UNIT 2: ANALOG & DIGITAL COMMUNICATION (EX-604(C))

Exam-Focused Short Notes | Based on RGPV Past Papers (2022-2025)

1.0 CATHODE RAY OSCILLOSCOPE (CRO) & TIME-BASE SYSTEMS

1.1 CRT Fundamentals & Electrostatic Deflection

• Construction of CRT:

  • Electron gun: Cathode (heated emitter), control grid (intensity control), focusing anode (electrostatic lens), accelerating anode (high voltage).

  • Deflection system: Two pairs of electrostatic plates (vertical/horizontal) inside vacuum envelope.

  • Fluorescent screen: Converts electron energy to visible light (phosphor coating).

• Electrostatic Deflection Principle:

  • Electron beam deflection angle $$\displaystyle \theta \propto \frac{V_d}{V_a} $$, where $$\displaystyle V_d $$ = deflecting voltage, $$\displaystyle V_a $$ = anode voltage.

  • Deflection Sensitivity ($$\displaystyle S_v $$): Vertical deflection per unit voltage (cm/V).

$$S_v = \frac{L_l}{2V_a} \cdot \frac{l}{d}$$

where $$\displaystyle L_l $$ = length from plate center to screen, $l$ = plate length, $d$ = plate spacing.

• Deflection Factor ($G$): Reciprocal of sensitivity (V/cm). $$\displaystyle G = 1/S_v $$.

• Post-Deflection Acceleration (PDA):

  • Role: Additional high-voltage electrode after deflection plates.

  • Significance: Increases beam velocity after deflection → reduces spot size (less magnification of deflection errors), improves brightness, and minimizes deflection distortion.

  • Effect: Higher final anode voltage $$\displaystyle V_a $$ → lower sensitivity $$\displaystyle S_v $$ but smaller spot.

[!TIP]

Exam Focus: Derive/define $$\displaystyle S_v $$ and $G$. PDA is asked for its effect on velocity and spot size (June 2025).

1.2 General Purpose CRO Block Diagram & Applications

• Block Diagram:

  
  [Input Signal] → Vertical Amplifier → [Vertical Deflection Plates]
  
                     ↓
  
  [Time Base Generator] → Horizontal Amplifier → [Horizontal Deflection Plates]
  
                     ↓
  
  [Trigger Circuit] (synchronizes sweep to signal)
  
                     ↓
  
  [Power Supply] → CRT & all circuits
  
  

• Four Key Applications:

  1. Voltage/Time Measurement: Amplitude, period, rise/fall times.

  2. Frequency Measurement: $$\displaystyle f = 1/T $$ from time base.

  3. Phase Difference: Dual-trace/beam comparison.

  4. Lissajous Patterns: Frequency ratio & phase from stationary figures.

1.3 Dual-Beam vs. Dual-Trace Oscilloscope

[!TIP]

June 2025 (7m): Contrast in terms of construction, bandwidth, timing accuracy. Dual-beam = two guns; dual-trace = electronic switch.

1.4 Time Base Circuits & Sweep Synchronization

• Time Base Generator: Generates sawtooth waveform.

  • Circuit: Typically an integrator (RC) with a reset (transistor/valve) triggered by a comparator.

  • Sweep: Linear rising ramp (time base) → sudden flyback.

• Sweep Synchronization:

  • Internal Trigger: Derived from vertical signal.

  • External Trigger: From separate source.

  • Effect on Display: Proper sync → stable, non-jittery waveform. No sync → rolling/shifting pattern. Sync ensures sweep starts at same phase of input → accurate time measurement.

1.5 Specialized Oscilloscopes

• Sampling Oscilloscope (Multi-input):

  • Principle: Sample input signal at high rate, reconstruct waveform (Nyquist). Used for very high frequencies (>1 GHz).

  • Precautions: Must sample above Nyquist rate; aliasing if undersampled.

• Wobbly Scope (Wobbler):

  • Construction: Sweep generator frequency modulated by audio signal.

  • Working: Creates "wobbly" Lissajous on screen.

  • Primary Application: Component testing in AF circuits (e.g., checking capacitor/inductor reactance by pattern shape).

• Graticules:

  • Internal: Etched on CRT inside (permanent, parallax-free).

  • External: Removable plastic sheet (adjustable, but parallax).

  • Grid patterns: 1×1 cm squares common for measurements.

2.0 AC BRIDGES FOR IMPEDANCE MEASUREMENT

2.1 Bridge Fundamentals & Errors

• General Balance Condition: $$\displaystyle Z_1 Z_4 = Z_2 Z_3 $$ (complex product). For AC: magnitude & phase balance.

