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 pressure chamber in which a first pressure sensor is to be disposed; one or more first sensors to determine a capacitance value from the first pressure sensor from a physical test performed on the first pressure sensor; the one or more first sensors to determine a first pull-in voltage value from a first electrical test performed on the first pressure sensor; a correlator to determine correlation coefficient values based on the capacitance value determined during the physical test on the first pressure sensor and the first pull-in voltage value determined during a first electrical test on the first pressure sensor; and a calibrator to determine calibration coefficient values to calibrate a second pressure sensor based on the correlation coefficient values and a second electrical test on the second pressure sensor.

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 the 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 performing tests on first pressure sensors during a training phase and calibrating second pressure sensors during a testing phase using correlation coefficient values determined during the training phase. By taking such an approach, the examples disclosed herein enable the efficient calibration of a large quantity of pressure sensors based on calibration coefficient values determined by testing a lesser number of pressure sensors. As such, the examples disclosed herein avoid the time-consuming process of calibrating pressure sensors by performing a pressure sweep on each pressure sensor positioned in a pressure chamber.

In some examples, the training phase includes performing physical and electrical tests on the first pressure sensors. The physical test(s) may include exposing the first pressure sensors to various pressures (e.g., performing a pressure sweep) and determining the resultant capacitance value(s). In some examples, Equation 1 is used to relate the pressure and capacitance values determined during the physical test and/or is used to account for the capacitance of the first pressure sensor at ambient pressure, where Cpxcorresponds to the capacitance at a particular pressure and Cp=1013hPacorresponds to the capacitance at 1013 hectopascals (hPa).
f(Cp)=Cpx−Cp=1014hPaEquation 1:

In some examples, the electrical test(s) includes applying various voltages (e.g., performing a voltage sweep) to the first pressure sensors and determining the pull-in voltage for the different pressure sensors. The voltages applied during the electrical test(s) may be direct current (DC) voltage. The pull-in voltage may be determined in various ways such as, for example, identifying a relatively significant capacitance increase as satisfying a threshold. As used herein, the pull-in voltage refers to the voltage beyond which it causes a diaphragm, plate and/or a membrane of a sensor to snap to the other plate-.

Based on the associated pressure and capacitance values and the pull-in voltages, in some examples, correlation coefficient values are determined using a polynomial function such as, for example, the second order polynomial function of Equation 2. Referring to Equation 2, a1corresponds to a first correlation coefficient, a2corresponds to a second correlation coefficient, a3corresponds to a third correlation coefficient, f(Cp) corresponds to the capacitance in the physical domain and f(Vpi) corresponds to the pull-in voltage, where f(Vpi)=Vpi.
f(Cp)=a1f(Vpi)2+a2f(Vpi)+a3Equation 2:

After the training phase, the testing phase may be performed. The testing phase may include performing electrical tests on second pressure sensors to determine the pull-in voltages for the different second pressure sensors. Based on the electrical tests performed on the second pressure sensors during the testing phase and the correlation coefficient values determined during the training phase, in some examples, capacitance values are determined for the second pressure sensors at different pressure values without performing the physical tests on the second pressure sensors. In some examples, Equation 3 is used to determine the capacitance value for a selected pressure value for the respective ones of the second pressure sensors.
Cpx=a1f(Vpi)2+a2f(Vpi)+a3+Cp=1013hPaEquation 3:

To extrapolate the capacitance and pressure values determined using equation 3, in some examples, a sensor equation fit is used such as, for example, the sensor equation fit of Equation 4. In some examples, the sensor equation fit uses Levenberg-Marquardt algorithm (LMA). Referring to Equation 4, Aprefers to the plate area of the pressure sensor being calibrated in the testing phase, ε0corresponds to the permittivity of the free space within the pressure sensor being calibrated in the testing phase and xpcorresponds to the peak plate displacement of the pressure sensor being calibrated in the testing phase as defined by Equation 5. Referring further to Equation 4, g0corresponds to the effective gap (e.g., 545.6 nanometers (nm)) of the pressure sensor being calibrated in the testing phase as defined by Equation 6, δxpcorresponds to the displacement adjustment (e.g., zero offset) of the pressure sensor being calibrated in the testing phase and Cparcorresponds to the parasitic offset (e.g., 3.2 picofarads (pF)) of the pressure sensor being calibrated in the testing phase.

