I am working on my final year project which involves the use of the Nitendo Wii Nunchuk. The Wii Nunchuk operates based on a 3-axis accelerometer, a joystick and two push buttons. I carried out a small theoretical research on the accelerometer, and in this wiki page I am going to briefly explain what an accelerometer is, how it works, types of accelerometers, characteristics of accelerometers, how to select an accelerometer for a project requirement, and shows some applications of accelerometers.
Physically, acceleration is a vector quantity having both direction and magnitude that is defined as the rate at which an object changes its velocity with respect to time. It is a measure of how fast speed changes . An object is accelerating when its velocity is changing. [1. ] In order to measure acceleration, an acceleration sensor called accelerometer is used. Accelerometer measures in units of g. A g is the acceleration measurement for gravity which is equal to 9.81 m/s². However, depending on altitude, this measurement can be 10 m/s² in some place.
The design of an accelerometer is based on the application of physics phenomenon. In aviation, accelerometers are based on the properties of rotating masses. In the world of industry, however, the design is based on a combination of Newton's law of mass acceleration and Hooke's law of spring action. This is the most common design applied to the making of accelerometers, and therefore, in this wiki page I will focus on explaining the accelerometer's working principle based on this combination of Newton's law and Hooke's law. Figure 1 shows a simplified spring-mass system. In figure 1a, the mass of mass m is attached to a spring at equilibrium position x0 which in turn is attached to the base. The mass can slide freely on the base. Suppose that the base friction is negligible. Figure 1b shows the mass is moving to the right by a displacement of Δx = x - x0. Since the mass is slowing down, the direction of acceleration vector is to the left. In this case, the mass is subject to the force according Newton's second law and Hooke's law.
Figure 1. A simplified spring-mass system accelerometer. [2]
Reprinted from Process Control Instrumentation Technology book
According to Newton's second law, if a mass, m, is undergoing an acceleration, a, then there must be a force, F, acting on the mass with a magnitude of
F = ma \quad (1) |
Hooke's law states that if a spring of spring constant k is extended from its equilibrium position (
x_0 |
\Delta x = x - x_0 |
x is the current position with reference to
x_0 |
F = k\Delta x (2) |
Equating equations (1) and (2) yields
ma = k \Delta x |
<=> a = \dfrac{k \Delta x}{m} (3) |
where k is spring constant in N/m
Δx is the displacement in m
m is the mass in kg
a is acceleration in m/s²
Equation (3) shows the measurement of acceleration in relation to mass, spring constant and spring extension. This is equivalent to the the linear equation y = λ x where y represents acceleration a, λ = k /m being a constant, and x being the displacement of the mass. This is how the design of an accelerometer is based on. The design and types of accelerometer based on spring-mass system differ in how this displacement measurement is made, and this comes to discussion on section 3 of this wiki page.
The equation (3) as a result of the analysis from figure 1 and b holds true on the assumption that there is no friction applied to the mass m. In practice, other parameters such as natural frequency and damping coefficient need to be considered since they have a profound effect on the application of accelerometers.
The mass-spring system exhibits oscillations at some characteristic natural frequency. This natural frequency is given by
f = \dfrac{1}{2π} √\frac{k}{m} |
where f is natural frequency in Hz
k is spring constant in N/m
m is seismic mass in kg
If there was no friction in the spring-mass system, the mass would oscillate forever. This is, however, not the case in reality. The friction that causes the system to rest is defined by a damping coefficient that has a unit of s^-1. The effect of oscillation is described by periodic damped signal which has the equation as follows. [2,2.]
XT(t) = X_0\mbox{e}^{-μt}sin(2πft) |
where XT(t) is transient mass position
μ is damping coefficient
f is natural frequency in Hz
Now two parameters that affect the accelerometer have been described. If the spring-mass system is exposed to a vibration, then the resultant acceleration is given by
a(t) = -w^2x_0sinwt (4) |
Applying equation (4) to equation (3) yields
\Delta x = \dfrac{-mx_0w^2sinwt}{k} |
Figure 2 a. Response of spring-mass system to vibration compared to w^2 prediction b. Effect of various peak motion [2,3]
Reprinted from Process Control Instrumentation Technology book
Define f as the applied frequency, and fN is the natural frequency of the accelerometer. When f < fN , the natural frequency has little effect on the operation of the accelerometer. when f > fN, the accelerometer output is independent of the applied frequency. An important point worth noting is that with the applied frequency much larger than the natural frequency, the accelerometer becomes a measurement of vibration displacement . At near the resonance of accelerometer's natural frequency, the output of the accelerometer becomes high non-linear.
