Abstract:
A band-pass filter made up by an operational amplifier and by an input circuit. The input circuit is formed by a capacitive filtering element, connected to the input of the operational amplifier; a coupling switch, coupled between an input node and the capacitive filtering element; a capacitive sampling element, coupled between the input of the filter and the input node; and a sampling switch, coupled between the input node and a reference-potential line. The coupling switch and the input sampling switch close in phase opposition according to a succession of undesired components sampling and sensing steps, so that the capacitive sampling element forms a sampler for sampling the undesired component in the undesired components sampling step, in the absence of the component of interest, and forms a subtractor of the undesired components from the input signal in the sensing step.

Description:
BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a switched-capacitor band-pass filter of a discrete-time type, in particular for cancelling offset and low-frequency noise of switched-capacitor stages. For example, the present band-pass filter can be used in the control loop for driving capacitive gyroscopes made using MEMS technology. 
     2. Description of the Related Art 
     As is known, the use of micro-electro-mechanical systems (MEMS) has become increasingly widespread in various sectors of technology and has yielded encouraging results especially in the construction of inertial sensors, microintegrated gyroscopes, and electromechanical oscillators for a wide range of applications. 
     MEMS of this type are usually based upon micro-electro-mechanical structures comprising at least one mobile mass connected to a fixed body (stator) through springs and mobile with respect to the stator according to preset degrees of freedom. The mobile mass is moreover coupled to the fixed body via capacitive structures (capacitors). The movement of the mobile mass with respect to the fixed body, for example on account of an external stress, modifies the capacitance of the capacitors; the variation of capacitance can be exploited to detect the relative displacement of the mobile mass with respect to the fixed body and thus the applied force. Vice versa, by supplying appropriate biasing voltages, it is possible to apply an electrostatic force to the mobile mass to set it in motion. In addition, to produce electromechanical oscillators, the frequency response of the inertial MEMS structures is exploited, which is typically of a second-order low-pass type. 
     Many MEMS (in particular, all the electromechanical oscillators and gyroscopes) envisage a driving device, which has the task of maintaining the mobile mass in oscillation. 
     Consequently, a driving system is provided, which controls in a precise way the movement of the mobile mass and includes a sensing amplifier operating in discrete-time mode. In order for the driving system to operate correctly with the desired precision level, it is useful to eliminate the offset of the sensing amplifier, as well as the so-called “flicker noise” or “l/f noise”, at low frequency, due, as is known, to random capture and release of charge carriers. In order not to interfere in the driving loop, filtering of the noise should not introduce phase shifts in the signal. 
     The same desires are also shared by other types of circuits, which would benefit from a discrete-time band-pass filtering, without the introduction of any phase shift. 
     In order to eliminate the offset of a micromechanical structure, derivative filters are normally used in the case of a continuous-time read chain; alternatively, a factory calibration is exploited. These solutions, in the case of drifts in the self-oscillation frequency of the mechanics due to ageing or temperature, do not enable a constant phase shift to be maintained, since the position of singularities, and thus the phase shift introduced at the frequency of interest, depends upon these parameters. 
     In literature, systems have been proposed using chopping techniques, which include a high-frequency offset modulation, filtering, and demodulation. These solutions require, however, a complex signal processing and are not able to offer a good control of the introduced phase shift. 
     BRIEF SUMMARY 
     One embodiment is a band-pass filter capable of solving the problems that afflict known systems, in particular eliminating the offset and attenuating the flicker noise of the preceding stage up to frequencies higher than the frequency of the signal of interest. 
     According to the present disclosure, a switched-capacitance band-pass filter and a corresponding method of operation are provided, as defined in claims  1  and  11 , respectively. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       For a better understanding of the present disclosure, preferred embodiments thereof are now described, purely by way of non-limiting example, with reference to the attached drawings, wherein: 
