Analog & Digital Communication (EX-604 (C)) - Unit 5 Short Notes

UNIT 5: ELECTRONIC INSTRUMENTATION AND MEASUREMENT SYSTEMS

I. CATHODE RAY OSCILLOSCOPES (CROs) AND DISPLAY DEVICES

A. Fundamentals of CRT

• Electrostatic deflection: Electron beam deflected by electric field between parallel plates.

• Deflection sensitivity: $$\displaystyle S = \frac{D}{V_d} $$ (cm/V), where $D$ = deflection on screen, $$\displaystyle V_d $$ = deflecting voltage.

• Deflection factor: $$\displaystyle F = 1/S $$ (V/cm).

• Post-deflection acceleration: High anode voltage after deflection plates increases beam velocity, reducing spot size and increasing brightness.

• Graticules:

  • Internal: Etched on inside of CRT face.

  • External: Transparent front panel with grid.

  • Types: cross-hatch, square grid, etc., for measurements.

B. Types and Configurations of Oscilloscopes

• Dual-beam CRO:

  • Two separate electron guns, deflection systems.

  • Simultaneous display of two signals.

  • Higher cost, alignment complexity.

• Dual-trace CRO:

  • Single gun, electronic switching (chopped for low freq, alternate for high freq).

  • Time-division multiplexing of signals.

• Time base circuits:

  • Sweep generator (ramp voltage), synchronization (triggering), hold-off.

  • Synchronization ensures stable waveform display; improper sync causes jitter or drift.

• Sampling oscilloscopes:

  • Stroboscopic sampling: sample input at different times, reconstruct waveform.

  • Multi-input sampling: multiple channels sampled sequentially.

  • Applications: high-frequency signals beyond bandwidth.

  • Precautions: signal conditioning, avoid aliasing, proper sampling rate.

• Wobbly scope:

  • Frequency-modulated sweep for low-frequency signals.

  • Displays stationary pattern for slow sweeps.

C. Waveform Analysis with CRO

• Lissajous patterns:

  • Formed by applying signals to X and Y plates.

  • Frequency ratio: $$\displaystyle \frac{f_y}{f_x} = \frac{N_x}{N_y} $$, where $$\displaystyle N_x $$ = horizontal tangencies, $$\displaystyle N_y $$ = vertical tangencies.

• Applications:

  • Voltage: compare with known reference.

  • Frequency: from Lissajous tangencies.

  • Phase: ellipse axes ratio.

  • Modulation: AM/FM demodulation by pattern analysis.

[!TIP] For Lissajous, always count tangencies carefully: $$\displaystyle f_y/f_x = N_x/N_y $$.

II. AC BRIDGE CIRCUITS FOR IMPEDANCE MEASUREMENT

A. General Bridge Principles

• Balance condition: $$\displaystyle Z_1 Z_3 = Z_2 Z_4 $$ (product of opposite arms).

• Measurement methodology: vary known impedance until null (minimum detector current).

• Sources of errors:

  • Stray capacitance/inductance.

  • Frequency instability.

  • Detector sensitivity.

• Error reduction techniques:

  • Shielding and guarding.

  • Wagner earth (for capacitance bridges).

• Q-meter:

  • Resonant circuit with known $L$ and $C$.

  • Measures Q-factor of unknown coil at high frequencies.

  • Circuit: coil under test in series with standard capacitor, driven by RF source.

B. Specific AC Bridges

1. Wien Bridge

   • Circuit: series-parallel RC network.

   • Balance equations:

$$ \frac{R_1}{R_2} = \frac{R_3}{R_4}, \quad \frac{C_2}{C_1} = \frac{R_4}{R_3} $$

• Frequency determination:

  \boxed{f = \frac{1}{2\pi\sqrt{R_1 R_2 C_1 C_2}}}

• Applications: frequency standard, RC oscillator.

2. Maxwell Bridge

   • Circuit: unknown $$\displaystyle L_x $$ with series $$\displaystyle R_x $$ in one arm; standard $$\displaystyle C_1 $$ adjacent; resistors $$\displaystyle R_2, R_3 $$ in other arms.

   • Balance equations:

     \boxed{L_x = R_2 R_3 C_1, \quad R_x = \frac{R_2 R_3}{R_1}}

   • Merits: direct reading of $L$ and $R$.

   • Demerits: requires precise $$\displaystyle C_1 $$, limited Q range (1 to 10).

   • Applicable for coils with storage factor $Q \in [1, 10]$.

