22-Agric-A5 Principles of Instrumentation · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A5 Principles of Instrumentation, National Exams May 2015 — a three-hour open-book exam; any non-communicating calculator is permitted. Questions 1 and 2 are compulsory (20 marks each); candidates then choose any three (3) of Questions 3-7 (20 marks each) for a 100-mark paper. All seven questions are worked here.
Reference texts. E.O. Doebelin, Measurement Systems: Application and Design, 5th ed. (calibration, standards, static/dynamic sensor characteristics, second-order step response); J.P. Bentley, Principles of Measurement Systems, 4th ed. (accuracy vs. precision, error propagation, signal conditioning); P. Horowitz and W. Hill, The Art of Electronics, 3rd ed. (Johnson noise, CMRR, ADC architectures, anti-aliasing); J. Fraden, Handbook of Modern Sensors: Physics, Designs, and Applications, 5th ed. (thermistors, thermocouples, capacitive and photo sensors).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
a) A standard is a physical artifact or a precisely reproducible physical phenomenon whose value of the measured quantity is known, fixed and traceable to an internationally agreed reference (ultimately the SI definitions). Calibration compares the instrument's output against the standard's known input so any systematic deviation of the instrument can be quantified and corrected.
b) The triple point of water (0.01°C, 611.657 Pa) is the unique combination of temperature and pressure at which solid, liquid and vapour phases coexist in equilibrium. Because that state occurs at exactly one point, it is completely self-defining — it needs no separate pressure measurement the way the boiling point does (which drifts with atmospheric pressure) — so it is reproducible to better than a millikelvin in a sealed triple-point cell in any properly equipped lab, making it an ideal fixed calibration point.
c) Saturation occurs when the input to a sensor exceeds the range over which the sensor can still produce a corresponding change in output — the output flattens (clips) at or near its maximum regardless of further increases in the input. Once saturated, the instrument's response is no longer a useful (or even monotonic) function of the measurand.
d) The lowest detectable limit is set by the sensor's own noise floor, not by an arbitrarily small signal: it is conventionally the smallest concentration whose signal exceeds the baseline (blank) noise by a stated margin, typically three standard deviations of the blank/noise measurement (the 3σ criterion). Below that level, a real signal cannot be reliably distinguished from random noise.
e) A single calibration run cannot separate random error from a genuine, repeatable instrument characteristic. Repeating the calibration several times lets the random scatter (precision/repeatability) be characterized statistically and averaged out, and confirms the calibration curve itself is stable from run to run rather than being a one-off fluke of that particular trial.
f) Hysteresis is determined by cycling the input over its full range twice — once increasing, once decreasing — and comparing the output reading at the same input value on the up-going and down-going branches. The maximum difference between the two branches, expressed as a percentage of full scale, is the hysteresis error.
g) Statistical methods (mean, standard deviation of repeated readings) characterize the spread of the readings around their own average — i.e. precision/repeatability, a random-error property. They say nothing about whether that average itself agrees with the true value, which is accuracy, a systematic-error property. An instrument can be very precise (tightly repeatable) while being consistently biased away from the true value, and no amount of statistics on its own readings will reveal that bias — only comparison against an independent traceable standard can.
h) A single-point calibration is adequate only if the rest of the calibration curve can be trusted from physics/design rather than being separately measured: the instrument's transfer function must be known to be linear over the working range, it must pass through a known origin (zero output at zero input, i.e. no offset error), and hysteresis and drift must be negligible. Under those assumptions, the single point fixes the one remaining unknown — the slope (sensitivity) — and the rest of the line follows.
i) For a non-linear calibration curve, sensitivity at any point is the local slope dOutput/dInput of that curve. The instrument is therefore most sensitive where that curve is steepest, not necessarily at the high or low end of the range — a small change in the measurand there produces the largest change in output.
j) No. A static calibration is a snapshot taken at one point in time; drift is by definition a slow change of the input-output relationship over time after that calibration was performed. A single calibration cannot reveal a change that has not yet happened relative to it — only periodic re-calibration, comparing the instrument's response at a later time against the same standard, can detect that the curve has shifted.
