Delta sigma modulator

State of the art

p0001The invention is based on a delta-sigma modulator, with a oscillating system with a natural frequency, with an electronics and with a regulating loop, which acts from the oscillating system on the electronics and from the electronics again on the oscillatory system.

p0002Microsystems in which micromechanical sensors are combined with an evaluation electronics are key components for modern systems in the car, such as ESP, airbag control, roll-over sensing and navigation. One possibility, which has many advantages, of combining the micromechanical sensor element with a microelectronic evaluation electronics is the construction of an electromechanical ΔΣ modulator.

p0003In the writings "<nplcit id="ncit0001" npl-type="s"><text>Surface Micromachined Accelerometers ", Bernhard E. Boser, Roger T. Howe, IEEE Journal of Solid State Circuits, vol. 31, No. 3, March 1996</text></nplcit> and <nplcit id="ncit0002" npl-type="b"><text>C. Lang "Modeling and realization of a low-noise electromechanical ΔΣ modulator for acceleration measurement according to the principle of force compensation", Shaker-Verlag, Aachen, 2001, ISBN 3-8265-8616-6</text></nplcit> Electromechanical delta-sigma modulators are described in the prior art.

p0004The print <nplcit id="ncit0003" npl-type="s"><text>In a recent study, IEEE International Symposium on Circuits and Systems (IEEE International Symposium on Circuits and Systems). Sydney, Australia, May 6-9, 2001</text></nplcit>, <nplcit id="ncit0004" npl-type="s"><text>IEEE International Symposium on Circuits and Systems, New York, NY: IEEE, US, Vol. 1 of 5, May 6, 2001 (2001-05-06), pages 453-456, XP010541174, ISBN: 0-7803- 6685-9</text></nplcit>, Describes electromechanical delta-sigma modulators, which have mechanical forces as input and have micromechanical transducers in the loops. It is proposed in the document to use a so-called complementary pulse-density-modulated signal (CPDM signal) in order to achieve a linear multibre coupling by means of microactuators.

Advantages of the invention

p0005The invention is based on a delta-sigma modulator, with a oscillating system with a natural frequency, with an electronics and with a regulating loop, which acts from the oscillating system on the electronics and from the electronics again on the oscillatory system. The core of the invention is that the control loop is designed in such a way that a gain in the control loop has an amplification increase in a frequency range around the natural frequency of the oscillatable system. Advantageously, the quantization noise of the electronics can be formed as a function of the frequency of the signal in the control loop.

p0006An advantageous embodiment of the invention provides that the oscillatable system is designed mechanically. Advantageously, in such a system, the functions of a measured-value sensor, in particular for accelerations or rotational data, can be combined with the function of a component, namely an integrator for shaping the quantization noise, in a delta-sigma modulator. In the electromechanical delta-sigma modulator, the integrating behavior of the mechanics is advantageously utilized to form the quantization noise of the ADC and the DAC. The mechanics reacts to a (Coriolis) acceleration with a deflection of a moving mass. The transfer function from acceleration to deflection involves two integrators. An integrator describes the conversion of acceleration into the velocity of the moving mass. The second integrator describes the conversion of velocity into deflection. In purely electronic delta-sigma modulators, purely electronic integrators (mostly switched capacitor circuits) are used to form the quantization noise of the DAC.

p0007It is advantageous that the delta-sigma modulator has a bandpass characteristic at an output. Advantageously, the delta-sigma modulator according to the invention with bandpass characteristics is suitable for processing signals with a specific or known bandwidth, such as, for example, a carrier frequency with modulated signals.

p0008It is advantageous that the electronics comprise an analog-to-digital converter (ADC), a digital-to-analog converter (DAC) and means for setting the gain in the control loop and / or the bandwidth of the delta-sigma modulator independently of an input signal of the Analog-to-digital converter (ADC).

p0009An advantageous embodiment of the ΔΣ modulator according to the invention provides that the electronics includes a multibit analog-to-digital converter and / or a multibit digital-to-analog converter. Advantageously, a defined gain, which is independent of the input signal of the analog-to-digital converter, can thereby be set at the analog-to-digital converter. Advantageously, the quantization error of the analog-to-digital converter can also be kept small. Dieselben advantages apply analogously for the digital-analog converter.

