Abstract:
A sensing device having a microelectromechanical structure made of semiconductor material, and a control loop for controlling the microelectromechanical structure, the microelectromechanical structure including a stator element and a rotor element electrostatically coupled together, and the control loop including a position interface supplying a position signal indicative of the position of the rotor element, and a one-bit quantizer receiving the position signal and supplying a corresponding bit sequence. The sensing device further includes a calibration device for calibrating the microelectromechanical structure, including a microactuator made of semiconductor material and coupled to the rotor element, and a driving circuit for driving the microactuator, and receiving the bit sequence and supplying to the microactuator a driving signal correlated to a mean value of the bit sequence in a given time window.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention regards a device and a method for automatic calibration of a microelectromechanical structure included in a control loop.  
           [0003]    In particular, the present invention finds an advantageous, but not exclusive, application in the compensation of the position offset of an inertial sensor, to which the ensuing treatment will explicitly refer, without this entailing any loss of generality.  
           [0004]    2. Description of the Related Art  
           [0005]    As is known, owing to their reduced size, excellent technical characteristics, high reliability and low cost, integrated inertial sensors manufactured using the micromachining technique are progressively laying claim to market segments up to now occupied by conventional inertial sensors.  
           [0006]    One of the main applications of the above inertial sensors is in the field of airbag systems for motor vehicles as a means for measuring the deceleration to which a motor vehicle is subjected upon impact.  
           [0007]    An inertial sensor, also known as accelerometric sensor or accelerometer, is a particular transducer device capable of measuring and converting an acceleration into an electrical signal, and is basically formed by two distinct elements: a sensor proper and an electrical interface.  
           [0008]    The sensor proper is the element that is able to carry out conversion between the quantity (acceleration), the value of which is to be determined, and a quantity that may be measured by means of circuitry of an electrical nature, whilst the second element of the transducer device is a capacitive reading interface, i.e., a charge integrator, capable of determining the capacitance variation due to the presence of an acceleration.  
           [0009]    An integrated rotary inertial sensor, i.e., the only movement of which is of a rotational nature, is described in the European Patent No. 99830568.4 filed on Sep. 10, 1999, in the name of the present applicant and is shown in FIG. 1.  
           [0010]    The inertial sensor, designated as a whole by 1, is made of semiconductor material, has a circular structure, and comprises an inner stator  2  integral with the die  3  in which the inertial sensor  1  is formed, and an outer rotor  4  electrostatically coupled to the stator  2 .  
           [0011]    The rotor  4  comprises a suspended mass  6  having an annular shape, a plurality of mobile arms  8  extending radially towards the stator  2  from the suspended mass  6 , identical to each other and angularly equispaced, and elastic-suspension and anchorage elements  10  (represented schematically as springs) elastically connecting the suspended mass  6  to fixed anchoring and biasing regions  12 , through which the suspended mass  6  and the mobile arms  8  are biased (typically at a potential of 1.5 V).  
           [0012]    The stator  2  comprises a plurality of pairs of fixed arms  14 ,  16 , one pair for each mobile arm  8  of the rotor  4 , which extend radially with respect to the suspended mass  6  towards the suspended mass  6  itself, are arranged in such a way that between each pair of fixed arms  14 ,  16  a corresponding mobile arm  8  of the rotor  4  is arranged, and are connected to respective fixed anchoring and biasing regions  18 ,  20 , through which the fixed arms  14 ,  16  are biased (typically at a potential ranging between 1.5 and 2.2 V).  
           [0013]    The fixed arms  14 ,  16  are connected, via the fixed anchoring and biasing regions  18 ,  20 , to a sensing circuit having the purpose of picking up, from the fixed arms  14 ,  16 , information regarding the relative position of the rotor  4  with respect to the stator  2 .  
           [0014]    The inertial sensor  1  can be electrically modeled as shown in FIG. 2, i.e., by means of two capacitive elements  21 ,  22  having a half-bridge configuration, wherein the two outer plates are defined by the fixed arms  14  and  16 , respectively, of the stator  2 , and the two inner plates are defined by the mobile arms  8  of the rotor  4 .  
           [0015]    When the suspended mass  6  is subjected to an angular acceleration, it undergoes a rotation such as to determine a modulation in phase opposition of the capacitances, indicated in FIGS.  2  as C S1  and C S2 , of the capacitive elements  21  and  22 , respectively, which, in the absence of angular acceleration or deceleration applied to the inertial sensor  1 , should assume the same value. Consequently, by measuring the capacitances C S1  and C S2  it is possible to measure the magnitude of the unknown inertial quantity, i.e., the acceleration or deceleration to which the inertial sensor  1  is subjected.  
