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Gyroscopes (angular rate sensors) are used to measure the rate of rotation of their host. They have attracted lots of attention during the past decade. They have several applications. They can be used with micromachined accelerometers to provide heading information for inertial navigation purposes. Low cost and high precision gyroscopes find use in the fields of advanced automotive safety and comfort systems for ride stabilization and rollover detection, people-to-people and people-to-device communication, robotics, and medicine. Conventional, rotating wheel, high precision fiber optic and ring laser, gyroscopes are all too expensive and too large for use in new applications. Also, fiber has limited lifetime. Micromachining can shrink the sensor size by orders of magnitude, reduce the fabrication cost significantly, and allow electronics to be integrated on the same silicon chip. Due to the large market scope, various groups are working on new designs, technologies, and readout concepts for micromachined gyroscopes.
This chapter introduces a complete analysis for the designed gyroscopes as well as accelerometers. First novel structure for micromachined accelerometer is present and analyzed, then all gyroscopes structures are given with brief discussion about principle of operation, driving and sensing mechanisms, matching operation, then the chapter is ended by brief comparisons between different analyzed types.
The following section demonstrates and investigates the improvements of the new approach on one of the best and recent surface micromachined accelerometer available in literature.
Novel Architecture for Micromachined Accelerometer
There has been a wide interest and research diversity in micromachined (MEMS) accelerometer. This is basically due to the fact that they can be easily integrated and vacuum operated by means of low power electronics and, accordingly, implemented in miniature inertial navigation systems (INS). Consequently, various design and fabrication approaches have been well covered, especially for rate grade surface micromachined, which are still apart from the desirable inertial grade. The focus on surface micromachined accelerometer is due to the fact that they can be monolithically integrated with their sense circuitry. This is the main limitation to their bulk micromachined counterparts. However, bulk micromachined accelerometers significantly outperform surface micromachined ones in performance and can operate in the inertial grade range, which has never been attainable for surface micromachined accelerometer. Most of the designs in literature focus on Silicon based accelerometer due to their better mechanical and electrical properties in addition to the ease of microfabrication of its compounds. Employing different materials in accelerometer, especially metals can further improve their performance due to their high density which in turn increases their proof masses and quality factor. This work presents various novel ideas and approaches which are generically suitable for Silicon and metal based accelerometers. The ideas behind such approaches have been built up logically after the inspection of the key design parameters in the basic analytical equations of typical second order mass-spring-damper systems, which hold for their miniature or MEMS schemes. The following equations are the fundamental equations relating the key design parameters for the second order mass-spring-damper systems [134-137]:
where w is the mechanical resonance frequency, k is the spring stiffness constant, m is the vibrating proof mass, q is the mechanical quality factor, b is the damping factor, Xstatic is the maximum static amplitude at resonance, TNEA is the total noise equivalent acceleration which represents the noise floor for an accelerometer, T is the absolute temperature in Kelvin, and K is the Boltzmann constant. The following section describes the new approaches for surface micromachined accelerometer.
3.1.1 Vertical Suspension
This design introduces a novel architecture for high performance micromachined inertial sensors based on Silicon on Insulator (SOI). The new sensors are essential for high precision inertial navigation systems (INS), which serve a wide range of applications varying from automotive to space. The architecture proposed for accelerometers is feasible due to the advantages of the available SOI technology. The common designs of micromachined accelerometers are in-plane, i.e. the suspension and the proof mass vibrate in the same plane (parallel to the substrate surface). Such in-plane architecture limits the area fill factor of the proof mass and the whole sensor. The limited fill factor affects directly the proof mass, thus affecting the performance of the sensor by raising the noise level and resonance frequency and reducing the quality factor. During this investigation, it has found that the key factor to consider in increasing the proof mass is the area fill factor of the proof mass. As a result, we introduce, for the first time, the vertically suspended micromachined accelerometer as shown in Fig. 1 . The novel sensors possess overall large value area fill factors in addition to the increased thickness, which consequently allows reducing the overall area of the sensor for comparable performance relative to literature or achieving a relatively much improved performance for the same overall sensor area. The performance of the new designs was analyzed using finite element analysis techniques to determine the natural mode shapes and frequencies for a wide range of geometries in addition to the mechanical stability. The results were compared to the best previously reported results of high performance designs. The proposed structure is shown schematically in Fig. 3.1.
