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206                                                                  Inertial Sensors

                 of the inner frame. The resulting signal is amplified and demodulated to produce the
                 rate signal output.
                    Other commercial gyroscopes are in the final stages of their commercialization
                 from companies such as Samsung and Sensonor.




          8.4   Future Inertial Micromachined Sensors

                 It is believed that in future years, the major innovation will come from multiaxis sen-
                 sors, both for linear and angular motion. As described above, three-axis accelerome-
                 ters using a single proof mass have been presented already as prototypes, but a
                 commercial version has not yet been implemented. As an ultimate goal, a single sen-
                 sor capable of measuring linear and angular motion for six degrees of freedom is
                 envisaged. Such a sensor can be fully integrated with the control and interface elec-
                 tronics on the same chip.
                    One interesting approach is to use a mechanical structure similar to the one
                 shown in Figure 8.16. Watanabe et al. [71] report a five-axis capacitive motion sen-
                 sor. Linear acceleration is sensed in the same way as described in the paper by
                 Mineta et al. [44]: Out-of-plane acceleration causes the proof mass to move along
                 the z-axis, and in-plane acceleration along either the x-or y-axes makes the proof
                 mass tilt. Additionally, the proof mass is vibrated along the z-axis with electrostatic
                 forces. Angular motion about the x- or y-axes induces a Coriolis-based tilting oscil-
                 lation of the proof mass. The oscillatory signals are of much higher frequency (about
                 2 kHz) as the signals caused by linear acceleration, and hence, they can be separated
                 easily in the frequency domain using electronic filters. In this way linear acceleration
                 and angular rate signals can be measured concurrently.
                    Another very promising approach towards such a sensor is to use a
                 micromachined disk that is levitated by electrostatic or magnetic forces and spun
                 about its main axes. This is similar to macroscopic flywheel type gyroscopes; how-
                 ever, the lack of a good bearing in the microworld has excluded this approach so far
                 for micromachined gyroscopes. Using a levitated object alleviates this problem. Any
                 angular motion perpendicular to the spin axis of the disk will cause it to recess, and
                 this can be detected by a capacitive position measurement to provide a measure of
                 the angular velocity. Using a levitated object for inertial sensing has several advan-
                 tages. First, since there is no mechanical connection from the substrate to the disk,
                 the effective spring constant is solely dependent on the electrostatic forces set up by
                 voltages or currents applied to surrounding electrodes; hence, the characteristics of
                 the sensor, such as bandwidth and sensitivity, can be adjusted on-line, according to
                 the application requirements. Second, when used as a gyroscope, quadrature error is
                 inherently ruled out. The comparable effect, due to the imbalance of the mass, will
                 manifest itself at the rotation frequency, whereas the Coriolis force will cause the
                 disk to recess at the rotational speed of the body of interest. These two frequencies
                 are several orders of magnitude apart and are easy to separate. Furthermore, there is
                 no need to tune the drive and sense resonant frequencies since the scale factor does
                 not depend on the matching of different modal frequencies. Linear acceleration
                 along the three axes can be measured simultaneously by measuring the displacement
                 of the disk.
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