Capacitive displacement sensor system with interdigitated combs

Abstract

A capacitive displacement sensor system (1) with interdigitated combs comprising a capacitive detection unit in a direction (y) perpendicular to the surfaces of the combs facing each other, said combs being subjected to a sinusoidal motion (A0.sin(ωt)) in said direction (y), comprising: - a device (2) for converting the capacitance delivered by the sensor (1) into a voltage; - an analog / digital converter (3) configured to digitize the voltage delivered by said conversion device (2) and to provide a digitized signal (Vadc); and - a control unit (4) comprising: - a harmonic estimator (5) configured to estimate the amplitudes of the harmonics of order less than or equal to a maximum order based on the digitized signal (Vadc) and a reference angle (a) corresponding to the instantaneous angle of the input angular frequency (ωt); and - a signal reconstruction module (6) for reconstructing a signal from the amplitudes provided by said harmonic estimator (5) and the reference angle and the digitized signal delivered by said analog / digital converter (3).

Description

TECHNICAL FIELD

[0001] The present invention relates to a capacitive displacement sensor system with interdigitated combs, comprising a capacitive detection unit in a direction perpendicular to the surfaces of the combs facing each other, the combs being subjected to a sinusoidal motion in said direction. BACKGROUND

[0002] The field of application of the present invention is sensors using capacitive combs as detection or feedback means.

[0003] Many sensors use the capacitive effect to determine a measured quantity or to inject a feedback force.

[0004] The basic capacitance C is generally composed of a fixed surface facing a moving surface, as shown in Figure 1 and can be expressed by the following relationship:

[0005] C = ε S / d

[0006] where:

[0007] S represents the area of the surfaces facing each other;

[0008] d represents the inter-surface distance;

[0009] ε represents the dielectric constant of the material.

[0010] To increase the surface area and thus its efficiency, these capacitances can be organized in the form of combs (two interdigitated combs). In addition to increasing the area of the surfaces facing each other, this arrangement allows operation along two axes, in this case the x and y axes.

[0011] As shown in Figure 2 the following quantities are noted:

[0012] n: number of teeth of the comb (unit of repetition of the pattern);

[0013] el: air gap 1 in meters (m);

[0014] e2: air gap 2 (which can be equal to air gap 1 in the case of symmetrical design), in m;

[0015] r: overlap of the combs, in m;

[0016] h: depth of the comb teeth (along the z axis), in m.

[0017] The capacitance can thus be expressed by the following relationship:

[0018] C = ε.n.h.r. (1 / el + 1 / e2)

[0019] Considering the detection and as described above, two types of displacements are possible:

[0020] Displacement along the x-axis: r = r0 + x (r0 corresponds to the value of r in the rest or equilibrium position); and

[0021] Displacement along the y-axis: e1 = e10 + y (e10 corresponds to the value of e1 in the rest or equilibrium position) and e2 = e20 - y (e20 corresponds to the value of e2 in the rest or equilibrium position).

[0022] Thus, the displacement along the x-axis gives a linear relationship between x and the capacitance variation:

[0023] C = ε.n.h.r0.(1 / e1 + 1 / e2) + ε.n.h.x.(1 / e1 + 1 / e2), which can be expressed as C0 + dC(x)

[0024] with dC = k.x, setting k = ε.n.h.(1 / e1 + 1 / e2).

[0025] This operating scenario does not have difficulties in handling the information, the displacement along the x-axis being directly and linearly included in the capacitance variation signal.

[0026] In the displacement along the y-axis, the capacitance can be expressed as:

[0027] C = ε.n.h.r.(1 / (e10 + y) + 1 / (e20 - y)).

