a
Understanding Accelerometer Scale Factor and Offset Adjustments
by Charles Kitchin
AN-396
APPLICATION NOTE
ONE TECHNOLOGY WAY
•
P.O. BOX 9106
•
NORWOOD, MASSACHUSETTS 02062-9106
•
617/329-4700
INTRODUCTION
The ADXL50 and ADXL05 accelerometers are small, low
cost, easy to use devices. These modern integrated cir-
cuits have an onboard buffer amplifier that allows the
user to change the output scale factor and 0
g
bias level.
The output scale factor of an accelerometer is simply
how many volts output are provided per
g
of applied
acceleration. This should not be confused with its reso-
lution. The resolution of the device is the lowest
g
level
the accelerometer is capable of measuring. Resolution
is principally determined by the device noise and the
measurement bandwidth.
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 VPR (the
preamplifier output) is equal to the
g
forces applied to
the sensor (along its sensitive axis) times the output
scale factor of the accelerometer. The ADXL50 has a pre-
set scale factor of 19 mV/
g
at its preamplifier output, VPR;
the ADXL05’s scale factor is 200 mV/
g
. The use of the
buffer is always recommended, even if the preset scale
factor is adequate, as the buffer helps prevent any fol-
lowing circuitry from loading-down the VPR output.
In Figure 1, the output scale factor is simply the output at
VPR times the gain of the buffer, which is simply the
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.
BUFFER
AMP
ADXL50 OR ADXL05
PRE-AMP
0.022µF
C1
C1
0.022µF
C2
COM
C3
0.1µF
+5V
V
OUT
V
IN–
V
PR
REF
+3.4V R3
1.8V
R1
2
3
4 1
5
6
9
810
OUTPUT SCALE FACTOR = ——— x V
PR
OUTPUT
R3
R1
V
PR
OUTPUT: ADXL50: 19mV/
g
, ADXL05: 200mV/
g
Figure 1. Basic Buffer Connections
The circuit of Figure 1 is entirely adequate for many ap-
plications, but its accuracy is dependent on the
pretrimmed accuracy of the accelerometer, and this will
vary by product type and grade. For the highest pos-
sible accuracy, an external trim is recommended. As
shown by Figure 2, this consists of a potentiometer, R1a,
in series with a fixed resistor, R1b.
BUFFER
AMP
ADXL50 OR ADXL05
PRE-AMP
0.022µF
C1
C1
0.022µF
C2
COM
0.1µF
+5V
V
OUT
V
IN–
V
PR
REF
+3.4V R1b R3
1.8V
R1a
2
3
41
5
6
9
810
OUTPUT SCALE FACT OR = —————— x V
PR
OUTPUT
R3
(R1a + R1b)
V
PR
OUTPUT: ADXL50: 19mV/
g
, ADXL05: 200mV/
g
Figure 2. External Scale Factor Trimming
–2–
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 VPR and the buffer input is
highly recommended. AC coupling virtually eliminates
any 0
g
drift and allows the maximum buffer gain with-
out 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 VPR by 3 dB at the corner frequency and it will con-
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 acceler-
ometers 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, pro-
vides 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
at +1.8 V, its summing junction, Pin 10, is also held con-
stant 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, IR3, is
equal to:
I
R
3=0.7
Volts
R
3
in Ohms
In order to force this current through R3, the same cur-
rent needs to flow from Pin 10 to ground through resis-
tor R2. Since Pin 10 is always held at +1.8 V, R2 is equal
to:
R
2=1.8
Volts
