§ 10.1Transducers: Classification & Basics
A transducer converts one form of energy/physical quantity into another; an electrical transducer (sensor) outputs an electrical signal. Generic measurement chain: sensor → signal conditioning (amplify/filter/linearize) → ADC → processing → display/control.
Classification axes (each pair is an MCQ)
- Active (self-generating) — produces its own EMF/charge, no external supply: thermocouple, piezoelectric, photovoltaic, tachogenerator, Hall (current-biased but generates EMF). Passive — modulates an external excitation by changing R, L or C: strain gauge, LVDT, RTD, capacitive, potentiometer.
- Primary (senses the quantity directly, e.g., bourdon tube) vs secondary (converts the primary's output to electrical).
- Analog (continuous) vs digital (encoder, quantized).
- By principle: resistive, inductive, capacitive, piezoelectric, thermoelectric, Hall, photoelectric (the syllabus list).
Static characteristics (define-and-distinguish set)
- Accuracy (closeness to true value) vs precision (repeatability/reproducibility) — accurate ≠ precise; sensitivity = Δoutput/Δinput; resolution (smallest detectable change); linearity; hysteresis (loading-vs-unloading difference); dead zone/threshold; drift; span/range; repeatability.
- Dynamic: speed of response, time constant, bandwidth, settling — first/second-order behaviour (Unit-3 §3.10).
- Errors: systematic (gross/instrumental/environmental — correctable) vs random (statistical — reduced by averaging); loading effect (the meter disturbing the measured circuit); calibration against standards (NPL).
UGC NET focus
Active vs passive classification (thermocouple/piezo/photovoltaic = active; LVDT/strain gauge/RTD = passive); accuracy vs precision distinction; sensitivity = Δo/Δi; systematic vs random errors; loading effect definition.
§ 10.2Resistive Transducers
Vary resistance \( R = \rho L/A \) with the measurand (passive — need excitation).
Potentiometric (resistive displacement)
- Wiper on a resistance track → V_out ∝ position; linear/rotary; cheap, high output, but friction, wear, finite resolution (wire-wound) and loading error.
Strain gauge (the workhorse)
Gauge factor
$$ GF = \frac{\Delta R/R}{\varepsilon} = 1 + 2\nu + \frac{\Delta\rho/\rho}{\varepsilon}; \qquad \varepsilon = \frac{\Delta L}{L} $$
- Metallic foil GF ≈ 2 (dimensional effect dominant); semiconductor (piezoresistive) GF ≈ 100–200 (resistivity effect — high sensitivity but temperature-sensitive, nonlinear).
- Read with a Wheatstone bridge; quarter/half/full bridge; temperature compensation via dummy gauge; the basis of load cells, pressure sensors, torque sensors (§10.9).
Resistance thermometers
- RTD (Pt100: 100 Ω at 0 °C): R increases with T, positive TC, near-linear \( R_T = R_0(1 + \alpha T) \) (Pt α ≈ 0.00385/°C); accurate, stable, −200…+850 °C; needs lead-compensation (3/4-wire).
- Thermistor: metal-oxide, large negative TC (NTC), exponential \( R = R_0e^{\beta(1/T - 1/T_0)} \); very sensitive but nonlinear, narrow range — temperature alarms, compensation.
UGC NET focus
GF = (ΔR/R)/ε; metal GF ≈ 2 vs semiconductor ≈ 100+; RTD positive-TC linear (Pt100) vs thermistor negative-TC exponential; bridge readout + dummy-gauge compensation; ρL/A dependence.
§ 10.3Inductive Transducers & LVDT
- Vary inductance/mutual inductance with the measurand: change reluctance (moving core), air gap, or coupling. \( L = N^2/\mathcal{R} \) (reluctance \(\mathcal R\)).
- Variable-reluctance and variable-air-gap sensors; eddy-current proximity probes (non-contact distance/vibration).
LVDT — Linear Variable Differential Transformer
One primary + two secondaries in series opposition; AC excitation on the primary. A movable ferromagnetic core sets the coupling: at the centre (null) the secondary outputs cancel (V_o ≈ 0); displacement unbalances them so |V_o| ∝ displacement and the phase (0°/180°) gives direction.
- Merits: frictionless (infinite mechanical life), high resolution (μm), good linearity over range, rugged, no electrical contact, can work in harsh environments; demerits: AC excitation + phase-sensitive (synchronous) detection needed, sensitive to stray fields/temperature.
- RVDT = rotary version (angular displacement); synchros/resolvers for shaft angle.
- Applications: precision displacement, level, force/pressure (via a spring/diaphragm converting force → displacement).
UGC NET focus
LVDT: two secondaries in series opposition, null at centre, |V_o| ∝ displacement, phase = direction; frictionless/high-resolution merits; needs AC + phase-sensitive detection; variable-reluctance principle L = N²/ℛ.
