., 9+' *I)1+:0

05(*)1&@ /0 (-29-1+.,1 9+11&@1 J'41&1,+.(01C (-./0.1+,0)'1C <-<&.01 (-)9*401 -) .-.N"

8+ ,-9-*-:&0 S(*+11&A)0T 01, 9'410.,40 1)' *+ Q:)'0 !"U" %0,,0 1-*),&-. 90'20, *0 Q*>

,'+:0 /01 /0)5 2-/01 /0 90',)'<+,&-.1" V**0 01, (-29-140 /I).0 &./)(,+.(0 /0 2-/0

/&34'0.,&0*C /I).0 &./)(,+.(0 /0 2-/0 (-22). 0, /01 (+9+(&,41 /0 Q*,'+:01 R %6

9-)' *0 2-/0 (-22). 0, %5 9-)' *0 2-/0 /&34'0.,&0*" W0*-. *01 &294/+.(01 '0190(>

,&=01 /01 1-)'(01 /0 90',)'<+,&-.1 0, /) '410+)C *+ (-2<&.+&1-. /0 (;02&.1 @-',020.,

&294/+.,1 J&./)(,+.(01N -) @+&<*020., &294/+.,1 J(+9+(&,4N 90'20, /I+&:)&**0' *01

(-)'+.,1 90',)'<+,0)'1 10*-. /01 (;02&.1 .0 90',)'<+., 9+1 *0 '410+)" %0 ,690 /0

1,')(,)'0 01, :4.4'+*020., (-X,0)5 0, =-*)2&.0)5" M0 9*)1C *0 Q*,'0 =-&, 1+ (+9+(&,4

Page 22: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%& '( )*+$,%( $-.*%$/0,1/(

!"#"$%&' &$ ()%*& +',-%&$.& .)' /&0 .1#210)$*0 2)00"+0 2',0&$*&$* !&0 ,/,#&$*0 2)3

')0"*&04

L_MD L_MC

C_x

C_yC_y

!"#$% 546 7 8"/*'&0 9:; 2)00"+0 <./)00"-%&0=

7 >&0 ?/*'&0 ).*"+0 0& .)').*,'"0&$* 2)' /@%0)A& !& .1#210)$*0 ).*"+0 B2)' &C&#2/& ;DE3

8:FG4 5/0 1$* /@"$*,'H* 2)' ')221'* )%C .1#210)$*0 2)00"+0 !@H*'& 2/%0 +)."/&#&$*

#"$")*%'"0)I/&0 &* 21*&$*"&//&#&$* 2/%0 2&'+1'#)$*04 9&2&$!)$*J .1$*')"'&#&$* )%C

?/*'&0 2)00"+0J "/0 $,.&00"*&$* %$& )/"#&$*)*"1$ ,/&.*'"-%&4 >&0 .1#210)$*0 ).*"+0 2&%K&$*

.1%K'"' !& /)'A&0 I)$!&0 !& +',-%&$.&0 #)"0 "$*'1!%"0&$* !% I'%"* 2)')0"*&J .& -%"J

)%3!&/L !@%$ .&'*)"$ 0&%"/J 2&%* H*'& AH$)$*4 F1%*&+1"0 .& I'%"* 2&%* 01%K&$* H*'&

#)M*'"0, N;OPQJR>SOTTU4

7 >&0 ?/*'&0 (VI'"!&0 -%" .1#I"$&$* %$& 2)'*"& ).*"K& &* %$& 2)'*"& 2)00"K&4 5/0 '&2',3

0&$*&$* %$ .1#2'1#"0 &$*'& /&0 !&%C )%*'&0 K&'0"1$0 .)' "/0 2&'#&**&$* !& ',!%"'& /)

*)"//& !& /@"$!%.*)$.& 0)$0 /) 0%22'"#&' NWXX

+PYJZ/"T[U4

E" $1%0 +)"01$0 %$& 0V$*(\0& !&0 !"],'&$*0 *V2&0 !& ?/*')A&J 1$ 2&%* $1*&' -%& /& ?/*')A&

2)00"+ &0* !,!", L %$ .1$K&'*"00&%' 02,."?-%& &* 2&%* "$*'1!%"'& !&0 &]&*0 "$!,0"')I/&0

.1##& /&0 ',01$)$.&0 )K&. /@"#2,!)$.& !% ',0&)%4 >& ?/*')A& ).*"+ -%)$! L /%"J .1$0"0*&

L .1$$&.*&' 0%' /& ',0&)% %$ .1$K&'*"00&%' 0%22/,#&$*)"'&J -%" K) A,$,'&' !&0 .1%')$*0

()'#1$"-%&0 21%' .1#2&$0&' .&%C -%" 01$* ,#"0 2)' %$& .()'A& 21//%)$*& -%&/.1$-%&4 9&

*V2& !& 0*'%.*%'& K) "$*'1!%"'& !&0 2&'*%'I)*"1$0 0%22/,#&$*)"'&0 B.1$!%"*&0 &* ')V1$$,&0G

!^&0 )%C .1##%*)*"1$0 ')2"!&04 _& 2/%0J /) .1##)$!& $%#,'"-%& 2&%* &//& #H#& H*'& %$&

01%'.& !& 2&'*%'I)*"1$0 &* !& +',-%&$.& ,/&K,& N91.YYU4 9@&0* 21%' ',!%"'& .&0 &]&*0 -%@1$*

,*, !,K&/122,0 /&0 ?/*'&0 (VI'"!&04

!" #$%& '( )*+$,%( $-.*%$/0,1/(

!"!# $%#&'() *+,-. /,0123'4-05

_&2%"0 -%&/-%&0 )$$,&0J /&0 "$A,$"&%'0 !@Z"'I%0 !,K&/122& /& 2'1`&* !& /@)K"1$ *1%* ,/&.3

*'"-%&4 5/0 1$* "#)A"$, %$ .1$.&2* )22&/, <R1a&'3IV3a"'&=J !)$0 /&-%&/ /@,$&'A"& ,/&.*'"-%&

0& !,2/).& 0%' /&0 0%'+).&0 !& K1/4 >&0 "$*,'H*0 !& .&0 0V0*\#&0 2/%0 ,/&.*'"-%&0 01$* %$&

Page 23: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$%&'%& &% #()&*%+,- .& /01%2.&

!"#$% !"# $ %&'()* &+(,-./0*( 1 23.4 45*6 )7/36

8)/6-(6)6,( '/89+/:&( (- 83/6' ,3;-(*'(" <6 (=(-> +(' '?'-@8(' A?4.)*+/0*(' )7(, +(*.'

+/0*/4(' /6B)88)2+(' C36,-/366(6- 1 A)*-( -(89&.)-*.( (- 9.(''/36" D( 9+*'> /+' 6&,('E

'/-(6- 4(' 4&4)+(' 4( -*?)*-(./(> 4( 9389(' (- 4( 7)66('" F( 93/4' )/6'/ &,3638/'& '*. +)

G9+382(./(H 93*..)/- '(.7/. 1 )*I8(6-(. +( 6382.( 4( 9)'')I(.' 9). 73+ (- +( 73+*8( 4(

,).2*.)6- (82).0*& JK7/LMN" F5)7/36 9+*' &+(,-./0*( ('- )*''/ '?636?8( 4( .32*'-(''( (-

45&,3638/( 4( 8)/6-(6)6,( )7(, +(' )7)6,&(' 4( +5&+(,-.36/0*( )*O3*.45A*/" F5)7/36 -3*-

&+(,-./0*( 65('- 9)' (6,3.( 93*. 4(8)/6 8)/' 4*.)6- +(' 4(.6/@.(' 4&,(66/('> +5&6(.I/( &+(,E

-./0*( ) 3,,*9& *6 .P+( ,.3/'')6- )* '(/6 4(' .&'()*Q 4( 23.4 )&.36)*-/0*('" R36 *-/+/')-/36

&-)/- )*-.(C3/' +/8/-&( 1 +) 6)7/I)-/36 (- 1 +5/6'-.*8(6-)-/36 4( 23.4" S*/'> (++( '5('- 9.3I.('E

'/7(8(6- 4&7(+399&( 93*. )8&+/3.(. +( ,36C3.- (- +( 4/7(.-/''(8(6- 4(' 9)'')I(.' T&,+)/.)I(>

,*/'/6(> &0*/9(8(6-' 7/4&3U" D( 63*7(++(' )99+/,)-/36' '36- (6'*/-( )99).*(' 93*. 39-/8/E

'(. +( C36,-/366(8(6- 4( +5)7/36> ,388( 9). (Q(89+( +) I('-/36 &+(,-./0*( 4(' ,388)64('

4( 73+ '*. +5K/.2*' KVWL 4)6' +(' )66&(' MX L TY+?E2?EZ/.(U"

F( 4&7(+399(8(6- 4( +5K/.2*' KV L ,36'-/-*( *6( &-)9( '*99+&8(6-)/.( 45/6637)-/36

)* 6/7()* 4(' -(,A63+3I/(' &+(,-./0*(' [

$ +( .&'()* &+(,-./0*( )+-(.6)-/C ('- 1 C.&0*(6,( 7)./)2+( TV\LE LL]^U>

$ +( '?'-@8( 4( '(,3*.' ('- (6-/@.(8(6- &+(,-./0*(>

$ 4(' ),-/366(*.' 1 9*/'')6,( &+(,-./0*( 36- &-& /6-.34*/-' (6 .(4364)6,( 93*. +('

,388)64(' 4( 73+"

S3*. +(' 9.3,A)/6(' I&6&.)-/36' 45)7/36' T_3(/6I ` `U> 45)*-.(' C36,-/36' '36- '*',(9-/2+('

45a-.( .&)+/'&(' &+(,-./0*(8(6-> ,388( 9). (Q(89+( +( C.(/6)I( 4(' .3*('> +( ,364/-/366(E

8(6- 45)/. 3* +( 4&8)..)I( 4(' 83-(*.'" b(--( &73+*-/36 4(' ).,A/-(,-*.(' &6(.I&-/0*(' ('-

'3*7(6- &730*&( 1 -.)7(.' +5(Q9.(''/36 G)7/36 9+*' &+(,-./0*(H Jc(/LV>d36XX>F)6L\N"

!"!# $% &'()%* ++,-(.%'

<6 .)''(82+)6- 4(' 9).-(6)/.(' (*.39&(6' 8)O(*.' 4( +5/64*'-./( )&.36)*-/0*(> 4(' 9.3E

O(-' 4( .(,A(.,A( .&,(6-'> -(+ 0*( SeK TS3Z(. e9-/8/^(4 K/.,.)C-U> fe<g Tf3.( e9(6

<+(,-./,)+ g(,A63+3I/('U (- !RR T!6637)-/7( R3+*-/36' C3. R?'-(8'U 36- 93*. )82/-/36 4(

Page 24: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 25: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'%& &% #()&*%+,- .& /01%2.&

" #$% &'()*'+),*$% #-.#-/0 $+ /1213-4 )5+ 6,% $5 7'*'&&8&$ &$9*% :)67;+$5:$% <$

:'*':+;*,%'+,)5= <$ 6'>+*,%$ <$% 6'+;*,'9? <,;&$:+*,@9$% $+ <$ +)9+$% &$% ;+'7$% <$

&' 6,%$ $5 A9B*$ <C95$ :;*'6,@9$ 69&+,:)9:D$ 7)9* &' *;'&,%'+,)5 <C95 :)5<$5%'E

+$9* F G)*+$ <$5%,+; <C;5$*H,$ %+):I;$J #$ 7*):;<; <$ <;7K+ <$ :;*'6,@9$ ;+9<,;= &'

%;*,H*'7D,$ L:)9:D$ 6,5:$M= $%+ &' B),$ <;B$&)77;$ '9 #-.#-/0 @9, *$:D$*:D$ <$%

:)**;&'+,)5% %+*9:+9*$N7*)7*,;+;% ;&$:+*,@9$% %9* &$% <$9? +O7$% <$ :;*'6,@9$J #$ 7*)E

:;<; <$ <;7K+ <$ :;*'6,@9$ ;+9<,; P &$ :)9&'H$ $5 ('5<$ L'B$: 6'>+*,%$ <$% ;+'+% <$

%9*G':$ $+ H*'5<$% <,6$5%,)5%M= %$*' &' B),$ <;B$&)77;$ '9 /1213-4 @9, %O5+D;+,%$

$+ 7*)7)%$ <$% G)*69&'+,)5% 7)9* &$% <$9? +O7$% <$ :;*'6,@9$J 1&% %)5+ '::)67'H5;%

<$ &C$?7$*+,%$ <$ &C,5<9%+*,$& 0Q2RS-2-T= 7)9* &$ 7'%%'H$ F &C;+'+ :)67)%'5+J

" #$% &'()*'+),*$% UV0&'( $+ -3.020 %)9+$59% 7'* &' :)67'H5,$ 4/4 L4)*$% /)6E

7)%'5+ 4$:D5)&)H,$%M %$ %)5+ ,5+;*$%%;% F &C;+9<$= &' 6)<;&,%'+,)5 $+ F &' *;'&,%'+,)5

<$% ,5<9:+'5:$% <$ W&+*'H$ 7)9* ;+$5<*$ &$9* 7&'H$ <$ G*;@9$5:$ <$ G)5:+,)55$6$5+

+)9+ $5 6,5,6,%'5+ &C$5:)6(*$6$5+J X,%7'5)EY9,Z'= 7'*+$5',*$ <9 7*)[$+= ' 7)9* )(E

[$:+,G &C,5<9%+*,'&,%'+,)5 <C95 W&+*$ /03 7'%%,G F :)67)%'5+ 6'H5;+,@9$ 95,@9$ 7)9*

95$ '77&,:'+,)5 V F \ I]J

!"#$% 1J^ " S,&+*$ /03 P 3)<$ :)6695 $+ 6)<$ <,_;*$5+,$& `a]]

+!bc

/$% +*'B'9? <$ +D8%$ %$ G):'&,%$5+ %9* &' *;<9:+,)5 <$ B)&96$ <$% :)67)%'5+% 6'H5;E

+,@9$% <$% W&+*$% /03= :C$%+ F <,*$ &$% ,5<9:+'5:$% <$ W&+*'H$ <$ 6)<$ :)6695 $+ <$ 6)<$

<,_;*$5+,$&J 05 $_$+= <'5% 95 W&+*$ /03= &$% :)67)%'5+% 6'H5;+,@9$% )::97$5+ F $9? %$9&%

7&9% <$ \!d <9 B)&96$ LS,HJ 1J^MJ /$% :)67)%'5+% %)5+ <)5: F ;+9<,$* 7*,)*,+',*$6$5+J

!"!# $%& '()*%& +,-

#C;&$:+*)5,@9$ <$ 79,%%'5:$ <$B$5'5+ <$ 7&9% $5 7&9% 7*;%$5+$ F ()*< <$% 'B,)5%= <$%

7*)(&86$% <$ 7$*+9*('+,)5% /03 '77'*',%%$5+J -W5 <$ &,6,+$* :$% 7$*+9*('+,)5% $+ &$% ,5E

+$*':+,)5% $5+*$ &$% '77'*$,&&'H$%= <$% 5)*6$% )5+ ;+; <;W5,$%J #$% 5)*6$% /03 *$H*)97$5+=

<C95$ 7'*+= &' <;W5,+,)5 <$% &,6,+$% 6'?,6'&$% <$ 7$*+9*('+,)5% *'O)55;$% $+ :)5<9,+$%=

<C'9+*$ 7'*+ &' <;W5,+,)5 <$% 5,B$'9? <C,6695,+; $5 :)5<9,+ )9 *'O)55; <$% ;@9,7$6$5+% $+=

Page 26: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%& '( )*+%$ ,-. /0$1 '( &$'* 12342&/(+ 3/5(6+78'$

!"#"$ %& '!()*+,-+." '!( /0-1.'!( !- '!( /.2!"( "0)!((&+*!( 3 %& 40*+#)&-+." '!( "+4!&56

'7+//5"+-0 !- '70/+((+." ,!*/!--&"- '! *!,*.'5+*! '!( /!(5*!( #&8%!( 9:;<=$ :1&==&>?

@%5(+!5*( -2,!( '! ".*/!( :AB !6+(-!"-? C)+$ ".5( "! 4!**."( D5! %& ".*/! E0"0*+D5!$

FGH I=J '!(-+"0! 3 %7&0*."&5-+D5!? F&"( )!--! ".*/! (."- *05"+!( -.5-!( %!( (,0)+#)&-+."(

(5* %!( ,10"./K"!( +"-!*4!"&"- !" &0*."&5-+D5! L 4+8*&-+."($ 4&*+&-+."( '! -!/,0*&-5*!$ &%H

-+-5'!$ 15/+'+-0$ E+4*&E!$ +"M&//&8+%+-0$ !-)? D5! '.+4!"- (5,,.*-!* -.5( %!( 0D5+,!/!"-(

!/8&*D50( (5* 5" &4+."? A%%! ,*0)+(! %!( E&8&*+-( 3 -!"+* (5* %!( ,!*-5*8&-+."( ,.54&"-

(5*4!"+* (5* %!( *0(!&56 !/8&*D50( N,+)( '! ).5*&"-(O-!"(+."$ +//5"+-0 3 %& P.5'*!Q &+"(+

D575"! (,0)+#)&-+." (5* %!( 0/+((+."(O+//5"+-0( '!( &,,&*!+%( 4+(H3H4+( '!( ,!*-5*8&-+."(

)."'5+-!(? A" -!*/!( '! ,!*-5*8&-+."( :AB )."'5+-!($ %& ".*/! '.""! 5" E&8&*+- '7&--0H

"5&-+." !" -!"(+." &56 8.*"!( '5 ;RCS N;0(!&5 R-&8+%+(&-!5* '7C/,0'&")! '! S+E"!Q NJ+E

C?TQ? S! P.")-+.""!/!"- '5 ;RCS (!*& '0-&+%%0 '&"( %! )1&,+-*! (5+4&"-?

!"#$% C?T U V+4!&5 /&6+/&% '! ,!*-5*8&-+."( )."'5+-!( &'/+((+8%!( NV.*/! FGH I=JQ

S7&--0"5&-+." !(- '0#"+! ).//! (5+- NAD?C? Q

Att(dB) = 20log|VRSIL||VRSIL0

| NC? Q

VRSIL !- VRSIL0(."- *!(,!)-+4!/!"- %!( -!"(+."( '7!"-*0! '5 ;RCS &4!) !- (&"( #%-*!?

S! *&,,.*- ,!5-HW-*! '0#"+ !" -!"(+." .5 !" ).5*&"- ,5+(D57+% !(- ,*+( &56 8.*"!( '!(

+/,0'&")!( ).""5!( '5 ;RCS? F&"( ".-*! 0-5'!$ ".5( 5-+%+(!*."( %! *&,,.*- '!( -!"(+."(?

!" #$%& '( )*+%$ ,-. /0$1 '( &$'* 12342&/(+ 3/5(6+78'$

!"!# $%&'()*#+,-./ 0. 1&*2&3#4+ *#54)+,-./ .4,-./

V.-*! 0-5'! !(- )+8%0! (5* %& *0'5)-+." '5 4.%5/! .))5,0 ,&* %!( )./,.(&"-( /&E"0H

-+D5!( '&"( %! #%-*! :AB? V.5( ".5( +"-0*!((."( '.") 5"+D5!/!"- 3 %& ,&*-+! +"'5)-+4! '5

#%-*!$ %!( )&,&)+-0( '! /.'! ).//5" !- '! /.'! '+X0*!"-+!%$ ).//5"0/!"- &,,!%0!( Cy

Page 27: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'%& &% #()&*%+,- .& /01%2.&

"# Cx$ %&'(& )*" +% (#,*-#*," .* /+#," 0-&,-*&# 1$23 (",4'# -4'(&.5,5"( '4' 64.&/%7+"( 08&9:

;:<3:

1"( -46=4(%'#( &'.*-#&>( ." /+#,%9" (4'# -4'(#&#*5( +" =+*( (4*?"'# ." ."*@ "',4*+"A

6"'#( ,5%+&(5 %*#4*, .B*' '4C%* "' 6%#5,&%* 6%9'5#&)*" .4*@$ -B"(# D .&," D >%&7+" -E%6=

-4",-&#&> FG1HIJ: 2"( 6%#5,&%*@ (4'# -%,%-#5,&(5( =%, ."( =,4=,&5#5( '4'A+&'5%&,"($ "' =%,#&A

-*+&",$ +% ,"+%#&4' "'#," +" -E%6= 6%9'5#&)*"H$ "# +B&'.*-#&4' 6%9'5#&)*" B: 2"##" ,"+%#&4'

"(# .5-,&#" =%, *' -C-+" .BEC(#5,5(&( #C=&)*" =,5("'#5 D +% /9*," ;:K:

!"#$% ;:K L 2C-+"( B(H) "# J(H) #C=&)*"( .B*' 6%#5,&%* 6%9'5#&)*":

1B&'.*-#&4' 6%9'5#&)*" B "(# .5/'&" =%, +B5)*%#&4' ;:!: 1% =4+%,&(%#&4' J "(# +% -4'#,&A

7*#&4' .* 6%#5,&%* >",,46%9'5#&)*"$ 4' =%,+" %*((& .B%&6%'#%#&4' M .* 6%#5,&%* 0M)*%A

#&4' ;:N3:

−→B = µ0

−→H +

−→J 0;:!3

−→J = µ0

−→M 0;:N3

1B5#%# &'&#&%+ .* 6%#5,&%* "(# .&# O.5(%&6%'#5P +4,()*" J "# H (4'# '*+(: Q4*6&( %

*'" "@-&#%#&4'$ +" 6%#5,&%* .5-,&# *'" -4*,7" ." =,"6&R," %&6%'#%#&4' )*& %##"&'# +% (%#*A

,%#&4': Q& -"##" "@-&#%#&4' "(# =5,&4.&)*" 4' 47(",?" *' -C-+" .BEC(#5,5(&(: 1"( =,&'-&=%+"(

=,4=,&5#5( .B*' -C-+" .BEC(#5,5(&( B(H) (4'# +" -E%6= -4",-&#&> Hc$ +B&'.*-#&4' ,56%'"'#"

Br$ "# "' '59+&9"%'# +BEC(#5,5(&($ +% =",65%7&+&#5 ,"+%#&?" .&S5,"'#&"++" µr: Q"+4' +B5)*%#&4'

;:!$ +B&'.*-#&4' ,56%'"'#" "# #4*T4*,( 59%+" D +% =4+%,&(%#&4' ,56%'"'#" 0Br U Jr3 =4*,

+B"'("67+" ."( 6%#5,&%*@ >",,46%9'5#&)*"(: 1% =",65%7&+&#5 ,"+%#&?" ="*# V#," .5/'&" D *'

=4&'# )*"+-4')*" .B%7(-&((" h (*, +" -C-+" B(H) =%, +% ,"+%#&4' ;:<: M++" "(# (4*?"'# .5/A

'&" =4*, h = 0$ (*, +% -4*,7" ." =,"6&R," %&6%'#%#&4'$ 4' +B%=="++" %+4,( +% =",65%7&+&#5

,"+%#&?" &'&#&%+":

µrh =1

µ0.∂B

∂HH=h0;:<3

W4*, +"( 6%#5,&%*@ D >4,#" =",65%7&+&#5 0µr X HH3 +"( -C-+"( B(H) "# J(H) (4'#

-4'>4'.*(: Y +B5-E"++" 6%-,4(-4=&)*" "# =4*, +% -4'-"=#&4'$ 4' *#&+&(" +" -C-+" B(H) .*

6%#5,&%*:

1"( =,4=,&5#5( -%,%-#5,&(#&)*"( .* 6%#5,&%* (4'# (4*?"'# .5="'.%'#"( .B%*#,"( 9,%'A

."*,( =EC(&)*"( #"++"( )*" +% #"6=5,%#*,"$ +"( -4'#,%&'#"( 65-%'&)*"($ +" #C=" "# +% >,5A

Page 28: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%& '( )*+%$ ,-. /0$1 '( &$'* 12342&/(+ 3/5(6+78'$ !

"#$%&$ '$ ()$*&+,-,+.% /($&,0+"#$1 2.33$ %.#4 ()-5.%4 '+, '-%4 (- 6-0,+$ 60/&/'$%,$7 +(

$*+4,$ '$#* ,86$4 '$ 6$0,#09-,+.%4 &.%'#+,$47 &$(($4 '$ 3.'$ &.33#% $, &$(($4 '$ 3.'$

'+:/0$%,+$(1 2$4 6$0,#09-,+.%4 .%, '$4 &-0-&,/0+4,+"#$4 ,0;4 '+:/0$%,$4 <=-9($ >1 ?1

!"#$ >1 @ A6/&+B&-,+.%4 '$4 6$0,#09-,+.%4 &.%'#+,$4

2-0-&,/0+4,+"#$4 C.'$ &.33#% C.'$ '+:/0$%,+$(

2+0&#(-,+.% D$9.#&(-E$ 6-0 3-44$ F.#&($

G36(+,#'$ '$4 &.#0-%,4 <G2? 3G 3G

G36(+,#'$ '$4 &.#0-%,4 <H2? I JG

K$ L.%&,+.%%$3$%, ')#% &.36.4-%, +%'#&,+L $4, L.%&,+.% '# ,86$ ')$*&+,-,+.% MFHNOPQ1

2$(#+R&+ +36.4$0- '$4 &.%'+,+.%4 '$ ,0-5-+( '+:/0$%,$4 6.#0 ($ 3-,/0+-# 3-E%/,+"#$ <&8&($4

')S84,/0/4+4 '+:/0$%,4?1 T.#4 6.#5.%4 '+4,+%E#$0 '$#* ,86$4 ')$*&+,-,+.% U

@ V*&+,-,+.% ')-36(+,#'$ 4-%4 &.36.4-%,$ &.%,+%#$ <BE1 >1 I <-??1 2$ ,86$ '$ &8&($

483/,0+"#$ 0$60/4$%,$ #% #4-E$ '$ ,86$ ,0-%4L.03-,$#0 3-+4 -#44+ &$(#+ ')#%$ +%'#&R

,-%&$ '$ B(,0-E$ '$ 3.'$ &.33#%1 K$ 3-,/0+-# 6.44;'$ E/%/0-($3$%, #%$ 6$03/-9+R

(+,/ /($5/$ <W III? 6.#0 E-0-%,+0 #% 9.% &.$X&+$%, '$ &.#6(-E$7 $, '$4 6$0,$4 L-+9($4

<G((+-E$ %-%.&0+4,-((+%7 6-0 $*$36($?1

@ V*&+,-,+.% '$ L-+9($ -36(+,#'$ -5$& #%$ L.0,$ &.36.4-%,$ &.%,+%#$ <BE1 >1 I <9??1

2$ &8&($ &.00$46.%' -#* +%'#&,-%&$4 '$ B(,0-E$ '$ 3.'$ '+:/0$%,+$(1 K- &.36.4-%,$

&.%,+%#$7 "#+ $4, ($ &.#0-%, '$ (+E%$7 6.44;'$ #%$ .%'#(-,+.% Y #%$ L0/"#$%&$ /($5/$

3-+4 ()-36(+,#'$ $4, 3.'/0/$1 K- L.0,$ &.36.4-%,$ &.%,+%#$ +36.4$ ')#,+(+4$0 #%

3-,/0+-# Y 9-44$ 6$03/-9+(+,/ <6.#'0$?7 .# #% &+0&#+, 3-E%/,+"#$ -5$& $%,0$L$07 6.#0

/5+,$0 (- 4-,#0-,+.%1

%&'()$ >1 I @ 28&($4 F<Z? 6.#0 '+:/0$%,4 ,86$4 ')$*&+,-,+.%4

K- 60.9(/3-,+"#$ '$ &$,,$ /,#'$ '$5+$%, '.%&7 &.33$%, 0/'#+0$ ($ 5.(#3$ '$4 &.36.R

4-%,4 3-E%/,+"#$4 4-&S-%, "#$ ($4 9$4.+%4 4.%, '+:/0$%,4 6.#0 ($4 '$#* ,86$4 '$ 6$0,#09-R

,+.%41 [%$ 4.(#,+.% $%5+4-E/$ 6.#0 0/E($0 &$ 60.9(;3$ $4, ()#,+(+4-,+.% '$ B(,0$4 S890+'$41

V% $:$,7 &$ ,86$ '$ B(,0$ 6$03$, '$ '+3+%#$0 (- ,-+(($ '# &.36.4-%, 3-E%/,+"#$ 3-+4 +(

-66.0,$ &$6$%'-%, '$4 6$0,#09-,+.%4 4#66(/3$%,-+0$41 T.#4 -5.%4 '.%& &S.+4+ '$ 0$4,$0

4#0 #%$ 4,0#&,#0$ '$ B(,0$ 6-44+L1 [%$ '$#*+;3$ 4.(#,+.% $4, '$ ,0.#5$0 #% 3-,/0+-# 6(#4

Page 29: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'%& &% #()&*%+,- .& /01%2.&

"#$%&$'()*+ '(,- -.,/ #0,-*(,* 1) '(*2$,(1 ,32(/ 4*&1* 31 '&,)- 5#(16&1" "/1- "#$%&$'()*7+

,/ -#$(,* 3289 1*,/,-2: ;( 3#$),<$# -&/1*,&)+ =1# )&1- (>&)- >&1/1 #0"/&,*#$ #-* 3# *$&1>#$

1)# -*$16*1$# 3# 6&'"&-()* '(?)2*,=1# 1),=1# =1, "#$'#* /# @/*$(?# 3#- 3#10 '&3#-+ #)

8&1()* -1$ /# '(*2$,(1 #* /( *&"&/&?,#:

!"!# $%&% '( )*&+%

!"!#$% &'() *+,')%-'. */0 #)/1/20

A# *B"# 3# 6&'"&-()* '(?)2*,=1#+ $2(/,-()* /# @/*$(?# 3#- 3#10 '&3#-+ ( 3289 3&))2 /,#1

9 "/1-,#1$- 5$#>#*- CD$#EF+G,/HI+J&,EE+ KL1E!+MNKOHF+M"(E!+P('EQ( !"#$% !"#$&'(

)*+, -*./. 01230124 .3314,5",.*+46

!"#$ 768 9 7+)1/,"+/24 )2 :3,52 ;<= > =*)2 /*##1+ 2, #*)2 ).?@52+,.23

AB C",2+, D D&E 88F AB C",2+, D $GG &DH

AB C",2+, D &8D 8G8 AB C",2+, % %EG $DI

B. 3J*+ 52K"5)2 L314 2+ )@,".34 324 L5*,*,ML24 /*3*5@4 /.N)24414 +*14 52#"501*+4 01J.34

4*+, '"4@4 415 32 #O#2 L5.+/.L2 >

9 A+ #",@5."1 P"1,2 L25#@"'.3.,@ Q2+ 5*1K2RK5.4 S*+/@T

9 A+ #",@5."1 '"442 L25#@"'.3.,@ Q2+ '321RK5.4 /3".5T

9 A+ )*1'32 '*'.+"K2 415 324 )21U #",@5."1U L25#2,,"+, ".+4. 32 L"44"K2 )24 V1U )2

#*)2 /*##1+ 2, )2 #*)2 ).?@52+,.23 L"5 324 )21U #",@5."1U6

;2,,2 ,*L*3*K.2 L25#2, )J*?5.5 )21U /P2#.+4 ).?@52+,4 L*15 324 V1U )2 #*)2 ).?@52+,.23

2, /21U )2 #*)2 /*##1+ /*##2 32 #*+,52 3" :K152 76EE6 C*15 /P"012 ,ML2 )2 V1U Q=;

*1 =WT 32 /*#L*4"+, 42 /*#L*5,2 /*##2 1+ /*#L*4"+, )2 #*)2 /*##1+ *1 )2 #*)2

).?@52+,.236

W"+4 32 )25+.25 '52-2, L5@42+,@ QAB C",2+, % %EG $DI )"+4 3" ,"'32 768T 42132 1+2

.+)1/,"+/2 )2 #*)2 /*##1+ 24, 5@"3.4@2 2, 32 :3,5"K2 )2 #*)2 ).?@52+,.23 24, "4415@ L"5

3" /"+"3.4",.*+ )1 V1U )2 S1.,2 )"+4 1+ ,*52 L3"/@ 2+N)244*146 ;2 )25+.25 L21, O,52 "144.

52#L3"/@ L"5 1+ K23 #"K+@,.012 XYZ=

+EE(6

Page 30: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%& '( )*+%$ ,-. /0$1 '( &$'* 12342&/(+ 3/5(6+78'$ !

!"#$% "# $ %&'()*+ ,) -./ ,) 01,) 2100.3 )* ,) 01,) ,456&)3*4)7

!"!#$%% &' ()*+),-./ 0%,+-.)$12%3-

8) 9)3*)& :1& ;1<)& =7)2*&1342+ >?+*)0+ @9;=>A ,) B4&C434' %)2D ' E&6+)3*6 .3)

31.F)77) 'EE&12D) E1.& 7G43*6C&'*413 ,)+ 43,.2*'32)+ ,) H9 )* HI J8HK

+ LM# "7 +G'C4*

,G.3 31?'. *1&4N.) O :'4P7) E)&06'P474*6 43*&1,.4* ,'3+ .3 31?'. ,) 01,) 2100.3 'F)2

.3 )3&1.7)0)3* +E624'7 @Q4C#"# RA# 8' E'&*42.7'&4*6 ,) 2)**) *1E171C4) )+* 7) P1P43'C) S)3

D.4*T N.4 E)&0)* ,G1&4)3*)& 7)+ -./ @H9 1. HIA# 8)+ 'F'3*'C)+ ,) 2)**) +*&.2*.&) +13*

7' +40E7424*6 C6106*&4N.) )* 7)+ -./ ,) :.4*) ,. *1&) ,) D'.*) E)&06'P474*6 N.4 )3 01,)

,456&)3*4)7 F4)33)3* &)3:1&2)& 7G43,.2*'32) ,) 01,) ,456&)3*4)7# 8' +*&.2*.&) E)&0)**&'4*

,G'**)43,&) .3 34F)'. 67)F6 ,G43,.2*'32) HI# 8)+ 'F'3*'C)+ +13* .3 :'4P7) F17.0) )* 7'

&6,.2*413 ,) 7' 713C.).& ,. U7 ,) 2.4F&)V E'& 213*&) 7' +E624U24*6 ,. P1P43'C) '.C0)3*)

7) 21W*# ;'& &'EE1&* O 7' F)&+413 ,4+2&X*)V 2) E&1*1*?E) 013*&) .3) &6,.2*413 ,. F17.0)

,) YL Z '43+4 N.G.3) &6,.2*413 ,) [ Z ,) U7 ,) 2.4F&) +'3+ ,6C&',)& 7' E)&:1&0'32)

,G'**63.'*413 1. 2'.+)& ,) C&'F)+ E&1P7X0)+ *D)&04N.)+ J8HK

+ LM#

Page 31: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'%& &% #()&*%+,- .& /01%2.&

!"#$% "# $ % &'()()*+, +'(+(-. +/' 0, 1&23

4/ -(56.). 76-+/8(93:6;/< /=,5 0/>:,00, 8(:- )'/=/600(8- -:' 0, +'(?,)< / @.56@. @A68@:-9

)'6/06-,' 5, +'()()*+,# 1,+,8@/8)< 0,- 06B6)/)6(8- -:' 0/ 5(B+0,C6). @: D(D68/E, /68-6 >:,

0, -:'9@6B,8-6(88,B,8) @: 8(*/: @, B(@, 5(BB:8 +(:' >:A60 ,8)(:', 0, 8(*/: @, B(@,

@6F.',8)6,0< (8) (D06E. G B(@6H,' 0/ './06-/)6(8 +'/)6>:, @: +'()()*+,# I/8- 5,)), 8(:=,00,

=,'-6(8< 0,- )(',- 8, -(8) +0:- 5(85,8)'6>:,- B/6- -:+,'+(-.- JK6E#"# LM#

!"#$% "# L % &'()()*+, +'(+(-. +/' 76-+/8(93:6;/

!"!# $%&'(#)* +* ,-%./+*

I/8- 5, 5N/+6)',< 8(:- /=(8- +'6- 5(8-56,85, @,- +'(D0OB,- >:A,8E,8@',8) 0/ 12P ,) 0,-

5(8)'/68),- -.=O',- @, 0A/.'(8/:)6>:,# I/8- 0, 5/@', @, 5,)), .):@,< 8(:- /=(8- './06-. :8,

',5N,'5N, D6D06(E'/+N6>:, +(:' @.5(:='6' +0:-6,:'- -)':5):',- @, 5(B+(-/8)- B/E8.)6>:,-

:86>:,-# I/8- 0/ -:6), @, 5,- )'/=/:C< 8(:- @,=(8- @/8- :8 +',B6,' ),B+-< 50/--,' 5,-

@6F.',8),- -)':5):',- ,) 0,- 5(B+/','# &(:' 5,0/< 8(:- @.)/600,'(8- 0/ B(@.06-/)6(8 @,-

5(B+(-/8)- B/E8.)6>:,-# &:6- 8(:- +'.-,8),'(8- @,:C -)':5):',- >:, 8(:- /=(8- './06-.,-

+(:' '.+(8@', G 8()', 5/N6,' @,- 5N/'E,-< @(8) :8, 68).E'., -:' &1Q#

Page 32: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&' ((

!"#$ %& '( )"*"'"+#& %, -".*"/(0) .(+01)#2,&

,0#2,&

!""#$%&

!" #$%&'()* +,-.(',/$,& .$ &010.02+' !

!! " # $%&' '( )*%+'(,' +' -#,.'/0& "1

!! " 2 3' ,45%6 +/ 7#.)0%#/ 7#8().%9/' ":

!! " , ;)<',.%5( +' 9/#.0' .5=5<58%'& >?

!" #$%&' () *+ ,%(-*&.+/&%0 1.2./3,)4 !

!! " # $%&'()(*' +, -# .,/0*/1#'2, +3 &-)/, "4

!! " #5( 6#7(,/ +,8 27#/9,8 :(8.#'*5;3(<# "4

!! " #5(( 67*(= +3 2#8 +, /%0%/,'2, "4

!! " > !')%/?) +, -@#../*27, A8B8)C1,D "E

!5 #%0./678/&%0 (7 ,%(3*) "

!! F # G# 0*'2)(*' *>H,2)(0 ,) -,8 2*')/#('),8 "I

!! F > J(8, ,' %K3#)(*'8 +3 8B8)C1, "L

!! F >5( :B.*)7C8,8 "L

!! F >5(( G@,'M(/*'',1,') +3 2*1.*8#') 1#9'%)(K3, "N

!! F >5((( G, 2*1.*8#') 1#9'%)(K3, FF

!! F >5(M G, 8B8)C1, 9-*>#- F4

!! F 2 O#-(+#)(*' +, -# 1(8, ,' %K3#)(*'8 .#/ 3' -*9(2(,- 2(/23() FE

!9 #%,:+6+&.%0 (). (&;;-6)0/). /%:%*%<&). #$

!! P # G, 2*3.-#9, +, 1*+, FE

!! P > $(82388(*' 83/ -,8 )*.*-*9(,8 /,),'3,8 FL

!! P >5( 6*1.#/#(8*' +,8 )*.*-*9(,8 FL

!! P >5(( Q/%5+(1,'8(*'',1,') +3 2*1.*8#') 1#9'%)(K3, PR

!! P >5((( !')%/?) +, -# 1*+%-(8#)(*' +3 2*1.*/),1,') +3 1#)%/(#3 1#9'%5

)(K3, +#'8 -# 1*+%-(8#)(*' A8B8)C1,D PS

!"#$!

! "#$%&'(! %()*!+'!, -$+* .+! %(!/&0(! %$('&!, 12&-!+'&3"$'&4+ -!* -&5)(!+'* 6$"'!.(*

6$74(&*$+' 1$ "4+"!%'&4+ -. "4/%4*$+' /$8+)'&9.! .+&9.!: ;$ /&*! !+ )7&-!+"! -!

"!* 6$"'!.(* $ %!(/&* 1$ *)1!"'&4+ -! %1.*&!.(* '4%4148&!* %4.( )'.-&!( 1!.(* &+<.!+"!*:

!''! )'.-! $ -4++) 1&!. = 1$ ()$1&*$'&4+ -2.+ /4-01! >*?*'0/!@ -)3+&**$+' 1!* '4%4A

148&!*, 12!+7&(4++!/!+' -!* "4/%4*$+'*, 1!* "4+'($&+'!* 8)4/)'(&9.!* !' %#?*&9.!*: !

/4-01! $ !+*.&'! %!(/&* 1$ "4/%$($&*4+ -!* '4%4148&!* !' 1$ ()-."'&4+ -! 12)'.-! = -!.B

'4%4148&!* %$('&".1&0(!* 9.& *!(4+' -)'$&11)!* -$+* 1! "#$%&'(! *.&7$+':

Page 33: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

!" #$%&'()* +,-(',.$,& /$ &010/02+'

"#$% &' ()'*+') ,-#(+.)'/ (&0%+'0)% 1)'2'.% %0) 3'% %.)0,.0)'% 3' ,4*(4%#$. *#5$6.+70'

0$+70' 4$. 6.6 ()6%'$.6%8 "#$% &# ()'*+9)' (#).+' 3' ,' ,-#(+.)'/ $40% #&&4$% #$#&:%')

,'% 3+;6)'$.% 1)'2'.% #<$ 3' 36.')*+$') %0) 70'&% =#,.'0)% %' 1#%') (40) &# )6#&+%#.+4$

30 ,4*(4%#$. 0$+70'8 >$%0+.'/ $40% $40% =4,#&+%')4$% %0) 0$ 6,-#$.+&&4$ 3' .4(4&45+'%

+&&0%.)#$. &?+$@0'$,' 3' ,'% =#,.'0)%8

!"!# $%&' '( )*%+'(,' +' -#,.'/0&

>$ #$#&:%#$. &'% 3+;6)'$.% 1)'2'.% ()6%'$.6% 3#$% &' ,-#(+.)' ()6,63'$. #+$%+ 70' &'%

,4*(4%#$.% *#5$6.+70'% 3' <&.)' A>B C.)#3+.+4$$'&D EF+58 G8HI/ $40% #24$% +3'$.+<6 3'0J

5)#$3'% =#*+&&'% K

L M'% ,4*(4%#$.% %:*6.)+70'%/ ,?'%. N 3+)' 34$. &'% +$30,.#$,'% ()4()'% %4$. +3'$.+70'%

EF+58 GG8 I

!"#$% GG8 L O4(4&45+' 1#%6' %0) &# 3+%%:*6.)+' 3'% .)#P'. 3' @0J

L M'% ,4*(4%#$.% 3+%%:*6.)+70'%/ ,?'%. N 3+)' 34$. &'% +$30,.#$,'% ()4()'% %4$. 3+;6Q

)'$.'% EF+58 GG8RI

!"#$% GG8R L O4(4&45+' 1#%6' %0) &# 3+%%:*6.)+' 3'% 141+$#5'%

>$%0+.'/ (40) ,-#70' 5)40('/ +& '%. (4%%+1&' 3' P40') %0) (&0%+'0)% (#)#*9.)'% %',4$Q

3#+)'% (40) 41.'$+) &?0$ 40 &?#0.)' 3'% ,4*(4%#$.% K

L M' 141+$#5'8

A4**' ()6%'$.6 3#$% &?#).+,&' STUV

+ W/ %+ $40% ,)64$% 0$' +$30,.#$,' 3' *43'

,4**0$ #2', 0$ 141+$#5' 3+%%:*6.)+70'/ #&4)% &# $4$ ,4*('$%#.+4$ 3'% @0J (')Q

*'. 3' )6#&+%') &' <&.)#5' 3' *43' 3+;6)'$.+'&8 X40% ,)6')4$% #&4)% 0$ ,4*(4%#$.

3+%%:*6.)+70'8

Page 34: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()* +,-(',.$,& /$ &010/02+' !

" #$ %&'($% )$ *+,-

#$. %&'($%. )$ *+, ./0% )123&$0%. $0%&$ 4$. 5$&%+&6'%1/0. )$ 7/)$. 8/77+0 $% 4$.

5$&%+&6'%1/0. )$ 7/)$ )123&$0%1$44$.- 9$ :'8%$+& $.% 144+.%&3 )'0. 4$ 8;'51%&$ < 5'& 4'

=>+&$ <- -

" #$ 7'%3&1'+ 7'>03%1?+$-

9$ :'8%$+& $.% )3%'1443 )'0. 4$ 5'&'>&'5;$ .+1@'0%-

!"!# $% &'()* +, -./01)., -.230/)4,%

A/+& 4' ?+'.1B%/%'41%3 )$. 7'%3&1'+, 7'>03%1?+$.C 4' 5$&73'6141%3 8;+%$ &'51)$7$0% '@$8

4D'+>7$0%'%1/0 )$ 4' :&3?+$08$- A4+. 4' 5$&73'6141%3 $.% 34$@3$ 54+. 4' &3./0'08$ 7'>03B

%1?+$ .$ 7'01:$.%$ $0 6'..$ :&3?+$08$ E4171%$ )$ F0/$GH- I$ 8$ :'1%C 4$ 8;/1, )D+0 7'%3&1'+

7'>03%1?+$ $.% '@'0% %/+% =,3 5'& 4' >'77$ )$ :&3?+$08$. )'0. 4'?+$44$ 14 $.% +%141.3-

#D+%141.'%1/0 )$. 7'%3&1'+, 7'>03%1?+$. 73%'441?+$. EJ$C '441'>$. J$F1C J$K1C '7/&5;$.

/+ 0'0/8&1.%'4410.H $0 :&3?+$08$ $0>$0)&$ )$. 5&/64L7$. 10;3&$0%. '+, :'164$. &3.1.%1@1%3.

)$ 8$. 7'%3&1'+, M

" 4' 5&/:/0)$+& )$ 5303%&'%1/0 δ EN?- <<- H- 9$%%$ 5&/:/0)$+& $.% 10@$&.$7$0% 5&/5/&B

%1/00$44$ O 4' &'810$ 8'&&3$ )$ 4' 8/0)+8%1@1%3 34$8%&1?+$ σ EΩ−1m−1HC )$ 4' 5$&73'B

6141%3 µC $% )$ 4' :&3?+$08$ f EPQH M

δ =

1

π.f.µ.σE<<- H

" 4$. 5$&%$. 5'& 8/+&'0%. )$ J/+8'+4% 413$. '+, 8/+&'0%. 10)+1%.- IL. 4/&. ?+$ 4D/0

'%%$10% +0$ )1Q'10$ )$ G14/;$&%Q $% ?+$ 4D/0 8;$&8;$ O &3'41.$& +0 8/75/.'0% 7'..1:

)/0% 4$. )17$0.1/0. ./0% >&'0)$. )$@'0% 4D35'1..$+& )$ 5$'+C 8$. 5&/64L7$. )$@1$00$0%

1&&373)1'64$.- 9D$.% 4' 5&10815'4$ 8/0%&'10%$ ?+1 O 8/0)+1% O +%141.$& )$. :$&&1%$. 5/+&

4$. 8/75/.'0%. 7'>03%1?+$. ;'+%$. :&3?+$08$.-

!"#$% <<-R " <44+.%&'%1/0 )$. 8/+&'0%. )$ J/+8'+4%

#$. 5&$71$&. 7'%3&1'+, O S%&$ +%141.3. 5/+& )$. '55418'%1/0. :&3?+$0%1$44$. ./0% 4$. :$&B

&1%$.- #$. :$&&1%$. )/+, &$>&/+5$0% %&/1. :'7144$. )$ 7'%3&1'+, T#$6UVW M

" #' 5&$71L&$ :'7144$ $.% 8$44$ )$. :$&&1%$. .510$44$. )$ 7'0>'0L.$BQ108 EX0BY0H +%141.3.

5/+& )$. :&3?+$08$. '44'0% )$ U GPQ O XPQ- 9$. 7'%3&1'+, ./0% 5&10815'4$7$0%

+%141.3. )'0. 4$. )/7'10$. )$ 4' 8/0@$&.1/0 )D30$&>1$ /+ 4$ %&'1%$7$0% )+ .1>0'4- #$+&

&3.1.%1@1%3 34$8%&1?+$ @'+% %Z51?+$7$0% Ωm-

" #' .$8/0)$ :'7144$ $.% 8$44$ )$. :$&&1%$. .510$44$. )$ 018G$4BQ108 $% )$ 018G$4BQ108B

8+1@&$ +%141.3. $0%&$ $% VUU XPQ- #$+& &3.1.%1@1%3 34$8%&1?+$ 5$+% '%%$10)&$ U[ Ωm-

Page 35: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

"#$$% &%' (%))*+%' ,-./-0 *&' '#-+ 1+*&*'2' 3#1) &4 )24&*'4+*#- 5% +)4-'(#)$4+%1)' #1

56*-517+4-7%'8

9 :-;-0 &4 +)#*'*<$% (4$*&&% %'+ 7%&&% 5%' (%))*+%' 5*+' =>?3%)()2@1%-7%'A B!0C D C!!

EFGH8 I- +)#1J% 54-' 7% K)#13% 5%' (%))*+%' 5% +?3% '3*-%&&% %+ 5% +?3% K)%-4+8 L&'

'#-+ 1+*&*'2' 3#1) &4 )24&*'4+*#- 5% 7#$3#'4-+' >?3%)()2@1%-7%' '327*;@1%' +%&' @1%

&%' 7*)71&4+%1)' B#1 *'#&4+%1)'H0 &%' ;&+)%' 477#)54M&%' %+ &%' 523>4'%1)'8

"#-7%)-4-+ &%' 433&*74+*#-' 3)4+*@1%' 5%' $4+2)*41N $4K-2+*@1%'0 &4 3#&4)*'4+*#- D '4.

+1)4+*#- 5%' (%))*+%' BO !0P QH %'+ *-(2)*%1)% D 7%&&%' 5%' $4+2)*41N $2+4&&*@1%' B 0 Q 3#1)

&% (%) 5#1NH8 :- )%J4-7>%0 &4 )2'*'+*J*+2 2&%7+)*@1% %'+ M*%- '132)*%1)% BC Ωm 3#1) &%' (%))*+%'

,-./- D 7#$34)%) D 10−7 Ωm 3#1) &% (%)H0 7% @1* %- (4*+ 5%' $4+2)*41N *))%$3&4R4M&%'

3#1) &%' 433&*74+*#-' D >41+% ()2@1%-7%8

S%' $4+2)*41N $4K-2+*@1%' $2+4&&*@1%' '#-+ 32-4&*'2' 34) &%1) (4*M&% )2'*'+*J*+2 2&%7+)*@1%

3#1) &%' 1+*&*'4+*#-' D >41+% ()2@1%-7%8 T24-$#*-'0 #- 3%1+ )%3#1''%) &%' %U%+' 5%' 7#1.

