Sensors and Electrical Transducers

Introduction and Context

Measurement is the foundation of engineering analysis, control, protection, automation, and scientific experimentation. A physical variable such as temperature, pressure, displacement, acceleration, light intensity, or chemical concentration cannot usually be processed directly by a digital controller or electrical instrument. It must first be detected and converted into a usable signal. Sensors and transducers perform this interface function.

A sensor detects a physical, chemical, or biological quantity and responds to it. A transducer converts energy from one form into another; in measurement systems, the term commonly refers to a device that converts a measurand into an electrical signal. The output may be voltage, current, resistance, capacitance, inductance, frequency, charge, or a digital code.

Modern electrical instrumentation increasingly combines sensing elements, signal conditioning, embedded computation, communication, and diagnostics. Consequently, the design of a sensor system requires more than selecting a sensing principle. It requires analysis of static and dynamic performance, loading, noise, calibration, reliability, safety, electromagnetic compatibility, and the intended measurement uncertainty.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Distinguish sensors, transducers, actuators, primary elements, and signal-conditioning stages.
2. Classify electrical transducers according to excitation, output, operating principle, and energy conversion.
3. Analyze sensitivity, linearity, hysteresis, resolution, repeatability, drift, uncertainty, and response time.
4. Explain the operating principles and limitations of resistive, inductive, capacitive, piezoelectric, thermoelectric, photoelectric, magnetic, and semiconductor sensors.
5. Select suitable sensors for industrial and research applications.
6. Design basic bridge and signal-conditioning arrangements.
7. Evaluate sensor systems in the presence of loading, noise, environmental effects, and calibration errors.
8. Apply sensor-fusion, digital-interface, and diagnostic concepts to contemporary instrumentation.

1. Measurement Chain and Sensor Terminology

A practical measurement system can be represented as:

measurand → sensing element → transduction element → signal conditioning → transmission or conversion → display, control, or storage

The measurand is the quantity being measured. The primary sensing element first responds to the measurand. A variable conversion element changes that response into a more convenient physical quantity, often an electrical one. Signal conditioning may include amplification, filtering, linearization, isolation, excitation, analog-to-digital conversion, and computation.

A transducer may be:

• Input transducer: converts a non-electrical quantity into an electrical quantity.
• Output transducer or actuator: converts an electrical signal into a physical action.
• Active transducer: generates an output without external excitation, as in a thermocouple or piezoelectric sensor.
• Passive transducer: requires external excitation, as in a strain gauge, resistance thermometer, or LVDT.
• Analog transducer: produces a continuously varying output.
• Digital transducer: produces discrete states, pulses, counts, or a digital data stream.
• Contact transducer: physically contacts the object being measured.
• Non-contact transducer: measures through electromagnetic, optical, acoustic, or other fields.

The terms sensor and transducer are often used interchangeably, but they are not identical. A sensor emphasizes detection and measurement, whereas a transducer emphasizes energy conversion. A complete sensor node may contain both a sensor and several transducers or electronic conversion stages.

2. Performance Characteristics

2.1 Static characteristics

Static characteristics describe performance when the measurand is constant or changes sufficiently slowly that dynamic effects are negligible.

If the output is y and the input measurand is x, the ideal transfer relationship is:

For a linear sensor, the model is often written as:

where y₀ is the zero offset and S is sensitivity, with units of output per unit input. If y is in volts and x is in degrees Celsius, S has units V/°C.

Range is the interval between the minimum and maximum measurable values. Span is the numerical difference between the upper and lower range values. Sensitivity is the slope of the calibration curve:

This finite-difference form is appropriate over a specified interval. For a nonlinear characteristic, local sensitivity is:

Resolution is the smallest input change that produces a detectable output change. It may be limited by noise, quantization, friction, or electronic threshold. Resolution must not be confused with accuracy.

Accuracy describes closeness to the accepted reference value. Precision describes the closeness of repeated readings to one another. A sensor may be precise but inaccurate if it has a systematic calibration error.

Linearity indicates the deviation of the actual calibration curve from a specified reference line. If emax is the maximum deviation and FSO is full-scale output, percentage full-scale nonlinearity is:

The reference may be a best-fit straight line, terminal-point line, or theoretical line. The stated reference is essential when comparing specifications.

Hysteresis is the difference in output for the same input when the input is approached from increasing and decreasing directions. It results from magnetic effects, mechanical friction, material memory, and other irreversible phenomena.

