AN737

M
AN737
Using Digital Potentiometers to Design
Low-Pass Adjustable Filters
INTRODUCTION
The most common filter found in a data acquisition
system signal path is a low-pass filter. This type of filter
is usually used to reduce A/D Converter (ADC) aliasing
errors. If there is more than one signal that is applied to
the A/D converter through a multiplexer, each signal
source may have its own set of filter requirements (i.e.,
settling time, fast transition region, etc.). Consequently,
a variety of filters may be required in the circuit prior to
the multiplexer. Usually these filters are implemented
with operational amplifiers (op amps) in combination
with fixed resistors and capacitors.
An alternative filter design solution is to have one filter
following the multiplexer. In this circuit, the low-pass
filter would need to be programmable. The obvious
advantage of having the filter serve many analog inputs
is that there is a reduction in chip count. An example of
this type of approach is shown in Figure 1.
Temperature 2
Temperature 3
Acceleration
Figure 2 shows the details of a single-supply, unity
gain, second-order, programmable low-pass Sallen
Key filter. This filter is implemented with two resistors
and two capacitors. The two resistors in this circuit are
replaced with the dual MCP42100, 100 kΩ, 8-bit, digital
potentiometer.
C1
R1
VIN
PW0
PA0
R2
Programmable
Low-Pass
Filter
Vibration
Pressure
12-bit
A/D Converter
FIGURE 1:
If a programmable low-pass
filter is used in the application circuit, it can be
placed after the analog multiplexer. The
programmability of the filter allows for a wide variety of input signals.
Programmable Low-Pass Filters
In this application note, a programmable, secondorder, low-pass filter will be presented in four different
scenarios. The first three scenarios will illustrate how a
dual digital potentiometer and a single amplifier can be
configured for low-pass second-order Butterworth,
Bessel and Chebyshev responses with a programma-
 2004 Microchip Technology Inc.
Single-Supply,
Rail-to-Rail Input
Op Amp
PW1
PB0
1/2
MCP42100
PA1
PB1
1/2
MCP42100
100 kΩ Digital
Potentiometers
Temperature 1
Analog
Multiplexer
ble corner frequency range of 1:100. An example of the
digital potentiometer setting for these designs is
summarized in Tables 1, 2 and 3. The fourth scenario
will show the same circuit design, where all three
approximation methods (Butterworth, Bessel and
Chebyshev) can coexist with a programmable corner
frequency range of 1:10. An example of the digital
potentiometer settings for this combination of
approximation methods is summarized in Table 4.
C2 MCP601
MCP3201
12-bit ADC
-
Bonnie C. Baker
Microchip Technology Inc.
+
Author:
VOUT
FIGURE 2:
The combination of a dual
digital potentiometer and a single-supply, rail-torail amplifier can be used to construct a programmable, second-order, Sallen-Key, low-pass filter.
Digital potentiometers can be used to adjust system
reference levels, gain errors and offset errors, while
offering the added capability of digital adjustment
control. Devices such as Microchip’s MCP41XXX and
MCP42XXX digital potentiometer families have three
resistive terminals for the single versions (MCP41010,
MCP41050 and MCP41100) and six resistive terminals
for the dual versions (MCP42010, MCP42050 and
MCP42100) and are illustrated in Figure 3. The
MCP41010 and MCP42010 are both 10 kΩ
potentiometers. The MCP41050 and MCP42050 are
both 50 kΩ potentiometers, while the MCP41100 and
42100 are both 100 kΩ potentiometers.
DS00737C-page 1
AN737
PA0 PW0 PB0
PA PW PB
RDAC2
RDAC1
Data Register 1
Data Register 0
D7
PW1 PB1
PA1
D7
D0
Digital
Potentiometer
Model
D0
RS
Decode
Logic
CS
D7
D0
PA PW PB
16-bit Shift Register
SI
SCK
SO
Mechanical
Potentiometer
Model
SHDN
Dual Digital Potentiometer
FIGURE 3:
The operation of the digital potentiometer as compared to the mechanical potentiometer is functionally the same. The adjustment of the digital potentiometer is done with a serial code to the
device. Although the mechanical potentiometer provides simplicity, the digital potentiometer provides
flexibility and reliability.
