170
3 Superposition et le théorème de l’extra-élément
1
1 0
100 1 10
3
×
1 10
4
×
1 10
5
×
1 10
6
×
20
−
0
20
40
50
−
0
50
arg H
3 i 2
⋅ π f
k
⋅
(
)
(
)
180
π
⋅
f
k
1
1 0
1 00 1 10
3
×
1 10
4
×
1 10
5
×
1 10
6
×
40
60
80
50
−
0
50
arg H
4 i 2
⋅ π f
k
⋅
(
)
(
)
180
π
⋅
f
k
H
1 s
( ) H
0
1
1
s
ω
1
+
⋅
:=
1
1 0
1 00 1 10
3
×
1 10
4
×
1 10
5
×
1 10
6
×
20
−
0
20
40
50
−
0
50
20 log H
1 i 2
⋅ π f
k
⋅
(
) 10
,
(
)
⋅
20 log H
2 i 2
⋅ π f
k
⋅
(
) 10
,
(
)
⋅
20 log H
1 i 2
⋅ π f
k
⋅
(
) 10
,
(
)
⋅
20 log H
1 i 2
⋅ π f
k
⋅
(
) 10
,
(
)
⋅
arg H
1 i 2
⋅ π f
k
⋅
(
)
(
)
180
π
⋅
f
k
H
2 s
( ) H
0 1
s
ω
1
+
⋅
:=
1
1 0
100 1 10
3
×
1 10
4
×
1 10
5
×
1 10
6
×
40
60
80
100
50
−
0
50
arg H
2 i 2
⋅ π f
k
⋅
(
)
(
)
180
π
⋅
f
k
( )
1
H f
( )
1
H f
∠
( )
2
H f
( )
2
H f
∠
(dB)
(dB)
(Hz)
(Hz)
Pôle
Zéro
( )
3
H f
( )
3
H f
∠
Pôle inversé
Zéro inversé
( )
4
H f
( )
4
H f
∠
(°)
(°)
(°)
(°)
(dB)
(dB)
500 Hz
-45°
37 dB
500 Hz
45°
43 dB
500 Hz
-45°
43 dB
500 Hz
45°
37 dB
H
3 s
( ) H
inf
1
1
ω
1
s
+
⋅
:=
H
4 s
( ) H
inf 1
ω
1
s
+
⋅
:=
0
H
0
H
H
∞
H
∞
f
1
500Hz
:=
ω
1
f
1 2
⋅ π
⋅
:=
H
0
100
:=
H
inf
100
:=
Figure 3.45 Les réponses dynamiques de pôle et zéro classiques et leurs équivalents inversés.