Correctly interpreting accuracy values for pressure sensors

Correctly interpreting accuracy values for pressure sensors

In the search for a suitable pressure transmitter, various factors will play a role. Whilst some applications require a particularly broad pressure range or an extended thermal stability, to others accuracy is decisive. The term “accuracy”, however, is defined by no standards. We provide you with an overview of the various values.

Although ‘accuracy’ is not a defined norm, it can nevertheless be verified from values relevant to accuracy, since these are defined across all standards. How these accuracy-relevant values are specified in the datasheets of various manufacturers, however, remains entirely up to them. For users, this complicates the comparison between different manufacturers. It thus comes down to how the accuracy is presented in the datasheets and interpreting this data correctly. A 0.5% error, after all, can be equally as precise as 0.1% – it’s only a question of the method adopted for determining that accuracy.

Accuracy values for pressure transmitters: An overview

The most widely applied accuracy value is non-linearity. This depicts the greatest possible deviation of the characteristic curve from a given reference line. To determine the latter, three methods are available: End Point adjustment, Best Fit Straight Line (BFSL) and Best Fit Through Zero. All of these methods lead to differing results.

The easiest method to understand is End Point adjustment. In this case, the reference line passes through the initial and end point of the characteristic curve. BSFL adjustment, on the other hand, is the method that results in the smallest error values. Here the reference line is positioned so that the maximum positive and negative deviations are equal in degree.

The Best Fit Through Zero method, in terms of results, is situated between the other two methods. Which of these methods manufacturers apply must usually be queried directly, since this information is often not noted in the datasheets. At STS, the characteristic curve according to Best Fit Through Zero adjustment is usually adopted.

The three methods in comparison:

Measurement error is the easiest value for users to understand regarding accuracy of a sensor, since it can be read directly from the characteristic curve and also contains the relevant error factors at room temperature (non-linearity, hysteresis, non-repeatability etc.). Measurement error describes the biggest deviation between the actual characteristic curve and the ideal straight line. Since measurement error returns a larger value than non-linearity, it is not often specified by manufacturers in datasheets.

Another accuracy value also applied is typical accuracy. Since individual measuring devices are not identical to one another, manufacturers state a maximum value, which will not be exceeded. The underlying “typical accuracy” will therefore not be achieved by all devices. It can be assumed, however, that the distribution of these devices corresponds to 1 sigma of the Gaussian distribution (meaning around two thirds). This also implies that one batch of the sensors is more precise than stated and another batch is less precise (although a particular maximum value will not be exceeded).

As paradoxical as it may sound, accuracy values can actually vary in accuracy. In practice, this means that a pressure sensor with 0.5% error in maximal non-linearity according to End Point adjustment is exactly as accurate as a sensor with 0.1% error of typical non-linearity according to BSFL adjustment.

Temperature error

The accuracy values of non-linearity, typical accuracy and measurement error refer to the behavior of the pressure sensor at a reference temperature, which is usually 25°C. Of course, there are also applications where very low or very high temperatures can occur. Because thermal conditions influence the precision of the sensor, the temperature error must additionally be included. More about the thermal characteristics of piezoresistive pressure sensors can be found here.

Accuracy over time: Long-term stability

The entries for accuracy in the product datasheets provide information about the instrument at the end of its production process. From this moment on, the accuracy of the device can alter. This is completely normal. The alterations over the course of the sensor’s lifetime are usually specified as long-term stability.  Here also, the data refers to laboratory or reference conditions. This means that, even in extensive tests under laboratory conditions, the stated long-term stability cannot be quantified precisely for the true operating conditions. A number of factors need to be considered: Thermal conditions, vibrations or the actual pressures to be endured influence accuracy over the product’s lifetime.

This is why we recommend testing pressure sensors once a year for compliance to their specifications. It is essential to check variations in the device in terms of accuracy. To this end, it is normally sufficient to check the zero point for changes while in an unpressurized state. Should this be greater than the manufacturer’s specifications, the unit is likely to be defective.

The accuracy of a pressure sensor can be influenced by a variety of factors. It is therefore wholly advised to consult the manufacturers beforehand: Under which conditions is the pressure transmitter to be used? What possible sources of error could occur? How can the instrument be best integrated into the application? How was the accuracy specified in the datasheet calculated? In this way, you can ultimately ensure that you as a user receive the pressure transmitter that optimally meets your requirements in terms of accuracy.

