Patent Publication Number: US-11650078-B2

Title: Demodulation phase calibration using external input

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of U.S. application Ser. No. 16/217,509, filed Dec. 12, 2018, and entitled “DEMODULATION PHASE CALIBRATION USING EXTERNAL INPUT,” which claims priority to U.S. Provisional Application No. 62/598,332, filed Dec. 13, 2017, and entitled “DEMODULATION PHASE CALIBRATION USING EXTERNAL INPUT,” and is a Continuation-in-Part of U.S. application Ser. No. 15/173,530, filed Jun. 3, 2016, now U.S. Pat. No. 10,267,650, and entitled “DEMODULATION PHASE CALIBRATION,” all of which are hereby incorporated by reference herein in their entireties. 
    
    
     BACKGROUND 
     Micro-electromechanical systems (MEMS) and their use has become prevalent. For example, MEMS may be used as an accelerometer, gyroscope, optical switching, microphones, silicon pressure sensor, magnetic sensor, etc., in various industries such as the airbag industry, the aviation industry, the display industry, the tire pressure industry, etc. Unfortunately, package stress and other causes may cause error and degradation in the performance of the MEMS structure. For example, package stress may induce an offset shift in a MEMS structure, e.g., a quadrature shift in a gyroscope, resulting in an error by introducing error in gyroscope demodulation phase angle. 
     SUMMARY OF THE INVENTION 
     Accordingly, a need has arisen to determine errors introduced, e.g., by package stress, and further to calibrate the MEMS structure in order to improve the performance of the MEMS device. Provided herein is a method and system for determining an error resulting from various factors such as package stress. The determined error may be used to calibrate the demodulation phase of a gyroscope in order improve performance of the gyroscope. 
     According to some embodiments, a method includes receiving a signal from a sensor, wherein the signal comprises a first in-phase component and a first quadrature component. The method further includes identifying the first in-phase component. The method also includes identifying the first quadrature component. A rate signal may be applied to the sensor, wherein the sensor in response to the applying the rate signal generates a sensed rate signal. A second in-phase component associated with the sensed rate signal and a second quadrature component associated with the sensed rate signal may be determined. A phase error may be determined based on the first and the second in-phase components, and the first and the second quadrature components. 
     The first in-phase component, the first quadrature component, and the second in-phase component and the second quadrature component can be identified through sequential demodulation of the signal and the sensed rate signal. The first in-phase component can be identified through demodulation of the signal using a first demodulator, and the first quadrature component can be identified through demodulation of the signal using a second demodulator. It is appreciated that the first demodulator may be independent from the second demodulator, and the first demodulator and the second demodulator may be configured to identify the first in-phase component and the first quadrature component simultaneously. 
     It is appreciated that the second in-phase component may be determined through demodulation of the sensed signal using the first demodulator, and the second quadrature component may be determined through demodulation of the sensed signal using the second demodulator, and the first demodulator and the second demodulator may be configured to identify the second in-phase component and the second quadrature component of the sensed rate signal simultaneously. 
     The method may further include applying a rotation to the sensor to generate the rate signal. In some embodiments, the method may include changing rotation rate of the sensor to generate a change in the rate signal. For example, the change in rotation rate may occur by applying an electrostatic force, a magnetic force, and a piezoelectric force. 
     The method may further include determining a difference of the first quadrature component and the second quadrature component to generate a quadrature difference, determining a difference of the first in-phase component and the second in-phase component to generate an in-phase difference, and determining the phase error by processing an arctangent of the quadrature difference and the in-phase difference. 
     In some embodiments, the method may further include reducing error in measurements associated with the sensor by dynamically compensating for the determined phase error. It is appreciated that a clock signal may be modified based on the determined phase error to reduce error, and the modified clock may be used in determining in-phase and quadrature components. 
     The method may further include changing a demodulation phase of a demodulator used to identify the first in-phase component, the first quadrature component, the second in-phase component, and the second quadrature component. 
     It is appreciated that the sensor device may be a micro-electromechanical system gyroscope. 
     It is appreciated that the phase error detection may occur in response to detecting a motion. The method may include periodically applying another rate signal to the sensor to generate another sensed signal, determining another in-phase component and another quadrature component associated with another sensed rate signal, and updating the phase error based on the determining another in-phase component and the another quadrature component associated with the another sensed rate signal. 
     It is appreciated that in some embodiments the method may include determining a difference of the first quadrature component and the second quadrature component to generate a quadrature difference, determining a difference of the first in-phase component and the second in-phase component to generate an in-phase difference, and determining sensitivity associated with the sensor based on the quadrature difference and the in-phase difference. 
     In some embodiments, a device may include a sensor device, a first demodulator, a second demodulator, and a processing unit. The sensor device may be configured to generate a signal comprising a first in-phase component and a first quadrature component. The first demodulator may be configured to identify the first in-phase component. The second demodulator may be configured to identify the second quadrature component. The processing unit may be configured to determine a phase error associated with the sensor device. It is appreciated that the phase error may be determined based on the first quadrature component and the first in-phase component and may be further based on a second in-phase component associated with a sensed rate signal and a second quadrature component associated with the sensed rate signal. It is appreciated that the first in-phase component may be determined by the first demodulator and the first quadrature component may be determined by the second demodulator. According to some embodiments, the sensed rate signal may be generated by the sensor device in response to application of a rate signal thereto. 
     In some embodiments, the device may further include a first filter coupled to the first demodulator. The first filter may be configured to generate an averaged in-phase component signal for transmission to the processing unit for determining the phase error. The device may also include a second filter coupled to the second demodulator. The second filter may be configured to generate an averaged quadrature component signal for transmission to the processing unit for determining the phase error. According to some embodiments, the first filter and the second filter are selected from a group consisting of a low pass filter, integrator, and a bandpass filter. 
     It is appreciated that the sensor device may be a micro-electromechanical system gyroscope. 
     The processing unit may be configured to calculate a difference between the first quadrature component and the second quadrature component to generate a quadrature component difference. It is appreciated that the processing unit may be further configured to calculate a difference between the first in-phase component and the second in-phase component to generate an in-phase component difference. In some embodiments, the processing unit is further configured to determine the phase error by calculating the arctangent of the quadrature component difference and the in-phase component difference. In some embodiments, the processing unit is selected from a group consisting of a central processor, a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC). 
     According to some embodiments, output readings from the sensor device may be calibrated to compensate for the phase error. 
     In some embodiments, the processing unit may be configured to calculate a difference between the first quadrature component and the second quadrature component to generate a quadrature component difference. The processing unit may further be configured to calculate a difference between the first in-phase component and the second in-phase component to generate an in-phase component difference. In some embodiments, the processing unit may be further configured to determine sensitivity of the sensor device based on the quadrature component difference and the in-phase component difference. 
     In some embodiments, a device may include a sensor device, a demodulator, and a processing unit. The sensor device may be configured to generate a signal comprising a first in-phase component and a first quadrature component. The demodulator may be configured to sequentially identify the first in-phase component and the first quadrature component. In some embodiments, the processing unit may be configured to determine a phase error associated with the sensor device. It is appreciated that the phase error may be determined based on the first quadrature component and the first in-phase component and is further based on a second in-phase component associated with a sensed rate signal and a second quadrature component associated with the sensed rate signal. According to some embodiments, the second in-phase component and the second quadrature component may be sequentially determined by the demodulator. In some embodiments, the sensed rate signal may be generated by the sensor device in response to application of a rate signal thereto. 
     The device may include a filter coupled to the demodulator. The filter may be configured to generate an averaged component signal received from the demodulator. In some embodiments, the filter is selected from a group consisting of a low pass filter, integrator, and a bandpass filter. According to some embodiments the averaged component signal may be transmitted to the processing unit for determining the phase error. 
     It is appreciated that the sensor device may be a micro-electromechanical system gyroscope. 
     The processing unit may be configured to calculate a difference between the first quadrature component and the second quadrature component to generate a quadrature component difference. In some embodiments the processing unit may be further configured to calculate a difference between the first in-phase component and the second in-phase component to generate an in-phase component difference. It is appreciated that the processing unit may further be configured to determine the phase error by calculating the arc-tangent of the quadrature component difference and the in-phase component difference. It is appreciated that the processing unit may be selected from a group consisting of a central processor, a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC). According to some embodiments, output readings from the sensor device is calibrated to compensate for the phase error. 
     In some embodiments of the present disclosure, a method for determining a phase error for a micro-electromechanical system (MEMS) device comprises receiving a first signal from the MEMS device, wherein the first signal comprises an in-phase component and a quadrature component, and applying an external signal to the MEMS device, wherein the phase of the external signal corresponds to the phase of the quadrature component. The method may further comprise receiving a second signal from the MEMS device, wherein the second signal is generated by the MEMS device based on the external signal, and wherein the second signal comprises a modified in-phase component and a modified quadrature component. The method may further comprise determining the phase error for the MEMS device based on the modified in-phase component and the modified quadrature component. 
