Abstract:
A position-sense interface with improved transfer characteristics. Electrical position detection circuitry, which may be substantially time-multiplexed or frequency-multiplexed, comprises a differential charge integrator with input-sensed output-driven common mode feedback. By placing sense capacitors in the feedback loop of said differential charge integrator with input-sensed output-driven common mode feedback, improved position sensing linearity is attained. In some embodiments of the invention, a compensating charge is applied to the sense capacitors in a fashion that minimizes the output common mode shift of the opamp. The magnitude of the compensating charge may be preset at a substantially constant level, or derived by a feedback loop that measures the shift in output common mode voltage in response to an excitation signal and adjusts the magnitude of the compensating charge to drive said shift towards zero.  
     The invention has numerous advantages for acceleration measurement in both open-loop and force-balanced accelerometers, as well as rotation rate measurement in a vibratory rate gyroscope. Other applications in which the invention may prove advantageous include: motion detection for an oscillation-sustaining feedback loop; position detection of actuators, including micro-actuators used for effecting controlled motion of a disk-drive read/write head, or effecting controlled motion of an optically active device, such as a positionable mirror for use in fiber-optic data communications; and application of electrostatic forces for large motions.

Description:
PRIORITY APPLICATION DATA  
       [0001]    This application claims priority to provisional application Ser. No. 60/177,114, POSITION SENSING WITH IMPROVED LINEARITY, filed Jan. 20, 2000. 
     
    
     GOVERNMENT INTEREST  
       [0002] This invention was made with Government support under contract #DAAMHO1-99-C-R215 awarded by DARPA. The Government has certain rights in the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE INVENTION  
         [0003]    This invention relates to an improved measuring device for open-loop and force-balanced accelerometers, and vibratory rate gyroscopes. In addition, the invention further relates to: position or velocity detection in an oscillation-sustaining feedback loop; position detection of actuators, including micro-actuators used for effecting controlled motion of a disk-drive read/write head, or effecting controlled motion of an optically active device, such as a positionable mirror used in data communications. The invention further relates to microelectromechanical systems formed by one or more micromachining operations.  
           [0004]    This invention utilizes charge-based sensing to attain a linear position-input to voltage-output transfer characteristic.  
         BACKGROUND OF THE INVENTION  
         [0005]    Accelerometers are sensors that measure acceleration. Accelerometers can be designed to measure rotational or translational acceleration. Vibratory rate gyroscopes are a type of accelerometer in which one or more proof-masses are forced into oscillation and a Coriolis acceleration is detected in response to a rate input. Accelerometers and rate gyroscopes have many uses in many commercial, military, and scientific applications including, but not limited to, inertial navigation, vehicular safety systems such as airbags, ride comfort control, platform stabilization, tilt sensing, vibration monitoring, shock and impact measurement, and weapons fusing.  
           [0006]    The heart of a displacement-based accelerometer is a mechanical proof-mass. Under an applied acceleration, this passive mechanical device moves with respect to the substrate. For an accelerometer with a linear suspension, it may be shown that for frequencies below the proof-mass resonant frequency along the sensitive axis, ω n ,the displacement of the proof-mass from its nominal position with respect to the substrate is given by 1/ω n   2  times the applied acceleration. By measuring the displacement of the proof-mass with an electrical interface, acceleration may be inferred.  
           [0007]    A sense-element may be operated either open-loop, or placed into a force-feedback loop. Enclosure of a sense-element in a force-feedback loop is commonly called force-balancing or force-rebalancing. In the open-loop configuration, the accelerometer output is given by the change in relative displacement of the proof-mass multiplied by the gain of the position sense interface. Often piezoelectric materials, piezoresistive materials, or sense capacitors are used in conjunction with an electrical position-sense interface to detect proof-mass displacements.  
           [0008]    In the force-balanced configuration the position-sense interface output is used to feed back a force in a manner that tends to restore the proof-mass to a defined nominal position. Note the accelerometer output is not a quantity representative of position, but rather is a quantity representative of the force necessary to keep the proof mass at its nominal position. Because force-balanced accelerometers maintain small displacements for acceleration inputs within the measuring range, electrostatic nonlinearities due to changes in air gap capacitance are attenuated. Closed-loop operation has been used to provide several advantages that are particularly important for miniature micromachined sensors including improved linearity, increased dynamic range, and extended bandwidth. In addition, since the output is the applied force, not displacement, the output typically is less sensitive to device dimensions, such as spring width, making the sensor typically less sensitive to variations in manufacturing. Sense capacitors or piezoelectric materials are often used to apply feedback forces to the proof mass.  
           [0009]    Note force-feedback is not practical or even desirable for many applications, however. As full scale ranges rise above approximately 50 G, it becomes increasingly difficult to force balance an accelerometer in a manner such that the feedback loop doesn&#39;t saturate, especially if electrostatic forces and low-voltage operation (i.e. 5V or less) are used to apply the restoring force feedback. Alternatively, when an application requires a low-cost, small, or simple accelerometer, the increased circuit area or added complexity may preclude usage of force-balanced topologies. Although some applications may not allow for force balancing, many of these same target applications will require good input-output linearity and a wide dynamic range that force balancing provides. Furthermore, it is often desirable that the sensor include a differential sense interface for improved rejection of undesired disturbances, such as power supply fluctuations.  