Referring to Equation 5, a corresponds to the plate radius of the pressure sensor being calibrated in the testing phase and D corresponds to the flexural rigidity of the pressure sensor being calibrated in the testing phase as defined in Equation 7.

Referring to Equation 6, gnooxcorresponds to the air gap of the pressure sensor being calibrated in the testing phase, toxcorresponds to the thickness of the oxide of the pressure sensor being calibrated in the testing phase and εr,axcorresponds to the relative permittivity of the oxide of the pressure sensor being calibrated in the testing phase.

Referring to Equation 7, E corresponds to Young's modulus, v corresponds to Poisson's ratio and t corresponds to the thickness of the plate (e.g., 8 micrometers(μm)) and D is the flexural rigidity of the pressure sensor being calibrated in the testing phase.

In some examples, to reduce the complexity of the solution, a polynomial fit (e.g., 5thorder polynomial) is performed on the squared inverted results of the sensor equation fit using, for example, Equation 8. Referring to Equation 8, C corresponds to the capacitance determined using Equation 4, aicorresponds to the polynomial coefficients and {circumflex over (P)} corresponds to the pressure result vector from the polynomial fit. In some examples, the polynomial fit performed is a 5thorder 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 system100includes an example training phase102that performs physical and electrical tests on a first pressure sensor104and uses the results of the physical and electrical tests to determine correlation coefficient values. While the illustrated example depicts one pressure sensor (i.e., the first pressure sensor104) in the training phase102, in other examples, any number of pressure sensors may be used during the training phase102.

To enable the physical tests to be performed on the first pressure sensor104during the training phase102, in the illustrated example, the calibration system100includes an example pressure controller106, an example pressure gauge and/or sensor108, an example pressure chamber110in which the first pressure sensor104is disposed and an example capacitance sensor111. In some examples, to perform the physical tests on the first pressure sensor104, the pressure controller106sets a pressure within the pressure chamber110via a pressure value input112and the pressure gauge108measures the actual pressure within the pressure chamber110to enable a determination to be made as to whether the pressure within the pressure chamber110has stabilized and/or whether the pressure value input112and a measured pressure114are within a threshold of one another.

In some examples, when the pressure within the pressure chamber110stabilizes and/or when the pressure value input112and the measured pressure114are within a threshold of one another, the capacitance sensor111measures a capacitance value(s)116from the first pressure sensor104based on the pressure applied. In some examples, results500of the physical tests conducted during the training phase102are plotted on a graph502depicted inFIG. 5where an x-axis504represents pressure and a y-axis506represents capacitance.

Referring back to the example ofFIG. 1, the pressure gauge108and/or the capacitance sensor111provide or otherwise enable an example correlator118to access the measured pressure value(s)114and the capacitance value(s)116for further processing. In this manner, in some examples, during the training phase102, the first pressure sensor104is exposed to a range of pressures by performing a pressure sweep on the first pressure sensor104and measuring the resultant capacitance values116from the first pressure sensor104using the capacitance sensor111. As used herein, the phrase “pressure sweep” refers to exposing a pressure sensor to a plurality of pressure values that may be incrementally or otherwise spaced from one another between a first pressure value (e.g., 600 hPa) and a second pressure value (e.g., 1013 hPa).

To enable the electrical tests to be performed during the training phase102, in the illustrated example, the calibration system100includes an example first voltage stimulator120and an example first “pull-in” voltage identifier122. While the illustrated example ofFIG. 1depicts the first pressure sensor104within the pressure chamber110when the electrical tests are being conducted, the electrical tests may be performed when the first pressure sensor104is disposed outside of the pressure chamber110. In other words, the physical tests of the training phase102may be performed with the first pressure sensor104disposed within the pressure chamber110and the electrical tests of the training phase102may be performed with the first pressure sensor104disposed inside or outside of the pressure chamber110.

