Abstract:
A modulator is provided in operative engagement with a sensor element having a plurality of electrodes. The modulator has a single-bit quantizer electrically connected to a digital accumulator. The accumulator accumulates output information received from the single-bit quantizer. The accumulator converts the accumulated output information received from the single-bit quantizer to a multi-bit feedback signal and sends the multi-bit feedback signal in a primary feedback loop back to the sensor element. The quantizer sends a single-bit feedback signal in a secondary feedback loop back to a point before the quantizer.

Description:
[0001]    This application claims the benefit of U.S. Provisional Application No. 61/451,144, filed Mar. 10, 2011, the entire contents of which are hereby incorporated by reference as if fully set forth herein, 
     
    
     TECHNICAL FIELD 
       [0002]    The invention relates to a method for using a sensor system having a single-bit quantizer and a multi-bit feedback loop. 
       BACKGROUND OF INVENTION 
       [0003]    High performance sensor systems are typically based on closed loop architectures to provide good linearity and large dynamic range. Systems typically use sigma-delta modulated single-bit feedback and let the sensing element act as a loop filter. A voltage driven micro-machined inertial sensor acts as a second order low pass filter where one order comes from the voltage to force (charge) conversion and the other order from force to displacement which is what is detected.  FIG. 1  is an illustrative example of a prior art system  10  of a second order accelerometer system. The prior art technology of  FIG. 1  limits the noise-shaping order of the system to two. One drawback is that the system  10  requires a large over-sampling ratio to achieve low in-band quantization noise density. A large over-sampling ratio drives up the power consumption mainly due to the charging and discharging of the force capacitors. The high-frequency phase-shift of the sensing element is close to 180 degrees. Therefore, a power-consuming phase compensating lead-lag is required to guarantee stability of the system. In most applications, e.g. battery operated, the power consumption can be equally or even more important than the signal-to-noise ratio. 
         [0004]    The required over-sampling ratio can be decreased by adding electrically determined poles to the transfer function of the system which increases the noise shaping order. The systems create a fifth order system by introducing three electrical poles. They still use single-bit feedback to the sensing element and they also make use of a phase compensating filter to ensure stability. 
         [0005]    The prior art systems use single-bit feedback. Single-bit noise shapers possess two attractive properties namely simplicity and linearity. It is significantly easier to build a single-bit quantizer than a multi-bit quantizer both in terms of quantization levels and power consumption. A single-bit feedback system is inherently more linear than a multi-bit system since mismatch of the feedback signal is no issue with only two levels. However, single-bit feedback systems are always be a compromise between quantization of the noise performance and the over-sampling ratio, i.e. power consumption. There is a need for a more effective system that operates reliably without suffering from the drawbacks described above. 
       SUMMARY OF INVENTION 
       [0006]    The method of the present invention provides a solution to the above-outlined problems. More particularly, a multi-bit sigma-delta modulator is provided in operative engagement with a sensor element that has a plurality of electrodes. The modulator has a single-bit quantizer electrically connected to a digital accumulator. The accumulator accumulates output information received from the single-bit quantizer. The accumulator converts the accumulated output information received from the single-bit quantizer to a multi-bit feedback signal and sends the multi-bit feedback signal in a primary feedback loop back to the sensor element. The quantizer sends a single-bit feedback signal in a secondary feedback loop back to a point before the quantizer. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0007]      FIG. 1  is a schematic view of a block diagram of the second order accelerometer system of a prior art system; 
           [0008]      FIG. 2  is a schematic view of a digital accumulator output for a large sensor input signal of the present invention wherein a 2 g, 50 Hz acceleration is applied; 
           [0009]      FIG. 3  is a schematic view of two feedback paths of the present invention wherein the primary feedback loop cancels the applied input signal while the secondary loop facilitates noise shaping and stability; 
           [0010]      FIG. 4  is a schematic view of a unit force DAC sensor and an error signal generation of the present invention; 
           [0011]      FIG. 5  is a table showing typical sensing element parameters; 
           [0012]      FIG. 6  is a schematic view of a magnitude response of sensor element conversion gain of the present invention; 
           [0013]      FIG. 7  is a schematic view transfer functions calculated from a linearized system model with an effective quantizer gain of 1.4; 
           [0014]      FIG. 8  is a schematic view of a spectrum of a transient simulation of the multi-bit voltage feedback system wherein an input acceleration is a 50 Hz 2 g sinusoidal signal and no kT/C or thermal noise has been added; 
           [0015]      FIG. 9  is a schematic view of an input acceleration, feedback signal and resulting instantaneous acceleration error for a 2 g, 50 Hz signal; 
           [0016]      FIG. 10  is a schematic view of a spectrum with applied white noise on a voltage across unit forces wherein the noise density is 18 nV/√Hz which corresponds to 0.4 μV in 500 Hz bandwidth and no mismatch is applied; 
           [0017]      FIG. 11  is a schematic view of a resulting spectrum of a transient simulation with 18 nV/√Hz white noise, 1% (3σ) mismatch and data weighted averaging to mitigate the mismatch; 
           [0018]      FIG. 12  is a schematic view of a spectrum of transient simulation when the sensor resonance frequency has been reduced to 530 Hz without changing any other system parameters; and 
           [0019]      FIG. 13  is a schematic view of a spectrum of transient simulation when a sensor resonance frequency has been increased to 880 Hz without changing any other system parameters. 
       
