the physics on which the technology is based.
Static Pressure. Pressure, P, is defined as force, F, per unit area, A:
|P = F/A||(1)|
liquids or gases. A container filled with a liquid (see Figure 1) has a
pressure (due to the weight of the liquid) at a point in the liquid of:
|P = F / A = hw||(2)|
|h||= distance from the surface to the point|
|w||= weight of the liquid (most liquids are nearly incompressible)|
Figure 1. The pressure at any given point in a confined liquid is determined
by the weight of the liquid and the distance from the point to the surface.
|w = mg/V||(3)|
|g||= gravitational acceleration|
of liquid in a tank by measuring the pressure.
a given height. Mercury is 13.6 3 denser than water, so would exert a pressure
13.6 3 that of water for a column of the same height. It should be noted
that the pressure due to the height of a column of liquid is in addition
to the atmospheric pressure acting on the surface of the liquid. The height
of a column of liquid is:
|h = P/g||(5)|
in a liquid is buoyed up by a force equal to the weight of the liquid displaced."
Given a block of material submerged in a container of liquid (see Figure
2) with area A and length L, the downward pressure exerted on the top face
|PD = hg||(6)|
Figure 2. Archimedes' principle states that an object submerged in a
confined liquid will be buoyed up by the weight of the liquid it displaces.
|PU = (h + L) g||(7)|
|PU - PD = Lg||(8)|
of the liquid displaced.
Figure 3. The pressure transmitted to a confined liquid is normal to
the liquid's surface, as can be observed by breaching one of the walls of
results. Pressure is transmitted to the inside of a container normal to
the surfaces, a fact that can be most easily proved by punching a hole in
a container of water and observing the stream as it exits the hole (see
Figure 3). This is important in the construction of dams, given
that they must resist the force of water. This pressure is called the static
results in a like increase at every other point in the liquid. This principle
is used in hydraulic systems such as jacks and automobile brakes and is
the fluidic equivalent of the principle of the lever, which allows large
forces to be generated easily by trading large movement of a small piston
for small movement of a large piston (see Figure 4).
Figure 4. Pascal's law states that an increase in pressure at any point
in a liquid causes a corresponding increase at every other point in the
parallel to the flow direction is called the impact pressure, PI. This is
due to the kinetic energy of the fluid:
|PI = VO²/2||(9)|
|= fluid density|
|VO||= fluid velocity|
|PS = PO + PI||(10)|
|PS||= stagnation (or total) pressure|
|PO||= static pressure|
of applications. Rearranging the equation gives:
Figure 5. A Pitot tube assembly can be used to measure the velocity of
a moving fluid.
in Figure 5. The tube facing the flow measures total pressure and the tube
normal to the flow measures static pressure. This approach is used in HVAC
applications and in aircraft to measure flow velocity.
compressible, and they completely fill any closed vessel in which they are
Figure 6. The compressibility of gases is illustrated by nonlinear atmosphere
pressure as a function of altitude.
6 is an example of the effect of the compressibility of gases.
or equilibrium conditions, but most real-life applications deal with dynamic
or changing pressure. For example, the measurement of blood pressure usually
gives the two steady-state values of systolic and diastolic pressure. There
is much additional information in the shape of the blood pressure signal,
however, which is the reason for the monitors used in critical-care situations.
be considered. As a rough approximation, the sensorfrequency response should
be 5-10 × the highest frequency component in the pressure signal. The
frequency response is defined as the highest frequency that the sensor will
measure without distortion or attenuation. Sometimes the response time is
given instead. For a first-order system, they are related as follows:
|FB = 1/2||(12)|
|FB||= frequency where the response is reduced by 50%|
|= time constant where the output rises to 63% of its final value following a step input change|
medium is used. Care must be taken to purge all air because its compressibility
will corrupt the waveform.
Absolute pressure is measured relative to a perfect vacuum. An
example is atmospheric pressure. A common unit of measure is pounds per
square inch absolute (psia).
points of measurement. This is commonly measured in units of pounds per
square inch differential (psid).
pressure is one example. Common measurement units are pressure per square
inch gauge (psig). Intake manifold vacuum in an automobile engine is an
example of a vacuum gauge measurement (vacuum is negative gauge pressure).