           [0016]    On account of the imperfect configuration of the elastic-suspension and anchoring elements  10  and on account of the residual mechanical stress of the material of which the inertial sensor  1  is made, the rotor  4  is generally affected by a position offset, i.e., the effective zero position of the rotor  4  does not coincide with the nominal zero position, centered with respect to the stator, envisaged in the design phase.  
           [0017]    The position offset consequently gives rise to a corresponding capacitive offset, defined as the difference between the capacitances of the capacitive elements  21 ,  22  in the absence of acceleration or deceleration, which has an adverse effect on the overall performance of the system comprising the inertial sensor  1  and the corresponding driving and measuring circuitry.  
           [0018]    To carry out compensation of the aforesaid capacitive offset, the inertial sensor  1  is provided with an integrated microactuator  24  made of semiconductor material, coupled to the rotor  4  and having the purpose of rotating the rotor  4  by an amount equal to the position offset to bring it back into the nominal zero position.  
           [0019]    In particular, the microactuator  24  comprises four distinct actuator groups  26 , each of which is arranged in a respective quadrant of the inertial sensor  1  and is formed by a plurality of actuator elements  28 , numbering four in the example illustrated in FIG. 1, identical to one another and angularly equispaced.  
           [0020]    In detail, each actuator element  28  is defined on the silicon wafer together with the suspended mass  6  of the rotor  4 , and comprises a mobile arm  30  integral with the suspended mass  6  (and consequently biased at the same potential as that of the suspended mass  6 ), extending radially outwards from the suspended mass  6 , and carrying a plurality of mobile electrodes  32  extending from either side of the respective mobile arm  30  in a substantially circumferential direction, arranged parallel to one another, and equispaced along the respective mobile arm  30 .  
           [0021]    Each actuator element  28  further comprises a pair of fixed arms  34 ,  36  which extend radially with respect to the suspended mass  6 , arranged on opposite sides of the corresponding mobile arm  30  and facing the latter, and connected to respective fixed anchoring and biasing regions  38 ,  40 , through which the fixed arms  34 ,  36  are biased (typically at a potential ranging between 1.5 and 5 V). Each of the fixed arms  34 ,  36  carries a plurality of fixed electrodes  42 ,  43  extending in a substantially circumferential direction towards the corresponding mobile arm  30  and interleaved, or “comb-fingered,” with the mobile electrodes  32  of the corresponding mobile arm  30 .  
           [0022]    The fixed arms  34 ,  36  of the actuator elements  28  are connected, through the fixed anchoring and biasing regions  38 ,  40 , to a driving circuit (not shown) having the purpose of applying a biasing voltage to either one or the other of the two fixed arms  34 ,  36  of each actuator element  28  in such a way that the potential difference between the fixed arm  34 ,  36  thus biased and the corresponding mobile arm  30  causes a rotation of the rotor  4  in one direction or the other, sufficient for bringing the rotor  4  back into the nominal zero position.  
           [0023]    In particular, as a result of the electrostatic coupling existing between each mobile arm  30  and the corresponding fixed arms  34 ,  36 , the rotor  4  is subjected to a transverse force proportional to the number of pairs of fixed arms and mobile arms  30 ,  34 ,  36 . This force tends to move the mobile arm  30  away from the fixed arm  34 ,  36 , with respect to which the mobile arm  30  has a smaller potential difference, and to bring the mobile arm  30  closer to the fixed arm  34 ,  36 , with respect to which the mobile arm  30  has a greater potential difference, thus causing rotation of the suspended mass  6 .  
           [0024]    Owing to the presence of the comb-fingered electrodes  32 ,  42 ,  43 , the force necessary to bring the rotor  4  back from the effective zero position to the nominal zero position is altogether independent of the amount of offset with respect to the nominal zero position itself.  
           [0025]    As regards implementation of the electrical interface of the inertial sensor  1 , there essentially exist two different solutions.  
           [0026]    The first solution consists in reading and amplifying the capacitance variation of the capacitive half-bridge of FIG. 2 caused by the angular acceleration to which the inertial sensor  1  is subjected. This technique represents a direct approach to the problem, whereby at output from the electrical interface there is a voltage directly proportional to the capacitance variation.  