The vertical suspension scheme presented in the previous section aims briefly to build the accelerometer's suspensions vertically or normal to the substrate direction rather than in the substrate lateral directions. Actually, this new architecture has been found to open the floor for bulk micromachined accelerometer possessing ultra large sense capacitance and proof mass which in turn results in relatively much larger quality factor and therefore large sensitivity. This is clearly due to the fact that the design of a second order mass-spring-damper is simple based on literature, and high performance accelerometer seems to be achievable through new and uncommon architectures rather than the common and well-settled simple models for mass-spring-damper systems.
Figure 3.1 Vertical suspensions Accelerometer 
In order to illustrate the advantage of the new architectures, Tables 3.1 reports some of the main specifications taken into comparison for micromachined accelerometers. The analytical inspection and comparison through the main design equations in literature reveals that the new sensors are expected to operate in the inertial grade range due to their large mass, and low resonance frequencies as well as the accordingly suppressed noise floor by more than an order of magnitude, increased signal sensitivity by more than two orders of magnitude, signal to noise ratio (SNR) up to three orders of magnitude, and reduced support losses for high performance vacuum operation. In fact, the micromachined accelerometers are expected to have sub-µg acceleration resolution.
Table 3.1: Comparison of the new architecture with the state of the art micro- accelerometer reported in 
Mechanical Noise Equivalent Acceleration
€¾ 0.2 pF/g
€¾ 0.98 pF/g
3.1.2 Lateral Suspension
Maximum Mass Design
In this design a large proof mass with lateral suspension is used to increase the static displacement according to equation (3). This design use a standard SOI wafer with 100 micrometer structural layer covered by 4 micrometer Sio2 on the two sides of the wafer. The process flow is typical as the table design process flow except the first five steps. In this design an efficient usage of the silicon area between supports is used to define more sense combs. A design for this structure is shown in Fig. 3.2.
Figure 3.2 Maximum mass design MEMS-Based accelerometer
Maximum Capacitance Design
In this design a large proof mass with lateral suspension is used to increase the static displacement according to equation 3.3. This design use a standard SOI wafer with 100 micrometer structural layer covered by 4 micrometer SiO2 on the two sides of the wafer. In this design an efficient usage of the silicon area between supports is used to define more sense combs, as shown in Fig. 3.3. An extra sense combs is used imbedded in the proof mass. As the above design the suspension is defined in the structural layer only and the proof mass is extended to one hundred micrometer in the wafer.
Figure 3.3 maximum capacitance design micromachined accelerometer.
Angular rate sensors or gyroscopes are used to measure the angular velocity or rotation rate of their host. Low cost, small size and high precision gyroscopes are required for many applications such as, inertial navigation system (INS), automotive safety and comfort systems etc. Keeping in focus the low cost factor, a clear tendency to use surface micromachining like processes can be observed. Compared to conventional surface micromachining, a large thickness of the layer containing the movable structures is desired to obtain higher inertial mass and thus higher accuracy.
Keeping in focus the small physical size, low power consumed light weight introduces us to micromachining gyroscopes.
Almost micromachined gyroscopes are vibratory gyroscopes, (i.e.) determine the rotation rate as a function of sensing the Coriolis force in the secondary mode of oscillations. Coriolis force, which is an apparent force induced on a body travel with velocity v with respect to a rotation frame of reference, the Coriolis force, , where m is the mass, v is the velocity and is the rotation rate. The cross product means that the Fc is in a plane perpendicular on the plane that contains v and the rotation rate. Keeping in focus the high accuracy factor the Coriolis force must be maximized by Use large mass as large as possible and achieve large drive amplitude as large as possible.
Vibratory gyroscopes principle is depend on the transfer of energy between two vibrating modes. When the drive force is at the resonance frequency of the drive mode, the drive mode amplitude is maximized by the mechanical quality factor of the drive mode. When the sense mode resonance frequency is matched with drive mode resonance frequency, the sense mode displacement is improved by the mechanical quality factor of the sense mode and so the sensor sensitivity also does.
Excitation of proof mass to resonant frequency can be done through many ways; piezoelectric; electromagnetic; and electrostatic actuations are available as been explained in chapter one. From different studies the electrostatic actuation is the best one due to simplicity in implementation, all silicon material used to reduce temperature sensitivity, linearization of force essay etc.
Sensing the output signal displacement can be done through many ways, among these piezoresistive, electromagnetic, and capacitive. Also, optical sensing is available, but very expensive to implement. Among these the capacitive one is more suitable to implement, accurate, electronic readout are simple etc.
Minimizing the stray and parasitic capacitances is required, which can be achieved through using silicon-on-insulator (SOI) wafer.