     In some embodiments of the present disclosure, a micro-electromechanical system (MEMS) device may comprise a suspended spring-mass system and a sense system, wherein the sense system receives a first signal based on movement of the suspended spring-mass system, wherein the first signal comprises an in-phase component and a quadrature component. The MEMS device may further comprise a drive system, wherein the drive system applies an external signal to the MEMS device, wherein the phase of the external signal corresponds to the phase of the quadrature component, wherein the sense system receives a second signal generated by the suspended spring-mass system based on the external signal, and wherein the second signal comprises a modified in-phase component and a modified quadrature component. The MEMS device may further comprise processing circuitry configured to determine a phase error for the MEMS device based on the modified in-phase component and the modified quadrature component. 
     In some embodiments of the present disclosure, a device may comprise a sensor device configured to generate a first signal and a second signal, wherein the first signal comprises an in-phase component and a quadrature component, wherein the second signal is based on an external signal applied to the sensor device and having a phase that corresponds to the phase of the quadrature component, and wherein the second signal generated by the suspended spring-mass system comprises a modified in-phase component and a modified quadrature component. The device may further comprise a processing unit configured to determine a phase error for the sensor device based on the modified in-phase component and the modified quadrature component. 
     These and other features and aspects of the concepts described herein may be better understood with reference to the following drawings, description, and appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other features of the present disclosure, its nature and various advantages will be more apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings in which: 
         FIGS.  1 A- 1 C  show orientation of Coriolis vector in phase domain for calculating a phase error in accordance with some embodiments of the present disclosure; 
         FIG.  2    shows a system for determining a phase error and for compensating the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  3    shows another system for determining a phase error and for compensating the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  4    shows one system for determining a phase error and for compensating the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  5    shows a single demodulator system for determining a phase error and for compensating the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  6    shows another single demodulator system for determining a phase error and for compensating the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  7    shows yet another single demodulator system for determining a phase error and for compensating the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  8    shows a flow diagram for determining a phase error and for compensating for the phase error in accordance with some embodiments of the present disclosure; 
         FIG.  9    shows an illustrative MEMS sensor including quadrature tuning electrodes in accordance with some embodiments of the present disclosure; 
         FIG.  10    shows a flow diagram for determining a phase error based on an applied quadrature drive signal in accordance with some embodiments of the present disclosure; 
         FIG.  11    shows a flow diagram for determining a phase error based on an applied signal from a quadrature tuning signal in accordance with some embodiments of the present disclosure; and 
         FIG.  12    shows a flow diagram for determining a phase error based on an applied signal from a quadrature tuning signal in accordance with some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Before various embodiments are described in greater detail, it should be understood by persons having ordinary skill in the art that the embodiments are not limiting, as elements in such embodiments may vary. It should likewise be understood that a particular embodiment described and/or illustrated herein has elements which may be readily separated from the particular embodiment and optionally combined with any of several other embodiments or substituted for elements in any of several other embodiments described herein. 
     It should also be understood by persons having ordinary skill in the art that the terminology used herein is for the purpose of describing the certain concepts, and the terminology is not intended to be limiting. Unless indicated otherwise, ordinal numbers (e.g., first, second, third, etc.) are used to distinguish or identify different elements or steps in a group of elements or steps, and do not supply a serial or numerical limitation on the elements or steps of the embodiments thereof. For example, “first,” “second,” and “third” elements or steps need not necessarily appear in that order, and the embodiments thereof need not necessarily be limited to three elements or steps. It should also be understood that, unless indicated otherwise, any labels such as “left,” “right,” “front,” “back,” “top,” “middle,” “bottom,” “forward,” “reverse,” “clockwise,” “counter clockwise,” “up,” “down,” or other similar terms such as “upper,” “lower,” “above,” “below,” “vertical,” “horizontal,” “proximal,” “distal,” and the like are used for convenience and are not intended to imply, for example, any particular fixed location, orientation, or direction. Instead, such labels are used to reflect, for example, relative location, orientation, or directions. It should also be understood that the singular forms of “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. 
     Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by persons of ordinary skill in the art to which the embodiments pertain. 
     A need has arisen to determine errors introduced, e.g., by package stress, and further to calibrate the MEMS structure in order to improve the performance of the MEMS device. Provided herein is a method and system for determining an error resulting from various factors such as package stress. The determined error may be used to calibrate the demodulation phase of a gyroscope in order improve performance of the gyroscope. 
     In an exemplary embodiment of the present disclosure, a phase error may be determined by applying an external force to a MEMS device. The external signal may have a phase that corresponds to a quadrature component of a received signal from the MEMS device. By applying a known external signal under certain conditions, and/or by varying the external signal, the overall response signal may be varied based solely on the known external signal. An in-phase component and a quadrature component may be determined from the response signal and compared to baseline signals, such as in-phase and quadrature signals previously determined from a prior response signal under baseline conditions (e.g., without application of the external signal, and with a known rate of rotation or with a minimal rate of rotation). Based on the known input of the quadrature-related external signal or signals, the values associated with the baseline conditions, and the measured response signal or signals associated with the quadrature-related external signal or signals, a phase error may be determined. This phase error may then be used to modify the calculation of rate of rotation, for example, by modifying a demodulation phase angle used to demodulate received rate signals or by modifying an output signal of the gyroscope. 
     In an exemplary embodiment, the external signal may be applied as a periodic signal, for example, using capacitive or piezoelectric forces. While the MEMS device (e.g., MEMS gyroscope) is being driven in a normal manner, the external force may also be applied, but such that the force is sensed by output components (e.g., sense electrodes) of the MEMS device as a change in the quadrature component of the sensed signal. In some embodiments, an additional signal may be applied to drive circuitry (e.g., drive electrodes that apply a force to a drive mass) that is out of phase (e.g., 90° out of phase) with the signal that drives the MEMS device. In additional embodiments, the external signal may be applied by other components, such as electrodes that are used for sensing movement of masses (e.g., drive sense electrodes configured to sense movement of a drive mass, intermediate masses, and/or sense masses) of a suspended spring-mass system of a sensor such as a MEMS gyroscope. It will be understood that depending on the relative location (e.g., on the same or a different mass of a suspended spring-mass system of a gyroscope) and orientation (e.g., direction in which the external signal can be applied) of the drive components applying the external signal, the external signal may be applied in a variety of different manners to cause a change in a quadrature component of the sensed signal that corresponds to the applied external signal (e.g., causing a proportional increase in the quadrature component of the sensed signal, for determination of phase error). 
     In some embodiments, the external signal may be applied as a DC signal that results in a change (e.g., a proportional increase) in the quadrature component of the sensed signal. For example, quadrature tuning electrodes may be located at a suitable location relative to driven masses of a suspended spring-mass system (e.g., of a gyroscope) such that a DC signal applied to the quadrature tuning electrodes imparts a force on the driven masses that corresponds to the phase of the quadrature component of the sensed signal, i.e., based on a change in overlap between the driven masses and the quadrature tuning electrodes. The external signal applied to the quadrature tuning electrodes may cause a change in a quadrature component of the sensed signal that corresponds to the applied external signal (e.g., causing a proportional increase in the quadrature component of the sensed signal, for determination of phase error). 
     The phase error may be determined at a variety of times and in a variety of manners, and compensation may be performed as described herein. In some embodiments, a phase error may be determined during a manufacturing, testing, and/or calibration process by applying an external signal to modify a quadrature component of the sensed signal and/or applying an external rate to modify an in-phase component of the sensed signal. In some embodiments, the applied external signal and/or rate may be applied in an iterative manner to determine phase error and test the accuracy of compensation techniques. For example, an initial estimate of phase error may be determined, a compensation technique may be applied to the MEMS device, and then a known rate of rotation may be applied to test the accuracy of the output of the sensor (e.g., angular velocity or an output determined from angular velocity). This process may be repeated until the output of the sensor is within a suitable threshold of a desired output. 
     In some embodiments, a phase error may be determined during the active operational life of the MEMS device. The external signal may be applied at suitable times, for example, during device startup, a periodic calibration routine, or when the sensed parameter (e.g., angular velocity) has been less than a threshold for a predetermined period of time. By applying the external signal at suitable times during the operational life of the MEMS device, phase drift over the life of the sensor may be identified and compensation and/or modification of sensor operation (e.g., modification of drive signals, scaling factors, etc.) may be performed to increase the accuracy and operational life of the MEMS device. 
     Referring now to  FIGS.  1 A- 1 C , orientation of Coriolis vector in phase domain for calculating a phase error in accordance with some embodiments is shown. According to some embodiments, the orientation of the Coriolis vector in the phase domain may be determined using a rate table characterization. It is appreciated that aligning the sense mode demodulation phase to the Coriolis vector, e.g., by changing the demodulation phase, may improve the performance of the gyroscope. Thus, the demodulation phase angle of the gyroscope can be trimmed to Coriolis signal, improving the performance of the gyroscope. 
       FIG.  1 A  shows the in-phase and the quadrature components of a gyroscope. It is appreciated that the true in-phase and the true quadrature components may be unknown. As such, the phase error, for example resulting from package stress, may also be unknown. It is appreciated that the in-phase error and the quadrature error components may be 
     
