Micromachined inertial sensors are very important sensors in any navigation systems. Inertial sensors consist of accelerometers and gyroscopes. They measure either linear acceleration as the accelerometer, or angular motion about one or several axes as the gyroscope. Until recently, medium to high performance inertial sensors were restricted to applications in which the cost of these sensors was not of essential concern, such as military and aerospace systems. The advantages of micromachining have generated the possibility of producing relatively high performance inertial sensors at a fractional of cost of conventional sensors. A variety of such applications already exists, mainly in the automotive industry for safety systems such as airbag deployment, seat belt control, active suspension, and traction control. Inertial sensors are used for military applications such as missile guidance and inertial navigation.
2.1 Micromachined Accelerometer
As discussed in the pervious chapter, the large amount of MEMS advantages made it a suitable technology for many fields. Accelerometers can be built using the MEMS technology resulting in low cost, small size, low power, high performance and more reliable sensors. This advantage of micromachined accelerometer finds its way for many applications that require special concern in size and cost of the sensors. This made the micromachined accelerometer highly participates in the automotive applications, such as air bags. However, the application of accelerometers covers a wide range where their small size and low cost are required. They are used in biomedical applications for activity monitoring; in numerous consumer applications, such as active stabilization of picture in camcorders, head mounted displays and virtual reality, three-dimensional mouse, and sport equipment; in industrial applications such as robotics and machine and vibration monitoring; in many other applications, such as tracking and monitoring mechanical shock and vibration during transportation and handling of a variety of equipment and goods; and in several military applications, including impact and void detection.
Many types of micromachined accelerometers have been developed and are reported in the literature; however, the vast majority has in common that their mechanical sensing element consists of a proof mass that is supported any way by a mechanical suspension system to a reference frame, as shown in Fig. 2.1.
Any inertial force due to acceleration will deflect the proof mass according to Newton's second law. The accelerometer model in its simple case is a second order mass-damper-spring system. The governing equation for such system is given as:
(2.1)
It can be described mathematically in the Laplace domain by:
(2.2)
Where x is the displacement of the proof mass, a is the acceleration to be measured, b is the damping coefficient, m is the mass of the proof mass and k is the mechanical spring stiffness of the suspension system. The natural resonant frequency of this system is given by:
(2.3)
2.1.1 Principle of Acceleration Sensing
As shown in Fig. 2.1, the simplest model of an accelerometer is a mass-spring-damper system. The applied acceleration on the system makes the mass to oscillate, and this vibration can be used to determine the magnitude of the acceleration.
Figure 2.1 shows a model of an accelerometer.
Let x be the displacement of the mass. When the system is experienced to an external acceleration a, thus one can find the equation of motion for this system is:
(2.4)
Where b and k are the damping coefficient and spring constant, respectively. Thus, the acceleration can be determined by measuring x, i.e., the net stretch or compression of the spring.
2.1.2 Structure
An accelerometer generally consists of a proof mass anchored to a fixed frame. The proof mass has a mass of m, the suspension beams have spring constant of k, and there is a damping factor b affecting the dynamic movement of the mass. The accelerometer can be modeled by a second-order mass-damper-spring system, as shown in Fig. 2.1. External acceleration displaces the support frame relative to the proof mass, which in turn changes the internal stress in the suspension spring. By using Newton's second law and the accelerometer model, the mechanical transfer function can be obtained as:
(2.5)
Where: is the external acceleration, x is is the proof mass displacement, is the natural resonance frequency, and is the quality factor. The resonance frequency of the structure can be increased by increasing the spring constant and decreasing the proof mass, while the quality factor of the device can be increased by reducing damping and by increasing proof mass and spring constant. The static sensitivity of the accelerometer is shown to be:
, (2.6)
On other words:
(2.7)
From equation 2.7, it implies that to sense very small acceleration, the accelerometer should operate at lower natural frequency. On other words, the static response of the device can be improved by reducing its resonant frequency.
The primary mechanical noise source for the device is due to Brownian motion of the gas molecules surrounding the proof mass and the Brownian motion of the proof mass suspension. The total noise equivalent acceleration (TENA) [m/s2] is [69]:
(2.8)
Where: kB is the Boltzmann constant and T is the temperature in Kelvin. This equation clearly shows that to reduce mechanical noise, the quality factor and proof mass have to be increased.