§ 10.4Capacitive Transducers
Three ways to vary C = εA/d
$$ C = \frac{\varepsilon_0\varepsilon_r A}{d}: \quad \text{change } d\ (\text{displacement, } C\propto 1/d,\ \text{nonlinear}),\ \ A\ (\text{linear}),\ \ \text{or } \varepsilon_r\ (\text{level, humidity}) $$
- Distance/displacement (vary d — high sensitivity, nonlinear → differential arrangement linearizes); area-vary (rotary/linear, linear); dielectric-vary (liquid level, moisture/humidity, grain).
- Merits: no friction, very high resolution/sensitivity, low power, good HF response, non-contact; demerits: tiny capacitance (pF) → stray-capacitance and cable sensitivity, needs guarding/AC bridge or oscillator readout, temperature/humidity effects.
- Read by AC bridge (Schering/Wien), capacitance-to-frequency (in a 555/oscillator), or charge amplifier.
- Applications: pressure (diaphragm moves a plate — capacitive pressure sensor), MEMS accelerometers (§10.19), touchscreens, proximity, humidity, level.
UGC NET focus
C = εA/d and which parameter senses what (d → displacement nonlinear, A → linear, ε_r → level/humidity); differential plates linearize the 1/d law; stray-capacitance problem → guarding; capacitive vs inductive sensitivity contrast.
§ 10.5Piezoelectric Transducers
- Active (self-generating): mechanical stress on a non-centrosymmetric crystal (quartz, Rochelle salt) or poled ceramic (PZT, barium titanate) or polymer (PVDF) produces a proportional surface charge.
Piezoelectric output
$$ Q = d\,F\ \ (d = \text{charge sensitivity, C/N}); \qquad V = \frac{Q}{C} = \frac{d\,F}{C} = g\,t\,P \ \ (g = \text{voltage sensitivity}) $$
- Dynamic only — charge leaks away → cannot measure static/DC quantities (steady force, constant pressure); ideal for vibration, shock, dynamic force/pressure, acceleration (seismic-mass accelerometer), AE.
- High output impedance → needs a charge amplifier (or high-Z buffer) and low-noise cable; high natural frequency → wide bandwidth, fast response; reversible (inverse piezoelectric effect → ultrasonic transmitters, buzzers, actuators, SAW devices).
- Applications: accelerometers, ultrasonic transducers/sonar, microphones, knock sensors, igniters, ink-jet, quartz frequency standards (Unit-4 §4.10).
UGC NET focus
Self-generating/active; Q = dF and V = Q/C; no static measurement (charge leakage) — the most-asked limitation; charge amplifier need; PZT/quartz materials; accelerometer/ultrasonic applications; inverse effect for actuators.
§ 10.6Thermoelectric Transducers
Seebeck effect
Two dissimilar metals joined at two junctions at different temperatures generate an EMF \( V = \alpha_{AB}(T_{hot} - T_{cold}) \) — the thermocouple. (Active/self-generating.)
- Cold-junction (reference) compensation is essential — the measured EMF depends on the difference; modern instruments measure the cold-junction temperature electronically and add the correction.
- Related: Peltier effect (current → heating/cooling at a junction → thermoelectric coolers) and Thomson effect.
- Standard types: J (Fe-Constantan), K (Chromel-Alumel, the general-purpose −200…+1260 °C), T (Cu-Constantan), R/S/B (Pt-PtRh, high temperature).
- Merits: wide range, rugged, cheap, self-powered, fast, point measurement; demerits: low output (mV, ~μV/°C → needs amplification), nonlinear (polynomial linearization), reference-junction handling, noise pickup.
- Thermopile = many thermocouples in series → larger output (IR/radiation thermometry, non-contact).
- Other temperature sensors recap: RTD/thermistor (§10.2, resistive), IC sensors (LM35: 10 mV/°C), pyrometers/radiation (Stefan–Boltzmann, non-contact, very high T).
UGC NET focus
Seebeck EMF ∝ ΔT and cold-junction compensation necessity; type K = general purpose; Peltier = cooling; thermocouple (mV, wide range) vs RTD (accurate, linear) vs thermistor (sensitive, NTC) comparison; thermopile = series stack.
§ 10.7Hall-Effect Transducers
Hall voltage
$$ V_H = \frac{B\,I}{n\,q\,t} = R_H\frac{BI}{t}, \qquad R_H = \frac{1}{nq} $$
- A current-carrying semiconductor slab in a transverse magnetic field develops a voltage ⊥ to both (Lorentz force separates carriers, Unit-1 §1.1). Output ∝ B (for fixed I) → magnetic-field/proximity sensor; ∝ I (for fixed B) → contactless current sensor (clamp meters).
