WO2011015302A1

WO2011015302A1 - Arrangement and method for capacitive pressure measurement

Info

Publication number: WO2011015302A1
Application number: PCT/EP2010/004605
Authority: WO
Inventors: Joachim Ihlefeld; Daniel Züllig; Amer Tarraf
Original assignee: Baumer Innotec Ag
Priority date: 2009-08-04
Filing date: 2010-07-28
Publication date: 2011-02-10
Also published as: DE102009035973A1; DE102009035973B4

Abstract

The invention relates to a pressure sensor (10) that can both be easily calibrated and have a high measurement accuracy. The pressure sensor (10) comprises an elastically deformable membrane (1) that is fixed at the edge thereof and can be deflected on the basis of a pressure difference, and at least two deflection sensors, wherein the deflection sensors detect the deflection of surface regions of the membrane that are spaced differently with respect to the middle of the membrane. The pressure sensor comprises a calculating device which calculates a value for the pressure difference on the membrane out of a deflection in the middle of the membrane from the deflections detected by the deflection sensors.

Description

Arrangement and method for capacitive pressure measurement

The invention relates to an arrangement and a

Method for capacitive pressure measurement. In particular, the invention relates to the calibration of pressure sensors.

Sensors for capacitive pressure measurement are known. Thus, DE 101 00 321 A1 shows a pressure sensor with a

A diaphragm having a dielectric portion that moves in a cavity near capacitor plates. If a pressure acts on the membrane and thus the dielectric section, then the

Capacitor plates this movement and generate due to the change in capacitance, an electrical output signal that represents the external pressure.

DE 103 13 908 B3 shows a pressure sensor with a conductive first electrode and spaced from this an opposite membrane. This membrane comprises a second electrode or acts as a second electrode itself.

When an external pressure deforms the membrane, the capacitance formed by the two electrodes is changed. A measuring signal representing the capacitance change is tapped. The capacity change represents the outer one

Pressure.

In order to calibrate pressure sensors, as they are known for example from the aforementioned two documents, a pressure-voltage curve can be traversed. This process is complicated. It would also be possible to have one

to use specified characteristic. This consists

BESTATIGUNGSKOPIE However, the problem that it is due to

Manufacturing tolerances in the pressure sensors may come to deviations from the characteristic, so that the measurement accuracy of the pressure sensor is impaired.

It is therefore an object of the invention to provide a pressure sensor which on the one hand is easy to calibrate and on the other hand has a high accuracy of measurement. This task is governed by the subject matter of the independent

Claims solved. Advantageous embodiments and

Further developments of the invention are specified in the respective dependent claims.

The invention is based on the finding that a calibration of the deflection of a membrane of a

Pressure sensor measuring sensor arrangement can be simplified if a plurality of measuring at a distance from the center axis of the membrane sensors are provided which determine the deflection of the membrane at the respective locations, wherein the measured distance, or

Deflection values on the deflection in the middle of the

Membrane to be back-calculated.

Accordingly, a pressure sensor is provided, which comprises an elastically deformable, fixed at its edge, deflectable due to a pressure difference membrane, as well as at least two displacement sensors, wherein the

Deflection sensors spaced the deflection of each of the center of the membrane, in particular in each case

spaced apart from the center of the membrane

Cover surface areas of the membrane, and wherein the

Pressure sensor comprises a computing device, which from the Displacements detected by the deflection sensors calculate a deflection in the middle of the membrane and from this a value for the pressure difference bearing on the membrane is calculated. A corresponding method for measuring a pressure by means of the pressure sensor based thereon, the deflection of each differently spaced from the center of the membrane surface areas of the membrane by means of

To detect deflection sensors and by means of

Calculation device from the deflections detected by the deflection sensors to calculate a deflection in the middle of the membrane and from it a value for the pressure difference on the diaphragm. According to a further embodiment of the invention, a measurement of the deflection can be made alternatively or additionally in the middle of the membrane.

The invention is also based on the knowledge that there are parameters which the characteristic of the sensor

Surprisingly, by a simple measurement of the resonant vibration of the membrane of

Have the pressure sensor determined. Such a measurement is in turn much faster and easier to implement than a complex measurement of a characteristic

different pressures.