A rule of thumb is that with f < fN, the safe maximum applied frequency should be f < 2/5 fN.With f > fN, the minimum applied frequency should be f > 5/2 fN.[2,4.] So to best avoid the severe effect of resonance, the accelerometer should not be used near the resonance of their frequency because the output will become non-linear. Furthermore, the accelerometer should not be used with the applied frequency larger than the natural frequency if the measurement system is meant to measure acceleration.This has an important implication in the selection of the accelerometer for an application.
The equation of motion of an accelerometer is given by:
M\frac{{d}^{2}x}{d{t}^2} + b\frac{dx}{dt} + kx = M\frac{{d}^{2}y}{d{t}^2} |
Where M (kg) is the seismic mass, x (m) is the displacement from its equilibrium, d²y/dt² is the acceleration applied to the accelerometer case, b is the damping coefficient.
To describe the relationship between the accelerometer input and output, a transfer function is used. Taking Laplace transformation from the above equation yields
M{s}^{2}X(s) + bsX(s) + kX(s) = -MA(s) [7,329] |
where X(s) and A(s) are the Laplace transforms of x(t) and d2y/dt2, respectively. Solving the above for X(s) we receive
X(s) = -\frac{MA(s)}{M{s}^{2} + bs + k} (5) |
Equation (5) represents a typical transfer function for accelerometer.
Figure 3. Mechanical characteristics of LIS3L02AL accelerometer
Reprinted from STMicroelectronics LIS3L02AL accelerometer datasheet [8]
Like any other sensors, a typical accelerometer possesses several characteristics which are needed to understand. Those characteristics are explained as follows:
Until now, all the basic characteristics of an accelerometer have been explained. One important characteristic is the sensitivity and the question is how to improve the sensitivity of the accelerometer. For analog-output sensors, sensitivity is ratiometric to supply voltage. Therefore, the sensitivity can be improved by increasing the supply voltage for the sensor as long as it does not exceed the maximum rating power supply specified by the datasheet. So this means that doubling the supply, for example, doubles the sensitivity. [9.]
Section characteristics of an accelerometer mentioned some of the most important characteristics of an accelerometer. Examples of these characteristics were taken from the LIS3L02AL accelerometer which is used in the Wii Nunchuk. Unfortunately, the schematic for interfacing between the LIS3L02AL accelerometer and other electronic circuits is not "open source". Therefore, in this section an ADXL203 accelerometer from Analog Devices and its signal conditioning circuit will be used instead. This circuit is an used for the EVAL-CN0189-SDPZ evaluation board from Analog Devices. Figure 4 shows how the PCB of this board looks like.
Figure 4. Analog Devices EVAL-CN0189-SDPZ evaluation board
Reprinted from Analog Devices [10]
Figure 5 shows a circuit schematics which includes a dual axis ADXL203 accelerometer and the AD7887 12-bit successive approximation analog to digital converter (ADC). This is a simplified schematics designed as a signal conditioning circuit for the evaluation board shown in figure 4.
Figure 5. ADXL203 accelerometer and its signal conditioning circuit.
Reprinted from Analog Devices [11]
The signals from the x axis and y axis are conditioned by using an AD8608 quad amplifier. The main purpose of the quad operational amplifier is to buffer, attenuate, and level shift the x axis and y axis signals of the ADXL203 accelerometer so that the signals are at proper levels for interfacing with, for example, an ADC. In particular, the quad AD8608 is used to create a 2-stage conditioning circuit. The first stage provides a signal gain of 1.2 and level shifts the common-mode voltage (VCM) to 2 V [10]. The gain can be calculated from a non-inverting amplifier formula as follows:
A(v) = \frac{Vout}{Vin}=1+\frac{Rf}{R2} |
where A(v) is the closed loop voltage gain; Rf (1KΩ) is a feedback resistor; R2 has a value of (5KΩ); Vin is the input voltage; Vout is the output voltage.
The second stage amplifier gives a voltage gain of 1.1 and establishes the common-mode output voltage of 1.7 V. Therefore, the total voltage of the is 1.32 after a signal from the accelerometer has gone through 2 stages of amplification . A common-mode voltage of 1.7 V after being conditioned is good enough to line up with the load device [10]. The load device in this case is an AD7887 ADC which needs an input voltage range of 0 to 3.3 V.