- Semiconductor (InSb, GaAs, Si) — high R_H (low carrier density) → large V_H; the sign of V_H gives carrier type.
- Forms: linear (analog ∝ B) and switch/latch (digital threshold). Merits: non-contact, no wear, solid-state, wide bandwidth, works at DC; demerits: temperature drift, offset (null) voltage, needs constant bias current.
- Applications: position/proximity, brushless-DC commutation, speed/RPM (gear-tooth), contactless current measurement, magnetometers, keyboards; gaussmeter.
UGC NET focus
V_H = BI/nqt and R_H = 1/nq; measures B (field/proximity) or I (current, contactless); semiconductor for large V_H; sign → carrier type; DC-capable non-contact merits; BLDC commutation application.
§ 10.8Photoelectric Transducers
| Device | Principle | Type / note |
|---|---|---|
| LDR / photoresistor (CdS) | photoconductive — R falls with light | passive; slow; cheap; light switches |
| Photodiode (PN/PIN) | photocurrent ∝ illumination | photoconductive (reverse-bias, fast) or photovoltaic (zero-bias) |
| Photovoltaic / solar cell | generates EMF from light | active (Unit-1 §1.15) |
| Phototransistor | photodiode + transistor gain (β) | higher current, slower than photodiode |
| APD | avalanche multiplication | internal gain, low-light (Unit-8 §8.16) |
| Photoemissive (PMT) | external photoemission + electron multiplication | extreme sensitivity, single photons |
- Cutoff: photons need \( h\nu \ge E_g \) (photoconductive) or work function (emissive); responsivity R = ηλ/1.24 A/W (§8.16). Categories: photoemissive, photoconductive, photovoltaic.
- Applications: light meters, optical encoders/counters, flame/smoke detectors, optocouplers (isolation), barcode readers, fiber receivers, pyranometers, CCD/CMOS imagers (Unit-2 §2.17).
UGC NET focus
LDR = photoconductive (R↓ with light, passive) vs solar cell = photovoltaic (active); photodiode fast vs LDR slow; phototransistor = gain; categories photoemissive/photoconductive/photovoltaic; hν ≥ E_g threshold.
§ 10.9Measurement of Mechanical Quantities
| Quantity | Primary sensing methods |
|---|---|
| Displacement | potentiometer, LVDT/RVDT, capacitive, optical encoder, eddy-current, ultrasonic/laser (non-contact) |
| Velocity | linear: differentiate displacement; rotary: tachogenerator (V ∝ ω, active), magnetic/optical pickup pulse rate, Doppler |
| Acceleration | seismic mass + spring + damper; piezoelectric (dynamic) or piezoresistive/capacitive MEMS accelerometer; a = displacement of mass × ω_n² region |
| Force / Weight | load cell = elastic element + strain gauges in a bridge; piezoelectric (dynamic); LVDT + spring |
| Torque | strain gauges (45° rosette) on a shaft in a bridge (slip-ring/telemetry); twist-angle (optical); reaction torque |
| Strain | strain gauge + Wheatstone bridge (§10.2); GF = (ΔR/R)/ε; quarter/half/full bridge for sensitivity & compensation |
- Force/pressure/torque all reduce to strain measurement via an elastic element — the unifying idea; bridge output \( V_o = \tfrac14 GF\,\varepsilon\,V_{ex} \) (quarter bridge), ×2/×4 for half/full.
- Accelerometer (seismic): below resonance, mass displacement ∝ acceleration; above, ∝ displacement (vibrometer) — choice of damping (ζ ≈ 0.7) flattens response.
- Velocity by integrating accelerometer or differentiating displacement (noise trade-offs, Unit-4 §4.12).
UGC NET focus
Sensor↔quantity matching (LVDT-displacement, tachogenerator-velocity, piezo/MEMS-acceleration, load cell-force, strain-gauge bridge-strain/torque); seismic-mass accelerometer regions; bridge output formula; force→strain unifying principle.
§ 10.10Measurement of Process Quantities
| Quantity | Methods |
|---|---|
| Temperature | thermocouple (Seebeck, wide range), RTD (Pt100, accurate/linear), thermistor (NTC, sensitive), IC (LM35), bimetallic, radiation pyrometer (non-contact, very high T) — §10.2/§10.6 |
| Pressure | elastic element (Bourdon tube, diaphragm, bellows, capsule) → displacement → LVDT/capacitive/strain-gauge readout; piezoresistive/capacitive MEMS; absolute/gauge/differential; vacuum: Pirani (thermal), ionization gauges |
| Flow | differential-pressure obstruction (orifice/venturi/nozzle, Q ∝ √Δp), rotameter (variable area), turbine, electromagnetic (Faraday, conductive liquids, no obstruction), ultrasonic (transit-time/Doppler), Coriolis (mass flow), vortex-shedding, hot-wire anemometer (gas) |
| Humidity | capacitive (polymer ε_r changes — dominant), resistive hygrometer, dew-point (chilled mirror), psychrometer (wet/dry bulb); relative vs absolute |
| Thickness | capacitive/inductive (eddy-current for coatings on metal), ultrasonic (echo time), beta/X-ray gauges (rolling mills), optical interferometry/ellipsometry (films, Unit-2) |
| pH | glass electrode + reference (Ag/AgCl) → potentiometric; \( E = E_0 - 0.059\,\text{pH} \) (V at 25 °C, Nernstian ~59 mV/pH); very high source impedance → electrometer/buffer amplifier; temperature compensation |
- Flow numerical: orifice \( Q = C_d A\sqrt{2\Delta p/\rho} \) (∝ √Δp — the square-root scale trap).