In some examples, the electrical tests include the first voltage stimulator120applying a first voltage value124to and/or across the first pressure sensor104and the first “pull in” voltage identifier122measuring the resultant capacitance value(s)116based on the voltage(s) applied. In some examples, the first “pull in” voltage identifier122determines when, for example, a capacitance value change satisfies a threshold and/or indicates that a first “pull-in” voltage value126has been achieved. In some examples, results600of the electrical tests are plotted on a graph602depicted inFIG. 6where an x-axis604represents voltage and a y-axis606represents capacitance and the increase in capacitance at reference number608is indicative of the pull-in voltage.

Referring back to the example ofFIG. 1, the first voltage stimulator120and/or the first “pull-in” voltage identifier122provide or otherwise enable the correlator118to access the first “pull-in” voltage value126for further processing and/or to determine correlation coefficient values128used when calibrating other pressure sensors. In some examples, the correlation coefficient value(s)128are determined for the different pressures by the correlator118based on the measured pressure values114, the capacitance values116and the first “pull-in” voltage value126by generating correlation curves using, for example, a second order polynomial function such as, Equation 2 above. In some examples, correlation curves700generated by the correlator118are plotted on a graph702as depicted inFIG. 7where an x-axis704represents the pull in voltage in the electrical domain f(Vpi) and a y-axis706represents the capacitance in the physical domain, f(Cp). As shown in the example ofFIG. 1, the correlation coefficient value(s) and corresponding pressure value(s)128are provided to a database130for storage.

FIG. 2illustrates an example implementation of the correlator118ofFIG. 1. In the illustrated example, the correlator118includes an example pressure/capacitance correlator202and an example pressure/voltage/capacitance correlator204.

In the illustrated example, to process the measured pressure values114and the capacitance values116associated with the physical tests of the training phase102, the pressure/capacitance correlator202receives and/or accesses the measured pressure values114and the capacitance values116and determines capacitance values206in the physical domain, f(Cp), using for example, Equation 1. In some examples, the capacitance values206in the physical domain, f(Cp), account for the capacitance (e.g., Cp=1013hPa) of the first pressure sensor104at ambient pressure.

In the illustrated example, to determine the correlation coefficient values128used to calibrate other pressure sensors, the pressure/voltage/capacitance correlator204receives and/or accesses the capacitance values206in the physical domain, f(Cp), and the first “pull-in” voltage126and determines the correlation coefficient values128for each of the pressure values having a corresponding capacitance value206in the physical domain, f(Cp), using, for example, Equation 2. In some examples, to associate the correlation coefficient values128with a corresponding pressure value, the pressure/voltage/capacitance correlator204generates a look-up table in which the correlation coefficient values128(e.g., a1, a2, a3) are associated with a respective pressure value (e.g., P1, P2, P3, etc.).

FIG. 3illustrates an example calibration system300that 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 system300includes an example testing phase302that calibrates a second pressure sensor304using the determined correlation coefficient values128and the results of electrical tests conducted on the second pressure sensor304. While the illustrated example depicts one pressure sensor (i.e., the second pressure sensor304) in the testing phase, in other examples, any number of pressure sensors may be used during the testing phase302.

To enable the electrical test(s) to be performed during the testing phase302, in the illustrated example, the example calibration system100includes an example second voltage stimulator306and an example second “pull-in” voltage identifier308. In some examples, the electrical tests include the second voltage stimulator306applying second voltage values310to and/or across the second pressure sensor304and the second “pull-in” voltage identifier308measuring the resultant capacitance value(s) based on the voltage(s) applied. In some examples, the second “pull-in” voltage identifier308determines when, for example, a capacitance value change satisfies a threshold and/or indicates that a second “pull-in” voltage value312has been achieved.

