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# Pressure sensor

## The physical quantity

Static pressure is the ratio of the perpendicular element of force to the element of surface it is exerted on.

ps = dF/dA

For the pressure inside a fluid we have:

ps = patm+ ρgh , where patm is the atmospheric pressure, ρ is the density of the fluid, g is the acceleration at the place of measurement, h is the distance from the free surface

The Si unit for pressure is pascal (Pa) which is equal to one newton per square metre (N/m2).

For liquids the total pressure can be expressed as:

p = ps + 0.5ρν, where ν is the velocity of the fluid

For gases, using the ideal gas equation the pressure is:

p = nkBT/V , where n, T and V are respectfully the number of molecules, the temperature and the volume of the gas, and kB is the Boltzmann constant

All those physical laws are implemented into the construction of devices designed for pressure measurements. They use different methods for sensing, converting and processing the signal. However, they have a common working principle explained in the following section.

## Working principle

The majority of pressure sensors do not measure the pressure directly. Being a composite sensor, it consists of a sensing element that takes a primary reading (most commonly deformation followed by displacement, force or strain) and translates it to another non-electric physical quantity. Another sensor then translates this into an electrical signal that represents the output of the pressure sensor.

Figure 1. Working principle of a composite pressure sensor.

## Types of pressure sensors

##### Pressure from resistance variation

In Figure 2A the applied pressure causes deformation of the sensing element (for example diaphragm), which is connected to a strain gauge that exhibits a change in resistance when mechanically strained. The value for pressure is then obtained by reading the variation of the output voltage which is proportional to the change in resistance of the strain gauge.

Figure 2A. Strain gauge pressure sensor.

Similarly, in Figure 2B a wiper (moveable electrical contact) is mechanically linked to the diaphragm and the applied pressure controls the wiper's position. This affects on the length of the wire (representing the resistance) between the wiper and the end of a potentiometer (variable resistance). The measurement for pressure is then obtained from the output voltage that reflects the resistance value.

Figure 2B. Potentiometric pressure sensor.

##### Pressure from capacitance variation

Here the sensing element, such as diaphragm, is connected to one of the electrodes of a capacitor. A change in the the distance between the plates, the effective area of the plates, or the relative permittivity of the dielectric creates a change in capacitance which reflects on the output voltage, from where the pressure can be derived.

Figure 3. Capacitive pressure sensors with a change in distance d, area A, or dielectric type.

##### Pressure from inductance variation

In magnetic circuits we talk about reluctance instead of resistance. A change in the distance between two magnetic devices causes a change in reluctance. In this type of sensor, the pressure acts on a part of the magnetic circuit (movable core) and changes the reluctance between the coils. The amplitude of the displacement is proportional to the output voltage which is used to calculate the applied pressure.

Figure 4. Inductive pressure sensor.

##### Pressure from piezoelectric effect

These types of sensors are used for dynamic pressure measurements. There are about 40 crystalline materials that generate electric charge when strained. Using such piezoelectrics as a sensing element, the strain produced from a stress on the diaphragm is converted to electric charge which is proportional to the pressure.

Figure 5. Piezo-electric pressure sensor.

##### Pressure from oscillation

These sensors use a vibrating element which frequency of vibration depends on the force applied to it. This element is made from ferromagnetic material and induces voltage between two magnets, which is consecutively amplified and measured. This voltage reflects the frequency of vibrations which follow a mathematical model to derive the pressure. The sensing element can be the vibrating element itself or connected to it.

Figure 6. Vibrating wire pressure sensor.

##### Pressure from light intensity variation

The displacement of the sensing element (vane) gives a variation in light intensity between the source LED and the measuring LED. The diaphragm connected to the vane is moved by pressure, and therefore, the amount of infrared light received changes. This change in light intensity corresponds to the pressure applied.

Figure 7. Optical pressure sensor.

##### Pressure from ion variation

The pressure of a gas can be derived from measuring the ion current flow. Electrical current is supplied and when the electrons entering the gauge hit the gas molecules, they form positive ions causing ion current flow. The amount of that ion current is related to the gas density which is proportional to its pressure.

Figure 8. Ionization gauge pressure sensor.

## Data reliability

All pressure sensors are intrusive. Therefore, an incorrect installation can disturb the measurand or compromise the reliability of the system.

