DE102020207895A1 - Method and sensor system for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor - Google Patents

Abstract

The invention relates to a method for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor, with a sensor capacitance of the pressure sensor having a non-linear dependency on an applied pressure, comprising the steps: Generating a digitized raw measured value for an applied pressure by evaluating the sensor capacitance of the pressure sensor and using an analog-to-digital converter and• determining a measured pressure value from the digitized raw measured value by means of an assignment function, the assignment function being formed by approximating the sensor capacitance using a model based on a parallel connection of at least two plate capacitors, each with a pressure-dependent capacitance, wherein the assignment function has a quotient of a first polynomial and a second polynomial and wherein the first polynomial and the second polynomial are each at least square of the digitized raw measurement value ert depend. The invention further relates to a corresponding sensor system.

Description

Technical area

The invention relates to a method for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor, a sensor capacitance of the pressure sensor having a non-linear dependence on an applied pressure.

The invention also relates to a corresponding sensor system.

State of the art

Pressure sensors are used more and more frequently in products such as smartphones, smartwatches, fitness trackers or in applications in the area of loT - Internet of Things. The use cases are not limited to weather measurements or the estimation of the altitude. Rather, applications are also conceivable in which, for example, the floor of a building is reliably identified from which an emergency number has been dialed. This requires very high levels of accuracy. For fitness and sports applications, resolutions in the centimeter range are required.

Current capacitive pressure sensors for consumer applications mostly consist of a sensor element, often a micromechanical sensor element, and sensor electronics, in many cases implemented in an ASIC - Application Specific Integrated Circuit. A sensor capacitance of the sensor element changes under the action of an applied pressure. The sensor electronics record a parameter for the capacitance and convert this into a digitized raw measured value for the applied pressure. Since the capacitance value of the sensor capacitance depends non-linearly on the applied pressure and an exact mathematical description of this relationship is extremely complex and in many cases even not possible, approximations are required for this. As a result, a digitized raw measured value is assigned to a measured pressure value for which there is as proportional a relationship as possible with the pressure actually applied.

It is known from practice to approximate the sensor capacitance of a pressure sensor with a higher order polynomial. But even with an approximation with a fourth order polynomial, a not inconsiderable error remains.

In another known solution, the pressure sensor is modeled by an ideal parallel plate capacitor and a pressure value is converted using a formula of the following form: $$p_{Out}={\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="DE102020207895A1\_0014.png,DE102020207895A1\_0015.png"\; state="\{\{state\}\}">p</figure-callout>}}_0+\frac{k_1}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">k</figure-callout>}}_2+p_{in}}$$

Here, pout is the measured pressure value, po is a pressure offset, k ₁ and k _{2 are} constants and pin is the digitized raw measured value. However, this relationship also only inadequately depicts the behavior that occurs in reality and a clear error remains.

Disclosure of the invention

• • Erzeugen eines digitalisierten Rohmesswerts für einen anliegenden Druck durch Auswerten der Sensorkapazität des Drucksensors und unter Verwendung eines Analog-Digital-Wandlers und
• • Bestimmen eines gemessenen Druckwerts aus dem digitalisierten Rohmesswert mittels einer Zuordnungsfunktion,

wobei die Zuordnungsfunktion über eine Approximation der Sensorkapazität durch ein Modell auf Basis einer Parallelschaltung aus mindestens zwei Plattenkondensatoren mit einer jeweils druckabhängigen Kapazität gebildet ist, wobei die Zuordnungsfunktion einen Quotienten aus einem ersten Polynom und einem zweiten Polynom aufweist und wobei das erste Polynom und das zweite Polynom jeweils mindestens quadratisch von dem digitalisierten Rohmesswert abhängen.In one embodiment, the present invention provides a method for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor, a sensor capacitance of the pressure sensor having a non-linear dependence on an applied pressure, comprising the steps:

• • Generating a digitized raw measured value for an applied pressure by evaluating the sensor capacitance of the pressure sensor and using an analog-to-digital converter and
• • Determination of a measured pressure value from the digitized raw measured value by means of an assignment function,

wherein the assignment function is formed via an approximation of the sensor capacitance by a model based on a parallel connection of at least two plate capacitors, each with a pressure-dependent capacitance, wherein the assignment function has a quotient of a first polynomial and a second polynomial and wherein the first polynomial and the second polynomial each depend at least quadratically on the digitized raw measured value.