    
    
     DETAILED DESCRIPTION 
       [0020]    With reference to  FIGS. 2-4 , the sensor system  100  (best seen in  FIG. 3 ) of the present invention has a sensor architecture that makes it possible to combine high performance with low power consumption. It has been surprisingly discovered that the combination of using a multi-bit primary feedback loop back to the sensor element in combination with a single-bit secondary feedback loop back to the electrical part provide an effective high-performance stable sensor system that requires a very low power consumption. The application of the present invention to an accelerometer is only used as an illustrative example to describe the features of the present invention and the sensor system is not limited to accelerometer applications. For example, the sensor system could be used in computer games for mobile computers so that the game is displayed in a certain direction regardless of whether the user turns the mobile computer or not. The mobile computer may use a built-in accelerometer to measure the acceleration of the movement of the earth such as gravitational forces relative to the movement of the mobile computer. Another preferred use of the invention is sensing for seismic exploration and surveillance there large number of sensor over large areas are needed and low energy consumption is a must for battery powering or manageable power cabling. 
         [0021]    The sensing element  102 , such as an inertial sensor, may be included as an integral part of an integrated circuit of an electrical part such as a multi-bit sigma-delta modulator  104 . Digital accumulation of quantizer output in a digital accumulator  106  achieves a multi-bit primary feedback  108  with a single-bit quantizer  110 . In other words, the accumulator  106  converts the accumulated single-bit output information received from the single-bit quantizer  110  to a multi-bit feedback signal and sending the multi-bit feedback signal  109  in a delayed primary feedback loop  108  back to the sensor element. 
         [0022]    The feedback  108  to the sensing element provides low noise and large dynamic range. To compensate for the relatively infrequent feedback signal  109 , single-bit feedback signal/information  111  is sequentially and preferably continuously sent in the secondary feedback loop  112  as each single bit of signal information  107  is received from the single-bit quantizer  110  directly into a electrical loop filter  114  to enhance stability making it possible to eliminate the need for phase compensating filters. It is thus better for the some of preliminary information at a higher frequency in feedback  112  about the position of the proof mass  124  to compensate for the delay and to preliminarily anticipate the change of the feedback signal  109  in feedback loop  108  although the single-bit information  111  in feedback loop  112  may not be as precise and the information of the feedback signal  109  in the primary feedback loop  108 . In other words, since the delay in the feedback loop  108  may be significant, the actual position of, for example, the proof mass  124  may have changed too much during the delay so that the sensor system may have very incorrect and old information. By using the very frequent information in the feedback loop  112 , the information that goes into the quantizer  110  can be preliminarily corrected, such as some preliminary information about the position of the proof mass  124 , while waiting for the more correct but relatively infrequent feedback signal  109  of feedback loop  108 . The information in the feedback loop  112  is used and accumulated in the integrators  115  of the modulator  104  so that the integrators in a way operate like digital accumulators. The information such as current information, in the feedback loop  112  may be subject to weighting factors b 0 , b 1  and b 2  as shown in  FIG. 3  before the information is received in the integrators. 