       
         
           
             
               
                 
                   
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     It is, however, appreciated that the in-phase component at zero rate output may be measured, as depicted as I error,ZRO  in  FIG.  1 A . Similarly, the quadrature component at zero output may be measured, as depicted as Q error,ZRO  in  FIG.  1 A . It is appreciated that the in-phase error and the quadrature error components for zero rate output may be measured and it may be 
     
       
         
           
             
               
                 
                   
                     
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     It is appreciated that the in-phase component at a rate input may be measured, as depicted as I error,+Cor  in  FIG.  1 B . Similarly, the quadrature component at a rate input may be measured, as depicted as Q error,+Cor  in  FIG.  1 B . It is appreciated that the in-phase error and the quadrature error components for the rate input may be measured and it may be 
     
       
         
           
             
               
                 
                   
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     It is further appreciated that the in-phase component at another rate input may be measured, as depicted as I error,−Cor  in  FIG.  1 C . Similarly, the quadrature component at another rate input may be measured, as depicted as Q error,−Cor  in  FIG.  1 C . It is appreciated that the in-phase error and the quadrature error components for another rate input may be measured and it may be 
     
       
         
           
             
               
                 
                   
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     Accordingly, the phase error may be determined.
 
ϕ error =arctan( B,A )  (5)
 
where  A=I   error,+Cor   −I   error,ZRO   =Cor ·cos(ϕ error )  (6)
 
and
 
 B=Q   error,ZRO   −Q   error,−Cor   =Cor ·sin(ϕ error ).  (7)
 
     In other words, the phase error that has been determined may be used to trim and align the phase of the gyroscope, e.g., by modifying the phase of the demodulator or changing the phase of the clock, to the Coriolis vector. It is appreciated that the sensitivity of the gyroscope may also be determined using the quadrature difference and the in-phase difference
 
| Cor |=√{square root over ( A   2   +B   2 )},  (8)
 