           [0010]    A substantially parallel-plate capacitor is defined here as a capacitor having a nonlinear relationship between capacitance and displacement along an axis of sensitivity; a significant component of capacitance being described by the equation K/g, where K is a geometrically determined constant and g is a characteristic distance between sense electrodes as measured orthogonally from the face of one sense electrode. Substantially parallel-plate capacitors may be advantageous in many applications because in addition to a typically higher sensitivity to changes in air-gap, substantially parallel-plate capacitors typically provide significantly higher air-damping than alternative configurations such as interdigitated comb fingers (see for example Tang et al U.S. Pat. No. 5,025,346 issued Jun. 18, 1991). Higher air damping is beneficial to many applications where underdamped mechanical resonances are undesirable including, but not limited to, accelerometers and open-loop actuators.  
           [0011]    [0011]FIG. 1 shows an example of a substantially parallel-plate capacitor with conductive electrodes  40  and  41 , each electrode having an area A equal to plate length/multiplied by plate width w. When the length and width are substantially greater than the separation gap g, the capacitance, C, between the two plates may be approximated by: 
           
         C≈ε 
         0 
         A/g 
       
           [0012]    As either plate width or plate length approach the gap dimension, the above approximation becomes less accurate, since fringing fields comprise a larger percentage of capacitance. Note that the capacitance is highly nonlinear with a 1/g dependence. To attain a representation of position that is linear, a position sense interface must account for this nonlinearity.  
           [0013]    A sense capacitor is defined, within the scope of this document, as one or more substantially parallel-plate capacitors connected in parallel. Note, in certain applications, a substantially parallel-plate capacitor may have gasses between electrodes at a reduced pressure, or vacuum, for lower mechanical damping. Furthermore, substantially parallel-plate capacitors may include between the electrodes any of a number of gasses including, but not limited to, one or more of the following: nitrogen, argon, hydrogen, helium, oxygen, or other gasses or combination of gasses.  
           [0014]    Often a position sense interface requires a pair of sense capacitors that change oppositely in value for a displacement in the same direction. A pair of sense capacitors that change in this manner provide a degree of symmetry that may result in reduced offset and drift over temperature. Furthermore, a pair of sense capacitors may enable the use of differential circuit techniques that reject certain environmental noise sources such as power supply ripple.  
         SUMMARY OF THE INVENTION  
         [0015]    The invention, roughly described, comprises a position-sense interface with improved transfer characteristics. In one embodiment of the invention, a single proof-mass includes two electrically decoupled sensing capacitors is shown. Electrical position detection circuitry, which may be substantially time-multiplexed or frequency-multiplexed, comprises a differential charge integrator with input-sensed output-driven common mode feedback. By placing the sense capacitors in the feedback loop of said differential charge integrator with input-sensed output-driven common mode feedback, improved position sensing linearity is attained.  
           [0016]    In an alternative embodiment of the invention two or more proof-masses are connected to form two electrically decoupled sensing capacitors.  
           [0017]    In yet another embodiment of the invention, a compensating charge is applied to the sense capacitors in a fashion that minimizes the output common mode shift of the opamp. The magnitude of the compensating charge may be set to a substantially constant level, or derived by a feedback loop that measures the shift in opamp output common mode voltage in response to an excitation signal and adjusts the magnitude of the compensating charge to drive said shift towards zero.  
           [0018]    The invention has numerous advantages for acceleration measurement in both open-loop and force-balanced accelerometers, as well as rotation rate measurement in a vibratory rate gyroscope. Other applications in which the invention may prove advantageous include: motion detection for an oscillation-sustaining feedback loop; position detection of actuators, including micro-actuators used for effecting controlled motion of a disk-drive read/write head, or effecting controlled motion of an optically active device, such as a positionable mirror for use in fiber-optic data communications; and application of electrostatic forces for large motions. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0019]    For a better understanding of the nature and objects of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, in which:  
         [0020]    [0020]FIG. 1 is a perspective view of a substantially-parallel plate capacitor.  
         [0021]    [0021]FIG. 2 is a schematic diagram of a novel proof-mass structure with dual sense capacitors.  
         [0022]    [0022]FIG. 3 is layout of a novel accelerometer having electrically decoupled sense capacitors.  
         [0023]    [0023]FIG. 4 is a schematic diagram of an accelerometer that measures in-plane acceleration comprising two proof-masses.  
         [0024]    [0024]FIG. 5 is a schematic diagram of an accelerometer that measures out-of-plane acceleration comprising two proof-masses.  
         [0025]    [0025]FIG. 6 is a schematic diagram of a first embodiment of the invention.  
