a ONE TECHNOLOGY WAY * P.O. AN-374 APPLICATION NOTE BOX 9106 * NORWOOD, MASSACHUSETTS 02062-9106 * 617/329-4700 Using Accelerometers in Low g Applications by Charles Kitchin INTRODUCTION Accelerometers can be used in a wide variety of low g applications such as tilt and orientation, vibration analysis, motion detection, etc. This application note explains how to best apply the ADXL50 (50 g) and ADXL05 (5 g) accelerometers when measuring signals at the low end of their respective full-scale ranges. Although each accelerometer is specified according to its full scale (clipping) g level, the limiting resolution of the device, i.e., its minimum discernible input level, is extremely important when measuring low g accelerations. The limiting resolution is predominantly set by the measurement noise "floor" which includes the ambient background noise and the noise of the accelerometer itself. The level of the noise floor varies directly with the bandwidth of the measurement. As the measurement bandwidth is reduced, the noise floor drops, improving the signal-to-noise ratio of the measurement and its limiting resolution. DEVICE BANDWIDTH VS. MEASUREMENT RESOLUTION The output noise of the ADXL50 and ADXL05 scales with the square root of the measurement bandwidth. The maximum amplitude of the noise, its peak-to-peak value, approximately defines the worst-case resolution of a measurement. The peak-to-peak noise is approximately equal to 6.6 times its rms value (for an average uncertainty of 0.1%). The bandwidth of the accelerometer can be easily reduced by adding low-pass or bandpass filtering. Figure 1 shows the noise vs. bandwidth characteristics of the ADXL50 and ADXL05 devices. As shown by the figure, device noise drops dramatically as the operating bandwidth is reduced. For example, when operated in a 1 kHz bandwidth, the ADXL05 typically has a peak-to-peak noise level of 130 mg. With 5 g applied accelerations, this 130 mg resolution limit is normally quite satisfactory; but for ADXL50 NOISE LEVEL - rms 150mg 15mg 1g 100mg ADXL05 1.5mg 10mg 150g 10 100 3dB BANDWIDTH - Hz Figure 1. Noise Level vs. 3 dB Bandwidth 1mg 1k NOISE LEVEL - Peak to Peak 10g 1.5g 0 g offset trimming, and output scaling. Two tables are included with the figure which provide practical component values for various full-scale g levels and approximate circuit bandwidths. For bandwidths other than those listed, use the formula: smaller acceleration levels the noise is now a much greater percentage of the signal. As shown by Figure 1, when the device bandwidth is rolled off to 100 Hz, the peak-to-peak noise level is reduced to approximately 40 mg, and at 10 Hz it is down to 10 mg. Alternatively, the signal-to-noise ratio may be improved considerably by using a microprocessor to perform multiple measurements and then compute the average signal level. When using this technique, the signal level will be increased directly with the number of measurements while the noise will only increase by their square root. For example, with 100 measurements, the signal-tonoise ratio will be increased by a factor of 10 (20 dB). Capacitor C4 (Farads ) = 2 x R3 () x 3 dB BW (Hz) or simply scale the value of capacitor C4 accordingly, i.e., for an application with a 50 Hz bandwidth, the value of C4 will need to be twice as large as its 100 Hz value. If further noise reduction is needed while maintaining the maximum possible bandwidth, then a 2- or 3-pole post filter is recommended. These provide a much steeper roll-off of noise above the pole frequency. Figure 3 shows a circuit that uses the buffer amplifier to provide 2-pole post filtering. Component values for the 2-pole filter were selected to operate the buffer at unity gain. Low-Pass Filtering The bandwidth of either accelerometer can be reduced by providing post filtering. Figure 