KR101433590B1 - Parametric amplification of a mems gyroscope by capacitance modulation - Google Patents

Abstract

The parameter amplification of the output of the MEMS gyroscope is obtained by modulating the auxiliary capacitance with the sense capacitance or the applied DC voltage. The capacitance modulation is generated by the driving motion of the gyroscope mechanism so that the pump signal of the parameter amplifier is not exposed to the phase error of the electronic device. The capacitance modulation affects the mechanical gain of the sensor as well as the electrical gain of the sensor (the transfer function from the sensor mechanism displacement to the output electrical signal) (the transfer function from the input force to the sensor mechanism displacement). The mechanical and electrical gains of the sensors are phase dependent, so that the undesired quadrature signal is attenuated while the Coriolis velocity signal is amplified.

MEMS, gyroscope, capacitance modulation, parametric amplification

Description

[0001] PARAMETRIC AMPLIFICATION OF A MEMS GYROSCOPE BY CAPACITANCE MODULATION [0002]

[Priority claim]

This patent application is a continuation-in-part of US patent application, entitled " PARAMETRIC AMPLIFICATION OF A MEMS GYROSCOPE BY CAPACITANCE MODULATION, " filed December 12, 2007, 61 / 013,041.

[Government Rights]

The present invention was made with support from the US government under Contract No. W15P7T-05-C-P609 and / or W15P7T-07-C-P609, as financed by the US Army. The US government may have certain rights to the invention.

A MEMS (Micro-ELectro-Mechanical System) gyroscope sensor consists of one or more movable inert mass masses connected to each other by a flexible suspending member or connected to a substrate. In general, inertial mass and suspending members are fabricated by etching strongly doped silicon, which is bonded to one or more upper and / or lower glass or silicon substrates.

The inertial mass is electrostatically driven at the resonant frequency of the "motor" mode. When the sensor is subjected to rotation, the speed of the motor-mode motion is subjected to the Coriolis force whose inertia mass is perpendicular to the motor speed and rotation axis. The motion of the inertial mass caused by the Coriolis force is capacitively sensed by the sensing electrode to produce an electrical output signal.

In various MEMS gyroscopes, the motor mode consists of two inertial masses moving at the same or opposite speed parallel to the substrate, with the two inertial masses along a line connecting the centers of the two inertial masses It moves. The motor mode resonance frequency may be in the range of 10 to 20 kHz. The MEMS gyroscope sensor may be designed to sense either a rotation parallel to the substrate or a rotation perpendicular to the substrate. The Coriolis force drives a "sense" resonance mode of the silicon mechanism consisting of two inertial masses moving in parallel or vertically opposite directions to the substrate as the axis of rotation is perpendicular or parallel to the substrate. A sensor designed to sense rotation about an axis parallel to the substrate is called an in-plane gyroscope (IPG), and a sensor designed to sense rotation about an axis perpendicular to the substrate may be a z-axis gyroscope or an OPG -of-plane gyroscope.

In a MEMS gyroscope, the resonance frequency of the sensing mode is typically 5% to 10% or less of the resonance frequency of the motor mode, so that the Coriolis force drives the sensor mode out of resonance. Other MEMS gyroscopes can operate with a sense resonance frequency as close as possible to the motor resonance frequency to maximize the scale factor. However, the bandwidth of such a sensor is very limited and can have safety problems.

Other MEMS gyroscopes may be quite different from the two inertial mass configurations described above. However, these moments can have a motor mode driven at their resonant frequency, receive the force of the Coriolis during rotation, and the Coriolis force drives the sense mode in which the motion is capacitively detected.

The sensor output signal at the MEMS gyroscope is an AC signal at the motor resonant frequency. A typical MEMS gyroscope has a large output error signal, meaning "quadrature", which is 90 degrees out of phase with the output signal generated by the Coriolis force. Phase sensitive detection allows the Coriolis velocity signal to be detected when there is a much larger quadrature signal. However, phase shifting in electronic devices and sensors causes quadrature signals to produce errors in Coriolis-phase signals.

Parameter amplification in a MEMS gyroscope using a pump signal consisting of an AC voltage applied to a sensing electrode has been previously described in US Pat. No. 6,715,353 (Burgess R. Johnson, Apr. 6, 2004) . The AC pump voltage can increase the mechanical gain (the transfer function from the input force to the sensor mechanism displacement) of the sensor, as well as the electrical gain of the sensor (the transfer function from sensor mechanical displacement to the output electrical signal). In addition, the mechanical and electrical gain of the sensor is phase-dependent, so that the Coriolis velocity signal can be amplified while the undesired quadrature signal is attenuated.

Oropeza-Ramos et al. Describe the use of parameter resonance to modify the characteristics of the driving mode of a MEM gyroscope (see "Parametric Resonance Amplification in a MEM Gyroscope," LA Oropeza-Ramos and KL Turner, Proceedings of the 2005 IEEE Sensors Conference , Pages 660-663, October 31 - November 3, 2005, California Irvine), the disclosure of which is incorporated herein by reference.

