Circular system and method for the digital correction of modulation effects in eletromechanical delta-sigma modulators

Abstract

The present invention relates to a circuit arrangement and a method for reading a capacitive vibratory gyroscope with an at least primary mass and at least one secondary mass that is connected to the primary mass, wherein the primary mass is excited to a primary vibration during operation, and wherein the secondary mass is deflected out of a resting position in a direction that is transversal to the primary vibration when the vibratory gyroscope rotates around a sensitive axis. The circuit arrangement comprises a delta-sigma modulator with at least one control loop to perform a force feedback that resets the secondary mass into its resting state by applying a reset signal, wherein the reset signal forms a modulator output signal of the delta-sigma modulator, a correction unit that receives the modulator output signal and that is operated to generate a corrected modulator output signal that corresponds to an actually acting feedback force, a demodulator that is connected to the correction unit for demodulation of the corrected modulator output signal, and a filter arrangement to filter the demodulated signals and to output a rotary rate signal.

Claims

1. A circuit arrangement to read out a capacitive vibratory gyroscope having transversely oriented primary and secondary masses, the circuit arrangement comprising: a delta-sigma modulator with at least one control loop having a force feedback which resets the secondary mass to its resting position by outputting a reset signal; a correction unit receiving the reset signal and generating a corrected modulator output signal that corresponds to an actually impacting reset force, the correction unit has a multiplying element that is configured to multiply the modulator output signal with a known value of a position of the primary mass and a weighting factor; a demodulator connected to the correction unit and demodulating the corrected modulator output signal; and a filter arrangement filtering the demodulated signal and outputting a rotary rate signal of the capacitive vibratory gyroscope.

2. The circuit arrangement according to claim 1, wherein the correction unit has an adding part that is configured to add the output of the multiplying element to the reset signal in order to generate the corrected modulator output signal.

3. The circuit arrangement according to claim 1, wherein the demodulator comprises a look-up table.

4. The circuit arrangement according to claim 1, wherein the correction unit and the demodulator are implemented by a combined look-up table.

5. The circuit arrangement according to claim 1, wherein the filter arrangement has a low-pass filter and a decimation filter connected in series.

6. The circuit arrangement according to claim 1, further comprising a controller to control a secondary resonance frequency, wherein the correction unit has a multiplying element that is connected to an output signal of the controller.

7. A Coriolis vibratory gyroscope comprising: at least one primary mass and at least one secondary mass that is connected to the primary mass, the primary mass being excited to a primary vibration during operation and the secondary mass being deflected in a direction that is transverse to the primary vibration when the Coriolis vibratory gyroscope rotates around a sensitive axis, and a circuit arrangement having: a delta-sigma modulator with at least one control loop with a force feedback which resets the secondary mass to its resting position by outputting a reset signal; a correction unit receiving the reset signal and generating a corrected modulator output signal that corresponds to an actually impacting reset force, the correction unit has a multiplying element that is configured to multiply the modulator output signal with a known value of a position of the primary mass and a weighting factor; a demodulator connected to the correction unit and demodulating the corrected modulator output signal; and a filter arrangement filtering the demodulated signal and outputting a rotary rate signal of the capacitive vibratory gyroscope.

8. A circuit arrangement to read out a capacitive vibratory gyroscope having transversely oriented primary and secondary masses, the circuit arrangement comprising: a delta-sigma modulator with at least one control loop having a force feedback which resets the secondary mass to its resting position by outputting a reset signal; and a correction unit receiving the reset signal and generating a corrected modulator output signal that corresponds to an actually impacting reset force, the correction unit has a multiplying element that is configured to multiply the modulator output signal with a known value of a position of the primary mass and a weighting factor.

9. The circuit arrangement according to claim 8, further comprising a demodulator connected to the correction unit and demodulating the corrected modulator output signal.

10. The circuit arrangement according to claim 9, further comprising a filter arrangement filtering the demodulated signal and outputting a rotary rate signal of the capacitive vibratory gyroscope.

Description

(1) The Figures show:

(2) FIG. 1 a schematic diagram of an electromechanical delta-sigma modulator;

(3) FIG. 2 a schematic display of the arrangement of feedback electrodes on the secondary mass of a capacitive acceleration sensor;

(4) FIG. 3 the temporal progression of the reset force for the arrangement of FIG. 1 in case of a switched-off primary vibration;

(5) FIG. 4 the temporal progression for the reset force for the arrangement of FIG. 1 under the influence of the primary vibration;

(6) FIG. 5 a spectrum of the delta-sigma bit stream of the arrangement from FIG. 1 in case of a switched-off primary vibration;

(7) FIG. 6 a spectrum of the delta-sigma bit stream of the arrangement from FIG. 1 for a nominal primary vibration;