         FIG. 1  is a circuit diagram of a first embodiment of the present band-pass filter; 
         FIG. 1   a  shows the plot of control signals used in the circuit of  FIG. 1 ; 
         FIG. 2  is a circuit diagram of a second embodiment of the present band-pass filter; 
         FIG. 2   a  shows the plot of control signals used in the circuit of  FIG. 2 ; 
         FIGS. 3   a - 3   c  show the circuit of  FIG. 2  in three different operating steps; 
         FIGS. 4   a  and  4   b  show two simulations regarding the circuit of  FIG. 2 ; and 
         FIG. 5  shows a block diagram of a charge amplifier connected to the filter of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a filter  1  of a switched-capacitor double-ended band-pass type, which uses the correlated-double-sampling technique at its input. 
     The filter  1  comprises an operational amplifier  2  having an inverting input  2   a , a non-inverting input  2   b , a non-inverting output  2   c , and an inverting output  2   d . Furthermore, the outputs  2   c  and  2   d  form the outputs of the filter  1 , and the two inputs  2   a ,  2   b  are at virtual ground. 
     A first feedback branch  3   a  is connected between the inverting input  2   a  and the non-inverting output  2   c ; a second feedback branch  3   b  is connected between the non-inverting input  2   b  and the inverting output  2   d.    
     The feedback branches  3   a  and  3   b  are equal and comprise a first feedback capacitor C a , connected between the respective input  2   a , respectively  2   b , and the respective output  2   c , respectively  2   d ; and a second feedback capacitor C 2 , connected in parallel to the first capacitor C a  through a pair of feedback switches  4  controlled by a same first phase signal Φ 1 . In addition, the second capacitor C 2  can be by-passed through a by-pass switch  5 , which is controlled by a second phase signal Φ 2 , in phase opposition with respect to the first phase signal Φ 1 , and enables reset of the second feedback capacitor C 2 , eliminating part of the charge injected during the phase Φ 1 , and thus determining the position of the pole of the high-pass filtering. 
     Furthermore, the inputs  2   a  and  2   b  of the operational amplifier  2  are connected to a first input branch  6   a , and a second input branch  6   b , respectively, which are equal. In detail, each input branch  6   a ,  6   b  comprises a filtering capacitor C 1  having a first terminal directly connected to the respective input  2   a  and  2   b  of the operational amplifier  2  and a second terminal connected to a node  10  through a coupling switch  11  controlled by the first phase signal Φ 1 ; an input sampling capacitor C s  connected between the node  10  and a respective input  15   a , respectively  15   b , of the filter  1 ; and an input sampling switch  16 , arranged between a respective node  10  and a common-potential line  17  (at a common-mode potential) and controlled by the second phase signal Φ 2 . 
     The transfer function of the filter  1  can be calculated as described hereinafter. 
     Consider initially the circuit  18  enclosed by the dashed line and formed by the operational amplifier  2 , single-ended (the input  2   b  is connected to common mode and no output  2   d  is present), just the first feedback branch  3   a , the filtering capacitor C 1 , and the coupling switch  11  of just the first input branch  6   a . These components form a single-ended high-pass filter. In the circuit  18 , in a first step, referred to also as read or sensing step, the first phase signal Φ 1  is active and the second phase signal Φ 2  is inactive and, in a second step, referred to also as undesired-components sampling step, the first phase signal Φ 1  is inactive and the second phase signal Φ 2  is active. 
     In the sensing step, the capacitors C 1 , C 2 , and C a  store a charge Q 1 , while in a second step, the capacitors C 1 , C a  store a charge Q 2 , with
 
 Q   1   =C   1   V   in +( C   2   +C   a ) V   out  
 
 Q   2   =C   1   V   in   z   −1   +C   a   V   out   z   −1  
 
     By applying the charge-conservation principle to the capacitors and equating the stored charges Q 1  and Q 2 , the transfer function T HP (z)=V out /V a  is obtained: 
                 T   HP     ⁡     (   z   )       =         -     C   1           C   2     +     C   a         ·       1   -     z     -   1           1   -       (       C   a         C   2     +     C   a         )     ⁢     z     -   1                     
which is also the transfer function of the fully differential double-ended high-pass filter, obtained considering also the second feedback branch  3   b , the filtering capacitor C 1 , and the coupling switch  11  of the second input branch  6   b.  
 