3. Schering Bridge

   • Circuit: unknown $$\displaystyle C_x $$ with loss tangent $\tan\delta$ in one arm; standard $$\displaystyle C_3 $$ adjacent; resistors $$\displaystyle R_4, R_2 $$ in other arms.

   • Balance equations:

     \boxed{C_x = C_3 \frac{R_4}{R_2}, \quad \tan\delta = \omega C_4 R_4}

   • High-voltage Schering Bridge:

     • Separate high-voltage supply.

     • Guard rings to reduce stray capacitance.

   • Applications: capacitor testing, insulation loss measurement.

4. De Sauty's Bridge

   • Simple capacitance comparison: two known capacitors, two resistors.

   • Assumes lossless capacitors; not suitable for dielectric loss measurement.

   • Compared to Schering: Schering measures $\tan\delta$, De Sauty does not.

5. Anderson Bridge

   • Modification of Maxwell bridge: adds capacitor in series with resistor.

   • Improves accuracy for high-Q coils.

   • More complex circuit topology.

C. Bridge Calculations and Problem-Solving

• Solve balance equations for unknown $R, L, C, \tan\delta$.

• Numerical problems: given bridge constants, compute equivalent impedance parameters.

[!TIP] Maxwell Bridge: $$\displaystyle L_x = R_2 R_3 C_1 $$; Schering: $$\displaystyle C_x = C_3 (R_4/R_2) $$, $$\displaystyle \tan\delta = \omega C_4 R_4 $$.

III. TRANSDUCERS AND SENSORS

A. Resistive Transducers

• Strain Gauges

  • Principle: $$\displaystyle \Delta R / R = GF \cdot \epsilon $$, where $\epsilon$ = strain.

  • Gauge factor: $$\displaystyle GF = \frac{\Delta R / R}{\epsilon} = 1 + 2\nu + \frac{\Delta \rho / \rho}{\epsilon} $$.

    • For metals: $GF \approx 2$ (due to Poisson effect).

    • For semiconductors: $GF \approx 50-200$ (piezoresistive effect).

  • Metal vs semiconductor:

    | Property | Metal Strain Gauge | Semiconductor Strain Gauge | |-------------------|--------------------|---------------------------| | Gauge Factor | ~2 | 50-200 | | Temp Sensitivity | Moderate | Very High |

  • Temperature compensation:

    • Dummy gauge in adjacent bridge arm.

    • Three-wire or four-wire connection.

  • Instrumentation amplifier adaptation:

    • Bridge circuit with differential amp (high CMRR).

    • DiagramCANVAS: Strain gauge in Wheatstone bridge with instrumentation amplifier

• RTDs and Thermistors

  • RTDs (Resistance Temperature Detectors):

    • Materials: Pt, Ni, Cu.

    • Linear resistance increase with temperature.

    • Range: -200°C to 850°C; accurate, stable.

  • Thermistors:

    • NTC: resistance decreases with temperature.

    • PTC: resistance increases with temperature.

    • Exponential curve; range: -50°C to 150°C; high sensitivity, nonlinear.

  • Measurement: bridge circuit or constant current source.

B. Inductive and Capacitive Transducers

• LVDT (Linear Variable Differential Transformer)

  • Construction: primary coil, two secondary coils (series opposing), movable ferromagnetic core.

  • Working: AC excitation on primary; core displacement induces voltage in secondaries; output $$\displaystyle V_{out} = V_{s1} - V_{s2} \propto $$ displacement.

  • Characteristics: linear region around null position; output phase indicates direction.

  • Advantages: frictionless, infinite resolution, robust, long life.

  • Limitations: needs AC excitation, sensitive to stray magnetic fields, limited bandwidth.

  • Applications: displacement, position, pressure (with diaphragm), force.

  • DiagramCANVAS: LVDT with primary coil, two secondary coils, movable core

C. Other Transducer Principles

• Hall Effect Transducers

  • Hall voltage: $$\displaystyle V_H = \frac{I B}{n e t} \cdot k $$, where $k$ = geometrical correction factor (accounts for non-uniform current distribution).

  • Applications: magnetic field measurement, current sensing, position detection.

• Piezoelectric Transducers

  • Modes of operation:

    • Charge generator: static force generates charge $$\displaystyle Q = d F $$.

    • Voltage generator: charge across internal capacitance $$\displaystyle V = Q/C $$.

    • Stiffness effect: force changes dimensions.