For this purpose, a method for calibrating a pressure sensor is provided, wherein a pressure sensor is used, which has a deformable, fixed at its edge membrane, on which as a result of a pressure to be measured

Pressure difference acts and at least one distance sensor which corresponds to the distance of the membrane to a

Area within the border to one of the membrane

opposite position generated corresponding signal, wherein the membrane is put into a resonant vibration and the resonant frequency of this resonant vibration is measured, and based on this resonant frequency the

mechanical stress is determined which the

Proportionality factor between a deflection of the membrane and a force acting on the membrane is determined or influenced, and wherein based on the

Proportionality factor a conversion rule

is created, which signals measured by the distance sensor in a pressure difference acting on the membrane

transformed. When measuring the resonance vibration, a known pressure is assumed. It lends itself in the

Generally, the calibration in unpressurized

Condition in which the same forces, or pressures act on the membrane on both sides to perform. For the analysis of the functionality of a pressure sensor, the wave model of a vibrating circular membrane can be used. This membrane is fixed on a fixed ring with the inner radius p _raax . The physical problem usually becomes with the partial differential equation for the simplified case of small displacement

: D θ ² A (p, φ) _| dA (p, φ) _| d ² A (p, φ) ₌ d ² A (p, φ)

dp ² p dp dφ v dt ²

described, wherein

p, φ denote the radius measured from the center of the membrane and the azimuth angle, hence polar coordinates represent, t denotes the time and v the

Propagation speed of the shaft.

For the velocity of the wave in the membrane also applies:

(2) v ² = -

Pmaterial

T designates the mechanical stress in force per area (N / m ² ) and pM _ater i _a i the mass coating or the density (kg / m ³ ).

The membrane is held on the edge and / or fixed, for example on a solid ring. Both at a vibration in resonance, as well as a deformation due to a pressurization is therefore the deflection φ) at the maximum radius p _ma χ, which measured the location at the fixed edge of the membrane from the center of

Represents membrane, always equal to zero. Under

Considering the Dirichlet boundary condition, one obtains the following general solution:

[3) A (p, t) = A _msii ύn {βvt + / 3 ₀ ) j ₀ (β, p) where J ₀ (β, p) denotes a Bessel function first

Genus. ß, ß ₀ are constants that result from the zeroes of the Bessel function, or from the equation

(4) Λ (/? A "J = 0 result.

The Bessel function has several zeros, and the partial differential equation thus has several solutions. For a measuring pressure sensor with an approximately constant area distribution of the pressure p (p, φ) over the membrane, the first zero point of the Bessel function of the first type can be used. The following then applies: (5) ßp _max = 2.4048

The membrane has several natural resonance frequencies (modes). For the case described above, it suffices to consider the lowest frequency:

(6) ω _res = βv

After insertion into (2) follows for the stress in

Resonance:

This means that from the measured resonance frequency as well as the previously known with sufficient accuracy

Constants the tension T and thus the restoring force of the membrane at a given deflection can be determined by simple means. The voltage T is in the context of the invention in this case of a mechanical stress

on the one hand and the elastic modulus together. Is the

Membrane, for example, completely tensionless fixed, so is the tension T equal to the elastic modulus. Conversely, a very thin, easily deformable

Membrane used, the parameter T is significantly determined by the applied mechanical stress.

Accordingly, it is provided in a preferred embodiment of the invention, a pressure sensor with a circular

Use membrane and determine the proportionality constant T by the relationship (7).

In general, this aspect of the invention is thus the

Principle underlying to determine a calibration of the membrane properties, or the pressure sensor based on one or more resonance frequencies of the membrane.

The invention will be described in more detail below with reference to FIGS

enclosed figures explained. Here, the same reference numerals designate the same or similar elements. Show it:

Fig. 1, the deflected membrane of a pressure sensor.

Fig. 2 is a pressure sensor with capacitive

deflection measurement,

3 shows an arrangement for calibrating a pressure sensor,

Fig. 4 is a self-calibrating sensor. 1 shows the membrane 1 of a pressure sensor, which is held at its edge, that is to say at the position with the radius p _ma measured from the center axis 5 of the membrane 1. For example, the membrane may be fixed on a ring 3. The diaphragm 1 is due to an applied pressure, or more precisely a pressure difference between the two sides along the center axis

deflected. The deflection causes the surface of the membrane at the edge opposite an undeflected position at an angle α. Due to the elastic deformation of the pressure difference acts in

Balance a force F contrary.