As described in U.S. Patent No. 6,715,353, the difficulty in using the AC pump voltage to provide parameter amplification is that the phase of the pump voltage must be precisely synchronized with the phase of the drive motion of the sensor mechanism. If not, the parameter amplification causes a phase shift of the sensor output signal relative to the phase of the input force at the sensor. As a result, a relatively large quadrature force with respect to the sensor mechanism can produce a sensor output at the Coriolis velocity phase, resulting in a zero-rate bias error.

Therefore, it is an object of the present invention to solve the problems of the prior art described above.

According to one embodiment of the present invention, parameter amplification of the output of the MEMS gyroscope is obtained by modulating an auxiliary capacitance having a sense capacitance or an applied DC voltage.

According to one embodiment of the present invention, the capacitance modulation is generated by the driving motion of the gyroscope mechanism so that the pump signal of the parameter amplifier is not exposed to the phase error of the electronic device.

FIG. 1 illustrates an exemplary Micro-ELectro-Mechanical System (MEMS) capacitance modulation device 100. An exemplary embodiment of the MEMS capacitance modulation device 100 includes a first vibrating mass 102, a second vibrating mass 104, one or more left motors 106, an upper center motor pick-off 108, The left center comb structure 114, the right center comb structure 116, the right comb structure 118, the left center comb structure 114, the left center comb structure 112, Includes an electrode (120), a right sensing electrode (122) and an output electrode (124) connected to one or more anchors (126).

The left motor 106 is capacitively coupled to the first vibrating mass 102 via the left comb structure 112. [ The right motor 110 is coupled with the second vibrating mass 104 through the right comb structure 118 in an abstraction. The center motor pick-offs 108 and 109 are capacitively coupled to the first vibrating mass 102 via the first central comb structure 114. The center motor pick-offs 108 and 109 are capacitively coupled to the second vibrating mass 104 via the second central comb structure 116. The left motor 106 and the right motor 110 are driven with a signal to give a vibration motion to the first vibrating mass 102 and the second vibrating mass 104 at a known frequency hereinafter referred to as the motor frequency. The center motor pick-off 108, 109 is biased to a DC voltage so that the motion of the inertial mass along the x-axis produces an AC current input to the electronic device that controls the signal applied to the motor comb.

The sensing electrodes 120 and 122 are capacitively coupled to the first and second vibrating masses 102 and 104 by a plurality of comb finger pairs 128. Each comb finger pair 128 has one comb finger attached to the vibrating mass and another comb finger attached to the sense electrode. The sensing electrodes 120 and 122 are connected to the anchor 130. In an exemplary embodiment, the comb finger pairs 128 are spaced from other comb finger pairs by a predetermined distance. Further, in some embodiments of the sensing electrodes 120, 122, the pairs of comb fingers have a corresponding pair such that the two pairs have a mirror symmetry with respect to the motor axis shown in Fig. Other configurations for the comb structure may be used in other embodiments of the MEMS capacitance modulation device 100.

The embodiment of the MEMS capacitance modulation device 100 employs various configurations in the structure of the comb finger pair 128 as described in more detail below. The structure of the comb finger pair allows the capacitance of the comb finger pair 128 to vary along the motor axis along with the displacement of the vibrating mass.

The embodiment of the MEMS capacitance modulation device 100 generates parameter amplification with the phase of the pump force precisely synchronized with the phase of the motor motion of the sensor mechanism. In some embodiments, this allows the motor motion to generate a modulation of the sensing capacitance at twice the motor frequency, thereby causing the sensing electrodes 120, 122 to be brought to bring the parameter pump force at twice the motor frequency due to the modulation of the electrostatic force in the sensing mode. Design can be achieved. Since the parameter pump force is generated by the motor motion of the inertia mass, the parameter pump force is precisely synchronized with the motor motion of the inertia mass.

The time-dependent electrostatic force F _y along the y-axis generated by the capacitance C, which is a function of time and y-axis displacement (i.e., sensing mode displacement), is given by:

Here, _Vbias is the voltage of the capacitor electrode, and dC / dy is a derivative of C with respect to y. Modulating dC / dy at twice the motor frequency causes the force F _y to be modulated to twice the motor frequency when V _bias is a DC voltage. Thus, F _y (t) provides parameter amplification of the mechanical response of the inertial mass to an input force (e.g., Coriolis force). Alternatively, or in addition, F _y (t) may be a pump force that provides suppression of the response to a quadrature force. The amplified mechanical response is generated in a manner similar to that described in U.S. Patent No. 6,715,353, except that the pump force of the present invention is generated by modulation of the sensing capacitance. The pump force described in U.S. Patent No. 6,715,353 was generated by applying an AC voltage to the sense capacitance, and V _bias ² was modulated to twice the motor frequency with a time independent dC / dy.