           [0027]    An alternative solution is proposed in “A Three-Axis Micromachined Accelerometer with a CMOS Position-Sense Interface and Digital Offset-Trim Electronics,” Mark Lemkin, Member IEEE, and Bernhard E. Boser, Member IEEE, IEE Journal of Solid-state Circuits, Vol. 34, No. 4, April 1999.  
           [0028]    This solution basically consists in inserting the inertial sensor in a fedback system consisting of a control loop that measures the displacement of the rotor  4  with respect to its nominal position and accordingly applies to the rotor  4  a torque such as to maintain the rotor  4  in the nominal position. The value of the unknown inertial quantity (angular acceleration) is then proportional to the feedback torque necessary for nullifying the displacement of the rotor generated by the external load.  
           [0029]    [0029]FIG. 3 illustrates the block diagram of the sensing device proposed in the above-mentioned publication.  
           [0030]    The sensing device, designated as a whole by  50 , comprises an inertial sensor  52  not provided with any actuator elements for compensation of the position offset, and a control loop  53  having the purpose of maintaining the rotor  4  in its nominal position and of measuring the acceleration to which the inertial sensor  52  is subjected.  
           [0031]    From the control standpoint, the sensing device  50  has a circuit structure similar to that of a sigma-delta converter widely used in analog-to-digital conversion, wherein the inertial sensor  52  is inserted instead of the integrator (constituting the sigma part of the AD converter) and performs the conversion of the angular acceleration to which it is subjected into a variation in the capacitances C S1  and C S2  of the capacitive elements  21 ,  22 .  
           [0032]    The control loop  53  operates in a time division mode in the two sensing and actuation steps; namely, it switches between an actuation operating condition in which, through the fixed anchoring and biasing regions  18 ,  20  of the fixed arms  14 ,  16 , it drives the rotor  4  to keep it in its nominal position, and a sensing operating condition in which, through the same fixed anchoring and biasing regions  18 ,  20 , it measures the angular acceleration to which the inertial sensor  52  is subjected.  
           [0033]    In particular, the control loop  53  comprises an adder  54  receiving at input an input acceleration ζ IN , the value of which is to be measured, and a feedback acceleration ζ RET  supplied by a feedback branch which will be described hereinafter, and supplies at output an error acceleration ζ ERR  equal to the difference between the input acceleration ζ IN  and the feedback acceleration ζ RET .  
           [0034]    The error acceleration ζ ERR  is supplied at input to the inertial sensor  52 , which supplies at output a capacitance variation ΔC S  indicative of the variation in the capacitances C S1  and C S2  of the capacitive elements  21 ,  22  of FIG. 2 caused by the error acceleration ζ ERR , the capacitance variation ΔC S  being calculated according to the following relation:  
         Δ                   C   S       =       ɛ   0     ·     S   gap                             
 
           [0035]    where S is the area of the plates of the capacitive elements  21 ,  22 , and gap is the variation in distance between the fixed arms  14 ,  16  of the stator  2  and the corresponding mobile arms  8  of the rotor  4  caused by the error acceleration ζ ERR .  
           [0036]    The control loop  53  further comprises a differential position interface  56  receiving at input the capacitance variation ΔC S  supplied by the inertial sensor  52  and supplying at output a voltage position signal V OUT  indicative of the position of the rotor  4  and is calculated according to the following relation:  
         V   OUT     =         Δ                   C   S         C   I       ·     V   M                             
 
           [0037]    wherein C I  and V M  assume the meanings described hereinafter.  
           [0038]    In particular, the position interface  56  is implemented using the differential circuit diagram shown in FIG. 4, i.e., using an operational amplifier  58  in fully differential configuration, the inverting and non-inverting input terminals of which are connected, through the capacitive elements  21 ,  22  in half-bridge configuration, to a voltage generator  60  supplying a square wave measurement voltage V M , and the inverting and non-inverting output terminals of which are respectively connected to the inverting and non-inverting input terminals via respective feedback capacitive elements  62 ,  64  having capacitance C I .  
           [0039]    With reference again to FIG. 3, the control loop  53  further comprises a one-bit quantizer  66  receiving at input the position signal V OUT  supplied by the position interface  56  and supplying at output a digital signal OUT assuming a first logic value, for instance 1, if the position signal V OUT  is positive, and a second logic value, in the example considered 0, if the position signal V OUT  is negative.  
