# Accelerometer

## Summary

### Introduction

One of the most common inertial sensors is the accelerometer, a dynamic sensor capable of a vast range of sensing. Accelerometers are available that can measure acceleration in one, two, or three orthogonal axes. They are typically used in one of three modes:

• As an inertial measurement of velocity and position;
• As a sensor of inclination, tilt, or orientation in 2 or 3 dimensions, as referenced from the acceleration of gravity (1 g = 9.8m/s2);
• As a vibration or impact (shock) sensor.

There are considerable advantages to using an analog accelerometer as opposed to an inclinometer such as a liquid tilt sensor – inclinometers tend to output binary information (indicating a state of on or off), thus it is only possible to detect when the tilt has exceeded some thresholding angle.

### Principles of Operation

Most accelerometers are Micro-Electro-Mechanical Sensors (MEMS). The basic principle of operation behind the MEMS accelerometer is the displacement of a small proof mass etched into the silicon surface of the integrated circuit and suspended by small beams. Consistent with Newton's second law of motion (F = ma), as an acceleration is applied to the device, a force develops which displaces the mass. The support beams act as a spring, and the fluid (usually air) trapped inside the IC acts as a damper, resulting in a second order lumped physical system. This is the source of the limited operational bandwidth and non-uniform frequency response of accelerometers. For more information, see reference to Elwenspoek, 1993.

### Types of Accelerometer

There are several different principles upon which an analog accelerometer can be built. Two very common types utilize capacitive sensing and the piezoelectric effect to sense the displacement of the proof mass proportional to the applied acceleration.

#### Capacitive

Accelerometers that implement capacitive sensing output a voltage dependent on the distance between two planar surfaces. One or both of these “plates” are charged with an electrical current. Changing the gap between the plates changes the electrical capacity of the system, which can be measured as a voltage output. This method of sensing is known for its high accuracy and stability. Capacitive accelerometers are also less prone to noise and variation with temperature, typically dissipate less power, and can have larger bandwidths due to internal feedback circuitry. (Elwenspoek 1993)

#### Piezoelectric

Piezoelectric sensing of acceleration is natural, as acceleration is directly proportional to force. When certain types of crystal are compressed, charges of opposite polarity accumulate on opposite sides of the crystal. This is known as the piezoelectric effect. In a piezoelectric accelerometer, charge accumulates on the crystal and is translated and amplified into either an output current or voltage.

Piezoelectric accelerometers only respond to AC phenomenon such as vibration or shock. They have a wide dynamic range, but can be expensive depending on their quality (Doscher 2005)

Piezo-film based accelerometers are best used to measure AC phenomenon such as vibration or shock, rather than DC phenomenon such as the acceleration of gravity. They are inexpensive, and respond to other phenomenon such as temperature, sound, and pressure (Doscher 2005)

#### Overview of other types that are less used in audio applications

Piezoresistive

Piezoresistive accelerometers (also known as Strain gauge accelerometers) work by measuring the electrical resistance of a material when mechanical stress is applied. They are preferred in high shock applications and they can measure acceleration down to 0Hz. However, they have a limited high frequency response.

Hall effect

Hall effect accelerometers work by measuring the voltage variations caused by the change in magnetic field around them.

Heat transfer

Heat transfer accelerometers consist in a single heat source centered in a substrate and suspended accross cavity. They include equally spaced thermoresistors on the four side of the heat source. They measure the internal changes in heat due to an acceleration. When there is zero acceleration, the heat gradient will be symmetrical. Otherwise, under acceleration, the heat gradient will become asymmetrical due to convection heat transfer

#### Other

There are many other types of accelerometer, including:

• Null-balance
• Servo force balance
• Strain gauge
• Resonance
• Optical
• Surface acoustic wave (SAW)

### Specifications

A typical accelerometer has the following basic specifications:

• Analog/digital
• Number of axes
• Output range (maximum swing)
• Sensitivity (voltage output per g)
• Dynamic range
• Bandwidth
• Amplitude stability
• Mass

Analog vs. digital: The most important specification of an accelerometer for a given application is its type of output. Analog accelerometers output a constant variable voltage depending on the amount of acceleration applied. Older digital accelerometers output a variable frequency square wave, a method known as pulse-width modulation. A pulse width modulated accelerometer takes readings at a fixed rate, typically 1000 Hz (though this may be user-configurable based on the IC selected). The value of the acceleration is proportional to the pulse width (or duty cycle) of the PWM signal. Newer digital accelerometers are more likely to output their value using multi-wire digital protocols such as I2C or SPI.