For the pressure p and the angle α, the following relationship holds:

, _p . p = constTtan (α) ∞constT α

The constant const results from the geometry of the

Membrane. At small deflections is the tangent

negligible, as well as the deflection A (p, φ) on the axis of symmetry is proportional to the angle.

The membrane is stretched by the applied pressure p. For the relative linear expansion ΔL / L the following applies:

The spring force within the membrane then results in: dA (p, φ)

(10a) F = 2πph

dp

H denotes the thickness of the membrane and p the radius. For the change of the deflection with the radius also applies for the edge area dA {p, φ)

(10b) ^f A (O, φ) = + / - 0.519, p = +/- p _n

dp i According to equation (10b), the first derivative of the

Deflection according to the radius in equation (10a) by means of

deflection

Center to be determined.

Combining equation (10b) with equation (10a) using the relationship F = p ^# A _m between pressure p,

Membrane area A _m and spring force F, is obtained as a relationship between the pressure on the diaphragm p, the

Membrane radius p _ma χ, the deflection A (O, φ) in the center of the membrane and by measuring the resonance frequency

certain tension T:

(10c) p = ^^ -h-T A {θ, φ)

In order to reliably measure a pressure acting on the membrane with high precision as absolute size, two steps can be carried out:

First, the deflection ^A {P>Φ> in the center of the membrane is measured or determined at the location of the center axis, and secondly A ^ P'Φ 'is converted by means of the voltage T into a pressure p taking into account the membrane constants. The constants can be calculated or experimentally determined once. Since a circular diaphragm is assumed, the argument of the azimuth angle weg is omitted below.

The constant K on the right side of the relationship (10c) before the product of voltage T and displacement A (O, φ), K = 0.519, represents a prefactor which

A ^ max

may differ from the correspondingly calculated values, but characteristic of a particular type of membrane with respect to the membrane material, its thickness and diameter. The pre-factor can therefore also be determined once for a particular type of membrane and be based on the calibration of the resonance frequency in the following. According to a preferred

Further development of the invention, therefore, the determination of the pressure by multiplying the determined voltage or proportionality constant T with the measured

Deflection in the middle of the membrane and a previously

determined or fixed factor.

The procedure for calibrating the sensor and the

The following measurement will be described below with reference to a

Pressure sensor with capacitive deflection sensors explained. A capacitive distance measurement is preferred because this is very easy to implement. In principle, however, other measuring methods for measuring the deflection of the membrane can also be implemented. For example, optical, magnetic, piezoelectric or inductive Distance measurements conceivable. In the preferred capacitive deflection sensors voltage changes are due to a caused by a deflection of the membrane

Change the capacitance of a capacitor whose one electrode is connected to the membrane or through the

Membrane is formed, captured. In order to detect a voltage change due to a deflection of the membrane, it is advantageous to use a bridge circuit and for this purpose to connect a further, constant capacitance in series.

It is also generally preferred to be annular

To use measuring ranges, in which the deflections of each in the form of annularly around the center of the membrane around extending surface areas of the membrane are detected. In the case of capacitive deflection sensors, ring-shaped electrodes spaced apart from the membrane can be used for this purpose in a simple manner. Fig. 2 shows an embodiment of a pressure sensor with capacitive deflection sensors, which changes in voltage on the basis of a deflection of the membrane

caused change in the capacitance of a capacitor whose one electrode is connected to the membrane or is formed by the membrane detect.

The membrane is low in tension as shown in Fig. 1 with a rigid ring 3, not shown in Fig. 2

connected and thus fulfilled exactly the Dirichletsche

Boundary condition. The membrane 1 may be a dielectric

Comprise material with an internal insulated metallic layer 11 or be itself metallically conductive. Parallel to and spaced from the membrane 1, a carrier 13 (for example, a ceramic carrier or a printed circuit board) is arranged. On this are several concentric to

A flat counter electrode 15 is provided, which is spaced from the annular electrodes 6, 7, 8 and arranged on the opposite side of the membrane-facing side of the annular electrodes 6, 7, 8 ,

In addition, a shield electrode 17 may be provided to reduce immunity to electrical noise

Improve fields. In the exemplary embodiment illustrated in FIG. 2, all the electrodes 6, 7, 9, 15 and 17 are arranged on or in the carrier 13. But it is also conceivable, for example, a series circuit of capacitors instead of a counter electrode 15 with separate, to the

To perform annular electrodes connected capacitors, or the counter electrode 15 in shape

single, the respective annular electrodes

build associated electrodes. Between the metallic layer 11 of the membrane 1 and the counter electrode 15, an alternating voltage UO can now be applied. Due to the AC voltage in the

annular electrodes 6, 7, 8 with the radii pi

Induced voltages Ui.