Figure 7. The same sensor can be used for all three types of pressure
measurement; only the references differ.
same sensor may be used for all three types; only the reference is different.
Differential pressures may be measured anywhere in the range—above, below,
and around atmospheric pressure.
As previously noted, pressure is force per unit area and historically
a great variety of units have been used, depending on their suitability
for the application. For example, blood pressure is usually measured in
mmHg because mercury manometers were used originally. Atmospheric pressure
is usually expressed in in.Hg for the same reason. Other units used for
atmospheric pressure are bar and atm. The following conversion factors should
help in dealing with the various units:
|1 psi||= 51.714 mmHg|
|= 2.0359 in.Hg|
|= 27.680 in.H2O|
|= 6.8946 kPa|
|1 bar||= 14.504 psi|
|1 atm.||= 14.696 psi|
Figure 8. The typical pressure sensor has three functional blocks.
units and that mmHg cancels.
Pressure is sensed by mechanical elements such as plates, shells, and
tubes that are designed and constructed to deflect when pressure is applied.
This is the basic mechanism converting pressure to physical movement. Next,
this movement must be transduced to obtain an electrical or other output.
Figure 9. The basic pressure sensing element can be configured as a C-shaped
Bourdon tube (A); a helical Bourdon tube (B); flat diaphragm (C); a convoluted
diaphragm (D); a capsule (E); or a set of bellows (F).
and the application. Figure 8 illustrates the three functional
The main types of sensing elements are Bourdon tubes, diaphragms, capsules,
and bellows (see Figure 9). The Bourdon tube is a sealed tube that
deflects in response to applied pressure. All except diaphragms provide
a fairly large displacement that is useful in mechanical gauges and for
electrical sensors that require a significant movement.
by the sensing element is read directly by a dial or pointer. These devices
are typically seen in low-performance applications, including blood pressure
measurement and automotive pressure gauges. The mechanical approach used
to couple the sensing element to the readout can introduce repeatability
Figure 10. Temperature has an effect on the offset of a pressure sensor.
also limits the frequency response and makes these sensors suitable only
for slowly changing measurements.
Pressure Sensors. Electromechanical pressure
sensors convert the applied pressure to an electrical signal. A wide variety
of materials and technologies has been used in these devices, resulting
in performance vs. cost tradeoffs and suitability for applications. The
electrical output signal also provides a variety of choices for various
|VOUT = kO + k1P||(13)|
|k1||= pressure sensitivity in V/pressure unit|
Figure 11. The sensitivity of a pressure sensor is also affected by temperature.
(also called null shift) and sensitivity (see Figures 10 and 11).
by Equation (13). One way to measure linearity is to use the least squares
method, which gives a best fit straight line (see Figure 12).
Figure 12. The least squares method can be used to measure a pressure
output with consecutive applications of the same pressure (see Figure 13).
output when the same increasing and then decreasing pressures are applied
consecutively (see Figure 14).
give the same output at a given temperature before and after a temperature
cycle. Repeatability and hysteresis effects are not easily compensated and
Figure 13. Repeatability refers to the ability of a pressure sensor to
provide the same output with successive applications of the same pressure.
defined as the ratio of the change in an electrical transduction parameter
over the full range of pressure to the value of that parameter at zero pressure.
|R||= base resistance|
|R||= resistance change with full-scale pressure, for example|
Figure 14. Hysteresis is a sensor's ability to give the same output at
a given temperature before and after a temperature cycle.
Potentiometric Pressure Sensors. Potentiometric pressure sensors
Figure 15. Potentiometric pressure sensors use a Bourdon tube, capsule,
or bellows to drive a wiper arm on a resistive element. Such sensors tend
to be inexpensive, but subject to repeatability and hysteresis errors.
element. For reliable operation the wiper must bear on the element with
some force, which leads to repeatability and hysteresis errors. These devices
are very low cost, however, and are used in low-performance applications
such as dashboard oil pressure gauges. An example is shown in Figure 15.
inductance or inductive coupling are used in pressure sensors. They all
require AC excitation of the coil(s) and, if a DC output is desired, subsequent
demodulation and filtering. The linear variable differential transformer
Figure 16. An LVDT pressure sensor, one configuration of inductive devices,
drives a moving core that varies the inductive coupling between the transformer
primary and secondary.
driving the moving core of the differential transformer (see Figure 16).