2 shows how the buffer amplifier can be connected to provide 1-pole post filtering, C2 1 4 +5V 1 0.022F ADXL50 OR ADXL05 1.8V C1 0.1F BUFFER AMP PRE-AMP 2 0.022F 9 C1 VOUT 3 5 COM 6 10 8 VPR +3.4V REF VIN- R1a R1b R3 OPTIONAL SCALE FACTOR TRIM* C4 R2 0g LEVEL 50k TRIM *TO OMIT THE OPTIONAL SCALE FACTOR TRIM , REPLACE R1a AND R1b WITH A FIXED VALUE 1% METAL FILM RESISTOR. SEE VALUES SPECIFIED IN TABLES BELOW. ADXL50 COMPONENT VALUES FOR VARIOUS FULL-SCALE RANGES AND BANDWIDTHS ADXL05 COMPONENT VALUES FOR VARIOUS FULL-SCALE RANGES AND BANDWIDTHS FULL SCALE mV per g 3dB BW (Hz) R1a k R1b k R3 k R2 k C4 F FULL SCALE mV per g 3dB BW (Hz) R1a k R1b k R3 k R2 k C4 F 10 g 200 100 5 21.5 249 100 0.0068 1 g 2000 10 10 24.9 301 100 0.056 20 g 100 100 5 23.7 137 100 0.01 2 g 1000 100 10 35.7 200 100 0.0082 10 g 200 10 5 21.5 249 100 0.068 4 g 500 200 10 35.7 100 100 0.0082 20 g 100 10 5 23.7 137 100 0.01 5g 400 300 10 45.3 100 100 0.0056 1 3dB BW = 2 R3 C4 1 3dB BW = 2 R3 C4 Figure 2. Using the Buffer Amplifier to Provide 1-Pole Post Filtering Plus Scale Factor and 0 g Level Trimming -2- pickup from ac line voltage. This can be minimized by physically moving the device away from power leads, or if that is not practical, using proper shielding and grounding techniques. In most cases, it is advisable to ground the cable's shield at only one end and connect a separate common lead between the circuits; this will help to prevent ground loops. Also, if the accelerometer is inside or near a metal enclosure, this should be grounded as well. Capacitors C3 and C4 were chosen to provide 3 dB bandwidths of 10 Hz, 30 Hz, 100 Hz, and 300 Hz. In this configuration, the nominal buffer amplifier output will be +1.8 V the scale factor of the accelerometer, either 19 mV/g for the ADXL50 or 200 mV/g for the ADXL05. An AD820 external op amp allows noninteractive adjustment of 0 g offset and scale factor. The external op amp offsets and scales the output to provide a +2.5 V 2 V output over a wide range of fullscale g levels. Another area to consider is mechanical resonance of the overall measurement system. The use of a highly flexible shielded wire will greatly help to prevent secondary resonance effects of wire vibrating at its natural frequency. A shielded cable with a silicone jacket and silicone insulation such as that produced by Cooner Wire Company of Chatsworth, California, is recommended. Additional Noise Reduction Techniques In addition to reducing circuit noise, any electromagnetic interference (EMI) needs to be considered. Shielded wire should be used for connecting the accelerometer to any equipment or circuitry that is more than a few inches away. A common problem is that of 60 Hz OPTIONAL CAPACITOR FOR 3-POLE FILTERING 1.8V PRE-AMP ADXL50 OR ADXL05 BUFFER AMP R5 VOUT 9 +5V 6 VPR VREF 10 8 VIN - 0.01F R5 42.2k C4 R4a R4b 2 R1 82.5k C3 R3 82.5k 2-POLE FILTER +3.4V 2-POLE FILTER COMPONENT VALUES 3dB BW (Hz) C3F C4F 300 0.027 0.0033 100 0.082 0.01 30 0.27 0.033 10 0.82 0.1 20k R7 71.5k 0g LEVEL TRIM R4a k R4b k R5 k 200 200 10 g 10.53 5 21.5 249 100 20 g 5.26 5 23.7 137 R4b k R5 k 1 g 2000 10.00 10 24.9 301 2 g 1000 4.98 10 35.7 2.00 OFFSET AND SCALING AMPLIFIER GAIN R4a k 400 4 MAX INPUT GAIN 5g 3 6 SCALE FACTOR IN mV/g mV per g 2.50 OUTPUT AD820 ADXL50 OFFSET AND SCALING AMPLIFIER COMPONENT VALUES FULL SCALE 500 7 R6 40.2k ADXL05 OFFSET AND SCALING AMPLIFIER COMPONENT VALUES 4 g SCALE FACTOR TRIM 10 35.7 100 10 45.3 100 Figure 3. Two-Pole Filtering Circuit with Gain and 0 g Offset Adjustment -3- Other methods for 0 g drift compensation include using a low cost temperature sensor such as the AD590 to supply a microprocessor with the device temperature. If the drift curve of the accelerometer is stored in the P, then a software program can be used to subtract out the drift. This method