an699 - anti-aliasing, analog filters for data acquisition systems-00699b

1999 Microchip Technology Inc. DS00699B-page 1

AN699Anti-Aliasing, Analog Filters for Data Acquisition Systems

INTRODUCTIONAnalog filters can be found in almost every electroniccircuit. Audio systems use them for preamplification,equalization, and tone control. In communication sys-tems, filters are used for tuning in specific frequenciesand eliminating others. Digital signal processing sys-tems use filters to prevent the aliasing of out-of-bandnoise and interference.This application note investigates the design of analogfilters that reduce the influence of extraneous noise indata acquisition systems. These types of systems pri-marily utilize low-pass filters, digital filters or a combina-tion of both. With the analog low-pass filter, highfrequency noise and interference can be removed fromthe signal path prior to the analog-to-digital (A/D) con-version. In this manner, the digital output code of theconversion does not contain undesirable aliased har-monic information. In contrast, a digital filter can be uti-lized to reduce in-band frequency noise by usingaveraging techniques.Although the application note is about analog filters, thefirst section will compare the merits of an analog filter-ing strategy versus digital filtering.Following this comparison, analog filter design param-eters are defined. The frequency characteristics of alow pass filter will also be discussed with some refer-ence to specific filter designs. In the third section, lowpass filter designs will be discussed in depth.The next portion of this application note will discusstechniques on how to determine the appropriate filterdesign parameters of an anti-aliasing filter. In this sec-tion, aliasing theory will be discussed. This will be fol-lowed by operational amplifier filter circuits. Examplesof active and passive low pass filters will also be dis-cussed. Finally, a 12-bit circuit design example will begiven. All of the active analog filters discussed in thisapplication note can be designed using Microchips Fil-terLab software. FilterLab will calculate capacitor andresistor values, as well as, determine the number ofpoles that are required for the application. The programwill also generate a SPICE macromodel, which can beused for spice simulations.

ANALOG VERSUS DIGITAL FILTERSA system that includes an analog filter, a digital filter orboth is shown in Figure 1. When an analog filter isimplemented, it is done prior to the analog-to-digitalconversion. In contrast, when a digital filter is imple-mented, it is done after the conversion from ana-log-to-digital has occurred. It is obvious why the twofilters are implemented at these particular points, how-ever, the ramifications of these restrictions are not quiteso obvious.

FIGURE 1: The data acquisition system signal chaincan utilize analog or digital filtering techniques or acombination of the two.There are a number of system differences when the fil-tering function is provided in the digital domain ratherthan the analog domain and the user should be awareof these.Analog filtering can remove noise superimposed on theanalog signal before it reaches the Analog-to-DigitalConverter. In particular, this includes extraneous noisepeaks. Digital filtering cannot eliminate these peaksriding on the analog signal. Consequently, noise peaksriding on signals near full scale have the potential tosaturate the analog modulator of the A/D Converter.This is true even when the average value of the signalis within limits.Additionally, analog filtering is more suitable for higherspeed systems, i.e., above approximately 5kHz. Inthese types of systems, an analog filter can reducenoise in the out-of-band frequency region. This, in turn,reduces fold back signals (see the Anti-Aliasing FilterTheory section in this application note). The task ofobtaining high resolution is placed on the A/D Con-verter. In contrast, a digital filter, by definition uses over-sampling and averaging techniques to reduce in bandand out of band noise. These two processes take time. Since digital filtering occurs after the A/D conversionprocess, it can remove noise injected during the con-version process. Analog filtering cannot do this. Also,the digital filter can be made programmable far more

Author: Bonnie C. BakerMicrochip Technology Inc.

AnalogInputSignal

AnalogLow PassFilter

A/DConversion

DigitalFilter

AN699

DS00699B-page 2 1999 Microchip Technology Inc.

readily than an analog filter. Depending on the digital fil-ter design, this gives the user the capability of program-ming the cutoff frequency and output data rates.

KEY LOW PASS ANALOG FILTER DESIGN PARAMETERSA low pass analog filter can be specified with fourparameters as shown in Figure 2 (fCUT-OFF , fSTOP ,AMAX, and M).