Figure 2 shows an assembly 200 comprising two pairs of sensing comb fingers that are part of a MEMS gyroscope according to the prior art, with one member of each pair being attached to a vibrating inertial mass 202. The total capacitance of the two comb finger pairs is independent of the displacement distance of the vibrating mass 202 along the x-axis. The assembly 200 includes an inertial mass 202, a left sensing electrode comb finger 204, and a right sensing electrode comb finger 206. The left sensing electrode comb fingers 204 and the right sensing electrode comb fingers 206 are attached to the corresponding sensing electrodes 208. The sensing electrode 208 is fixed to an anchor attached to a substrate (not shown). The left sensing electrode comb fingers 204 and the right sensing electrode comb fingers 206 are capacitively coupled to the comb fingers 210 and 212 of the inertial mass 202, respectively. The motor motion induced in the inertial mass 202 along the x-axis does not cause capacitance fluctuations between the sensing electrode comb fingers 204, 206 and the comb fingers 210, 212 of the inertial mass.

3 shows the capacitance as a function of the motor displacement distance delta x of the assembly 200 according to the prior art. The inertia-mass motor motions follow the x-axis. Motor motion produces the same and opposite variations in the left and right capacitances of the sensing electrode comb fingers 204, 206 and the comb fingers 210, 212. Thus, the total capacitance is independent of motor motion.

FIG. 4 illustrates an assembly 400 that includes two instances of an exemplary embodiment of a sensing comb finger pair 128 that provides modulation of sensing capacitance. Assembly 400 may be part of a MEMS gyroscope. The assembly 400 includes an inertial mass 402, a left sensing electrode comb finger 404 and a right sensing electrode comb finger 406. The inertial mass 402 has a left inertial mass comb electrode 408 that provides capacitive coupling with the corresponding sense electrode comb fingers 404 in the interval 410. The inertial mass 402 has a right inertial mass comb electrode 412 that provides capacitive coupling with the corresponding sensing electrode comb fingers 406 at an interval 414. The right inertial mass comb electrode 412 has a capacitance The sensing electrode comb fingers 404 and 406 are attached to the sensing electrode 416. The sensing electrode 416 is fixed to an anchor attached to a substrate (not shown).

The sensing electrode comb fingers 404 and 406 are defined by an end portion 418 and an attachment portion 420 that fixes to the corresponding sensing electrode 416. Inertial mass comb fingers 408 and 412 are defined by an attachment portion 424 that secures end 422 and inertial mass comb fingers 408 and 412 to inertial mass body 426.

The separation between the inertial mass comb fingers 408, 412 and the sensing electrode comb fingers 404, 406 defines an interval 410, 414. The spacing 410 and 414 define the capacitive coupling (capacitance) between the sensing electrode comb fingers 404 and 406 and the inertial mass comb fingers 408 and 412.

In Figure 4, the comb finger end 418 has a width that is greater than the width of the comb finger attaching portion 420. Alternatively, the inertial mass comb fingers 408 and 412 are wider than the portion 424 attached to the body 426 of the inertial mass 402. (In other embodiments, the comb finger portions 418,420 have the same width, while the comb finger portion 422 is wider than the comb finger portions 424.) / Or the difference in width of the comb finger portions 422 and 424 causes a variation in the spacing 410 and 414 when the motor movement is induced in the inertial mass 402. In an exemplary embodiment, the sensing electrode comb fingers 404 and 406 are modulated at twice the motor frequency.

The motor movement induced in the inertial mass 402 leading to the motor displacement distance delta x along the x-axis shown is dependent on the capacitance between the sensing electrode 416 and the inertial mass 402 as the spacing 410, Lt; / RTI > The derivative of the capacitance with respect to the displacement along the y-axis also varies according to the motor displacement? X. As a result, when a DC bias voltage is applied between the sensing electrode 416 and the inertial mass 402, the electrostatic force along the y-axis given by equation (1) varies with the x-axis displacement of the inertial mass. According to Fig. 5, the capacitance is configured to decrease in accordance with the positive and negative motor displacement distances? X. For positive delta x, the average spacing separation between the comb fingers 406 and 412 is reduced relative to delta x = 0, and the average spacing separation between the comb fingers 404 and 408 is constant. Therefore, the total capacitance decreases as compared to the value when? X = 0. Because of the mirror symmetry of assembly 400, the negative value of delta x causes a decrease in capacitance.

FIG. 6 shows an assembly 600 having two cases for an exemplary embodiment of a sensing comb finger pair 128 that provides modulation of the sensing capacitance. Assembly 600 may be part of a MEMS gyroscope. The assembly 600 includes an inertial mass 602, a left sensing electrode comb finger 604 and a right sensing electrode comb finger 606. The inertial mass 602 has a left inertial mass comb electrode 608 that provides capacitive coupling with the left sensing electrode comb fingers 604 at an interval 610. The inertial mass 602 has a right inertial mass comb electrode 612 that provides capacitive coupling with the right sensing electrode comb fingers 606 at an interval 614. [ The sensing electrode comb fingers 604 and 606 are attached to the sensing electrode 616. The sensing electrode 616 is fixed to an anchor attached to a substrate (not shown).

