MEMS Gyroscope

How a MEMS gyroscope works

A classical gyroscope keeps a heavy wheel spinning and watches how it resists being turned. A MEMS gyroscope has no wheel and nothing that rotates continuously. Instead it exploits a different consequence of rotation: the Coriolis force. The trick is to give the device its own internal velocity by vibrating a small silicon mass — the proof mass — back and forth along a fixed line. As long as that mass is moving and the whole chip is being rotated, the laws of mechanics demand a sideways force, and the size of that sideways force tells you how fast you are rotating.

The device runs two mechanical modes at once. The drive mode is a deliberate oscillation: comb-shaped electrostatic actuators push and pull the proof mass along the drive axis (call it x) at the structure's resonant frequency, building up a large, clean velocity. The sense mode is an orthogonal direction (call it y) that is normally still. When the package rotates about the third axis (z), the Coriolis force appears along y, in proportion to the drive velocity and the rotation rate. The mass starts oscillating along y too, and a separate set of capacitive comb fingers measures that motion.

The chain of cause and effect is therefore: electrostatic drive → resonant velocity along x → rotation Ω about z → Coriolis force along y → tiny sense oscillation along y → capacitance change → amplified, demodulated voltage → rate output. Crucially the sense motion is in phase with the drive velocity, which lets the electronics use synchronous demodulation to dig the real signal out from far larger noise and error terms.

Coriolis force on the proof mass (vector form):

  F_c = -2 m (Ω × v)

  m  = proof-mass value (~10⁻⁹ to 10⁻⁷ kg)
  Ω  = angular rate of the chip (rad/s)        ← what we want
  v  = drive velocity of the mass (m/s)

For drive along x and rotation about z, the force is along y:

  F_c,y = 2 m Ω_z v_x

If the drive motion is x = X·sin(ω_d t), then v_x = X ω_d cos(ω_d t), so:

  F_c,y = 2 m Ω_z X ω_d cos(ω_d t)

→ a y-force that oscillates at the drive frequency ω_d,
  with amplitude proportional to the rotation rate Ω_z.

The governing equation: amplifying a sub-atomic deflection

The sense mass is a damped, driven harmonic oscillator. Its steady-state displacement amplitude depends on how close the sense resonant frequency ω_s sits to the drive frequency ω_d, and on the mechanical quality factor Q_s:

Sense displacement amplitude:

  y₀ = (2 Ω_z X ω_d) / √[ (ω_s² − ω_d²)² + (ω_d ω_s / Q_s)² ]

Two design philosophies:

  Mode-MATCHED   (ω_s ≈ ω_d):  y₀ ≈ 2 Ω_z X Q_s / ω_d
                 → multiplied by Q_s (thousands) — huge gain, but
                   narrow bandwidth and tight temperature control needed.

  Mode-SPLIT     (ω_s ≠ ω_d):  y₀ ≈ 2 Ω_z X ω_d / (ω_s² − ω_d²)
                 → lower gain, but flat response and robust to drift.
                   This is what most consumer parts ship.

Scale factor (volts or LSB per °/s) is set by y₀ and the
capacitive pickoff sensitivity ∂C/∂y.

Put numbers to it. A typical part drives the mass to X ≈ 5 µm at ω_d = 2π·20 kHz. For a rotation rate of just 1 °/s (0.0175 rad/s), the mode-split sense amplitude works out to the order of a few picometres — roughly one-hundredth the diameter of a silicon atom. The pickoff converts this into a capacitance change of a few attofarads (10⁻¹⁸ F) across the sense combs. That such a vanishingly small motion becomes a clean digital number is the entire engineering achievement: resonant drive concentrates energy at one frequency, the high-Q structure multiplies the response, and lock-in demodulation rejects everything that is not at the drive frequency and in phase with the drive velocity.

Reading attofarads: the comb-drive pickoff

Both the drive actuator and the sense pickoff use interdigitated combs — interlocking sets of silicon fingers, one set fixed to the substrate and one set on the moving mass. Applying a voltage across the drive combs creates an electrostatic force that pulls the mass; this is how energy is pumped into the drive mode each cycle. On the sense side, the geometry is arranged so motion changes the overlap or gap of parallel-plate capacitors, and a differential pair of capacitors lets the electronics subtract out common-mode effects.

Differential capacitance for a parallel-plate sense gap g moving by y:

  C₊ = ε A / (g − y)        C₋ = ε A / (g + y)

  ΔC = C₊ − C₋ ≈ (2 ε A / g²) · y      (for y ≪ g)

The sense interface is a charge amplifier / lock-in:
  charge amp → bandpass at ω_d → multiply by drive-velocity
  reference (cos ω_d t) → low-pass → output ∝ Ω_z.

A dedicated quadrature reference (sin ω_d t) demodulates the
90°-out-of-phase leakage so it can be measured and nulled.

Because the raw sense signal is buried under a much larger quadrature term (drive motion that leaks into the sense axis through imperfect etch geometry), the phase of the demodulation matters enormously. The real Coriolis signal tracks the drive velocity; the quadrature error tracks the drive position, exactly 90° away. Synchronous demodulation against the velocity reference passes the rate and rejects the leakage. Any phase error in that reference, however, mixes some quadrature back into the output as a bias — which is why phase-locked loops and automatic-gain-control loops wrap around the drive oscillator to hold both its frequency and its phase rock-steady over temperature.

Real-world parts and specs

Part / class	Axes	Full-scale range	Bias instability	Typical home
Consumer IMU (e.g. phone-class 6-axis)	3 gyro + 3 accel	±2000 °/s	~10 °/h	Phones, earbuds, game controllers
Drone / robotics IMU	3 + 3	±2000 °/s	3 to 8 °/h	Flight controllers, gimbals, robots
Automotive rate sensor (AEC-Q100)	1 to 3	±300 °/s	2 to 10 °/h	ESC, rollover detect, navigation dead-reckoning
Industrial / tactical-grade MEMS	1 to 3	±450 °/s	0.3 to 3 °/h	Platform stabilization, survey, AHRS
High-end MEMS (quartz / closed-loop)	1 to 3	±200 °/s	0.05 to 0.5 °/h	Guidance, north-finding, GNSS-denied nav
Reference: ring-laser / fiber-optic gyro (not MEMS)	1	varies	0.001 to 0.01 °/h	Aircraft & submarine inertial nav

The numbers that matter most are bias instability (the floor of slow bias wander, quoted in °/h) and angle random walk (ARW, the integrated white noise, quoted in °/√h). A consumer gyro might post 10 °/h bias instability and 0.5 °/√h ARW; a tactical-grade MEMS pushes both down by one to two orders of magnitude. Unit economics drive the split: a 6-axis consumer IMU costs roughly US$1 to US$3 in volume, an automotive-qualified part US$3 to US$10, and a tactical-grade MEMS hundreds of dollars — while the optical gyros that beat them all on drift cost thousands and don't fit on a chip.

MEMS gyroscope vs other rotation sensors

	MEMS vibratory gyro	Spinning-rotor gyro	Ring-laser gyro (RLG)	Fiber-optic gyro (FOG)
Physical principle	Coriolis force on a resonator	Conservation of angular momentum	Sagnac effect (counter-rotating light)	Sagnac effect (light in fiber coil)
Moving parts	Vibrating silicon, no rotation	High-speed spinning wheel + gimbals	None (dithered)	None
Bias instability	0.05 to 20 °/h	0.01 to 1 °/h	0.001 to 0.01 °/h	0.001 to 0.05 °/h
Size	mm-scale die	Fist-sized assembly	~10 cm ring	Coil + optics box
Cost	US$1 to a few hundred	Thousands	Tens of thousands	Thousands to tens of thousands
Warm-up / startup	Milliseconds	Seconds to minutes (spin-up)	Seconds	Sub-second
Shock / vibration tolerance	Very high (no bearings)	Low (bearing wear)	High	Very high
Typical home	Phones, drones, cars	Legacy aircraft, museums	Airliners, ships	Missiles, AUVs, survey

Design tradeoffs and architecture choices

• Mode-matched vs mode-split. Matching the sense resonance to the drive frequency multiplies sensitivity by the sense quality factor Q_s — a gain of thousands — but collapses the bandwidth and makes the scale factor brutally sensitive to temperature, since the resonant frequencies drift apart by tens of ppm/°C. Mode-split designs sacrifice raw gain for a flat, robust response and are the default for consumer parts; high-end devices mode-match and then add closed-loop force-feedback and active frequency tuning to tame the temperature problem.
• Tuning-fork (anti-phase) topology. Driving two proof masses 180° out of phase makes the device differential: real rotation drives them in opposite sense directions (the signals add when subtracted), while linear shock drives them together (common mode cancels). This buys huge rejection of the engine and motor vibration that would otherwise swamp the picometre-scale signal, and it balances momentum so little energy leaks into the package, keeping Q high.
• Open-loop vs closed-loop (force-rebalance) sense. Open-loop reads the free sense deflection — simple and cheap. Closed-loop applies an electrostatic counter-force to hold the sense mass nearly still and measures the force needed; this linearizes the scale factor, widens bandwidth, and improves stability at the cost of more electronics. Tactical-grade MEMS are almost always closed-loop.
• Vacuum packaging. The drive Q (and, if mode-matched, the sense Q) depends on gas damping, so the resonator is sealed in a getter-pumped cavity at sub-millibar pressure. A slow vacuum leak over years raises damping, lowers Q, and degrades the scale factor — a real long-term reliability concern.
• Quadrature cancellation. Manufacturing asymmetry leaks drive motion into the sense axis at a level often hundreds of times the true signal. Designers add dedicated quadrature-nulling electrodes that apply an electrostatic torque to cancel the leakage, and rely on phase-accurate demodulation to reject what remains.

Where MEMS gyroscopes are used

• Phones and tablets. Optical and electronic image stabilization, screen-rotation, AR/VR head tracking, and pedestrian dead reckoning when GPS drops out indoors. Fused with the accelerometer and magnetometer in a 6- or 9-axis IMU.
• Drones and gimbals. The flight controller integrates gyro rate to hold attitude at hundreds of hertz; the camera gimbal uses its own gyro to counter-rotate brushless motors and keep the horizon level.
• Automotive. Yaw-rate sensors feed electronic stability control (ESC) — comparing commanded steering to actual yaw to brake individual wheels — plus rollover detection for curtain airbags and dead-reckoning navigation through tunnels.
• Game controllers and wearables. Motion-aiming, gesture recognition, and step/activity tracking.
• Industrial and defense. Antenna and platform stabilization, GNSS-denied navigation for UAVs and munitions, north-finding gyrocompasses, and structural-health and machine-condition monitoring.

Common misconceptions and pitfalls

• "The gyro tells me which way I'm pointing." No — it tells you how fast you are turning (rate, °/s). Heading is the time-integral of rate, and any bias in the rate integrates into a heading error that grows without bound. Treating the gyro as an absolute orientation sensor is the single most common beginner mistake; it must be fused with an accelerometer/magnetometer.
• "Calibrate it once at the factory and you're done." Bias drifts with temperature (often tens of °/h across the automotive −40 to +85 °C range) and changes slightly every power-up (turn-on-to-turn-on bias repeatability). Good systems re-zero the bias whenever the device is detected to be stationary.
• "Vibration doesn't matter — it averages out." Vibration near the drive frequency is the gyro's worst enemy. A resonant disturbance can couple straight into the sense axis or even modulate the drive, producing a false rate. This is why drone IMUs are vibration-isolated on soft mounts and why the tuning-fork common-mode rejection is so prized.
• "Higher Q is always better." High Q boosts sensitivity but narrows bandwidth and lengthens the ring-down time, so a high-Q mode-matched gyro reacts sluggishly to fast rate changes and needs tight temperature control. There is no free lunch — Q trades against bandwidth and robustness.
• "It's a tiny version of the spinning gyroscope in a museum." Mechanically unrelated. The museum gyroscope works by angular-momentum conservation and gimbal precession; the MEMS device has no net angular momentum and no continuous rotation — it senses the Coriolis force on a linear vibration. They share only the name and the job.
• "More g-force will damage it like a spinning gyro." The opposite: with no bearings and a stiff silicon structure, MEMS gyros survive thousands of g of shock, which is exactly why they replaced spinning-rotor units in launch vehicles and munitions.