• • einen kapazitiven Drucksensor mit einer Sensorkapazität, wobei die Sensorkapazität von einem anliegenden Druck nichtlinear abhängig ist,
• • einen Analog-Digital-Wandler, der zum Erzeugen eines digitalisierten Rohmesswerts durch Digitalisieren eines durch den Drucksensor gewonnenen Rohmesswerts ausgebildet ist,
• • eine Zuordnungseinheit, die zum Zuordnen eines gemessenen Druckwerts zu dem digitalisierten Rohmesswert mittels einer Zuordnungsfunktion ausgebildet ist,

wobei die Zuordnungsfunktion über eine Approximation der Sensorkapazität durch ein Modell auf der Basis einer Parallelschaltung aus mindestens zwei Plattenkondensatoren mit jeweils einer druckabhängigen Kapazität gebildet ist, wobei die Zuordnungsfunktion einen Quotienten aus einem ersten Polynom und einem zweiten Polynom aufweist und wobei das erste Polynom und das zweite Polynom jeweils mindestens quadratisch von dem digitalisierten Messwert abhängen.In a further embodiment, the present invention provides a sensor system for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor, comprising:

• • a capacitive pressure sensor with a sensor capacitance, whereby the sensor capacitance is non-linearly dependent on an applied pressure,
• • an analog-to-digital converter which is designed to generate a digitized raw measured value by digitizing a raw measured value obtained by the pressure sensor,
• • an allocation unit which is designed to allocate a measured pressure value to the digitized raw measured value by means of an allocation function,

wherein the assignment function is formed via an approximation of the sensor capacitance by a model based on a parallel connection of at least two plate capacitors, each with a pressure-dependent capacitance, wherein the assignment function has a quotient of a first polynomial and a second polynomial and wherein the first polynomial and the second Polynomials each depend at least quadratically on the digitized measured value.

In one embodiment, this sensor system is designed to carry out the method.

According to the invention, it has been recognized that a relatively simple model of the sensor capacitance of a capacitive pressure sensor based on a parallel connection of several plate capacitors, each with a pressure-dependent capacitance, allows the real behavior of the sensor capacitance to an applied pressure to be simulated very precisely. This allows an assignment function to be specified which enables a measured pressure value to be assigned relatively precisely to a raw measured value of the capacitive pressure sensor.

A pressure-dependent capacitance C of an ideal plate capacitor can be described by the fact that the plate spacing of the ideal plate capacitor changes linearly with an applied pressure p. The pressure-dependent capacity can thus be calculated as follows: $$\mathrm{C.}=\epsilon \cdot \frac{\mathrm{A.}}{d_0-x\cdot p}$$

Here, ε is the permittivity, A is the area of the plates and d _{0 is} the plate spacing in the state of rest. x can be viewed as a constant factor that describes a correlation between a change in distance and an applied pressure.

This equation can be solved for the pressure p: $$p=\frac{d_0}{x}-\frac{\epsilon \cdot \mathrm{A.}}{x}\cdot \frac{1}{\mathrm{C.}}$$

bringt eine Verbesserung, kann das Vorhandensein deutlicher Fehler aber nicht vermeiden.If a real capacitive pressure sensor would behave like an ideal plate capacitor, the above equation could be parameterized by recording the capacitance C at two different pressures. Since a real capacitive sensor does not behave like an ideal plate capacitor, this modeling results in not inconsiderable errors. An addition of a pressure-independent capacitance value Co to the capacitance value C of the above equation, namely: $$\mathrm{C.}=\epsilon \cdot \frac{\mathrm{A.}}{d_0-x\cdot p}+{\mathrm{C.}}_0$$

brings an improvement, but cannot avoid the presence of clear errors.

If a model is used in which several pressure-dependent plate capacitors (which can also be viewed as “virtual” pressure sensors) are connected in parallel, the real behavior of the pressure sensor can be approximated much better. A parallel connection of two "virtual" pressure sensors leads to the following capacity: $$\mathrm{C.}=\mathrm{C.}\text{'}-\mathrm{C.}\text{''}=\epsilon \cdot \frac{\mathrm{A.}\text{'}}{d_0^{\text{'}}-x\text{'}\cdot p}+{\mathrm{C.}}_0^{\text{'}}+\epsilon \cdot \frac{\mathrm{A.}\text{''}}{d_0^{\text{''}}-x\text{''}\cdot p}+{\mathrm{C.}}_0^{\text{''}}$$

This equation can be solved for the pressure p and can be represented in the following form: $$p=\frac{pOlynOm1\left(\mathrm{C.}\right)}{pOlynOm2\left(\mathrm{C.}\right)}$$

The maximum order of the two polynomials corresponds to the number of “virtual” pressure sensors. If two “virtual” pressure sensors are used, a quotient of second-order polynomials is created - depending on the parameterization.

