Theory Pressure Sensors

Pressure sensors have very diverse applications. For this, they must possess different properties. There are several technologies for measuring pressure. Depending on the scenario, the measured pressure may need to be compared with a different reference. There are also various ways to process the signals and then output them. These and other aspects of pressure sensors will be discussed in more detail here.


Pressure sensors

Pressure sensors have very diverse applications. For this, they must possess different properties. There are several technologies for measuring pressure. Depending on the scenario, the measured pressure may need to be compared with a different reference. There are also various ways to process the signals and then output them. These and other aspects of pressure sensors will be discussed in more detail here.

 

 

Resistive sensors

Resistive sensors operate with one or more resistances that change due to strain. These resistances are integrated into a Wheatstone bridge. By measuring the voltage differences at points A and B in Figure 1, the compression or elongation of the respective resistances can be derived. Most resistive pressure sensors are based on this principle. However, the carrier membrane on which the resistances are applied can have a variety of different designs.

Wheatstone-bridge

Silicon pressure sensors

Silicon pressure sensors are piezo-resistive sensors in which impurity atoms are applied to a silicon membrane, acting like strain-dependent resistors. "Piezo" because the variation of resistance is based on crystalline structures. The membrane thickness is normally 10-50 µm. The bottom side of the membrane is quite resistant to gases and aggressive liquids. The top side, on the other hand, which is populated with foreign atoms, is much more susceptible. Silicon pressure sensors can still be equipped with an additional, chemically stable outer membrane to circumvent this problem, whereby the space between the two membranes is filled with an oil for pressure transfer. The disadvantage of this arrangement, however, is the risk of leaking oil if the sensor is damaged, which can have expensive consequences, especially in pharmaceutical or food applications.
Piezo-resistive silicon sensors have high accuracy and are particularly suitable for the low pressure ranges. On the other hand, they are not very shock resistant.

Ceramic thick-film sensors

In ceramic thick-film sensors, resistors are applied to the ceramic diaphragm using a pressure process. The ceramics are very resistant to aggressive media and are suitable for medium pressure ranges. They are also inexpensive to manufacture.

Metal thin-film sensors

In metal thin-film sensors, the resistors are applied to a stainless steel membrane. Metal thin-film sensors are not suitable for use as absolute pressure sensors, since the generation of a vacuum behind the metal diaphragm is very complex. On the other hand, they are more resistant to overpressure, high temperatures and vibrations. They are generally more suitable for the higher pressure ranges, up to several 1000 bar.

Capacitive sensors

In capacitive sensors, the capacitance is measured between the sensor backplate and a membrane. The closer these two electrodes are, the higher the capacitance. From the measurement of this capacitance, more precise and higher-resolution pressure values can be read out than is the case with resistive designs. Furthermore, capacitive sensors are position-independent. This means that it has no influence on the measurement whether the sensor is mounted sideways or downwards, for example. Capacitive sensors also have a low energy consumption, which is an advantage especially in battery-powered systems. A disadvantage, however, is the drift, i.e. the correct reading of the pressure value over a longer period of time. Capacitive pressure sensors tend to be more expensive to manufacture than resistive designs.

Structure of a capacitive pressure sensor

Piezoelectric sensors

Another technology that can be used for pressure measurements is piezoelectricity. Piezoelectric sensors should not be confused with piezoresistive sensors. In piezoresistive sensors, a crystal generates a voltage dependent on the pressure applied to it. However, this voltage drops over time as the pressure remains constant. This technology is therefore not suitable for static pressure measurement. On the other hand, dynamic pressure changes can be measured very precisely and, above all, accurately even in very high pressure ranges. Since the voltage generated by the crystal has a very high impedance, the amplifying electronics must be designed very carefully, otherwise interference signals can quickly render the measurement unusable.

Calibration and compensation

The simplest form of sensor is the uncalibrated, uncompensated sensor. These sensors output a simple signal, usually in the range of 20-200 mV. This signal must then be calibrated and compensated for each individual sensor. Calibration in this context means correcting the signal for offset and span. Compensating means compensating for temperature effects.
Sensors can be compensated and calibrated, however, depending on the application, an amplifier is still missing. The temperature influence can either be compensated directly by a temperature dependent resistor. Alternatively, this is done electronically using a separate temperature sensor. In each case, calibration is performed directly at the factory. However, the output signal of such a sensor still shows disturbances, e.g. the linearity still has to be corrected.

uncalibrated, not compensated sensors (Fujikura FGM)

Differences in signal output

The signal output of sensors can be done in different ways. On the one hand, a distinction must be made between digital and analog output signals. For digital signals, some standards such as I²C or SPI have become established.


