Pressure Sensors: Types, Measurement, and Applications

A pressure sensor is a device used to detect pressure. In general, matter is classified into two categories: solids and fluids (liquids and gases). By varying pressure, it’s possible to change a liquid into a gas and vice versa.

As we know, it’s impossible to apply pressure to a fluid in any direction except normal to its surface. At any angle other than 90 degrees, the fluid will slide or flow. For a fluid at rest, pressure can be defined as the force $F$ exerted perpendicularly on a unit area $A$ of a boundary surface:

$p = \frac{dF}{dA}$

Pressure is a mechanical term and depends on mass, length, and time.

Pressure $dp = -w \cdot dh$, where $w$ is the specific weight of the medium and $h$ represents vertical height. Pressure is unaffected by the shape of the confining boundaries, which is why pressure sensors come in various shapes and dimensions.

The kinetic theory of gases states that pressure can be viewed as a measure of the total kinetic energy of the molecules:

$p = \frac{2}{3} \cdot \frac{KE}{V} = \frac{1}{3} \cdot (\rho \cdot C^2) = N \cdot R \cdot T$

Where:

• $KE$ = Kinetic Energy
• $V$ = Volume
• $C^2$ = Average value of the square of molecular velocities
• $\rho$ = Density
• $N$ = Number of molecules per unit volume
• $R$ = Specific gas constant
• $T$ = Absolute temperature

Whether gas pressure is above or below the pressure of ambient air, we speak about overpressure or vacuum. Pressure is called “relative” when it is measured with respect to ambient pressure. It is called “absolute” when it is measured with respect to a vacuum at 0 pressure. The pressure of a medium may be static when it is referred to fluid at rest, or dynamic when it is referred to the kinetic energy of a moving fluid.

Unit of Pressure

The SI unit of pressure is the pascal: $1 Pa = 1 N/m^2$; one pascal equals one newton of force uniformly distributed over 1 square meter of surface. In technical systems, “atmosphere” (atm) is sometimes used. One atmosphere is the pressure exerted on 1 square centimeter by a column of water having a height of 1 meter at a temperature of +4 °C and normal gravitational acceleration.

A pascal can be converted into other units using these relationships:

$Pa = 1.45 \times 10^{-4} \frac{lb}{in^2} = 9.869 \times 10^{-6} atm = 7.5 \times 10^{-4} cm Hg$

$1 atm = 760 torr (Torricelli) = 101325 Pa$

$1 psi = 6.89 \times 10^3 Pa = 0.0703 atm$

Pressure Measurement Methods

There are three different pressure measurement methods:

1. Absolute pressure: Relative to 0 Pa.
2. Gauge pressure: Relative to ambient atmospheric pressure.
3. Differential pressure: Relative to another pressure point in the system rather than ambient pressure.

Mercury Pressure Sensor

A simple and efficient pressure sensor is based on the communicating vessels principle. It’s primarily used for measuring gas pressure. A U-shaped wire is immersed in mercury, which shorts its resistance in proportion to the height of mercury in each column. The resistors are connected into a Wheatstone bridge circuit, which remains balanced as long as the differential pressure in the tube is zero.

Pressure applied to one arm of the tube unbalances the bridge, resulting in an output signal. The higher the pressure in the left tube, the higher the resistance of the corresponding arm and the lower the resistance of the opposite arm.

The output voltage is proportional to the difference in resistances $\Delta R$ of the wire arms not shunted by mercury:

$V_{out} = V \cdot \frac{\Delta R}{R}$

The sensor can be directly calibrated in units of torr.

Bellows, Membranes, Thin Plates

In pressure sensors, a sensing element is a mechanical device that undergoes structural changes under strain. These devices include bourdon tubes (C-shaped, twisted, and helical), corrugated, catenary diaphragms, capsules, bellows, barrel tubes, and other components whose shape changes under pressure.

A bellows converts pressure into a linear displacement, measured by an appropriate sensor. Thus, the bellows performs a first step in converting pressure into an electrical signal. A popular example of pressure conversion into a linear deflection is a diaphragm in an aneroid barometer.

A deflecting device always forms at least one wall of a pressure chamber and is coupled to a strain sensor, such as a strain gauge, which converts deflection into electrical signals. Currently, the majority of pressure sensors are fabricated with silicon membranes using micro-machining technology.

Piezoresistive Pressure Sensor

To make a pressure sensor, two essential components are required: a plate (membrane) with a known area ($A$) and a detector that responds to the applied force ($F$). Both components can be fabricated from silicon.

A silicon diaphragm pressure sensor consists of a thin silicon diaphragm as an elastic material and piezoresistive gauge resistors made by diffusing impurities into the diaphragm. When stress is applied to a semiconductor resistor with initial resistance $R$, the piezoresistive effect results in a change in resistance $\Delta R$:

$\frac{\Delta R}{R} = \pi_l \cdot \rho_l + \pi_t \cdot \rho_t$

Where $\pi_l$ and $\pi_t$ are the piezoresistive coefficients in the longitudinal and transverse directions, respectively. Stresses in the longitudinal and transverse directions are designated $\rho_l$ and $\rho_t$.

Capacitive Pressure Sensor

A silicon diaphragm can be used with another pressure-to-electric output conversion process: a capacitive sensor. Here, the diaphragm displacement modulates capacitance with respect to a reference plate. This conversion is especially effective for low-pressure sensors.

An entire sensor can be fabricated from a solid piece of silicon, maximizing its operational stability. The diaphragm can be designed to produce up to a 25% capacitance change over the full range, making these sensors candidates for direct digitization.

When designing a capacitive pressure sensor, maintaining the flatness of the diaphragm is crucial for good linearity. Traditionally, these sensors are linear only over displacements much less than their thickness. One way to improve the linear range is to make a diaphragm with grooves and corrugations using micro-machining technology.

Piezoelectric Pressure Sensor

Piezoelectric sensors rely on quartz crystals rather than a resistive bridge transducer. Electrodes transfer charge from the crystals to an amplifier built into the sensor. These crystals generate an electrical charge when they are strained.

Piezoelectric pressure sensors do not require an external excitation source and are very rugged. However, these sensors require charge amplification circuitry and are susceptible to shock and vibration.

Optoelectronic Pressure Sensor

When measuring low-level pressures or when thick membranes are required to enable a broad dynamic range, diaphragm displacement may be too small to assure sufficient resolution and accuracy. In addition, most piezoresistive sensors, and some capacitive sensors, are quite temperature sensitive, which requires additional thermal compensation.

An optical readout has several advantages over other technologies, namely simple encapsulation, small temperature effects, high resolution, and high accuracy. Optoelectronic sensors operating with light interference phenomena are especially promising.

Such sensors use a Fabry-Perot (FP) principle to measure small displacements. The sensor consists of the following essential components: a passive optical pressure chip with a membrane etched in silicon, a light-emitting diode (LED), and a detector chip.