Repeatability is agreement among repeated measurements under the same conditions. Reproducibility concerns agreement when conditions such as operator, equipment, location, or time are changed.

2.2 Dynamic characteristics

When the measurand varies with time, a sensor cannot generally respond instantaneously. A first-order sensor is modeled by:

where τ is the time constant, K is the static sensitivity, x(t) is the input, and y(t) is the output. The model assumes linear behavior, constant parameters, and negligible higher-order effects.

For a step input x(t) = X₀u(t), with zero initial output, the response is:

At t = τ, the output reaches approximately 63.2% of its final value. At approximately 4τ, it reaches about 98.2%; at 5τ, about 99.3%.

A second-order sensor may be represented by:

where ωₙ is the undamped natural angular frequency in rad/s and ζ is the damping ratio. This model is useful for accelerometers, mechanical pickups, and resonant sensors. Underdamping may produce overshoot and ringing; overdamping produces a slower response.

The frequency response is commonly described by magnitude ratio and phase shift. A sensor must have adequate bandwidth for the frequency content of the measurand. Filtering can reduce noise, but excessive filtering introduces delay and may suppress important transient information.

2.3 Error and uncertainty

Measurement error is commonly separated into systematic and random components. Systematic error may arise from calibration, loading, zero offset, drift, or environmental sensitivity. Random error varies unpredictably and is often characterized statistically.

For independent input quantities q₁, q₂, …, qₙ and a result y = f(q₁, q₂, …, qₙ), the first-order law of propagation of standard uncertainty is:

This expression assumes small uncertainties, a sufficiently smooth model, and uncorrelated input quantities. If inputs are correlated, covariance terms must be included.

For a linear resistance measurement using a voltage divider,

where Vₛ is excitation voltage, Rₛ is the sensor resistance, and Rᵣ is the reference resistance. The formula assumes negligible loading by the measuring instrument. If the instrument input resistance is comparable with the divider resistance, it must be included in the circuit model.

3. Resistive Transducers

Resistive transducers operate through a change in resistance caused by displacement, strain, temperature, or another measurand.

3.1 Strain gauges

A metallic strain gauge consists of a fine wire or foil pattern bonded to a specimen. Mechanical strain changes its length and cross-sectional area. The gauge factor is:

where R is nominal resistance, ΔR is resistance change, and ε is mechanical strain, expressed as a dimensionless ratio. For a metallic gauge, GF is commonly close to 2, although the exact value depends on construction and material.

For a quarter-bridge circuit with one active gauge and small strain, the bridge output is approximately:

where Vₑ is bridge excitation. The approximation assumes one active arm, matched bridge completion resistors, small resistance change, and negligible lead-wire effects.

Strain gauges are used in load cells, pressure transmitters, torque meters, structural monitoring, and weighing systems. Temperature compensation is necessary because gauge resistance and specimen dimensions also vary with temperature. Three-wire and four-wire arrangements help reduce lead resistance effects.

3.2 Resistance temperature detectors

An RTD uses the predictable resistance variation of a metal, most commonly platinum. Over a moderate temperature range, the relationship may be approximated by:

where R₀ is resistance at reference temperature T₀, α is the temperature coefficient, and T is temperature. The linear expression is an approximation. For wider ranges, a standardized polynomial such as the Callendar–Van Dusen equation is used for platinum RTDs.

RTDs provide good stability and accuracy but require excitation, and self-heating can create error. Two-wire connections include lead resistance in the measurement. Three-wire connections compensate approximately for equal lead resistances, while four-wire Kelvin connections provide the best accuracy.

3.3 Thermistors

Thermistors are semiconductor resistors with large temperature coefficients. For many negative-temperature-coefficient thermistors:

where temperatures T and T₀ are in kelvin and B is a material constant in kelvin. The equation is empirical and valid only over the specified operating range.

Thermistors are inexpensive and highly sensitive but nonlinear. They are widely used for temperature compensation, battery monitoring, medical probes, and thermal protection.

4. Inductive and Electromagnetic Transducers

4.1 Variable-reluctance sensors

A variable-reluctance transducer detects displacement through a change in magnetic reluctance. For a magnetic circuit with an air gap, reluctance is approximately:

where ℜ is reluctance, l is magnetic path length, μ is permeability, and A is cross-sectional area. The approximation assumes a uniform field and negligible leakage and fringing.