         [0026]    [0026]FIG. 7 is a schematic diagram of an opamp suitable for an input-sensed output-driven common mode feedback loop.  
         [0027]    [0027]FIG. 8 are calculated plots of output vs. displacement for the present invention and a prior-art position-sense interface.  
         [0028]    [0028]FIG. 9 is a schematic diagram of a second embodiment of the invention.  
         [0029]    [0029]FIG. 10 is a schematic diagram of a third embodiment of the invention.  
         [0030]    [0030]FIG. 11 is a schematic diagram of a fourth embodiment of the invention. 
     
    
       [0031]    Like reference numerals refer to corresponding parts throughout all the views of the drawings.  
       DETAILED DESCRIPTION OF THE INVENTION  
       [0032]    Measurement of proof-mass displacement from a nominal position is attained using a differential charge integrator, with novel Input-Sensed Output-Driven Common Mode Feedback loop (termed ISODCMFB), in conjunction with two or more substantially parallel-plate capacitors. The invention comprises a charge integrator having an ISODCMFB circuit and one or more proof-masses, each proof-mass having at least one substantially parallel-plate capacitor that varies with displacement of the proof-mass along a sensitive axis.  
         [0033]    [0033]FIG. 2 schematically illustrates a novel proof-mass structure with dual sense capacitors. The structure of FIG. 2 may be formed using a micromachining technology, for example as described in copending United States patent application Ser. No. 09/322,381, May 28, 1999, inventors Clark, et. al, hereby fully incorporated by reference. Gaps between capacitor electrodes are typically 0.25 to 4 microns wide, and the structure thickness is typically 2 to 50 microns thick. This novel structure comprises proof-mass sections  52  and  62 , mechanically attached, but electrically isolated by a dielectric-lined isolation trench  59 . Each proof-mass section includes conductive electrodes  52   a,b,    62   a,b  that form one electrode of a substantially parallel-plate capacitor. In addition to providing a mechanical restoring force when the proof-mass undergoes a deflection, suspensions  53   a,b,    63   a,b  provide electrical connectivity from anchor points  54   a,b,    64   a,b  to electrodes  52   a,b    62   a,b.  Anchor points  54   a,b,    64   a,b  are electrically isolated from substrate  58  by dielectric-filled trenches. Although suspensions  53   a,b,    63   a,b  include one fold to provide strain relief as illustrated, the presence of a fold is not necessary. Alternatively, to attain a structure with a low resonant frequency a number of folds may be used to increase compliance. Conductive electrodes  50   a,b,    60   a,b  form second electrodes of substantially parallel-plate capacitors. Conductive electrodes  50   a,b,    60   a,b  are mechanically attached to substrate  58  by dielectric-filled trenches at anchor points  51   a,b,    61   a,b.  Thus, the structure illustrated FIG. 2 comprises a single proof-mass with capacitors formed by the following pairs of electrodes:  60   a,    62   a;    60   b,    62   b;    50   a,    52   a;    50   b,    52   b.  Electrical connections may be constructed between electrodes  60   a  and  60   b  forming one sense capacitor having a value that increases for proof-mass displacements along the positive direction of the axis of sensitivity. Likewise, electrical connections may be constructed between electrodes  50   a  and  50   b  forming a second sense capacitor having a value that decreases for proof-mass displacements along the positive direction of the axis of sensitivity.  
         [0034]    [0034]FIG. 3 shows a layout of a sense-element  66  comprised of a plurality of structures  66   a,  similar to the structure shown in FIG. 2, for acceleration measurement. Adjacent structures  66   a  are isolated by additional dielectric-isolation trenches  65   b.  Dielectric-isolation trenches  65   a  electrically isolate adjacent conductive electrodes. Two isolated sense capacitors are constructed by electrically connecting like substantially parallel-plate capacitors using conductive interconnect  69   a  through  69   e  in conjunction with electrical contacts  67 . Note the resulting capacitor pair has four independent terminals, each capacitor having two terminals; a first terminal pair formed by  69   a,d  and a second terminal pair formed by  69   b,e.  This is in contrast to prior-art planar sense-elements in which the proof-mass acts as a common terminal to both capacitors. For improved performance, isolation trench pair  65   c,  in conjunction with conductor  69   c  and its corresponding electrical contacts, greatly attenuates parallel parasitic-capacitance coupling with sense capacitors.  