     Referring now to  FIG.  2   , a system for determining a phase error and for compensating the phase error in accordance with some embodiments is shown. It is appreciated that  FIG.  2    depicts an embodiment for implementing the determination of the phase error, for example due to package stress, determination of the sensitivity of the gyroscope as well as compensating for the determined error in order to improve performance of the gyroscope. 
     System  200  includes a sensor  210 , e.g., a gyroscope, demodulators  220  and  230 , a processing unit  240 , and an error compensator  250 . The sensor  210  may be a gyroscope, a magnetometer, etc., and it may include various components such as a piezo element. The sensor  210  receives an input signal, e.g., zero rate output according to  FIG.  1 A , a rate input according to  FIGS.  1 B and  1 C  or an input signal resulting from movements, rotation, electrostatic force, a magnetic force, etc. 
     The sensor  210  may then output signal  212  to the demodulator  220  and it may output signal  214  to the demodulator  230 . The output signal from the sensor  210  may be the sensed signal due to zero rate output or other rate inputs. It is appreciated that according to some embodiments the two separate paths are configured to detect the in-phase and the quadrature components. For example, signal  212  input to the demodulator  220  may identify the in-phase component whereas signal  214  input to the demodulator  230  may identify the quadrature component of the signal. 
     According to some embodiments, the demodulator  220  may output the in-phase component  222  to the processing unit  240  and the demodulator  230  may output the quadrature component  224  to the processing unit  240 . It is appreciated that the in-phase and the quadrature components may include the zero rate output, and two rate inputs as discussed with respect to  FIGS.  1 A- 1 C . It is appreciated that the processing unit  240  may be configured to determine the phase error based on the received signals from the demodulators  220  and  230  and according to equations (1)-(8). It is appreciated that a change in rotation may cause a change in the rate input. In some embodiments, the change in rotation may be achieved using one or more actuators. It is appreciated that according to some embodiments, the actuator may be configured to periodically change the rotation rate. Accordingly, the phase error may be periodically estimated and corrected. 
     It is further appreciated that the sensitivity of the sensor  210  may also be determined by the processing unit  240 . The processing unit  240  may output the readings  244  and  242 . Output signals  244  may be used as the output reading of the device. 
     Signal  242  may be input to the error compensator  250 . Signal  242  may be the phase error that has been determined by the processing unit  240  and according to equations (1)-(8) above. The error compensator  250  may be configured to use the determined phase error to modify the operation of the demodulators  220  and  230  respectively to adjust for the determined error. For example, the error compensator  250  may transmit a signal  252  to the demodulator  220  in order to modify the operation of the demodulator  220  in order to compensate for the determined error associated with the in-phase component. Similarly, the error compensator  250  may transmit a signal  254  to the demodulator  230  in order to modify the operation of the demodulator  230  in order to compensate for the determined error associated with the quadrature component. 
     It is appreciated that in some embodiments, the processing unit  240  may be configured to trigger a phase error calculation in response to a change in the rate signal or a quadrature component. For example, a first in-phase and quadrature components (e.g., at zero rate) may be determined before application of the change in the rate signal (e.g., through an actuator) or the quadrature component (e.g., by application of the external signal, as described herein). The in-phase and the quadrature components associated with the change in rate signal or the quadrature component may be determined after the rate signal or external signal is changed, e.g., by using an actuator or applying the external signal. 
     It is appreciated that the processing unit  240  may be triggered to calculate phase errors in response to a difference between the first and second rate signals or first and second quadrature components (e.g., difference between the zero rate and change in the rate signal, or difference between no external signal applied and an applied external signal that increases the quadrature component) exceeding a threshold. In some embodiments, the processing unit  240  may be triggered to calculate phase errors in response to a difference between the first and second in-phase components or first and second quadrature components exceeding a threshold. The first and the second in-phase components may be components associated with two different rate signals, e.g., zero rate and a changed rate for instance. The first and the second quadrature components may be components associated with two different external signals, e.g., zero magnitude external signal and a changed external signal for instance. It is appreciated that according to some embodiments, the processing unit  240  may be triggered to calculate phase errors in response to a difference between the first and second quadrature components exceeding a threshold. The first and the second quadrature components may be components associated with two different rate signals, e.g., zero rate and a changed rate for instance, or in some embodiments, changes in an applied external signal. It is appreciated that the processing unit  240  may be triggered to calculate phase errors in response to a difference between the first and second sensed signal exceeding a threshold. It is appreciated that the first and the second sensed signals may be output signals of the sensor  210  in response to various rate inputs or external signal inputs, e.g., at zero rate and at a changed rate or a change in an applied external signal. According to some embodiments, the zero rate may be associated with no motion and a changed rate may be associated with a constant rate, a transient rate or a rotation. 
     According to some embodiments, the phase error correction may be applied, e.g., by the error compensator  250 , in response to a change in rotation rate or the applied external signal, e.g., zero rate and a changed rate or an increase in an applied external signal. In some embodiments, the change in rate signal may be a difference in average rates over a period of time. 
     Referring now to  FIG.  3   , another system for determining a phase error and for compensating the phase error in accordance with some embodiments is shown. System  300  is substantially similar to that of  FIG.  2   . However, the error compensator  250  is replaced with a clock  350  component. The clock  350  may receive the determined phase error and it may adjust the phase of the clocking signal for the demodulators  220  and  230 . As such, the demodulators  220  and  230  may be aligned with the Coriolis signal and quadrature signal respectively. 
     Referring now to  FIG.  4   , one system for determining a phase error and for compensating the phase error in accordance with some embodiments is shown. The system  400  is substantially similar to that of  FIG.  2    except that filters  410  and  420  associated with the demodulators  220  and  230  respectively are used to average the signals before transmission to the processing unit  240 . It is appreciated that the filters  410  and  420  may be a low pass filter, integrator, a bandpass filter, or any combination thereof. 
     It is appreciated that  FIG.  2 - 4    depict embodiments where the in-phase and the quadrature components can be determined simultaneously because of different paths, one for the in-phase path and another for the quadrature path. It is also appreciated that the determination of the phase error, the sensitivity, and the compensation for the error may occur at a manufacturing site where the error is compensated for or it may alternatively occur dynamically during use and in response to detecting a motion, e.g., movement, rotation, etc. For example, the phase error determination may occur in response to detecting a movement, a rotation, etc., and the phase error may be corrected and compensated for resulting therefrom. It is also appreciated that the phase error determination may occur periodically (e.g., predetermined periods), such as once every hour, once a day, once a month, etc., in order to calibrate the device. 