The potentiometer can be configured for two modes:
the Rheostat mode and Voltage Divider mode. In the
Rheostat mode, the wiper (terminal PW) is shorted to
either the PA or PB terminal of the device. This
configuration is shown in Figure 4. When used in the
Voltage Divider mode (Figure 4.b), all three terminals
are connected to differing nodes in the circuit. For the
analog filter example in this application note, the digital
potentiometer will be configured in the Rheostat mode.
By adjusting the two digital potentiometers in Figure 2,
the frequency cutoff and the filter approximation
method of this second-order low-pass filter can be
changed.
The design equation
configuration is:
for
this
low-pass
filter
V
K/ ( R R C C )
OUT
1 2 1 2
----------------- = --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------V
2
IN
s + s ( 1/R 1 C 1 + 1/R 2 /C 1 + 1/ R 2 C 2 – K/R 2 C 2 ) + 1/R 1 R 2 C 1 C 2
Where: K = 1
PW
PW
PA
PB
PA
(a) Rheostat Mode
RX = ±30% accurate
500 ppm/°C
PA
PB
PB
PW
(b) Voltage Divider Mode
RA/RB = ±3% accurate
15 ppm/°C
FIGURE 4:
A digital potentiometer can
be configured in the (a) Rheostat mode or (b)
Voltage Divider mode.
The operational amplifier used in this application circuit
is a single-supply, rail-to-rail out device. The MCP601
is a single amplifier that belongs to the MCP601/2/3/4
family of operational amplifiers. The MCP603 is also a
single amplifier with a Chip Select feature. The dual
version is the MCP602, while the quad version is the
MCP604. These amplifiers are optimized for high
speed, low offset voltage and single-supply operation.
DS00737C-page 2
With this formula, the appropriate resistance and capacitance can be calculated. An alternative to this tedious
design exercise is to determine the capacitor and resistor values using the FilterLab® software, a filter design
program that can be downloaded from Microchip’s web
site at www.microchip.com.
The Circuit screen in this program allows the user to
adjust the capacitors to desired values (C 1 and C2 per
Figure 2). When these capacitors are set, the software
changes the resistors in the circuit to appropriate
values for the circuit implementation. There may be a
corner frequency and stability error with low-pass filters
that are designed at frequencies higher than 100 kHz.
This error is introduced by the parasitic capacitance of
the digital potentiometer. As a general guideline, C1
and C2 should be larger than 10 nF.
For more detailed information concerning anti-aliasing
filters, please refer to Microchip’s Application Note 699,
entitled “Anti-Aliasing, Analog Filters for Data
Acquisition Systems” (DS00699).
 2004 Microchip Technology Inc.
AN737
TABLE 1:
A BUTTERWORTH FILTER DESIGN ADJUSTING THE RESISTORS THROUGH A
DIGITAL POTENTIOMETER
Specifications: Programmable cutoff frequency range of 100 Hz to 10 kHz by using capacitors of C1 = 0.047 µF,
C2 = 0.018 µF and adjusting the resistors through a digital potentiometer.
Closest
FilterLab
FilterLab
Nominal
Closest
Calculated 1% Digital Pot. R1 Digital Pot. R1 Calculated 1% Digital Pot. R2 Digital Pot. R2
Cutoff
Frequency, Hz R1 Value, kΩ
Value, kΩ
Code, decimal R2 Value, kΩ
Value, kΩ
Code, decimal
100
32.2
32.031
82
92.8
92.969
238
200
16.1
16.016
41
46.4
46.484
119
300
10.7
10.156
26
30.9
30.859
79
1000
3.22
3.125
8
9.28
9.375
24
2000
1.61
1.563
4
4.64
4.688
12
3000
1.07
1.172
3
3.09
3.125
8
10000
322
0.391
1
928
0.781
2
Butterworth Second-Order Low-Pass
Filters
When a Butterworth filter is required, the Sallen Key
configuration shown in Figure 2 can have an adjustable
frequency range of 1:100. The frequency behavior of
the Butterworth filter is maximally flat in the magnitude
response in pass band. The rate of attenuation in
transition band is better than the Bessel filter, though
not as good as the Chebyshev filter. There is no ringing
in the stop band. The step response of the Butterworth
filter has some overshoot and ringing in the time
domain, though this is less than the Chebyshev filter.