)4-+' *-51*+' %- 5*$*-14-+ &6234*''%1) 5% &64&&*4K% $2+4&&*@1%8 V7+1%&&%$%-+0 &%' *-51'+)*%&'

'#-+ 7434M&%' 5% '?-+>2+*'%) 5%' )1M4-' 4$#)3>%' #1 -4-#7)*'+4&&*-' 561-% J*-K+4*-% 5%

$*7)#$<+)% 56234*''%1) W,%+XXY8

!"#$% LL8Z 9 [7>2$4 562&4M#)4+*#- 561- )1M4- -4-#7)*'+4&&*- W,%+XXY

L& %'+ 3#''*M&% D 34)+*) 5% 7%' )1M4-' 5% (4M)*@1%) 5%' +#)%' =%-)#1&2'A @1* '%)J*)#-+

%-'1*+% D &4 )24&*'4+*#- 56*-517+4-7%' #1 5% +)4-'(#)$4+%1)'8 S%' 7#$3#'4-+' 4*-'* #M+%.

-1' #-+ 5%' 3)#3)*2+2' +#1+ D (4*+ *-+2)%''4-+%' 54-' &4 K4$$% 5%' $#?%--%' ()2@1%-7%'8

S%' $4+2)*41N -4-#7)*'+4&&*-'0 527#1J%)+' D &4 ;- 5%' 4--2%' C\X! W]]XX0]]X\Y0 '#-+ 5%'

'+)17+1)%' $*N+%'0 3)2'%-+4-+ 5%' K)4*-' 5#-+ &%' 5*$%-'*#-' '% '*+1%-+ 54-' &4 K4$$% 5%

@1%&@1%' -$ D C! -$ %-J*)#-0 54-' 1-% $4+)*7% 4$#)3>% W^%)\_Y8 ^4)$* 7%' $4+2)*41N0

#- 3%1+ 7*+%) 5%' 72)4$*@1%' 5#-+ &%' 3)#3)*2+2' $274-*@1%' '#-+ *-+2)%''4-+%'0 5%' '%$*.

7#-517+%1)' -4-#7)*'+4&&*-' B'*&*7*1$ 34) %N%$3&%H0 5%' 7#$3#'*+%' J4)*2' B3)27*3*+4+*#-' 5%

-4-#K)4*-' '%$*.7#-517+%1)' 54-' 5%' J%))%' 56#N?5%'H %+ 5%' $4+2)*41N $4K-2+*@1%' 5#1N

#1 51)'8 L& %N*'+% 5*U2)%-+%' (4$*&&%' 5%' $4+2)*41N -4-#7)*'+4&&*-' M)%J%+2%' 34) 5*U2)%-+'

Page 36: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()* +,-(',.$,& /$ &010/02+' !

"#$%&'(")*& $+#' *)& ,-#+./01 ,-#+.)(21 3"'.)(2 )' 4"#)2)'5 6)& -**"-7)& #-#+8("&'-**"#&

&+#' "&&%& $) 2-'9("-%: 2-7#9'";%)& -2+(./)&5 6)& 2-'9("-%: <&+"' = >-&) $) 4)( +% 6+?

>-*'@ &) $"&'"#7%)#' .-( *)%( 8+2.+&"'"+# )' *)%(& ')2.9(-'%()& $) 6%(") 9*)A9) <B CDDE6@1

8) ;%" *)%( 8+#FG() %#) >+##) &'->"*"'9 )# ')2.9(-'%()5 H#) F+"& *) (%>-# -2+(./) 9*-?

>+(91 %# ()8%"' $) 8("&'-**"&-'"+# )&' -*+(& )I)8'%91 -.(G& *- 2"&) )# J%A() &+%& F+(2) $)

8+2.+&-#' <'+() )#(+%*9@ )' &+%& %#) -'2+&./G() #)%'() <7-K "#)(') .+%( 9A"')( $L9A)#?

'%)**)& +:0$-'"+#&@5 M- ')2.9(-'%() <)#'() NDD )' NNDE6@ )' *- $%(9) $) ()8%"' $9.)#$)#'

-*+(& $) *- 8+2.+&"'"+# $) *L-2+(./) .(98%(&)%( )' $)& 7(-#$)%(& $L%&-7) ()8/)(8/9)& .+%(

*L-..*"8-'"+#5 6) ()8%"' $) 8("&'-**"&-'"+# ()#$ *)& 2-'9("-%: #-#+8("&'-**"#& '(G& F(-7"*)&

)' #+#?$%8'"*)5 M- .(9F9()#8) )&' $+#8 $) 8+#&'(%"() *)& 8+2.+&-#'& -A-#' $L)I)8'%)( 8)

()8%"'5 O-( -"**)%(&1 8) ()8%"' .)(2)' $) $9A)*+..)( $L):8)**)#')& .(+.("9'9& 2-7#9'";%)&5

P(Q8) = *)%( '-%: ()*-'"A)2)#' "2.+('-#' )# F)( <.-( (-..+(' -%: F)(("')&@ *)& 2-'9("-%:

#-#+8("&'-**"#& .+&&G$)#' $)& "#$%8'"+#& = &-'%(-'"+# 9*)A9)& <!5 = !5R S)&*-@5 T-*7(9 %#)

'(G& F-">*) (9&"&'"A"'9 <!!N µΩm@1 *- F-">*) 9.-"&&)%( $% (%>-# 29'-**";%) .)(2)' $) *"2"')(

*)& )I)'& $) *- F(9;%)#8) $-#& *) 8"(8%"' 2-7#9'";%)5 U)& '(-"')2)#'& -$-.'9& $%(-#' *)

()8%"' $% 2-'9("-% .)(2)'')#' $) (97*)( *- A-*)%( $) *L-#"&+'(+.") "#$%"') )' $+#8 $L-V%&')(

*- F+(2) $% 808*) $L/0&'9(9&"&5 6)& +.9(-'"+#& -%'+("&)#' -*+(& %# -V%&')2)#' .(98"& $) *-

.)(29->"*"'9 ()*-'"A) ;%" )&' '0.";%)2)#' 8+2.("&) )#'() DDDD )' CDDDDD .+%( $)& ()8%"'&

&+%& 8/-2.& 2-7#9'";%)&5

O+%( .(98"&)( V%&;%L= ;%)**) F(9;%)#8) "* )&' .(9F9(->*) $L%'"*"&)( ')* '0.) $) 2-'9("-%

.*%'W' ;%L%# -%'()1 *)& 9A+*%'"+#& $) *- .)(29->"*"'9 )# F+#8'"+# $) *- F(9;%)#8) $L%#

-**"-7) F)((+2-7#9'";%) #-#+8("&'-**"# )' $L%# F)(("') &."#)**) T#?X# ().(9&)#'-'"F& $) *L9'-'

$) *L-(' &+#' .(9&)#'9)& &%( *- Y7%() ZZ5N5 M) F)(("') &9*)8'"+##9 )&' %# F)(("') &."#)**) $)

.%"&&-#8) T#?X# +.'"2"&9 .+%( %# F+#8'"+##)2)#' = !DD [3K1 DD 2S )' !DD

65 \-

.+*-("&-'"+# 2-7#9'";%) = &-'%(-'"+# A-%' D1NN S1 &- ')2.9(-'%() $) 6%(") ND

65 ML-**"-7)

#-#+8("&'-**"# &) .(9&)#') &+%& *- F+(2) $L%# (%>-# $) !] µ2 $L9.-"&&)%( )' $) 8+2.+&"'"+#

8/"2";%) Fe73.5B7Cu1Si15.5Nb35 \- .+*-("&-'"+# 2-7#9'";%) = &-'%(-'"+# A-%' !1 S1 &-

(9&"&'"A"'9 !!N µΩcm )' &- ')2.9(-'%() $) 6%(") CDD

65

6)'') Y7%() #+%& 2+#'() ;%) *- .)(29->"*"'9 $)& #-#+8("&'-**"#& )&' &%.9(")%() = 8)**)

$)& F)(("')& )' 8)*- 2^2) = /-%')& F(9;%)#8)&5

,+%& .+%A+#& $+#8 ()')#"( *)& .+"#'& &%"A-#'& _

` *)& F)(("')& &."#)**)&1 +#' = *- ')2.9(-'%() $) F+#8'"+##)2)#' $)& 8+#A)('"&&)%(&

<!DDE6@1 $)& .)(')& &)2>*->*)& -%: #-#+8("&'-**"#& .+%( %#) "#$%8'"+# $) D1 S

)' %#) F(9;%)#8) $) !DD [3K5 O+%( $)& "#$%8'"+#& "#F9(")%()& )' $)& F(9;%)#8)& .*%&

9*)A9)&1 *)& F)(("')& &+#' .*%& .)(F+(2-#'&5 O+%( $)& "#$%8'"+#& &%.9(")%()& )' $)&

F(9;%)#8)& .*%& >-&&)&1 *)& #-#+8("&'-**"#& &+#' .*%& .)(F+(2-#'& a

` *)& #-#+8("&'-**"#& .(9&)#')#' %#) >+##) &'->"*"'9 $) *)%(& .)(')& '+'-*)& )# F+#8'"+#

$) *- ')2.9(-'%() <("&;%) $L)2>-**)2)#' '/)(2";%) (9$%"'@ a

` *)& #-#+8("&'-**"#& &) .(9&)#')#' -%V+%($L/%" &+%& *- F+(2) $) (%>-# ()*-'"A)2)#'

F(-7"*) <ZZ5C@5 6)8" *"2"') *)& .+&&">"*"'9& $) 2"&) )# F+(2) )# 8+2.-(-"&+# -%: F)(("')&

&."#)**)& ;%) *L+# '(+%A) &)*+# $)& F+(2-'& .*%& 8+2.*):)& )' .+%( $)& 8+b'& 2+$9(9& a

` *)& #-#+8("&'-**"#& +#'1 = 2+0)##) F(9;%)#8)1 $)& .)(29->"*"'9& '(G& &%.9(")%()& =

8)**)& $)& F)(("')&5

c# &L+(")#')(- $+#8 $) .(9F9()#8) A)(& *)& 2-'9("-%: #-#+8("&'-**"#& _

Page 37: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

!"#$% !!"# $ %&'()*)+,&- ./, (/*'0)1+2+30, /- 4&-53+&- ./ 2) 4*067/-5/ 89/*:;<

$ (&7* ./, 4*067/-5/, ./ 4&-53+&--/'/-3 '&.0*0/, => ?@@ ABCD .)-, 2/, )((2+5)3+&-,

./ (7+,,)-5/ =3*)-,4&*')3/7*, &7 +-.753)-5/, (&7* 5&-E/*3+,,/7*,D F

$ (&7* ./, )((2+5)3+&-, &G +2 /,3 +'(&*3)-3 ./ .+,(&,/* ./ (/*'0)1+2+30, 02/E0/, =+-+H

3+)2/, &7 .I)'(2+37./DJ 'K'/ (&7* ./, 4*067/-5/, )33/+L-)-3 67/267/, '0L)M/*3C N

5&-.+3+&- 67/ 2/, (/*3/, -/ ,&+/-3 (), 5&-3*)+L-)-3/, =O23*)L/ /- '&./ 5&''7-D"

9&7* /'(K5M/* 7-/ )7L'/-3)3+&- ./, (/*3/, ()* 5&7*)-3, ./ P&75)723 .)-, 2I+-.75H

3)-5/J 7- 5Q30 ./ 2) ,7*4)5/ .7 *71)- /,3 +,&20 ()* 7-/ 5&75M/ '+-0*)2/ O-/ 67+ ,/

5&'(&,/ L0-0*)2/'/-3 ./ RLS 89/3@ <"

%/(/-.)-3J 5&''/ -&7, 2I)E&-, .03)+220 .)-, 2) (*&120')3+67/ .7 5&'(&,)-3 7-+67/J

2/, (/*37*1)3+&-, ./ '&./ 5&''7- /3 ./ '&./ .+T0*/-3+/2 -I)U)-3 (), 2/, 'K'/, 5)*)5H

30*+,3+67/,J ./7V 3U(/, ./ ')30*+)7V ,&-3 73+2+,0," W/, 5&'(&,)-3, ./ O23*)L/ ./ '&./

5&''7- ,&-3 2/, ')30*+)7V XM)73/ (/*'0)1+2+30 Y =/- *&7L/ZL*+, 4&-50 ,7* 2/, ,5M0'),D

5+30 5+H./,,7, =P/**+3/ &7 [)-&5*+,3)22+- /3 P/[+ /- 4)+12/ 0()+,,/7*D"

9&7* 2/, (/*37*1)3+&-, ./ '&./ .+T0*/-3+/2J -&7, ./E&-, -&7, 3&7*-/* E/*, ./, ')30*+)7V

.+\5+2/'/-3 ,)37*)12/,J 5I/,3 N .+*/ ./, ')30*+)7V )E/5 ./, 5M)'(, ./ ,)37*)3+&- Hs 3*],

L*)-.,J ')+, )7,,+ 73+2+,)12/, N M)73/, 4*067/-5/," ^0-0*)2/'/-3J &- 5&-3&7*-/ 2) .+\57230

,&+3 /- 73+2+,)-3 2/, )22+)L/, 4/**&')L-03+67/, /- (&7.*/,J ,&+3 /- 73+2+,)-3 ./, -&U)7V ')H

L-03+67/, N /-3*/4/*, 2&5)2+,0," W/, (&7.*/, ,I&13+/--/-3 ()* E&+/ 5M+'+67/ =.05&'(&,+3+&-

./ 4/*H5)*1&-U2/D 5/ 67+ 5&-.7+3 N ./, L*)+-, .I/-E+*&- ?@ -'" _22/, ,&-3 /-,7+3/ +,&20/,

02/53*+67/'/-3J 5&'(*+'0/, N 2) 4&*'/ /3 ,&7E/-3 /-*&10/, .)-, 7-/ *0,+-/ ./ (*&3/53+&-"

S- (/73 )7,,+ 3*&7E/* ./, )22+)L/, )'&*(M/, &7 -)-&5*+,3)22+-, (&7* ./, 3&*/, ./ '&./

.+T0*/-3+/2 ')+, 5/, )22+)L/, &-3 030 */57+3, ,&7, ./, 5&-3*)+-3/, ()*3+572+]*/, ='05)-+67/

&7 5M)'( ')L-03+67/ 3*)-,E/*,/D" %/, ')30*+)7V &-3 ./, (/*'0)1+2+30, */2)3+E/, ./ 2I&*.*/

./ 2) 5/-3)+-/ =/- 12/7ZL*+, 52)+* ,7* 2/, ,5M0'),D"

Page 38: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()* +,-(',.$,& /$ &010/02+' !

!"#$% ""#$ % &'()*+*,- ./ '01(2 .3(++*()/ 2(245'*6,(++*2

!"!# $%&'#()*+ ,' -./(0' (*1*&*2)'3

7 8(',*' ./ +3-,0./ 1*1+*4)'(89*:0/ /, ./ +( .-,/';*2(,*42 ./6 <(5,/0'6 *2=0/2>(2, +( ,4?

84+4)*/@ 2406 (A426 .-,/';*2- :0(,'/ 6,'05,0'/6 ./ 54;846(2, ;()2-,*:0/ 8/';/,,(2, +3(,?

,-20(,*42 ./6 540'(2,6 ./ ;4./ 54;;02 /, ./ ;4./ .*B-'/2,*/+# C40' 594*6*' 5/6 6,'05,0'/6@

2406 (A426 .3(14'. <(*, +( .*6,*25,*42 /2,'/ 54;846(2,6 6D;-,'*:0/6 /, .*66D;-,'*:0/6# C0*6

2406 (A426 (E2- +( .*6,*25,*42 840' A4*' +3*2=0/25/ ./6 8('(;F,'/6 6/542.(*'/6# G/6 54;?

846(2,6 642, '/8'-6/2,-6 6406 <4';/ ,4'*:0/6 840' ./6 '(*6426 ./ 6*;8+*5*,- 659-;(,*:0/#

G( 54;8('(*642 ./6 ,484+4)*/6 /6, '-(+*6-/ 6(26 8'/2.'/ /2 54;8,/ +( )-4;-,'*/ .(26 5/,,/

8(',*/#

C(';* +/6 ,484+4)*/6 .*66D;-,'*:0/6@ 2406 (A426 594*6* 02 54;846(2, (A/5 02 141*2()/

.*66D;-,'*:0/# H/,,/ ,484+4)*/ /6, 1(6-/ 60' 02 ,4'/ ./ ;(,-'*(0 ;()2-,*:0/ (A/5 02

141*2()/ (D(2, 02 24;1'/ ./ 68*'/6 (0 8'*;(*'/ IJKL .*B-'/2, .0 24;1'/ ./ 68*'/6 (0

6/542.(*'/ IJ L I&*)# ""# L#

M(26 5/ 54;846(2,@ 2406 230,*+*6426 :0302 6/0+ ;(,-'*(0 ;()2-,*:0/# M3(8'F6 +/ ,9-4?

'F;/ .37;8F'/ 60' +/ 24D(0 ;()2-,*:0/@ +/ 59(;8 ./ 84+('*6(,*42 I/2 ;4./ .*B-'/2,*/+L

Hp 63-5'*, ./ +( ;(2*F'/ 60*A(2,/ 60' +( +42)0/0' ;4D/22/ .0 ,4'/ ILmoyL#

Hp =(N1 −N2)IDC

Lmoy

I""# L

G/ 59(;8 ./ 84+('*6(,*42 .4*, N,'/ 60E6(;;/2, 8/,*, ./A(2, +/ 59(;8 ./ 6(,0'(,*42 .0

;(,-'*(0 840' :0/ 5/ ,D8/ ./ ,484+4)*/ 64*, /E5(5/ /2 ;4./ .*B-'/2,*/+# G( 8'/;*F'/ *.-/

6/'(*, .425 ./ 594*6*' ./6 ;(,-'*(0O (A/5 ./6 59(;86 ./ 6(,0'(,*42 -+/A-6# H/8/2.(2,@ 5/6

,D8/6 ./ ;(,-'*(0 42, ./6 8/';-(1*+*,-6 ./ +34'.'/ ./ +( 5/2,(*2/@ 5/ :0* ( 840' 5426-:0/25/

./ .*;*20/' +/6 8/'<4';(25/6 .0 54;846(2, /2 ;4./ 54;;02# J406 ./A426 .425 ,'40A/'

02 54;8'4;*6# C40' .*;*20/' +/ 59(;8 ./ 84+('*6(,*42@ 2406 (A426 ./0O 8466*1*+*,-6 P

% Q(O*;*6/' Lmoy@ 5/+( 6*)2*R/ ./ 594*6*' 02 24D(0 ;()2-,*:0/ ./ )'(2. 8-'*;F,'/ 5/

:0* A( S +3/2542,'/ ./ +( ;*2*;*6(,*42 .0 A4+0;/ .0 54;846(2,# J406 (A426 .425

594*6* ./ 8'/2.'/ +( +42)0/0' ;4D/22/ .0 54;846(2, T*68(24?U0*V( LmoyW X 5;

% Q*2*;*6/' N1 − N2@ 5/+( 6*)2*R/ ./ 8'/2.'/ 02 24;1'/ ./ 68*'/6 (0 8'*;(*'/ /, (0

6/542.(*'/ ,'F6 8'459/# J406 (A426 594*6* ./ RO/' 5/,,/ A(+/0' .(26 +/ 5(6 +/ 8+06

<(A4'(1+/ S N1 −N2 = 1

Page 39: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

"#$ %&'$()*+,-(&'$ '&.$ )*/'($$#'- .' %0,12 )# 2&3,+($,-(&' Hp )# 45 6718 "# %0,12

)# 2&3,+($,-(&' '&.$ ,19'# : %&'$()*+#+ )#$ 1,-*+(,.; ','&%+($-,33('$ : %<%3# %&.%0*=

)#$ ,33(,>#$ ,1&+20#$ &. )#$ 2&.)+#$ )&'- 3#$ 2#+1*,?(3(-*$ '@#;%9)#'- 2,$ 3#$ A.#3A.#$

1(33(#+$8 B,'$ %#--# 2+#1(9+# ,22+&%0#= '&.$ '&.$ $&11#$ /;*$ 3#$ C,3#.+$ )@(').%-,'%#$

). %,0(#+ )#$ %0,+>#$ D($2,'&EF.(G, HI,?3# JJ8KL8 M&.$ )#C&'$ )&'% -+&.C#+ 3# %&12+&1($

N2 µr S A.( +*,3($# 3#$ C,3#.+$ )@(').%-,'%#$ 1('(1,3#$8 N@*-.)# 2+*3(1(',(+# '&.$ , 2#+1($

)# %0&($(+ .' 1,-*+(,. 1,>'*-(A.# 2&.+ %# %&12&$,'- )# 2#+1*,?(3(-* 1&<#''# Hµr )#

OPPP #'C(+&'L8

N# )#.;(91# >+&.2#1#'- %&'%#+'# 3#$ -&2&3&>(#$ $<1*-+(A.#$= '&.$ ,C&'$ %0&($( Q

R N# %&12&$,'- ?+#C#- HSF T,-#'- U=UOK= !L

J3 $@,>(- )# )#.; -&+#$ %&'%#'-+(A.#$ 1,($ 3@&+(#'-,-(&' )#$ -+,V#-$ )# W.; $# X,(- #'

V&.,'- $.+ 3, X&+1# )# 3@.' )#$ -&+#$ 23.-Y- A.# $.+ 3#$ ?&?(',>#$8

!"#$% JJ8Z R I&2&3&>(# ?,$*# $.+ 3, X&+1# )#$ 1,-*+(,.; 1,>'*-(A.#$

R N# %&12&$,'- D($2,'&EF.(G,

M&.$ 3@,C&'$ +#2+*$#'-* (%( #' C#+$(&' %&'%#'-+(A.#= )*C#3&22*# 2,+ 3# 3,?&+,-&(+#

"T[F= 2&.+ 23.$ )# C($(?(3(-*8 T,+ ,(33#.+$= %&11# '&.$ '# '&.$ ('-*+#$$&'$ 2,$ ,.

W.; )# X.(-# ),'$ %#--# 2,+-(#= %#--# +#2+*$#'-,-(&' '@, ,.%.'# %&'$*A.#'%#8

!"#$% JJ8O R I&2&3&>(# "T[F

B,'$ %#--# -&2&3&>(#= 3, )($$<1*-+(# #$- %+**# 2,+ 3# ?&?(',># #' \0.(-]8 "# ?&?(',>#

1&)(/# 3, %(+%.3,-(&' ). W.; ),'$ 3#$ )#.; -&+#$ #'-+# 3@#'+&.3#1#'- 2+(1,(+# #-

3@#'+&.3#1#'- $#%&'),(+#8

R N# %&12&$,'- ,C#% .' #'-+#X#+

"#--# -&2&3&>(# %&'$($-# #' .' -&+# .'(A.# ,C#% .'# V,1?# %#'-+,3# 2&$$*),'- .' #'E

Page 40: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&' () *+ ,%(-*&.+/&%0 1.2./3,)4 !

"#$%$# &'()* ++*,-* .$""$ /012)3#4"(01 5$#6$" 7809#(# 43: ;3: 7$3: /<$6(1= 7(9>#$1"=*

?4 5#>=$1/$ 7$ @8$1"#$%$# 5$#6$" 7$ /#>$# 31 "#4A$" 7$ ;3: 4B$/ 31$ 5$#6>4C(@("> 45D

54#$1"$ 5@3= %4(C@$ =41= 503# 43"41" /<41)$# 7$ 64">#(43* ?$ C0C(14)$ E341" F @3(

$=" (7$1"(E3$ F /$@3( 7831$ (173/"41/$ 7$ 607$ /06631*

!" #$%&' () *+ ,%(-*&.+/&%0 1.2./3,)4

G41= @4 54#"($ 5#>/>7$1"$H 103= 4B01= =>@$/"(011> E34"#$ "050@0)($= 503B41" #>4@(=$#

@4 %01/"(01 7$ 2@"#4)$ 7$ 607$ /06631 $" 7$ 607$ 7(9>#$1"($@* I21 7$ /0654#$# /$=

"050@0)($= $" 78(7$1"(2$# @$= %4/"$3#= @$= 5@3= 5$#"(1$1"=H 103= 4B01= >@4C0#> 31 607J@$*

?0#=E3$ @801 54#@$ 7$ 2@"#4)$H 01 >B0E3$ =03B$1" @$ "$#6$ 78$K/4/("> 03 7$ 5$#%0#641/$ 7831

7(=50=("(%* G41= @4 5#$6(J#$ 54#"($H 103= 4@@01= 7>"4(@@$# 10"#$ 7>21("(01 7$ @4 5$#%0#641/$H

/$@@$ E3( =$#4 $:5@0(">$ 741= @4 =3("$ 73 6413=/#("* ?$= A3="(2/4"(01= 7$ @4 607>@(=4"(01

L=M="J6$N =01" 5#>=$1">$= 741= 31$ 7$3:(J6$ 54#"($*

!"!# $%&'()(*' +, -# .,/0*/1#'2, +3 &-)/,

!"!#$% &#'%() *(+ ,'#)-(+ .%+/#01$23%4#

I21 7$ 7(6$1=(011$# @$ /0650=41" 64)1>"(E3$ 31(E3$H @4 /0654)1($ O(=5410DP3(Q4

103= 4 %03#1( 31 /4<($# 7$= /<4#)$= (650=41" 7$= B4@$3#= 78(173/"41/$= $1 %01/"(01 7$ @4

%#>E3$1/$ &R4C@$ ++*,-*

!"#$ ++*, S .4<($# 7$= /<4#)$= O(=5410DP3(Q4

+173/"41/$ '#>E3$1/$

LMC 3.5mH 15 kHz

1.4mH 100 kHz

400µH 1MHz

LMD 200µH 150 kHz

.$5$1741"H /$= B4@$3#= 1$ 103= 5$#6$""$1" 54= 7$ 7(6$1=(011$# $" 7$ /<0(=(# @$ 64">#(43

64)1>"(E3$* T1 $9$"H $@@$= =01" 7>5$1741"$= 7$ @4 )>06>"#($H 73 106C#$ 7$ =5(#$= $" 7$

@4 5$#6>4C(@("> 503# @4 #>4@(=4"(01 7$ @8(173/"41/$* .$5$1741"H $@@$= 103= 5$#6$""$1" 7$

7>"$#6(1$# @$ =$3(@ 6(1(636 F #$=5$/"$#* U03= 4B01= 701/ 7>/(7> 7$ #$)4#7$# @4 7>21("(01

7$ 5$#%0#641/$ 741= @$= 10#6$= .TV*

!"!#$%% &'1%5 *3 ,#+ *( )676)(0,(

?4 10#6$ GWD,XY 1$ /017("(011$ @$ 1(B$43 7$ 5$#"3#C4"(01= 43: C0#1$= 73 ZP+? E38F

54#"(# 7$ ,!Y [OQ &'()*+*\-* V4@<$3#$3=$6$1"H @$ =5$/"#$ %#>E3$1"($@ 7$= 5$#"3#C4"(01=

/0173("$= =8>"4@$ 7$ E3$@E3$= 7(Q4(1$= 7$ O$#"Q F ,!Y VOQ* ]03# @4 5@4)$ 7$ %#>E3$1/$

$1 7$==03= 7$ ,!Y [OQH 43/31$ 6$=3#$ 184 >"> ="4174#7(=>$* ?4 =0/(>"> O(=5410DP3(Q4 4

7>B$@055> =4 5#05#$ 6>"<07$ 7$ /4#4/">#(=4"(01* ?$ 2@"#$ $=" /011$/"> F 31$ =03#/$ G. 7$

[ 4B$/ 31$ (65>741/$ 7>21($H /$ E3( @$3# 5$#6$" 784B0(# 31 )4C4#(" $1 4"">134"(01*

Page 41: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

"# $%&'# ()&*+ $,-.-$& /-0 1- 0%2'(# 3*4$5# /-' 650/-$%78259-+ $%20 -:%$0 3*(53* 3# (%$057

3*'#' 2$ -2&'# ;-<-'5& =25 0#'- :-1-<1# 02' &%2&# 1- /1-;# 3# >'*=2#$(# 3# 1,*&23#? @%2'

(#1-+ $%20 -:%$0 (A%505 3# 3*4$5' (%BB# 3-$0 1- $%'B# "C7D!E+ 1# ('5&F'# 02' 1- :-1#2'

3# 1- &#$05%$ -2G <%'$#0 3,#$&'*# 32 H8IJ KL=? I?DM? I1 $# '#0&-5& /120 =2,N (A%505' (# ('57

&F'#? 85 1,%$ 0# '*>F'# -2 41&'# OLP &'-35&5%$$#1+ 51 . - 2$ (%B/%0-$& B-;$*&5=2# /%2'

(A-=2# B%3#+ #$ 1,%((2''#$(# 2$# 5$32(&-$(#? J# (-A5#' 3#0 (A-';#0 650/-$%78259- - 4G*

1#0 :-1#2'0 B5$5B-1#0 3# (#0 5$32(&-$(#0 KQ-<1# II?DM? R%20 -:%$0 3%$( (A%505 3# /'#$3'#

3#0 5$32(&-$(#0 (%2/1*#0 K05B51-5'# N 3#0 (%B/%0-$&0 /-'>-5&0M -:#( (#0 :-1#2'0 B5$5B-1#0

(%BB# (-0 3# '*>*'#$(#? O#&&# 0%12&5%$ '#/'*0#$&# 3#2G (%B/%0-$&0 B-;$*&5=2#0 350('#&0

KPO #& P"M -:#( 3#0 :-1#2'0 B5$5B-1#0 N '#0/#(&#' KS5;? II?TM?

L_MD L_MC

Composant magnétique

!"#$% !" # $%& '( )*+*)(,-( . /(& 0,'1-2%,-(& -314/*(&

5( ,06(%1 '( 4()21)7%203,& 8%908%/ %'80&&07/( -3))(&43,' '3,- : /% 6%/(1) '( /% 2(,&03,

%19 73),(& '1 ;< 5 '1 -%& '( )*+*)(,-(! =, (>(2? &0 /% 2(,&03, '1 -3843&%,2 1,0@1( (&2

0,+*)0(1)( : -(//( '1 -%& '( )*+*)(,-( %/3)& 0/ % 1,( 8(0//(1)( %22*,1%203, '(& 4()21)7%203,&!

!"!# $%&'(% )* +,-..'/01* 2343%56*7

A31) 372(,0) /% 4()+3)8%,-( '1 B/2)(? ,31& '(63,& '3,- 8(&1)() /(& 2(,&03,& %19 73),(&

'1 ;< 5! $(4(,'%,2? /% 6%/(1) '( -(22( 2(,&03, '*4(,' '1 2C4( '( 4()21)7%203,& 8%0&

%1&&0 '1 B/2)( $=D @1( /E3, 4/%-( 431) B/2)() -(& 4()21)7%203,&! $( -3,&2%2 ,31& %8F,( :

-3,&0'*)() /( &C&2F8( '%,& &% G/37%/02* -388( 0//1&2)* &1) /% BG1)( !HI!

Source de

perturbations

Capacités

Cx et Cy

Composant

magnétiqueRSIL

Filtre CEM

!"#$% !HI # D3'F/( J&C&2F8(K '1 -3843&%,2 8%G,*20@1( (2 '( &3, (,60)3,,(8(,2

=, +3,-203, '(& 7(&30,& 'E1,( *21'( (2 '1 '(G)* '( -384/(902* 'E1, &C&2F8( -3,&0'*)*?

1, ,06(%1 'E%44)3-L( '0>*)(,2 '302 M2)( -L30&0! =, 2()8( '( &081/%203,? -(-0 &( 2)%'102 4%)

1, -384)380& (,2)( /% -384/(902* '1 83'F/( -L30&0? '( /% 4)*-0&03, &31L%02*( '(& )*&1/2%2&

(2 '1 2(84& '( -%/-1/! 5% BG1)( !HI )(4)*&(,2( /E%44)3-L( 'E1, &C&2F8( -384/(9( 4%)

'*-3843&0203, (, &31&N&C&2F8(&! O0(, &P)? ,32)( *21'( &( /0802( %1 B/2)( $=D (2 4/1& 4%)N

20-1/0F)(8(,2 (,-3)( %1 -3843&%,2 8%G,*20@1(! / (&2 '3,- 4)*+*)%7/( 431) ,31& '( 431630)

G%)'() J/E(,60)3,,(8(,2K '1 -3843&%,2 8%G,*20@1( -3,&2%,2 %B, 'E*21'0() &3, 0,Q1(,-(

Page 42: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*'+$% ,) -$,./0 !

"#$ %&" '&$(#$)*(+,-". /,#$ 0&%*1 -,#" *2,-" 345-+ %& "6"(78& &- ",#"9"6"(78&" :;,#$0&

3& '&$(#$)*(+,-"1 0*'*0+(4"1 0,8',"*-( 8*<-4(+=#& &( >;?@A. B,88& +-3+=#4 "#$ %* 59

<#$& ??.CD1 0E*=#& ",#"9"6"(78& '&#( 3,-0 F($& 2# 0,88& #- =#*3$+'G%&. B&" =#*3$+'G%&"

'&#2&-( F($& $&'$4"&-(4" ",#" %* H,$8& 3& 8*($+0& 3& ($*-"H&$( %+*-( %&" (&-"+,-" &( 0,#$*-("

3I&-($4& *#J (&-"+,-" &( 0,#$*-(" 3& ",$(+& :'*$ &J&8'%& ',#$ %& 0,8',"*-( 8*<-4(+=#&

??.CCA.

V2_out

V1_out

V2_in

V1_in

I1_in

I2_in

I1_out

I2_out

I1_c

I2_c I2_d

I1_d

!"#$% ??.CC K ;0E48* 3# =#*3$+'G%& L0,8',"*-( 8*<-4(+=#&M

@I4(#3& 3I#-& -,#2&%%& (,',%,<+& 3& 0,8',"*-( 8*<-4(+=#& &-<&-3$&$* #-+=#&8&-( %*

8,3+50*(+,- 3& %* 8*($+0& 3& ($*-"H&$( 3# 0,8',"*-( 8*<-4(+=#&.

!" #$%&'()*'+$% ,) -$,./0

!"!# $# %&'()*&' &+,-()*% -) .-/ (&')0#*')-/

N- *4$,-*#(+=#&1 %* 8*""& &"( #- 0$+(7$& +8',$(*-( =#I+% H*#( ,'(+8+"&$. B,88& -,#"

-& -,#" +-(4$&"",-" =#I*# 0,8',"*-( 8*<-4(+=#& &( =#& %&" *%%+*<&" ,-( =#*"+8&-( %* 8F8&

8*""& 2,%#8+=#&1 -,#" *2,-" 340+34 3& $43#+$& %& 2,%#8& 3# 0,8',"*-( 8*<-4(+=#&. O,#"

*2,-" 3,-0 0E,+"+ %& 2,%#8& *''*$&-( 0,88& H,-0(+,- ,)P&0(+H :Q+<. ??.C A.

!"#$% ??.C K R45-+(+,- 3& %* "&0(+,- *''*$&-(& 3I#- 0,8',"*-(

@&" 0,-($*+-(&" ',#$ %&" 0,8',"*-(" ",-( 3& 3&#J (6'&". RI#-& '*$( %&" 0,-($*+-(&"

<4,84($+=#&"1 ,- '&#( 0+(&$ S

Page 43: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

" #$% &'()*+,$% &$% +-,$% ./'()*+,$ $0+1,'$2, .Dext34 /'()*+,$ '5+1,'$2,.Dint33

" 6' 7( +-8-7-9'$ &-'+ (:-', 25 $5+,$;$, .<5+,$;$, .Ent34 =3

" >-2+$% 7$% +-8-7-9'$% %-5+ ?-?'51$% .@-)?,$ &$ %8',$% N 4 = $+ 5-)?,$ $5+'$,3

" #$ 5-)?,$ &$ %8',$% &-'+ A+,$ B-5+$52 &(5% 7( ;$5A+,$ &$ ?-?'5(9$C D(, $0$)87$E 8-2,

25 +-,$ %')87$ ?-?'51 (:$B 25 F7 &$ &'()*+,$ .Dfil3 G

N Dfil = π (Dint −Dfil) .HHCI3

#$ B-$JB'$5+ &$ ;-'%-55$)$5+ %$,( 8,'% $5 B-)8+$ &(5% 7$ BK(8'+,$ HL 8-2, 7M-8+')'N

%(+'-5 (:$B 7$% B-5+,('5+$% '5&2%+,'$77$%C

<+ &M(2+,$ 8(,+ 7$% B-5+,('5+$% &$ 8$,;-,)(5B$C O-))$ 5-2% 7M(:-5% &1F5' 8,1B1&$)N

)$5+E 7( :(7$2, &$ 7( +$5%'-5 (20 ?-,5$% &2 P6H# &-'+ A+,$ (2 )-'5% '5;1,'$2,$ Q B$77$ &2

B(% &$ ,1;1,$5B$E B$ R2' B-,,$%8-5& Q 25$ )$'77$2,$ (++152(+'-5C @-2% 5-2% %-))$% 7')'+1%

Q %'0 :(7$2,%E R2' %-5+ 7$% +$5%'-5% &$ )-&$ B-))25 $+ 7$% +$5%'-5% &$ )-&$ &'S1,$5+'$7 Q

+,-'% ;,1R2$5B$% .T=UVWE T==UVW $+ TXVW3 R2' B-,,$%8-5&$5+ Q BK(R2$ &1B(&$ &$ 7( 87(9$

;,1R2$5+'$77$ Q 7(R2$77$ 7$ B-)8-%(5+ %$,( %-2)'%C

!"!# $%&' '( )*+,-%.(& /+ &0&-12'

!"!#$% &'()*+,-.-

#$% )(+1,'(20 )(951+'R2$% -5+ 25 B-)8-,+$)$5+ 5-5 7'51(',$C @-2% (:-5% &1F5' 7$

B-)8-,+$)$5+ )(951+'R2$ &2 )(+1,'(2 YK(2+$ 8$,)1(?'7'+1Z 8(, 25$ 7-' $5 (,B+(59$5+$

8-2, 8,$5&,$ $5 B-)8+$ 7( %(+2,(+'-5 .<RCHHC[3C

Js $%+ 7( 8-7(,'%(+'-5 Q %(+2,(+'-5 &2 )(+1,'(2 )(951+'R2$C

µri $%+ 7( 8$,)1(?'7'+1 ,$7(+':$ '5'+'(7$ &2 )(+1,'(2 )(951+'R2$C

µ0 $%+ 7( 8$,)1(?'7'+1 &2 :'&$C

H $%+ 7$ BK()8 )(951+'R2$C

J $%+ 7( 8-7(,'%(+'-5 &2 )(+1,'(2 )(951+'R2$C

J(H,µri) =2 Jsπ

arctan(πµ0(µri − 1)H)

2 Js.HHC[3

D(, ('77$2,%E 8-2, 7$% )(+1,'(20 ?(%%$% 8$,)1(?'7'+1%E 5-2% (:-5% F01 7( 8$,)1(?'7'+1

Q µr \ I==C O$++$ 8$,)1(?'7'+1 B-,,$%8-5& (2 +-,$ &2 B-)8-%(5+ Y?(%%$ 8$,)1(?'7'+1Z

&MV'%8(5-N62'W( $+ $%+ $5 (BB-,& (:$B 7$% )(+1,'(20 )(951+'R2$% 1:-R21% &(5% 7( 8(,+'$

8,1B1&$5+$C @-2% (:-5% B$8$5&(5+ F01 B$++$ :(7$2, (2 7'$2 &$ 8,$5&,$ 25 )-&*7$ &$ )(+1N

,'(2 (:$B 25$ 7-' $5 (,B+(59$5+$ 82'%R2$ 7$ BK()8 &$ %(+2,(+'-5 &2 )(+1,'(2 $%+ +,*% 7-'5

&2 BK()8 B,11 8(, 7$ B-2,(5+ 8-,+$2, &$ ]^E 5-2% 5M(:-5% &-5B 8(% &$ %(+2,(+'-5 8-2, 7(

%$B+'-5 &-551$C @-2% 8,$5&,-5% 5-+$ &$ :1,'F$, 7$ B,'+*,$ (:$B 7$% &')$5%'-5% -?+$52$%C

/(5% 5-+,$ )-&*7$ %_%+*)$E 5-2% :-27-5% &1F5', &$% )(+,'B$% &$ +,(5%;$,+ &$ BK(R2$ %-2%N

%_%+*)$ R2$ 5-2% 8-2,,-5% $5%2'+$ )$++,$ $5 B(%B(&$C /M25 8-'5+ &$ :2$ 5-,)(+';E 7M1+2&$

&$% 8$,+2,?(+'-5% &$ )-&$ B-5&2'+ .)-&$% B-))25 $+ &'S1,$5+'$73 %$ ;('+ 8(, 7M(5(7_%$ &$

7M(++152(+'-5 &$% +$5%'-5% (20 ?-,5$% &2 P6H#C OK(B25 &$ B$% )-&$% $%+ +,(&'+'-55$77$)$5+

&1F5' B-))$ %2'+ G

Page 44: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*'+$% ,) -$,./0 !

VMC = V1+V2

2

VMD = V1 − V2

IMC = I1 + I2IMD = I1−I2

2

"##$%&

'( )*+,-(+ ./)01 /. 2.+0,3- 4- 5.11.6- "7& "89$ ##$:&$

VMD

IMD

VMC

IMC

=

1 −1 0 0

0 0 12

−12

12

12 0 0

0 0 1 1

V1

V2

I1I2

"##$:&

!"!#$%% &'()*%+,))(-(). /0 1,-2,34). -45)6.%70(

&( 89 &

;. ()02- <'=>:? ()@1 ,25)1- 4-1 AB#;1 .C.(+ @(- ,25D4.(3- 4DE(,- 5.0 /. E6@0- ##$>F$

<- 5/@1G /. 2-1@0- ()02.+,H- .@I *)0(-1 4@ AB#; 4),+ J+0- -K-3+@D- 1@0 @(- ,25D4.(3-

4- %? Ω -+ @(- 3.5.3,+D 4- >? µF 4),+ J+0- 5/.3D- -( -(+0D- 4- 3-/@,=3,$

!"#$% !"# $ %& ' ()*+,-

'- %& ' *./0/123 4)567./,0- 78-4 07 9)+5-3 -1. 4)91./.*2 :;2025-9.1 6711/<1 /:27*= >?/@!

!"AB!

!"#$ !C $ D70-*+1 :-1 4)56)179.1 :* %& '

LRSIL RRSIL CRSIL RsRSIL CsRSIL

5µH 50Ω 0.75µF 0.7Ω 10µF

'- +21-7* -1. *9 ,*1 E(! ()55- 9).+- 2.*:- 6)+.- 1*+ 0- 4)56)+.-5-9. <+2F*-9./-0 :*

Page 45: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

Vreseau

L_RSILI_L

L_RSIL

I_B2_RSIL I_B1_RSIL

C_RSIL

R_RSIL R_RSIL

C_RSILCs_RSIL

Rs_RSIL

Cs_RSIL

Rs_RSIL

I_s1_RSIL

I_s2_RSILV1_in

V2_in

I1_in

I2_in

I1_out

I2_out

V2_out

V1_out

!"#$% ""#$% & '()*+, -. /'"0 (1+2,34567 ,87( 6, 91:+7 ;<=$>!

?@?3A+7 73 79 2,:34(.647: -. B63:7C 91.? 21.819? (19?4-*:7: 6D4+2*-,9(7 -. :*?7,. (1++7

9.667# 07 ?()*+, -. /'"0 7?3 ,61:? ?4+264B* EF4G# ""#$HI#

I_L

I_B2_RSIL I_B1_RSIL

C_RSIL

R_RSIL R_RSIL

C_RSIL

2*L_RSIL

V1_in

V2_in

I1_out

I2_out

V2_out

V1_out

!"#$% ""#$H & '()*+, -. /'"0

J 2,:34: -. ?()*+, *67(3:4K.7C 91.? 21.819? 79 -*-.4:7 6, +,3:4(7 -. /'"0 E/'"0I

ELK# ""#MI#

I1out = −IL − IB1RSIL

I2out = IL − IB2RSIL

E""#NI

V1

V2

I1I2

out

=

1 0

0 1

−( 12∗ZLRSIL

+ 1ZCRSIL

+ZRRSIL

) 12∗ZLRSIL

12∗ZLRSIL

−( 12∗ZLRSIL

+ 1ZCRSIL

+ZRRSIL

)

[

V1

V2

]

in

E""#MI

! "#$%&' (' )'%*$%+!*,#-"

"6 7O4?37 26.?47.:? +1-A67? -7 ?1.:(7? -7 27:3.:5,3419? PLQ E37+21:76? 1. R:*K.793476?I

S0,5$!T# 07? 37()94K.7? -7 +1-*64?,3419 7O4?3,937? :721?793 ?.: 6, :72:*?793,3419 -7? ?1.:(7?

-7 27:3.:5,3419? 2,: -7? G*9*:,37.:? *K.48,6793? E-7 379?419 1. -7 (1.:,93I 73 67? ()7+49?

-7 2:12,G,3419 2,: -7? :*?7,.O -D4+2*-,9(7?# ;,9? 913:7 *3.-7C 91.? ,819? ()14?4 6, +1-*=

64?,3419 3@27 U 51437 914:7 V# P7 3@27 -7 +1-*64?,3419 9D, 2,? 21.: 5.3 -7 (1+2:79-:7 -D1W

Page 46: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*'+$% ,) -$,./0 !

"#$%&'(('() *'+ "'#),#-.)&$(+ /0,( 1$(%'#)&++',# +',* 2.&+ /' #')#.(+1#&#' *' 1$2"$#)'2'()

/' *0&()'#1$(('3&$( /' "*,+&',#+ +)#,1),#'+ +,# ,( 242' #5+'., ".# ,(' 2$/5*&+.)&$( +&2"*'

') 65(5#&7,' /' 18.1,(9 :'+ )#.%.,3 +0."",&'() +,# ,(' &/'()&;1.)&$( /' )<"' = -$&)' ($&#'

> ') ,( "#$)$1$*' /' 2'+,#' ./.")5 7,& "'#2') /' #'(+'&6('# ,( 2$/?*' 1$2"$+5 /' +$,#1'+

') /0&2"5/.(1'+ @A&69 BB9!CD EAFGHIJKKL!HM9 N(' O$&+ #'(+'&6(5J %, /, -,+ 1$()&(, /0.*&P

2'().)&$( ') /' *. )'##'J *' 2$/?*' +' 1$2"$#)' 1$22' *. +)#,1),#' 1$(+&/5#5' ') 65(?#'

*'+ 242'+ "'#),#-.)&$(+ /' 2$/' 1$22,( ') /' 2$/' /&Q5#'()&'*9 :'"'(/.()J *' 2$/?*'

(' "'#2') ".+ /0&/'()&;'# 7,'**'+ +$() *'+ +$,#1'+ /' "'#),#-.)&$(+ ., +'&( /' *. +)#,1),#'9

:' )<"' /' 2$/5*&+.)&$( '+) ,( '31'**'() $,)&* /0.(.*<+' ') "'#2') ,(' 5),/' . "$+)'#&$#&

/0,( +<+)?2' 6*$-.* 2.&+ (0'+) ".+ ./.")5 R *. "#5/&1)&$( /'+ "'#),#-.)&$(+ &()#&(+?7,'+ R

,(' +)#,1),#'9 S' "*,+J *' 2$/?*' '+) /5;(& "$,# ,( 1$(%'#)&++',# .%'1 ,(' 18.#6' /$((5'J

10'+) R /&#' "$,# ,( "$&() /' O$(1)&$(('2'()9 T$,# *0&(+).()J .,1,(' 5),/' (' "'#2') /'

"#5%$&# *. 2$/&;1.)&$( /, 2$/?*' +& *0$( 2$/&;' *. 18.#6'J /'+ )#.%.,3 /' #'18'#18' +$()

'( 1$,#+ +,# +$( ./.").)&$( @)8?+' /' U'('%&?%' A#.()V ., UWX*.-D9 Y. "#'2&?#' 5)."'

1$(+&+)' /$(1 R #'(+'&6('# 1'+ /&Q5#'()+ 5*52'()+9 Y. /5;(&)&$( /' *. +$,#1' .%'1 1' )<"'

/' 2$/?*' /'2.(/' ,(' 1'#).&(' #5Z'3&$( +,# *'+ 1$(/&)&$(+ /0&/'()&;1.)&$(9 Y'+ 2'+,#'+

/$&%'() 4)#' ./.")5'+ ') -&'( 18$&+&'+9

Z_s3

Z_s2Z_s1

I_Z_s2

I_Z_s1

I_Z_s3

I_S1

I_S2

I1_in

I2_in

V2_in

V1_in

!"#$% BB9!C [ F1852. /' *. +$,#1' /' "'#),#-.)&$(+ @)<"' =-$&)' ($&#'>D

\ ".#)&# /, +1852. 5*'1)#&7,'J ($,+ "$,%$(+ '( /5/,&#' *. 2.)#&1' /' *. +$,#1' /'

"'#),#-.)&$(+ @F]N^:XD@X79 BB9!HD9

I1in = IZs1 + IZs3 − IS1I2in = IZs2 − IZs3 − IS2

@BB9ID

[

1Zs1

+ 1Zs3

− 1Zs3

−1 0

− 1Zs3

1Zs1

+ 1Zs3

0 −1

]

V1

V2

I1I2

in

=

[

IS1IS2

]

@BB9!HD

S.(+ ($)#' 1.+J *05),/' 5).() .35' +,# *' 1$2"$+.() ') ($( *. +$,#1' /' "'#),#-.)&$(+J

($,+ (0.%$(+ /$(1 ".+ .""#$O$(/& *. "8.+' /0&/'()&;1.)&$(9 T$,# #5+$,/#' 1' "#$-*?2'J

($,+ .%$(+ /51&/5 /' O.&#' ,(' ./.").)&$( /0&2"5/.(1' '()#' *. +$,#1' /' "'#),#-.)&$( ')

*' ^FBY9 F$,+ *' )'#2' ./.").)&$( /0&2"5/.(1'J ($,+ "$,%$(+ )#$,%'# /',3 /5;(&)&$(+9 Y.