         [0035]    Practice of the invention does not require a single proof-mass with distinct electrical nodes; many existing fabrication technologies are unable to form proof-masses with distinct electrical nodes. (See, for example, Kung, et al., U.S. Pat. No. 5,504,026; Montague et al., U.S. Pat. No. 5,798,283; and Sherman, et al., U.S. Pat. No. 5,847,280, each of which is fully incorporated by reference herein). FIG. 4 schematically illustrates a sense element for measuring in-plane acceleration comprising two proof-masses, each proof-mass providing one sense capacitor. A sense capacitor having a value that increases for proof-mass displacements along the positive direction of the axis of sensitivity is formed by pairs of anchored electrodes  72   b  and electrodes  74   b  attached to a conductive proof-mass  76   b.  Like stationary electrodes are attached to one another via electrical interconnect  78   b,  forming one terminal of a sense capacitor. Proof-mass  76   b  is mechanically attached to and electrically isolated from substrate  80  via compliant suspension  75   b  and anchors  71   b.  Electrical interconnection to proof-mass  76   b  is attained via interconnect  79   b,  forming a second terminal of a sense capacitor. A sense capacitor having a value that decreases for proof-mass displacements along the positive direction of the axis of sensitivity is formed by pairs of anchored electrodes  72   a  and electrodes  74   a  attached to a conductive proof-mass  76   a.  Like stationary electrodes are attached to one another via electrical interconnect  78   a,  forming one terminal of a sense capacitor. Proof-mass  76   a  is mechanically attached to and electrically isolated from substrate  80  via compliant suspension  75   a  and anchors  71   a.  Electrical interconnection to proof-mass  76   a  is attained via interconnect  79   a,  forming a second terminal of a sense capacitor. Electrostatic shields  73   a,b  are used to ensure that only one side of each electrode  72   a,b  forms a capacitor with electrodes  74   a,b.  To minimize electrostatic forces, electrostatic shields  73   a,b  may be set to a DC potential similar to the proof-mass potential, with interconnect to proof-mass electrodes  79   a,b  being connected to the input terminals of a differential opamp in feedback thereby being kept at a substantially constant voltage. Electrostatic shields  73   a,b  are preferably not connected to the proof-mass since this would create a large, constant parasitic capacitance in parallel with the sense-capacitor that may cause deleterious effects as described below. Often further electrical shielding  81   a,b , disposed above and electrically isolated from substrate  80 , will be formed under each proof-mass to prevent, for instance, undesired electrostatic forces. In this case shielding  80  is also preferably not connected to the proof-mass since this would create a large, constant parasitic capacitance in parallel with the sense-capacitor. Instead, shielding  80  may be connected to the same DC potential as electrostatic shields  73   a,b.    
         [0036]    [0036]FIG. 5 schematically illustrates a sense element for measuring out-of-plane acceleration. This sense-element may be formed in a suitable fabrication technology such as disclosed in (Kung, et al., U.S. Pat. No. 5,504,026 issued Apr. 2, 1996; Montague et al., U.S. Pat. No. 5,798,283 issued Aug, 25, 1998; and Sherman, et al., U.S. Pat. No. 5,847,280 issued Dec. 8, 1998). First-proof mass  96   a  comprises two substantially planar regions  91   a  and  91   b  connected by lever  95   a.  Rotationally-compliant member  93   a  acts as a fulcrum, member  93   a  mechanically anchored to substrate  90  on both ends by anchors  94   a.  Member  93   a  is located closer to the center of mass of planar region  91   a  than the center of mass of planar region  91   b . Anchors  94   a  provide connectivity to electrical conductors  97   a,b  electrically distinct from substrate  90 . Due to the relative dispositions of planar regions  91   a,b  with respect to member  93   a,  when substrate  90  undergoes a positive acceleration along the axis of sensitivity the proof-mass tends to rotate clockwise as drawn. Thus, conductive region  92   a,  electrically isolated from and superposed to substrate  90 , in conjunction with the portion of planar region  91   a  facing conductive region  92   a,  form two electrodes of a substantially-parallel plate capacitor that decreases in response to a positive acceleration along the axis of sensitivity. Likewise, conductive region  92   b,  electrically isolated from and superposed to substrate  90 , in conjunction with the portion of planar region  91   d  facing conductive region  92   b,  form two electrodes of a substantially-parallel plate capacitor that increases in response to a positive acceleration along the axis of sensitivity. Note that for large angular displacements these sense capacitors deviate from an ideal parallel-plate capacitor due to a rotational component of motion. Improved approximation to an ideal parallel-plate capacitor may be attained by increasing the length of levers  95   a,b.    
         [0037]    A first embodiment of the present invention is schematically illustrated in FIG. 6. In this embodiment, position sense interface  150  comprises a differential opamp  115  having an ISODCMFB circuit and a negative feedback loop, the feedback loop operating in a sampled-data, i.e. time-multiplexed, fashion. Position sense interface  150  further comprises sense capacitors  100   a,b  each having a nominal sense capacitance C s , reference capacitors  104   a,b  each having a capacitance of Cref, feedback coupling capacitors  101   a,b,  feedforward capacitors  123   a,b,  output terminals  105   a,b,  opamp output terminals  106   a,b,  unity-feedback switches  103   a,b,  output zeroing switches  102   a,b,  and feedforward compensation switches  120   a,b  and  121   a,b.  Switches may be formed using, for example a NMOS transistor, a PMOS transistor, or both a NMOS and a PMOS transistor.  