The sensing electrode comb fingers 604 and 606 are defined by an attachment portion 620 that fixes the sensing electrode comb fingers 604 and 606 to the end portion 618 and the corresponding sensing electrode 616. The inertial mass comb fingers 608 and 612 are defined by an attachment portion 624 that secures the end portion 622 and the inertial mass comb fingers 608 and 612 to the inertial mass body 626.

The separation between the inertial mass comb fingers 608, 612 and the sensing electrode comb fingers 604, 606 defines an interval 610, 614. The spacing 610 and 614 define the capacitive coupling (capacitance) between the sensing electrode comb fingers 604 and 606 and the inertial mass comb fingers 608 and 612.

In Figure 6, the width of the comb finger end 618 is smaller than the width of the portion 620. The inertial mass comb fingers 608 and 612 have ends 622 that are less than the width of the portion 624 attached to the body 626 of the inertial mass 602. [ (In other embodiments, portions 618 and 620 have the same width, while end portion 622 has a width that is narrower than portion 624.) Portions 618 and 620 and / or portion 622 , 624 causes a variation in the capacitance of the spacing 610, 614 when the motor movement is induced in the inertial mass 602. In the exemplary embodiment, the comb fingers 604 and 606 are modulated at twice the motor frequency. Thus, the capacitance is shown as a function of motor displacement in FIG.

The motor movement induced in the inertial mass 602 which yields the motor displacement distance delta x along the x-axis shown is dependent on the capacitance between the sensing electrode 616 and the inertial mass 602 as the intervals 610 and 614 change, Lt; / RTI > The derivative of the capacitance with respect to the displacement along the y-axis also varies according to the motor displacement? X. As a result, when a DC bias voltage is applied between the sensing electrode 616 and the inertial mass 602, the electrostatic force along the y-axis given by equation (1) varies with the x-axis displacement of the inertial mass. According to Fig. 7, the capacitance is configured to increase in accordance with the positive and negative motor displacement distances? X. For positive delta x, the average spacing separation between the comb fingers 606 and 612 is reduced relative to delta x = 0, and the average spacing separation between the comb fingers 604 and 608 is constant. Therefore, the total capacitance increases with respect to the value when? X = 0. Because of the mirror symmetry of assembly 600, the negative value of delta x causes an increase in capacitance.

FIG. 8 illustrates an assembly 800 having two cases for an exemplary embodiment of a sensing comb finger pair 128 that provides modulation of the sensing capacitance. Assembly 800 may be part of a MEMS gyroscope. Assembly 800 includes inertial mass 802, left sensing electrode comb finger 804 and right sensing electrode comb finger 806. The inertial mass 802 has a left inertial mass comb electrode 808 that provides capacitive coupling with the left sensing electrode comb fingers 804 at interval 810. The inertial mass 802 has a right inertial mass comb electrode 812 that provides capacitive coupling with the right sensing cathodic finger 806 in the interval 814. The sensing electrode comb fingers 804 and 806 are attached to the sensing electrode 816. The sensing electrode 816 is fixed to an anchor attached to a substrate (not shown).

The sensing electrode comb fingers 804 and 806 are defined by an attachment portion 820 that secures the sensing electrode comb fingers 804 and 806 to the end portion 818 and the corresponding sensing electrode 816. Inertial mass comb fingers 808 and 812 are defined by an attachment portion 824 that secures end 822 and inertial mass comb fingers 808 and 812 to inertial mass body 826. The separation between the inertial mass comb fingers 808, 812 and the comb fingers 804, 806 define the intervals 810, 814. Spacing 810 and 814 define capacitive coupling (capacitance) between sensing electrode comb fingers 804 and 806 and inertial mass comb fingers 808 and 812.

8, sensing electrode comb fingers 804 and 806 have a corrugated end 818 and a non-corrugated end 820. Alternatively, the inertial mass comb fingers 808, 812 include a corrugated end 822 and a non-corrugated attachment portion 824. The corrugation of the portion 818 and / or portion 822 may cause the motor motion to induce the inertial mass 802. In other words, Resulting in variations in the capacitance of the spacing 810, 814. In an exemplary embodiment, the sensing electrode 816 has a capacitance modulated twice the motor frequency. Therefore, the capacitance increases with the motor displacement. The capacitance is shown as a function of the motor displacement in FIG.

Motor motions induced in the inertial mass 802 that yield a motor displacement distance delta x along the depicted direction (x-axis) are determined by sensing electrodes 816 and inertial masses 802 Lt; RTI ID = 0.0 > capacitance. ≪ / RTI > The derivative of the capacitance with respect to the displacement along the y-axis also varies according to the motor displacement? X. As a result, when a DC bias voltage is applied between the sensing electrode 816 and the inertial mass 802, the electrostatic force along the y-axis given by equation (1) varies with the x-axis displacement of the inertial mass. According to Fig. 9, the capacitance is configured to increase in accordance with the positive and negative motor displacement distances? X. For positive and negative delta x, the average of the inverse of the interval separations in intervals 810 and 814 increases relative to delta x = 0. Therefore, the total capacitance increases with respect to the value when? X = 0. Because of the mirror symmetry of assembly 800, the negative value of delta x causes an increase in capacitance.