• Sources of Errors:

  • Stray capacitance/inductance, contact resistance, frequency/voltage dependence, lead inductance.

• Error Reduction:

  • Shielding (guard rings), Kelvin connections (4-terminal), proper layout, operate at proper freq/voltage.

2.2 Specific Bridge Circuits & Applications

Wien Bridge:

• Circuit: Series $R$-$C$ in one arm, parallel $R$-$C$ in opposite arm, ratio arms $R$.

• Balance Equations:

$$f = \frac{1}{2\pi R C} \quad \text{(when } R_1/R_2 = C_2/C_1\text{)}$$

Used in Wien bridge oscillator for frequency determination.

• Numerical (Dec 2024): Given $$\displaystyle R_3=R_4=8.8\,\text{k}\Omega $$, $$\displaystyle R_1=10\,\text{k}\Omega $$, $$\displaystyle R_2=4.7\,\text{k}\Omega $$, $$\displaystyle f=13\,\text{kHz} $$ → $$\displaystyle C_1 = \frac{1}{2\pi f R_1} \cdot \frac{R_2}{R_3} = \boxed{1.38\,\text{nF}} $$, $$\displaystyle C_2 = C_1 \cdot \frac{R_1}{R_2} = \boxed{2.93\,\text{nF}} $$.

Maxwell's Inductance-Capacitance Bridge:

• Circuit: $$\displaystyle L_x $$-$$\displaystyle R_x $$ in one arm, $$\displaystyle C_1 $$ (standard) in adjacent arm, ratio arms $$\displaystyle R_1 $$, $$\displaystyle R_2 $$, $$\displaystyle R_3 $$ (non-inductive).

• Balance Equations:

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

Applicability: Coils with Q-factor (storage factor) between 1 and 10.

Merits: Independent $$\displaystyle R_x $$ and $$\displaystyle L_x $$ balance controls.

Demerits: Requires precise $$\displaystyle C_1 $$; $$\displaystyle R_3 $$ must be non-inductive.

• Numerical (June 2025): Given $$\displaystyle C_1=0.01\,\mu\text{F} $$, $$\displaystyle R_1=470\,\text{k}\Omega $$, $$\displaystyle R_2=5.1\,\text{k}\Omega $$, $$\displaystyle R_3=100\,\text{k}\Omega $$ →

  $$\displaystyle L_x = R_2 R_3 C_1 = \boxed{5.1\,\text{H}} $$, $$\displaystyle R_x = \frac{R_2 R_3}{R_1} = \boxed{1.085\,\text{k}\Omega} $$.

Schering Bridge:

• Circuit: Measures capacitance ($$\displaystyle C_x $$) and dissipation factor (tanδ).

  Arms: $$\displaystyle C_x $$ (with $$\displaystyle R_x $$ parallel for loss), $$\displaystyle C_2 $$ (standard), $$\displaystyle R_1 $$, $$\displaystyle R_2 $$ (ratio).

• Balance Equations:

$$C_x = C_2 \frac{R_1}{R_2}, \quad \tan\delta = \omega C_x R_x = \frac{1}{\omega C_2 R_1}$$

High Voltage Schering Bridge: Uses guarded shielding, high voltage supply for insulation testing.

• Numerical (May 2024): Given $$\displaystyle R_1=100\,\Omega $$, $$\displaystyle R_2=300\,\Omega\parallel 0.5\,\mu\text{F} $$, $$\displaystyle C_2=100\,\text{pF} $$, $$\displaystyle f=50\,\text{Hz} $$ →

  $$\displaystyle C_x = C_2 \frac{R_1}{R_2} = \boxed{33.3\,\text{pF}} $$, $$\displaystyle \tan\delta = \omega C_x R_x = \boxed{0.0105} $$ (Power factor = 0.0105).

De Sauty's Bridge:

• Simple $C$-$C$ bridge (no $$\displaystyle R_x $$). Suitable only for low-loss capacitors; cannot measure dielectric loss (unlike Schering).

Anderson Loop:

• Motivation: Measure low-Q coils (Q<1). Uses additional standard capacitor and resistors to avoid standard inductor need.

2.3 Q-Meter

• Principle: Series resonance ($$\displaystyle X_L = X_C $$) in a coil under test.

• Circuit: Known $C$, variable freq → resonance when $$\displaystyle f = 1/(2\pi\sqrt{LC}) $$.

• Q-factor: $$\displaystyle Q = \frac{\omega L}{R} = \frac{V_C}{V_R} $$ (voltage across $C$ vs. $R$).

• Applications: Measure $Q$, $L$, $C$ of coils.

