Transducers and Potentiometers

Transducers

• These are electromechanical devices converting mechanical changes like displacement or force into electrical signals.
• The electrical signals from transducers can be monitored as voltage after conditioning.
• Transducer characteristics, including range, linearity, sensitivity, and operating temperature, are determined primarily by incorporated sensors.

Potentiometers: Slide-Wire Resistance

• These potentiometers can be used for displacement measurement.
• The relationship of values are given via the following formulas: v₀ = (x/l)vi or x = (v₀/vi)l
• Slide-wire resistance potentiometers are not feasible for all situations.
• The resistance of short wire lengths causes excessive power requirements from the voltage source.

Potentiometers: Wire-Wrapped Resistance

• Wire-wrapped resistance potentiometers are used to avoid low resistance issues from slide-wire resistance potentiometers.
• Applications include measurement of linear displacement (see Fig. 5.2 a) and angular displacement (see Fig. 5.2 b).
• Resistance ranges from 10 to 10^6 Ω, based on coil length, wire type and diameter.
• Resistance increases stepwise.
• The step change in resistance limits potentiometer resolution to L/n, where n is the number of turns in the length of the coil.
• Linear potentiometers are available up to 1 m in length.

Differential Transformers

• These are based on a variable-inductance principle and are used to measure displacement.
• LVDT is short for Linear Variable Differential Transformer.
• These consist of 3 symmetrically spaced coils wound onto an insulated bobbin (Fig. 5.3 a).
• They feature a magnetic core that moves without contact through the bobbin, which provides a magnetic flux linkage path between coils.
• The position of the magnetic core controls mutual inductance between the primary (center) coil, and the secondary (outer) coils (Fig. 5.3b).
• The differential voltage, v₀, is equal to v1 - v2
• The output voltage is a linear function of core position (Fig. 5.4).

Strain-Gauged Element

• This is the basic form of an electrical resistance strain gauge.
• Strain gauges consist of a flat length of metal wire, metal foil strip, or a strip of semi-conductor material
• Similar to a postage stamp it can be stuck onto surfaces.
• When the wire, foil, strip or semiconductor is stretched, its resistance R changes.
• The fractional change in resistance ΔR/R is proportional to strain ε, where ΔR/R = Gε.
• G, the constant of proportionality, is also termed the gauge factor.
• Metal strain gauges usually have gauge factors around 2.0.
• The resistance increases when a metal strain gauge is stretched and the resistance decreases when it's compressed.

Capacitance Elements

• These are parallel plate capacitors defined as: C = εrε₀A/d.
  • εr is the relative permittivity of the dielectric between the plates.
  • ε₀ is a constant termed the permittivity of free space.
  • A is the area of overlap between the two plates.
  • d is the plate separation.
• Capacitance changes occur when the plate separation d changes, area A of overlap changes, or a dielectric slab is moved into or out of the plates. All affecting variations in **ε*r.
• All methods can be used to determine displacement.

Capacitance Sensor

• This consists of a target plate and a second plate (sensor head) (Fig. 5.11 a).
• The two plates are separated by an air gap of thickness h, forming the terminals of a capacitor.
• In operation h changes to h + Δh: C + ΔC = εrε₀A / (h+Δh) → ΔC / C = - Δh/h / 1+(Δh/h)
• ΔC/C is nonlinear, so the change in impedance due to the capacitor is measured to avoid difficulty employing a capacitance sensor with a nonlinear output.
• Fringing in the electric field produces nonlinearities when (h + Δh) exceeds D/4.
• The linear range is extended ≈D/2 by surrounding the sensor with a guard ring (Fig. 5.11 b)

Capacitance Sensor: Advantages

• Not contacting and can be used with most materials
• Rugged and can be subjected to high shock loads (5000 g) and intense vibratory environments.
• Impressive for use as a sensor at high temperatures.
• Constructed to withstand temperatures up to 2000°F (1111.1°C).
• Exhibit a constant sensitivity S over a broad temperature range: (74° - 1600°F) = (41.1°C – 888.89°C).

