Understanding the vocabulary and performance metrics that define a professional measurement system: the foundation for everything that follows in this course.
Every measurement system can be decomposed into a standard signal chain. Understanding each stage is essential for diagnosing errors and designing reliable systems.
The physical quantity being measured (temperature, pressure, strain, velocity, etc.). The measurand is the true value your system is trying to observe.
Converts the measurand into an electrical signal (voltage, current, resistance, charge). The transducer introduces the first opportunity for error.
Amplification, filtering, impedance matching, and linearization applied to the raw transducer output before digitization or display.
Digitizes the conditioned analog signal (ADC) and transfers it to a computer or microcontroller for storage or further processing.
The final displayed or recorded value. The indication is what we report — ideally equal to the measurand, but always affected by the chain above it.
Accuracy describes the closeness of a measurement to the true value. It is typically expressed as a percentage of full-scale output (FSO) or as an absolute value. A highly accurate instrument may not be precise, and vice versa.
Accuracy = |(Indicated Value - True Value)| / Full-Scale Range x 100%
Precision describes how consistently an instrument returns the same reading for the same input, regardless of whether that reading is close to the true value. Precision is quantified statistically by the standard deviation of repeated measurements.
The smallest change in the measurand that produces a detectable change in the instrument output. For a digital display, resolution equals one count. For an ADC, resolution = Full-Scale Range / 2^N where N is the number of bits.
Resolution (V/count) = V_ref / 2^N
The slope of the instrument's output-vs-input curve (transfer function). Units are output units per input unit (e.g., mV/N for a force sensor, or mV/°C for a thermocouple). Higher sensitivity means a larger output signal per unit of input, which generally improves signal-to-noise ratio.
The deviation of the actual calibration curve from a specified straight line, usually expressed as a percent of full-scale. A linear sensor simplifies signal processing; a nonlinear sensor requires a linearization table or equation.
The difference in output for the same input value depending on whether the input is increasing or decreasing. Hysteresis is caused by friction, magnetic effects, or mechanical play. It is expressed as a percentage of full-scale and represents a fundamental limit on accuracy.
The range of input values over which there is no change in output. Deadband is common in mechanical linkages, relay-controlled systems, and backlash-prone actuators. It is distinct from resolution: deadband refers to a zone of insensitivity, not the minimum detectable increment.
The ratio of the maximum measurable value to the minimum measurable value (or minimum detectable signal), often expressed in decibels: Dynamic Range (dB) = 20 · log10(Max / Min).
When a sensor is connected to a circuit or mechanical system, it inevitably draws energy from that system and alters the quantity being measured. This is a loading effect.
The goal is to select instruments whose impedance (electrical or mechanical) is dramatically different from the source impedance — typically by a factor of 100:1 or more — to limit loading error to below 1%.
Temperature is the most common environmental variable affecting sensor accuracy. Nearly all electronic components have temperature-dependent characteristics. Other environmental effects include humidity, vibration, electromagnetic interference (EMI), and supply voltage variation. Instrument datasheets specify these as "temperature coefficient," "sensitivity error," or "EMI susceptibility."
The number of discrete digital levels for a 12-bit ADC is 212 = 4096.
Resolution = V_ref / 2N = 3.3 V / 4096 = 0.000806 V/count
Resolution ≈ 0.806 mV/count
Mean = (98.2 + 98.4 + 98.1 + 98.3 + 98.2) / 5 = 491.2 / 5 = 98.24 kPa
Accuracy error = |98.24 − 100.0| = 1.76 kPa (1.76% of true value — systematic error, likely a bias).
Standard deviation = √[(sum of squared deviations)/4] ≈ 0.114 kPa (high precision — readings cluster tightly).
The sensor is precise (low scatter) but inaccurate (systematic bias of ~1.76 kPa below true value).
Sensitivity = ΔOutput / ΔInput = (24.8 − 0) mV / (500 − 0) N
Sensitivity = 0.0496 mV/N
Dynamic Range (dB) = 20 · log10(10 V / 0.005 V) = 20 · log10(2000)
= 20 · 3.301 = 66.02 dB
Dynamic Range ≈ 66 dB