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AN3984 Datasheet(PDF) 12 Page - STMicroelectronics

Part # AN3984
Description  The purpose of this document is to provide a tool to calculate
PDF  46 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN3984 Datasheet(HTML) 12 Page - STMicroelectronics

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Second-order filter design
AN3984
12/46
Doc ID 022240 Rev 1
The coefficients in the APWorkbench are consequently calculated as follows:
Equation 24
4.3
Shelf filters
The coefficient gain is defined in Equation 25.
Equation 25
The coefficients
α and β are calculated as follows:
Equation 26
4.3.1
Low-shelf filter
The coefficients for an LSF can be calculated as follows:
Equation 27
The coefficient to load in APWorkbench can be calculated by applying the calculation
already shown in Equation 11.
BoostValue
W
K
Q
Gain
b
t
Coefficien
BoostValue
W
Q
K
t a
Coefficien
BoostValue
W
a
t
Coefficien
BoostValue
W
K
Q
Gain
t b
Coefficien
BoostValue
W
b
t
Coefficien
+
⋅
+
⋅
=
+
−
−
=
−
=
+
⋅
−
=
−
=
1
2
1
2
1
1
2
)
1
(
1
2
0
2
1
2
1
)
40
(
10
dB
Gain
Gain
=
()
Gain
S
Gain
Gain
c
⋅
⋅
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛ −
⋅
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
+
⋅
=
α
β
ϑ
α
2
2
1
1
1
2
sin
() (
)
() (
)
() (
)
() (
)
()
() (
)
()
() (
)
()
β
ϑ
ϑ
β
ϑ
β
ϑ
ϑ
β
ϑ
−
⋅
−
−
+
⋅
=
⋅
+
−
−
⋅
⋅
=
+
⋅
−
−
+
⋅
=
−
⋅
−
+
+
=
⋅
+
+
−
⋅
−
=
+
⋅
−
+
+
=
c
c
c
c
c
c
Gain
Gain
Gain
b
Gain
Gain
Gain
b
Gain
Gain
Gain
b
Gain
Gain
a
Gain
Gain
a
Gain
Gain
a
cos
1
1
cos
1
1
2
cos
1
1
cos
1
1
cos
1
1
2
cos
1
1
2
1
0
2
1
0



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