     Referring now to  FIG.  5   , a single demodulator system for determining a phase error and for compensating the phase error in accordance with some embodiments is shown.  FIG.  5    is similar to that of  FIG.  2    except that in this embodiment the in-phase component and the quadrature component are determined using the same path and therefore the same components. In other words, the in-phase components, e.g., zero rate output, rate inputs, external signals, etc., may occur in sequence with respect to one another and further with respect to the quadrature components for zero rate output, rate inputs, etc. In other words, the system  500  determines the in-phase components for the zero rate out, and the rate inputs sequentially. Similarly, the system  500  determines the quadrature components for the zero rate out, and the rate inputs sequentially. The processing unit  240  may use the in-phase components and the quadrature components that have been received sequentially to determine the phase error. The error compensator  250  may use the determined phase error in order to compensate for the error similar to that of  FIG.  2   . 
     Referring now to  FIG.  6   , another single demodulator system for determining a phase error and for compensating the phase error in accordance with some embodiments is shown.  FIG.  6    operates substantially similar to that of  FIG.  5    except that the error compensator  250  has been replaced by the clock  350  where it operates similar to that of  FIG.  3   . 
     Referring now to  FIG.  7   , yet another single demodulator system for determining a phase error and for compensating the phase error in accordance with some embodiments is shown.  FIG.  7    operates substantially similar to that of  FIG.  5    except that the filter  410  is introduced in order to average the signals being transmitted to the processing unit  240 . The operation of the filter  410  is similar to that described in  FIG.  4   . 
     It is appreciated that  FIGS.  5 - 7    depict embodiments where the in-phase and the quadrature components are determined sequentially by sharing the same path for the in-phase path and the quadrature component. It is also appreciated that the determination of the phase error, the sensitivity, and the compensation for the error may occur at a manufacturing site where the error is compensated for or it may alternatively occur dynamically during use and in response to detecting a motion, e.g., movement, rotation, etc. For example, the phase error determination may occur in response to detecting a movement, a rotation, etc., and the phase error may be corrected and compensated for resulting therefrom. It is also appreciated that the phase error determination may occur periodically (e.g., predetermined periods), such as once every hour, once a day, once a month, etc. in order to calibrate the device. 
     Referring now to  FIG.  8   , a flow diagram  800  for determining a phase error and for compensating for the phase error in accordance with some embodiments is shown. At step  810 , a signal e.g., zero rate output, is received from the sensor, e.g., MEMS, gyroscope, etc., as discussed above with respect to  FIGS.  1 A- 7   . At step  820 , the first in-phase and the first quadrature components may be identified, e.g., by using one or more modulators as described above with respect to  FIGS.  1 A- 7   . It is appreciated that the first in-phase and the first quadrature components may be determined sequentially using the same demodulator or simultaneously through independent modulators as described above. 
     At step  830 , a rate signal, e.g., magnetic force, electrostatic force, rotation, movement, etc., is applied to the sensor. Accordingly, the sensor generates a sensed signal. At step  840 , the second in-phase and the second quadrature components associated with the sensed signal may be identified, e.g., by using one or more modulators as described above with respect to  FIGS.  1 A- 7   . It is appreciated that the first in-phase and the first quadrature components may be determined sequentially using the same demodulator or simultaneously through independent modulators as described above. 
     At step  850 , the phase error may be determined based on the first in-phase and quadrature components and further based on the second in-phase and quadrature components. For example, in some embodiments, the phase error may be determined based on a difference between the quadrature components (e.g., zero rate output and the rate signal) and further based on a difference between the in-phase components (e.g., zero rate output and the rate signal). In some embodiments, the phase error may be an arctangent of the two differences. It is appreciated that in some embodiments, the phase error may be the ratio of the two differences. 
     It is appreciated that the determination of the phase error may occur periodically, in response to detecting a motion, or during the manufacturing process in order to calibrate the device, or any combination thereof. For example, the in-phase and the quadrature components may be periodically identified and determined in response to detecting a motion or in response to application of another rate signal. A new phase error may therefore be calculated periodically or the old phase error may be updated. 
     At step  860 , the error may be reduced by using the determined phase error in order to control the operation of the demodulator(s), as described in  FIGS.  1 A- 7   , in order to dynamically compensate for the determined error. For example, the clock signal used for the demodulator(s) may be modified based on the determined phase error, thereby changing the demodulation phase of the in-phase and the quadrature components. 
     It is appreciated that in some embodiments the same or a different rate signal may be applied to the sensor periodically and the process may be repeated in order to recalculate the phase error. As such, the device may be recalibrated periodically. It is appreciated that in one optional embodiment, at step  870 , the sensitivity of the sensor may be calculated and determined based on the quadrature difference and the in-phase difference. For example, the sensitivity may be based on equation (9) above. 
       FIG.  9    shows an illustrative MEMS sensor including quadrature tuning electrodes in accordance with some embodiments of the present disclosure. In the exemplary embodiment depicted in  FIG.  9   , a proof mass  906  is depicted relative to a plurality of quadrature tuning electrodes  902  and  904 . In the simplified representation depicted in  FIG.  10   , a single proof mass  906  is depicted occupying a first plane (e.g., within a MEMS layer of a MEMS device) and the quadrature tuning electrodes  902  and  904  are located below the proof mass (e.g., on a substrate of a CMOS layer of the MEMS device) on a plane that is parallel to the lower surface of the proof mass  906 . However, it will be understood that a variety of numbers, sizes, shapes, and relative locations of proof masses and quadrature tuning electrodes may be implemented in accordance with the present disclosure. 
     In the exemplary embodiment of  FIG.  9   , the proof mass  906  and quadrature tuning electrodes  902  and  904  are depicted at three different relative locations with respect to each other, with plot  908  depicting a force experienced by the proof mass  906  at those three locations and other points between. The proof mass  906  may be caused to move as a result of a drive motion imparted on a suspended spring-mass system associated with the proof mass, oscillating within the MEMS plane along a drive axis (e.g., the x-axis) at a drive frequency. In an embodiment of a MEMS gyroscope, a rotation about an axis perpendicular to the drive axis may result in a Coriolis force perpendicular to the drive axis and the axis of rotation, and may be sensed as described herein and as will be understood by a person of skill in the art, for example, by in-plane or out-of-plane sense electrodes along a sense axis associated with the Coriolis force. 