3.0 TRANSDUCERS

3.1 Transducer Fundamentals

• Definition: Device converting physical quantity → electrical signal.

• Primary vs. Secondary:

  • Primary: Directly senses input (e.g., thermocouple senses temperature → voltage).

  • Secondary: Converts primary output (e.g., LVDT converts displacement → voltage).

• Input Characteristics: Static (linearity, sensitivity), dynamic (response time, frequency), loading effect, transfer function.

3.2 Resistive Transducers

• Strain Gauge:

  • Principle: Piezoresistive effect → $$\displaystyle \Delta R/R = GF \cdot \varepsilon $$.

  • Gauge Factor (GF):

$$GF = \frac{\Delta R / R}{\varepsilon} = 1 + 2\nu + \frac{\Delta \rho / \rho}{\varepsilon}$$

For metals: $GF \approx 1+2\nu$ (2~5). For semiconductors: $GF \approx 100+$ (high, temperature sensitive).  

• Numerical (May 2024): $$\displaystyle GF=2 $$, $$\displaystyle \varepsilon=1\times10^{-6} $$, $$\displaystyle R=130\,\Omega $$ → $$\displaystyle \%\Delta R = GF \cdot \varepsilon \times 100 = \boxed{0.0002\%} $$.

• Instrumentation Amp: Used in Wheatstone bridge to amplify small $\Delta R$.

• RTD: Pt (200–800°C), Ni (–60–300°C), Cu (–50–150°C). Positive TCR, linear.

• Thermistor: NTC (most common) → high sensitivity, nonlinear. PTC → overcurrent protection.

3.3 Inductive Transducers

• LVDT:

  • Construction: Primary winding, two secondary windings (series opposing), movable ferromagnetic core.

  • Working: AC excitation on primary. Core displacement → imbalance in secondary voltages → output $$\displaystyle V_o \propto $$ displacement $x$, phase indicates direction.

  • Characteristics: Linear ± few mm around null; infinite resolution (analog).

  • Advantages: No contact, high reliability, frictionless.

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

3.4 Piezoelectric Transducers

• Piezoelectric Effect: Direct (stress → charge $$\displaystyle Q = d F $$), Converse (voltage → strain).

• Modes: Thickness expansion (d33), thickness shear (d15), face shear.

• Equivalent Circuit: Voltage source $$\displaystyle V = d_{33} F / C $$ in series with $C$ (crystal capacitance).

• Numerical (May 2024): Quartz $$\displaystyle d_{33}=21\,\text{C/N} $$, size $2\times2\times1\,\text{mm}$, strain $$\displaystyle \varepsilon=10^{-6} $$.

  Stress $$\displaystyle \sigma = Y \varepsilon = 86\times10^{10} \times 10^{-6} = 86\times10^4\,\text{N/m}^2 $$.

  Force $$\displaystyle F = \sigma \cdot A = 86\times10^4 \times (2\times10^{-3})^2 = \boxed{344\,\text{N}} $$.

  Charge $$\displaystyle Q = d_{33} F = 21 \times 344 = \boxed{7224\,\text{pC}} $$.

  $$\displaystyle C = \varepsilon_r \varepsilon_0 A / t = 40.6\times8.85\times10^{-12} \times 4\times10^{-6} / 10^{-3} = \boxed{1.44\,\text{pF}} $$.

  Voltage $$\displaystyle V = Q/C = \boxed{5.02\,\text{V}} $$.

• Applications: Force/pressure/acceleration sensors, ultrasonic generators.

3.5 Magnetic & Hall Effect Transducers

• Hall Effect:

  • Hall Voltage: $$\displaystyle V_H = \frac{R_H I B}{t} $$ where $$\displaystyle R_H $$ = Hall coefficient, $I$ = current, $B$ = flux density, $t$ = thickness.

  • Geometrical Correction Factor ($$\displaystyle r_H $$): Accounts for non-uniform current/field distribution; $$\displaystyle V_H = \frac{r_H R_H I B}{t} $$.

  • Applications: Magnetic field measurement, current sensing (Hall effect current transformer), position sensing (brushless encoders).

3.6 Thermal Transducers

• Thermocouple:

  • Principle: Seebeck effect → two dissimilar metals at junction produce $\Delta V \propto \Delta T$.

  • Materials: Type K (Ni-Cr/Ni-Al), Type J (Fe-CuNi), Type T (Cu-CuNi).

  • Cold Junction Compensation: Reference junction at known temp (ice bath or electronic compensation).

3.7 Photoelectric Transducers

3.8 Digital Multiplexing in Transducer Interfacing

• Concept: Time-division multiplexing (TDM) → multiple sensors share single ADC/processor via fast analog switches.