         [0038]    Position sense interface  150  operates over two recurring, discrete, nonoverlapping time periods Phi 1  (φ 1 ) and Phi 2  (φ 2 ). Typical period frequencies are between 1 kHz and 10 MHz. During Phi 1 , switches  103   a,b  are closed, placing opamp  115  into unity-gain feedback and setting the differential voltage at opamp input terminals  109   a,b  to a value substantially equal to the opamp offset plus a random component due to flicker and other noise. The ISODCMFB circuit measures the input common mode voltage and drives the output common mode voltage so that the input common mode is driven towards a reference value typically midway between the opamp output common mode voltage range, defined here as V cm . Reference voltage V cm  may be provided by any of a number of well known circuits for providing a constant voltage, and may be derived from a bandgap reference. Since switches  103   a,b  are closed, the output common mode voltage is equal to the input common mode voltage, which is driven substantially equal to reference voltage V cm . Note that both the differential and common mode feedback loops are typically designed so that the loop gain is greater than 100. Switches  102   a,b  are also closed during Phi 1 , connecting output node  105   a,b  to a reference voltage V outcmref . Note that while input nodes  109   a,b  have a small voltage difference due to opamp noise and offset, output terminals  105   a,b  are forced equal. Reference voltage V outcmref  may be, but is not necessarily, equal to V cm . If V outcmref  is chosen equal to V cm , however, only a very small error voltage component is presented across sense capacitors  100   a,b  during Phi 1 ; thus, undesired electrostatic attraction is minimized. Reduced electrostatic attraction during Phi  1  results in better linearity, especially for systems with high mechanical compliance such as a low-G accelerometer. Improved linearity is due to reduced electrostatic forces affecting the proof-mass in a manner similar to a nonlinear mechanical spring. By closing switches  111  and  120   a,b  during Phi  1 , reference capacitors  104   a,b  and feedforward capacitors  123   a,b  are initialized so that they may inject controlled amounts of charge during Phi 2 .  
         [0039]    During Phi 2  output nodes  105   a,b  are released by opening switches  102   a,b,  and opamp  115  is removed from unity-gain feedback and placed into charge-integration mode by opening switches  103   a,b.  A sense-charge pulse equal to C ref  *V s  is generated by opening switch  111  and closing switch  112 , where sense voltage V s  is a constant voltage typically between 0.1 and 5 Volts. A combination of differential feedback and ISODCMFB through capacitors  100   a,b  and  101   a,b  drive input nodes  109   a,b  towards V cm,  integrating sense-charge onto the sense capacitors. The position-sense interface output, V out , is equal to the voltage difference between nodes  105   a,b  (v(ch_outm)-v(ch_outp)), and is taken during Phi 2  after the electronics have had time to properly settle. V out  as a function of the sense capacitance C s  is given by the following equation: 
           V   out   =−V   s ( C   ref /( C   p   +C   s+ )− C   ref /( C   p   +C   s− )) 
         [0040]    where C s+ and C s− are sense capacitors  100   a,b,  and C p  is a term representing parasitic capacitance in parallel with sense capacitors  100   a,b .  
         [0041]    When parallel plates comprising either sense capacitor physically touch, sense capacitors are no longer acting as a capacitor and the position sensing interface ceases to function. Physical collision between the plates may have adverse consequences including sticking or welding, especially if the touching members, upon contact, have a voltage difference. Overrange collison may be prevented via equi-potential bumpers that stop movement before capacitor plates touch. Alternatively, the probability of sticking or welding may be reduced upon detection of an impending overrange by applying an equal voltage to electrodes about to collide. Impending collision may be detected, for instance, by periodically or continuouly comparing the position-sense interface output to a pre-determined threshold.  
         [0042]    Note that in response to the voltage shift at input node  110 , a large output common mode shift must occur at output terminals  105   a,b.  To minimize the amount of output common mode swing necessary at opamp outputs  106   a,b,  and enable larger values of V s , switches  120   a,b  are opened and switches  121   a,b  are closed during Phi  2 , applying a charge to the output terminals  105   a,b  via feedforward capacitors  123   a,b.  Voltage V c  is applied to nodes  122   a,b  and may be a constant value that is estimated to minimize output common mode shift. Alternatively, a separate feedback loop may be used to measure shift in output common mode value in response to application of a sense-pulse and adjust V c  in a fashion to drive this shift, over time, towards zero. When V c  is generated using a feedback loop the feedback loop may include a switched capacitor integrator that integrates the difference in opamp output common mode voltage between before and after application of the sense pulse. Switched capacitor integrator design is well known by those skilled in the art. Injecting a feedforward charge through capacitors  123   a,b  to output nodes  105   a,b , reduces output common-mode swing of opamp  115  and allows larger sense voltages to be used.  
         [0043]    A further advantage of the invention is that during Phi 2  substantially equal charges are applied to sense capacitors  100   a,b.  For the substantially parallel-plate sense capacitors used in the position sense interface, attractive force between the plates is approximately proportional to charge squared, with fringing fields and parasitic capacitance causing a slight deviation. Thus, substantially equal amounts of force are applied to both capacitors over their full range of motion, thereby greatly attenuating the effects of spring softening, electrostatic pull-in or snap-in, and nonlinear electrostatic effects inherent with constant voltage prior-art solutions.  