For use with ADCs commonly used for music interaction systems, analog accelerometers are usually preferred.

Number of axes: Accelerometers are available that measure in one, two, or three dimensions. The most familiar type of accelerometer measures across two axes. However, three-axis accelerometers are increasingly common and inexpensive.

Output range: To measure the acceleration of gravity for use as a tilt sensor, an output range of ±1.5 g is sufficient. For use as an impact sensor, one of the most common musical applications, ±5 g or more is desired.

Sensitivity: An indicator of the amount of change in output signal for a given change in acceleration. A sensitive accelerometer will be more precise and probably more accurate.

Dynamic range: The range between the smallest acceleration detectable by the accelerometer to the largest before distorting or clipping the output signal.

Bandwidth: The bandwidth of a sensor is usually measured in Hertz and indicates the limit of the near-unity frequency response of the sensor, or how often a reliable reading can be taken. Humans cannot create body motion much beyond the range of 10-12 Hz. For this reason, a bandwidth of 40-60 Hz is adequate for tilt or human motion sensing. For vibration measurement or accurate reading of impact forces, bandwidth should be in the range of hundreds of Hertz. It should also be noted that for some older microcontrollers, the bandwidth of an accelerometer may extend beyond the Nyquist frequency of the A/D converters on the MCU, so for higher bandwidth sensing, the digital signal may be aliased. This can be remedied with simple passive low-pass filtering prior to sampling, or by simply choosing a better microcontroller. It is worth noting that the bandwidth may change by the way the accelerometer is mounted. A stiffer mounting (ex: using studs) will help to keep a higher usable frequency range and the opposite (ex: using a magnet) will reduce it.

Amplitude stability: This is not a specification in itself, but a description of several. Amplitude stability describes a sensor's change in sensitivity depending on its application, for instance over varying temperature or time (see below).

Mass: The mass of the accelerometer should be significantly smaller than the mass of the system to be monitored so that it does not change the characteristic of the object being tested.

Other specifications include:

• Zero g offset (voltage output at 0 g)
• Noise (sensor minimum resolution)
• Temperature range
• Bias drift with temperature (effect of temperature on voltage output at 0 g)
• Sensitivity drift with temperature (effect of temperature on voltage output per g)
• Power consumption

### Output

An accelerometer output value is a scalar corresponding to the magnitude of the acceleration vector. The most common acceleration, and one that we are constantly exposed to, is the acceleration that is a result of the earth's gravitational pull. This is a common reference value from which all other accelerations are measured (known as g, which is ~9.8m/s^2).

Digital output

Accelerometers with PWM output can be used in two different ways. For most accurate results, the PWM signal can be input directly to a microcontroller where the duty cycle is read in firmware and translated into a scaled acceleration value. (Check with the datasheet to obtain the scaling factor and required output impedance.) When a microcontroller with PWM input is not available, or when other means of digitizing the signal are being used, a simple RC reconstruction filter can be used to obtain an analog voltage proportional to the acceleration. At rest (50% duty-cycle) the output voltage will represent no acceleration, higher voltage values (resulting from a higher duty cycle) will represent positive acceleration, and lower values (<50% duty cycle) indicate negative acceleration. These voltages can then be scaled and used as one might the output voltage of an analog output accelerometer. One disadvantage of a digital output is that it takes a little more timing resources of the microcontroller to measure the duty cycle of the PWM signal. Communication protocols could use I2C or SPI.

Analog output

When compared to most other industrial sensors, analog accelerometers require little conditioning and the communication is simple by only using an Analog to Digital Converter (ADC) on the microcontroller. Typically, an accelerometer output signal will need an offset, amplification, and filtration. For analog voltage output accelerometers, the signal can be a positive or negative voltage, depending on the direction of the acceleration. Also, the signal is continuous and proportional to the acceleration force. As with any sensor destined for an analog to digital converter, the value must be scaled and/or amplified to maximally span the range of acquisition. Most analog to digital converters used in musical applications acquire signals in the 0-5 V range.