FIGURE 2: The key analog filter design parametersinclude the 3dB cut-off frequency of the filter (fcutoff),the frequency at which a minimum gain is acceptable(fstop) and the number of poles (M) implemented withthe filter.The cut-off frequency (fCUT-OFF) of a low pass filter isdefined as the -3dB point for a Butterworth and Besselfilter or the frequency at which the filter responseleaves the error band for the Chebyshev.The frequency span from DC to the cut-off frequency isdefined as the pass band region. The magnitude of theresponse in the pass band is defined as APASS asshown in Figure 2. The response in the pass band canbe flat with no ripple as is when a Butterworth or Besselfilter is designed. Conversely, a Chebyshev filter has aripple up to the cut-off frequency. The magnitude of theripple error of a filter is defined as .By definition, a low pass filter passes lower frequenciesup to the cut-off frequency and attenuates the higherfrequencies that are above the cut-off frequency. Animportant parameter is the filter system gain, AMAX.This is defined as the difference between the gain in thepass band region and the gain that is achieved in thestop 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 bot-tom of the ripple. The stop band frequency, fSTOP , isthe frequency at which a minimum attenuation isreached. Although it is possible that the stop band hasa ripple, the minimum gain (ASTOP) of this ripple isdefined at the highest peak.As the response of the filter goes beyond the cut-off fre-quency, it falls through the transition band to the stopband region. The bandwidth of the transition band isdetermined by the filter design (Butterworth, Bessel,Chebyshev, etc.) and the order (M) of the filter. The filterorder is determined by the number of poles in the trans-fer function. For instance, if a filter has three poles in itstransfer function, it can be described as a 3rd order fil-ter.Generally, the transition bandwidth will become smallerwhen more poles are used to implement the filterdesign. This is illustrated with a Butterworth filter inFigure 3. Ideally, a low-pass, anti-aliasing filter shouldperform with a brick wall style of response, where thetransition band is designed to be as small as possible.Practically speaking, this may not be the best approachfor an anti-aliasing solution. With active filter design,every two poles require an operational amplifier. Forinstance, if a 32nd order filter is designed, 16 opera-tional amplifiers, 32 capacitors and up to 64 resistorswould be required to implement the circuit. Additionally,each amplifier would contribute offset and noise errorsinto the pass band region of the response.

FIGURE 3: A Butterworth design is used in a lowpass filter implementation to obtain various responseswith frequency dependent on the number of poles ororder (M) of the filter.Strategies on how to work around these limitations willbe discussed in the Anti-Aliasing Theory section ofthis application note.

M = Filter Order

Gai

n (dB

)

APASS

ASTOP

AMAX

Pass BandTransition

Stop Band

Frequency(Hz)

fCUTOFF

fSTOP

Band

. . . . . . .

1.0

0.1

0.01

0.001

Ampl

itude

Re

spon

se VO

UT/V

IN

0.1 1.0 10

n = 16

n = 32

n = 1

n = 2

n = 4

n = 8

Normalized Frequency


AN699ANALOG FILTER DESIGNSThe more popular filter designs are the Butterworth,Bessel, and Chebyshev. Each filter design can be iden-tified by the four parameters illustrated in Figure 2.Other filter types not discussed in this application noteinclude Inverse Chebyshev, Elliptic, and Cauerdesigns.Butterworth FilterThe Butterworth filter is by far the most popular designused in circuits. The transfer function of a Butterworthfilter consists of all poles and no zeros and is equatedto:

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 Butter-worth design. Although the order of a Butterworth filterdesign theoretically can be infinite, this table only listscoefficients up to a 5th order filter.

As shown in Figure 4a., the frequency behavior has amaximally flat magnitude response in pass-band. Therate of attenuation in transition band is better thanBessel, but not as good as the Chebyshev filter. Thereis no ringing in stop band. The step response of theButterworth is illustrated in Figure 5a. This filter typehas some overshoot and ringing in the time domain, butless than the Chebyshev.Chebyshev FilterThe transfer function of the Chebyshev filter is only sim-ilar to the Butterworth filter in that it has all poles and nozeros with a transfer function of:

VOUT/VIN = G/(a0 + a1s + a2s2+... an-1sn-1 + sn)Its frequency behavior has a ripple (Figure 4b.) in thepass-band that is determined by the specific placement ofthe poles in the circuit design. The magnitude of the rippleis defined in Figure 2 as . In general, an increase in ripplemagnitude will lessen the width of the transition band.The denominator coefficients of a 0.5dB ripple Cheby-shev design are given in Table 2. Although the order ofa Chebyshev filter design theoretically can be infinite,this table only lists coefficients up to a 5th order filter.