Movement of a ferromagnetic target changes the air gap and therefore the inductance. These sensors are robust and suitable for speed sensing, proximity detection, and position measurement, but their output depends on target material, geometry, and excitation frequency.

4.2 Linear variable differential transformer

An LVDT contains a primary winding and two secondary windings arranged symmetrically around a movable ferromagnetic core. The secondary windings are connected in series opposition. At the null position, induced voltages cancel. Core displacement changes the coupling and produces a differential output whose phase indicates direction.

LVDTs offer excellent resolution, low friction, good repeatability, and electrical isolation between excitation and output. Their limitations include the need for AC excitation and demodulation, sensitivity to electromagnetic interference, and dependence on mechanical alignment.

4.3 Eddy-current sensors

An alternating magnetic field induces eddy currents in a conductive target. The target modifies coil impedance, which is related to separation, conductivity, permeability, and frequency. Eddy-current sensors are non-contact devices used for shaft displacement, vibration, crack detection, and thickness measurement. They are unsuitable for nonconductive targets unless a conductive target layer is added.

5. Capacitive Transducers

A parallel-plate capacitor has capacitance:

where ε is permittivity, A is overlapping plate area, and d is separation. A capacitive transducer can therefore measure displacement by changing A or d, or detect material properties through changes in ε.

Capacitive sensors are sensitive and require very little mechanical force. They are used for displacement, thickness, liquid level, humidity, pressure, and touch sensing. Their main limitations are stray capacitance, cable effects, contamination, dielectric variation, and sensitivity to shielding and grounding.

For small changes, a differential capacitive arrangement improves linearity and rejects common-mode environmental effects. Guard electrodes can reduce fringe-field and parasitic-capacitance errors. High-frequency excitation and charge-amplifier circuits are often used to reduce the influence of cable capacitance.

6. Piezoelectric, Thermoelectric, and Photoelectric Transducers

6.1 Piezoelectric sensors

Certain crystals and ceramics generate electric charge when mechanically stressed. In a simplified charge model:

where Q is generated charge, d is the piezoelectric charge coefficient, and F is applied force. The coefficient and tensor form depend on material orientation and mode of operation.

Piezoelectric sensors are excellent for dynamic force, vibration, impact, and acoustic measurements. They are not ideal for static measurements because leakage and finite insulation cause the output to decay. A charge amplifier is commonly used to make the measurement less sensitive to cable capacitance.

6.2 Thermocouples

A thermocouple produces a voltage because of the Seebeck effect. Over a restricted temperature interval, the output may be approximated as:

where S is the effective Seebeck coefficient, Tₕ is hot-junction temperature, and T𝚌 is reference-junction temperature. In practice, thermocouple voltage is nonlinear, and reference-junction compensation is required.

Thermocouples are rugged, inexpensive, and capable of high-temperature operation. Their disadvantages include low output voltage, susceptibility to noise, material inhomogeneity, and the need for correct extension wire and reference compensation.

6.3 Photoelectric sensors

Photodiodes convert incident optical power into photocurrent. Within a suitable operating region:

where Iₚ is photocurrent, Rλ is responsivity in A/W at wavelength λ, and Pₒₚₜ is incident optical power. Dark current, temperature, wavelength, and reverse bias influence the actual response.

Photodiodes are used in optical communication, encoders, flame detection, instrumentation, and biomedical systems. Photovoltaic operation generates a voltage without external bias; photoconductive operation uses reverse bias to improve speed and linearity at the expense of dark current.

7. Semiconductor and Smart Sensors

Semiconductor sensors exploit changes in junction voltage, carrier concentration, resistance, or field effect. Examples include Hall-effect sensors, magnetoresistive sensors, integrated temperature sensors, MEMS accelerometers, pressure sensors, and chemical sensors.

A Hall sensor produces a transverse voltage when current flows through a semiconductor exposed to a magnetic field. Ideally:

where Vᴴ is Hall voltage, Kᴴ is a material-dependent coefficient, I is bias current, B is magnetic flux density, and t is active-layer thickness. Practical devices include offset, temperature dependence, and nonlinearities.

MEMS sensors integrate mechanical structures with semiconductor electronics. Capacitive MEMS accelerometers, for example, detect inertial displacement of a proof mass. Their performance depends on mechanical resonance, damping, electrostatic forces, package stress, and electronic noise.

A smart sensor combines sensing, signal conditioning, local processing, calibration data, diagnostics, and communication. Digital interfaces such as I²C, SPI, UART, CAN, and industrial Ethernet improve integration but introduce requirements for timing, cybersecurity, grounding, firmware validation, and protocol management.