p0010A further advantageous embodiment of the ΔΣ modulator according to the invention provides for the electronics to include a low-pass filter with a quality enhancement, in particular a digital filter, such that the ΔΣ modulator has a bandpass characteristic with a band center frequency at the natural frequency of the oscillatable system. Advantageously, the bandwidth can thereby be set independently of the input signal. The following and other equivalent circuits are also advantageous.

p0011Another advantageous embodiment of the ΔΣ modulator according to the invention provides that the electronics comprise a bandpass filter, in particular a digital filter, and a phase slider, such that the electromechanical ΔΣ modulator has a bandpass characteristic with a band center frequency at the natural frequency of the oscillatable system. Advantageously, the bandwidth can also be adjusted independently of the input signal. A digital design of the two aforementioned filters is particularly advantageous.

p0012A further advantageous embodiment provides for the electronics to include means for deriving a vibration frequency of the oscillatable system, in particular a phase regulating circuit, by means of which the band center frequency is controlled. Advantageously, the phase rotation of the low-pass filter with a quality increase at the driving resonance frequency is advantageously independent of tolerances in the production process. This ensures the stability of the ΔΣ modulator.

p0013A particularly advantageous embodiment of the delta-sigma modulator according to the invention provides that the digital-to-analog converter has a centered pulse-width-modulated output signal, which in particular acts for feedback on the oscillatory system. A constant magnitude (amplitude) of the feedback signal (the feedback voltage) is thereby advantageous. It is also advantageous to quantize and linearize the feedback signal (the feedback force) of the ΔΣ modulator in the time domain. Finally, the centering of the feedback voltage pulse is also advantageous in such a way that the temporal center of gravity of the pulse always lies in the same clock phase. This prevents phase shifts of the oscillation of the oscillatable system due to different feedback signals.

p0014Further advantageous embodiments are to be found in the subclaims.

drawing

p0015Exemplary embodiments of the invention are illustrated in the drawing and explained in more detail in the following description.<ul><li><figref idrefs="f0001">FIG</figref> Shows the construction of an electro-mechanical ΔΣ modulator in the prior art.</li><li><figref idrefs="f0001">FIG</figref> Shows a mechanical sensor element as a differential capacitor.</li><li><figref idrefs="f0001">FIG</figref> Shows the comparator characteristic of an analog-to-digital converter.</li><li><figref idrefs="f0002">FIG</figref> Shows the analog-digital transmission function of a typical oscillating sensor element with a quality increase.</li><li><figref idrefs="f0002">FIG</figref> Shows the construction of an electromechanical ΔΣ modulator with multibit converters.</li><li><figref idrefs="f0002">FIG</figref> Shows the characteristics of a multibit ADU.</li><li><figref idrefs="f0003">FIG</figref> Shows the characteristic of a multi-bit DAU.</li><li><figref idrefs="f0004">FIG</figref> Shows gain frequency responses in the control loop of an embodiment of the ΔΣ modulator according to the invention.</li><li><figref idrefs="f0005">FIG</figref> Shows, by way of example, the ZPWM signal of the multibit DAC in one embodiment of the ΔΣ modulator according to the invention.</li></ul>

DESCRIPTION OF EXEMPLARY EMBODIMENTS

p0016The invention is described in detail with reference to the embodiments described in the following.

p0017<figref idrefs="f0001">FIG</figref> Shows the construction of an electro-mechanical ΔΣ modulator in the prior art. Before the characteristics are discussed, the function is to be presented. In<figref idrefs="f0001">FIG</figref> The block circuit diagram of such a microsystem is shown. A force F acts on a mechanical oscillator 100, in this example on a sensor element. This force F can, for example, be the quantity to be measured in an acceleration sensor or the Coriolis force in a rotational speed sensor. This force results in a change in capacitance in the sensor element 100, which is converted into an analog voltage by a capacitance-voltage converter (C / U converter) 110. This analog voltage is compared as input signal from a clocked comparator 120 (1-bit analog-to-digital converter, ADU) with a single threshold and thus converted into the digital. Depending on the output signal of the comparator 120, a digital-to-analog converter 140 (D / F, DAU) running at the same clock frequency generates a force impulse. The DAU 140 can produce two possible force shocks. Both forces have the same amount. They differ only in their sign. To illustrate this fact,<figref idrefs="f0001">FIG</figref>. A digital output signal of the ΔΣ modulator is applied to a digital output circuit 130. The reference symbols 1 indicate that all signals in the digital part of the ΔΣ modulator have the same bit width.