Micromachined Accelerometer Types
This section classified the micromachined accelerometer depending on their mechanical sensing schemes. The device named according to the mechanical function of applied to sense the input accelerations.
Piezoresistive Devices
As been described in the previous chapter, the piezoresistivity of a material is that some materials change its resistivity according to applied stress. The first micromachined accelerometer was piezoresistive [69-71]. These accelerometers integrate silicon piezoresistors in their suspension beam. As the support frame moves relative to the proof mass, the suspension beams will stretch or compress, which changes the stress and hence the resistivity of the piezoresistors.
The main advantage of piezoresistive accelerometers is the simplicity of their structure and fabrication process, as well as their readout circuitry, since the resistive bridge generates low output impedance. However, piezoresistive accelerometers have larger temperature sensitivity, and smaller overall sensitivity. The early development of bulk micromachining technology helped the initial development of piezoresistive microaccelerometers using bulk micromachining and wafer bonding technology [72- 75].
Tunneling Devices
These devices use the tunneling current between a tip on the proof mass and another one on the fixed electrode. Sensing the tunneling current, results in a high sensitive sensor. This scheme able to sense proof mass deflection as lower as a few angstroms.
Figure 2.3 Idea of the tunneling accelerometer [76]
Fig. 2.3 [76] shows the general operating principal of a micromachined tunneling accelerometer. As the tip is brought sufficiently close to its electrode using electrostatic force generated by the bottom deflection electrode, a tunneling current is established. Once the proof mass is displaced due to acceleration, the readout circuit responds to the change of current and adjusts the bottom deflection voltage to move the proof mass back to its original position, thus maintaining a constant tunneling current. Acceleration can be measured by reading out the bottom deflection voltage in this closed loop system. Tunneling accelerometers can achieve very high sensitivity with a small size since the tunneling current is highly sensitive to displacement, typically changing by a factor of two for each angstrom of displacement [76]. However, these devices have larger low-frequency noise levels [77].
Resonant Devices
The resonance device is a device in which it has an element vibrating at resonance that exhibit some form of changes in its resonance parameters such as frequency, amplitude or phase as a result of the presence of the physical phenomena (value to be measured). The conversion from the measured quantity to the change of the resonance parameters could be accomplished by the means of change in stress, strain, shape etc. of the resonator. The use of resonant silicon structures is a well known way to realize sensitive sensors due to the excellent mechanical properties of the single crystal silicon, such as high quality factor. The resonant sensors have an advantage of direct digital output. For these advantages of silicon and resonant devise, many micromachined accelerometers were fabricated and operated on the principle of resonant devices.
The resonant accelerometers were fabricated using quartz micromachining [78], [79]. Silicon resonant accelerometers are operates based on the transferring of the proof mass inertial force to axial force on the resonant beams and hence changing their frequency [80]. Many micromachined high sensitivity resonant accelerometers have been reported [81], [82]. The devices use wafer thick proof mass and achieve high resolution and very good stability. However, these devices typically have small bandwidth. Also recently, surface micromachined resonant accelerometers are developed [83], [84].
Thermal Devices
Thermal devices depend on measuring the position of the mass that affected by the amount of heat flow due to the conduction through the gas between the proof mass and the encapsulation. The variation of heat flow results in temperature difference between the heated part and the heat sink, which depend on the position of mass and hence the acceleration.
One of the first thermal accelerometers used the principle that the temperature flux between a heater and a heat sink plate is inversely proportional to their separation [85]. Hence, by measuring the temperature using thermopiles, the change in distance between the plates can be measured. A novel thermal accelerometer was reported that does not have any moving mechanical parts. Its operation is based on free convection heat transfer of a small hot air bubble in a sealed chamber [86]. The device consists of a thermally isolated heater that forms a hot air bubble. The heat distribution of this bubble changes in the presence of an acceleration and becomes asymmetric with respect to the heater. This heat profile can be sensed by two symmetrically placed temperature sensors and is a measure of the acceleration. Many devices operates on the thermal idea were fabricated and reported [87-90].
Capacitive Devices
The most common applied physical phenomena are the electrostatic force. Electrostatic means when two opposite charged particles are near enough, an electrostatic force is produced. This is the common idea for the sensors and actuators depending on this criterion. In actuators a parallel plate or a comb finger assembly are used. In parallel plate one fixed plate is connected to a driving AC voltage signal, where as the moving plate is put at a polarized voltage. The same is applicable for interdigitated comb fingers. In sensors the idea is reversed, if a two metal plates separated by a gap exists, a capacitance between them will appear. If one of these plates is moving with respect to other, a variation of capacitance will be produced. Sensing this capacitance will give a good indication for the displacement of the moving plate, which is produced as a result of acceleration. The capacitive sensors have the advantages of variation of capacitance with very small displacement is enough to be sensed.
