Methods and apparatus to calibrate micro-electromechanical systems

Methods and apparatus to calibrate micro-electromechanical systems are disclosed. An example pressure sensor calibration apparatus includes a mechanical lift to move a pressure sensor between a first height, a second height, and a third height; one or more sensors to measure first pressure and capacitance values at the first height, second pressure and capacitance values at the second height, and third pressure and capacitance values obtained at the third height; and a calibrator to determine calibration coefficient values to calibrate the pressure sensor based on the first pressure and capacitance values obtained at the first height, the second pressure and capacitance values at the second height, and the third pressure and capacitance values obtained at the third height.

FIELD OF THE DISCLOSURE

This disclosure relates generally to micro-electromechanical systems, and, more particularly, to methods and apparatus to calibrate micro-electromechanical systems.

BACKGROUND

Micro-electromechanical systems (MEMS) such as, for example, pressure sensors are relatively nonlinear devices. Based on this nonlinearity and differences between pressure sensors, typically, each pressure sensor is individually calibrated. Such an approach may increase the capital cost of equipment used to calibrate the pressure sensors and/or increase the time dedicated to calibrating each of the pressure sensors.

DETAILED DESCRIPTION

The examples disclosed herein relate to calibrating micro-electromechanical systems (MEMS) such as, for example, pressure sensors and/or capacitive based barometric pressure sensors. Specifically, the examples disclosed herein relate to calibrating pressure sensors based on values obtained when testing the pressures sensors at different positions. By taking such an approach, the examples disclosed herein enable the efficient calibration of a large quantity of pressure sensors at, for example, ambient pressure using equipment that may be obtained at a relatively low cost.

In some examples, the testing includes positioning a pressure sensor at different heights and measuring the capacitance and pressure at the respective heights. For example, an example calibration system may measure a first pressure value, Ph1, and a first capacitance value, Ch1, at a first height, h1, a second pressure value, Ph2, and a second capacitance value, Ch2, at a second height, h2, and a third pressure value, Ph3, and a third capacitance value, Ch3, at a third height, h3.

Based on the pressure values determined at the different heights, in some examples, Equation 1 is used to determine an average pressure, Pavg1,2, between the first and second pressure values, P1, P2, and Equation 2 is used to determine an average pressure, Pavg2,3, between the second and third pressure values, P2, P3.

Based on the capacitance values determined at the different heights, in some examples, Equation 3 is used to determine an average capacitance, Cavg1,2, between the first and second capacitance values, C1, C2and Equation 4 is used to determine an average capacitance, Cavg2,3, between the second and third capacitance values, C2, C3.

Based on the pressure and capacitance values determined at the different heights, in some examples, Equation 5 is used to represent the capacitance-pressure sensitivity, SCP1,2, at the first and second heights and Equation 6 is used to represent the capacitance-pressure sensitivity, SCP2,3at the second and third heights.

To determine attributes of the pressure sensor being calibrated such as, for example, an effective gap, geff, and/or the plate thickness, t, in some examples, Equations 7 and 8 are used in combination with the results of the testing and/or Equations 1-6, for example. Referring to Equations 7 and 8, ε0refers to the permittivity of the free space within the pressure sensor being calibrated, Aprefers to the plate area of the pressure sensor being calibrated and Cparrefers to the parasitic capacitance and/or the parasitic offset (e.g., 3.2 picofarads (pF)) of the pressure sensor being calibrated. Referring further to Equations 7 and 8, Cdynrefers to the dynamic capacitance of the pressure sensor being calibrated, a refers to the plate radius of the pressure sensor being calibrated, v refers to Poisson's ratio, and E refers to Young's modulus.

To determine other values and/or to extrapolate the capacitance and pressure values determined when positioning the pressure sensor at different heights, in some examples, a sensor equation fit is used such as, for example, the sensor equation fit of Equation 9. In some examples, the sensor equation fit is based on a non-linear fitting algorithm called Levenberg-Marquardt. Referring to Equation 9, xprefers to the peak plate displacement of the pressure sensor being calibrated as defined by Equation 10 and δxprefers to the displacement adjustment (e.g., zero offset) of the pressure sensor being calibrated.

