Abstract:
A device for controlling the frequency of resonance of an oscillating micro-electromechanical system includes: a microstructure, having a first body and a second body, which is capacitively coupled to the first body and elastically oscillatable with respect thereto at a calibratable frequency of resonance, a relative displacement between the second body and the first body being detectable from outside; and an amplifier coupled to the microstructure for detecting the relative displacement. DC decoupling elements are arranged between the amplifier and the microstructure.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]     This application is a continuation of International Application No. PCT/EP2006/061118, filed Mar. 28, 2006, and claims priority from European Patent Application No. 05425185, filed Mar. 31, 2005, which applications are incorporated herein by reference in their entirety. 
     
    
     BACKGROUND  
       [0002]     1. Technical Field  
         [0003]     The present invention relates to a device for controlling the frequency of resonance of an oscillating micro-electromechanical system.  
         [0004]     2. Description of the Related Art  
         [0005]     Various types of oscillating micro-electromechanical systems (MEMS) are known, which include a micro-electromechanical structure and a reading and driving circuit associated thereto. The micro-electromechanical structure comprises a fixed body or stator and a movable body constrained to the stator by elastic connection elements, in accordance with a mass-spring-damper model. In particular, the connection elements are configured so as to enable small oscillations of the movable body about a position of equilibrium selectively with respect to pre-determined degrees of freedom. The oscillating motion of the movable body with respect to the stator is characterized by a natural frequency of resonance that depends both upon the elastic constant of the connection elements and upon the mass of the movable body itself.  
         [0006]     Furthermore, the movable body and the stator are capacitively coupled by means of a plurality of respective comb-fingered electrodes. The relative position of the movable body with respect to the stator determines the total coupling capacitance between the electrodes. Consequently, the total coupling capacitance between the electrodes can be measured by the reading and driving circuit to arrive at the relative position of the movable body with respect to the stator and hence to the force acting on the movable body itself. Vice versa, the reading and driving circuit can apply a controlled electrostatic force between the stator and the movable body by appropriately biasing the electrodes.  
         [0007]     Application of a constant electrostatic force determines a non-zero mean displacement of the movable body with respect to the position of equilibrium and has the same effect of a (fictitious) elastic constant that is added to the elastic constant of the connection elements between the movable body and the stator. In practice, also the natural frequency of resonance of the mass-spring-damper system can be modified.  
         [0008]     This possibility is very important in the fabrication of micro-electromechanical devices such as MEMS resonators or gyroscopes, in which the value of the natural frequency of resonance has a decisive role. In fact, since said value can be calibrated on the finished device instead of during its fabrication, the processes of fabrication are extremely less critical and hence simpler.  
         [0009]     The reading and driving circuits include, among other things, a differential amplifier, which detects capacitive variations at the electrodes of the stator and supply a feedback quantity, typically a voltage. The feedback voltage generates an electrostatic force between the stator and the movable body.  
         [0010]     A limit of the current reading and driving circuits lies in the fact that the dynamics available for calibration of the frequency of resonance is rather limited. In particular, the electrodes of the stator remain permanently coupled to the inputs of the differential amplifier, which must, however, be biased at a value of common-mode voltage (normally, the common-mode voltage is central with respect to the available maximum and minimum supply voltages). The voltages on the inputs of the differential amplifier must not depart significantly from the common-mode voltage in order to prevent saturation of the differential amplifier. Consequently, also the voltages that can be supplied to the electrodes of the stator to modify the elastic constant and the natural frequency of resonance of the MEMS can exploit only a limited part of the maximum available dynamics. In other words, the frequency of resonance of the MEMS can be calibrated only within of a small range of values.  
       BRIEF SUMMARY  
       [0011]     The aim of the present invention is to provide a device for controlling the frequency of resonance of an oscillating micro-electromechanical system which will be free from the drawbacks described above.  
         [0012]     According to the present invention, a device for controlling the frequency of resonance of an oscillating micro-electromechanical system is provided, as defined in claim  1 . 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0013]     For a better understanding of the invention, there is now described an embodiment, purely by way of non-limiting example and with reference to the attached drawings, wherein:  
         [0014]      FIG. 1  illustrates a simplified block diagram of a micro-electromechanical resonator incorporating a device for controlling the frequency of resonance according to the present invention;  
         [0015]      FIG. 2  is a schematic top plan view of a microstructure included in the system of  FIG. 1 ;  
         [0016]      FIG. 3  shows a detail of the microstructure illustrated in  FIG. 2  at an enlarged scale;  
         [0017]      FIGS. 4   a  and  4   b  are simplified circuit diagrams of the device for controlling the frequency of resonance incorporated in the system of  FIG. 1 , in two different operating configurations;  
         [0018]      FIG. 5  is a graph showing plots of quantities regarding the device illustrated in  FIG. 4 ; and  
         [0019]      FIG. 6  is a simplified circuit diagram of a part of the device for controlling the frequency of resonance illustrated in  FIG. 4 . 
     
