Inertial sensors

An inertial sensor comprising:

• a substantially planar, rotationally symmetric proof mass mounted to a fixed substrate by a plurality of flexible support legs so as to be laterally moveable in a first in-plane sensing direction in response to an applied linear acceleration in said first sensing direction and to be laterally moveable in a second in-plane sensing direction in response to an applied linear acceleration in said second sensing direction, said second sensing direction being offset from the first sensing direction by a non-zero acute angle;
• four pairs of electrodes arranged around the proof mass such that each electrode within a pair is diametrically opposite the other electrode in said pair, wherein a first pair of electrodes is substantially aligned with the first sensing direction, a second pair of electrodes is substantially aligned with the second sensing direction, a third pair of electrodes is substantially aligned perpendicular to the first pair of electrodes and a fourth pair of electrodes is substantially aligned perpendicular to the second pair of electrodes;
• a capacitive pick-off circuit connected to the proof mass, the pick-off circuit being arranged to provide a sensing signal dependent on any applied linear acceleration and/or angular rate;
• and
• an electrical drive circuit connected to the four pairs of electrodes, wherein the drive circuit is arranged to:
• apply first in-phase and anti-phase pulse width modulation (PWM) drive signals with a first frequency to the first and third electrode pairs, such that one electrode in each pair is provided with in-phase PWM drive signals and the other electrode in each pair is provided with anti-phase PWM drive signals;
• and
• apply second in-phase and anti-phase PWM drive signals with a second frequency, different to the first frequency, to the second and fourth electrode pairs, such that one electrode in each pair is provided with in-phase PWM drive signals and the other electrode in each pair is provided with anti-phase PWM drive signals;
• wherein the first and second in-phase and anti-phase PWM drive signals are modulated such that the drive signals applied to the first and second electrode pairs are modulated with an in-phase resonance signal at a resonant frequency of the proof mass and the third and fourth electrode pairs are modulated with a quadrature resonance signal at the resonant frequency of the proof mass such that the in-phase and quadrature resonance signals cause the proof mass to oscillate in-plane in a cos 2θ mode of vibration.