[0028] The restriction to a finite expansion of order 3 gives the following relationship:

[0029] C = ε.n.h.r.[e10 -1 .(1 - y / e10 + y 2 / e10 2 - y3 / e10 3 ) + e20 -1 .(1 + y / e20 + y 2 / e20 2 + y 3 / e20 3 )] which can be expressed as C0 + dC(x)

[0030] This thus gives C = k10 + k11.y + k12.y 2 + k13.y 3 + k20 + k21.y + k22.y 2 + k23.y 3 corresponding to C0 + dC(y)

[0031] where:

[0032] C0 = k10 + k20

[0033] dC = (k11+k21).y + (k21+k22).y 2 + (k31+k32).y 3 = k1.y + k2.y 2 + k3.y 3 ; and

[0034] k0 = ε.n.h.r / e10 + ε.n.h.r / e20

[0035] k1 = -ε.n.h.r / e10 2 + ε.n.h.r / e20 2

[0036] k2 = ε.n.h.r / e10 3 + ε.n.h.r / e20 3

[0037] k3 = -ε.n.h.r / e10 4 + ε.n.h.r / e20 4

[0038] It appears that the use of movements along the y axis leads to the appearance of harmonic terms. In some architectures, so-called complementary combs are implemented, operating in the opposite way, that is to say, when the capacitance of one side increases, the capacitance of the complementary side decreases. The displacement information is then obtained by subtracting the two complementary edges: this arrangement eliminates some common-mode defects and significantly eliminates (or greatly reduces) even harmonic terms, but doubles the odd terms.

[0039] In the case of processing operations related to certain high-precision resonant sensors for which it is necessary to obtain a real image of the mechanical displacement, the presence of these harmonic terms can prove to be detrimental.

[0040] The document US 9797750 describes a method of linearization of capacitive detection. This method uses four electrodes to generate signals with phases of 0°, 90°, -90° and 180°. The signal is linearized by performing a radiometric calculation on the quadrature signals.

[0041] In addition, depending on the architecture of the sensor, the production of the electrodes that provide the signal at 90° can exhibit production difficulties. This document also does not demonstrate the degradation of the linearization performance (that is to say, the degradation of the phase between the relative electrodes) in the event of defects in the production of the set of electrodes. SUMMARY

[0042] One aim of the present invention is to overcome the problems mentioned above, and in particular to allow a correction by processing while preserving the conventional electrodes.

[0043] Therefore, according to one aspect of the present application, it is proposed a capacitive displacement sensor system with interdigitated combs, comprising capacitive detection cells in a direction perpendicular to the surfaces of the combs facing each other, the combs being subjected to a sinusoidal motion in said direction, comprising:

[0044] - a device for converting the capacitance delivered by the sensor into a voltage;

[0045] - an analog / digital converter configured to digitize the voltage provided by the conversion device and to provide a digitized signal; and

[0046] - a control unit comprising:

[0047] - a harmonic estimator configured to estimate the amplitudes of the harmonics of order less than or equal to a maximum order based on the digitized signal and on a reference angle corresponding to the instantaneous angle of the input angular frequency; and

[0048] - a signal reconstruction module for reconstructing the signal from the amplitudes provided by the harmonic estimator and from the reference angle and from the digitized signal delivered by the conversion device.

[0049] Such a system makes it possible to reconstruct a displacement signal from which its harmonics have been removed, providing better performance in the case of processing operations of so-called "resonant" sensors, such as microelectromechanical system (or Mems for the acronym) gyroscopes.

[0050] According to one embodiment, the harmonic estimator comprises a phase-locked loop locked to the digitized signal delivered by the analog / digital converter, a delivery of the reference angle, and an estimation module for estimating the amplitudes of the harmonics of order less than or equal to a maximum order.

[0051] It is thus possible to reuse a phase-locked loop that is usually already present in the case of resonant sensor processing operations.

[0052] In one embodiment, the phase-locked loop comprises a phase comparator, a low-pass filter and a loop corrector module, and a phase accumulator, all arranged in series, the phase comparator receiving at the input the digitized signal delivered at the output of the phase accumulator and the reference angle, and delivering at the output a phase error signal to the low-pass filter and the loop corrector module, the low-pass filter and the loop corrector module filtering the terms of high frequency greater than a threshold and correcting the reference angle, delivering at the output a frequency setpoint to the phase accumulator, which determines the reference angle by summing a basic phase step.