(8) FIG. 7 the noise in the signal band (IBN) as a function of the primary vibration amplitude for the arrangement of FIG. 1;

(9) FIG. 8 a schematic diagram of a known correction circuit;

(10) FIG. 9 a schematic principle display of a further electromechanical delta-sigma modulator with quadrature control and control of the secondary resonance frequency;

(11) FIG. 10 an exemplary spectrum of the control signal for the frequency control in the arrangement from FIG. 9;

(12) FIG. 11 the noise in the signal band (IBN) for the calibrated and the controlled bit stream from the arrangement of FIG. 9 in case of different rotary rates;

(13) FIG. 12 the signal noise ratio (SNR) for the calibrated and the controlled bit stream from the arrangement of FIG. 9 in case of different rotary rates;

(14) FIG. 13 the spectrum of the delta-sigma bit stream of the arrangement from FIG. 9 in case of a switched-off frequency control;

(15) FIG. 14 the spectrum of the delta-sigma bit stream of the arrangement from FIG. 9 in case of a switched-on frequency control;

(16) FIG. 15 the temporal progression of test signals that have been fed in for detection of the secondary resonance frequency in the arrangement of FIG. 9;

(17) FIG. 16 a schematic display of the digital correction according to a first advantageous embodiment of the present invention;

(18) FIG. 17 the temporal progression of the reset force under application of the digital correction according to FIG. 16;

(19) FIG. 18 the spectrum of the digitally corrected bit stream for the arrangement of FIG. 16;

(20) FIG. 19 the noise in the signal band (IBN) for the uncorrected and the corrected bit stream as a function of the primary vibration amplitude;

(21) FIG. 20 the used correction amplitudes as a function of the primary vibration amplitude;

(22) FIG. 21 a schematic display of the digital correction according to a further advantageous embodiment of the present invention;

(23) FIG. 22 a schematic display of the digital correction according to a further advantageous embodiment of the present invention;

(24) FIG. 23 the spectrum of the uncorrected bit stream for the arrangement of FIG. 22 in case of a high rotary rate;

(25) FIG. 24 the spectrum of the corrected bit stream for the arrangement of FIG. 22 in case of a high rotary rate;

(26) FIG. 25 the noise in the signal band (IBN) for the calibrated, the uncorrected and the corrected bit stream as a function of the rotary rate;

(27) FIG. 26 the signal noise ratio (SNR) for the calibrated, the uncorrected and the corrected bit stream as a function of the rotary rate.

(28) With reference to FIG. 16, a first advantageous embodiment of the present invention will be explained in greater detail in the following.

(29) According to the invention, the feedback force that is not temporally constant in terms of its amount due to the primary vibration is digitally reproduced to minimize the effects that are based on the primary vibration. Then, each of the sample values of the bit stream will not be assigned the value 1 and/or 1 but a digital value, which corresponds to the mean force effect for this sample value, for the further steps (demodulation, filtering, downsampling). An exemplary structure for the implementation of such a digital correction is illustrated in FIG. 16.

(30) The arrangement of the electromagnetic delta-sigma modulator (emM) thereby corresponds to the display from FIG. 1. For the purpose of simplification, only the measurement loop and the digital signal processing 100 are shown in FIG. 16.

(31) According to the present invention, the output bit stream of the emM is weighted with the current mean force effect. Subsequently, the further digital processing of the corrected bit stream takes place. As shown in FIG. 16, the digital signal processing 100 according to the present invention comprises a digital correction unit 102.

(32) Further processing of the corrected data takes place by means of a lookup table (LUT) for the demodulation 104 as well as a filter arrangement with a low-pass filter 106 and a decimation filter 108.

(33) As the primary vibration is usually controlled both in frequency as well as in amplitude, a known primary vibration and also a known current primary position can be assumed. Alternatively, the primary vibration can be measured on the outputs of the readout circuit (C/V converter) of the primary vibration. This known primary position is used as an input signal for the correction unit 102. Furthermore, a correction factor all.sub.o is calculated based on the capacitive deviation factor a described above and also led into the digital correction unit 102. Therefore, the digital correction unit 102 calculates a corrected bit stream out of the output bit stream 110 of the emM according to the equation (6) derived above:

(34) $\begin{matrix} F_{ges, dr} = F_{ges} .Math. (1 + .Math. \frac{x_{p}}{l_{0}}) & (6) \end{matrix}$

(35) The mean force effect F.sub.mean can be determined via the feedback time used by means of integration of the current force effect according to equation (6). For the case that feedback forces are constantly applied, we obtain t.sub.s=1f.sub.s, whereas f.sub.s designates the sample frequency of the emM. The following will apply:

(36) $\begin{matrix} F_{mean} = \frac{1}{t_{s}}_{t_{N}}^{t_{N} + t_{s}} F_{ges, dr} d t \\ = F_{ges} .Math. (1 + \frac{}{l_{0} .Math. t_{s}}_{t_{N}}^{t_{N} + t_{s}} x_{p} d t) \\ = F_{ges} .Math. (1 + \frac{}{l_{0} .Math. t_{s}}_{t_{N}}^{t_{N} + t_{s}} {\hat{x}}_{p} .Math. \cos (2 f_{p} .Math. t +) d t) \end{matrix}$

(37) In the structure shown in FIG. 16, the intervals for the emM are generated through a phase-locked control loop (phase locked loop, PLL) in the block frequency control of FIG. 1 in a way that f.sub.s=8.Math.f.sub.p applies. Furthermore, the frequencies f.sub.s and f.sub.p are in phase so that it can be assumed that =0.

(38) Hence, the following applies for the weighting values G.sub.N of each sampling value N that are needed for the correction:

(39) $\begin{matrix} \begin{matrix} F_{mean} = F_{ges} .Math. (1 + \frac{}{l_{0} .Math. t_{s}}_{t_{N}}^{t_{N} + t_{s}} {\hat{x}}_{p} .Math. \cos (\frac{2 f_{s}}{8} .Math. t) d t) \\ = F_{ges} .Math. (1 + \frac{.Math. {\hat{x}}_{p}}{l_{0}} \cos (\frac{2 t_{N}}{8 t_{s}} + \frac{}{8})) \end{matrix} F_{mean, N} = F_{ges} .Math. (1 + A_{ges} .Math. \cos (\frac{2}{8} (N + 0.5))) G_{N} = \frac{F_{mean, N}}{F_{ges}} = (1 + A_{ges} .Math. \cos (\frac{2}{8} (N + 0.5))) & (18) \end{matrix}$

(40) The weighting values G.sub.N of each sampling value N that are required for the correction can be calculated in advance due to the controlled primary vibration. In addition, only 8 correction values, which subsequently repeat themselves, are needed due to the existing relationship between the primary and the sampling frequency. In the case displayed here, the weighting values for the digital correction are derived in relation to:
G.sub.1:8=1+A.sub.ges.Math.0.924.Math.[1 0.4140.414110.414 0.414 1](19)

(41) In this context, the weighting value A.sub.ges is dependent on the primary amplitude {circumflex over (x)}.sub.p and multiplied with an additional constant factor in order to enable a simpler implementation of the LUT.

(42) As a single-bit quantizer is used in the present embodiment, a multiplication step for the performance of the weighting is not required. Only the plus/minus sign of the weighting values is adapted as a function of the output value of the quantizer. FIG. 17 shows a section of the corrected bit stream in an exemplary way together with the actual force effect. FIG. 18 shows the associated spectrum of the corrected bit stream. If this display is compared to the spectrum from FIG. 6, it becomes clear that an improvement of the signal noise ratio by 12 dB can be achieved. This corresponds to an improved resolution by approximately 2 bit.

(43) FIGS. 19 and 20 show the noise in the signal band of the corrected bit stream as well as the required correction amplitudes A.sub.gee for the primary amplitudes shown in FIG. 7. A linear relationship between the primary amplitude v.sub.p and the used correction amplitude A.sub.ges leads in the present case to the ability to achieve a noise in the signal band that is nearly independent from the primary amplitude. This can be seen in FIG. 19. The solid curve thereby designates the non-corrected bit stream whereas the dashed curve denominates the corrected bit stream.

(44) For further simplification of the digital correction, the LUT of the digital correction and of the demodulation can be combined so that a common LUT with the following values is formed in the present structure for the correction and demodulation:
G.sub.1:8,comb=[0.414 1 1 0.4140.414110.414].Math.G.sub.1:18(20)

(45) Due to the relationship used between the primary frequency and the sampling frequency as well as the controlled primary vibration, these values can also be calculated in advance in ideal cases. The simplified structure with a combined LUT is shown in FIG. 21. The digital correction can hereby be performed with a very low extra digital workload.

(46) To minimize the interference effects during matched-mode-operation, each sampling value of the bit stream is weighed, according to a preferred further development of the present invention, as a function of the voltage U.sub.Mode in a way that the reset force that is changed due to the frequency control will be digitally reproduced. For the further steps (demodulation, filtering, downsampling), a sample value of the bit stream is by contrast not assigned the value 1 and/or 1, but a digital value that corresponds to the mean force effect for this sample value.

(47) Ideally, the frequency control in this process is performed in a way that a change of the voltage U.sub.Mode can only occur at the sampling times. Therefore, the effects can only change at the sampling times, which facilitates the calculation of the correction values.