Characteristic curve, hysteresis, measurement error: Terminology in pressure measurement technology

Characteristic curve, hysteresis, measurement error: Terminology in pressure measurement technology

The first data sources for users of pressure measurement technology are often the data sheets supplied by the manufacturers. Of particular interest here is usually the accuracy data. In this context, a large number of terms appear whose comprehension is of great importance in assessment of that particular measurement instrument.

On the topic of accuracy, it can be fundamentally stated that the term itself is not subject to any defined standard. This, however, is not the case for the terminology arising in association with accuracy specifications, including characteristic curve, hysteresis, non-linearity, non-repeatability, and measurement error. In the following, we will briefly explain these terms.

Characteristic curve

The characteristic curve indicates the dependence of the output signal (measured value) upon the input signal (pressure). In the ideal scenario, the characteristic curve will be a straight line.

Non-linearity

The greatest deviation (positive or negative) of the characteristic curve from a reference line is described as non-linearity. The reference line itself can be determined by three different methods: End Point adjustment, Best Fit Straight Line(BFSL) and Best Fit Through Zero. Each of these methods arrives at different results, with Limit Point adjustment being the most commonly used method in Europe. The reference line here runs through the start and end point of the characteristic curve.

Measurement error

The measurement error, or measurement deviation, describes the shift of the displayed value from the “correct” value. This “correct” value is an ideal one, which in practice can only be attained with a highly accurate measuring device under reference conditions, such as a primary standard as would be used in calibration. The measurement error is expressed as either an absolute or a relative error. Absolute error is listed in the same units as the measured value, whereas relative error refers to the correct value and remains unit-free.

Zero point and span errors

In sensor production, there are deviations from the reference device (standard). Measurement deviations at the measuring range start and end points are referred to as zero point and span errors. The latter relates to the difference between the two values. The zero point error is the difference between the ideal zero point of the target characteristic line and the true output value of the actual characteristic curve.

Zero point error can be easily read off by the user in an unpressurized state. In order to eliminate it, the user must then enter this as an offset into the evaluation unit. Elimination of the span error is somewhat more difficult, since the pressure at the end of the measuring range must be approached precisely.

Hysteresis

The displayed value measured depends not only on the input variable (here, pressure), but also on the values measured previously from the input variable.

If the characteristic curve of the measuring device is recorded with continuously increasing pressure and then compared with the characteristic curve at continuously decreasing pressure, it is noticeable that the output signals, despite identical pressures, are not themselves exactly identical. The maximum deviation between these two characteristic curves is termed hysteresis and is expressed as a percentage of full scale (% FS).

Non-repeatability

Even when measured under identical conditions, electronic pressure transmitters are subject to stochastic influences, because of which the output signal is not identical at the same pressure values over successive measurements. The biggest deviation over three successive measurements taken from the same direction of approach is thus expressed as non-repeatability. A reliable pressure measuring device is recognized by users from its lowest possible non-repeatability.

Similar to hysteresis, non-repeatability cannot be compensated for.

Temperature error

Temperature changes directly affect the characteristics of a pressure sensor. The electrical resistance of semiconductors, as used in piezoresistive pressure transmitters, decreases with increasing temperature, for example. Manufacturers therefore optimize their products by way of a balanced thermal characteristic. Temperature-related errors are either compensated for directly on the sensor or are performed electronically. Some devices also have a temperature sensor that directly compensates for these temperature-related errors. All the same, errors such as this can only be minimized but not completely eliminated. This residual temperature error is indicated by some manufacturers as a temperature coefficient.

Overload pressure – Overpressure

The specified error limits are exceeded into the overload range. The pressure transmitter, however, suffers no lasting damage.

Burst pressure

The burst pressure indicates the pressure at which deformation of the pressure transducer occurs, where it becomes mechanically damaged.

Long-term stability

External influences affect the measuring instrument. For this reason, the characteristic curve does not remain constant over years of use. The long-term stability (also long-term drift) is determined by manufacturers under laboratory conditions and listed in data sheets as a percentage of full scale per annum.

The actual operating conditions of the device can however differ significantly from the test conditions. Test procedures between manufacturers can also vary widely, which makes comparability of the data even more difficult. In general, it is recommended that the pressure transducer be calibrated at regular intervals and, if necessary, adjusted.