This approach is used in the present invention. For this purpose, the sensor capacitance is approximated by a model based on a parallel connection of at least two plate capacitors with pressure-dependent capacitance. As a result, an assignment function can be formed with which an assignment of a pressure value to a raw measured value of the pressure sensor is possible. The assignment function has a quotient of a first polynomial and a second polynomial, the first polynomial and the second polynomial each depending at least quadratically on the digitized raw measured value.

The “digitized raw measured value” indicates a value that represents the size of the sensor capacitance at a pressure applied to the pressure sensor. This digitized raw measured value can be in the form of a capacitance value. However, the digitized raw measured value can also include a voltage that is used as a bridge voltage on a Wheatstone Bridge being tapped. The digitized raw measured value can also be characterized by a frequency that an oscillating circuit with the sensor capacitance assumes as the resonance frequency. This short exemplary list, which is neither conclusive nor restrictive, shows how flexibly the digitized raw measured value can be generated and displayed. Depending on the digitized raw measured value, the coefficients of the first and second polynomials will have to be adapted accordingly.

The “measured pressure value” is a pressure value that is calculated by approximating the characteristic curve of the pressure sensor by connecting several “virtual” pressure sensors in parallel. The measured pressure value corresponds approximately to the actually applied pressure value, with an approximation error occurring. However, this approximation error is small, preferably less than 0.1%, particularly preferably less than 0.01%.

In one embodiment, the order of the first polynomial and / or the order of the second polynomial is in each case equal to the number of parallel-connected plate capacitors of the approximation. This enables a good approximation of the real behavior of the pressure sensor to be achieved.

The approximation of the real behavior of the pressure sensor becomes more and more precise as the number of “virtual” pressure sensors increases. However, every additional "virtual" pressure sensor means an increase in the order of the polynomials, so that the calculation effort can be considerable with a large number of "virtual" pressure sensors. In one embodiment, the number of plate capacitors can therefore be limited to a maximum of five. In one embodiment, the approximation of the sensor capacitance is formed by three plate capacitors, so that here the first polynomial and / or the second polynomial is a third order polynomial. In this way, a good approximation is created with at the same time manageable calculation effort.

The model's plate capacitors can be parameterized as required. In one embodiment, a rough approximation of the sensor capacitance is carried out using a first plate capacitor of the model from the at least two plate capacitors, while a second plate capacitor from the at least two plate capacitors improves the rough approximation. If the model includes a third plate capacitor, in this embodiment the third plate capacitor further improves the already improved approximation, and so on. This makes the approximation more accurate. In this way, a model is created whose approximation can be reliably more accurate with each additional plate capacitor.

• könnte „für mindestens zwei Potenzen“ bedeuten, dass mindestens zwei der Parameter N₀, N₁, N₂ und N₃ und/oder mindestens zwei der Parameter D₀, D₁, D₂ und D₃ ungleich 0 sind. Eine derartige Parametrierung bietet einen guten Kompromiss zwischen Berechnungsaufwand und Genauigkeit der Approximation. Der Fall „für mindestens zwei Potenzen größer als 0“ könnte bedeuten, dass mindestens zwei der Parameter N₁, N₂ und N₃ und/oder mindestens zwei der Parameter D₁, D₂ und D₃ ungleich 0 sind. Dabei kann ergänzend der Parameter D₀ als ungleich 0 festgelegt sein. Eine derartige Parametrierung verbessert die Approximation bei gleichzeitig vertretbarem Berechnungsaufwand.

In a further embodiment, the first polynomial and / or the second polynomial have coefficients for at least two powers, preferably coefficients for at least two powers greater than 0, each unequal 0. If, for example, the approximation is made by three “virtual” sensors and the quotient from the first and second polynomial has the following form: $$p_{lin}=\frac{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="DE102020207895A1\_0014.png,DE102020207895A1\_0015.png"\; state="\{\{state\}\}">N</figure-callout>}}_0+{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="DE102020207895A1\_0015.png,DE102020207895A1\_0016.png"\; state="\{\{state\}\}">N</figure-callout>}}_1\cdot adcp+{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">N</figure-callout>}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+N_3\cdot adc{p}^3}{{\mathrm{D.}}_0+{\mathrm{D.}}_1\cdot adcp+{\mathrm{D.}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+{\mathrm{D.}}_3\cdot adc{p}^3}$$

• could mean “for at least two powers” that at least two of the parameters N ₀ , N ₁ , N ₂ and N ₃ and / or at least two of the parameters D ₀ , D ₁ , D ₂ and D _{3 are} not equal to 0. Such a parameterization offers a good compromise between calculation effort and accuracy of the approximation. The case “for at least two powers greater than 0” could mean that at least two of the parameters N ₁ , N ₂ and N ₃ and / or at least two of the parameters D ₁ , D ₂ and D _{3 are} not equal to 0. In addition, the parameter D ₀ can be defined as not equal to 0. Such a parameterization improves the approximation while at the same time making the computation work justifiable.

