Séance de TP n°4 : le pont diviseur et les limites du filtrage passif

!
!
LSM$2$$&$Mesures$physiques$&$Instrumentation$
Séance'de#TP#n°4!:"le"pont"diviseur"et"
les$limites$du$filtrage$passif!
!"#$%&'()*"#"+'#,-"#./01/+)-'"#'(2+#%01/(')-'"#3"#&45&".'(/-%6,"#0/3"(-"7#8)(#"9"01&":#1/,(#
(5)&%+"(#3"+#0"+,("+#3"#+%*-),9#3"#'(2+#$)%;&"#1,%++)-."#%&#"+'#34);/(3#-5."++)%("#3"#1/,</%(#
&"+#%+/&"(#3"+#+%*-),9#1)()+%'"+#"'#-/')00"-'#3,#;(,%'#5&".'(/-%6,"#3"+#),'("+#./01/+)-'+7#
=4"+'#>#."#0/0"-'#6,4%-'"(<%"-'#&"#$%&'("7#?&#1"(0"'#3"#(53,%("#&)#;)-3"#1)++)-'"#3,#3%+1/+%'%$#
"'# 3"# &)# ."-'("(# +,(# &"# +%*-)&# ># 5',3%"(7# @)-+# ."# .)+# &"+# +%*-),9# "-# 3"A/(+# 3"# ."''"# ;)-3"#
1)++)-'"#+/-'#"-&"<5#B/-#3%'#6,4%&+#+/-'#./,15+C:#1/,(#-"#&)%++"(#6,"#&"#+%*-)&#34%-'5(D'7##@)-+#
&"+# 3%+1/+%'%$+# ).',"&+# </,+# 1/,<"E# )%-+%# ("'(/,<"(# ;"),./,1# 3"# ./01/+)-'+# 6,%# +"(<"-'# ),#
$%&'()*":#1)(#"9"01&"#3)-+#&"+#'5&51A/-"+#1/(');&"+:#1/,(#%+/&"(#&)#$(56,"-."#./(("+1/-3)-'#>#
&)#1/('",+"#3"#</'("#+%*-)&7#F/,+#'(/,<"("E#),++%#;"),./,1#3"#$%&'("+#3)-+#&"+#)01&%$%.)'",(+#
),3%/7# ?&+# 1"(0"''"-'# 34/1'%0%+"(# &"# +%*-)&# ),3%/# "-# "-&"<)-'# -/')00"-'# &"+# "$$"'+# 3"#
+/,$$&"+7#G,(#."(')%-"+#.A)%-"+#),3%/:#%&+#1"(0"''"-'#),++%#3"#0/3%$%"(#&"#+%*-)&#B&)#0,+%6,"#%.%C#
"-#0"'')-'#1)(#"9"01&"#1&,+#3"#1,%++)-."#+,(#&"+#;)++"+#"'#0/%-+#+,(#&"+#)%*,"+#BH)++#H//+'C7#
8/,(#&"+#.A)%-"+#),3%/#&"+#1&,+#+/1A%+'%6,5"+#</,+#1/,<"E#0D0"#0/3%$%"(#1&,+%",(+#1&)*"+#3"#
$(56,"-."+#I#.4"+'#&45*)&%+",(7##
@)-+# ."# ./-'"9'"# %&# "9%+'"# ;"),./,1# 3"# 'J1"+# 3%$$5("-'+# 3"# $%&'("+7# K-# 1",'# 3%+'%-*,"(# 3",9#
*()-3"+# .&)++"+#I# &"+# $%&'("+# ).'%$+# "'# &"+# $%&'("+# 1)++%$+7# 8/,(# ."# L8# -/,+# -/,+# %-'5("++"(/-+#
+",&"0"-'#),#$%&'()*"#1)++%$#"'#-/,+#<"((/-+#+"+#&%0%')'%/-+7#?&#$),'#),++%#+)</%(#6,"#'/,+#&"+#
$%&'("+# -"# 0)(.A"-'# 1)+# 3)-+# &"+# 0D0"+# *)00"+# 3"# $(56,"-."7# F/%.%# ,-"# 1"'%'"# &%+'"# 3"#
3%$$5("-'+#'J1"+#3"#$%&'("+#I#
• $%&'("+#).'%$+#I#&%0%')'%/-#"-#$(56,"-."#1)(#&"+#.)().'5(%+'%6,"+#3"#&4)01&%$%.)'",(#,'%&%+5#
• $%&'("+#>#'()-+$"('#3"#.A)(*"+#I#$/-35+#+,(#&"+#./00,')'%/-+#()1%3"+#3"#."&&,&"+#=MKG#
B!
