Abstract:
A force-balance accelerometer having a pick-off coil responsive to displacement of a seismic mass from a balance position for providing an output corresponding to the displacement, includes a digital signal processor including tow pulse width modulation generators for converting the output of the pick-up coil to a digital signal, and a torque coil responsive to the digital signal for rebalancing the seismic mass by restoring the mass to the balance position. The processor outputs the digital signal as first and second PWM signals, which control the digital signal.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to force-balance accelerometers and, more particularly, to feedback loops for the pick-off coils of force-balance accelerators. 
   2. Description of the Related Art 
   In U.S. Pat. No. 4,088,027, issued May 9, 1978 to Hernandez et al., there is disclosed a force balance servo accelerometer including a D&#39;Arsonval type mechanism for rebalancing, between a pair of sensing coils, a seismic mass moved by acceleration. The D&#39;Arsonval type mechanism comprises a pair of suspension beams mounted in parallel planes in a liquid filled cylindrical housing. A pair of axially aligned taut wires support a torque coil between the suspension beams. The coil surrounds a permanent magnet fixedly mounted in the housing. An arm extending outwardly from the coil, transverse to the axis of the taut wires, supports the seismic mass between the sensing coils, which are mounted in the housing. The sensing coils form two arms of a bridge circuit energized by an oscillator connected across one pair of opposing terminals of the bridge. The signal developed across the other pair of opposing terminals is applied to a differential amplifier. The resultant difference signal is sine wave multiplied with the output of the oscillator in a quadrature detector. The output of the quadrature detector, which is related to the acceleration of the seismic mass, is applied to the coil of the D&#39;Arsonval mechanism to rebalance the seismic mass. A bellows mounted on one end of the housing allows the liquid in the housing to expand and contract as the temperature of the environment in which the D&#39;Arsonval type mechanism is located changes. 
   In U.S. Pat. No. 4,315,434, issued Feb. 16, 1982 to Marcus R. Eastman, there is disclosed an accelerometer, the output of which is sent to a pulse width modulating digitizing circuitry comprising a comparator to generate a PWM signal, a flip-flop steering circuit, an “H” switch to toggle a torquer constant current either positive or negative, and an AND gate to gate clock pulses for the output. 
   The accelerometer taught in the afore-said U.S. Pat. No. 4,315,434 has the disadvantage of a continuous torquer current, i.e. a bipolar current through a torque coil, and therefore a large power consumption. Furthermore, with reference to FIG. 2 of Eastman, it is clear that the feedback loop from a pick-off coil ( 14 ) to a torque coil ( 24 ) consists entirely of analog components, with exception of the flip-flop ( 22 ). Therefore, the accelerometer of the Eastman reference is very susceptible to aging and drift of components, temperature, and noise sources. The Eastman reference does not provide a technique to compensate for the above effects on the components, and therefore must be returned to the manufacturer for calibration. 
   An additional disadvantage of that accelerometer is that it does not provide a measured value for the acceleration, but instead, provides a digital pulse train that is proportional to the sensed acceleration (see column 2, line 6). Clearly, additional circuitry is required in order to obtain a measurement of the acceleration. 
   That prior accelerometer has the disadvantage of including much of the feedback loop of the accelerometer in the analog domain, which makes it overly sensitive to temperature, manufacturing and aging tolerances. 
   BRIEF SUMMARY OF THE INVENTION 
   In a first aspect of the present invention, there is provided a force-balance accelerometer comprising a movable seismic mass, a pick-off coil responsive to displacement of the seismic mass from a balance position for providing an output corresponding to the displacement, means for converting the output of the pick-up coil to a digital signal, and a torque coil responsive to the digital signal for rebalancing the seismic mass by restoring the mass to the balance position. 
   In a second aspect of the present invention, there is provided a force-balance accelerometer comprising a movable seismic mass, a pick-off coil responsive to displacement of the seismic mass from a balance position for providing an output corresponding to the displacement, means for converting the output of the pick-up coil to a digital signal, a torque coil responsive to the digital signal for rebalancing the seismic mass by restoring the mass to the balance position, and means for outputting the digital signal as first and second PWM signals. 