The rate of attenuation in the transition band is steeperthan Butterworth and Bessel filters. For instance, a 5thorder Butterworth response is required if it is to meetthe transition band width of a 3rd order Chebyshev.Although there is ringing in the pass band region withthis filter, the stop band is void of ringing. The stepresponse (Figure 5b.) has a fair degree of overshootand ringing.Bessel FilterOnce again, the transfer function of the Bessel filter hasonly poles and no zeros. Where the Butterworth designis optimized for a maximally flat pass band responseand the Chebyshev can be easily adjusted to minimizethe transition bandwidth, the Bessel filter produces aconstant time delay with respect to frequency over alarge range of frequency. Mathematically, this relation-ship can be expressed as:

C = * fwhere:

C is a constant, is the phase in degrees, and f is frequency in Hz

Alternatively, the relationship can be expressed indegrees per radian as:

C = / where:

C is a constant, is the phase in degrees, and 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 aregiven in Table 3. Although the order of a Bessel filterdesign theoretically can be infinite, this table only listscoefficients up to a 5th order filter.

The Bessel filter has a flat magnitude response inpass-band (Figure 4c). Following the pass band, therate of attenuation in transition band is slower than theButterworth or Chebyshev. And finally, there is no ring-ing in stop band. This filter has the best step responseof all the filters mentioned above, with very little over-shoot or ringing (Figure 5c.).

M a0 a1 a2 a3 a42 1.0 1.41421363 1.0 2.0 2.04 1.0 2.6131259 3.4142136 2.61312595 1.0 3.2360680 5.2360680 5.2360680 3.2360680

TABLE 1: Coefficients versus filter order for Butter-worth designs.

M a0 a1 a2 a3 a42 1.516203 1.4256253 0.715694 1.534895 1.2529134 0.379051 1.025455 1.716866 1.1973865 0.178923 0.752518 1.309575 1.937367 1.172491

TABLE 2: Coefficients versus filter order for 1/2dBripple Chebyshev designs.

M a0 a1 a2 a3 a42 3 33 15 15 64 105 105 45 105 945 945 420 105 15

TABLE 3: Coefficients versus filter order for Besseldesigns.

AN699


FIGURE 4: The frequency responses of the more popular filters, Butterworth (a), Chebyshev (b), and Bessel (c)..

FIGURE 5: The step response of the 5th order filters shown in Figure 4 are illustrated here.

ANTI-ALIASING FILTER THEORYA/D Converters are usually operated with a constantsampling frequency when digitizing analog signals. Byusing a sampling frequency (fS), typically called theNyquist rate, all input signals with frequencies belowfS/2 are reliably digitized. If there is a portion of theinput signal that resides in the frequency domain abovefS/2, that portion will fold back into the bandwidth ofinterest with the amplitude preserved. The phenomenamakes it impossible to discern the difference betweena signal from the lower frequencies (below fS/2) andhigher frequencies (above fS/2). This aliasing or fold back phenomena is illustrated inthe frequency domain in Figure 6.

In both parts of this figure, the x-axis identifies the fre-quency of the sampling system, fS. In the left portion ofFigure 6, five segments of the frequency band are iden-tified. Segment N =0 spans from DC to one half of thesampling rate. In this bandwidth, the sampling systemwill reliably record the frequency content of an analoginput signal. In the segments where N > 0, the fre-quency content of the analog signal will be recorded bythe digitizing system in the bandwidth of the segmentN = 0. Mathematically, these higher frequencies will befolded back with the following equation:

FIGURE 6: A system that is sampling an input signal at fs (a) will identify signals with frequencies below fs/2 as well asabove. Input signals below fs/2 will be reliably digitized while signals above fs/2 will be folded back (b) and appear as lowerfrequencies in the digital output.

