AN699

AN699
Anti-Aliasing, Analog Filters for Data Acquisition Systems
Author:
Bonnie C. Baker
Microchip Technology Inc.
INTRODUCTION
Analog filters can be found in almost every electronic
circuit. Audio systems use them for preamplification,
equalization, and tone control. In communication systems, filters are used for tuning in specific frequencies
and eliminating others. Digital signal processing systems use filters to prevent the aliasing of out-of-band
noise and interference.
This application note investigates the design of analog
filters that reduce the influence of extraneous noise in
data acquisition systems. These types of systems primarily utilize low-pass filters, digital filters or a combination of both. With the analog low-pass filter, high
frequency noise and interference can be removed from
the signal path prior to the analog-to-digital (A/D) conversion. In this manner, the digital output code of the
conversion does not contain undesirable aliased harmonic information. In contrast, a digital filter can be utilized to reduce in-band frequency noise by using
averaging techniques.
Although the application note is about analog filters, the
first section will compare the merits of an analog filtering strategy versus digital filtering.
Following this comparison, analog filter design parameters are defined. The frequency characteristics of a
low pass filter will also be discussed with some reference to specific filter designs. In the third section, low
pass filter designs will be discussed in depth.
The next portion of this application note will discuss
techniques on how to determine the appropriate filter
design parameters of an anti-aliasing filter. In this section, aliasing theory will be discussed. This will be followed by operational amplifier filter circuits. Examples
of active and passive low pass filters will also be discussed. Finally, a 12-bit circuit design example will be
given. All of the active analog filters discussed in this
application note can be designed using Microchip’s FilterLab software. FilterLab will calculate capacitor and
resistor values, as well as, determine the number of
poles that are required for the application. The program
will also generate a SPICE macromodel, which can be
used for spice simulations.
 1999 Microchip Technology Inc.
ANALOG VERSUS DIGITAL FILTERS
A system that includes an analog filter, a digital filter or
both is shown in Figure 1. When an analog filter is
implemented, it is done prior to the analog-to-digital
conversion. In contrast, when a digital filter is implemented, it is done after the conversion from analog-to-digital has occurred. It is obvious why the two
filters are implemented at these particular points, however, the ramifications of these restrictions are not quite
so obvious.
Analog
Input
Signal
Analog
Low Pass
Filter
A/D
Conversion
Digital
Filter
FIGURE 1: The data acquisition system signal chain
can utilize analog or digital filtering techniques or a
combination of the two.
There are a number of system differences when the filtering function is provided in the digital domain rather
than the analog domain and the user should be aware
of these.
Analog filtering can remove noise superimposed on the
analog signal before it reaches the Analog-to-Digital
Converter. In particular, this includes extraneous noise
peaks. Digital filtering cannot eliminate these peaks
riding on the analog signal. Consequently, noise peaks
riding on signals near full scale have the potential to
saturate the analog modulator of the A/D Converter.
This is true even when the average value of the signal
is within limits.
Additionally, analog filtering is more suitable for higher
speed systems, i.e., above approximately 5kHz. In
these types of systems, an analog filter can reduce
noise in the out-of-band frequency region. This, in turn,
reduces fold back signals (see the “Anti-Aliasing Filter
Theory” section in this application note). The task of
obtaining high resolution is placed on the A/D Converter. In contrast, a digital filter, by definition uses oversampling and averaging techniques to reduce in band
and out of band noise. These two processes take time.
Since digital filtering occurs after the A/D conversion
process, it can remove noise injected during the conversion process. Analog filtering cannot do this. Also,
the digital filter can be made programmable far more
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KEY LOW PASS ANALOG FILTER
DESIGN PARAMETERS
A low pass analog filter can be specified with four
parameters as shown in Figure 2 (fCUT-OFF , fSTOP ,
AMAX, and M).
M = Filter Order
ε
.......
fCUT–OFF
Gain (dB)
APASS
fSTOP
AMAX
ASTOP
Pass Band
Transition
Band
Stop Band
Frequency(Hz)
FIGURE 2: The key analog filter design parameters
include the –3dB cut-off frequency of the filter (fcut–off),
the frequency at which a minimum gain is acceptable
(fstop) and the number of poles (M) implemented with
the filter.
The cut-off frequency (fCUT-OFF) of a low pass filter is
defined as the -3dB point for a Butterworth and Bessel
filter or the frequency at which the filter response
leaves the error band for the Chebyshev.