For a capacitive MEMS gyroscope it is required to maximize the mass as well as the capacitance of the sensor to achieve high sensitivity.
In the following subsections, many parameter and definition concerning the gyroscope will be discussed briefly.
3.2.1 Quality Factor definition
The mechanical quality factor Q is a measure for the energy losses of the resonator or in other words, a measure for the mechanical damping . The Q factor is defined as the ratio between the total energy stored in the vibration and the energy loss per cycle.
Low energy losses imply a high Q-factor. The Q-factor cannot be determined directly, but instead can be deduced from the steady-state frequency response of a resonator. If a resonator excited by a harmonic force with constant amplitude:
High Q-factor means a sharp resonance peak and has several advantages which are lowering the energy required to maintain the vibration, minimizing the effect of the electronic circuitry on the oscillation frequency and reduce sensitivity towards mechanical disturbances.
3.2.2 Resonance Frequency
The idea of resonance frequency and Q can be explained in terms of an example of a single mass spring system . Consider Fig. 3.4, the proof mass has a mass of m, the suspension beam has an effective spring constant of k, and damping factor b affecting the dynamic movement of the mass. By using Newton's second law and the shown figure, the mechanical transfer function can be obtained as:
Where: is the external acceleration, is the proof mass displacement, is the natural resonant frequency and is the quality factor. The frequency response is:
Note that when the resonator operates under matching condition the response is amplified by the Q-factor.
Figure 3.4: Simple second order mass-damper-spring system.
3.2.3 Actuation Schemes
As micromachined vibratory gyroscopes are MEMS devices, all schemes for MEMS actuation can be applied here. The actuation mechanisms used to drive the vibrating element into its primary mode of vibration are electrostatic, electromagnetic, or piezoelectric. Although many other schemes introduced in the first chapter can be used, the application requirements limit us to temperature insensitive gyroscopes. Piezoelectric actuation is not suitable for gyroscopes, because silicon is not a piezoelectric material, then we require depositing thin film of a piezoelectric material. This introduces the gyroscope to temperature sensitivity problems. Although electromagnetic has large drive force, it requires more complicated structure. Electrostatic actuation more suitable and can be implemented in comb-drive scheme as well as parallel plate scheme. It is less expensive, easy to implement, and has a suitable driving force .
126.96.36.199 Electrostatic actuation
Electrostatic actuation is the most common type of electromechanical energy conversion scheme in micromechanical system. The fundamental actuation principle behind electrostatic actuators is the attraction of two oppositely charged plates. Their use is extensive in MEMS devices, since it is simple to fabricate closely spaced gaps with conductive plates on opposite sides.
For a parallel plate capacitor, the energy (W) stored at a given voltage (V) is equal to:
Where: C is the capacitance between plates and then, the force between the plates is:
Comb-drive type actuators make use of a large number of finite inter-digitated fingers that are actuated by applying a voltage between them, see Fig. 3.5. .
Figure 3.5 Schematic diagram shows a part of the comb drive assembly.
3.2.4 Sensing Schemes
To sense the Coriolis induced force or vibrations in the secondary mode, capacitive, piezoresistive, or piezoelectric detection mechanisms can be used. Optical detection is also feasible, but it is too expensive to implement . Among these schemes capacitive sensing is very easy to implement, less expensive, more reliable.
188.8.131.52 Capacitive Sensing
Capacitive sensing is one of the most important precision sensing mechanisms and includes one or more fixed conducting plates with one or more moving conducting plates. Capacitive sensing relies on the basic parallel-plate capacitor equation shown below. As capacitance is inversely proportional to the distance between the plates, sensing of very small displacements is extremely accurate . The capacitance is:
Where: is the permittivity of free space = 8.854*10-12 Fm-1, is the relative permittivity of material between the plates, is the overlapping plate area, and is the plate separation distance.
Principle of operation
The capacitive sensor works on the principle of change the capacitance that may be caused by:
Change in overlapping area (A).
Change in the distance between the plates (d).
Change in dielectric constant.
Advantages of capacitive sensors
They require extremely small forces to operate them.
They are extremely sensitive.
They have a good frequency response.
Sense capacitance Analysis
Consider the schematic shown in Fig. 3.6, it represent a part of the senor element. The gray part is the moving element which moves up and down in y-direction. Due to its motion, a variation in the capacitance appears between the moving and fixed finger of the comb drive. Due to the non-perfect decoupling, the sensor may be has some unwanted motion in the x-direction.