In one embodiment, with a parallel connection of n virtual sensors - with n as a natural number greater than or equal to 3 - the coefficient for the nth power in the first polynomial is equal to 0 and all other coefficients are not equal to 0. With the form of the assignment function and shown above with n = 3 it could result that N _{3 is} equal to 0 and the coefficients N ₀ , N ₁ , N ₂ , D ₀ , D ₁ , D ₂ and D _{3 are} each not equal to 0. The approximation can thus be further improved.

In one embodiment, with a parallel connection of n virtual sensors - with n as a natural number greater than or equal to 2 - all coefficients in the first polynomial and the second polynomial are not equal to 0 for all powers. This allows the approximation to be improved even further.

In one embodiment, coefficients of the first polynomial and / or coefficients of the second polynomial are example-specific or type-specific, coefficients for powers of lower order are preferably example-specific. "Specimen-specific" means that the coefficients have been determined with the specific pressure sensor in which a measured pressure value is assigned to a raw measured value. The determination of specimen-specific parameters can, for example, during a calibration measurement after completion of the sensor or during an initial start-up of the sensor at various known pressures applied. "Type-specific" means that the coefficients are determined with one or more identical pressure sensors and not with a specific pressure sensor.

können in einer Ausführungsform die Koeffizienten N₀, N₁, N₂, D₁ und D₂ jeweils exemplarspezifisch sein. In einer alternativen Ausführungsform können die Koeffizienten N₀, N₁, N₂ und D₁ jeweils exemplarspezifisch sein. In einer weiteren alternativen Ausführungsform können die Koeffizienten N₀, N₁, N₂, D₁ und D₃ jeweils exemplarspezifisch sein. Bei all diesen Ausführungsformen von exemplarspezifischen Koeffizienten kann der Koeffizient D₀ zusätzlich ungleich 0 gewählt sein.With a representation of the assignment function in the form $$p_{lin}=\frac{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="DE102020207895A1\_0014.png,DE102020207895A1\_0015.png"\; state="\{\{state\}\}">N</figure-callout>}}_0+{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="DE102020207895A1\_0015.png,DE102020207895A1\_0016.png"\; state="\{\{state\}\}">N</figure-callout>}}_1\cdot adcp+{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">N</figure-callout>}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+N_3\cdot adc{p}^3}{{\mathrm{D.}}_0+{\mathrm{D.}}_1\cdot adcp+{\mathrm{D.}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+{\mathrm{D.}}_3\cdot adc{p}^3}$$

In one embodiment, the coefficients N ₀ , N ₁ , N ₂ , D ₁ and D _{2 can} each be specific to the example. In an alternative embodiment, the coefficients N ₀ , N ₁ , N ₂ and D _{1 can} each be example-specific. In a further alternative embodiment, the coefficients N ₀ , N ₁ , N ₂ , D ₁ and D _{3 can} each be specific to the example. In all of these embodiments of example-specific coefficients, the coefficient D _{0 can} also be selected to be unequal to 0.

In one embodiment, poles of the assignment function are arranged outside a measuring range of the sensor. Poles of the assignment function arise when the second polynomial has zeros. These poles lead to discontinuities in the assignment function and to digitized raw measured values that cannot be clearly assigned to a measured pressure value. By arranging the poles outside the measuring range of the sensor, the effects of the poles on the assignment can be avoided. The poles can be positioned or selected in such a way that the poles remain outside the measuring range even if there is a fluctuation in ambient conditions, signs of aging and / or other changes in the framework conditions of a pressure measurement. In this way, the reliability can be further improved.

According to one embodiment, the lower limit of the measurement range is less than or equal to 50 kPa, according to another embodiment less than or equal to 30 kPa and according to a further embodiment less than or equal to 20 kPa. The upper limit of the measurement range is greater than or equal to 100 kPa according to one embodiment, greater than or equal to 110 kPa according to another embodiment and greater than or equal to 150 kPa according to a further embodiment.

