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Texas Instruments Incorporated
Amplifiers: Op Amps
Using the infinite-gain, MFB filter topology
in fully differential active filters
By Thomas Kuehl
Senior Applications Engineer
Active filters are commonly employed in analog signal-
conditioning applications. Some of the more common appli-
cations include tailoring a signal’s bandwidth to reduce
noise.Oneexampleofthisisalow-passanti-aliasingfilter
in front of an analog-to-digital converter (ADC); another is
an anti-imaging filter that follows the output of a delta-
sigma digital-to-analog converter (DAC) to remove
unwanted high-frequency content. These filters—most
commonly low-pass, high-pass, and band-pass filters—are
often used to manage the amplitude response within a
particular frequency range. The amplitude response may be
tailored to track a particular pass-band or stop-band
characteristic such as one provided by a Butterworth,
Chebyshev, or Bessel filter. Filter-synthesis software is
available from several sources, including Texas Instruments
(TI). The synthesis programs and various on-line calcula-
tors allow for quick realization of practical filter designs.
TI’s FilterPro™ software accommodates all of the filters
just mentioned.
Differential-amplifier and differential-input mixed-signal
circuits such as ADCs are recognized for their inherent
ability to reject common-mode signals and noise.
1
This
ability provides a distinct advantage over the performance
of single-ended-input/output ADCs, where unintended
noise and signals may be processed along with the intended
signal. Both the circuit complexity and the passive compo-
nent count increase for a differential circuit, but maximiz-
ing system performance may easily justify the increased
complexity. Like the basic differential-amplifier stages,
differential active filters reject common-mode signals.
Designers often need to filter a signal as it is processed
through the circuit’s signal chain. In most instances the
applicationcallsforalow-passfilter.Otherfilterssuchas
the band-pass, high-pass, band-reject, or an all-pass (used
to create a specific time delay) are sometimes needed, but
not nearly as often as the low-pass filter.
The Sallen-Key and infinite-gain, multiple-feedback
(MFB) filter topologies are well-documented in filter liter-
ature, books, and on-line resources. Their popularity may
stem from the fact that they require only one operational
amplifier per second-order stage. Alternate topologies are
available that provide a very precise filter response and
offer lower component sensitivity; but they require two to
four operational amplifiers per second-order stage, plus
severaladditionalprecisepassivecomponents.Usingone
or more cascaded Sallen-Key or MFB stages often provides
the necessary level of filter performance without resorting
to more complex topologies.
The MFB configuration is one of the few topologies that
readily lends itself to an application requiring a fully differ-
ential active filter because typical feedback paths run from
the amplifier output back to only one input circuit—the
inverting input circuit. The noninverting input is either
biased at a common-mode potential or grounded, and no
feedback is applied to it in its most common connection.
The basic single-ended MFB filter topology can be used as
the basis for developing a differential filter that has equiv-
alent response characteristics. Nearly all other filter topol-
ogies require one or more feedback paths to each input of
the operational amplifiers and are therefore more difficult
to apply.
Transforming a single-ended-input/output filter
into a fully differential filter
Filter handbooks and software don’t always include topol-
ogies for differential filters, so knowing how to convert a
single-ended-input/output filter to a fully differential filter
when needed can save design time. For example, TI’s
FilterPro includes a provision for selecting a fully differen-
tial low-pass or high-pass filter but not a fully differential
band-pass filter. Suppose the latter is needed. A basic
single-ended MFB filter created with FilterPro can be used
33
Analog Applications Journal
3Q 2009
www.ti.com/aaj
High-Performance Analog Products
Amplifiers: Op Amps
Texas Instruments Incorporated
as a starting point. The 10-kHz second-order Butterworth
filter (Q = 0.707) shown in Figure 1 is used here as an
example. Butterworth filters have a maximally flat pass-
band response, which is a desirable trait for most analog
signal paths. A higher-order Butterworth filter further flat-
tens the pass-band response and provides higher attenua-
tion in the stop band. The second-order filter used in this
example provides an amplitude roll-off rate of –40 dB/
decade, beyond the –3-dB cutoff frequency. For now, a
value of 100 nF is selected for C2, and all the other com-
ponents are allowed to float to their calculated values.
FilterPro allows the designer to enter a capacitor value or
a seed value for the input resistor; in this case, C2’s value of
100nFisentered.Oncethefilterrequirementsareentered
into the program, the resulting values are displayed within
a schematic of the filter.
A helpful FilterPro feature is that it selects standard
capacitance values and then calculates the required resist-
ancesthatmeetthefilterresponse.Oftentheresistor
values are within the range of resistors with 1% tolerance.
Capacitors with a tolerance of better than 5%, such as 2 or
1%, have limited availability. Resistors, by comparison, are
commonly available with a tolerance of 1% and even 0.1%.
Therefore, most of the filter component values can be
covered without resorting to parallel or series combinations;
but keep in mind that components with tight tolerances
are required if a precise filter response is to be achieved.
The 10-kHz Butterworth low-pass filter shown in Figure 1
usesanOPA211precisionoperationalamplifier,whichis
well suited for this application because of its wide band-
width and high gain at the filter’s critical frequencies.
