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10 / 15 page –10– ADXL150/ADXL250 REV. 0 DEVICE BANDWIDTH VS. MEASUREMENT RESOLUTION Although an accelerometer is usually specified according to its full-scale g level, the limiting resolution of the device, i.e., its minimum discernible input level, is extremely important when measuring low g accelerations. 3dB BANDWIDTH – Hz 100m g 1m g 10m g 10 1k 100 660m g 66m g 6.6m g Figure 19. ADXL150/ADXL250 Noise Level vs. 3 dB Bandwidth (Using a “Brickwall” Filter) The limiting resolution is predominantly set by the measure- ment noise “floor,” which includes the ambient background noise and the noise of the ADXL150/ADXL250 itself. The level of the noise floor varies directly with the bandwidth of the mea- surement. As the measurement bandwidth is reduced, the noise floor drops, improving the signal-to-noise ratio of the measure- ment and increasing its resolution. The bandwidth of the accelerometer can be easily reduced by adding low-pass or bandpass filtering. Figure 19 shows the typical noise vs. bandwidth characteristic of the ADXL150/ ADXL250. The output noise of the ADXL150/ADXL250 scales with the square root of the measurement bandwidth. With a single pole roll-off, the equivalent rms noise bandwidth is π divided by 2 or approximately 1.6 times the 3 dB bandwidth. For example, the typical rms noise of the ADXL150 using a 100 Hz one pole post filter is: Noise rms ()=1mg/ Hz × 100 1.6 ()=12.25mg Because the ADXL150/ADXL250’s noise is, for all practical purposes, Gaussian in amplitude distribution, the highest noise amplitudes have the smallest (yet nonzero) probability. Peak- to-peak noise is therefore difficult to measure and can only be estimated due to its statistical nature. Table I is useful for esti- mating the probabilities of exceeding various peak values, given the rms value. Table I. Nominal Peak-to- % of Time that Noise Will Exceed Peak Value Nominal Peak-to-Peak Value 2.0 × rms 32% 4.0 × rms 4.6% 6.0 × rms 0.27% 6.6 × rms 0.1% 8.0 × rms 0.006% RMS and peak-to-peak noise (for 0.1% uncertainty) for various bandwidths are estimated in Figure 19. 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 ADXL150/ADXL250 typically have an rms noise level of 32 mg. When the device bandwidth is rolled off to 100 Hz, the noise level is reduced to approximately 10 mg. Alternatively, the signal-to-noise ratio may be improved consid- erably by using a microprocessor to perform multiple measure- ments and then to compute the average signal level. Low-Pass Filtering The bandwidth of the accelerometer can easily be reduced by using post filtering. Figure 20 shows how the buffer amplifier can be connected to provide 1-pole post filtering, zero g offset trimming, and output scaling. The table provides practical component values Cf R2 1M +VS RT 200k 0 g TRIM SCALE FACTOR TRIM (OPTIONAL) R3 100k +VS 0.1 F R1a 75k VOUT 0.1 F +VS 2 SELF-TEST 25k 5k ADXL150 GAIN AMP OFFSET NULL COM C1 0.1 F BUFFER AMP DEMODULATOR SENSOR +VS TP (DO NOT CONNECT) 14 9 10 7 5 CLOCK OP196 3 4 6 2 8 7 +VS 2 R1b 50k EXT AMP GAIN R3 VALUE F.S. RANGE DESIRED OUTPUT SCALE FACTOR Cf ( F) 100Hz Cf ( F) 30Hz Cf ( F) 10Hz 0.0082 0.0056 0.0033 0.0015 0.027 0.022 0.010 0.0056 0.082 0.056 0.033 0.015 76mV/ g 25 g 2.0 200k 100mV/ g 20 g 2.6 261k 200mV/ g 10 g 5.3 536k 400mV/ g 5 g 10.5 1M Figure 20. One-Pole Post Filter Circuit with SF and Zero g Offset Trims |
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