- pH electrode's ~59 mV/decade slope and GΩ impedance → the classic high-input-impedance amplifier requirement (ties to op-amp/in-amp, Unit-4).
UGC NET focus
Bourdon tube → pressure; orifice/venturi Q ∝ √Δp; electromagnetic flowmeter (Faraday, conductive, no obstruction); capacitive humidity; glass-electrode pH with 59 mV/pH and high-Z amplifier; method↔quantity matching.
§ 10.11Measurement of R, L, C: Bridges
Bridges measure an unknown impedance by null balance (detector reads zero) → high accuracy, independent of supply magnitude. DC for R, AC for L/C.
Wheatstone bridge (DC, resistance)
$$ \text{Balance: } \frac{R_1}{R_2} = \frac{R_3}{R_4} \;\Rightarrow\; R_x = R_3\frac{R_2}{R_1} \quad (\text{medium R, 1 Ω–1 MΩ}) $$
| Bridge | Measures | Key feature / balance |
|---|---|---|
| Wheatstone | medium R | R_x = R₃R₂/R₁; strain-gauge readout |
| Kelvin (double) | low R (< 1 Ω) | eliminates lead/contact resistance (4-wire) |
| Megohm / guarded | very high R | insulation resistance |
| Maxwell (Maxwell–Wien) | L (medium Q) | L via a parallel R-C standard; L_x = R₂R₃C₁, balance frequency-independent |
| Hay | high-Q L | series R-C standard; balance is frequency-dependent |
| Anderson | low-Q L | extends Maxwell, accurate low Q |
| Schering | C & dielectric loss (tan δ) | HV capacitance/insulation testing |
| De Sauty | C (lossless) | simple capacitance comparison |
| Wien | frequency / C | f = 1/2πRC — frequency-selective (oscillator, Unit-4 §4.10) |
- AC bridge general balance: \( Z_1Z_4 = Z_2Z_3 \) → two equations (magnitude + phase / real + imaginary) → solves for the unknown's R and L (or C) and its quality.
- Quality factor: Maxwell for low-medium Q, Hay for high Q (Q > 10) — the standard discriminator MCQ; Schering for capacitance & loss angle (HV dielectric testing).
- Detector: galvanometer (DC), headphones/tuned amplifier/null indicator (AC); shielding and Wagner earth eliminate stray-capacitance errors.
UGC NET focus
Wheatstone R_x = R₃R₂/R₁; Kelvin for low R; Maxwell (low-Q) vs Hay (high-Q) inductor; Schering for C/tan δ; Wien for frequency; AC bridge needs two balance conditions; L_x = R₂R₃C₁ (Maxwell).
§ 10.12Potentiometers
- DC potentiometer (Crompton/slide-wire): measures an unknown EMF by balancing it against a known voltage drop — at null no current is drawn from the source → no loading, measures true EMF (not terminal voltage). Standardized against a standard cell (Weston, 1.0186 V) to fix the working current.
- Uses: precise EMF/voltage, and by extension current (drop across a standard resistor), resistance (ratio), and calibration of voltmeters/ammeters; \( E_x = \dfrac{l_x}{l_s}E_s \).
- AC potentiometer: measures magnitude and phase of AC voltage — polar type (magnitude + phase dial) and coordinate/Cartesian type (in-phase + quadrature components); needs a phase reference and frequency match. Used for AC voltage/current, power-factor, transformer testing, magnetic measurements.
- Advantage over a voltmeter: null method → infinite input resistance at balance → no loading error (the recurring exam point).
UGC NET focus
Potentiometer = null method, draws no current → measures true EMF without loading; standard-cell (Weston) standardization; DC (magnitude) vs AC (polar/coordinate — magnitude + phase); E_x = (l_x/l_s)E_s.
§ 10.13Voltage, Current, Power & Energy
Analog meters (PMMC core)
- PMMC (D'Arsonval): torque ∝ current, DC only, responds to average, linear scale; basic movement = a microammeter.