• Efficiency Improvement:

  • Reduced wiring cost & complexity.

  • Single high-precision ADC instead of multiple.

  • Centralized processing/calibration.

  • Used in industrial data acquisition systems (e.g., PLC input modules).

4.0 SIGNAL GENERATORS & WAVE ANALYZERS

4.1 Function/Arbitrary Waveform Generator

• Block Diagram:

  [Frequency Control (VCO)] → [Function Core (Wien bridge/RC oscillator)] → [Waveform Shaper (square/triangle)] → [Sine Filter] → [Attenuator/Amplifier]

• Sine Wave Generation:

  • Wien bridge oscillator (stable, low distortion).

  • Or filter square wave (harmonic rejection).

• VCO Control: External voltage → changes oscillator frequency (e.g., varactor diode in RC network).

4.2 Specific Oscillator Types

• Beat Frequency Oscillator (BFO):

  • Mix two close frequencies $$\displaystyle f_1 $$, $$\displaystyle f_2 $$ → beat frequency $$\displaystyle |f_1-f_2| $$ in audio range.

  • Used for AF testing (e.g., telegraphy, audio frequency response).

• Wein Bridge Oscillator:

  • Positive feedback via Wien network ($R$-$C$ series-parallel).

  • Gain set by non-linear element (lamp, diodes) for stability.

  • Frequency: $$\displaystyle f = \frac{1}{2\pi RC} $$.

4.3 Sweep & Fixed-Frequency Generators

4.4 Wave Analyzers

• Frequency Selective (Filter-Based):

  • Tuned filters (LC/RC) → select one frequency.

  • Limitations: Poor selectivity (adjacent freq leakage), low sensitivity.

• Heterodyne Wave Analyzer:

  • Operation:

    1. Mix input with local oscillator (LO) → sum/difference frequencies.

    2. IF amplifier (narrowband, high gain) → selects difference freq.

    3. Detector → output.

  • Advantages: High selectivity (IF filter), high sensitivity (IF gain).

  • Block Diagram: [Input] → [Mixer + LO] → [IF Amplifier] → [Detector] → [Output]

[!TIP]

May 2024 (7m): Heterodyne vs. filter type → superior sensitivity & selectivity due to IF stage.

5.0 DIGITAL MEASUREMENT INSTRUMENTS

5.1 Digital Voltmeter (DVM) Types

• General Advantages: High accuracy, noise immunity, auto-zero, direct reading.

• Ramp/Integrating Type (Dual-Slope):

  • Principle:

    1. Charge period ($$\displaystyle T_1 $$): Input $$\displaystyle V_i $$ charges capacitor → slope $$\displaystyle \propto V_i $$.

    2. Discharge period ($$\displaystyle T_2 $$): Reference $$\displaystyle -V_{ref} $$ discharges → slope $$\displaystyle \propto V_{ref} $$.

    3. $$\displaystyle T_2 $$ measured by counter → $$\displaystyle V_i = V_{ref} \cdot T_2/T_1 $$.

  • Advantages: Excellent noise rejection (integrates input), high accuracy.

  • Disadvantages: Slow (conversion time $$\displaystyle \propto T_1 $$).

• Successive Approximation Type (SAR):

  • Principle: DAC + comparator + SAR logic. Binary search → $n$ clock cycles for $n$-bit.

  • Comparison: Faster than dual-slope, but more sensitive to noise.

• 3½ Digit Voltmeter Concepts:

  • Resolution: Smallest change = $1$ count. For $n$½ digits: $$\displaystyle 10^n $$ counts full scale.

    Example: 3½ digit → 1999 counts → resolution = $$\displaystyle V_{FS}/2000 $$.

  • Display Examples (May 2024):

    • 11.52V on 10V range → Overrange (display shows "1" or "OL").

    • 0.5234V on 1V range → 0.5234 (4 digits).

    • 0.5234V on 10V range → 0.523 (3½ digits → 0.523).

5.2 Digital Frequency Meter

• Block Diagram:

  [Input Conditioning (amp/shaper)] → [Gate Circuit (controlled by timebase)] → [Counter] → [Display]

  Timebase: Crystal oscillator → precise time interval $T$.

• Working: Count input cycles $N$ in fixed $T$ → $$\displaystyle f = N/T $$.

  Error: ±1 count → $$\displaystyle \Delta f = \pm 1/T $$.

5.3 Data Logger vs. Data Acquisition System (DAS)

6.0 DISPLAY & RECORDING DEVICES

6.1 Display Technologies

• LED: Electroluminescence (pn junction). Low voltage, bright, fast. Driving: Current-limiting resistor.

