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David E. Thompson



The use of integrated circuit based sensors and microprocessors has revolutionized instrumentation.  Many of today’s transducers can be called smart systems because they are capable of self-calibration, translation of the sensor reading to engineering units, compensation for environmental effects on the sensor, communication systems for sending data to a digital system, and more.  In the following sections, we will look at the more common sensors.

Position Sensors


Position sensors are those which transduce a rotary or linear displacement into a resistance, voltage, or current change.




There are a huge variety and number of types of variable resistors, termed potentiometers or “pots”, in use today.  Some of the types of these devices are wirewound, composite, rotational, linear, digital, harmonic output, log output, and more.    The concept is simple, a rotational or translational input is transduced, or changed, into a change in resistance between the three device pins..


In Figure 1, the potentiometer has two inputs, E1 and E2, and an output E3.  The output voltage is a linear sweep between these two voltages as portrayed in the following plot.

Figure 1.  The voltages in a potentiometer.

The most common configuration in signal manipulation is where one end of the pot is grounded, and the output voltage is a fraction of the input voltage, or Eout kEin.  This is shown in Figure 2 along with the shorthand notation to its right.

Figure 2.  Potentiometer used as a ratiometric device.

There are many interesting potentiometer variants.  Some of these include:

  • Nonlinear windings to produce an output proportional to the log of the input or other functions like sine and cosine.
  • Both straight and rotational windings.
  • Wirewound and composite materials are used.
  • Single- and multi-turn potentiometers.
  • Printed circuit board and panel mountings.
  • Vernier indicator systems with optional locking to hold the setting.
  • Variations on mounting (servo, screw, gang mounts).



Linear Variable Differential Transformers


These transducers are based on a variable coupling between input and output windings in a special transformer as shown in Figure 3.  A sinusoidal voltage is applied to the input and when the core is centered, the signals from the left and right output coils cancel on another, but with a small offset voltage, Eoff.



Figure 3. Electrical schematic for an LVDT position sensor.

Note that the amplitude of the output signal increases linearly in each direction, but there is a 180o phase shift between the input and output signal in the positive and negative directions.  It is possible to detect this change in phase for use in making the transducer more useable.

Figure 4.  A DC LVDT with internal signal conditioning.

A shown in Figure 4, it is now possible to configure all the signal conditioning inside the instrument, so that one merely provides a DC voltage and the output is a voltage linearly related to the position of the core with no offset voltage effect.  The transformer core is shown below the LVDT, but it is normally fitted on a threaded, non-magnetic rod attached to the object to be tracked, and then inserted into the LVDT body.



Hall Effect Sensors


These transducers track changes in magnetic flux density.  Some of these sensors are linear in their response, while others are bipolar.  A typical application is shown in Figure 5.

Figure 5.  Linear Hall effect position sensor (Allegra Model A1302 shown).

As the magnet and its associated field moves across the face of the sensor, the transducer’s output voltage changes.  These sensors can also be used to monitor the Earth’s magnetic field and monitor tilt angle (inclinometer) in one or two dimensions.  Note that the sensor output is scaled by the magnet’s pole-to-pole distance as well as the strength and direction of its magnetic field.  These devices require careful calibration.


One unique application of a Hall effect device is a “tiltmeter” to sense the position of the sensor relative to the Earth’s magnetic field.


Ultrasonic Sensors


These transducers actually use the speed of sound in air (or any other medium) to determine distances computed from the time for a pulse to make a round trip.  The speed of sound in air is given by the equation

                                                                                                                   Eqn 1

where k is the ratio of specific heats, k=Cp/Cv, R is the gas constant, and T the absolute temperature.  For air, this is approximately 1130 ft/sec.  The principle is as shown in Figure 6, where an ultrasonic pulse travels from a source through the medium, reflects off of a target, and is returned to the receiver.  In most instances, the transducer that generates the pulse can also be used as a receiver.



Figure 6.  The distance between source and target is computed from the transit time.

Unfortunately, small intervening targets will reflect the pulses (usually a high frequency train of 10 or more pulses) based on the target’s reflectivity and size.   A typical sensor and its interface electronics board are shown in Figure 7.  Most of these devices come with an on-board microprocessor to perform the time to distance calculations and to ignore small reflections.  They also frequently have options to allow them to communicate with a separate data storage and control computer.

