3 Sensor Specifications

3.2.1 The Core Specification Set

3.2.2 Beginner Examples

Start by a temperature sensor with fine resolution can show small changes, but the reading is still limited by its accuracy and calibration evidence. Then a fast response time matters for alarms and control loops; slower response may be acceptable for trend logging. Next a wide operating range matters when the installation sees outdoor, refrigerated, heated, humid, or dusty conditions. Finally a low unit price is not enough if the sensor drifts quickly, corrodes, or requires frequent field replacement.

For timing claims, distinguish response time from a simple time constant. Response time is the time needed for the output to settle inside a named tolerance band after the input changes; a rising step and a falling step can have different settle or decay times. An RC-like time constant is usually shorter than the final response-time specification, so an alarm or control record should name the tolerance band, step direction, and test condition.

3.2.3 Overview Knowledge Check

3.3.1 How It Works: Read the Specification Chain

Start by start with the decision. State the alarm, control action, trend, report, or diagnostic that depends on the measurement. Then set the measurement envelope. Record the physical range, operating environment, response-time need, and mounting constraint. Next separate accuracy, precision, and resolution. Ask which error is systematic, which variation is random, and which display step is merely output granularity. After that check calibration and drift. Identify the reference, calibration interval, offset or scale factor, repeatability check, and review trigger. Finally close with evidence. Keep datasheet conditions, bench checks, installation notes, field validation readings, and exceptions that would force re-selection.

3.3.2 Specification Review Ledger

A blood-pressure transducer might be specified with a range of -50 mmHg to +450 mmHg and a sensitivity of 10 mV/V/mmHg (10 millivolts of output per volt of excitation per mmHg of applied pressure). A bench check against a reference could show the installed part delivering closer to 7.8 mV/V/mmHg — a sensitivity error that the range and accuracy numbers alone would not reveal.

3.3.3 Intermediate Example

A greenhouse controller triggers irrigation from soil moisture readings. The selection record should not start with the cheapest part. It should state the irrigation threshold, soil type, installation depth, expected moisture range, acceptable uncertainty around the threshold, response-time need, corrosion risk, power budget, calibration method, and field-check schedule. A sensor that is inexpensive but drifts or fails after repeated wetting can be more expensive than a durable sensor once replacement visits are counted.

3.3.4 Practitioner Knowledge Check

3.4.1 Advanced Example

A cold-chain monitor needs more than a temperature value. The record should name the allowed storage window, sensor accuracy under that window, calibration reference, enclosure thermal lag, sampling interval, alarm rule, battery behavior at low temperature, data retention during connectivity loss, and evidence retained after a temperature excursion. A reading that appears valid on the dashboard is not enough if the sensor was mounted where it responds slowly to the product temperature.

3.4.2 Error-Boundary Checklist

Start by offset: The sensor is consistently high or low; calibration may subtract the bias if the reference is valid. Then scale: The output changes too much or too little across the span; calibration may need more than one point. Next linearity: The output departs from a straight-line fit to the ideal response; quoted as the maximum gap between the measured and ideal curve, expressed as a percentage of full-scale span rather than a single value, because the departure grows with how far the input swings from the calibration point — a nonlinearity that looks negligible near one operating point can still turn a fast-oscillating input, such as vibration on an accelerometer, into a steady false offset instead of averaging away. After that resolution: The output step is too coarse for the required change; software cannot invent missing measurement detail. Continue by noise: Repeated readings vary under stable conditions; averaging can help only when the process can tolerate delay. Continue by hysteresis: The reading depends on whether the condition approached from above or below; record direction-sensitive behavior. Continue by drift: The same condition produces a different reading over time; define recheck, recalibration, or replacement triggers. Finally response lag: The reading trails the physical event; test whether the delay is acceptable for the decision.

