AN-396
a
ONE TECHNOLOGY WAY • P.O. BOX 9106
Understanding Accelerometer Scale Factor and Offset Adjustments
INTRODUCTION
The ADXL50 and ADXL05 accelerometers are small, low
cost, easy to use devices. These modern integrated circuits have an onboard buffer amplifier that allows the
user to change the output scale factor and 0
The output scale factor of an accelerometer is simply
how many volts output are provided per
acceleration. This should not be confused with its resolution. The resolution of the device is the lowest
the accelerometer is capable of measuring. Resolution
is principally determined by the device noise and the
measurement bandwidth.
g
•
by Charles Kitchin
g
bias level.
of applied
g
level
NORWOOD, MASSACHUSETTS 02062-9106
APPLICATION NOTE
C2
ADXL50 OR ADXL05
4 1
0.022µF
C1
0.022µF
C1
COM
PRE-AMP
2
3
5
6
8
REF
V
PR
R1
+3.4V
OUTPUT SCALE FACTOR = ——— x VPR OUTPUT
VPR OUTPUT: ADXL50: 19mV/g, ADXL05: 200mV/
617/329-4700
•
1.8V
BUFFER
AMP
10
V
IN–
R3
R3
R1
+5V
C3
0.1µF
9
V
OUT
g
The 0
g
bias level is simply the dc output level of the
accelerometer when it is not in motion or being acted
upon by the earth’s gravity.
SETTING THE ACCELEROMETER’S SCALE FACTOR
Figure 1 shows the basic connections for using the
onboard buffer amplifier to increase the output scale
factor. The nominal output level in volts from V
preamplifier output) is equal to the
g
forces applied to
PR
(the
the sensor (along its sensitive axis) times the output
scale factor of the accelerometer. The ADXL50 has a preset scale factor of 19 mV/
the ADXL05’s scale factor is 200 mV/
g
at its preamplifier output, VPR;
g
. The use of the
buffer is always recommended, even if the preset scale
factor is adequate, as the buffer helps prevent any following circuitry from loading-down the V
output.
PR
In Figure 1, the output scale factor is simply the output at
V
times the gain of the buffer, which is simply the
PR
value of resistor R3 divided by R1. In all cases, never use
more gain than is needed to provide a convenient scale
factor, as the buffer gain not only amplifies the signal
but any noise or drift as well. Too much gain can
also cause the buffer to saturate and clip the output
waveform.
Figure 1. Basic Buffer Connections
The circuit of Figure 1 is entirely adequate for many applications, but its accuracy is dependent on the
pretrimmed accuracy of the accelerometer, and this will
vary by product type and grade. For the highest possible accuracy, an external trim is recommended. As
shown by Figure 2, this consists of a potentiometer, R1a,
in series with a fixed resistor, R1b.
C2
0.022µF
0.022µF
COM
ADXL50 OR ADXL05
4
C1
2
PRE-AMP
3
C1
5
6
+3.4V
REF
OUTPUT SCALE FACTOR = —————— x VPR OUTPUT
VPR OUTPUT: ADXL50: 19mV/g, ADXL05: 200mV/
8
V
PR
R1a
R1b
R3
(R1a + R1b)
1.8V
10
V
IN–
BUFFER
AMP
g
1
9
R3
0.1µF
V
OUT
+5V
Figure 2. External Scale Factor Trimming
SETTING THE ACCELEROMETER’S 0 g BIAS LEVEL,
AC COUPLED RESPONSE
If a dc (gravity sensing) response is not needed, then the
use of ac coupling between V
and the buffer input is
PR
highly recommended. AC coupling virtually eliminates
any 0
g
drift and allows the maximum buffer gain without clipping. The basic ac coupling circuit is shown in
Figure 3. Resistor R1 and Capacitor C4 together form a
high pass filter whose corner frequency is 1/(2 π R1 C4).
This means that this simple filter will reduce the signal
from V
by 3 dB at the corner frequency and it will con-
PR
tinue to reduce it at a rate of 6 dB/octave (20 dB per
decade) for signals below the corner frequency.
The 0
g
offset level of the ADXL50 and ADXL05 accelerometers is preset at +1.8 V. There are two simple ways
to change this to a more convenient level, such as +2.5 V
which, being at the middle of the supply voltage, provides the greatest output voltage swing.