Page 47: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

"#$%&'#$ $() *+$ )$,-+&.*$ $+ /0$,)#&,&)/ "$#%$))1+) 234")&%&($# 0$ )#1+(5$#) 23*+$ "*&(6

(1+,$ /0$,)#&.*$ $+)#$ *+ /%$))$*# 7(4*#,$8 $) *+ #/,$")$*# /0$,)#&.*$ 7,-1#9$8 : $+ "#/($+,$

23*+$ 0&9+$ 2$ )#1+(%&((&4+; 03&%"/21+,$ 2* #/,$")$*# 24&) <)#$ /910$ = 03&%"/21+,$ ,1#1,6

)/#&()&.*$ 2$ ,$00$6,& "4*# />&)$# 0$( #/?$@&4+(A B1 2$*@&'%$ ($ #/5'#$ = 01 )-/4#&$ 2$( 4+2$(;

03121")1)&4+ 23&%"/21+,$ "$#%$) 23$%"<,-$# 01 +1&((1+,$ 23*+$ 4+2$ #/?/,-&$A C$))$ 2/D6

+&)&4+ >1 21+( 0$ ($+( 4E (1+( D0)#$ CFG; )4*)$( 0$( "$#)*#H1)&4+( "#42*&)$( "1# 01 (4*#,$

($ #$)#4*>$+) (*# 0$ IJKB $) 24+, (4+) )#1+(%&($( 1* #/($1*A L4*( 1>4+( 104#( 2/D+& 01

(4*#,$ 1>$, 0$( %<%$( &%"/21+,$( .*$ 0$ IJKB :

Zs1 = Zs2 = ZBRSIL

Zs3 = 2 ∗ ZLRSIL

7KKAMM8

B$( ,10,*0( 2/)1&00/( 2$ 03121")1)&4+ 23&%"/21+,$ 1&+(& .*3*+$ 1+10N($ (*# 03$@&()$+,$ 2$

,4*"019$ $+)#$ 0$( "$#)*#H1)&4+( 2$ %42$ ,4%%*+ $) 0$( "$#)*#H1)&4+( 2$ %42$ 2&O/#$+)&$0

(4+) "#/($+)/( 21+( 031++$@$ PA B1 ,4+,0*(&4+ /)1+) .*$ (& 0$( &%"/21+,$( 2$( H#1+,-$( 2$ 01

(4*#,$ (4+) (N%/)#&.*$( 104#( &0 +3N 1 "1( 2$ ,4*"019$ 2$ %42$A C$ .*& $() 0$ ,1( 21+( +4)#$

,4+D9*#1)&4+ 23121")1)&4+ 23&%"/21+,$A C$01 (&9+&D$ .*$ 031))/+*1)&4+ $+ %42$ ,4%%*+

($#1 4H($#>/$ "1# *+$ $@,&)1)&4+ $+ %42$ ,4%%*+ $) 2$ %<%$ "4*# 0$ %42$ 2&O/#$+)&$0 $)

.*$ 0$( %42$( "$*>$+) <)#$ (/"1#/( 21+( 01 (4*#,$A

B1 +4#%$ QR6MST 2/D+&) 2$( 91H1#&)( 231))/+*1)&4+ .*& 24&>$+) <)#$ #$("$,)/( $+ %42$

,4%%*+ $) $+ %42$ 2&O/#$+)&$0A C$"$+21+) +4*( +$ ,4++1&((4+( "1( 01 "1#) 2$ %42$

,4%%*+ $) 01 "1#) 2$ %42$ 2&O/#$+)&$0 21+( +4)#$ /)*2$; +4*( 1>4+( 24+, D@/ 2$( >10$*#(

&2$+)&.*$( "4*# 0$( 2$*@ %42$( 1D+ 234H($#>$# 031))/+*1)&4+ )4)10$A J& 034+ ($ #/5'#$ 1*@

/.*1)&4+( 2$ ,-1+9$%$+) 2$ H1($ 7F.A KKAU8 $) 1*@ #/(*0)1)( 2$ ,4*"019$ 2$ %42$ "4*# 01

(4*#,$ 2$ "$#)*#H1)&4+( 7F.A VAW8; ,$01 #$>&$+) = IS1 = −3 IS2A R+ D@$ 1#H&)#1&#$%$+) 01

>10$*# 2$ IS1 = M PA

!" #$%$#&'(" )* !' )+

X+ D0)#$ CFG "1((&5 Y,01((&.*$Z $() ,4+()&)*/ 23*+ H04, ,1"1,&)/ $) 23*+ H04, &+2*,)1+,$

7[&9AKA\8A B$ (4*(6(N()'%$ ,1"1,&)/( 2$>&$+) ,$0*& 2/,#&) 21+( 01 D9*#$ KKAM]A

Cx I_Cy1

I_Cy2

I_Cx

Cy2 Cy1

I1_in

I2_inV1_in

V2_inV2_out

I2_out

I1_out

V1_out

!"#$% KKAM] ^ J,-/%1 2$( ,1"1,&)/( C@ $) CN 2* D0)#$ CFG

Page 48: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*'+$% ,) -$,./0

!"#$ !!" # $%&'()* +'* ,%-%,./0*

Cx Cy

20µF 50 nF

1 -%)/.) +( *,203% 0&',/).4('5 67(* -7(876* '6 +0+(.)' &% 3%/).,' +( *7(* *9*/:3' ,%-%,./0

;<1=1>;?4" !!"@ >"

V 1in = V 1outV 2in = V 2outI1in = ICx + ICy1 + I1outI2in = −ICx + ICy2 + I2out

;!!"@A>

V1

V2

I1I2

in

=

1 0 0 0

0 1 0 0

jw(Cx+ Cy) −jwCx 1 0

−jwCx jw(Cx+ Cy) 0 1

V1

V2

I1I2

out

;!!"@ >

!"!#$%%% &' ()*+),-./ *-0.1/%23'

B6 -'(/ +0C6.) &' ,73-7*%6/ 3%D60/.4(' ,733' (6 4(%+).-E&' ;F.D" !!"@G> +76/ &%

3%/).,' .3-0+%6,' '*/ +7660' +%6* &H04(%/.76 !!"@I"

I1_in

I2_in

V1_in

V2_in

I1_out

I2_out

V2_out

V1_out

%&'()$ !!"@G # J,203% D060)%& +( ,73-7*%6/ 3%D60/.4(' (6.4('

[

V1

V2

]

=

[

Z11 Z21

Z12 Z22

] [

I1I2

]

;!!"@I>

=%) +0C6./.765 (6' 3%/).,' .3-0+%6,' '*/ *930/).4(' +H7K Z12 LZ21" B6 -'(/ '6*(./'

+0C6.) &% 3%/).,' +' /)%6*M')/ +( ,73-7*%6/ 3%D60/.4(' ;!NOP<> +' &% 3%6.:)' *(.8%6/' Q

V1

V2

I1I2

in

=

1 0 Z11 Z12

0 1 Z12 Z22

0 0 1 0

0 0 0 1

V1

V2

I1I2

out

;!!"@R>

Page 49: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

"#$% &'()$* +#,#-#./* 01/20$&+(2&*3 2#$4 (5#24 0672/ -* 4&'68( %6-$&+(2+ &#%%*4,#29

0(2+: ; ,(%+/% 0* &*++* %*,%64*2+(+/#23 2#$4 (5#24 06+*%8/26 -*4 5(-*$%4 0*4 /8,60(2&*4

*2 <#2&+/#2 0*4 ,(%(8=+%*4 .6#86+%/)$*4 *+ 8(.26+/)$*4: >*4 0/?6%*2+*4 .%(20*$%4 4#2+

-/4+6*4 &/90*44#$4:

w = 2π f #@ < 6+(2+ -( <%6)$*2&*:

µrhp A -( ,*%86(B/-/+6 %*-(+/5* 0$ 8(+6%/($ 8(.26+/)$* C'($+* ,*%86(B/-/+6D:

µrbp A -( ,*%86(B/-/+6 %*-(+/5* 0$ 8(+6%/($ 8(.26+/)$* CB(44* ,*%86(B/-/+6D:

µ0 A -( ,*%86(B/-/+6 0$ 5/0*:

S A -( 4*&+/#2 8#E*22* 0$ +#%*

l A -( -#2.$*$% 8#E*22* 0$ +#%* C'($+* ,*%86(B/-/+6D

N A -* 2#8B%* 0* 4,/%*4:

Ent A -1*2+%*<*%:

"#$% -16+$0* 4*-#2 -( 2#%8* FG9HIJ3 #2 $+/-/4* -* &'(2.*8*2+ 0* %6<6%*2+/*- 0672/ ,(%

-16)$(+/#2 KK:L: F(24 -( B(4* MNOMF3 -( 8(+%/&* 0$ &#8,#4(2+ 8(.26+/)$* 0*5/*2+ (-#%4 A

[

VMD

VMC

]

=

[

Z11 − 2Z12 + Z22Z11−Z22

2Z11−Z22

2Z11+2Z12+Z22

4

] [

IMD

IMC

]

PKK:HIQ

;$ 5$ 0* &*++* 8(+%/&*3 #2 ,*$+ 0#2& 0672/% -1/8,60(2&* 0* 8#0* 0/?6%*2+/*- PZMDQ

*+ -1/8,60(2&* 0* 8#0* &#88$2 PZMCQ PR):KK:HSQ:

ZMC = Z11+2Z12+Z22

4

ZMD = Z11 − 2Z12 + Z22PKK:HSQ

"(% (/--*$%43 2#$4 ,#$5#24 0672/% $2 &#*T&/*2+ 0* &#$,-(.* *2+%* 8#0*3 2#+6 kmd PR):

KK:HUQ:

kmd =Z11−Z22

2√Z2

MC+Z2

MD

PKK:HUQ

!"#$% KK:HV W X(%/(+/#2 0$ &#*T&/*2+ 0* &#$,-(.* 0* 8#0* *2 <#2&+/#2 0* Y

Page 50: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*'+$% ,) -$,./0 !

"# $%#&$'#() #*) +,-#(+.() /

0 +# 1. +'**23,)4'# +5 $%3-%*.() *54 $#* +#56 1'7(#*8 9%5* (%33#4%(* :6: 1. ;4.$)'%(

+# +'**23,)4'# +5 $%3-%*.() <Z11 = xZ22=8 "# $%#&$'#() #*) (%( (51 5('>5#3#()

#( $.* +# +'**23,)4'# +5 $%3-%*.()? >5#1 >5# *%') 1# $%#&$'#() +# $%5-1.7# #()4# 1#*

#(4%51#3#()*8 @# -15*? '1 #*) A%4(, #()4# BC #) C8

0 +5 $%#&$'#() +# $%5-1.7# #()4# 1#* #(4%51#3#()* *54 1# (%2.5 3.7(,)'>5#? (%), k12<-.4 +,D(')'%( Z12 = k12

√Z11Z22=8

!"#$% EE8FG 0 H.4'.)'%( +5 $%#&$'#() +# $%5-1.7# +# 3%+# #( ;%($)'%( +# ICF

J( 7,(,4.1? 1%4*>5# +#56 #(4%51#3#()* *%() 4,.1'*,* *54 5( 3K3# (%2.5 3.7(,)'>5#? (%5*

%A)#(%(* +#* $%#&$'#()* +# $%5-1.7# -4%$L#* +# C #( M.1#54 .A*%15#8 @.(* $# $.* +# D754#?

(%5* -%5M%(* 4#3.4>5#4 >5# *' 1# $%#&$'#() +# 3%+# #*) (%( (51? *. M.1#54 *#4. .5**' )4N*

-4%$L# +# C #( M.1#54 .A*%15#8

!"!#$%& '( )*)+,-( ./0#1/

O.'()#(.() >5# (%5* .M%(* )%5)#* 1#* 3.)4'$#* +# )4.(*;#4) +#* $%3-%*.()* +5 *2*)N3#?

(%5* +#M%(* 1#* 3#))4# #( $.*$.+# $%33# '(+'>5, *54 1. D754# EE8CG8

[

V1

V2

]

RSIL

= [[Source] [Capa]−1 [Induc]−1 [RSIL]]−1

[

Is1Is2

]

<EE8CP=

9%5* -%5M%(* +%($ +,D('4 V 1NRSIL#) V 2NRSIL

>5' *%() 1#* )#(*'%(* .56 A%4(#* +# 1.

4,*'*).($# +5 QRES <J>8EE8FG=8 J(*5')#? (%5* -%5M%(* 4#M#('4 +.(* 1. A.*# O"TO@ 74U$#

V 1:,>5.)'%( EE8!8

V 1NRSIL=

V 1RSIL ZRRSIL

ZRRSIL+ZCRSIL

V 2NRSIL=

V 2RSIL ZRRSIL

ZRRSIL+ZCRSIL

<EE8FG=

Page 51: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

!"!# $%&'(%)'*+ (, &% -'., ,+ /01%)'*+. 2%3 1+ &*4'#',& #'3#1')

"#$ %& '()*#&) $+,)& (-)*,.)& /0,)*-*&11&2 $+.3 0'+$3 -4+*3* %& -+/50)&) 1&3 )(3.1,0,3

+6,&$.3 50) -&,,& /(,4+%& 0'&- -&.7 +6,&$.&3 50) .$& 3*/.10,*+$ 3+.3 1& 1+8*-*&1 -*)-.*,

9:;<=> 9?*8@ AA@BC>@ D+.3 0'+$3 -4+*3* %& -+/50)&) 1& -03 %& )(E()&$-&2 -F&3, G %*)& 1& #1,)&

-+/51&, ,&1 H.& )&5)(3&$,( 3.) 10 #8.)& !"! #$ %$ &'( )*($+,-,(. /0$( 10$%0/( %-+2&') /0(

*3)2,$)'( 4-,)232'++'(!

!"#$% !56 7 8041-)-2(0/ '/,)' +' +09232'+ 32)3$2, ', +:*3)2,$)' 4-,)232'++'

!" #$%&'(')*$+ ,-* ,)./(-+0-* 0$&$1$2)-*

!"!# $% &'()*#+% ,% -',%

;0$( -%0/( %$ <$' &-/( +' 3-( &:$/ 30410(-/, 4-9/*,2<$' &2((=4*,)2<$'. /0$( -%0/(

+:-11-)2,20/ &:$/ ,')4' &' 30$1+-9' &' 40&' &-/( +- >-(' ?8@?A BC<! !6DE! #F/ &'

&*,')42/') +:2/G$'/3' &' 3' H-3,'$) ($) +'( 1')H0)4-/3'( &$ 30410(-/, $/2<$'. /0$( -%0/(

&*32&* &' )*-+2(') +:*,$&' ($2%-/,'! A-/( $/ 1)'42') ,'41(. /0$( -%0/( FI* +'( 1')H0)4-/3'(

42/24-+'( J -,,'2/&)' BC<! !55E! + (:-92, &$ 30410(-/, &*F/2 1-) +' 3-K2') &'( 3K-)9'(

L2(1-/0MN$2O- BP->+' !6E! Q'( 2/&$3,-/3'( BQE (0/, ,)-&$2,'( '/ 241*&-/3' BRE 1-) +-

)'+-,20/ BC<! !56E 0S H '(, +- H)*<$'/3' '/ BLOE!

Z = 2π fL B !56E

# 1-),2) &$ (=(,T4' &:*<$-,20/( !55. /0$( 10$%0/( &*F/2) +'( %-+'$)( &' Z11. Z12. Z22

'/ H0/3,20/ &' kmd ', &0/3 +- 4-,)23' &$ 30410(-/, 4-9/*,2<$'!

ZMC = Z11+2Z12+Z22

4

ZMD = Z11 − 2Z12 + Z22

kmd

L2MC + L2

MD = L11−L22

2

B !55E

Page 52: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'(')*$+ ,-* ,)./(-+0-* 0$&$1$2)-* !

"#$%& ' () *+,& &- %),%).& .&, *)/#+%&, .& /#)-,0&#/ .1 ,2,/3*&4 -51, 65175-, )+-,+

.89-+# (&, /&-,+5-, .& *5.& %5**1- &/ .& *5.& .+:8#&-/+&( &- 05-%/+5- .& kmd; <=875(1/+5-

.& %&, /&-,+5-, &,/ #&6#8,&-/8& ,1# (&, >#)6?+@1&, %+A.&,,51, BC+>; DD;EE &/ C+>; DD;E F;

!"#$% DD;EE G D-H1&-%& .1 %516()>& .& *5.& ,1# () /&-,+5- .& *5.& %5**1-

!"#$% DD;E G D-H1&-%& .1 %516()>& .& *5.& ,1# () /&-,+5- .& *5.& .+:8#&-/+&(

I () (&%/1#& .& %&, %51#J&,4 -51, &- .8.1+,5-, @1& (& %516()>& .& *5.&4 %=&,/ ' .+#&

(=)1>*&-/)/+5- .1 %5&K%+&-/ kmd4 ) 651# &:&/ .=)1>*&-/&# (&, /&-,+5-, .& *5.& %5**1-

&/ .& *5.& .+:8#&-/+&(4 &/ %& ,1# /51/& () 6()>& .& 0#8@1&-%&; L& @1+ ) 651# %5-,8@1&-%&

.& .8>#).&# (&, 6&#05#*)-%&, .1 %5*65,)-/; <=8/1.& ) 8/8 %5-.1+/& )1,,+ )7&% 1-& ,51#%&

@1+ -& >8-3#& @1& .&, 6&#/1#J)/+5-, .& *5.& %5**1- &/ @1& .&, 6&#/1#J)/+5-, .& *5.&

.+:8#&-/+&(4 (&, #8,1(/)/, #&,/&-/ +-%?)->8,; <) .+,,2*8/#+& .1 %5*65,)-/ -=&,/ .5-% 6), 1-

%#+/3#& 0)75#)J(& 651# (& %5*65,)-/ 1-+@1&;

Page 53: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

!"!# $%&'(&&%)* &(+ ,-& .)/),)0%-& +-.-*(-&

!"!#$% &'()*+*%,'- ./, 0')'1'2%/,

"#$ %& '()*+,&, -&. %/01,&$2&. 2(*(-(3/&.4 $(5. +6($. '7&,'71 8 .+6(/, -+95&--& +5,+/2

-& *-5. *&2/2 6(-5)& *(5, %&. *&,:(,)+$'&. )/$/)+-&. #;1&.< =(5. $(5. .())&. +**5>1.

.5, 2(52&. -&. 12+*&. *,1'1%&$2&. %1',/2&. %+$. '& '7+*/2,& +#$ %& '($.2,5/,& -& *,(3,+))&

%& )/$/)/.+2/($ *(5, '7+95& 2(*(-(3/&<

&'-,0+340%'- ./, (*0+%4/,

? =(5. +6($. %1#$/ 5$ )+21,/+5 )+3$12/95& *+, 5$& '(5,@& &$ +,'2+$ AB9< CC<DE<

F&. %&5; *+,+)G2,&. %& '& )(%G-& .($2 H Js -+ *(-+,/.+2/($ 8 .+25,+2/($ &2 µri -+

*&,)1+@/-/21 /$/2/+-& %5 )+21,/+5< =(5. +6($. '7(/./ %& :+/,& -I125%& +6&' 5$ +--/+3&

$+$(',/.2+--/$ %& '+,+'21,/.2/95&. H JsJ K<L M &2 µri = 30000< N&. '+,+'21,/.2/95&.

'(,,&.*($%&$2 +5 )+21,/+5 )+3$12/95& 52/-/.1 *(5, -I/$%5'2+$'& %& )(%& '())5$

%5 '()*(.+$2 %& ,1:1,&$'&< O$& 125%& %& -+ 6+,/+2/($ %& -+ *&,)1+@/-/21 + 121 )&$1&

&2 -&. ,1.5-2+2. .($2 *,1.&$21. .5, -+ #35,& CC<LP<

? =(5. +6($. &$.5/2& /$/2/+-/.1 -&. 3,+$%&5,. 31()12,/95&. A.&'2/($4 -($35&5,4 $()@,&.

%& .*/,&.E< F&. 6+-&5,. %&. 3,+$%&5,. /$/2/+-&. ($2 121 %12&,)/$1&. *+, 5$& 125%&

*,1+-+@-& .5, -&. *&,:(,)+$'&. 8 +22&/$%,&< Q,R'& 8 '&. 6+-&5,.4 $(5. +6($. %12&,)/$1

-&. '(&S'/&$2. Z11 &2 Z22 %& -+ )+2,/'& C=TON AB9< CC<KPE

? U+, +/--&5,.4 $(5. +6($. '7(/./ -& '(&S'/&$2 %& '(5*-+3& &$2,& -&. %&5; @(@/$+3&.

k12JV<WW< N& '7(/; '(,,&.*($% 8 %&5; @(@/$+3&. 2,G. @/&$ '(5*-1.4 '& 95/ &.2 -& '+.

.5, %&. $(>+5; 2(,/95&. '())& 2(52&. -&. 2(*(-(3/&. 95& $(5. +6($. '7(/./&.< N&22&

6+-&5, *&,)&2 %& %12&,)/$&, -&. '(&S'/&$2. Z12 &2 kmd %& -+ )+2,/'& C=TON AB9<

CC<KPE<

? =(5. +6($. %($' *5 %12&,)/$&, -+ 2&$./($ +5; @(,$&. %5 XYCF *+, -& *,(%5/2 %&.

)+2,/'&. %& 2,+$.:&,2 *5/.95& 2(5. -&. *+,+)G2,&. 12+/&$2 %1#$/.<

? =(5. +6($. %1#$/ '())& '($2,+/$2& 95& -+ 2&$./($. +5; @(,$&. %5 XYCF %& '7+95&

2(*(-(3/& %&6+/2 Z2,& /$:1,/&5,& 8 '&--& %5 '()*(.+$2 %& ,1:1,&$'& *,1.&$21 %+$. -+

.&'2/($ L %& '& '7+*/2,& &2 $(5. +6($. '7(/./ -+ :($'2/($ (@[&'2/: %5 )(%G-& '())&

12+$2 -& 6(-5)& +**+,&$2 %& '7+95& '()*(.+$2<

56,310*0 ./, (%-%(%,*0%'-,

" *,&)/G,& 65&4 $(5. ,&2,(56($. 5$ ,1.5-2+2 -(3/95&< " .+6(/, 95& *-5. -& 6(-5)& &.2

3,+$%4 *-5. -+ 2(*(-(3/& &.2 *&,:(,)+$2&4 'I&.2 8 %/,& 95& -&. 2&$./($. +5; @(,$&. %5 XYCF

%/)/$5&$2< C- $(5. :+52 %($' 2,(56&, 5$ '()*,()/. &$2,& *&,:(,)+$'& &2 6(-5)&< NI&.2

*(5,95(/ $(5. +6($. '7(/./ %& *,1.&$2&, -&. ,1.5-2+2. .(5. :(,)& %& '(5,@&. %& U+,&2(

,&*,1.&$2+$2 -& 6(-5)& +**+,&$2 %& '7+95& '()*(.+$2 &$ :($'2/($ %& -+ 2&$./($ +5; @(,$&.

%5 XYCF A\N &2 \TE< F&. 2&$./($. ($2 121 *,/.&. 8 -+ :,195&$'& %& KPV ]^_< N&22& 6+-&5,

'(,,&.*($% +5 '&$2,& %& -+ *-+3& :,195&$2/&--& &2 + -I+6+$2+3& %& ,&$%,& 6/./@-& -I&0&2 %5

'(5*-+3& %& )(%& .5, -+ 2(*(-(3/& %/..>)12,/95& A`/3< CC<LL4 `/3< CC<L E< F+ 6+,/+2/($ %&.

2&$./($. +5; @(,$&. %5 XYCF &.2 %a& 8 -I+53)&$2+2/($ (5 -+ %/)/$52/($ %5 $/6&+5 %&

2&$./($ %5 '+. %& ,1:1,&$'&4 'I&.2 8 %/,& %5 $/6&+5 %& *&,:(,)+$'& )/$/)+- #;1 .5, -&

Page 54: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'(')*$+ ,-* ,)./(-+0-* 0$&$1$2)-* !

"#$ %& '()('&*"&+ ,#*$ *-.'& (./%&0 *-/$ 1-/2-*$ /* "-34-$#*. 5/6 $-6. #/$$6 &7"#"&

&* 82.'#9& 4-/' 2&$ %&/: 3-%&$0 ; %()#/. %& )#6'& 2<(./%& %</*& #4426"#.6-* 4'("6$&+ =-/$

#1-*$ %-*" %(8*6 /*& .&*$6-* 3->&**& *-'3(& ?VRSILmoyennorme@ #6*$6 5/</* 1-2/3& *-'3(

?V olumenorme@ #8* %& 4-/1-6' "-34#'&' %& 3#*6A'& (5/6.#B2& "C#5/& .-4-2-96& ?D5+ EE+F @+

VRSILmoyennorme=

VMCVMCmax

+VMD

VMDmax

2

V olumenorme =V olapparent

V olapparentmax

?EE+F @

!"#$% !"# $ %&'()* +,,+-*./ 0( 1'/-* *. 2&.3/4&. 0* '+ /*.54&. +(6 7&-.*5 0( 89 :

!"#$% !"; $ %&'()* +,,+-*./ 0( 1'/-* *. 2&.3/4&. 0* '+ /*.54&. +(6 7&-.*5 0( 89 :

<µri=>???@

9(- '* A-+,B4C(* 0* 3&(-7*5 .&-)+'45D*5 <E4A! !"#@F .&(5 3&.1-)&.5 C(* '+ /&,&'&A4*

7+5D* 5(- '+ 0455G)D/-4* */ 0&.3 '* 3&(,'+A* 0* )&0* .H*5/ ,+5 '+ ,'(5 2+I&-+7'*! J* 3*//*

1A(-*F .&(5 ,&(I&.5 -*/*.4- 0*(6 /&,&'&A4*5 4./D-*55+./*5 ,&(- '+ -D+'45+/4&. 0( 3&),&5+./

Page 55: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%& '( )* +$,$)$-%( '. /$0,$1*2+ 0*-23+%4.( .2%4.(

"#$%"& ' (& )*+,*-.#/ 012&(*,,1 ,.3 4$-,.#*56"$7. &/ (& )*+,*-.#/ 8 &#/3&9&3 &/ +./13$."

"#$%"&:

;*++& &<,($%"1 0.#- (& 01="/ 0& )& ,.3.>3.,?&@ #*"- .2*#- 9.$/ "#& 1/"0& )*+,(1+&#5

/.$3& &# 9.$-.#/ 2.3$&3 (. ,&3+1.=$($/1 $#$/$.(& 0" +./13$." +.>#1/$%"& %"$ 1/.$/ 0& A!!!!: B)$

,*"3 "#& ,&3+1.=$($/1 0& C!!! DE$>: BB:FGH@ )*33&-,*#0.#/ 8 (. ,&3+1.=$($/1 ).()"(1& ,*"3

(& ,3*/*/I,& 0$--I+1/3$%"&@ #*"- #*/*#- (& +J+& *303& 0&- )*"3=&- &/ (. #*#5)*#)"33&#)&

0" ,3*/*/I,& .2&) (& )*",(.>& 0& +*0&:

!"!#$%% &'($)%*+,-%.,,+*+,/ )0 1.*2.-3,/ *34,(/%50+

6$ (K*# -K$#/13&--& 0.#- "# ,3&+$&3 /&+,- ."< 0$+&#-$*#- *=/&#"&- DL.=(& BB: &/ BB:GH@

#*"- )*#-/./*#- %"& ,*"3 0&- 2*("+&- .,,.3&#/- -$+$(.$3&- D0& (K*303& 0& 3 cm3H@ (& )*+5

,*-.#/ 4$-,.#*56"$7. &-/ 0& 9*3+& ,("/M/ )I($#03$%"& D0$.+N/3& &</13$&"3 ,("- ,&/$/ %"&

(. ?."/&"3H /.#0$- %"& (& )*+,*-.#/ 8 &#/3&9&3 &-/ ,("/M/ 0& 9*3+& .,(./$&: O.3 .$((&"3-@

#*"- 3&+.3%"*#- %"& (&- 0&"< ,3*/*/I,&- -&+=(&#/ .2*$3 0& +&$((&"3&- ,&39*3+.#)&- %"&

(& )*+,*-.#/ 0& 31913&#)& D2*$3 (&- P>"3&- BB:FQ &/ BB:FRH ." +*$#- &# +*0& )*++"#: S&-

31-"(/./- -*#/ 0*#) &#)*"3.>&.#/-:

!"#$% BB:FQ T ;*+,.3.$-*# 0&- ,&39*3+.#)&- 0& (. /*,*(*>$& 4$-,.#*56"$7. .2&) (& ).-

0& 31913&#)&

&'()% BB: T S& )*+,*-.#/ 012&(*,,1 ,.3 4$-,.#*56"$7.

DextMC DintMC HautMC DextMD DintMD HautMD Nspires

D++H D++H D++H D++H D++H D++H

C:!G A: A:A C:!A A: C:A G

Page 56: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'(')*$+ ,-* ,)./(-+0-* 0$&$1$2)-* !

!"#$% ""#$% & '()*+,+-.(/ 01. *1,2(,)+/31. 01 4+ 5(*(4(6-1 +713 1/5,121, +713 41 3+. 01

,828,1/31

&'()% ""#9 & :1 3()*(.+/5 ; 1/5,121, 15 )+58,-+< </-=<1

Dext(mm) Dint(mm) Haut(mm) Ent(mm) Nspires

$$ !9 9#> ?#! !9

!"!#$%%% &'()*' +, -. /0+(-%1.'%0& +2 30/40)',/,&' +2 /.'()%.2 /.5&('%62,

+.&1 -. /0+(-%1.'%0& 7181'9/,:

@,A31 +< )(0B41 C.D.5B)1E /(<. +7(/. *< 08F/-, </ 1/7-,(//1)1/5 3())</ *(<,

3()*+,1, 41. 0-G8,1/51. 5(*(4(6-1. 01 3()*(.+/5 )+6/85-=<1 </-=<1# '1551 85<01 /(<. +

*1,)-. 0H-01/5-F1, 41. 01<I 5(*(4(6-1. 41. *4<. *1,2(,)+/51.# '1*1/0+/5J 0+/. 4+ 08F/-5-(/

0< )+58,-+< )+6/85-=<1J /(<. /(<. .())1. 3(/51/58. 0H</1 08F/-5-(/ K+.-=<1 +713 </1 4(-

1/ +,35+/61/51# L+/. 41 F45,1 3()*415J 41 )+58,-+< )+6/85-=<1 .1,+ .(<)-. ; 01. 3(/5,+-/51.

.<, </1 4+,61 *4+61 01 2,8=<1/31 )+-. +<..- ; 01. 3M+)* 01 *(4+,-.+5-(/ 5,B. 0-G8,1/5. 1/5,1

41 )(01 3())</ 15 41 )(01 0-G8,1/5-14# "4 1.5 0(/3 /831..+-,1 01 *,1/0,1 1/ 3()*51 01

)+/-B,1 *4<. F/1 41. 3+,+358,-.5-=<1. )+6/85-=<1. 0< )+58,-+< 0+/. 4+ )(084-.+5-(/# '1551

/(<71441 0(//81 1.5 2+3-41)1/5 -/586,+K41 ; 4+ )(084-.+5-(/ 1I-.5+/51 *<-.=<H-4 .<N5 01

3()*4851, 41 )(0B41 0< )+58,-+< 0+/. 4+ )+5,-31 01 5,+/.21,5 0< 3()*(.+/5 )+6/85-=<1

15 01 4H-)*48)1/51, 0+/. 4+ )(084-.+5-(/ 1I-.5+/51#

Page 57: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 58: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&' (((

!"#$%&'(%!) "* +!,-!&')( ,'.)#(%/*0

!""#$%&

!"#$%&'()*+($, %- .$/0$)*,+ /*1,&+(2-3

!!! " # $%& '#(#')*(+&)+,-%& .%& /#)*(+#-0 /#12*)+,-%& 33

!!! " #4+ 56/76()%/%2) 8(*,-%2)+%9 33

!!! " #4++ !2:-%2'% .% 9# 769#(+&#)+62 3;

!456$(7 %- /$%8'3 0$-9 '3 .$/0$9+3/3,+ :9&2-3,+(3' !

!!! < # =%7(*&%2)#)+62 *9%')(+,-% *,-+>#9%2)% ? /6.@9%& 196A#-0 3B

!!! < A C6.@9% .% '+('-+)& /#12*)+,-%& *,-+>#9%2)& 3D

!;<+('()*+($, %- /$%8'3 .$/0$)*,+ /*1,&+(2-3 %*,) '* /$%&'()*=

+($, )>)+8/3 !"

!!! E # F(+&% %2 '6/7)% .- '6/76()%/%2) 8(*,-%2)+%9 ;G

!!! E #4+ C6.*9+&#)+62 .%& '#7#'+)*& Cx %) Cy ;"

!!! E #4++ H0%/79% .- '+('-+) (*&62#2) $5 ;"

!!! E #4+++ C6.*9+&#)+62 /#12*)+,-% ? 9%& +2.-')#2'%& C5ICJ ;3

!!! E A F(+&% %2 '6/7)% .% 9# 769#(+&#)+62 &-( 9% )(#K%) .% :-0 .% /6.% .+L*(%2)+%9 ;B

!? @(/-'*+($, %- :('+93 5A# .$/0'3+ !#

!"#$!

! "#$%&'(! %()*!+'!, -$+* .+! %(!/&0(! %$('&!, 1!* "$($"')(&*'&2.!* &/%3('$+'!* -!*

/$')(&$.4 /$5+)'&2.!* 6 %(!+-(! !+ "3/%'! %3.( .+ "3/%3*$+' .'&1&*) !+ 71'($5! *.(

.+! 1$(5! %1$5! -! 8()2.!+"!9 :&;)(!+'* '<%!* -! /3-)1&*$'&3+ *3+' %()*!+')* $=!" 1!.(*

$=$+'$5!* !' 1!.(* &+"3+=)+&!+'*9 >! /3-01! 5<($'!.(?"$%$"&') (!'!+. !*' !+*.&'! -)?

'$&11)9 >@&+')(A' -! 1$ %(&*! !+ "3/%'! -!* =$(&$'&3+* 8()2.!+'&!11!* !' 1!.( &+B.!+"! *.(

1!* %!(83(/$+"!* -. 71'(! !*' /&* !+ )=&-!+"!9

Page 59: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

!" #$%&'()*+($, %- .$/0$)*,+ /*1,&+(2-3

!"!# $%& '#(#')*(+&)+,-%& .%& /#)*(+#-0 /#12*)+,-%&

!"#$ %& '"()& (& #*+)& ",,%-'"+-*#. %& '*/,*$"#+ /"0#1+-23& &$+ $*3/-$ 4 (&$ ,&)+3)5

6"+-*#$ $3) 3#& %")0& ,%"0& (& 7)123&#'&$ 8(& 23&%23&$ 9:; 4 %" '&#+"-#& (& <:;= &+ 4

3# '>"/, (& ,*%")-$"+-*#. Hp. ,*3) %&$ ,&)+3)6"+-*#$ '*#+&#"#+ 3#& '*/,*$"#+& '*#+-#3&

&# '*3)"#+ 8,&)+3)6"+-*#$ (& /*(& (-?1)&#+-&%=@ A&$ '")"'+1)-$+-23&$ *#+ 3# &?&+ $3) %&

'*/,*)+&/&#+ (3 /"+1)-"3 /"0#1+-23&@ B #*+)& #-C&"3. #*3$ "C*#$ (1'-(1 (D-#+10)&) %&$

'>"#0&/&#+$ (& ,)*,)-1+1$ (&$ /"+1)-"3E. (3&$ "3E '*#(-+-*#$ (D3+-%-$"+-*#. "F# (& ,)1(-)&

,%3$ F#&/&#+ %& '*/,*)+&/&#+ (3 '*/,*$"#+ /"0#1+-23&@

!"!#$% &'()'*+,(,-+ .*/01,-+%,2

A*//& (1+"-%%1 ("#$ %& '>",-+)& GG. %" ,&)/1"6-%-+1 '>3+& )",-(&/&#+ "C&' %D"30/&#5

+"+-*# (& %" 7)123&#'&@ A&++& C")-"+-*# &$+ %-1& 4 %" ')1"+-*# (& '*3)"#+$ -#(3-+$ ("#$ %&

/"+1)-"3@

!"#$% GGG@H I J")-"+-*# (& %" ,&)/1"6-%-+1 &# 7*#'+-*# (& %" 7)123&#'&

K&$ /&$3)&$ (& ,&)/1"6-%-+1 *#+ 1+1 )1"%-$1&$ $3) 3# +*)& (D"%%-"0& #"#*')-$+"%%-# )&'3-+

$*3$ '>"/, +)"#$C&)$& 8L*)& <A= &+ 3# +*)& (& ,*3()& (& 7&) 8L*)& <!= (*#+ %&$ (-/&#$-*#$

$*#+ (*##1&$ ("#$ %& +"6%&"3 GGG@H@

&'()% GGG@H I !-/&#$-*#$ (&$ -#(3'+"#'&$ (& F%+)"0&

DextMC(mm) DintMC(mm) HautMC(mm) NMCspires LMC(mH)

MN MO P@M HQ HP@P

DextMD(mm) DintMD(mm) HautMD(mm) NMDspires LMD(µH)

RO MO HO HQ MON

S3) %&$ (&3E '*3)6&$ (& ,&)/1"6-%-+1 8T-0@ GGG@H=. #*3$ ,*3C*#$ )&/")23&) 23& %&$

/"+1)-"3E 6"$$&$ ,&)/1"6-%-+1$ $*#+ ,%3$ $+"6%&$ &# 7)123&#'&@ U# &?&+. ,*3) '& +V,& (&

/"+1)-"3. (3 7"-+ (& %&3)$ $+)3'+3)&$ &# ,*3()&$ '*/,"'+1&$. %&$ &?&+$ (&$ '*3)"#+$ -#(3-+$

Page 60: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&' () *%(+,- .%)/ ,- 0%*.%/1-*-21 3/45)-21&-, !

"#$% &'"'()*" + ,*" -./01*$2*" 3)1" /)*&/*"4 56 3*.-#.76$2* ,1 2#73#"6$% 1$'01* /%6$%

)'/* + )6 &6)*1. ,* )8'$,12%6$2* ,* 9)%.6:* *% ,#$2 + )6 3*.7/6(')'%/; "#$ 2#73#.%*7*$%

-./01*$%'*) ,#'% ,#$2 $/2*""6'.*7*$% <%.* 3.'" *$ 2#73%*4

!"!#$%% &'()&*) +) ,# -.,#/%0#1%.&

5#."0181$ 76%/.'61 76:$/%'01* (#('$/ *"% *=2'%/ 36. 1$ 2#1.6$% 2#$%'$1; ') *"% "#17'"

+ 1$ 2>673 ,* 3#)6.'"6%'#$ Hp4 ?6$" )* 26" ,1 2#73#"6$% 76:$/%'01* 1$'01*; %#1" )*"

76%/.'61= 1%')'"/" "1. )*" %.6@*% ,* A1= ,* 7#,* ,'B/.*$%'*) "#$% "#17'" + 1$ 2>673 ,*

3#)6.'"6%'#$4 C1. )6 9:1.* DDD4E; $#1" 3#1&#$" 2#$"%6%*. 01* 3)1" )* 2>673 ,* 3#)6.'"6%'#$

*"% :.6$,; 3)1" )6 3*.7/6(')'%/ 2>1%*4 F* 3>/$#7G$* *"% 36.%'21)'G.*7*$% &'"'()* "1. )*"

76%/.'61= + -6'()* 2>673 2#*.2'%'- H2#77* )*" 6))'6:*" $6$#2.'"%6))'$" .*3./"*$%/" "1. )6

9:1.* DDD4E HI#.* JFKK4 L$ *B*%; 1$ -6'()* 2>673 ,* 3#)6.'"6%'#$ "1M% + "6%1.*. )* 76%/.'61

*% ,#$2 + -6'.* 2>1%*. )6 3*.7/6(')'%/4 ?6$" )* 26" ,*" 6))'6:*" $6$#2.'"%6))'$"; )* 2>673

2#*.2'%'- *"% ,* )8#.,.* ,* )6 ,'N6'$* ,8673G.* 36. 7G%.* %6$,'" 01* 3#1. ,*" 3#1,.*" ,*

-*.; ') *"% ,* )8#.,.* ,* )6 2*$%6'$* ,8673G.* 36. 7G%.* OF#1PQ;R#N!ST4

!"#$% DDD4E U D$A1*$2* ,* )6 3#)6.'"6%'#$ "1. )*" 2#1.(*" ,* 3*.7/6(')'%/ .*)6%'&* *$

-#$2%'#$ ,* )6 -./01*$2* V µr W 36.%'* ./*))*; µi W 36.%'* '76:'$6'.*

X9$ ,* $* 3)1" $/:)':*. 2*" ,*1= -62%*1." '$A1*$%" "1. )*" 3.#3.'/%/" ,1 76%/.'61

76:$/%'01* *% ,#$2 )6 3*.-#.76$2* ,1 2#73#"6$% 1$'01*; $#1" ,*&#$" )*" 3.*$,.* *$

2#73%* ,6$" $#%.* 7#,/)'"6%'#$4

!" #$%&' () *%(+,- .%)/ ,- 0%*.%/1-*-21 3/45)-21&-,

5* (1% ,* $#%.* 7#,G)* *"% ,* .*3.#,1'.* )* 2#73#.%*7*$% ,* $#%.* 2#73#"6$% 76:$/Y

%'01* &'" + &'" ,* )6 -./01*$2* *% ,* )6 3#)6.'"6%'#$4 Z#1" 3./"*$%#$" ,6$" )*" 36.6:.63>*"

"1'&6$%" ,'&*."*" "#)1%'#$" *% ,/%6'))#$" 2*))* 01' $#1" 6336.6[% )6 3)1" 3*.%'$*$%* 3#1. $#%.*

3.#()/76%'01*4

Page 61: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

!"!# $%&'()%*+#+,-* (.%/+',01% (01,2#.%*+% 3 4-56.%) 7.-8#19

!"#$% &'(')

"#$ %&$'()&$ *+,-.(+# /+#*(*.$ 0 &$%&1*$#.$& ,$ /+'%+*2#. '23#1.(4-$ %2& -# /(&/-(.

%,-* +- '+(#* /+'%,$5$ /+'%+*1 6$ &1*(*.2#/$*7 68(#6-/.2#/$* $. 6$ /+#6$#*2.$-&* (612-57

6$ '2#()&$ 0 &$%&+6-(&$ ,$ /+'%+&.$'$#. 6$ ,8('%162#/$ 9(* 0 9(* 6$ ,2 :&14-$#/$ 6-

/+'%+*2#. '23#1.(4-$ &1$,; <2#* #+.&$ /2*7 (, :2-6&2(. 6+#/ .&+-9$& -# '+6),$ 262%.1

%+-& /=24-$ /+'%+*2#. LMD $. LMC ; >$/( *$&2(. .+-. 0 :2(. :2(*2?,$ $. (#/+&%+&2?,$ 62#*

6$* ,+3(/($,* 6$ .@%$ /(&/-(.; >$%$#62#.7 ?($# *+-9$#.7 %,-* ,$ */=1'2 14-(92,$#. /+'%+&.$

681,1'$#.*7 %,-* +# %$&6 6$ *$#* %=@*(4-$ A%+-& /=24-$ #+-9$2- /+'%+*2#. 2B+-.1C; D#

$E$.7 ,$* 92,$-&* 6$* /+'%+*2#.* *+#. (6$#.(F1* 0 %2&.(& 6$ '$*-&$* %+-& &$%&+6-(&$ -#

/+'%+&.$'$#. :&14-$#.($,; <2#* /$..$ 2%%&+/=$7 ,8(#G-$#/$ 6- '2.1&(2-7 6$ ,2 31+'1.&($7

6- #+'?&$ 6$ *%(&$* $*. *+-9$#. .&+% /+'%,$5$7 9+(&$ ('%+**(?,$ 0 2#2,@*$&; H+-& /=24-$

#+-9$,,$ /+#F3-&2.(+#7 (, :2-. ?($# *+-9$#. &1I(6$#.(F$& .+-.$* ,$* 92,$-&* 6$* /+'%+*2#.*

6- '+6),$ 14-(92,$#.; >$ .&292(, $*. ,+#3 $. :2*.(6($-5 $. #+# 262%.1 0 -#$ %&+/16-&$ 68+%.(I

'(*2.(+#; >$%$#62#.7 /$..$ 2%%&+/=$ 2 1.1 26+%.1$ %+-& ,2 '+61,(*2.(+# 6$* /+#6$#*2.$-&*

Cx $. Cy A/+''$ #+-* ,$ 9$&&+#* -# %$- %,-* ,+(#C7 /2& ?($# 4-$ #+.&$ .&292(, *$ /+#/$#.&$

-#(4-$'$#. *-& ,$* /+'%+*2#.* '23#1.(4-$*7 #+-* 9+-,+#* &$%&+6-(&$ 6$ '2#()&$ ,2 %,-*

&12,(*.$ %+**(?,$ ,$ /+'%+&.$'$#. 6- F,.&$ /+'%,$.; J$* /2%2/(.1* #81.2#. %2* 6$* 1,1'$#.*

0 +%.('(*$& 62#* #+.&$ 1.-6$7 /$ '+6),$ $*. %$&.(#$#.;

(% *!"#$% +,"-./0,.% %/ /10,23!1*0/%-1 40130+/

!"#$% KKK;L M N/=1'2 6- '+#.23$ 6$ H&2?=2O2&2# $. 2,; 62#* PHNQRS

T %2&.(& 6$ '$*-&$* 68('%162#/$ *-& /$..$ (#6-/.2#/$7 #+-* %+-9+#* 61.$&'(#$& ,$

/+'%+&.$'$#. 1,$/.&+*.2.(4-$ $. '23#1.(4-$ 6- 6(*%+*(.(: $. &12,(*$& -# '+6),$ /+#*.&-(.

0 %2&.(& 68-# &1*$2- 68(#6-/.2#/$* $. 6$ .&2#*:+&'2.$-&* %2&:2(.*; <(9$&*$* '1.=+6$* 6$

'$*-&$* 68('%162#/$* +#. 1.1 619$,+%%1$*; D,,$* +#. .+-.$* 6$* 292#.23$* $. 6$* (#/+#I

91#($#.* PU2#7V2#S; J$ /=+(5 $#.&$ /$* 6(E1&$#.$* '1.=+6$* 61%$#6 6$ ,2 32''$ 6$ :&1I

Page 62: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&' () *%(+,- .%)/ ,- 0%*.%/1-*-21 3/45)-21&-, !

"#$%&$' ()*+,(-.#/$ /# &0*+, *,,(-"#1' (* ,21&-3-4% /13-21$ *-%3- "#$ (* 3-+,(-&-.1 /$ +-3$

$% 5#62$7 8)*,,*2$-( "#- &422$3,4%/ ($ +-$#9 : &$3 &2-.;2$3 3$+<($%. =.2$ ()*%*(>3$#2 /)-+?

,1/*%&$' %4#3 *64%3 /4%& &04-3- @A-($%. BC @ D@A-E7 F4#.$G4-3' ($3 %-6$*#9 /$ ()43&-((*.$#2

-%.$2%$ 2$3.$%. .2;3 G*-<($3 2$3.2$-A%*%. %43 +$3#2$3 : /$3 %-6$*#9 /)-%/#&.-4% G*-<($7 H4#2

&4%.4#2%$2 &$ ,24<(;+$' H2*<0*I*2*% $. *(7 /*%3 DHJKBE 4%. +-3 *# ,4-%. #%$ &4%LA#2*.-4%

3,1&-L"#$ ,4#2 (* +$3#2$ /)-+,1/*%&$ : /$3 %-6$*#9 /)-%/#&.-4% 1($61$7 M% *+,(-L&*.$#2

/$ ,#-33*%&$ $3. -%.24/#-. $%.2$ ()*%*(>3$#2 /)-+,1/*%&$ $. ($ 3#,,42. /$ ()1&0*%.-((4%7 N$3

34%/$3 /-O12$%.-$(($3 /$ &4#2*%.3 $. /$ .$%3-4%3 34%. #.-(-31$3 ,4#2 *<*-33$2 ()*+,(-.#/$ /$3

3-A%*#9 *,,(-"#13 21.24*&.-6$+$%. *#9 <42%$3 /$ ()*%*(>3$#2 /)-+,1/*%&$ PQ-A7 RRR7ST7

H4#2 *..$-%/2$ (* &*2*&.12-3*.-4% /# &4+,42.$+$%. +*A%1.-"#$ U#3"#): VK WXY' %4#3

*64%3 &04-3- /$ +4/1(-3$2 ($ &4+,42.$+$%. 1($&.243.*.-"#$ /# %4>*#7 Z4#3 #.-(-34%3 #%$

*,,24&0$ A(4<*($' <-$% /1&2-.$ /*%3 /$3 .2*6*#9 *%.12-$#23 D8[Q\KS'\][KC*'W[K!E7 8$

/1.*-( /# ,24.4&4($ $9,12-+$%.*( $3. ,213$%.1 /*%3 ()*2.-&($ $% *%%$9$ \7 ]$3 +$3#2$3

,$2+$..*%. /$ &4%&$64-2 #% +4/;($ /1&2-6*%. ($3 3,$&.2$3 /$ ,$2+1*<-(-.1 &4+,($9$ /)#%

.42$ /)*((-*A$ %*%4&2-3.*((-% PF*<($ RRR7BT7

!"#$ RRR7B ^ ]*2*&.12-3.-"#$ /# .42$ %*%4&2-3.*((-%

N$9. P++T N-%. P++T X P++T 8+ P++T J$&.-4% Pmm2T ZV ZB

V! VK7! _7B S7` V`7_ VV VV

%&'()$ RRR7 ^ ]-2&#-. 1"#-6*($%. /$ ()-%/#&.*%&$

8* &4%&(#3-4% /$ &$..$ 1.#/$ $3. ()4<.$%.-4% /)#% &-2&#-. 1"#-6*($%. ,$2+$..*%. /$ +4/1?

(-3$2 ($ &4+,42.$+$%. 1($&.243.*.-"#$ $. +*A%1.-"#$ PQ-A7 RRR7 T7 ]$ +4/;($ ,$2+$. /)4<?

.$%-2 ($3 &*2*&.12-3.-"#$3 +*A%1.-"#$3 $% G4%&.-4% /$ (* G21"#$%&$ /$ +*%-;2$ .2;3 ,21?