   In a third aspect of the present invention, there is provided a force-balance type accelerometer having a negative feedback network and one or more feedback paths. The negative feedback network is operable to rebalance a mass accelerated by an external force. Each of the feedback paths provides an analog-to-digital conversion of a system variable that is monitored by the negative feedback network for changes in a parametric value. The negative feedback network compensates for the changes in the parametric values, thereby calibrating the accelerometer. 
   In a fourth aspect of the present invention, there is provided a high resolution digital to analog converter for converting a digital signal to an analog signal that comprises first and second low resolution PWM generators, first and second switches and first and second current sources. The first and second PWM generators provide first and second PWM signals respectively. The first PWM generator is controlled by a most significant word of the digital signal, and the second PWM generator is controlled by a least significant word of the digital signal. The first and second switches are controlled by the first and the second PWM signals respectively. The first and second current sources have first and second currents respectively. The first and second currents are switched by the first and the second switches, thereby providing first and second switched currents respectively. The analog signal is obtained by the combination of the first and second switched currents. 
   In a fifth aspect of the present invention, there is provided a method of providing a high resolution DAC for converting a digital signal to an analog signal comprising the steps of providing a first PWM signal having a duty cycle corresponding to the most significant word of the digital signal; providing a second PWM signal having a duty cycle corresponding to the least significant word of the digital signal; providing a first electrical signal, said first electrical signal having a duty cycle equal to the duty cycle of the first PWM signal; providing a second electrical signal, said second electrical signal having a duty cycle equal to the duty cycle of the second PWM signal; and combining the first the second electrical signals to provide the analog signal. 
   The present invention is preferably embodied as a seismic motion sensor and, more particularly, as a broadband type of force-balance accelerometer used to measure signals in a wide range of amplitudes and frequencies, the performance of which strongly depends on the performance of a feedback loop. 
   The feedback loop is digital with a minimum number of components, designed using primarily integrated circuits, and relying on an optimized way of current switching to reduce the required space sand to improve temperature stability and noise immunity, in comparison to prior art accelerometers using an analog feedback loop, while maintaining good dynamic performance. 
   State of the art pulse width modulation (PWM) generators in digital signal processors are limited by fifteen bits of resolution, and therefore the dynamic range of a digital-to-analog converter comprising one of these low resolution PWM generators is limited to fifteen bits of resolution. 
   The technique of the present invention overcomes this limitation by providing a digital-to-analog converter of substantially greater dynamic range by combining two or more low resolution PWM generators that, in combination with additional circuitry, theoretically provide any number of bits of accuracy. For example, the preferred embodiment of the invention illustrates a twenty four bit, high resolution digital-to-analog converter, the output of which is applied to the torque coil, which is achieved by combining two low resolution PWM generators that produce respective PWM signals. 
   The PWM signals from respective PWM generators each contribute to the high resolution output by varying its respective duty cycle and, therefore, an electrical signal, i.e. a current and/or voltage signal, applied to the torque coil. The current flowing through the torque coil is discrete and, in contrast to the well known PWM patterns, also includes amplitude control. The amplitude of the current flowing through the torque coil is controlled by providing a feedback path for the voltage signal across the torque coil. This provides an additional level of control of energy delivered to the load, i.e. the torque coil. 