!"# =1#MNEC#
• $%&'("+#05.)-%6,"+#I#>#(5+/-)'",(+#5&".'(/O05.)-%6,"+#B./-<"(+%/-#3P,-#+%*-)&#
5&".'(%6,"#"-#<%;()'%/-+:#Q#RNES$SQTTRNEC#
• $%&'("+#-,05(%6,"+#I#&"#-/0;("#345.A)-'%&&/-+#'()%'5+#),*0"-'"#)<".#&4/(3("#3,#$%&'("#
B1/,(#,-"#0"%&&",("#(5U".'%/-C#34/V#'"01+#3"#.)&.,&#"'W/,#-/0;("#3"#.%(.,%'+#6,%#
),*0"-'"#B&%0%'"(#1)(#&"#.(%'2("#GA)-/-C#
• $%&'("+#1)++%$+#>#5&50"-'+#3%+.("'+I#X!=#"-#5.A"&&"#.&)++%6,":#3"#+'(,.',("+#+%01&"+#
U,+6,P>#QTMNE:#(5)&%+);&"+#U,+6,P>#Y#ZNE#)<".#3"+#1(5.),'%/-+#
#

!
!
Objectifs$du$TP$:$
!
• "#$%&'()!(*+#)&,(-.$%(,(-.!/-!0&1)$,,(!0(!230(!43,+%(.!56$&-!(-!.(-'&3-!7!+8$'(9!0:/-!
;&%.)(!
• <./0(!0(!0&;;#)(-.'!;&%.)('!+$''&;'!0/!+)(,&()!(.!0/!'(43-0!3)0)(!
• =-;%/(-4(!0(!%$!48$)1(!'/)!%('!+)3+)&#.#'!0/!;&%.)(>!
Prérequis$:$Connaitre!le!formalisme!complexe!pour!décrire!un!circuit!linéaire.!Connaitre!la!
notion!de!fréquence!de!coupure
I. Etude$du$filtre$passe&haut$:$$$$$$$$$$$$$$$$$$
a. Filtre$à$vide$(rappel)$
• ?(''&-()!%(!'48#,$!#%(4.)&@/(!0A/-!;&%.)(!+$''&;!0/!B()!3)0)(!0(!.C+(!+$''(!8$/.!$D(4!/-(!
4$+$4&.#!!!(.!/-(!)#'&'.$-4(!!>!E-!-3.()$!!!(!)!%$!.(-'&3-!$++%&@/#(!(-!(-.)#(!0/!4&)4/&.!(.!
!!(!)!!%$!.(-'&3-!(-!'3).&(!0/!4&)4/&.>!
• "#$%&'()!%(!,3-.$1(!$D(4!!=1!FGH!!=1!IJ>!6#-#)()!/-(!.(-'&3-!'&-/'3K0$%(!$D(4!%(!62G!
5483&'&''(L!$)M&.)$&)(,(-.!%$!;)#@/(-4(9>!G&*()!%:$,+%&./0(!0(!%$!.(-'&3-!0:(-.)#(!
!!(!)!!1#-#)#(!+$)!%(!62G!N!OP!"QR>!EM'()D()!!!(!)!!!(.!!!(!)!,!)('+(4.&D(,(-.!'/)!%('!voies'1'
et'2!0(!%:3'4&%%3'43+(>!Sur'quelle'voie'faite'vous'le'déclanchement'(trigger)'?'
• S)$4()!%(!0&$1)$,,(!0(!230(!(*+#)&,(-.$%!T!!!/!!!>!"$++(%'!T!/-!0&$1)$,,(!0(!M30(!'(!
0#43,+3'(!(-!0(/*!+$).&('!T!
o ?:/-!4U.#!%(!1$&-!!!=!!(!)