         [0044]    Another advantage of the invention is that thermal noise caused by structure resistance is amplified less than prior-art position measurement interfaces. The improved noise performance arises from including the sense capacitors in the feedback loop. Prior-art interfaces amplified thermal noise by a factor dependent on the amount of parasitic capacitance  
         [0045]    Due to manufacturing imperfections there will be a certain amount of mismatch between sense capacitors, as well as between reference capacitors. Mismatch may result in an undesired offset. Scale factor will also vary due to mismatch and variations between sense capacitors and reference capacitors. Both offset and scale factor may be trimmed using two binary weighted capacitor arrays, such as that described in (M. Lemkin, B. E. Boser, “A three-axis micromachined accelerometer with a CMOS position-sense interface and digital offset-trim electronics,” IEEE JSSC, April, 1999, pp 456-468), one array in parallel with each reference capacitor. Alternatively, if a large scale-factor trim range is necessary, the reference capacitors may be replaced by a pair of binary weighted capacitor arrays.  
         [0046]    [0046]FIG. 7 shows CMOS differential opamp  199  with portion of a switched-capacitor ISODCMFB circuit. The ISODCMFB loop is closed when the opamp is used in a configuration with output to input feedback, such as shown in the first embodiment of the invention. Opamp  199  comprises NMOS bias network  190 , PMOS bias network  188 , differential input pair  187 , PMOS current sources  186   a,b,  PMOS cascodes and gain-boost amplifiers  184   a,b    185   a,b,  and NMOS cascodes and gain-boost amplifiers  182   a,b    183   a,b.  NMOS transistors  180   a,b  act as adjustable current sinks to enable adjustment of output common mode. Bias stack  191  in conjunction with replica transistor  181  sets up a reference voltage at terminal  181   c  used in the generation of voltage applied to node  180   c.  Each of capacitor  198   a,b  is connected at one end to an opamp input terminal  187   a,b,  and node  180   c  at the other end. Capacitors  198   a,b  are typically chosen to be equal for symmetry. Switches  195   a,b,c,d  and  196   a,b,c,d  open and close in two, nonoverlapping phases. In conjunction with capacitors  197   a,b,  switches  195   a,b,c,d  and  196   a,b,c,d  set up the correct voltage across capacitors  198   a,b  so that when the input common-mode voltage equals V cm , NMOS transistors  180   a,b  are biased at approximately the correct value. Note that in ISODCMFB, the input common-mode is measured and the output common-mode is controlled. To attain common-mode feedback, the loop must be closed external to the opamp—in a feedback network. This is in contrast to prior-art in which the output common-mode is both measured and controlled. There are certainly many different opamp configurations that may be used instead of, or in conjunction with a folded cascode topology with gain boosting, including, but not limited to: folded cascode, telescopic, class AB, constant transconductance. In fact, almost any differential opamp topology may be used, as long as the opamp includes a means for adjusting output common mode dependent on the input common-mode value. However, cascoding of the input transistors is desirable to prevent Miller capacitance from degrading linearity. Other ways of effecting an adjustable output common mode are well known by those skilled in the art including, but not limited to triode current-regulation. Note different electronic technologies may be used to form electronic circuits including CMOS, JFET, BiCMOS, or a combination thereof.  
         [0047]    [0047]FIG. 8 shows plots demonstrating calculated nonlinearity for the present invention as compared to a conventional differential position detection interface, such as in (M. Lemkin, B. E. Boser, “A three-axis micromachined accelerometer with a CMOS position-sense interface and digital offset-trim electronics,” IEEE JSSC, April, 1999, pp 456- 468).  Since linearity of the present invention is a function of how well sense-capacitors are modeled by an ideal parallel-plate capacitor, nonlinearity over displacement was calculated in the presence of a constant parasitic capacitance in parallel with sense capacitors. Parasitic capacitance in parallel with the sense capacitors may arise, for example, from interconnection capacitance (i.e. from two parallel metal wires) or from fringing field capacitance from structural electrodes; this parasitic capacitance is typically easy to minimize as compared to parasitic capacitance to a substrate node, for instance. Parameters for these calculations are: sense capacitance C s  2pF each, sense voltage V s  1V, gap width 2 microns, reference capacitance C ref  2pF each, C p  varies between 0.1 pF and 0.5 pF. As evidenced by FIG. 8 a,  scale factor is slightly dependent upon parasitic capacitance in parallel with the sense capacitors. FIG. 8 b  shows a measure of linearity - the Integral Nonlinearity Profile, which is a plot of the deviation of the output from a straight line passing through the two endpoints of the output. Even in the presence of a parasitic capacitance of 25% the sense capacitance, linearity over closing 75% of the gap remained better than 1% of full scale. Smaller values of parasitic capacitance yield even better linearity. FIG. 8 c,  shows the output vs. displacement for the parasitic-insensitive approach described in Lemkin, et. al.; the transfer function is clearly quite nonlinear. FIG. 8 d  shows the Integral Nonlinearity Profile. Nonlinearity approaches 30% of full scale over a 1.5 micron displacement: approximately two orders of magnitude worse than the linearity attained by the present invention.  