     DC signals may be applied to the respective quadrature tuning electrodes  902  and  904  to impart a force on the proof mass  906  (e.g., based on a capacitance between the quadrature tuning electrodes and the proof mass). In the embodiment of  FIG.  9    quadrature tuning electrode  904  may have a positive voltage applied thereto while quadrature tuning electrode  902  may have a negative voltage applied thereto. When the proof mass  906  is stationary or located at a center point of its oscillation along the x-axis, as depicted by the middle representation of proof mass  906  and quadrature tuning electrodes  902  and  904 , the overlap between the proof mass  906  and the quadrature tuning electrodes  902  and  904  may be equal, such that no force is imparted on the proof mass by the quadrature tuning electrodes. When the proof mass  906  is oscillated in the positive x-axis direction, as depicted by the right-side representation of proof mass  906  and quadrature tuning electrodes  902  and  904 , the overlap between the proof mass  906  and the quadrature tuning electrode  902  is minimized, while the overlap between the proof mass  906  and the quadrature tuning electrode  904  is maximized. As a result of the positive DC voltage applied to quadrature tuning electrode  904 , proof mass  906  experiences a force that causes it to move in the positive z-direction, which can be sensed by sense electrodes and which corresponds to a quadrature component of the sensed signal. When the proof mass  906  is oscillated in the negative x-axis direction, as depicted by the left-side representation of proof mass  906  and quadrature tuning electrodes  902  and  904 , the overlap between the proof mass  906  and the quadrature tuning electrode  904  is minimized, while the overlap between the proof mass  906  and the quadrature tuning electrode  902  is maximized. As a result of the negative DC voltage applied to quadrature tuning electrode  902 , proof mass  906  experiences a force that causes it to move in the negative z-direction, which can be sensed by sense electrodes and which corresponds to a quadrature component of the sensed signal. 
       FIGS.  10 - 12    depict exemplary steps for identifying and compensating for a phase error according to some embodiments of the present disclosure. Although  FIGS.  10 - 12    are described in the context of the present disclosure, it will be understood that the methods and steps described in  FIGS.  10 - 12    may be applied to a variety of sensor and gyroscope designs, and to methodologies for applying a signal that modifies a quadrature component of a sensed signal in a predictable manner. Although a particular order and flow of steps is depicted in  FIGS.  10 - 12   , it will be understood that in some embodiments one or more of the steps may be modified, moved, removed, or added, and that the flow depicted in  FIGS.  10 - 12    may be modified. Although  FIGS.  10 - 12    may be described in the context of a MEMS gyroscope, it will be understood that the disclosure of  FIGS.  10 - 12    may be applied to other sensor types. 
       FIG.  10    shows a flow diagram for determining a phase error based on an applied quadrature drive signal in accordance with some embodiments of the present disclosure.  FIG.  10    depicts two exemplary phases of operation, a calibration stage  1000  and an operations stage  1010 . The calibration stage  1000  may determine an initial baseline of values for determining phase error, for example, by applying a known rate to a MEMS gyroscope. The calibration stage  1000  may occur under controlled conditions, such as during manufacturing, testing, service, or in-field calibration procedures where an applied rate of rotation can be provided with reasonable certainty. During the operations stage  1010 , the external signal may be applied at appropriate times, such as during startup or when a measured rate of rotation is less than a threshold. The external signal may modify the quadrature component of the received signal in a predictable manner, based at least in part on known characteristics of the sensor from the calibration stage  1000 . Thus, operations stage  1010  may allow the phase error for the sensor to be measured during the life of the sensor, thus providing more accurate measurement of rate of rotation over the life of the sensor. 
     At step  1002  of calibration stage  1000 , a known rate of rotation may be applied to a MEMS gyroscope, as described herein. By applying the known rate and measuring the in-phase and quadrature components of the sense signal, a phase of the MEMS sense displacement in response to the applied rate of rotation (ϕ Cor,1 ) may be determined as described herein (e.g., measuring in-phase components and quadrature components at different rates, and using the arctangent of the two signals or their ratio). 
     Processing may then continue to step  1004 , at which an external signal may be applied to the sensor in a manner that modifies the quadrature component of the sensed signal. A phase of the MEMS sense displacement in response to the external force (ϕ ST,1 ) may be determined as described herein (e.g., measuring in-phase components and quadrature components in response to different external forces, and using the arctangent of the two signals or their ratio). Processing may then continue to step  1006 , at which a calibration value ϕ DIFF  may be determined based on the sense displacements measured in steps  1002  and  1004 , e.g., as ϕ diff =ϕ Cor,1 −ϕ ST,1 . Processing may then exit the calibration stage  1006  and continue to step  1012  of the operational stage  1010 . 
     At step  1012 , it may be determined whether a criteria for performing operational testing is met. Operational testing may be performed at a variety of times, such as during startup or periodically while a sensor is operational (not depicted). It may also be determined whether the rate is below a threshold (e.g., less than a minimum signal that is recognized as a sensed rate versus noise) such that a response to providing an external signal may principally modify a quadrature component of a received sense signal in a predictable manner. If the measured rate is not less than the threshold, the MEMS gyroscope may continue to check the signal at step  1012 . If the measured rate is less than the threshold, processing may continue to step  1014 . 
     At step  1014 , an external signal may be applied to the MEMS gyroscope, for example, by drive electrodes or drive sense electrodes (e.g., temporarily used as drive electrodes). In an exemplary embodiment the external signal may be a periodic signal having the same frequency as the drive signal. In an embodiment where the external signal is applied at a drive mass of the MEMS gyroscope, the external signal may have a predetermined phase difference (e.g., 90 degrees) from the drive signal, i.e., such that the effect of the external signal is to modify the quadrature component of the sensed signal. In other embodiments, the external signal may be applied to other masses (e.g., directly to a proof mass or to intermediate or Coriolis masses). The magnitude of the external signal may vary based on the desired change to the quadrature component of the sensed signal from the proof mass. Once the external signal has been applied to the MEMS gyroscope, processing may continue to step  1016 . 
     At step  1016 , the MEMS sense displacement may be calculated based on the applied external signal and the modification to the quadrature component caused by the applied external signal, as described herein. In an exemplary embodiment where the applied external force has the same magnitude as the external force that was applied at step  1004  of the calibration stage, any difference in response due to the external signal corresponds to changes in the operating characteristics of the MEMS gyroscopes. In other embodiments, the magnitude of the external force applied at step  1014  may be scaled compared to the external force applied at step  1004 , and the resulting quadrature component output from the sense signal may be similarly scaled. The resulting effect of the external signal applied at step  1014  may then be determined as ϕ ST,2 , which may be used to calculate a MEMS sense displacement value ϕ Cor,2  based on the effect of the external signal and the calibration phase difference, i.e., as ϕ Cor,2 =ϕ ST,2 +ϕ diff . Once the phase shift has been determined, processing may continue to step  1018 . 