works well, removing both the linear and nonlinear components of the drift. But due to device-to-device variation, it requires that the drift curve of each individual accelerometer be known (or measured). Alternatively, various drift compensation circuits can be used to subtract out the linear portion of the accelerometer's drift by using a temperature sensor and op amp to supply a small compensation current. This hardware approach does not use a P but does require calibrating the compensation circuitry for each device. For more details on software and hardware drift compensation, refer to application note AN-380. OFFSET DRIFT CONSIDERATIONS When using an accelerometer with a dc (gravity sensing) response, the 0 g offset level will exhibit some temperature drift. When the accelerometer must measure low g levels over wide temperature ranges, the 0 g drift can become large in proportion to the signal amplitude. If a dc response is truly needed, there are a number of design options available. One very straightforward approach is to use a low cost crystal oven to maintain the accelerometer at a constant temperature. These ovens are particularly useful in high accuracy tilt applications. After the circuit has been built and is operating correctly, the crystal oven can be mounted over the accelerometer and powered off the same +5 V power supply. Figure 4 shows the basic circuit. The ovens may be purchased from Isotemp Research, Inc., P.O. Box 3389, Charlottesville, VA 22903, phone 804-2953101. For more details on crystal oven compensation, refer to application note AN-385. C2 ADXL50 OR ADXL05 4 0.022 F +5V 1 1.8V C1 C3 0.1F ISOTEMP M050570 BUFFER AMP PRE-AMP 2 0.022F 9 VOUT VOUT 3 +5V C1 VPR 1 +VDC 5 2 COM 6 +3.4V REF 8 10 VIN- VPR R1 3 0VDC R3 0g OUTPUT - +2.5V 3dB Bw - 1Hz CF FS MEASUREMENT RANGE* OUTPUT SENSITIVITY BUFFER GAIN R1 R3 ADXL50 10 g 100mV/g 5.26 26.1k 137k 1F ADXL05 2 g 500mV/g 2.50 40.2k 100k 1.5F DEVICE CF *FS RANGE NUMBERS ARE CONSERVATIVE TO ALLOW FOR VPR 0g TOLERANCE. Figure 4. Low g DC Coupled (Tilt) Circuit Using Crystal Oven Compensation -4- NC AC Coupling If a dc (gravity) response is not required--for example in motion sensing or vibration measurement applications--ac coupling can be used between the preamplifier output and the buffer input as shown in Figure 5. NORMALIZED OUTPUT LEVEL - dB 20 Because ac coupling removes the dc component of the output, the preamp output signal may be amplified considerably without increasing the 0 g level drift. If capacitor C5 is added to the ac coupling circuit, forming a 1-pole low-pass filter, then a bandpass function is provided that will attenuate any signals other than those within the pass band. A typical ac coupled frequency response is shown in Figure 6. LOW FREQUENCY ROLL-OFF ( FL ) 0 -10 HIGH FREQUENCY ROLL-OFF ( FH ) -20 -30 0.1 The low frequency roll-off, FL, due to the ac coupling network is: FL = 10 1 10 FREQUENCY - Hz 100 1k Figure 6. Typical Output vs. Frequency Curve when AC Coupling VPR to the Buffer 1 2 R1 C 4 Note that capacitor C4 should be a nonpolarized, low leakage type. If a polarized capacitor is used, tantalum types are preferred, rather than electrolytic. With polarized capacitors, VPR should be measured on each device and the positive terminal of the capacitor connected toward either VPR or VIN--whichever is more positive. In this case, the high frequency roll-off, FH, is determined by the 1-pole post filter R3, C5. If ac coupling is used, the self-test feature must be monitored at VPR, rather than at the buffer output (since the self test output is a dc voltage). ADXL50 OR ADXL05 COMPONENT VALUES ARE APPROXIMATE. FOR MAXIMUM ACCURACY, SCALE FACTOR TRIMMING SHOULD BE EMPLOYED. 