         [0048]    In a second embodiment of the present invention, shown in FIG. 9, feedforward capacitors are removed, enabling opamp output  206   a,b  to be coupled directly to sense capacitors  200   a,b  during Phi 2 . Opamp  215  may be similar to opamp  199  described in the first embodiment, and includes an ISODCMFB circuit. Offset cancellation may be maintained by including the switches  201   a,b  and  202   a,b.  However, if offset cancellation is undesired, or will be performed at a later stage, switches  201   a,b  may be replaced by a wire and  202   a,b  may be removed. Position sense interface  250  operates over two recurring, discrete, nonoverlapping time periods Phi 1  ((φ 1 ) and Phi 2  ((φ 2 ) Typical period frequencies are between 1 kHz and 10 MHz. During Phi 1 , switches  203   a,b  are closed, placing opamp  215  into differential unity-gain feedback and setting the differential voltage at opamp input terminals  209   a,b  to a value substantially equal to the opamp offset plus a random component due to flicker and other noise. Since switches  203   a,b  are closed, the output common mode voltage is equal to the input common mode voltage, which is driven substantially equal to reference voltage V cm . Switches  202   a,b  are also closed (and  201   a,b  are open) during Phi 1 , connecting node  205   a,b  to a reference voltage V outcmref . Note that while the input nodes  209   a,b  have a small voltage difference due to opamp noise and offset, output terminals  205   a,b  are forced equal. Reference voltage V outcmref  may be, but is not necessarily, equal to V cm . If V outcmref  is chosen equal to V cm , however, only a very small error voltage component is presented across sense capacitors  200   a,b  during Phi 1 ; thus, undesired electrostatic attraction is minimized. By closing switch  211 , reference capacitors  204   a,b  are initialized so that they may inject a controlled amount of charge during Phi 2 .  
         [0049]    During Phi 2  V outcmref  is disconnected from the sense capacitors by opening switches  202   a,b,  and opamp  215  is removed from unity-gain feedback and placed into charge-integration mode by opening switches  203   a,b  and closing switches  201   a,b  respectively. A sense-charge pulse equal to C ref  {circumflex over (V)} s  is generated by opening switch  211  and closing switch  212 , where sense voltage V s  is a constant voltage typically between 0.1 and 5 Volts. Differential feedback and ISODCMFB through capacitors  200   a,b  drive input nodes  209   a,b  towards V cm , integrating sense-charge onto the sense capacitors. The output is taken as the voltage difference between output nodes  206   a,b.  Since this embodiment does not utilize feedback coupling capacitors, this embodiment typically benefits from faster settling, compared to the first embodiment. However, this embodiment does not provide for feedforward charge cancellation, and thus is limited to smaller sense-pulse voltages.  
         [0050]    A third embodiment of the present invention is shown in FIG. 10. Position sense interface  350  operates in the continuous-time, or frequency multiplexed, domain. Opamp  315  may be similar to opamp  199  described in the first embodiment, and includes an ISODCMFB circuit. A modulation signal, which may be a sinusoid or a square wave for example, is applied to input terminal  310 . Typical frequencies are between 1 kHz and 10 MHz with a magnitude from 0.1 to 5V. Resistors  303   a,b  are large valued and set the low-frequency voltage at the input terminals  309   a,b  while minimally affecting the response of the position-sense interface at frequencies close to the modulation frequency. Resistors  303   a,b  may be formed by a MOS transistor operating in subthreshold regime, for example. Likewise, resistors  302   a,b  set the low-frequency voltage at the output terminals  305   a,b.  The position-sense signal is reconstructed by demodulating the differential output voltage from output terminals  305   a,b  via a demodulator such as a synchronous demodulator synchronized to the voltage at node  310 . To minimize an undesirably large output common mode shift at opamp output terminals  306   a,b,  a modulated feedforward charge is applied to the output terminals  305   a,b  via feedforward capacitors  323   a,b.  Modulated voltage V, is applied to nodes  320   a,b  and may have a constant amplitude and phase relation to the voltage at node  310 , the amplitude and phase estimated to minimize output common mode shift. Alternatively, a separate feedback loop may be used to measure shift in output common mode value in response to modulation signal applied to node  310  and adjust the amplitude of modulation voltage V c  in a fashion to drive this shift, over time, towards zero. When V c  is generated using a feedback loop the feedback loop may include a synchronous demodulator with a continuous time integrator configured in a manner such that the difference in opamp output common-mode voltage in response to changes in the amplitude of the voltage at node  310  is first correlated with the modulation signal and then integrated over time.  