&-3$ DW@]

+VVE7 8)4<.$%.-4% /$3 &4#2<$3 /$ ,$2+1*<-(-.1 3$ G*-. ,*2 (* ,2-3$ $% &4+,.$ /#

Page 63: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

"#"$%&'( () *(+ ,&-&./)-(+ '0#.0)-$12(+ *2 %#3&2 .&'%0)$12(4 5(6& +$'%$7( 12( 68$*(%)$9

7:&)$#% %8(+) ;&6&"6( 12( ,#2- 2% %#."-( *( +,$-(+ () 2%( '0#.0)-$( *#%%0(4 <&%+ %#)-(

0)2*(= %#2+ +#2>&$)#%+ *$++#:$(- 6(+ ,&-&./)-(+ ,>3+$12(+ ?:8(+) @ *$-( .&'%0)$12(A *(+

,&-&./)-(+ '0#.0)-$12(+ ,#2- *(+ "(+#$%+ *8#,)$.$+&)$#% 26)0-$(2-(4 B(+ .#*/6(+ '6#"&2C

%( +#%) *#%: ,&+ &*&,)0+ @ %#)-( 0)2*(4

!"!# $%&'() &) *+,*-+./ 01234.+5-)/ 45-+61()3./

B(+ .#*/6(+ ,&- :$-:2$)+ .&'%0)$12(+ 012$;&6(%)+ +#%) *(+ .#*/6(+ 12$ *07%$++(%) 2%(

&%&6#'$( (%)-( 6(+ '-&%*(2-+ 06(:)-$12(+ () 6(+ '-&%*(2-+ .&'%0)$12(+4

!"#$ DDD4E F G%&6#'$( *(+ ;&-$&"6(+

5$-:2$) 06(:)-$12( 5$-:2$) .&'%0)$12( ?H062:)&%)A 5$-:2$) .&'%0)$12( ?5&,&:$)0A

I(%+$#% ?;A J#-:( .&'%0)#.#)-$:( ?K..A J#-:( .&'%0)#.#)-$:( ?K..A

5#2-&%)?$A J62C ?ΦA <0-$;0( *2 L2C ?

dΦdtA

H0+$+)&%:( ?HA H062:)&%:( ?R

!"#$%&'()('* +σ ,-./*01(2('* +µ

!030&('* +! ,-./*0#&- +P

!40.5- +6 72%8 +Φ

,-./(''()('* +ǫ ,-./*01(2('* +µ

! "#$%&! '(&)*+,-+

,.-#"#9 %#- (#$%&'0#&- .*02(9*- : 30.'(. $;%# #"<0% /05#*'(6%- -' $;%# 1"1(#05- &"#'-#0#'

= 93(.-9> ?0 &(.&%20'("# $% &"%.0#' +( $0#9 2- 1"1(#05- (#$%(' %# @%8 /05#*'(6%- $0#9

2- #"<0% +φ > A( "# 0332(6%- 20 2"( $;B"3C(#9"# : &-''- (#$%&'0#&- +D6> EEE>F G 20 H".&-

/05#*'"/"'.(&- +fmm 3-%' I'.- (#'-.3.*'*- &"//- %#- 6%0#'('* $- H".&- 6%( /-' -#

&(.&%20'("# 2- @%8 +φ $0#9 2- &(.&%(' /05#*'(6%->

fmm = Ni = Rφ +EEE>F

J0#9 2- &09 $;%# /0'*.(0% /05#*'(6%- 2(#*0(.- +KLµ0µr H -' 90#9 3-.'-9G 20 fmm -9'

3."3".'("##-22- 0% @%8> ?0 .*2%&'0#&- R +-# B

!

$-)(-#' 2;0#02"5%- $- 20 .*9(9'0#&- M +-#

Ω -# *2-&'.(&('* -' $0#9 2- &(.&%(' /05#*'(6%- 2- @%8 /05#*'(6%- φ = fmmR -9' 0#02"5%- 0%

&"%.0#' *2-&'.(6%- i = vR> !- /"$N2- 109* 9%. $-9 .*9(9'0#&-9 3"%. 2-9 &"/3"90#'9 /05#*O

'(6%-9 -9' 033-2* 2- /"$N2- .*2%&'0#' PQRMSTGB0/SUG$,$AMTVW +X012-> EEE>U > !- /"$N2-

-9' '.N9 %'(2(9* 3"%. $-9 3.*O$(/-#9("##-/-#'9 $- /0&4(#-9 *2-&'.(6%-9 PJ-YTZG =-$FFW>

,"%.'0#'G &- /"$N2- -9' 109* 9%. %#- &"#)-#'("# 6%( )0 : 2;-#&"#'.- $- 20 &"#'(#%('* $-

2;*#-.5(- 3%(96%;%#- .*2%&'0#&- /05#*'(6%- 9'"&C- $- 2;*#-.5(- '0#$(9 6%;%#- .*9(9'0#&- *2-&O

'.(6%- -# $(99(3-> !- 3."12N/- $;(#'-.3.*'0'("# -9' 30.'(&%2(N.-/-#' &.%&(02 -# *2-&'."#(6%-

$- 3%(990#&- 3%(96%- 2-9 .-20'("#9 *#-.5*'(6%-9 9"#' $- 3.-/(N.-9 (/3".'0#&-9> J- 32%9G

2-9 &(.&%('9 /05#*'(6%-9 -' *2-&'.(6%-9 (#'-.05(99-#' -#'.-O-%8G &- 6%( "12(5- : 0#02<9-. 2-

9<9'N/- $0#9 90 52"102('*>

Page 64: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&' () *%(+,- .%)/ ,- 0%*.%/1-*-21 3/45)-21&-, !

! "#$%&! '()*+!,)-.*/*.0+1

"#$%%&'()* +,&$-*.&/($%$(0-1 $ 1-1 213*4'%%1* *5 6!78 9:$;! < =.578< =>>!6?@ A*

;'2B4* *C- D$C1 C.& 4$ -)1'&0* 2*C +&$%)*C 2* 40*5C@ "$ -)1'&0* 2*C +&$%)*C 2* 40*5C< $%%*41*

$.CC0 D'52 +&$%) *5 $5+4$0C< $ 1-1 05-&'2.0-* *5 6!E8 %$& :*5&, F@ G$,5-*& 9G$,E8? %'.&

2*C .C$+*C *5 ;1($50H.* *- *5 $.-';$-0H.*@ A*--* -)1'&0* $ 1-1 *5C.0-* .-040C1* 2$5C 4*

;'52* 2* 4#14*(-&'50H.* 2* %.0CC$5(* %$& FC)*& 9FC)!I?@

J5 +&$%)* 2* 40*5C *C- .5* &*%&1C*5-$-0'5 +&$%)0H.* 'K 4*C ('55*L0'5C *5-&* 4*C (';%'/

C$5-C C'5- *L%40(0-*C@ "*C +&$%)*C 2* 40*5C C'5- D$C1C C.& .5* *L%&*CC0'5 15*&+1-0H.* 2* 4$

2,5$;0H.* 2*C C,C-B;*C@ J5 C,C-B;* *C- 2030C1 *5 C'.C/C,C-B;*C< *- 4* +&$%)* 2* 40*5C 2.

C,C-B;* 0520H.* (';;*5- 4#15*&+0* *C- 1()$5+1* *5-&* 4*C C'.C/C,C-B;*C@ "* ;'2B4* 2#.5

C'.C/C,C-B;* 0520H.* (';;*5- 4#15*&+0* *C- C-'(M1*< ;'20N1* '. 21+&$21* O 4#05-1&0*.& 2.

D4'(@ P$5C (*--* $%%&'()*< 4$ Q;; &*C-* $5$4'+.* O 4$ -*5C0'5 R3S %$& ('5-&* 4* ('.&$5-

R0S ('&&*C%'52 O 4$ 21&031* 2. T.L ;$+51-0H.* 2φU2- RVH@ WWW@XS@ A*--* $5$4'+0* &*C%*(-*

4$ ('5C*&3$-0'5 2* 4$ %.0CC$5(* *5-&* 4* 2';$05* 14*(-&0H.* *- 4* 2';$05* ;$+51-0H.* %$&

.5 C0;%4* &$%%'&- 2* %&'%'&-0'55$40-1@ "* %$CC$+* 2. 2';$05* 14*(-&0H.* $. 2';$05* ;$/

+51-0H.* R*- 053*&C*;*5-S C* Q$0-< ;$-1&0*44*;*5-< %$& 4* D'D05$+*@ W4 *L0C-* .5 (';%'C$5-

%$&Q$0-*;*5- $2$%-1 2$5C 4$ ;'2140C$-0'5 %$& +&$%)* 2* 40*5C %'.& &*%&1C*5-*& (* 2*&/

50*&< 04 C#$+0- 2. (';%'C$5- Y,&$-*.& RZ0+@ WWW@[S 9\]^!8?@ A* (';%'C$5- $ 4$ %&'%&01-1

2#05-*&()$5+*& 4$ -*5C0'5 *- 4* ('.&$5-< 04 *C- +'.3*&51 %$& 4*C &*4$-0'5C WWW@X@

p(t) = v(t) · i(t) = Ndφ(t)

dt· i(t) = Ni(t) · dφ(t)

dt= fmm · dφ(t)

dtRWWW@XS

"* &$%%'&- 2* %&'%'&-0'55$40-1 13'H.1 %4.C )$.- *C-< 2$5C 4* ($C 2#.5 D'D05$+*< 4* 5';D&*

2* C%0&*C _@ P$5C 4* ($C 2#.5* '%-0;0C$-0'5< 5'.C %'.&&'5C $4'&C ()$5+*& .50H.*;*5- (*

%$&$;B-&* *- 3'0& 4#05T.*5(* C1%$&1* 2* (* 2*&50*& C.& 4*C %*&Q'&;$5(*C 2. C,C-B;*@ "$

&1C0C-$5(* C1&0* 2. D'D05$+* %*.- `-&* $a'.-1* .4-1&0*.&*;*5- %$& .5 141;*5- 20CC0%$-0Q@

!"#$% WWW@[ b ^*%&1C*5-$-0'5 2#.5 +,&$-*.&

"#$5$4'+0* *5-&* 4* (';%'&-*;*5- ;$+51-0H.* *- 14*(-&0H.* *C- 'D-*5.* O %$&-0& 2* c

b 4$ 4'0 2* (';%'&-*;*5- ;$+51-0H.* O D$C ()$;% R2$5C 4* 2';$05* 4051$0&*S@

B = µ0µr H RWWW@IS

b 2* 4$ 21N50-0'5 2* 4$ %*&;1$D040-1 (';%4*L*

µr = µreel − jµimag RWWW@ S

Page 65: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

!" #$ #%& !" '$()"## "* +",-&%* &*./0,$#" 1-& %* -233%-" #$ -"4.&%* !2 *%5$2 6$0*/.&72"

4%*-.$*." 1899 ". #:&*!24.&%* B 6%5"**" !$*- 4".." -2,;$4"<

φ = BS 1===<>9

!" #:$33#&4$.&%* !2 .?/%,@6" !:A63@," -2, #" .%,"

H =NI

l1===<B9

4" 72& *%2- !%**" #$ ,"#$.&%* -2&+$*." C

NI = (µreel · l

µ0 ·S · (µ2reel + µ2

imag)+ j

µimag · lµ0 ·S · (µ2

reel + µ2imag)

)φ 1===<D9

8& #:%* +"2. .,$!2&," #" -.%4E$0" ". #" !&--&3$.&%* !:/*",0&" $+"4 #"- +$,&$F#"- NI ".

dφdtG

*%2- !"+%*- ;$&," #:$*$#%0&" $+"4 2* 4&,42&. HI -/,&" $#&6"*./ 3$, 2*" -%2,4" !" ."*-&%*

NI< J* $33#&72$*. #$ #%& !"- 6$&##"- K 4" 4&,42&.G *%2- %F."*%*- #$ ,"#$.&%* ===<L<

NI = Rdφ

dt+

1

C

dt1===<L9

M,N4" $2( /72$.&%*- ===<D ". ===<LG *%2- 3%2+%*- &!"*.&O", #"- "(3,"--&%*- !" H ". I "*

;%*4.&%* !"- 3$,$6@.,"- 0/%6/.,&72"- !2 .%," ". !" -%* 4%63%,."6"*. 6$0*/.&72"G &##2-.,/

3$, #$ 3",6/$F&#&./<

C =µ0 ·S · (µ2

reel + µ2imag)

µreel · l1===<P9

R =µimag · l

µ0 ·w ·S · (µ2reel + µ2

imag)1===<QR9

M,N4" K 4" 6%!@#"G 4?$72" 3$,.&" !2 4&,42&. 6$0*/.&72" 3"2. S.," "(3,&6/" "* ;%*4.&%*

!"- 0,$*!"2,- H ". I TJ$.PLU< V$, $&##"2,-G #"- 3$,$6@.,"- 6$0*/.&72"- /.$*. !/4%,,/#/- !"-

3$,$6@.,"- 0/%6/.,&72"-G #"- -&62#$.&%*- 3"2+"*. S.," ,/$#&-/"- 3%2, !&W/,"*."- 0/%6/.,&"-

-$*- 6%!&O4$.&%* !" #$ -.,24.2,"< X" 4" ;$&. 4".." 6%!/#&-$.&%* "-. !%*4 .%2. K ;$&. $!$3./"

K *%.," /.2!" 3%2, *%.," 3?$-" !:%3.&6&-$.&%* 2#./,&"2,"< Y%2- $+%*- !%*4 4%*-",+/ 4"

4?%&( 3$, #$ -2&."<

!" #$%&%'($%)* +, -)+.&/ 0)-1)'(*$ -(2*3$%4,/ +(*' &(

-)+3&%'($%)* '5'$.-/

'$&*."*$*. 72" *%2- $+%*- !/.",6&*/ #" 6%!@#" 3%2, !/4,&," #" 4%63%,."6"*. 6$0*/Z

.&72" !2 4%63%-$*.G *%2- !"+%*- *%2- &*./,"--", K #$ ;$[%* !" #:&*4#2," !$*- #$ 6%!/#&-$.&%*

-5-.@6" "(&-.$*."<

!"!# $%&'( () *+,-.( /0 *+,-+%.(,(). 1%230().&(4

X$*- 4".." 3$,.&"G *%2- $##%*- !/.$&##", #$ 6$*&@," !%*. #" 4%63%,."6"*. ;,/72"*.&"# !2

6$./,&$2 6$0*/.&72" $ /./ 3,&- "* 4%63." !$*- #" 6%!@#" 05,$."2,Z4$3$4&./< A23$,$+$*.G

*%2- !/.$&##%*- #" 6%!@#" ;,/72"*.&"# $!%3./ 3%2, #"- 4$3$4&./- Cx ". Cy $O* !" !/4,&,"

4%63#@."6"*. #" O#.," IJ'<

Page 66: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&%'($%)* +, -)+.&/ 0)-1)'(*$ -(2*3$%4,/ +(*' &( -)+3&%'($%)* '5'$.-/ !

!"!#$% &'()*%+#,%'- (.+ /#0#/%,)+ Cx ., Cy

"#$$% &#'( )*+,#&( ,' -+&( )% ./+0123% 445 )%( ,+)%'3( -%( .+0+.126( Cx %2 Cy (#&2

786%( 0+3 91(0+&#:;'1<+ =>+?)% 44@AB@ "%( ,+)%'3( -6.31,%&2 )%'3 .#$0#32%$%&2 1-6+)@ C&

03%$1D3% +003#81$+21#&5 '& .#&-%&(+2%'3 (% $#-6)1(% -% E+F#& 0)'( 36+)1(2% G3H.% I .%(

.+3+.2631(21J'%( %((%&21%))%( =K1G@ 444@LB M

N )+ ,+)%'3 -% )+ .+0+.126 ="B

N )+ 36(1(2+&.% (631% =C;OB

N )*1&-'.2+&.% (631% =C;PB

C ESR ESL

!"#$% 444@L N Q#-D)% -*'& .#&-%&(+2%'3

R 0+3213 -%( $%('3%( I )*+&+)S(%'3 -*1$06-+&.% RG1)%&2 TUVTR ('3 -%( .#&-%&(+2%'3( -%

2S0% .63+$1J'% =CyWRQ":XYZ %2 CxW [\O =I ?+(% -% ]+> 1^ABB5 &#'( +,#&( 0' 62+?)13

)% $#-D)% 6J'1,+)%&2 +,%. (%')%$%&2 !_ -*%33%'3 =K1G@ 444@\B@

!"#$% 444@\ N "#$0+3+1(#& -%( $%('3%( %2 -' $#-D)% 0#'3 "8 %2 "S

P%( 0+3+$D23%( -' $#-D)% (#&2 036(%&26( -+&( )% 2+?)%+' 444@T@

&'()% 444@T N Q#-D)% 36%) -%( .+0+.126(

"8 =-%'8 %& 0+3+))D)%B "S

" V@ TT µF TV@TV &K

C;P Z@`L &9 TT@U\ &9

C;O U@A! $Ω !@UVL $Ω

!"!#$%% 12.30*. (4 /%5/4%, 5)+'-#-, 67

Y#'3 ,+)1-%3 &#23% +003#./% -% $#-6)1(+21#& aGS3+2%'3:.+0+.126b5 &#'( +,#&( ./#1(1 '&

.+( 2%(2 (1$0)% %2 E+.1)%$%&2 $%('3+?)% M '& .13.'12 P" 0+3+))D)%@ P% .#$0#(+&2 1&-'.21E P

(%3+ $#-6)1(6 0+3 '& $#-D)% -% 2S0% GS3+2%'3:.+0+.126@

Page 67: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

"#$%&'()*%(+ +,) '% )-.+ %*%-(.$,)*//$% &-%) /+, (*.*()0.$,)$1'+, ,-%) 2.0,+%)0+, &*%, /+

)*3/+*' 4445 5

!"#$ 4445 6 7*.*()0.$,)$1'+ &+ /#$%&'()*%(+

8+9) :;;< 8$%) :;;< =*') :;;< >3 ,2$.+,

!? !@ ? A@

%&'()$ 4445? 6 B+,'.+, &#$;20&*%(+ &+ /#$%&'()*%(+ +) &' (-%&+%,*)+'.

C%+ (*.*()0.$,*)$-% D.01'+%)$+//+ &+ (E*1'+ (-;2-,*%) ,02*.0 +,) .0*/$,0+ *F+( '% *%*G

/H,+'. &#$;20&*%(+ IJ$/+%) A!KAI :L$J5 4445?<5 >-', 2-'F-%, .+;*.1'+. /#*22*.$)$-% &+

&+'9 2$(, &+ .0,-%*%(+ ,'. /* ;+,'.+ &+ /#$%&'()*%(+5 7+ 2E0%-;M%+ +,) &N *'9 (*2*($)0,

2*.*,$)+, +%).+ ,2$.+, O E*')+, D.01'+%(+,5

P-'. 2.+%&.+ +% (-;2)+ /* F*.$*)$-% D.01'+%)$+//+ &+ /#$%&'()*%(+ +) &+ /* (*2*($)0

&*%, /* ,$;'/*)$-% :QR$;'/*)$-% *F+( F*/+'., &+ " +) 7S L$J5 4445T@<U %-', 2.-(0&-%, &+ /*

;*%$M.+ ,'$F*%)+5 >-', ')$/$,-%, '% /-J$($+/ &+ )H2+ ($.('$) (*2*3/+ &+ J0%0.+. '%+ 32*&'(*5

C%+ 32*&'(* +,) '% V(E$+. )+9)+ 1'$ .+).*%,(.$) /+ ,(E0;* 0/+().$1'+ +% %W'&, +) /* F*/+'.

&#$;20&*%(+ &+, 3.*%(E+,5 7#+,) &*%, (+ V(E$+. )+9)+ 1'+ %-', ;-&$V-%, /+, F*/+'., &+ " +)

7 2-'. (E*1'+ D.01'+%(+5 P-'. (-;2*.+. (+, .0,'/)*), *' ;-&M/+ )'3+ &+ X'9 :QR$;'/*)$-%

*F+( F*/+'., &+ " :)'3+ &+ X'9< +) 7S L$J5 4445T@<U %-', 2.-(0&-%, 1'*,$;+%) &+ /* ;Y;+

;*%$M.+5 Z% +[+)U %-', .+;2/*\-%,U &*%, /+ ,(E0;* 2.0(0&+%)U /#$%&'()*%(+ " 2*. %-).+

;-&M/+ JH.*)+'.G)'3+ &+ X'9 :F-$. L$J5 4445K<5 ]% .+).-'F+ &*%, (+ ,(E0;*U /+ JH.*)+'.

*F+( /+, 0/0;+%), ^T +) 7T 1'$ ,-%) D-%()$-% &+, &$;+%,$-%, &' ($.('$) ;*J%0)$1'+ *$%,$

1'+ &+ /* 2+.;0*3$/$)0 (-;2/+9+ +) ^! (-..+,2-%&*%) O /* .0,$,)*%(+ &' 3-3$%*J+5 8*%,

(+))+ ).-$,$M;+ ,$;'/*)$-%U %-', ;-&$V-%, &-%( '%$1'+;+%) /+, F*/+'., &+, (-;2-,*%)+,

.0+//+, +) $;*J$%*$.+, &+ /* 2+.;0*3$/$)05

Page 68: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&%'($%)* +, -)+.&/ 0)-1)'(*$ -(2*3$%4,/ +(*' &( -)+3&%'($%)* '5'$.-/ !

!"#$% """#$ % &'()*+ ,- *.,/01 234+51-46'+7+'85) ,1 098:,-'5+:'1 ;.-; <=>&

?+ @2-41 """#AB '.*7.451 54.8; '.-4C1; D-1 :.-; 74);1:5.:; '86,1;;.-; E

% ?+ '.-4C1 FG1;-41 +- 7.:5 ,98*7),+:'1H 1;5 0+ '.-4C1 ,98*7),+:'1 *1;-4)1 +-

7.:5 ,98*7),+:'1 ,1 091:;1*C01 ,- '84'-85 ?> 7+4+00/01

% ?+ '.-4C1 F&8*-0+58.: +I1' I+01-4; ,1 ? 15 >H 1;5 0+ '.-4C1 ,98*7),+:'1 ;8*-0)1J

1: 8*7.;+:5 7.-4 '(+D-1 K4)D-1:'1 01; I+01-4; *1;-4)1; ,1 ? 15 >#

% ?+ '.-4C1 F&8*-0+58.: +I1' I+01-4; ,1 ? L5-C1 ,1 M-NO 15 >H 1;5 0+ '.-4C1 ,98*7)6

,+:'1 ;8*-0)1J 1: 8*7.;+:5 7.-4 '(+D-1 K4)D-1:'1 01; I+01-4; *1;-4)1; ,1 0+ 714*)+6

C8085) '.*701N1 ,+:; 01 *.,/01 P34+51-46Q-C1 ,1 M-N 7.-4 01 '.*7.;+:5 8:,-'58K 15

01; I+01-4; *1;-4)1; ,1 098*7),+:'1 7.-4 >#

!"#$% """#AB % >.*7+4+8;.: 1:541 01 *.,/01 234+51-46'+7+'85) 15 0+ *1;-41

Page 69: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

"# $%&' ()*+ ,&% -%. /%&0 .*1&-2'*)#. .)#' %# 3)# 244)+/ 2(%4 -2 1%.&+% 5&.,&67 &#%

8+9,&%#4% /6%#(*+)# :;<= >2 /*(%+?%#4% %#'+% -%. /%&0 8+9,&%#4%. /% +9.)#2#4% .9+*%

2$+@. :;< $%&' A'+% -*9% 2&0 42$24*'9. $2+2.*'%. /%. %#+)&-%1%#'. %' 2&0 *#/&4'2#4%. /%

8&*'%= B%$%#/2#'C /2#. 4%''% ?211% /% 8+9,&%#4%C -2 42$24*'9 %.' 4)#.'2#'%C /% .)+'% ,&% -2

(2+*2'*)# /% -2 .%4)#/% 8+9,&%#4% /% +9.)#2#4% $%&' A'+% 2''+*3&9% 7 &#% *#/&4'2#4% $2+2.*'%

/% 4D3-2?% %.'*19% 7 EE #;= "# 4)#.'2'% ,&% -%. /%&0 1)/@-%. .% 4)1$)+'%#' ,&2.*1%#'

7 -6*/%#'*,&% (*. 7 (*. /% -2 8+9,&%#4%= F)'+% 2$$+)4G% HIJ*1&-2'*)# 2(%4 (2-%&+. /% >

H'&3% /% K&0L %' BML 4)1$)+'%C 4%$%#/2#' &# 2(2#'2?%C $2+ +2$$)+' 7 -2 42+24'9+*.2'*)#

.9$2+9% /% 4G2,&% 4)1$).2#' HIJ*1&-2'*)# 2(%4 (2-%&+. /% > %' BMLC %--% #)&. $%+1%'

/9.)+12*. /% 4)#.*/9+%+C -%. '+25%'. /% K&0C -%. /*1%#.*)#. /& 4*+4&*' 12?#9'*,&%C 2*#.* ,&%

-% #)13+% /% .$*+%. /% 12#*@+% *#/9$%#/2#'%= B%''% 2$$+)4G% #)&. .%+2 /)#4 '+@. &'*-% $)&+

-6)$'*1*.2'*)# /% #). 4)1$).2#'. 12?#9'*,&%.= B%$%#/2#'C 4)11% #)&. -62()#. .)&-*?#9

$+949/%11%#'C #)&. #% $+%#)#. $2. %# 4)1$'% -%. 9-91%#'. $2+2.*'%. /& 4*+4&*'=

!"!#$%%% &'()*%+#,%'- .#/-),%012 3 *2+ %-(14,#-42+ &56&7

N)&+ -2 /%+#*@+% 9'2$% /% (2-*/2'*)# /% #)'+% 1)/@-%C #)&. 2()#. /94*/9 /% -% '%.'%+ .&+

&# /*.$).*'*8 $+)4G% /% -2 .'+&4'&+% '+2/*'*)##%--% /% O-'+% :B )& :P= F)&. 2()#. 4G)*.*

/% 42+24'9+*.%+ /%&0 ')+%. /2#. -2 1A1% 4)#O?&+2'*)# ,&% 4%--% $+9.%#'9% .&+ -2 O?&+% QQ=R=

BG2,&% *#/&4'2#4% 4)&$-9% 9'2#' +%1$-249% $2+ &# #)S2& 12?#9'*,&% H&# '&3% /% K&0L %'

&# 3)3*#2?% H&# )& $-&.*%&+. ?S+2'%&+.L= >% $+%1*%+ ')+% %.' %# $)&/+% /% 8%+ H:*4+)-*'%L

4)++%.$)#/2#' 7 &#% $%+1923*-*'9 *#*'*2-% /% T UC *- .%+2 /9#)119 I')+%VNM HW23-%= QQQ=XL=

>% .%4)#/ ')+% %.' %# 2--*2?% #2#)4+*.'2--*# 4)++%.$)#/2#' 7 &#% $%+1923*-*'9 *#*'*2-% /% YU

UUUC *- .%+2 /9#)119 I')+%;NM HW23-%= QQQ= L= >% 3)3*#2?% %.' O09 7 EE .$*+%. 2& $+*12*+%

%' 2& .%4)#/2*+% /% 4G2,&% ')+% HFEZFTZEEL=

!"#$ QQQ=X [ B2+24'9+*.'*,&%. /& ')+% VN

P%0' H11L P*#' H11L ;2&' H11L

!U T EX

P2#. &# $+%1*%+ '%1$.C #)&. +92-*.)#. -%. 3)3*#2?%. %' #)&. -%. 4)##%4')#. %# .9+*%=

N&*.C #)&. +92-*.)#. &#% .9+*% /% 1%.&+% 7 -62#2-S.%&+ /6*1$9/2#4% H\*?= QQQ=ETL= F)&. 2()#.

%]%4'&9 /%&0 'S$%. /% 1%.&+%. ^ &#% %# 1)/% /*]9+%#'*%- H:PL %' &#% %# 1)/% 4)11&#

H:BL= N2+ -2 .&*'%C #)&. 2()#. +92-*.9 -% 1)/@-% ?S+2'%&+_'&3% /% K&0 /& /*.$).*'*8 H\*?=

QQQ=EEL=

` $2+'*+ /% 4%''% +%$+9.%#'2'*)# /2#. &# -)?*4*%- 4*+4&*'C #)&. 2()#. 94+*' -%. -)*. /%.

#a&/. %' /%. 12*--%. $)&+ /9'%+1*#%+ -2 12'+*4% %#'+9%b.)+'*% /% 4% /*.$).*'*8 Hc,= QQQ=EEL=

F)&. $)&()#. /9'%+1*#%+ -% $2..2?% 9-%4'+*,&%b12?#9'*,&% $2+ -%. /%&0 12'+*4%. ?S+2'%&+

%' -2 12'+*4% 12?#9'*,&% /% 12#*@+% *#/9$%#/2#'%= >%. *1$9/2#4%. ZHP %' ZBP 4)++%._

$)#/%#' 7 -6*1$9/2#4% 9,&*(2-%#'% /% -2 1*.% %# .9+*% /% -2 +9.*.'2#4% %' -2 42$24*'9 /&

1)/@-% '&3% /% K&0= B% .)#' /62*--%&+. 4%. (2-%&+. ,&* .)#' 1)/*O9%. 7 4G2,&% 8+9,&%#4%

$)&+ $+%#/+% %# 4)1$'% -% 4)1$)+'%1%#' +9%- /& 12'9+*2&= B)11% /2#. -2 $2+'*% $+949_

/%#'%C -%. 42+24'9+*.'*,&%. /& 3)3*#2?% H#)13+% /% .$*+%. %' +9.*.'2#4%L .)#' *#'+)/&*'%.

/2#. -% 3-)4 ?S+2'%&+ '2#/*. ,&% -%. $+)$+*9'9. /%. #)S2&0 12?#9'*,&%. .)#' +%#'+9%. /2#.

-% 1)/@-% '&3% /% K&0 HdCBL=

Page 70: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&%'($%)* +, -)+.&/ 0)-1)'(*$ -(2*3$%4,/ +(*' &( -)+3&%'($%)* '5'$.-/

R_BP

C_BPC_HP

R_HP

N

N

N

N

!"#$% !!!"## $ %&'()* +,-./*0-12.3.24/5 '*6 '*07 48'02/.82*6

[

V1

V2

]

=

[

N 0

0 N

] [

ZHP+ZBP

4ZHP−ZBP

4ZHP−ZBP

4ZHP+ZBP

4

] [

1N

0

0 1N

][

I1I2

]

9!!!"##:

;*6 -560)/./6 '* ). 64<0)./4&8 6&8/ -*3-56*8/56 60- ). =+0-* !!!"#> */ 2&<3.-56 .07

-560)/./6 *735-4<*8/.07"

!"#$% !!!"#> $ ?&<3.-.46&8 *8/-* )* <&'()* +,-./*0-12.3.24/5 */ ). <*60-* 60- 08 2&<1

3&6.8/ -5*)

@&06 3&0A&86 8&/*- 08* B&88* .'5C0./4&8 *8/-* )*6 64<0)./4&86 */ )*6 <*60-*6 D06C0EF

G %HI" ;*6 '4A*-+*82*6 &B/*80*6 .01'*)F 6&8/ '0*6 .07 2.3.24/56 3.-.64/*6 '*6 B&B48.+*6

C04 8* 6&8/ 3.6 3-46*6 *8 2&<3/* '.86 2* <&'()*"

Page 71: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

!"!# $%&'( () *+,-.( /( 01 -+01%&'1.&+) '2% 0( .%13(. /( 425 /( ,+/(

/&67%().&(0

"#$ %&'()*+$ ,# -&,# ,./0(#*+.#1 2&$$3,#*+4 2&'( *&+(# )221.%)+.&*4 '*# %&-2&$)*+#

%&*+.*'# ,# 15&(,(# ,# 6 78)91# :;<=; >#1) $.?*.@# A'# 1#$ -)+0(.)'B -)?*0+.A'#$ $# +(&'C

D)*+ $'( 1# +()E#+ ,' F'B ,# -&,# ,./0(#*+.#1 +()D).11#(&*+ )'+&'( ,5'* 2&.*+ ,# 2&1)(.$)+.&*

Hp A'. 2#'+ G+(# %)1%'10 2)( 1# +H0&(3-# ,56-23(# 7IA; :::;!=; "&($A'# %# %H)-2 ,# 2&1)(.C

$)+.&* #$+ 2#+.+ ,#D)*+ 1# %H)-2 ,# $)+'()+.&* ,' -)+0(.)' -)?*0+.A'#4 &* 2#'+ )$$.-.1#( 1#

%&-2&(+#-#*+ ,' -)+0(.)' J '*# 1&. 1.*0).(# 7IA; :::;K=; I* )221.A')*+ 1# +H0&(3-# ,56-C

23(#4 $'( 1# +&(# LM #* N.%&1.+# 78)91#; :::;!=4 *&'$ +(&'D&*$ O2 P <QQQ 6R-; :1 *5S )'()

,&*% )'%'*# .*F'#*%# $'( 1#$ %&'(9#$ ,# 2#(-0)9.1.+0 ,#$ -)+0(.)'B 9)$$#$ 2#(-0)9.1.+0$

A'. &*+ ,#$ %H)-2$ ,# $)+'()+.&* ,# 15&(,(# ,# 21'$.#'($ -.11.#($ ,5)-23(# 2)( -3+(#; I*

(#D)*%H#4 2&'( 1#$ -)+0(.)'B A'. &*+ '* %H)-2 ,# $)+'()+.&* 21'$ 9)$4 %&--# 1#$ )11.)?#$

*)*&%(.$+)11.*$ 7OP Q6R- -)B.-'-=4 .1 *&'$ T)',() 2(#*,(# #* %&-2+# 1) ,0?(),)+.&*

,# 1) 2#(-0)9.1.+0 #* T&*%+.&* ,# 1) 2&1)(.$)+.&* 7U.?; :::;V=;

W)*$ 1# %H)2.+(# 2(0%0,#*+4 *&'$ )D.&*$ .,#*+.@0 A')+(# +&2&1&?.#$ ,&*+ '*# #*+.3(#-#*+ #*

)11.)?# *)*&%(.$+)11.* )D#% '* #*+(#T#(; M&'( %#++# +&2&1&?.# J -)+0(.)' '*.A'# 7U.?; ::;<=4

*&'$ ,#D&*$ ,&*% .*+0?(#( 1# %)1%'1 ,' %H)-2 ,# 2&1)(.$)+.&* ,)*$ 1) -&,01.$)+.&*; X&'$

$'22&$#(&*$ 15#*+(#T#( 2#+.+ 2&'( *0?1.?#( 1#$ F'B ,# T'.+# #+ 1502)*&'.$$#-#*+ ,' F'B4 %#

A'. #$+ 1# %)$ ,)*$ 1# 2(#-.#( ,.-#*$.&**#-#*+ 7I*+(#T#( P Q;< --=;

!"#$% :::;<K Y >&*+&'( ,56-23(# $'( 1) +&2&1&?.# )D#% #*+(#T#(

M&'( ,0+#(-.*#( 1) D)1#'( ,' %H)-2 ,# 2&1)(.$)+.&* HP ,)*$ 1# -)+0(.)' J 15).,#

,' +H0&(3-# ,56-23(#4 *&'$ ,#D&*$ 2(&%0,#( 2)( 0+)2#; W)*$ '* 2(#-.#( +#-2$4 *&'$

)221.A'&*$ 1# +H0&(3-# ,56-23(# $'( '* ,#-. %&-2&$)*+ ,0@*. $'( 1) @?'(# :::;<K 7IA;

:::;<V=;

HMC1 ∗ lMC1 +Hjambe ∗ ljambe +Hair ∗ Ent = NI 7:::;<V=

"# -)+0(.)' *50+)*+ 2)$ 1.*0).(#4 *&'$ *# 2&'D&*$ 2)$ 0%(.(# 150A')+.&* #* 2#+.+$ $.?*)'B

7IA; :::;K=; X&'$ )D&*$ )1&($ (0)1.$0 '* -#$'(# F'B-0+(.A'# $'( 1# -G-# 0%H)*+.11&* )@*

,5&9+#*.( $&* %S%1# ,5HS$+0(0$.$ $+)+.A'# ,'A'#1 *&'$ ,0,'.$&*$ 1) 1&. L7O= 7U.?; :::;<Z=;

I* .*D#($)*+ %#++# %&'(9# 71&. O7L== #+ #* 1) %&-9.*)*+ )' +H0&(3-# ,56-23(# 7IA;

:::;<V=4 *&'$ &9+#*&*$ '*# 0A')+.&* J '*# $#'1# .*%&**'# A'. *&'$ 2#(-#+ ,# ,0+#(-.*#(

15.*,'%+.&* ,# 2&1)(.$)+.&* Bp 7IA; :::;<K=;

Hp(Bp) ∗ lmat +Bp

µ0∗ Ent = NIp 7:::;<K=

Page 72: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()$*+ ,& -')./ 012 3*%4'/) !

!"#$% """#$% & '()*+ ,-./ 0 $11 2.3

4567 89:7 5:+ 8+;:6<;+ =>9?+@ :A57 ;+>;A5BA:7 *+ )C92? 8+ ?A*9;679>6A: Hp ?9; *9 *A6

.-,/# D9:7 :A>;+ )97@ 9B+) *+ ?;=862+:76A::+2+:> 85 )C9?6>;+ ""@ :A57 >;A5BA:7 5: Hp 8+

1#$EFG2# H;I)+ 0 )+>>+ B9*+5; +> 95 ;=7+95 8+ )A5;J+7 2+75;=+7 -K6L# """#M ! "#$% &#$'#"%

()*+,-."+, /0 &+,-)01./.*) 2#-&/+3+ (+% -0*),.0$3 -04")*.5$+% &#/0,.%)%6 7#$% "#*#"%

5$+ /+ 280-& (+ &#/0,.%0*.#" +%* *,9% :0.1/+6 ;+* +<+* +%* ($ = /0 &,)%+"2+ (+ />+"*,+:+, 5$.

0 *+"(0"2+ = 0&/0*., /+ 2?2/+6 ;>+%* />."@$+"2+ ($ 280-& ()-04")*.%0"*6

A$ '$ (+ 2+**+ )*$(+! "#$% &#$'#"% 2#"2/$,+ 5$+ 4,B2+ = /0 &,)%+"2+ (+ />+"*,+:+,! "#$%

"+ *,0'0.//#"% &0% &,#28+ (+ /0 C#"+ (+ %0*$,0*.#" ($ -0*),.0$6 7#$% ">0'#"% (#"2 &0%

1+%#." (+ &,+"(,+ 2+* +<+* (+ &#/0,.%0*.#" +" 2#-&*+ &$.%5$+ 2+/$.D2. %+,0 ")4/.4+01/+6 ;+D

&+"(0"*! %. $"+ *#&#/#4.+ #$ $" -0*),.0$ ")2+%%.*0.* (+ &,+"(,+ +" 2#-&*+ /0 &#/0,.%0*.#"!

"#$% %+,.#"% *#$* = :0.* +" -+%$,+ (+ /+ :0.,+6

!" #$%&'()$*+ ,& -')./ 012 3*%4'/)

E,B2+ = /0 ,)0/.%0*.#" (+% 1/#2% 2#-&#,*+-+"*0$3 +" :,)5$+"2+ ($ F/*,+ ;GH! "#$%

&#$'#"% &,)(.,+ /+ 2#-&#,*+-+"* ($ F/*,+6 7#$% 0'#"% ,)0/.%) 2+**+ )*$(+ %$, /+ 2#-&#%0"*

I.%&0"#DJ$.C06 G" +<+*! 2+ 2#-&#%0"* )*0"* 2#"%*.*$) (+ (+$3 *#,+%! "#$% /+% 0'#"% %)&0,)

+* "#$% 0'#"% ,)0/.%) (+$3 2#-&#%0"*% (.%2,+*% &#$, #1%+,'+, />."@$+"2+ (+ /0 -#()/.%0*.#"6

K+% "#$'+//+% '0/+$,% (>."($2*0"2+% (+ ,):),+"2+ %#"* (#"")+% (0"% /+ *01/+0$ 2.D(+%%#$%

LM01/+6 NNN6O 6

AF" (+ '#., />."@$+"2+ (+ /0 &,.%+ +" 2#-&*+ ($ 2#-&#,*+-+"* :,)5$+"*.+/ ($ F/*,+!

"#$% 0'#"% ,)0/.%) *,#.% %.-$/0*.#"% (.<),+"*+% %$, /+ F/*,+ (+ ,):),+"2+ LP.46 NN6Q 6

R K0 &,+-.9,+ +" "+ &,+"0"* 5$+ (+% 2#-&#%0"*% .()0$3! = /0 :#.% &#$, /+% ."($2*0"2+%

+* /+% 2#"(+"%0*+$,% L%28)-0 S NNN6OT LU)%$/*0*% S NNN6OV! 2#$,1+ A 6

Page 73: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$%&'()*'#+ $, -#./#()+* .)0+%*'1,2

!"#$% """#$ % &'()*+ ,- ./012 345 +62' '7*879+:09 '+8+';0;<9 20 ;:,-'0;<9 ;,)+-=

% >+ 92'7:,2 2: :2 812:+:0 ?-2 ,29 '7*879+:09 ;,)+-= 87-1 /29 ;:,-'0+:'29 20 /2

*7,@/2 1)2/ 87-1 /29 '+8+';0)9 AB)9-/0+09 C """#$DE '7-1F2 GH#

% /+ 017;9;@*2 2: 812:+:0 07-029 /29 '+1+'0)1;90;?-29 1)2//29 A9'()*+ C """#$IHAB)9-/0+09 C """#$DE

'7-1F2 3H#

!"#$% """#$I % &'()*+ ,- ./012 345 +62' '7*879+:09 1)2/9

3282:,+:0E /+ J)7*)01;2 )0+:0 -: 82- 8/-9 '7*8/2=2E 87-1 8/-9 ,2 /;9;F;/;0)E :7-9

+67:9 K 2*8+?-20) L '210+;:29 8+10;29# M;:9;E /29 JN1+02-1 20 /+ 1)9;90+:'2 9)1;2 97:0

1+992*F/)9 ,+:9 /2 F/7' +882/) K F7F;:2 L# >29 F71:29 A2OE 2PH ,)9;J:2:0 /29 F71:29 ,-

'Q0) )/2'01;?-2 20 A*OE *P H ,)9;J:2:0 /29 F71:29 ,- 'Q0) *+J:)0;?-2# >29 )/)*2:09

,):7**)9 K R-=S0-F2S53 L 20 K R-=S0-F2S 5T L 1281)92:02:0 12982'0;62*2:0

/29 07129 ,2 *7,2 '7**-: 20 ,2 *7,2 ,;U)12:0;2/#

4: +:+/N9+:0 '29 '7-1F29E :7-9 12*+1?-7:9 ,+:9 /2 92'7:, '+9E /V+88+1;0;7: ,2 017;9 <1)P

?-2:'29 ,2 1)97:+:'2 2: '7:9;,)1+:0 /2 *7,@/2 1)2/ ,29 '+8+';0)9# 329 <1)?-2:'29 ,2 1)97P

:+:'2 '7112987:,2:0 +-= <1)?-2:'29 8178129 ,2 1)97:+:'2 ,29 '+8+';0)9 Cx W XX! YZ[ 20

Cy W \E]$ 5Z[# ^7-1 /+ 017;9;@*2 9;*-/+0;7:E :7-9 7F92167:9 ?-2 /+ 81;92 2: '7*802 ,-

'7*87102*2:0 *+J:)0;?-2 2: <1)?-2:'2 ,;*;:-2 /29 821<71*+:'2 ,- ./012 +81@9 \E]$ 5Z[#

_1`'2 W /+ ,)82:,+:'2 <1)?-2:0;2//2 ,2 :7012 *7,@/2 /2 '7*87102*2:0 ,V-: ./012 345

W 01+a209 ,2 R-= 53 20 5T ,;U)12:09 290 81)6;9;F/2 9-1 -:2 01@9 /+1J2 8/+J2 ,2 <1)?-2:'29#

Page 74: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()$*+ ,& -')./ 012 3*%4'/) !

"#$#%&'%() %*(+# ,*-+.# &# $#+(-+/'(0*%, %12('%( 3-1-% 4*&56#) %*-, %# $*-7*%, $',

.*4$'+#+ .#, ,04-6'(0*%, 8 &#, 4#,-+#, ,-+ 6# ,9,(54# :6*/'6; "# 4*&56# ' 61'7'%(':# &#

,2$'+#+ 6#, $'+'45(+#, :2*42(+03-#, &#, $'+'45(+#, $<9,03-#,; =6 7' &*%. %*-, $#+4#((+#

&# 4*&260,#+ 6#, &0>2+#%(#, (*$*6*:0#, &# .*4$*,'%( -%03-# #( &# 6#, *$(040,#+ #% 7- &#

610%&-,(+0'60,'(0*%;

!"#$% ===;?@ A =%B-#%.# &# 6' $+0,# #% .*4$(# &# 6' C+23-#%.# ,-+ 6# 4*&56#

Page 75: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 76: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&' ()

!"#$#%&"#'( )" *+&,#%&"#'( -. /'$!'%&("

$&0(+"#1.)

!""#$%&

!"# $%&'()*+ ),(-&./.+0&.(1 )* 20 &(-(2(3.* !

!" # $ %&'()*+$,*&- '. )$ ,&/&)&0*. $1.2 .-,3.4.3 56

!" # 7 8&-2,*&- &79.2,*4 5:

!" # 2 ;<&*= '. )>$)0&3*,<?. '>&/,*?*+$,*&- 55

!"4 5%+62&0&+ )* 2,(-&./.+0&.(1 "

!" 6 $ ;&-,3$*-,.+ )*(+ $@ ?$,(3*$@ ., $@ 7&7*-$0. 5A

!" 6 7 B-,3.4.3 ?*-*?$) 3($)*+$7). C#

!"7 8090:&%9.+0&.(1 )6 :(/-(+01& #$

!"; 8(1:26+.(1 #%

!"#$!

! "#$%&'(! %()*!+'!, -$+* .+! %(!/&0(! %$('&!, 1$ /2-)1&*$'&2+ !' 132%'&/&*$'&2+ -.

"2/%2*$+' .+&4.! 5 !+'(!6!(7 8%(0* 1$ 9$1&-$'&2+ -! 13)"(&'.(! /$'(&"&!11! -. "2/%2:

*$+', 1$ /)'#2-! -32%'&/&*$'&2+ %!(/!''$+' 1$ %(&*! !+ "2/%'! -!* "2+'($&+'!* !*' %():

*!+')!7 ;3)'!+-.! -. -2/$&+! -! *21.'&2+* $ )') $+$1<*)!7 =$+* .+ *!"2+- '!/%*, 1!*

"2+'($&+'!* &+-.*'(&!11!* 2+' )') )9$1.)!* !' &+')>()!* 5 132%'&/&*$'&2+ !' .+ %(2'2'<%!

$ )') ()$1&*)7

Page 77: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

!"# $%&'()*+ ),(-&./.+0&.(1 )* 20 &(-(2(3.*

"# $%&'()%* +,(,*', -%'+ &# .%/0&)$#()%* -,+.,( /, $0-#+,+ &,$ 1+#*/,'+$ 10%.0(+)2',$

/,$ 1+#*/,'+$ .#1*0()2',$3 4,( #5#*(#1, *%'$ -,+.,( /6%-().)$,+ &, 5%&'., /' 7%.-%$#*(

'*)2', -%'+ '* .#(0+)#' .#1*0()2', /%**03

!"#"$ %&'()*+$,*&- '. )$ ,&/&)&0*. $1.2 .-,3.4.3

8 -#+()+ /' $790.# /, &# (%-%&%1), #5,7 ,*(+,:,+ ;<)13 ==3>?@ *%'$ #5%*$ /0(,+.)*0 &,

$790.# 0&,7(+)2', 02')5#&,*( ;<)13 =A3>?3

!"#$% =A3> B C%-%&%1), #5,7 ,*(+,:,+

4,((, D1'+, +,-+,*/ &, .%/E&, 1F+#(,'+G7#-#7)(0 ;D1'+, ===3H? /07+)( #' 79#-)(+, -+0G

70/,*(3 ",$ 0&0.,*($ /0*%..0$ I C'J,KL'MKN4> O@ I C'J,KL'MK N4! O ,( I C'J,K

L'MK P#.J, O@ +,-+0$,*(,*( +,$-,7()5,.,*( &,$ ! /,.)G(%+,$ ,( &# P#.J, 7,*(+#&,3 ", /,+*),+

0&0.,*( I C'J,KL'MK #)+ O +,-+0$,*(, &6,*(+,:,+ 2') #5,7 &, :%+.#&)$., +,(,*' ,$( .%/0&)$0

-#+ '*, 7#-#7)(03

Q#*$ '* -+,.),+ (,.-$@ *%'$ #5%*$ +0#&)$0 &, 7#&7'& /, &# .#(+)7, ,*(+0,R$%+(), /'

7%.-%$#*( /, .#*)E+, S )*(01+,+ 7,&')G7) /#*$ &# /,$7+)-()%* $F$(E., -+0$,*(0, #' 79#-)(+,

== 2', *%'$ #5%*$ ,*$')(, 7%.-#+0 #' .%/E&, 7)+7')( ;<)13 =A3!?3

!"#$% =A3! B A0+)D7#()%* /, &607+)('+, .#(+)7),&&,

T%'+ 5#&)/,+ 7,((, .)$, ,* 02'#()%*@ '*, 7%.-#+#)$%* /,$ -,+('+J#()%*$ %J(,*',$ $'+

&, UV=" ,*(+, &, &%1)7),& 7)+7')( ;W'7$? ,( &, 7#&7'& 5)# *%(+, .#(+)7, /, (+#*$:,+( ,$( /%**0,

$'+ &# D1'+, =A3!3 "# 7%*7%+/#*7, /,$ +0$'&(#($ *%'$ -,+.,( /, 5#&)/,+ *%(+, 07+)('+,

Page 78: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*+ ),(-&./.+0&.(1 )* 20 &(-(2(3.* !

"#$%&'&())(* +#&,$(,#,$ -%.'( / )# 0%&1( (, '2"0$( 1&"3)$#,4( 5(1 0#%#"6$%(1 -42"4$%&73(1

($ 5(1 0#%#"6$%(1 "#-,4$&73(18 ,231 #))2,1 02392&% "(,(% 3,( 4$#0( 5:20$&"&1#$&2, 5( '($$(

$202)2-&( 5( '2"021#,$*

!"#"$ %&'()*&' &$+,()*-

!""# #$%&'()* +,-. &# /0,%'12# 334 &5!67#/1'8 +# /#11# *1)+# #.1 &, 2*+)/1'!- +) 9!:

&)"# +) /!"%!.,-1 ",;-*1'()# /!-12,'-1# %,2 +#. %#28!2",-/#. ,) "!'-. *()'9,&#-1#. <

&, .!&)1'!- +# 2*8*2#-/#= ># 9!&)"# +# /0,()# 1!%!&!;'# +*%#-+ +# %&).'#)2. %,2,"?12#.

;*!"*12'()#. @

A ># +',"?12# #$1*2'#)2 +) 1!2# BDextC

A ># +',"?12# '-1*2'#)2 +) 1!2# BDintC

A >, 0,)1#)2 +) 1!2# BHautC

A >5#-12#8#2 BEntC

A ># -!"62# +# .%'2#. BNC=

D!). +#9!-. +!-/ )1'&'.#2 )- ,&;!2'10"# +5!%1'"'.,1'!- .)2 /#. E %,2,"?12#.= #%#-:

+,-14 /#. %,2,"?12#. .!-1 /!-12,'-1. %,2 +#. *(),1'!-. ;*!"*12'()#. #1 %0F.'()#. ()' &':

"'1#-1 &5#.%,/# +#. .!&)1'!-. B#- 6&,-/ .)2 &#. G;)2#. 3H=I4 3H=J4 3H=EC= K!)2 %!)9!'2

'-1#2%2*1#2 &# +!",'-# +#. .!&)1'!-.4 -!). ,9!-. +*/'+* +# %2*.#-1#2 +#. /!)%#. LM +# /#&)':

/'= M#)$ +#. %,2,"?12#. .!-1 ,&!2. 9,2',6&#. #1 1!). &#. ,)12#. G$*.= N)2 &#. ;2,%0'()#. &#.