Range extension $$ \text{Ammeter: shunt } R_{sh} = \frac{I_mR_m}{I - I_m}; \qquad \text{Voltmeter: series } R_s = \frac{V}{I_m} - R_m;\qquad \text{sensitivity} = \frac{1}{I_{fsd}}\ \Omega/V $$
- Moving-iron (reads RMS, AC+DC, nonlinear, cheap — panel meters); electrodynamometer (RMS, AC+DC, used as a transfer/wattmeter standard); rectifier-type (PMMC + diode, calibrated RMS for sinusoids → form-factor error on non-sinusoids); thermocouple meter (true RMS at RF).
- Loading: a voltmeter of 20 kΩ/V loads less than one of 1 kΩ/V — sensitivity matters.
Power & energy
- Wattmeter (electrodynamometer): current coil (in series) + pressure/voltage coil (across) → deflection ∝ VI cos φ = true (active) power; compensate for pressure-coil current; three-wattmeter / two-wattmeter method for 3-phase (P = W₁ + W₂; tan φ = √3(W₁−W₂)/(W₁+W₂)).
- Energy meter (induction/watt-hour): an aluminium disc driven by voltage + current fluxes rotates at speed ∝ power; revolutions ∝ energy (kWh); meter constant (rev/kWh). Modern electronic meters use Hall/shunt sensing + a multiplier IC.
UGC NET focus
PMMC = DC/average/linear; shunt & multiplier formulas; sensitivity 1/I_fsd Ω/V and loading; moving-iron/dynamometer = RMS; wattmeter ∝ VIcosφ; two-wattmeter 3-phase relations; energy-meter constant rev/kWh.
§ 10.14Frequency, Time & Phase Measurement
- Digital frequency counter: count input cycles over a precise gate time T → f = N/T; reciprocal counter (measure period, invert) better at low f; time-base from a crystal/oven oscillator sets accuracy; ±1 count quantization error (dominant at low f → measure period instead).
- Time-interval/period: count a high-frequency clock between start/stop edges → resolution = clock period; averaging improves it.
- CRO methods: frequency from the time-base (T_period = div × time/div, f = 1/T); Lissajous figures (X = signal, Y = reference):
Lissajous frequency ratio $$ \frac{f_y}{f_x} = \frac{\text{tangencies on horizontal (top) edge}}{\text{tangencies on vertical (side) edge}} $$ellipse shape gives phase: \( \sin\phi = y_{intercept}/y_{max} \) (1:1 figure — straight line 0°/180°, circle 90°).
- Phase also by dual-trace time-shift (φ = 360°·Δt/T), XOR/zero-cross digital phase meter, or vector voltmeter; phase-sensitive detection (lock-in) for noisy signals.
- Heterodyne/wavemeter methods at microwave (Unit-7 cavity wavemeter).
UGC NET focus
f = N/gate-time and ±1-count error (use period at low f); Lissajous frequency ratio (count tangencies) and phase from the ellipse; phase φ = 360°Δt/T; reciprocal counter rationale.
§ 10.15Digital Multimeter (DMM)
- Core = ADC (Unit-5 §5.12) + signal conditioning + digital display; measures DCV/ACV/DCI/ACI/R (and often C, f, diode, continuity, temperature).
- Dual-slope (integrating) ADC is the classic DMM converter: ratiometric (R, C, clock cancel), excellent noise/mains rejection (integrates over a multiple of the 50/60 Hz period), high accuracy at modest speed — bench/handheld meters; high-speed DMMs use SAR/ΣΔ.
- Resolution: "3½ digits" = 0–1999 counts (≈ 11 bits), "4½" = 0–19999; accuracy spec = ±(% of reading + counts).
- Functions: ACV via precision rectifier (average-responding RMS-calibrated) or true-RMS converter (analog computer/thermal — needed for non-sinusoids); resistance by constant-current + voltage measure (4-wire/Kelvin for low R); high input impedance (10 MΩ) → low loading.
- DMM vs analog VOM: higher accuracy/resolution, no parallax, auto-range, high Z, but needs power and may alias fast transients.
UGC NET focus
Dual-slope ADC core (ratiometric + 50 Hz rejection); 3½/4½ digit count meaning; true-RMS vs average-responding; accuracy = ±(%reading + counts); 10 MΩ input low loading; 4-wire for low R.
§ 10.16CRO & Digital Storage Oscilloscope
Analog CRO
- Blocks: CRT (electron gun → focusing/accelerating anodes → vertical & horizontal deflection plates → phosphor screen) + vertical amplifier (Y, with delay line) + horizontal amplifier + time-base (sweep) generator (sawtooth) + trigger circuit + power supplies.
- Sweep & trigger: the sawtooth moves the spot left→right at a calibrated time/div; the trigger starts each sweep at the same point on the waveform → a stationary display. Modes: auto/normal/single; edge/level/slope.