[0053] It is thus given a reference angle that can be directly used by the harmonic estimator.

[0054] According to one embodiment, the estimation module for estimating the amplitudes of the harmonics of order less than or equal to the maximum order comprises, for each harmonic amplitude, a first multiplier which multiplies the reference angle by the order of the harmonic amplitude, a cosine module in the case where the order is even, a sine module in the case where the order is odd, the sine or cosine module receiving at the input the output of the first multiplier, a second multiplier which multiplies the output of the cosine or sine module by the digitized signal, and a low-pass filter having a static gain inversely related to the coefficients of the trigonometric development, delivering the harmonic amplitude of order.

[0055] This method thus remains highly economical by limiting the implementation surface, since it only evaluates the selected harmonic terms.

[0056] In one embodiment, the signal reconstruction module comprises:

[0057] a sine module which receives at the input the reference angle delivered by the harmonic estimator and delivers at the output its sine value,

[0058] an addition module for adding to the power of the order the sine of the reference angle for each harmonic amplitude of order less than or equal to the maximum order, a third multiplier which multiplies the output delivered by the addition module by the harmonic amplitude of order delivered by the harmonic estimator,

[0059] a summer which receives at the input the output of the third multiplier, and

[0060] a subtracter configured to subtract from the digitized signal the sum delivered by the summer.

[0061] This method thus remains highly economical by limiting the implementation surface, since it only evaluates the selected harmonic terms.

[0062] According to one embodiment, the system operates in closed loop mode, comprising a feedback loop which feeds back to the harmonic estimator the reconstructed signal at the output of the reconstruction module.

[0063] The operation in closed loop mode thus makes it possible to correct other harmonic defects possibly introduced by the analog formatting chain, for example, and thus to eliminate the desired harmonic terms overall. In the same way, it is possible to compensate for a temporal drift in the amplitude of the harmonic terms, since the operation in closed loop mode continuously cancels the selected harmonics.

[0064] In one embodiment, the reconstructed signal replaces the input signal at the input of the second multiplier and the corrector having the function of integration replaces the low-pass filter.

[0065] In one embodiment, the maximum order is 3. BRIEF DESCRIPTION OF DRAWINGS

[0066] The application will be better understood by studying some embodiments described by way of purely non-limiting example and illustrated by the attached drawings, in which:

[0067] [ Figure 1 ] a basic capacitance of a fixed surface facing a mobile surface according to the prior art is schematically shown;

[0068] [ Figure 2 ] a capacitive displacement sensor with interdigitated combs according to the prior art is schematically shown;

[0069] [ Figure 3 ] a capacitive displacement sensor system with interdigitated combs according to an aspect of the application is schematically shown;

[0070] [ Figure 4 ] a capacitive displacement sensor system with interdigitated combs according to an aspect of the application is schematically shown;

[0071] [ Figure 5 ] a capacitive displacement sensor system with interdigitated combs according to an aspect of the application is schematically shown; and

[0072] [ Figure 6 ] a capacitive displacement sensor system with interdigitated combs according to an aspect of the application is schematically shown.

[0073] Throughout the drawings, elements of the same reference number are similar. DETAILED DESCRIPTION

[0074] Figure 3 A capacitive displacement sensor system 1 with crossed combs is shown, according to an aspect of the application, comprising capacitive detection cells in a direction y perpendicular to the facing surfaces of the combs, which are subjected to a sinusoidal motion A0.sin(ωt) in said direction y, comprising

[0075] - a device 2 for converting the capacitances transmitted by the sensor 1 into voltages;

[0076] - an analog / digital converter 3, or ADC in acronym, configured to digitize the voltages V transmitted by the conversion device 2, and to provide a digitized signal Vadc; and

[0077] - a control unit 4, comprising:

[0078] - a harmonic estimator 5 configured to estimate the amplitudes of the harmonics of order less than or equal to a maximum order, based on the digitized signal Vadc and a reference angle a corresponding to the instantaneous angle of the input angular frequency a = ωt; and

[0079] - a signal reconstruction module 6 for reconstructing the signal from the amplitudes and the reference angle a provided by the harmonic estimator 5 and the digitized signal Vadc transmitted by the converter 3.