     The input sampling capacitors C s  have the purpose of sampling and storing the undesired components (input offset, flicker noise and/or possible noise of any other type at low frequency, where “low frequency” indicates a much lower frequency, for example by one order of magnitude, than the switching frequency of the phase signals) during the second step and of cancelling it during the first step. This introduces, on the useful signal, a low-pass type filtering and an attenuation. In fact, by computing the charge balance at node  10 , the following transfer function T LP (z) between V in  and V a : 
     
       
         
           
             
               
                 T 
                 LP 
               
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               
                 
                   C 
                   S 
                 
                 
                   
                     C 
                     1 
                   
                   + 
                   
                     C 
                     S 
                   
                 
               
               · 
               
                 1 
                 
                   1 
                   - 
                   
                     
                       ( 
                       
                         
                           C 
                           1 
                         
                         
                           
                             C 
                             1 
                           
                           + 
                           
                             C 
                             S 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         1 
                       
                     
                   
                 
               
             
           
         
       
     
     The overall transfer function T BP (z) of the filter  1  derives from the combination of the transfer functions T HP (z) and T LP (z): 
     
       
         
           
             
               
                 
                   
                     
                       T 
                       BP 
                     
                     ⁡ 
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           LP 
                         
                         ⁡ 
                         
                           ( 
                           z 
                           ) 
                         
                       
                       · 
                       
                         
                           T 
                           HP 
                         
                         ⁡ 
                         
                           ( 
                           z 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             - 
                             
                               C 
                               1 
                             
                           
                           ⁢ 
                           
                             C 
                             S 
                           
                         
                         
                           
                             ( 
                             
                               
                                 C 
                                 1 
                               
                               + 
                               
                                 C 
                                 S 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 C 
                                 a 
                               
                               + 
                               
                                 C 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         
                           1 
                           - 
                           
                             z 
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     
                                       C 
                                       1 
                                     
                                     
                                       
                                         C 
                                         1 
                                       
                                       + 
                                       
                                         C 
                                         S 
                                       
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     
                                       C 
                                       a 
                                     
                                     
                                       
                                         C 
                                         a 
                                       
                                       + 
                                       
                                         C 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   z 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     By applying the bilinear transformation 
     
       
         
           
             f 
             = 
             
               
                 
                   f 
                   ck 
                 
                 π 
               
               · 
               
                 ( 
                 
                   
                     1 
                     - 
                     
                       z 
                       p 
                     
                   
                   
                     1 
                     + 
                     
                       z 
                       p 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     the position of the singularities of the continuous-time equivalent of the filter  1  is: 
     
       
         
           
             
               
                 
                   
                     f 
                     z 
                   
                   = 
                   0 
                 
               
             
             
               
                 
                   
                     f 
                     
                       p 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         f 
                         ck 
                       
                       π 
                     
                     . 
                     
                       ( 
                       
                         
                           C 
                           2 
                         
                         
                           
                             2 
                             ⁢ 
                             
                               C 
                               a 
                             
                           
                           + 
                           
                             C 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   
                     f 
                     
                       p 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         f 
                         ck 
                       
                       π 
                     
                     · 
                     
                       ( 
                       
                         
                           C 
                           S 
                         
                         
                           