- Reading: amplitude = (vertical div)×(volts/div); period = (horizontal div)×(time/div), f = 1/T; rise time t_r relates to bandwidth (\( t_r ≈ 0.35/BW \), Unit-3). Probes: ×1/×10 (×10 = 10 MΩ, less loading, must be compensated). Dual-trace via chop/alternate; X-Y mode for Lissajous (§10.14).
- Deflection sensitivity, bandwidth, and writing speed are key specs.
Digital Storage Oscilloscope (DSO)
- Signal → attenuator → sample-and-hold + ADC → acquisition memory → DSP → LCD; sampling per Nyquist (Unit-3 §3.17).
- Advantages: stores waveforms (capture single-shot/transients, pre-trigger view), measurement/maths/FFT, deep memory, automated parameters, connectivity; real-time vs equivalent-time sampling; sample rate ≥ 2.5–5× BW; watch aliasing from undersampling.
- Specs: bandwidth, max sample rate (GS/s), record length, vertical resolution (8-bit typical), number of channels; MSO adds digital channels.
UGC NET focus
CRT block diagram + electrostatic deflection; trigger gives a stable display; amplitude/period reading from div × setting; ×10 probe (10 MΩ, compensation); DSO = sample+ADC+memory → single-shot/pre-trigger/FFT; aliasing if undersampled.
§ 10.17Spectrum Analyzer
- Displays signal amplitude vs frequency (frequency domain) — the complement of the oscilloscope's amplitude-vs-time.
- Swept-tuned (superheterodyne) type: a swept LO mixes the input down to a fixed IF; a narrow resolution-bandwidth (RBW) filter + detector trace amplitude as the LO sweeps across the span. RBW sets frequency resolution and noise floor (narrow RBW → finer resolution, lower floor, slower sweep); video bandwidth (VBW) smooths the trace.
- FFT (real-time) analyzer: digitizes the signal and computes the DFT/FFT (Unit-3 §3.19) → captures transients, full span at once, fast; bandwidth limited by ADC/sample rate.
- Measures: spectral occupancy, harmonic & intermodulation distortion, spurious/noise, modulation (sidebands), phase noise, occupied/channel power, EMI/EMC; dynamic range and sensitivity are key specs.
- Contrast: oscilloscope = time domain, spectrum analyzer = frequency domain, network analyzer = ratio (S-parameters) vs frequency.
UGC NET focus
Amplitude vs frequency (frequency domain); swept-superheterodyne with RBW filter (resolution vs sweep-speed trade); FFT analyzer for transients; uses (harmonics, distortion, modulation, EMI); spectrum analyzer vs oscilloscope vs network analyzer.
§ 10.18Biomedical Instruments: ECG, EEG, BP
Common front-end needs: µV–mV signals riding on large common-mode (mains, electrode offset) → instrumentation amplifier (Unit-4 §4.14) with very high CMRR (>100 dB), high input impedance, isolation (patient safety — optical/transformer), driven-right-leg circuit, and band-limiting filters.
| Instrument | Signal & band | Essentials |
|---|---|---|
| ECG (heart) | ~0.5–4 mV, 0.05–100 Hz | Einthoven's triangle, 12 leads (I/II/III, aVR/aVL/aVF, V1–V6); P-QRS-T waves; Ag/AgCl electrodes + gel; 50 Hz notch; diagnoses arrhythmia/ischaemia |
| EEG (brain) | ~10–100 µV, 0.5–100 Hz | scalp electrodes (10–20 system); rhythms δ (<4), θ (4–8), α (8–13), β (13–30), γ Hz; highest-gain/lowest-noise front end; epilepsy/sleep studies |
| Blood pressure | systolic/diastolic mmHg | indirect: sphygmomanometer + cuff — Korotkoff sounds (auscultatory) or oscillometric (automatic, MAP at peak oscillation); direct: catheter + strain-gauge/piezoresistive transducer |
- Other biopotentials: EMG (muscle, mV, to ~1 kHz), EOG, ERG; transducers used: piezoresistive/capacitive pressure (BP, respiration), thermistor (temperature), pulse oximeter (two-wavelength photoplethysmography → SpO₂), photodiode/IR.
- Safety: leakage-current limits, isolation barriers, defibrillation protection — patient-safety standards dominate biomedical design.
UGC NET focus
ECG ~mV with Einthoven's triangle/12 leads and P-QRS-T; EEG ~µV with α/β/δ/θ bands; BP via Korotkoff/oscillometric; in-amp + high CMRR + isolation as the common front end; signal amplitude/bandwidth values.
§ 10.19MEMS & Sensors for IoT
MEMS (Micro-Electro-Mechanical Systems)
- Micron-scale mechanical structures (beams, membranes, combs, masses) integrated with electronics, fabricated by silicon micromachining — bulk (anisotropic KOH etch, Unit-2 §2.6) and surface (sacrificial-layer release) — plus LIGA/DRIE (Bosch).