[0080] The capacitive detection will be considered along the y axis, operating and subjected to a sinusoidal mechanical motion A0.sin(wt). As mentioned above, the electrical signal, which is the image of the capacitance variation, is affected by harmonic defects. The device converting the capacitance C into a voltage V, like a charge amplifier, can add other harmonic defects. The information processing chain can be summarized as follows:

[0081] - the comb is subjected to a sinusoidal motion along the y axis;

[0082] - the capacitance transmitted by the sensor 1 (charge amplifier, switched capacitor or other similar device) is converted 2 into a voltage, then analog / digital converted 3;

[0083] - then, the digital information Vadc is processed in an electronic control unit 4 comprising a harmonic estimator 5 and a signal reconstruction module 6.

[0084] The idea is to estimate the harmonic terms in order to be able to recover the initial displacement signal from the sensor comb. In the following description, the harmonics of order 2 and 3 will be considered, but without limitation, since the present invention can be applied in the same way to higher harmonics.

[0085] It is considered that the conversion of the capacitance into a voltage (by amplification) eliminates the DC component (DC is the acronym for Direct Current, corresponding to the term k0).

[0086] The high order terms include the transfer function of the conversion device 2 and of the converter 3, and the equation is simplified with A0=1, but without limitation.

[0087] Due to the non-linearity of the comb, the digitized signal Vadc has the following form:

[0088] Vadc = k1.sin(wt) + k2.[sin(wt)] 2 + k3.[sin(wt)] 3

[0089] However, since sin 2 (wt) = [1 - cos(2wt)] / 2 and sin 3 (wt) = [3sin(wt) - sin(3wt)] / 4, the following relations are obtained:

[0090] Vadc = [k1+ .k3].sin(wt) + [- k2 .k2].cos(2wt) + [- k3 .k3].sin(3wt)

[0091] The DC component term related to the coefficient k2 is not retained because it has been assumed that the capacitive to voltage conversion (C→V) does not retain the DC component.

[0092] The terms in cos(2ωt) and sin(3ωt) appear, weighted by the 2nd and 3rd order nonlinearities. The first embodiment of the harmonic estimation can be a DFT or FFT, which makes it possible to return the coefficients k2 and k3 based on the three lines at ωt, 2ωt and 3ωt. Although this approach can be taken, it exhibits the drawback of having to perform a DFT or FFT, which can prove greedy in terms of implementation (silicon surface, computation time) if precision is required.

[0093] As shown in Figure 4 the harmonic estimator 5 comprises a phase-locked loop 7, which is locked to the digitized signal Vadc delivered by the analog / digital converter 3, a delivery reference angle a, and an estimation module 8 for estimating the amplitudes of the harmonics of order less than or equal to the maximum order.

[0094] The approach taken is to use a phase-locked loop 7, or PLL for short, which is locked to the signal from the analog / digital converter 3.

[0095] The phase-locked loop 7 comprises a phase comparator 9, a low-pass filter and loop corrector module 10 and a phase accumulator 11, all arranged in series, the phase comparator 9 receiving at the input the digitized signal Vadc delivered at the output of the phase accumulator 11 and the reference angle a, and delivering at the output a phase error signal EP to the low-pass filter and loop corrector module 10, which filters the terms having a high frequency greater than a threshold and corrects the reference angle, delivering at the output a frequency setpoint to the phase accumulator, which determines the reference angle by summing a basic phase step.

[0096] The output of the phase accumulator is thus the instantaneous angle of the input angular frequency a = ωt.

[0097] Thanks to the presence of the PLL 7, it is possible to perform a coherent demodulation of the input signal Vadc, which is equivalent to performing a discrete Fourier transform, or DFT for short, only for the frequencies of interest. The amplitude ratio of the fundamental wave, combined with the loop filter of the PLL, allows the PLL to be locked to the fundamental wave.

