Today 's sensor market offers a wide variety of pressure sensors for designers to use in their systems.They range from the very basic transducer to more complex, fully integrated devices with onchip circuitry.Because of those differences,designers must ascertain and, if necessary,compensate for the measurement error of the pressure sensor chosen.This is a vital step in the design process to ensure that the sensor complies with the design and application requirements.In some cases,compensation may also be done to improve the sensor 's overall performance in the application.

The intent of this article is to help application designers through that critical process.The following findings are based on studies done using Motorola 's pressure sensor devices.Regardless of the application,the concepts covered are applicable and are of value in the design-in phase.

The mainstay of the Motorola pressure sensor portfolio is the single-chip, piezoresistive device,with three levels of sophistication:

• basic, or uncompensated;
• calibrated and temperature--compensated;and
• calibrated, compensated and amplified.

Offset and span calibration,as well as temperature compensation,are performed by means of a thin-film resistor network that is laser-trimmed during the assembly process.

The sensor is typically coupled with a microcontroller device whose embedded software possesses a mathematical model of the sensor.Once the microcontroller reads the voltage output,the model is employed,with the help of an analog-to-digital converter, to express the signal as a pressure measurement.

The simplest expression of the mathematical model is the sensor's typical transfer function.The model can be refined throughout the calibration process;the level of sophistication increases with each calibration point.

Measurement error has a rather strict definition from a metrology standpoint: It 's the difference be- tween the measured pressure and the real pressure.The latter is usually not directly known,but it can be estimated with an appropriate pressure standard. As a target, metrologists typically accept standard instruments with an accuracy at least 10 times better than the device under test.With that in mind,we can begin.

Since a noncalibrated system uses only typical sensitivity and offset values to convert the output voltage into pressure,the measured pressure produces an error as reported in Fig.1.

That raw error has many contributing factors:

• Offset error.A vertical shift that remains constant over the whole pressure range,offset error is caused by the variability of the transducer-diffusion and laser-trim processes.
• Sensitivity error,with a magnitude proportional to pressure. If the device sensitivity is higher than the typical value,the sensitivity error is an increasing function of pressure (as in Fig.1). If the opposite is true, it is a decreasing function.This error is also due to variability in the diffusion process.
• Linearity error. This is a minor offender. It 's basically due to the silicon's physical nonlinearity but, for amplified sensors, also includes the amplifier's nonlinearity. The linearity-error profile shows a concave or convex curve.
• Hysteresis error.This error is negligible in most cases because of the silicon 's high mechanical rigidity. Hysteresis error should be considered only in the event of large pressure variations.

Calibration eliminates or greatly reduces these error factors.The compensation technique consists of determining the actual transfer-function parameters,instead of using their typical values. Potentiometers,adjustable resistors and other hardware can be used to perform calibration. Software is a much more flexible approach that can handle the job as well.

A one-point calibration compensates the offset error by nullifying the shift from zero of the transfer function. This type of calibration is also known as autozero.

Offset calibration is usually performed at zer pressure, especially in the case of differential sensors, because the differential pressure is zer at nominal conditions.For absolute sensors,the offset calibration is a bit trickier.It requires either a pressure-reading system, to measure the calibration pressure value when performed at ambient atmospheric pressure, or a pressure controller,to apply the desired pressure.

Zero-pressure calibration for differential sensors is very accurate since the calibration pressure is strictly equal to zero. On the other hand, the calibration accuracy at pressures not equal to zero depends on the pressure controller or the performance of the measurement system.

Pick your pressure

The choice of calibration pressure is critical,because this is what determines the pressure range in which the accuracy is optimal.In fact,after calibration the offset error is minimal at the calibration point and remains weak there.

Therefore,the calibration point has to be selected according to the target pressure range,which is not necessarily the same as the operating range.

To convert the output voltage into pressure, the typical sensitivity value is used in the mathematical model to perform one-point calibration.This is done because the actual sensitivity is unknown.

In Fig.2,the red curve represents the error profile after offset calibration (PCAL =0).Notice its vertical shift with the black curve,which represents the error before calibration.

This calibration is more restricting than one-point calibration and is probably more expensive. Nevertheless,compared with one-point calibration,it significantly improves the performance accuracy because it calibrates not only the offset but also the sensor's sensitivity. Thus the actual, not the typical,value is used in the error calculations.

The green curve in Fig.2 illustrates the accuracy improvement. Here, the calibration is performed at 0 and 500 mbar (full scale).The error is nearly zer at the calibration points.Therefore,it is critical to set those points appropriately so as to have a minimum measurement error within the desired pressure range.

Certain applications require higher accuracy levels

throughout the entire pressure range.For such applications,a multipoint calibration process yields the best results.In this method of calibration, not only are offset and sensitivity errors addressed, but a large portion of linearity error will also become a nonissue,as shown in the magenta curve in Fig.2.The mathematical model in this case is the same as the two-point calibration for each calibration interval (between two calibration points).

Three-point calibration, minus one

As previously stated,the linearity error has a consistent form,with a predictable shape and magnitude that fits a quadratic function.This is especially true of nonamplified sensors,since their nonlinearity is basically me- chanical (it 's due to silicon membrane stress).

Characterization of the part must be carried out on a representative sample to determine the coefficients of the polynomial function (a x 2 +bx +c)by calculating the average linearity-error profile.Once a,b and c are determined,the model remains valid for any sensor of the same type.That efficiently compensates for the linearity error without the third point.

Fig.3 shows an example of compensation performed on Motorola 's MPX2300,a temperature-compensated sensor used mainly in invasive blood-pressure measurement applications.The polynomial model has been extracted from the average linearity error of 10 sensors. The remaining error after compensation is 10 to 20 times smaller than the maximum raw linearity error,as shown by the dotted curves in Fig.3.

This method of error compensation transforms a low-cost sensor into a high-performance device (better than 0.05 percent of full-scale)with a mere two-point calibration.

The designer,of course,will choose the most suitable calibration method according to the application 's accuracy requirements.Nevertheless,that choice is also a matter of system cost.

Thanks to the diversity of integration levels and compensation techniques,designers have a wide range of options for appropriately addressing each design challenge.