!!(!)!@/&!.)$0/&.!%$!D$)&$.&3-!0:$,+%&./0(!(-!;3-4.&3-!0(!%$!
;)#@/(-4(!5(-!0M!'/)!+$+&()!'(,&V%319!!
o W:(D3%/.&3-!0(!%$!phase'(-.)(!%(!'&1-$%!0:(-.)#!(.!%(!'&1-$%!0(!'3).&(!(-!;3-4.&3-!0(!%$!
;)#@/(-4(!5'/)!+$+&()!'(,&V%319>!
!X3,,(-.!D3/'!C!Y.('VD3/'!+)&'!+3/)!;$&)(!%(!0&$1)$,,(!Z!!
• [/(%!('.!%(!1$&-!,$*&,/,!(-!.(-'&3-!@/(!D3/'!,('/)()!Z!X3,+$)()!$D(4!%$!D$%(/)!.8#3)&@/(>!
?#.(),&-()!N!+$).&)!0(!D3.)(!1)$+8&@/(!%$!+(-.(!0:$..#-/$.&3-!0(!4(!;&%.)(!(-!0270(4$0(>!
X3,+$)(L!N!%$!D$%(/)!.8#3)&@/(>!
• ?#.(),&-()!(*+#)&,(-.$%(,(-.!5N!%:$&0(!0(!%:3'4&%%3'43+(9!%$!;)#@/(-4(!0(!43/+/)(!!!
!!53/!
+/%'$.&3-!0(!43/+/)(!
!9!0(!4(!;&%.)(!(.!43,+$)()!N!%$!D$%(/)!.8#3)&@/(,(-.!$..(-0/>![/(%%(!
('.!$%3)'!%$!D$%(/)!0/!1$&-!(-!.(-'&3-!!=!!
!
!
!(.!0/!1$&-!(-!0#4&M(%'!!!"!!+3/)!4(..(!
;)#@/(-4(!(.!@/:(%%(!('.!%$!D$%(/)!0(!%$!+8$'(!$''34&#(!Z!!!

!
!
b. Influence$du$courant$de$sortie$sur$les$propriétés$du$filtre$$
E-!&-'\)(!,$&-.(-$-.!/-(!)#'&'.$-4(!0&.(!0(!48$)1(!!!!(-!'3).&(!0/!;&%.)(!+)#4#0(-.>!=%!(-!)#'/%.(!/-!
43/)$-.!0(!'3).&(!!!!N!+)&3)&!!-3-!-/%>![/(%'!D3-.!Y.)(!N!D3.)(!$D&'!%('!43-'#@/(-4('!Z!
!
• G$&)(!%(!'48#,$!0/!-3/D($/!4&)4/&.>!
• X$%4/%()!%$!-3/D(%%(!;3-4.&3-!0(!.)$-';().!0/!;&%.)(!Z!X3,+)(-0)(!+$)!%(!4$%4/%!43,,(-.!%$!
)#'&'.$-4(!548$)1(9!!!!!&-;%/(!'/)!%$!;)#@/(-4(!0(!43/+/)(!0/!;&%.)(>!S)$4()!%$!43/)M(!!
!!(-!
;3-4.&3-!0(!!!!+3/)!]!≤!!≤2000!
• "(+)(-0)(!%(!,3-.$1(!+)#4#0(-.!(.!$^3/.()!/-(!)#'&'.$-4(!0(!48$)1(!!!!D$)&$M%(!43-'.&./#(!
0:/-!+3.(-.&3,\.)(!]!VB!IΩ!!(.!,/-&!0:/-(!)#'&'.$-4(!0(!+)3.(4.&3-!0(!200!H!+(),(..$-.!0(!
%&,&.()!%(!43/)$-.!0#M&.#!%3)'@/(!%(!+3.(-.&3,\.)(!('.!N!]>!6$)0()!%('!,Y,('!)#1%$1('!+3/)!%(!
62G>!G$&.(!D$)&()!%$!)#'&'.$-4(!0(!48$)1(!(.!0#.(),&-()!+3/)!@/(%@/('!D$%(/)'!0&;;#)(-.('!0(!
4(..(!0()-&\)(!%$!;)#@/(-4(!0(!43/+/)(!$''34&#(>!S)$4(L!$D(4!)(1)(''&!3/!'/)!+$+&()!
,&%%&,#.)#!%$!;3-4.&3-!!
!(!!)!!
• G&*()!,$&-.(-$-.!!!!!N!200!>>!X3,,(-.!43-.)U%(LVD3/'!%$!D$%(/)!0(!%$!)#'&'.$-4(!Z![/(%%(!
('.!%$!+/&''$-4(!,$*&,/,!0&''&+#(!$/!-&D($/!0(!%$!)#'&'.$-4(!0(!48$)1(!5+3/)!4(..(!D$%(/)9!Z!
_$)!@/(%@/('!,('/)('!N!0&;;#)(-.('!;)#@/(-4('H!0#.(),&-()!'/)!%(!1)$+8&@/(!B!5@/&!D3/'!'()$!
0&'.)&M/#9!%$!43/)M(!43))('+3-0$-.!$/!-3/D($/!0&$1)$,,(!0(!230(!0/!;&%.)(!
II. Cascades$de$filtres$passifs:$
a. Réalisation$d'un$filtre$d'ordre$2$:$
• ?(!@/(%!.C+(!0(!;&%.)(!':$1&.V&%>![/(%!('.!%$!;)#@/(-4(!0(!43/+/)(!0/!B()!;&%.)(!&'3%#!(.!0/!
'(43-0!;&%.)(!&'3%#!Z!`!D3.)(!$D&'!@/:(%%(!('.!%$!;)#@/(-4(!0(!43/+/)(!.8#3)&@/(!0('!0(/*!
;&%.)('!(-!'#)&(!Z!!

!
!
• "#$%&'()!%(!,3-.$1(!(-!!+)(-$-.!C=1!FH!R=1!k>>!X3-'()D()!%('!)#1$%('!0/!62G>!
?#.(),&-()!(*+#)&,(-.$%(,(-.!%$!;)#@/(-4(!0(!43/+/)(>!!
• _$)!@/(%@/('!,('/)('!N!0&;;#)(-.('!;)#@/(-4('H!0#.(),&-()!'/)!%(!1)$+8&@/(!B!5@/&!D3/'!'()$!
0&'.)&M/#9!%$!43/)M(!43))('+3-0$-.!$/!0&$1)$,,(!0(!230(!0(!4(!;&%.)(>!?#.(),&-()!%$!+(-.(!
0(!%:$..#-/$.&3-!(-!0270(4$0(>!X3,+$)(L!$D(4!%(!;&%.)(!0(!%$!+$).&(!+)#4#0(-.(>!
b. Réalisation$d’un$filtre$passe&bande$:$
• "#$%&'()!%(!,3-.$1(!(-!+)(-$-.!C=1!FH!R=1!k>>!X3-'()D()!%('!)#1$%('!0/!62G>!
• <./0&()!@/$%&.$.&D(,(-.!%(!)$++3).!!!(ω)/!!(ω)!!(-!;3-4.&3-!0(!%$!;)#@/(-4(>!?#.(),&-()!%$!
;)#@/(-4(!0&.(!4(-.)$%(H!+3/)!%$@/(%%(!%(!1$&-!('.!,$*&,/,>![/(!D$/.!$%3)'!4(!1$&->!
• =0(-.&;&()!'/)!%(!1)$+8&@/(!;3/)-&!%(!0&$1)$,,(!0(!230(!$''34&#!N!4(..(!4$'4$0(!X"a"X>!
?#.(),&-()!1)$+8&@/(,(-.!%$!M$-0(!+$''$-.(!0(!4(!;&%.)(!+$''(VM$-0(>!
"$++(%'!T!W$!M$-0(!+$''$-.(!('.!0#;&-&(!43,,(!ΔωbωOVωB!$D(4!ωO!(.!ωB!.(%%('!@/(!!65ωOcω49b6,$*7√O!
(.!65ωBdω49b6,$*7√O>!ωO!(.!ωB!'3-.!%('!;)#@/(-4('!0(!43/+/)(!8$/.(!(.!M$''(!0/!;&%.)(>!
!