The LVDT uses the moving core to vary the inductive coupling between the
transformer primary and secondary.
use a thin diaphragm as one plate of a capacitor. Applied pressure causes
the diaphragm to deflect and the capacitance to change. This change may
or may not be linear and is typically on the order of several picofarads
out of a total capacitance of 50-100 pF. The change in capacitance may
be used to control the frequency of an oscillator or to vary the coupling
of an AC signal through a network. The electronics for signal conditioning
should be located close to the sensing element to prevent errors due to
|C = µA/d||(15)|
|µ||= dielectric constant of the material|
between the plates
|A||= area of the plates|
|d||= spacing between the plates|
Figure 17. The basic capacitive pressure sensor consists of two plates
with a vacuum between them.
constant, errors may result. Capacitive absolute pressure sensors with a
vacuum between the plates are ideal in this respect. Because the capacitance
of this sensor depends only on physical parameters, sensors with good performance
can be constructed using materials with low coefficients of thermal expansion.
Since the device has to be fairly large to obtain a usable signal, frequency
response may be a problem in some applications. Also, low-pressure capacitive
sensors exhibit acceleration and vibration sensitivity due to the necessity
for a large, thin diaphragm. A basic capacitive sensor is shown in Figure
17 and a more complex differential pressure capsule is shown in
transducers capable of converting stress into an electric potential and
vice versa. They consist of metallized quartz or ceramic materials. One
important factor to remember is that this is a dynamic effect, providing
an output only when the input is changing. This means that these sensors
can be used only for varying pressures. The piezoelectric element has a
Figure 18. A more complex capacitive pressure sensor can be built to
detect differential pressure.
by the interface electronics. Some piezoelectric pressure sensors include
an internal amplifier to provide an easy electrical interface (see Figure
used a metal diaphragm with strain gauges bonded to it. A strain gauge measures
the strain in a material subjected to applied stress. Consider a strip of
metallic material (see Figure 20) with electrical resistance given
|RO = L/WT||(16)|
|L, W, T||= length, width, thickness|
a change in resistance. A stress applied to the strip causes it to become
slightly longer, narrower, and thinner, resulting in a resistance of:
| R = (L + L) / (W - W)(T - T), or|
R RO(1 + 3)
small, on the order of 0.1% of the base resistance.
Figure 21. A silicon bar can be bonded to a diaphragm to yield a strain
gauge sensor with a relatively high output.
into a silicon diaphragm, because the response to applied stress is an order
of magnitude larger than for a metallic strain gauge. When the crystal lattice
structure of silicon is deformed by applied stress, the resistance changes.
This is called the piezoresistive effect. Following are some of the types
of strain gauges used in pressure sensors.
Photo 1. IC processing is used to form the piezoresistors on the surface
of a silicon wafer to fabricate an integrated piezoresistive pressure sensor.
a diaphragm by means of thin film deposition. This construction minimizes
the effects of repeatability and hysteresis that bonded strain gauges exhibit.
These sensors exhibit the relatively low output of metallic strain gauges.
to a diaphragm to form a sensor with relatively high output. Making the
diaphragm from a chemically inert material allows this sensor to interface
with a wide variety of media (see Figure 21).
to form the piezoresistors on the surface of a silicon wafer (see Photo
1). There are four piezoresistors within the diaphragm area on
the sensor. Two are subjected to tangential stress and two to radial stress
when the diaphragm is deflected.
Figure 22. Piezoresistive integrated semiconductor pressure sensors incorporate
four piezoresistors in the diaphragm. When the diaphragm is deflected, two
resistors are subjected to tangential stress and two to radial stress. The
four are connected to a four-element bridge.
configuration (see Figure 22) and provide the following output:
|VOUT/VCC = R / R||(18)|
|VCC||= supply voltage|
|R||= base resistance of the piezoresistor|
|R||= change with applied pressure and is typically ~2.5% of the full R|
Figure 23. The back of a wafer is etched out to form the diaphragm of
a piezoresistive pressure sensor.