10 illustrates an assembly 1000 having two cases for an exemplary embodiment of a sense comb finger pair 128 that provides modulation of the sense capacitance. Assembly 1000 may be part of a MEMS gyroscope. The assembly 1000 includes an inertial mass 1002, a left sensing electrode comb finger 1004 and a right sensing electrode comb finger 1006. The inertial mass 1002 has a left inertial mass comb electrode 1008 that provides capacitive coupling with the left sensing electrode comb fingers 1004 in the interval 1010. The inertial mass 1002 has a right inertial mass comb electrode 1012 that provides capacitive coupling with the right sensing electrode comb fingers 1006 in the interval 1014. The sensing electrode comb fingers 1004 and 1006 are attached to the sensing electrode 1016. The sensing electrode 1016 is fixed to an anchor attached to a substrate (not shown).

The sensing electrode comb fingers 1004 and 1006 are defined by an attachment portion 1020 that fixes the sensing electrode comb fingers 1004 and 1006 to the end portion 1018 and the corresponding sensing electrode 1016. The inertial mass comb fingers 1008 and 1012 are defined by an attachment portion 1024 that secures the end portion 1022 and the inertial mass comb fingers 1008 and 1012 to the inertial mass body 1026. The separation between the inertial mass comb fingers 1008, 1012 and the comb fingers 1004, 1006 defines an interval 1010, 1014. The spacing 1010 and 1014 define the capacitive coupling (capacitance) between the sensing electrode comb fingers 1004 and 1006 and the inertial mass comb fingers 1008 and 1012.

10, the sensing electrode comb fingers 1004 and 1006 have a corrugated end portion 1018 and a non-corrugated end portion 1020. In this embodiment, the corrugated portion of the comb finger 1004 faces the corrugated portion of the comb finger 1008, and the corrugated portion of the comb finger 1006 faces the corrugated portion of the comb finger 1012.

The corrugation of portion 1018 and / or portion 1022 causes a variation in capacitance at intervals 1010 and 1014 when motor motion is induced in inertial mass 1002. In an exemplary embodiment, sensing electrode 1016 has a capacitance modulated twice the motor frequency. Thus, the capacitance decreases with the motor displacement. The capacitance is shown as a function of motor displacement in FIG.

Motor motions induced in the inertial mass 1002 that yield a motor displacement distance delta x along the direction (x-axis) shown are dependent on the sensing electrode 1016 and the inertial mass 1002 Lt; RTI ID = 0.0 > capacitance. ≪ / RTI > The derivative of the capacitance with respect to the displacement along the y-axis also varies according to the motor displacement? X. As a result, when a DC bias voltage is applied between the sensing electrode 1016 and the inertial mass 1002, the electrostatic force along the y-axis given by equation (1) varies with the x-axis displacement of the inertial mass. According to Fig. 11, the capacitance is configured to decrease in accordance with the positive and negative motor displacement distances? X. For positive and negative delta x, the mean of the reciprocal of the interval separations at intervals 1010 and 1014 decreases relative to delta x = 0. Therefore, the total capacitance decreases as compared to the value when? X = 0. Because of the mirror symmetry of assembly 1000, the negative value of delta x causes a decrease in capacitance.

12 illustrates an assembly 1200 having two cases for an exemplary embodiment of a sense comb finger pair 128 that provides modulation of the sense capacitance. Assembly 1200 may be part of a MEMS gyroscope. Assembly 1200 includes an inertial mass 1202, a left sensing electrode comb finger 1204 and a right sensing electrode comb finger 1206. The inertial mass 1202 has a left inertial mass comb electrode 1208 that provides capacitive coupling with the left sensing electrode comb fingers 1204 in the interval 1210. The inertial mass 1202 has a right inertial mass comb electrode 1212 that provides capacitive coupling with the right sensing electrode comb fingers 1206 at an interval 1214. The sensing electrode comb fingers 1204 and 1206 are attached to the sensing electrode 1216. The sensing electrode 1216 is fixed to an anchor attached to a substrate (not shown).

The sensing electrode comb fingers 1204 and 1206 are defined by an attachment portion 1220 that fixes the sensing electrode comb fingers 1204 and 1206 to the end portion 1218 and the corresponding sensing electrode 1216. Inertial mass comb fingers 1208 and 1212 are defined by an attachment portion 1224 that secures end 1222 and inertial mass comb fingers 1208 and 1212 to inertial mass body 1226. [

The separation between the inertial mass comb fingers 1208 and 1212 and the sensing electrode comb fingers 1204 and 1206 defines the intervals 1210 and 1214. Intervals 1210 and 1214 define the capacitive coupling (capacitance) between sensing electrode comb fingers 1204 and 1206 and inertial mass comb fingers 1208 and 1212.