In the presence of external acceleration, the support frame of an accelerometer moves from its rest position, thus the capacitance between the proof mass and a fixed electrode separated from it with a small gap will be changed. This capacitance can be measured using read out electronic circuit. Silicon capacitive accelerometers have numerous advantages that make them very attractive for various applications ranging from small size, low cost, massed produce automotive accelerometers [91], [92] to high precision inertial grade microgravity devices [93-98]. As been described in chapter one the capacitive sensing has high sensitivity, good DC response and noise characteristic, small drift, low temperature sensitivity, low energy dissipation, easy to implement using micromachining process and a simple structure. Some of the most widely used structures for capacitive accelerometers are vertical and lateral structures, as shown in Fig. 2.4.
Figure 2.4: Left, vertical accelerometer and Right, lateral accelerometer.
Many capacitive accelerometers utilize the vertical structure, where the proof mass is separated by a small air gap from a fixed electrode, forming a parallel plate sense capacitor [92-99]. In these devices, the proof mass moves in the direction perpendicular to the substrate plane (z-axis) and changes the air gap. In a lateral accelerometer, a number of moving sense fingers are attached to the proof mass, and the sense capacitance is formed between these and the fixed fingers parallel to them. The sense direction in lateral accelerometers is in the proof mass plane (x-y directions) [91].
A number of capacitive microaccelerometers with medium resolution have been fabricated using the bulk silicon dissolved wafer process [100- 106].
Surface micromachined accelerometers [97- 99] offer the opportunity to integrate the sensor and interface circuitry on a single chip. These devices utilize deposited polysilicon layers to form the sense element and are well suited for both vertical and lateral capacitive accelerometers.
Also, by employing a vertical and two lateral accelerometers, an integrated three-axis accelerometer system has been designed by researchers at Berkeley and fabricated through Sandia National Laboratory's process [107]. The same group has also developed a three axis accelerometer with a single sense element [108]. Surface micromachining devices have small proof mass and hence high mechanical noise unless the device is packaged in vacuum.
Although bulk micromachined devices can attain higher resolution due to their large proof mass, they generally require wafer bonding. These devices, if not formed using only silicon wafers, could have large temperature coefficients. An all-silicon, fully symmetric, high-precision accelerometer has been developed [98], as shown in Fig. 2.5.
Figure 2.5 shows the micro accelerometer structure [98]
This device [98] uses a combined surface and bulk micromachining process to obtain a large proof mass, controllable small damping, and a small air gap for large capacitance variation all by using a single silicon wafer. Sense electrodes are created by depositing polysilicon on the wafer. These electrodes, while thin, are made very stiff by embedding thick vertical stiffeners in them so that force rebalancing of the proof mass becomes possible. There are eight suspension beams, which are symmetric with respect to the proof mass centerline and result in low cross axis sensitivity. This device is operated closed loop using an over sampled Σ/Δ modulator [109]. It achieves a high sensitivity of 2 pF/g with a full bridge supports a low noise level, and low temperature sensitivity, which enable it to attain mg and sub- µg performance.
Position Measurement with Capacitance
By investigating the above presented different type of sensors, it is clear that the capacitive sensors are the one suitable one for the advantages of capacitance. Advantages of capacitance include, and not limited to, small physical size, minimum temperature sensitivity, easy to implement, low power consumption, wide dynamic range, senses very small displacement and very high sensitivity.
There are many methods of direct position measurement, for example, capacitance change, inductance change, optical methods, and scanning-probe tips. Of these, capacitance change is the most widely used in micro accelerometers. Inductance change is widely used in macrosensors. Optical position sensing in microstructures is a sensitive scheme but difficult to implement and expensive. Position measurement with scanning probe tips, specifically electron tunneling tips, has very interesting features.
Capacitance measurement is one of the most versatile methods of position measurement. Fig. 2.6 illustrates several types of capacitors that are in common use.
Figure 2.6: shows capacitive sensing schemes; a) parallel plate, b) digitated comb fingers.