,$#. .!-1 ;2,+)*. #- O .)2 &5'-1#29,&&# +# 9,2',1'!- +# /0,()# %,2,"?12#=

A K,2 #$#"%&#4 %!)2 &, /!-12,'-1# +# 6!- .#-. %!)2 &,()#&&# M',"?12# #$1*2'#)2 BDextCP

M',"?12# '-1*2'#)2BDintC=

!"#$% 3H=I A Q.%,/# +#. .!&)1'!-. %!)2 &, /!-+'1'!- ;*!"*12'()# &!;'()# +#. +',"?12#.

A N' &, 1!%!&!;'# +!'1 ,9!'2 )- #-12#8#2 BQ-12#8#2 BEntCP RC

A S!)1#. &#. 1!%!&!;'#. .!-1 6!6'-*#. BN P RC

A ># -!"62# +# .%'2#. +!'1 T12# /!-1#-) +,-. &5#.%,/# +# 6!6'-,;#= K,2 #$#"%&#4 %!)2

)- 1!2# ,9#/ )- 6!6'-,;# %2'",'2# #1 .#/!-+,'2# +# D .%'2#. /0,/)-4 6!6'-* ,9#/ )-

G& +# +',"?12# BDfilC4 #- /!-.'+*2,-1 )- /!#U/'#-1 +# 8!'.!--#"#-1 +# V @

N Dfil <π

2(Dint −Dfil) B3H=VC

K!)2 )- -!"62# +# .%'2#. ",$'")" G$* .)2 )-# .#)&# /!)/0#4 &5#.%,/# +#. .!&)1'!-.

#.1 %2*.#-1* .)2 &, G;)2# 3H=J=

Page 79: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

!"#$% "#$! % &'()*+ ,+' '-./01-2' (-/3 .) *-2,101-2 ,+ 4-412)5+ '/3 /2+ '+/.+ *-/*6+

(-/3 78 9: '(13+' ,+ ;. ,</2 ,1)=>03+ ,+ ?$ ==

% @) *-2,101-2 ,+ 2-2 ')0/3)01-2 ,/ 0-3+$ &2 +A+0B =C=+ '1 2-/' )D1-2' D/ E/+ (-/3

.) 0-(-.-51+ )D+* +203+F+3B .+ 0-3+ 2<G0)10 ()' ')0/3GB 1. +'0 (3GFG3)4.+ ,+ .+ F)13+ 03)H

D)1..+3 ,)2' ') I-2+ .12G)13+B *<+'0 J ,13+ )D)20 .+ *-/,+ ,+ ')0/3)01-2$ K+00+ *-2,101-2

+'0 1../'03G+ ()3 .<GE/)01-2 "#$9B L' G0)20 .) (-.)31')01-2 J ')0/3)01-2 ,/ =)0G31)/

=)52G01E/+$ &2 (3+2)20 /2 *-20-/3 ,<M=(>3+ '/3 /2 ,+=1 *-=(-')20 N

HMC1 ∗ lMC1 +Hjambe ∗ ljambe +Hair ∗ Ent = NI O"#$PQ

&2 =-,+ ,1AG3+201+.B .+ R/S (3-,/10 ,)2' .+ 43)' TK? '<)22/.+ ()3 *+./1 (3-,/10 ()3

.+ 43)' TKPB 1. 2-/' 3+'0+ ).-3' N

B

µ0µr

∗ ljambe +B

µ0∗ Ent = NI avecB < 0.85 ∗ Js O"#$9Q

!"#$% "#$U % &'()*+ ,+' '-./01-2' (-/3 .) *-2,101-2 ,+ 03)D)1. ,)2' .) I-2+ .12G)13+ ,/

0-3+

M ()3013 ,+ .) *-/34+ "#$UB 2-/' (-/D-2' ,G0+3=12+3 .) D).+/3 ,+ .<+203+F+3 =121=).B

*+ E/1 *-33+'(-2, J /2+ D).+/3 ,+ :$?PU == (-/3 /2 2-=43+ ,+ '(13+' ;SG J P?$ V)2'

Page 80: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*+ ),(-&./.+0&.(1 )* 20 &(-(2(3.* !

"# $%&'( )( *( +#,#-,#+.(/ 01 +0%,,# 10'(, 2%( "($ 3#"(%,$ )4(1',(5(, ',0%36($ $01'

'0%70%,$ $%+6,&(%,($ 8 *(''( 3#"(%, *019,:#1' #&1$& "4.;+0'.<$( )( 101 $#'%,#'&01 )%

'0,( =>2? @A?BC?

D($ *01',#&1'($ )( +(,50,:#1*( 3&(11(1' 6-#"(:(1' $4#70%'(,? E0::( 10%$ "4#301$ )6F

91& +,6*6)(::(1'/ "# 3#"(%, )( "# '(1$&01 #%G H0,1($ )% IJ@D )0&' K',( #% :0&1$ &156,&(%,(

8 *(""( )% *#$ )( ,656,(1*(/ *( 2%& *0,,($+01) 8 %1( :(&""(%,( #''61%#'&01?

L0%, $#30&, $& 10',( *0:+0$#1' ($' ,6#"&$#H"(/ 10%$ 10%$ $0::($ &1'6,($$6$ 8 "46'(1)%(

)% )0:#&1( )( $0"%'&01$ #3(* "($ ,("#'&01$ )( *01',#&1'($? M#1$ %1 +,(:&(, '(:+$/ 10%$

,(:#,2%01$ 2%( "( 10:H,( :#G&:%: )( $+&,($ )6+(1) )% )&#:<',( &1'6,&(%, )% '0,( =>2?

@A?NC? M( +"%$/ "# *01',#&1'( )( $#'%,#'&01 14($' +#$ +,6$(1'6( #3(* "($ :K:($ +#,#:<',($?

>1 (O('/ +0%, +0%30&, 0H$(,3(, "# $#'%,#'&01 )#1$ "( :K:( ,(+<,(/ &" 10%$ 5#%' 9G(, "($

3#"(%,$ )4#%',($ +#,#:<',($ =N (' EntC? P91 )40H$(,3(, "4&1Q%(1*( )($ *01',#&1'($/ 10%$

#301$ ,6#"&$6 %1( 6'%)( *0:+#,#'&3( =R#H"( @A?NC? D($ 3#"(%,$ )4(1',(5(, *0,,($+01)(1' #%G

3#"(%,$ :&1&:#"($ +0%, "( 10:H,( )( $+&,($ *.0&$&?

!"#$ @A?N S @1Q%(1*( )($ *01',#&1'($ $%, "( )0:#&1( )($ $0"%'&01$

>1' T U?UVWN :: >1' T U?NX! :: >1' T U?BN ::

Y$+&,($ T N!

Y$+&,($ T XN &:+0$$&H"(

D($ )(%G +,(:&<,($ *01',#&1'($ )691&$$(1' %1 ',&#1-"(/ )#1$ "( +"#1 Dext/Dint 8 #%',($

3#"(%,$ 9G6($ (' &:+0$(1' "($ )&:(1$&01$ :&1&:#"($ )($ )&#:<',($ (G'6,&(%, (' &1'6,&(%,?

E($ 3#"(%,$ $01' (1 #**0,) #3(* "( +,(:&(, )&:(1$&011(:(1' ,6#"&$6 $0%$ Z#'.*#) )#1$ "(

*.#+&',( +,6*6)(1'? L#, #&""(%,$/ 10%$ ,(:#,2%01$ 2%( "( )0:#&1( )($ $0"%'&01$ $4#-,#1)&'

"0,$2%401 #%-:(1'( "# 3#"(%, )( "4(1',(5(,/ *( +.610:<1( ($' )[ 8 "# 101 $#'%,#'&01 )%

:#'6,&#%? \1 +(%' ,(:#,2%(, 2%48 +#,'&, )4%1( *(,'#&1( 3#"(%, )4(1',(5(,/ *(''( *01',#&1'(

14# +"%$ )4&1Q%(1*( $%, "( )0:#&1( )( $0"%'&01?

Page 81: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

!"#"$ %&'() *+ ,-.,/'0(1&2+ *-'31(2(4.1('5

!"# $% &'()*%' +% ,%-++%)' .%) $% */'-/0+%1 2)- ,-#-,-1% +% *(+),%3 #()1 /*(#1 45%'456

)# /+7('-&5,% 1-,8+% %& '/8-$% 9:;<=>? @# %A%&3 #()1 4(##/-11(#1 +B('$'% $% 7'/#$%)' $%1

$-,%#1-(#1 /*%4 +% 8'%,-%' 8'6C$-,%#1-(##%,%#& 1()1 D/&54/$3 %# $6"#-11/#& )#% 8+/7%

$% $(##6%1 /)&()' $% 4%1 */+%)'13 4%+/ $-,-#)% +/ $)'6% $B6&)$% %# '6$)-1/#& +B%18/4% $%

1(+)&-(# /) $(,/-#% )&-+%? E()1 /*(#1 45(-1- $%1 */+%)'1 ,-#-,/+%1 $% <?FG H(-1 8+)1 8%&-&%1

%& $%1 */+%)'1 ,/I-,/+%1 $% F H(-1 8+)1 7'/#$%1 2)%+1 2)% 1(-%#& +%1 8/'/,J&'%1?

K% 8'%,-%' /+7('-&5,% &%1&6 1()1 D/&+/0 8%',%&&/#& 4% &L8% $% ,($6+-1/&-(# %1& +/ H(#4C

&-(# fminsearchbnd3 $6*%+(886% 8/' )# )&-+-1/&%)' %& &6+645/'7%/0+% 1)' +% M "+%%I45/#7% N

$) 1-&% $% ,/&5O('P1? K/ H(#4&-(# fminsearchbnd %1& %,8+(L6% %I/4&%,%#& 4(,,% +/ H(#4C

&-(# fminsearch Q2)-3 %++%3 %1& )#% H(#4&-(# 4'66% 8/' +%1 $6*%+(88%)'1 $% ,/&5O('P1R 1/)H

2)B%++% 8%',%& $% $(##%' )# %#4/$'%,%#& $%1 */'-/0+%1 $B%#&'6%1 Q0('#%1 ,-# %& ,/IR3

4% 2)- #B%1& 8/1 8(11-0+% /*%4 +/ H(#4&-(# ('-7-#%++% fminsearch? K/ H(#4&-(# fminsearch

8%',%& $% &'()*%' +% ,-#-,), $B)#% H(#4&-(# ,)+&-*/'-/0+% 1/#1 4(#&'/-#&% %# )&-+-1/#&

)#% ,6&5($% 1/#1 $6'-*6%? fminsearch 8%',%& /+('1 4/+4)+%' +% ,-#-,), $B)#% H(#4&-(#

14/+/-'% $% 8+)1-%)'1 */'-/0+%1 S 8/'&-' $% +B%1&-,/&-(# -#-&-/+%? @++% %1& 0/16% 1)' +/ ,6&5($%

$% E%+$%'CD%/$ 9KTUUV=3ED G>?

!"#$% WX? Y @*(+)&-(# $) 1-,8+%I% $% E%+$%' %& D%/$ Q+% 1-,8+%I% ('-7-#/+ %1& %#

8(-#&-++6R

K/ ,6&5($% $% E%+$%' %& D%/$3 /88%+6% /)11- '.%5*0, 01 (&'$/,6,3 4(#1-1&% S H/-'%

6*(+)%' )# 1-,8+%I% *%'1 )# ,-#-,-1%)' $% +/ H(#4&-(# (0.%4&-H 8/' $%1 %I8/#1-(#1 () $%1

4(#&'/4&-(#1 1)44%11-*%1 $) 1-,8+%I% %# H(#4&-(# $% +/ &(8(+(7-% +(4/+% QZ-7? WX? R? [# 1-,C

Page 82: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*+ ),(-&./.+0&.(1 )* 20 &(-(2(3.* !

"#$%$ &$ &'($)*'+) 4 $*, #-$).$#+""$ /+).$%$ &$ 45# .$/,$01* #')23'1$($), ')&2"$)&3),*4

4 $*, #3 &'($)*'+) &$ #-$*"3/$ +5 #3 6+)/,'+) +78$/,'6 "1$)& /$* .3#$01*4 93 "1$(':1$ 2,3"$

/+)*'*,$ ; $)#$.$1 #$ "+'), &0 *'("#$%$ +5 #3 6+)/,'+) $*, (3%'(3#$ $, ; #$ 1$("#3/$1 "31

#3 12<$%'+) &$ /$ "+'), "31 13""+1, 30 /$),1$ &$ =13.',2 &$* > "+'),* 1$*,3),*4 ?' /$ "+'),

$*, ($'##$01@ +) 2,'1$ #$ *'("#$%$ &3)* /$,,$ &'1$/,'+)4 ?')+)@ +) $*, &3)* 0)$ .3##2$@ $, +)

12&0', #$ *'("#$%$ "31 0)$ *'('#',0&$ /$),12$ *01 #$ "+'), &0 *'("#$%$ +5 #3 6+)/,'+) $*,

(')'(3#$4

A$, 3#=+1',B($ &$ >$#&$1 $, C$3& "$1($, &$ ,1+0.$1 0)$ *+#0,'+) *'("#$($), &3)* #3

"#0"31, &$* /3* *3)* )2/$**',$1 #$ /3#/0# &0 =13&'$),4 9-')/+).2)'$), &$ /$, 3#=+1',B($ $*,

D0$ #3 6+)/,'+) 1$/B$1/B$ 0) (')'(0( #+/3# $, $*, &+)/ ,1:* &2"$)&3),$ &$* /+)&','+)*

')','3#$*4 E1 &3)* )+,1$ /3*@ )+0* &$.+)* ,1+0.$1 0) (')'(0( =#+73#4 F+01 /+),1$1 /$

"1+7#:($@ "#0*'$01* *+#0,'+)* *+), "+**'7#$* G

H 93 "1$(':1$ *+#0,'+) /+)*'*,$ ; /B3)=$1 317',13'1$($), $, 0) )+(71$ 2#$.2 &$ 6+'*

#$* /+)&','+)* ')','3#$*4 9$ (')'(0( =#+73# *$13 #$ "#0* "$,', &$* (')'(3 #+/30%4

A$,,$ (2,B+&$ $*, #+)=0$ $, 63*,'&'$0*$4 I$ "#0*@ #$ )+(71$ J2#$.2K &-',213,'+)*

2,3), 3#23,+'1$ &-0)$ +",'('*3,'+) ; 0)$ 30,1$ $, #$* /+)&','+)* ')','3#$* "3* 6+1/2($),

'&23#$($), /B+'*'$*@ )+0* )$ *+(($* "3* /$1,3') &$ ,1+0.$1 #$ (')'(0( =#+73#4

H 93 &$0%':($ *+#0,'+) /+)*'*,$ $) #-0,'#'*3,'+) &-0) 3#=+1',B($ =2)2,'D0$4 9-'),21L, &$

/$ ,M"$ &-3#=+1',B($ $*, D0-'# "31/+01, ,+0, #$ &+(3')$ &$ *+#0,'+)* ,1:* 13"'&$($),

"+01 ,1+0.$1 #-+1'$),3,'+) &$ #3 ($'##$01$ *+#0,'+)4 A$"$)&3),@ '# )$ "$1($, "3* &-36N

O1($1 D0$ #3 *+#0,'+) ,1+0.2$ *+', #$ (')'(0( =#+73#4 A$, 3#=+1',B($ $*, &2,3'##2

&3)* #$ "313=13"B$ *0'.3),4

H 93 &$1)':1$ *+#0,'+) $*, #3 /+(7')3'*+) &$* &$0% 3#=+1',B($* "12/2&$),*4 P) $Q$,@

#-3#=+1',B($ =2)2,'D0$ "$1($,,13 13"'&$($), &-+7,$)'1 0)$ *+#0,'+) 3""1+/B2$ &0

(')'(0( =#+73# $, #-3""#'/3,'+) &$ #3 6+)/,'+) fminsearchbnd "$1($,,13 &$ #$ &2N

,$1(')$14

9$* 3#=+1',B($* =2)2,'D0$* 3""31,'$))$), ; #3 63('##$ &$* 3#=+1',B($* 2.+#0,'+))'*,$*

RS+#[email protected]@WWXYZ4 9$01 70, $*, &-+7,$)'1 0)$ *+#0,'+) 3""1+/B2$ ; 0) "1+7#:($ &-+"N

,'('*3,'+)@ #+1*D0-'# )-$%'*,$ "3* &$ (2,B+&$ $%3/,$ [+0 D0$ #3 *+#0,'+) $*, ')/+))0$\ "+01

#$ 12*+0&1$ $) 0) ,$("* 13'*+))37#$4 9$* 3#=+1',B($* =2)2,'D0$* 0,'#'*$), #3 )+,'+) &$ *2N

#$/,'+) )3,01$##$ $, #-3""#'D0$), ; 0)$ "+"0#3,'+) &$ *+#0,'+)* "+,$),'$##$* 30 "1+7#:($

&+))24 ]) 3#=+1',B($ =2)2,'D0$ .3 63'1$ 2.+#0$1 0)$ "+"0#3,'+) &3)* #$ 70, &-$) 3(2#'+1$1

#$* ')&'.'&0*4 P, /-$*, &+)/@ ; /B3D0$ =2)213,'+)@ 0) $)*$(7#$ &-')&'.'&0* D0' *$13 ('* $)

3.3), $, )+) 0) ')&'.'&0 "31,'/0#'$14 >+0* +7,'$)&1+)* &+)/ 0) $)*$(7#$ &$ *+#0,'+)* "+01

0) "1+7#:($ $, "3* 0)$ *+#0,'+) 0)'D0$4 9$* *+#0,'+)* ,1+0.2$* *$1+), =2)213#$($), &'Q2N

1$),$*@ (3'* *$1+), &-0)$ D03#',2 2D0'.3#$),$4 9$ &21+0#$($), &-0) 3#=+1',B($ =2)2,'D0$

"$0, L,1$ &2/+0"2 $) /')D "31,'$* G

H 93 /123,'+) &$ #3 "+"0#3,'+) ')','3#$

H 9-2.3#03,'+) &$* ')&'.'&0*

H 93 /123,'+) &$ )+0.$30% ')&'.'&0*4 A$,,$ 2,3"$ /+)*'*,$ ; "1$)&1$ &$* (+1/$30% &$

*+#0,'+) &$ /$1,3')* ')&'.'&0* $, &-30,1$* (+1/$30% &-30,1$* ')&'.'&0* "+01 /12$1 &$*

)+0.$30% ')&'.'&0* D0'@ +) #-$*":1$@ *$1+), &$ ($'##$01$* *+#0,'+)* ; )+,1$ "1+7#:($4

^# $*, ,+0, ; 63', "+**'7#$ &$ /B+'*'1 &$* ')&'.'&0* 30 B3*31& $, &$ #$* (2#3)=$1 3#23N

,+'1$($), "+01 /12$1 &$ )+0.$30% ')&'.'&0*4 _+0,$6+'*@ )+0* 3.+)* /B+'*' #$ "1')/'"$

&$ #-2#','*($4 A$,,$ (2,B+&$ &$ *2#$/,'+) "$1($, &$ ($,,1$ $) 3.3), #$* ($'##$01*

Page 83: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

!"#$% "#$% & '()*+, -. /012(1/. -. 34,356017)+. 5*2*7189.

12-1:1-9; -. 3, /6/93,7162$ <. ;627 -62( 3.; 12-1:1-9; 3.; /39; /06+.77.90; 891 :627

/,071(1/.0 = 34,+*3160,7162 -. 2670. /6/93,7162$ <.77. +*7)6-. , 34,:,27,5. -. /.0>

+.770. 92. (62:.05.2(. ?/39;@ 0,/1-. -.; ;6397162;A +,1; ,9 -*701+.27 -. 3, -1:.0;17*

-.; 12-1:1-9;$ B2 /0.2- .2 .C.7 3. 01;89. -4*(,07.0 -.; 12-1:1-9; -. /1D70. 89,317*A

+,1; 891 ,90,17 /9 ,//607.0 -. 8961 (0*.0 -. 70D; E622.; ;6397162; -,2; 3.; 5*2*0,7162;

;91:,27.;$

& F412;.07162 -.; 269:.,9G 12-1:1-9; -,2; 3, /6/93,7162

& F, 0*17*0,7162 -9 /06(.;;9;

F.; ,356017)+.; 5*2*7189.; 627 34*260+. ,:,27,5. -. /69:610 H70. ,//3189*; -,2; 92

50,2- 26+E0. -. -6+,12.; -. 0.().0(). -. ;6397162A 360;89413 24.;7 /,; 2*(.;;,10. -4,:610

3, ;6397162 6/71+,3.A 891 /0.2-0,17 /,0 .G.+/3. 706/ -. 7.+/; .7 -. 0.;;690(.; /690 H70.

(,3(93*.$ F, ;6397162 .;7 ,//06()*. /,0 IE62-;J ;9((.;;1K;A (6++. -,2; 92. /06(*-90. -.

;*/,0,7162 .7 *:,39,7162A = (.(1 /0D; 89. (. ;627 -.; K60+93.; 891 ;627 0.().0()*.; .7 262

/39; -10.(7.+.27 -.; :,3.90;$ L77.27162A 92 ,356017)+. 5*2*7189. +,G1+1;. 92. K62(7162

6EM.(71KA 13 K,97 -62( 0,M697.0 92 ;152. +612; 69 12:.0;.0 3, :,01,E3.$ N,2; 2670. (,;A 269;

,:62; ()61;1 -. +.770. 92 ;152. +612; = 3, K62(7162 6EM.(71K$

!"# $%&'()*)& +, (-./)010&*)0.2

L /,0710 -.; (6270,127.; -*O21.; (1>-.;;9; .7 -. 3, -*O217162 -9 :639+. ,//,0.27 -9

760.A 269; 6E7.262; 3. -1+.2;1622.+.27 ;91:,27 ?P,E3. "#$Q@ R

<. 0*;937,7 .;7 70D; .2(690,5.,27 /91;89413 /.0+.7 -. 0*-910. 3. :639+. -9 (6+/6;,27

+,52*7189. -. S T /,0 0,//607 ,9G (6+/6;,27; -. 0*K*0.2(. ?14.4cm3@$ LO2 -. /,0K,10.

Page 84: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*)& +, (-./)010&*)0.2 !

!"#$ "#$% & '( )*+,*-./0 1 (/02(3(2 (0 +.0425.6 6/576( 8,2(+5(2 95+(/-5*//(+(/0:

Dext(mm) Dint(mm) Haut(mm) Ent(mm) Nspires V olume(cm3)

;%$< =>$ ;$ ?$%?< ;% @$>

AB4069( 9( )(00( 0*,*A*C5( (/ D6( 9( -. 24.A5-.05*/E /*6- /*6- -*++(- 5/042(--4- 9( ,A6-

,2F- .6G )*/02.5/0(- 9B5/96-025.A5-.05*/ 9B6/ 0(A )*+,*-./0$

!"#"$ %&'()$*'(+, -*., $/ 0$(.)*$/ +( $/ 1&1*'$2+

H/ ,.--./0 1 A. ,I.-( 9( 24.A5-.05*/E /*6- .D*/- 9J ,2(/92( (/ )*+,0( ,A6-5(62- ,.K

2.+F02(- 5/96-025(A-$ L./- 6/ ,2(+5(2 0(+,-E A(- )*/02.5/0(- 9( 3.5-.M5A504 -*/0 A54(- 1 A.

95-,*/5M5A504 9(- +.0425.6G (0 9(- M*M5/(6-(- 95-,*/5MA(-$ N*6- .D*/- 9*/) 2.O*604 )*++(

)*/02.5/0( P

& '. A.2C(62 9( M./9( 95-,*/5MA( 765 )*/9505*//( A. I.60(62 +5/5+.A( (0 +.G5+.A( 96

0*2( 8@ ++E $% ++E > ++E =? ++E =@ ++E %? ++ (0 %@ ++:$

& '( 95.+F02( /4)(--.52( ,*62 3.52( ,.--(2 A. /.D(00( 9( A. M*M5/(6-( 765 )*/9505*//(

A( 95.+F02( 5/0425(62 96 0*2( 8Q*6- A(- 95.+F02(- ,.52- )*+,25- (/02( =? (0 ;? ++:

%&'()$ "#$> & R*M5/.C( 9B6/ 0*2(

S(,(/9./0E .D() AB.AC*250I+( C4/40576(E */ 94T/50 6/( ,A.C( 9( -*A605*/- (0 /*/

,.- 9(- -*A605*/- ,2494T/5(-$ S(- )*/02.5/0(- D*/0 9*/) /*6- .+(/(2 1 94T/52 A(-

M*2/(- +5/5+.A(- (0 +.G5+.A(- 9( AB(-,.)( 9(- -*A605*/-$ '. -*A605*/ 02*6D4(E /(

)*22(-,*/92. ,.- 3*2)4+(/0 1 6/ 95.+F02( *6 6/( I.60(62 -0./9.29$ '( )*+,*-./0

T/.A .62. .A*2- 9(- 95.+F02(- (0 I.60(62- -0./9.29- O6-0( -6,425(62( ,*62 .--62(2 A(-

,(23*2+./)(-$

& '( 3*5-*//(+(/0 9(- M*M5/.C(- ,25+.52( (0 -()*/9.52( 9( ?$! 765 )*/9505*//( A(

/*+M2( 9( -,52(- +.G5+.A($ "/3*2+.05*/ 9*//4( ,.2 A. -*)5404 QSQ$

'. 0*,*A*C5( 76( /*6- .D*/- (/D5-.C4( ,*62 24.A5-(2 )( )*+,*-./0 )*22(-,*/9 1 A. -*A6K

05*/ 5/505.A( 8U5C$ ""$=:$ S(,(/9./0E ,*62 24.A5-(2 )(00( 0*,*A*C5(E 6/( -*A605*/ )*/-5-0(2.50

1 ,*5/V*//(2 (0 (+,5A(2 ,A6-5(62- 3(65AA(- 9B.AA5.C( /./*)25-0.AA5/ )*++( 9./- A( ).- 9(-

0WA(- ,*62 A(- 02./-3*2+.0(62- ,.2 (G(+,A($ S( /B(-0 ,.- (/D5-.C(.MA( 5/96-025(AA(+(/0 D6

A. 32.C5A504 9( AB.AA5.C( /./*)25-0.AA5/$ '(- -(6A- )52)650- 24.A5-.MA(- -*/0 9(- /*X.6G (/2*6K

A4-$ Y*62 24.A5-(2 /*02( -026)062( 9( )*+,*-./0 6/576(E /*6- 9(D*/- 94)*6,(2 6/( M.22(

9( /./*)25-0.AA5/ (0 A. ,A.)(2 .6 +5A5(6 9B6/ 0*2( ,*62 24.A5-(2 A. O.+M( )(/02.A( 0*60 (/

Page 85: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

"#$%&'( )"#*+,#-.'( %& /&%.0" 1. %2.'(".3."4 560, &/6', .'/+,&$# ("6+, ,("0*(0"., 1+7#".'(.,

89&:%. ;<4=>4

!"#$ ;<4= ? 9"6+, ,("0*(0"., 1. %& (6)6%6$+. &/.* .'(".3."

@&', %. (6". A0" %. (6". B' 1C-.

D& )".-+E". 1., (6)6%6$+., *6',+,(. F )%&*." 0'. :&"". 1. '&'6*"+,(&%%+' 1&', %. (6".4

G.).'1&'(H %. )6,+(+6''.-.'( 1. *.((. :&"". .,( 1+I*+%. +'10,("+.%%.-.'(H *. J0+ .,( )"#K0L

1+*+&:%. )60" %. "#$%&$. )"#*+, 1. %& /&%.0" 1. %2.'(".3."4 D& ,.*6'1. .'%E/. %& *6'("&+'(. 1.

)6,+(+6''.-.'( 1&', %. (6". -&+, %. ("&K.( 1. M0N 1. -61. 1+7#".'(+.% ).0( &""+/." ).").'L

1+*0%&+".-.'( F %& 1+".*(+6' 1. %&-+'&$. 10 "0:&' 8,.%6' %. ,.', 10 3.0+%%.(&$. 1. %& :&"".>H

*. J0+ '2.,( )&, 3&/6"&:%.4

D& 1."'+E". (6)6%6$+. .,( %& )%0, ,+-)%. F -.((". .' O/".4 B%%. "#,60( %., )"6:%E-., 1.

("&K.( 1. M0N ).").'1+*0%&+". *.).'1&'( .%%. .,( 1#3&/6"&:%. )60" %. /6%0-. &))&".'( 10

*6-)6,&'( 8P+$4 ;<4Q!>4

D2&16)(+6' 1. *.((. '60/.%%. 36"-. '60, & &-.'# F .'/+,&$." 0'. 1."'+E". *6'("&+'(.4

B' .7.(H )60" -&N+-+,." %. )&,,&$. 10 M0N 10 (6". F %& K&-:. *.'("&%. .' -61. 1+7#".'(+.%H

'60, $&"16', %2#)&+,,.0" [email protected](L@+'(>RS> 10 (6". .( 1. %& K&-:. *.'("&%. *6',(&'(. -&+, %.,

T&0(.0", 1., 1.0N #%#-.'(, ).0/.'( U(". 1+7#".'(.,4 G.).'1&'(H %& T&0(.0" 10 (6". "#&%+,&'(

%& K&-:. *.'("&%. 16+( U(". :6"'#.4 B' .7.(H ,+ .%%. .,( ("6) $"&'1.H .%%. /& V1#)&,,."W 10

(6". ,6*%. .( 16'* .%%. '. ,."& )&, 0(+%. )60" %. )&,,&$. 10 M0N4 X60" *.%&H '60, 1#*+16',

1. %+-+(." %. 1#)&,,.-.'( VNW F !4Y -- 8P+$4 ;<4Z>

%&'()$ ;<4Z ? A*T#-& .N)%+*&(+3 1. %& %+-+(&(+6' .' T&0(.0"

560, &/6', 1#['+ %. /6%0-. &))&".'( 1. *.((. (6)6%6$+. *6--. 1#*"+( ,0" %& [$0".

;<4Q! )60" ".,(." &0 )%0, )"E, 1., *"+(E"., 1. -&,,. +-)6,# )&" %2&#"6'&0(+J0.4

Page 86: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*)& +, (-./)010&*)0.2 !

!"#$% "#$!% & #'()*+ ,--,.+/0 1) 2'*-'3,/0 )/45)+

!"#"$ %&'()*)( +,&,+-. (/-.,0-$.)

! "#$%# &#'#()*(% +( '*"*,-%"# .+/ #$% )0'#()*(% )#$ &1(%"*/(%#$ /()+$%"/#!!#$ 2 !3#(4

%"#5#"6 7( #8#%9 !* "+:1$/%0 )#$ ;*()#$ )# (*(1&"/$%*!!/($9 !3*$$#,;!*:# )+ %1"# #% )# !*

<*,;# &#(%"*!# (1+$ /,'1$# +( #(%"#5#" ,/(/,*!6 =(# $0"/# )# ,#$+"#$ '1+" )0%#",/(#"

&#%%# >*!#+" )*($ !# &*)"# )# !* $%"+&%+"# #( 51",# )# )?,# * 0%0 (0&#$$*/"#6 @1+$ *>1($

&A1/$/ )#+B %C'#$ )30&A*(%/!!1($ )# ,D,#$ )/,#($/1($ EF*;!# G6HI 2

!"#$ G6H J K*"*,-%"#$ :01,0%"/.+#$ )#$ 0&A*(%/!!1($

L1(:+#+" ,1C#((# M#&%/1( ,1C#((# @1,;"# )# $'/"#$

N &, 0.14 cm2OP

J )#$ %1"#$ "#&+/%$ $1+$ &A*,' %"*($>#"$# #% "#&1+>#"%$ )3+(# "0$/(# 2 Q%1"#$ /,'"0:(0$R

J )#$ %1"#$ "#&+/%$ $1+$ &A*,' %"*($>#"$#9 "#&1+>#"%$ )3+(# "0$/(#9 )0&1+'0$ #( )#+B

#% $+"5*&0$ 2 Q%1"#$ /,'"0:(0$9)0&1+'0$R

L* "0$/(# '#",#% )# "#()"# !# ,*%0"/*+ ,1/($ &*$$*(% S !* )0&1+'#6 L# $+"5*T*:# #%

!30;*>+"*:# '#",#%%#(% )# "#%/"#" !#$ &1+"%4&/"&+/%$ #(%"# 5#+/!!#$9 )# "#()"# !* 5*&# )0&1+4

'0# #% )1(& )# &1(%*&% '!+$ !/$$# #% )# )/,/(+#" */($/ !3#(%"#5#"6

U '*"%/" )# &#$ )#+B %C'#$ )30&A*(%/!!1($9 (1+$ *>1($ &1($%"+/% %"1/$ $%"+&%+"#$ ;1;/4

(0#$ 2

J Q%1"# /,'"0:(0R '1+" )0%#",/(#" !#$ &*"*&%0"/$%/.+#$ /(%"/($-.+#$ )+ &/"&+/% ,*:(04

%/.+# EV/:6 G6OOI6

%&'()$ G6OO J M&A0,* )+ Q%1"# /,'"0:(0R

J Q%1"# /,'"0:(09 )0&1+'09 "#51",0R #( '!*T*(% !#$ )#+B )#,/ %1"#$ #( >/$ S >/$ EV/:6

G6OWI

X#%%# $%"+&%+"# '#",#% )# )0%#",/(#" !# '!+$ '#%/% #(%"#5#" "0*!/$*;!# #(%"# )#+B

$+"5*&#$ '*"5*/%#,#(% !/$$#$ #% %"*>#"$0#$ '*" +( Y+B !1(:/%+)/(*!6 7!!# (1+$ )1((#"*

+(# /()/&*%/1( )# !* ;1"(# ,/(/,*!#6

J Q%1"# /,'"0:(0 Z )#,/4<*,;# R #( '!*T*(% +( )#,/ %1"# $+" +( %1"# /,'"0:(0 EV/:6

G6O[I6

Page 87: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

!"#$% "#$%! & '()*+ ,-.*/01/2 3/4)5./2 *+6)*-/7

!"#$% "#$%8 & '()*+ ,-.*/01/ 9 3+-,:;<-=+ 7

>+((+ ?(*54(5*+ .+*-+( 3+ 3/(+*-,1+* @A+1(*+6+* */<@,?<=@+ +1(*+ @< (*<14B+ 35 ()*+

+( @< ;<-=+ 4+1(*<@+$ C*D4+ <5E 3,F/*+1(? /4B<1(,@@)1?2 1)5? <G)1? */<@,?/ .@5?,+5*?

?(*54(5*+? ,3+1(,H5+? .)5* )=(+1,* 51+ G<@+5* -)I+11+$ J< G<@+5* 3+ 4+( +1(*+6+* 3),(

K(*+ ?5./*,+5*+ <5 4<? .*/4/3+1( .5,?H5+ @+? ?5*6<4+? +1 4)1(<4( 1+ ?)1( .<? @,??+?

+( @+ L5E (*<G+*?+ 4+@@+?:4, .+*.+13,45@<,*+-+1($ M1 +F+(2 ?, 1)5? *+0<*3)1? .@5?

<((+1(,G+-+1( @< N05*+ "#$%82 1)5? 4)1?(<()1? H5+ @+? ?5*6<4+? 3+ @< ;<-=+ 4+1(*<@+

.*/<@<=@+-+1( /=<G5*/+? ?+ *+(*)5G+1( +1 4)1(<4( <G+4 @< (*<14B+ 3+? *5=<1? 4<* @+

()*+ +?( +1*)5@/$

O<1? 51 .*+-,+* (+-.?2 1)5? */<@,?)1? @+ ?4B/-< */@54(<1( 3+? (*),? ?(*54(5*+? =)=,1/+?$

J+? */@54(<14+? ?)1( 3/N1,+? .<* "#$P )Q @ +( R ?)1( *+?.+4(,G+-+1( @< @)105+5* +( @< ?+4(,)1

-)I+11+ 35 1)I<5 +( µr ?< .+*-/<=,@,(/ *+@<(,G+$ J+ .*+-,+* /4B<1(,@@)1 1)5? .+*-+( 3+

3/(+*-,1+* @< G<@+5* -)I+11+ 3+ @< */@54(<14+ 3A51 ()*+ ,-.*/01/$

R =l

Sµ0µr

S"#$PT

U)5* 4B<H5+ ?(*54(5*+2 1)5? */<@,?)1? 3+? -+?5*+? <5 .)1( 3A,-./3<14+ V @A,-./3<14+

.*).*+ SZ0T <,1?, H5+ 3+? -+?5*+? +1 -)3+ 4)--51 SW>T$ X .<*(,* 3+ 4+((+ ,16)*-<(,)12

1)5? */45./*)1? @+? G<@+5*? 3+ .+*-/<=,@,(/? ,1,(,<@+? .+*-+((<1( 3+ 3/(+*-,1+* @< */@54:

(<14+ ()(<@+ 3+ @A/4B<1(,@@)1$ M1 1)5? =<?<1( ?5* @+? G<@+5*? 3+ R')%.-&)1 &'$-.3+. +( @+?

?4B/-<? */@54(<1(? 1)5? <G)1? .5 3/(+*-,1+* H5+ @A+1(*+6+* -,1,-<@+ */<@,?<=@+ /(<,( 3+ !

µ-$

J< 3+*1,Y*+ ).(,-,?<(,)1 =<?/+ ?5* @+? 4)1(*<,1(+? ,135?(*,+@@+? 1)5? 3)11+ @+? 3,-+1:

?,)1? ?5,G<1(+? .)5* @< ?(*54(5*+ +1 3Z-+ S[<=@+ "#$ T$

Page 88: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*)& +, (-./)010&*)0.2 !

!"#$ "#$% & '()*+,-./)-0. 1*2 3/+/3)(+-2)-45*2 15 6)0+* -,7+(8.(9:;-8$ "#$<<=

>?</@A?</ :Z0= >?</@A?<B :CD=

A3E(,/ +(F53)/.)

R_impNI 2*NI

R_imp

G(25F)/)2 R -,7H1.27 ∗ 105H−1 R -,7H 1.28 ∗ 105H−1

!"#$ "#$I & J+0)030F* 1* ,*25+* 705+ F/ 1()*+,-./)-0. 1* FK*.)+*L*+ ,-.-,/F

A3E(,/ +(F53)/.)

NI

R_imp/2

R_imp/2

R_ent/2

R_ent/2

R_imp/2 R_imp/2

R_ent/2

R_ent/2

NI

R_imp/2

>45/)-0. R :>?</@A?</=HR -,7MR *.) R :>?I@A?I=HNR *.)M

34R -,7

>.)+*L*+ 8µm 27µm

!"#$ "#$ & O* 30,702/.) P *.)+*L*+ *) ,/)(+-/5 5.-45* :1-,*.2-0..*,*.) -.152)+-*F=

Dext(mm) Dint(mm) Haut(mm) Hautjambe(mm) Ent(mm) Nspires

!I$< NQ$R % R$% ?$<Q NN$S

%&'()$ "#$<Q & D0,7/+/-20. 1*2 7*+L0+,/.3*2 15 7+0)0)T7* U./F /V*3 F* 30,702/.) 1*

+(L(+*.3*

Page 89: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

"# $%&' ($()*'%$' +, -.'&)/(/0 $%&' -,1(-2&%$' 3($' &$ 4-,1#,- /,14' 2&, )5,$/-,6,-

,'/ 7#,$ '&4.-#,&- 8 )5,$/-,6,- 1#$#1&1 -.()#'(7),0 +,//, /%4%)%9#, ,'/ 3%$+ -.()#'(7),: ;(-

(#)),&-'0 %$ +%$'/(/, 2&, ),' 3#(1</-,' ,/ =(&/,&-' $, +%--,'4%$3,$/ 4(' 8 3,' 3#1,$'#%$'

'/($3(-3': >,//, +%$/-(#$/, ?( 3%$+ $%&' (1,$,- 8 4-.6.-,- 3,' 3#(1</-,' ,/ =(&/,&-' '/($@

3(-3' 4)&' 9-($3,' 4%&- (''&-,- ),' 4,-6%-1($+,' 1(#' +%11, ), 3#(1</-, ,A/.-#,&- ,/ )(

=(&/,&- 3& /%-, $, +=($9,$/ 4('0 +,)( $, 1%3#B,-( 4(' ), ?%)&1, (44(-,$/ 3& +%14%'($/

CD#9: EF:GHI: J%&' %7/,$%$' &$ ?%)&1, (44(-,$/ 3, 11.68 cm3+%$/-, 14.4 cm3

'%#/ &$,

-.3&+/#%$ 3& ?%)&1, 3, KH L: "# %$ -.&''#''(#/ 8 #$/.9-,- )( M(17, +,$/-(), 3($' ), +%14%@

'($/0 ), ?%)&1, 3& +%14%'($/ &$#2&, ',-(#/ 3, 6.6 cm3+%$/-, 14.4 cm3

0 '%#/ &$, 3#1#$&/#%$

3, NN L: ;(- (#)),&-'0 &$, (&/-, 4#'/, 8 ./&3#,- ',-(#/ 3, -.()#',- )( M(17, +,$/-(), (?,+

&$ 3,1#@/%-, %7)%$9 (B$ 3, -.3&#-, '( =(&/,&- ,/ 3%$+ '%$ ?%)&1,: O( /%4%)%9#, 4-%4%'.,

',-( 3%$+ 4)&' 4,-6%-1($/,0 1%#$' ?%)&1#$,&',:

!"# $%&%'()&*+%(*,- ./ ',01,+%-(

;%&- 3,' -(#'%$' 3, 6(+#)#/. #$3&'/-#,)), ,/ ,$ (++%-3 (?,+ ),' -.'&)/(/' 35%4/#1#'(/#%$0

$%&' (?%$' +=%#'# ),' 3#1,$'#%$' '&#?($/,' CP(7), EF:QI:

!"#$ EF:Q R O, +%14%'($/ 8 ,$/-,6,- ,/ 1(/.-#(& &$#2&, C3#1,$'#%$$,1,$/ B$()I

Dext(mm) Dint(mm) Haut(mm) Hautjambe(mm) Ent(mm) Nspires

ST K! N GH H:G! KK

O, 4-%/%/*4, (+/&,) ,'/ -.()#'. (?,+ &$ +%))#,- 3, ',--(9, 1(#' (4-<' 3#'+&''#%$ (?,+ ),'

#$9.$#,&-' 3, P>P0 &$ 7%#/#,- (?,+ &$, +(), (1(9$./#2&, (M&'/.,0 4,&/ U/-, -.()#'. 4%&- )(

4=(', 35#$3&'/-#()#'(/#%$:

%&'()$ EF:GN R ;=%/% 3& +%14%'($/ 1(9$./#2&, &$#2&, (?,+ ,$/-,6,-

VB$ 3, ?()#3,- $%/-, +%14%'($/ B$()0 $%&' ?%&)%$' +%14(-,- +,' 4,-6%-1($+,' 8 )(

'#1&)(/#%$: >,4,$3($/0 $, 3#'4%'($/ 4(' 3, )( '%&-+, 3, 4,-/&-7(/#%$'0 $%&' (?%$' +%14(-.

),' #14.3($+,' ,$ 1%3, +%11&$ ,/ ,$ 1%3, 3#W.-,$/#,) CD#9: EF:GTI:

J%&' +%$'/(/%$' 2&, ),' #14.3($+,' +%--,'4%$3,$/ 8 +,)),' '#1&).,' M&'2&58 G XYZ0

Page 90: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#" $%&'()*+%& !

!"#$% "#$%& ' ()*+,-,./)0 12/ .*+31,042/ 205-2 62 -3/765,5 12 68)+5.*./,5.)0 25 62

4)*+)/,05 90,6

,7 126: 62/ +;30)*<02/ +,-,/.52/ =.200205 205,4;2- 6, *2/7-2 +7./>72 0)7/ 08,=)0/ +,/

*)136./3 62/ 4,+,4.53/ +,-,/.52/$ (2552 4)04)-1,042 0)7/ +2-*25 12 4)0467-2 >72 6, +2-?)-@

*,042 17 4)*+)/,05 70.>72 2/5 1)04 /2*A6,A62 : 0)/ +-3=./.)0/$ B)7/ ,=)0/ 1)04 -3,6./3

70 4)*+)/,05 *,C035.>72 70.>72D *).0/ =)67*.027E 25 +67/ +2-?)-*,05 >72 62 4)*+)/,05

-3,6./3 +,- F./+,0)@G7.H, +)7- 0)5-2 /)7-42 12 +2-57-A,5.)0/$ I2/ =,627-/ 12/ .01745,042/

12 *)12 1.J3-205.26 25 12 *)12 4)**70 4)09-*2 0)/ -3/765,5/ "#$K$

&'()% "#$K ' "01745,042/ 17 4)*+)/,05 : 205-2?2- 25 *,53-.,7 70.>72

LMC LMD

L% *F %KM µF

(2+201,05D 62 4)*+)/,05 F./+,0)@G7.H, , 353 1.*20/.)003 +)7- 702 /)7-42 12 +2-57-@

A,5.)0/ 1.J3-2052/ 12 6, 0)5-2$ "6 /2-,.5 1)04 .053-2//,05 18.1205.92- 62/ +,-,*<5-2/ 12 6,

/)7-42D >7. +)7--,.5 +2-*255-2 12 -21.*20/.)002- 0)5-2 4)*+)/,05 ,./3*205 25 18)A520.-

62/ 4)7-A2/ 4)*+,-,5.=2/ /7- 62 /N/5<*2 -326$

!"# $%&'()*+%&

!"#$ % &' (!)*$ $+ #,-(.$ /0 #,-(,!.$-$+. !1$& /0 -'.1!)'0 -'2+1.)30$ $+ 4,+#.),+

/$ &' (,&'!)*'.),+ $. /$ &' 4!130$+#$5 +,0* '6,+* (0 (!1/)!$ &$ #,-(,!.$-$+. !1$& /0 7&.!$

89: /'+* *,+ $+6)!,++$-$+.; <+$ -1.=,/$ /$ -)+)-)*'.),+ +,0* ' ($!-)* /$ /1.$!-)+$!

&$* #'!'#.1!)*.)30$* 21,-1.!)30$* 7+'&$* /$ &' .,(,&,2)$ .,0. $+ )+#,!(,!'+. &$* #,+.!')+.$*

/0$* % *,+ )+/0*.!)'&)*'.),+; >$ (!,.,.?($ /$ #,-(,*'+. -'2+1.)30$ 0+)30$ ,@.$+0 ($!-$.

0+$ !1/0#.),+ /$ 6,&0-$ /$ AB C ('! !'((,!. '0 #,-(,*'+. $D)*.'+. /'+* &E$+6)!,++$-$+.

30$ +,0* +,0* *,--$* 7D1*; F& $*. )-(,!.'+. /$ (!$+/!$ $+ #,-(.$ 30$ #$ !1*0&.'. /1($+/ G

H /$ +,.!$ -,/1&)*'.),+; 9+ $I$.5 $&&$ /,). J.!$ '-1&),!1$ '7+ /$ (!$+/!$ $+ #,-(.$ &$*

Page 91: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! !" #$%&'&()%&*+ ,% -.)/&()%&*+ 01 2*'$*()+% ')3+.%&41,

"#"$%&'( )*+*(,'%(- .% )#/(0 #1,2%&',34*',5& 2% #* (5/+4% 2% )%+'/+6*',5&( +"%##% %' %&

)*+',4/#,%+ #* )*+' 2% )%+'/+6*',5&( 2% $52% 45$$/& %' 2% $52% 2,7"+%&',%# 8/% &5/(

*95&( )+,( *+6,'+*,+%$%&' ":*#%( 25,9%&' ;'+% $%(/+"%(- <%( $%(/+%( )%+$%''+5&' 2%

9"+,3%+ #1%=4*4,'" 2/ )+5'5'>)% %' 2% 45$)*+%+ (%( )%+?5+$*&4%( *9%4 #% 45$)5(*&'

%@,('*&'-

A 2%( 45&'+*,&'%( '%4B&5#5:,8/%(- C* +"*#,(*',5& 21/& 65,',%+ 45&'%&*&' #* D*$6% 4%&'+*#%

)%+$%''*&' 2% 3@%+ #* 9*#%/+ 2% #1%&'+%?%+ 25,' ;'+% 9*#,2"%- <%''% "'*)% &% 2%9+*,'

)*( )5(%+ 2% )+56#E$% $*,( %&:%&2+% /& 45F' (/))#"$%&'*,+%-

Page 92: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&' (

!"# $% &'()'#*%+ (*,%-+./$! $%./$! .%+-,"*01!

#$" 234

!""#$%&

!" #$%&'()*+'%,& -.* /01 23- 4,56,-+&'- 5+)&('%7.3- !

! " # $%&'#' () *%#+' ,-

! " . /010*023) (4 506107#8' 6#28&'394) ,:

! " 5 !)++047 ')5;80*02394)7 #5'4)*7 104+ *%38'&2+#'308 74+ <=> -?

!8 #3 93**,. '34:&,;,)%7.3 23 ;+ 5%-3 3& <,*53 !"

! @ # A&5041) () *%#60+1;) 1+&54+7)4+ -@

! @ . B)543' () 8#805+37'#**37#'308 -C

! @ .D3 =087'+45'308 (%48 E04+ () +)543' 7047 F+208 GH(+02&8& -I

! @ .D33 =#*3.+#'308 (4 5H5*) () +)543' -J

!= #3 93**,. '34:&,;,)%7.3 2. *34.%' -,.- 4:+56 '*+&-93*-3 -.*

23- 4+2*3- !#

! C # <+38531) (4 (371073'3E -:

! C . =08'+#38')7 74+ *) (36)873088)6)8' :?

! C 5 !#*3(#'308 )' +&#*37#'308 (4 (371073'3E :"

! C ( B&74*'#'7 )K1&+36)8'#4K :@

!> ?&'()*+'%,& -.* /01 3' 4+*+4'(*%-+'%,& #$

! I # A36)873088)6)8' (4 <=> :L

! I . =06107#8' 6#28&'394) 38'&2+& 74+ <=> :J

!@ 0,&4;.-%,& #%

!"#$!

! "#$%&'(! %()*!+'! ,-&+')(.' /!* "01%0*$+'* *2( 3 45 6$+* 2+! %(!1&7(! %$('&!8

+02* %()*!+'!(0+* 2+ ($%&/! )'$' /! ,-$(' /!* "01%0*$+'* 1$9+)'&:2!* %$**&;* &+')<

9()* *2( 3 45 =2 >2 /!* $>$+'$9!* /!* $,,&$9!* +$+0"(&*'$,,&+*8 +02* %()*!+'!(0+*

2+! '0%0,09&! /! "01%0*$+' &+')9($?,! *2( 3 4 !' +02* !@%0*!(0+* ,!* /&A"2,')* /!

()$,&*$'&0+5 6$+* 2+! *!"0+/! %$('&!8 +02* %(0%0*!(0+* 2+! '!"#+&:2! $B+ /! /)%$**!(

,!* %(0?,71!* /! 1&*! !+ ;0(1! /! ,-$,,&$9! +$+0"(&*'$,,&+5 6$+* ,$ '(0&*&71! %$('&!8

+02* /)'$&,,!(0+* ,$ ()$,&*$'&0+ /-2+ /&*%0*&'&; /-$%%,&"$'&0+ /-2+ "#$1% ,0(* /2 (!"2&'

/!* "$/(!* +$+0"(&*'$,,&+* !' +02* "0+",2(0+* *2( ,!* ()*2,'$'*5 C$ /!(+&7(! %$('&! /)<

10+'(! ,$ ;$&*$?&,&') /-2+ "01%0*$+' 1$9+)'&:2! !+ $,,&$9! +$+0"(&*'$,,&+ *2( 3 4 !'