Let, the motion in y-direction which is the dominant motion is y, the motion in the x-direction which is not wanted is Δx, the change in the over lap distance is varied from (lo+ Δy) to (lo- Δy) according to the upper and lower capacitors, and the change in the gap spacing changes within each capacitor from (go+ Δx) to (go- Δx), using equation (3-11).
consider Fig. 3.6, which represent the potential diveder connection scheme for the snese capacitors.
From the above analysis, it is evidence that the motion in the x-direction does not affect the sensor seriously.
Fig. 3.6 Schematic diagram shows part of a comb drive and its equivalent electrical circuit.
During the last decades MEMS has received more attention. Its processes are large and in advance to achieve large inertial mass for those sensors that require large mass, high aspect ratio, less damping. In general, silicon micromachining processes for fabrication of vibratory gyroscopes fall into one of four categories: 1) silicon bulk micromachining and wafer bonding; 2) polysilicon surface micromachining; 3) metal electroforming and LIGA; and 4) combined bulk-surface micromachining or the so-called mixed processes .
Different Gyroscope Structures
Michael Kranz at Carnegie Mellon University designed and implemented Elastically Gimbaled Gyroscope (EGG) . A schematic diagram of the designed gyroscope is given in Fig. 3.7. This gyroscope was implemented through CMOS-MEMS process. The structure is 5 μm thick. The gyroscope is electrostatically driven and capacitively senses the induced-Coriolis force.
Figure 3.7 A schematic diagram of elastically gimbaled gyroscope (EGG) .
W. Geiger, et al, designed and implemented a new decoupled micro gyroscope based on the principle of decupling drive and sense modes using Decoupled Angular Velocity Detector (DEAVD), principle [170,171]. Three designs were introduced; doubly rotary drive and sense modes (RR- structure), doubly linear motion drive and sense mode (LL-structure), and doubly decupled micro gyroscope (DDMG).
Figure 3.8 a schematic diagram shows the layout structure of decoupled micro gyroscope (DDMG) 
Micromachined Vibratory Gyroscope design
The actual determination of the physical parameters of the above designs is not simple. The design process begins by sizing the drive mode to achieve a visible oscillation. The internal and external elements must be sized simultaneously to keep the resonance frequencies of the two modes matched. For EGG the sensor has an inner spring constant in both the x and y directions, and an external spring constant in both directions also. Ideally, the inner mass is suspended by springs that are compliant in the y-direction, but infinitely stiff in the x-direction, and the outer frame is suspended by springs that are compliant in the x-direction, but infinitely stiff in the y-direction. The other structures have four sets of springs to fully decouple the drive and sense modes completely. Beams 1, 2 and 4 are of the same type, which are crab-leg springs. Beam 3 is simple beam type. Driving the sensor to primary mode oscillation is done electrostatically by means of a set of comb-finger. Sensing the drive mode displacement amplitude is done capacitively by means of a set of comb-finger. The secondary mode displacement is sensed capacitively by means of two sets of comb fingers connected as voltage potential divider. Matching condition is then applied to determine the total mass of the sensor. Then resonance frequencies of drive and sense modes can be determined.
Two types of springs are used here. The crab-leg spring is shown schematically in Fig 3.9. It consists of two segments, thigh (show in figure) and arm. The thigh has length and width of la, and wa, respectively. The arm has length and width of lb, and wb respectively. The total spring constants for the four beams along x and y directions can be expressed as :
Where E is Young's Modulus of elasticity, and h is the structure thickness.
Figure 3.9: Crab-leg spring layout.
The simple beam springs are formed of one segment having a total spring constant given by :
Where: l and w are the length and width of the beam, respectively.
Figure 3.10: Schematic diagram shows a part of the comb drive assembly
Comb-drive fingers are used to produce the required electrostatic force. Consider the inter-digitated structure shown in Fig 3.10, the produced electrostatic force, Fd, is given by .
Where N is the number of finger, h is the structure thickness, V is the applied potential between fingers, go is the initial gap between fingers, andis the free space permittivity. It is evident from Eq. (3.21) that maximizing the force requires using large number of comb fingers, large structure thickness, and small gap between fingers, at the same potential deference.
If this force has the same frequency of the drive mode, the drive mode displacement is amplified by the quality factor of the drive mode, Qx. This force results in a maximum displacement of the excited mode Xd, calculated as :
Where Kx is the spring stiffness in the x-direction
Using a parallel plate approximation, the capacitive of a comb-drive like that of Fig 3.10 is given by,
(Change in overlap distance) (3.17)
(Change in gap separation) (3.18)
Where N is the number of fingers, h is the structure height, lo is the initial overlap, go is the gab separation, x is the lateral displacement, and y is the transverse displacement.