           [0040]    The digital signal OUT supplied by the one-bit quantizer  66  defines a sequence of bits generally referred to as “bitstream,” a term that will be used also in the ensuing treatment.  
           [0041]    Finally, the control loop  53  comprises a main feedback branch  67  having the function of driving the rotor  4  to maintain it in its nominal position, and essentially formed by a main actuator  68  receiving at input the bitstream OUT supplied by the one-bit quantizer  66  and supplying at output the aforementioned feedback acceleration ζ RET , which is indicative of the acceleration (and hence the torque) applied to the rotor  4  to maintain it in its nominal position, and the absolute value and sign of which define the intensity and direction of the feedback necessary for maintaining the rotor  4  in its nominal position.  
           [0042]    In particular, the main actuator  68  acts directly on the biasing of the fixed arms  14 ,  16  of the stator  2 , and consequently on the mobile arms  8  of the rotor  4 , to maintain the rotor  4  in its nominal position, and is implemented using the differential circuit diagram shown in FIG. 5, in which the capacitive elements  21 ,  22  defined by the fixed and mobile arms  8 ,  14 ,  16  are shown.  
           [0043]    In detail, the main actuator  68  basically comprises two pairs of switches, designated by  70 ,  72  and  74 ,  76 , controlled by the bitstream OUT supplied by the one-bit quantizer  66 .  
           [0044]    The switches  70 ,  72  of the first pair are respectively controlled by the bitstream OUT and by the negated bitstream {overscore (OUT)} (obtained by means of a simple NOT logic gate—not shown) and connect selectively, and in phase opposition, the fixed arms  14  of the stator  2  to a supply line  78  set at a supply voltage V RET  and to a ground line  80  set at a ground voltage V GND , whilst the switches  74 ,  76  of the second pair are also respectively controlled by the negated bitstream {overscore (OUT)} and by the bitstream OUT, and connect selectively, and in phase opposition, the fixed arms  16  of the stator  2  to the supply line  78  and to the ground line  80 .  
           [0045]    The biasing voltage actually applied to the fixed arms  14 ,  16  of the stator  2  thus comes to be a voltage correlated to the bitstream OUT, namely, a pulse modulated voltage modulated by the bitstream OUT (PDM—Pulse Density Modulation), and consequently also the feedback acceleration ζ RET  applied to the rotor  4  to keep it in its nominal position is correlated to the bitstream OUT.  
           [0046]    The closed loop control of the position of the rotor of the inertial sensor  52  and, consequently, the measurement of the angular acceleration to which the inertial sensor  52  is subjected performed by the circuit structure of FIG. 3, are, however, adversely affected both by the position offset existing between the rotor  4  and the stator  2  and by the voltage offsets present in the active electronic devices, such as operational amplifiers and comparators, and by the mismatches of the passive electronic components, such as resistors and capacitors, that are present in the control loop  53 .  
           [0047]    In particular, owing to the factors referred to above, in the absence of angular acceleration applied to the inertial sensor  52 , the bitstream OUT supplied by the one-bit quantizer  66  has a non-zero mean value, whereby, in this operating condition, the value of the feedback acceleration ζ RET  generated by the main actuator  68  is non-zero and thus causes, at best, a reduction in the intervention dynamics of the control loop  53 , whilst, at worst, it may even lead to complete saturation of the control loop  53 .  
           [0048]    In fact, the control loop  53  is typically able to recover capacitance variations ΔC S  of the order of the fF, whereas the capacitance variations ΔC S  generated by the offsets and mismatches referred to above may reach values that are even decidedly higher. Consequently, in the presence of sufficiently small offsets and mismatches, the dynamics of the control loop  53  is reduced by the part necessary for recovering the said offsets and mismatches, whereas, in the presence of high offsets and mismatches, the control loop  53  is completely saturated, and its dynamics is consequently reduced to zero.  
           [0049]    It has moreover been experimentally verified by the present applicant that the above-mentioned offsets and mismatches rarely assume sufficiently small values, such as to lead to a negligible, or in any case not too significant, reduction in the dynamics of the control loop  53 ; on the contrary, they often assume values such as to bring the control loop  53  to complete saturation. Consequently, the recovery of the aforementioned offsets and mismatches is increasingly becoming an indispensable requirement in this type of applications.  
         BRIEF SUMMARY OF THE INVENTION  
         [0050]    The disclosed embodiments of the present invention provide a sensing device and an automatic calibration method thereof that will enable the drawbacks described above to be overcome at least in part.  