100

-10-20-30-40-50-60-70

0.1 1 10Normalized Frequency (Hz)

Mag

nitu

de (d

B)10

0-10-20-30-40-50-60-70


Ma

gnitu

de (d

B)

100

-10-20-30-40-50-60-70


Ma

gnitu

de (d

B)

(c) 5th Order Bessel Filter(b) 5th Order Chebyshev with 0.5dB Ripple(a) 5th Order Butterworth Filter

(c) 5th Order Bessel Filter (b) 5th Order Chebyshev with 0.5dB Ripple(a) 5th Order Butterworth Filter

Time (s)

Ampl

itude

(V)

Time (s)

Ampl

itude

(V)

Time (s)Am

plitu

de (V

)

fALIASED fIN NfS=

N = 1N = 0 N = 2 N = 3 N = 4

0 fs/2 fs 3fs/2 2fs 5fs/2 3fs 6fs/2 4fs

Anal

og In

put

(1) (2)

(3)(5)(4)

N = 0

(1)(2)

(3)(5)(4)

0 fs/2 fs

Sam

pled

O

utpu

t R

epr

ese

nta

tion

a) b)


AN699For example, let the sampling rate, (fS), of the systembe equal to 100kHz and the frequency content of:

fIN(1) = 41kHzfIN(2) = 82kHzfIN(3) = 219kHzfIN(4) = 294kHzfIN(5) = 347kHz

The sampled output will contain accurate amplitudeinformation of all of these input signals, however, fourof them will be folded back into the frequency rangeof DC to fS/2 or DC to 50kHz. By using the equationfOUT = |fIN - NfS|, the frequencies of the input signalsare transformed to:

fOUT(1) = |41kHz - 0 x 100kHz| = 41kHzfOUT(2) = |82kHz - 1 x 100kHz| = 18kHzfOUT(3) = |219kHz - 2 x 100kHz| = 19kHzfOUT(4) = |294kHz - 3 x 100kHz| = 6kHzfOUT(5) = |347kHz - 4 x 100kHz| = 53kHz

Note that all of these signal frequencies are betweenDC and fS/2 and that the amplitude information hasbeen reliably retained.This frequency folding phenomena can be eliminatedor significantly reduced by using an analog low pass fil-ter prior to the A/D Converter input. This concept isillustrated in Figure 7. In this diagram, the low pass filterattenuates the second portion of the input signal at fre-quency (2). Consequently, this signal will not be aliasedinto the final sampled output. There are two regions ofthe analog low pass filter illustrated in Figure 7. Theregion to the left is within the bandwidth of DC to fS/2.The second region, which is shaded, illustrates thetransition band of the filter. Since this region is greaterthan fS/2, signals within this frequency band will bealiased into the output of the sampling system. Theaffects of this error can be minimized by moving thecorner frequency of the filter lower than fS/2 or increas-ing the order of the filter. In both cases, the minimumgain of the filter, ASTOP , at fS/2 should less than the sig-nal-to-noise ratio (SNR) of the sampling system. For instance, if a 12-bit A/D Converter is used, the idealSNR is 74dB. The filter should be designed so that itsgain at fSTOP is at least 74dB less than the pass bandgain. Assuming a 5th order filter is used in this example:

fCUT-OFF = 0.18fS /2 for a Butterworth FilterfCUT-OFF = 0.11fS /2 for a Bessel FilterfCUT-OFF = 0.21fS /2 for a Chebyshev Filter with

0.5dB ripple in the pass bandfCUT-OFF = 0.26fS /2 for a Chebyshev Filter with

1dB ripple in the pass band

FIGURE 7: If the sampling system has a low passanalog filter prior to the sampling mechanism, highfrequency signals will be attenuated and not sampled.

ANALOG FILTER REALIZATIONTraditionally, low pass filters were implemented withpassive devices, ie. resistors and capacitors. Inductorswere added when high pass or band pass filters wereneeded. At the time active filter designs were realizable,however, the cost of operational amplifiers was prohibi-tive. Passive filters are still used with filter design whena single pole filter is required or where the bandwidth ofthe filter operates at higher frequencies than leadingedge operational amplifiers. Even with these two excep-tions, filter realization is predominately implementedwith operational amplifiers, capacitors and resistors.Passive FiltersPassive, low pass filters are realized with resistors andcapacitors. The realization of single and double polelow pass filters are shown in Figure 8.