23). The high output of the bonded strain gauge is combined with the low
hysteresis of the deposited strain gauge in this design, due to the integrated
construction and the nearly perfect elasticity of single-crystal silicon.
The cost of the sensing element is low since a large number of devices fit
on a silicon wafer. Typical die size is 0.1 in. square with a 50 mil square
Figure 24. Piezoresistive pressure sensors can be configured to provide
absolute, differential, or gauge pressure readings, depending on the reference.
The diaphragm is shown here as it deflects under applied differential pressures.
and calibration may also be included on the same IC. Various pressure ranges
are accommodated by varying the diaphragm thickness and, for very low pressures,
Photo 2. This totally integrated silicon pressure sensor measures 0.52
in. long by 0.44 in. wide by 0.75 in. high, including the port.
absolute, differential, and gauge pressure sensors, depending on the reference
(see Figure 24).
can have a great deal of mounting and port interface flexibility. Also,
the small size means that it has a wide frequency response and may be used
for dynamic pressure measurements without concern about errors. Mechanical
vibration and acceleration have a negligible effect.
Photo 3. The recently developed microbridge mass airflow sensor consists
of a thin thermally isolated bridge structure suspended over a cavity in
the silicon IC. The chip is 67 mil square.
measurement in applications where a small flow across the sensing element
may be tolerated. The sensor consists of a thin film thermally isolated
bridge structure suspended over a cavity in the silicon IC.
milliwatts of power are required to achieve high air flow sensitivity. By
calibrating the device with a flow restriction for a specified pressure
drop, a sensor capable of measuring pressures of a few inches of water results.
This is ideal for airflow measurement in HVAC applications, for example.
directed across the surface of the sensing element (see Figure 25).
Figure 25. A silicon bar can be bonded to a diaphragm to yield a strain
gauge sensor with a relatively high output.
the inlet and outlet ports of the package (see Photo 4). The sensor
Photo 4. The output voltage of the microbridge mass air flow sensor varies
in proportion to the mass flow of air or other gas through the inlet and
outlet ports of the package. The packaged sensor is 1.20 in. wide by 1.24
in. long by 0.61 in. high.
It consists of a thin film, thermally isolated, bridge structure containing
a heater and temperature-sensing elements. The bridge structure provides
a sensitive and fast response to the flow of air over the chip. Dual sensing
elements flanking a central heating element indicate direction as well as
rate of flow. A specially designed housing precisely directs and controls
the airflow across the sensing microstructure. Highly effective thermal
isolation for the heater and sensing resistors is attained by the etched
cavity air space beneath the flow sensor bridge. The small size and thermal
isolation of the microbridge mass airflow sensor are responsible for the
remarkably fast response and high sensitivity to flows.
other pressure measuring means with a precision snap switch, can provide
precise single-point pressure sensing. Alternatively, simple electronic
switches may be combined with electrical sensors to construct a pressure
switch with an adjustable set point and hysteresis.
a pressure sensor to avoid corrupting the signal by noise or 60 Hz AC pickup.
If the signal must be run some distance to the interface circuitry, twisted
and/or shielded wire should be considered. A decoupling capacitor located
at the sensor and connected from the supply to ground will also filter noise,
as will a capacitor from output to ground.
have a 2-wire interface and modulate the supply current in response to applied
pressure. Obviously, wire resistance has no effect and noise must change
the loop current, not simply impress a voltage on the signal. The industry
standard interface is:
|PL = 4 mA||(19)|
|PH = 20 mA||(20)|
|PL||= low pressure range limit|
|PH||= high pressure range limit|
Figure 26. Dead-weight testers, used to calibrate pressure sensors, incorporate
calibrated weights that exert force on a piston which in turn acts on a
fluid to produce a test pressure. Oil-type testers like the one shown here
are commonly used for high pressures; pneumatic air bearing devices are
the usual choice for lower pressures.