The frequency span from DC to the cut-off frequency is
defined as the pass band region. The magnitude of the
response in the pass band is defined as APASS as
shown in Figure 2. The response in the pass band can
be flat with no ripple as is when a Butterworth or Bessel
filter is designed. Conversely, a Chebyshev filter has a
ripple up to the cut-off frequency. The magnitude of the
ripple error of a filter is defined as ε.
By definition, a low pass filter passes lower frequencies
up to the cut-off frequency and attenuates the higher
frequencies that are above the cut-off frequency. An
important parameter is the filter system gain, AMAX.
This is defined as the difference between the gain in the
pass band region and the gain that is achieved in the
stop band region or AMAX = APASS − ASTOP.
In the case where a filter has ripple in the pass band,
the gain of the pass band (APASS) is defined as the bottom of the ripple. The stop band frequency, fSTOP , is
the frequency at which a minimum attenuation is
reached. Although it is possible that the stop band has
a ripple, the minimum gain (ASTOP) of this ripple is
defined at the highest peak.
As the response of the filter goes beyond the cut-off frequency, it falls through the transition band to the stop
band region. The bandwidth of the transition band is
determined by the filter design (Butterworth, Bessel,
Chebyshev, etc.) and the order (M) of the filter. The filter
order is determined by the number of poles in the transfer function. For instance, if a filter has three poles in its
transfer function, it can be described as a 3rd order filter.
Generally, the transition bandwidth will become smaller
when more poles are used to implement the filter
design. This is illustrated with a Butterworth filter in
Figure 3. Ideally, a low-pass, anti-aliasing filter should
perform with a “brick wall” style of response, where the
transition band is designed to be as small as possible.
Practically speaking, this may not be the best approach
for an anti-aliasing solution. With active filter design,
every two poles require an operational amplifier. For
instance, if a 32nd order filter is designed, 16 operational amplifiers, 32 capacitors and up to 64 resistors
would be required to implement the circuit. Additionally,
each amplifier would contribute offset and noise errors
into the pass band region of the response.
1.0
Amplitude Response VOUT/VIN
readily than an analog filter. Depending on the digital filter design, this gives the user the capability of programming the cutoff frequency and output data rates.
n=1
n=2
0.1
n = 16
0.01
0.001
0.1
n=4
n=8
n = 32
1.0
Normalized Frequency
10
FIGURE 3: A Butterworth design is used in a low
pass filter implementation to obtain various responses
with frequency dependent on the number of poles or
order (M) of the filter.
Strategies on how to work around these limitations will
be discussed in the “Anti-Aliasing Theory” section of
this application note.
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 1999 Microchip Technology Inc.
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ANALOG FILTER DESIGNS
The more popular filter designs are the Butterworth,
Bessel, and Chebyshev. Each filter design can be identified by the four parameters illustrated in Figure 2.
Other filter types not discussed in this application note
include Inverse Chebyshev, Elliptic, and Cauer
designs.
Butterworth Filter
The Butterworth filter is by far the most popular design
used in circuits. The transfer function of a Butterworth
filter consists of all poles and no zeros and is equated
to:
VOUT /VIN = G/(a0sn + a1sn-1 + a2sn-2... an-1s2 + ans + 1)
where G is equal to the gain of the system.
Table 1 lists the denominator coefficients for a Butterworth design. Although the order of a Butterworth filter
design theoretically can be infinite, this table only lists
coefficients up to a 5th order filter.
M
a0
a1
a2
a3
2
1.0
1.4142136
3
1.0
2.0
4
1.0
2.6131259 3.4142136 2.6131259
5
1.0
3.2360680 5.2360680 5.2360680 3.2360680
The rate of attenuation in the transition band is steeper
than Butterworth and Bessel filters. For instance, a 5th
order Butterworth response is required if it is to meet
the transition band width of a 3rd order Chebyshev.
Although there is ringing in the pass band region with
this filter, the stop band is void of ringing. The step
response (Figure 5b.) has a fair degree of overshoot
and ringing.