   The primary purpose of the pulse amplitude control is to compensate for the electrical drifts in the torque coil, caused, for example, by aging or temperature change, thus allowing low frequency components to be differentiated from the electrical drifts and promoting proper distribution of the currents related to each PWM generator. The dynamic method of the PWM signal pulse amplitude control reduces the amount of noise generated by current switching, for example, it reduces power supply noise. 
   The frequency and period of the pulse stream does not affect the delivered energy, which depends only on the duty cycle. Moreover, using the symmetric driving pattern described herein, linearity of the system is dramatically improved by removing the effects of transient processes, making the delivered energy directly proportional to the pulse width. The amplitude control is a kind of calibration that is performed in run time without interruption of the data acquisition process. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be more readily understood from the following description of an embodiment thereof given, by way of example only, with reference to the accompanying drawings, in which:— 
       FIGS. 1A ,  1 B &amp;  1 C show block diagram views according to one embodiment of the present invention; 
       FIG. 2  shows a schematic view of elements of an accelerometer of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C; 
       FIG. 3  shows a block diagram view of the accelerometer and a negative feedback loop of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C; 
       FIGS. 4A &amp; 4B  show diagrammatic views of a digital to analog converter of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C; 
       FIG. 5  shows a diagrammatic view of the resolution of the digital-to-analog converter of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C; 
       FIG. 6  shows a graphical view of electrical energy delivered to a torque coil of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C; 
       FIGS. 7A &amp; 7B  shows a graphical views of pulse width modulated signals of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C; and 
       FIGS. 8A ,  8 B,  8 C &amp;  8 D show a schematic view of the embodiment of  FIGS. 1A ,  1 B &amp;  1 C. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Referring to the figures and firstly to  FIGS. 1A ,  1 B,  1 C &amp;  2 , there is a force balance-type accelerometer indicated generally by reference numeral  11 , which has a fluid-damped metal-flexure suspension. There is a pick-off coil  10  and an unbalanced weight  13  attached to a shaft  15  forming a pendulum, which is suspended in a permanent magnetic field and is free to move in one degree of freedom only. When subjected to acceleration, this pendulum moves with respect to the accelerometer frame. 
   The pick-off coil  10  provides an angular position signal  12 , e.g. a voltage signal, which is applied to a position detector  14 , which is a differential position sensor in this example. The position detector  14  electronically senses the movement of the pick-off coil  10  and provides an analog output signal  16 . The output signal  16  of the position detector  14  is applied to a high resolution analog-to-digital converter (ADC)  18 , which provides a twenty four bit digital signal  20  representative of the angular position signal  12 . The ADC  18  samples the output signal  16  once every sampling period T SAMPLE  ( FIGS. 7A &amp; 7B ). 
   The digital signal  20  is inputted into a digital signal processor  22  over a communication bus  23 , where it is used in an algorithm to provide a feedback signal  36  ( FIGS. 4A &amp; 4B ) to the pick-off coil  10 . The processor  22  comprises a first pulse width modulation (PWM) generator  24 , a second PWM generator  26  and an arithmetic logic unit (ALU)  28 . The processor  22  also comprises a memory (not shown), which stores instructions representative of the algorithm, and which are executed by the processor  22 . 
   The ALU  28 , when configured by the instructions of the algorithm, comprises a multiplier  30  and a digital feedback network  32 , which is a proportional-integral-derivative filter in this embodiment. The digital feedback network  32  is part of a negative feedback loop that controls the angular position of the pick-off coil  10 , and has a transfer function optimized for this purpose. 
   Transfer functions in negative feedback loops are well developed in the art, and the particular transfer function used in the digital feedback network  32  is a design decision. In other embodiments, the digital feedback network  32  can be a fuzzy logic network that adapts the parameters of the transfer function of the network  32  depending on the angular position signal  12 , or can comprise the common regulator algorithm, i.e. the Kalman regulator, which is a predictive algorithm that attempts to differentiate noise from the signal  12 . 