Figure 7. Ultrasound transceiver and electronics module with a 2" inch diameter sensor.

One limitation is that most ultrasound sensors have a resonant frequency, so when the transducer is “pinged”, it has a mechanical resonance that produces a ringing phenomenon that lasts for a period of time before it can be used as a receiver and listen for a returned pulse train.


Optical Position Encoders


There are both linear and rotary versions of this sensor.  They are a form of analog (position) to digital converters.  They range in complexity from a simple rotational and direction count to absolute n-bit encoders.  A typical encoder has a glass plate with a row of photocells arrayed radially.  A pattern on the glass plate then interrupts the light passing through the plate to achieve multiple position bits.  A typical pattern is shown in Figure 8.



 Figure 8.  A typical 4-bit optical encoder pattern.



Temperature Sensors


There are similarly many different kinds of temperature sensors.  These include:

Mercury-in-glass thermometers, thermocouples, thermistors, semiconductor sensors, thermal color strips and paints, bimetallic, infrared, wireless, and more. 

Table 1.  Types of temperature sensors and the basis of their operation.

Galileo is credited with inventing the first density-based thermometer which he called a “thermoscope”.  In an open container of colored alcohol, he placed a long glass tube with a sphere at the upper end in this liquid after warming the sphere with his hands. The air in the sphere would then cool and contract, drawing alcohol into the tube. Then as the air temperature changed, the air in the sphere would expand or contract causing the colored alcohol to move up or down in the tube. Modern day Galileo thermometers use sealed vials of various densities in a liquid. As the temperature rises and the density of the liquid decreases, more of the vials sink to the bottom. The temperature can be read by marking each of the vials in turn with the temperature at which it sinks.

Following the thermoscope, water-based, open-ended thermometers were used. These were superseded by closed-glass liquid thermometers much like those we use today. Mercury has become the de factostandard liquid for precision thermometry due to its uniform expansion.

In the mid 1700's, John Harrison invented the bi-metallic strip for temperature compensation in clocks. Two metals with different coefficients of expansion are bonded together. Heating them equally will cause the strip to bend in one direction, cooling will cause them to bend in the other direction. Such a temperature-dependent deflection can be usefully applied to indicate temperature. A simple form of this device is widely used in thermostats and breaker switches. Helical bi-metallic springs are often used in common dial thermometers.


Resistance Thermometers


The electrical resistance of metals has been observed to be temperature dependent.  The resistance usually increases with increasing temperature, termed a positive temperature coefficient of resistance. Some new ceramic materials have negative temperature coefficients.  The most accurate thermometers use the resistance of platinum as the measured indicator. The laboratory standard is known as the "bird-cage" element. A helical platinum coil is suspended in a cage-like configuration to minimize strain-induced resistance changes. A more robust construction uses a film of platinum deposited on a ceramic substrate which is highly stable.

The resistance of a platinum thermometer is low (10-100 ohms) and the temperature coefficient is also low (0.385 ohms/°C at 0°C) so the resistance measuring equipment must be sensitive and accurate. The resistance of the connecting wire must be minimized since it can have a dramatic effect on the measurement. The usual method for measuring resistance with a Wheatstone Bridge where the platinum resistor forms one arm of the bridge. A three wire bridge is used to control for any temperature effects on the leads going to the thermometer.  The problems encountered with resistance thermometers include self- heating (must be subtracted from the measurement), thermal shunting (heat is conducted away from the system), and slow response time.





In 1821, while making tea, an Estonian physician named Thomas Seebeck discovered a new and interesting phenomenon: when two dissimilar metals are joined together, a current flows as long as one junction (termed a thermocouple) is at a higher temperature than the other.  He subsequently became famous for this natural phenomenon and this effect has been named for him.

Figure 9. Seebeck Effect (Adapted from Figliola & Beasley)


Years later, Jean Peltier found that when thermal energy crosses a thermocouple junction, energy is either liberated or absorbed.  The direction of the current flow determines the direction of the energy flow. A Seebeck current that exists at the hotter junction will result in energy absorption at that junction and an equal amount of thermal energy release at the other junction.  Here is a summary of the findings ofSeebeck and Peltier:

  1. The voltage (emf) developed by the thermocouple of two dissimilar metals will report the relative temperature of the two junctions.  This effect is irrespective of the temperature increases and decreases along the wires.
  2. A third metal in the circuit can introduce new voltage potentials unless both junctions are at the same temperature.  This is called the Law of Intermediate Metals.

