Instrumentation and Measurement
Instrumentation and measurement tests sensor selection, bridge and signal-conditioning circuits, uncertainty, calibration, resolution, sampling and noise. The exam expects defensible measurement statements: value, unit, uncertainty and conditions.
Core rules
- A Wheatstone bridge is balanced when R1/R2=R3/R4. A small strain-gauge change produces ΔV≈Vex(ΔR/R)/4 for a single active gauge.
- ADC resolution is Vref/2^n; quantization error is up to ±½ LSB. Nyquist requires fs>2fmax, with anti-alias filtering before sampling.
- Combined independent uncertainties add in quadrature: u_total=√(u1²+u2²+…).
- Sensitivity is output change per input change; resolution is the smallest detectable change; accuracy is closeness to true value, distinct from precision.
- Thermocouples need cold-junction compensation; RTDs are more linear but slower; strain gauges need excitation and bridge completion.
Worked example
A 12-bit ADC has Vref=5 V and unipolar range 0–5 V. Resolution=5/4096=1.22 mV. For Vin=1.25 V, ideal code=round(1.25/5×4095)=1024. The represented voltage is 1024×5/4095=1.2503 V, so the quantization error is about +0.3 mV, within half an LSB.
Traps
- Using 2^n−1 for resolution but 2^n for code scaling inconsistently.
- Ignoring sensor loading: a high-impedance source feeding a low-impedance ADC loses gain.
- Reporting precision as accuracy.
- Missing aliasing when sampling a fast vibration signal.
- Forgetting bridge excitation drift or lead-wire resistance in strain measurement.