         [0023]    As explained in detail below, a unit force digital-to-analog converter (DAC)  118  is disposed in the feedback branch. A multi-level force is created by splitting the electrodes into several smaller units and driving them individually. 
         [0024]    One important feature of the present invention is the digital accumulation in the digital accumulator  106  of the output information  107  received from the single-bit quantizer  110 . To achieve really low power-consumption, the electrical loop filter and quantizer need to be as simple as possible. It is therefore advantageous to use a single-bit quantizer  110  due to the low power-consumption. However, the signal being fed back to the sensing element  102  is preferably a multi-level signal in the multi-bit primary feedback  108  to reduce the quantization noise and to increase the large signal handling. Therefore, one feature of the present invention is to use the single-bit quantizer  110  and to generate a multi-bit feedback control value by digitally integrating the quantifier output of the sinusoidal acceleration movement, as seen in  FIG. 2 ,  FIG. 2  thus illustrates a digital accumulated feedback signal  116  of the primary feedback loop  108  as the digital accumulator output for a large sensor input signal. In the illustrated example, the input signal is a 2 g, 50 Hz acceleration that may be applied to an illustrative example based on the parameters described in  FIG. 5  which is described in more detail below. The multi-bit control is preferably converted to a corresponding electrostatic force which counteracts the applied acceleration. The moving average of this multi-level signal can be close to the peak value. In a single-bit sigma-delta system the moving average can typically only be driven to half the peak value. This means that the multi-level system makes more efficient use of the available electrostatic force, reducing the required actuator drive voltage, which in turn enables lower power-consumption for the same full scale acceleration, 
         [0025]    Compared to a multi-bit quantizer, the digital accumulator  106  introduces significant delay of the feedback signal of the feedback  108 . It takes several clock cycles to change from full positive feedback to full negative feedback. In other words, the fact that the output signal  107  from the single-bit quantizer  110  must be accumulated in the digital accumulator  106  takes time and makes the frequency or rate of the primary feedback  108  too slow. In conventional sigma-delta modulators such a delay would typically result in an unstable system. The system of the present invention overcomes this stability issue by introducing a secondary feedback loop as seen in  FIG. 3 . The low latency single-bit quantizer output  107  is fed directly into the electrical loop filter  114  of the forward path/signal of the electronics without going through the digital accumulator  106 . An additional important advantage of the secondary feedback loop is that it provides enough stability-margin to make it possible to eliminate the power consuming analog lead-lag filter to compensate for the phase-shift of the sensing element. 
         [0026]    Inertial sensors of prior art systems typically have a single pair of actuator electrodes. The most intuitive implementation of a multi-bit feedback force is consequently to control the voltage across this electrode pair. This could be done by driving the electrode pair with an electrical DAC. However, noise or imperfections added in the feedback path of ΣΔ-ADCs cannot be suppressed by the loop. The DAC would therefore need to be both linear and have low noise. The method of the present invention, on the other hand, focuses on the total required electrostatic force. This is the quantity that needs multi-bit properties and it can be achieved more efficiently by replacing the commonly large single outer electrodes into several smaller electrodes disposed inside the sensor element  102 , as shown in  FIG. 4 . The plurality of electrodes in the sensor element  102  enables the use of multi-rate primary feedback loop  108 , as explained in detail below. The digital-to-analog converter (DAC)  118  may have an upper glass carrier  120  and a lower glass carrier  122  with a proof mass common electrode  124  hanging freely in vacuum therebetween so that it may move relative to the carriers  120  and  122 . If the sensor element  102  is moved in one direction such as upwardly, the distance between the proof mass  124  and the carrier  122  will shorten and the distance between the proof mass  124  and the carrier  120  will lengthen. This means the capacitance values will also change since that depends (inversely proportional) upon the distance. This change of the capacitance values may be measured as an error signal that is either plus or minus. In other words, each electrode pair may then create a small unit force, F i  to attempt to pull back the proof mass to the initial resting position. The sign of the unit force depends on the applied voltages V vi  and V Li . One problem is that the created pull back force, such as a positive force, may be too large so that is must be compensated by a negative force that may also be too large. The forces may then be switched back and forth until the correct pull back forces are applied to the proof mass to bring it back to the initial resting position. By combining several individually controlled unit forces, the total electrostatic force obtains multi-bit properties. In other words, the number of positive unit forces compared to the number of negative forces is adjusted to try to find an accumulated force that is about right to pull back the proof mass to the initial resting position which reduces the total quantizer error and makes it possible to correct the error quicker and reduce the need for sampling speed. 
         [0027]    This unit force DAC  118  requires no operational amplifier or other power consuming circuitry. Instead, the DAC  118  is sufficient to have simple switches allowing the outer electrodes to be connected either to ground or supply. 
         [0028]    Mismatch of the unit force DAC  118  is preferably mitigated by dynamically selecting which of the unit elements to use for each sample. This technique may be referred to as dynamic element matching and may be used in purely electrical sigma-delta modulated systems. This technique may be applied to electro-mechanical inertial sensors prior to the invention. 
         [0029]    One application of the present invention that has been carefully investigated is electro-mechanical inertial sensor. With the novel architecture of the present invention it is possible to design an accelerometer with a full scale input of 2 g, close to 130 dB signal-to-noise ratio in 300 Hz bandwidth and a power consumption as low as 3 mW. The required supply voltage may be limited to 5 V. The sample rate could be 256 kHz. Preferably, the sensing element is a bulk micro-machined device consisting of a silicon proof mass suspended between two glass plates. The parameters  126  of the sensing element  102  parameters are summarized in  FIG. 5  and its sensor transfer function  128  showing a magnitude response of sensor element conversion gain is shown in  FIG. 6 . 
         [0030]    With reference to  FIG. 4 , electrostatic forces F i  are applied to the proof mass  124  such that forces caused by acceleration and gravity are cancelled and the proof mass  124  remains almost fixed relative to its surrounding electrodes. Minimizing the movement of the proof mass  124  and variation in capacitance improves linearity compared to an open loop system. Displacement of the proof mass  124  relative to its nominal position is monitoring by measuring the error charge generated when the charge is shifted between the upper and lower capacitances. In other words, the acceleration of the proof mass  124  may be measured by monitoring the electrostatic forces F i  required to counteract the acceleration. 
         [0031]    Assuming that the proof mass  124  is perfectly centered between the outer glass plates  120 ,  122  if no force is applied, then the capacitances of the unit elements can be described by equation (1) below: 
         [0000]    
       