I
R
3
Therefore, for an ac coupled connection and a +2.5 V 0
g
output:
R
2=1.8
Volts
×
R
3
0.7
Volts
=2.57 ×
R
3
BUFFER
AMP
ADXL50 OR ADXL05
PRE-AMP
0.022µF
C1
C1
0.022µF
C2
COM
C3
0.1µF
+5V
V
OUT
V
IN–
V
PR
REF
+3.4V
R2
R3
1.8V
C4 R1
2
3
4 1
5
6
9
810 BUFFER GAIN = ——
R3
R1
C4 = ————
1
2π R1 F
L
FOR A +2.5V 0
g
LEVEL,
IN AN AC COUPLED
CONFIGURATION,
R2 = 2.57 R3
ADXL05 RECOMMENDED COMPONENT VALUES
SCALE DESIRED R2 VALUE
FULL- FACTOR LOW R1 CLOSEST R3 IN kΩ FOR
SCALE IN FREQUENCY IN C4 IN +2.5V 0
g
RANGE mV/
g
LIMIT, FLkΩVALUE kΩLEVEL
±2
g
1000 30Hz 49.9 0.10µF 249 640
±5
g
400 30Hz 127 0.039µF 249 640
±2
g
1000 3Hz 49.9 1.0µF 249 640
±5
g
400 1Hz 127 1.5µF 249 640
±5
g
400 0.1Hz 127 15µF 249 640
ADXL50 RECOMMENDED COMPONENT VALUES
SCALE DESIRED R2 VALUE
FULL- FACTOR LOW R1 CLOSEST R3 IN kΩ FOR
SCALE IN FREQUENCY IN C4 IN +2.5V 0
g
RANGE mV/
g
LIMIT, FLkΩVALUE kΩLEVEL
±10
g
200 30Hz 24 0.22µF 249 640
±20
g
100 10Hz 24 0.68µF 127 326
±10
g
200 3Hz 24 2.2µF 249 640
±20
g
100 1Hz 24 6.8µF 127 326
±10
g
200 0.1Hz 24 68µF 249 640
Figure 3. Typical Component Values for AC Coupled Circuit
–3–
SETTING THE ACCELEROMETER’S 0
g
BIAS LEVEL, DC
COUPLED RESPONSE
When a true dc (gravity) response is needed, the output
from the preamplifier, VPR, must be dc coupled to the
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 ap-
proximate and the buffer is operated a low gain, a single
fixed resistor, R2, can still be used. But to obtain the
exact 0
g
output desired or to allow the maximum out-
put voltage swing from the buffer, the 0
g
offset will
need to be externally trimmed using the circuit of
Figure 4. Normally, a value of 100 kΩ is typical for R2.
OPTIONAL SCALE
FACTOR TRIM
BUFFER
AMP
ADXL50 OR ADXL05
PRE-AMP
0.022µF
C1
C1
0.022µF
C2
COM
0.1µF
+5V
V
OUT
V
IN–
V
PR
REF
+3.4V
50kΩ
R1b
R2
R3
0
g
LEVEL
TRIM
1.8V
R1a
2
3
41
5
6
9
810
R1
100kΩ
SF = ——
R1 ≥ 20kΩ
R3
R1
ADXL05 0
g
TRIM ONLY,
RECOMMENDED COMPONENT VALUES FOR
VARIOUS OUTPUT SCALE FACTORS
FULL mV R1 R3
SCALE PER
g
kΩkΩ
±1
g
2000 30.1 301
±2
g
1000 40.2 200
±4
g
500 40.2 100ߜ
±5
g
400 49.9 100
ADXL50 0
g
TRIM ONLY,
RECOMMENDED COMPONENT VALUES FOR
VARIOUS OUTPUT SCALE FACTORS
FULL mV R1 R3
SCALE PER
g
kΩkΩ
±10
g
200 23.7 249
±20
g
100 26.1 137
±40
g
50 39.2 105
±50
g
40 49.9 105
ADXL05 WITH 0
g
AND SF TRIMS
FULL mV R1a R1b R3
SCALE PER
g
kΩkΩkΩ
±1
g
2000 10 24.9 301
±2
g
1000 10 35.7 200
±4
g
500 10 35.7 100
±5
g
400 10 45.3 100
ADXL50 WITH 0
g
AND SF TRIMS
FULL mV R1a R1b R3
SCALE PER
g
kΩkΩkΩ
±10
g
200 5 21.5 249
±20
g
100 5 23.7 137
±40
g
50 10 34.0 105
±50
g
40 10 45.3 105
Figure 4. Typical Component Values for Circuit with External 0 g or 0 g and Scale Factor Timing
–4–
PRINTED IN U.S.A. E2009–9–5/95
Increasing its resistance above this value makes trim-
ming the offset easier, but may not provide enough trim
range to set VOUT equal to +2.5 V for all devices.
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
PR
Times the Max
Applied Acceleration in gs
Note that the value of R1 should be kept as large as pos-
sible, 20 kΩ or greater, to avoid loading down the VPR
output.
The device scale factor and 0
g
offset levels can be cali-
brated using the earth’s gravity as explained in the
ADXL50 and ADXL05 data sheets.