The ADXL203 accelerometer has an internal resistor of 32KΩ at each output, one from the x axis output and one from the y axis output. The tolerance of the internal resistor vary as much as ±25%[12]. Each of the internal resistors are connected with a capacitor of 10μF to make a low-pass filtering circuit for antialiasing and removing high frequency components of noise. The bandwidth of the low-pass filter can be calculated using the following formula.
f(-3dB) = \frac{1}{2πRC} |
where R is the internal resistor (32KΩ for ADXL203 accelerometer), and C is the capacitor.
To help quickly determine the value of a capacitor for a particular bandwidth, table 1 shows the values of capacitors and the corresponding low-pass filter bandwidth.
Table 1. Filter capacitor selection for a bandwidth
Data gathered from Analog Devices data sheet [12]
| Bandwidth (Hz) | Capacitor (μF) |
|---|---|
| 1 | 4.7 |
| 10 | 0.47 |
| 50 | 0.10 |
| 100 | 0.05 |
| 200 | 0.027 |
| 500 | 0.01 |
Apart from the capacitors used for the low-pass filtering circuits, there are also some other passive components used for the signal conditioning circuit. Eight resistors are used for the quad op amp. The values of them can be seen in figure 5. The ADXL203 accelerometer can be powered between 3 to 6V. However, it is recommended that the sensor be powered from a 5V power supply for optimum overall performance[10]. To reduce the effect of noise from the power supply for the accelerometer, two decoupling capacitors are used, one 0.1μF capacitor and one 10μF capacitor. The ADXL203 noise has the characteristics of white Gaussian noise, which contributes equally at all frequencies.
Until now, the signals from the x axis and y axis of the accelerometer are properly conditioned, and they are actually analog signals. In order to convert these analog signals to digital ones, the AD7887 12-bit successive approximation analog to digital converter is used as shown in figure 5. The ADC operates from a 2.7V to 5.25V power supply. It is capable of sampling signal with a sampling rate of 125Khz. The output coding for the AD7887 is straight binary. The ADC can be configured by software to operate at either dual channel or single channel via the on-chip control register. Regarding communication, the ADC supports an SPI interface which can be used to interface with an embedded processor.
The circuit shown in figure 5 itself possesses errors including offset error and sensitivity mismatch error. In order to compensate those errors, two techniques are used to calibrate the circuit. The first technique is called no-turn calibration and the second one is called multiple turn calibration.
So far, I have discussed mainly spring-mass based accelerometers since it is the focus of this wiki page. In addition to that, there are many other accelerometers that are designed based on other physical phenomenon. In fact, what makes a difference between the types is the sensing element and their operating principles. There are many types of accelerometers in real life applications such as capacitive, piezoelectric, piezoresistive, Hall effect, magnetoresistive, heat transfer, MEMS-based accelerometers, to name just a few. Commonly used accelerometers, however, will be represented in this wiki page.
This is a type of an accelerometer which bases its working principles on the spring-mass system. The potentiometric accelerometer employs a mass (seismic mass), a spring, a dashpot, and a resistive element. The seismic mass is connected between a spring and a dashpot. The wiper of the potentiometer is connected to the mass.The following figure illustrates the structure of the potentiometric accelerometer.
Figure 6. Structure of a potentiometric accelerometer [3]
The way it works is simple. It measures the motion of the seismic mass by attaching the wiper arm to the spring-mass system. When the mass is moving, the position of the wiper changes according, thus changing the resistance of the resistive element. Since the natural frequency fN of the potentiometer accelerometer is generally less then 30Hz, this type of accelerometer should be used in low frequency vibration measurements.
Hall effect accelerometer is based the working principles of on spring-mass system. The output voltage varies according to a change in magnetic field from the magnet which is attached on a seismic mass. The mass deflects because of the forces due to acceleration. The output Hall voltage is calibrated in terms of acceleration.
Figure 7. Simplified structure of a Hall effect accelerometer [4,3]
Capacitive accelerometer operates based on spring-mass system working principles. It differs from Hall effect accelerometer and potentiometric accelerometer in its sensing element. Figure 8 shows the structure of a capacitive accelerometer, The sensing electrodes are in stationary state, and the diaphragm which is attached to the seismic mass is sandwiched in between the two sensing electrodes creating two capacitors. 
Figure 8. Structure of capacitive accelerometer [5]
The vibration because of the forces due to acceleration causes the seismic or proof mass to move. The motion of the mass leads to the capacitance change of the sensing electrodes so as to determine the acceleration. The movement of the diaphragm causes a capacitance shift by altering the distance between the two parallel plates, with the diaphragm itself being one of the plates.
Unlike the three types of accelerometers mentioned above, Piezoresistive accelerometers do not use a spring. Instead of that, the mass is attached to cantilever beam which in turn is sandwiched in between strain gages.