FIGURE 8: A resistor and capacitor can be used toimplement a passive, low pass analog filter. The inputand output impedance of this type of filterimplementation is equal to R2.The output impedance of a passive low pass filter is rel-atively high when compared to the active filter realiza-tion. For instance, a 1kHz low pass filter which uses a0.1F capacitor in the design would require a 1.59kresistor to complete the implementation. This value ofresistor could create an undesirable voltage drop ormake impedance matching difficult. Consequently,passive filters are typically used to implement a singlepole. Single pole operational amplifier filters have theadded benefit of isolating the high impedance of thefilter from the following circuitry.

(1)

0 fs/2 fs

Ana

log

Out

put (2)

Low Pass Filter

20

0

-20

Gai

n (dB

)

Frequency (Hz)100 1k 10k 100k 1M

VOUTVIN

11+sRC

=

R2VOUTVIN

fc = 1/2p R2C2

C2

20dB/decade

AN699


FIGURE 9: An operational amplifier in combination with two resistors and one capacitor can be used to implement a1st 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, pas-sive filter at the input of a Delta-Sigma A/D Converter.In this case, the high output impedance of the filterdoes not interfere with the conversion process.Active FiltersAn active filter uses a combination of one amplifier, one tothree resistors and one to two capacitors to implement oneor two poles. The active filter offers the advantage of pro-viding isolation between stages. This is possible by tak-ing advantage of the high input impedance and low outputimpedance of the operational amplifier. In all cases, theorder of the filter is determined by the number of capacitorsat the input and in the feedback loop of the amplifier.Single Pole FilterThe 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.Double Pole, Voltage Controlled Voltage SourceThe Double Pole, Voltage Controlled Voltage Source isbetter know as the Sallen-Key filter realization. This fil-ter is configured so the DC gain is positive. In theSallen-Key Filter realization shown in Figure 10, the DCgain is greater than one. In the realization shown inFigure 11, the DC gain is equal to one. In both cases,the order of the filters are equal to two. The poles ofthese filters are determined by the resistive and capac-itive values of R1, R2, C1 and C2.

FIGURE 10: The double pole or Sallen-Key filterimplementation has a gain G = 1 + R4 /R3. If R3 is openand R4 is shorted the DC gain is equal to 1 V/V.

FIGURE 11: The double pole or Sallen-Key filterimplementation with a DC gain is equal to 1V/V.

Gai

n (dB

)

Frequency (Hz)

60

40

20

100 1k 10k 100k 1M

VOUTVIN

1 + R2 / R11+sR2C2

=

R2VOUT

VIN

fc = 1/2pi R2C2

C2

R1

a. Single pole, non-inverting active filter b. Single pole, inverting active filter c. Frequency response of single polenon-inverting active filter

VOUTVIN

R2 / R11+sR2C2

=

R2VOUT

VREF

C2

VIN

1 + R2 / R1

R1

MCP601 MCP601

20dB/decade

R2

VOUT

VIN

C2

R1

R4R3

C1

Sallen-Key

VOUTVIN

K/(R1R2C1C2)s2+s(1/R1C2+1/R2C2+1/R2C1 K/R2C1+1/R1R2C1C2)

=

K = 1 + R4/R3

MCP601

R2

VOUT

VIN

C1

R1 C2

Sallen and Key

MCP601


AN699Double Pole Multiple FeedbackThe double pole, multiple feedback realization of a 2ndorder low pass filter is shown in Figure 12. This filtercan also be identified as simply a Multiple FeedbackFilter. The DC gain of this filter inverts the signal and isequal to the ratio of R1 and R2. The poles are deter-mined by the values of R1, R3, C1, and C2.

FIGURE 12: A double pole, multiple feedback circuitimplementation uses three resistors and two capacitorsto implement a 2nd order analog filter. DC gain is equalto R2 / R1.