Figure 12 shows that x-axis movement of sensing electrode comb fingers 1204 and 1206 provides capacitance modulation of spacing 1210 and 1214. [ The sensing electrode comb fingers 1204 and 1206 and the inertial mass comb fingers 1208 and 1212 are tilted at a shallow angle relative to the x-axis so that motor movement of the inertial mass 1202 along the x-axis results in capacitance spacings 1210 and 1214 In a nonlinear manner on one side of the inertial mass 1202 and on the other side. Since the capacitance is inversely proportional to the spacing, the total capacitance increases by the x-axis displacement. In an exemplary embodiment, the non-linear dependence of the capacitance on the spacing 1210, 1214 provides a capacitance modulation in which the sloping sensing electrode has a dependence on the approximate parabola of the capacitance to the motor displacement, .

In Figure 13, the capacitance is shown as a function of motor displacement for the assembly of Figure 12. The capacitance is a nonlinear function of the motor displacement distance delta x along the x-axis shown. The derivative of the capacitance with respect to the displacement along the y-axis also varies according to the motor displacement? X. As a result, when a DC bias voltage is applied between the sensing electrode 1216 and the inertial mass 1202, the electrostatic force along the y-axis given by equation (1) varies with the x-axis displacement of the inertial mass.

The assembly 1200 can be configured to have a frequency response that is greater than that of the motor displacement when the frequency component of the capacitance modulation at twice the motor frequency is greater than when the capacitance is proportional to the absolute value of the motor displacement for the same amplitude of the motor displacement, The nonlinear capacitance as a function of the x-axis displacement of the inertial mass 1202 can provide more efficient parameter amplification than the electrodes of the assembly shown in Figures 4, 6, and / or 8. However, since the inclined electrode shown in Fig. 12 may be difficult and / or impractical to manufacture when the comb finger is very long, the configuration of Figs. 4, 6, and / or 8 may be desirable for a given situation have.

Also, the modulation of the capacitance produced by the matched comb fingers of the comb finger pair 128 shown in Figures 4, 6, 8, 10, and / or 12 is due to the first and second order of the capacitance for the displacement along the y- Generates the modulation of the derivative. The modulation of these derivatives is a source of parametric amplification that is the subject of various embodiments.

Modulating the sensing capacitance can affect the mechanical gain of the sensor (the transfer function between input and inertial mass sides) as well as the electrical gain (transfer function between inertial mass displacement and electrical output signal) of the MEMS gyro sensor. The effect on the mechanical gain is described below.

Figure 14a, 14b and 14c are exemplary four sensing capacitance that can be modulated at twice the motor frequency in the example _{C +1 (x, y 1)} , C -1 (x, y 1), C +2 (x , y ₂ ), and C _-2 (x, y ₂ ). For clarity, Figures 14a, 14b and 14c do not show the detailed capacitance shapes required for modulation. 14A, 14B, and 14C illustrate three methods for applying a sense bias voltage to the MEMS gyroscope 1400 and corresponding methods for coupling a charge amplifier for generating an output voltage proportional to the rotational speed.

14A shows two polarities of the sense bias voltage on the sense plate and a single-eneded amplifier whose input is AC coupled to the sense plate. The sensing capacitance is biased at DC bias voltages V ₊ (positive) and V _- (negative) which may have the same magnitude and opposite polarity in some embodiments. Figure 14B shows differential charge amplifier 1408 with DC _bias coupled to the sensing plate with a single polarity of sense bias voltage, V _bias , on inertial masses 1404, 1406. Differential charge amplifier 1408 is typically configured so that the input is held at virtual ground. As a result, the voltage on the sensing plate is maintained at virtual ground. Figure 14c shows the two polarities of the sense bias voltage on the sensing plate and the single terminal amplifier with the input DC coupled to the inertial mass. The sensing capacitance is biased at DC bias voltages V ₊ (positive) and V _- (negative) which may have the same magnitude and opposite polarity in some embodiments.

The x-axis displacements of the two inertial masses 1404 and 1406 have the same magnitude (denoted as "x" in Figures 14A, 14B and 14C) but in the opposite direction. Rotation about an axis orthogonal to the motor axis (x axis) and the sensing axis (y axis) creates Coriolis forces on the inertial mass along the sensing axis. The displacement of the inertial mass as a result of the four detected change the capacitance hanyeo, Fig. 14a, 14b and 14c of the time-varying (time-varying) of the sensing capacitance input to the charge amplifier shown in charges q ₊ (t) and q _- (t).

The output of the system incorporating the sensor / charge amplifier shown in Figs. 14A, 14B, and 14C is designed to be sensitive only to the differential sense axis motion generated by the Coriolis force. Equation (2) describes the differential motion.

Here, y _S (t), which is a sense axis differential motion of inertia masses 1404 and 1406, referred to as sense mode motions, is defined by Equation (3).