   The algorithm is a feedback algorithm which accepts the digital signal  20  and provides the digital feedback signal  34 , which is a twenty four bit word as shown in  FIGS. 4A &amp; 4B . The digital feedback signal  34  is representative of a duty cycle for a feedback signal  36  that is applied to a torque coil  38 . The feedback signal  36  is a high resolution, pulse width modulated signal which also varies in amplitude. The unbalanced weight  13  is brought back into balance by applying the correct feedback signal  36  to the torque coil  38 . 
   The algorithm in the processor  22  calculates the required twenty four bit digital feedback signal  34 , i.e. the duty cycle value, and splits it into two segments according to the following procedure. The digital feedback signal  34  comprises a most significant word (MSW) and a least significant word (LSW). The MSW comprises the top fourteen bits of the twenty four bit digital feedback signal  34 , and the LSW comprises the lower ten bits of the twenty four bit digital feedback signal  34 . If the MSW is less than one thousand and twenty four (1024), then the MSW is multiplied by sixteen, to extend it up to a fourteen bit value, providing an MSW segment  40 . If the MSW is greater than or equal to one thousand and twenty four (1024) then its value is unmodified and provides an MSW Full Scale segment  42 . The LSW provides an LSW segment  44 . 
   The MSW segment  40  and the MSW Full Scale segment  42  are used to set the duty cycle of a first PWM signal  46  ( FIGS. 1A ,  1 B &amp;  1 C), which is a digital signal, from the PWM generator  24 . In each of the sampling periods T SAMPLE , only one of the segments  40  or  42  is used, i.e. the segments  40  and  42  are mutually exclusive, since the MSW of the digital feedback signal  34  is constant for each sampling period T SAMPLE . The LSW segment  44  is used to set the duty cycle of a second PWM signal  48 , which is a digital signal, from the PWM generator  26 . 
   The processor  22  provides the first and second PWM signals  46  and  48  and first and second control signals  52  and  54  to a multiplexor  50 . The first control signal  52  indicates whether the duty cycle of the first PWM signal  46  is controlled by the MSW segment  40  or the MSW Full Scale segment  42 . The second control signal  54  controls the direction of the feedback signal  36  through the torque coil  38 , as will be explained in more detail below. 
   The multiplexor  50  provides eight switch control output signals  56 ,  58 ,  60 ,  62 ,  64 ,  66 ,  68  and  70  that control switches SW 1 -SW 8 , respectively. The switches SW 1 -SW 8  are preferably solid state switches, such as a MOSFET device, but can be other types of switches, such as mechanical switches. 
   The switch control signals  56  and  62  correspond to the first PWM signal  46  when the MSW full scale segment  42  controls the duty cycle of the signal  46 . The switch control signals  58  and  64  correspond to the first PWM signal  46  when the MSW segment  40  controls the duty cycle of the signal  46 . The switch control signals  60  and  66  correspond to the second PWM signal  48 , whose duty cycle is controlled by the LSW segment  44 . 
   The switch control signals  68  and  70  determine the direction of the feedback signal  36  in the torque coil  38 . The switches SW 1 -SW 8  and the switch control signals  56 - 70  together establish six channels  72 - 82  of electrical energy, i.e. current and/or voltage, which are selectively switched on to create the feedback signal  36 . Table 1 below indicates which of the switches SW 1 -SW 8  are on for each of the channels  72 - 82 . The column labelled “Direction” indicates the direction the current in the respective channel flows through the torque coil  38 . The quiescent current in each of channels  72 ,  74 ,  76 ,  78 ,  80  and  82  is substantially determined by resistors R 1 , R 2 , R 3 , R 4 , R 5  and R 6 , respectively, in this example. 
   The multiplexer  50  selects which of the channels  72 - 82  are to be driven. For each of the sampling periods T SAMPLE , there are four channel combinations that may be selected. A first combination includes channels  72  and  76 , a second combination includes channels  74  and  76 , a third combination includes channels  78  and  82  and a fourth combination includes channels  80  and  82 . In each of the combinations mentioned above, each of the channels  72 - 82  is selected mutually exclusively of the other channel, in this example. 
   