    
     DETAILED DESCRIPTION  
       [0020]     In the ensuing description, reference will be made to the use of the invention in an electromechanical resonator. This must not, however, be considered as in any way limiting the sphere of application in so far as the invention can advantageously be applied also to oscillating micro-electromechanical systems of a different type, such as for example MEMS gyroscopes, and in any case to all micro-electromechanical structures of which it is necessary to control the natural frequency of oscillation.  
         [0021]      FIG. 1  illustrates a micro-electromechanical resonator  1 , comprising a micro-electromechanical structure  2  (hereinafter referred to as microstructure  2 , for simplicity) and a reading and driving circuit  3  associated and connected thereto so as to form a feedback loop  4 . The micro-electromechanical resonator  1  has a natural frequency of resonance (OR determined by the mechanical characteristics of the microstructure  2 , as clarified hereinafter. The reading and driving circuit  3  maintains the microstructure  2  in vibration at a controlled frequency and forms, with the microstructure  2  itself, a device for controlling the frequency of resonance of the micro-electromechanical resonator  1 .  
         [0022]     The reading and driving circuit  3  includes a differential stage  5  and a feedback stage  6 . The feedback stage  6 , in itself known, is for example based upon a variable-gain amplifier (VGA), typically a voltage-controlled one, and sets conditions of oscillation as regards magnitude and phase on the feedback loop  4  according to the Barkhausen criterion. In particular, the condition of oscillation is guaranteed by a square-wave feedback signal S FB  of controlled amplitude and phase. The micro-electromechanical resonator  1  is connected to a control unit  7 , which supplies a calibration signal S CAL  for calibration of the frequency of resonance of the micro-electromechanical resonator  1 .  
         [0023]     As shown in detail in  FIGS. 2 and 3 , the microstructure  2  is integrated in a semiconductor chip  8  and comprises a fixed portion or stator  10  and a movable body  11 . The movable body  11  is constrained to the stator  10  by springs  12 , which are also made of semiconductor material and are configured so that the movable body  11  may oscillate along an axis Y about an equilibrium position, designated by Y 0  in  FIG. 3 .  
         [0024]     The stator  10  and the movable body  11  are capacitively coupled. In greater detail ( FIG. 3 ), the stator  10  is provided with a plurality of first fixed electrodes  13   a  and a plurality of second fixed electrodes  13   b , insulated from one another, whilst the movable body  11  is provided with a plurality of movable electrodes  14 . The first and second fixed electrodes  13   a ,  13   b  and the movable electrodes  14  are all shaped as plane semiconductor plates extending perpendicular to the axis Y and are comb-fingered. More precisely, the stator  10  and the movable body  11  are arranged so that each movable electrode  14  faces, on one side, a respective fixed electrode  13   a  and, on the opposite side, a respective second fixed electrode  13   b , thus forming a first capacitor  15   a  and a second capacitor  15   b , respectively. Furthermore, the first fixed electrodes  13   a  are electrically connected in parallel to a first stator terminal  17   a , and the second fixed electrodes  13   b  are connected in parallel to a second stator terminal  17   b . The movable electrodes  14  are connected to a common terminal  18  through the movable body  11  and the springs  12 , all of which are made of semiconductor material.  
         [0025]     The movable body  11  can oscillate about the equilibrium position Y 0  with a motion characterized by the natural frequency of resonance ω R  given by: 
 
ω R   =√{square root over (K M /M)}   (1) 
 
         [0026]     where K M  is the (mechanical) elastic constant associated to the springs  12 , and M is the mass of the movable body  11 .  
         [0027]     When the movable body  11  has a displacement ΔY with respect to the equilibrium position Y 0  and, moreover, the first and second fixed electrodes  13   a ,  13   b  are biased with a same shift voltage Vs with respect to the movable electrodes  14 , each movable electrode  14  is subjected to two opposite electrostatic forces F E1 , F E2  along the axis Y (see  FIG. 3 ), which are given by:  
                 F     E   ⁢           ⁢   1       =       1   2     ⁢         C   NOM     ⁢     Y   G   2     ⁢     V   S   2             Y   G     ⁡     (       Y   G     -     Δ   ⁢           ⁢   Y       )       2           ⁢     
     ⁢       F     E   ⁢           ⁢   2       =       -     1   2       ⁢         C   NOM     ⁢     Y   G   2     ⁢     V   S   2             Y   G     ⁡     (       Y   G     -     Δ   ⁢           ⁢   Y       )       2                   (   2   )             
 