p0018<figref idrefs="f0001">FIG</figref> Shows a mechanical oscillator in the form of a mechanical sensor element 100 as a differential capacitor. A center electrode CM is shown between two external electrodes CP and CN. The center electrode CM is movable. The outer electrodes CP and CN are stationary. If a positive force impact is to be applied, a constant voltage is applied between CP and CM during a predetermined period of time. CM and CN are short-circuited. The resulting electrostatic force pulls the center electrode in the direction of CP. In the case of a negative force impulse, the same voltage is applied between the electrodes CM and CN over the same period of time. The electrodes CP and CM are short-circuited. The resulting force impulse pulls the center electrode in the direction of CN. A series of force surges compensates on average the force F to be measured and the movable electrode CM is kept at rest on average.

p0019The essential properties of this process are as follows:

p0020If the sensor element 100 were not guided by the electronics by means of the impulses induced by means of the DAU 140 by means of the electrodes, and would thus be bound, but could move freely, a deflection-dependent mechanical spring constant of this oscillator would be a non-linearity in the entire measuring system. The guidance of the sensor element 100 in the electromechanical ΔΣ modulator thus prevents a deflection of the middle mass of the mechanical oscillator and thus eliminates the danger of non-linearity by the sensor element 100. The mechanical properties of the sensor element 100 are thus linearized.

p0021As a result of the fact that the resetting force acting in the center is composed of individual force impingement quanta, all of which have the same magnitude and there are only two possible feedback force surges, the characteristic curve of the digital-to-analog converter DAU is always ideally linear. A straight line can always be drawn through two points. The restoring force is thus also linearized.<figref idrefs="f0001">FIG</figref> This is illustrated by the comparator characteristic curve.

p0022<figref idrefs="f0001">FIG</figref> Shows the comparator characteristic of an analog-to-digital converter. The input voltage U_in of the analog / digital converter ADU is compared with a single threshold and the output voltage U_out of the analog-to-digital converter can only assume two values. If U_out is positive, a positive force impact is fed back and reversed. In return, the arrangement described has the disadvantage that the slope of the straight line in FIG<figref idrefs="f0001">FIG</figref> Is not defined. To indicate this, there are three straight lines 300 with different slopes in<figref idrefs="f0001">FIG</figref> Is shown. Which of these three straight lines 300 actually describes the amplification of the analog-to-digital converter ADU depends on the statistical distribution of the voltage U_in. The gain of the series connection of the analog-to-digital converter ADU and the digital-to-analog converter DAU is therefore not defined but depends on the input signal of the analog-to-digital converter ADU as described in the document "<nplcit id="ncit0005" npl-type="s"><text>Surface Micromachined Accelerometers ", Bernhard E. Boser, Roger T. Howe, IEEE Journal of Solid State Circuits, vol. 31, No. 3, March 1996</text></nplcit> Described. This results in the disadvantage of a loop gain (gain in the control loop) in the delta-sigma modulator, which is dependent on the input signal and can thus not be set in a defined manner. Since the bandwidth of the ΔΣ modulator is a function of the loop amplification, this too can not be set and is signal-dependent. The bandwidth of the delta-sigma modulator can be several orders of magnitude higher than the bandwidth which the measuring system is intended to detect at all. This can result in a great problem if the micromechanical sensor element has interfering resonant frequencies in a frequency range which is also detected by the variable bandwidth of the ΔΣ modulator. The consequence of this can be a signal-dependent instability of the ΔΣ modulator which makes the product unusable.

p0023<figref idrefs="f0002">FIG</figref> Shows the analog-digital transmission function of a typical mechanical oscillator, using the example of an oscillating sensor element with a quality increase. The analog-to-digital converter ADU quantizes the analog input signal into two possible digital values. This digital value decides on the polarity of the back-coupled force impulse. The sensor element is then subjected to relatively high frequency with force pulses and reacts to the force pulses according to a second-order integrator. In<figref idrefs="f0002">FIG</figref> The transmission flection (deflection x in response to a force F) of a typical sensor element with a quality increase over the frequency f is shown. The Kraftstö SSE are at a frequency f_K Is applied to the sensor element which is above the sensor resonance frequency f_R, Of the natural frequency of the oscillatable system. In this frequency range, the characteristic falls at 40 dB per decade. The actual quantization error of the analog-to-digital converter ADU is ultimately also integrated in the sensor element and in turn influences the future decisions of the analog-to-digital converter ADU. Thus, over a longer period, the quantization errors are filtered by the sensor element. The quantization noise is formed. At the output of the system, the quantization noise is smallest in the frequency range in which the sensor element has the greatest gain.