The capacitor values in this circuit are kept constant
while the resistive elements are adjusted. The two
capacitors should be carefully selected to be constants
in the FilterLab software so that the digital potentiometer resistances are the only values that are changing.
These capacitive values can easily be found in the
FilterLab software through experimentation.
Verification of the performance of the Butterworth filters
that use 1% discrete resistors can be performed with
the SPICE listing that is provided as an output from the
FilterLab software. The SPICE simulations for the
100 Hz, 200 Hz, 300 Hz and 1,000 Hz filters using the
values calculated by the FilterLab software are shown
in Figure 5.
To validate the digital potentiometer design, SPICE
simulations can be performed on the Butterworth filters
using the digital potentiometer values. The 100 Hz,
200 Hz, 300 Hz and 1,000 Hz filters using the
calculated nominal resistance values of the digital
potentiometers, per Table 2, are shown in Figure 6.
From these two SPICE simulations, it is easy to see
that the filters from Figure 5 behave fundamentally the
same over frequency as compared to Figure 6.
As an example, a programmable second-order, lowpass Butterworth filter with a corner frequency that
ranges from 100 Hz to 10 kHz can be designed by
setting C1 = 0.047 µF and C2 = 0.018 µF. The values
calculated by the FilterLab software for this filter design
are summarized in Table 1. Table 1 also includes the
closest values for R1 and R 2 from the digital
potentiometer, along with the digital program code for
the MCP42100.
 2004 Microchip Technology Inc.
DS00737C-page 3
AN737
FIGURE 5:
SPICE simulation of four Butterworth, second-order low-pass filters with corner
frequencies of 100 Hz, 200 Hz, 300 Hz and 1,000 Hz. In this simulation, 1% resistor values were used.
FIGURE 6:
SPICE simulation of four Butterworth, second-order low-pass filters with corner
frequencies of 100 Hz, 200 Hz, 300 Hz and 1,000 Hz. In this simulation, nominal digital potentiometer
resistor values, per Table 1, were used.
TABLE 2:
A PROGRAMMABLE BESSEL FILTER DESIGN USING A DUAL 100 KΩ DIGITAL
POTENTIOMETER.
Specifications: A programmable Bessel filter with a cutoff frequency range of 100 Hz to 10 kHz can be implemented
with C1 = 0.033 µF, C2 = 0.018 µF and a dual 100 kΩ digital potentiometer.
Closest
FilterLab
FilterLab
Nominal
Closest
Calculated 1% Digital Pot. R 1 Digital Pot. R1 Calculated 1% Digital Pot. R2 Digital Pot. R2
Cutoff
Value, kΩ
Code, decimal R2 Value, kΩ
Value, kΩ
Code, decimal
Frequency, Hz R1 Value, kΩ
100
28.7
28.516
73
91.5
91.406
234
200
14.3
14.453
37
45.7
43.75
117
300
9.57
9.375
24
30.5
30.469
78
1000
2.87
2.734
7
9.15
8.984
23
2000
1.43
1.563
4
4.57
4.688
12
3000
0.957
0.781
2
3.05
3.125
8
10000
0.287
0.391
1
0.915
0.781
2
DS00737C-page 4
 2004 Microchip Technology Inc.
AN737
Bessel Second-Order Low-Pass Filters
Chebyshev 2nd Order Low-Pass Filters
When a Bessel filter is desired, the Sallen Key
configuration, shown in Figure 2, can have an adjustable frequency range of 1:100. As with the Butterworth
filter, the frequency response of the Bessel filter has a
flat magnitude response in the pass band. Following
the pass band, the rate of attenuation in the transition
band is slower than the Butterworth or Chebyshev.
Finally, there is no ringing in the stop band. This filter
has the best step response of all of the filters mentioned in this application note, with very little overshoot
or ringing.