To operate the device in the matched mode, the resonant frequencies, of the modes must be nearly equal. The modal frequencies are matched by sizing the springs, the outer frame, and the inner mass simultaneously. From the analysis performed in chapter three for double mass gyroscope, the resonance frequency for the secondary and primary modes respectively can be written as:
ms = total sense mode mass.
md = total drive mode mass, and
Ky = spring stiffness in y-direction.
Equating the resonance frequency of the two modes (Eq. (3.25), gives the required condition on the mass as:
The frequency of the Coriolis force is equal to the resonance frequency of the drive mode, and its amplitude is modulated by the maximum drive mode displacement, Xd, and the rate of the external rotation, Ω as clear from Eq. (3.27).
If the sense mode is at the resonant frequency of the drive mode, the resulting displacement of the sensed mode can be calculated as:
The mechanical sensitivity, Sm, of the sensor can be obtained by dividing Eq. (3.22) by the input rotation rate, Ω,
In general, the output is connected as a capacitor voltage divider. For a carrier signal of , the output voltage at the center of the divider is at the frequency of the carrier signal, and has amplitude of:
, (Change in overlap distance) (3.24)
, (Change in gab separation) (3.25)
It is evident from Eqs. (3.24), and (3.25) that the electrical sensitivity can be represented by the second term in the above equations. Typical values of lo and go are 20 μm and 2 μm respectively, it shows that the electrical sensitivity is 0.25 V/ μm, and 2.5 V/ μm respectively. Although Eq. (3.25) shows high electrical sensitivity, it has a nonlinear operation and small dynamic range.
Symmetric and Decoupled MEMS Gyroscope
MEMS vibratory gyroscopes are based on transferring energy between two modes of oscillation. Applying an appropriate AC voltage across the drive comb-finger produces an electrostatic force. This force is a function of the number of comb fingers, structure thickness, applied potential and gap separation between fingers . If the drive force is at the resonance frequency of the drive mode, the drive mode displacement is amplified by the mechanical quality factor of the drive mode. When exposed to external rotation rate around the z-axis, an induced Coriolis force is produced along the y-axis. This force is a function of the drive mode velocity, the external rotation rate, and the mass. Accordingly, maximizing the drive mode amplitude and the structure mass are required to sense small input rotation rates. The Coriolis force excites the sense mode oscillation (secondary mode along the y-axis). If the resonance frequency of the sense mode is the same as the drive oscillation frequency, the sense displacement amplitude is amplified by the mechanical quality factor of the sense mode.
Fig. 3.11 shows a schematic diagram of the adopted gyroscope that was originally introduced in Ref. . It consists of an outer drive mass an inner mass (proof mass), and a sense mass element. The outer drive has a mass md and is anchored to the substrate by the first beam suspension, (beam 1). It carries two comb assemblies; these combs are used to produce the required driving electrostatic force, and to maintain constantly the drive oscillations. The inner mass (mi) is attached to the outer drive and sense element masses via two identical suspensions (beams 2 and 3 in Fig. 3.11). By this suspension scheme, the inner mass decouples the drive mode from the sense mode oscillations. The sense element supports the sense combs. It is anchored to the substrate through suspension beam 4, and to the inner mass via a simple beam (beam3), and has a mass ms. The mechanical crosstalk is minimized due to the decoupling between the drive and sense masses.
Fig. 3.11 The symmetric and decoupled micromachined gyroscope 
Fully Symmetric completely Decoupled Micromachined Gyroscope
Micromachined gyroscope is one of the most microelectromechanical sensors in the complexity of its design and operation. The sensor must be exited to produce an output signal. The device has lots of requirements to increase its performance. First, the devise should have a large mass to increase the induced Coriolis force and to decrease the Brownian noise, which is technology process limitation. Second, it requires matched mode operations to increase the performance by the quality factor of the sense mode. Third, it should be decoupled the vibration of drive and sense modes to decrease the mechanical crosstalk and to minimize the zero rate output. Forth, the gap spacing between comb fingers should be minimized to increase the sense capacitance, which is a process technology limitation. Fifth, increase the drive amplitude by increasing the drive force, and decrease the parasitic capacitance. Here a new fully symmetric and completely decoupled micromachined gyroscope (FSCDMG) is presented.