                             2 
                             ⁢ 
                             
                               C 
                               1 
                             
                           
                           + 
                           
                             C 
                             S 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     In practice, in the undesired-components sampling step, when the first phase signal Φ 1  is inactive and the second phase signal Φ 2  is active, the sampling capacitors C s  store the undesired components on the inputs  15   a ,  15   b . In this step, the filtering capacitors C 1  hold the signal of interest, since the coupling switches  11  are open and the nodes A of the filtering capacitors C 1  are floating. In the next read or sensing step, when the first phase signal Φ 1  is active and the second phase signal Φ 2  is inactive, the signal of interest is supplied to the filtering capacitors C 1 , and the undesired components are subtracted by the sampling capacitors C s . In this step, the nodes A are biased through the input sampling capacitors C s  by charge sharing. Consequently, in neither of the two steps are the nodes A directly connected to the common-potential line  17 ; this prevents the signal of interest stored on the filtering capacitors C 1  from being cancelled. 
     In practice, the signal of interest and the undesired components on the input (offset of the preceding stage and flicker noise) are treated differently. In fact, the signal of interest, which is supplied only in the sensing step, sees a band-pass filter (for example, in the case of a control loop for driving a gyroscope, with passband of approximately 400 Hz to 40 kHz, necessary for maintaining the loop in oscillation), and the undesired components, present also in the undesired-components sampling step, see a high-pass filter (in the considered case, for example with lower limit of the band at approximately 20 kHz). 
       FIG. 2  shows a filter  100  that further enables elimination of the offset and of the flicker noise of the band-pass filter, and uses a third phase signal Φ R  (referred to also as reset signal), which commands a reset step. 
     The filter  100 , in addition to the components of the filter  1  of  FIG. 1 , comprises a pair of output sampling capacitors C cds , each connected between a respective output  2   c ,  2   d  of the operational amplifier  2  and a respective output terminal  100   a ,  100   b  of the filter  100 . In addition, an output reset switch  101  is arranged between the outputs  2   c ,  2   d  of the operational amplifier  2  and is controlled by a reset signal Φ R , the time plot whereof is shown in  FIG. 2   a . Two output sampling switches  102  are arranged between a respective output  100   a , respectively  100   b , of the filter  100  and the common-potential line  17  and are controlled by the second phase signal Φ 2 . Two input reset switches  103  are arranged between a respective input  15   a , respectively  15   b  of the filter  100  and the common-potential line  17 . 
     In  FIG. 2 , in order to prevent the first feedback capacitors C a  (which store the signal of interest) from being discharged during offset and sampling, instead of the feedback switches  4  a single insulation switch  104  is provided in series to each first feedback capacitor C a . 
     Operation of the filter  100  of  FIG. 2  will now be explained with reference to  FIGS. 3   a ,  3   b , and  3   c , which regard respectively the reset step, the undesired-components sampling step, and the sensing step. In particular, during the reset step ( FIG. 3   a ), the reset signal Φ R  and the second phase signal Φ 2  are high and the first phase signal Φ 1  is low. Consequently, the switches  101 - 103 ,  16  and  5  are closed, the switches  11  and  104  are open, and the input sampling capacitors C s  and the output sampling capacitors C cds  are completely discharged. 
     During the undesired-components sampling step ( FIG. 3   b ), the second phase signal Φ 2  is high, the reset signal Φ R  and the first phase signal Φ 1  are low, and thus the switches  16 ,  5 , and  102  are closed and the switches  103 ,  11 ,  104  and  101  are open. Consequently, the low-frequency undesired input component V n  (typically due to the offset of the preceding stage and to the flicker noise) is stored as V n1  and V n2  on the input sampling capacitors C s , and the low-frequency undesired output component V nAMP1 , V nAMP2  (due mainly to the offset of the operational amplifier  2 ) is stored on the output sampling capacitors C cds . In the undesired-components sampling step, as in the preceding reset step, the first feedback capacitors C a  are insulated from the rest of the circuit and thus do not lose the signal stored, preventing the transfer function of the filter from being altered. 