Bessel Filter
Once again, the transfer function of the Bessel filter has
only poles and no zeros. Where the Butterworth design
is optimized for a maximally flat pass band response
and the Chebyshev can be easily adjusted to minimize
the transition bandwidth, the Bessel filter produces a
constant time delay with respect to frequency over a
large range of frequency. Mathematically, this relationship can be expressed as:
C = −∆θ * ∆f
where:
a4
C is a constant,
θ is the phase in degrees, and
2.0
f is frequency in Hz
TABLE 1: Coefficients versus filter order for Butterworth designs.
As shown in Figure 4a., the frequency behavior has a
maximally flat magnitude response in pass-band. The
rate of attenuation in transition band is better than
Bessel, but not as good as the Chebyshev filter. There
is no ringing in stop band. The step response of the
Butterworth is illustrated in Figure 5a. This filter type
has some overshoot and ringing in the time domain, but
less than the Chebyshev.
Chebyshev Filter
The transfer function of the Chebyshev filter is only similar to the Butterworth filter in that it has all poles and no
zeros with a transfer function of:
VOUT/VIN = G/(a0 + a1s + a2s2+... an-1sn-1 + sn)
Its frequency behavior has a ripple (Figure 4b.) in the
pass-band that is determined by the specific placement of
the poles in the circuit design. The magnitude of the ripple
is defined in Figure 2 as ε. In general, an increase in ripple
magnitude will lessen the width of the transition band.
The denominator coefficients of a 0.5dB ripple Chebyshev design are given in Table 2. Although the order of
a Chebyshev filter design theoretically can be infinite,
this table only lists coefficients up to a 5th order filter.
M
a0
a1
a2
a3
2
1.516203
1.425625
3
0.715694
1.534895
1.252913
4
0.379051
1.025455
1.716866
1.197386
5
0.178923
0.752518
1.309575
1.937367
a4
1.172491
Alternatively, the relationship can be expressed in
degrees per radian as:
C = −∆θ / ∆ω
where:
C is a constant,
θ is the phase in degrees, and
ω is in radians.
The transfer function for the Bessel filter is:
VOUT/VIN = G/(a0 + a1s + a2s2+... an-1sn-1 + sn)
The denominator coefficients for a Bessel filter are
given in Table 3. Although the order of a Bessel filter
design theoretically can be infinite, this table only lists
coefficients up to a 5th order filter.
M
a0
a1
a2
a3
2
3
3
3
15
15
6
4
105
105
45
10
5
945
945
420
105
a4
15
TABLE 3: Coefficients versus filter order for Bessel
designs.
The Bessel filter has a flat magnitude response in
pass-band (Figure 4c). Following the pass band, the
rate of attenuation in transition band is slower than the
Butterworth or Chebyshev. And finally, there is no ringing in stop band. This filter has the best step response
of all the filters mentioned above, with very little overshoot or ringing (Figure 5c.).
TABLE 2: Coefficients versus filter order for 1/2dB
ripple Chebyshev designs.
 1999 Microchip Technology Inc.
DS00699B-page 3
AN699
(b) 5th Order Chebyshev with 0.5dB Ripple
Magnitude (dB)
0.1
1
10
Normalized Frequency (Hz)
FIGURE 4:
10
0
-10
-20
-30
-40
-50
-60
-70
0.1
1
10
Normalized Frequency (Hz)
0.1
1
10
Normalized Frequency (Hz)
The frequency responses of the more popular filters, Butterworth (a), Chebyshev (b), and Bessel (c)..
(b) 5th Order Chebyshev with 0.5dB Ripple
Amplitude (V)
Amplitude (V)
(a) 5th Order Butterworth Filter
Time (s)
FIGURE 5:
10
0
-10
-20
-30
-40
-50
-60
-70
(c) 5th Order Bessel Filter
Amplitude (V)
Magnitude (dB)
10
0
-10
-20
-30
-40
-50
-60
-70
(c) 5th Order Bessel Filter
Magnitude (dB)
(a) 5th Order Butterworth Filter
Time (s)
Time (s)
The step response of the 5th order filters shown in Figure 4 are illustrated here.
ANTI-ALIASING FILTER THEORY
A/D Converters are usually operated with a constant
sampling frequency when digitizing analog signals. By
using a sampling frequency (fS), typically called the
Nyquist rate, all input signals with frequencies below
fS/2 are reliably digitized. If there is a portion of the
input signal that resides in the frequency domain above
fS/2, that portion will fold back into the bandwidth of
interest with the amplitude preserved. The phenomena
makes it impossible to discern the difference between
a signal from the lower frequencies (below fS/2) and
higher frequencies (above fS/2).
