Method for operating a micromechanical inertial sensor

Abstract

A method for operating a micromechanical inertial sensor, including: translating an acceleration into a deflection of two detection electrodes that are displaced in opposite directions; ascertaining a difference in the spacing of the two detection electrodes; converting the difference in the spacing into an acceleration value using a scaling factor; and applying a linearization process to the acceleration value.

Claims

1. A method for operating a micromechanical inertial sensor, the method comprising: translating a mechanical acceleration into a deflection of two detection electrodes that are displaced in opposite directions; ascertaining a difference in a spacing of the two detection electrodes; converting the difference in the spacing into an acceleration value using a scaling factor; and applying a linearization process of a characteristic curve of the micromechanical inertial sensor to the acceleration value, wherein the linearization process processes the following mathematical system of equations: TABLE-US-00003 u.sub.0g = dC.sub.0g/(2*C0) u.sub.1g = dC.sub.1g/(2*C0) k1 = u.sub.0g/(u.sub.1g−u.sub.0g) k2 = u.sub.1g/(u.sub.1g−u.sub.0g) a_NL = (a.sub.in+k1)/k2 if a_NL ≠ 0 v = −1/(2*a_NL*u.sub.1g.sup.2)+sign(a_NL)/abs(u.sub.1g)*(1/(2*a_NL*u.sub.1g).sup.2+1).sup.0.5 else  v = 0 end a.sub.out = v−(1−v)*k1 where:
C(x)=C0/(1+x/d)  (1)
dC(x)=C0/(1−x/d)−C0/(1+x/d)  (2), where: a.sub.in is an acceleration at the inertial sensor, a.sub.out is an acceleration indicated by the inertial sensor, C0is a base capacitance of the inertial sensor for each of the two detection electrodes C1 and C2, dC.sub.0g is a value of equation (2) when an acceleration of 0 g is present, dC.sub.1g is a value of equation 2 when an acceleration of 1 g is present, u.sub.0g is a parameter derived from dC.sub.0g, u.sub.1g is a parameter derived from dC.sub.0g, k1, k2, a_NL, v are intermediate variables to simplify the equations, sign is a function that returns the sign of its argument (>0: =1; <0: −1), and abs is a function that returns the absolute value of its argument.

2. The method of claim 1, wherein the linearization process is carried out by a computer.

3. The method of claim 1, wherein the method being carried out at least partly in hardware and at least partly as a computer program product.

4. A micromechanical inertial sensor, comprising: a translating device to translate a mechanical acceleration into a deflection of two detection electrodes that are displaced in opposite directions; an ascertaining device to ascertain a difference in the spacing of the two detection electrodes; a converting device to convert the difference in spacing into an acceleration value using a scaling factor; and a linearization device to apply a linearization process of a characteristic curve of the micromechanical inertial sensor to the acceleration value, wherein the linearization process processes the following mathematical system of equations: TABLE-US-00004 u.sub.0g = dC.sub.0g/(2*C0) u.sub.1g = dC.sub.1g/(2*C0) k1 = u.sub.0g/(u.sub.1g-u.sub.0g) k2 = u.sub.1g/(u.sub.1g-u.sub.0g) a_NL = (a.sub.in + k1)/k2 if a_NL ≠ 0 v = −1/(2 * a_NL * u.sub.1g.sup.2) + sign(a_NL )/ abs(u.sub.1g) * (1/(2 * a_NL * u.sub.1g).sup.2 + 1).sup.0.5 else  v = 0 end a.sub.out = v − (1 − v) * k1, where:
C(x)=C0/(1+x/d)  (1)
dC(x)=C0/(1−x/d)−C0/(1+x/d)  (2), where: a.sub.in is an acceleration at the inertial sensor, a.sub.out is an acceleration indicated by the inertial sensor, C0is a base capacitance of the inertial sensor for each of the two detection electrodes C1 and C2, dC.sub.0g is a value of equation (2) when an acceleration of 0 g is present, dC.sub.1g is a value of equation 2 when an acceleration of 1 g is present, u.sub.0g is a parameter derived from dC.sub.0g, u.sub.1g is a parameter derived from dC.sub.0g, k1, k2, a_NL, v are intermediate variables to simplify the equations, sign is a function that returns the sign of its argument (>0: =1; <0: −1), and abs is a function that returns the absolute value of its argument.