If additional electronics are omitted, the output signal can be directly proportional to the input voltage, which is usually in the range of a few hundred mV. This is cheaper in production and energy consumption, but makes the output signal additionally dependent on voltage fluctuations in the supply. Regulated voltage sources are therefore required for the operation of such sensors.


If the output signal is output in a standard voltage range such as 0-5 V, this must be regulated by internal electronics, which makes such sensors independent of voltage fluctuations in the power supply.
 
Via a further circuit, the voltage signal can then also be converted into a current signal. This is especially common for pressure transmitters, since a current signal is less susceptible to interference.

Pressure types

Pressure sensors differ in the property relative to which pressure is measured. On the one hand, pressure can be measured relative to vacuum. In such so-called absolute pressure sensors, a vacuum is created in the chamber behind the diaphragm, which is then sealed, usually with the aid of anodic bonding. This results in a vacuum that is as permanent as possible, thus avoiding excessive long-term drift. Absolute pressure sensors are primarily used to measure barometric and altimeter air pressure.
 
In certain applications, however, a vacuum as a reference is not necessary or even undesirable. Often it is sufficient to measure the pressure relative to the ambient pressure. Such sensors are called "gauge pressure sensors". In certain situations, however, the pressure difference between two systems is of interest. In such cases differential pressure sensors are used.


Pressure measuring cells

Pressure sensing elements can be constructed in different ways. In principle, however, it is a pressure sensor that is installed in a small, cylindrical housing. Depending on the application, this simplifies the design-in process.


The market of pressure sensing elements is dominated by two types: oil-filled cells and ceramic cells. In the case of oil-filled pressure cells, a pressure sensor is installed in a steel cylinder, one end of which has a diaphragm, which is classically made of stainless steel. In the case of ceramic pressure sensing elements, the entire housing is often made of ceramic. Ceramic cells offer high resistance to aggressive media. Oil-filled measuring cells, for example, have the advantage that the temperature in the measuring cell is very homogeneous when the ambient and medium temperatures change. This leads to fewer measurement errors in the event of strong temperature fluctuations.


For the output signals of measuring cells, the entire range is available, from unamplified and uncompensated to digital output signal.


Pressure transmitter and transducer

Depending on the application, it makes sense to install the sensor in a standardized housing before it is used further. Transmitters/transducers contain sensors or measuring cells that have already been calibrated and compensated. The output signal is processed and standardized. The terms "transmitter" and "transducer" are largely used synonymously in the industry. Originally, the terms differ at the signal output: the transmitter outputs a current signal, the transducer outputs a voltage signal. The current signal of a transmitter is in most cases 4-20mA. With the Transducers there are clearly more variants. For example, the output can be 0-5V, 0.5-4.5 or 0-10V. Mostly this signal is regulated by the transducer, but it can also be relative or ratiometric to the supply voltage. The advantage of the current output is the low susceptibility to interference. The voltage of a voltage output drops differently depending on the resistance and length of the signal line, which can lead to measurement errors. A transmitter has a rather higher energy consumption compared to a transducer.
There are also transmitters / transducers with digital signal output, which is why the terms were additionally mixed. The digital signals range from simple protocols such as I2C or SPI to industrial standards such as IO-Link.
The main advantage of transmitters and transducers compared to mountable pressure sensors or measuring cells is the reduced development effort. A transmitter is also much easier to replace after a failure.

Pressure transmitters in steel housings with different electrical and process connections (APSP PEWA200)

Measuring accuracy and other specifications

The accuracy specified in a data sheet is usually divided into the following three components: Repeatability, linearity (or non-linearity) and hysteresis.

A term that is often found in connection with repeatability is precision. Precision is comparable to repeatability. However, precision normally refers to longer periods of time. Repeatability, in relation to sensors, refers to measurements within a few hours. Precision tends not to be specified for sensors, but in principle would describe "repeatability over several months, including long-term drift."


