22-Agric-A5 Principles of Instrumentation · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A5 Principles of Instrumentation, National Exams May 2018 — 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, sampling and ADCs); 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, op-amp signal conditioning); 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) Infra-red detection relies on picking up very small differences in thermal (blackbody) radiation from the scene, but the CCD's own detector elements, mounting, and surrounding electronics are themselves at ambient temperature and radiate (and thermally generate dark-current electrons) at a level that can swamp the weak scene signal. Cooling to liquid-nitrogen temperature ($\approx77\,\text{K}$) suppresses both the detector's own thermal dark-current noise and its self-emitted infra-red radiation by many orders of magnitude, letting the genuine scene signal be resolved.
b) Instrument drift is mainly caused by slow changes in the physical properties of the sensor's own components (aging of materials, chemical/mechanical degradation, contamination) and by their sensitivity to ambient conditions — especially temperature — that change gradually over time (thermal drift of resistors, offset voltages, mechanical creep). Because these changes occur slowly compared with the measurement itself, they are not caught by a single calibration and instead require periodic recalibration to correct.
c) A Faraday cage is an enclosure made of a conductive material (solid or fine mesh) that surrounds a circuit or measurement to shield it from external electric fields. External time-varying fields induce charge redistribution on the cage's outer conductive surface, which cancels the field inside the enclosure (the interior conductor sits at a uniform potential), so no significant electric field — and hence no capacitively-coupled interference — reaches the shielded circuit inside.
d) Insertion error (loading error) is the error introduced by the act of inserting the measuring instrument or sensor into the system itself — the sensor inevitably draws some energy, current, or mass/heat from the system it is measuring (finite input impedance, thermal mass, flow obstruction), which perturbs the very quantity being measured away from what it would have been with no instrument present at all.
e) Most electrical interference (power-line hum, ignition noise, atmospheric static) is predominantly amplitude noise — it adds directly to an amplitude-modulated (AM) signal's information-carrying amplitude and is demodulated right along with the wanted signal. A frequency-modulated (FM) signal carries its information in the instantaneous frequency, not amplitude, of the carrier; an FM receiver (limiter + discriminator) strips off amplitude variations entirely before demodulating, so additive amplitude noise picked up along the transmission path is largely rejected, giving FM a much better noise/interference immunity for the same transmitted power.
f) An explosion-proof measurement system is designed so that it cannot provide the ignition source for a surrounding flammable atmosphere — either by containing any internal spark or arc inside a housing strong enough to withstand and vent an internal explosion without igniting the outside atmosphere, or (intrinsic safety) by limiting all internal electrical energy levels (voltage, current, stored energy) below the minimum needed to ignite the specified gas/dust, so a spark simply cannot occur with enough energy to ignite the surroundings.
g) Disposable sensors add error sources beyond a normal (reusable, individually characterized) sensor because each unit is used only once and is typically not individually calibrated: manufacturing/lot-to-lot variability between nominally identical units (each disposable sensor may have a slightly different true sensitivity than the batch-average calibration applied to it), storage/shelf-life degradation before use, and handling/activation errors (e.g. incomplete wetting, air bubbles, improper insertion) that a trained operator would catch and correct on a reusable, repeatedly recalibrated instrument but that go undetected on a single-use device.
h) Common mode error is the residual error that appears at the output of a differential measurement (e.g. a differential amplifier) due to a signal that is common to both inputs (ground-potential differences, shared interference) leaking through instead of being perfectly rejected, because the amplifier's common-mode rejection ratio (CMRR) is finite rather than infinite. It is minimized by using an amplifier with the highest practical CMRR, keeping the source impedances of the two input legs closely matched (CMRR degrades badly with impedance imbalance), and reducing the size of the common-mode signal itself at its source (better grounding, shielding, breaking ground loops).
i) A digital signal only needs to be correctly resolved as one of two discrete logic levels, so it tolerates substantial noise and attenuation along the transmission path before a bit is misread, and it can be regenerated (re-clocked, error-checked, even error-corrected) at repeaters to restore a perfect copy. An analog signal's information is carried continuously in its amplitude, so any noise picked up along the path adds directly and irreversibly to the measurement, with no way to separate signal from noise once summed, and the corruption only accumulates through each repeater/amplifier stage.
j) Sensitivity is the size of response per unit of the intended input — achieved, in general, by making the sensor respond as strongly as possible to any stimulus in its physical operating mechanism. Selectivity is the ability to respond only to the intended measurand and reject all other similar stimuli (interferents). Increasing the general responsiveness of the underlying sensing mechanism to boost sensitivity very often also increases its responsiveness to closely related interfering species/effects that share the same underlying physical or chemical mechanism, so pushing sensitivity up frequently erodes selectivity unless the two are decoupled by a more specific recognition element (see Q6a).
