Sensors

Sensors respond to a physical quantity with a measurable electrical change. Learn static and dynamic characteristics — range, sensitivity, accuracy, precision, resolution, linearity, hysteresis — and the common temperature, position, pressure and light sensors.

Every automated system begins with sensing: a thermostat needs temperature, a car needs wheel speed, a phone needs orientation. A sensor converts a physical quantity (the measurand) into a change in resistance, voltage, current, capacitance or frequency that electronics can read.

Choosing a sensor means understanding its characteristics — not just what it measures, but how well, how fast and under what conditions.

An analogy

A sensor is like a translator: it listens to the physical world's language (heat, pressure, light) and repeats the message in electrical language. A good translator is accurate, quick and doesn't change the conversation it's listening to.

Key static characteristics

These describe how a sensor behaves for steady inputs.

• Range/span: the inputs it can measure.
• Sensitivity: output change per input change.
• Resolution: smallest detectable change.
• Accuracy: closeness to the true value; precision (repeatability): closeness of repeated readings to each other.
• Linearity, hysteresis (different output rising vs falling), offset and drift.

Common sensor types

Temperature: thermocouples, RTDs, thermistors, IC sensors. Position/motion: potentiometers, encoders, Hall sensors, LVDTs, accelerometers, gyros. Force/pressure: strain gauges, piezoelectric, capacitive. Light: photodiodes, phototransistors, LDRs. Level/flow: ultrasonic, magnetic flow meters, float switches.

Dynamic characteristics

Most sensors respond like a first-order system: a step input reaches 63 % of the final reading after one time constant τ. A thermocouple in a thick sheath may take 10 s; a bare one milliseconds. For fast signals, bandwidth and phase lag matter as much as accuracy.

Accuracy vs precision

A sensor can be precise but inaccurate (tight readings, all offset — fixable by calibration) or accurate on average but imprecise (noisy — reduced by averaging). Specifications distinguish %FS errors from % of reading errors; at low readings, %FS errors dominate.

Smart and MEMS sensors

MEMS accelerometers, gyros and pressure sensors integrate micromachined structures with signal conditioning, ADCs and digital interfaces (I²C, SPI) on one chip. They include calibration, temperature compensation, filtering and even sensor fusion, which has changed sensor selection from 'which element' to 'which data sheet'.

Formulas

• Sensitivity: S = Δy / Δx
• Pt100 RTD: R(T) = R₀(1 + αT), α = 0.00385 /°C
• NTC thermistor: R(T) = R₀ · e^{B(1/T − 1/T₀)} (T in K)
• Non-linearity: max |y − y_fit| / FS × 100 %

Worked example: NTC resistance at 50 °C

Given: R₀ = 10 kΩ at 25 °C; B = 3950 K

Find: Resistance at 50 °C.

• T = 323.15 K, T₀ = 298.15 K
• B(1/T − 1/T₀) = 3950 × (−0.0002595) = −1.025
• R = 10k × e^(−1.025) = 3.59 kΩ

Answer: ≈ 3.59 kΩ

Worked example: Resolution of an IC temperature sensor

Given: LM35: 10 mV/°C; 10-bit ADC, 3.3 V reference

Find: Temperature resolution.

• LSB = 3.3/1024 = 3.22 mV
• Resolution = 3.22/10 = 0.32 °C

Answer: 0.32 °C per count

Common mistakes

• Wrong: Confusing resolution with accuracy. — Right: A display can show 0.01 °C resolution while the sensor is only ±0.5 °C accurate.
• Wrong: Ignoring self-heating. — Right: Excitation current heats resistive sensors (P = I²R); keep it low or specify it.

Applications

• Battery packs: NTC thermistors on cells feed the BMS, which limits charging when cells are too cold or hot.
• Automotive: A modern car has 100+ sensors: MAP, oxygen, wheel speed, crankshaft position, rain, radar.
• Industry 4.0: Vibration and temperature sensors on motors enable predictive maintenance.

Key takeaways

• Sensors convert physical quantities into electrical signals.
• Know range, sensitivity, resolution, accuracy, precision, linearity and response time.
• RTDs are linear, thermistors sensitive, thermocouples wide-range.
• Resolution is not accuracy — calibrate and compensate.

Going further

• Steinhart–Hart equation: 1/T = A + B ln R + C (ln R)³ fits NTC thermistors to ±0.01 °C over wide ranges, much better than the simple B-equation.
• Sensor fusion: Combining accelerometer, gyroscope and magnetometer with a Kalman or complementary filter gives orientation that no single sensor can provide reliably.
• Calibration traceability: Accurate measurements trace back through calibrated references to national standards (NIST, NPL, PTB), with documented uncertainties at each step (ISO/IEC 17025).