- Transduction: capacitive (dominant), piezoresistive, piezoelectric, thermal, electrostatic actuation.
- Flagship devices: accelerometer (proof mass + comb capacitors — airbags, phones, IMUs), gyroscope (Coriolis), pressure sensor (piezoresistive diaphragm), microphone (MEMS mic), inkjet/optical (DMD micromirrors), RF-MEMS switches/resonators, microfluidics/lab-on-chip, gas sensors.
- Advantages: tiny, low power, low cost (batch fabrication), integrable, sensitive — the enabler of cheap ubiquitous sensing.
Sensors for IoT
- IoT (Unit-8 §8.18) needs low-power, low-cost, small, smart sensors. Smart sensor = sensing element + signal conditioning + ADC + µC + (often) wireless on one module → calibrated, self-diagnosing digital output.
- Common buses: I²C, SPI (short, on-board), 1-Wire, UART, analog; digital sensors output engineering units directly.
- Sensor zoo: temperature/humidity (DHT/SHT, BME280), MEMS accelerometer/gyro/magnetometer (IMU), pressure/altitude, ambient light, PIR motion, gas/air-quality (MQ, CO₂), proximity (capacitive/Hall/ToF), GPS, microphone, biosensors/wearables, soil-moisture (agriculture).
- Design drivers: ultra-low-power (duty-cycling, sleep, energy harvesting), edge pre-processing, calibration/drift, wireless interfacing (BLE/Zigbee/LoRa), and security (Unit-8). Smart sensors offload the host and enable plug-and-play IoT nodes.
UGC NET focus
MEMS = silicon micromachining (bulk vs surface), capacitive accelerometer as the flagship; MEMS merits (small/low-power/cheap/batch); smart sensor = sensor + conditioning + ADC + µC + comms; I²C/SPI digital interfaces; low-power as the IoT-sensor design driver.
§ 10.20Unit-10 Formula Sheet
| Topic | Result | Notes |
|---|---|---|
| Gauge factor | GF = (ΔR/R)/ε | metal ≈ 2, semiconductor ≈ 100–200 |
| RTD | R_T = R₀(1 + αT) | Pt100, α ≈ 0.00385/°C, positive TC |
| Thermistor | R = R₀ e^{β(1/T − 1/T₀)} | NTC, nonlinear |
| LVDT | |V_o| ∝ displacement; phase = direction | null at centre; 2 secondaries opposing |
| Capacitive | C = εA/d | d (nonlinear), A (linear), ε_r (level/humidity) |
| Piezoelectric | Q = dF; V = Q/C | dynamic only; charge amplifier |
| Thermocouple | V = α_AB(T_hot − T_cold) | cold-junction compensation; type K general |
| Hall voltage | V_H = BI/nqt; R_H = 1/nq | measures B or I (contactless) |
| Responsivity | R = ηλ/1.24 A/W | photodiode (§8.16) |
| Strain bridge | V_o = ¼ GF·ε·V_ex (quarter) | ×2/×4 half/full |
| Orifice flow | Q = C_d A√(2Δp/ρ) ∝ √Δp | venturi/nozzle similar |
| pH electrode | E = E₀ − 0.059·pH (25 °C) | ~59 mV/pH; high-Z amp |
| Wheatstone | R_x = R₃R₂/R₁ | medium R |
| Maxwell | L_x = R₂R₃C₁ | low-Q L, freq-independent |
| AC bridge balance | Z₁Z₄ = Z₂Z₃ | two conditions; Hay = high-Q |
| Potentiometer | E_x = (l_x/l_s)E_s | null → no loading; Weston std cell |
| Ammeter shunt | R_sh = I_m R_m/(I − I_m) | voltmeter R_s = V/I_m − R_m |
| Voltmeter sensitivity | 1/I_fsd Ω/V | higher → less loading |
| Wattmeter | P ∝ VI cosφ | 2-W method: P = W₁+W₂ |
| Frequency counter | f = N/T_gate | ±1 count error |
| Lissajous | f_y/f_x = h-tangencies/v-tangencies | phase from ellipse |
| Phase by time-shift | φ = 360°·Δt/T | dual-trace CRO |
| CRO rise time | t_r ≈ 0.35/BW | ×10 probe = 10 MΩ |
| DMM | dual-slope ADC; 3½ digit = 0–1999 | ratiometric, 50 Hz rejection |
| EEG bands | δ<4, θ 4–8, α 8–13, β 13–30 Hz | ECG ~mV, EEG ~µV |
§ 10.21Quick Revision Notes — Unit 10 in 25 Points
Rapid-fire recap (last-day revision)
- Active (self-generating): thermocouple, piezoelectric, photovoltaic, Hall, tachogenerator. Passive (need excitation): strain gauge, LVDT, RTD, capacitive, potentiometer.