1.8V BUFFER AMP PRE-AMP VPR VOUT 9 10 8 VPR VIN- R1 R3 C4 R2 C5 ADXL50 SCALE FACTOR IN mV/g DESIRED LOW FREQUENCY LIMIT, FL R1 VALUE IN k CLOSEST C4 VALUE DESIRED HIGH FREQUENCY LIMIT, FH R3 IN k 200 30 24 0.22F 300 249 0.002F 640k 100 10 24 0.68F 300 127 0.0039F 326k 200 3 24 2.2F 100 249 0.0068F 640k 100 1 24 6.8F 100 127 0.01F 326k 200 0.1 24 68F 10 249 0.068F 640k DESIRED HIGH FREQUENCY LIMIT, FH R3 IN k CLOSEST C5 VALUE VALUE OF R2 FOR +2.5V 0g LEVEL ADXL05 SCALE FACTOR IN mV/g DESIRED LOW FREQUENCY LIMIT, FL R1 VALUE IN k 1000 30 49.9 0.10F 300 249 0.002F 640k 200 30 249 0.022F 300 249 0.002F 640k 1000 3 49.9 1.0F 100 249 0.0068F 640k 200 1 249 0.68F 100 249 0.0068F 640k 200 0.1 249 6.8F 10 249 0.068F 640k CLOSEST C4 VALUE CLOSEST C5 VALUE VALUE OF R2 FOR +2.5V 0g LEVEL Figure 5. AC Coupling the VPR Output to the Buffer Input -5- GAIN SELECTION ISSUES The uncommitted amplifier incorporated into the ADXL50 and ADXL05 devices allows the user to readily set the scale factor to the desired voltage output per g of applied acceleration. However, some caution is advised in not setting the scale factor, too high as the output buffer could run out of "headroom," i.e., the buffer's output can go as low as 0.25 volts and as high as 4.75 volts. This means the buffer's maximum output swing is +2.5 V 2.25 V. If the gain is too high, the buffer can clip on periodic transient accelerations; or it can clip due to the fact that the 0 g offset drift is also amplified along with the signal. 0g (a) 0g (b) -1g (c) +1g (d) E2007-9-3/95 INDICATED POLARITY IS THAT OCCURING AT VPR Therefore, use only enough gain in the buffer as is necessary to override any transmission losses between the accelerometer and any following circuitry (i.e., to keep the system's signal to noise ratio high). Figure 7. Using the Earth's Gravity to Calibrate the ADXL50 and ADXL05 Accelerometers If the optional scale factor trimmer, R1a, is to be used, it should be adjusted next. The package axis should be oriented as in "c" (pointing down) and the output reading noted. The package axis should then be rotated 180 to position "d" and R1a adjusted so that the output voltage indicates a change of 2 gs in acceleration. For example, if the circuit scale factor at the buffer output is 200 mV per g, then the scale factor trim should be adjusted so that an output change of 400 mV is indicated. Using the Earth's Gravity to Calibrate the Accelerometer Both the 0 g offset and scale factor of the ADXL50 and ADXL05 devices may be roughly calibrated by using the 1 g (average) acceleration of the Earth's gravity. Figure 7 shows how gravity and package orientation affect the output polarity. Note that the output polarity is that which appears at VPR; the output at VOUT will have the opposite sign (due to the buffer amplifier's inverting configuration). With its axis of sensitivity in the vertical plane, the accelerometer should register a 1 g acceleration, either positive or negative, depending on orientation. With the axis of sensitivity in the horizontal plane, no acceleration (0 g) should be indicated. Adjusting the circuit's scale factor will have some effect on its 0 g level, so this should be readjusted, as before, but this time checked in both positions "a" and "b." If there is a difference in the 0 g reading, a compromise should be selected so that the reading in each direction is equal distant from +2.5 V. Scale factor and 0 g offset adjustments should be repeated until both are correct. Calibrate the accelerometer by placing it on its side with its axis of sensitivity oriented as shown in "a." The 0 g offset potentiometer, RT, (as shown in Figure 2) is then roughly adjusted for midscale: +2.5 V at the buffer output. PRINTED IN U.S.A. APPLICATIONS ASSISTANCE For applications assistance contact Charles Kitchin, Accelerometer Applications, Analog Devices Semiconductor, 831 Woburn St., Wilmington, MA 01887. Phone: 617-937-1665. -6-