Referring to Equation 10, D corresponds to the flexural rigidity of the pressure sensor being calibrated as defined in Equation 11.

Referring to Equation 11, E refers to Young's modulus, v refers to Poisson's ratio and t refers to the thickness of the plate determined using Equations 7 and 8.

In some examples, to reduce the complexity of the solution, a polynomial fit is performed on the squared inverted results of the sensor equation fit using, for example, Equation 12. Referring to Equation 12, C refers to the capacitance determined using Equation 9, airefers to the polynomial coefficients and {circumflex over (P)} refers to the pressure result vector from the polynomial fit. In some examples, the polynomial fit performed is a 4th order polynomial fit and the output includes calibration coefficient values to calibrate the second pressure sensors.

FIG. 1illustrates an example calibration system100that can be used to calibrate micro-electromechanical systems (MEMS) including pressure sensors in a cost effective and efficient manner. In the illustrated example, the calibration system100performs physical tests on a pressure sensor104and uses the results of the physical tests to determine calibration coefficient values. While the illustrated example depicts one pressure sensor (i.e., the pressure sensor104), in other examples, any number of pressure sensors may be used. To enable the physical tests to be performed on the pressure sensor104, in the illustrated example, the calibration system100includes an example pressure sensor and/or gauge108and an example capacitance sensor110.

In the example ofFIG. 1, to perform the physical tests on the pressure sensor104, the calibration system100positions the pressure sensor104at different heights112,114,116using a lift117and the pressure sensor108and the capacitance sensor110determine pressure and capacitance values at the different heights. The calibration system100may move the pressure sensor104to the different heights112,114,116, etc. in different ways such as, for example, using a movable platform, an elevator or any other device (e.g., a mechanical device, an electro-mechanical device) or, more generally, the lift117, that can move the pressure sensor104between different positions.

In the illustrated example, when the calibration system100positions the pressure sensor104at the first height112, the second height114and the third height116, the pressure sensor108measures first, second and third pressure values118,120and122at the respective heights112,114,116. Similarly, in the illustrated example, when the calibration system100positions the pressure sensor104at the different heights112,114,116, the capacitance sensor110measures first, second and third capacitance values124,126and128at the respective heights112,114,116. In other examples, the pressure values118,120,122may be determined using an equation(s) that relates height and pressure such as Equation 13. Referring to Equation 13, P0refers to the reference pressure at h1, R* refers to the gas constant, M refers to molar mass of Earth's air: 0.0289644 kg/mol, g refers to the gravitational acceleration: 9.80665 m/s2, z refers to the height change from h1and T refers to the the temperature at h1.
P=P0e−Mgz/R*TEquation 13:

In such examples, the pressure sensor104may not be included. In some examples, results300of the physical tests conducted on the pressure sensor104are plotted on a graph302depicted inFIG. 3, where an x-axis304represents pressure and a y-axis306represents capacitance.

Referring back to the example ofFIG. 1, the pressure gauge108and/or the capacitance sensor110provide or otherwise enable an example calibrator130to access the first, second and third pressure value(s)118,120and122and the first, second and third capacitance value(s)124,126,128for further processing. In some examples, the further processing includes the calibrator130determining calibration coefficient values132that can be used to calibrate the pressure sensor104and/or are stored on a data store134of the pressure sensor104. The calibration coefficient values132may be determined based on the first, second and third pressure values118,120,122, the first, second and third capacitance values124,126and128and/or pressure sensor data and/or associated parameters136from a database138.

In some examples, the pressure sensor data and/or associated parameters136include, for example, a permittivity of the free space within the pressure sensor104, ε0, a plate area of the pressure sensor104, Ap, the dynamic capacitance of the pressure sensor104, Cdyn, and/or a parasitic offset of the pressure sensor104, Cpar. In some examples, the pressure sensor data and/or associated parameters136include, for example, a plate radius of the pressure sensor104, a, Young's modulus, E, Poisson's ratio, v, the thickness of the plate, t, the peak plate displacement of the pressure sensor104, xp, the displacement adjustment (e.g., zero offset) of the pressure sensor104, δxp, and/or the flexural rigidity of the pressure sensor104, D.