  • Applications: force, pressure, acceleration sensors; ultrasonic transducers.

  • Calculations: given strain, compute force, charge, voltage using material constants.

• Photo-transducers

  • Photovoltaic: solar cell; generates voltage/current when illuminated; no bias needed.

  • Photoconductive: LDR; resistance decreases with light; requires bias.

  • Photodiode: reverse-biased PN junction; current proportional to light; low dark current.

  • Comparison: photodiodes most suitable for low-intensity light due to low noise and high sensitivity.

• Thermocouples

  • Seebeck effect: two dissimilar metals joined, temperature difference generates voltage.

  • Voltage: $$\displaystyle V = \alpha (T_1 - T_2) $$, where $\alpha$ = Seebeck coefficient.

  • Materials: Type K (Chromel-Alumel), Type J (Iron-Constantan), etc.

  • Cold-junction compensation: reference junction at known temperature (ice bath or electronic).

D. Transducer Interfacing and Systems

• Digital multiplexing: time-division multiplexing (TDM) of sensor signals; improves wiring efficiency, reduces cost in industrial systems.

• Primary vs secondary transducers:

  • Primary: senses physical quantity directly (e.g., thermocouple).

  • Secondary: converts primary output to electrical (e.g., strain gauge converts strain to resistance change).

• Transducer input characteristics: impedance, loading effect, frequency response.

[!TIP] For strain gauges, metal GF ~2, semiconductor GF ~50-200. Hall effect geometrical factor corrects for non-ideal geometry.

IV. SIGNAL GENERATORS AND SPECTRUM ANALYSIS

A. Function Generators

• Block diagram: waveform generator (sine, square, triangle), VCO, attenuator, output amplifier.

• Sine wave generation:

  • RC oscillators (Wein bridge).

  • Function synthesis: integrate triangle wave to approximate sine.

• Frequency control by external voltage (VCO): voltage controls capacitor/inductor in oscillator tank circuit.

B. Specialized Oscillators

• Beat Frequency Oscillator (BFO):

  • Two close-frequency oscillators; beat note in audio range.

  • Applications: radio direction finding, audio testing.

• Wein Bridge Oscillator:

  • Positive feedback via RC network.

  • Frequency: \boxed{f = \frac{1}{2\pi RC}}

  • Stable, low distortion.

C. Sweep and Wave Analysis

• Sweep Generators:

  • Fixed-frequency: single tone.

  • Sweep-frequency: frequency varies linearly with time; used for frequency response testing.

• Wave Analyzers:

  • Frequency selective: tuned filters (LC/RC); narrow bandwidth, limited sensitivity.

  • Heterodyne: input mixed with local oscillator, IF amplifier, detector; high sensitivity and selectivity due to narrow IF bandwidth.

• Spectrum Analyzers:

  • Block diagram: swept local oscillator, IF filter, detector, display.

  • Importance: displays signal in frequency domain.

  • Applications: harmonic analysis, interference detection, signal characterization.

[!TIP] Heterodyne wave analyzer uses frequency conversion for superior selectivity vs fixed filters.

V. DIGITAL MEASUREMENT INSTRUMENTS

A. Digital Voltmeters (DVMs)

• Ramp Type:

  • Linear ramp generator, comparator, counter.

  • Measures time to charge capacitor to input voltage.

  • Simple but sensitive to noise.

• Dual-Slope Integrating Type:

  • Integrate input for fixed time $$\displaystyle T_1 $$, then integrate reference voltage $$\displaystyle V_{ref} $$ until zero.

  • Count during $$\displaystyle T_2 $$ proportional to input.

  • Advantages: excellent noise rejection (averages over $$\displaystyle T_1 $$), high accuracy.

  • Slower than successive approximation.

• Successive Approximation Type:

  • SAR ADC: successive approximation register controls DAC.

  • Fast, moderate accuracy.

  • Comparison: dual-slope better noise rejection, SAR faster.

• Specifications:

  • Resolution: $$\displaystyle 1/2^n $$ for n-digit display.

  • 3.5 digit: maximum 1999 counts.

    • Resolution on range $$\displaystyle V_{range} $$: $$\displaystyle V_{range}/2000 $$.

    • Example: 10V range → resolution = 5 mV.

  • Display examples:

    • 11.52V on 10V range: overrange → shows "1" or "OL".

    • 0.5234V on 1V range: resolution 0.5 mV → displays 0.523V.