When using the ac coupled circuit of Figure 3, only a
single resistor, R2, is required to swing the buffer output
to +2.5 V. Since the “+” input of the buffer is referenced
0.022µF
0.022µF
C2
4 1
C1
2
3
C1
5
COM
+3.4V
REF
ADXL50 OR ADXL05
PRE-AMP
6
8 10
V
PR
C4
R1
1.8V
at +1.8 V, its summing junction, Pin 10, is also held constant at +1.8 V. Therefore, to swing the buffer’s output to
the desired +2.5 volt 0
g
bias level, its output must move
up +0.7 V (2.5 V–1.8 V = 0.7 V). Therefore, the current
needed to flow through R3 to cause this change, I
equal to:
Volts
0.7
I
=
R
3
3
in Ohms
R
In order to force this current through R3, the same current needs to flow from Pin 10 to ground through resistor R2. Since Pin 10 is always held at +1.8 V, R2 is equal
to:
Volts
1.8
R
2 =
I
R
3
Therefore, for an ac coupled connection and a +2.5 V 0
output:
V
R2
BUFFER
AMP
IN–
R3
1.8
R
2 =
+5V
C3
0.1µF
V
OUT
2π R1 F
0.7
1
9
BUFFER GAIN = ——
C4 = ————
FOR A +2.5V 0g LEVEL,
IN AN AC COUPLED
CONFIGURATION,
R2 = 2.57 R3
Volts×R
L
Volts
R3
R1
3
= 2.57 ×
R
3
, is
R3
g
ADXL05 RECOMMENDED COMPONENT VALUES
FULL- FACTOR LOW R1 CLOSEST R3 IN kΩ FOR
SCALE IN FREQUENCY IN C4 IN +2.5V 0
RANGE mV/
±2
g
±5
g
±2
g
±5
g
±5
g
SCALE DESIRED R2 VALUE
g
1000 30Hz 49.9 0.10µF 249 640
400 30Hz 127 0.039µF 249 640
1000 3Hz 49.9 1.0µF 249 640
400 1Hz 127 1.5µF 249 640
400 0.1Hz 127 15µF 249 640
LIMIT, F
kΩ VALUE kΩ LEVEL
L
ADXL50 RECOMMENDED COMPONENT VALUES
FULL- FACTOR LOW R1 CLOSEST R3 IN kΩ FOR
SCALE IN FREQUENCY IN C4 IN +2.5V 0
RANGE mV/
±10
g
±20
g
±10
g
±20
g
±10
g
SCALE DESIRED R2 VALUE
g
200 30Hz 24 0.22µF 249 640
100 10Hz 24 0.68µF 127 326
200 3Hz 24 2.2µF 249 640
100 1Hz 24 6.8µF 127 326
200 0.1Hz 24 68µF 249 640
LIMIT, F
kΩ VALUE kΩ LEVEL
L
Figure 3. Typical Component Values for AC Coupled Circuit
–2–
g
g
SETTING THE ACCELEROMETER’S 0 g BIAS LEVEL, DC
COUPLED RESPONSE
When a true dc (gravity) response is needed, the output
from the preamplifier, V
, must be dc coupled to the
PR
buffer input.
With a dc coupled connection, any difference between a
nonideal +1.8 V 0
g
level at VPR and the fixed +1.8 V level
at the buffer’s summing junction will be amplified by the
gain of the buffer. If the 0
g
level only needs to be approximate and the buffer is operated a low gain, a single
fixed resistor, R2, can still be used. But to obtain the
exact 0
put voltage swing from the buffer, the 0
g
output desired or to allow the maximum out-
g
offset will
need to be externally trimmed using the circuit of
Figure 4. Normally, a value of 100 kΩ is typical for R2.
C2
4
0.022µF
C1
2
0.022µF
3
C1
5
COM
+3.4V
REF
50kΩ
ADXL50 OR ADXL05
PRE-AMP
6
V
PR
0
g
LEVEL
TRIM
ADXL05 0g TRIM ONLY,
RECOMMENDED COMPONENT VALUES FOR
VARIOUS OUTPUT SCALE FACTORS
FULL mV R1 R3
SCALE PER
±1
g
±2
g
±4
g
±5
g
g
2000 30.1 301
1000 40.2 200
500 40.2 100ߜ
400 49.9 100
kΩ kΩ
1.8V
BUFFER
AMP
8
R1
R1a
100kΩ
R2
10
R1b
OPTIONAL SCALE
FACTOR TRIM
V
IN–
1
9
R3
+5V
0.1µF
V
OUT
R3
SF = ——
R1
R1 ≥ 20kΩ
ADXL05 WITH 0g AND SF TRIMS
FULL mV R1a R1b R3
SCALE PER
±1
g
±2
g
±4
g
±5
g
g
2000 10 24.9 301
1000 10 35.7 200
500 10 35.7 100
400 10 45.3 100
kΩ kΩ kΩ
RECOMMENDED COMPONENT VALUES FOR
ADXL50 0g TRIM ONLY,
VARIOUS OUTPUT SCALE FACTORS
FULL mV R1 R3
SCALE PER
±10
g
±20
g
±40
g
±50
g
g
200 23.7 249
100 26.1 137
50 39.2 105
40 49.9 105
kΩ kΩ
Figure 4. Typical Component Values for Circuit with External 0 g or 0 g and Scale Factor Timing
–3–
ADXL50 WITH 0g AND SF TRIMS
FULL mV R1a R1b R3
SCALE PER
±10
g
±20
g
±40
g
±50
g
g
200 5 21.5 249
100 5 23.7 137
50 10 34.0 105
40 10 45.3 105
kΩ kΩ kΩ
Increasing its resistance above this value makes trimming the offset easier, but may not provide enough trim
range to set V
equal to +2.5 V for all devices.
OUT
The buffer’s maximum output swing should be limited
to ± 2 volts, which provides a safety margin of ±0.25 volts
before clipping. With a +2.5 volt 0
g
level, the maximum
gain the buffer should be set to (R3/R1) equals:
2
Volts
Output Scale Factor at V
Times the Max
PR
Applied Acceleration ings
Note that the value of R1 should be kept as large as possible, 20 kΩ or greater, to avoid loading down the V
output.
The device scale factor and 0 g offset levels can be calibrated using the earth’s gravity as explained in the
ADXL50 and ADXL05 data sheets.
PR
E2009–9–5/95
–4–
PRINTED IN U.S.A.
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