The annular electrodes 6, 7, 8 each form together with the metallic layer 11 on the one hand and the Counter electrode 15 capacitors, or capacitors. For each of the annular electrodes 6, 7, 8 results in a series circuit of the capacitors, which are formed of counter electrode and annular electrode and metallic layer 11 and annular electrode.

The field lines are largely parallel, therefore, for the model of a plate capacitor can be applied. The capacitors in question are denoted by Ci ₁ or C ₂₁ . The capacitance of the capacitors C ₂ i is constant, whereas the capacitance of the

Capacitors Ci ₁ is variable due to the changing in a deflection of the membrane distance between the ring electrode and the metallic layer 11. Through this

Arrangement can parasitic effects in the measurement

be taken into account.

In the notation, the argument φ

omitted, since this dependency is not needed for the considered case.

The voltage Ui across the capacitors Ci _{1 is} calculated according to the voltage divider rule which follows from the series connection of the capacitors Ci ₁ and C ₂₁ :

Here denote ω the angular frequency of the AC voltage, Ci ₁ , C _21, the capacities of the arrangement of the

Ring electrode with the index i and the metallic layer 11, and the counter electrode 15th If one sets the relations of the capacities for

Plate capacitors, it follows from equation (11):

U _t {jώ)

(12) U _n d _{ + d ₂ / ε _r

In this case, ε _r denotes the relative dielectric constant of the substrate, which as a multiplier in capacity of each of the ring electrodes 6, 7, 8 and the

Counter electrode 15 formed capacitors received. The plate spacings of the capacitors Ci _f i and C ₂ , i are denoted by di and d ₂ , respectively.

Furthermore, for the distances: (13) d, = A (p _l ) + A_off,

In this case, A_offi denotes the offset displacement of the ith ring to the plane of the membrane. In other words, A_offi denotes the distance of the annulus to the undeflected membrane.

Substituting equation (12) into equation (13) and resolving after A \ p _t ) yields:

(14) A (P ₁ ) = ^ ^UXJω) -A off

K ^Pl) ε (U ₀ -U ₁ Uω)) - ^JJ>

Equation (14) can be used for a precise calibration. For this the membrane is e.g. by an external sound wave, or magnetic in harmonic

Vibrations offset, and it will be over the Capacitors Cn occurring voltage waveforms recorded. The voltage minima and maxima are determined separately for each capacitor from these voltage time courses. Advantageously, these can also be averaged. The difference of the minimum and maximum

Deflection gives twice the amplitude, the sum twice the offset:

(15a) 2Λ (p) = ^{2 2 U} '^ ^ώ) ^ ^d * ^U> ( ^jώ) ™ "

^Kμ>) ε (U ₀ -U, (jω) _{m! Α} ) ε (U ₀ -U, (jω) _m )

(15b) -IA off

The offsets determined according to (15) can be used in (14), the ratio - represents a substrate constant ε

and can be considered as a good approximation as constant. The substrate constant is available in all terms so that it can be used after calibration of the sensitivity if required.

Now consider a system consisting of three rings. By subtraction from the signals of two adjacent rings one obtains from (14):

J ₂ ^U ₀ ^(U ₃ U ^a) - ^U ₂ Un ⁾⁾

A (P ₃ ) _-A (p ₂ ) = _-ε ₍ _{Uo + UiUω) HUo _U2} ₍ _jω ₎₎

(15d) The offsets A_off i determined from (15b) for each ring are the same for an ideal design of the pressure measuring head, ie for parallelism of membrane and electrode carrier. If the parallelism is violated, the characteristic of the sensor becomes non-linear. Therefore, the variance of the measured offsets A_off i is a measure of the nonlinearity of the

Sensors.

A particularly efficient measure of the non-linearity can be formed from the ratio of the amplitude differences:

A (p ₂ ) -A ( _P1 ) (U ₂ (J (O) -U _x U ω)) (-U ₀ + U ₃ Qω))

₍₁₅ _e) ^A (P ₃₎ ^{"A (P} ₂₎ ^~ (CZ ₀ - t /, ^0" ω)) (CZ ₃ O ^'ω) - ^[/ ₂ C / ^"ω))

This ratio depends only on the average diameters Pi _r P2r P _{3 of} the rings. If there is an angular deviation, then a substantially reproducible arises

non-linear characteristic.