ANTI-ALIASING FILTER DESIGN EXAMPLEIn the following examples, the data acquisition systemsignal chain shown in Figure 1 will be modified as fol-lows. The analog signal will go directly into an active lowpass filter. In this example, the bandwidth of interest ofthe analog signal is DC to 1kHz. The low pass filter willbe designed so that high frequency signals from theanalog input do not pass through to the A/D Converterin an attempt to eliminate aliasing errors. The imple-mentation and order of this filter will be modified accord-ing to the design parameters. Excluding the filteringfunction, the anti-aliasing filter will not modify the signalfurther, i.e., implement a gain or invert the signal. Thelow pass filter segment will be followed by a 12-bit SARA/D Converter. The sampling rate of the A/D Converterwill be 20kHz, making 1/2 of Nyquist equal to 10kHz.The ideal signal-to-noise ratio of a 12-bit A/D Converterof 74dB. This design parameter will be used whendetermining the order of the anti-aliasing filter. The filterexamples discussed in this section were generatedusing Microchips FilterLab software.

Three design parameters will be used to implementappropriate anti-aliasing filters:1. Cut-off frequency for filter must be 1kHz or

higher.2. Filter attenuates the signal to -74dB at 10kHz.3. The analog signal will only be filtered and not

gained or inverted.Implementation with Bessel Filter DesignA Bessel Filter design is used in Figure 13 to imple-ment the anti-aliasing filter in the system describedabove. A 5th order filter that has a cut-off frequency of1kHz is required for this implementation. A combinationof two Sallen-Key filters plus a passive low pass filterare designed into the circuit as shown in Figure 14.This filter attenuates the analog input signal 79dB fromthe pass band region to 10kHz. The frequencyresponse of this Bessel, 5th order filter is shown inFigure 13.

FIGURE 13: Frequency response of 5th order Besseldesign implemented in Figure 14.

R3

VOUT

VINR1

C2

R2C1

VOUTVIN

1/R1R3C5C6

s2C2C1 + sC1 (1/R1 + 1/R2 + 1/R3) + 1/(R2R3C2C1)=

MCP601

Frequency (Hz)

Ga

in (d

B)

90

0

-90

-180

-270

-360

-450

-540

-630

-720

10

0

-10

-20

-30

-40

-50

-60

-70

-80

Phas

e (de

grees

)

100 10,0001,000

gain

phase

AN699


FIGURE 14: 5th order Bessel design implemented two Sallen-Key filters and on passive filter. This filter is designed tobe an anti-aliasing filter that has a cut-off frequency of 1kHz and a stop band frequency of ~5kHz.Implementation with Chebyshev DesignWhen a Chebyshev filter design is used to implementthe anti-aliasing filter in the system described above, a3rd order filter is required, as shown Figure 15.

FIGURE 15: 3rd order Chebyshev design implemen-ted using one Sallen-Key filter and one passive filter.This filter is designed to be an anti-aliasing filter that hasa cut-off frequency of 1kHz -4db ripple and a stop bandfrequency of ~5kHz.

Although the order of this filter is less than the Bessel,it has a 4dB ripple in the pass band portion of the fre-quency response. The combination of one Sallen-Keyfilter plus a passive low pass filter is used. This filter isattenuated to -70dB at 10kHz. The frequency responseof this Chebyshev 3rd order filter is shown in Figure 16.

FIGURE 16: Frequency response of 3rd orderChebyshev design implemented in Figure 15.This filter provides less than the ideal 74dB of dynamicrange (AMAX), which should be taken into consider-ation.The difference between -70dB and -74dB attenuationin a 12-bit system will introduce little less than 1/2 LSBerror. This occurs as a result of aliased signals from10kHz to 11.8KHz. Additionally, a 4dB gain error willoccur in the pass band. This is a consequence of theripple response in the pass band, as shown inFigure 16.

VIN

VOUT

MCP601

MCP601

2.94k

33nF

18.2k

4.7nF

10nF

10.5k 1.96k 16.2k

10nF

33F

VOUT

VINMCP601

9.31k 2.15k

68nF

330nF

20k

2.2nF

Frequency (Hz)

Gai

n (dB

)90

0

-90

-180

-270

-360

-450

-540

-630

-720

10

0

-10

-20

-30

-40

-50

-60

-70

-80

Phas

e (d

egre

es)

100 10,0001,000

gain

phase


AN699

FIGURE 17: 4th order Butterworth design implemented two Sallen-Key filters. This filter is designed to be ananti-aliasing filter that has a cut-off frequency of 1kHz and a stop band frequency of ~5kHz.Implementation with Butterworth DesignAs a final alternative, a Butterworth filter design can beused in the filter implementation of the anti-aliasing fil-ter, as shown in Figure 17.For this circuit implementation, a 4th order filter is usedwith a cut-off frequency of 1kHz. Two Sallen-Key filtersare used. This filter attenuates the pass band signal80dB at 10kHz. The frequency response of this Butter-worth 4th order filter is shown in Figure 18.The frequency response of the three filters describedabove along with several other options are summarizedin Table 4.