Figure 10. Thermocouple circuit.


In Figure 10, there are three important temperatures shown that determine the accuracy and validity of the voltage measurements.  The unknown temperature, Tx, is the one temperature we want to influence the measurements.  The introduction of a less expensive wire from the measurement site to a remotely mounted instrument is a common practice.  To assure that this third metal doesn’t create a new emf to be dealt with, we must be certain that the temperatures of both connections at Tcon are at the same temperature.  We must take similar precautions at Tmeter, because the metal of the meter may be altogether a different alloy than the wires or the thermocouple.  The thermocouple emf generated will be proportional to the difference between Tx and Tmeter, as if the reference junction were at Tmeter.


The most common practice is to connect the thermocouple as shown in Figure 11.  Here a known reference temperature, Tref = 0oC, is used.  Tables of the generated voltage for this reference temperature are widely available for all standard types of thermocouples.  It is importat that Tconn = Tmeter or one introduces a new thermocouple into the calculation.


The use of thermocouples is robust and simple, and we can maximize the size of the emf generated by properly choosing the materials we use. Some examples of common matches include Chromel-Alumel(most popular and widely available, Type K: Chromel-Alumel), Chromel-Constantan (Non-magnetic, Type E), and Iron-Constantan (Type J), Copper-Constantan (Type T), Platinum-Rhodium (high temperature, standard calibration is melting point of gold, Type S).  Use the common Type K thermocouple, Chromel-Alumel, unless you have a reason not to do so.  Thermocouples are non-linear devices, but can have accuracies of better than 0.5oF, if these nonlinearities are taken into account.


Most measurement errors are caused by unintentional thermocouple junctions.  In addition, most thermocouples are made of thin wire to minimize response times.  Such thin wire can result in a high junction resistance making it sensitive to noise. A typical 32AWG wire (0.25mm diameter) junction will have a resistance of approximately 15 ohms/meter.  Special thermocouple extension wires that match the composition of the thermocouple are available that have larger gauges and are shielded and are thus less problematic.

Figure 11.  Ice junction reference temperature.

As shown in Figure 12 for a copper-constantan thermocouple, over a wide range of temperatures thermocouple voltage are highly non-linear.  Temperature interpolation is usually derived from polynomial fits of around 5th order and higher.

Figure 12.  Calibration for a type 'T' thermocouple with a 0oC reference junction.

Over a small range of temperatures, it is possible to represent the temperature using a simple linear approximation as T = T0+b(e-e0).  We can use tables to then compute the unknown temperature.


A simple formula representing the above data for a type ‘T’ thermocouple (copper-constantan) over the range -200oC to +400oC is given in Table 1.  This particular formula is of value because it only requires eight arithmetic operations per evaluation, each with a precision of slightly greater than that of the result.  This formula can be readily programmed into a spreadsheet, pocket calculator, or an analysis package.


Table 2. Simple formula, table of coefficients for type 'T' voltages to oC.

Another approach used to reduce the number of computations was introduced by Omega Engineering (www.omega.com).  The usual formulation for computing temperature requires 4 additions and 8 multiplications for a 5th order computation,

As shown below, by factoring, we can dramatically reduce the computational time.

The 5th order computation requires only 5 additions and 5 multiplications (which take the most time).  The difficulty of this task is highlighted by the fact that it typically takes a 9th order polynomial to obtain ±1oC accuracy.  Table 3 lists the National Bureau of Standards’ (now NIST) polynomial coefficients for standard commercial thermocouples.  Be careful to stay within the temperature limits shown, because the polynomial calculation errors grow rapidly outside these bounds.

Table 3. NBS polynomial coefficients for standard thermocouple types.

For your use as a quick reference on the range of voltages produced by the various types of thermocouples over their useable temperature range, refer to Figure 13.  Chromel-constantan has the greatest output, but its temperature range is more limited than others.

Figure 13. Voltage from standard thermocouple types with a 0oC reference junction.



Semiconductor Electronic Thermometers


It is now practical to integrate temperature sensors into standard semiconductor chips. Such devices have become cheap and readily available.  Some include A/D conversion on-chip and some even have signal conditioning and communications capability. The Dallas Semiconductor DS1820 is an example of just how capable and useful this new technology can be.