The filter in Figure 2 can also be designed in the
Chebyshev approximation for an adjustable range of
1:100. With the Chebyshev filter, the frequency behavior
exhibits a ripple in the pass-band that is determined by
the specific placement of the poles in the circuit design.
With the design discussed in this application note, the
ripple is 3 dB. In general, an increase in ripple magnitude
will lessen the width of the transition band. The rate of
attenuation in the transition band is steeper than
Butterworth and Bessel filters. Although there is ringing
in the pass-band region with this filter, the stop band is
devoid of ringing. The step response has a fair degree
of overshoot and ringing.
In Table 3, a programmable Bessel filter is designed
with a corner frequency range of 100 Hz to 10 kHz, by
setting C1 = 0.033 µF and C2 = 0.018 µF. Once again,
in the FilterLab software, the capacitor values are kept
constant, while the resistive elements are adjusted.
TABLE 3:
An example of the digital potentiometer settings for a
2nd order, low-pass Chebyshev filter is given in
Table 3.
CHEBYSHEV FILTER DESIGN
Specification: Chebyshev, 3 dB Ripple, 100 to 10 kHz cutoff, C1 = 0.15 µF, C 2 = 0.015 µF
Cutoff
Frequency, Hz
FilterLab
Calculated 1%
R1 Value, kΩ
Closest
Nominal Digital
Pot. R1 Value,
kΩ
Digital Pot. R1
Code, decimal
FilterLab
Calculated 1%
R2 Value, kΩ
Closest Digital
Pot. R 2 Value,
kΩ
Digital Pot. R 2
Code, decimal
100
21.0
21.094
54
75.6
75.781
194
200
10.5
10.547
27
37.8
37.891
97
300
7.01
7.031
18
25.2
25.391
65
1000
2.10
1.953
5
7.56
16.016
41
10
2000
1.05
1.563
4
3.78
3.9063
3000
0.701
0.781
2
2.52
2.344
6
10000
0.210
0.391
1
0.756
0.781
2
TABLE 4:
THE BUTTERWORTH, BESSEL AND CHEBYSHEV APPROXIMATION METHODS
Specifications: The Butterworth, Bessel and Chebyshev approximation methods can be designed into the circuit in Figure 2 by
using a dual potentiometer and capacitive values of C1 = 0.015 µF, C2 = 0.0022 µF. The adjustable cutoff frequency range of these
filters is 1,000 Hz to 10 kHz.
Cutoff Frequency,
Hz
Filter
Approximation
Method
Closest Digital
Pot. R1 Value, Ω
Digital Pot. R1
Code, decimal
Closest Digital
Pot. R 2 Value, Ω
Digital Pot. R2
Code, decimal
1,000
Butterworth
8.203
21
94.141
241
Bessel
5.078
13
93.359
239
Chebyshev
(3 dB Ripple)
3.516
9
33.984
87
Butterworth
3.906
10
47.266
121
Bessel
2.344
6
46.484
119
Chebyshev
(3 dB Ripple)
15.625
40
17.188
44
Butterworth
2.734
7
31.250
80
Bessel
1.563
4
31.250
80
Chebyshev
(3 dB Ripple)
10.547
27
11.328
29
Butterworth
0.781
2
9.375
24
2,000
3,000
10,000
Bessel
0.391
1
9.375
24
Chebyshev
(3 dB Ripple)
3.125
8
3.516
9
 2004 Microchip Technology Inc.
DS00737C-page 5
AN737
Combining Butterworth, Bessel and
Chebyshev Second-Order Low-Pass
Filters
All three approximation methods can be combined,
with some limitations, in this circuit. Since there is a
large variety of pole locations, the cutoff frequency
range is 1:10. An example of a programmable filter with
a cutoff frequency range of 1,000 Hz to 10 kHz is
shown in Table 4.
CONCLUSION
It is possible to design second-order, low-pass,
programmable filters with one dual digital
potentiometer, one amplifier and two capacitors.
REFERENCES
AN699, “Anti-Aliasing, Analog Filters for Data
Acquisition Systems”, Bonnie C. Baker,
Microchip Technology Inc., DS00699, 1999.
