What are inertial sensors?

Inertial sensors are used to transduce inertial force into measurable electrical signals to measure an object's acceleration, tilt, and vibration. Micromachining technology has made it possible to produce MEMS (Micro Electromechanical System) inertial sensors using single-crystal silicon sensing elements. These micrometer-sized sensors meet all key system design drivers such as low cost, high performance, high accuracy, and small form factor. Based on the same principles as macroscopic inertial sensors, MEMS inertial sensors can detect the smallest change in the position, orientation and acceleration of an object several meters long using a sensor unit with dimensions as small as a few micrometers.

There are mainly two types of MEMS inertial sensors – accelerometers that measure linear acceleration in one or more axes and gyroscopes that measure angular motion. These sensors are manufactured for use in specific applications, as each application requires inertial sensors with different bandwidth, resolution and dynamic range. For example, the inertial sensor used in the automotive airbag release system must have a bandwidth of up to 0.5 KHz, a resolution of around 500 mG and a dynamic range of around +/-100G. While the inertial sensor used in a space microgravity measuring instrument may have a bandwidth of 0-10 Hz, but must have a resolution as accurate as <1 µG and dynamic range less than +/- 1G.

Inertial sensors are often part of a larger control system in any application or device. Mere information about an object's acceleration or angular motion is useless. The information collected from the inertial sensor is always used to control the movement of the device itself or to activate an actuator, such as opening a car's airbag.

Inertial sensor applications
There was a time when building inertial sensors was expensive and their use was restricted to military and aerospace applications. The development of MEMS inertial sensors has opened up the possibilities and use of inertial sensors in the automotive and various consumer electronics segments.

In the automotive industry, the accelerometer is used for airbag release control, traction control, seat belt control, active suspension, anti-lock braking system (ABS) and vehicle vibration monitoring. While the gyroscope is used for rollover protection, automatic indicators, power steering and to control vehicle dynamics.

In the consumer segment, inertial sensors are used in a variety of applications, such as platform stabilization in video cameras, virtual reality headsets, computer pointing devices, smart toys, and gaming keyboards. All smartphones and tablets nowadays have inertial sensors to detect screen rotation, games and augmented reality applications.

Inertial sensors are also used to monitor the position and orientation of robotic manipulators and unmanned robotic vehicles. In medical applications, these sensors are used to monitor patients with specific conditions, such as to monitor patients with Parkinson's disease. State-of-the-art inertial sensors are used in military and aerospace applications such as smart ammunition, aircraft dynamics control, crash detection, aircraft seat ejection system, and microgravity measurement.

Accelerometers
Accelerometers consist of a mechanical sensing element that can measure acceleration in one or more axes. The sensing element consists of a test mass fixed to a reference by a mechanical suspension system. In MEMS sensors, the test mass is an extremely small seismic mass and the suspension system is constructed from silicon springs.

Top view micrograph of an accelerometer quadrant

The test mass deviates from its stable position whenever the sensor experiences any inertial force due to acceleration. Newton's second law of motion governs this. The deflection of the test mass for acceleration is expressed by a Laplace equation as follows:
x/a = 1/(s ² + b/m + shit*k/m)
Where,
x is the displacement of the test mass,
a is acceleration,
s is the Laplace operator,
b is the damping coefficient,
m is the mass of the test mass,
k is the mechanical spring constant of the suspension system.

The following equation gives the sensor resonance frequency:
_fn = √(k/m)

The following equation provides the quality factor:
Q = √(m*k)/b

The following equation provides the sensor sensitivity (in open loop):
S = m/k

You can see, then, that if the sensitivity increases, the resonant frequency decreases and vice versa. This compensation can be adjusted with a closed loop system. The damping coefficient determines the maximum bandwidth of the accelerometer. In MEMS accelerometers, the damping coefficient is often variable and increases with the displacement of the test mass.

In all types of micromachined accelerometers, the displacement of the test mass is measured by position measurement interfaces, as in a capacitive measurement, there are movable plates attached to the test mass that move along the test mass between fixed capacitive electrodes . There are many types of sensing mechanisms used in accelerometer design. Some of the common detection methods include piezoresistive, capacitive, piezoelectric, optical, and tunneling current.

The accelerometer can have an open loop or closed loop system. If the electrical signals from the position measurement interface are directly used as output signals, it is called an open-loop accelerometer. Most accelerometer sensors are open circuit as they are easy to build. However, open-loop accelerometers have to deal with high tolerances due to the variable spring constant, variable damping coefficient, and nonlinear mass displacements.

In a closed-loop accelerometer, there is a feedback system that applies a feedback force to the test mass proportional to its acceleration, placing the test mass back to its rest position. In this way, nonlinear factors are canceled, sensitivity is dependent on feedback control, and sensor dynamics can be precisely controlled using an electrical signal controller. The test mass can be returned to its resting position using electrostatic, thermal or magnetic actuation. The feedback signal that controls the feedback strength can be analog or digital. All of this adds more complexity to the sensor design.