(48) FIG. 22 shows the fundamental structure with a digital correction of the bit stream in case of a control of the secondary resonance frequency based on the arrangement shown in FIG. 9. The bit stream is calculated according the present invention with the scaled digital output value of the frequency control for each sample value. Hereby, the scaling k is chosen in a way that the following allocation applies for the value of the bit stream after the correction:

(49) $\begin{matrix} 1 -> \frac{U_{Mode}}{U_{FB}} & (21) \end{matrix}$

(50) Through this correction, the reset forces generated according to equation (11) are reproduced, due to which both the described change of the scale factor is corrected and also the noise convolution effects are minimized.

(51) Alternatively, a structure that is similar to the arrangement from FIG. 16 can be used in which only the deviations due to the frequency regulations are calculated and added. The calculation of the deviation can usually be implemented more efficiently as is specified in M. Sarhang-Nejad, G. C. Temes: A high-resolution multibit ADC with digital correction and relaxed amplifier requirements, IEEE J. Solid-State Circuits, 28(6):648-660, 1993.

(52) As a further alternative, the correction can also take place in the further course of the digital signal processing. The digital signal processing steps that have already taken place prior to the correction have to be taken into account for the correction in order to achieve a correction of the noise convolution effects and of the scale factor. A separate processing of the deviations is possible as well.

(53) FIGS. 23 and 24 show an exemplary display of the spectrum of a non-corrected bit stream and a bit stream corrected in this way in a comparative way. Compared to the spectrum of the uncorrected bit stream, a clear improvement of the IBN can be seen. Compared to the calibrated, uncontrolled system (FIG. 13), it shows that most of the influences on the inband noise have been compensated through the correction.

(54) FIGS. 25 and 26 show the IBN as well as the signal noise ratio for different rotary rates with and without correction compared to the IBN and/or SNR of a calibrated, unregulated system. The solid curves thereby refer respectively to the uncorrected bit stream whereas the dashed curves refer to the calibrated bit stream and the dashed/dotted curves show the IBN and/or SNR of the bit stream corrected according to the invention. It becomes clear that the influences of the effects described with reference to FIG. 9 can be compensated through the digital correction. The correction is hereby independent of the existing rotary rate according to the above relationship (21).

(55) In summary, the levels of the feedback of the sigma-delta modulator are not regarded as temporally constant as usual up to present according to the present invention, but it is assumed that a temporal change of these levels occurs due to further influences. Furthermore, no analogous measures will be taken in order to keep the levels of the feedback forces constant.

(56) The temporally modifiable feedback forces are compensated, in contrast to the state of the art, in a way that a weighting of the respective sample value of the sigma-delta modulator is performed in accordance with the actually impacting feedback forces in the digital post-processing of the bit stream. This leads to an elimination or at least to a minimization of the negative influences of the feedback forces (e.g. increased noise) that are not temporally constant.

(57) This comes with the advantage that no measures have to be taken to keep the reset forces, in particular the value of the reset forces, constant. Therefore, no additional analog circuit components are required especially during generating the voltages to be applied to the sensor.

(58) The negative effect of the non-constant feedback forces is suppressed by digitally reproducing the actually impacting reset forces and by using this digital reproduction in the further signal processing. In addition, also temporal changes that are more complex than the ones observed in this context can be inhibited through a digital weighting and by using respectively adapted weighting values or corresponding calculations.

(59) Due to the digital implementation, this solution offers the possibility of energy and space savings compared to a suppression by means of analog circuits. Another advantage of the digital implementation is theta calibration by means of setting digital parameters is possible very easily. Therefore, this solution can be adapted very easily to other sensors or other technologies, which is only to a limited extent the case for an analog implementation.

(60) In addition, it shall be mentioned that this method takes full advantages of the benefits of the technology scaling in case of an implementation as an application-specific integrated circuit (ASIC) because the displayed solution is structured in a completely. digital way. Due to the digital implementation, a change of the technology used would in addition be possible in an easier way as the layout can be generated automatically for digital parts of the ASIC.

(61) Furthermore, the weighting values that are necessary for compensation of the drive effect can be integrated in the LUT that is required for demodulation of the rotary rate so that only very little additional hardware is needed.

(62) Hence, an improvement of the system is possible with a low and purely digital additional effort, which contributes to an improvement of the system parameters and to the reduction of costs compared to other solutions.

Circular system and method for the digital correction of modulation effects in eletromechanical delta-sigma modulators

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G01C19/5712

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G01C19/5726

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G01C19/5776

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G01C25/005

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B41J3/00

PERFORMING OPERATIONS; TRANSPORTING

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G01C25/00

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G01C19/5726

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G01C19/5712

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Abstract

Claims

Description