FIG. 2illustrates an example implementation of the calibrator130ofFIG. 1. In the illustrated example, the calibrator130includes an example pressure sensor attribute determiner202, an example data fitter204and an example determiner206. In the illustrated example, to determine different attributes208of the pressure sensor104such as, for example, the effective gap, geff, and/or the plate thickness, t, of the pressure sensor104, the pressure sensor attribute determiner202accesses the first, second and third pressure values118,120,122, the first, second and third capacitance values124,126,128and the pressure sensor data and/or associated parameters136and processes these values using, for example, Equations 7 and 8 to determine the pressure sensor attributes808.

To determine other and/or extrapolate the pressure and capacitance values118,120,122,124,126,128, in the illustrated example, the data fitter204accesses the pressure sensor attributes208and the pressure and capacitance values118,120,122,124,126,128from the pressure sensor attribute determiner202and the pressure sensor data and/or associated parameters136and determines other values and/or extrapolates and/or fits pressure and capacitance values210using the sensor equation fit of Equation 9 and then places the data in a simpler form using the 5th order polynomial fit equation of Equation 12.

To determine the calibration coefficient values132to be used to calibrate the pressure sensor104, the determiner206accesses the other pressure and capacitance values210from the data fitter204and processes the other pressure and capacitance values210to determine the calibration coefficient values132. Thus, using the examples disclosed herein, the example calibrator130determines the calibration coefficient values132based on physical tests performed on the pressure sensor104without performing more extensive testing on the pressure sensor104, such as, physical testing involving a pressure chamber.

While an example manner of implementing the example of implementing the example calibrator130ofFIG. 1is illustrated inFIG. 2, one or more of the elements, processes and/or devices illustrated inFIG. 2may be combined, divided, re-arranged, omitted, eliminated and/or implemented in any other way. Further, the example pressure sensor attribute determiner202, the example data fitter204, the example determiner206and/or the example calibrator130ofFIG. 2may be implemented by hardware, software, firmware and/or any combination of hardware, software and/or firmware. Thus, for example, any of the example pressure sensor attribute determiner202, the example data fitter204, the example determiner206and/or the example calibrator130ofFIG. 2could be implemented by one or more analog or digital circuit(s), logic circuits, programmable processor(s), application specific integrated circuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or field programmable logic device(s) (FPLD(s)). When reading any of the apparatus or system claims of this patent to cover a purely software and/or firmware implementation, at least one of the example pressure sensor attribute determiner202, the example data fitter204, the example data fitter206and/or the example calibrator130ofFIG. 2is/are hereby expressly defined to include a tangible computer readable storage device or storage disk such as a memory, a digital versatile disk (DVD), a compact disk (CD), a Blu-ray disk, etc. storing the software and/or firmware. Further still, the calibrator130ofFIG. 1may include one or more elements, processes and/or devices in addition to, or instead of, those illustrated inFIG. 2, and/or may include more than one of any or all of the illustrated elements, processes and devices.

FIG. 3illustrates the example graph302including resultant capacitances of the pressure sensor104being exposed to different pressures at different heights. The graph302ofFIG. 3includes the x-axis304that represents pressure and the y-axis306that represents capacitance.

A flowchart representative of example machine readable instructions for implementing the example calibrator130ofFIGS. 1 and 2are shown inFIG. 4. In this example, the machine readable instructions comprise a program for execution by a processor such as the processor512shown in the example processor platforms500discussed below in connection withFIG. 5. The program may be embodied in software stored on a tangible computer readable storage medium such as a CD-ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), a Blu-ray disk, or a memory associated with the processor512, but the entire program and/or parts thereof could alternatively be executed by a device other than the processor512and/or embodied in firmware or dedicated hardware. Further, although the example program is described with reference to the flowchart illustrated inFIG. 4, many other methods of implementing the example calibrator130may alternatively be used. For example, the order of execution of the blocks may be changed, and/or some of the blocks described may be changed, eliminated, or combined.

