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Accelerometer
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An accelerometer is a device that measures acceleration.
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The measurement of acceleration relies on classical Newton’s mechanics.
𝐹 = 𝑚𝑎 = −𝑘𝑥, 𝒂(𝒕) = −(𝒌⁄𝒎)𝒙(𝒕)
Fundamental equation of accelerometers
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Some form of damping is required, otherwise the system would oscillate at its natural
frequency for any input signal.
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Accelerometer characteristics
1. Sensitivity is the ratio of an electrical output to the mechanical input.
[volts per unit of acceleration] V/g, The sensitivity is typically measured at a single
Reference frequency of a sine-wave shape. fref: 100Hz for USA and 160Hz for Europe
2. Frequency response is the outputs signal over a range of frequencies where the sensor
should be operating.
3. Resonant frequency in an undamped sensor shows as a clearly defined peak that can be
3~4 dB higher than the response at the reference frequency.
4. Zero stimulus output is specified for the position of the sensor where its sensitive
(active) axis is perpendicular to Earth’s gravity. That is, in the sensors that have a DC
component in the output signal, the gravitational effect should be eliminated before the
output as no mechanical input is determined.
5. Linearity of the accelerometer is specified over the dynamic range of the input signals.
ME 568
Page 2 of 5
1. Capacitive accelerometers
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A capacitive acceleration sensor essentially contains at least two components, where the
first is a “stationary” plate (i.e., connected to the housing) and the other is a plate attached
to the inertial mass, which is free to move inside the housing. These plates form a
capacitor whose value is function of a distance d between the plates.
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An internal mass is sandwiched between the upper cap and the base.
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C1: a parallel capacitor between the mass and the cap electrode
C2: a parallel capacitor between the mass and the base electrode
C0: a parallel capacitor at rest
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When the mass moves toward the upper plate, d1 can be reduced by an amount Δ and
d2 increases by Δ.
𝛥 = 𝐹𝑚 ⁄𝑘 , 𝐹𝑚 : 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒
𝑉𝑠𝑒𝑛𝑠𝑒 ⁄𝑉0 = 𝛥𝐶 ⁄𝐶0 (by capacitance to voltage converter)
ME 568