FIGURE 18: Frequency response of 4th orderButterworth design implemented in Figure 17.

VIN

VOUTMCP601

MCP6012.94k10nF

33nF

26.1k

6.8nF

2.37k 15.4k

100nF

Frequency (Hz)

Gai

n (dB

)

90

0

-90

-180

-270

-360

-450

-540

-630

-720

10

0

-10

-20

-30

-40

-50

-60

-70

-80

Phas

e (de

gree

s)

100 10,0001,000

phase

gain

FILTERORDER,

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 acut-off frequency of 1kHz.

AN699


CONCLUSIONAnalog filtering is a critical portion of the data acquisi-tion system. If an analog filter is not used, signals out-side half of the sampling bandwidth of the A/DConverter are aliased back into the signal path. Once asignal is aliased during the digitalization process, it isimpossible to differentiate between noise with frequen-cies in band and out of band.This application note discusses techniques on how todetermine and implement the appropriate analog filterdesign parameters of an anti-aliasing filter.

REFERENCES Baker, Bonnie, Using Operational Amplifiers for Ana-log Gain in Embedded System Design, AN682, Micro-chip Technologies, Inc.Analog Filter Design, Valkenburg, M. E. Van, OxfordUniversity Press.Active and Passive Analog Filter Design, An Introduc-tion, Huelsman, Lawrence p., McGraw Hill, Inc.


AN699NOTES:

2002 Microchip Technology Inc.

Information contained in this publication regarding deviceapplications and the like is intended through suggestion onlyand may be superseded by updates. It is your responsibility toensure that your application meets with your specifications.No representation or warranty is given and no liability isassumed by Microchip Technology Incorporated with respectto the accuracy or use of such information, or infringement ofpatents or other intellectual property rights arising from suchuse or otherwise. Use of Microchips products as critical com-ponents in life support systems is not authorized except withexpress written approval by Microchip. No licenses are con-veyed, implicitly or otherwise, under any intellectual propertyrights.

Trademarks

The Microchip name and logo, the Microchip logo, FilterLab,KEELOQ, microID, MPLAB, PIC, PICmicro, PICMASTER,PICSTART, PRO MATE, SEEVAL and The Embedded ControlSolutions Company are registered trademarks of Microchip Tech-nology Incorporated in the U.S.A. and other countries.

dsPIC, ECONOMONITOR, FanSense, FlexROM, fuzzyLAB,In-Circuit Serial Programming, ICSP, ICEPIC, microPort,Migratable Memory, MPASM, MPLIB, MPLINK, MPSIM,MXDEV, PICC, PICDEM, PICDEM.net, rfPIC, Select Modeand Total Endurance are trademarks of Microchip TechnologyIncorporated in the U.S.A.

Serialized Quick Turn Programming (SQTP) is a service markof Microchip Technology Incorporated in the U.S.A.

All other trademarks mentioned herein are property of theirrespective companies.

2002, Microchip Technology Incorporated, Printed in theU.S.A., All Rights Reserved.

Printed on recycled paper.

Microchip received QS-9000 quality system certification for its worldwide headquarters, design and wafer fabrication facilities in Chandler and Tempe, Arizona in July 1999. The Companys quality system processes and procedures are QS-9000 compliant for its PICmicro 8-bit MCUs, KEELOQ code hopping devices, Serial EEPROMs and microperipheral products. In addition, Microchips quality system for the design and manufacture of development systems is ISO 9001 certified.

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 knowl-

edge, 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.