Fig. 3.12 shows schematic diagram of the proposed gyroscope structure code named fully symmetric decoupled micromachined gyroscope (FSDMG_A). It consists of outer frame, inner mass, and sense element. The outer frame, which consists of two C-shaped frames, is anchored to the substrate through a crab-leg beam suspension. It carries two combs assembly, and has a mass md. The first comb is used as drive actuator, and is assembled as four combs that are arranged symmetrically around the outer frame. The second comb is a control and sense combs. The sense one used to sense the drive mode displacement for feedback control purposes. The control combs have a control signal for electrostatic tuning. The inner mass as shown in Fig. 3.12 is attached to the outer frame via another crab-leg suspension, and to the sense element through folded beam, it has a function of decoupling the drive and sense elements from each other's, and has a mass mi. The sense element consists from two masses and supports the sense combs. It is anchored to substrate through another set of crab-leg suspension, and to the inner mass through a set of folded beam, as shown schematically in Fig. 3.12, and has a mass ms. The mechanical crosstalk is minimized due to the decoupling between the drive and sense masses.
Fig. 3.12 Schematic diagram shows the main component of a fully symmetric completely decoupled micromachined gyroscope (FSCDMG_A) .
The structure is fully symmetric about x- and y- axes; also complete decoupling is achieved by separating the drive and sense elements via the intermediate mass and the decoupling beams. This design alleviates most of the micromachined gyroscope drawbacks such as asymmetry, and coupling. Furthermore, it allows actuating the primary mode with higher electrostatic force, and increases the sense capacitance (Fig. 3.13).
The proposed sensor, as shown in Fig. 3.13, is composed mainly of three masses namely the drive mass, the intermediate mass and the sense mass. The design under consideration enables exciting primary mode oscillations along the x-axis in either differential or common mode. In addition, the amplitude of the drive mode vibration is kept constant all the time using a sense and feedback control system connected to the drive mass, also four sets of control combs are used to tune the resonance frequency externally via electric voltage. Using intermediate mass and decoupling beams achieve the complete decoupling. The second part of the sensor is the intermediate mass, which has two degrees of freedom. This mass is designed to decouple the primary and secondary mode oscillations to minimize the mechanical crosstalk. The sense mass consists of two identical sense elements each of which carries two sense capacitors (Fig. 3.13). These capacitors are connected differentially to cancel any interference of the drive mode motion into the output signal.
Figure 3.13: Schematic diagram shows the main component of a fully symmetric completely decoupled micromachined gyroscope (FSCDMG_B) .
It looks like the second version except for the folded beam suspension position and the decoupling beams are eliminated. It has low crowding around the drive actuators that enabling building the actuator to have large drive mode displacement in the linear region of the comb finger behavior.
Figure 3.14: Schematic diagram shows the main component of a fully symmetric completely decoupled micromachined gyroscope (FSCDMG_C) .
All the above structures have the same principle of operation. They are electrostatically driven to the resonance frequency of the primary mode, and capacitively sense the secondary mode displacement.
The comb-finger actuator applies an electrostatic force, produced by the potential difference between the fingers. This force excites the drive mode mass into linear oscillations along the x-direction. If the force is at the resonance frequency of the drive mode, the x-direction displacement is amplified by the quality factor of the drive mode. When the gyroscope is exposed to an angular displacement around the z-axis, Coriolis force is generated along the y-axis, which has the same resonance frequency as the drive mode. The induced-Coriolis force drives the inner mass to linear oscillations along the y-axis. If the sense mode has the same resonance frequency as that of the drive mode, the oscillation amplitude is amplified with the quality factor of the sense mode. Accordingly, the sensitivity of the sensor is amplified with the quality factor of the sense mode, Qy. The induced motion is sensed with a pair of comb-finger capacitors connected as a differential capacitive voltage divider.
This section introduces a comparison between different designs based on the analytical analysis. The numerical analysis will be introduced in chapter four. Table 3.2 summarize the main analytical results for the above four designs. Based on the same wafer type (SOI- 100 orientation), same driving and sensing schemes and by investigating table 3.2, it is clear that the third design (fully symmetric and completely decoupled micromachined gyroscope the third version) has the best performance at the same area. This is due to efficient usage of silicon area and relaxation of the design complexity to achieve large driving amplitudes.
Table 3.2 Comparison between discussed gyros parameters.
Drive Force (μN)
Resonant frequency (Hz)
Coriolis Force (nN/(°/s))
Drive amplitude (μm)
Sense amplitude (nm)