The parallel-plate capacitor can vary either with vertical motion of a movable plate, single or differential, modifying the gap, or by transverse motion of one plate relative to another, modifying the effective area of the capacitor. Inter digitated comb finger capacitors vary with the degree of appointment of the fingers. Also, displacement of one of the electrodes out of the plane of the substrate would modify the capacitance, but this is not a configuration in common use.
Figure 2.7 differential capacitors and their equivalent circuit model
Fig. 2.7 illustrates differential capacitors that can be used for position sensing. In these two examples, there are three electrodes used for the measurement, with two capacitors that are nominally of equal size when the moveable component is centered. Motion of the moveable component in the indicated direction increases one capacitance and decreases the other. A variant of the parallel plate differential capacitor would have the middle and lower plate fixed and only the upper plate moveable. In this configuration, motion of the upper plate modifies one capacitor while the other remains constant.
Figure 2.8 typical circuit used in a differential capacitor
Differential capacitors have the virtue of canceling many effects to first order, providing a signal that is zero at the balance point and carries a sign that indicates the direction of motion. From a system point of view, a differential capacitor accomplishes linearization about the balance point. Consider the parallel plate example, with the gap of the upper capacitor G1 and that of the lower capacitor G2. We assume equal area of both capacitors. A voltage (+Vs) is applied to the upper plate. Simultaneously, a voltage (-Vs) is applied to the lower plate. The voltage that appears at the output is [110]:
Since the areas are equal, this can be rearranged to yield:
If the two gaps are equal, the output voltage is zero. However, if the middle plate moves so that one gap is larger than the other, the output voltage is a function of this displacement change results in an indication of the acceleration.
Micromachined Gyroscopes
Gyroscopes are sensors used to measure the rotation rate of their host. The gyroscope has a keen sense of direction, which explains why man has used this device for guidance and navigation. It is used to control or guide a vehicle in a constant direction, in a circle, or in accordance with a planned program. The mechanical gyroscope in its simplest form consists of a flywheel rotating at very high speed with axis is mounted on gimbals. This allows the spin axis to stay fixed while its host moves in all directions. Some gyroscopes that appear in nature are the earth spinning on its axis. The earth rotates once every 24 hours, so its rotation rate is 15 (deg / h) [111].
Gyroscopes and accelerometers are essential components in any navigation system. Guidance system directs the vehicle to a terminal or aiming point with the desired restrictions on velocity and arrival time. Guidance may be supplied to vehicles such as the missile, satellite, airplane, submarine, ship, torpedo, undersea probe, and space probe. Attitude guidance is required to keep the vehicle horizontal and headed in a predetermined direction. A gravity sensor, either a pendulum or vertical gyroscope, can meet the horizontal requirement while a heading gyroscope maintains the direction. This system requires two guidance loops, as demonstrated on Fig. 2.9 [112].
Navigation system is a space transducer, which determines the location of its vehicle. There are numerous types of navigators, but for convenience, two general categories are defined: non-inertial and inertial navigation system. The non-inertial navigation system consists of many types: pioltage; celestial navigation; radio, radar, Loran; dead reckoning; Doppler radar. Dead reckoning is a mathematical mean to determine present position when the vehicle starts from a known point and moves at known velocity.
Gyroscopes and accelerometers are the main components of an inertial navigation system (INS), which provide the necessary signal for automatic navigation. Gyroscopes measure rotation, and accelerometers measure acceleration. Integrating the accelerometers output signal twice gives travel distance, and the gyroscopes provide information about acceleration direction, so heading and distance are determined. The INS is build of a navigation computer and a set of gyroscopes and accelerometers, which are called inertial sensors. The computer and three axis accelerometers and three axis gyroscopes integrated together formulate a complete inertial measurement unit (IMU). The inertial sensors might be mounted in a set of gimbals, navigation platform, or can be attached to the vehicle, strap-down system. Inertial platforms use gyroscopes to maintain the accelerometers in a fixed attitude. In strap-down system, the gyroscopes and accelerometers are rigidly mounted to the vehicle structure so that they move with the vehicle. i.e., the strap-down gyros must measure the angles turned up and the expected maximum rotation rate [112].
The family of gyroscopes is large one. There are many types such as mechanical gyroscope which is the classical type of gyroscopes. Optical gyroscopes are available and have a very high resolution. Also, macro scale vibratory gyroscopes find its way for many applications. All the above types are bulky, in size and weight, and more expensive to be used in most of modern applications. Using the MEMS technology, the gyroscope size can be shrinking to microscale dimensions at the relatively same performance and a fraction of cost. This makes the micromachined gyroscopes more suitable for most of modern applications.
