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) The characteristics that matter when specifying an ADC for a measurement task are: resolution (number of bits, i.e. the size of one LSB relative to full scale); sampling rate/bandwidth (how fast it can convert, which must satisfy Nyquist for the signal of interest); accuracy and linearity (integral and differential non-linearity, INL/DNL, and monotonicity); conversion time/latency; input voltage range; and noise floor. A converter can have excellent resolution on paper yet still deliver poor effective accuracy if its linearity or noise performance is poor.
b) Integrating the input over exactly 1/60 s — one full period of the North American 60 Hz mains frequency — means any interference component at 60 Hz (or its harmonics) that has leaked onto the input contributes a net area of essentially zero to the integral, because a symmetric periodic waveform integrates to zero over exactly one of its own full periods. Mains hum from nearby AC wiring, transformers or fluorescent-lighting ballasts is therefore automatically averaged out by the conversion process itself, which is why dual-slope (integrating) converters are the classic choice for precision digital multimeters operating on 60 Hz mains (and are commonly switched to 1/50 s integration time in 50 Hz countries).
c) A successive-approximation converter resolves the input one bit at a time over several clock cycles, comparing the (fixed) input against a sequence of trial DAC voltages in a binary search. That comparison sequence is only valid if the input voltage being compared is the same value throughout the whole conversion; if the input were free to change mid-conversion, each bit decision would effectively be made against a different, moving target and the resulting code would not correspond to any single instant of the real signal. A sample-and-hold stage freezes (holds) one instantaneous sample of the input for the full duration of the conversion so every bit decision is self-consistent.
d) Aliasing occurs when a signal is sampled at a rate below the Nyquist rate for its highest frequency component ($f_s<2f_{max}$). The under-sampled high-frequency content cannot be distinguished, after the fact, from a lower, false ("alias") frequency that the same sample sequence would also be consistent with — the sampled data folds that high-frequency energy down into the baseband as spurious, misleading low-frequency content. Because this distortion is created at the moment of sampling, no amount of digital processing afterward can remove it; it must be prevented beforehand by an anti-aliasing (analog low-pass) filter ahead of the sampler.
e) A pre-amplifier's functions are: amplifying the sensor's weak raw signal up to a robust level (improving SNR for everything downstream, per Q2i); impedance buffering/matching — presenting a high input impedance to the sensor (so it isn't loaded, per Q2b) while driving a low output impedance capable of feeding a cable and the rest of the signal chain; and often some initial filtering or excitation (e.g. supplying bridge excitation voltage, or basic noise/bandwidth limiting) before the signal reaches the anti-aliasing filter and ADC.
f) The required gain is set by matching the sensor's expected full-scale output signal to the ADC's (or the rest of the signal chain's) full-scale input range: $$\text{Gain}=\dfrac{\text{ADC full-scale input range}}{\text{sensor's maximum expected output}}.$$ Too little gain wastes the ADC's resolution (the signal only exercises a small fraction of the available codes); too much gain saturates/clips the amplifier or the ADC input before the sensor's own maximum signal is reached. The right gain uses the full dynamic range available without ever clipping.