Resistance Temperature Detectors (RTDs)

• These are based on the change in resistance of metals with temperature, providing the basis for a family of temperature sensors.
• Resistance increases in a linear manner after the following calculations: Rt = R₀ * ( 1 + α ΔT ) -Rt: The resistance at a temperature t°C. -R₀: The resistance at a temperature 0°C. -α: A constant for the metal; the temperature coefficient of resistance.
• RTDs are composed of a conductor built either as a wire-wound coil, or a film or foil grid.
• RTDs are able to be used in ovens and furnaces.
• Platinum is used for sensor fabrication:
  • It the most stable metal
  • It is the least sensitive to contamination
  • It operates over a wide range of temperatures (4K to 1064°C; TK = TC + 273.15)

Thermocouplers

• These consist of two dissimilar materials in thermal and electrical contact
• A potential develops at the interface as temperature changes.
• The "Seebeck effect" describes the thermoelectric phenomenon.
• Figure 5.27 shows a typical thermocouple circuit
• J2 represents a reference junction where T2 is a reference temperature.
• J₁ is place in contact with the body at a point where a temperature measurement is performed. -Added junctions (J3 and J4) do not affect output voltage v₀ when meter terminals are at the same temperature (T3 = T4). v₀ = SA/B(T₁ - T₂): An equation that describes overall relation. -T1 = Temperature at junction 1 -T2 = Temperature at junction 2 -SA/B: the material sensitivity combination A and B; reference Table 5.4

Thermocouples: Practical Notes

• A thermocouple can be used with the reference junction at a temperature other than 0°C (The cold junction)
• Tables assume 0°C junction, so compensation is applied before use.
• Correction uses the law of intermediate temperatures: Vt,o = Vt,I + V₁,O -Vt,o = combined voltage -Vt₁ * T₁ = Temperature at junction 1 -VO = output voltage
• Can use software temperature correction measuring reference voltage with a precision temperature sensor.
• Use TC effectively by twisting wires from the TC to the reference junction, then wrapping them with ground foil sheath
• Measurement junction is intended to be grounded.

Thermistors

• These are semiconductor temperature sensors that are composed of metal oxide mixtures.
• In thermistors, resistance decreases in a nonlinear manner as temperature increases.
• Thermistors are rugged and small, which has allowed for temperature monitoring at virtually any point.
• Thermistors have a small thermal capacity due to their size, and respond rapidly to any change in temperature.
• Temperature range will depend on the thermistor used, but ranges typically stay within -100°C and +300°C.
• These feature large resistance change per degree variance, and can achieve accuracies of ±0.1°C within a small range.

Piezoelectric Sensors

• These produce charge when subjected to force or pressure.
• Quartz is an example of a material that can do that (single-crystal), along with polycrystalline barium titanate.
• Materials contain molecules featuring asymmetrical charge distributions, so the crystal deforms upon pressure being applied, prompting relative displacement of the positive and negative surfaces within.
• Displacement then produces external charges of opposite signals on the external crystal surfaces (Fig. 5.15).
• If the piezoelectric material is coated via metallic electrodes, measured charge q can be calculated from circuit voltage: q = vC
  • Where C is the capacitance of the associated piezoelectric crystal.
• Charge q is related to applied pressure p: q=SqAp -Sq = charge sensitivity of the associated piezoelectric crystal, e.g. quartz SiO₂ is 2.2 -A = electrode area
• Most piezoelectric transducers are generally fabricated from single-crystal quartz.
• The sensor acts like a capacitor (Fig. 5.16).
• Time available for voltage readout: τ = RₑCₑ = (RₚRA / (Rₚ + Rᴀ))(Cₚ + Cₗ + CA)
• Time constants usually range from 1000 to 100000 s