8. Signal Conditioning and Interface Design

A sensor output is rarely suitable for direct conversion or transmission. Signal conditioning may include:

• excitation-current or excitation-voltage sources;
• instrumentation amplifiers with high input impedance and high common-mode rejection;
• bridge completion and balancing;
• isolation amplifiers or isolated converters;
• anti-aliasing filters;
• linearization and temperature compensation;
• rectification and demodulation for AC sensors;
• sample-and-hold circuits and analog-to-digital conversion.

The differential output of a Wheatstone bridge can be written generally as:

where R₁ through R₄ are the four arm resistances and Vₑ is excitation voltage. The sign depends on the chosen polarity. A balanced bridge satisfies R₁R₄ = R₂R₃ under the corresponding arm arrangement.

An instrumentation amplifier should provide adequate gain without saturating, low input-referred noise, high common-mode rejection, and acceptable input bias-current error. Gain selection must account for sensor offset and the complete input range of the ADC.

Sampling introduces aliasing when signal components above half the sampling frequency are present. Therefore, an analog low-pass anti-aliasing filter is required before an ADC unless the sensor interface and sampling architecture provide an equivalent protection. The Nyquist condition is necessary but not sufficient in practical systems because real filters have finite roll-off.

Ground loops, electromagnetic interference, thermoelectric junctions, cable motion, and common-mode voltage can dominate a low-level measurement. Shielding, twisted pairs, differential transmission, proper grounding, isolation, and physical separation from power conductors are often more effective than merely increasing amplifier gain.

9. Calibration, Traceability, and Sensor Selection

Calibration establishes the relationship between sensor output and reference input under specified conditions. A calibration procedure should define the reference standard, environmental conditions, input points, loading, stabilization time, acceptance criteria, and treatment of uncertainty.

A linear calibration may use:

where a is estimated offset and b is estimated sensitivity. Calibration coefficients should not be used outside the range and conditions for which they were established. Polynomial or lookup-table linearization may be required for nonlinear sensors, but increasing model complexity does not automatically improve accuracy if the reference data are poor.

Sensor selection should consider:

Sensor selection is therefore a systems decision rather than a comparison based only on nominal accuracy.

10. Worked Examples

Example 1: Strain-gauge bridge output

A quarter-bridge load cell has gauge factor GF = 2.05, strain ε = 600 με, and excitation Vₑ = 5 V. Estimate the small-signal bridge output.

Since 600 με = 600 × 10⁻⁶,

Therefore, Vₒ ≈ 1.54 mV. The result assumes one active gauge, a balanced bridge, small strain, and negligible lead and amplifier errors. An instrumentation amplifier is required because the signal is much smaller than the excitation voltage.

Example 2: First-order temperature response

A temperature sensor has time constant τ = 8 s and static sensitivity K = 10 mV/°C. A step change of 20 °C is applied. Find the output change after 8 s.

The final output change is KX₀ = 10 mV/°C × 20 °C = 200 mV. At t = τ, the response is 63.2% of final value:

Thus the output change is approximately 126 mV after 8 s. The sensor has not reached its final value, so using its instantaneous output as though it represented the final temperature would produce a dynamic error.

11. Illustrative Case Study: Condition Monitoring of an Induction-Motor Drive

Background

A manufacturing plant experiences intermittent failures in a 75 kW induction motor driving a conveyor. Failures appear as increased vibration and eventual bearing damage. The plant wishes to introduce predictive maintenance without disrupting production.

Problem

The measurement system must detect bearing-related vibration, monitor winding temperature, and distinguish mechanical faults from inverter-generated electrical interference. The system must operate continuously in a dusty industrial environment.

Analysis

A piezoelectric accelerometer is selected for high-frequency vibration because it has broad bandwidth and good sensitivity to impacts. An RTD is installed near the bearing housing for temperature measurement. A Hall-effect current sensor monitors motor current and can support electrical-fault diagnosis.

The accelerometer requires a constant-current excitation and charge-compatible signal-conditioning unit. The RTD is connected in a four-wire arrangement to reduce lead resistance error. Shielded twisted-pair cables are routed separately from inverter output conductors. Sampling frequency is selected above the highest diagnostic frequency of interest, and an anti-aliasing filter is installed before digitization.

