22-Agric-A5 Principles of Instrumentation · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A5 Principles of Instrumentation, National Exams May 2016 — 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) Apply a known, sharply-defined time-varying test input — ideally a step or an impulse, since both excite the full frequency range at once — and record the instrument's output versus time. From that trace extract the dynamic parameters: for a first-order sensor, the time constant $\tau$ (63.2% rise time); for a second-order (underdamped) sensor, the natural frequency $\omega_n$ (from the ringing period) and damping ratio $\zeta$ (from the overshoot), from which the settling time and usable bandwidth follow.
b) Per the Nyquist criterion, the sampling rate must be at least twice the highest frequency component present in the signal, $f_s\ge2f_{max}$; in practice a comfortable margin above the bare minimum (5-10× the signal's highest significant frequency, or at minimum 2-4× after the anti-aliasing filter's cutoff) is used so the filter's finite roll-off does not let residual energy alias back into the sampled band.
c) Noise is an inherent, generally random, broadband property of the sensor/signal-conditioning chain itself (thermal/Johnson noise, shot noise, 1/f noise) that exists even with no external source coupling in — it cannot be shielded away, only reduced by bandwidth-limiting or averaging. Electrical interference is an unwanted signal injected from an external source (power-line hum, switching transients, radiated RF) that couples into the measurement circuit via capacitive, inductive or conductive (ground-loop) paths — because it has an identifiable external origin and coupling path, it can in principle be eliminated by shielding, grounding, filtering at its specific frequency, or physically separating the source from the signal path.
d) A differential amplifier ideally responds only to the difference between its two inputs, $V_+-V_-$, and rejects any signal common to both (the common-mode signal, $V_{cm}=(V_++V_-)/2$) — such as ground-loop offsets or interference picked up equally by both wires of a twisted pair. The common mode rejection ratio (CMRR) is the ratio of differential gain to common-mode gain, expressed in dB; a high CMRR means the amplifier passes the wanted differential signal essentially undiminished while suppressing the unwanted common-mode noise by many orders of magnitude.
e) The measuring instrument's own presence must draw negligible energy/current from the system under test, i.e. its input impedance must be made very high relative to the source impedance of the system being measured (for a voltage measurement) — or, more generally, the sensor must be chosen/sized so that its own mass, heat capacity, flow restriction, etc. is negligible compared with the system being measured, so that attaching the sensor does not itself perturb the very quantity it is trying to read (the general "loading effect").
f) A digital signal only has to be distinguished as one of two discrete logic levels (high/low), so it tolerates a large amount of additive noise or attenuation along the transmission path before a receiver mis-reads a bit — and it can be regenerated (re-clocked, error-checked, even error-corrected) at intermediate repeaters to restore a perfect copy. An analog signal's information is carried in its continuous amplitude, so any noise picked up along the path is added directly and permanently to the measurement, with no way to distinguish "signal" from "noise" once they have summed, and it only gets worse with each repeater/amplifier stage.
g) A cable shield grounded at both ends forms a closed loop between the two ground points; if those two grounds are not at exactly the same potential (which they almost never are, due to ground currents elsewhere in the building), the potential difference drives a circulating current through the shield loop (a ground loop), and that current's magnetic field couples directly into the signal conductors it is supposed to protect. Grounding the shield at only one end (single-point grounding) breaks this loop — the shield still intercepts and drains capacitively /inductively coupled interference to that one ground reference, but no current can circulate through it, eliminating the ground-loop coupling mechanism.
h) Locating the preamplifier immediately at the sensor amplifies the (often very small) raw sensor signal to a much larger level before it has to travel any significant length of cable. Any noise or interference picked up by the cable is then a small addition to an already-large signal (a good signal-to-noise ratio), whereas if the raw small signal were carried unamplified over a long cable first, the same absolute noise pickup would represent a much larger fraction of the (still tiny) signal — potentially burying it entirely.
i) Thermocouples generate their signal from the Seebeck effect at a junction of two dissimilar metals, and the two lead wires running back to the measuring instrument form a natural differential (twisted) pair, both legs of which pick up essentially the same interference from a shared external source — that common-mode pickup is then rejected by the differential measurement (part d). In addition, because thermocouples are inherently low-impedance, capacitively-coupled interference currents produce only a small voltage across that low impedance ($V=IZ$), further reducing the interference's effect relative to a high-impedance sensor picking up the same coupled current.
j) The number of bits $N$ must give a quantization step $Q=FSR/2^N$ (full-scale range divided into $2^N$ levels) that is small enough that the quantization error it introduces is negligible compared with the sensor's own noise floor and the required measurement resolution — there is no benefit to bits finer than the analog signal's own noise, since that noise will dither the reading across several quantization levels anyway. In practice $N$ is chosen so $Q$ is a small fraction (e.g. ≤ 1/4 to 1/2) of the smallest change that must be resolved, rounded up to the next available converter word length (8/10/12/16/24-bit).