     
       
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
               Channel 
               SW1 
               SW2 
               SW3 
               SW4 
               SW5 
               SW6 
               SW7 
               SW8 
               Direction 
             
             
                 
             
           
           
             
               72 
               on 
               off 
               off 
               off 
               off 
               off 
               off 
               on 
               positive 
             
             
               74 
               off 
               on 
               off 
               off 
               off 
               off 
               off 
               on 
               positive 
             
             
               76 
               off 
               off 
               on 
               off 
               off 
               off 
               off 
               on 
               positive 
             
             
               78 
               off 
               off 
               off 
               on 
               off 
               off 
               on 
               off 
               negative 
             
             
               80 
               off 
               off 
               off 
               off 
               on 
               off 
               on 
               off 
               negative 
             
             
               82 
               off 
               off 
               off 
               off 
               off 
               on 
               on 
               off 
               negative 
             
             
                 
             
           
        
       
     
   
   The first combination corresponds to the PWM signal  46 , controlled by the MSW full scale segment  42 , and the PWM signal  48  providing positive electrical energy, i.e. current and/or voltage, to the torque coil  38 . The second combination corresponds to the PWM signal  46 , controlled by the MSW segment  40 , and the PWM signal  48  providing positive electrical energy to the torque coil  38 . 
   The third combination corresponds to the PWM signal  46 , controlled by the MSW full scale segment  42 , and the PWM signal  48  providing negative electrical energy, i.e. current and/or voltage, to the torque coil  38 . The fourth case corresponds to the PWM signal  46 , controlled by the MSW segment  40 , and the PWM signal  48  providing negative currents to the torque coil  38 . 
   The channels  74  and  80 , which correspond to positive and negative current contributions of the PWM signal  46  controlled by the MSW full scale segment  42 , are used to extend the pulse duration and to decrease the pulse amplitude to deliver the same amount of energy in order to reduce the overall amplitude of the current being switched, and, therefore, reduce the amount of noise caused by the switching. 
   The positive electrical signal of the channel  72 , which is applied to the torque coil  38 , corresponds to the negative electrical signal of the channel  78 , which is also applied to the coil  38 . The electrical signals of the channels  72  and  78  are substantially equal in magnitude and opposite in direction. In the present embodiment, in order to achieve substantially equal magnitudes of the electrical signals of the channels  72  and  78 , resistors R 1  and R 4  are preferably well matched in value. 
   In a similar manner, resistors R 2  and R 5  are preferably well matched in value so that the electrical signals of the channels  74  and  80  are substantially equal in magnitude, and resistors R 3  and R 6  are preferably well matched in value so that the electrical signals of the channels  76  and  82  are substantially equal in magnitude. In other embodiments, it is possible to use active current sources instead of resistors in order to achieve highly matched electrical signals in respective corresponding channels  72  &amp;  78 ,  74  &amp;  80  and  76  &amp;  82 . 
   The current signals of the channels  72  and  78 , corresponding to the MSW full scale segment  42 , are greater in magnitude than the current signals of the channels  76  and  82 , which correspond to the LSW segment  44 . This aspect allows the two low resolution PWM generators  24  and  26 , which are fifteen bit PWM generators in this example, to provide a digital-to-analog converter of twenty four bit resolution, and therefore increased dynamic range. This is diagrammatically illustrated in  FIG. 5 . 