Approach and solution

Baseline vibration spectra are recorded under normal load and speed. Features such as root-mean-square vibration, crest factor, selected band energy, and temperature trend are stored. A simple threshold is supplemented by trend analysis because absolute vibration levels depend on mounting and operating condition. Measurements are synchronized with motor speed so that order-related components can be interpreted.

A diagnostic model compares vibration features with temperature and current. If vibration increases without corresponding temperature rise, imbalance or looseness is considered. If vibration and bearing temperature rise together, lubrication or bearing damage becomes more likely. If current harmonics change simultaneously, electrical or inverter-related causes are investigated.

Outcome

The system identifies a gradual increase in high-frequency vibration several weeks before a scheduled inspection. Inspection confirms early bearing surface damage. Replacing the bearing during planned downtime avoids an unplanned production stoppage.

Learning points

1. A sensor must be selected according to the frequency content and failure mechanism, not merely the measurand name.
2. Installation, cabling, grounding, and mounting can be as important as sensor specifications.
3. Sensor fusion reduces ambiguity that cannot be resolved by a single measurement.
4. Baselines and operating context are essential for reliable condition monitoring.
5. Predictive analytics must remain traceable to validated measurements and engineering reasoning.

12. Limitations, Safety, Ethics, and Contemporary Development

Every sensor has a finite operating range and failure mode. Saturation, drift, fatigue, contamination, electrical breakdown, moisture ingress, and communication failure must be considered. Critical applications should use redundancy, plausibility checks, watchdogs, fail-safe outputs, and proof testing where appropriate.

In safety-related systems, sensor failure must be evaluated through hazard analysis and applicable standards. Isolation may be required where a sensor is connected to hazardous voltages. Intrinsically safe designs are necessary in explosive atmospheres. Calibration records and traceability are important wherever measurements affect product acceptance, energy billing, environmental compliance, or human safety.

Smart sensors and artificial-intelligence methods can support anomaly detection, adaptive calibration, and sensor fusion. However, machine-learning outputs depend on training data, sensor health, operating distribution, and model validation. AI should not conceal uncertainty or replace a calibrated measurement chain. Data integrity, cybersecurity, access control, firmware authenticity, and privacy become relevant when sensors are networked.

Best practice is to specify the complete measurement requirement, model dominant error sources, validate the installation, calibrate against traceable standards, monitor sensor health, and document assumptions. A highly accurate sensor used with poor wiring or an unsuitable sampling system may produce a less reliable result than a moderate sensor integrated correctly.

Chapter Summary

Sensors detect physical or chemical quantities, while transducers convert energy or information from one form to another. Electrical transducers may be active or passive, analog or digital, contact or non-contact. Their performance is described through sensitivity, range, accuracy, precision, resolution, linearity, hysteresis, repeatability, drift, bandwidth, and dynamic response.

Resistive devices include strain gauges, RTDs, and thermistors. Inductive devices include variable-reluctance sensors, LVDTs, and eddy-current sensors. Capacitive sensors measure displacement, dielectric properties, level, and related quantities. Piezoelectric sensors are particularly useful for dynamic measurements; thermocouples measure temperature through the Seebeck effect; photodiodes convert optical power into current; and semiconductor and MEMS devices provide compact, integrated sensing solutions.

A complete measurement system requires excitation, signal conditioning, filtering, isolation, digitization, calibration, and interpretation. Bridge circuits, instrumentation amplifiers, anti-aliasing filters, shielding, and appropriate grounding are central to practical design. Sensor selection must account for the measurand, range, bandwidth, environment, loading, uncertainty, reliability, safety, and lifecycle cost. Modern systems increasingly use smart sensors, sensor fusion, diagnostics, and networked data, but these developments do not eliminate the need for traceability, validation, uncertainty analysis, and engineering judgment.

Key Terms

Sensor: Device that detects a physical, chemical, or biological quantity.

Transducer: Device that converts energy or information from one form into another.

Measurand: Quantity intended to be measured.

Sensitivity: Change in output per unit change in input.

Resolution: Smallest detectable change in the measurand.

Accuracy: Closeness of a measurement to an accepted reference value.

Precision: Closeness among repeated measurements.

Linearity: Agreement of a sensor characteristic with a specified reference line.

Hysteresis: Difference in output for the same input approached from opposite directions.

Repeatability: Agreement under the same measurement conditions.

Drift: Gradual change in output or sensitivity with time or environment.

Time constant: Parameter describing the response speed of a first-order sensor.