5. The micromechanical inertial sensor of claim 4, wherein the micromechanical inertial sensor includes a micromechanical acceleration sensor or a micromechanical rotational rate sensor.

6. A method for producing a micromechanical inertial sensor, the method comprising: providing a translating device to translate a mechanical acceleration into a deflection of two detection electrodes that are displaced in opposite directions; providing an ascertaining device to ascertain a difference in the spacing of the two detection electrodes; providing a converting device to convert the difference in spacing into an acceleration value using a scaling factor; and providing a linearization device to apply a linearization process of a characteristic curve of the micromechanical inertial sensor to the acceleration value, wherein the linearization process processes the following mathematical system of equations: TABLE-US-00005 u.sub.0g = dC.sub.0g/(2*C0) u.sub.1g = dC.sub.1g/(2*C0) k1 = u.sub.0g/(u.sub.1g-u.sub.0g) k2 = u.sub.1g/(u.sub.1g-u.sub.0g) a_NL = (a.sub.in + k1)/k2 if a_NL ≠ 0 v = −1/(2 * a_NL * u.sub.1g.sup.2) + sign(a_NL )/ abs(u.sub.1g) * (1/(2 * a_NL * u.sub.1g).sup.2 + 1).sup.0.5 else  v = 0 end a.sub.out = v − (1 − v) * k1, where:
C(x)=C0/(1+x/d)  (1)
dC(x)=C0/(1−x/d)−C0/(1+x/d)  (2), where: a.sub.in is an acceleration at the inertial sensor, a.sub.out is an acceleration indicated by the inertial sensor, C0is a base capacitance of the inertial sensor for each of the two detection electrodes C1 and C2, dC.sub.0g is a value of equation (2) when an acceleration of 0 g is present, dC.sub.1g is a value of equation 2 when an acceleration of 1 g is present, u.sub.0g is a parameter derived from dC.sub.0g, u.sub.1g is a parameter derived from dC.sub.0g, k1, k2, a_NL, v are intermediate variables to simplify the equations, sign is a function that returns the sign of its argument (>0: =1; <0: −1), and abs is a function that returns the absolute value of its argument.

7. A non-transitory computer readable medium having a computer program, which is executable on a processor, comprising: a program code arrangement having program code for operating a micromechanical inertial sensor, by performing the following: translating a mechanical acceleration into a deflection of two detection electrodes that are displaced in opposite directions; ascertaining a difference in a spacing of the two detection electrodes; converting the difference in the spacing into an acceleration value using a scaling factor; and applying a linearization process of a characteristic curve of the micromechanical inertial sensor to the acceleration value, wherein the linearization process processes the following mathematical system of equations: TABLE-US-00006 u.sub.0g = dC.sub.0g/(2*C0) u.sub.1g = dC.sub.1g/(2*C0) k1 = u.sub.0g/(u.sub.1g-u.sub.0g) k2 = u.sub.1g/(u.sub.1g-u.sub.0g) a_NL = (a.sub.in*k1)/k2 if a_NL ≠ 0 v = −1/(2 * a_NL * u.sub.1g.sup.2) + sign(a_NL )/ abs(u.sub.1g) * (1/(2 * a_NL * u.sub.1g).sup.2 + 1).sup.0.5 else  v = 0 end a.sub.out = v − (1 − v) * k1, where:
C(x)=C0/(1+x/d)  (1)
dC(x)=C0/(1−x/d)−C0/(1+x/d)  (2), where: a.sub.in is an acceleration at the inertial sensor, a.sub.out is an acceleration indicated by the inertial sensor, C0is a base capacitance of the inertial sensor for each of the two detection electrodes C1 and C2, dC.sub.0g is a value of equation (2) when an acceleration of 0 g is present, dC.sub.1g is a value of equation 2 when an acceleration of 1 g is present, u.sub.0g is a parameter derived from dC.sub.0g, u.sub.1g is a parameter derived from dC.sub.0g, k1, k2, a_NL, v are intermediate variables to simplify the equations, sign is a function that returns the sign of its argument (>0: =1; <0: −1), and abs is a function that returns the absolute value of its argument.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a schematic representation of an exemplary embodiment of an micromechanical inertial sensor.