(U ₂ U ω) - U ^ ω)) (-U ₀ + U ₃ U ω))

K: = - ^•

(U ₀ -U ₁ (Yes)) (U ₃ (J ⁽ O) -U ₂ U ω))

(15f!

After measuring the ratio K can therefore be a

predefined characteristic curve selected and the sensor

Getting corrected. Therefore, it is useful from a lot of linearity errors afflicted sensors for a

Concrete construction present relationship between the voltage / pressure characteristic and the value K to determine and store in a database. In production, only k is calculated. In the memory of the arithmetic unit, such as a connected microcomputer then the corresponding or a lot more similar

Characteristic curves as a function of the parameter Cabled, and then the required characteristic is selected.

The value K can also be obtained online through accumulation of

Measured values and / or the fitting of parameters and the recording behavior are determined. For example, if the sensor is exposed to mechanical stress due to heating, the value K may change. In this case, the characteristic can be switched, or generally adapted to the changed value K. For this it makes sense to accumulate K over a longer period of time. Accordingly, in the invention, the pressure sensor with capacitive deflection sensors with annular, concentric and arranged at a distance from the membrane annular electrodes in which by an applied between the membrane and a counter electrode AC voltage Uo the frequency jω AC voltages Ui (jω), U ₂ (jω ), U ₃ (jω), where the amplitude of the induced AC voltage is detected by the displacement sensors as a measured quantity, adapted to determine the value of the parameter K according to the equation (15f) given above, a voltage / pressure characteristic based on the parameter K TO determine and then determine pressure values based on the determined characteristic curve.

It is also apparent from equation (15e) that the calibration and measurement procedure described above for capacitive displacement sensors can also be applied to other displacement sensors, provided that at least three centerline diaphragm displacement sensors are provided, the ratio of the differences in the measured deflections , respectively the

Displacement representative of measured values can be formed. This ratio, corresponding to the parameter K, is then used to determine a characteristic, such as by selection from a stored list of ratios. It is also possible to change the offset,

or to determine the distance of a circular ring to undeflected membrane A_off online. These occur e.g. due to temperature change, consequence would be a change in the sensitivity of the sensor. For correction, first the deflection of the innermost and the

considered subsequent ring.

-V ₀ (P ₁ )

^{~ A} - ^Off

(15g)

d ₂ U ₂ U ω)

-Vo (P ₂ ) = _{e (} U ₀ - U ₂ U ")) - ^A - ^Off

(15h)

This system of equations can be resolved to A_off. It follows: (15i)

A_OFF: d = ₂ (J ₀ (P ₂₎ (/ ^'0' ω) U _{0 +} J ₀ (P ₂₎ U ₁ (J ω) ω CZ ₂ O) + J ₀ _(Pl) CZ ₂ O ^" ω) CZ ₀

- J ₀ (P ₁ ) CZ ₁ O CO) CZ ₂ O ω)) / (ε (-J ₀ (p ₂ ) U _{0 +} J ₀ (P ₂ ) U ₀ U ₂ (J (O)

+ J ₀ (P ₂ ) CZ ₁ O CU) CZ ₀ - J ₀ (P ₂ ) c / O ω) cz ₂ θ ω) + J ₀ ( _Pl ) cz _o ² - J _o ( _Pl ) cz.o ω ) c / ₀

-J ₀ (P ₁ ) U ₂ (Jω) CZ _{0 +} J ₀ (P ₁ ) CZ ₁ OCO) CZ ₂ OCO)))

It should be noted that the Bessel function J ₀ (P ₂ ) should not be too small, because then the measurement accuracy decreases. Therefore, as can be seen from equations (15g) to (15i), it is convenient to choose the innermost and the subsequent ring with the radii pi and _pΣ . This means that the A_off can also be determined during operation. This is done over a longer period A_off

accumulated. Subsequently, A_off is corrected in the arithmetic unit, for example a microcomputer integrated in the sensor. Another way to determine the A_off value online is to read the reading,

preferably over the largest ring to compare with the measured value over a capacitive voltage divider and to close from the voltage difference to A_off.