(a)
(b)
Figure 2.9 block diagram loops for Attitude guidance, in (a) horizontal loop and (b) direction loop [112]
Principle of operation
Virtually all micromachined gyroscopes rely on a mechanical structure that is driven into resonance and excites a secondary oscillation in either the same structure or in a second one, due to the Coriolis force. The Coriolis force is a virtual force that depends on the inertial frame of the observer. It is produced as a result of rotating a frame carrying a travelling body with a direction perpendicular to the rotation plane. The induced Coriolis force is in other plane, which is at right angles with the plane contains the vibration and rotation. The amplitude of this secondary oscillation is directly proportional to the angular rate signal to be measured. Imagine a person on a spinning disk, rolling a ball radially away from him self, with a velocity υr. The person in the rotating frame will observe a curved trajectory of the ball. This is due to the Coriolis acceleration that gives rise to a Coriolis force acting perpendicularly to the radial component of the velocity vector of the ball. A way of explaining the origin of this acceleration is to think of the current angular velocity of the ball on its way from the center of the disk to its edge, as shown in Figure 2.10. The angular velocity Vang increases with the distance of the ball from the center (Vang = r Ω), but any change in velocity inevitably gives rise to acceleration in the same direction. This acceleration is given by the cross product of the angular velocity Ω of the disk and the radial velocity vr of the ball: Coriolis acceleration: ; Coriolis force:
Figure 2.10 A ball rolling from the center of a spinning disk is subjected to Coriolis acceleration and hence shows a curved trajectory.
Macroscopic mechanical gyroscopes typically use a flywheel that contains the most gyroscope mass and spin at high speed and hence a large angular momentum which counteracts all external torque and creates an inertial reference frame that keeps the orientation of the spin axis constant. This approach is not very suitable for a micromachined sensor. Consequently, nearly all MEMS gyroscopes use a vibrating structure that couples energy from a primary, forced oscillation mode into a secondary, sense oscillation mode. In Figure 2.11, a lumped model of a simple gyroscope suitable for a micromachined implementation is shown. The proof mass is excited to oscillate along the x-axis with a constant amplitude and frequency. Rotation about the z-axis couples energy into an oscillation along the y-axis whose amplitude is proportional to the rotational velocity. Similar to closed loop micromachined accelerometers, it is possible to incorporate the sense mode in a force-feedback loop. Any motion along the sense axis is measured and a force is applied to counterbalance this sense motion. The magnitude of the required force is then a measure of the angular rate signal.
Figure 2.11 Lumped model of a vibratory rate gyroscope [113].
One problem is the relatively small amplitude of the Coriolis force compared to the driving force. One way to increase the displacement is to fabricate sensing elements with a high Q structure and then operate the sensor on the matched mode, i.e. drive mode resonance equals to the sense mode resonance. Very high Q structures, however, require vacuum packaging. In addition, the bandwidth of the gyroscopes is proportional to the ratio between the resonance frequency and the quality factor; thus, if a quality factor of 10,000 or more is achieved in vacuum, the bandwidth of the sensor is reduced to only a few hertz. Lastly, it is difficult to design structures for an exact resonance frequency, due to manufacturing tolerances. A solution is to design the sense mode for a higher resonant frequency than the drive mode and then decrease the resonant frequency of the sense mode by tuning the mechanical spring constant using electrostatic forces [113].
A second fundamental problem with vibratory rate micromachined gyroscopes is due to the quadrature error. This type of error is produced as a result of manufacturing errors. As a result, a small value of the driven motion will be along the sense axis. Even though the misalignment angle is very small, due to the small Coriolis acceleration, the resulting motion along the sense axis may be much larger than the motion caused by the Coriolis acceleration.
Gyroscope Concepts
The gyroscope has three axes. First, a spin axis, which is define the gyroscope strength or moment, the other two axes are the primary axis, about which the body is vibrate, and the secondary axis, about which the output is sensed. These three axes are orthogonal to each other. As shown in Fig. 2.12, the gyroscope rotates around the spin axis (in this case z-axis). The primary axis vibrates the whole gyroscope in the plane of the page (x-axis in this case), and the secondary axis oscillates the gyroscope up and over into the page. The source of the gyroscopic effect papers around the spin axis. The primary axis is the input or driving axis and the secondary axis is the output or sense axis [114].