및

이며, 차분 코리올리-위상 및 직각 위상 힘은 수학식 4에 의해 정의된다.The first and second time derivatives of y _S (t)

And

, And the differential Coriolis-phase and quadrature phase forces are defined by Equation (4).

Where [omega] is the drive frequency of motor motion along the x-axis, and [psi] is the phase factor. The phase of the drive motor motion is defined by equation (5).

The other variables in equation (2) are defined as follows.

m is the mass of each inertial mass,

is a damping parameter for the sensing mode,

ω _SM is the mechanical resonance frequency of the sensing mode (resonance frequency when no voltage is applied)

Is the magnitude of the V _bias to the embodiment of the size or (size is assumed to be the same) Figure 14b example _- V is Figures 14a and 14c in Example V and ₊ V in the.

The first term on the right side of equation (2) is the differential electrostatic force generated by the sensing capacitance. The displacements y ₁ (t) and y ₂ (t) are generally small. Thus, it is useful to develop the capacitance in the Taylor series at y ₁ (t) and y ₂ (t) and ignore the second order term or higher. x, y ₁ and y ₂ are assumed to be the same as if all four sense capacitances at 0, equation (2) is as shown in equation (6).

Here, C is calculated as a derivative of _{"+ 1} (x, 0), C for the _{y 1" +1 (x, y} 1), y 1 = time zero.

The motor motion modulates C " _{+ 1} (x, 0) as a function of time. The modulation consists of harmonics twice the motor frequency omega, as defined by equation (7).

Here,? ₀ "and? _N " are time-independent coefficients. The reflection symmetry of the sense capacitors along the x-axis (as shown in FIGS. 4, 6, 8, 10 and 12) causes the odd harmonics of the motor frequency to be zero and also sin (2nωt) in the Fourier series of sense capacitances. Quot; 0 "

The terms in equation (7) higher than n = 1 do not have a significant effect on y _s (t) and can therefore optionally be ignored. Substituting Equation (7) into Equation (6), Equation (8) is obtained.

Here, the electrostatically softened detection frequency? _S is defined by Equation (9).

Equation (8) has the form of the well-known Mathieu equation. Because of modulation of C " ₊ (x, 0) by motor motion of the inertial mass, the sense resonance frequency is modulated to twice the motor frequency. This modulation of the sense frequency provides parameter amplification in the embodiment.

Since the driving force F (t) is at a frequency? That is close to the sensing resonance frequency? _S with a large mechanical response, the sensing mode response y _S (t) given by solving equation (8) is mainly at the motor frequency?. The terms at other frequencies are far from the sense resonance frequency and therefore do not provide a large contribution to y _S (t). This is also the reason why (8) excludes terms at C " _{+ 1} (x, 0) with a frequency greater than 2?.

Assuming that the solution to equation (8) is of the form of equation (10) and ignoring the brake term, the solution can be expressed as equation (11).

Here, the phase? Is the same as the phase? Of the force F (t). The sign of the denominator in equation (11) is negative for? = 0 (Coriolis) and positive for? =? / 2 (quadrature). Equation 11 shows that if the sign of? ₁ "is equal to the sign of? _S ² -ω ² , then the amplitude of the response (? = 0) of y _S (t) to the Coriolis- phase force is increased by the capacitance modulation, The response to the quadrature phase force shows a decrease in amplitude.

The representation of the electrical gain of the sensor, which is a transfer function from the inertial mass sensing axis displacement to the electrical output, is derived here. The nonlinear mixing between the capacitance modulation and the sensing mode displacement of the inertial mass makes the electrical gain dependent on the phase so that the electrical signal for the Coriolis-phase signal can be larger than for the quadrature signal.

Charges q ₊ and q _- on the sensing capacitance are defined by equation (12).

Here, V _± may be a bias voltage on the sense of whether the capacitance of the polarity of the positive or negative as defined in Figures 14a and 14c, is a bias voltage (V _bias) applied to the inertial mass (1404, 1406) in Figure 14b.

y ₁ and deploy the capacitance as a Taylor series in y _2, and x, y ₁ and y ₂ are Assuming all four sense capacitances are to be the same as zero, equation (12) as defined by equation (13) is smaller y ₁ and may be approximated with respect to y _2.

The first derivative C ' _{+ 1} (x, 0) for the capacitance C ₊₁ (x, 0) and y ₁ is calculated using Equation 14 and Equation 12 in a similar manner to Equation 7 for C " ₊₁ Lt; RTI ID = 0.0 > Fourier < / RTI >

Here, α ₀ , α ₀ ', α _n and α _n ' are time-independent variables. Equations (14) and (15) are substituted into Equation (13), and the form for _yS (t) given by Equation (10) is assumed.

In equation (16), the term having a frequency higher than 2? Is ignored. The reading electronics of MEMS gyroscopes use phase sensitive detection to reject signals at frequencies other than the desired motor frequency ω, so that only the motor frequency component of the sensor output is of interest. In addition, since the configuration of the bias voltage combined with the selection of a single terminal or differential charge amplifier in the embodiment of Figs. 14A, 14B and 14C invalidates the contribution of these terms at the charge amplifier output, The term does not contribute to the gyroscope output.