           [0051]    According to one embodiment of the invention, a sensing device is provided that includes a microelectromechanical structure made of semiconductor material, a control loop for controlling the microelectromechanical structure, the microelectromechanical structure including a stator element and a rotor element electrostatically coupled together, and the control loop including an interface circuit coupled to the microelectromechanical structure and supplying a position signal indicative of the position of the rotor element; and a calibration circuit for calibrating the structure, the calibration circuit including at least one actuator made of semiconductor material and coupled to the rotary element, the first driving circuit for driving the at least one actuator including a first driving circuit receiving a position signal and supplying to the at least one actuator a driving signal correlated to a mean value of the position signal.  
           [0052]    In accordance with another embodiment of the invention, a method for automatic calibration of a sensing device is provided, the sensing device including a microelectromechanical structure made of semiconductor material and a control loop for controlling the same, a microelectromechanical structure including a stator element and a rotor element electrostatically coupled together, the control loop including an interface circuit coupled to the microelectromechanical structure and configured to supply a position signal indicative of the position of the rotor element. The method includes the step of repositioning the rotor element to overcome voltage offset and component mismatches, which further includes the steps of providing an actuator made of semiconductor material and coupled to the rotor element; and supplying to the actuator a driving signal correlated to a mean value of the position signal.  
           [0053]    In accordance with another aspect of the foregoing method of the present invention, the control loop includes a quantizer for receiving the position signal and supplying a corresponding sequence of samples, and the step of driving the actuator includes the step of supplying to the actuator a driving signal correlated to a mean value of the sequence of samples. 
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)  
       [0054]    For a better understanding of the present invention, two preferred embodiments thereof are now described, purely to furnish non-limiting examples, with reference to the attached drawings, in which:  
         [0055]    [0055]FIG. 1 is a schematic representation of the structure of a rotary inertial sensor;  
         [0056]    [0056]FIG. 2 shows an equivalent electrical circuit of the inertial sensor of FIG. 1;  
         [0057]    [0057]FIG. 3 shows the block diagram of a prior art sensing device, formed by an inertial sensor and a control loop for controlling the inertial sensor;  
         [0058]    [0058]FIG. 4 shows the circuit structure of a position interface forming part of the control loop of FIG. 3;  
         [0059]    [0059]FIG. 5 shows the circuit structure of a main actuator forming part of the control loop of FIG. 3;  
         [0060]    [0060]FIG. 6 shows the block diagram of a sensing device according to one embodiment of the present invention, formed by the inertial sensor of FIG. 1 and a control loop for controlling this inertial sensor; and  
         [0061]    [0061]FIG. 7 shows a flowchart relative to the method for calibration of the sensing device of FIG. 6 in accordance with another embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0062]    The present invention stems from the realization that, in the sensing device of FIG. 3, the position offset of the inertial sensor, the voltage offset present in the active electronic devices used in the control loop, and the mismatches of the passive electronic components also used in the control loop are “seen” by the control loop as virtual accelerations applied to the inertial sensor.  
         [0063]    Consequently, by using an inertial sensor of the type shown in FIG. 1, namely, one provided with actuator elements for compensating the position offset, and by appropriately modifying the control loop in the way described in detail hereinafter, it is possible to obtain that the control loop will handle these virtual accelerations in the same way as it handles the accelerations actually applied to the inertial sensor  1 , consequently nullifying the effects of the above-mentioned offsets and mismatches.  
         [0064]    In other words, by appropriately intervening on the control loop, it is possible to obtain that, just as the control loop acts to nullify the effects on the position of the rotor of the accelerations actually applied on the inertial sensor, it will likewise act to nullify the effects, again on the position of the rotor, of the aforesaid virtual accelerations (i.e., of the aforesaid offsets and mismatches), thus achieving an effective automatic calibration procedure for calibrating the inertial sensor, because there is in fact a substantial nullification of all the negative effects produced by the above-mentioned offsets and mismatches on the control of the position of the rotor and on the measurement of the angular acceleration to which the inertial sensor is subjected.  
         [0065]    In greater detail, according to the present invention a sensing device is provided that comprises an inertial sensor  1  equipped with actuator elements for compensating the position offset, and a control loop formed by a main feedback branch identical to that of FIG. 3 and of a secondary feedback branch having the purpose of estimating, on the basis of the bitstream OUT supplied by the one-bit quantizer  66 , the extent of the offsets and mismatches present in the inertial sensor and in the active and passive devices used in the control loop, and of acting accordingly on the biasing of the fixed arms  34 ,  36  of the actuator elements  28  in such a way as to nullify the effects of said offsets and mismatches on the position of the rotor  4 .  