und mehrere Koeffizienten auf, wobei die Koeffizienten reelle Zahlen sind. Diese Darstellung bietet insbesondere dahingehend Vorteile, dass die Koeffizienten der einzelnen Potenzen problemlos bestimmt und festgelegt werden können.The assignment function can be represented in various ways as long as the assignment function has a quotient of a first polynomial and a second polynomial. In one embodiment, however, the assignment function for the measured pressure value has the form: $$p_{lin}=\frac{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="DE102020207895A1\_0014.png,DE102020207895A1\_0015.png"\; state="\{\{state\}\}">N</figure-callout>}}_0+{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="DE102020207895A1\_0015.png,DE102020207895A1\_0016.png"\; state="\{\{state\}\}">N</figure-callout>}}_1\cdot adcp+{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">N</figure-callout>}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+N_3\cdot adc{p}^3}{{\mathrm{D.}}_0+{\mathrm{D.}}_1\cdot adcp+{\mathrm{D.}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+{\mathrm{D.}}_3\cdot adc{p}^3}$$

and a plurality of coefficients, the coefficients being real numbers. This representation offers advantages in particular in that the coefficients of the individual powers can be easily determined and fixed.

und mehrere Nullstellen und mehrere Polstellen auf, wobei die Polstellen vorzugsweise außerhalb eines Messbereichs des Sensors angeordnet sind. Diese Darstellung bietet den Vorteil, dass Polstellen einfach ermittelt werden können.In one embodiment, the assignment function for the measured pressure value (p _lin ) has the form: $$p_{lin}=k_{\mathrm{P.}lin}\cdot \frac{\left(adcp-{\mathrm{<figure-callout\; id="1"\; label="Z"\; filenames="DE102020207895A1\_0015.png,DE102020207895A1\_0016.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{1,}\mathrm{P.}lin}\right)\left(adcp-{\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\text{2}\text{,}\mathrm{P.}lin}\right)\left(adcp-Z_{\text{3}\text{,}\mathrm{P.}lin}\right)}{\left(adcp-{\mathrm{P.}}_{\mathrm{1,}\mathrm{P.}lin}\right)\left(adcp-{\mathrm{P.}}_{\text{2}\text{,}\mathrm{P.}lin}\right)\left(adcp-{\mathrm{P.}}_{\text{3}\text{,}\mathrm{P.}lin}\right)}$$

and a plurality of zero points and a plurality of poles, the poles preferably being arranged outside a measuring range of the sensor. This representation offers the advantage that poles can be easily determined.

In one embodiment, the sensor system for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor comprises a host system that is designed to read out a digitized raw measured value and / or a measured pressure value via an interface and / or in which the assignment unit is at least partially implemented . The host system can interact with the sensor system and / or control the sensor system. In one embodiment, the host system can at least partially implement components of the sensor system. These components can include the allocation unit. By using a host system and the computing resources that are usually better there, faster calculations are possible.

In one embodiment, the pressure sensor comprises sensor electronics. This sensor electronics can comprise a non-volatile memory. In one embodiment, coefficients of the first and second polynomials are stored in the non-volatile memory, which coefficients can be loaded from the non-volatile memory for the assignment of the measured pressure value to a raw measured value. In another embodiment, zeros and poles of the assignment function are stored in the non-volatile memory, which can be loaded from the non-volatile memory for the assignment of the measured pressure value to a raw measured value.

The values stored in the non-volatile memory can have a wide variety of bit widths. The larger the bit width, the more precise the results are. However, the computational effort increases as the bit width increases. In one embodiment, the bit width of the values stored in the non-volatile memory is therefore not greater than 32 bits, in a further embodiment not greater than 24 bits.

The sensor electronics can be implemented in various ways. In one embodiment, the sensor electronics are implemented by hardware. In another embodiment, the sensor electronics are implemented by a combination of software and hardware. An ASIC — Application Specific Integrated Circuit — can be used, it being possible for the ASIC to contain a microprocessor core and / or a signal processor core.

Measured pressure values that have been assigned to a raw measured value by embodiments of the method or the sensor system can be used in further calculations. In this way, a measured pressure value can be temperature-compensated or error-compensated in some other way. The measured pressure value or the error-compensated measured pressure value can then be used in an application that runs on the host system, for example. For example, an application can determine a floor of a building or a change in the floor, to name just a single example from a multitude of possibilities.

Further important features and advantages of the invention emerge from the subclaims, from the drawings, and from the associated description of the figures on the basis of the drawings.

It goes without saying that the features mentioned above and those yet to be explained below can be used not only in the respectively specified combination, but also in other combinations or on their own, without departing from the scope of the present invention.

Preferred designs and embodiments of the invention are shown in the drawings and are explained in more detail in the following description, with the same reference symbols referring to the same or similar or functionally identical components or elements.