In both parts of this figure, the x-axis identifies the frequency of the sampling system, fS. In the left portion of
Figure 6, five segments of the frequency band are identified. Segment N =0 spans from DC to one half of the
sampling rate. In this bandwidth, the sampling system
will reliably record the frequency content of an analog
input signal. In the segments where N > 0, the frequency content of the analog signal will be recorded by
the digitizing system in the bandwidth of the segment
N = 0. Mathematically, these higher frequencies will be
folded back with the following equation:
f A LI A S E D = f I N – NfS
This aliasing or fold back phenomena is illustrated in
the frequency domain in Figure 6.
a)
b)
(1)
N=1
N=2
N=3
(2)
(3)
0
fs/2
N=4
fs
3fs/2
2fs
5fs/2
(4)
3fs
(5)
6fs/2
N=0
Sampled Output
Representation
Analog Input
N=0
4fs
0
(2)
(4)
(1)
(3)
(5)
fs/2
fs
FIGURE 6: A system that is sampling an input signal at fs (a) will identify signals with frequencies below fs/2 as well as
above. Input signals below fs/2 will be reliably digitized while signals above fs/2 will be folded back (b) and appear as lower
frequencies in the digital output.
DS00699B-page 4
 1999 Microchip Technology Inc.
AN699
For example, let the sampling rate, (fS), of the system
be equal to 100kHz and the frequency content of:
Low Pass Filter
fIN(4) = 294kHz
fIN(5) = 347kHz
The sampled output will contain accurate amplitude
information of all of these input signals, however, four
of them will be folded back into the frequency range
of DC to fS/2 or DC to 50kHz. By using the equation
fOUT = |fIN - NfS|, the frequencies of the input signals
are transformed to:
fOUT(1) = |41kHz - 0 x 100kHz| = 41kHz
fOUT(2) = |82kHz - 1 x 100kHz| = 18kHz
fOUT(3) = |219kHz - 2 x 100kHz| = 19kHz
fOUT(4) = |294kHz - 3 x 100kHz| = 6kHz
fOUT(5) = |347kHz - 4 x 100kHz| = 53kHz
Note that all of these signal frequencies are between
DC and fS/2 and that the amplitude information has
been reliably retained.
This frequency folding phenomena can be eliminated
or significantly reduced by using an analog low pass filter prior to the A/D Converter input. This concept is
illustrated in Figure 7. In this diagram, the low pass filter
attenuates the second portion of the input signal at frequency (2). Consequently, this signal will not be aliased
into the final sampled output. There are two regions of
the analog low pass filter illustrated in Figure 7. The
region to the left is within the bandwidth of DC to fS/2.
The second region, which is shaded, illustrates the
transition band of the filter. Since this region is greater
than fS/2, signals within this frequency band will be
aliased into the output of the sampling system. The
affects of this error can be minimized by moving the
corner frequency of the filter lower than fS/2 or increasing the order of the filter. In both cases, the minimum
gain of the filter, ASTOP , at fS/2 should less than the signal-to-noise ratio (SNR) of the sampling system.
For instance, if a 12-bit A/D Converter is used, the ideal
SNR is 74dB. The filter should be designed so that its
gain at fSTOP is at least 74dB less than the pass band
gain. Assuming a 5th order filter is used in this example:
fCUT-OFF = 0.18fS /2 for a Butterworth Filter
fCUT-OFF = 0.11fS /2 for a Bessel Filter
fCUT-OFF = 0.21fS /2 for a Chebyshev Filter with
0.5dB ripple in the pass band
fCUT-OFF = 0.26fS /2 for a Chebyshev Filter with
1dB ripple in the pass band
 1999 Microchip Technology Inc.
(2)
(1)
0
fs
fs/2
FIGURE 7:
If the sampling system has a low pass
analog filter prior to the sampling mechanism, high
frequency signals will be attenuated and not sampled.
ANALOG FILTER REALIZATION
Traditionally, low pass filters were implemented with
passive devices, ie. resistors and capacitors. Inductors
were added when high pass or band pass filters were
needed. At the time active filter designs were realizable,
however, the cost of operational amplifiers was prohibitive. Passive filters are still used with filter design when
a single pole filter is required or where the bandwidth of
the filter operates at higher frequencies than leading
edge operational amplifiers. Even with these two exceptions, filter realization is predominately implemented
with operational amplifiers, capacitors and resistors.