         [0066]    [0066]FIG. 6 shows the block diagram of a sensing device according to the present invention, wherein the parts that are identical to those of FIG. 3 are designated by the same reference numbers.  
         [0067]    The sensing device, designated as a whole by  50 ′, has a circuit structure similar to that of the sensing device  50  and comprises an inertial sensor  52  of the type shown in FIG. 1, hence represented by an inertial sensor designated by  1 , and a corresponding control loop, designated by  53 ′.  
         [0068]    The control loop  53 ′ comprises, as does the control loop  53 , an adder  54 , a position interface  56 , a one-bit quantizer  66 , and a main feedback branch  67  formed by a main actuator  68 , all of which, consequently, will not be described again.  
         [0069]    According to one feature of the present invention, the control loop  53 ′ further comprises a secondary feedback branch  81  arranged in parallel to the main feedback branch  67  and mainly consisting of a calibration device  82 .  
         [0070]    The calibration device  82  comprises a computation circuit  84  receiving at input the bitstream OUT supplied by the one-bit quantizer  66  and supplying at output a dimensionless number MBS equal to the mean value of the bitstream OUT within a pre-set time window.  
         [0071]    In particular, the computation circuit  84  sums together the logic values of a number N of bits supplied by the one-bit quantizer  66 , for example N= 2   15 , and divides the said sum by the number N itself; namely, it implements the following formula:  
       MBS   =       1   N     ·       ∑     i   =   1     K                     bit        (   i   )                                 
 
         [0072]    where bit(i) may assume only the values +1 and −1.  
         [0073]    In fact, with reference to the meanings assumed by the individual bits of the bitstream OUT, it may be understood how a bit having logic value  1  involves application, to the rotor  4 , of a torque in a given direction, whilst the arrival of a bit having logic value 0 involves application to the rotor  4  of a torque (angular acceleration) in the opposite direction. In the above formula, therefore, any bit of the bitstream OUT having logic value 0 is mathematically considered as having logic value −1.  
         [0074]    In practice, the computation circuit  84  may be implemented by means of a moving average filter of length N.  
         [0075]    It is moreover emphasized that the mean value MBS of the bitstream OUT supplied at output by the computation circuit  84  represents an estimate of the offsets and mismatches present in the inertial sensor  52  and in the active and passive devices used in the control loop  53 . In fact, a mean value MBS of the bitstream OUT equal to zero indicates the absence of offsets and mismatches, whilst a mean value MBS of the bitstream OUT equal to +1 or to −1 indicates the presence of offsets and mismatches of such amounts as to saturate the control loop  53  completely.  
         [0076]    The calibration device  82  further comprises a processing circuit  86  receiving at input the mean value MBS of the bitstream OUT supplied by the computation circuit  84  (one at each sampling instant) and supplying at output a calibration voltage V CAL , which is applied to the fixed arms  34 ,  36  of the actuator elements  28  to bring about the application to the rotor  4  of a torque sufficient for compensating the above-mentioned offsets and mismatches.  
         [0077]    In particular, the actuator elements  28  are represented in FIG. 6 by means of a secondary actuator  88  receiving at input the calibration voltage V CAL  and supplying at output a calibration acceleration ζ CAL  which, when applied to the rotor  4 , brings about compensation of the aforementioned offsets and mismatches.  
         [0078]    In particular, the calibration acceleration ζ CAL  is supplied at input to the adder  54 , which supplies at output an error acceleration ζ ERR  equal to the algebraic sum of the input acceleration ζ IN , the feedback acceleration ζ RET , and the calibration acceleration ζ CAL .  
         [0079]    The calibration voltage V CAL  is determined by the processing circuit  86 , not only according to the mean value MBS of the bitstream OUT, but also according to the mechanical characteristics (moment of inertia) of the inertial sensor  1 , in so far as the said calibration voltage V CAL  must be such as to apply to the rotor  4  a torque sufficient for compensating the offsets and mismatches, and consequently cannot fail to take into account the mechanical characteristics of the inertial sensor  1 .  
