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to the force of gravity, ie, parallel to the earth s surface Figure 1565 shows that the change in projection of a 1 g gravity-induced acceleration vector on the axis of sensitivity of the accelerometer will be more signi cant if the axis is tilted 10 degrees from the horizontal than if it is tilted by the same amount from the vertical
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Axis of sensitivity 1g
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Axis of sensitivity
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Figure 1565 Tilt sensitivity
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However, the car may not always be level when the alarm is activated, and while the zero g offset can be recalibrated for any initial inclination, effectively the farther from the horizontal the axes of sensitivity are, the less sensitive the system will be to tilt (see ADXL202 datasheet) In most cases, this should not be of great concern, since the sensitivity only declines by about 25 mg per degree of tilt when inclination goes from zero (horizontal) to thirty degrees of tilt Nevertheless, installation guidelines should recommend that the tilt sensing module containing the accelerometer be mounted such that the axes of sensitivity be as level as possible Implementation In general we are interested in knowing if the inclination of the car has changed more than 5 degrees from its inclination when initially parked When the car is turned off, a measurement of the car s inclination is made If the car s inclination is changed by more than 5 degrees, an alarm is triggered Alternatively, the rate of change of tilt may be evaluated and if its absolute value is above 02 degrees per second for several seconds the alarm may be triggered Each technique has certain advantages The former algorithm is better at false alarm rejection due to jostling of the car, while the rate of change algorithm may be set up to react more quickly Algorithms using a combination of both techniques may be used as well It is left to the reader to decide which technique is best for their application While all of the concepts presented here are valid for both algorithms, for consistency this application note will describe the former (absolute inclination) algorithm For the purpose of the following discussion, we will assume a less than perfect tilt sensitivity for the accelerometer of 15 mg per degree of tilt, or 75 mg for 5 degrees The ADXL202 will be set up to have a bandwidth of 200 Hz so that vibration may be detected A 200 Hz bandwidth will result in
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a noise oor of: Noise = 500 g Hz ( 200 15) rms Noise = 85 mg rms or 34 mg peak-to-peak of noise (using a peak-to-peak to rms ratio of 4:1), well within our 75 mg requirement For reliability purposes, we would like to have a noise oor about 10 times lower than this, or around 8 mg Since towing a car takes at least a few seconds, we are free to narrow the bandwidth to lower the noise oor An analog or digital low pass lter may be used, but since low pass ltering in the digital domain is very simple, it is the preferred method By taking the average of 16 samples we reduce the effective bandwidth to 125 Hz (200 Hz/16 samples) The resulting noise performance is approximately 87 mg peak-to-peak, close enough to our target Lowering the noise oor even further, by taking up to 128 samples for example, would result in about 3 mg peak-to-peak of noise, which would allow us to easily detect the 15 mg of static acceleration resulting from a change in tilt of less than a degree The typical zero g drift due to temperature for the ADXL202 is 2 mg/ C Since our trigger point for a tilt alarm could be as low as 15 mg, it is conceivable that temperature drift alone would cause a false alarm (a car parked overnight could easily experience more than 75 C in ambient temperature change) Therefore we will include a differentiator to reject temperature drift In the event of the car being jacked up or lifted for towing, we would expect the rate of change in tilt to be faster than ve degrees or 75 mg per minute (or 125 mg per second) Each time the acceleration is measured it is compared to the previous reading If the change is less than 125 mg per second we know that the change in accelerometer output is due to temperature drift We can now add an auto-zero block that adjusts our zero g reference (that is the static acceleration sensed when the car was initially parked) to compensate for zero g drift due to temperature Shock Sensing Generally for automotive shock/vibration sensing we are interested in signals between 10 and 200 Hz Since the response of the ADXL202 extends from DC to 5 kHz, a band pass lter will have to be added to remove out of band signals This band pass lter is most easily implemented in the analog domain (Figure 1566 shows a simple 10 Hz high pass lter) When coupled with the 200 Hz low pass lter (from X lt and Y lt on the ADXL202), a 10 to 200 Hz bandpass lter is realized
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