# Do MEMS accelerometers have a lower frequency limit?

Being a higher level programmer by education I have no deeper knowledge of electronics and electromechanics, so feel no obligation to answer this.

I'm wondering about MEMS accelerometers. I heard a claim from a coworker the other day that MEMS accelerometers have a lower limit to what acceleration frequencies they can pick up.

Due to the ODR, (Output Data Rate), we have a finite rate at which we receive distinct samples of the measured accelerometer waveform. Usually (or always?), these accelerometers also employ some sort of lowpass-filter. Thus, we have an upper limit of what wave-frequencies we can reconstruct with the data gathered (due to the Nyquist theorem, at most half of the ODR.) This is known.

But is there any lower limit to what frequencies the accelerometer can pick up, at least to an extent that we can isolate and/or reconstruct it?

Intuitively, my best guess is that it can pick up arbitrarily low frequencies, as long as we have a sufficiently high ODR, and there are detectable forces acting on the accelerometer, - I mean, it can pick up static "forces" such as gravity, so why not low or really low frequencies as well?

• It would be good to check the datasheets of any few MEMS accelerometer products. As you said, if an accelerometer can pick up gravity, it means the device works up to 0 Hz.
– AJN
Commented Dec 1, 2020 at 13:07
• Yes, this is what I have done. But I can't find anything that would relate to a lower limit of detectable frequencies. Intuitively I'm pretty sure there is no such thing. The argument itself feels as ridiculous as claiming an ordinary car has a lower limit to speed (which in practice is just stupid). But I'm no expert in signal theory or microelectronics, and I wish to drive the hypothesis with no preconceptions! :) Commented Dec 1, 2020 at 13:19
• Think about their common usage for phone screen orientation. Does your phone flip back after a few seconds? No. That said there often is hysteresis in the software interpretation, and sometimes the overall decision algorithm can yield undesirable behavior if you're at a less than definite angle with the phone mostly laying flat, but that's not the sensor but rather the way the software is reacting to an unclear reality. Commented Dec 1, 2020 at 16:35
• And do quadcopter drones slowly capsize and crash? No. Actually they react to perturbations with rate gyros feeding the rotation-nulling loop, but use MEMS accelerometers (where fitted) in an outer loop to seek a level orientation as the one at which their rotation is nulled. Commented Dec 1, 2020 at 16:38
• The issue is that at low frequencies, an acceleration that is high enough to measure with reasonable accuracy implies a large amplitude of motion. As a numerical example, since any accelerometer may be measuring +/-1g under static conditions, let's assume that acceleration changes of 0.1g can be measured accurately enough to be useful. At a frequency of 1Hz, that means a vibration amplitude of about 5mm peak-to-peak. At 0.1Hz, it means 0.5m peak-to-peak. Whether those amplitudes are physically realistic depends on the system you are measuring. Commented Dec 1, 2020 at 22:25

Capacitive MEMS (yours, probably) and piezo-resistive accelerometers have a DC-response and are almost always DC-coupled, so they can measure down to 0 Hz without problems.

Piezo-electric accelerometers, however, are almost always AC-coupled and can't go below a few Hz, and can't measure static acceleration.

There is no lower limit to the frequency response of the acceleration to output transfer function. As the other answers have said, they detect orientation, which means detecting gravity all the way down to DC.

However, be aware that all accelerometers, regardless of technology, suffer from the velocity to acceleration transfer function falling by 6dB per octave towards DC, and the position to acceleration transfer function falling by 12dB/octave, as the shaking frequency decreases. At lower frequencies, the same acceleration is going to correspond to larger amplitudes and higher velocities, so it will certainly seem like the sensitivity falls towards DC.

• You may want to elaborate on your second paragraph to make it more clear. What you're saying basically is that very slow velocity / position changes result in very little g's (per-second changes are small), thus get buried in the noise. Commented Dec 1, 2020 at 15:30

From what I recall, some accelerometers use 4_leg capacitive bridges, etched out of the top silicon layers to provide tiny suspended masses that respond to changes in force.

Because capacitance measurements have no lower limits (using AC_stimuli to detect bridge imbalance), you should be able to sense down to DC.

Such a lower limit would not make much sense and would render the device unusable for detecting the orientation.

A MEMS accelerometer will (typically) output the acceleration from Earth's gravity when it's resting. You will see this as "-1" or "+1" in the Z or Y axis, depending on its definition. This would not work if it could not detect frequencies all they way down to 0 Hz.

I've looked at datasheets for accelerometers before, and checked a couple just now to be sure.

I don't remember seeing a lower limit for detection frequencies - the spot check confirms this.

As you said, they can detect the "static" gravity of the Earth, so there's no reason they couldn't detect an abitrarily low frequency as well.

That's not to say that they couldn't have a really wild looking frequency response that has some really bad dips between "0" and the Nyquist limit - it's just that I've never seen one that has any kind of frequency response chart. That leaves the assumption that they are pretty flat (frequency response wise) from 0 to the Nyquist limit.

A piezo accelerometer yes, but a MEMS one only if they build it that way for some reason.