According to a further development of the invention, therefore, the pressure sensor is provided with deflection sensors with annular, concentric and spaced from the membrane annular electrodes, in which by an applied between the membrane and a counter electrode AC voltage Uo the frequency jω AC voltages

Ul (jω), U2 (jω), U3 (jω) are induced as

Measured variable, the amplitude of the induced AC voltage is detected by the displacement sensors, and wherein the Calculator is adapted to the distance A_off between the annular electrodes to the membrane by equation (15i), in which again J ₀ a Bessel function, Pi and p _2, the mean radii of the smaller of the three annular electrodes, Ui and U ₂ in this

ε, the dielectric constant of the material between the counter electrode and the annular electrodes, and Uo denote the applied AC voltage, and / or by

Measurement of the voltage difference of the induced

AC voltage on at least one of the annular

Electrode and a capacitive voltage divider too

determine.

In the embodiment of the invention with capacitive

Auslenkungssensoren with annular, concentric and spaced from the membrane electrodes are in particular by the between the membrane and a

Counterelectrode applied AC voltage U ₀

AC voltages Ui induced, wherein as a measure of the amplitude of the induced AC voltage of the

Deflection sensors is detected, and wherein the deflection A (P ₁ ) and the distance A_offi of the ith annulus to the undeflected membrane are determined by the relationships (15a) and (15b), where p _{t is} the radius of the i-th annular electrode , d ₂ denotes the distance of the i-th annular electrode to the counter electrode and ε the dielectric constant of the medium between the i-th annular electrode and the counter electrode.

Generally speaking, with the calibration described above, the actual displacement as a function of obtained by the displacement sensors measured variable, the measured variable in the case of capacitive

Deflection sensors is given by the amplitude of the induced AC voltage. It is clear, however, that this calibration can also be transferred to deflection sensors based on other measurement principles.

Accordingly, in a more general development of the invention, a method for pressure measurement is provided, in which the membrane is set into harmonic oscillations, the values of the measured variable of the deflection sensors are determined at the deflection maxima of the membrane and, based on these values of the measured variable, a calibration of the deflection of the membrane in FIG

Dependence of the value of the measured variable is made.

In particular, a calibration according to equation (10c) can be carried out as described above.

The excitation of the resonant vibration may be in an external device, such as a Kundschen tube. Fig. 3 shows schematically such an arrangement for calibration.

As shown in FIG. 3, the speaker 19 is in

Slidably disposed longitudinally in a Kundt tube 18. By shifting the loudspeaker 19 in the Kundt tube 18 it is achieved that a standing wave is formed in the Kundt tube. As a result, at a defined distance between the opening of the Kundt tube 18 and the pressure sensor 10 arranged in front of the opening, a constant sound pressure is applied to the membrane 1 of the

Pressure sensor 10 acts. Furthermore, the phase and the frequency of the radiated sound waves, the Resonance frequency of the assembly 10 are aligned. From the resonance frequency, the diameter, the thickness and the modulus of elasticity of the membrane, its sensitivity can be calculated.

According to yet another embodiment of the invention, the pressure sensor 10 itself may be provided with means for exciting vibrations of the diaphragm 1. 4 shows schematically a pressure sensor 10 with such a device for exciting vibrations of the membrane 1 in the form of a coil 21. The coil 21 is in this example arranged centrally to the membrane on the support 13, on which also the annular electrodes 6, 7, 8 are located. In order to be able to exert a force on the membrane via the magnetic field generated by the coil by means of a current, the membrane is here provided with a magnetizable material at least in the region of the field of the coil. The coil 21 can now be energized with an alternating current whose frequency is changed until the periodically attracted by the coil 21 in this way 1 in

Resonance vibration device. Alternatively, for example, piezoelectric

Actuators for vibration excitation of the membrane 1 possible.

By the means for exciting vibrations of the membrane, the pressure sensor as a self-calibrating

Sensor equipped in field use,

for example, calibrated at fixed intervals controlled by the computing device 9 itself. Unlike in 4, the device for exciting vibrations of the membrane can also act on the membrane from the outside. This can be favorable in order to avoid or at least reduce signal couplings to the deflection sensors.

Furthermore, the resonance frequency and the voltage T are also slightly dependent on the temperature. Therefore, in the

Pressure sensor in an advantageous manner as shown in Fig. 2, a temperature sensor 24 may be provided. With the values measured by this temperature sensor, the previously determined value for the voltage T and / or the determined pressures can then be corrected, or the

temperature-dependent change of the voltage T in the

Calculation of the pressure by the computing device

be included. For this purpose, for example, a corresponding characteristic can be stored in the computing device.