   The current signals of the channels  74  and  80 , which correspond to the MSW segment  40 , are also greater in magnitude than the current signals of the channels  76  and  82 , which correspond to the LSW segment  44 , but less in magnitude than the current signals of the channels  72  and  78 , which correspond to the MSW full scale segment  42 . However, since the MSW segment  40  is derived by multiplying the MSW of the digital feedback signal  34  by sixteen, the time base of the current signals of the channels  74  and  78  are extended. The current signals of the channels  74  and  78  are therefore applied over a greater period of time, and the effective resolution is therefore equivalent to the MSW full scale segment. This is diagrammatically illustrated in  FIG. 6 . 
   The acceleration is calculated based on the digital feedback signal  34  and the electrical signals of the channels  72 - 82 , and in particular the current signals of the channels, since the acceleration is proportional to the total current through the torque coil  38 . The total current through the torque coil is proportional to the current signals of each the channels  72 - 82  and the respective duty cycles of those current signals. An equation for calculating total current through the torque coil  38  is illustrated in  FIGS. 4A &amp; 4B . 
   In addition to the feedback loop described above for the angular position signal  12 , there are additional feedback paths that are used to compensate for temperature effects, power supply drift, amplifier offset of the position detector  14  and changes in the parametric values of the resistors R 1 -R 6 , the switches SW 1 -SW 6  and the torque coil  38 . When these parametric values change, then accordingly the values of the electrical signals of the channels  72 - 82 . 
   Recalling that the measured value of acceleration is based on calculating the total current through the torque coil, which is proportional to the current signals of the channels  72 - 82  and their respective duty cycles, if the current signals of the channels  72 - 82  change then the measured value of the acceleration changes as well. Therefore in order to provide ongoing calibration of the accelerometer, these changes must be tracked and compensated for. 
   By providing the above multiple feedback paths, the digital accelerometer of the present invention is able to track and compensate for very low frequency signals, such as drift, while simultaneously measuring the angular position signal  12 , even when the signal  12  is also a comparably low frequency signal. 
   Referring again to  FIGS. 1A ,  1 B &amp;  1 B, there is a calibration analog-to-digital converter  92 , a temperature sensor  94  and a voltage divider  96 . The temperature sensor  94  provides an analog measurement of the ambient temperature in the form of a temperature signal  98 . The voltage divider provides a power supply signal  100 , which is a scaled version of a power supply voltage. 
   The calibration analog-to-digital converter  92  converts the temperature signal  98 , the power supply signal  100 , an amplifier offset signal  102  and torque coil signals Cal− and Cal+ into corresponding digital signals used by the algorithm, and in particular the digital feedback network  32 , to compensate the PWM signals  46  and  48  for changes in these signals over time. 
   Referring again to  FIG. 3 , there is a block diagram of the force-balance type accelerometer  11  and the negative feedback network described above. A controller block  33  comprises the multiplier  30  and the digital feedback network  32 . A PWM generator block  35  comprises the PWM generators  24  and  26 . A three level switch block  37  comprises the multiplexor  50 , the switches SW 1 -SW 8  and the resistors  72 - 82 . 
   Referring now to  FIGS. 7A &amp; 7B , the operation of the accelerometer, and more particularly the feedback signal  36 , is now described for a sampling period T SAMPLE.    FIGS. 7A &amp; 7B  has a first graph  84  illustrating the first PWM signal  46  when the duty cycle is being controlled by the MSW full scale segment  42 , a second graph  86  illustrating the first PWM signal  46  when the duty cycle is being controlled by the MSW segment  40 , a third graph  88  illustrating the second PWM signal  48  and a fourth graph  90  illustrating a voltage across the torque coil  38 . The graphs  84 ,  86 ,  88  and  90  illustrate two consecutive sampling periods T SAMPLE . The horizontal axes of the graphs  84 ,  86 ,  88  and  90  represent time and the vertical axes represent voltage. The horizontal axes of the graphs  84 ,  86 ,  88  and  90  of  FIGS. 7A &amp; 7B  refer to the following stages: 
   