p0024The higher the clock frequency, the wider the frequency band to which the quantization noise power is distributed. It follows that, with a constant quantization noise power, the noise power density in the system bandwidth decreases with increasing clock frequency.

p0025One way to achieve a high signal-to-noise ratio is to increase the clock frequency. This possibility, however, reaches limits when the input circuit can no longer settle in the predetermined clock slots.

p0026Another way to increase the signal-to-noise ratio is to increase the order of the delta-sigma modulator. This means, by means of frequency-selective circuits, to ensure that the loop gain is maximum in the range of the system bandwidth and the loop gain falls as steeply as possible outside the system bandwidth. However, this procedure entails the great danger that the system may become unstable, especially if the system bandwidth can be dimensioned only with difficulty due to a 1-bit analog-to-digital converter, and any non-functionalities of the sensor element lead to interference resonances in the sensor element Which adversely affect the loop reinforcement.

p0027Since the ΔΣ-modulator operates as a closed control circuit, which always returns the movable electrode of the sensor element to the rest position, sensor elements can be operated as vibration systems with high mechanical quality. As a result, a high signal-to-noise ratio can be achieved.

p0028The implicit A / D conversion of the ΔΣ principle has the advantage that the output signal of the ΔΣ modulator can be processed directly digitally. This digital processing also has the advantage that the design is very robust against electromagnetic interference, that no long-term drifts and temperature dependencies are to be expected, that very few external components are required, and that very large time constants can be realized.

p0029A further development to the previously described state is described in the book by C. Lang "Model formation and realization of a low-noise electromechanical ΔΣ modulator for acceleration measurement according to the principle of force compensation", Shaker-Verlag, Aachen, 2001, ISBN 3-8265-8616-6 Using the example of an acceleration sensor. In the following, those points from the work of C. Lang are presented which are important for the understanding and assessment of the ideas described in the context of this invention. Used to describe the essential points<figref idrefs="f0002">FIG</figref>.

p0030<figref idrefs="f0002">FIG</figref> Shows the construction of an electromechanical ΔΣ modulator with multibit converters. The schematic diagram shows one of<figref idrefs="f0001">FIG</figref> Further developed electromechanical ΔΣ modulator. Instead of a comparator (1-bit ADC) 120, a flash multi-bit ADU 500 is now proposed. This offers the advantage that the quantization error of the A / D conversion can be reduced compared to the 1-bit ADU 120, resulting in a smaller quantization noise.

p0031A further proposal in the prior art consists in using a filter 510, in particular a digital low-pass filter, after the multibit ADU 500. This has the advantages that the quantization noise of the digital-to-analog converter DAU is strongly shaped at low frequencies, whereby the signal-to-noise ratio can be increased at small bandwidths. A further advantage is that the current consumption of the filter is very low and that the filter is very robust against temperature fluctuations and electromagnetic disturbances.

p0032A further proposal in the prior art consists in the use of a multi-bit DAU 530 according to FIG <figref idrefs="f0002">FIG</figref>. This converter offers the advantages that the quantization error is reduced compared to the 1-bit converter, whereby the noise of the sensor can be decisively reduced. This is done without sacrificing linearity.

p0033The invention, unlike the prior art, is to dimension the bandwidth of the delta-sigma modulator in such a way that it is not greater than required. This has the advantage that the frequency band in which disturbing resonance frequencies of the sensor element could act is kept as small as possible. This increases the robustness against interference modes and their scattering in the sensor element and also against manufacturing tolerances in the electronics. In contrast to the low-pass characteristic of the electromechanical ΔΣ modulator, which is referred to as the prior art, this means that the loop gain of the ΔΣ modulator is set as small as possible in the frequency range from zero to the drive resonance frequency of the sensor element. As a result, the electromechanical ΔΣ modulator obtains a band-pass characteristic.

p0034In a first embodiment according to the invention, the electronics is implemented as a low-pass filter with an increase in the quality at the driving resonance frequency. As a result, the quantization noise of the digital-to-analog converter DAU is particularly strongly shaped in the region of the drive resonance frequency. Instead of a low-pass filter with resonance amplification, the combination of a bandpass filter which has the center frequency at the driving resonance frequency and a phase-rotating member can also be used in a second embodiment according to the invention. In general, controller types can also be used which have a particularly large gain at the drive resonance frequency.