Figure 2.12 Gyroscope Axis
Fundamentals of Gyroscopes
Classes of gyroscopes
The generalized mechanical gyroscope is an instrument that senses the change in direction of its momentum. Thus, the property of a body to resist any change in the direction of its momentum is the principle by which the gyroscope operates (Newton's laws.) The gyroscopes can be classified in respect to momentum and number of sensing axes. The more insight classification is based on its performance, which may be rate grade, tactical grade, or inertial grade performance [115].
Kinds of gyroscopes
In general there are mainly three types of gyroscopes; mechanical (spinning mass) gyroscope; optical gyroscope; and vibrating gyroscope. Spinning mass gyroscope is the classical gyroscope that has a mass rotating steadily about free movable axis. Angular velocity sensor is rate sensor. Dry tuned gyroscope, dynamically tuned gyroscope (DTG) is a type of rotating mass gyroscope, which has been designed to provide very small mechanical constraints once the rotating speed reaches to particular speed. Optical gyroscopes are operating on the properties of light. To understand this idea, consider laser ray reflected round around many time within the enclosure. When the enclosure exposed to external rotation, the duration between the moments of laser emission beams to final reception will be different in phase. In a ring laser gyroscope (RLG), the laser beams is done by set of mirrors inside the enclosure. In a fiber optic gyroscope (FOG), the light source is done by a coil of optical fiber. The third type is the vibrating gyroscopes. As vibrating element rotates, it is subjected to the Coriolis force that causes secondary vibration normal to the primary vibrating direction. By sensing this vibration, the rate of rotation can be detected. All the primary vibration (driven) and secondary vibration (detection) can be done by piezoelectric, electrostatic, or optical etc [116].
Performance Measure of a Gyroscope
The scale factor, zero rate output, dynamic range, bandwidth and resolution are the main performance that determines the sensor specifications. The scale factor is the ratio of the change in output signal to the change in the input signal and specified in (mV/°/sec). Some scale factor error specifications include linearity error; which is the deviation of the output from a best curve fit of the input/output data, Nonlinearity; which is the systematic deviation from the straight line that defines the nominal input-output relationship and Asymmetry error; which is the difference between the scale factor measured with positive input and that measured with negative input, specified as a fraction of the scale factor measured over the input range. Bias or zero rate output (ZRO) is the average over a specified time of gyro output measured at specified operating condition that has no correlation with input rotation. Bias is typically expressed in (°/sec) or (°/hr). The zero-rate output drift rate specifications include random drift rate; which is usually defined in terms of the Allan variance components as angle random walk (ARW); which is the angular error buildup with time that is due to white noise in angular rate, typically expressed in (°/) or (°/s/) and Bias Instability: which is the random variation in bias as computed over specified finite sample time and averaging time intervals, characterized by a 1/f power spectral density, typically expressed in °/hr. The dynamic range or operating range is the range of positive and negative angular rates that can be detected without saturation. The resolution is the largest value of the minimum change in input that produces a change in output equal to some specified percentage of the change in output expected using the nominal scale factor. The Bandwidth is the range of frequency of the angular rate input that the gyroscope can detect. Typically specified as the cutoff frequency or the -3dB point [117- 119].
Applications and Their Requirement
The gyroscope has a keen sense of direction, so man has used this device for guidance and navigation. It is used to control or guide a vehicle in a constant direction, in a circle, or in accordance with a designed program. It may be used for heading information for inertial navigation purposes or other areas; including automotive applications such as ride stabilization and roll over detection; some consumer electronic application, such as video camera stabilization, and inertial mouse for computer; robotics applications; a wide range of military application. Based on the performance of the gyroscope, many categories are given for each type of applications. Automotive applications lay on the rate grade devices, because of the lower performance requirements. Military application requires tactical grade performance, while application such as inertial navigation requires inertial grade performance. Table 2.1 summarizes the requirements of each one of these categories [120].
Table 2.1 Performance Requirements for Different Classes of Gyroscope [121].