[0098] Furthermore, the locked angle a serves as a basis for easily generating the signals 2a and 3a and the terms cos(2ωt) and sin(3ωt).

[0099] The estimation module 8 for estimating harmonic amplitudes of orders less than or equal to the maximum order includes: a first multiplier 12, which multiplies the order of the harmonic amplitude by a reference angle α for each harmonic amplitude (in this case, the 2nd and 3rd orders); a cosine module 13, which multiplies the order by the digitized signal Vadc, or the sine module receiving the output of the first multiplier 12 at its input; a second multiplier 14, which multiplies the output of the cosine or sine module 13 by the digitized signal Vadc; and a low-pass filter 15 having a static gain negatively correlated with the trigonometric expansion coefficients, transmitting the harmonic amplitude ki of order i.

[0100] This harmonic estimator 5 constitutes the part for estimating harmonics. Its principle is not limited to the second and third orders; it can be extended to higher orders.

[0101] In the case of harmonic estimation for the second and third order terms, the reference signals cos(2ωt) and sin(3ωt) are multiplied by the digitized input signal Vadc. This is equivalent to estimating the powers of the second and third order terms by returning these levels to the DC current:

[0102] - Low-pass filtering can retain the DC component and filter out high-frequency terms;

[0103] - Gain 2 can compensate for the factor caused by multiplying two sine terms. ;as well as

[0104] A gain of -2 or -4 can compensate for harmonic gains (see equation Vadc = [k1 + ... .k3].sin(ωt)+[- .k2].cos(2ωt)+[- .k3].sin(3ωt)).

[0105] This method allows for the dynamic estimation of terms k2 and k3 for harmonic levels.

[0106] like Figure 5 As shown, the signal reconstruction module includes:

[0107] - Sine module 16, which receives the reference angle α transmitted by harmonic estimator 5 at the input and transmits its sine value at the output;

[0108] - Adding module 17, for each harmonic amplitude whose order is less than or equal to the maximum order, the adding module is used to add the sine of the reference angle to the power of the order, and the third multiplier 18, which multiplies the output transmitted by the adding module 17 by the harmonic amplitudes k2, k3 of the order transmitted by the harmonic estimator 5.

[0109] - An adder 19 that receives the output of the third multiplier 18 at its input; and

[0110] - a subtracter 20 configured to subtract the sum delivered by the adder 19 from the digitized signal Vadc.

[0111] The output of the harmonic estimator 5 is then used by the reconstruction module 6, aiming at reconstructing the linearized signal, as Figure 5 illustrated.

[0112] The reference angle a makes it possible to recreate the terms [sin(ωt)] 2 and [sin(ωt)] 3 . The principle of inverse harmonic correction consists in weighting these terms by the harmonic estimations k2 and k3, so as to subtract them from the input signal. This thus reconstructs the original motion signal Ao.sin(ωt), which can be used for the rest of the signal processing. This principle can easily be extended to higher harmonic orders, or limited to specific harmonic orders.

[0113] It should be noted that such a method is based on a 1 / 2 and 3 / 4 weighting of the harmonic terms (Vadc = [k1 .k3].sin(ωt) + [- k2].cos(2ωt) + [- k3].sin(3ωt)). The harmonic estimator 5 reuses this weighting in reverse to obtain the coefficients k2 and k3. More generally, this device can be considered to be in an "open loop mode", and the bias or imperfections in the processing stage can lead to estimation errors of the terms k2 and k3 (quantification imperfections, calculation resolution, etc.). This is even more the case when the manipulated amplitude remains low with respect to the base signal.

[0114] Then, as illustrated, an alternative of "closed loop mode" can be considered, comprising a feedback loop of the reconstructed signal A0sin(ωt) at the output of the reconstruction module 6 to the harmonic estimator 5.

[0115] Figure 6 This alternative implements two integrators 21 in the harmonic estimation part and uses the linearized output information. The harmonic estimator 5 thus seeks to directly cancel the harmonic terms on the output signal, and makes it possible to dynamically eliminate the targeted harmonic terms.