Figure list

• 1 ein Fehlerdiagramm für eine mittels Polynom vierter Ordnung approximierten Kennlinie eines bekannten Drucksensors,
• 2 ein Fehlerdiagramm für eine Kennlinie eines Drucksensors, die in bekannter Weise als Plattenkondensator approximiert ist,
• 3 ein Diagramm einer genormten Kapazität eines idealen Plattenkondensators und eines realen Drucksensors,
• 4 ein Ablaufdiagramm mit Schritten einer Ausführungsform eines erfindungsgemäßen Verfahrens,
• 5 ein Fehlerdiagramm einer Approximation gemäß einer Ausführungsform des erfindungsgemäßen Verfahrens,
• 6 ein Blockdiagramm mit Funktionseinheiten einer Ausführungsform eines erfindungsgemäßen Sensorsystems,
• 7 eine beispielhafte Ausführungsform eines kapazitiven Drucksensors, dessen Rohmesswerte bei dem erfindungsgemäßen Verfahren zugeordnet werden können und
• 8 ein Schaltbild mit einer Parallelschaltung dreier Plattenkondensatoren zur Approximation der Sensorkapazität.

It shows:

• 1 an error diagram for a characteristic curve of a known pressure sensor approximated by means of a fourth order polynomial,
• 2 an error diagram for a characteristic curve of a pressure sensor, which is approximated in a known manner as a plate capacitor,
• 3 a diagram of a standardized capacitance of an ideal plate capacitor and a real pressure sensor,
• 4th a flowchart with steps of an embodiment of a method according to the invention,
• 5 an error diagram of an approximation according to an embodiment of the method according to the invention,
• 6th a block diagram with functional units of an embodiment of a sensor system according to the invention,
• 7th an exemplary embodiment of a capacitive pressure sensor, the raw measured values of which can be assigned in the method according to the invention and
• 8th a circuit diagram with a parallel connection of three plate capacitors to approximate the sensor capacitance.

Embodiments of the invention

the 1 and 2 represent error diagrams for known approximations of the characteristic curve of a pressure sensor, whereby a pressure error is plotted against the applied pressure and the axis labels each have kilo-Pascal as a unit. at 1 is an approximation with a fourth order polynomial, at 2 an approximation was used as an ideal plate capacitor with a pressure-independent capacitance component. It can be seen that a not insignificant approximation error remains.

3 shows a diagram in which a standardized capacity is plotted against an applied pressure in kilo-Pascal. The upper, dashed curve represents the case in which the pressure sensor is modeled by a plate capacitor, the plate spacing of which changes linearly with an applied pressure. The lower, solid curve represents a real characteristic of a pressure sensor. It can be seen that the real conditions deviate from the behavior of an ideal plate capacitor over large parts of the measuring range.

4th shows a flow chart of an embodiment of a method according to the invention. In step S1 a digitized raw measured value is generated for a pressure that is applied to a sensor element of a capacitive pressure sensor. For the Generating the digitized raw measured value, the sensor capacity of the pressure sensor is evaluated and an analog-to-digital converter is used. In step S2 parameters of an assignment function, for example from a non-volatile memory, are loaded, the assignment function assigning a raw measured value to a measured pressure. The assignment function is formed by a model based on a parallel connection of at least two plate capacitors and has a quotient of a first polynomial and a second polynomial. These parameters can be coefficients of powers of the raw measured value or zeros and poles of the assignment function. In step S3 a measured pressure is determined from the digitized raw measured value by means of the assignment function.

5 shows an error diagram in which an error is plotted against an applied pressure, the axis labeling in each case referring to values in kilo-Pascal. The error describes the deviation of the measured pressure value, which has been determined by an embodiment of the method according to the invention, and an actually applied pressure. It can be seen that the approximation by the assignment function represents a very good approximation of the real behavior.