         [0051]    A fourth embodiment of the present invention is shown in FIG. 11. Position sense interface  450  operates in the continuous-time domain. Opamp  415  may be similar to opamp  199  described in the first embodiment, and includes an ISODCMFB circuit. A modulation signal, which may be a sinusoid or a square wave for example, is applied to input terminal  410 . Typical frequencies are between 1 kHz and 10 MHz with a magnitude from 0.1 to 5V. Resistors  403   a,b  are large valued and set the low-frequency voltage at the input terminals  409   a,b  while minimally affecting the response of the position-sense interface at frequencies close to the modulation frequency. The position-sense signal is reconstructed by demodulating the differential output voltage from output terminals  406   a,b  via a demodulator such as a synchronous demodulator synchronized to the voltage at node  410 .  
         [0052]    The present invention further provides for application of a force quasi-constant over displacement, but with a controlled variation over time. In the context of the present invention, electrostatic forces acting on plates of sense capacitors are substantially independent of proof mass position. During position-sensing, nominally equal forces are applied to the proof-mass or proof-masses due to equal amounts of charge provided by reference capacitors. However, by intentionally applying unequal charges to two sense capacitors a net force may be generated. Unequal charges may be produced, for example, by applying different sense voltages to two equal reference capacitors. Advantages of using the position sense interface in a forcing capacity include: elimination of the snap-in voltage/displacement limitation of voltage-based forcing, and attenuation of spring softening nonlinearities that may cause undesired dynamic response. Note that while the forces are substantially independent of displacement, the forces are approximately dependent on the square of the sense-charge pulse and hence the voltage applied to the reference capacitors. If a linear voltage to force relationship is desired, a square-root function may be used to substantially cancel the square charge dependence. Square-root circuits are well known by those skilled in the art and may include in their implementation a translinear loop or a MOSFET.  
         [0053]    Note that the present invention includes many alternate configurations. For example, feedforward capacitors may be switched into a capacitively-coupled output temporarily, for enough time to transfer a majority of the feedforward charge to the output nodes, and then disconnected from the sensing circuit. In this manner feedback-loop settling characteristics are improved because the capacitive loading due to the feedforward capacitors is removed after the feedforward capacitors have applied the feedforward charge. Alternatively, feedforward capacitors may be replaced by a voltage source which is temporarily switched to the output nodes, and then disconnected from the sensing circuit.  
         [0054]    The invention may be co-fabricated with integrated circuitry on a single chip using many fabrication methods including, but not limited to: surface micromachining, reactive ion etching, SOI-based micromachining, epi-polysilicon micromachining, or similar fabrication methods or technologies. Examples of some applicable fabrication technologies may be found in, for example: copending United States application Ser. No. 09/543,936 filed Apr. 5, 2000; U.S. Patent application Ser. No. 09/322,381, filed May 28, 1999; and U.S. Patents: Tsang et al., U.S. Pat. No, 5,326,726, issued Jul. 5, 1994; Spangler et al., U.S. Pat. No. 5,343,064, issued Aug. 30, 1994; Bashir et al., U.S. Pat. No. 5,747,353, issued May 5, 1998; Montague et al., U.S. Pat. No. 5,798,283, issued Aug. 25, 1998; Zhang et al, U.S. Pat. No. 5,506,175 issued Apr. 19, 1996; Kung, U.S. Pat. No. 5,504,026, issued Apr. 12, 1996, each of which is specifically incorporated by reference.  
         [0055]    Alternatively, different components comprising the invention may be formed as discrete elements. For example, the sense element may be formed on a silicon or quartz substrate and the interface, control and signal processing circuitry may be formed on one or more separate substrates as described in, for example, U.S. Patents: MacDonald et al., U.S. Pat. No. 5,198,390, issued Mar. 30, 1993; Diem et al., U.S. Pat. No. 5,576,250, issued Nov. 19, 1996; and Field et al., U.S. Pat. No. 5,882,532, issued Mar. 16, 1999; as well as Smith, T. et. al., “A 15b Electromechanical Sigma-Delta Converter for Acceleration Measurements,” ISSCC Dig. Tech. Papers, pp. 160-161, 1994, each of which is specifically incorporated by reference. Alternatively, the sense-element may be bulk-micromachined by any of a number of well known methods, interface, control and signal processing circuitry may be formed on one or more separate substrates, and the electrical and mechanical substrates may be connected by one or more wire bonds.  
         [0056]    The foregoing description, for the purposes of explanation, used specific nomenclature, terminology and dimensions to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the invention. Thus, the foregoing descriptions of specific embodiments of the invention are presented for the purposes of illustration and description. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed; obviously many modifications and variations are possible in view of the above teachings. For example, the sense-element need not necessarily be micromachined; the invention may be included in a larger system comprising a force feedback loop; the invention may be included in a larger system comprising additional signal processing circuitry; the sense-interface may be mixed domain, meaning the sense-interface may be substantially frequency-multiplexed, with periodic resets occurring to reset the input common mode voltage, a reset comprising a period in which one or more switches are briefly closed and subsequently opened or vice versa.