Data Acquisition System & Signal Processing – Comprehensive Study Notes

Analogue Instruments: General Concepts

• An analogue device gives a continuously-varying output that maintains a fixed (usually linear) relationship to the input over time.
• Despite the higher accuracy, stability and input impedance of digital meters, analogue meters remain popular because:
– Pointer–scale movement makes deviations visually obvious on control panels.
– Generally passive (no local power required).
– Lower susceptibility to certain noise / isolation problems.

Measurands Commonly Addressed by Analogue Meters

• Electrical quantities: voltage, current, power, energy, frequency, resistance, etc.
• Display generally via a dial & pointer.

Major Classification Axes for Analogue Meters

• By measured quantity: Ammeter, Voltmeter, Watt-meter, Frequency-meter …
• By current type:
– Direct-Current (DC) only.
– Alternating-Current (AC) only.
– AC + DC universal instruments.
• By operating principle (producing deflecting torque):
– Magnetic effect
– Thermal effect
– Electrostatic effect
– Induction effect
– Hall effect
• By indication mode:
– Indicating (instantaneous value only)
– Recording (continuous trace over time)
– Integrating (time-integrated quantity, e.g. energy meters)
• By measurement method:
– Direct-reading (transducer energy directly drives pointer)
– Comparison (unknown compared with a standard – e.g.
AC/DC bridges)
• By mechanical construction:
– Electromechanical
– Electronic

Indicating Instruments

• Pointer moves over a calibrated scale showing magnitude.
• Typical examples: moving-coil voltmeter, moving-iron ammeter.

Recording Instruments

• Provide a continuous paper or chart record over a period.
• Used where trends are important (e.g. strip-chart recorders).

Integrating Instruments

• Sum the measured quantity over time (e.g. $\int i\,dt$ for charge, $\int P\,dt$ for energy).

Operating Principles (Torque-Producing Effects)

• Magnetic (Most common): current in a conductor produces a magnetic field that interacts with another field to yield torque.
• Thermal: measurand heats an element; attached thermocouple converts ∆T→emf.
• Electrostatic: electrostatic force between charged plates displaces a moving element.
• Induction: eddy currents in a non-magnetic conducting disc placed in an AC field produce torque.
• Hall: transverse magnetic field in a conductor carrying current generates a Hall voltage proportional to $I\,B$.

Moving-Coil (D’Arsonval) Galvanometer & Derivatives

• Coil in a radial permanent-magnet field; spring provides restoring torque.
• Theoretical torque: $T = B I h w N$ (N·m).
• With uniform field, $T = K I$ → linear scale.
• Variants by added resistors:
– Voltmeter: high series resistance $R<em>s$ limits current. – Ammeter: low shunt $R</em>p$ bypasses majority of current.
– Ohmmeter: internal source + calibration resistor $R_o$ drive current through unknown R.
• Strengths: high sensitivity, uniform scale, shielding feasible.
• Weaknesses: inherently DC; requires rectifier or converter for AC.

Moving-Iron Instruments (AC or DC)

Attraction Type

• Soft-iron vane is drawn into coil’s stronger field region when current flows.
• Deflecting force $F \propto H^2 \propto i^2$ ⇒ pointer deflection $\theta = k i^2$.
• Scale non-linear (compressed near zero, expanded near full scale).

Repulsion Type

• Two iron vanes magnetised with like polarity repel as coil current increases.
• Mechanical layout: fixed coil, fixed iron vane, moving iron vane on spindle, pointer, hairspring control, air-piston damping.

Merits / Limitations

• Work on AC & DC; rugged & cheap.
• Less sensitive, non-uniform scale; lower accuracy than moving-coil.

Electrostatic Voltmeters

• Use force between charged plates; suited for very high voltages (>10 kV).
• Torque arises from change in stored electrostatic energy as movable plate rotates.

Thermocouple (Thermo-ammeter / RF Ammeter)

• Heater element carries measurand current; junction emf $E \propto \Delta T \propto I_{\text{rms}}^2$.
• PMMC indicator reads resultant DC.
• Can measure true RMS of RF or irregular waveforms.

Rectifier-Type Instruments

• Diode rectifier + PMMC movement → measures AC by rectifying to DC.
• Accuracy limited by diode non-linearity and waveform dependence; best for sinewaves.