The program ofFIG. 4begins with the calibrator130and/or the pressure sensor attribute determiner202accessing the first pressure and first capacitance values118,124associated with the physical tests performed on the pressure sensor104at the first height112(block402). The calibrator130and/or the pressure sensor attribute determiner202accesses the second pressure and second capacitance values120,126associated with the physical tests performed on the pressure sensor104at the second height114(block404). The calibrator130and/or the pressure sensor attribute determiner202accesses the third pressure and third capacitance values122,128associated with the physical tests performed on the pressure sensor104at the third height116(block406).

The calibrator130and/or the pressure sensor attribute determiner202determines attributes208of the pressure sensor104based on the first, second and third pressure values118,120,122and the first, second and third capacitance values124,126,128(block408). In some examples, the attributes include the effective gap, geff, of the pressure sensor104and/or the plate thickness, t, of the pressure sensor104. The calibrator130and/or the data fitter204accesses the pressure sensor attributes208, the pressure and capacitance values118,120,122,124,126,128and the pressure sensor data and/or associated parameters136and determines other values and/or extrapolates and/or fits the pressure and capacitance values210using an example sensor equation fit and/or places the data in a simpler form using an example 5th order polynomial fit equation (block410).

The calibrator130and/or the determiner206determines the calibration coefficient values132to be used to calibrate the pressure sensor104by processing the other pressure and capacitance values210to determine the calibration coefficient values132(block412). The calibration coefficient values132are stored on the pressure sensor104(block414).

FIG. 5is a block diagram of an example processor platform500capable of executing the instructions ofFIG. 4to implement the calibrator130ofFIGS. 1 and 2. The processor platform500can be, for example, a server, a personal computer, a mobile device (e.g., a cell phone, a smart phone, a tablet such as an iPad™), a personal digital assistant (PDA), an Internet appliance, or any other type of computing device.

The processor platform500of the illustrated example includes a processor512. The processor512of the illustrated example is hardware. For example, the processor512can be implemented by one or more integrated circuits, logic circuits, microprocessors or controllers from any desired family or manufacturer. In this example, the processor512implements the example pressure sensor attribute determiner202, the example data fitter204and the example determiner206and the example calibrator130.

The processor512of the illustrated example includes a local memory513(e.g., a cache). The processor512of the illustrated example is in communication with a main memory including a volatile memory514and a non-volatile memory516via a bus518. The volatile memory514may be implemented by Synchronous Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random Access Memory (RDRAM) and/or any other type of random access memory device. The non-volatile memory516may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory514,516is controlled by a memory controller.

The processor platform500of the illustrated example also includes an interface circuit520. The interface circuit520may be implemented by any type of interface standard, such as an Ethernet interface, a universal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices522are connected to the interface circuit520. The input device(s)522permit(s) a user to enter data and commands into the processor512. The input device(s) can be implemented by, for example, an audio sensor, a microphone, a camera (still or video), a keyboard, a button, a mouse, a touchscreen, a track-pad, a trackball, isopoint and/or a voice recognition system.

The processor platform500of the illustrated example also includes one or more mass storage devices528for storing software and/or data. Examples of such mass storage devices528include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, RAID systems, and digital versatile disk (DVD) drives.

The coded instructions532ofFIG. 4may be stored in the mass storage device528, in the volatile memory514, in the non-volatile memory516, and/or on a removable tangible computer readable storage medium such as a CD or DVD.

From the foregoing, it will be appreciated that the above disclosed methods, apparatus and articles of manufacture relate to calibrating micro-electromechanical systems (MEMS) such as, for example, pressure sensors and/or capacitive based barometric pressure sensors. Specifically, the examples disclosed herein relate to calibrating pressure sensors based on obtained values when the pressure sensors are at different positions and/or heights and/or other sensor attributes determined and/or estimated. By taking such an approach, the examples disclosed herein enable the efficient calibration of a large quantity of pressure sensors.