2002 Microchip Technology Inc.

MAMERICASCorporate Office2355 West Chandler Blvd.Chandler, AZ 85224-6199Tel: 480-792-7200 Fax: 480-792-7277Technical Support: 480-792-7627Web Address: http://www.microchip.comRocky Mountain2355 West Chandler Blvd.Chandler, AZ 85224-6199Tel: 480-792-7966 Fax: 480-792-7456

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ASIA/PACIFICAustraliaMicrochip Technology Australia Pty LtdSuite 22, 41 Rawson StreetEpping 2121, NSWAustraliaTel: 61-2-9868-6733 Fax: 61-2-9868-6755China - BeijingMicrochip Technology Consulting (Shanghai)Co., Ltd., Beijing Liaison OfficeUnit 915Bei Hai Wan Tai Bldg.No. 6 Chaoyangmen Beidajie Beijing, 100027, No. ChinaTel: 86-10-85282100 Fax: 86-10-85282104China - ChengduMicrochip Technology Consulting (Shanghai)Co., Ltd., Chengdu Liaison OfficeRm. 2401, 24th Floor, Ming Xing Financial TowerNo. 88 TIDU StreetChengdu 610016, ChinaTel: 86-28-6766200 Fax: 86-28-6766599China - FuzhouMicrochip Technology Consulting (Shanghai)Co., Ltd., Fuzhou Liaison OfficeUnit 28F, World Trade PlazaNo. 71 Wusi RoadFuzhou 350001, ChinaTel: 86-591-7503506 Fax: 86-591-7503521China - ShanghaiMicrochip Technology Consulting (Shanghai)Co., Ltd.Room 701, Bldg. BFar East International PlazaNo. 317 Xian Xia RoadShanghai, 200051Tel: 86-21-6275-5700 Fax: 86-21-6275-5060China - ShenzhenMicrochip Technology Consulting (Shanghai)Co., Ltd., Shenzhen Liaison OfficeRm. 1315, 13/F, Shenzhen Kerry Centre,Renminnan LuShenzhen 518001, ChinaTel: 86-755-2350361 Fax: 86-755-2366086Hong KongMicrochip Technology Hongkong Ltd.Unit 901-6, Tower 2, Metroplaza223 Hing Fong RoadKwai Fong, N.T., Hong KongTel: 852-2401-1200 Fax: 852-2401-3431IndiaMicrochip Technology Inc.India Liaison OfficeDivyasree Chambers1 Floor, Wing A (A3/A4)No. 11, OShaugnessey RoadBangalore, 560 025, IndiaTel: 91-80-2290061 Fax: 91-80-2290062

JapanMicrochip Technology Japan K.K.Benex S-1 6F3-18-20, ShinyokohamaKohoku-Ku, Yokohama-shiKanagawa, 222-0033, JapanTel: 81-45-471- 6166 Fax: 81-45-471-6122KoreaMicrochip Technology Korea168-1, Youngbo Bldg. 3 FloorSamsung-Dong, Kangnam-KuSeoul, Korea 135-882Tel: 82-2-554-7200 Fax: 82-2-558-5934SingaporeMicrochip Technology Singapore Pte Ltd.200 Middle Road#07-02 Prime CentreSingapore, 188980Tel: 65-334-8870 Fax: 65-334-8850TaiwanMicrochip Technology Taiwan11F-3, No. 207Tung Hua North RoadTaipei, 105, TaiwanTel: 886-2-2717-7175 Fax: 886-2-2545-0139

EUROPEDenmarkMicrochip Technology Nordic ApSRegus Business CentreLautrup hoj 1-3Ballerup DK-2750 DenmarkTel: 45 4420 9895 Fax: 45 4420 9910FranceMicrochip Technology SARLParc dActivite du Moulin de Massy43 Rue du Saule TrapuBatiment A - ler Etage91300 Massy, FranceTel: 33-1-69-53-63-20 Fax: 33-1-69-30-90-79GermanyMicrochip Technology GmbHGustav-Heinemann Ring 125D-81739 Munich, GermanyTel: 49-89-627-144 0 Fax: 49-89-627-144-44ItalyMicrochip Technology SRLCentro Direzionale Colleoni Palazzo Taurus 1 V. Le Colleoni 120041 Agrate BrianzaMilan, Italy Tel: 39-039-65791-1 Fax: 39-039-6899883United KingdomArizona Microchip Technology Ltd.505 Eskdale RoadWinnersh TriangleWokingham Berkshire, England RG41 5TUTel: 44 118 921 5869 Fax: 44-118 921-5820

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