Wheatstone Bridge (Comparison Instrument for Resistance)

• Four arms $AB, BC, CD, DA$ with resistances $P, Q, R, S$ (S variable, R unknown).
• At balance (galvanometer current $=0$): $\dfrac{P}{Q}=\dfrac{R}{S}$ ⇒ $R = \dfrac{P}{Q} S$.
• High accuracy because indication is null rather than deflection magnitude.

Digital Multimeter (DMM)

• Core element: Analogue-to-Digital Converter (ADC).
• Functional blocks:
– Calibrated attenuator / buffer amplifier (DCV path).
– Precision rectifier + converter (AC paths).
– Current-to-voltage converters for current ranges.
– Constant-current source + ADC for resistance ranges.
– Microcontroller/logic drives LCD/LED display (typically 4½ digits).
• Zero-reference and auto-ranging improve usability.

Analogue-to-Digital Conversion Fundamentals

• ADC links analogue transducers to digital processing.
• Characteristics:
– Input: analogue voltage (commonly 0–10 V, ±5 V, etc.).
– Output: binary integer (count).
• Resolution: $2^n$ discrete codes for n-bit converter.
– Example: 10 V span, 0.01 V resolution ⇒ need 1000 steps ⇒ $2^{10}=1024$ ⇒ 10 bits.
– Step size: $\text{LSB} = \dfrac{\text{range}}{2^n}$.
• Sampling theory:
– Nyquist criterion: sampling rate $\ge 2 f_{\text{max}}$ of analogue signal.
– Data rate = (samples/s) × (bits/sample).
• Errors:
– Quantisation error ±½ LSB.
– Aliasing if sampling below Nyquist.
• Improving fidelity: increase n (resolution) and/or sampling frequency.

Oscilloscope Essentials

• Displays voltage (Y) versus time (X); many models offer XY, FFT, cursor measurement.
• Input impedance ≈ $1\,\text{M}Ω$ || 15–20 pF → minimal loading.
• Measures amplitude, frequency, phase, rise time, noise, distortion.
• Bandwidth: frequency where gain falls by 3 dB (×0.707).
• Rise-time relation: $\text{BW} \times \text{rise time} \approx 0.35$.
• Accuracy modest (±1 % best, ±5 % cheap units); use where qualitative/approximate results suffice.

Transmission of Measurement Signals

Voltage Mode (Unconditioned)

• Simplest; suffers attenuation (wire resistance) & noise pickup.
• Remedies: pre-amplification, shielded twisted pair, short runs.

4–20 mA Current Loop

• Voltage-to-current converter sends analogue as current; immunity to resistance & noise.
• Range 4 mA (zero) – 20 mA (full scale); zero-current alarm denotes fault.
• At receiving end, convert back via precision resistor & op-amp: $V = I R$.

A.C. Carrier Transmission (Modems)

• Embed low-level DC signal onto AC carrier via amplitude modulation (AM) or frequency modulation (FM):
$V_s = V \sin \omega t$, then vary amplitude or $\omega$ proportional to measurand.
• Demodulate at receiver to recover original DC.
• AM susceptible to noise affecting amplitude; FM more robust.

Fibre-Optic Transmission

• Advantages: intrinsic safety, immunity to EMI, low attenuation over distance.
• Cost higher (terminating opto-transducers, cable), but drops as length increases.

Cable Construction

• Core (glass/plastic) with refractive index $n<em>1$, cladding n2 < n_1, protective jacket.

Modes

• Single-mode (core ≈6 µm): straight-line propagation, minimal dispersion, high bandwidth.
• Multimode (50–200 µm): multiple ray paths → modal dispersion unless mitigated.
– Step-index: abrupt $n$ change; zig-zag rays cause broadening.
– Graded-index: gradual $n$ drop with radius; faster outer rays equalise delays.

Total Internal Reflection Condition

• Snell: $n<em>0 \sin \alpha</em>0 = n<em>1 \sin \alpha</em>1$, $n<em>1 \sin \beta</em>1 = n<em>2 \sin \beta</em>2$.
• Critical angle $\alpha<em>c$ when $\beta</em>2 = 90°$ → beyond this all light reflects.

Multiplexing

• Wavelength-Division Multiplexing (WDM): each sensor modulates unique λ.
• >100 wavelengths possible on one single-mode fibre (≈9 µm).

Wireless Telemetry

• Eliminates physical media; uses radio or optical free-space links.
• Same modulation/demodulation ideas; extra issues: licensing, power, antenna alignment, interference.