ERROR ANALYSIS OF
PROGRAMMABLE FILTERS
AN219, “Comparing Digital Potentiometers to
Mechanical Potentiometers”, Bonnie C. Baker,
Microchip Technology Inc., DS00219, 2000.
Absolute Accuracy of Circuit Elements
AN691, “Optimizing Digital Potentiometer Circuits to
Reduce Absolute and Temperature Variations”,
Bonnie C. Baker, Microchip Technology Inc.,
DS00691, 2001.
The nominal resistance of a 100 kΩ digital potentiometer (MCP42100), per data sheet specifications, varies
approximately ±30%. If the 10 kΩ digital potentiometer
(MCP42010) is substituted for the MCP42100, the
nominal resistance variance from part-to-part is
specified at ±20% for the MCP42010. When the 10 kΩ
potentiometer is substituted, the capacitive values
should be increased by 10X. For instance, in the
Butterworth example of Table 1, C1 should be changed
to 0.47 µF and C2 changed to 0.18 µF. When this is
done, the codes to the potentiometer that can stay the
same, remain unchanged. The change of the potentiometer from the MPC42100 (100 kΩ) to the
MCP42010 (10 kΩ) will, in fact, decrease the values,
as stated in Table 1, by 10X.
In this application circuit, it is suggested that the dual
version of the digital potentiometer be used because
there can be part-to-part variation of the nominal
resistance (±30% for the MCP42100 and ±20% for the
MCP42010). With the dual potentiometer, resistor-toresistor variation on chip is specified to a typical value
of 0.2%. The resistance variation of these digital
potentiometers is primarily dependent on the process
variation of the sheet-rho of a diffused p-silicon layer
and the on-resistance of the internal switches.
If 20% accurate capacitors are used, the variability of
this filter in a manufacturing environment is dominated
by the capacitors.
Wiper resistance
The wiper resistance of the MCP42100 digital
potentiometer is approximately 125Ω (typ) when
VDD = 5.5V. This wiper resistance appears as an error
in the resistance value of the digital potentiometer only
at lower programmed settings. For instance, with the
MCP42100, the nominal resistance step for each code
is equal to 100 kΩ/256, or 390.625Ω. With a digital
code setting of ‘1’, the ideal nominal resistance is
390.625Ω. However, with the added wiper resistance,
this resistance is nominally 515.625Ω.
DS00737C-page 6
 2004 Microchip Technology Inc.
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DS00737C-page 7
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Tel: 91-80-2290061 Fax: 91-80-2290062
Japan
Benex S-1 6F
3-18-20, Shinyokohama
Kohoku-Ku, Yokohama-shi
Kanagawa, 222-0033, Japan
Tel: 81-45-471- 6166 Fax: 81-45-471-6122
Durisolstrasse 2
A-4600 Wels
Austria
Tel: 43-7242-2244-399
Fax: 43-7242-2244-393
Regus Business Centre
Lautrup hoj 1-3
Ballerup DK-2750 Denmark
Tel: 45-4420-9895 Fax: 45-4420-9910
France
Parc d’Activite du Moulin de Massy
43 Rue du Saule Trapu
Batiment A - ler Etage
91300 Massy, France
Tel: 33-1-69-53-63-20
Fax: 33-1-69-30-90-79
Germany
Steinheilstrasse 10
D-85737 Ismaning, Germany
Tel: 49-89-627-144-0
Fax: 49-89-627-144-44
Italy
Via Quasimodo, 12
20025 Legnano (MI)
Milan, Italy
Tel: 39-0331-742611
Fax: 39-0331-466781
Netherlands
P. A. De Biesbosch 14
NL-5152 SC Drunen, Netherlands
Tel: 31-416-690399
Fax: 31-416-690340
United Kingdom
505 Eskdale Road
Winnersh Triangle
Wokingham
Berkshire, England RG41 5TU
Tel: 44-118-921-5869
Fax: 44-118-921-5820
01/26/04
DS00737C-page 8
 2004 Microchip Technology Inc.