    • 0.5234V on 10V range: resolution 5 mV → displays 0.525V (rounded to nearest 5 mV).

B. Other Digital Instruments

• Digital Frequency Meters:

  • Block diagram: input conditioning, gate circuit, counter, timebase, display.

  • Gate time (e.g., 1 s) controls counting period.

  • Accuracy depends on timebase stability.

• Digital Tachometers:

  • Optical or magnetic pickup generates pulses per revolution.

  • Count pulses over time to compute RPM.

[!TIP] Dual-slope DVM rejects power-line noise because integration period $$\displaystyle T_1 $$ is integer multiple of AC cycle.

VI. DATA ACQUISITION, INTERFACING, AND CONTROL

A. Data Systems

• Data Logger: stores data locally with timestamp; limited real-time control.

• Data Acquisition System (DAS): real-time acquisition, processing, control; often with computer interface.

B. Communication Interfaces

• RS232C:

  • Serial, point-to-point.

  • Voltage levels ±3 to ±15 V.

  • Speed up to 115.2 kbps; distance up to 15 m.

• IEEE-488 (GPIB):

  • Parallel 8-bit bus.

  • Up to 1 Mbps; up to 15 devices (talker/listener).

  • Used in laboratory instrumentation.

• Comparison with modern interfaces:

  • USB: plug-and-play, up to 480 Mbps (USB 2.0), short distance.

  • Ethernet: networked, long distance, TCP/IP; used in distributed systems.

  • GPIB/RS232C: slower, but robust for lab; USB/Ethernet: higher speed, flexible.

[!TIP] GPIB allows multiple instruments on one bus; RS232C is point-to-point only.

VII. RECORDERS AND PLOTTERS

A. X-Y Recorders

• Analog X-Y Recorder:

  • Two servo-motors move pen on X and Y axes.

  • Input signals control positions via amplifiers.

  • Suitable for low-frequency plots; limited by pen speed and friction.

• Digital X-Y Recorder:

  • ADC samples inputs, step motors or digital plotter.

  • Higher accuracy, no wear, data storage.

• Applications: plotting characteristics (e.g., transfer function), control system response, process monitoring.

[!TIP] Analog recorders have mechanical inertia; digital ones offer precision and programmability.

VIII. DISPLAY TECHNOLOGIES

A. Light-Emitting and Liquid Crystal Displays

• LEDs:

  • PN junction emits light when forward biased.

  • Low power, bright, wide viewing angle.

  • Used in digital readouts, indicators.

• LCDs:

  • Liquid crystal between polarizers.

  • Twisted nematic (TN): field untwists crystal, blocks light.

  • Dynamic scattering: field scatters light.

  • Advantages: very low power, slim, no backlight for reflective types.

  • Comparison: LCDs consume less power but slower response; LEDs brighter, higher power.

B. Specialized Displays

• Electrophoretic image display (e-ink):

  • Charged particles in fluid move under electric field.

  • Bistable: image persists without power.

  • Used in e-readers.

• Liquid vapor display:

  • Heated electrodes vaporize liquid to create opaque spots.

  • High power consumption, temporary image.

  • Used in some calculators.

• Comparison:

  | Feature | Electrophoretic (e-ink) | Liquid Vapor | |-----------------------|-------------------------|--------------------| | Power consumption | Very low (bistable) | High | | Image persistence | Long | Short | | Applications | E-readers, signage | Calculators |

IX. SPECIAL TOPICS AND APPLICATIONS

A. Measurement Quality Metrics

• Total Harmonic Distortion (THD):

  \boxed{\text{THD} = \frac{\sqrt{V_2^2 + V_3^2 + \cdots + V_n^2}}{V_1} \times 100%}

  • $$\displaystyle V_1 $$: fundamental amplitude, $$\displaystyle V_2, V_3,... $$: harmonic amplitudes.

  • Significance: measures signal purity in audio and power systems.

B. Safety and Grounding

• Wagener's earthing device:

  • Safety device to prevent electric shock.

  • Provides low-resistance path to earth for instrument chassis.

C. Integrated Applications

• CRO applications:

  • Voltage measurement (with probe).

  • Frequency (Lissajous or time base).

  • Phase shift (X-Y mode).

  • Modulation analysis (AM/FM demodulation).

• X-Y recorders in industry:

  • Plotting process variables (e.g., temperature vs pressure).

  • Control system calibration, characteristic plotting.

[!TIP] THD is critical for assessing distortion in audio amplifiers and power systems.