         [0028]     In Equations (2), Y G  is the distance between each movable electrode  14  and the first and second fixed electrodes  13   a ,  13   b  adjacent thereto, when the movable body  11  is in the equilibrium position Y 0 , and C NOM  is the capacitance of the capacitors  15   a ,  15   b , once again with the movable body  11  in the equilibrium position Y 0 . The resultant electrostatic force F ER  applied to each movable electrode  14  is:  
               F   ER     =         F     E   ⁢           ⁢   1       +     F     E   ⁢           ⁢   2         =       2   ⁢       C   NOM     ⁡     (     Δ   ⁢           ⁢     Y   /     Y   G         )       ⁢     V   S   2             Y   G     ⁡     (     1   -       (     Δ   ⁢           ⁢     Y   /     Y   G         )     2       )       2                 (   3   )             
 
         [0029]     and, on the hypothesis of small displacements (Y G &lt;&lt;ΔY):  
               F   ER     =       2   ⁢       C   NOM     ⁡     (       Δ   ⁢           ⁢   Y     -     Y   G       )       ⁢     V   S   2         Y   G   2               (   3   )             
 
         [0030]     Equation (4) shows a direct proportionality between the resultant electrostatic force F ER  and the displacement ΔY. The effect of the resultant electrostatic force F ER  is equivalent to that of a fictitious elastic force with negative elastic constant. It is hence possible to introduce an electrostatic elastic constant K E  given by:  
               K   E     =       -       ⅆ     F   ER         ⅆ   Y         =     -       2   ⁢     C   NOM     ⁢     V   S   2         Y   G   2                   (   5   )             
 
         [0031]     As may be noted from Equation (5), the electrostatic elastic constant K E  is correlated to the shift voltage V S . Consequently, when the fixed electrodes  13   a ,  13   b  are biased at the shift voltage V S  with respect to the movable electrodes  14 , the motion of the movable body is characterized by an equivalent elastic constant K EQ  and by a translated frequency of resonance ω RS  given by: 
 
 K   EQ   =K   M   +K   E   (6) 
 
ω RS   =√{square root over (K EQ /M)}   (7) 
 