In real-time operation, the deflections for each radius pi. calculated according to (14) and the offset subtracted.

Among other things, for constructive reasons, it has proved to be cheaper, the deflection on the axis A (0,0) not directly to measure, which is why the invention

Deflection is respectively detected differently from the center of the membrane spaced surface areas of the membrane. It is favorable, the measurements by a

Summarize bestfitalgorithm. It is the Deflection A (O) is sought, which produces the smallest mean squared error ^σ :

After differentiation of (16) and solving the equation, one obtains the following displacement A (O) for the smallest quadratic error:

ΣJO (Pp ₁ ) A (P ₁ )

[H) A (O) =

ΣJOissp,) ²

In other words, according to this development, the computing device of the pressure sensor is adapted to perform the calculation of the deflection A (O) in the middle of the membrane according to the relationship (17), wherein in equation (17) p _{t is} generally the distance of the i th

Displacement sensor from the center of the diaphragm, A (p _t ) the

Deflection of the membrane at the location of the i-th

Deflection sensor, J _{0 is} the Bessel function of the first type with the index 0 and ß a constant that from the

The boundary condition follows that the Bessel function has a zero at the edge of the membrane.

The advantage of this calculation method is that caused in particular by mounting tolerances

Measurement errors are averaged. A weighted sum of the measured values is obtained.

Claims

claims

1. Pressure sensor comprising an elastic

deformable, fixed at its edge and deflectable due to a pressure difference membrane, and at least two deflection sensors, wherein the deflection sensors detect the deflection of each differently from the center of the membrane spaced surface areas of the membrane, and wherein the pressure sensor comprises a computing device, which from the of the deflection sensors

detected deflections a deflection in the middle of the membrane and from this a value for the pressure on the diaphragm pressure difference calculated.

2. Pressure sensor according to the preceding claim,

characterized in that the computing means is adapted to the deflection of the membrane in the middle by a bestfit algorithm from the detected by the deflection sensors

Calculate deflections.

3. Pressure sensor according to the preceding claim, wherein the membrane is circular and wherein the

Computing device is set up to the

Calculation of the deflection A (O) in the middle of the membrane according to the following relationship

to carry out:

where p _{t is} the distance of the ith displacement sensor from the center of the diaphragm, A (p,) the displacement of the Membrane at the measuring location of the ith displacement sensor, Jo the Bessel function of the first type with the index 0 and ß a constant that follows from the boundary condition that the Bessel function has a zero at the edge of the membrane.

4. Pressure sensor according to one of the preceding claims, characterized by capacitive

Deflection sensors, which changes in voltage on the basis of a change in the capacitance caused by a deflection of the membrane

Capacitor whose one electrode is connected to the membrane or is formed by the membrane.

5. Pressure sensor according to the preceding claim, wherein the deflection of the membrane with capacitive

Displacement sensors with annular, concentric and spaced from the membrane annular electrodes is measured, in which by a between the membrane and a

Alternating voltage U _{0 of} the frequency jω alternating voltages Ui (jω), U ₂ (jω), U ₃ (jω) are induced, the measured variable being the

Amplitude of the induced AC voltage is detected by the displacement sensors, and wherein the

Computing device is adapted to the value of a parameter K according to the equation

(U ₂ (JCO) - U ₁ U ω)) (-t / ₀ + C / ₃ (/ ω))

K ^{: "~} (CZ ₀ - U ₁ U ω)) (CZ ₃ C / ω) - U ₂ U ω)) to determine a voltage / pressure characteristic of the parameter K, and subsequently to determine pressure values based on the determined characteristic curve.

6. Pressure sensor according to one of the two preceding

Claims, wherein the deflection of the membrane with capacitive deflection sensors with annular, concentric and arranged at a distance from the membrane annular electrodes is measured, in which by an applied between the membrane and a counter electrode AC voltage Uo the frequency jω AC voltages Ui (jω), U _2nd (jω), U ₃ (jω) are induced, the measured variable being the

Amplitude of the induced AC voltage is detected by the displacement sensors.