Strain gauge: Resistive sensor whose resistance changes with mechanical strain.

RTD: Resistance temperature detector using a temperature-dependent metal resistance.

Thermistor: Semiconductor resistor with a large temperature coefficient.

LVDT: Differential inductive displacement transducer.

Piezoelectric sensor: Sensor producing charge in response to mechanical stress.

Thermocouple: Temperature sensor using the Seebeck effect.

Smart sensor: Sensor incorporating signal processing, diagnostics, calibration, and communication.

Sensor fusion: Combination of information from multiple sensors to improve estimation or diagnosis.

Review Questions

Short Answer Questions

1. Distinguish between a sensor and a transducer.
2. Define sensitivity, resolution, accuracy, and precision.
3. Why is a piezoelectric sensor generally unsuitable for static force measurement?
4. State two advantages of a four-wire RTD connection.
5. What is the purpose of an anti-aliasing filter?

Long Answer Questions

1. Explain the static and dynamic characteristics of electrical transducers, including first-order response.
2. Describe the construction, operating principle, applications, and limitations of strain gauges and Wheatstone bridges.
3. Compare RTDs, thermistors, and thermocouples for industrial temperature measurement.
4. Explain the operation of an LVDT and discuss its advantages and practical limitations.
5. Discuss the complete signal-conditioning chain for a low-level sensor output in an industrial environment.

Analytical / Application Questions

1. A quarter-bridge strain-gauge system has GF = 2.0, strain = 800 με, and excitation = 10 V. Estimate the bridge output using the small-signal expression and identify two practical error sources.
2. A first-order sensor has a time constant of 5 s. Determine the approximate percentage of final response after 15 s and explain the significance for a rapidly changing measurand.
3. Select suitable sensors and signal-conditioning methods for monitoring vibration, temperature, and shaft speed in an inverter-fed induction motor. Justify the selection with reference to bandwidth, interference, installation, and calibration.

Multiple Choice Questions with Answers

Question 1

Which characteristic is defined as the change in output per unit change in input?

A. Sensitivity

B. Resolution

C. Hysteresis

D. Repeatability

Correct Answer: A. Sensitivity

Question 2

At one time constant, the ideal first-order step response reaches approximately:

A. 37% of its final value

B. 50% of its final value

C. 63.2% of its final value

D. 99.3% of its final value

Correct Answer: C. 63.2% of its final value

Question 3

Which transducer is particularly suitable for dynamic vibration measurement but generally unsuitable for static force measurement?

A. RTD

B. Piezoelectric sensor

C. Potentiometric displacement sensor

D. Thermistor

Correct Answer: B. Piezoelectric sensor

Question 4

For a quarter-bridge strain gauge with GF = 2, strain = 500 με, and excitation = 4 V, the approximate output is:

A. 0.5 mV

B. 1.0 mV

C. 2.0 mV

D. 4.0 mV

Correct Answer: B. 1.0 mV

Question 5

Which connection most effectively eliminates lead-resistance effects in an RTD measurement?

A. Single-wire connection

B. Two-wire connection

C. Three-wire connection

D. Four-wire Kelvin connection

Correct Answer: D. Four-wire Kelvin connection

Question 6

An LVDT primarily measures:

A. Chemical concentration

B. Linear displacement

C. Optical wavelength

D. Liquid conductivity

Correct Answer: B. Linear displacement

Question 7

The main purpose of an anti-aliasing filter is to:

A. Increase sensor excitation voltage

B. Prevent unwanted high-frequency components from folding into sampled data

C. Remove all sensor offset

D. Convert resistance directly into temperature

Correct Answer: B. Prevent unwanted high-frequency components from folding into sampled data

Question 8

In a thermocouple measurement, reference-junction compensation is required because thermocouple voltage depends on:

A. Only the hot-junction resistance

B. The temperature difference between junctions

C. Only the cable length

D. The sensor’s mechanical displacement

Correct Answer: B. The temperature difference between junctions

Question 9

Which sensor uses a change in capacitance caused by separation, area, or dielectric permittivity?

A. Capacitive transducer

B. Thermocouple

C. Piezoelectric accelerometer

D. Hall sensor

Correct Answer: A. Capacitive transducer

Question 10

A smart sensor generally combines sensing with:

A. Only a mechanical spring

B. Signal processing, diagnostics, or communication

C. A permanent reference thermometer only

D. An actuator without measurement electronics

Correct Answer: B. Signal processing, diagnostics, or communication