Measuring Tilt with Silicon Designs Accelerometers

Download the SDI App Note: Measuring Tilt

Sensor Resolution as a Function of Tilt Angle

The resolution of a tilt sensor is the rate of change in voltage output relative to the change in tilt angle:

R = dV/dθ = –g × S × sin(θ)

This means resolution is highest when the angle θ is 90°, i.e. when the sensor’s sensitive axis is perpendicular to gravity (the “zero-G” position). At this position, signal output is at its minimum but resolution is maximized. Conversely, resolution approaches zero when the sensor is parallel to gravity (±1G position), where output is at its peak.

This relationship applies universally to all ±2G accelerometers.

The maximum resolution of a ±2G accelerometer, by definition, is 17.453 mg/degree, occurring when the sensor is perpendicular to the gravity vector.

Understanding Noise in Tilt Measurements

When selecting a tilt sensor, a critical specification parameter for consideration is noise. For example, the noise level specification of the ±2G version of Silicon Designs Model 1521 industrial-grade surface mount MEMS DC accelerometer is:

With this noise specification, a typical noise error for a 1Hz bandwidth measurement would be:

In contrast, if another accelerometer manufacturer’s ±2G sensor has a noise spec of 20ug/root Hz, then the equivalent error would be four times as great, or

In this example, based upon a comparison of the two noise specifications of these ±2G parts, the SDI Model 1521 accelerometer would be three times more accurate for tilt sensing.

Note that by using two sensors mounted perpendicularly, the sensitivity vs angle curve can be flattened. Each sensor will have its own estimate of the angular error. For example, if tilt sensor A is mounted with the sensitive axis in line with the gravity vector, and tilt sensor B is positioned with its sensitive axis perpendicular to gravity, then two separate estimates of theta are provided, one from sensor A and one from sensor B.

If these estimates are combined according to the formula:

Then the combined angular error can be flattened over the actual input error. The chart below shows a simple excel simulation of this. Angular error values for the estimates of theta for tilt sensors A and B are plotted in purple and blue respectively. Note that the error from tilt sensor A is maximum when theta is zero and the sensor is in the +1G position but goes down as the sensor is turned to the zero g position.