3.4.3 Response Time Beyond a Single Time Constant

A sensor whose output settles like a charging capacitor is a first-order system: one time constant, one exponential curve, no overshoot. Many sensors are not that simple. A sensor with moving mass or a resonant structure — an accelerometer proof mass, a pressure diaphragm, a thermal probe with a spring-loaded mount — behaves more like a mass-spring-damper system, and its step response depends on a natural frequency and a damping ratio rather than a single time constant. An underdamped sensor overshoots the final value and rings before settling, so a fast reading taken right after a step can briefly sit past the true value in the wrong direction. A critically damped sensor reaches the final value in close to the shortest possible time without overshoot. An overdamped sensor approaches the final value slowly with no overshoot, trading speed for stability.

This matters for the response-time specification because a datasheet's stated settle time and tolerance band assume one of these shapes. A control loop or alarm that samples a fast sensor immediately after a step can be fooled by overshoot into recording a value more extreme than the true one, and a system that only checks whether the reading is still moving can mistake ringing for real oscillation in the process being measured. Reviewing a fast sensor's actual step response, not just its published response-time number, is the only way to know which of these shapes applies.

3.4.4 Resolution, Noise, and Effective Bits

Resolution begins with span, not with the largest printed code. An ideal $n$-bit ADC divides an input span $V_{\text{span}}$ into $2^n$ code bins, so one least-significant bit is

For a bipolar $\pm10\ \text{V}$ input, $V_{\text{span}}=20\ \text{V}$. With 16 bits,

That number is ideal code width, not yet trustworthy measurement resolution. If repeated readings at a constant input occupy a 16-count noise band, the bottom four bits are not stable because $16=2^4$. A useful first estimate is therefore

This range-based estimate is intentionally conservative and is not the same as the sine-wave ENOB calculated from SINAD. State which method produced the number. Also check missing codes, INL, reference noise, and drift: averaging can reduce random variation, but it cannot repair a nonlinear transfer curve or a moving reference.

For independent, zero-mean samples with standard deviation $\sigma$, the mean of $N$ samples has

If the input noise is 8 counts RMS, averaging 64 independent samples gives $8/\sqrt{64}=1$ count RMS. The price is time. At 1 ksample/s, a single result takes about 1 ms while a non-overlapping 64-sample mean spans 64 ms, an eightfold noise improvement for a sixty-fourfold observation window. Correlated noise, 1/f drift, mains pickup, or a changing measurand will not follow this square-root rule.

The workbench below turns that trade-off into a sensor specification decision. It opens on a 3.30 V, 12-bit converter with 2.00 count RMS independent noise, one sample per result, 1000 sample/s, and the LM35 sensitivity of 0.0100 V/deg C. Walk through the orange uncertainty band and live readouts first: the starting result is only 9.19 useful bits and 0.564 deg C effective resolution. Then change only Average count from 1 to 64. The useful result reverses to 11.6 bits and 0.107 deg C, but the acquisition window grows from 1.00 ms to 64.0 ms. That visible exchange is why a module specification must record both resolution and observation time instead of quoting nominal ADC bits alone.

Sensitivity must use the same count convention. For a 12-bit converter spanning $-1$ to $+1\ \text{V}$,

A $\pm4$-count decision band is therefore $\pm1.953\ \text{mV}$ about the mean. Its full lower-to-upper width is $8q=3.906\ \text{mV}$ peak to peak. Calling the result simply “1.9 mV p-p” mixes a one-sided threshold with a peak-to-peak band; preserve the sign and count definition in the specification record. If a 0—1 V sensor represents 0—1000 engineering units, its scale is $1\ \text{mV/unit}$, so a $\pm1.953\ \text{mV}$ threshold corresponds to roughly $\pm2$ units before accuracy, nonlinearity, and drift are added.

3.4.5 Evidence That Makes a Specification Trustworthy

3.4.6 Under-the-Hood Knowledge Check

3.5.1 Predict Which Specification Wins

• Predict: A valve fault develops in 20 ms, but the displayed value uses the 64 ms mean. Can the display prove the peak was captured? Check: No. The averaging window can smooth or delay the brief pressure event.
• Predict: The package survives 85 °C storage but lists only 60 °C operating temperature. May it measure at 75 °C? Check: Not from the storage rating; operation and unpowered survival are different specification limits.