,!* ;$"'!2(* /! /&1!+*&0++!1!+' /2 "&("2&' 3 45

Page 93: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

!" #$%&'()*+'%,& -.* /01 23- 4,56,-+&'- 5+)&('%7.3-

!"!# $%&'#' () *%#+'

"#$%&'()*&$+% ,-. /+01+.*%&. 1*..$2. .3) 4-. 567 85)$%&-, 6$)/3$& 7+*),9: -.& 3%-

.+43&$+% ,- 143. -% 143. 14';$./$&'- 1+3) 4* )',3/&$+% ,3 <+430- ,-. /+01+.*%&. =>?@ABC "-

143. .+3<-%&: 4#$%,3/&*%/- -.& )'*4$.'- D 4#*$,- ,- 1$.&-. ,- /3$<)-. -% .1$)*4- -& ,#3% /$)/3$&

0*(%'&$E3- )-1+)&' ,- 1*)& -& ,#*3&)- ,3 567C F3) 4* G(3)- HC@: -.& 0+%&)' 4#-I-014- ,-

,-3I -%)+34-0-%&. -% .1$)*4-. )'*4$.*%& 4- 1)$0*$)- -& 4- .-/+%,*$)- ,#3% &)*%.2+)0*&-3)

,+%& 4- /$)/3$& 0*(%'&$E3- -%4*/- 4- 567C

!"#$% HC@ J 5)$%/$1- ,- &)*%.2+)0*&-3) 14*%*)

6- &K1- ,- /+01+.*%&. 1)'.-%&- ,- %+0;)-3I $%&')L&. M')$&'. ,-. 1)+/','. ,- 2*;)$/*N

&$+% ,- 567C O% -P-&: 4-. /+01+.*%&. )'*4$.'. .3) 567 1)'.-%&-%& 3%- &)Q. 2*$;4- ,$.1-).$+%C

R- 143.: /-)&*$%-. &+1+4+($-. 1-)0-&&-%& ,#3&$4$.-) 4-. 1$.&-. /+00- 1)-0$Q)- *)0*&3)- ,-.

/+%,-%.*&-3). 6K -& 6I 1+3) )'*4$.-) 3%- .&)3/&3)- ,- G4&)- "6 =66S

+ATBC "#$%&'()*&$+%

.3) 567 1-)0-& *3..$ 4#*3(0-%&*&$+% ,- 4* ,-%.$&' ,- 13$..*%/- ,-. /+%<-)&$..-3). -&

0-& -% -I-)(3- 4-. 1)+;4Q0-. ,- )-2)+$,$..-0-%& ,-. /+01+.*%&. =F5U

+AA: F5UAVBC R-

0L0- 4* 1)+I$0$&' ,- 1$.&-. /+%,3/&)$/-. 1-3<-%& 0-%-) D ,-. '4'0-%&. 1*)*.$&-. 143. $0N

1+)&*%&. E3$ ,$0$%3-%& 4-. /*)*/&')$.&$E3-. M*3&-. 2)'E3-%/-. ,-. G4&)-. 6O>C O%G%: /-.

/+01+.*%&. .3) 567 3&$4$.-%& ,-. /$)/3$&. 0*(%'&$E3-. -% 2-))$&- ,+%& 4-. 1-)&-. 0*(%'N

&$E3-. )',3$&-. 2*<+)$.-%& 4-. )-%,-0-%&. $01+)&*%&.C R- 143.: /-. 0*&')$*3I 1)'.-%&-%&

,-. /+W&. -I&)L0-0-%& )',3$&.: /- E3$ )-%2+)/- 4-3) $%&')L& ,*%. ,- %+0;)-3.-. *114$/*N

&$+%.C "- 1+$%& ,#*/M+11-0-%& ,- /-. 0*&')$*3I )'.$,- ,*%. 4-3) 2)*($4$&' E3*%, +% 3&$4$.-

,-. 2*$;4-. '1*$..-3). &-44-. E3- )-E3$.-. 1+3) 4-. %+K*3I 14*%*).C 6-&&- 2)*($4$&' )-%, 1*)

-I-014- ,$X/$4- 4#-%&-))-0-%& /+014-& ,3 %+K*3 E3$ 1-3& /*..-) 4+). ,-. '&*1-. ,- 1)-.N

.*(-. ,-. 034&$/+3/M-. =Y4$@VBC 5+3) .3)0+%&-) /-. ,$X/34&'.: 3%- .&)3/&3)- -% 0+.*ZE3-

E3$ /+%.$.&- D 3&$4$.-) ,-. 0+)/-*3I ,- 2-))$&- 1+3) )'*4$.-) 4- %+K*3 ,*%. 4- 567 * '&'

1)+1+.'- ,*%. =6[S

+A :[6S

+A!:US\

+A]BC 6-&&- &-/M%$E3- $%&)+,3$& *4+). 3% -%&)-2-)

-%&)- /M*E3- 1$Q/- /- E3$ )',3$& 4* 1-)0'*;$4$&' ,3 %+K*3C R- 143.: 4-. /*)*/&')$.&$E3-.

Page 94: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*+'%,& -.* /01 23- 4,56,-+&'- 5+)&('%7.3- !

"#$%&'()* +(, '(+'-.,/*012("3 4-,' 5%0*(' 2#()*'(6(' (* 2$ /$""(7 ,)( "*',/*,'( .#0).,/*$)/(

() 6-'8( .( /$.'( () 6(''0*( $ 5*5 ()9) +'-+-"5( .$)" :;20<=> ?@0A3 B3=C3

!"#$% B3= D E).,/*$)/(" 6(''0*( 0)*5A'5(" .$)" 2( 4FG :;20<=>

; 2#H(,'( $/*,(22(7 2(" "(,2" 8$*5'0$,I 8$A)5*0J,(" ()*(''5" .$)" 2(" 4FG "-)* .-)/

2(" 6(''0*("3 F(+().$)*7 .$)" 2(" /-8+-"$)*" .( 92*'$A( .0"/'(*7 2( 8$*5'0$, 8$A)5*0J,( 2(

+2," ,*020"5 +-,' 2(" 0).,/*$)/(" .( 8-.( /-88,) ("* 2#$220$A( )$)-/'0"*$220)3 K-," $%-)"

.-)/ %-,2,7 8$2A'5 2(" .0L/,2*5" .( 80"( () 6-'8( +'5"()*5(" .$)" 2( /H$+0*'( EE7 '5$20"('

)-*'( /-8+-"$)* M +$'*0' .#,) $220$A( )$)-/'0"*$220) $, %, .( "(" +'-+'05*5" 8$A)5*0J,("3

!"!# $%&%'%()* +, -%.&%/012 .0(132)4,*

K-," $%-)" /-)/2, .$)" 2( /H$+0*'( +'5/5.()* J,( 2$ *-+-2-A0( $%(/ ()*'(6(' +('8(*N

*$0* .( '5.,0'( 2( %-2,8(7 2( /-O* (* .#$,A8()*(' 2#$**5),$*0-)3 ;9) .( '5.,0'( ()/-'( 2(

%-2,8( ., /-8+-"$)*7 )-," )-," "-88(" $2-'" 0)*5'(""5" M /(**( 8P8( *-+-2-A0( 0)*5A'5(

.$)" ,) 4FG3 K-," $%-)" .-)/ ()*'(+'0" .( '5$20"(' ,)( 0).,/*$)/( .( 8-.( /-88,) ()

$220$A( )$)-/'0"*$220) +-,' 2$J,(22( ,) ()*'(6(' ("* 0)*'-.,0* ",' 2( *'$Q(* .(" R,I .( 8-.("

.0S5'()*0(2"3 4-,' "$*0"6$0'( /(" /-).0*0-)"7 )-," $%-)" 08$A0)5 2$ *-+-2-A0( ",0%$)*( ?@0A3

B3TC3

a

c

b

!"#$% B3T D U/H58$ .( +'0)/0+( ., /-8+-"$)* ,)0J,( ",' 4FG ?VF M A$,/H( (* VW M

.'-0*(C

E2 "#$A0* .( .(,I 0).,/*$)/(" .( 8-.( /-88,) '5$20"5(" $,*-,' .( .(,I )-X$,I 8$N

A)5*0J,(" *'&" +2$*"7 J,0 "-)* ",+('+-"5(" .( 8$)0&'( M 0)*'-.,0'( ,) ()*'(6(' ?(C ()*'( 2("

/0'/,0*"3 Y(" )-X$,I "-)* '5$20"5" +$' ,) (8+02(8()* .( ',1$)" )$)-/'0"*$220)" .#5+$0""(,'

,)0*$0'( =Z µ8 .5/-,+5" () 6-'8( .( /$.'(3

Page 95: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

"#$% &' &(#)*+,'- *. %/#0*+ 1' 1234$+,', .# 5#*%#6*.*+2 1/7$ +'. &43)4%#$+ *$+20,2 %7,

89:; <'% 1*3'$%*4$% 1'% &#1,'% $' %4$+ 14$& )#% &(4*%*'% 1#$% 7$ %47&* 1' 1*3'$%*4$$'=

3'$+ 17 &43)4%#$+ 3#*% 1' ),#+*&*+2 1' 3*%' '$ >7?,' @A#6.' !" #$ %&'(# !)* !

!"#$ !" + ,-.#/0-1/ 2#0 342(#0 /4/13(-0$455-/0

a(mm) b(mm) c(mm)

67!8 9:!7 ;!8

!"!# $%%&'( )$#*+&,&-./'$( 0#)'$,( 1&'% ,2.+)3-%0).&+ ('% 456

<=-/$>&(4$-1/ 0'( ?@A 2#0 31.B104/$0 .4&/>$-C'#0 #/ 455-4&# /4/13(-0$455-/ 31..#/3#

D 0'03-$#( 5=-/$>(E$ 4' F' 2#0 B#(G1(.4/3#0 2' .4$>(-4'! @#B#/24/$H 5#0 455-4&#0 /4/13(-0I

$455-/0 01/$ #J$(E.#.#/$ G(4&-5#0! ,4/0 5#0 B(13>2>0 2# G4K(-34$-1/H 3=#0$ 21/3 54 K4/2#

2=4.1(BL# B(>3'(0#'( C'- #0$ #/(1'5># 0'( #55#I.E.#H B'-0 (#3'-$# B1'( /4/13(-0$455-0#( 5#

.4$>(-4'! M/# G1-0 5# /1N4' (#3'-$ #$ /4/13(-0$455-0> $1'$# .-0# #/ G1(.# '5$>(-#'(# #0$

C'40- -.B100-K5#! O 5=L#'(# 43$'#55#H 54 0#'5# 015'$-1/ B1'( 2>31'B#( 2#0 $1(#0 #/ 455-4&#

/4/13(-0$455-/ #0$ 2# 5=-.B(>&/#( 01'0 F-2# 2='/# (>0-/# 4%/ 2# 015-24(-0#( 5#0 ('K4/0 4F4/$

54 2>31'B#! @=#0$ 2=4-55#'(0 3#$$# .>$L12# C'- 4 >$> '$-5-0># 24/0 5# 3L4B-$(# B(>3>2#/$!

,4/0 P? Q""RH 5#0 4'$#'(0 1/$ 2>31'B> 2#0 ('K4/0 2# 54(&#'( $(S0 G4-K5# T" ..* B1'( B#(I

.#$$(# 5=#/$#((#.#/$ 24/0 5# ?@A! @# /=#0$ 3#B#/24/$ B40 54 F1-# C'# /1'0 4F1/0 (#$#/'#!

<4 2#'J-S.# 31/$(4-/$# 2=-/$>&(4$-1/ 2# 3#0 455-4&#0 #0$ 5#'( 31.B1($#.#/$ #/ G(>C'#/3#!

U/ #V#$H 2='/# .4/-S(# &>/>(45#H 5#0 /1N4'J 2#0$-/>0 D E$(# '$-5-0>0 #/ >5#3$(1/-C'# 2#

B'-004/3#H 0'K-00#/$ '/ (#3'-$ 01'0 3L4.B .4&/>$-C'# $(4/0F#(0# 4%/ 2# B(>0#/$#( '/#

B#(.>4K-5-$> B5'0 (>2'-$# T#/31(# 2# 5=1(2(# 2# C'#5C'#0 "W WWW 5# B5'0 01'F#/$* #$ '/

3N35# 2=LN0$>(>0-0 C'40- 5-/>4-(#! <# 3L4.B .4&/>$-C'# 4 451(0 B1'( #V#$ 2=-/$(12'-(# '/#

4/-01$(1B-# '/-I4J-45# 24/0 5# .4$>(-4' D .E.# 2=-.B10#( 2#0 0$('3$'(#0 #/ 21.4-/#0 B#(I

B#/2-3'54-(#.#/$ D 54 2-(#3$-1/ 2' 3L4.B 2=#J3-$4$-1/!

X5 #0$ >&45#.#/$ B100-K5# 2=-/2'-(#H 24/0 3#0 455-4&#0H '/# 4/-01$(1B-# B4( 5=43$-1/ 2='/#

31/$(4-/$# .>34/-C'# 4BB5-C'># 2'(4/$ 5# (#3'-$ 2# 3(-0$455-04$-1/ TY-&! !7* PQZ;9R! <#0

B#(.>4K-5-$>0 0=>$45#/$ 451(0 2# C'#5C'#0 3#/$4-/#0 D C'#5C'# .-55-#(0!

!" #$ %$&&'( )$*+,'-'./0($ 1$ -2 3/4$ $, 5'&3$

[1'0 4F1/0 F' C'# 5#0 455-4&#0 /4/13(-0$455-/0 >$4-#/$ G(-4K5#0H 3# C'- 5-.-$# 5#'( .-0#

#/ G1(.#! ,4/0 3#$$# B4($-#H /1'0 B(1B101/0 '/# .>$L12# B1'( 0=4V(4/3L-( 2# 54 G(4&-5-$>

2# 3#$ 455-4&# 4%/ 2# B#(.#$$(# 2=4'$(#0 .-0#0 #/ G1(.#H #/ B4($-3'5-#( 5#0 342(#0 B(>0#/$>0

3-I2#00'0! <#0 342(#0 /4/13(-0$455-/0 01/$ (>45-0>0 D B4($-( 2='/ ('K4/ 2=4.1(BL# B(>3'(0#'(H

3# 2#(/-#( >$4/$ K#4'31'B .1-/0 G(4&-5#! [1'0 4F1/0 451(0 B#/0> D (>45-0#( 54 .-0# #/ G1(.#H

3=#0$ D 2-(# 54 2>31'B# #/ 342(#H 0'( 5# ('K4/ 4.1(BL# B(>3'(0#'(H B'-0 (#3'-(# 5#0 342(#0

B1'( 5#0 /4/13(-0$455-0#( 24/0 '/ 0#31/2 $#.B0!

Page 96: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1$ -2 3/4$ $, 5'&3$ !

!"#$% "#$ % &'()*+ ,-.'+/010+2+ +/3/245*+ ,* )-3))236* 7378(12+/3))27

Fe73.5Cu1Nb3Si13.5B9 9:*1;<=

!"#$% "#> % &851?*+ ,-32@37/3/287 3A1B+ 1*(52/ A851 ,2C*1+*+ C3)*51+ ,* )3 (87/1327/*

,* /13(/287 σ 9DE;F=

Page 97: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

µ

Page 98: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1$ -2 3/4$ $, 5'&3$ !

!"#$% "#$ % &'()*+( ,( ,-./0*( *12 -+(.32/4-2/56/7

897 ,:/;3(762 ,(5 *2-.656/75 ,( ,-./0*( 51365<165173(5= 7/05 7/05 5/))(5 673-2(55-5 > +1

,-./0*( *12 -+(.32/4-2/56/7# ?:-+(.32/4-2/56/7 (53 07 *2/.-,- ,:05671@( A06 ./75653( > (7+(B(2

,( +1 )136C2( ,175 07( *6C.( (7 036+65173 ,(5 12.5 -+(.326A0(5# D(33( 3(.E76A0( 5( .121.3-265(

*12 5/7 1*3630,( > 0567(2 3/05 +(5 )13-2610' ./7,0.3(025 ,( +:-+(.326.63- F)-310'= 1++61@(5=

.12;02(5= @21*E63(5= (3.#G A0(++( A0( 5/63 +(02 ,02(3- (3 *(2)(3 ,:/;3(762 ,(5 *2-.656/75

,( ,-./0*(= ,( +:/2,2( ,( H#I ))# J/05 1B/75 036+65- +:-+(.32/4-2/56/7 *12 9+# ?(5 20;175

6763610' ,( ,6)(756/75 KL#M'N$#L )) 5/73 ,-./0*-5 > +:16,( ,:07 )1556./3# O+5 5/73 (75063(

*265 (7 517,P6.E (732( ,(0' *+1A0(5 ./7,0.326.(5 (3 +:(75();+( (53 ,:1;/2, *(2.- (3 (75063(

,-./0*- *12 -+(.32/4-2/56/7 10' 1;/2,5 ,0 9+ *12./020 *12 07 ./02173 ./73670# ?:673(7563-

,0 ./02173 (53 9'-( *12 21**/23 > +:-*1655(02 ,(5 20;175 (3 +1 316++( ,( +:(75();+( ()*6+-#

?/25 ,0 *2/.(5505 ,( ,-./0*( ,( +:(75();+( ,(5 <(06++(5= +( 2-@+1@( ,( +:673(7563- ,175 +(

9+ (53 32C5 ,-+6.13# Q7 ('.C5 ,( ./02173 67,063 ,(5 3()*-21302(5 6)*/23173(5 (3 (7321R7(

+:1**12636/7 ,( )6.2/45/0,02(5 (732( +(5 20;175# S12 ./732( ,0 */673 ,( B0( ,( +1 2-1+65136/7

,0 *2/3/3T*(= .( *E-7/)C7( 7:1U/03( A0( *(0 ,( ,6V.0+3-5 .12 .(5 */6735 ,( 5/0,02( 5/73

<1.6+()(73 ./0*-5 > +:16,( ,:07( +1)( 97( 3(+ A0:07 .033(2#

?/25 ,( .(33( -31*( ,( ,-./0*(= +(5 .1,2(5 5/73 *+/7@-5 ,175 07 ;167 ,:E06+(# J/05 2-14

+65/75 ,/7. 07( -31*( 50**+-)(73162( F1B173 +( 2(.063 ,( 717/.26531++65136/7G ,( 7(33/T1@(

,175 07 ;167 > 0+3215/75 */02 (7+(B(2 +(5 2-56,05 ,( ,-./0*(#

!"!# $%&'() *% +,+-&.(/),00(/,)(-+

?:-31*( ,( ,-./0*( ,(5 .1,2(5 -3173 B1+6,-(# J/05 7/05 5/))(5 673-2(55-5 > +1 *E15(

,( 717/.26531++65136/7 ,(5 -.E1736++/75# S/02 *155(2 ,( +:1)/2*E( *2-.025(02 > +:1++61@(

717/.26531++67= +( )13-2610 )1@7-36A0( 1 ;(5/67 ,:W32( .E10X-# ?> 10556 *+056(025 )-3E/,(5

('653(73 Y

% ?( 2(.063 321,636/77(+# ?:-.E1736++/7 (53 *+1.- ,175 07 </02 5/05 13)/5*EC2( 67(23(

Page 99: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

"# $ %&'(# &)" *+)#,"- &) ./0("1 "# &)" 2"%3")#" ") #"*.,1/#&1" 3+)#140,"% /5) 2"

*/6#1(%"1 %/ %#1&3#&1" )/)+31(%#/00()"7

8 9" : 1"3&(# ;/%< =- .0&% 3+))& %+&% 0" #"1*" /)>0/(% :;/%< /))"/0()>= "%# &)" *,#<+2"

?&( 3+)%(%#" @ A/(1" ./%%"1 &) 3+&1/)# 2/)% 0B,3</)#(00+) .")2/)# &) #"*.% #1C% 3+&1#

D3")#/()" 2" *%E7 F/1 "G"# H+&0"- 0/ #"*.,1/#&1" 2" 0B,3</)#(00+) I/ 31+6#1" "# 0"

.1+3"%%&% 2" 31(%#/00(%/#(+) %"1/ 2,30")3<,7 J"##" #"3<)(?&" / I& 0" K+&1 ") LM !

NH/> O-P9Q !R7 S"% /I/)#/>"% %+)# T

L7 0B,0,I/#(+) 2" #"*.,1/#&1" 1/.(2" D0/ I(#"%%" 2" 3</&G/>" "# 2" 1"A1+(2(%%"*")#

"%# 2" 0B+121" 2" LU!VLUW XY*()E Z

[7 0/ .+%%('(0(#, 2B+'#")(1 2"% >1/()% .0&% 5)% /&>*")#/)# /()%( 0/ ."1*,/'(0(#,

N\PUUR Z

O7 0/ %(*.0(3(#, 2" 3+*'()"1 0" 1"3&(# /I"3 0B/..0(3/#(+) 2" 3+)#1/()#" *,3/)(?&"

N]0IULR7

8 9/ 31(%#/00(%/#(+) /I/)# 0B")1+&0/>" 2& #+1" %&1 &) */)21() 3</&G, +& ./1 ./%%/>"

%&1 &) 2(%.+%(#(A 2" 3</&G/>" 2" ?&/1#^ N_]` !R7

8 9" 1"3&(# 0/%"1 %&1 &)" '/)2" 21+(#" N99MWR7

F+&1 2"% 1/(%+)% 2" 3+**+2(#, "# 2B"a."1#(%" /& %"() 2& 0/'+1/#+(1"- )+&% /I+)% 3<+(%(

2B&#(0(%"1 0" 1"3&(# #1/2(#(+))"07

!"!#$% &'()*+,-*%'( ./,( 0',+ .1 +1-,%* )',) 2+3'( 45.+'36(6

b/)% &) .1"*("1 #"*.%- )+&% /I+)% 2& 1,/0(%"1 &) A+&1 2" 1"3&(# Dc(>7 d7 E7

!"#$% d7 8 9" A+&1 2" 1"3&(#

9"% 1"3&(#% #1/2(#(+))"0% 2+(I")# e#1" 1,/0(%,% %+&% /#*+%.<C1" ()"1#" /5) 2B,I(#"1 0B+a$V

2/#(+) ") %&1A/3" 2& */#,1(/&7 Q) ./1#(3&0("1- 3"00" 2"% /#+*"% 2" f+1" ?&( %+)# 0"% .0&%

Page 100: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1$ -2 3/4$ $, 5'&3$ !

"#$"%&'#" ()* +,- .#//# 01234/%0$ #$5#$36# 3#" 37849/" #$ "9684:# ;9% %$<9#$/ "96 '4 "/69:=

/96# #$ 30>4%$#" #/ >?$# @ 3#" :A4>B" :0#6:%/%8" B'9" %>B06/4$/"- C4 B'9B46/ 3#" 8096"

%$39"/6%#'" "0$/ 7;9%B7" B096 6#:9%6# "09" 3%A23605?$#- D4$" '# :436# 39 '4&064/0%6#E $09"

4F0$" 0B/7 B096 3#" 6#:9%/" "09" G650$ H236057$7- C#" /#>B764/96#" 3# 6#:9%/ B096 '#"

$4$0:6%"/4''%$" 4//#%5$#$/ IJJ

. >41%>9>- K09" 3#F0$" 30$: :0$"/69%6# 9$ "2"/?># ;9%

"9BB06/# :#//# /#>B764/96#-

K0/6# 8096 #"/ :0$"/%/97 3#" 7'7>#$/" "9%F4$/" L

M N$ &'0: :A49O4$/ #$ :9%F6# P3# /2B# GQR- .S#"/ 9$ :2'%$36# 3# TJ >> 3# 3%4>?/6#

%$/#6$# #/ 3# '0$59#96 UJJ >> PV%5- W-XR-

M N$# 67"%"/4$:# :A49O4$/#- Y' "S45%/ 3S9$ /A#6>0:041 &0&%$7 #$ 309&'# A7'%:# PB096

$# B4" :67#6 3# :A4>B >45$7/%;9#RE 3%6#:/#>#$/ "96 '# &'0: :A49O4$/- C4 67"%"/4$:#

#"/ 4'%>#$/7# "09" Q!JW = QJG >41E "0%/ 9$# B9%""4$:# 3# Q!JJ Z PV%5- W-XR-

!"#$% W-X M C# &'0: :A49O4$/ &0&%$7

M N$ /9&# 3SY$:0$#' 34$" '#;9#' F%#$/ "# 5'%""#6 '# &'0: :A49O4$/- C#" &459#" #$ :9%F6#

39 &'0: :A49O4$/ B#6>#//#$/ '# :#$/645# 34$" '# /9&# 3SY$:0$#'-

M G 'S#1/76%#96 3# :# /9&# 3SY$:0$#'E 9$ /9&# 3# :9%F6# 4""964$/ '4 :%6:9'4/%0$ 3# 'S#49

B096 '# 6#860%3%""#>#$/ 3#" #1/67>%/7" 39 8096 #"/ &64"7-

*46 4%''#96"E B096 '4 >%"# #$ 80$:/%0$$#>#$/ #/ 'S%$"/69>#$/4/%0$E $09" 4F0$" 49""%

;9#';9#" 4BB46#%''45#" 4$$#1#" PV%5- W-QJR L

M N$ 5609B# 3# F%3# "#:0$34%6# *V[YVV[\ HY=.N][ J J 4F#: "4 "0$3# *#$$%$5^*%64$$%-

Y' B#6>#/ 3S4//#%$36# 3#" F%3#" 4''4$/ _9";9S@ 10−4 >&46-

M N$# &09/#%''# 3SG650$ H236057$7# PX! ` G6 a ! ` H+R 4F#: 9$ 37/#$3#96- C4

B6#""%0$ @ '4 "06/%# #"/ 675'7# "96 Q &46-

M N$ :%6:9%/ 3S#49 B096 6#860%3%6 'S7'7>#$/ :A49O4$/- [$ B46/%:9'%#6 '#" #1/67>%/7" ;9%

30%F#$/ 6#"/#6 #$ 3#""09" 3# +JJ

. B096 $# B4" 37/76%06#6 '#" _0%$/" 3S7/4$:A7%/7 #/

'S%$"/69>#$/4/%0$-

M N$# 4'%>#$/4/%0$ "/4&%'%"7# :0$/6b'7# cDd CGe]DG J=Q!JW J=QJG

M N$ 6759'4/#96 3# /#>B764/96# [960/A#6> U!J P309&'# &09:'#E B60564>>4&'#R ;9%

:0$/6b'# #$ J=QJW 'S4'%>#$/4/%0$ cDd CGe]DG-

M N$ 063%$4/#96 ;9% B#6>#/ 3# B60564>>#6E 3%4'059#6 4F#: '# 6759'4/#96 3# /#>B764=

/96# #/ 3# 64B4/6%#6 3#" 30$$7#" 3# /#>B764/96# F%4 'S#$6#5%"/6#96 30$$7#" )>754

c.J -

Page 101: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

!"#$% "#$% & '()*+,- .)/*012-)*3 41 5(10 4- 0-61.*

78+)* 9+ 2./- -) 2+06:- 41 5(10 4- 0-61.*; <1-9<1-/ =(.)*/ 6016.+1> ()* 3*3 830.?3/ @

& A-/ 0-61.*/ /()* 03+9./3/ -) /10=0-//.() =+0 0+==(0* B 9+ =0-//.() +*2(/=:30.<1- /(1/

70,() CD40(,3)3# E(1/ 4-8()/; 4+)/ 1) =0-2.-0 *-2=/; 5+.0- 9- 8.4- 4+)/ 9F-)6-.)*-

=(10 9+ 0-2=9.0 4- ,+G .)-0*- 4+)/ 1) /-6()4 *-2=/# H9 -/* 4()6 -//-)*.-9 4- 830.?-0

9F:-023*.6.*3 4- 9F-)6-.)*- IJ(.)*/; /(1410-K# A-/ -//+./ 03+9./3/ 2()*0-)* <1- )(1/

+**-.,)()/ 4-/ L()/ 8.4-/ =0.2+.0-/ IJ1/<1FB 10−4 2L+0K; 6- <1. 6-0*.?- 9F+L/-)6- 4-

51.*-#

& M- =91/; 9F:(2(,3)3.*3 4- 9+ *-2=30+*10- 4+)/ 9F-)6-.)*- 41 5(10 + 3*3 6()*0N93- B

9F+.4- 4-/ 2-/10-/ 03=3*3/ =+0 =91/.-10/ *:-02(6(1=9-/ B 4.8-0/ -)40(.*/# O10 )(*0-

4./=(/.*.5; 9+ =+0*.- 6-)*0+9- 41 5(10 I2.9.-1 41 L9(6 6:+1P+)*K -/* :(2(,Q)-# R(10

=+99.-0 +1 =0(L9Q2- 4F:(2(,3)3.*3; 9+ =91=+0* 4-/ 5(10/ .)41/*0.-9/ /()* 3<1.=3/ 4F1)

4./=(/.*.5 4- L0+//+,- 41 ,+G#

!"!#$%% &'(%#)'*%+, -. /0/(1 -1 )1/.%*

7?) 4- =0(634-0 B 9+ )+)(60./*+99./+*.() 4- )(/ 6+40-/ -) +2(0=:- =03610/-10; )(1/

+8()/ 4-2+)43 B 9+ /(6.3*3 STS 4- )(1/ 5(10).0 9-/ 6+0+6*30./*.<1-/ 4-/ 6D69-/ 4- 0-61.*

IU.,# "#$$K#

& './- /(1/ +*2(/=:Q0- +8-6 ,+G .)-0*- I$K

& '()*3- -) *-2=30+*10- =0(,0-//.8- IVK

& '()*3- -) *-2=30+*10- =91/ 9-)*- IWK# T- 0+9-)*.//-2-)* -/* .2=(/3 =(10 ,+0+)*.0 9+

Page 102: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1$ -2 3/4$ $, 5'&3$ !

!"#$% "#$$ % &''()* +( ,-,'* +* )*,(./

)01('2/.34 *4 /*560)2/()* 2( 535*4/ +* '2 )02,/.34 *73/8*)5.9(* +* ,).:/2''.:2/.34#

% ;2'.*) +* /*560)2/()* 63() 2,8*<*) '2 ,).:/2''.:2/.34 =>?#

% @*A)3.+.::*5*4/ B '2 <./*::* +( A3() =C?#

% ;2'.*) 63() 0/2D'.) '2 6*)502D.'./0 +( 52/0).2( 4243,).:/2''.:0 =E?#

% @*A)3.+.::*5*4/ B '2 <./*::* +( A3() =!?#

&F4 +* <2'.+*) 43/)* 6)3,0+0 +* 4243,).:/2''.:2/.34G 43(: 2<34: )02'.:0 'H0/(+* ,3562I

)2/.<* :(.<24/* B 62)/.) +* 6'(:.*(): 0,824/.''34: +H253)68* 6)0,():*() 6)062)0 ,8*J KLK

=K2D'* "#M? N

&'()% "#M % L2)2,/0).:/.9(*: +*: 0,824/.''34:

Dext(mm) Dint(mm) H(mm)

$! $O#! E#M

% P4 /3)* )*,(./ :24: ,8256 +24: '* A3() .4+(:/).*' ,8*J KLK

% P4 /3)* )*,(./ :24: ,8256 +24: 43/)* A3() 2( '2D3)2/3.)*

;3() 3D:*)<*) '*: ,2)2,/0).:/.9(*: +*: 0,824/.''34:G 43(: 2<34: )02'.:0 (4* 5*:()* Q(7I

50/).9(* B O#O$ RJ 2F4 +H3D/*4.) '*: ,-,'*: :/2/.9(*: =S.1# "#$M?#

T2 A)21.'./0 +*: )(D24: 43(: .4+.9(* 9(* '* 52/0).2( 2 D.*4 0/0 4243,).:/2''.:0# L*6*4I

+24/G 2( <( +* ,*: 6)*5.*): )0:('/2/:G 43(: 63(<34: 43/*) 'H3)+)* +* 1)24+*() +( ,8256

,3*),./.A +( 52/0).2(G Hc +H*4<.)34 $O &U5 63() 43/)* )*,(./ ,3562)0 2( $#M &U5 63()

'* )*,(./ .4+(:/).*' */ 43(: 63(<34: )*52)9(*) 9(* 'H0,824/.''34 )*,(./ 2( '2D3)2/3.)* *:/

6'(: V,3(,80W 9(* ,*'(. 9(* 'H0,824/.''34 )*,(./ .4+(:/).*''*5*4/# ;'(:.*(): A2,/*(): 6*(<*4/

*41*4+)*) ,* 680435X4*#

Y3(: 63(<34: :(663:*) 9(* '* <.+* 9(* 43(: A2.:34: 4H*:/ 62: 2::*J 63(::0 */U3( 9(*

43/)* 2/53:68X)* 4H*:/ 62: 2::*J )0+(,/).,*# Z4 '2.::24/ '2 6356* B <.+* *4 52),8* /3(/*

(4* 4(./G 43(: 3D/*434: '* 5[5* <.+* 9(* :3(: '*:9(*': :34/ A2./ '*: *::2.: 2( D3(/ +H(4*

8*()* +* 635621*# \24: '*: ,-,'*: .4+(:/).*':G .' *:/ )*,35524+0 +* A2.)* (4 <.+* :*,34+2.)*

:3./ 10−7 5D2)# &<*, 43/)* +.:63:./.A 2,/(*'G 43(: 4* 63(<34: +34, 62: ]3(*) :() ,* A2,/*()#

P4* 2(/)* 8-63/8X:* *:/ 'H37-+2/.34 +( 52/0).2( 52140/.9(*# Z4 *^*/G '* 52/0).2( 6*(/

2'3): :H37-+*) *4 :()A2,* ,* 9(. 63())2./ *76'.9(*) 'H2(15*4/2/.34 +( ,8256 ,3*),./.A# T*:

Page 103: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

!"#$% !"#$ % &'()*+*,-'. /0- 12130- /452-67+7-,- -6*6,890- )'9+ 30- /09: +019,6-"

/7;*96- 0. -9+;*10 )09<0.6 1'.-,/7+*=30(0.6 /7>+*/0+ 30- 1*+*167+,-6,890- (*>.76,890-? 0.

)*+6,193,0+ -9+ /0- +9=*.- @.-" A.0 -'396,'. 1'.-,-60 B ,.6+'/9,+0 /0- 7)'.>0- 0. 6,6*.0?

89, 1*)60 0. 5*960 60()7+*69+0 34':2>C.0 )+7-0.6? *@. /0 +7/9,+0 34':2/*6,'. /9 (*67+,*9"

&0)0./*.6? 30 1')0*9 76*.6 6+') 37>0+? ,3 * 767 *-),+7 *9 ;'./ /9 ;'9+ 3'+- /0 .'6+0 0--*,"

D9,-890 1039,E1, .476*,6 )*- )+'150 /9 6'+0? .'9- .0 )'9<'.- /'.1 )*- 1'.139+0 1*+ .'9-

.4*<'.- )39- /4*96+0- 715*.6,33'.- B /,-)'-,6,'."

D*+ *,3309+-? 30 ;'9+ ,./9-6+,03 0-6 (9., /49. -2-6C(0 /0 =+*--*>0 /0 34*6('-)5C+0 *@.

/0 +0./+0 3* 60()7+*69+0 5'('>C.0? 10 89, .40-6 )*- .'6+0 1*-" F. 0G06? /*.- .'6+0 ;'9+?

10 -2-6C(0 76*,6 6+') /,H1,30 B (066+0 0. )3*10 *9 <9 /0- /,(0.-,'.-" I, 34'. <096 '=60.,+

/0- .*.'>+*,.-? ;*<'+*=30- *9 (*>.76,-(0 /'9:? ,3 0-6 .710--*,+0? /49.0 )*+6? /0 ;*<'+,-0+

3* .9137*6,'. /0 >0+(0- 1+,-6*33,.- 3* )39- 5'('>C.0 )'--,=30 06 /4*96+0 )*+6 /0 3,(,60+ 3*

1+',--*.10 /0 10- >0+(0- 06 309+ 1'*30-10.10 JD0+KLM" N45'('>7.7,67 /0 3* 60()7+*69+0 -9+

6'96 34715*.6,33'. ;*<'+,-0 3* 1+',--*.10 /0- >+*,.- /0 (*.,C+0 9.,;'+(0 /*.- 30 (*67+,*9?

)'9+ )*33,0+ B 10 )+'=3C(0 .'9- *<'.- 0.<,-*>7 /0 +7/9,+0 3* )0.60 /0 ('.670 0. 60()7E

+*69+0 *@. /4'=60.,+ 9.0 1+',--*.10 )39- 30.60 /0- .*.'1+,-6*9:" &0- 0--*,- .4'.6 0.>0./+7

*919. 15*.>0(0.6 /9 12130" O*.- .'6+0 *))3,1*6,'.? .'9- -'95*,6'.- P1'9150+Q 30 12130

/452-67+7-,-" N0 ;*,6 /4*<',+ 9. *33,*>0 .*.'1+,-6*33,. /7RB 9. )09 1'9157 .4* /'.1 )*- 767

R9>7 6+') 1'.6+*,>.*.6 /*.- 9. )+0(,0+ 60()- 06 .'9- *<'.- +0(,- B )39- 6*+/ 34*(73,'+*6,'.

/0 .'6+0 /,-)'-,6,;"

S*3>+7 30- )+'=3C(0- 0:)7+,(0.6*9:? .'9- *<'.- /71,/7 /0 )'9+-9,<+0 .'6+0 769/0

)9,-890 .'9- *<'.- <*3,/7 890 30- (*67+,*9: 76*,0.6 .*.'1+,-6*33,-7- (T(0 -4,3- .476*,0.6

Page 104: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1( &$*(/) 2'(2 *+345 )&3,2%$&2$ 2(& 1$2 *31&$2 !

"#$ %&'%())*'+,*-$ . %*(/ )0#-,$0$ "#) -*$ ,'1($+),*-$2

!" #$ %$&&'( )$*+,'-'./0($ 1( &$*(/) 2'(2 *+345 )&3,2%$&2$

2(& 1$2 *31&$2

!"!# $%&'(&)* +, +&-).-&/&0

3&44* '&($ -5#6&'$ 6( 1#'$ -# "#)+,* ")0%01*'+*7 -*$ #--,#8*$ '#'&%),$+#--,'$ $&'+

%&'%())*'+$ 1*$ 9*)),+*$ . :#(+*$ 9)0;(*'%*$ $, ,-$ &'+ 0+0 )*%(,+$ $&($ %:#4" 4#8'0+,;(*

+)#'$6*)$*2

!"#$% <2=> ? @""-,%#+,&' 15(' %:#4" +)#'$6*)$* $() (' '&A#( +&),;(*

B#'$ -* ")&%010 ,'1($+),*-7 -*$ +&)*$ $&'+ "-#%0$ $() ('* +,8* $() (' #/* +)#6*)$#'+ -#

-&'8(*() 1( 9&()2 C'* D&D,'* 1* %:#4" "-#%0* #(+&() 1( 9&() 1#'$ -* $*'$ 1* -# -&'8(*()

"*)4*+ 15#""-,;(*) (' %:#4" 4#8'0+,;(* 9&)+ EF *' 4#(6*G8),$ 9&'%0H E"&() -*$ 0+#"*$ >

. I 1( %A%-* 1* )*%(,+H "&() ,'1(,)* ('* #',$&+)&",* EJ,82 <2=>H2

B#'$ '&+)* %#$7 -# ;(*$+,&' $* "&$* "&() #""-,;(*) (' %:#4" +)#'$6*)$* -&)$ 1( )*%(,+

1*$ %#1)*$2 K# $+)(%+()* <2=L # 0+0 ,4#8,'0* 1#'$ %* D(+2

!"#$% <2=L ? B,$"&$,+,9 15#""-,%#+,&' 1( %:#4"

M- $5#8,+ 15('* N#4D* %*'+)#-* 4#8'0+,;(* $() -#;(*--* '&($ D&D,'&'$ 1*$ $",)*$ 1* %(,6)*2

K*$ %#1)*$ )*"&$*'+ $() ('* $+)(%+()* #4#8'0+,;(*2 K* O(/ ")&1(,+ "#) -# %,)%(-#+,&' 1(

Page 105: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

"#$%&'( )&'* +& ,#,-'. .*( .'*$-(. /$-)0 1&% +& 2#%3. .' 4 ). +& 5&3,. )&'* $' .31-+.3.'(

). "&)%.* 1$-* *. %.,#$"+. 1&% +& "$+&**. 3&/'0(-6$.7 8. (#$( .*( ,+#6$0 1&% ).* "#$9.%"+.*

&3&/'0(-6$.* :;-/7 <7=>?7 8& "-%"$+&(-#' )$ @$A .*( -')-6$0. 1&% +.* @B"C.* 9.%(.* "+&-%.*7

!"!# $%&'()*&'+, ,-( .+ /*0+&,*%&&+0+&'

D. )-*1#*-(-2 9& E(%. 1+&"0 F +G-'(0%-.$% )$ 2#$%7 H#$* *#33.* )#'" "#'2%#'(0 F 1+$*-.$%*

1%#,+B3.* I

=7 8.* 3&(0%-&$A )#-9.'( *$11#%(.% ).* (.310%&($%.* ). J!!

D7 H#$* ).9#'* 9.-++.% F

$(-+-*.% ).* 3&(0%-&$A )#'( +& (.310%&($%. ). 2$*-#' .*( +&%/.3.'( *$10%-.$%. F ".((.

+-3-(.7

K7 L9." +G0+09&(-#' ). +& (.310%&($%.M +.* &++-&/.* *. )02#%3.'(7 4+ .*( )#'" -31#%(&'( ).

"C#-*-% ).* 3&(0%-&$A &9." ).* "#.N"-.'(* )G.A1&'*-#' (C.%3-6$. ). 3E3. #%)%. ).

/%&').$% 1#$% 09-(.% ).* )02#%3&(-#'* (%#1 -31#%(&'(.* ). +& *(%$"($%. #$ ). 1%09#-%

+.* &5$*(.3.'(* 30"&'-6$.* &11%#1%-0*7

O7 8#%* ). +& 1C&*. ). '&'#"%-*(&++-*&(-#'M +G&3#%1C. 1%0"$%*.$% *. "#'(%&"(.7 8& "%0&(-#'

). /%&-'* αP;.Q- )&'* +& 3&(%-". &3#%1C. )-3-'$. +.* )-3.'*-#'* )$ %$,&' RS.% !T7

UG&1%B* +.* )#''0.* 2#$%'-**.$%* :VDV?M +.* %."$-(* ). '&'#"%-*(&++-*&(-#' 1.$9.'(

.'/.')%.% $'. %0)$"(-#' ). +#'/$.$% ). !7W X F = X7

>7 U$ 2&-( ).* 1C0'#3B'.* ). )-+&(&(-#' .( ). "#'(%&"(-#' ).* 3&(0%-&$A )$%&'( +. %.P

"$-(M '#$* ).9#'* )#'" 1%09#-% ).* 5.$A 30"&'-6$.* .'(%. +.* )-Y0%.'(.* 1-B".*7 Q- ".*

1C0'#3B'.* '. *#'( 1&* /E'&'(* )$ 1#-'( ). 9$. 30"&'-6$.M -+ +. *#'( ,.&$"#$1 1+$*

)$ 1#-'( ). 9$. 3&/'0(-6$.7 Z' .Y.(M +.* .'(%.2.%* "%00* .'/.')%.'( +G&11&%-(-#' ).

"C&31 )03&/'0(-*&'( RU./ KT7 L "#$%(.* )-*(&'".*M +.* -'(.%&"(-#'* )-1#+&-%.* .'(%.

3#3.'(* 3&/'0(-6$.* *#'( '0/+-/.&,+.* ).9&'( ".++.* )G0"C&'/.M 3&-* .++.* )#3-'.'(

F /%&').* )-*(&'".*7 8G&"(-#' )-1#+&-%. )01.') ). +& 1#*-(-#' %.+&(-9. ).* 1#-'(* "#'*-P

)0%0* ). +G0"C&'(-++#' .( ). +G.A-*(.'". #$ '#' )G$'. &-3&'(&(-#' .' ".* 1#-'(*7 Z++.

*. 3&'-2.*(. 1&% $'. -'@$.'". &)9.%*.M 2#'"(-#' ). +& /0#30(%-.M 6$. +G#' (%&)$-( .'

(.%3.* ). "C&31 )03&/'0(-*&'( Hd 6$- *G#11#*. F +G&-3&'(&(-#' M )$ 3&(0%-&$ .(

9-.'( *. *#$*(%&-%. &$ "C&31 )G.A"-(&(-#' H7 D.( .Y.( '#$* &3B'. )#'" F &$/3.'(.%

+. "C&31 )G.A"-(&(-#' 1#$% *&($%.% +. 3&(0%-&$7

[7 8. ).%'-.% 1#-'( & 0($)-.% .*( +. "#31#%(.3.'( ).* 3&(0%-&$A 3&/'0(-6$.* .' 2#'"(-#'

). +& (.310%&($%.7 Q$% ". 1#-'(M '#$* ).9#'* )-*(-'/$.% +. 3&(0%-&$ ). +& *(%$"($%.

:"$+&**. .( 5&3,. ".'(%&+.? .( +.* "&)%.* )G&++-&/.* F %."$-%.7 \#$% +& 1%.3-B%. "&(0P

/#%-.M '#$* &9#'* "C.%"C0 ).* 3&(0%-&$A 2.%%#3&/'0(-6$.* "&1&,+.* ). *$11#%(.% +&

(.310%&($%. ). J!!

D7 8.* "&%&"(0%-*(-6$.* 3&/'0(-6$.* ).* 1%-'"-1&$A &++-&/.* 2.%P

%#3&/'0(-6$.* $(-+-*0* .' 0+."(%#(."C'-6$. .( +.$%* (.310%&($%.* ). 2#'"(-#''.3.'(

*#'( 1%0*.'(0.* )&'* +. (&,+.&$ <7=[7

8& 2&3-++. 2.%P"#,&+( 1%0*.'(. +.* '-9.&$A )G-')$"(-#' F *&($%&(-#' +.* 1+$* 0+.90* ).*

&++-&/.* 2.%%#3&/'0(-6$.* :5$*6$GF KM> V? .( #Y%. ).* 1#**-,-+-(0* ). 2#'"(-#''.% F ).*

(.310%&($%.* 0+.90.* :Tc] [!

D?7 L$ 9$ ). '#(%. &11+-"&(-#' .( ). *.* "&%&"(0%-*P

(-6$.*M '#$* &9#'* "C#-*- $' &++-&/. .' ;.%PD#,&+( ). (^1. L;_[!K 6$- "#%%.*1#')

F [! XD# )&'* +. (&,+.&$ <7=[7 \#$% +.* "&)%.* )G&3#%1C. 1%0"$%*.$%M F +& (.310P

%&($%. ). J!!

DM +G&3#%1C. .*( 1&%&3&/'0(-6$.7 D.+& *-/'-`. 6$. +.* /%&-'* αP;.Q-

Page 106: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1( &$*(/) 2'(2 *+345 )&3,2%$&2$ 2(& 1$2 *31&$2 !

!"#$% "#!$ % &'(')*+(,-*,./0- 1'23+*,./0- 45'66,'20- 70((81'23+*,./0- 9&8/ :; &8/ <;

"= !>

-83* 03*8/(+- 45/30 1'*(,)0 ./'-, '1'23+*,./0; -01?6'?60 @ 65',( @ )0**0 *01A+('*/(0#

B0 1'*+(,'/ 0-* 483) -,1,6',(0 @ /3 1'*+(,'/ )81A8-,*0 483* 6' 7(')*,83 C86/1,./0

'C8,-,30 60- DE F# B0 )G'1A 4+1'23+*,-'3* 03*(0 60- 2(',3- 0* 6' 1'*(,)0 '1'23+*,./0

@ HEE

& C' 483) (+4/,(0 6' A86'(,-'*,83 @ -'*/('*,83 @ I- J E#! K 0* 6' A0(1+'?,6,*+

4/ 1'*+(,'/ L/-./5@ µi = 40 !"#$%&'

!"!# $%&'$(&)* +( ,-$%&.$(&)* '/ '&.0).&(&1

()*+ ,"+ -)#./"+ -#0102"*."+3 *45+ )64*+ 20."#7/*0 ,"+ 7).0#/)58 7)9*0./:5"+ ;<"=4 ".

1)2#" 2>)74#-?" -#015#+"5#@ ". ,) 90470.#/" 25 2/+-4+/./A ;"* +)1?)*. :5>/, 24/. #"*.#"# 2)*+

," A45# 2" B% 77 2" 2/)7C.#"@' D* A4*1./4* 2"+ 14*.#)/*."+ 2" 2/,).)./4*3 2" 14*.#)1./4*

". 2"+ 2/7"*+/4*+ 25 1)2#"3 *45+ )64*+ 06),50 5* "*.#"A"# 7)8/7), -"*2)*. ," #"15/.

2" %'E 77 "*.#" ,"+ 1)2#"+ ". ,) 15,)++" "* <"=4' F, *45+ #"+." G 20."#7/*"# ," *47H#"

2>)7-C#"I.45# G A)/#" 1/#15,"# 2)*+ ,) H4H/*" -45# +).5#"# ,"+ 1)2#"+' J45# 1",)3 *45+

)64*+ #0),/+0 5*" +/75,)./4* +45+ ," ,49/1/", <,58 E( 2>)-#C+ ,"+ 2/7"*+/4*+ 25 +K+.C7"

2"++/*0 +45+ L4,/2D29" ;</9' M'NO@'

P"+ #0+5,.).+ 2"+ +/75,)./4*+ *45+ )7C*"*. G 14*1,5#" :5>5* 145#)*. 2" QR% )7S

-C#"+I.45# +"#)/. *01"++)/#"' T/"* +U# 2)*+ ,) -#)./:5"3 *45+ *" -4564*+ -)+ #0),/+"# 5*"

+"5," +-/#" 2" 15/6#" 2" +"1./4* #"1.)*95,)/#" .45. "* )K)*. 5* #)K4* 2" 145#H5#" +5V+)*.

-45# #"*.#"# 2)*+ ," 2/+-4+/./A' W45+ )64*+ 4-.0 2)*+ 5* -#"7/"# ."7-+ -45# 5*" H4H/*"

"*25/." 2" 10#)7/:5" #0+/+.)*." G ,) ."7-0#).5#" )X* 2>06/."# ," 14*.)1. "*.#" ,"+ +-/#"+

". ," 14*.)1. )6"1 ,) 15,)++"' ="-"*2)*.3 ,) 10#)7/:5" 0.)*. 1)++)*." ". *>)2?0#)*. -)+ )5

15/6#"3 *45+ )64*+ 5./,/+0 5*" 9)/*" /+4,)*." .?"#7/:5" G ,) -,)1"' =".." 9)/*" "* ./++5 "+.

