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.
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.
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.
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.
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