hat. Die Koeffizienten N₀, N₁, N₂, N₃, D₀, D₁, D₂ und D₃ sind jeweils reelle Zahlen, wobei der Index jeweils die Potenz der Variabel adcp wiedergibt. 6th shows a block diagram with functional units of an embodiment of a sensor system according to the invention. The sensor system 1 includes a pressure sensor 2 , a temperature sensor 3 , a sensor electronics 4th and a host system 5 . The pressure sensor 2 is made by an excitation signal generator 6th acted upon by an excitation signal. The pressure sensor 2 can be connected in a Wheatstone bridge, not shown here, with excitation signal generator 6th can be connected to one end or to both ends of the Wheatstone bridge and the bridge voltage can be tapped as an analog sensor signal. This analog sensor signal forms a raw measured value obtained by the sensor 7th that into an analog-to-digital converter 8th is entered. The analog-to-digital converter 8th may additionally comprise an amplifier and / or analog filter circuits. The analog-to-digital converter 8th is a digital filter 9 downstream, which can carry out a digital filtering. At the output of this digital filter 9 if a digitized raw measured value adcp is available, it is stored in an allocation unit 10 is entered. The allocation unit 10 _{assigns a measured pressure value p lin} to a raw measured value adcp by means of an assignment function, the assignment function having a quotient of a first polynomial f ₁ and a second polynomial f ₂ and the form: $$p_{lin}=\frac{f_1\left(adcp\right)}{f_2\left(adcp\right)}=\frac{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="DE102020207895A1\_0014.png,DE102020207895A1\_0015.png"\; state="\{\{state\}\}">N</figure-callout>}}_0+{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="DE102020207895A1\_0015.png,DE102020207895A1\_0016.png"\; state="\{\{state\}\}">N</figure-callout>}}_1\cdot adcp+{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">N</figure-callout>}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+N_3\cdot adc{p}^3}{{\mathrm{D.}}_0+{\mathrm{D.}}_1\cdot adcp+{\mathrm{D.}}_2\cdot a\mathrm{<figure-callout\; id="2"\; label="d\; c\; p"\; filenames="DE102020207895A1\_0016.png,DE102020207895A1\_0017.png"\; state="\{\{state\}\}">d</figure-callout>}c{p}^{}{}^2+{\mathrm{D.}}_3\cdot adc{p}^3}$$

has. The coefficients N ₀ , N ₁ , N ₂ , N ₃ , D ₀ , D ₁ , D ₂ and D ₃ are each real numbers, the index representing the power of the variable adcp.

The allocation unit 10 is with a non-volatile memory 11th connected, in which various parameters for assigning the digitized raw measured value to a measured pressure value are stored. These parameters include in particular the aforementioned coefficients N ₀ , N ₁ , N ₂ , N ₃ , D ₀ , D ₁ , D ₂ and D ₃ . In the allocation unit 10 the measured pressure value can also be temperature compensated by taking a temperature reading from the temperature sensor 3 after digitization by the analog-to-digital converter 8th and possible filtering by the digital filter 9 has been digitized and processed.

The allocation unit 10 outputs a measured pressure value p _lin to a register 12th and a FIFO control unit 13th out. In the register 12th a current measured pressure value p _{lin can be} stored, it being possible for the stored measured pressure value to be provided with a time stamp. The FIFO control unit 13th _{several pressure values p lin} measured one after the other - possibly provided with a time stamp - in a FIFO 14th - First In First Out memory - store so that in the FIFO 14th a certain number of historical measured pressure values, for example 16, 132 or 200 pressure values, can be stored.

The host system 5 is through an interface 15th with the sensor electronics 4th connected. The interface 15th be formed by I ² C, I3C or SPI. Other configurations of the interface are also possible. Via this interface 15th can the host system 5 a current measured pressure value p _lin from the register 12th or several measured pressure values p _lin on the FIFO 14th read out.

In 7th is an exemplary embodiment of a capacitive pressure sensor 2 shown, which is designed as a MEMS - micro-electro-mechanical system. The pressure sensor 2 includes a sensor capacitance 16 by a ground electrode 17th and a deflectable sensor electrode 18th is formed. The deflectable sensor electrode is dependent on an applied pressure p 18th different distances in the direction of the ground electrode 17th emotional.

8th shows a circuit diagram with a parallel connection of three plate capacitors C, C 'and C ″. These plate capacitors have a pressure-dependent capacitance and, in one embodiment of the method according to the invention, can be a model for approximating the sensor capacitance 16 form.

Although the present invention has been described on the basis of preferred embodiments, it is not restricted thereto, but rather can be modified in many ways.

Claims (11)