-#065" -45# #0+/+."# G 2"+ ."7-0#).5#" 2" OR%

=3 1" :5/ 14*6/"*. H/"* G *4.#" )--,/1)./4*'

Y5 65 2" ,>"+-)1" 2/+-4*/H," 2)*+ ," 2/+-4+/./A 2>)--,/1)./4* 25 1?)7-3 *45+ )64*+ -5

#0),/+"# Z +-/#"+ )6"1 5* X, 75,./H#/*+ 2" +"1./4* 2.5 mm2' J45# 20,/6#"# ," 145#)*.3 *45+

)64*+ H#)*1?0 "* -)#),,C," 2"58 ),/7"*.)./4*+ [(\ P)7H) ;%SNR%M %SQRY@ 20,/6#)*. 5*

145#)*. .4.), 2" EO Y'

!"!' 2-./%($(. +30-,&4+*($/3

P4#+ 25 -#"7/"# "++)/ 2" #"15/. 2"+ 1)2#"+ +45+ 1?)7- .#)*+6"#+"3 *45+ #"7)#:54*+ :5"

,>/*.#4251./4* 25 2/+-4+/./A 2)*+ ," A45# "*9"*2#" 5* 20#C9,"7"*. 2" ,) #095,)./4*' D* "]".3

Page 107: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

!"#$% "#$% & '()*+,-(./ 0* 121-3)4 05,66+(7,-(./ 0* 78,)6 -9,/1:4914 ; %<<

= 1.*1

>+*? !@ A$BC ,* :* 041 12)D-9(41E

!"#$% "#$F & G8.-. 041 7,0941 /,/.79(1-,++(1D1 0,/1 +4 0(16.1(-(H 05,66+(7,-(./ 0* 78,)6

Page 108: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$ %$&&'( )$*+,'-'./0($ 1( &$*(/) 2'(2 *+345 )&3,2%$&2$ 2(& 1$2 *31&$2 !

"#$%%&'()%%&*&+, &+ -./'$+, 0&()&+, )+%,$1"&2 3& 456+.*7+& &%, 08 9 "$ +$,/'& *:*& 0/

0)%4.%),); </) %& -.*4.',&= (/ 0/ ;./'= -.**& /+& 4&',/'1$,).+ ".)+ 0#:,'& +6>")>&$1"&2 ?+

&@&,= "& 0)%4.%),); .--/4& "$ *.),)6 0/ (."/*& /,)"& 0#/+& 4$',2 ?, 0#$/,'& 4$',= )" ($ %&

-.*4.',&'= ,./A./'% (/ 0/ ;./'= -.**& /+& %./'-& 0& -5$"&/' B'&,$'06&C= 0/ ;$), 0& %.+

)+&',)&2 D" &%, 0.+- )+0)%4&+%$1"& 0& '6>"&' "& -.''&-,&/' EDF 0$+% -&,,& -.+G>/'$,).+2

HG+ 0& -$'$-,6')%&' +.% -$0'&%= +./% $(.+% -.+I/ /+& 4&,),& 1.J,& &+ 4"$%,)</& 4&'*&,K

,$+, "& 1.1)+$>& 4')*$)'& &, %&-.+0$)'& %$+% &+0.**$>&' "&% 6-5$+,)"".+% LM)>2 N2OPQ2

!"#$% N2OP R F)%4.%),); 0& -$'$-,6')%$,).+ 0&% -$0'&% +$+.-')%,$"")%6%

S.'% 0& +.% '&-/),% $(&- "& +./(&$/ EDF= +./% $(.+% 4/ '&*$'</&' 4"/%)&/'% -5.%&%2

S& -T-"& 0#5T%,6'6%)% &%, *.)+% -./-56 </& +.,'& '&-/), %$+% -5$*4 %/' "& ,.'&2 3&4&+K

0$+,= $T$+, 0&% 0./,&% %/' -& '&-/),= +./% 4'6;6'.+% -.*4$'&' "&% '&-/),% 0& -$0'&% %./%

-5$*4 ,'$+%(&'%& LU&-/), %./% -5$*4Q $/ '&-/), 0/ ,.'& %$+% -5$*4 -5&V W3W LU&-/),

W3WQ2 X./% +.,.+% </& "& -T-"& &%, 4"/% -./-56 </& "& '&-/), %$+% -5$*4 0& W3W= -&

!"#$% N2O R 3T-"& 0#5T%,6'6%)% 0&% -$0'&% '&-/), %./% -5$*4 ,'$+%(&'%&

</) +./% 06*.+,'& "#)+Y/&+-& 0/ -5$*4 *$>+6,)</& 4&+0$+, "& '&-/), LM)>2N2O Q2 X./%

.1,&+.+% 4./' -& *$,6')$/ /+& 4&'*6$1)"),6 0& "#.'0'& 0& OZZ ZZZ 9 O!Z ZZZ -.+,'& [ZZ

ZZZ 4./' /+ '&-/), %$+% -5$*42 S&% *&%/'&% 0& 4&'*6$1)"),6 %.+, &@&-,/6&% 4$' *&%/'& $/

4.+, 0#)*460$+-& 9 /+& ;'6</&+-& 0& \Z]V 4./' /+& $*4"),/0& 0& Bc 0& Z2! W2 S#.'0'&

Page 109: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

Hc

Hc

Page 110: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()%*+$ ,-( ./0 1% 2)()2%&(*,)%*+$ !

!"#$% "#$% & '()*+(,+ -* ,./01 23/(45+34+ 4*3 6+ ,7,6+ -8.7429394:4

!" #$%&'()%*+$ ,-( ./0 1% 2)()2%&(*,)%*+$

!"!# $%&'()%*(('&'(+ ,- ./0

;/(4 *( 13+0:+3 2+014< (=*4 (=*4 4=00+4 :(293+4494 /*> ,/3/,293:42:?*+4 -+4 ,:3,*:24

@AB4# C( (=*4 D/4/(2 4*3 6+4 /D/?*+4 E=*3(:+4 1/3 6/ 4=,:929 F:41/(=GH*:I/ 4*3 6+*34 *4/J+4

,=*3/(24 K6+ 271+ -+ @AB K91/:44+*3 %#L 00M< 6+4 6/3J+*34 -+ ,*:53+ *2:6:49+4< 6+4 ,=(23/:(2+4

-89695/2:=( -+ 2+0193/2*3+ K$N

AMM< (=*4 /5=(4 -92+30:(9 6+ (=0D3+ -+ 41:3+4 0/>:0/6

39/6:4/D6+ 4*3 *( ,O29 -* ,/-3+ KP/D6+ "#QM#

&'()% "#Q & A/3/,293:42:?*+4 -+4 1:42+4 -+ ,*:53+ 4*3 6+ @AB

Epaisseurpiste Largeurpiste Espaceentrepistes Nspiresmax

%N! µ0 N#R 00 N#LR 00 Q$

A+22+ 92*-+ /7/(2 1=*3 D*2 -+ -90=(23+3 6/ E/:4/D:6:29 -* ,=01=4/(2 +2 (=( -+ 39/6:4+3

*( ,=01=4/(2 391=(-/(2 139,:490+(2 /* ,/.:+3 -+4 ,./3J+4< (=*4 /5=(4 ,.=:4: -+ 39/6:4+3

6+ ,=01=4/(2 /5+, 6+ (=0D3+ -+ 41:3+4 0/>:0*0# A+ ,.=:> / 1=*3 =DS+,2:E -8/*J0+(2+3

68:(-*,2/(,+ -+ 0=-+ ,=00*(# C( +T+2< 68:(-*,2/(,+ -91+(- 13:(,:1/6+0+(2 -* (=0D3+ -+

41:3+4< -+ 6/ 4+,2:=( -+ 0/293:/* 0/J(92:?*+ +2 -+ 6/ 1+309/D:6:29# U=23+ ,.=:> 4+ S*42:V+

1/3 6/ 0/W23:4+ (=( 1/3E/:2+ -* -+3(:+3 E/,2+*3# X+ -+*>:Y0+ E/,2+*3 ?*/(2 Z 6*: 92/(2

,=(-:2:=((9 1/3 6/ 0:4+ +( E=30+ -+ 6/ 423*,2*3+ -/(4 6+ @AB#

@=*3 ,+22+ -+*>:Y0+ 1./4+< 16*4:+*34 4=6*2:=(4 1+*5+(2 [23+ +(5:4/J9+4< ,+1+(-/(2 ,+32/:(+4

Page 111: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! ! "#$ %& '()*($+&, )+-&.,/0%" %&/0%" /&,.-#+12" $%# 345

"#$%&'($%)* +#(,)$% -%&) ($%./&.)* 0

1 2)* "'+&)* +3'44('/)* $'$#"&(*%'44($* .%'$% )5%&-6)6)$% 7&'/(4)*8 4' *%&9"%9&) :;<

+#(% ',#(& 9$) ")&%'($) &(/(+(%.=

1 23)$%&)7)& )$%&) 4)* +)95 ($+9"%'$")* +#(% -%&) >'&7'(%)6)$% 6'?%&(*.= @#9* ',#$*

+#$" )$,(*'/. +) >&)$+&) 9$ *9>>#&% '6'/$.%(A9) >#9& &.'4(*)& 43)$%&)7)&=

1 2)* ($+9"%'$")* +#(,)$% -%&) B#B($.)* )$ *.&()= @#9* +),#$* '4#&* %&#9,)& 9$ 6#C)$

+3($"49&) 4) 6'%.&('9 6'/$.%(A9) )% +) &.'4(*)& 4)* *>(&)* 7'"(4)6)$% '9%#9&=

!"#$% D=EE 1 D9) +) "#9>) *"F.6'%(A9) +) 43($+9"%'$") +'$* 4) :;<

G$ >&)$'$% )$ "#6>%) ")* "#$*(+.&'%(#$* )% ,#94'$% 9$) *%&9"%9&) &.'4(*'B4) &'>(+)6)$%8

$#9* ',#$* #>%. >#9& 9$) *%&9"%9&) )$ 7#&6) +) B#?%) HI(/= D=EEJ=

2' &(/(+(%. +9 +(*>#*(%(7 )*% #B%)$9) >'& +)95 >4'A9)* +) :;< +) K=! 66 HLJ= 2)* "'+&)*

$'$#"&(*%'44($* *#$% ($%&#+9(%* +'$* +)* )6>4'")6)$%* &'($9&.* +'$* 4) :;<= LM$ +) $)

>'* "'**)& 4)* >4'A9)* +) :;< 4#&* +9 &'($9&'/)8 $#9* ',#$* "F#(*( +) &.'4(*)& 9$ .,(+)6)$%

+) K 66 +) >&#7#$+)9&= ;)%%) ,'4)9& M5) '4#&* 4' *)"%(#$ +) 43($+9"%'$")= 23)$%&)7)& )*%

&.'4(*. >'& 9$) 7)9(44) +) N'>%#$ +3.>'(**)9& O=K 66 H<J8 .>'(**)9& 6($(6'4) &.'4(*'B4)=

2' ,'4)9& +) 43)$%&)7)& )*% +#$" M5.) >'& 43.>'(**)9& +9 P'>%#$ )% +)* >(*%)* +) "9(,&)= 2)*

+(Q.&)$%)* >(R")* +) 4' *%&9"%9&) *#$% 6'($%)$9)* )$%&) )44)* >'& +)* ,('* 6.%'44(*.)*= ;)*

,('* '**9&)$% '9**( 4' "#$%($9(%. +)* *>(&)* '9%#9& +9 6'%.&('9 6'/$.%(A9)=

!"!# $%&'%()*+ &),*-+./01 .*+-,2- (02 3$4

S&T") '95 +(Q.&)$%)* ','$".)* *9& 4) 6'%.&('9 )% U $#* "#$*(+.&'%(#$* *9& 4) +(6)$*(#$V

$)6)$% +9 :;<8 $#9* *#66)* '"%9)44)6)$% )$ "#9&* +) &.'4(*'%(#$ +9 >&#%#%C>)=

!" #$%&'()*$%

W'$* ") "F'>(%&)8 $#9* ',#$* )$,(*'/. +3($%./&)& +)* '44('/)* $'$#"&(*%'44($* +'$* +9

:;<= ;)%%) .%9+) $3'C'$% >'* .%. 6)$.) '9>'&','$%8 $#9* $#9* *#66)* "#$7&#$%.* U

+(Q.&)$%* ,)&&#9* %)"F$#4#/(A9)* )% >&#B4R6)* )5>.&(6)$%'95= 2) >&)6()& ,)&&#9 +) 4'

6(*) )$ 7#&6) +) 43'44('/) ' .%. &.*#49 >'& 4' +."#9>) +) 43'6#&>F) >&."9&*)9& ',)" *9""R*=

2) *)"#$+ ,)&&#9 %)"F$#4#/(A9) +9 &)"9(% *#9* "F'6> %&'$*,)&*) +)* "'+&)* $#9* ' '6)$. U

Page 112: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"! #$%&'()*$% !

"#$%&'()'* ($ +#(' %#(% ,'-#$ ./0'#-1$12 , 345*('* 6"&(*37 3* +#(' *%& #81'6&)#$$*3 *& 0#$$*

3)*( 9 0*% '*"()&% '*8'#0("&):3*%2 ;*8*$06$&7 36 <(*%&)#$ 0* 34#=/06&)#$ 0*% >6&1')6(= '*%&*

9 688'#+#$0)'2 ?6 "#$"*8&)#$ 0( 0)%8#%)&)+ 046883)"6&)#$ 0( "56>8 &'6$%@*'%* $#(% 6 8*'>)%

046@#)' ($* @63)06&)#$ 8'13)>)$6)'* 0* 34)$A(*$"* 0( "56>8 %(' $#% "60'*%2 ;* '1%(3&6& *%&

0#$" 8'#>*&&*(' 8#(' 0* $#(@*33*% &#8#3#-)*% 0* "#>8#%6$&% >6-$1&)<(*% $6$#"')%&633)$%2

?4)$&1-'6&)#$ %(' B;C 6 0#$$1 3)*( 9 0*% '1A*=)#$% %(' 36 '163)%6&)#$ 8'6&)<(* 0( "#>8#%6$&

>6)% $#(% $* 0)%8#%#$% 86% 0* "#>8#%6$& D$63 9 345*('* 6"&(*33* +6(&* 0* &*>8% 6@6$& 36

'*%&)&(&)#$ 0( >6$(%"')&2

Page 113: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 114: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&'!" () *(+&*(#)',(&

! "#$%$&' $ !( )*(# *+,!-"&. '/0"(1! !" '$ #0$'&2$"&*3 1/(3 -*4)*2$3" 4$530"&6(! (3&6(!

)*(# (3 7'"#! 89: ! -*4)*2$3" $ 0"0 -*3;( )*(# #01(&#! '!2 )!#"(#+$"&*32 -*31(&"!2 1!

4*1! -*44(3 !" 1! 4*1! 1&<0#!3"&!' !3 $4*3" 1/(3 -*3%!#"&22!(# = >= ? @A 1!2"&30 B

'/$0#*3$("&6(!: C*"#! *+,!-"&. 0"$&" $'*#2 '$ #01(-"&*3 1! '$ 4$22! -*3"#$&3" )$# (3 -$D&!#

1!2 -D$#5!2 101(&" 1! '$ 2*'("&*3 !E&2"$3"!: =$32 '! +(" 1/$))#0D!31!# '! )#*+'F4! 1(

1&4!32&*33!4!3" *)"&4&20 1! -! -*4)*2$3" !" '! -*3"!E"! $))'&-$"&.G 3*(2 $%*32 10-*4)*20

-! 404*&#! !3 -&36 -D$)&"#!2:

=$32 '! )#!4&!# -D$)&"#!G '$ )#*+'04$"&6(! 1! 7'"#$5! )$# (3 -*4)*2$3" 4$530"&6(! (3&6(!

$ 0"0 !E)'&-&"0!: H!2 3*"&*32 1! -*4)$"&+&'&"0 0'!-"#*4$530"&6(! !" !3 )$#"&-('&!# 1!2 )!#"(#>

+$"&*32 -*31(&"!2 *3" 0"0 $'*#2 10-#&"!2: H!2 -#&"F#!2 &4)*202 )$# '!2 3*#4!2G !3 )$#"&-('&!#

'$ =I>JKLMG *3" 0"0 )#02!3"02: N )$#"&# 1! -!2 &3.*#4$"&*32G '!2 -*3"#$&3"!2 1! -*3-!)"&*3

1! -!2 -*4)*2$3"2 *3" 0"0 105$50!2 $( "#$%!#2 1/(3 0"$" 1! '/$#" 1!2 1&<0#!3"!2 "*)*'*>

5&!2 !E&2"$3"!2: O*(# -D$-(3!G '!2 )*&3"2 2)0-&76(!2 1! -*3-!)"&*3 *3" 0"0 $3$'P202 !" (3!

$""!3"&*3 )$#"&-('&F#! $ 0"0 )*#"0! 2(# '! -*4)*2$3" #0$'&20 )$# Q&2)$3*>R(&S$:

N '/&22(! 1! -!""! $3$'P2!G )'(2&!(#2 .$-"!(#2 1/&3T(!3-! *3" 0"0 4&2 !3 0%&1!3-! -*44! '$

2P40"#&!G 1( 4$"0#&$( 4$530"&6(! !" 1!2 "#$,!"2 1! T(E: 83 3*(2 +$2$3" 2(# -!2 .$-"!(#2

3*(2 $%*32 )( #01(&#! 3*"#! 0"(1! B 6($"#! "*)*'*5&!2 1&2"&3-"!2: N73 1! '!2 -*4)$#!#G

3*(2 $%*32 1U 10"!#4&3!# (3 -#&"F#! 1! -*4)$#$&2*3 $))'&-$"&.: N&32&G '!2 "!32&*32 $(E

+*#3!2 1( VRWH *+"!3(!2 )*(# (3 7'"#! 1$32 (3 !3%&#*33!4!3" "D0*#&6(! 2)0-&70 )$#

3*2 2*&32 $ 0"0 1073& -*44! #0.0#!3-!: /!2" B -!""! $#"&-('$"&*3 1!2 "#$%$(E 6(! 2! 2&"(!

$'*#2 (3 1!2 )*&3"2 1! 1&2-(22&*3 &4)*#"$3" )(&26(! -/!2" B )$#"&# 1! -!2 -D*&E 6(! '!

-(#2!(# !3"#! 2)07-&"0 1! '/$))'&-$"&*3 !" 5030#&-&"0 1! '/$))#*-D! !2" )*2&"&*330: O$# '$

2(&"!G -D$6(! "*)*'*5&! $ 0"0 4&3&4&20! !3 "!#4! 1! %*'(4! )$# #$))*#" $( -*4)*2$3" 1!

#0.0#!3-!: O*(# -!'$G 3*(2 $%*32 -D*&2& (3! 4*10'&2$"&*3 2P2"F4! 1! '/!32!4+'! 1! '$ -D$X3!

0'!-"#&6(! YR*(#-! 1! )!#"(#+$"&*32G M&'"#!G VRWHZ: 83 !<!"G '$ )!#.*#4$3-! 10)!31 1( "P)!

1! )!#"(#+$"&*32 4$&2 $(22& 1( 7'"#! 89 6(! '/*3 )'$-! )*(# 7'"#!# -!2 )!#"(#+$"&*32: W' !2"

1*3- &4)*#"$3" 1! -*32&10#!# '/!3%&#*33!4!3" 1( 7'"#! -*32"$3" )*(# )*(%*&# '!2 -*4)$#!#:

[3! $1$)"$"&*3 1/&4)01$3-! $ 0"0 4&2! !3 )'$-! !3"#! '! VRWH !" '$ 2*(#-! 1! )!#"(#+$"&*32

$73 1! 2/$<#$3-D&# 1! '$ )#*+'04$"&6(! 1/&1!3"&7-$"&*3 1! '$ 2*(#-!: !""! )#!4&F#! 0"$)!

1! 4*10'&2$"&*3 3*(2 $ )!#4&2 1/0-$#"!# '!2 -*4)*2$3"2 4$530"&6(!2 1&22P40"#&6(!2 6(&

.$%*#&2!3" '! -*()'$5! 1! 4*1!2 !" 3! 2*3" )$2 -*3-(##!3"&!'2 !3 "!#4! 1! )!#.*#4$3-!2:

Page 115: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!! "#$%&'()#$ *+ ,*-(,*%+).*(

/')+* 0 %*++* ,-*1)2-* 3+4,* 5* 1#53&)(4+)#$6 $#'( 4.#$( -*+*$' &*( 5*'7 +#,#&#8)*( &*(

,&'( 454,+3*(9 "*,*$54$+6 $#+-* +-4.4)& 3+4$+ 473 ('- &* 14+3-)4' 148$3+):'*6 $#'( 4.#$(

53%)53 5;4,,-#<#$5)- (4 1#53&)(4+)#$ 4=$ 5* ,-35)-* &* %#1,#-+*1*$+ -3*& 5' =&+-*9 >4$( &*

=&+-* %#1,&*+6 &* 14+3-)4' 148$3+):'* *(+ (#'1)( 0 5*( %#$+-4)$+*( ('- '$* &4-8* ,&48* 5*

<-3:'*$%* 14)( 4'(() 0 5*( *7%)+4+)#$( 5)?3-*$+*( (').4$+ &* 1#5* %#11'$ #' 5)?3-*$+)*&9 @*

%A4,)+-* +-#)( *(+ 535)3 0 &4 ,-)(* *$ %#1,+* 5' %#1,#-+*1*$+ 148$3+):'* 5' %#1,#(4$+ B*$

<-3:'*$%* *+ *$ ,#&4-)(4+)#$C9 @* 1#52&* '+)&)(36 8D-4+*'-E%4,4%)+3 D *(+ 53+4)&&39 @;4.4$+48*

5* %* 1#52&* *(+ &4 (3,4-4+)#$ 5*( ,4-412+-*( ,AD():'*( *+ 5*( ,4-412+-*( 83#13+-):'*(6

%* :') <4%)&)+* &;#,+)1)(4+)#$ '&+3-)*'-*9 "*,*$54$+6 %*++* 1#53&)(4+)#$ (* %4$+#$$*6 )%)6 4'7

%#1,#-+*1*$+( 148$3+):'*( *+ &*( *?*+( %4,4%)+)<( ,4-4()+*( $;#$+ ,4( 3+3 ,-)( *$ %#1,+*6

%* :') &)1)+* 4 ,#(+*-)#-) &4 ,&48* 5* <-3:'*$%* 5* $#+-* 1#52&*9

>4$( &* %A4,)+-* :'4+-*6 $#'( 4.#$( 53+4)&&3 &*( 5)?3-*$+*( 13+A#5*( 5;#,+)1)(4+)#$ (#'(

%#$+-4)$+*(9 F-G%* 0 &4 %#1H)$4)(#$ 5;'$ 4&8#-)+A1* 83$3+):'* *+ 5;'$ 4&8#-)+A1* 5* -*E

%A*-%A* 5* 1)$)1'1 &#%4& B()1,&*7*C6 $#'( 4.#$( %#$.*-83 -4,)5*1*$+ .*-( '$ 5)1*$()#$E

$*1*$+ 5* &4 +#,#&#8)* 4.*% *$+-*<*-9 I' .' 5* &4 -34&)(4+)#$ )$5'(+-)*&&* 5* %* ,-#+#+D,*6

$#'( 4.#$( *$(')+* ,-)( *$ %#1,+* 5*( %#$+-4)$+*( 5* <4H-)%4+)#$ B&4-8*'- 5*( -'H4$(6 H#H)E

$48*6 *+%9C9 I &;)(('* 5* %*++* ,A4(*6 $#'( 4.#$( #H+*$' &*( 5)1*$()#$( =$4&*( 5' ,-#+#+D,*9

"* 5*-$)*-6 '$* <#)( -34&)(36 4 3+3 %#1,4-3 4.*% ('%%2( 4'7 ,*-<#-14$%*( 5' ,-3 5)1*$()#$E

$*1*$+9 "*( +-4.4'7 #$+ 5#$% ,*-1)( 5* -34&)(*- '$ %#1,#(4$+ 148$3+):'* '$):'* ,#'- '$

=&+-48* "JK 4.*% '$* -35'%+)#$ 5* L! M 5' .#&'1* *+ 5* 1*)&&*'-*( -35'%+)#$( +A3#-):'*(

5*( ,*-+'-H4+)#$( 5* 1#5* %#11'$ *+ 5)?3-*$+)*& :'* &* %#1,#(4$+ N)(,4$#E/')O46 ,#'-

$#+-* (#'-%* 5* ,*-+'-H4+)#$(9

>4$( &* 5*-$)*- %A4,)+-*6 $#'( 4.#$( %A*-%A3 0 +)-*- ,-#=+ 5* &4 +#,#&#8)* 53.*&#,,3* 4.*% '$

*$+-*<*- *$ 4&&)48* $4$#%-)(+4&&)$ *+ 0 &;)$+38-*- 4' P"Q9 @4 %#1,&*7)+3 5* %* +-4.4)& -3()54)+

5;'$* ,4-+ 54$( &4 <-48)&)+3 5' 14+3-)4' 148$3+):'* *+ 5;4'+-* ,4-+6 54$( &4 -34&)(4+)#$ 5;'$

-*%')+ (#'( %A41, +-4$(.*-(* ,#'- &*( %45-*( 148$3+):'*(9 P4- &;)$.*-()#$ 5*( 3+4,*( 5*

53%#',* *+ 5* -*%')+ 5*( -'H4$(6 $#'( 4.#$( ,' 53=$)- '$ 5)(,#()+)< *7,3-)1*$+4& (,3%)=:'*9

J$ *?*+6 ,#'- 4.#)- &*( ,-#,-)3+3( 148$3+):'*( $3%*((4)-*( 0 $#+-* 4,,&)%4+)#$6 &* %)-%')+

148$3+):'* 5#)+ R+-* -*%')+ (#'( %A41, +-4$(.*-(*9 >4$( '$ ,-*1)*- +*1,(6 $#'( 4.#$(

5#$% -34&)(3 '$ <#'- 5* -*%')+ (#'( 4-8#$ AD5-#83$3 ,')( '$ (D(+21* 5;4,,&)%4+)#$ 5'

%A41, 454,+3 0 $#+-* +#,#&#8)* *+ '+)&)(4H&* 54$( &* <#'-9 @*( -3('&+4+( 5* -*%')+ (#'(

%A41, +-4$(.*-(* (#$+ *$%#'-48*4$+( ,')(:'* 5*( ,*-134H)&)+3( 5* &;#-5-* 5* !! !!! #$+

3+3 #H+*$'*(9 "*( .*--#'( +*%A$#&#8):'*( &*.3(6 &;)$+38-4+)#$ 5*( 4&&)48*( $4$#%-)(+4&&)$(

54$( 5' P"Q *(+ 5#$% *$.)(48*4H&* ,#'- &4 -34&)(4+)#$ 5* %#1,#(4$+( ,&4$4-9

J$ %#$%&'()#$6 &* H'+ 5* %*( +-4.4'7 4 3+3 4++*)$+ 4.*% &4 -34&)(4+)#$ 5;'$ %#1,#(4$+

148$3+):'* 5* =&+-48* '$):'* *+ 1#)$( .#&'1)$*'79 @* ,-#%353 5* -*%')+ 5*( %45-*( 4&&)48*(

$4$#%-)(+4&&)$( 4 3+3 .4&)53 *+ $#'( 4 ,*-1)( 5;4++*)$5-* 5*( ,*-134H)&)+3( 5* &;#-5-* 5*

!! !!!9 "* +D,* 5* %#1,#(4$+ *(+ 5#$% ,4-<4)+*1*$+ *$.)(48*4H&* ,#'- &4 -34&)(4+)#$ 5*

5)(S#$%+*'-( 5)?3-*$+)*&( )$+38-4H&*( ('- P"Q9 "*,*$54$+6 ,&'()*'-( ,*-(,*%+).*( ,*'.*$+

R+-* *$.)(483*( ,#'- %*( +-4.4'79 J&&*( ,*'.*$+ R+-* -*8-#',3*( *$ 5*'7 %4+38#-)*(9

Page 116: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#$%&'!" () *(+&*(#)',(& -.-

/0%"( *1+)2 30%" *!'") 3( ,%( 3( $1 4!35$'&1)'!" &6&)74( 8

9 :1 #!4*1+1'&!" 3(& 3(%; )!*!$!<'(& => 41)5+'1% %"'?%( () @'&*1"!AB%'C1D &%+ 3(&

4!37$(& 3( &!%+#(& ,5+')1E$(& #( ?%' *(+4())+1') 301**!+)(+ %"( ,1$'3')5 &%**$54("A

)1'+( > #(& )+1,1%;F G$ (&) 3!"# "5#(&&1'+( 3( +51$'&(+ $05)%3( 3( $1 3(&#+'*)'!" 3( $1

&!%+#( 3( *(+)%+E1)'!"&F

9 :05)%3( 3( $1 3'&&645)+'( 3% H$)+( IJF K!%& 1,!"& 5)%3'5 *$%&'(%+& L1#)(%+& '"M%("A

N1") $1 )!*!$!<'( 3% #!4*!&1") 41<"5)'?%( %"'?%(F ())( 5)%3( "!%& 1 *(+4'& 3(

#!"#$%+( &%+ $( 35&1,1")1<( 30%" #!4*!&1") 41<"5)'?%( 3'&&645)+'?%(F (*("31")2

#())( 5)%3( 1 5)5 4("5( 1,(# $(& ,1$(%+& 3( #1*1#')5& Cx () Cy '4*!&5(& *1+ $( #1A

O'(+ 3(& #O1+<(&F P"( 5)%3( #!4*$54(")1'+( &%+ $1 )!*!$!<'( #!4*$7)( 3% H$)+( IJ

= !4*!&1") 41<"5)'?%( () #1*1#')5&D *(+4())+1') 3( #!4*$5)(+ #(& #!"#$%&'!"&2 ("

"!%& E1&1") &%+ $(& )+1,1%; 35Q> +51$'&5& 31"& RS!E--TF

9 :1 *+!E$541)'?%( 3( $0'3(")'H#1)'!" 3(& 5$54(")& *1+1&')(& () $(%+ *+'&( (" #!4*)(

31"& $1 4!35$'&1)'!" 3(& H$)+(& IJ 1H" 305)("3+( $1 <144( 3( L+5?%("#(& #!%,(+)(&F

())( 5)%3( *(%)AU)+( 4("5( &!') *1+ 3(& #14*1<"(& 3( 4(&%+(& &%+ $(& #!4*!&1")&

(;'&)1")& RV W.XET2 &!') *1+ 3(& &'4%$1)'!"& "%45+'?%(& (" 14!") 3( $1 #!"#(*)'!"F

9 :1 *O1&( 30!*)'4'&1)'!" 3% #!4*!&1") 41<"5)'?%( *(%) U)+( 145$'!+5( (" 1Q!%)1")

$(& <+1"3(%+& 41<"5)'?%(& #!44( *1+147)+(& 3% 4!37$( 1H" 3( 35)(+4'"(+ $( 41A

)5+'1% 41<"5)'?%( $( *$%& 131*)5 > $1 )!*!$!<'(F

I) 301%)+( *1+)2 30%" *!'") 3( ,%( 3(& 1,1"#5(& )(#O"!$!<'?%(& 8

9 :1 +51$'&1)'!" 3( )!*!$!<'( 3% ?%1)+'74( #O1*')+( 1,(# %" )!+( !E$!"< *!%+ +53%'+(

$( ,!$%4( 3% #!4*!&1")F

9 :0145$'!+1)'!" 3% 3'&*!&')'L 3( +(#%') 3% $1E!+1)!'+( () 3( #!4*+("3+( $(& *O5"!47"(&

1**1+%& $!+& 3% +(#%') &1"& #O14*F

9 :0'")5<+1)'!" 3% #!4*!&1") 41<"5)'?%( 5)1") ,1$'35(2 '$ (&) (",'&1<(1E$( 3( +51$'&(+

%" H$)+( IJ '")5<+5F I" (Y()2 $(& #1*1#')5& *(%,(") U)+( ($$(& 1%&&' '")5<+5(& +("31")

$( H$)+( )+7& #!4*1#)F RZ$'-[TF

9 :1 +51$'&1)'!" 3% \ V *(%) U)+( 1%&&' 145$'!+5(F I" (Y()2 (" +51$'&1") 3(& #13+(&

41<"5)'?%(& (" 451"3+( #!44( 31"& RZO4-.T2 $(& E!E'"1<(& &!") +51$'&5& 31"& $(

4U4( *$1"2 #( ?%' "!%& *(+4())+1') 3( +53%'+( > 3(%; #!%#O(& 3( \ V $( #!4*!&1")

H"1$ 1% $'(% 3( )+!'& () 1'"&' 3( 3'4'"%(+ $0(")+(L(+ > $05*1'&&(%+ 3(& *'&)(& 3( #%',+(F

Page 117: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 118: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"#!$%&'()!*

!"#$% & !'()* (+, - "./0.1.2 ! 3(44*56 60* 78169 :.9 39656+1*+) ;*);<:96=/6+>?

86('()6 >/996+1 :9.0 @.A*+) 1;9./); 1;6 )9./+,6, *+569169 ;6(1 4*+' .:

(+ (,B/41(C86<4366, 0.1.9 ,9*56 4?41602 DEEE -F!GH!I-DJGH JG

DG"KH-FL !MMNDI!-DJGHO PQ RQSQ$TQSSUO S##$2

!)*% !)*86+1 QV#PWE -641 X*Y1/96O !"#$%&'( $() *"#+&," -$(.$/0 12&/"(%

3",4('/'2&"*0 5$(6 78896

:14-98; <6 14-$)&6 ='-!'*$(% -$2(>%&?." &(%>2#> "( $//&$2" @"A&=#=. !'.# /

>/",%#'(&?." )" !.&**$(,"6 B4C %4"*&*0 D(&+"#*&%> )" E#"('F/"0 78986

:1/&97; G6 1/&6 A'.+"//"* $#,4&%",%.#"* &(%>2#>* )" H/%#" =IG 4JF#&)"6 B4C %4"*&*0

I,'/" ('#-$/" K.!>#&".#" )" =$,4$(0 78976

:1/+89; @6 1/+"*6 @/$*4 *%#"** $(("$/&(2* &( ($(',#J*%$//&(" $//'J* L'# ("M &().,%&+"

,'-!'("(%*6 56 G$2(6 G$2(6 G$%"#60 77N O9PQ8R9PQ70 78896

:1*4QS; E6G6 1*4"#6 34" #'F.*% -')"//&(2 'L +$#&$F/" %'!'/'2J ,&#,.&%* .*&(2 F'()

2#$!4*6 B#',"")&(2* 'L K=K ='(L"#"(," T=<EGUQS0 !$2"* 97NR9S90 9QQS6

:1+&89; 1+&'(&,* %')$J0 ,%'F"# 78896

:<<V98; 16=6 <$&*)"(0 C6 <'#'J"+&,40 $() @"& V$(26 E"("#$/&W") %"#-&($/ -')"/&(2

'L "/",%#'-$2("%&, &(%"#L"#"(,"6 TIII 3#$(*$,%&'(* '( T().*%#J 1!!/&,$%&'(*0

PN O78NXR78YQ0 78986

:<=Z8Q$; 16 <"*#&0 [6 =4$W$/0 $() 56 B6 Z"#$)",6 =$!$,&%&+" F"4$+&'# 'L 4L !'M"# %#$(*\

L'#-"#* O E/'F$/ $!!#'$,4 %' )#$M #'F.*% "?.&+$/"(% ,&#,.&%* $() "]!"#&-"(\

%$/ ,4$#$,%"#&W$%&'(6 TIII T(%"#($%&'($/ T(*%#.-"(%$%&'( $() G"$*.#"-"(%

3",4('/'2J ='(L"#"(,"0 788Q6

:<=Z8QF; 16 <"*#&0 [6 =4$W$/0 $() 56 B6 Z"#$)",6 =$!$,&%&+" F"4$+&'# 'L 4L !'M"# %#$(*\

L'#-"#* O E/'F$/ $!!#'$,4 %' )#$M #'F.*% "?.&+$/"(% ,&#,.&%* $() "]!"#&-"(\

%$/ ,4$#$,%"#&W$%&'(6 TIII T(%"#($%&'($/ T(*%#.-"(%$%&'( $() G"$*.#"-"(%

3",4('/'2J ='(L"#"(,"0 788Q6

:<CEQX; 56 <"$.,/$&#0 B6 C"/+&(?.&"#0 $() 56 B6 E#'*6 3#$(*L'#-$%".#* "% &().,%$(,"*6

3",4(&?."* )" /^(2>(&".#0 %#$&%> E>(&" >/",%#&?."0 9QQX6

:<"/99; G6 <"/%#$-&(&6 ='(%#&F.%&'( _ /U'!%&-&*$%&'( )" /U"(*"-F/" ,'(+"#%&**".# `

H/%#"* )" *'#%&" +&* _ +&* )"* ,'(%#$&(%"* =IG $+&'(6 B4C %4"*&*0 T(*%&%.%

A$%&'($/ B'/J%",4(&?." )" 3'./'.*"0 78996

Page 119: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!" #$#%$&'()*+$,

-#./0 1 23 #./.4563 7844.9:;<85=>93 ?3 @:< A.>54:<B C.9D:<EF G0 3

-#H<I!1 (3 J3 #H<58<K:L63 ) ;8<84:M=/8B L=4LH=5 9.B8M N.4 9HM5=O=<B=<; =<BHL5=P8

B8P=L83 $,,, Q4:<>3 2:;<3F R SR0F GI!3

-#@@G 1 *3'3 #M:<T8< :<B U3U3%323 @:< @M84T8<3 2.B8M=<; .N 8M8L54.9:;<85=L >E>589>3

$,,, Q4:<>3 2:;<3F VI S"0!GW"0 0F GG 3

-#JJ

+!G1 U3 #=8M:F )3 J=4569H8MM84F (3 J:8>D8F 23 %3 +8MBO8=<F X3 (:;;MF :<B U3 J3

X.M:43 *:>>=P8 :<B :L5=P8 6EK4=B =<58;4:58B 89= YM584>3 $,,, Q4:<>3 *.O84

,M8L54.<3F V"Z0[R\ S ]"!W ]"GF V!!G3

-CC^

+!]1 (3 C68<F 73 C:<:M8>F #3 :<;F *3 #:4K.>:F U3?3 P:< JETF :<B 73C3 %883

$<58;4:5=.< .N 8M8L54.9:;<85=L D:>>=P8 L.9D.<8<5> =< BD> N4.<5[8<B BL_BL

L.<P84584 S ) L.9D:4:5=P8 >5HBE .N B=`848<5 =<58;4:5=.< >58D>3 )DDM=8B *.O84

,M8L54.<=L> C.<N848<L8 :<B ,aD.>=5=.< Z)*,C\F V S ]IW "VF V!!]3

-C'^

+!I1 b3 C68<F c3 '.<;F d3 :<;F c3 J:<;F :<B %3 c6:<;3 ?8>=;< L.<>=B84:5=.<>

N.4 D:>>=P8 >HK>54:58 O=56 N844=58 9:584=:M> 89K8BB8B =< D4=<58B L=4LH=5 K.:4B

ZDLK\3 *.O84 ,M8L54.<=L> eD8L=:M=>5> C.<N848<L8 Z*,eC\F D:;8> !"]W !"IF

V!!I3

-C6:!!:1 '3'3 C6:9D=.53 C.9D:5=K=M=5f fM8L54.9:;<f5=gH8 S A.49:M=>:5=.<F 4f;M898<[

5:5=.< 85 98>H483 Q8L6<=gH8> B8 Mh<;f<=8H4F 54:=5f 'f<=8 fM8L54=gH8F ? ] !F

V!!!3

-C6:!!K1 )3 C6:4.E3 *:4:>=58> 85 D845H4K:5=.<> B8> fM8L54.<=gH8> S #M=<B:;8F 7=M548>F

CiKM8> KM=<Bf>3 ?H<.B 58L6F V!!!3

-C6:!!L1 )3 C6:4.E3 *:4:>=58> 85 D845H4K:5=.<> B8> fM8L54.<=gH8> Q.98 S e.H4L8> [

C.HDM:;8 [ ,`85>3 ?H<.B 58L6F V!!!3

-C.LGG1 U3[%3 C.LgH848MM83 C3,323 85 fM8L54.<=gH8 B8 DH=>>:<L83 C.MM8L5=.<> eL=8<L8>

85 Q8L6<.M.;=8>F GGG3

-C.>!!1 73 C.>5:3 C.9D:5=K=M=5f fM8L54.9:;<f5=gH8 L89 S *4f>8<5:5=.< ;f<f4:M83

Q8L6<=gH8> B8 Mh<;f<=8H4F 54:=5f 'f<=8 fM8L54=gH8F ? ]!!F V!!!3

-C.HG"1 '3 C.HB84L6.<3 )MM=:;8> N84[<=LT8M 85 N84[L.K:M5 [ D4.D4=f5f> 9:;<f5=gH8>3 Q8L63

$<;3F ?V ]!F GG"3

-C.HGj1 '3 C.HB84L6.<3 )MM=:;8> 9:;<f5=gH8> B.Ha3 Q8L6<=gH8> B8 Mh<;f<=8H4F 54:=5f

'f<=8 fM8L54=gH8F 2]0!F GGj3

-C(G!1 73 C.>5: :<B '3 (.k:53 C89 8< fM8L54.<=gH8 B8 DH=>>:<L8 S e.H4L8> B8 D84[

5H4K:5=.<>F L.HDM:;8>F >893 Q8L6<=gH8> B8 Mh<;f<=8H4F 54:=5f 'f<=8 fM8L54=gH8F

? ] VG!F ?]VG!3

-Cc!j1 ,BO=< X3 *3 C6.<; :<B e5:<=>M:O +3 c:T3 )< $<54.BHL5=.< 5. &D5=9=/:5=.<3

J=M8E[$<584>L=8<L8F 56=4B 8B=5=.<F V!!j3

-?:PG 1 % 3 ?:P=>3 +:<BK..T .N '8<85=L )M;.4=569>3 @:< A.>54:<B (8=<6.MBF GG 3

-?8;GV1 U3 ?8;:HgH83 2:;<f5=>98 85 9:5f4=:Ha 9:;<f5=gH8> S =<54.BHL5=.<3

U&l(A)% ?, *+^e$bl, $@ [ C.MM.gH8 C]F V S W ]F GGV3

-?8/!j1 ,3 ?8/=MM83 C.<L8D5=.< 85 .D5=9=>:5=.< Bm:L5=.<<8H4> 8M8L54.98L:<=gH8> B:<>

M8 L:B48 B8 M: D4.58L5=.< K:>>8 58<>=.<3 *6? 568>=>F '48<.KM8 $A*F V!!j3

Page 120: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "!#$%&'(!) *+,

-./"0+12 3454 .6789:;<=>8<? $4)4 /9:@? 04A4 "9BCDE9:;? >BC '454 0;>F>;9:4 EGH :;>FI6C

>F<8I@<E: F6;>G F>JB6;97 7<FI<B6B;? A>87@ K++14

-C'C0%+12 68;8>BC CE '6G<EL C6 0>9B; %<F>9B4 A<CMG9:>;9<B C6: >7;9<BB6E8:

MG67;8<F>JBM;9DE6: I>8 8M:6>EL C6 8MGE7;>B76:4 N8M>;9<B COEB <E;9G FM;968

CMC9M >E I86C9F6B:9<BB6F6B; I>8 <I;9F9:>;9<B4 '@. ;@6:9:? PB9Q68:9;M 5<R

:6I@ /<E8968? K++14

-)>;ST2 A4)4 )>;<B4 &CC9BJ UEL I>;@: ;< :I976V >B>GW;97>G 7>I>X9G9;W 9FI8<Q6: ;@6

6>:6 >BC >77E8>7W <= :9FEG>;9BJ I<Y68 7987E9;:4 &IIG96C '<Y68 )G67;8<B97:

N<B=686B76 >BC )LI<:9;9<B N<B=686B76 '8<766C9BJ: Z@98;66B;@ &BBE>G?

* [\T1]\SK? *SST4

-/86SK2 ^4 %97@>8C /86C6897H4 !B;6J8>;6C 6G67;8<F>JB6;97 9B;68=686B76 _G;68? 5>BE>8W

*SSK4

-/0`+S2 A4 /<9::>7? 54R"4 07@>B6B? >BC N4 <GG>9864 G>7H X<L 6F7 F<C6G =<8 I<Y68

6G67;8<B97: 7<BQ68;684 !))) )B68JW 7<BQ68:9<B 7<BJ86:: >BC 6LI<:9;9<B? K++S4

-$Na

++T2 b4 $<BJ? c4 N@6B? d4 a>BJ? 4 aE>B? ^4 /6BJ? >BC b4 >BJ4 .6:9JB <= @9J@

I<Y68 C6B:9;W C7RC7 7<BQ68;68 X>:6C <B 6FX6CC6C I>::9Q6 :EX:;8>;64 '<Y68

)G67;8<B97: 0I679>G9:;: N<B=686B76 e')0Nf? I>J6: Kg\]Kgg? K++T4

-$9G+\2 $9GF<864 N<FF<BRF<C6hC9i686B;9>GRF<C6 7@<H6? K++\4

-$")Tj2 A4 %4 54 $9XX:? .4 (4 "66? >BC 54 )4 )Q6;;:4 .7 F>JB6;97RI8<I68;96: <= F6;>GG97

JG>::6: >=;68 U>:@ >BB6>G9BJ4 !))) Z8>B:4 A>JB4? K+e,f [*\g\]*\g,? *STj4

-$<GTS2 .>Q9C )4 $<GCX68J4 $6B6;97 &GJ<89;@F: 9B 06>87@? #I;9F9k>;9<B? >BC A>7@9B6

"6>8B9BJ4 &CC9:<BR 6:G6W '8<=6::9<B>G? *STS4

-(>FS\2 .4 (>F9GG4 "EFI6C 6DE9Q>G6B; 7987E9;: <= F>JB6;97 7<FI<B6B;: [ Z@6 JW8>;<8R

7>I>79;<8 >II8<>7@4 !))) ;8>B:>7;9<B: <B I<Y68 6G67;8<B97:? T [Sg]*+\? *SS\4

-(>FSj2 .4N4 (>F9GG4 $W8>;<8R7>I>79;<8 F<C6G9BJ [ > X6;;68 Y>W <= EBC68:;>BC9BJ

F>JB6;97 7<FI<B6B;:4 &IIG96C '<Y68 )G67;8<B97: N<B=686B76 >BC )LI<:9;9<B?

N<B=686B76 '8<766C9BJ:? *SSj4

-(>B2 !FI6C>B76 A6>:E86F6B; (>BX<<H? &J9G6B; Z67@B<G<J96:4

-(68S+2 $4 (68k684 $8>9B :9k6 C6I6BC6B76 <= 7<6879Q9;W >BC I68F6>X9G9;W 9B B>B<78W:R

;>GG9B6 =688<F>JB6;:4 !))) Z8>B:4 A>JB4? K1 [*\Sg]*j+K? *SS+4

-((+j2 %>BCW "4 (>EI; >BC 0E6 )GG6B (>EI;4 '8>7;97>G $6B6;97 &GJ<89;@F:? 067<BC

)C9;9<B4 ^9G6W #BG9B6 "9X8>8W? K++j4

-(lS12 4 (<=F>BB >BC (4 l8<BFmGG684 0;86::R9BCE76C F>JB6;97 >B9:<;8<IW 9B B>R

B<78W:;>GG9B6 =67EBX:9X >GG<W4 5<E8B>G <= A>JB6;9:F >BC A>JB6;97 A>;689>G:?

*,K [S*]ST? 5>BE>8W *SS14

-5>JT\2 Z4 5>J96G9B:H94 /G>:@ >BB6>G9BJ <= >F<8I@<E:R>GG<W:4 !))) Z8>B:4 A>JB4?