The image at right depicts an amplification and offset circuit, including the on-board operational amplifier in the adxl 105, minimizing the need for additional IC components. The gain applied to the output is set by the ratio R2/R1. The offset is controlled by biasing the voltage with variable resistor R4. Accelerometers output bias will drift according to ambient temperature. The sensors are calibrated for operation at a specific temperature, typically room temperature. However, in most short duration indoor applications the offset is relatively constant and stable, and thus does not need adjustment. If the sensor is intended to be used in multiple environments with differing ambient temperatures, the bias function should be sufficient for analog calibration of the device. If the ambient temperature is subject to drastic changes over the course of a single usage, the temperature output should be summed into the bias circuit. Smart sensors may even take this into consideration.

The resolution of the data acquired is ultimately determined by the analog to digital converter. It is possible, however, that the noise floor is above the minimum resolution of the converter, reducing the resolution of your system. Assuming that the noise is equally distributed across all frequencies, it is possible to filter the signal to only include frequencies within the range of operation. The filter required depends upon both the type of acquisition as well as the location of the sensor. The bandwidth is primarily influenced by the three different modes of operation of the sensor.

### Uses

The acceleration measurement has a variety of uses. The sensor can be implemented in a system that detects velocity, position, shock, vibration, or the acceleration of gravity to determine orientation (Doscher 2005)

A system consisting of two orthogonal sensors is capable of sensing pitch and roll. This is useful in capturing head movements. A third orthogonal sensor can be added to the network to obtain orientation in three dimensional space. This is appropriate for the detection of pen angles, etc. The sensing capabilities of this network can be furthered to six degrees of spatial measurement freedom by the addition of three orthogonal gyroscopes.

As a shock detector, an accelerometer is looking for changes in acceleration. This jerk is sensed as an overdamped vibration.

Verplaetse has outlined the bandwidths associated with various implementations of accelerometers as an input device. These are:

Location Usage Frequency Acceleration
Hand , Wrist, Finger Cont. 8-12 Hz 0.04-1.0 g
Hand, Arm, Upper Body Cont. 0-12 Hz 0.5-9.0 g
Foot, Leg Cont. 0-12 Hz 0.2-6.6 g

Depending on the sensitivity and dynamic range required, the cost of an accelerometer can grow to thousands of dollars. Nonetheless, highly accurate inexpensive sensors are available.

## Devices

Description Low-cost, +/- 2 g, dual-axis accelerometer with duty cycle output Digikey CAN\$ 21.69
Datasheet pdf
Resources

Notes This accelerometer is available in a several IC formats.
Variants

Description High-precision, +/- 1.1 g, dual-axis accelerometer with signal conditioned voltage outputs. Digikey CAN\$ 20.64
Datasheet pdf
Resources

Notes

Variants

Description Small, Low Power, 3-Axis +/-3.6g Accelerometer, for Motion- and Tilt-Sensing Applications Digikey CAN\$ 6.74
Datasheet pdf
Resources

Notes

Variants

Description 3-axis accelerometer, +/- 16 g, I^2C/SPI digital output. Sparkfun US\$ 27.95
Datasheet pdf
Resources

Notes click and double click recognition, free fall detection
Variants

STMicroelectronics LIS302DL Sources
Description 3-axis accelerometer, +/- 2.3 or 9 g, I^2C/SPI digital output. Digikey CAN\$ 4.20
Datasheet pdf
Resources

Notes LGA-14 surface mount package, click and double click recognition, free fall detection
Variants

Dimension Engineering DE-ACCM2G Sources
Description Buffered ±2g 2-axis Accelerometer Robotshop CAN\$ 24.37
Datasheet pdf
Resources

Notes Integrated op amp buffers for direct connection to a microcontroller's analog inputs, based on Analog Devices ADXL332
Variants

Dimension Engineering DE-ACCM3D2 Sources
Description Buffered ±3g Tri-axis Accelerometer Robotshop CAN\$ 37.53
Datasheet pdf
Resources

Notes Integrated op amp buffers for direct connection to a microcontroller's analog inputs
Variants

Description Single-axis, ± 70g or 250g accelerometer with a 22 kHz bandwidth Digikey CAN\$ 35.21
Datasheet pdf
Resources

Notes Of interest as a precursor to an accelerometer-based contact microphone (O'Reilly et al.)
Variants

Freescale Semiconductor MMA2301 Sources
Description Dual-axis, surface mount silicon capacitive ±200g accelerometer Digikey CAN\$ 7.28
Datasheet pdf
Resources

Notes Features integrated signal conditioning and 4-pole low pass filter
Variants