Method for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor, wherein a sensor capacitance (16) of the pressure sensor (2) has a non-linear dependence on an applied pressure (p), comprising the steps: • Generating (S1) a digitized raw measured value (adcp ) for an applied pressure (p) by evaluating the sensor capacitance (16) of the pressure sensor (2) and using an analog-digital converter (8) and • determining a measured pressure value (p _lin ) from the digitized raw measured value (adcp) using an assignment function, the assignment function being formed via an approximation of the sensor capacitance (2) by a model based on a parallel connection of at least two plate capacitors (C, C ', C ") each with a pressure-dependent capacitance, the assignment function being a quotient of a first Polynomial (f ₁ (adcp)) and a second polynomial (f ₂ (adcp)) and where the first polynomial (f ₁ (adcp )) and the second polynomial (f ₂ (adcp)) each depend at least quadratically on the digitized raw measured value (adcp). Procedure according to Claim 1 , characterized in that the order of the first polynomial (f ₁ (adcp)) and / or the order of the second polynomial (f ₂ (adcp)) are each equal to the number of parallel-connected plate capacitors (C, C ', C ") of the Approximation is. Procedure according to Claim 1 or 2 , characterized in that the approximation is formed by three plate capacitors (C, C ', C "), so that the first polynomial (f ₁ (adcp)) and / or the second polynomial (f ₂ (adcp)) is a third order polynomial is. Method according to one of the Claims 1 until 3 , characterized in that a rough approximation of the sensor capacitance is carried out by a first plate capacitor (C) of the model from the at least two plate capacitors (C, C ', C "), while another plate capacitor / other plate capacitors (C', C") improve the rough approximation from the at least two plate capacitors (C, C ', C "). Method according to one of the Claims 1 until 4th , characterized in that in the first polynomial (f ₁ (adcp)) and / or in the second polynomial (f ₂ (adcp)) coefficients for at least two powers, preferably coefficients for at least two powers greater than 0, are each not equal to 0 . Method according to one of the Claims 1 until 5 , characterized in that coefficients of the first polynomial (f ₁ (adcp)) and / or coefficients of the second polynomial (f ₂ (adcp)) are specimen-specific or type-specific, with coefficients for powers of lower order are preferably specimen-specific. Method according to one of the Claims 1 until 6th , characterized in that poles of the assignment function are arranged outside of a measuring range of the sensor. Method according to one of the Claims 1 until 7th , characterized in that the assignment function for the measured pressure value (p _lin ) has the form: $$p_{lin}=\frac{N_0+N_1\cdot adcp+N_2\cdot adc{p}^2+N_3\cdot adc{p}^3}{{\mathrm{D.}}_0+{\mathrm{D.}}_1\cdot adcp+{\mathrm{D.}}_2\cdot adc{p}^2+{\mathrm{D.}}_3\cdot adc{p}^3}$$

and a plurality of coefficients (N ₀ , N ₁ , N ₂ , N ₃ , D ₀ , D ₁ , D ₂ , D ₃ ), the coefficients (N ₀ , N ₁ , N ₂ , N ₃ , D ₀ , D ₁ , D ₂ , D ₃ ) are real numbers. Method according to one of the Claims 1 until 7th , characterized in that the assignment function for the measured pressure value (p _lin ) has the form: $$p_{lin}=k_{\mathrm{P.}lin}\cdot \frac{\left(adcp-Z_{\mathrm{1,}\mathrm{P.}lin}\right)\left(adcp-Z_{\text{2}\text{,}\mathrm{P.}lin}\right)\left(adcp-Z_{\text{3}\text{,}\mathrm{P.}lin}\right)}{\left(adcp-{\mathrm{P.}}_{\mathrm{1,}\mathrm{P.}lin}\right)\left(adcp-{\mathrm{P.}}_{\text{2}\text{,}\mathrm{P.}lin}\right)\left(adcp-{\mathrm{P.}}_{\text{3}\text{,}\mathrm{P.}lin}\right)}$$

and several zeros (Z _{1, Plin,} Z _{2, Plin} , Z _{3, Plin} ) and several poles (P _{1, Plin} , P _{2, Plin} , P _{3, Plin} ,), the poles (P _{1, Plin} , P _{2, Plin} , P _{3, Plin} ,) are preferably arranged outside a measuring range of the sensor. Sensor system for assigning a measured pressure value to a raw measured value of a capacitive pressure sensor, comprising: • a capacitive pressure sensor (2) with a sensor capacitance (16), the sensor capacitance (16) being non-linearly dependent on an applied pressure (p), • an analogue Digital converter (8) designed to generate a digitized raw measured value (adcp) by digitizing a raw measured value (7) obtained by the pressure sensor (2), • an allocation unit (10) which is used to allocate a measured pressure value (p _lin ) in addition digitized raw measured value (adcp) is formed by means of an assignment function, the assignment function being formed via an approximation of the sensor capacitance (16) by a model based on a parallel connection of at least two plate capacitors (C, C ', C ") each with a pressure-dependent capacitance, where the assignment function has a quotient of a first polynomial (f ₁ (adcp)) and a second polynomial (f ₂ (adcp)) and where the first polynomial (f ₁ (adcp)) and the second polynomial (f ₂ (adcp) ) each depend at least quadratically on the digitized measured value (adcp). Sensor system according to Claim 10 , characterized by a host system (5) which is designed to read out a digitized raw measured value (adcp) and / or a measured pressure value (p _lin ) via an interface (15) and / or in which the (10) assignment unit is at least partially is implemented.

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