*Se,f [*SK,]*SKg? *ST\4

-56;+T2 N4 56;;>B>:6B4 A<CMG9:>;9<B I>8 >II8<7@6 DE>C89I<G>986 C6: 7<E8>B;: C6

F<C6 7<FFEB C>B: G6: >::<79>;9<B: 7<BQ68;9::6E8:RF>7@9B6: 6B >M8<B>E;9DE6 n

<I;9F9:>;9<B CE _G;8>J64 '@. ;@6:9:? )7<G6 N6B;8>G6 C6 "W<X? K++T4

-5<BSS2 %4!4 5<B6:4 Z@6 F<86 6G67;897 >9878>=; [ ;@6 I>:; >BC ;@6 =E;E86 o )G67;897>G

A>7@9B6: >BC 0W:;6F: =<8 ;@6 A<86 )G67;897 &9878>=? *SSS4

Page 121: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!" #$#%$&'()*+$,

-.+/

+ 0 +123 .456 312.1 +786 9123 /:86 912;1 9<6 =1291 %>>6 =1231 &?6 78@ 31231 +:8A1

) 8>B 7CD55>EF4G7H B48@48A G:55:8 5:@> G?:I> G7J7KH> :L 7EE>8<7E48A

@4M>F>8E47H 5:@> 8:4C>1 *:B>F ,H>GEF:84GC 78@ ,;;, )C47 N$;*, O ,;;,P

;:8L>F>8G>6 J7A>C QQ!RQQS6 T! 1

-.%!"0 )L>L N=4F>GE><F @> J<KH4G7E4:8P .>@:<C2%>K:<G1 U7EVF47<W 57A8VE4X<>C >8

AV84> VH>GEF4X<> 1 YF74EV ,',U6 T!!"1

-.U(Z!0 =1 .7F8:JJ6 =1 %1 U7FA:H4C6 78@ (1 ;1 (:C>8K>FA1 3DCE>5 =D8754GC [ )

\84]>@ )JJF:7G?1 +7F@G:^>F6 ZZ!1

-%7K !0 =1 %7KF:<CC>1 )5VH4:F7E4:8 @>C E>G?84X<>C @_>CE457E4:8 @>C J>FE<FK7E4:8C

G:8@<4E>C [ 7JJH4G7E4:8 ` <8> G?7a8> @> EF7GE4:8 @> ^V?4G<H> VH>GEF4X<>1 *?=

E?>C4C6 bG:H> 8:F57H> C<JVF4><F> @> ;7G?786 T! !1

-%78!"0 &1 %78AH:4C1 ;:8G>JE4:8 @c8 FVC>7< @> C>G:<FC VH>GEF4X<> J:<F HdVF:87<E4X<>1

*?= E?>C4C6 $8CE4E<E 87E4:87H J:HDE>G?84X<> @> Y:<H:<C>6 T!!"1

-%#U

+ 0 e1 %<:6 =1 #:F:D>^4G?6 *1 U7EE>^>HH46 .1 fA:6 78@ =1 '4H?751 )8 48E>AF7E>@

G:55:8 5:@> 78@ @4M>F>8E47H 5:@> G?:I> L:F >54 C<JJF>C4:8 <C48A 57A8>E4G

>J:WD 54WE<F>1 )JJH4>@ *:B>F ,H>GEF:84GC ;:8L>F>8G> 78@ ,WJ:C4E4:86 J7A>C

g SR gT!6 T! 1

-%>K!S0 (1 %>K:<FA>:4C1 e>FF4E>C @:<W J:<F H VH>GEF:84X<> @> J<4CC78G>1 Y>G?1 $8A16

T!!S1

-%.e#!h0 .1 %7:<75F46 912*1 .>F7@>G6 912*1 e>FF4><W6 78@ 91 #7FK7F:<W1 =4>H>GEF4G H:CC>C

:L G7J7G4E:F 78@ L>FF4E> G:F> 48 78 HGE G:5J:8>8E1 $,,, YF78C7GE4:8C :8

U7A8>E4GC6 hZ [ SgQR Sgg6 T!!h1

-%%ZS0 %1 %78:EE> 78@ i1 %78:EE41 f78:5>EF4G GFDCE7HH4j7E4:8 :L L>G<8KC4K KD H7C>F

788>7H48A1 91 )JJH1 *?DC16 gkNSP [hSh RhShh6 3>JE>5K>F ZZS1

-%U/

+ !0 ( %746 l1 U74HH>E6 e1 /78A6 31 /78A6 (1 #<FA:C6 78@ =1 #:F:D>^4G?1 )8 48E>2

AF7E>@ >54 G?:I> L:F @4M>F>8E47H25:@> 78@ G:55:825:@> 8:4C> C<JJF>CC4:81

$,,, YF78C7GE4:8C :8 *:B>F ,H>GEF:84GC6 TS [ShZRSQQ6 U7FG? T! !1

-%(//Zk0 91;1 %7A7F47C6 91 )1 (>>@C6 U1 +1 /F4A?E6 78@ *1 ,1 /F4A?E1 ;:8^>FA>8G> JF:2

J>FE4>C :L E?> 8>H@>F25>7@ C45JH>W 5>E?:@ 48 H:B @45>8C4:8C1 3$)U 9:<F87H

:L &JE454j7E4:86 Z [ TR Qg6 ZZk1

-U);

+ 0 e1 U>C5486 #1 )?57@46 +1 ;?7j7H6 )1 .>@:<C2%>K:<G6 78@ e1 34W@>84>F1 $52

JF:^48A F>H47K4H4ED :L 57A8>E4G 5<E<7H 45J>@78G> 5>7C<F>5>8E 7E ?4A? >WG4E72

E4:8 H>^>H1 $,,, $8E>F87E4:87H $8CEF<5>8E7E4:8 78@ U>7C<F>5>8E Y>G?8:H:AD

;:8L>F>8G>6 T! 1

-U780 k +48EC L:F 3<GG>CCL<H $5J>@78G> U>7C<F>5>8EC6 )A4H>8E6 )JJH4G7E4:8 f:E>

hQ"2Q !"m!!1U1 l:<8A6 Y?> Y>G?84G7H /F4E>F_C +78@K::I1 U4HH i7HH>D6 ;) [

\84^>FC4ED 3G4>8G>6 ZkZ1

-U7F!h0 U1 U7F@4A<4781 U78<>H JF7E4X<> @> G:5J7E4K4H4EV VH>GEF:57A8VE4X<>1 ?>F5nC>

CG4>8G>C6 Tn5> >@4E4:86 T!!h1

-U>Ekk0 +4E7G?4 U>E7HC6 Zkk1

-U'!!0 f1 U<F4HH: 78@ 91 ':8j7H>j1 ,M>GE :L E?> 788>7H48A G:8@4E4:8C 78@ AF748 C4j>

:8 E?> C:LE 57A8>E4G G?7F7GE>F :L L>G<N8KmE7PC4K 878:GFDCE7HH48> 7HH:DC1 91

U7A81 U7A81 U7E>F16 T kN P [ShRSZ6 T!!!1

Page 122: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "!#$%&'(!) *+,

-./+,0 12 .34567489 39: ;2 '2 /743:7<2 =7>?59 8@ 7A6?B3C79D <?4<6?D> 39: <E343<D74?F

G3D?89 >D43D75H @84 9F?9I6D <86IC7: ?9:6<D84>2 !))) J439>3<D?89> 89 !9:6>D4H

&IIC?<3D?89>K LM N*LOPPK P++,2

-.Q*+0 12 .? 39: R2 Q7:32 &:B39<7: .?<48S3B7 T?4<6?D> 39: RH>D7U> N !9D7543D7:

'3>>?B7> @84 (?5EFV47A679<H &IIC?<3D?89>2 W6UX74 TE3ID74 *M2 !9J7<EK &I4?C

P+*+2

-.6>+,0 '2 .6>G9?<Y?2 !:79D?Z<3D?89 :7> I74D64X3D?89> T). <89:6?D7> :39> C7>

<89B74D?>>764> >D3D?A67> I34 C3 U[DE8:7 :6 ZCD47 :7 \?79742 'E= DE7>?>K !9>F

D?D6D W3D?893C '8CHD7<E9?A67 :7 $4798XC7K P++,2

-.]+^0 W2 .84D79>89 39: $2 ]79Y3D343U39392 &9 3<D?B7 <8UU89 U8:7 7U? ZCF

D74 @84 >S?D<E?95 <89B74D74>2 P++^ !777 !9:6>D4H &IIC?<3D?89> R8<?7DH &9963C

.77D?95KK ]8C> *F_ N`M`O`LPK P++^2

-W7:**0 2 W7:a342 .8:[C?>3D?89 X3>[7 >64 C3 U[DE8:7 :7> 4[>736b :7 I74U[39<7> 79

B67 :7 CcID?U?>3D?89 :7 U3<E?97> >H9<E4897> d >?UIC7 7D d :86XC7 7b<?D3D?892

'E= DE7>?>K )<8C7 984U3C7 >6I[4?764 :7 T3<E39K P+**2

-W.`_0 ;2 &2 W7C:74 39: %2 .73:2 & >?UIC7b U7DE8: @84 @69<D?89 U?9?U?G3D?892

T6UI6D74 ;86493CK *L NM+^OM*MK *e`_2

-#V&+P0 R2 #53>3S343K .2 V6a?Y3S3K 39: (2 &Y35?2 & ISU 47<D?Z74f?9B74D74 >H>D7U

<3I3XC7 8@ >6II47>>?95 X8DE E34U89?<> 39: 7U?2 )C7<D4?<3C )95?9774?95 ?9

;3I39K *L* N_eO`^K P++P2

-#8?ee0 #8?2 TE8Y7 <8?C @84 7C?U?93D?95 <8UU89FU8:7 98?>7 39: 984U3CFU8:7 98?>7K

W8B7UX47 *eee2

-#'^P0 /2 ;2 #B74>E8DD 39: .2 (2 '4?<72 JE7 7g7<D 8@ 39973C?95 <89:?D?89 89 DE7

I8S74 C8>> 8@ 3U84IE7> 4?XX89>2 !))) J439>2 .3592K *^h`i N*MeLK W8B7UX74

*e^P2

-'36^e0 T2%2 '36C2 & <8UI34?>89 8@ DE7 <89D4?X6D?89> 8@ <8UU89FU8:7 39: :?g7479D?3C

U8:7 <64479D> ?9 43:?3D7: 7U?>>?89>2 !))) J439>3<D?89> 89 )C7<D48U3597D?<

T8UI3D?X?C?DHK M*hPi N*^eO*eMK .3H *e^e2

-'36+`0 T2%2 '36C2 !9D48:6<D?89 D8 7C7<D48U3597D?< <8UI3D?X?C?DH2 ;8E9 \?C7H j R89>K

P++`2

-'3H`+0 (794H &2 '3H9D742 &93CH>?> 39: =7>?59 8@ )95?9774?95 RH>D7U>2 JE7 .!J

'47>>K *e`+2

-'74e,0 ;2T2 '744892 .3D[4?36b @7448U359[D?A67> 3U84IE7> 7D 9398<4?>D3CC?9>2 J7<E2

!952K *ee,2

-'7D+P0 ;2 '7DG8C:2 &:B39D357> 8@ >8@DU3597D?< 9398<4H>D3CC?97 U3D74?3C> @84 U8:749

7C7<D489?< 3IIC?<3D?89>2 ;86493C 8@ .3597D?>U 39: .3597D?< .3D74?3C>K PLPO

PL_ N^LO^eK P++P2

-'"%]**0 .2T2 =? '?3GG3K .2 "693K & 2 %356>3K 39: $2 ]?D3C72 &9 ?UI48B7: <8UU89

U8:7 3<D?B7 ZCD74 @84 7U? 47:6<D?89 ?9 B7E?<6C34 U8D84 :4?B7>2 ]7E?<C7 '8S74

39: '48I6C>?89 T89@7479<7 h]''TiK I357> *O^K P+**2

-'R+P0 R2 '43XE3Y3439 39: T2 %2 R6CC?B392 !UI7:39<7 393CHG74 U73>647U79D 8@ E?5EF

@47A679<H I8S74 I3>>?B7> N D7<E9?A67> @84 E?5E I8S74 39: C8S ?UI7:39<72 !)))

?9:6>D4H 3IIC?<3D?89> >8<?7DHK P++P2

Page 123: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!" #$#%$&'()*+$,

-*.+ / 01 *23456 '1 .4789:6 4;< '1 +78=781 >2?: @4A;7:BC ;4;2C8D9:433B;7 @4:78B439

?28 ECF 7@F7<<7< B;<GC:289 H 2E:B@B94:B2; ?28 IBAI ?87JG7;CD 4EE3BC4:B2;1

$;:78;4:B2;43 C2;?787;C7 2; 92?: @4A;7:BC @4:78B439 K>LL M!N6 M! 1

-(2F / (1 (2FG:731 ,:G<7 <79 C2@E294;:9 E499B?9 E2G8 3OP37C:82;BJG7 <7 EGB994;C7 Q

I4G:7 :7@EP84:G87 H 4EE3BC4:B2; 4G R3:87 0,L <O7;:8P71 *IS :I79B96 $T>)

<7 %D2;6 M! 1

->IGUV/ >IG9:78@4;1 02@FB;7< <BW787;:B43X@2<7 C2@@2;X@2<7 ;2B97 R3:786 UUV1

->*Y

+!!/ S1 L1 >:GFF96 >1 +1 *G3526 )1 Z1 YB35B;92;6 #1 YB392;6 [1 0I89B:B47;96 4;<

\1 )3348:1 ,@F7<<7< E499B]7 C2@E2;7;:9 4;< ECF 9B=7 H :I78@43 7W7C:91

LBC82737C:82;BC9 B;:78;4:B2;436 ^ H^_ !6 M!!!1

->*Y!M/ S1 L1 >:GFF96 >1 +1 *G3526 4;< )1 Z1 YB35B;92;1 ); B;]79:BA4:B2; 2? :I7

97;9B:B]B:D 2? 7@F7<<7< E499B]7 C2@E2;7;: :7@E784:G879 :2 ECF 9:8GC:G871

$,,, :84;94C:B2; 2; C2@E2;7;:9 4;< E4C54AB;A :7CI;232AB796 M`KVN H^! _^!^6

S7C7@F78 M!!M1

-a)b"V/ a)b#1 ,W7C: 2? :I7 I74:B;A 84:7 G97< <G8B;A 9:8799 873B7? 4;;743B;A 2; :I7

@4A;7:BCXE82E78:B79 2? 4@28EI2G9X4332D91 Z )EE3 *ID96 `` H ^^`_ ^^^6 U"V1

-b\>L!M/ a1 bCIB<46 a1 c1 \4:9GDG5B6 \1 >GAB:4;B6 4;< \1 L494@B1 %C R3:78 dB:I

C4E4CB:28 737C:82<7 E34:7 ;2: B;:78?78B;A dB:I eGf 2? :d2 C2B396 T2]7@F78 M!!M1

-bE4UV/ )1 \1 bE4<ID4D1 $;:7A84:7< C2@@2; @2<7 4;< <BW787;:B43 @2<7 B;<GC:28

<7]BC76 @4D UUV1

-.#U / Z1 .78<G; 4;< Z1X01 #4]4D1 )33B4A79 ?78X9B3BCBG@1 a7CI1 $;A16 SM !6 UU 1

-.B;!U/ # .B;C7;:1 $<7;:BRC4:B2; <7 92G8C79 P37C:82@4A;P:BJG79 @G3:BE234B879

PJGB]437;:79 E48 R3:84A7 9E4:B43 H )EE3BC4:B2; Q 34 0,L 84D2;;P7 E2G8 379

C2;]78:B997G89 <OP37C:82;BJG7 <7 EGB994;C71 *IS :I79B96 $;9:B:G: ;4:B2;43 E2X

3D:7CI;BJG7 <7 '87;2F376 M!!U1

-Y7B!g/ Z1)1 Y7B@781 aI7 8237 2? 737C:8BC @4CIB;79 4;< <8B]79 B; :I7 @287 737C 4B8C84?:1

$;:78;4:B2;43 737C:8BC @4CIB2;79 4;< <8B]79 C2;?787;C76 H _ `6 ZG;7 M!!g1

-YcT

+!U/ Z1 Y4;A6 h1 c4;A6 +1 TBG6 i1 Y4;A6 4;< Z1 %BG1 *CF B;:7A84:7< :84;9?28@78

C2@E297< dB:I ?788B:7 @294BC9 ?28 33C 8792;4;: C2;]78:781 ,;78AD 02;]789B2;

02;A8799 4;< ,fE29B:B2; K,00,N6 E4A79 !gM_ !g"6 M!!U1

-c4@Uj/ c4@4AGCIB1 0I257 C2B3 ?28 73B@B;4:B;A C2@@2;X@2<7 ;2B97 4;< <BW787;:B43X

@2<7 ;2B976 UUj1

-c4@U"4/ c4@4<41 0I257 C2B3 ?28 9GEE8799B;A C2@@2;X@2<7 ;2B97 4;< ;28@43X@2<7

;2B976 &C:2F87 UU"1

-c4@U"F/ c4@4AGCIB1 0I257 C2B3 ?28 9GEE8799B;A C2@@2;X@2<7 ;2B97 4;< ;28@43X@2<7

;2B976 )GAG9: UU"1

-c29"g/ T1 c29IBIB941 0G::B;A @7:I2< 2? @4A;7:BC 9:773 9:8BE6 S7C7@F78 U"g1

-cc""/ c1 c29IB=4d4 4;< \1 c4@4GCIB1 02@@2; @2<7 CI257 C2879 G9B;A :I7 ;7d

?7XF497< 4332D9 C2@E297< 2? G3:84R;7 A84B; 9:8GC:G871 Z )EE3 *ID96 jV Hj!VV6

T2]7@F87 U""1

Page 124: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

! "!#$%&'(!) *+,

-../,0 .1 .23456787 79: ;1 .7<7=>451 )?@>A3 2B <7C9@A5>DE@F: 799@7F59C

29 <7C9@A5>DGH2G@HA5@3 59 =FAH7E9@ >HI3A7FF59@ B@D>=D9JD35DJ 7FF2I31 !)))

K%&LM&NK!#LM #L O&$L)K!NMP QR STTQUVTTQWP *,/,1

Page 125: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite
Page 126: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!!"#" $ %&'(&()*! %+),'-%&!." "( .*/'0&1" %"

,*%" %" 0& 2*/3." %" '"3(/34&()*!2

!"#$"$%&' !(%)#*!"'+,

!"#$%$&#

!" #$ #%&$'()"$' #$* +,-$.'* /0.' -$* )(/%#,"1$* #$ -, *0.'1$2 "0.* ,+0"* 130)*) -$

1')&4'$ #5,#,/&,&)0" #5)(/%#,"1$ $"&'$ -, *0.'1$ $& -$ 6789: 95,#,/&,&)0" #5)(/%#,"1$*

/$'($& *0)& #50/&)()*$' -$ &',"*;$'& #5."$ /.)**,"1$ %-$1&')<.$ $"&'$ ." %($&&$.' =*0.'1$>

$& ." '%1$/&$.' %-$1&')<.$ =13,'?$>2 *0)& #$ *5,@',"13)' #$* '%A$B)0"* #50"#$* $" /'%*$"1$

#5."$ -)?"$ #$ &',"*()**)0": C5$*& 1$ *$10"# 1')&4'$ <.$ "0.* 10"*)#%'0"*: D" $@$&2 -$ !-&'$

CDE $*& ,-0'* +. 10(($ ." 1)'1.)& <.) /$'($& F -5)"+$'*$ #$ (,B)()*$' -$* '%A$B)0"*

#$ (,")4'$ F 1$ <.$ -$ '%*$,. =6789> *0)& %/,'?"% /,' -$* /$'&.'G,&)0"* ?%"%'%$* /,' -,

*0.'1$: 7,"* !-&'$2 -, *)&.,&)0" $B&'H($ $*& ,-0'* 0G&$".$ -0'*<.$ &0.&$* -$* /$'&.'G,&)0"*

&',"*)&$"& #$ -, *0.'1$ ,. 6789 *,"* '%A$B)0": C5$*& #0"1 "0&'$ 130)B /0.' -5$*&)(,&)0" #$

-5)(/%#,"1$ #$ -, *0.'1$ =I)?: J:KL>:

M,' 10"+$"&)0" -$* 0"#$* )"1)#$"&$* =,> $& '%A%13)$* =G> *0"& #%!")$* /,' -, !?.'$ J:KN:

v

i

a

b

!"#$% J:KN O P%!")&)0" #$* 0"#$* )"1)#$"&$* $& '%A%13)$*

M0.' &0.* -$* 1,-1.-*2 -$* +,'),G-$* *0"& '%;%'$"1%$* /,' ',//0'& F Z0 -5)(/%#,"1$ 1,',1Q

&%')*&)<.$ #$ -, *0.'1$:

V =√Z0+

I = √Z0

=J:R>

9$* &$"*)0"* $& -$* 10.',"&* *0"& 10"*)#%'%* 10(($ -, *0(($ $& -, #)@%'$"1$ #$* ,(Q

/-)&.#$* 10(/-$B$* #5."$ 0"#$ )"1)#$"&$ $& #5."$ 0"#$ '%A%13)$:

+ = a+ b

) = a− b=J:K>

Page 127: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"##$%$ " & "'()*(*+,# '-+.)/'(#0$ $* 0,1)2(3$ '$ .,'$ '$ 2( 4,150$ '$ )$5*156(*+,#4

7( )5/4$#0$ '1 82*5$ '$95( ',#0 '/4('()*$5 2$4 +.)/'(#0$4:

I_L

I_B2_RSIL I_B1_RSIL

C_RSIL

R_RSIL R_RSIL

C_RSIL

2*L_RSIL Z_s3

Z_s2Z_s1

I_Z_s2

I_Z_s1

I_Z_s3

I_S1

I_S2

!"#$% ;:!< = >?4*@.$ 0,.),4/ '$ 2( 4,150$ '$ )$5*156(*+,#4 $* '1 A>B7

!"#$" %& "! '!()*#& *'+,%!-#& %$ ./.(0'&

>+ 2-,# 4-+#*/5$44$ (1 4?4*@.$ 1#+C1$.$#* 0,.),4/ '$ 2( 4,150$ $* '1 A>B7 DE+3: ;:!<FG

,# )$1* 5/'1+5$ 2$ 40H/.( /2$0*5+C1$ DE+3: ;:!IF (8# '$ 0(2012$5 2( .(*5+0$ +.)/'(#0$ '1

4?4*@.$: J$**$ /*()$ $4* +#'+4)$#4(62$ ),15 '/*$5.+#$5 2$4 9(2$154 C1$ ',+9$#* )5$#'5$ 2$4

+.)/'(#0$4 '$4 65(#0H$4 '$ 2( 4,150$ '$ )$5*156(*+,#4:

I_B2_RSILI_B1_RSIL

C_RSIL

R_RSIL R_RSIL

C_RSIL

2*L_RSIL Z_s3

Z_s2

Z_s1

V_S2 V_S1

I2

I1

!"#$% ;:!I = >?4*@.$ 5/'1+* '$ 2( 4,150$ '$ )$5*156(*+,#4 $* '1 A>B7

(9$0

ZB = ZCRSIL+ ZRRSIL

Z3 = Zs3//(2 ∗ ZLRSIL)

VS1 = IS1 ∗ Zs1

VS2 = IS2 ∗ Zs2

K1 0L*/ '$ 2( 0H(53$G ,# )$1* /05+5$ 2( .(*5+0$ 41+9(#*$ M

I1 = V 1−V 2Z3

+ V 1ZB

I2 = −(V 1−V 2)Z3

+ V 2ZB

D;:NF

[

V 1

V 2

]

=

[

ZB(Z3+ZB)Z3+2∗ZB

Z2

B

Z3+2∗ZBZ2

B

Z3+2∗ZB

ZB(Z3+ZB)Z3+2∗ZB

] [

I1

I2

]

D;:<F

Page 128: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!!"#" $ %&'(&()*! %+),'-%&!." "( .*/'0&1" %" ,*%" %" 0& 2*/3." %" '"3(/34&()*!2556

7/ .8(- %" 0& 2*/3."9 : '&3()3 %"2 -;/&()*!29 *! '"/( %-("3,)!"3 0"2 "#'3"22)*! %" <5 "(

<=>

V 1 = VS1 − Zs1I1

V 2 = VS2 − Zs2I2?@>AB

!"#$%&'#() *+ ,-&*&.'&'#() /0" )('"+ !'0*+

C*/2 &D*!2 2/''*2- ;/" 0"2 )!%/.(&!."2 -(&)"!( )%"!();/"2 ?E;>@>FB>

Zs1 = Zs2 = ZB

Zs3 = 2 ∗ ZLRSIL

?@>FB

'&3()3 %" ."((" 2),'0)G.&()*!9 !*/2 &D*!2 .&0./0- 0"2 *!%"2 )!.)%"!("2 "( 0"2 *!%"2

3-H-.I)"2>

a1 = VS1

2√ZB

a2 = VS2

2√ZB

b1 =√ZB(VS1−VS2)4(Z3+ZB)

b2 = −√ZB(VS1−VS2)4(Z3+ZB)

?@>JB

K*/3 D-3)G"3 !*(3" IL'*(IM2"9 !*/2 &00*!2 *42"3D"3 0+&,'0)(/%" %"2 *!%"2 2"0*! 0" ,*%"

%+"#.)(&()*!>

E! "#.)(&()*! %" ,*%" .*,,/!9 %+&'3M2 0"2 3"0&()*!2 %" '&22&1" VS1 = VS29 !*/2

3",&3;/*!2 ;/" 45N4=NO> <0 !+L & '&2 %+*!%" 3-H-.I)"9 0& (3&!2,)22)*! "2( (*(&0"9 !*/2

&D*!2 4)"! /!" &%&'(&()*! %+),'-%&!.">

E! "#.)(&()*! %" ,*%" %)P-3"!()"09 %+&'3M2 0"2 3"0&()*!2 %" '&22&1" VS1 = −VS29 !*/2

3",&3;/*!2 ;/" &5N$&= "( 45N$4=> Q*/( 0"2 *!%"2 "!D*L-"2 '&3 0& 0)1!" 5 3"D)"!!"!( 2/3

0& 0)1!" => C*/2 &D*!2 %*!. /!" .)3./0&()*! %" ,*%" %)P-3"!()"0> R".) D-3)G" %*!. !*(3"

.&0./0>

!"#$%&' (' )!(' * +,-.+' (' /0#%+%-,!1 ('/ )!('/ 2 324

S& 2*/3." %" '"3(/34&()*!2 %-G!)" %&!2 0" .I&')(3" << "2( /!" 2*/3." %" '"3(/34&()*!2

)%-&0" '/)2;/" !*/2 !+&D*!2 '&2 T&)( %+)%"!()G.&()*! "#'-3),"!(&0"2> R"'"!%&!(9 !*/2 &D*!2

D*/0/ D-3)G"3 2) 0& 2*/3." '*/D&)( 1-!-3"3 ;/" %"2 .*/3&!(2 %" ,*%" %)P-3"!()"0 */ %"2

.*/3&!(2 %" ,*%" .*,,/!> K*/3 ."0&9 !*/2 &D*!2 T&)( 0" '3*%/)( %"2 ,&(3)."2 "!(3-"U2*3()"

VW<SUW*/3." ?2&!2 0" G0(3" REXB @>Y>

[

V1

V2

]

Reseau

= [[Source] [RSIL]]−1

[

Is1Is2

]

?@>YB

K*/3 2&D*)3 2+)0 "#)2(" /! .*/'0&1" %" ,*%" &/ !)D"&/ %" 0& 2*/3."9 !*/2 %"D*!2 3"D"!)3

%&!2 0& 4&2" XRUX7 .*,," %-G!) '&3 0"2 -;/&()*!2 <<>A>

Z! *4()"!( &0*32 0& 3"0&()*! ,&(3).)"00" 2/)D&!(" ?E;> @>[B9 &D". 0"2 D&0"/32 %"2 ),'-$

%&!."2 %" 0& 2*/3." %-("3,)!-"2 D)& 0" .3)(M3" %+&%&'(&()*! %+),'-%&!.">

Page 129: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!"##$%$ " & "'()*(*+,# '-+.)/'(#0$ $* 0,1)2(3$ '$ .,'$ '$ 2( 4,150$ '$ )$5*156(*+,#4

VMD

VMC

IMD

IMC

=

−ZB

4−ZB

4−ZBZLRSIL

2(ZB+ZLRSIL)

ZBZLRSIL

2(ZB+ZLRSIL)

12

12

14

−14

[

Is1Is2

]

789:;

<,15 =/5+>$5 4-+2 $%+4*$ 1# 0,1)2(3$ '$ .,'$? #,14 '$=,#4 ',#0 =/5+>$5 @1$ 4+ 2-,# +#A$0*$

1#+@1$.$#* '1 0,15(#* '$ .,'$ 0,..1#? 2( *$#4+,# '$ .,'$ '+B/5$#*+$2 ',+* C*5$ #122$

$* +#=$54$.$#* ),15 2$ 0,15(#* '$ .,'$ '+B/5$#*+$29 "1 =1 '$ 2( .(*5+0$ !"# $%&'( )*&+

$& ,-& +.-' .)(&+.+'! /&' 01'-2(3(' .+( 1(1 $.+4051' 630 7&-8 '*5-23(*.+' '.-' 2& 2.9*$*&2

$*0$-*( :;<=!

Page 130: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

!!"#" $ % &'()(*+"),-(+,.! ./

0(1!"+,* 2")0"(3,4,+5 62"*+)( 76,!1 3.+' 87#0"+),*

(!9 ,02"9(!*" (22).(*'"6

Page 131: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

Improving reliability of magnetic mutual impedance

measurement at high excitation level

F. Mesmin, B. Ahmadi, H. Chazal, A. Kedous-Lebouc

Grenoble Electrical Engineering Laboratory (G2Elab),

Grenoble INP – UJF Grenoble 1 - CNRS UMR 5269

38402 Saint Martin d’Hères Cedex, France

[email protected]

F. Sixdenier

Université Lyon 1, CNRS UMR 5005 AMPERE,

43, Bld du 11 Novembre 1918,

Villeurbanne 69622 Cedex, France

Abstract— Power electronic designers are interested in

characterization of the magnetic cores permeability up to 10MHz

and at high induction level. To achieve this aim, different

experimental setups are used to measure mutual impedance

spectra. First, impedance measurement methods are carried out

on toroidal wound core of 20 µm nanocrystalline ribbons.

Measurement uncertainties are estimated and a confidence factor

is introduced as a useful consistency test to improve

measurement reliability. Then a lumped equivalent circuit is

identified to model electrostatic and magnetic frequency behavior

of the device under test. It allows calculating complex

permeability spectra over the resonance frequency of the device

under test. Finally, we point out the limitation due to high

excitation level. According to that, a flux-metric experimental

setup is described and elliptical hysteresis-loops are measured.

These results allow to consider magnetic linear behavior until a

few 10mT and to extend complex permeability calculations to

high induction level with good reliability.

Keywords-impedance measurement; flux-metric measurement ;

nanocrystalline; confidence factor; common mode choke

I. INTRODUCTION

Nanocrystalline FeNbCuSiB alloys (Finemet type) are ultra-soft magnetic materials. Besides, when annealed under transversal magnetic field, they exhibit a very high Snoek’s product µr fc, where µr is the low frequency initial relative permeability and fc is the related cutoff frequency. These characteristics make them suitable for common-mode chokes (CMC) in electromagnetic compatibility (EMC) filter for power applications [1]. These applications in medium-to-high frequency range (from a few kHz to a few MHz) call for using Mn-Zn ferrites. Those are very soft magnetic and quasi insulating materials. According to these characteristics, Mn-Zn ferrites require specific characterization considering their high permeability and high permittivity values as described in [2]. As a result of resonance phenomena and Snoek’s limit, nanocrystalline materials are preferred to Mn-Zn ferrites for common mode chokes.

The large Snoek’s product of nanocrystalline involves wide frequency range measurements of complex permeability. These measurements are those required for understanding and predicting the behavior of magnetic cores as described in [3]. The complex permeability spectra can be deduced from mutual impedance measurements if the magnetic behavior is assumed

linear. However, even if induction level remains far from saturation and typically below 100mT, magnetic behavior could deviate from linear characteristic. To check consistency of linear behavior, hysteresis-loop measurements under various excitation levels and over a wide range of frequency are performed. To achieve these aims, an experimental set-up, which involves flux-metric measurements, was designed to provide frequency and induction requirements up to 100mT at 10MHz. The flux-metric method requires voltage and current acquisitions and skew delay correction. In order to calibrate our measurements and to define the measurement protocol, results are compared to mutual impedance for induction levels below 5mT. First the accuracy of the mutual impedance measurement method is investigated and then the results are compared to the flux-metric ones to improve its reliability.

II. MUTUAL IMPEDANCE MEASUREMENT

A. Impedance Measurement Apparatus

Various methods have been developed for measuring impedance. They all have advantages and drawbacks [4], [5]. The choice between these different methods depends on the frequency range, the magnitude of the applied field, the desired accuracy and also the simplicity of implementation. Apparatus that best match these criteria appeared to be impedance analyzer so we choose Agilent 4294A which combines the 4-terminal pair measurement method into an auto-balanced bridge circuit [6].

B. Device Under Test

Device Under Test (DUT) is a toroidal wound core of 20µm nanocrystalline ribbons. Primary and secondary windings of respectively Np and Ns turns are wound in diametrical CMC topology to carry out mutual impedance measurement. Sample specifications are summarized in table 1.

TABLE I. SAMPLE SPECIFICATIONS

a. See section II.C.3.

Outer

diameter

(mm)

Inner

diameter

(mm)

Height

(mm)

Average

length

Lm

(mm)

Cross

section

area

AE

(mm2)

Primary

number

of turns

(Np)

Secondary

number of

turns

(Ns)

17 10.7 6.2 43.5 15.6 11 7 (11)a

Page 132: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

C. Mutual Impedance Measurement Methods

Three different methods are investigated in order to measure mutual impedance of a quadripole. First, some useful notations that are used throughout the article are given. Then, so called indirect and direct measurement methods, as described in [4] are briefly reminded. Then, open and short-circuit measurements are performed and we discuss how these measurements are suitable to deduce mutual impedance.

1) Useful notations (Table 2): Impedance measurements

are denoted for example: “ZAB_CDo”, where the first

subscript indicates the connected ports to the impedance

analyzer test fixture (A and B) and the second indicates the

short-circuited “s” or open-circuited “o” ports (C and D).

Compensation measurement Ztfs refers to impedance

measurement where sample test fixture is short-circuited as

described in [7]. All impedances are measured using test

fixture Agilent 16047E and we perform open-short

compensations to cancel wiring impact. Configuration of the

analyzer is chosen as shown in Table 3.

2) Indirect measurement method: the mutual impedance

Z12i is deduced from Common Mode (CM) and Differential

Mode (DM) impedance measurements as follow

Z12i = 1/4 (ZCM - ZDM). (1) (1)

In these measurements, primary and secondary voltages are connected respectively in series and in series opposition. To avoid non-linear magnetic behavior, maximum allowed induction level is estimated. This induction corresponds to a voltage oscillator level of the analyzer, which is estimated according to the faraday law assuming non-equal Ns and Np neglecting impedance in series. According to (1), mutual impedance modulus and phase are calculated and shown in Fig.1.

TABLE II. MEASUREMENT PROTOCOL

Table of measurement protocol

Compensation

measurement

Impedance

measurement Short name

ZAB_CDo Zo (m1) Ztfs

ZAB_CDs Zs (m2)

ZCD_ABo Z’o (m3) ZCDs_ABs

ZCD_ABs Z’s (m4)

ZAB_ACs (m5)

ZAB_BCs (m6)

ZBD_ACs ZCM (m7) Ztfs

ZAD_BCs ZDM (m8)

TABLE III. MEASUREMENT CONDITIONS

Measure parameter : IMPEDANCE MAG PHASE

Adapter : NONE

Sweep type : LOG

Number of points : 801

OSC level : 5, 20 or 100 mV

DC bias : OFF

Bandwidth (BW) : 4

Sweep averaging : OFF

Point averaging : OFF

3) Direct measurement method: As described in [4],

16047E test fixture is customized to allow direct mutual

impedance measurement. Ports B and D of the DUT are

connected together and to the L (Low) terminals of the

apparatus. The H (High) terminals are electrically separated

and used to connect A and C ports. Measured mutual

impedance, denoted Z12d, is shown in Fig.1. We emphasize

that direct measurement method requires equal Np and Ns.

Otherwise, impedance spectra show an unexplained

discontinuity at 15MHz.

4) Open/Short measurement method: As described in

previous studies [7] [8], open-circuit and short-circuit

measurements are suitable to characterize magnetic

components. In order to calculate the mutual impedance, three

measurements are needed. According to [9], a measurement

protocol was specified to avoid disconnections as soon as

possible (Table 2). The mutual impedance Z12 is deduced from

the two open-circuit and a short-circuit measurements as

follow

Ζ12 = (Ζ’sΖ o − Ζ’o Ζs)1/2, (2)

where Z’s and Z’o are related to the impedances measured from one side of the transformer (secondary) and Zs and Zo

from the other side (primary). The four impedances are shown in Fig. 2 and modulus and phase spectra of mutual impedance Z12 are shown in Fig.1.

D. Experimental Results and Accuracy Estimation

Impedance measurements are performed using Agilent 4294A in which synchronous detection techniques are used. We mean that the complex impedance values are obtained from two components: a component that is in-phase with the excitation reference (Real component) and a component that is 90° out-of-phase with the excitation reference (Imaginary component). As a consequence, uncertainties are estimated applying formula given by Agilent [1] on R (Real) and X (Imaginary) components.

Page 133: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

Figure 1. Mutual impedance modulus (left) and phase (right) according to direct,indirect and open/short measurement methods (symbols) and simulation results

Figure 2. Open and short circuit impedance modulus (left) and phase (right) measurements

In order to calculate uncertainties of three measurement methods, we apply error propagation law using standard deviations on (1) and (2). In Fig.3, measurement errors on impedance moduli are shown. We notice that uncertainties are considerable in low frequency range, due to large errors on the real component, and above the resonance frequency, due to large errors on imaginary component.

As depicted in Fig.3, Open/Short measurement method seems to be more accurate than the others. Consequently, we chose to investigate further the measurement of complex permeability using complete characterization of the DUT as detailed in the following subsection.

E. Complete Characterization and Modeling of the DUT

To achieve the magnetic behavior characterization up to 10MHz, and so above the resonance frequency, we chose to model the electrostatic behavior of the DUT. We use a global approach, well described in previous work [2],[8],[10]. According to table 2, measurement protocol includes to additional measurements, denoted (m5) and (m6). These two measurements, in addition to Z0, provide the experimental data for deducing the resonance frequencies that are needed to calculate stray capacitance values. The complete electrical scheme is shown in Fig.4, where all values are calculated to reduce model error below 1% up to 10 MHz.

Page 134: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

.

Figure 3. Estimation of mutual measurement uncertainties applying Agilent

formula given in [1] and error propagation law.

Then, electrical circuit simulations, with PSpice software, are compared to experimental results as shown in Fig.1. As a result, we are able to simulate all our measurements and all show good agreement. Moreover, the magnetic behavior was well defined up to 10 MHz and allows to accurately calculate complex permeability as follow:

µ~ = (Zm Lm)/(ω Np Ns AE µ0). (4)

The real and imaginary components of the complex permeability are shown in Fig.5 and are compared to those measured by flux-metric method as detailed in section 3.

Figure 4. Electrical equivalent circuits of the DUT

Figure 5. Complex permeability spectra deduce from mutual impedance

measurement and from hysteresis loops measurement at 10mT (symbols)

F. Measurement Reliability Improvement

In [9], the confidence factor was introduced as a useful consistency test to improve measurement reliability. It should be noticed that for a two-port passive circuit, the impedance matrix is symmetrical. In other words, one can say that only three independent equations are needed to fully characterize a quadripole. In (2), we use Z's, Zo and Z'o as equations required to deduce Z12. As mentioned in [9], Zs was used to introduce redundancy in our measurements and to define the confidence factor (CF) as follow:

CF = |(ΖoΖ's)/ (Ζ’oΖs)|. (3) (

It was pointed out that confidence factor is normally equal to 1 and a careful attention should be paid to any deviation from 1. Some examples of common causes that induce deviation of CF are listed in [9] and CF is used here to assess on uncertainty estimation. It could be noticed that impedance moduli (Zo, Z’o, Zs and Z’s shown in Fig. 2) are not close to resolution limits depicted by black lines (respectively given by the impedance modulus of a 10 nH inductor and that of a 1 pF capacitor). Moreover, our measurements seem more accurate than Agilent estimation let us suppose as shown in Fig.6. Besides, the noise level observed on confidence factor, without average technique (Table 3), is very small compared to error estimations. So accuracy of our apparatus is not incriminated in the deviation of the confidence factor.

To check the assumption of linear magnetic behavior, oscillator voltage level is increased from 5 mV to 100 mV and the confidence factor under these operating conditions is calculated as shown in Fig.6. We observe that CF deviates from 1 in the low frequency range. That highlights the non linear magnetic behavior of the core due to higher induction excitation level. We also notice that CF shows the same deviation from 1 about 20% in the high frequency range. To avoid any deviation at high frequency, we simulate the effect of a stray capacitance of 0.3 pF in parallel with the largest impedance Z0 as shown in Fig.6.

Page 135: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

To conclude, we are able to distinguish a deviation of about 2% on the confidence factor. It means that non linear magnetic behavior should be discriminated efficiently even when induction level remains very low, typically under 50 mT.

Figure 6. Confidence factor: in green with OSC = 5 mV, in red with OSC =

100mV and in blue compute with 0.3pF in parallel of Z0

III. FLUX-METRIC MEASUREMENT METHOD

Impedance analyzers are limited to low excitation levels. To overcome this drawback, authors in [11] have developed a specific setup for impedance measurement at high induction level. A power amplifier is introduced between the impedance analyzer and the test sample support. Current and voltage differential probes are used to step down the signals applied back to the impedance analyzer terminals. In this experiment, the test frequency is 155 kHz, so the compensation of the phase error introduced by the current and the voltage differential probes could be neglected. In our case, specific protocol is required to compensate inaccurate phase and amplitude measurements at high frequencies (f > 1 MHz).

The flux-metric measurements are related to mutual impedance ones but are not limited to linear magnetic behavior. Indeed, time-domain acquisition allows tracing magnetic hysteresis-loops up to saturation. In common-mode chokes applications, magnetic excitations are weak (e.g. 10 mT) but are applied at higher frequencies up to 10 MHz. To achieve high induction level flux-metric measurements, a home experimental setup is developed following the described approach depicted in [12] to characterize power Mn-Zn ferrite materials.

A. Experimental Setup

Sinusoidal waveforms are provided using a 100 MHz signal generator (Tektronix AFG3102) controlled via a GPIB and Matlab® interface. The DUT is fed with sinusoidal voltage thanks to a high frequency power amplifier (NF electronics instruments 4055 ) which allows an output voltage up to 70 V on a 50 Ohms load at 10 MHz. Shunts are inserted in series with DUT to measure the current in the primary side of the core. A resistance film fired onto a flat ceramic substrate known to be non-inductive up to MHz range (MP930 – 100

Ohms - 1%) is chosen to realize this function. Power package is mounted on heat sink to avoid self-heating. The resistance value was measured using four-terminal pair micro-ohmmeter

apparatus at 99.5 Ohms ± 0.1 Ohm. The non-inductive behavior of the shunt was confirmed by frequency measurement on impedance analyzer Agilent 4294A. The shunt voltage is measured with a differential probe in order to limit stray capacitance introduced by the additional electric connections to the DUT. This probe consists of a Lecroy DA1855A differential amplifier and DXC5100 differential passive voltage probe pair (10 MOhms of input resistance and 400 MHz of bandwidth). The differential amplifier allows a typical common mode rejection ratio (CMRR) of 90dB at 1 MHz and x10 gain (downgraded to 40dB due to the unbalance

of voltage probes specified at x100 ±1.75%). The common mode voltage is here about 50% (see Fig.7) of the differential voltage and the common mode error is below 10 mV. The input referred noise density levels are about 80 nV/vHz at 10 kHz and 4 nV/vHz at 1 MHz. When referred to the terminal probes, the noise level and the signal to noise ratio are respectively about 0.8 mV and 2% at 10 kHz (0.4 mV and lower that 1% at 1MHz). To measure the voltage at the secondary side of the DUT, we use a P3010 10x 100 MHz Tektronix passive voltage probe. The AC gain is calibrated using square waveforms and the accuracy is estimated at 1%. Data are acquired using a TDS3014B Tektronix oscilloscope. Waveforms are digitized simultaneously according to 9-bit resolution ADC and the record length is fixed to 10000 samples. We use an average acquisition mode to reduce uncorrelated noise and improve the measurement accuracy (64 acquisitions).

B. Measurement Protocol and Delay Compensation

In flux-metric method, measuring the phase shift between the primary current and the secondary voltage could be a tricky task, especially when concerning low loss magnetic materials [13][14]. A residual phase shift between the measured current and voltage signals appears and should be compensated.

This phase shift could be due to the acquisition system but also due to the inductive behavior of the shunt, the stray capacitance, and the limited bandwidth of the acquisition devices and probes. To compensate the measurements, the overall acquisition chain is characterized using a specific DUT free of magnetic core which represents the same size and windings as the main DUT.

The used core-less DUT is theoretically characterized by a 90° phase shift (quadrature) between the current and the voltage; however the measurement shows a deviation from this value which is an intrinsic property of the overall acquisition chain. This shift corresponds to a time delay which should be introduced numerically to correct the measurements. The measurements with magnetic core are then compensated with this same time delay. The hysteresis-loops at 5 mT and 10 mT and 40 kHz are shown in Fig.8. They all have elliptical shapes and can be described by a complex permeability value assuming a linear magnetic behavior. This result is predicted by the Confidence Factor, seen in Fig.6, which shows that the non-linear magnetic behavior vanishes over 30 kHz. As a consequence, complex permeability values are deduced from hysteresis-loops characteristics as follow:

Page 136: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

µ~ = 1/µ0.(Bm/Hm)

.exp(jδ), (5)

where Bm and Hm respectively define the maximum

amplitude of the induction and the magnetic field, and δ is given by

δ = arcsin(Pm/(π.f

.Hm

.Bm)) (6)

where Pm is the magnetic power loss and f the frequency.

Figure 7. Flux-metric experimental setup

Figure 8. Hysteresis-loops measured at 5 mT and 10 mT at 40 kHz

C. Conclusions

The Fig.5 shows a good agreement between flux-metric measurements and mutual impedance ones. According to that magnetic characterization at high excitation level should be achieved with a good reliability up to 10 MHz at 50 mT.

REFERENCES

[1] T. Waeckerle, F. Alves, P.L. Reydet, J. Degauque, G. Pourroy, “Magnetic behaviour of a nanocrystallized Fe/sub 73/Si/sub 15/B/sub 8/Nb/sub 3/Cu/sub 1/ alloy”, J.M.M.M., pp. 254-255, 2003.

[2] K. Laouamri, J. P. Keradec, J. P. Ferrieux, J. Barbaroux, "Dielectric losses of capacitor and ferrite core in an LCT component", Magnetics, IEEE Transactions on, vol. 39, no. 3, pp. 1574-1577, May 2003.

[3] B. Ahmadi, H. Chazal, T. , J. Roudet, “Effect of Anisotropy and Direction of Magnetization on Complex Permeability of Ferromagnetic Rectangular Thin Slabs,” Magnetics, IEEE Transactions on, vol. 46, n°. 12, p. 4001-4008, 2010.

[4] Impedance Measurement Hanbook, Agilent Technologies, July 2006, ref. 5950-3000.

[5] 8 Hints for Successful Impedance Measurements, Agilent, Application Note 346-4 06/00.M. Young, The Technical Writer's Handbook. Mill Valley, CA: University Science, 1989.

[6] Agilent 16047E Test Fixture, Operation and service manual, Agilent Technologies, Jan. 2001.

[7] X. Margueron, J. P. Keradec, “Identifying the Magnetic Part of the Equivalent Circuit of n-Winding Transformers,” Instrumentation and Measurement, IEEE Transactions on, vol. 56, n°. 1, p. 146-152, 2007.

[8] X. Margueron, J. P. Keradec, “Design of Equivalent Circuits and Characterization Strategy for n-Input Coupled Inductors,” Industry Applications, IEEE Transactions on, vol. 43, n°. 1, p. 14-22, 2007.

[9] A. Besri, H. Chazal, J. P. Keradec, X. Margueron, “Using Confidence Factor to Improve Reliability of Wide Frequency Range Impedance Measurement. Application to H.F. Transformer Characterization,” IEEE International Instrumentation and Measurement Technology Conference, Singapore, 2009.

[10] A. Besri, H. Chazal, J. P. Keradec, “Capacitive Behavior of HF Power Transformers: Global Approach to Draw Robust Equivalent Circuits and Experimental characterization,” presented at the IEEE International Instrumentation and Measurement Technology Conference, Singapore, 2009.

[11] S. Prabhakaran, C. R. Sullivan “Impedance analyzer measurement of high-frequency power passives : techniques for high power and low impedance” IEEE industry applications society, 2002.

[12] C. Beatrice, F. Fiorillo, F. Landgraf, V. Lazaro-Colan, S. Janasi, and J. Leicht, “Magnetic loss, permeability dispersion, and role of eddy currents in Mn-Zn sintered ferrites,” Journal of Magnetism and Magnetic Materials, vol. 320, n°. 20, pp. e865-e868, Oct. 2008.

[13] Yongtao Han and Yan-Fei Liu, “A Practical Transformer Core Loss Measurement Scheme for High-Frequency Power Converter”, IEEE Trans. Ind. Electron, vol. 55, No. 2, Feb 2008.

[14] Baguley et al., “A new Technique For Measuring Ferrite Core Loss Under DC Bias Conditions ”, IEEE Trans. On Magn. Vol44. No11 2008.pp.4127-30.

Page 137: Mat eriaux magn etiques et solutions innovantes de ltrage ... · Mat eriaux magn etiques et solutions innovantes de ltrage CEM pour applications a eronautiques Fanny Mesmin To cite

Résumé

L'industrie aéronautique, dans le cadre de l'avion plus électrique, met en œuvre le remplacement d'actionneurs pneumatiques

ou hydrauliques par des actionneurs électromécaniques. Cela permet de réduire le nombre de réseaux de distribution présents

dans l'avion, de faciliter la maintenance et d'améliorer le rendement. Le but final est de réduire la masse et d'améliorer

l'efficacité énergétique globale d'un avion pour réduire sa consommation en carburant. Les travaux de ce mémoire de thèse

s'inscrivent donc la logique de réduction de la masse des convertisseurs tout en assurant des critères de perturbations CEM

(Compatibilité ElectroMagnétique). En effet, les normes CEM sont de plus en plus contraignantes, en particulier les domaines

sensibles tel que l'aéronautique. Les filtres CEM sont donc de plus en plus nombreux. Dans ces filtres, les composants

magnétiques occupent plus de 50 % de la place et surtout de la masse. L'objectif de cette thèse est de faire émerger des

solutions innovantes, en dotant les filtres CEM passifs d'un composant magnétique unique pour les perturbations de mode

conduites afin de réduire sa masse. Afin de comprendre leur fonctionnement, suite à une étude bibliographique, nous avons

réalisé une étude comparative de topologies à composant magnétique unique. Nous avons développé un outil de modélisation

fréquentielle du composant magnétique unique. A partir d'une modélisation <<système>> nous avons pu prendre en compte

l'environnement du composant magnétique (Réseau Stabilisateur d'Impédance de Ligne (RSIL), Source de perturbations,

Capacités) et une modélisation plus fine des propriétés magnétiques du composant. Grâce à un modèle gyrateur-capacité, nous

avons pu prédire les performances du filtre complet dans son environnement et l'optimiser. Cette étude nous a permis de

réaliser une topologie de composant magnétique unique plus compacte et plus performante que la topologie existante. Par

ailleurs, nous avons démontré la faisabilité de l'intégration sur PCB (Printed Board Circuit) d'alliage nanocristallin en réalisant

une autre topologie de composant unique basée sur les mêmes facteurs que la précédente mais intégrée dans un PCB. Les

verrous technologiques auxquels nous avons été confrontés et les solutions que nous avons proposées pour les résoudre sont

détaillés dans le mémoire.

Abstract

In the context of the more electric aircraft, the industry replaces pneumatic or/and hydraulic actuators for electromechanical

actuators. The ultimate goal is to reduce the weight and improve the overall energy efficiency of an aircraft to reduce fuel

consumption. This thesis aims the mass reduction converters while providing criteria EMC interference (electromagnetic

compatibility). In fact, EMC standards are becoming more stringent, particularly in sensitive areas such as aeronautics. EMC

filters are more numerous. In these filters, the magnetic components have more than 50% of the space and weigth. The

objective of this thesis is to design innovative EMC filters solutions, using a single magnetic component, to reduce conducted

disturbances (common and differential modes). Following a review of the literature, we conducted a comparative study of single

magnetic component topologies. We have developed a modeling tool frequency magnetic single component. From a modeling

<<system>> we have to take into account the environment of the magnetic component (Impedance Stabilization Network Line

(LISN), Source disturbances and capacities) and a finer modeling of magnetic properties of component. With a gyrator-capacitor

model, we could predict the performance of the complete filter in its environment and optimize it. This study has allowed us to

achieve a unique magnetic topology component more compact and efficient than the existing topology. In addition, we have

demonstrated the feasibility of integrating PCB (Printed Circuit Board) of nanocrystalline alloy by performing another single

component topology based on the same factors as above but integrated into a PCB. The technological obstacles which we

faced and solutions we have proposed to solve them are detailed in the report.

Mots-clés :

Filtrage CEM, Alliage nanocristallin, recuit sous champ, intégration sur PCB.