Parameter
Rate-grade
Tactical-grade
Inertial-grade
Angle random walk, ° / √ h
> 0.5
0.5 - 0.05
< 0.001
Bias drift, ° / h
10 - 1000
0.1 - 10
< 0.01
Scale factor accuracy, %
0.1 - 1
0.01 - 0.1
< 0.001
Full scale range, ° / s
50 - 1000
> 500
> 400
Max. Shock in 1 msec, g's
103
103 - 104
103
Bandwidth, Hz
> 70
~ 100
~ 100
Today, optical gyroscopes are the most accurate gyroscopes. RLG has demonstrated inertial-grade performance, while FOG is mainly used in tactical-grade applications. Achieving "tactical-grade and inertial-grade" performance levels has proven to be a tough challenge for micromachined gyroscopes [122]. But, conventional rotting wheel as well as precision FOG and RLG are all too expensive and too large for use in most application. Also, laser emitter detorioltes with time and the fiber has its life [112].
Research Prototypes
Gyroscope is an important sensor in any navigation system. Due the highly advantages of MEMS technology and wide range of gyroscope applications, micromachined gyroscope had got a more attention during the last two decades. Researchers in academia and industry have worked on the field of micromachined gyroscope, to increase their performance, reduce mechanical and electrical noise affected their operation and introduce a new technology to fabricate such devices. As a result a large amount of published paper and fabricated devices was available. Based on the fabricated technology, micromachined gyroscope can be implemented using surface micromachining [123- 129], bulk micromachining [130-135], LIGA process [136- 142] and dissolved wafer process [143- 145]. Based on the actuation and sensing principles, they can be categorized as piezoelectric [146, 147], magnetic [148], thermal [149], or electrostatic [150-155]. According to the gyroscope type, they can be tuning fork [156, 157], vibrating beam [158] or vibrating ring [159].
Surface micromachined gyroscope was the early sensors. Fig. 1.13 shows the structure of the symmetric and decoupled gyroscope [160]. The anchors of the structure are placed at the outermost corners and connected to the movable drive and sense electrodes simple suspension beams. This connection prevents mechanical coupling, since the oscillations of the two vibration modes do not affect each other. The gyroscope is fabricated through a surface-micromachining process. The fabricated gyroscope has dimensions measured as (1mm Ã- 1mm). The thickness of the structural layer is 2µm. Due to the thin structural layer, the capacitances of the drive and sense modes are very small, which limits the sensor performance. The sensor is driven to primary mode resonance using electrostatic concept and senses the output signal capacitevely. Surface micromachining has some drawbacks such as very small structural layer, low dimensions and highly effected by stresses.
Figure 1.13: surface micromachined gyroscope [160].
Bulk micromachining technology is a solving for most of surface micromachining drawbacks such as small mass, and stress. But surface micromachining has the advantages of integrating the sensor with its readout circuit. This is results in decreasing the parasitic capacitance. Integrating the readout electronic circuit with sensor in bulk micromachining technology is difficult and needs a wafer bonding process. A bulk micromachining gyroscope with slots structure working at atmosphere is presented [161]. The sensor consists of a proof mass with slots linked up to substrate via a suspension beams and fabricated through silicon glass bonding and deep reactive ion etching. The sensor driven electrostatically and senses the output signal capacitevely. The designed gyroscope has a resonance frequency of 460.4 and 549.6 Hz for drive and sense mode respectively with a quality factor of 102.5 and 106.5 for the same modes in the same order. This results in a very low bandwidth which is only a fraction of 1 Hz.
Figure 1.14: bulk micromachining gyroscope [161].
The LIGA microchining technology finds its way to build very high gyroscope structure that has a large proof mass. Fig. 1.15 shows an exploded schematic view of a designed LIGA type gyroscope. The structure of a rotational gyroscope with a wheel-like rotor housed by stator electrodes, based on LIGA-type technology is fabricated. A top glass plate and a bottom glass plate are used as substrates for carrying electrodes and interconnections. The stator electrodes, composed of axial levitation electrodes, radial levitation electrodes, rotation electrodes and common electrodes, are symmetrically arranged around the rotor to form capacitors for capacitive detection, electrostatic levitation and rotation. On the bottom or top stator, thin film electrodes are formed. Four pairs of axial levitation electrodes are symmetrically disposed along the X-axis and Y-axis. On the inner side of the levitation electrodes, rotation electrodes for 3-phase driving are formed. Besides the thin film electrodes, on the periphery of the bottom stator, four pairs of radial levitation electrodes made of electroplating nickel are also symmetrically distributed along the x-axis and y-axis. There is a common electrode between the two neighboring pairs of the axial levitation electrodes. To increase the common capacitance, a ring-shaped pick-up electrode is formed on the center of each glass. All the common electrodes, used for signal pick-off or exciting, are connected together to form a large common electrode.
