User Manual

AN48
2
2. Design Steps
Step 1: Determine the required pass band gain,
H
o
. The circuit parameters require that the magni-
tude of H
o
be greater than or equal to one. H
o
is
also negative due to the inverting op-amp configu-
ration.
Step 2: Determine the minimum input impedance.
Step 3: Select the desired filter type, Butterworth,
Bessel, etc. and the corner frequency, F
c
,forthefi-
nal design. The filter response and corner frequen-
cy determine the pass band phase and amplitude
response. The filter type determines the pole-loca-
tions and therefore alpha and beta. Table 1 lists
the normalized pole locations for several filter
types.
Table 1: Normalized Pole Locations
Step 4: Select convenient values for C5 and C2.
Notice in Step 5 that K and H
o
must be selected
such that is real.
Step 5: Given F
c
,H
o
,C2,C5, alpha and beta, cal-
culate R1,R2 and R3 using the following equa-
tions.
FILTER TYPE αβ
Butterworth 0.7071 0.7071
Bessel 1.1030 0.6368
0.01 dB Chebyshev 0.6743 0.7075
0.1 dB Chebyshev 0.6104 0.7106
_
C5
R3R1
C2
+
R4
Figure 2. Multiple-Feedback Low-Pass
Filter
_
R1
R1
R4
R4
+
Figure 3. Differential Input Circuit
ζ
2
K 1 H
o
–()–
ζ
α
α
2
β
2
+
----------------------=
ω
o
2πF
c
α
2
β
2
+=
K
C
5
C
2
-----=
R
1
R
4
H
o
–()
--------------=
R
3
1
ω
o
C
2
ζζ
2
K 1 H
o
–()–±[]
--------------------------------------------------------------------=
R
4
ζζ
2
K 1 H
o
–()–±
ω
o
C
5
⋅
-------------------------------------------------=