Method for operating a micromechanical inertial sensor

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:
• u0g = dC0g/(2*C0)
• u1g = dC1g/(2*C0)
• k1 = u0g/(u1g-u0g)
• k2 = u1g/(u1g-u0g)
• a_NL = (ain + k1)/k2
• if a_NL ≠ 0
• v = −1/(2 * a_NL * u1g2) + sign(a_NL )/
• abs(u1g) * (1/(2 * a_NL * u1g)2 + 1)0.5
• else
• v = 0
• end
• aout = v − (1 − v) * k1,
• where:
• C(x)=C0/(1+x/d) (1)
• dC(x)=C0/(1−x/d)−C0/(1+x/d) (2),
• where:
• ain is an acceleration at the inertial sensor,
• aout 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,
• dC0g is a value of equation (2) when an acceleration of 0 g is present,
• dC1g is a value of equation 2 when an acceleration of 1 g is present,
• u0g is a parameter derived from dC0g,
• u1g is a parameter derived from dC0g,
• 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.

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:
• u0g = dC0g/(2*C0)
• u1g = dC1g/(2*C0)
• k1 = u0g/(u1g-u0g)
• k2 = u1g/(u1g-u0g)
• a_NL = (ain + k1)/k2
• if a_NL ≠ 0
• v = −1/(2 * a_NL * u1g2) + sign(a_NL )/
• abs(u1g) * (1/(2 * a_NL * u1g)2 + 1)0.5
• else
• v = 0
• end
• aout = v − (1 − v) * k1,
• where:
• C(x)=C0/(1+x/d) (1)
• dC(x)=C0/(1−x/d)−C0/(1+x/d) (2),
• where:
• ain is an acceleration at the inertial sensor,
• aout 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,
• dC0g is a value of equation (2) when an acceleration of 0 g is present,
• dC1g is a value of equation 2 when an acceleration of 1 g is present,
• u0g is a parameter derived from dC0g,
• u1g is a parameter derived from dC0g,
• 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.

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:
• u0g = dC0g/(2*C0)
• u1g = dC1g/(2*C0)
• k1 = u0g/(u1g-u0g)
• k2 = u1g/(u1g-u0g)
• a_NL = (ain*k1)/k2
• if a_NL ≠ 0
• v = −1/(2 * a_NL * u1g2) + sign(a_NL )/
• abs(u1g) * (1/(2 * a_NL * u1g)2 + 1)0.5
• else
• v = 0
• end
• aout = v − (1 − v) * k1,
• where:
• C(x)=C0/(1+x/d) (1)
• dC(x)=C0/(1−x/d)−C0/(1+x/d) (2),
• where:
• ain is an acceleration at the inertial sensor,
• aout 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,
• dC0g is a value of equation (2) when an acceleration of 0 g is present,
• dC1g is a value of equation 2 when an acceleration of 1 g is present,
• u0g is a parameter derived from dC0g,
• u1g is a parameter derived from dC0g,
• 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.