Infrared Temperature Measurement


As given below, all objects emit energy as a function of their surface temperature.

As surfaces emit more and more energy, they shift the peak radiance from the infrared (IR) to visible wavelengths (incandescence).  A good comparison is to note that standing next to a radiator used in room heating, one can feel the infrared heat being radiated and can only see the reflected light off of its surface.  Similarly, holding your hand next to a light bulb you feel the IR energy and also see its electromagnetic radiation.


Optical sensors and lenses that function in the IR regime allow one to make non-contact temperature measurement devices with fast response times (100 msec). They can be used for any object with an emissivity greater than 0.1 (polished metals or mirrors will give inexact readings).  Examples of such devices include medical thermometers and tire temperature recorders.


Calibration and Reference Temperatures


We frequently need exact temperatures to use as calibration test points or as reference junction temperatures.  There are some physical phenomena that are readily observed and consistent in nature.   The International Practical Temperature Scale established 11 such reference points as depicted in Table 4.

Table 4. Reference temperatures established by ITPS in 1968.


Two other commonly used, practical references are the freezing point of water (0oC) and the boiling point of water (100oC), both at a specific pressure of 1 atmosphere.



Pressure Sensors


There are many different kinds of pressure measurement devices.  The most common are described in this section.  Some of these devices measure absolute pressure, and others measure a differential pressure.  When the reference pressure of a differential pressure sensor is atmospheric pressure, the sensor is said to read “gage” pressure.

Bourdon Tube Gauges

In 1849 the Bourdon tube pressure gauge was patented in France by Eugene Bourdon. It is one of the most widely used instruments for measuring the pressure of liquids and gases of all kinds, including steam, water, and air up to pressures of 100,000 pounds per square inch (psi). Eugene Bourdon founded the Bourdon Sedeme Company to manufacture his invention.


The pressure sensing mechanism consists of a closed coiled tube (called a Bourdon tube) connected to the chamber or pipe in which pressure is to be sensed. As the pressure increases the tube will try to straighten (uncoil), while a reduced pressure will cause the tube to coil more tightly. This motion is transferred through a link to a gear train connected to an indicating needle. The needle is presented in front of a card face inscribed with the pressure indications associated with particular needle deflections.  While this device is normally a gage pressure device, if the housing around the Bourdon tube is sealed, it can be calibrated to read out in absolute pressure.

Figure 14.  Bourdon Tube pressure gauge mechanism.




The oldest known pressure measurement device is the U-tube manometer, shown both with no pressure and with pressure applied in Figure 15.  As the differential pressure increases, the weight of the liquid on the low pressure side balances the pressure difference.  The greater the density of the manometer fluid, the smaller the height change for a given pressure.

Text Box:   Figure 15. A U-tube manometer showing a differential pressure reading of 4 (the addition of the left and right scales).

If the reference pressure is atmospheric pressure, the manometer is a gage device.  While this may be a simple device, it is important for you to calibrate it periodically because fittings develop leaks, fluid may evaporate, changing the density of the remaining liquid, and other factors.  One improvement to the manometer is to use a large volume reservoir (with an area much larger than that of the tube) to allow for a direct reading of the pressure difference.  An example of this type of manometer is shown in Figure 16.


Figure 16.  Well type manometer with a pressure difference scale reading of 6.

There are examples where many manometer tubes share a common, large well and reference pressure.


Diaphragm Transducers


Two basic types of strain-gage transducers are used in practical pressure measurements are shown in Figure 17.  In (a), the deflection of the pressure-sensitive diaphragm with a stylus bends the beam which has strain gages near its root to measure bending.  A simpler arrangement is shown in (b), where the strain gages are affixed directly to the spring element and respond to the stress developed in the element's material. The gages are made of metal foil, vacuum-deposited or sputtered films and semiconductor material.


There are many different housing constructions for these devices.  If the body is sealed, it becomes an absolute pressure device.  Some units are constructed with two pressure ports so that you can record differential pressure or gage pressure.

Figure 17.  Two types of diaphragm pressure transducers.






Several of the figures and tables in this tutorial have been adapted from materials at the following locations:

Omega Instruments:  www.omega.com

TE Connectivity: http://www.te.com


Wikipedia:  http://en.wikipedia.org/wiki/Pressure_gauge