Figure 9. Piezoresistive accelerometer [4,2]
Piezoresistive accelerometer's working principle is based on piezoresistive effect. As far as the piezoresistive effect is concerned, applied mechanical stress changes the resistivity of a semiconductor. The force exerted by the seismic mass changes the resistance of the strain gages. Piezoresistive accelerometers are used in high shock applications, and they can also measure accelerations down to zero Hz or up to ±1000g. But, the disadvantage is that they have limited high frequency response. [6.]
MEMS stands for Micro-Electro Mechanical System. It is the technology which is based advanced technologies used to form small structures with dimensions in micrometer scale. MEMS technology is now being employed to manufacture state-of-the-art MEMS-based accelerometers.
Initially, MEMS accelerometers was designed using piezoresistors. Since piezoresistors are less sensitive than capacitive detection, the majority of MEMS accelerometers nowadays use capacitive sensing principle. MEMS-based accelerometer typically consists of a proof mass with plates attached through a mechanical suspension system to a reference frame. Movable plates (part of the seismic mass) and the outer plates in stationary state form differential capacitor. Because of the forces due to acceleration, the seismic mass deflects; the deflection is measured in terms of capacitance change. [4,3.]
Figure 10. MEMS-based accelerometer structure [4,3]
The datasheet of the LIS3L02AL accelerometer gives very little information about the materials used for manufacturing the sensor as well as how it is manufactured since the information about these is proprietary. What is known publicly is that the suspended structures which are attached to the substrate in anchors are made of silicon. There is no information about the manufacturing process of the sensor from STMicroelectronics. Fortunately, some other manufactures are generous enough to give some information about the manufacturing process of their sensor. The following gives steps in manufacturing accelerometers from IMV corporation.
The ceramic is put into the silicon oil heated approx.200℃ and high voltage 1-2kV/mm is added between the electrodes.Then, the random polarities are arranged in field direction are arranged to be in the same field direction. Thea piezoelectricity becomes apparent.
Step 14 - Checks: Polarized ceramics are checked. Check points include
The whole manufacturing process is completed after checking is done. [12.]
In order to make a decision on which accelerometer can be used based on the requirements, it is necessary to understand the specifications of the accelerometer. These specifications can be found from the datasheet of an accelerometer. They include dynamic specifications, electrical specifications and mechanical specifications. Some of the important ones are as follows:
In addition to understanding some of the important specifications just mentioned, it should be noted that if the measurement is meant to measure acceleration, then the applied frequency f should be less than the natural frequency fN of the accelerometer.
As a rule of thumb, in low-frequency applications (having a bandwidth on orders from 0 to 10 Hz), position and displacement measurements generally provide good accuracy. In the intermediate-frequency applications (less than 1 kHz), velocity measurement is usually favored. In measuring high-frequency motions with appreciable noise levels, acceleration measurement is preferred. [7,327.]
Accelerometers have many different applications ranging from industry, entertainment, sports to education. These applications can be, for example, triggering airbag deployments or monitoring of nuclear reactors. Accelerometers can also be used to measure static acceleration (gravity), tilt of an object, dynamic acceleration in an aircraft, shock to an object in a car, orientation or vibration of an object. Cell phones, washing machines or computers nowadays also have accelerometers.
STMicroelectronics. LIS3L02AL MEMS inertial sensor datasheet [online]. STMicroelectronics; May 2006.
URL: http://www.e-brt.com/upload/files/20111011111758_77.pdf. Accessed 9 April 2014.
Analog Devices. ACCELEROMETER SPECIFICATIONS - QUICK DEFINITIONS [online]. Analog Devices.
URL: http://www.analog.com/en/content/td_accelerometer_specifications_definitions/fca.html. Accessed 9 April 2014.
Analog Devices. Circuit Note CN-0189 - Tilt Measurement Using a Dual Axis Accelerometer [online]. Analog Devices; 2012.
URL: http://www.analog.com/static/imported-files/circuit_notes/CN0189.pdf. Accessed 20 April 2014.
Analog Devices. Precision +-1.7g, +-5g, +-18g Single-/Dual-Axis iMEMS Accelerometer ADXL103/ADXL203 Data Sheet [online]. Analog Devices.
URL: http://www.analog.com/static/imported-files/data_sheets/ADXL103_203.pdf. Accessed 20 April 2014.
IMV Corporation. Manufacturing Process of Accelerometer [online]. IMV Corporation.
URL: https://www.imv.co.jp/e/pr/pickup/. Accessed 1 May 2014.