In the illustrated example, the second voltage stimulator306and the second “pull-in” voltage identifier308provide or otherwise enable an example calibrator314to access the second “pull-in” voltage value(s)312for further processing. In some examples, the further processing includes the calibrator314determining calibration coefficient values316that can be used to calibrate the second pressure sensor304and/or stored on a data store318of the second pressure sensor304. The calibration values316may be determined based on the electrical tests performed on the second pressure sensor304, the correlation coefficient value(s)128from the correlator118, pressure sensor data and/or associated parameters320from a database322and/or an ambient pressure value(s)324measured by a pressure gauge and/or sensor326.

In some examples, the pressure sensor data and/or associated parameters320include, for example, a plate area of the second pressure sensor304, Ap, a plate radius of the second pressure sensor304, a, a permittivity of the free space within the second pressure sensor304, ε0, a relative permittivity of an oxide of the second pressure sensor304, εr,axand/or a peak plate displacement of the second pressure sensor304, xp. Additionally and/or alternatively, in some examples, the pressure sensor data and/or associated parameters320include, for example, a displacement adjustment of the second pressure sensor304, δxp, an effective gap of the second pressure sensor304, g0, an air gap of the second pressure sensor304, gnoox, a thickness of the oxide of the second pressure sensor304, tox, a parasitic offset of the second pressure sensor304, Cpar, flexural rigidity of the second pressure sensor304, D, Young's modulus, E and/or Poisson's ratio, v.

FIG. 4illustrates an example implementation of the calibrator314ofFIG. 3. In the illustrated example, the calibrator314includes an example re-constructor402, an example data fitter404and an example determiner406. In the illustrated example, to determine the resultant capacitance values when the second pressure sensor304is exposed to different pressures without actually performing physical tests on the second pressure sensor304, the re-constructor402accesses and/or receives the correlation coefficient values128and corresponding pressure values, the second “pull-in” voltage value312and the ambient pressure value324and predicts resultant capacitances408that the second pressure sensor304would generate if the second pressure sensor304were actually exposed to different pressures using Equation 2. In some examples, the re-constructor402uses Equation 2 to predict the capacitance that the second pressure sensor304would generate if the second pressure sensor304were actually exposed to different pressures. Thus, by selecting the correlation coefficient values128associated with a respective pressure, the example re-constructor402can predict the capacitance values in the physical domain for the second pressure sensor304without actually performing physical tests on the second pressure sensor304.

To determine other and/or extrapolate capacitance and pressure values408determined by the re-constructor402, in the illustrated example, the data fitter404accesses the pressure sensor data and/or associated parameters320and the pressure and capacitance values408and determines other and/or extrapolates and/or fits the pressure and capacitance values410using the sensor equation fit of Equation 4 and the places the data in a simpler form using the 5thorder polynomial fit equation of Equation 8.

To determine the calibration coefficient values316to be used to calibrate the second pressure sensor304, the determiner406accesses the other pressure and capacitance values410from the data fitter404and processes the other pressure and capacitance values410to determine the calibration coefficient values316. Thus, using the examples disclosed herein, the example correlator118determines the correlation coefficient values128by performing physical and electrical tests on the first pressure sensor104and the example calibrator314determines the calibration coefficient values316based on the correlation coefficient values128and electrical tests performed on the second pressure sensor304. In some examples, these calibration coefficient values316are stored in a memory to be later used to calibrate each sensor individually.

While an example manner of implementing the example correlator118ofFIG. 1is illustrated inFIG. 2and an example of implementing the example calibrator314ofFIG. 3is illustrated inFIG. 4, one or more of the elements, processes and/or devices illustrated inFIGS. 2 and/or 2may be combined, divided, re-arranged, omitted, eliminated and/or implemented in any other way. Further, the example pressure/capacitance correlator202, the example pressure/voltage/capacitance correlator204, the example correlator118, the example re-constructor402, the example data fitter404, the example determiner406and/or the example calibrator314ofFIGS. 2 and/or 4may be implemented by hardware, software, firmware and/or any combination of hardware, software and/or firmware. Thus, for example, any of the example pressure/capacitance correlator202, the example pressure/voltage/capacitance correlator204, the example correlator118, the example re-constructor402, the example data fitter404, the example determiner406and/or the example calibrator314ofFIGS. 2 and/or 4could 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/capacitance correlator202, the example pressure/voltage/capacitance correlator204, the example correlator118, the example re-constructor402, the example data fitter404, the example determiner406and/or the example calibrator314is/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 example correlator118ofFIG. 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. 5illustrates the example graph502including resultant capacitances of the first pressure sensor104being exposed to different pressures during the training phase102and/or predicted capacitance/pressure combinations for the second pressure sensor304in the testing phase302. The graph502ofFIG. 5includes the x-axis504that represents pressure and the y-axis506that represents capacitance.