p0035Since a delta-sigma modulator with a 1-bit converter has a signal-dependent loop gain and thus a signal-dependent bandwidth, such a converter is not suitable for the bandwidth reduction according to the invention. The use of a multi-bit ADC defines the gain of the converter and is thus independent of the input signal of the converter. The same applies to the use of the multi-bit DAC.

p0036<figref idrefs="f0002">FIG</figref> Shows the characteristics of a multibit ADU and <figref idrefs="f0003">FIG</figref> Shows the characteristic of a multi-bit DAU. The figures show that the transducers have a defined gain. It is possible to draw only one straight line through both transducer characteristics in order to describe the amplification. This distinguishes the multibit converter from the 1-bit converter (comparator), in which one can place different lines with different amplifications by means of the characteristic curve. A further advantage of the multibit converters is that the deviation from the line which describes the gain is significantly smaller than in the case of the 1-bit converter. The deviation from this line is also referred to as a quantization error. A smaller quantization error means smaller quantization noise. In<figref idrefs="f0002">FIG</figref> and <figref idrefs="f0003">FIG</figref> The characteristics of the converters are shown by way of example.

p0037The multibit flash analog-to-digital converter is advantageously implemented as described in the document of C. Lang.

p0038In the case of the multi-bit digital-to-analog converter (multi-bit DAC), the requirements for the DAC according to the invention and, subsequently, a design according to the invention are discussed.

p0039The task of the multibit DAC is to provide a feedback signal which is used to compensate for the Coriolis force to be measured. The invention relates to the fact that this restoring force is generated by the electrostats in the sensor element and the task of the electronics is to apply corresponding voltages to the sensor element. There is the problem that the relationship between the voltage and the resulting force is square. A linearization must therefore take place.

p0040A further component of the invention is the selective use of a multi-bit DAC in order to assign a defined gain to the converter and thus to be able to adjust the loop gain and the bandwidth of the ΔΣ modulator in a defined manner and thus increase with respect to loop gain and bandwidth independently of the input signal of the ΔΣ modulator will.

p0041The demands for linearization and multibit conversion can be solved by the use of a centered pulse width modulated signal (centered PWM signal or ZPWM signal) described below.

p0042In <figref idrefs="f0005">FIG</figref> The assignment between the control bits and the possible feedback signals is shown. The level of the feedback voltage is constant; Both the quantization and the linearization takes place in the time domain. In<figref idrefs="f0005">FIG</figref> The feedback signal of the delta-sigma modulator is plotted over time. The upper partial figure applies in case the input of the DAU assumes the value DAU_in = -3. The uppermost time beam describes the voltage U_C_neg at the electrode CN. The second time beam from above describes the voltage U_C_pos at the electrode CP. In the time section designated as "feedback period", the said signals are in phase opposition. While the reference voltage U_ref is applied to one of the two electrodes, the other electrode is short-circuited with the average mass. The time integral over the voltage applied during the feedback period determines the effective restoring force. In the time section described as a "time multiplex", no feedback is provided. This time section can be used for other purposes such as measuring the deflection. The figures for DAU_in = -2, DAU_in = -1 and DAU_in = 3 show the curves of the feedback voltages for other DAC input signals. The voltage profiles U_C_neg and U_C_pos applied during the feedback period differ depending on the signal DAU_in in the length of the period of time for which the voltage U_ref is applied to the sensor element. This time span is quantized in the time domain. The input signal of the DAC is periodically updated. Accordingly, the voltages U_C_neg and U_C_pos applied to the sensor element for feedback purposes are also embedded in a periodic pattern. This pattern always consists of a "feedback period" of constant duration and a "time multiplexing period" of constant duration. Depending on the signal DAU_in, only the distribution of the voltage pulses on the two feedback electrodes is varied in the feedback period.

p0043A further inventive feature of the feedback PWM signal is the fact that it is centered. Irrespective of the width of a feedback pulse, the temporal center of gravity of the pulse is always in the same clock phase. As a result, the time center of gravity of the feedback pulse does not become signal-dependent and thus no signal-dependent corruption of the feedback signal can take place. This avoids the output signal of the ΔΣ modulator becoming non-linear.

p0044A further advantage of the described procedure is that periodic recurring time slots can be kept free, which can be used to implement functions which are independent of the feedback function in the time division multiplex. Another difference to the multi-bit digital-to-analog conversion described in the book by C. Lang is that a single pulse is not generated per LSB of the DA converter drive (return to zero), but the LSB in the ZPWM signal is simply connected to one another (Non-return to zero). This has the advantage that, in the case of the ZPWM signal, the maximum feedback force is greater than in the embodiment described in the document of C. Lang. The reason is that no feedback time is lost to zero by jumpbacks.