[0116] In the same way, this device in "closed loop mode" can be extended to higher harmonic orders, or limited to specific harmonic orders, for example the 3rd order.

[0117] In the same way, this device in "closed loop mode" can be extended to higher harmonic orders, or limited to specific harmonic orders, for example the 3rd order.

[0118] ​This system makes it possible to completely eliminate the selected harmonic terms, since it can be implemented in the form of a loop system: in this respect, it makes the entire detection chain completely linear, including the electronic signal formatting phase, which can also increase the non-linearities leading to harmonic terms: the overall performance of the detection phase is thus improved.

[0119] Another advantage of the application is to directly use the main signal without the need to add a complementary signal and its formatting.

Claims

1. A capacitive displacement sensor system with interdigitated combs, comprising a capacitive detection unit in a direction perpendicular to surfaces of the combs facing each other, the combs being subjected to a sinusoidal motion in the direction, comprising: a conversion device for converting a sensor transmitted capacitance into a voltage; an analog / digital converter configured to digitize the voltage transmitted by the conversion device and to provide a digitized signal; and a control unit comprising: a harmonic estimator configured to estimate harmonic amplitudes of an order less than or equal to a maximum order based on the digitized signal and a reference angle corresponding to an instantaneous angle of an input angular frequency; and a signal reconstruction module for reconstructing a signal from the amplitudes provided by the harmonic estimator and the reference angle and the digitized signal transmitted by the analog / digital converter.

2. The system of claim 1, wherein, the harmonic estimator comprising: a phase locked loop locked to the digitized signal transmitted by the analog / digital converter, transmitting the reference angle, and an estimation module for estimating the harmonic amplitudes of the order less than or equal to the maximum order.

3. The system of claim 2, wherein, the phase locked loop comprising a phase comparator, a low pass filter and a loop corrector module, and a phase accumulator, all arranged in series, the phase comparator receiving at input the digitized signal transmitted at output of the phase accumulator and the reference angle, and transmitting at output a phase error signal to the low pass filter and loop corrector module, the low pass filter and loop corrector module filtering terms of high frequency greater than a threshold value and correcting the reference angle, transmitting at output a frequency setpoint to the phase accumulator, the phase accumulator determining the reference angle by summing a base phase step.

4. The system of claim 2 or 3, wherein, the estimation module for estimating the harmonic amplitudes of the order less than or equal to the maximum order comprising: a first multiplier multiplying the reference angle by the order of the harmonic amplitude for each harmonic amplitude; a cosine module in case the order is even, or a sine module in case the order is odd, the cosine or sine module receiving at input the output of the first multiplier; a second multiplier multiplying the output of the cosine or sine module by the digitized signal; and a low pass filter having a static gain inversely related to a triangle expansion coefficient, transmitting the harmonic amplitude of the order.

5. The system of one of claims 1 to 3, wherein, the signal reconstruction module comprising: a sine module receiving at input the reference angle transmitted by the harmonic estimator and transmitting at output a sine value thereof; an addition module for adding to the power of the order the sine of the reference angle for each harmonic amplitude of order less than or equal to the maximum order; a third multiplier multiplying the output transmitted by the addition module by the harmonic amplitude of the order transmitted by the harmonic estimator; a summer receiving at input the output of the third multiplier; and a subtracter configured to subtract from the digitized signal the sum transmitted by the summer.

6. The system according to one of claims 1 to 3, operating in a closed loop mode, comprising a feedback loop feeding back a reconstructed signal at the output of the reconstruction module to the harmonic estimator.

7. The system of claim 4, operating in a closed loop mode, comprising a feedback loop feeding back a reconstructed signal at the output of the reconstruction module to the harmonic estimator, wherein, The reconstructed signal replaces the input signal at the input of the second multiplier, and wherein a corrector with an integrating function replaces the low pass filter.

8. The system of one of claims 1 to 3, wherein, The maximum order is 3.

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