(2) FIG. 2 shows a diagram of an effect of the method according to the present invention on an acceleration signal of the inertial sensor.

(3) FIG. 3 shows a schematic sequence of a specific embodiment of a method for producing the micromechanical inertial sensor.

DETAILED DESCRIPTION

(4) An important aspect of the present invention is in particular to provide an improved measurement or sensing characteristic of a micromechanical inertial sensor. Using the proposed method, an output signal of an inertial sensor, e.g. of an acceleration sensor or of a rotational rate sensor, is linearized, so that measurement can take place over the entire dynamic range with constant precision, and the non-linearity resulting from the configuration of the conventional dC evaluation method is avoided.

(5) The more precise signal results in improvements for various specification parameters of an inertial sensor. This includes the linearity in itself, so that applications in which higher acceleration values occur (e.g. more than 10 times the acceleration of the earth's gravitational field) benefit from more precise measurement values.

(6) This yields the possibility of replacing more elaborate and thus more expensive evaluation circuits for meeting greater linearity requirements by the simpler dC circuit in combination with the linearization described in the following, in order to advantageously save production costs.

(7) FIG. 1 shows a schematic specific embodiment of a proposed micromechanical inertial sensor 10.

(8) Depicted is an ascertaining device having a first stage in the form of a translation device 1. Using translation device 1, a mechanical acceleration acting on the inertial sensor is translated into a deflection, e.g. by a spring-suspended mass. This element is generally very linear for the relevant deflections x. The deflection x changes the electrode spacing of two detection electrodes C1, C2 (not shown) of inertial sensor 10, which are displaced in opposite directions.

(9) Through a difference formation:
dC(x)=C1(x)−C2(x)

(10) of a subsequent stage in the form of a difference formation device 2, a signal is obtained that is approximately proportional to the deflection x; in the following, this is also referred to as the known “dC principal.” Due to the non-linear function of the capacitance of the electrode spacing:
C(x)=C0/(1+x/d)  (1)

(11) the output signal dC(x) is correspondingly nonlinear:
dC(x)=C0/(1−x/d)−C0/(1+x/d)  (2)

(12) with the parameters:

(13) C0 . . . resting capacitance

(14) d . . . electrode spacing of the detection electrodes C1, C2

(15) If an initial deflection of the electrodes xoff caused by the production process is taken into account, and xoff is substituted for x, the following is obtained:
dC(u)=2*C0*u/(1−u.sup.2)  (3)

(16) where

(17) u=(x−xoff)/d . . . normed deflection

(18) The evaluation electronics in inertial sensor 10 converts the signal dC(u) from equation (3), through multiplication by a scaling factor, into an acceleration value a.sub.out, so that this equation can also be represented in the form:
a.sub.out=const*a.sub.in/(1−a.sub.in.sup.2)  (4).

(19) Here it was also taken into account that the parameter u is a linear function of a.sub.in.

(20) From equation (4), it can be seen that for small normed deflections u<<1, or x<<d, it holds approximately that dC=2*C0*u; i.e. the relationship is linear, while for larger deflections the term u.sup.2 in the denominator can no longer be disregarded, and the characteristic curve is thus “deformed” or “bent” to a certain extent.

(21) This deformation is made computationally reversible, which, together with the required computing unit, enables a linearization of the characteristic curve of micromechanical inertial sensor 10.