p0045A further component of the invention is the use of a low-pass filter with a quality increase in the electromechanical delta-sigma modulator. Instead of this low-pass filter, a combination of bandpass filter and phase shifter could also be used.

p0046In general, a controller type can be used which has a gain amplification in the region of the driving resonance frequency. The band-pass characteristic of the filter in connection with the band-pass characteristic of the mechanical sensor element has the advantage that the frequency range in which the loop gain of the ΔΣ modulator is greater than one is limited to a frequency range which is centered around the sensor resonance frequency and which is selected as narrow as possible In order to increase the robustness against disturbing resonance modes. In addition, there is a strong formation of the DAU quantization noise. The quantization noise of the ADU is through the mechanics. These facts are described in<figref idrefs="f0004">FIG</figref> Respectively.

p0047<figref idrefs="f0004">FIG</figref> Shows gain frequency responses in the control loop of an embodiment of the ΔΣ modulator according to the invention. On the x-axes of the partial figures of<figref idrefs="f0004">FIG</figref> The frequency is plotted on logarithmic scale. The upper partial figure describes the amount of amplification from the input of the sensor element 100 in FIG<figref idrefs="f0002">FIG</figref>. To its exit. The middle sub-figure describes the amount of gain from the input of the digital filter 510 in FIG<figref idrefs="f0002">FIG</figref> To the output of this digital filter. The lower partial figure describes the amount of amplification from the input of the sensor element 100 in FIG<figref idrefs="f0002">FIG</figref> To the output of the digital filter 510 in FIG <figref idrefs="f0002">FIG</figref>.

p0048The upper part figure in <figref idrefs="f0005">FIG</figref> Shows the amount of the transfer function (deflection as a function of the acceleration) of the sensor element. One sees the resonance increase at the resonance frequency f_R. The middle partial figure shows the magnitude of the amplification path of the electronic bandpass at a logarithmic scale. In the lower partial figure, the resulting amplification path is obtained, which results when the sensor element and the electronic bandpass filter are connected in series. At the sensor resonance frequency, a large amplification amplification is achieved by the combination of the two amplification paths. In the closed control loop of the electromechanical delta-sigma modulator, this high gain is responsible for the fact that the quantization noise of the DAC at the output of the delta-sigma modulator is very strongly suppressed in the region of the sensor resonance frequency.

p0049The quantization noise of the ADC is suppressed according to the gain of the sensor element shown in the upper partial figure. This results in an electromechanical ΔΣ modulator of the fourth order, which consists of a second-order mechanical component (the sensor element) and an electronic component of the second order (for example, the low-pass filter with an increase in the quality). This electronic low-pass filter has additional memory in the microsystem , Which can store the effect of the DAU quantization error.

p0050The digital design of the low-pass filter with an increase in the quality or the replacement solutions (for example, bandpass and phase shifters) leads to the advantage that problems with long-term drift, electromagnetic compatibility (EMV) and temperature dependencies are avoided. In addition, inaccuracies due to process tolerances are circumvented. Furthermore, the digital filter can be realized with a very low loss power consumption.

p0051A further component of the invention is to make the clock frequency of the low-pass filter dependent on the driving resonance frequency of the sensor element, with the increase in the quality or the replacement solutions (for example, bandpass and phase shifters). This leads to the advantage that the center frequency of the bandpass is always exactly at the drive resonance frequency of the sensor element since it is automatically followed. This in turn has the effect that an optimal noise shaping of the DAU quantization noise is ensured. In addition, the loop gain and thus the bandwidth of the ΔΣ modulator is independent of the fluctuations of the drive resonance frequency of the sensor element.

p0052An advantage of the digital filter according to the invention is that the phase rotation of the low-pass filter with quality enhancement or the replacement solution always corresponds exactly to the designed value at the drive resonance frequency. The risk of scattering, for example due to tolerances in the manufacturing process, does not exist. This ensures the stability of the electromechanical ΔΣ modulator.

p0053The invention is not limited to electromechanical ΔΣ modulators, ie ΔΣ modulators with a mechanical oscillator. Also conceivable are other oscillatable systems as a component of the ΔΣ modulator according to the invention.

p0054Other exemplary embodiments are also conceivable.