         [0032]     In  FIG. 4 , where the differential stage  5  is illustrated in detail, the microstructure  2  is represented from the electrical standpoint by the first and second stator terminals  17   a ,  17   b , the common terminal  18 , a first equivalent capacitor  19   a  and a second equivalent capacitor  19   b , and parasitic capacitors  20 . The first equivalent capacitor  19   a  is connected between the first stator terminal  17   a  and the common terminal  18  and has a variable capacitance, equal to the sum of the capacitances of all the first capacitors  15   a ; likewise, the second equivalent capacitor  19   b  is connected between the second stator terminal  17   b  and the common terminal  18  and has a variable capacitance, equal to the sum of the capacitances of all the second capacitors  15   b . The parasitic capacitors  20  represent, instead, the parasitic capacitances associated to the stator terminals  17   a ,  17   b  and to the common terminal  18  (towards ground). Furthermore,  FIGS. 4   a  and  4   b  show a local oscillator  16 , which generates a reading and driving signal S SENSE  and a reset signal S RES , both of which are square-wave signals. The reading and driving signal S SENSE  is supplied to the common terminal  18 , whereas the reset signal S RES  is used for clocking the differential stage  5 . As illustrated in  FIG. 5 , the reading and driving signal S SENSE  and the reset signal S RES  preferably have the same period T and opposite logic values. Furthermore, the reading and driving signal S SENSE  is at a high level for a time longer than one half-period (for example, ⅔ of the period T), and, obviously, the reset signal S RES  is at a high level for a time shorter than one half-period (for example, ⅓ of the period T).  
         [0033]     The differential stage  5  comprises a fully differential switched-capacitor charge amplifier, hereinafter referred to more simply as differential amplifier  21 , and further includes DC decoupling capacitors  23 , feedback capacitors  25 , a common-mode voltage source  26 , and a shift voltage source  27 , here schematically represented as supply lines.  
         [0034]     The differential amplifier  21  has two inputs  28  and two outputs  30  and is in charge-amplifier configuration.  
         [0035]     Through respective first switches  31  actuated by the reset signal S RES , the inputs  28  of the differential amplifier  21  are selectively connectable to the common-mode voltage source  26 , which supplies a common-mode voltage V CM . Preferably, the common-mode voltage V CM  is the average between a maximum supply voltage V DD  and a minimum supply voltage V SS  supplied to the differential amplifier  21  by respective supply lines  32 ,  33 .  
         [0036]     The inputs of the differential amplifier  21  are moreover connected to first terminals of respective DC decoupling capacitors  23 , which have second terminals connected to the first stator terminal  17   a  and to the second stator terminal  17   b , respectively. The DC decoupling capacitors  23  are sized so as to obtain DC decoupling between the inputs  28  of the differential amplifier  21  and the stator terminals  17   a ,  17   b  of the microstructure  2 . Electrical signals with non-zero frequency, in particular with a frequency around the natural frequency of resonance (OR, can instead be transmitted through the DC decoupling capacitors  23 .  
         [0037]     Through respective second switches  35  actuated by the reset signal S RES , the second terminals of the DC decoupling capacitors  23 , and consequently also the first and second stator terminals  17   a ,  17   b  of the microstructure  2 , are selectively connectable to the shift voltage source  27 , which supplies an adjustable shift voltage V S  independent of the common-mode voltage V CM . As illustrated in  FIG. 6 , the shift voltage source  27  comprises a controllable voltage generator  36 , which supplies the shift voltage V S , and a regulator circuit  37 , connected to the control unit  7  for receiving the calibration signal S CAL . The regulator circuit  37  acts on the variable-voltage generator  36  to control the shift voltage V S  according to the calibration signal S CAL .  
         [0038]     With reference once again to  FIG. 4 , the feedback capacitors  25  are each connected between a respective output  30  of the differential amplifier  21  and the second terminal of a respective DC decoupling capacitor  23 .  
         [0039]     Across the outputs  30  of the differential amplifier  21 , there is an output voltage V O  correlated to the displacement of the movable body  11  of the microstructure  2  with respect to the stator  10 .  
         [0040]     Operation of the device for controlling the frequency of resonance of the electromechanical resonator  1  envisages two steps which are cyclically repeated.  
         [0041]     In a reset step ( FIG. 4   a ), the first switches  31  and second switches  35  are in a circuit-closing condition (see also  FIG. 5 , which illustrates the waveform of the reset signal S RES ). Consequently, the inputs  28  of the differential amplifier  21  are connected to the common-mode voltage source  26  and are at the common-mode voltage V CM , whereas the first and second stator terminals  17   a ,  17   b  of the microstructure  2  are connected to the shift voltage source  27  and receive the shift voltage V S . In the reset step, the inputs  28  of the differential amplifier  21  and the stator terminals  17   a ,  17   b  of the microstructure  2  can be biased at voltages independent of one another thanks to the DC decoupling capacitors  23 , which operate as batteries and, in the embodiment described herein, are charged at the voltage V S -V CM .  
         [0042]     In a subsequent read step ( FIG. 4   b ), the first switches  31  and second switches  35  are opened so as to disconnect the inputs  28  of the differential amplifier  21  and the stator terminals  17   a ,  17   b  of the microstructure  2  from the voltage sources  26 ,  27 . In this step, the DC decoupling capacitors  23  operate as batteries and apply the shift voltage V S  on the first and second stator terminal  17   a ,  17   b . Consequently, the electromechanical resonator  1  is forced to oscillate at a translated resonance frequency ω RS , which is given by the value of the shift voltage V S  according to Equations (5)-(7) and differs from the natural frequency of resonance ω R . Clearly, the value of the translated frequency of resonance ω RS  can be calibrated by acting on the second voltage source  27  by means of the calibration signal S CAL .  
         [0043]     In the reading step, the differential amplifier  21  reads charge packets ΔQ provided or absorbed by the stator terminals  17   a ,  17   b  and due partly to the capacitive unbalancing between the capacitances of the first and second equivalent capacitors  19   a ,  19   b  and partly to the reading and driving signal S SENSE  applied to the common terminal  18 . The charge packets ΔQ are converted by the differential amplifier  5 , which generates the output voltage V O , oscillating at the translated frequency of resonance ω RS . The DC decoupling capacitors  23  can be sized in such a way that their effect on the output voltage V O  is negligible.  
         [0044]     As emerges from the above description, the invention advantageously enables substantial exploitation of the entire dynamics made available by the minimum and maximum supply voltages of the micro-electromechanical resonator for calibrating the frequency of resonance. In particular, the constraint set by the connection between the inputs of the differential amplifier and the stator terminals of the microstructure is removed, it being thus possible for said inputs of the differential amplifier and said stator terminals of the microstructure to receive independent shift voltages. Also the frequency of resonance can hence be calibrated within a very wide range of values. Furthermore, the DC decoupling capacitors  23  enable a reduction in the output electronic noise and in the offset.  
         [0045]     Finally, it is clear that modifications and variations may be made to the device described herein, without thereby departing from the scope of the present invention, as defined in the annexed claims.  
         [0046]     In particular, the invention can be exploited with micro-electromechanical devices other than resonators, such as for example gyroscopes. The microstructure could, for example, be of a rotational type or with a number of translational and/or rotational degrees of freedom. Each movable electrode can be coupled to an individual fixed electrode, instead of being set between two fixed electrodes. The shift voltage can be supplied to the common terminal instead of being supplied to the stator terminals.