Question 2 of 7: Sensor Principles

Question 2: Sensor Principles (20 marks)

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) Sensitivity is highest at high air speeds. A Pitot tube measures the dynamic pressure $\Delta p=\tfrac12\rho V^2$ (stagnation minus static pressure); its sensitivity is $d(\Delta p)/dV=\rho V$, which grows linearly with speed. At low $V$, $\Delta p$ is tiny (it falls off as $V^2$) and is easily lost in transducer noise/resolution, whereas at high $V$ the same small change in speed produces a much larger, easily resolved change in $\Delta p$.

b) A reference electrode maintains a fixed, known, stable electrical potential that is independent of the composition of the solution being measured — typically a silver/silver-chloride (Ag/AgCl) or calomel electrode with a defined internal fill solution and a porous liquid junction to the sample. It supplies the stable "other half" of the electrochemical cell so that the pH-sensitive glass electrode's own potential can be interpreted, via the cell voltage, as a pH value; without it there is no fixed zero point against which to read the glass electrode.

c) Because the response is diffusion-limited rather than instantaneous, its speed is specified as a response time to a step change in gas concentration — conventionally $t_{90}$, the time for the output to reach 90 % of its final steady value — rather than a bandwidth or single time constant, since a purely diffusive approach to equilibrium is not a simple first-order exponential.

d) Add damping to the mechanical vibration itself (a viscous dashpot, elastomeric damping pad, or added mass/stiffened mounting to shift the cell's resonant frequency away from the exciting vibration) rather than filtering the electrical output. Because damping is applied to the mechanical structure, the static (DC) deflection that encodes the applied load is unaffected — only the dynamic ringing is removed — whereas a heavy electrical low-pass filter would also slow the cell's response to genuine load changes.

e) A piezoelectric crystal generates a charge (and hence a voltage across its own capacitance) directly and almost instantaneously in response to applied mechanical stress, via the piezoelectric effect — there are no moving parts beyond the crystal's own elastic deformation. Because the charge output tracks the instantaneous strain with no intermediate mechanical linkage, and the crystal's own natural frequency is high, the sensor has a very wide bandwidth and fast response compared with sensors that rely on bulk mechanical motion of a proof mass against a spring.

f) Current through a coil suspended in a fixed permanent-magnet radial field experiences a torque $\tau=BANI$ ($B$ field, $A$ coil area, $N$ turns, $I$ current) that deflects the coil against a calibrated restoring spring. The steady-state deflection angle is directly proportional to the coil current, read off a calibrated scale — the classic d'Arsonval/galvanometer movement.

g) A thermocouple's Seebeck voltage is generated by the temperature difference between its measuring (hot) junction and its reference (cold) junction — it has no absolute-temperature output of its own. Without fixing or independently knowing the reference junction's temperature, the same measured voltage could correspond to many different hot-junction temperatures, so the reference junction anchors the scale and lets the voltage be converted to an actual temperature.

h) A phototransistor is, in effect, a photodiode whose photo-generated base current is further amplified by the transistor's own current gain ($h_{FE}$); for the same incident light level it therefore delivers a much larger output current than a bare photodiode junction photocurrent alone — at some cost in response speed and linearity compared with the photodiode.

i) To suppress thermally generated dark current and the noise that rides on it. In a photodetector, carriers are excited across the band gap by heat as well as by light, and that thermal generation rate scales roughly as $\exp(-E_g/2kT)$ — so for the narrow-band-gap detectors used in the infrared (InSb, HgCdTe, extrinsic Si/Ge) the dark current at room temperature is large enough to saturate the readout and its shot/generation-recombination noise swamps a weak optical signal. Johnson noise in the detector and its load resistance also falls with $\sqrt{T}$. Cooling to liquid nitrogen (77 K) cuts the dark current by orders of magnitude, drops the noise floor and so raises the detectivity $D^{*}$, letting very weak (and long-wavelength) signals be measured; it also stabilises responsivity and reduces the detector's own thermal background emission.

j) A Hall effect sensor exploits the Hall effect: a current-carrying conductor or semiconductor placed in a magnetic field perpendicular to the current develops a small transverse voltage proportional to the product of current and field strength ($V_H\propto I\!\times\!B$). It is used to sense magnetic field directly, and, through that, proximity, position, rotational speed, or current (via the field a current-carrying conductor produces).