• LCD: Light modulation by liquid crystal alignment (twisted nematic). Advantages: Low power, flat, no glare. Disadvantages: Slow, viewing angle sensitive, temperature limited.

• E-ink vs. Liquid Vapor Display:

  | | E-ink | Liquid Vapor | |---|---|---| | Principle | Electrophoresis (charged particles in fluid) | Liquid crystals in vapor state | | Applications | E-readers, signage | Rare, obsolete | | Merits | Bistable (image without power), sunlight readable | — | | Demerits | Slow refresh, limited color | Complex, high power |

6.2 Recorders

• Analog X-Y Recorder:

  • Servo-motors move pen (X & Y) proportional to input voltages.

  • Applications: Plot $I$-$V$ curves, process variables.

• Digital XY Recorder:

  • Data acquisition → digital storage → digital plotter (pen/matrix).

  • Advantages: High accuracy, no wear, storage, scaling, multiple plots.

• Comparison:

  | | Analog | Digital | |---|---|---| | Accuracy | Low (mechanical hysteresis) | High | | Wear | Pen/paper wear | No wear | | Storage | Paper only | Digital memory | | Cost | Lower | Higher |

7.0 INTERFACES & COMMUNICATION IN INSTRUMENTATION

7.1 Standard Instrumentation Interfaces

• RS-232C (Serial):

  • Point-to-point, asynchronous, 20 mA current loop or voltage (±12V).

  • Limitations: Slow (115.2 kbps max), short distance (15 m), single master.

• IEEE-488 (GPIB):

  • Parallel 8-bit bus, up to 15 devices.

  • Roles: Talker (sends), Listener (receives), Controller (manages).

  • Advantages: Fast (1 Mbps), multi-drop, standard commands (SCPI).

7.2 Modern Interfaces & Comparison

[!TIP]

June 2025 (7m): Compare RS232C, GPIB, USB, Ethernet in terms of speed, distance, topology, cost, complexity. Ethernet = long distance, networking; USB = plug-play, power delivery.

8.0 ADDITIONAL TOPICS FROM PAST PAPERS

8.1 Specific Device Short Notes

• Thermocouple (June 2025, Dec 2024):

  Seebeck effect → two dissimilar metals → $$\displaystyle \Delta V = \alpha \Delta T $$. Cold junction compensation essential. Materials: Type K (general), Type T (cryogenic), Type S (high temp).

• Hall Effect Transducer (June 2025, Dec 2024):

  $$\displaystyle V_H = \frac{R_H I B}{t} $$. Geometrical factor $$\displaystyle r_H $$ corrects for non-idealities. Applications: magnetic field, current, position sensing.

• LVDT (June 2025, May 2024, May 2023):

  See 3.3. Infinite resolution, no contact, linear region ± core travel.

• Digital Tachometer (June 2025):

  Optical/magnetic pickup → pulses per revolution → counter → RPM = $$\displaystyle \frac{60 \times \text{pulse count}}{\text{time}} $$. Non-contact.

• Multi-input Sampling Oscilloscope (June 2025, May 2023):

  Sample each channel sequentially at high rate → reconstruct. Used for high-speed digital signals. Precautions: Sampling rate > 2× highest freq, avoid aliasing.

• Heterodyne Wave Analyzer (June 2025, Dec 2024):

  See 4.4. Mixer + LO + IF → high selectivity/sensitivity.

• Sweep Generator (June 2025, Dec 2024):

  Frequency varies linearly with time → used for Bode plots, filter testing.

• Wobbly Scope (June 2025, Dec 2024):

  Sweep frequency modulated by AF signal → wobbly Lissajous → component testing.

• GPIB (June 2025, Dec 2024):

  See 7.1. Parallel bus, talker/listener/controller, SCPI commands.

• Digital pH meter (Dec 2024):

  Glass electrode → high impedance amp (FET input) → ADC → digital display. Temperature compensation needed.

8.2 Miscellaneous

• Wagener's Earthing Device (May 2022):

  Safety grounding for CRO. Spring-loaded contact → earth the CRT chassis → prevent electric shock from high voltage anode.

• Total Harmonic Distortion (THD) (May 2023):

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

Measures distortion in periodic signals; lower THD = purer sine wave.

• Applications of CROs (May 2022):

  1. Voltage/time/frequency measurement.

  2. Phase difference.

  3. Lissajous patterns (frequency ratio).

  4. Debugging digital/analog circuits.

  5. Noise analysis.

  6. Displaying waveforms from sensors.

END OF UNIT 2 NOTES
Always cross-check formulas with RGPV syllabus and past papers. Practice numericals from Maxwell, Schering, Wien bridges and 3½ digit DVM display.