Otheroperationalamplifierswillalsoworkbutmusthave
sufficient gain bandwidth (GBW) to support the filter’s
performance. More will be mentioned about this later.
Transforming the single-ended-input/output low-pass
filter to a fully differential filter is really quite simple. The
procedure is as follows: (1) Create a mirror of the single-
ended filter circuit; (2) combine the circuit elements that
connect to ground; and (3) replace the operational ampli-
fier and its mirror with a fully differential operational
amplifier. Viewing the circuit in Figure 2, which shows the
single-ended low-pass filter and its mirror, aids under-
standing of this procedure.
The fully differential amplifier does not require the
ground reference that a conventional operational amplifier
uses, so the ground points in the circuit are no longer
needed. Also, when the mirror was created, an extra
input-voltage source and output meter were created; they
Figure 1. A 10-kHz single-ended Butterworth
MFB input/output low-pass filter
Figure 2. Mirroring the single-ended MFB
input/output low-pass filter
R2
2.4 k
R2
2.4 k
R1
2.4 k
R3
15.4 k
C1
680 pF
R1
2.4 k
R3
15.4 k
C1
680 pF
–V
U1
OPA211
Op
Amp
4
C2
10 nF
2
–
C2
10 nF
–
V
IN
3
6
+
V
IN
+
+
V
OUT
+
7
V
OUT
–
+V
–
0
Op
Amp
–
V
OUT
–20
+
+
V
IN
C2
10 nF
–
–40
C1
680 pF
R1
2.4 k
R3
15.4 k
–60
R2
2.4 k
–80
100
1 k
10 k
100 k
1 M
Frequency
(
Hz
)
34
High-Performance Analog Products
www.ti.com/aaj
3Q 2009
Analog Applications Journal
Texas Instruments Incorporated
Amplifiers: Op Amps
are redundant and not required either. The capacitor C2
and the mirrored C2 are required, but their individual
reactancescanbecombinedinonecapacitor.Oncetheir
ground connections are removed and they are connected
together, they form a series connection. Therefore, C2
becomes common to both sides of the filter’s input circuit,
and its value is half of the original value. In the original
low-pass filter, C2 had a value of 10 nF, but once the filter
has been transformed, C2’s final value is 5 nF. Lastly, the
two conventional operational amplifiers are removed and
replaced with one fully differential operational amplifier.
Inthiscase,ahigh-performanceaudioOPA1632isselected.
The transformed fully differential second-order low-pass
filter is shown in Figure 3. A plot of gain versus frequency
shows that the response is exactly the same for the fully
differential and the single-ended filters.
By now it may be apparent why the value of C2 was pre-
set to 10 nF. When a low-pass filter undergoes the transfor-
mation process, the capacitor ends up at half the original
value. Selecting a capacitor value of 10 nF or 20 nF results
in a transformed capacitor value of 5 nF or 10 nF, respec-
tively. All of these are standard capacitor values. If C2 had
originally been 4.7 nF, the transformed value would have
been 2.35 nF, which isn’t a standard value. Fortunately,
when FilterPro synthesizes a fully differential filter, it
always selects standard capacitor values and adjusts the
resistor values to provide the correct response.
The transformation procedure may be just as easily
applied to high-pass and band-pass filters. The resistors
and capacitors of these filters lie in different positions
within the MFB circuit than do those of low-pass filters.
As a result, instead of the one capacitor and its mirror
being reduced to one capacitor, a resistor and its mirror
are combined into one resistor. That resistor requires
twice the resistance of that used by the single-ended filter.
Figure 3. A transformed 10-kHz fully differential
second-order Butterworth low-pass filter
R2
2.4 k
R1
2.4 k
R3
15.4 k
C1
680 pF
–V
U1
OPA1632
–
+
C2
5 nF
V
OCM
V
OUT
V
IN
En
–
+
+V
R4
2.4 k
R6
15.4 k
C3
680 pF
R5
2.4 k
0
–20
–40
–60
–80
100
1 k
10 k
100 k
1 M
Frequency
(
Hz
)
35
Analog Applications Journal
3Q 2009
www.ti.com/aaj
High-Performance Analog Products
Amplifiers: Op Amps
Texas Instruments Incorporated
Figure 4 provides an example of a band-pass filter with
a center frequency of 10 kHz, a –3-dB bandwidth of 1 kHz,
and a gain of 10 V/V, with Q
bp
= 10 (f
C
/BW
–3 dB
). This filter
was transformed via the same steps described earlier for
the low-pass fully differential filter. Keep in mind that R3
is double the resistance required in a single-ended filter.
The differential-input, single-ended-output
active filter
Uptothispoint,single-ended-input/outputandfullydiffer-
ential active filters have been discussed. There are times,
however, when an application requires a filter function
provided by a differential input but requires only a single-
ended output. System applications sometimes are config-
ured with the input transducer or sensor entering the
circuit differentially, while the remainder of the circuitry
after the input stage operates in a single-ended fashion.
