MEGR 3171  |  UNC Charlotte Mechatronics 2
Dr. Roger Tipton
Mechanical Engineering & Engineering Science
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Week 1 — Module 1: Precision Measurement & Signal Science

Measurement System Performance

Understanding the vocabulary and performance metrics that define a professional measurement system: the foundation for everything that follows in this course.

Learning Objectives

1. The Measurement System Chain

Every measurement system can be decomposed into a standard signal chain. Understanding each stage is essential for diagnosing errors and designing reliable systems.

Measurand

The physical quantity being measured (temperature, pressure, strain, velocity, etc.). The measurand is the true value your system is trying to observe.

Transducer / Sensor

Converts the measurand into an electrical signal (voltage, current, resistance, charge). The transducer introduces the first opportunity for error.

Signal Conditioning

Amplification, filtering, impedance matching, and linearization applied to the raw transducer output before digitization or display.

Data Acquisition (DAQ)

Digitizes the conditioned analog signal (ADC) and transfers it to a computer or microcontroller for storage or further processing.

Indication / Output

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.

2. Static Performance Metrics

Accuracy

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 (% FSO)
Accuracy = |(Indicated Value - True Value)| / Full-Scale Range x 100%

Precision (Repeatability)

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.

Resolution

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.

ADC Resolution
Resolution (V/count) = V_ref / 2^N

Sensitivity

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.

Linearity

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.

Hysteresis

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.

Deadband

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.

Dynamic Range

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).

3. Loading Effects

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.

Key Principle A voltmeter with finite input impedance loads the circuit it measures. A pressure transducer with a finite compliance volume changes the pressure in a small cavity. Loading effects are never zero — they can only be minimized by proper instrument selection.

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%.

4. Environmental Effects

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."

Practice Problems

Problem 1 — Resolution A 12-bit ADC has a reference voltage of 3.3 V. What is its voltage resolution in millivolts per count?

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
Problem 2 — Accuracy vs. Precision Five repeated measurements of a 100.0 kPa reference pressure yield: 98.2, 98.4, 98.1, 98.3, 98.2 kPa. Characterize the accuracy and precision of this instrument.

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).
Problem 3 — Sensitivity A load cell produces an output of 0 mV at 0 N and 24.8 mV at 500 N. What is its sensitivity in mV/N?

Sensitivity = ΔOutput / ΔInput = (24.8 − 0) mV / (500 − 0) N

Sensitivity = 0.0496 mV/N
Problem 4 — Dynamic Range A data acquisition system can measure signals from a minimum of 5 mV to a maximum of 10 V. Express the dynamic range in decibels.

Dynamic Range (dB) = 20 · log10(10 V / 0.005 V) = 20 · log10(2000)

= 20 · 3.301 = 66.02 dB

Dynamic Range ≈ 66 dB