7. Pressure sensor according to one of the preceding claims, with deflection sensors with annular,

concentric and arranged at a distance from the membrane annular electrodes, in which by an applied between the membrane and a counter electrode AC voltage Uo the frequency jω AC voltages Ul (jω), U2 (jω),

U3 (jω) are induced, wherein the amplitude of the induced AC voltage is detected by the displacement sensors as a measured variable, and wherein the computing device is adapted to the

Distance A_off between the annular electrodes to the membrane by the equation A_off: = d ₂ (-J ₀ (P ₂ ) U ₁ (J (O) U _{0 +} J ₀ (P ₂ ) U _x U (O) U ₂ (J ω) + J ₀ (P ₁ ) U ₂ (J (O) U ₀

- J ₀ (P ₁ ) U _x U (O) u ₂ u (o)) / (ε (-J ₀ (P ₂ ) U ₀ ² + J ₀ (P ₂ ) t / ₀ t / ₂ (/ ω )

+ -Z ₀ (P ₂ ) f / .O ^' ω) U ₀ - J ₀ (P ₂ ) U ₁ U ⁽ O) U ₂ U (O) ₊ J ₀ (P ₁ ) U ₀ - J ₀ (P _x ) U _x U ω) U ₀ - J ₀ (P ₁ ) U ₂ U (O) U _{0 +} J ₀ (P _x ) U _x U ⁽ o) U ₂ U (O)))

in which Jo is a Bessel function, pi and p ₂ the

middle radii of the smaller of the three

annular electrodes, Ui and U ₂ in this

induced ring-shaped electrodes

Alternating voltages, ε the dielectric constant

of the material between the counter electrode and the

annular electrodes, and Uo the applied

Designate AC voltage,

and / or by measuring the voltage difference of

induced AC voltage on at least one of the annular electrode and a capacitive

Determine voltage divider.

8. Method for measuring a pressure by means of a

Pressure sensor, which has an elastically deformable, fixed at its edge and due to a

Pressure difference deflectable membrane, and at least two deflection sensors, wherein the

Deflection sensors the deflection of each

spaced apart from the center of the membrane

Cover surface areas of the membrane, and wherein

the pressure sensor comprises a computing device with which of the deflection sensors

detected deflections a deflection in the middle of the membrane and from this a value for on the

Membrane load bearing pressure difference is calculated.

9. Method according to the preceding claim, in which the diaphragm is harmonically oscillated, the values of the measured variable measured by the deflection sensors are determined at the deflection maxima of the diaphragm and, on the basis of these values

Measured variable is carried out a calibration of the deflection of the membrane as a function of the value of the measured variable.

10. The method according to the preceding claim, wherein the deflection of the membrane with capacitive

Counterelectrode applied AC voltage Uo

AC voltages U _{1 are} induced, wherein the measured variable is the amplitude of the induced

AC voltage is detected by the displacement sensors, and wherein the deflection A (p _t ) and the distance

A_offi of the i-th annulus to the undeflected membrane by relationships

2A (P ₁ ) = ^ ^UXJω) - ^ - ^{UXJω) ™} , and

ε {U ₀ -UXJώ) _mm ) ε (U ₀ -U, Uω) _mm )

_ U ₂ U, (Jω \ U, Uω \

-2A_off, =

ε (U ₀ -U, (jω) _max ) ε (U ₀ -U ₁ (jω) _mn )

it is determined

where P _{1 is} the radius of the ith annular

Electrode, d ₂ the distance of the ith annular electrode to the counter electrode and ε the

Dielectric constant of the medium between the ith annular electrode and the counter electrode describe.

11. The method according to any one of the preceding claims, wherein for calibration, the diaphragm is set at a known pressure difference in a resonant vibration and the resonance frequency of this resonant vibration is measured, and wherein based on this

Resonance frequency, the mechanical stress is determined, which the proportionality factor between a deflection of the membrane and a on the

Membrane acting force determined, and wherein on the basis of the proportionality factor

Conversion rule is created, which transforms signals measured by the distance sensor into a pressure difference acting on the membrane.

12. The method according to the preceding claim, wherein the proportionality constant T based on

relationship

where P _{1113x represents} the location at the fixed edge of the membrane as measured from the center of the membrane, and a> _res _denote the resonance frequency of the membrane and p _malenal the mass _{coating of} the membrane.

13. The method according to the preceding claim, characterized in that the determination of the pressure by multiplying the determined

Proportionality constant T with the measured deflection in the middle of the membrane and one before determined pre-factor occurs.

14. Method according to one of the two preceding

Claims, characterized in that measured with a temperature sensor of the pressure sensor temperatures and the temperature-dependent change in the proportionality constant T is included in the calculation of the pressure by the computing device.