     
       
             
             
           
         
             
                 
             
             
               Stage 
               Name 
             
             
                 
             
           
           
             
               A 
               PRELOAD 
             
             
               B 
               MSW (or MSW FULL SCALE) 
             
             
               C 
               MSW WAIT 
             
             
               D 
               COMPENSATION 
             
             
               E 
               WAIT COMPENSATION 
             
             
               F 
               LSW 
             
             
               G 
               IDLE 
             
             
                 
             
           
        
       
     
   
   The PWM cycle starts with a PRELOAD pulse at stage A that charges the torque coil  38 . The PRELOAD pulse is always present regardless of the duty cycle. After the PRELOAD pulse, a MSW (or MSW Full Scale) pulse is generated at stage B with a duration that matches the MSW (upper fourteen or ten bits) of the digital feedback signal  34 . After the MSW pulse there is a MSW WAIT period at stage C, which is initiated to allow the coil to discharge. The MSW WAIT period duration is fixed. 
   After the MSW WAIT period, a COMPENSATION pulse is generated at stage D to compensate for the presence of the PRELOAD pulse. The COMPENSATION pulse is generated in the opposite direction of the PRELOAD pulse. There is an additional WAIT COMPENSATION period initiated at stage E to wait for the coil to discharge. 
   After the WAIT COMPENSATION pulse, a LSW pulse is fired to generate the residual LSW at stage F. An IDLE period at stage G after the LSW is variable in length and its purpose is only to add up time up to the next cycle and to allow for the torque coil  38  to discharge. A full period of the cycle T SAMPLE  represents both the sampling and the PWM update frequency. 
   It is an advantage of the present invention to use the combination of the PRELOAD pulse and the equal but opposite COMPENSATION pulse. The COMPENSATION pulse cancels the transient energy delivered to the torque coil  38  caused by the PRELOAD pulse activating the switches SW 1  or SW 2 , thereby ensuring that the total energy delivered to the torque coil  38  is controlled precisely by the PWM signal  46  and  48 , and therefore the digital feedback signal  34 . The current signals of the channels  76  and  82  are relatively small, in this example, and therefore not much transient energy is created when switching on the switches SW 3  and SW 6 . 
   Assuming that the pulse amplitude, i.e. the amplitude of the current signals through the torque coil  38 , is stable, its compensation does not take place every cycle. The compensation takes place either on a random basis or at a fixed period. The pulse has to be of a certain duration to provide enough time for the ADC  18  to complete the conversion. If the required pulse width, at the time when amplitude measurement is to take place, is too small, then the pulse width gets extended up to the point that the analog to digital conversion may successfully complete. The extra amount of time added to MSW (or MSW Full Scale) to allow for the analog to digital conversion of the ADC  18  to complete is compensated by the extended duration of the COMPENSATION pulse. This technique entirely encapsulates the process of calibration normally invisible from the data collection point of view. 
   The force generated by the torque coil  38  due to the feedback signal  36  on the unbalanced weight  13  is in a direction opposite to force created by the input acceleration, and rises in value until the force generated matches the force of input acceleration, i.e. the current through the torque coil  38  is directly proportional to the acceleration. Thus, the acceleration is directly obtained by reading the digital feedback signal  34 , i.e. the PWM duty cycle value, which actually is the output of the system. 
   The feedback signal  36  has a significant amount of high frequency components related to the PWM switching that are eliminated by a low pass filter, preferably an FIR type, to provide a linear phase response. 
   In other embodiments, it is possible to overlap the MSW stage (or the MSW FULL SCALE stage) and the LSW stage. As an example, this is possible when the electrical signals of the channels  72 - 80  are provided by current sources. In this situation, the electrical signals are added together and applied to the torque coil  38 . 
   Referring to  FIGS. 1A ,  1 B,  1 C &amp;  3 , there is an output filter block  106  which receives as an input the digital feedback signal  34 . The digital feedback signal  34  is an extremely accurate, controlled feedback signal that may be used for other purposes. The output filter removes high frequency components introduced as a result of switching on and off the switches SW 1 -SW 6 . 
   Referring now to  FIGS. 8A ,  8 B,  8 C and  8 D, there is shown a schematic diagram of the embodiment of  FIGS. 1A ,  1 B and  1 C. 
   As apparent to those skilled in the art, various modifications can be made to the above described solution within the scope of the appended claims. For example, the resistors R 1 , R 2 , R 3 , R 4 , R 5  and R 6  can be replaced by current sources, or by the resistors of different values to allow for different scale factors. By varying the bandwidth of the low pass FIR filter the overall system bandwidth can be changed to allow for different dynamic response and/or output noise level (dynamic resolution). Also, the output FIR filter can be replaced by a more sophisticated estimator, such as Kalman regulator, to further reduce the amount of noise. Moreover, the output FIR filter can be removed from the circuitry to allow for non-real time signal processing to facilitate use of more sophisticated and complex algorithms normally not deployed in real time due to the required processing power. The current distribution (ratio of the currents in the channels  72 ,  74  and  76  and in channels  78 ,  80  and  82 ) can be achieved in many different ways to allow for different implementation of the current source, duty cycle, sampling frequency, etc. The proposed solution relates to a single axis acceleration measurement but the circuit can be easily modified to obtain two- and triaxial acceleration measurement. In that case, a single DSP with six channel PWM generators can be used to simultaneously drive three double level PWM signals for three channels through three different multiplexers and three H bridges. The discussed PWM drive can also be applied in different applications wherever a high resolution D/A conversion in form of PWM is required. 
   As will be apparent to those skilled in the art, various modifications may be made in the above-described embodiment of the present invention within the scope of the appended claims.