Calculating Equation 16 for the Coriolis-phase (θ = 0) and quadrature (θ = π / 2) sense mode displacements and ignoring the first three terms of the right side, the charge on the sense capacitance is defined by equations 17 and 18 do.

Equations 17 and 18 show that the magnitude of the sensed capacitance charge is dependent on the phase of the sense mode displacement y _S (t). Thus, the electrical gain of the sensor is phase dependent, so that the electrical gain for the Coriolis-phase signal can be greater than for a quadrature signal.

Another way to modulate the sensing capacitance is to provide a set of auxiliary electrodes whose capacitance is modulated by motor motion. If a DC bias voltage is applied to such an auxiliary electrode and the second derivative of the capacitance with respect to the sensing axis displacement is modulated by the motor motion, then these electrodes can modulate the sensing frequency and generate parameter amplification. The parameter amplification is generated by modifying the mechanical gain of the sensor as expressed by Equation (11). Since the electrical gain is determined by the sensor electrode, the electrical gain of the sensor is not modified. Thus, the use of an auxiliary electrode can provide greater flexibility in designing the electrical and mechanical gains of the sensor independently.

The above-described embodiments of the comb finger pairs have been described in connection with the MEMS OPG. Embodiments may also be implemented in a MEMS IPG, MEMS accelerometer, or other MEMS device employing a comb pair that is operated to produce a sensed capacitance. Alternative embodiments for the MEMS capacitance modulation device 100 may also include sensing electrodes, inertial masses, and / or differently arranged corresponding comb fingers, or may be provided with a sensing electrode, an inertial mass, and / More or less.

While the preferred embodiments of the present invention have been illustrated and described, many modifications may be made without departing from the spirit and scope of the present invention, as set forth above. Therefore, the scope of the present invention is not limited by the disclosure of the preferred embodiments. Instead, the invention should be determined entirely only by reference to the following claims.

An embodiment of the invention in which an exclusive right or privilege is required is defined as follows.

Preferred and alternative embodiments of the present invention have been described above with reference to the following drawings.

1 shows an embodiment of a MEMS (Micro-ELectro-Mechanical System) capacitance modulation apparatus.

Figure 2 shows a sensing electrode of a conventional MEMS gyroscope with a time-independent sensing capacitance.

Figure 3 shows the capacitance as a function of the motor displacement distance [delta] x of the MEMS gyroscope according to the prior art of Fig.

Figures 4, 6, 8, 10 and 12 show the spacing between the electrodes which varies with motor displacement.

Figures 5, 7, 9, 11 and 13 show the capacitance as a function of the motor displacement distance delta x in the embodiment shown in Figures 4, 6, 8, 10 and 12, respectively; And,

Figures 14A, 14B and 14C illustrate a MEMS gyroscope sensor with four sensing capacitances.

Claims (10)

Inertial masses (426, 626, 826, 1026, 1226) having at least one inertial mass comb finger (408, 608, 808, 1008, 1208); A sensing electrode having at least one sensing electrode comb finger 404, 604, 804, 1004, 1204 spaced from the inertial mass comb finger by an interval 410, 610, 810, 1010, 1210; And An electrical output section operative to output a time-varying electrical output; / RTI > The inertial mass comb fingers 408, 608, 808, 1008, Inertial mass comb finger tips 422, 622, 822, 1022, 1222; And An inertial mass finger attachment portion coupling the inertial mass comb finger end to the inertial mass; Lt; / RTI > The gap defines a variable capacitive coupling between the inertial mass comb finger and the sensing electrode comb finger, The sensing electrode comb finger may include: Sensing electrode comb finger ends 418, 618, 818, 1018, 1218; And Sensing electrode comb finger attachments 420, 620, 820, 1020, 1220 that couple the sensing electrode comb finger ends 418, 618, 818, 1018, 1218 to the anchors 416, 616, 816, 1016, ; / RTI > Wherein the time-varying electrical output is amplified by a variation of the variable capacitive coupling generated by the motor movement of the inertial mass and the shape of the sensing electrode, and the shape of the sensing electrode is a shape Wherein the time-varying electrical output is amplified by a variation in the sensing capacitance, MEMS sensors. The method according to claim 1, Wherein at least one of the inertial mass comb finger end and the sensing electrode comb finger end is wider than its corresponding attachment portion such that the spacing increases as a function of displacement along the direction of the motor movement, Characterized in that the variable capacitive coupling decreases as the gap increases. ≪ RTI ID = 0.0 > MEMS sensors. The method according to claim 1, Wherein at least one of the inertial mass comb finger ends (422, 622, 822, 1022, 1222) and the sensing electrode comb finger ends (418, 618, 818, 1018, 1218) As a function of the displacement along the circumferential direction. ≪ RTI ID = 0.0 > MEMS sensors. delete delete delete delete delete delete delete

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