to verify the accuracy of their production test equipment. These include
dead weight testers and temperature-controlled servo-rebalance testers using
Bourdon tubes made from high-stability quartz.
that exert force on a piston which then acts on a fluid to produce a test
pressure. For high pressures (>500 psi), oil is typically used (see Figure
26); for lower pressures, pneumatic air bearing testers are available
and are much more convenient as well as less messy to use.
may be used for gauge, differential, and absolute measurements with a suitable
reference. It is useful mainly for lower pressure work because the height
Figure 27. The mercury manometer, another calibration option for pressure
sensors, can be used on gauge, differential, and absolute sensors with a
suitable reference. The difference between column heights gives the pressure
reading. Manometers are used mainly to calibrate sensors designed to measure
in the lower pressure ranges.
in column heights gives the pressure reading (see Figure 27).
available pressure sensors are furnished with individual test data. A sensor
with excellent repeatability and hysteresis makes an excellent low-cost
in-house pressure calibration reference when combined with a pneumatic pressure
regulator and a source of air pressure (see Figure 28).
Selection of a pressure sensor involves consideration of the medium for
compatibility with the materials used in the sensor, the type (gauge, absolute,
differential) of measurement, the range, the type of electrical output,
and the accuracy required. Manufacturer's specifications usually apply to
Figure 28. A sensor with excellent repeatability and hysteresis can be
combined with a pneumatic pressure regulator and a source of air pressure
to yield an inexpensive in-house pressure calibration reference.
is smaller, for example, the errors should ratio down. Total error can be
computed by adding the individual errors (worst-case) or by computing the
geometric sum or root sum of the squares (RSS). The latter is more realistic
since it treats them as independent errors that typically vary randomly.
Following is a comparison of the two methods.
- Linearity = 1% F.S.
- Null calibration = 1% F.S.
- Sensitivity calibration = 1% F.S. Temperature errors are sometimes
given as coefficients per ºC referenced to 25ºC. Simply multiply
the coefficient by the temperature range of the application to obtain the
- Temperature error = 0.5% F.S.
- Repeatability and hysteresis = 0.1% F.S.
|Worst case error = 1 + 1 + 1 + 0.5 + 0.1 = 3.6%||(22)|
Industrial. Fluid level in a tank: A gauge pressure sensor
located to measure the pressure at the bottom of a tank can be used for
a remote indication of fluid level using the relation:
|h = P/g||(23)|
a pressure drop. This approach is widely used to measure flow because the
pressure drop may be kept small in comparison to some other types of flowmeters
and because it is impervious to clogging, which may otherwise be a problem
when measuring flow of a viscous medium or one containing particulate matter.
The relation is:
measured in the presence of common-mode pressures of thousands of pounds
per square inch. These pressure sensors are built with elaborate mechanisms
to prevent damage due to the high common-mode pressures and also frequently
have remotely controllable pressure ranging.
modern electronically controlled auto. Among the most important are:
use the speed-density approach to intake air mass flow rate measurement.
The mass flow rate must be known so that the optimum amount of fuel can
be injected. MAP is used in conjunction with intake air temperature to compute
the air density. This requires a 15 psia range or higher (for supercharged
or turbocharged engines). It is also desirable to include an altitude correction
in the control system, and this requires measurement of barometric absolute
pressure (BAP). Some systems use a separate sensor, but it is more common
for the MAP sensor to do double duty since it reads atmospheric pressure
for two conditions. One, before the engine begins cranking and two, whenever
the throttle is wide open.
10-15 psig. The oil pump is sized to achieve this pressure at idle and
the pressure increases with engine speed. A potentiometric gauge or pressure
switch is used for this function since precision isn't required.
modern fuel systems are not vented to the atmosphere. This means that fumes
resulting from temperature-induced pressure changes in the fuel tank are
captured in a carbon canister and later recycled through the engine. Government
regulations require that leaks in this system be detected by the onboard
diagnostics system. One approach is to pressurize the system and measure
pressure decay over a fixed time interval. A 1 psig sensor is used for this
tire has prompted development of a remote tire pressure measurement system.
The reason is that a flat tire of this type is difficult to detect visually
and the distance over which it can be used without any pressure is limited.