FIG. 6illustrates the example graph602including resultant capacitances of the first pressure sensor104being exposed to different voltages during the training phase102and/or predicted capacitance/voltage combinations for the second pressure sensor304in the testing phase302. The graph602ofFIG. 6includes the x-axis604that represents voltage and the y-axis606that represents capacitance.

FIG. 7illustrates the example graph702including the correlation curves700generated using Equation 3 where the x-axis704represents the capacitance in the electrical domain f(Cpi) and the y-axis706represents the capacitance in the physical domain, f(Cp).

Flowcharts representative of example machine readable instructions for implementing the example correlator118and the example calibrator314ofFIGS. 1-4is shown inFIGS. 8-10. In this example, the machine readable instructions comprise a program for execution by a processor such as the processors1112,1212shown in the example processor platform1100,1200discussed below in connection withFIGS. 11, 12. 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 processors1112,1212, but the entire program and/or parts thereof could alternatively be executed by a device other than the processor1111,1212and/or embodied in firmware or dedicated hardware. Further, although the example program is described with reference to the flowchart illustrated inFIGS. 8-10, many other methods of implementing the example correlator118and the example calibrator314may 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. 8begins with the correlator118determining the correlation coefficient values128for different pressure values (block802). In some examples, the correlation coefficient values128are determined based on first values114,116,126determined during first tests on the first sensor104. The calibrator314determines the calibration coefficient values316to be used to calibrate the second sensor304(block804). In some examples, the calibration coefficient values316are determined based on second values312,320,324and the correlation coefficient values128. The calibration coefficient values316are stored on the second pressure sensor304(block806).

FIG. 9illustrates an example of performing the processes of block802to determine the correlation coefficient values128. The program ofFIG. 9begins with the pressure/capacitance correlator202of the correlator118accessing the measured pressure values114(block902) and accessing the capacitance values116(block904) from the physical tests performed on the first pressure sensor104during the training phase102. The pressure/capacitance correlator202processes the pressure values114and the capacitance values116using, for example, Equation 1, to determine the capacitance values206in the physical domain, f(Cp) (block906).

The pressure/voltage/capacitance correlator204of the correlator118accesses the first “pull-in” voltage value126(block908). The pressure/voltage/capacitance correlator204processes the capacitance values206in the physical domain, f(Cp) and the first “pull-in” voltage value126to determine the correlation coefficient values128for each of the pressure values having a corresponding capacitance value206in the physical domain, f(Cp), using, for example, Equation 2 (block910). The database130stores the correlation coefficient values128and the associated values in the database130(block912). The process then returns toFIG. 8.

FIG. 10illustrates an example of performing the processes of block804to determine the calibration coefficient values316for the second sensor304. The program ofFIG. 10begins with the re-constructor402of the calibrator314accessing the second “pull-in” voltage312(block1002) from the electrical tests performed on the second pressure sensor304. The re-constructor402selects a pressure value to predict the resultant capacitance value of the second pressure sensor304if the second pressure sensor304were actually physically exposed to the pressure (block1004). The re-constructor402selects the associated correlation coefficient values128associated with the selected pressure from, for example, a look-up table generated by the pressure/voltage/capacitance correlator204(block1006).