Passive Filters
Passive, low pass filters are realized with resistors and
capacitors. The realization of single and double pole
low pass filters are shown in Figure 8.
20
VOUT
VIN
1
=
1+sRC
Gain (dB)
fIN(3) = 219kHz
Analog Output
fIN(1) = 41kHz
fIN(2) = 82kHz
R2
VIN
VOUT
fc =1/2p R2C2
0
20dB/decade
-20
C2
100
1k
10k
100k
Frequency (Hz)
1M
FIGURE 8: A resistor and capacitor can be used to
implement a passive, low pass analog filter. The input
and output impedance of this type of filter
implementation is equal to R2.
The output impedance of a passive low pass filter is relatively high when compared to the active filter realization. For instance, a 1kHz low pass filter which uses a
0.1µF capacitor in the design would require a 1.59kΩ
resistor to complete the implementation. This value of
resistor could create an undesirable voltage drop or
make impedance matching difficult. Consequently,
passive filters are typically used to implement a single
pole. Single pole operational amplifier filters have the
added benefit of “isolating” the high impedance of the
filter from the following circuitry.
DS00699B-page 5
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VOUT
VIN
=
b. Single pole, inverting active filter
1 + R 2 / R1
VOUT
1+sR2C2
VIN
C2
MCP601
–R2 / R1
60
1+sR2C2
C2
R1
R2
R1
=
c. Frequency response of single pole
non-inverting active filter
Gain (dB)
a. Single pole, non-inverting active filter
VOUT
VIN
40
20dB/decade
20
R2
VIN
fc =1/ 2π R2C2
1 + R 2 / R1
VOUT
MCP601
100
VREF
1k
10k
100k
Frequency (Hz)
1M
FIGURE 9: An operational amplifier in combination with two resistors and one capacitor can be used to implement a
1st order filter. The frequency response of these active filters is equivalent to a single pole passive low pass filter.
It is very common to use a single pole, low pass, passive filter at the input of a Delta-Sigma A/D Converter.
In this case, the high output impedance of the filter
does not interfere with the conversion process.
Active Filters
Sallen-Key
C2
C1
R1
An active filter uses a combination of one amplifier, one to
three resistors and one to two capacitors to implement one
or two poles. The active filter offers the advantage of providing “isolation” between stages. This is possible by taking advantage of the high input impedance and low output
impedance of the operational amplifier. In all cases, the
order of the filter is determined by the number of capacitors
at the input and in the feedback loop of the amplifier.
VOUT
Single Pole Filter
VIN
The frequency response of the single pole, active filter
is identical to a single pole passive filter. Examples of
the realization of single pole active filters are shown in
Figure 9.
R2
VIN
VOUT
R4
R3
=
MCP601
K/(R1R2C1C2)
s2+s(1/R1C2+1/R2C2+1/R2C1 – K/R2C1+1/R1R2C1C2)
K = 1 + R4 /R3
FIGURE 10: The double pole or Sallen-Key filter
implementation has a gain G = 1 + R4 / R3. If R3 is open
and R4 is shorted the DC gain is equal to 1 V/V.
Double Pole, Voltage Controlled Voltage Source
The Double Pole, Voltage Controlled Voltage Source is
better know as the Sallen-Key filter realization. This filter is configured so the DC gain is positive. In the
Sallen-Key Filter realization shown in Figure 10, the DC
gain is greater than one. In the realization shown in
Figure 11, the DC gain is equal to one. In both cases,
the order of the filters are equal to two. The poles of
these filters are determined by the resistive and capacitive values of R1, R2, C1 and C2.
Sallen and Key
C1
R2
VIN
R1
C2
MCP601
VOUT
FIGURE 11: The double pole or Sallen-Key filter
implementation with a DC gain is equal to 1V/V.
DS00699B-page 6
 1999 Microchip Technology Inc.
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Double Pole Multiple Feedback
The double pole, multiple feedback realization of a 2nd
order low pass filter is shown in Figure 12. This filter
can also be identified as simply a Multiple Feedback
Filter. The DC gain of this filter inverts the signal and is
equal to the ratio of R1 and R2. The poles are determined by the values of R1, R3, C1, and C2.
Three design parameters will be used to implement
appropriate anti-aliasing filters:
1.