Accuracy: Non-conformity of a curve

As mentioned at the outset, “accuracy“ is not a fixed value. Another term occasionally used for accuracy is non-conformity of a curve. This describes the maximum total error according to IEC 770 and comprises the linearity deviation and hysteresis, as well as non-repeatability. It is therefore the deviation from the ideal characteristic line at the end value of the measurement range and is expressed as a percentage.

Download the free STS infographic on total error here:

The Long-Term Stability of Pressure Sensors

The Long-Term Stability of Pressure Sensors

Factors such as temperature and mechanical stress can have negative effects on the long-term stability of pressure sensors. However, the effects can be minimized by diligent testing during production.

Manufacturers usually indicate the long-term stability of their pressure sensors in data sheets. The value given in these data sheets is determined under laboratory conditions and it refers to the expected maximum change of zero point and output span in the course of a year. For example, a long-term stability of < 0.1 % FS means that the total error of a pressure sensor may deteriorate by 0.1 percent of the total scale in the course of one year.

Pressure sensors usually take some time to “settle in”. As already mentioned, zero point and sensitivity (output signal) are the main factors to be mentioned here. Users usually notice zero point shifts as they are easy to recognize and to adjust.

How can the long-term stability be optimized?

In order to achieve the best possible long-term stability, which means that only minor shifts occur during the product lifetime, the core element must be right: the sensor chip. A high-quality pressure sensor is the best guarantee for optimal long-term functionality. In the case of piezoresistive pressure sensors, this is the silicon chip on which the Wheatstone bridge is diffused. The foundation of a stable pressure sensor is already laid at the beginning of the production process. A diligent qualification of the silicon chip is hence paramount to the production of pressure sensors with great long-term stability.

The assembly of the sensor is decisive as well. The silicon chip is glued into a casing. Due to the effects of temperature and other influences, the glued-in chip may move and thus also effect the mechanical stress exerted on the silicon chip. Increasingly inaccurate measurement results are the consequence.

Practice has shown that a new sensor takes some time to really stabilize – especially in the first year. The older a sensor, the more stable it is. In order to keep undesirable developments to a minimum and to be able to better assess the sensor, it is aged and subjected to some testing before it leaves production.

How this is done varies from manufacturer to manufacturer. To stabilize new pressure sensors, STS treats them thermally for over a week. The “movement”, which is prone to occur in the sensor in the first year, is thus anticipated to a large extent. Therefore, the thermal treatment is a form of artificial aging.

Image 1: Thermal treatment of piezoresistive pressure measurement cells

The sensor is subjected to further tests in order to characterize it. This includes assessing the behavior of the individual sensor under various temperatures as well as a pressure treatment in which the device is exposed to the intended overpressure over a longer period of time. These measurements serve to characterize each individual sensor. This is necessary in order to make reliable statements about the behavior of the measuring instrument at different ambient temperatures (temperature compensation).

Hence, long-term stability largely depends on the production quality. Of course, regular calibrations and adjustments can help correct any shifts. However, this should not be necessary in most applications: Properly produced sensors will work realiably for a really long time.

How relevant is the long-term stability?

The relevance of long-term stability depends on the application. However, it is certainly of greater importance in the low pressure range. On the one hand, this is due to the fact that external influences have a stronger effect on the signal. Small changes in the mechanical stress of the chip have a greater effect on the precision of the measurement results. Furthermore, pressure sensors produced for low pressure applications are based on a silicon chip whose membrane thickness is often smaller than 10 μm. Therefore, special care is required here during assembly.

Image 2: Detailed view of a bondend and glued silicon chip

Despite all care, an infinite long-term stability and also accuracy is physically impossible. Factors such as pressure hysteresis and temperature hysteresis cannot be completely eliminated. They are, so to speak, the characteristics of a sensor. Users can plan accordingly. For high-accuracy applications, for example, pressure and temperature hysteresis should not exceed 0.02 percent of the total scale.

It should also be mentioned that the laws of physics place certain limits on a sensor’s long-term stability. Wear and tear is to be expected in particularly demanding applications such as applications with fluctuating, high temperatures. Constant high temperatures beyond 150 °C eventually destroy the sensor: the metal layer, which serves to contact the resistors of the Wheatstone bridge, diffuses into the silicon and literally disappears.

Users who use pressure measurements under such extreme conditions or demand the highest level of accuracy should therefore thoroughly discuss options with manufacturers in advance.

Total error or accuracy?