Certainly the fully differential filter could be employed
with one or the other output, but the amplifier involved
likely offers more capability than is needed. Numerous
fully differential operational amplifiers are available, but
their parametric variety is limited when compared to the
vast selection offered by conventional operational ampli-
fiers. Thus, for the differential-input, single-ended-output
filter, a conventional operational amplifier is a logical and
often lower-cost option.
The differential-input, single-ended-output filter can be
viewed as having similarities to the difference amplifier,
which is comprised of a single operational amplifier and
four resistors or impedances. An example schematic for a
difference amplifier is shown in Figure 5. Note the differ-
ential inverting and noninverting inputs and the single-
ended output. The ratios of R2 to R1 and R3 to R4 are
Figure 4. A 10-kHz (Q = 10) fully differential
second-order Butterworth band-pass filter
C1
47 nF
R2
6.8 k
R1
340
C2
47 nF
–V
U1
OPA1632
–
+
R3
35.6
V
OCM
V
OUT
V
IN
En
–
+
+V
R4
6.8 k
R3
340
C4
47 nF
C3
47 nF
20
0
–20
–40
Figure 5. The basic difference amplifier
100
1 k
10 k
100 k
1 M
Frequency (Hz)
R1
10 k
R2
100 k
20
Op
Amp
18
V
IN
–
R3
100 k
16
+
+
V
OUT
R4
10 k
14
–
12
9.0k
9.5k
10.0 k
10.5 k
11.0 k
OUTI
=×
−
R
R
2
1
R
RR
4
34
1
R
R
2
1
V
V
+
×
+
Frequency(Hz)
×
36
High-Performance Analog Products
www.ti.com/aaj
3Q 2009
Analog Applications Journal
Texas Instruments Incorporated
Amplifiers: Op Amps
precisely matched such that the rejection of common-
mode signals is maximized, and the amplification of differ-
ential signals is achieved with high gain accuracy. When it
comes to the filter’s case, the components are arranged to
provide the differential filter function and to maintain
input balance, just as the difference amplifier does.
The procedure for transforming the single-ended filter to
the differential-input, single-ended-output filter is the same
as it was for creating the fully differential filter. A conven-
tional operational amplifier replaces the fully differential
operational amplifier and, since there is a single output, the
circuit is connected a little differently. Instead of connect-
ing from a differential output back to the noninverting
input, the lower feedback network simply connects to
ground. Viewing Figure 6 makes the connection easy to
understand. The circuit and response are shown for a
50-kHz differential-input, single-ended-output, second-order
0.5-dB Chebyshev filter that has a gain of +10 V/V. The
differential-input, single-ended-output configuration can
be just as easily applied to band-pass and high-pass filters.
Considerations for practical active filters
UsingfiltersoftwaresuchasFilterProcanmakedesigning
filters straightforward and easy, but be aware that the
component values resulting from such software or even
from manual calculations may not always be completely
satisfactory. The resistor and capacitor values derived
may place impractical loading on the sensors that drive
the filter, or on the operational amplifiers used in and/or
around the filter circuit. This includes the input and feed-
back resistors in the filter. When using fully differential
operationalamplifierssuchastheOPA1632,thedesigner
should review the data sheet before using the feedback
resistor value returned by a filter program or calculation.
TheOPA1632isaverylow-noiseoperationalamplifier
with a noise spectral density of about 1.3 nV/√H
–
(10 kHz).
There may be the temptation to use large-value resistors
to minimize capacitances, but those resistors can easily
produce noise on their own that exceeds that of the
OPA1632.Thecapacitanceassociatedwithamplifierinput
in conjunction with a large feedback resistance creates a
pole in the response that degrades the amplifier’s closed-
loop bandwidth and phase margin. Therefore wideband
amplifiersliketheOPA1632mostoftenusesmall-value
feedback resistors to preserve the amplifier’s bandwidth.
The same precautions must be observed whether the
operational amplifier is conventional or fully differential.
Circuit designers are sometimes surprised to find that
the filter response of the actual filter is not as expected.
The filter exhibits inexact gain, incorrect cutoff or center
Figure 6. A 50-kHz, differential-input, single-
ended-output, second-order 0.5-dB Chebyshev
low-pass filter (A
V
= +10 V/ V)
R2
19.1 k
C1
22 pF
R1
1.9 k
R3
10.7 k
–V
U1
OPA211
4
2
–
C2
750 pF
V
IN
3
6
+
+
V
OUT
7
–
+V
R4
1.9 k
R6
10.7 k
C3
22 pF
R5
19.1 k
40
20
0
–20
–40
–60
–80
500
5 k
50 k
500 k
5 M
50 M
Frequency (Hz)
frequencies, or incorrect pass-band or stop-band response
characteristics. Most often this is the result of the opera-
tional amplifier having insufficient closed-loop gain at
frequencies critical to the filter’s performance. Surprisingly
high GBW may be required of the operational amplifier,
especially when a filter’s operating frequency is increased,
the stage gain is high, and the filter must accurately repro-
duce the pass-band ripple characteristics. For best MFB
performance, it is recommended that any one stage’s filter
Q be 10 or less.
37
Analog Applications Journal
3Q 2009
www.ti.com/aaj
High-Performance Analog Products
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