         [0080]    According to a further feature of the present invention, calibration of the inertial sensor  1  is performed by the calibration device  82  executing a two-step calibration procedure, which is described hereinafter with reference to the flowchart of FIG. 7, wherein in the first step of said procedure, a rough calibration is performed which enables recovery of large capacitance variations ΔC S  generated by the above-mentioned offsets and mismatches, whilst in the second step a finer calibration is performed that enables recovery of small capacitance variations ΔC S , and hence refinement of the calibration of the inertial sensor  1 .  
         [0081]    In particular, as illustrated in FIG. 7, in the first step of the calibration procedure, the main actuator  68  drives the inertial sensor  1  in such a way as to apply to the rotor  4  a torque M 1  greater than the torque that is applied thereto during normal operation of the inertial sensor  1 , and in particular the said torque M 1  is generated by biasing the supply line  78  of the main actuator  68  at a supply voltage V RET1  greater than the one used during normal operation of the inertial sensor  1  (block  100 ).  
         [0082]    Experimental tests carried out by the present applicant have shown that, given the values generally assumed by the above-mentioned offsets and mismatches, a torque M 1  approximately eight times greater than that applied during normal operation of the inertial sensor  1  (and hence, given the quadratic link between torque and voltage, a supply voltage V RET1  approximately {square root}{square root over ( 8 )} times higher than the one used during normal operation of the inertial sensor  1 ) is sufficient for recovering a fair proportion of the capacitance variations ΔC S  generated in the aforesaid offsets and mismatches.  
         [0083]    At this point, the computation circuit  84  determines the mean value MBS 1  of the bitstream OUT resulting from the application to the rotor  4  of the torque M 1  (block  110 ), and the mean value MBS 1  is supplied to the processing circuit  86 , which stores it and accordingly calculates a corresponding calibration voltage V CAL1  in the way described in detail hereinafter (block  120 ).  
         [0084]    The calibration voltage V CAL1  is then applied to the actuator elements  28 , and the consequent rotational movement of the rotor  4  performs a compensation of a fair proportion of the offsets and mismatches that are present (block  130 ).  
         [0085]    The remainder of the offsets and mismatches are compensated in the second step of the calibration procedure, in which the main actuator  68  drives the inertial sensor  1  in such a way as to apply to the rotor  4  a torque M 2  equal to the torque applied thereto during normal operation of the inertial sensor  1 , and in particular the said torque M 2  is generated by biasing the supply line  78  of the main actuator  68  at a supply voltage V RET2  equal to the one used during normal operation of the inertial sensor  1  (block  140 ).  
         [0086]    The computation circuit  84  then determines the mean value MBS 2  of the bitstream OUT resulting from the application to the rotor  4  of the torque M 2  (block  150 ), and the mean value MBS 2 , which by now assumes a value close to zero, is supplied to the processing circuit  86 , which stores it and accordingly calculates a corresponding calibration voltage V CAL2  in the way described hereinafter (block  160 ).  
         [0087]    The said calibration voltage V CAL2  is then applied to the actuator elements  28 , and the consequent rotational movement of the rotor  4  performs complete compensation of the offsets and mismatches that are present (block  170 ).  
         [0088]    According to a further feature of the present invention, the two calibration voltages V CAL1  and V CAL2  applied to the actuator elements  28  in the first and second steps of the calibration procedure and described with reference to blocks  120 ,  160  are generated by pulse width modulating (PWM—Pulse Width Modulation) the same maximum calibration voltage V MAX , which is a square wave voltage having an amplitude variable between a zero value and a maximum value corresponding to the maximum torque that it is intended to apply to the rotor  5 , and a duty-cycle that can be modulated according to the mean values MBS 1  and MBS 2  of the bitstream OUT that are calculated in the blocks  110  and  150 .  
         [0089]    In particular, the calibration voltage V CAL1  applied to the actuator elements  28  at the end of the first step of the calibration procedure is generated by pulse width modulating the maximum calibration voltage V MAX  in proportion to the mean value MBS 1 , whilst, since the calibration voltage V CAL2  applied to the actuator elements  28  at the end of the second step of the calibration procedure is a refinement of the calibration voltage V CAL1 , it is generated by pulse width modulating the maximum calibration voltage V MAX  in proportion to a mean value MBS 3 =MBS 1 +αMBS 2 , where α is the ratio between the torques M 1  and M 2  applied to the rotor  4  respectively in the second step and in the first step of the calibration procedure (in the example considered, α= ⅛).    