      
       C 
       Ui 
       =C 
       0i 
       +ΔC 
       i  
      
     
         [0000]    
       
      
       C 
       Li 
       =C 
       0i 
       −ΔC 
       i  
      
     
         [0000]    where C 0i  is the nominal capacitance and ΔC i  is the capacitance deviation resulting from a net force leading to a displacement of the proof mass since the loop gain of the sensor system is large, the proof mass  124  will be kept close to its nominal position and ΔC i  can be approximated to be zero. The net electrostatic force on unit i can then be described by equation (2) below: 
         [0000]    
       
         
           
             
               
                 
                   
                     F 
                     t 
                   
                   = 
                   
                     
                       
                         2 
                          
                         
                           C 
                           
                             0 
                              
                             I 
                           
                           2 
                         
                          
                         
                           V 
                           
                             0 
                              
                             I 
                           
                         
                       
                       
                         ɛ 
                          
                         
                             
                         
                          
                         A 
                       
                     
                      
                     Δ 
                      
                     
                         
                     
                      
                     
                       V 
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where V 0i  and ΔV i  are described in equation (3) below: 
         [0000]        V   0i =( V   Ui   +V   Li )/ 2    
         [0000]      Δ V   i =±( V   Ui   =V   Li )/ 2  
 
         [0032]    When ΔV i  changes sign, the charge is transferred between the upper and lower capacitors. If C Ui ≠C Vi  an error charge will be transferred to C f , resulting in an voltage error signal, V err , at the output of the operation amplifier in  FIG. 4 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           error 
                         
                         = 
                           
                          
                         
                           
                             Q 
                             error 
                           
                           / 
                           
                             C 
                             f 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               4 
                                
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 C 
                                 i 
                               
                             
                             
                               C 
                               f 
                             
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0033]    As can he seen from equation (4) above, the error signal depends on the sign of the applied feedback signal ΔV i . This is not explicitly shown in the block diagrams but this should be accounted for. In a differential design this is straight forward. 
         [0034]    To achieve a low quantization noise level for a larger bandwidth, an electrical resonator has been added, coefficient b 2 . This creates a notch in the noise transfer function  130  at 250 Hz calculated from a linearized system model with an effective quantizer gain of 1.4, as shown in  FIG. 7 . The high frequency notch at 706 Hz may be set by the sensor resonance frequency. Preferably, the loop filter has sufficient degrees of freedom to both optimize the signal and noise transfer functions. 
         [0035]    The electrical loop filter coefficients may be designed such that full-scale becomes 2 g, but the system can typically handle 1 dB more before it is overloaded and becomes unstable.  FIG. 8  shows a spectrum  132  of a transient simulation without noise or DAC mismatch. The spectrum  132  is of a transient simulation of the multi-bit voltage feedback system. The input acceleration is set at 50 Hz 2 g sinusoidal signal. No kT/C or thermal noise is added. The feedback signal  134  and resulting instantaneous acceleration error  136  of such a transient simulation is shown in a diagram  138  in  FIG. 9 .  FIG. 10  shows the simulated spectrum  140  when kT/C noise of the unit force DAC is included. The noise density is 18 nV/√Hz. This corresponds to 0.4 μV in 500 Hz bandwidth and no mismatch is applied. 
         [0036]    The unit force DAC  118  (best shown in  FIG. 4 ) may consist of 12 unit elements. The currently implemented DEM is data weighted averaging (DWA), i.e. thermometer coding of the unit forces and rotating the control signals. This creates first order high frequency shaping of the mismatch errors. 
         [0037]    The system&#39;s sensitivity to parameter variations has also been analyzed and taken into account during optimization of the loop filter coefficients. The robustness of the system is greatly enhanced by the secondary feedback loop that is an essential part of the invention. Transient simulations prove that the system of the present invention can handle a sensor element resonance frequency shift down to 530 Hz (best seen in  FIG. 12 ) and up to 880 Hz (best seen in  FIG. 13 ) before it becomes unstable. More particularly,  FIG. 11  shows a resulting spectrum  142  of a transient simulation with 18 nV/√Hz white noise, 1% (3σ) mismatch and data weighted averaging to mitigate the mismatch.  FIG. 12  is a schematic view a spectrum  144  of transient simulation when the sensor resonance frequency has been reduced to 530 Hz without changing any other system parameters.  FIG. 13  shows a schematic view a spectrum  146  of transient simulation when a sensor resonance frequency has been increased to 880 Hz without changing any other system parameters. 
         [0038]    While the present invention has been described in accordance with preferred compositions and embodiments, it is to be understood that certain substitutions and alterations may be made thereto without departing from the spirit and scope of the following claims.