     At step  1018 , the phase drift during operation of the sensor Δϕ Cor  may be determined based on the original MEMS sense displacement ϕ Cor,1  from the calibration stage  1000  and the MEMS sense displacement ϕ Cor,2  from the operational stage  1010 , e.g., as Δϕ Cor =ϕ Cor,2 −ϕ Cor,1 . Processing may then then continue to step  1020 , at which the demodulation phase angle may be updated based on the phase drift Δϕ Cor , and to step  1022  at which the angular velocity may be calculated based on the updated demodulation phase angle. Processing may then continue to step  1024 . 
     At step  1024 , it may be determined whether a re-calibration is possible, for example, during service or during a user-initiated calibration. If a re-calibration is available, processing may continue to step  1002  of calibration stage  1000 . Otherwise, processing may return to step  1012 . 
       FIG.  11    shows a flow diagram for determining a phase error based on an applied signal from quadrature tuning electrodes in accordance with some embodiments of the present disclosure. In the exemplary embodiment of  FIG.  11   , a DC signal may be applied to components such as quadrature tuning electrodes to impart a periodic force on a proof mass based on the drive motion of a mass that periodically overlaps the quadrature tuning electrodes, e.g., as described herein. In the exemplary embodiment of  FIG.  11   , the phase error may be determined at suitable times during operation of the sensor, such as during start-up of the MEMS gyroscope or at suitable times during operation. 
     At step  1102 , the rate of rotation of a MEMS gyroscope may be measured, for example, to identify conditions where there is no rotation or very little rotation. In some embodiments, step  1102  may be associated with instructions to a user, such as to place the device including the MEMS gyroscope on a flat and stationary surface. In other embodiments, a predetermined rate signal may be applied. Processing may continue to step  1104 , at which it may be determined whether the measured rate of rotation is less than a threshold. If the measured rate of rotation is not less than the threshold, processing may return to step  1102 . If the measured rate of rotation is less than the threshold, processing may continue to step  1106 . 
     At step  1106 , the sense output of the MEMS gyroscope may be analyzed to determine an Offset 1  value from the sensed signal, which may correspond to a measured gyroscope output signal when there is no rotation of the sensor and when no quadrature tuning signal is applied to the MEMS gyroscope. Processing may then continue to step  1108 . 
     At step  1108 , the external signal may be applied to the quadrature tuning electrodes as a DC signal, with a corresponding modification to a quadrature component of the sensed signal as described herein. Processing may then continue to step  1110 , in which the sense output of the MEMS gyroscope may be analyzed to determine an Offset 2  value, which may be representative of a measured gyroscope output with the applied external signal modifying the quadrature component and with the effect of the rate of rotation on the in-phase component being minimal. Processing may then continue to step  1112 . 
     At step  1112 , a demodulation phase angle may be applied to the sense signal. An initial demodulation phase angle may be selected to enable an iterative search routine, i.e., to identify a demodulation phase angle that substantially eliminates the quadrature component of the sensed signal while minimizing the time required for testing (e.g., to limit the amount of time that the MEMS gyroscope must remain at a zero or low rate during testing). Once the demodulation phase angle is applied, a new value for Offset 2  may be determined and may represent the degree to which the demodulation phase angle is capable of removing the quadrature component of the signal from the measured output of the sensed signal. Processing may then continue to step  1114 . 
     At step  1114 , a difference between Offset 1  and Offset 2  may be determined as Offset DIFF , which may be compared to a threshold. A low value for Offset DIFF  may correspond to the selected demodulation angle removing most of the quadrature component of the sense signal from the rate output. If Offset DIFF  is greater than the threshold, processing may continue to step  1116  in which the demodulation phase angle is updated and applied to the quadrature component due to the external signal. If Offset DIFF  is less than the threshold, processing may continue to step  1118 . 
     At step  1118 , the demodulation phase angle that resulted in the desired reduction of the quadrature component of the sense signal may be stored for usage in determining rate of rotation. In some embodiments, this demodulation phase angle may not be used to directly modify the demodulation of the sense signal, but may be used in post-processing to properly remove the quadrature component of the signal. The external signal applied to the quadrature tuning electrodes may be removed, and processing may continue to step  1120  to determine rate of rotation based on the updated demodulation phase angle. This processing may continue until it is desired to recalibrate the demodulation phase angle at step  1122 , at which time processing may return to step  1102 . 
       FIG.  12    shows a flow diagram for determining a phase error based on an applied signal from a quadrature tuning signal in accordance with some embodiments of the present disclosure. In the exemplary embodiment of  FIG.  12   , the gyroscope output signal and the quadrature component of a sensed signal under first conditions (e.g., zero or minimal rate and no applied external signal) and second conditions (e.g., zero or minimal rate and an applied external signal) may be used to modify the processing of a received sense signal during normal operation. 
     At step  1202 , the rate of rotation of the MEMS gyroscope may be measured. In some embodiments, step  1202  may be associated with instructions to a user, such as to place the device including the MEMS gyroscope on a flat and stationary surface. Processing may continue to step  1204 , at which it may be determined whether the measured rate of rotation is less than a threshold. If the measured rate of rotation is not less than the threshold, processing may return to step  1202 . If the measured rate of rotation is less than the threshold, processing may continue to step  1206 . 
     At step  1206 , the sense output of the MEMS gyroscope may be analyzed to determine an Offset 1  value from the sensed signal, which may correspond to a measured gyroscope output signal when there is no rotation of the sensor and when no quadrature tuning signal is applied to the MEMS gyroscope. The sense output may also be analyzed to determine a Quad 1  value from the sensed signal, which may correspond to the quadrature component of the sensed signal. Processing may then continue to step  1208 . 
     At step  1208 , the external signal may be applied to the quadrature tuning electrodes as a DC signal, with a corresponding modification to a quadrature component of the sensed signal as described herein. Processing may then continue to step  1210 , in which the sense output of the MEMS gyroscope may be analyzed to determine an Offset 2  value, which may be representative of a measured gyroscope output with the applied external signal modifying the quadrature component and with the effect of the rate of rotation on the in-phase component being minimal. The sense output of the MEMS gyroscope may also be analyzed to determine a Quad 2  value from the sensed signal, which may correspond to the quadrature component of the sensed signal when the external signal is applied. Processing may then continue to step  1212 . 
     At step  1212 , phase error may be determined from the Offset 1 , Quad 1 , Offset 2 , and Quad 2  values. In an exemplary embodiment, this phase error Δϕ Cor  may be determined based on the arctangent of these values, as follows: 
     