     During the sensing step ( FIG. 3   c ), the first phase signal Φ 1  is high, the reset signal Φ R  and the second phase signal Φ 2  are low, and thus the switches  104  and  11  are closed and the switches  16 ,  5 , and  101 - 103  are open. Consequently, by appropriately sizing the filter, the undesired d.c. and low-frequency components are subtracted (practically, they are filtered out) and the signal V, downstream of the input sampling capacitors C s  is no longer affected by the undesired components V a . In addition, in this same step, the useful signal V, thus obtained is sampled, filtered, and immediately outputted as V out , without undergoing any delay. 
     Operation of the filter  100  was simulated at a frequency f ck =164 kHz, and the transfer function was obtained, having the plot vs. frequency shown in  FIGS. 4   a  and  4   b , relative to magnitude and phase, respectively. As may be noted, the filter  100  shows a zero in the origin, a first pole at f p1 =400 Hz and a second pole at f p2 =40 kHz; the useful signal of the filter  1  has a frequency f s =4 kHz. 
     The filter  100  of  FIG. 2  can be used to eliminate the offset and the flicker noise of a charge amplifier  20  arranged upstream of the filter  100 , as shown in  FIG. 5 . The charge amplifier  20 , of a switched-capacitor discrete-time type, has inputs respectively connected to a first feedback reading terminal  21   a  and to a second feedback reading terminal  21   b.    
     The charge amplifier  20  comprises a fully differential operational amplifier  37  in charge-integrator configuration, with integration capacitors  38  arranged between a respective input and a respective output, and an output reset switch  43 , controlled by the reset signal Φ R . Alternatively, instead of the output reset switch  43 , the reset switches  103 , shown in  FIG. 2 , may be provided. 
     During the reset step, the output switch  43  is closed. In this way, the nodes of the operational amplifier  37  are fixed to the common-mode voltage W CM  and, as described with reference to  FIG. 3   a , the input sampling capacitors C s  are discharged. 
     In the undesired-components sampling step, the output reset switch  43  is open and the undesired low-frequency components are stored on the input sampling capacitors C s . 
     Next, in the sensing step, the reading signal V R  across the inputs  21   a ,  21   b  of the charge amplifier  37  is amplified and supplied to the filter  100 , which suppresses the undesired components, as above described with reference to  FIG. 3   b.    
     The band-pass filter described herein presents numerous advantages. 
     In particular, it enables elimination of the undesired d.c. and low-frequency components by precisely controlling the introduced phase shift. This is particularly advantageous in the case of use in a gyroscope driving control loop and in all the circuits where it is important not to modify the phase of the signal. 
     The present band-pass filter enables filtering of disturbance up to a higher frequency than the working one. For example, in prototypes obtained by the applicant, it is capable of filtering the 1/f noise up to 10-20 kHz, with a working frequency of 4 kHz. 
     In addition, in the described filter, the positions of the pole and of the zero are directly linked to the frequency of the phases f ck , as appears clearly from Eq. (1), and shift as the frequency of oscillation varies, maintaining their own relative position with respect to the signal to be processed. This is particularly advantageous in the case of use in the gyroscope driving control loop, where the phases are generated by exploiting a self-oscillation of the electromechanical system, the resonance frequency whereof can vary from piece to piece on account of the spread of the production process and of ageing. With the present band-pass filter, variations of the oscillation frequency due to process spread, temperature variations, and ageing are recovered by shifts of the singularities of the transfer function of the filter. Frequency and phase shift are consequently well controlled. 
     Finally, it is clear that modifications and variations may be made to the filter described and illustrated herein, without thereby departing from the scope of the present disclosure, as defined in the attached claims. For example, the solution described is also applicable to a single-ended structure. 
     The various embodiments described above can be combined to provide further embodiments. All of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet are incorporated herein by reference, in their entirety. Aspects of the embodiments can be modified, if necessary to employ concepts of the various patents, applications and publications to provide yet further embodiments. 
     These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.