         [0090]    In this way, the calibration torque M CAL  applied to the rotor  4  by the actuator elements  28  is simply proportional to the ratio between the time interval T ON  in which the maximum calibration voltage V MAX  assumes a high logic value and the time interval T OFF  in which the maximum calibration voltage V MAX  assumes a low logic value; namely:  
         M   CAL     =           T   CN         T   CN     +     T   OFF         ·     M   MAX       =       T   ON     ·   f   ·     M   MAX                               
 
         [0091]    where f= 1 (T ON +T OFF ) is the frequency of the maximum calibration voltage V MAX , and M MAX  is the maximum torque corresponding to the maximum calibration voltage V MAX .  
         [0092]    Once the frequency of the maximum calibration voltage V MAX  has been fixed, by simply acting on the duration T ON  it is possible to apply the aforementioned different torques in the two steps of the calibration procedure.  
         [0093]    As regards the practical implementation of the pulse width modulation of the maximum calibration voltage V MAX , this may be simply done by using a B-bit counter receiving a clock signal CK having a period T CK . In fact, if the torque applied to the rotor  4  is kept at the maximum value for the first n clock pulses, we have T ON =n·T CK , and T ON +T OFF =1/f=2 B ·T CK , and hence:  
         M   CAL     =       n     2   B       ·       M   MAX     .                             
 
         [0094]    Consequently, we have 0&lt;M CAL &lt;M MAX , with a resolution equal to ΔM CAL =M MAX /2 B .  
         [0095]    From an examination of the characteristics of the sensing device according to the present invention, the advantages that the said sensing device affords emerge evidently.  
         [0096]    In particular, with the present invention it is possible to perform automatic calibration of the inertial sensor  1  by means of simple operations, the practical implementation of which involves the use of equally simple electronic circuits, in this way eliminating all the problems of reduction in the dynamics or of saturation of the control loop that afflict the sensing devices according to the prior art.  
         [0097]    Finally, it is clear that modifications and variations may be made to the inertial sensor described and illustrated herein, without thereby departing from the sphere of protection of the present invention.  
         [0098]    For example, the quantizer present in the control loop might not be a one-bit quantizer, but an n-bit quantizer supplying at output a sequence of samples, each of n bits.  
         [0099]    In addition, the calibration procedure described above could be performed using, in both steps, the same supply voltage V RET  that is used during normal operation of the inertial sensor  1 . This would inevitably involve an increase in the number of steps necessary for reaching a mean value MBS of the bitstream OUT equal to zero, and hence for reaching the calibration voltage V CAL  that enables complete nullification of the offsets and mismatches; however, this would in no way jeopardize the final result, namely the final value of the calibration voltage V CAL , but it would simply affect the number of steps required for achieving the said result.  
         [0100]    Furthermore, should, in certain particular applications, at the end of the second step of the calibration procedure the mean value MBS 2  of the bitstream OUT fail to be exactly zero, which would be an indication of a not yet perfect calibration, it is always possible to perform further steps similar to the previous ones.  
         [0101]    In this case, the multi-step calibration procedure for calibrating the inertial sensor  1  could be performed using, in the various steps, supply voltages V RET  that are different from one another, for example ones that are progressively decreasing until they reach the value of the supply voltage used during normal operation of the inertial sensor  1 , or else could be performed, as regards the first two steps, in a way similar to that described previously (namely, using in the first step a supply voltage higher than the one used during normal operation, and in the second step a supply voltage equal to the one used during normal operation), and using, instead, in the steps after the second, always a supply voltage V RET  equal to the one used during normal operation.  
         [0102]    In addition, the number of actuator groups  26  and the number of actuator elements  28  in each actuator group  26  of the inertial sensor  1  could be different from what has been described. In particular, even a single actuator element  28  connected to the suspended mass  6  could be provided, or else four actuator elements  28 , each arranged in a respective quadrant, or else two actuator elements  28  arranged on diametrically opposite sides of the suspended mass  6 , or again two actuator groups  26  arranged on diametrically opposite sides of the suspended mass  6 .  
         [0103]    Furthermore, the inertial sensor  1  could be of a linear type, in which the microactuator  24  is driven in such a way as to impress on the rotor  4  a translational movement with respect to the stator in a rectilinear direction, the fixed and mobile arms of the rotor and of the stator extend from the suspended mass orthogonally to the said direction, and the fixed and mobile electrodes extend from the said arms parallel to the said direction.  
         [0104]    From the foregoing it will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention is not limited except as by the appended claims and the equivalents thereof.