To predict the resultant capacitance values in the physical domain for the second pressure sensor304, the re-constructor402processes the correlation coefficient values128for the selected pressure, the second “pull-in” voltage value312and/or the ambient pressure value324and determines the capacitance value408for the selected pressure (block1008). The database322stores the associated pressure and capacitance values408in the database322(block1010). If another pressure is selected at block1012, control advances to block1014.

However, if another pressure is not selected at block1012, the data fitter404accesses the pressure and capacitance values408and/or the pressure sensor data and/or associated parameters320and determines other and/or extrapolates and/or fits the pressure and capacitance values410using an example sensor equation fit and/or places the data in a simpler form using an example 5thorder polynomial fit equation (block1016).

The determiner406determines the calibration coefficient values316to be used to calibrate the second pressure sensor304by processing the other pressure and capacitance values410(block1018). The process then returns toFIG. 8.

The processor platform1100of the illustrated example includes a processor1112. The processor1112of the illustrated example is hardware. For example, the processor1112can be implemented by one or more integrated circuits, logic circuits, microprocessors or controllers from any desired family or manufacturer. In this example, the processor1112implements the example pressure/capacitance correlator202, the example first voltage/capacitance correlator204and the example correlator118.

The processor1112of the illustrated example includes a local memory1113(e.g., a cache). The processor1112of the illustrated example is in communication with a main memory including a volatile memory1114and a non-volatile memory1116via a bus1118. The volatile memory1114may 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 memory1116may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory1114,1116is controlled by a memory controller.

The processor platform1100of the illustrated example also includes an interface circuit1120. The interface circuit1120may 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 devices1122are connected to the interface circuit1120. The input device(s)1122permit(s) a user to enter data and commands into the processor1112. 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 platform1100of the illustrated example also includes one or more mass storage devices1128for storing software and/or data. Examples of such mass storage devices1128include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, RAID systems, and digital versatile disk (DVD) drives.

The coded instructions1132of FIGS.FIGS. 8-10may be stored in the mass storage device1128, in the volatile memory1114, in the non-volatile memory1116, and/or on a removable tangible computer readable storage medium such as a CD or DVD.

The processor platform1200of the illustrated example includes a processor1212. The processor1212of the illustrated example is hardware. For example, the processor1212can be implemented by one or more integrated circuits, logic circuits, microprocessors or controllers from any desired family or manufacturer. In this example, the processor1212implements the example re-constructor402, the example data fitter404, the example determiner406and the example calibrator314.

The processor1212of the illustrated example includes a local memory1213(e.g., a cache). The processor1212of the illustrated example is in communication with a main memory including a volatile memory1214and a non-volatile memory1216via a bus1218. The volatile memory1214may 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 memory1216may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory1214,1216is controlled by a memory controller.

The processor platform1200of the illustrated example also includes an interface circuit1220. The interface circuit1220may 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 devices1222are connected to the interface circuit1220. The input device(s)1222permit(s) a user to enter data and commands into the processor1212. 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.

One or more output devices1224are also connected to the interface circuit1220of the illustrated example. The output devices1224can be implemented, for example, by display devices (e.g., a light emitting diode (LED), an organic light emitting diode (OLED), a liquid crystal display, a cathode ray tube display (CRT), a touchscreen, a tactile output device, a light emitting diode (LED)). The interface circuit1220of the illustrated example, thus, typically includes a graphics driver card, a graphics driver chip or a graphics driver processor.

The processor platform1200of the illustrated example also includes one or more mass storage devices1228for storing software and/or data. Examples of such mass storage devices1228include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, RAID systems, and digital versatile disk (DVD) drives.

The coded instructions1232of FIGS.FIGS. 8-10may be stored in the mass storage device1228, in the volatile memory1214, in the non-volatile memory1216, and/or on a removable tangible computer readable storage medium such as a CD or DVD.

From the foregoing, it will appreciate 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 performing tests on first pressure sensors during a training phase and calibrating second pressure sensors during a testing phase using correlation coefficient values determined during the training phase. By taking such an approach, the examples disclosed herein enable the efficient calibration of a large quantity of pressure sensors based on calibration coefficient values determined by testing a lesser number of pressure sensors.