Figure 1.15: Exploded schematic view of a designed LIGA type gyroscope [162].
Although this technique allows the gyroscope to have large proof mass, small capacitive gap spacing, it suffers from temperature sensitivity problems as different materials were used as well as the difficulty of monolithic integration
Ring gyroscope structure is developed by researchers at General Motors and the University of Michigan [163]. Fig. 1.16 shows the sensor schematically. This device consists of a ring, eight semicircular support springs, and drive, sense, and balance electrodes, which are located around the structure. The ring is electrostatically vibrated into an in-plane elliptically shaped primary flexural mode with fixed amplitude. When it is subjected to rotation around an axis normal to the substrate, excites the sense mode. The vibrating ring structure has some important features. At the first place, the structure is completely symmetric, makes it less sensitive to spurious vibrations. Then, the matched mode operation with the identical flexural suspension is used, makes the sensitivity of the sensor to be amplified by the quality factor of the structure. In addition, lower temperature sensitivity problems, since the vibration modes are affected equally by temperature. Lastly, electronic tuning of the structure is possible. Any frequencies mismatch due to mass or stiffness asymmetries that occur during the fabrication process can be electronically compensated by use of the balancing electrodes that are located around the structure.
Figure 2.16 Vibrating ring structure gyroscope. A secondary mode at 45° is a measure of the angular rate and is sensed capacitively [163].
The family of micromachined gyroscope is very large. Among these a combination of surface/ bulk mixed process, dissolved wafer process as well as the former discussed processes that using a combination of different actuating and sensing schemes are available.
Commercial Micromachined Gyroscopes
Silicon Sensing Systems is producing a very successful commercial gyroscope based upon a ring-type sensing element [164]. It uses magnetic actuation and detection, which may prove to be problematic for further device size reduction. The ring has diameter of 6 mm and is connected by eight radially compliant spokes to a support frame with the dimensions of mm2. It is fabricated by deep reactive ion etching of a 100 µm thick silicon wafer. Current carrying conductor loops are deposited on the surface of the ring structure. These loops, together with the magnetic field, set up by the permanent magnet provide the signal pick-off and primary oscillation mode drive. This gyroscope has a resolution of 0.005 °/sec, a bandwidth of 70 Hz, and a noise floor of 0.1 °/sec in a 20-Hz bandwidth. A picture of the sensor is shown in Figure 2.17. Currently, they are developing a capacitive sensor without a permanent magnet, by this means allowing for further size reduction [165].
Analog Devices has recently released the ADXRS [166] family of integrated angular rate-sensing gyroscopes, which contains the ADXRS300 (with dynamic range of ±300 °/sec) and the ADXRS150 (with dynamic range of ±150 °/sec). It is the first fully integrated commercial gyroscope. A picture of the chip is shown in Figure 2.18(a). It uses a 5V supply for operation over the temperature range of -40°C to +85°C and is available in a 32-pin surface mount IC package measuring mm3. Both are priced at approximately $30 per unit in thousand-piece quantities. Because the internal resonators require 14V to 16V for proper operation, ADI includes on-chip charge pumps to boost an applied TTL level voltage. Both the ADXRS150 and ADXRS300 are essentially z-axis gyroscopes based on the principle of resonant-tuning-fork gyroscopes. In these systems, two polysilicon sensing structures each contain a so-called dither frame that is driven electrostatically to resonance. Interestingly, the gyroscope includes two identical structures to enable differential sensing in order to reject environmental shock and vibration. Figure 2.18(b) shows one structure schematically. A rotation about the z-axis, orthogonal to the plane of the chip, will induces a Coriolis force that displaces the inner frame at right angles (normal) to the plan of the vibratory motion. This Coriolis motion is sensed by a series of capacitors structures placed on the edges of the inner frame. The resulting signal is farther processed to extract the rate of rotation signal output.
Figure 2.17: Commercial micromachined gyroscope from Silicon Sensing Systems [132].
Figure 2.18 (a) Die photo of the surface-micromachined gyroscope from Analog Devices with the interface and control electronics integrated on the same chip. It contains two identical mechanical structures to achieve differential sensing. (b) Schematic drawing of one of the two identical gyroscope elements.