(22) Proposed is a micromechanical inertial sensor 10 having an evaluation method based on the dC configuration, an electronic linearization device 4 for characteristic curve correction (e.g. a microcontroller, digital signal processor (DSP), or a “hardwired” discrete logic circuit situated internally or externally to the sensor), and a correction algorithm 5 carried out by linearization device 4, explained in more detail in the following as a specific exemplary embodiment. Advantageously, a partitioning of the execution of the proposed correction algorithm 5 can be freely selected as a computer program product or as a hardwired discrete logic circuit.

(23) Through a further transformation of equation (3), from the distorted dC one can infer, via deflection x, the applied acceleration a. As input variables, here the following are required: the measured (i.e. not yet linear) acceleration a.sub.in, normed to 1 g and freed from the offset; the rest capacitance of sensor C0; and the dC signal at acceleration values 0 g and 1 g, dC.sub.0g, dC.sub.1g.

(24) Description/meaning of the parameters and symbols used:

(25) a.sub.in “true” acceleration at the inertial sensor

(26) a.sub.out . . . measured acceleration indicated by the inertial sensor

(27) C0. . . base capacitance of the inertial sensor for each of the two detection electrodes C1 and C2; i.e. the value of equation (1) for x=0

(28) dC.sub.0g . . . value of equation (2) when an acceleration of 0 g is present (rest state, or the corresponding sensing axis parallel to the earth's gravitational field). Is ascertained for each inertial sensor during the sensor trimming before delivery.

(29) dC.sub.1g . . . value of equation 2 when an acceleration of 1 g is present (deflection in the earth's gravitational field). Is ascertained for each inertial sensor during the sensor trimming before delivery.

(30) u.sub.0g . . . parameter derived from dC.sub.0g (substitution to simplify the equations).

(31) u.sub.1g . . . parameter derived from dC.sub.1g (substitution to simplify the equations).

(32) k1, k2, a_NL, v . . . intermediate variables to simplify the equations.

(33) sign: function that returns the sign of its argument (>0: =1; <0: −1).

(34) abs: function that returns the absolute value of its argument.

(35) With the following system of equations or correction algorithm 5, the characteristic curve is linearized:

(36) TABLE-US-00002 u.sub.0g = dC_0g/(2*C0) u.sub.1g = dC_1g/(2*C0) k1 = u.sub.0g/(u.sub.1g−u.sub.0g) k2 = u.sub.1g/(u.sub.1g−u.sub.0g) a_NL = (a_in+k1)/k2 if a_NL ≠ 0  v = −1/(2*a_NL*u.sub.1g.sup.2)+sign(a_NL)/abs(u.sub.1g)*(1/(2*a_NL*u.sub.1g).sup.2+1).sup.0.5 else  v = 0 end a.sub.out = v−(1−v)*k1

(37) As a result, the linearized output signal a.sub.out is obtained.

(38) The listed equations have the purpose of providing a maximally ideal characteristic curve of an acceleration sensor having the form:
a.sub.out=a.sub.in  (6)

(39) Here, the acceleration a.sub.out indicated by the acceleration sensor is equal to the actual acceleration a.sub.in.

(40) Without this correction, corresponding to equation (4) there would result a “bent” characteristic curve 20 that is shown as an illustration in FIG. 2. Using equation (5), the bent characteristic curve 20 can be transformed into the linear characteristic curve 30 of the function a.sub.out=a.sub.in, as indicated in FIG. 2 by an arrow.

(41) FIG. 3 shows a schematic sequence of a proposed method for producing a proposed micromechanical inertial sensor 10.

(42) In a step 20, a translation device 1 for translating acceleration into a deflection of two detection electrodes displaced in opposite directions is provided.

(43) In a step 21, an ascertaining device 2 for ascertaining a difference in spacing of the two detection electrodes is provided.

(44) In a step 22, a conversion device 3 for converting the spacing difference into an acceleration value a.sub.out using a scaling factor is provided.

(45) In a step 23, a linearization device 4 for applying a linearization process to the acceleration value a.sub.out is provided.

(46) The person skilled in the art may also realize specific embodiments of the present invention that are not disclosed or are only partly disclosed without departing from the core of the present invention.