22-Agric-A5 Principles of Instrumentation · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams, 04-Agric-A5, Principles of Instrumentation. 3 hours, open book. Questions 1 and 2 are mandatory (20 marks each); the Marking Scheme table requires 3 of Questions 4–7 (Note 3's own wording is looser, “any other THREE questions,” which would also admit Question 3 — the source is self-inconsistent on this point). All FIVE optional questions (3–7) are answered below so this set is a complete study resource regardless of which reading is correct.
Reference texts: Doebelin, Measurement Systems: Application and Design, 5th ed.; Bentley, Principles of Measurement Systems, 4th ed.; Horowitz & Hill, The Art of Electronics, 3rd ed.; Fraden, Handbook of Modern Sensors, 5th ed.; Skoog, Holler & Crouch, Principles of Instrumental Analysis, 7th ed.
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) By coupling the signal through a non-galvanic (no direct wire) path: optical coupling (LED/phototransistor opto-isolator or a fibre-optic link), inductive/magnetic coupling (a small transformer), capacitive coupling, or RF/wireless telemetry. All of these transfer the information while leaving the sensor's and the data-acquisition system's electrical grounds and supplies completely isolated from one another.
b) Two noise sources are fundamental, physical, and unavoidable at any temperature above absolute zero: thermal (Johnson–Nyquist) noise, generated by the random thermal motion of charge carriers in any resistance, and shot noise, arising from the discrete, quantized nature of charge carriers crossing a junction. Neither is a design flaw to be engineered away — both can only be REDUCED (lower temperature, lower bandwidth, lower source resistance/current), never eliminated.
c) A LOW-PASS filter, applied to the analog signal BEFORE it is sampled (an anti-aliasing filter). It must attenuate any signal content above half the sampling rate (the Nyquist frequency) so that content cannot fold back into the sampled baseband and masquerade as a false low-frequency component.
d) Shielding (a grounded conductive enclosure or cable shield), twisted-pair wiring (which cancels induced common-mode pickup), proper single-point grounding (avoiding ground loops), physically routing signal wiring away from interference sources (motors, power lines), and using differential rather than single-ended signal transmission — each attacks a different coupling mechanism (capacitive, inductive, or conducted).
e) Every stage in a cascaded amplifier chain adds its own noise, but that noise is amplified by all of the GAIN STAGES THAT FOLLOW it, while the first stage's noise is amplified by the gain of the entire remaining chain. A low-level signal therefore has the first stage's own noise contribution dominate the system's total output noise almost completely (the Friis cascade result) — a noisy first stage cannot be fixed by a quiet second stage, so the first stage alone must be low-noise/high-precision.
f) An electrode that maintains a fixed, known, stable half-cell potential regardless of the composition of the solution being measured, providing a constant reference against which a sensing/working electrode's potential is compared (e.g. a silver/silver-chloride or saturated calomel electrode).
g) A phototransistor has internal current GAIN: the light-generated photocurrent acts as the transistor's base current, which the transistor then amplifies by its own current gain $h_{FE}$ before it appears at the output. A photodiode has no such internal amplification — its output is simply the raw photocurrent itself, so for the same incident light a phototransistor delivers a much larger output signal (at the cost of a slower response and a less linear relationship to light level).
h) Resistive temperature sensors (RTDs, thermistors) must be excited with a small measuring current to sense their resistance; that current dissipates $I^2R$ power directly IN the sensing element itself, raising its own temperature above the true surrounding temperature being measured. The resulting error grows with excitation power and is worse for sensors with a poor dissipation constant (poor heat transfer to their surroundings, e.g. in still air or gas rather than a flowing liquid).
i) Shot noise is the fluctuation that results from the discrete, quantized nature of electric charge/photons: a current is really a stream of individual carriers crossing a potential barrier (or photons striking a detector) at random, statistically independent instants (a Poisson process), so the instantaneous current scatters around its time-average value even with an otherwise perfectly steady applied voltage. Its RMS value is $i_n=\sqrt{2qI\,\Delta f}$, growing with the average current $I$ and the measurement bandwidth $\Delta f$.
j) Differentiation is a high-pass operation — for a sinusoidal component its gain rises in proportion to frequency — so it amplifies whatever high-frequency noise rides on the measured signal far more than it amplifies the (typically lower-frequency) signal itself. Taking a numerical or analog derivative of real, noisy measurement data therefore hugely magnifies the point-to-point noise/scatter, producing a derivative signal with a much worse signal-to-noise ratio than the original data, even when the underlying physical derivative is smooth.
