ADXL202/ADXL210
initial offset. The easiest way to null this offset is with a calibra-
tion factor saved on the microcontroller or by a user calibration
for zero
g.
In the case where the offset is calibrated during manu-
facture, there are several options, including external EEPROM
and microcontrollers with “one-time programmable” features.
DESIGN TRADE-OFFS FOR SELECTING FILTER
CHARACTERISTICS: THE NOISE/BW TRADE-OFF
Table IV gives typical noise output of the ADXL202/ADXL210
for various C
X
and C
Y
values.
Table IV. Filter Capacitor Selection, C
X
and C
Y
Bandwidth
10 Hz
50 Hz
100 Hz
200 Hz
500 Hz
C
X
, C
Y
0.47
µF
0.10
µF
0.05
µF
0.027
µF
0.01
µF
rms Noise
1.9 mg
4.3 mg
6.1 mg
8.7 mg
13.7 mg
Peak-to-Peak Noise
Estimate 95%
Probability (rms 4)
7.6 mg
17.2 mg
24.4 mg
35.8 mg
54.8 mg
The accelerometer bandwidth selected will determine the mea-
surement resolution (smallest detectable acceleration). Filtering
can be used to lower the noise floor and improve the resolution
of the accelerometer. Resolution is dependent on both the ana-
log filter bandwidth at X
FILT
and Y
FILT
and on the speed of the
microcontroller counter.
The analog output of the ADXL202/ADXL210 has a typical
bandwidth of 5 kHz, much higher than the duty cycle stage is
capable of converting. The user must filter the signal at this
point to limit aliasing errors. To minimize DCM errors the
analog bandwidth should be less than 1/10 the DCM frequency.
Analog bandwidth may be increased to up to 1/2 the DCM
frequency in many applications. This will result in greater dy-
namic error generated at the DCM.
The analog bandwidth may be further decreased to reduce noise
and improve resolution. The ADXL202/ADXL210 noise has
the characteristics of white Gaussian noise that contributes
equally at all frequencies and is described in terms of
µg
per root
Hz; i.e., the noise is proportional to the square root of the band-
width of the accelerometer. It is recommended that the user limit
bandwidth to the lowest frequency needed by the application, to
maximize the resolution and dynamic range of the accelerometer.
With the single pole roll-off characteristic, the typical noise of
the ADXL202/ADXL210 is determined by the following equation:
Noise rms
=
500
µg
/
Hz
×
BW
×
1.5
At 100 Hz the noise will be:
Noise rms
=
500
µg
/
Hz
×
100
×
(1.5)
=
6.12 mg
Often the peak value of the noise is desired. Peak-to-peak noise
can only be estimated by statistical methods. Table III is useful
for estimating the probabilities of exceeding various peak values,
given the rms value.
Table III. Estimation of Peak-to-Peak Noise
CHOOSING T2 AND COUNTER FREQUENCY: DESIGN
TRADE-OFFS
The noise level is one determinant of accelerometer resolution.
The second relates to the measurement resolution of the
counter when decoding the duty cycle output.
The ADXL202/ADXL210’s duty cycle converter has a resolu-
tion of approximately 14 bits; better resolution than the acceler-
ometer itself. The actual resolution of the acceleration signal is,
however, limited by the time resolution of the counting devices
used to decode the duty cycle. The faster the counter clock, the
higher the resolution of the duty cycle and the shorter the T2
period can be for a given resolution. The following table shows
some of the trade-offs. It is important to note that this is the
resolution due to the microprocessors’s counter. It is probable
that the accelerometer’s noise floor may set the lower limit on
the resolution, as discussed in the previous section.
Table V. Trade-Offs Between Microcontroller Counter Rate,
T2 Period and Resolution of Duty Cycle Modulator
ADXL202/
ADXL210
R
SET
Sample
T2 (ms) (k ) Rate
1.0
1.0
1.0
5.0
5.0
5.0
10.0
10.0
10.0
124
124
124
625
625
625
1250
1250
1250
1000
1000
1000
200
200
200
100
100
100
Counter-
Clock
Counts
Rate
per T2 Counts Resolution
(MHz)
Cycle
per
g
(mg)
2.0
1.0
0.5
2.0
1.0
0.5
2.0
1.0
0.5
2000
1000
500
10000
5000
2500
20000
10000
5000
250
125
62.5
1250
625
312.5
2500
1250
625
4.0
8.0
16.0
0.8
1.6
3.2
0.4
0.8
1.6
( )
( )
Nominal Peak-to-Peak
Value
2.0
×
rms
4.0
×
rms
6.0
×
rms
8.0
×
rms
% of Time that Noise
Will Exceed Nominal
Peak-to-Peak Value
32%
4.6%
0.27%
0.006%
The peak-to-peak noise value will give the best estimate of the
uncertainty in a single measurement.
–8–
REV. B
AD [ ANALOG DEVICES ]