- Accuracy = closeness to true; precision = repeatability; sensitivity = Δo/Δi; resolution = smallest detectable; loading effect = meter disturbs circuit; systematic vs random error.
- Strain gauge GF = (ΔR/R)/ε; metal ≈ 2, semiconductor ≈ 100–200; read by Wheatstone bridge with dummy-gauge compensation.
- RTD: positive TC, linear, Pt100, accurate. Thermistor: NTC, exponential, very sensitive, narrow range.
- LVDT: two secondaries in series opposition, AC excitation, null at centre, |V_o| ∝ displacement, phase gives direction; frictionless, high resolution; needs phase-sensitive detection.
- Capacitive C = εA/d: vary d (displacement, nonlinear), A (linear), or ε_r (level/humidity); high sensitivity but stray-capacitance/guarding issues.
- Piezoelectric: active, Q = dF, V = Q/C; dynamic only — no static measurement; charge amplifier; accelerometers/ultrasonics; reversible (actuators).
- Thermocouple (Seebeck): V ∝ ΔT, cold-junction compensation essential, type K general-purpose, mV output needs amplification; Peltier = cooling; thermopile = series stack.
- Hall: V_H = BI/nqt, R_H = 1/nq; senses B (proximity) or I (contactless current); semiconductor for large V_H; works at DC; BLDC commutation.
- Photoelectric: LDR (photoconductive, R↓, passive, slow) vs solar cell (photovoltaic, active); photodiode fast; phototransistor adds gain; hν ≥ E_g.
- Sensor↔quantity: LVDT-displacement, tachogenerator-velocity, piezo/MEMS-acceleration, load cell-force, strain bridge-strain/torque; force/pressure/torque all reduce to strain.
- Seismic-mass accelerometer: below resonance mass-displacement ∝ acceleration; ζ ≈ 0.7 flattens response.
- Pressure: Bourdon/diaphragm → displacement readout; flow: orifice/venturi Q ∝ √Δp, electromagnetic (Faraday, conductive, no obstruction); humidity: capacitive; pH: glass electrode 59 mV/pH + high-Z amp.
- Bridges (null balance): Wheatstone R_x = R₃R₂/R₁; Kelvin for low R; Maxwell (low-Q L, L_x = R₂R₃C₁) vs Hay (high-Q L); Schering for C/tan δ; Wien for frequency; AC bridge Z₁Z₄ = Z₂Z₃ (two conditions).
- Potentiometer: null method draws no current → true EMF, no loading; Weston standard cell; AC type = polar/coordinate (magnitude + phase).
- PMMC: DC, average-reading, linear scale; shunt R_sh = I_mR_m/(I−I_m), multiplier R_s = V/I_m − R_m; sensitivity 1/I_fsd Ω/V (higher = less loading).
- Moving-iron/dynamometer = RMS, AC+DC; rectifier-PMMC = RMS-calibrated (form-factor error on non-sinusoids); thermocouple meter = true RMS at RF.
- Wattmeter (dynamometer) ∝ VIcosφ; 3-phase two-wattmeter P = W₁+W₂, tanφ = √3(W₁−W₂)/(W₁+W₂); energy meter = induction disc, constant rev/kWh.
- Frequency counter f = N/gate, ±1 count error (use period at low f); Lissajous ratio = h-tangencies/v-tangencies, phase from ellipse; φ = 360°Δt/T.
- DMM = dual-slope ADC (ratiometric, 50 Hz rejection); 3½ digit = 0–1999; true-RMS vs average-responding; 10 MΩ input; 4-wire for low R.
- CRO: CRT + electrostatic deflection + sawtooth time-base + trigger (stable display); amplitude = div×V/div, T = div×time/div; ×10 probe (10 MΩ, compensate); t_r ≈ 0.35/BW.
- DSO = S/H + ADC + memory → single-shot/transient capture, pre-trigger, FFT/maths; sample ≥ 2.5–5× BW; beware aliasing.
- Spectrum analyzer = amplitude vs frequency; swept-superheterodyne (RBW filter sets resolution vs sweep speed) or FFT (transients); oscilloscope = time domain, network analyzer = S-parameters.
- Biomedical: ECG ~mV/Einthoven's triangle/12 leads/P-QRS-T; EEG ~µV/α-β-δ-θ bands; BP via Korotkoff or oscillometric; common front end = in-amp + high CMRR + isolation.
- MEMS = silicon micromachining (bulk vs surface); capacitive accelerometer flagship; small/low-power/cheap/batch. Smart sensor = sensor + conditioning + ADC + µC + comms over I²C/SPI; low-power is the IoT-sensor driver.