##### Range

Different pressure sensors have optimal working ranges. The process defines the operating range and the pressure sensor must be able to behave stable within that range. The range can vary from nPa for ionisation to GPa for strain gauges.

##### Sensitivity

The sensitivity of pressure sensors varies greatly between different types. Sensors based on strain gauge, ionisation, induction principles are very sensitive. Some ionisation pressure sensors can detect changes of 0.1 nPa. Potentiometric sensors have relatively low sensitivity.

##### Accuracy

The accuracy of a pressure sensor depends on the signal chain. It is the cumulative errors of each link of the chain. Typically ±0.1%. The most accurate pressure sensors are based on oscillation. Optical types have low accuracy.

##### Drift

All pressure sensor are subjected to drift over time. This is mainly because they undergo expansion and contraction when pressure is applied. The magnitude of drift depends on the usage (how frequently the pressure changes and to what extend) and the mechanical and thermal stability of the materials it is made of.

## Applications

Pressure sensors are widely applied in energy generation industry where a constant monitoring and control of pressures is crucial for the operation of the power plants. Another application is in robotics where a pressure measurement is required in controls or as a substitute for touch. The proper operation of machines can be related to data from pressures of compressed air, gas, vapor, oil or other fluids. Some common applications are listed below.

##### Touch screen devices

Smart phones and some computer devices come with pressure sensors. Sensors in those devices determine where the pressure has been applied and inform the processor by generating electric signal. There are two or more sensors fitted at the the corner of the screen to give precise location where actually the pressure has been applied.

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Figure 9. Pressure indication on a mobile phone with a touchscreen.

##### Automotive industry and security

Pressure sensors have a great application in automotive industry and security systems. They help to monitor oil and coolant pressure by regulating appropriate power pressure in accelerators and brakes. Pressure sensors are usually incorporated in the radiator's fill cap and the pressure inside the radiator ranges from 0.6 bar to 1.0 bar.

Figure 10. Pressure control in a relief valve.

When the temperature of the coolant rises up then the pressured in the closed system also increases. This is then notified by the pressure sensor which opens the valve and the excess fluid is dumped into the overflow container.

Besides, pressure sensors have very important role in security system such as anti-locking braking system (ABS) and air bag system. Pressure sensors fitted into the automobiles work under ECU. ECU detects uneven (fast/slow) rotation of wheels during driving which then informs the pressure sensor to detect the specific parts of the problem and apply more or less pressure to give an even wheel rotation.

Similarly, when the pressure is applied to the airbag control unit, then the pressure sensor fitted into the system determines the direction of impact and the restraint device is activated within 15-30 millisecond of the crash. This  quick response of the system helps to prevent the passenger from possible dangers.

##### Biomedical instrumentation

-       Digital blood pressure monitors and ventilators.

##### Industrial uses

-       Monitor gases and their partial pressures.

-       Determine the depth in oil industry while exploring.

##### Aviation industry

-       Pressure sensors are used to balance the atmospheric pressure with the airplanes’ control system.

-       Give appropriate external environmental situation to the system.

-       Help to create a breathing condition in the cockpit.

##### Marine industry

-       Sensors in ships and submarines help to detect the actual depth creating a safe situation.

-       Sensors are of great use in underwater projects. They help to study the oxygen level and demand.

## References

1. Ripka, P. and Tipek, A., 2007. Modern sensors handbook. 1st ed. Newport Beach, CA: ISTE USA.
2. Huddleston, C., 2007. Intelligent sensor design using the microchip dsPIC. 1st ed. Amsterdam: Elsevier/Newnes.
3. Engineersgarage.com, (2014). Pressure Sensors: Working Principle & Types of Pressure Sensor - EngineersGarage. [online] Available at: http://www.engineersgarage.com/articles/pressure-sensors-types-working [Accessed 30 April. 2014].
4. Futek.com, (2014). Pressure Sensor selection. [online] Available at: http://www.futek.com/pressure_sensor_selection.aspx [Accessed 30 April. 2014].
5. Controls.engin.umich.edu, (2014). PressureSensors - ControlsWiki. [online] Available at: https://controls.engin.umich.edu/wiki/index.php/PressureSensors [Accessed 30 April. 2014].

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