2.
3.
Cut-off frequency for filter must be 1kHz or
higher.
Filter attenuates the signal to -74dB at 10kHz.
The analog signal will only be filtered and not
gained or inverted.
Implementation with Bessel Filter Design
R1
VIN
C2
VOUT
VIN
=
C1
R3
MCP601
VOUT
–1/R1R3C5C6
2
s C2C1 + sC1 (1/R1 + 1/R2 + 1/R3) + 1/(R2R3C2C1)
A Bessel Filter design is used in Figure 13 to implement the anti-aliasing filter in the system described
above. A 5th order filter that has a cut-off frequency of
1kHz is required for this implementation. A combination
of two Sallen-Key filters plus a passive low pass filter
are designed into the circuit as shown in Figure 14.
This filter attenuates the analog input signal 79dB from
the pass band region to 10kHz. The frequency
response of this Bessel, 5th order filter is shown in
Figure 13.
ANTI-ALIASING FILTER DESIGN
EXAMPLE
In the following examples, the data acquisition system
signal chain shown in Figure 1 will be modified as follows. The analog signal will go directly into an active low
pass filter. In this example, the bandwidth of interest of
the analog signal is DC to 1kHz. The low pass filter will
be designed so that high frequency signals from the
analog input do not pass through to the A/D Converter
in an attempt to eliminate aliasing errors. The implementation and order of this filter will be modified according to the design parameters. Excluding the filtering
function, the anti-aliasing filter will not modify the signal
further, i.e., implement a gain or invert the signal. The
low pass filter segment will be followed by a 12-bit SAR
A/D Converter. The sampling rate of the A/D Converter
will be 20kHz, making 1/2 of Nyquist equal to 10kHz.
The ideal signal-to-noise ratio of a 12-bit A/D Converter
of 74dB. This design parameter will be used when
determining the order of the anti-aliasing filter. The filter
examples discussed in this section were generated
using Microchip’s FilterLab software.
 1999 Microchip Technology Inc.
Gain (dB)
FIGURE 12: A double pole, multiple feedback circuit
implementation uses three resistors and two capacitors
to implement a 2nd order analog filter. DC gain is equal
to –R2 / R1 .
10
90
0
0
-10
-90
-20
-180
-270
-30
phase
-360
-40
-450
-50
gain
-60
-630
-70
-80
100
-540
Phase (degrees)
R2
-720
1,000
Frequency (Hz)
10,000
FIGURE 13: Frequency response of 5th order Bessel
design implemented in Figure 14.
DS00699B-page 7
AN699
33nF
10nF
18.2kΩ
VIN
10.5kΩ
4.7nF
2.94kΩ
1.96kΩ
16.2kΩ
MCP601
10nF
33µF
MCP601
VOUT
FIGURE 14: 5th order Bessel design implemented two Sallen-Key filters and on passive filter. This filter is designed to
be an anti-aliasing filter that has a cut-off frequency of 1kHz and a stop band frequency of ~5kHz.
When a Chebyshev filter design is used to implement
the anti-aliasing filter in the system described above, a
3rd order filter is required, as shown Figure 15.
Although the order of this filter is less than the Bessel,
it has a 4dB ripple in the pass band portion of the frequency response. The combination of one Sallen-Key
filter plus a passive low pass filter is used. This filter is
attenuated to -70dB at 10kHz. The frequency response
of this Chebyshev 3rd order filter is shown in Figure 16.
330nF
VIN
2.15kΩ
68nF
20kΩ
90
0
0
-10
2.2nF
MCP601
VOUT
FIGURE 15: 3rd order Chebyshev design implemented using one Sallen-Key filter and one passive filter.
This filter is designed to be an anti-aliasing filter that has
a cut-off frequency of 1kHz -4db ripple and a stop band
frequency of ~5kHz.
Gain (dB)
9.31kΩ
10
-90
phase
-20
-180
-30
-270
-40
gain
-360
-50
-450
-60
-540
-70
-630
-80
100
Phase (degrees)
Implementation with Chebyshev Design
-720
1,000
Frequency (Hz)
10,000
FIGURE 16: Frequency response of 3rd
Chebyshev design implemented in Figure 15.
order
This filter provides less than the ideal 74dB of dynamic
range (AMAX), which should be taken into consideration.
The difference between -70dB and -74dB attenuation
in a 12-bit system will introduce little less than 1/2 LSB
error. This occurs as a result of aliased signals from
10kHz to 11.8KHz. Additionally, a 4dB gain error will
occur in the pass band. This is a consequence of the
ripple response in the pass band, as shown in
Figure 16.
DS00699B-page 8
 1999 Microchip Technology Inc.
AN699
33nF
100nF
26.1kΩ
VIN
2.37kΩ
10nF
2.94kΩ
15.4kΩ
MCP601
6.8nF
MCP601
VOUT
FIGURE 17: 4th order Butterworth design implemented two Sallen-Key filters. This filter is designed to be an
anti-aliasing filter that has a cut-off frequency of 1kHz and a stop band frequency of ~5kHz.
As a final alternative, a Butterworth filter design can be
used in the filter implementation of the anti-aliasing filter, as shown in Figure 17.
The frequency response of the three filters described
above along with several other options are summarized
in Table 4.
90
0
0
-90
-10
phase
-20
Gain (dB)
For this circuit implementation, a 4th order filter is used
with a cut-off frequency of 1kHz. Two Sallen-Key filters
are used. This filter attenuates the pass band signal
80dB at 10kHz. The frequency response of this Butterworth 4th order filter is shown in Figure 18.
10
-180
-30
-270
-40
-360
gain
-50
-450
-60
-540
-70
-630
Phase (degrees)
Implementation with Butterworth Design
-720
-80
100
1,000
Frequency (Hz)
10,000
FIGURE 18: Frequency response of 4th
Butterworth design implemented in Figure 17.
order
FILTER
ORDER,
M
BUTTERWORTH,
AMAX (dB)
BESSEL, AMAX
(dB)
CHEBYSHEV, AMAX (dB)
W/ RIPPLE ERROR OF
1dB
CHEBYSHEV, AMAX (dB)
W/ RIPPLE ERROR OF
4dB
3
60
51
65
70
4
80
66
90
92
5
100
79
117
122
6
120
92
142
144
7
140
104
169
174
TABLE 4: Theoretical frequency response at 10kHz of various filter designs versus filter order. Each filter has a
cut-off frequency of 1kHz.
 1999 Microchip Technology Inc.
DS00699B-page 9
AN699
CONCLUSION
REFERENCES
Analog filtering is a critical portion of the data acquisition system. If an analog filter is not used, signals outside half of the sampling bandwidth of the A/D
Converter are aliased back into the signal path. Once a
signal is aliased during the digitalization process, it is
impossible to differentiate between noise with frequencies in band and out of band.
Baker, Bonnie, “Using Operational Amplifiers for Analog Gain in Embedded System Design”, AN682, Microchip Technologies, Inc.
This application note discusses techniques on how to
determine and implement the appropriate analog filter
design parameters of an anti-aliasing filter.
DS00699B-page 10
Analog Filter Design, Valkenburg, M. E. Van, Oxford
University Press.
Active and Passive Analog Filter Design, An Introduction, Huelsman, Lawrence p., McGraw Hill, Inc.
 1999 Microchip Technology Inc.
AN699
NOTES:
 1999 Microchip Technology Inc.
DS00699B-page 11
Note the following details of the code protection feature on PICmicro® MCUs.
•
•
•
•
•
•
The PICmicro family meets the specifications contained in the Microchip Data Sheet.
Microchip believes that its family of PICmicro microcontrollers is one of the most secure products of its kind on the market today,
when used in the intended manner and under normal conditions.
There are dishonest and possibly illegal methods used to breach the code protection feature. All of these methods, to our knowledge, require using the PICmicro microcontroller in a manner outside the operating specifications contained in the data sheet.
The person doing so may be engaged in theft of intellectual property.
Microchip is willing to work with the customer who is concerned about the integrity of their code.
Neither Microchip nor any other semiconductor manufacturer can guarantee the security of their code. Code protection does not
mean that we are guaranteeing the product as “unbreakable”.
Code protection is constantly evolving. We at Microchip are committed to continuously improving the code protection features of
our product.
If you have any further questions about this matter, please contact the local sales office nearest to you.
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and may be superseded by updates. It is your responsibility to
ensure that your application meets with your specifications.
No representation or warranty is given and no liability is
assumed by Microchip Technology Incorporated with respect
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patents or other intellectual property rights arising from such
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