a ONE TECHNOLOGY WAY * P.O. AN-396 APPLICATION NOTE BOX 9106 * NORWOOD, * 617/329-4700 MASSACHUSETTS 02062-9106 Understanding Accelerometer Scale Factor and Offset Adjustments by Charles Kitchin 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 g bias level. C2 ADXL50 OR ADXL05 4 C1 1 +5V 1.8V 0.022F C3 0.1F BUFFER AMP PRE-AMP 2 0.022F 9 VOUT 3 C1 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 resolution. 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 preset 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 following 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. 5 COM 6 +3.4V REF 10 8 VPR VIN- R1 R3 R3 OUTPUT SCALE FACTOR = ------ x VPR OUTPUT R1 VPR OUTPUT: ADXL50: 19mV/g , ADXL05: 200mV/g 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 ADXL50 OR ADXL05 4 1 +5V 1.8V 0.022F 0.1F BUFFER AMP C1 2 PRE-AMP 0.022F 9 VOUT 3 C1 5 COM 6 +3.4V REF 10 8 VPR VIN- R1a R1b R3 R3 OUTPUT SCALE FACTOR = ------------ x VPR OUTPUT (R1a + R1b) VPR OUTPUT: ADXL50: 19mV/g, ADXL05: 200mV/g 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 VPR and the buffer input is 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 R1 C4). This means that this simple filter will reduce the signal from V PR by 3 dB at the corner frequency and it will continue to reduce it at a rate of 6 dB/octave (20 dB per decade) for signals below the corner frequency. 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, IR3, is equal to: IR 3 = 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: 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. R2 = 1 1.8 Volts x R 3 0.7 Volts +5V 1.8V 0.022F C1 R2 = ADXL50 OR ADXL05 4 1.8 Volts IR 3 Therefore, for an ac coupled connection and a +2.5 V 0 g output: 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 C2 0.7 Volts R 3 in Ohms PRE-AMP 2 C3 0.1F BUFFER AMP 0.022F 9 VOUT 3 C1 5 COM 6 +3.4V REF 8 VPR R3 BUFFER GAIN = ---- R1 10 C4 R1 VIN- R3 1 C4 = -------- 2 R1 F L FOR A +2.5V 0 g LEVEL, IN AN AC COUPLED CONFIGURATION, R2 = 2.57 R3 R2 ADXL05 RECOMMENDED COMPONENT VALUES FULLSCALE RANGE 2g 5g 2g 5g 5g SCALE FACTOR IN mV/g 1000 400 1000 400 400 DESIRED LOW FREQUENCY LIMIT, FL 30Hz 30Hz 3Hz 1Hz 0.1Hz R1 IN k 49.9 127 49.9 127 127 CLOSEST C4 VALUE 0.10F 0.039F 1.0F 1.5F 15F R3 IN k 249 249 249 249 249 R2 VALUE IN k FOR +2.5V 0g LEVEL 640 640 640 640 640 ADXL50 RECOMMENDED COMPONENT VALUES FULLSCALE RANGE 10g 20g 10g 20g 10g SCALE FACTOR IN mV/g 200 100 200 100 200 DESIRED LOW FREQUENCY LIMIT, FL 30Hz 10Hz 3Hz 1Hz 0.1Hz R1 IN k 24 24 24 24 24 CLOSEST C4 VALUE 0.22F 0.68F 2.2F 6.8F 68F R3 IN k 249 127 249 127 249 R2 VALUE IN k FOR +2.5V 0g LEVEL 640 326 640 326 640 Figure 3. Typical Component Values for AC Coupled Circuit -2- = 2.57 x R 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. 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 g output desired or to allow the maximum output 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 k is typical for R2. 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 C2 ADXL50 OR ADXL05 4 +5V 1 1.8V 0.022F 0.1F BUFFER AMP C1 2 PRE-AMP 0.022F 9 VOUT 3 C1 5 COM 6 +3.4V REF 8 VPR 10 R1 VIN- R1a 100k 50k 0g LEVEL TRIM R1b R3 OPTIONAL SCALE FACTOR TRIM R2 R3 SF = ---- R1 R1 20k ADXL05 0g TRIM ONLY, RECOMMENDED COMPONENT VALUES FOR VARIOUS OUTPUT SCALE FACTORS FULL SCALE 1g 2g 4g 5g mV PER g 2000 1000 500 400 R1 k 30.1 40.2 40.2 49.9 ADXL05 WITH 0g AND SF TRIMS R3 k 301 200 100oe 100 FULL SCALE 1g 2g 4g 5g ADXL50 0g TRIM ONLY, RECOMMENDED COMPONENT VALUES FOR VARIOUS OUTPUT SCALE FACTORS FULL SCALE 10g 20g 40g 50g mV PER g 200 100 50 40 R1 k 23.7 26.1 39.2 49.9 mV PER g 2000 1000 500 400 R1a k 10 10 10 10 R1b k 24.9 35.7 35.7 45.3 R3 k 301 200 100 100 ADXL50 WITH 0g AND SF TRIMS R3 k 249 137 105 105 FULL SCALE 10g 20g 40g 50g mV PER g 200 100 50 40 R1a k 5 5 10 10 R1b k 21.5 23.7 34.0 45.3 Figure 4. Typical Component Values for Circuit with External 0 g or 0 g and Scale Factor Timing -3- R3 k 249 137 105 105 Increasing its resistance above this value makes trimming the offset easier, but may not provide enough trim range to set VOUT equal to +2.5 V for all devices. Note that the value of R1 should be kept as large as possible, 20 k or greater, to avoid loading down the VPR output. 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: 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. E2009-9-5/95 2 Volts PRINTED IN U.S.A. Output Scale Factor at VPR Times the Max Applied Acceleration in gs -4-