Linearity also needs to be investigated. Linearity describes how closely the measurement curve correlates with a straight line over the entire measurement range.


When developing a sensor, the aim is to achieve as linear a relationship as possible between the measured quantity and the output. The linearity specification then describes the maximum deviation of the measurement from an ideal straight line in % of the entire measuring range.

Possible linearization. The red arrow describes the specification linearity in % of the span.

Finally, the hysteresis must be taken into account. It describes the difference at the output signal when the same pressure is measured, but this is approached once from above and once from below. The same effect can also be observed in relation to the temperature, in this case it is called temperature hysteresis. However, temperature hysteresis is not included in the accuracy specification.


So any measured value should be within the specified accuracy taking into account repeatability, linearity and hysteresis. It is important to note that the accuracy is specified in % Full Scale. The percentage value therefore refers to the entire measuring range. This means that the maximum deviation is "absolutely" constant over the entire measuring range. The error relative to the measuring range, on the other hand, is considerably larger in the lower measuring range. It is therefore worthwhile to configure a sensor only to the required measuring range, otherwise it becomes very inaccurate in the lower measuring range.

Illustration of the hysteresis

Another figure, which can sometimes be found on data sheets, is the "Total Error Band" (TER). The TER describes the worst-case scenario, taking into account accuracy and all temperature-dependent influences.


With varying temperature, both zero and span can shift. In addition, the temperature hysteresis already mentioned plays a role here.


If it is known that the sensor will only be used in a narrow temperature window, the "accuracy" may be sufficient as a reference. In many cases, however, the temperature varies, which is why the TER should then be decisive.

Components of accuracy and total error band

A simplifying straight line can be placed over the actual curve in different ways. The straight line can be drawn through the calibrated end points of the curve. This way, the deviation is in most cases completely in the positive or negative range.


In total, the method of least squares offers the least deviation.


An intermediate solution is the method of fixing the straight line at 10% and 90% of the span respectively. In this way, the deviation is distributed much more evenly in many cases than with the first-mentioned method, without excessive effort during calibration.


If, on the other hand, the sensor is mostly used in the room temperature range, it may also make sense to draw the line through the real 25°C mark. In this way, the deviation over the entire temperature range may be larger, but in the most relevant range for this application, it is significantly more accurate.

Typical vs. Maximal

For specifications in connection with accuracy, a distinction must be made between typical and maximum values.


Strictly speaking, the maximum error is the three-σ deviation of the normal distribution of all sensors. This means that 99.7% of the sensors fulfill this limit. The typical error describes the single-σ deviation, i.e. only 68.2% of the sensors fulfill the limit.


In general usage, however, the maximum error can be understood as a guarantee that a sensor must fulfill. For the typical error, the matter is less clear. Sometimes the average accuracy of a sufficiently large sample is declared as typical error. It is not always directly obvious whether accuracy specifications are typical or maximum values. In case of doubt, such questions should definitely be clarified with the supplier or distributor.

Resolution

Resolution is a term that should not be confused with accuracy. Resolution can refer to two different values for a sensor. For an amplified sensor with an analog output, the resolution refers to the analog-to-digital converter (ADC). This takes the analog signal from the sensor membrane, compensates it using stored values, and then outputs a quasi-analog signal. Quasi-analog because the signal is output as a "staircase" (see Fig. XX). The resolution now describes how high these stair steps are. It is given in bits.

It is important that the resolution in all cases does not allow a direct statement on the accuracy. The resolution must be at least as high as the accuracy. But a higher resolution does not increase the accuracy. A small calculation example:

Conversion of an analog signal into an amplified, quasi-analog signal

The sensor has a measuring range of 0-2 bar, a TER of 1.5% and an ADC resolution of 16-bit. The output is analog with 4-20mA.


The resolution has 16Bit = 65'535 steps. Translated to the output this means that the smallest step (20mA - 4mA) / 65535 = 0.000244mA = 0.244uA. Now the conclusion could be that the signal is therefore accurate to 0.000244mA / (20mA - 4mA) * 100 = 0.001525%. However, it turns out that the accuracy of 1.5% means a current range of (20mA - 4mA) * 1.5% = 0.24mA. So, in this example, the accuracy can deviate by almost 1000 steps of the resolution.


For further signal processing the resolution is quite important, especially for sensors with a digital output. However, it must be treated independently of the accuracy.


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