Acceleration detection methods
There are many ways that accelerometers detect acceleration in a specific axis. Some of the acceleration detection methods are described below:

1. Piezoresistive accelerometers – In this type of accelerometers, the test mass is fixed to a piezoresistor. The resistor is connected to the readout electronic circuit. When there is displacement in the test mass, there is a change in the resistance of the piezoresistor proportional to the applied force. These types of accelerometers are the first to see mass production. The biggest disadvantage of this type of accelerometers is their thermal stability. Peizoresistance can change significantly due to thermal noise and can lead to false outputs.
   

   Example showing the working principle of piezoresistive accelerometers

2. Capacitive accelerometers – In capacitive accelerometers, capacitive sensing fingers are attached to the test mass which move along a given axis with the displacement of the test mass. Each moving plate is placed between two electrodes. When there is an acceleration, the test mass moves in the opposite direction to the direction of movement and the variable plate moves along the test mass. Change in the position of the variable plate along an axis causes change in its distance with fixed electrode plates and causes symmetric change in capacitance. This is then measured as electrical output by an electronic readout system. Capacitive accelerometers are thermally stable, but are prone to electromagnetic interference, where they can provide false outputs due to parasitic capacitance.
   

   Example showing the working principle of capacitive accelerometers

3. Piezoelectric Accelerometers – Most macroscopic accelerometers use piezoelectric materials to detect movement of the test mass. Many micromachined accelerometers also use the same principle. These accelerometers have a large bandwidth, but have an extremely low resonance frequency due to leakage currents. The piezoelectric material produces electrical signals proportional to the displacement of the test mass on a given axis.
   

   Example showing the working principle of piezoelectric accelerometers

4. Tunneling accelerometers – These types of accelerometers use tunneling current to measure the displacement of the test mass. The tunneling current between a sharp tip and an electrode changes exponentially with the tip-electrode distance. The following equation gives the tunneling current:

i = i ₀ * exp(-ᵦ√(φz))

Example showing the working principle of tunneling accelerometers

Where,
I is the tunneling current between the tip and the electrode,
EU ₀ is sizing the current depending on the material used,
ᵦ is the conversion factor,
φ is the height of the tunnel barrier in eV,
and z is the distance from the electrode tip.

5. Resonant Accelerometers – In a resonant accelerometer, the test mass is attached to a resonator. The displacement of the test mass changes the deformation of the resonator and, therefore, its resonant frequency. The change is that the frequency is converted into digital electrical signals using a frequency counter circuit. These accelerometers are quite immune to noise and highly reliable as frequency changes can be converted directly to digital format.
   

   Example showing the working principle of resonant accelerometers

6. Optical accelerometers – These accelerometers use optical fibers and waveguides coupled to the test mass. However, fiber optic type accelerometers are not suitable for batch manufacturing as the fiber needs to be manually installed close to the test mass in the sensor assembly. Another type of optical accelerometers uses LED and PIN photodetectors to measure the displacement of the test mass. Optical accelerometers have the advantage of being free from electrostatic and electromagnetic interference. But because they usually involve complex assembly and readout circuitry, they are not very popular.
   

   Example showing the working principle of optical accelerometers

Gyroscopes

A gyroscope measures the rotation of an object. MEMS gyroscopes use the principle of Coriolis force. When a mass moves in a rotating system, it experiences a force perpendicular to the axis of rotation and the direction of motion. This is called the Coriolis force. A MEMS gyroscope consists of a mechanical structure that resonates due to the Coriolis force and excites secondary oscillation in the same or a secondary structure. The secondary oscillation is proportional to the rotation of the structure on a given axis. The Coriolis force has relatively small amplitude compared to its driving force. This is why all MEMS gyroscopes use a vibrating structure that uses the Coriolis force phenomenon.

Example showing the working principle of the MEMS gyroscope

The vibrating structure consists of a test mass that is connected to an internal structure by a pair of springs. The internal structure is connected to an external structure by another set of orthogonal springs. There are capacitive sensing fingers between the inner frame and outer frame fixed along the orthogonal springs. The Coriolis force is proportional to both the angular speed of the rotating object and the speed of the object toward or away from the axis of rotation. The test mass is continuously actuated in a sinusoidal fashion along the internal springs. When the system experiences rotation, the resonant probe mass experiences the Coriolis force along the orthogonal springs fixed between the inner and outer structure. This changes the distance between the capacitive sensing fingers and thus an electrical signal proportional to the Coriolis force is emitted. As the Coriolis force is proportional to the angular velocity, the electrical signal due to it is also proportional to the angular velocity of the system.