       
         
           
             
               
                 
                   
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     Once the phase error has been determined at step  1212 , processing may continue to step  1214 . At step  1214 , the demodulation phase angle may be modified based on Δϕ Cor  to reduce the phase error, as described herein. In some embodiments, this demodulation phase angle may not be used to directly modify the demodulation of the sense signal, but may be used in post-processing to properly remove the quadrature component of the signal. The external signal applied to the quadrature tuning electrodes may be removed, and processing may continue to step  1216  to determine rate of rotation based on the updated demodulation phase angle. This processing may continue until it is desired to recalibrate the demodulation phase angle at step  1218 , at which time processing may return to step  1202 . 
     While the embodiments have been described and/or illustrated by means of particular examples, and while these embodiments and/or examples have been described in considerable detail, it is not the intention of the Applicants to restrict or in any way limit the scope of the embodiments to such detail. Additional adaptations and/or modifications of the embodiments may readily appear to persons having ordinary skill in the art to which the embodiments pertain, and, in its broader aspects, the embodiments may encompass these adaptations and/or modifications. Accordingly, departures may be made from the foregoing embodiments and/or examples without departing from the scope of the concepts described herein. The implementations described above and other implementations are within the scope of the following claims. 
     Although the present disclosure has described, for example, determining a phase error by applying an external signal as a periodic signal (e.g., at drive or drive sense electrodes of a gyroscope) or applying a DC signal (e.g., by quadrature tuning electrodes) to determine a phase shift, it will be understood that the present disclosure may be applied to other methods of applying an external signal that modifies a quadrature component of a received signal of the sensor (e.g., gyroscope) in a particular manner, such that a phase error may be determined based on the change in the quadrature component. 
     The foregoing description includes exemplary embodiments in accordance with the present disclosure. These examples are provided for purposes of illustration only, and not for purposes of limitation. It will be understood that the present disclosure may be implemented in forms different from those explicitly described and depicted herein and that various modifications, optimizations, and variations may be implemented by a person of ordinary skill in the present art, consistent with the following claims.