Cirrus Logic AN048 User Manual
AN48
Application Note
DESIGNNOTESFORA2-POLEFILTERWITH
DIFFERENTIAL INPUT
by Steven Green
AIN-
AIN+
R1
R4
R1
R3
C2
C2
Figure 1. 2-Pole Low-Pass Filter with Differential Input
R4
R3
C5
_
+
C5
1. Introduction
Many of today’s Digital-to-Analog Converters
(DACs) require a circuit that has a differential input
and will remove common-mode errors, reduce the
out-of-band noise produced by the delta-sigma
modulator and produce a single-ended output. The
circuit in Figure 1 includes a differential input and a
two-pole analog filter to achieve these design requirements. This application note outlines the design steps required to select component values.
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Copyright Cirrus Logic, Inc. 2003
(All Rights Reserved)
Notice the similarities between Figure 1 and the
multiple-feedback low-pass filter shown in
Figure 2. The 2-Pole Low-Pass Filter with Differential Input is easily designed using the design equations for the multiple-feedback low-pass filter. Also,
notice the similarities between Figure 1 and
Figure 3. The differential input function is accomplished by simply duplicating the component values generated in the filter design
MAR ‘03
AN48REV2
1
AN48
R4
C5
R3R1
C2
Figure 2. Multiple-Feedback Low-Pass
Filter
_
+
2. Design Steps
Step 1: Determine the required pass band gain,
H
. The circuit parameters require that the magni-
o
tude of H
also negative due to the inverting op-amp configuration.
be greater than or equal to one. Hois
o
R4
R1
R1
Figure 3. Differential Input Circuit
_
+
R4
Step 4: Select convenient values for C5 and C2.
Notice in Step 5 that K and H
such that is real.
Step 5: Given F
ζ2K 1 Ho–()–
,C2,C5, alpha and beta, cal-
c,Ho
must be selected
o
culate R1,R2 and R3 using the following equa-
tions.
Step 2: Determine the minimum input impedance.
Step 3: Select the desired filter type, Butterworth,
Bessel, etc. and the corner frequency, F
,forthefi-
c
nal design. The filter response and corner frequency determine the pass band phase and amplitude
response. The filter type determines the pole-locations and therefore alpha and beta. Table 1 lists
the normalized pole locations for several filter
types.
Table 1: Normalized Pole Locations
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
----------------------=
α
2πFcα2β2+=
C
5
-----=
C
2
R
--------------=
--------------------------------------------------------------------=
ω
oC2
α
2β2
+
4
Ho–()
1
ζζ2K 1 Ho–()–±[]
ζ
ω
o
K
R
1
R
3
ζζ2K 1 Ho–()–±
R
-------------------------------------------------=
4
ω
oC5
⋅
2
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