Force-balance accelerometers

Fig. 16 without the capacitor C represents the circuit of a force-balance accelerometer (FBA), a device that is widely used for earthquake strong-motion recording, for measuring tilt, and for inertial navigation.

By equating the inertial and the electromagnetic force, it is easily seen that the responsivity (the output voltage per ground acceleration) is

$$U_{out}/\ddot x = M R / E$$ (37)

where M is the seismic mass, R the total resistance of the feedback path, and E the responsivity of the forcer (in N/A). The conversion is determined by only three passive components of which the mass is error-free by definition (it defines the inertial reference), the resistor is a nearly ideal component, and the force transducer can be very precise because the motion is small. Some accelerometers don't have a built-in feedback resistor; the user can insert a resistor of his own choice and thus select the gain. The responsivity in terms of current per acceleration is then simply $I_{out}/\ddot x=M/E$.

FBAs work down to zero frequency but the servo loop becomes uneffective at some upper corner frequency f₀ (usually a few hundred to a few thousand Hz), above which the arrangement acts like an ordinary inertial displacement sensor. The feedback loop behaves like an additional stiff spring; the response of the FBA sensor corresponds to that of a mechanical pendulum with the free period f₀, as it is schematically represented in the left panels of Fig. 6.