Total error or accuracy?

The topic of precision is often the main consideration for end users when purchasing a pressure transmitter. A variety of terminology relevant to accuracy is involved, which we have previously explained here. Accuracy, however, is only a partial aspect of another concept, total error, which also appears in the data sheets for pressure transmitters. In the following, we will explain how this designation is to be understood in data sheets and what role it should play in selection of the appropriate pressure sensor.

It can be firstly stated that accuracy does not provide information about the total error. This depends on various factors, such as under which conditions the pressure sensor is actually used. We can see in Figure 1 the three aspects of which total error consists: Adjustable errors, accuracy and thermal effects.

Figure 1: Origins of total error

As we see in the illustration above, the partial aspect of adjustable error consists of the zero point and span errors. The designation ‘adjustable error’ results from the fact that zero point and span errors can each be easily identified and adjusted. These are thus errors that users need not live with and indeed both have already been factory-corrected in pressure sensors of STS manufacture.

Long-term stability, also known as long-term error or long-term drift, is the cause of zero point and span errors during operation. This means that these two adjustable errors may reappear or even “worsen” after prolonged use of the sensor. By means of calibration and subsequent adjustment, this long-term drift can thus be corrected again. Read more about calibration and adjustment here.

Accuracy

The partial aspect of accuracy also appears in data sheets under the term ‘characteristic curve deviation’. This lack of conceptual clarity comes down to the fact that the term “accuracy” itself is not subject to any statutorily defined standard.

The term encompasses the errors of non-linearity, hysteresis (pressure) and non-repeatability (see Figure 2). Non-repeatability describes those deviations observed when a pressure is applied several consecutive times. Hysteresis refers to the fact that the output signals can differ at the exact same pressure when this is approached from a “rising” and “falling” direction. Both of these factors, however, are very minor in piezoresistive pressure transducers.

The biggest influence on accuracy, and thus also on total error, comes down to non-linearity. This is the greatest positive or negative deviation of the characteristic curve from a reference line at increasing and decreasing pressure. Read more on the terminology here.

Figure 2: The greatest difference in the characteristic curve when the pressure to be measured is approached several times is termed non-linearity.

Thermal effects

Temperature fluctuations have an influence on the measured values of a pressure sensor. There is also an effect known as temperature hysteresis. In general, hysteresis describes the deviation of a system when the same measuring point is approached from opposing directions. In the case of temperature hysteresis, this hysteresis describes the difference (error) of the output signal at a certain temperature when that specific temperature is approached from a lower or from a higher temperature. At STS this is typically listed at 25 °C.

More on the thermal characteristics of piezoresistive pressure transducers can be found here.

Figure 3: The typical appearance of thermal effects in pressure transmitters.

Total error or accuracy?

The important question that arises from these various aspects, of course, is what users should pay the most attention to in sensor selection. This will vary on a case-by-case basis. Since the aspect of adjustable errors has already been corrected at the factory, this plays only a subordinate role. In this instance, the sensor should in general be recalibrated and adjusted after one year of use.

When purchasing a new sensor, the dual aspects of accuracy and thermal effects now become decisive. The key question in this context is, “Do I perform my pressure measurements under controlled conditions?” This means that when users carry out their measurements near the reference temperature during calibration (typically 25 ° C), the thermal effects can essentially be ignored. The total error designation, however, does become important when pressure measurement is performed over a wide range of temperatures.

Lastly, we will look at a data sheet on the ATM.1st piezoresistive pressure transmitter from STS (Figure 4):

Figure 4: Excerpt from a data sheet (ATM.1st)

The technical specifications for the ATM.1st display both accuracy and total error, where the accuracy entries are broken down into their respective pressure ranges. The given values are derived from non-linearity, hysteresis and non-repeatability at room temperature. Users wishing to perform measurements under controlled temperature conditions (room temperature) can therefore orient themselves toward these accuracy values specified.

The total error depicted in the data sheet, on the other hand, does include thermal effects. In addition, total error is supplemented with the entries of “typ.” and “max.”. The first of these describes the typical total error. Not all pressure sensors are absolutely identical and their accuracy can vary slightly. The precision of the sensors correspond to the Gaussian normal distribution. This means that 90% of the measured values over the entire pressure and temperature range of a sensor correspond to the value designated under typical total error. Those remaining measured values are then attributed with maximum total error.  

Download our free infographic on the subject: