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" ) !) ! *! "" +$! , -
!% " " ! ! ! ! , - " .!$ * ϕm .!$ / GM "
! T (jω) , - " 01 01 01 +
!" # !$ 2 ! $ * 2" ! 2 !) ! ,3 2
# !$ %
&
H 3 (p) =
e−^2 p 1 + 4p H 4 (p) =
0 , 5 (1 + 2p)^3 " ! , 3 ! < !! ! + $ A@ $! T i ! T d ! ! ! @ * ! ! ! , 3 ! ) @ ! ! A B !
# A = 10 # T 3 (p) T 4 (p) !" '
C T 3 (p) =
A · e−^2 p 1 + 4p
@ ! ! ! A ) ! @ ) ! ! A·e−^2 p^ +1+4p = 0 → < ! ! C T 4 (p) =
A · 0 , 5 (1 + 2p)^3
@ ! ! ! A ) ! @ ) ! ! → A · 0 , 5 + (1 + 2p)^3 = 0 → ) @ ) < ! !
D ! ! $ !% ! $! % ! ! ! ! ) ! < ! ) !) ! !! ! ! ! ! E ! ! ! F D ! ! $ !% ! $! , -@ $! % , + ! ! ! % $! , -
G%< ! @ ! < $H ! @
ω ! *$ ! ! ! @ I! !% % ) ! @ ! ! ! ! !
S√2 (^) ωt
ϕ
s(t) E√ ωt
e(t)
H(jω)
D ) !) ! *! H(jω) ! J p ! jω ) !) ! ! * H(p)
H 3 (jω) H 4 (jω)
H 3 (jω) =
e−^2 jω 1 + 4jω H 4 (jω) =
0 , 5 (1 + 2jω)^3
D $! , - ! ) !) ! H ! EHdB F ) * H ! $! EKF
H 3 (jω) ω |H 3 | H 3 dB ϕH 3 (rad) ϕH 3 (K) & & & & &@ &@L #&@: #&@24 #@ &@"2 &@( # #@"L #(@: &@2 &@2 #( #"@ #"&@( &@" #"@ #@ #L&@: " &@" #4@ #2@2 #"@ → + ! H 3 (jω) , - ! H
H 4 (jω) ω |H 4 | H 4 dB ϕH 4 (rad) ϕH 4 (K) & &@2 #: & & &@ &@( #:@2 #&@2L #@L &@"2 &@: #4@L #@L #(L@( &@2 &@4 #2 #"@: # 4 , 5. 10 −^2 #"( #@" #L&@ " 7 , 1. 10 −^3 #"@L #@L4 #"" → + ! H 4 (jω) , - ! H
)) .
! ! ! $! E @! ! D 1 ) F@ ! Etr5%F @ ! $ $! 2, E!$$ !F O GM O (, E!$$ F % @ ! GM = 6dB &KE!$$ !F O ϕM O :&KE!$$ F % @ ! ϕM = 45K
! T (jω)
+ >< ! H(p) , -@ ! ! ! ! T (p) ? ! ! % T (jω) = H(jω) × C(jω) C + @ 3,? ! |T (jω)| = |H(jω)| × |C(jω)| 0 GT dB = GC dB + GH dB C * 3,? ϕT = ϕC + ϕH
+ !! ! < ! ! C(p) = A@ GT dB = 20logA + GH dB @ ϕT = 0 + ϕH = ϕH D $ D $ $ 20 logA + $! , -@ ! $ ! C ! $ ! ! < EA > 1 F ! C ! $ )! ! < EA < 1 F ! " ; E P A > 1 F ! ! !% !
ϕT
G (^) BO =20log( (^) ⎜T (^) ⎜)
C
-180˚
A=
T 4 (jω) !! ! $! , - H 4 (jω) H @ ! ! H T 4 (jω) ! A = 5 A = 20 ! *% ! C + ! ! , 3 ! A = 5 → stable@ A = 20 → instableenBF C 0 @ ! ! !$ $ GM * ϕM A = 5 → GM = 10dB; ϕM = 50K
? ! !! ! ! ! A = 1
+ @ C(p) = 1+
1 Tip
C(jω) = 1+
1 jTiω
, - T (jω)@ ! ! C(jω) C Q ω → 0 @ ! C(jω) ≈
1 jTiω
+ |C| → +∞ GC dB → +∞ R ϕC → − π 2 C Q ω → ∞@ ! C(jω) ≈ 1 + |C| → 1 GC dB → 0 R ϕC → 0 ? ) $! *% GH dB + GC dB ϕH + ϕC ! ! ! T (jω)
ϕT
G BO
C
-180˚
H(jω)
Black
!$ ϕM $ GM D ? % GT → +∞ % ω → 0 + T (p) → +∞ % ω → 0 @ ! ! ! ;
s = lim p→ 0 p(p) =
∆W 1 + T (p) @ ! % s = 0 01 @ !A ! ! !
! %
H 3 (jω)
!! ! $! , - H 3 (jω) ! H "@ ! ! H T 3 (jω) ! !! ! ! C(p) = A(1 + (^) T i^1 p ) A = 1 T i = 4s ω |H 3 | GH 3 dB ϕH 3 (K) |C| GC dB ϕC EKF GT 3 dB ϕT 3 (K) & & & +∞ +∞ #L& +∞ #L& &@ &@L #&@: #@ "@( 4@: #:4@" (@L: #&@ &@"2 &@( # #(@: @ #2 & #4@: &@2 &@2 #( #"&@( @" &@L( #":@: #:@& #(@ &@" #"@ #L&@: @& &@": # #"@& #"&@: " &@" #4@ #"@ @& &@ #(@ #4 #L@"
A = 1 + @ C(p) = 1+Tdp C(jω) = 1+jTdω ! ! ! $! , - T (jω)@ ! ! C(jω) C Q ω → 0 @ ! C(jω) ≈ 1 + |C| → 1 GC dB → 0 R ϕC → 0 C Q ω → ∞@ ! C(jω) ≈ jTdω + |C| → +∞ GC dB → 0 R ϕC → +∞ ϕC → + π 2
ϕT
G BO
C
-180˚
H(jω)
Black
!$ * ϕM ↗ $ GM ↘ D H 1 !! D ! ! ! @ %
D ! T (jω) , - ! ! ! ,3@ ! ! ! $!S H !$ * $ EϕM GM F D , - ! ! ! ! !) ! ) ! E ! ! ! D 1 @ ! ! @ ! tr 5 %F
! $! , -@ ) ;$!! ! $ E $F * E * F@
!% ) ,3 ! EϕT @GT F EϕF @GF F@ ! ) ,? < ,3 !
!! ! T 3 (jω) E !! ! ! ! F ! % , -# * % ;$! < H " 0 ! ! $ ) ! !% * ,3 ϕF = − 10 K@ − 90 K − 120 K
T (jω) ! N P GBF > 0 @ ! ! $ ! $ @ ! ;$!! ! # ! C ! ! @ ! T (jω) ! ! $ GBF > 0 C ! " ! < ωr @ ! T (jω) $ < ! $ GBF = 2, 3 dB
-270 -240 -210 -180 -150 -120 -90 -60 -30 0
0
10
20
Gain (dB)
Phase (˚)
Diagramme de Black de H 3 et T 3
-270 -240 -210 -180 -150 -120 -90 -60 -30 0
0
10
20
Diagramme de Black de H 4 et T 4
Gain (dB)
Phase ( )
Plan de Black.
-0,5 dB
-1 dB
-3 dB
-4 dB
-6 dB
-8 dB
-12 dB
6 dB
4 dB
1,4 dB
1 dB
0,5 dB
0,25 dB
-1
0,
-5
2,3 dB
-8
3 dB -10
8 dB
-90
0
4
8
12
16
20
24
28
32
36
-360 -340 -320 -300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0
phase en BO
gain logarithmique en BO
-120 -60
-50
-40
-30
-20
-150
-2 dB
