Electronic Instrumentation (EX-604 (A)) - Unit 4 Short Notes

UNIT 4: Electronic Instrumentation

I. Cathode Ray Oscilloscopes (CRO)

CRT Fundamentals

• Electrostatic Deflection: Electron beam deflected by electric field between parallel plates. Deflection $$\displaystyle D \propto V_d $$ (deflecting voltage).

• Post-Deflection Acceleration:

  • Significance: Increases beam velocity after deflection to enhance brightness and reduce spot size.

  • Effect: Higher final anode voltage $$\displaystyle V_a $$ → higher beam velocity $$\displaystyle v = \sqrt{\frac{2eV_a}{m}} $$ → smaller spot size due to reduced electrostatic repulsion.

• Deflection Sensitivity ($S$):

  • Definition: Deflection per unit deflecting voltage (cm/V).

$$S = \frac{D}{V_d} = \frac{L_l L_s}{2d V_a}$$

where $$\displaystyle L_l $$ = length of deflection plates, $$\displaystyle L_s $$ = distance from plate center to screen, $d$ = plate spacing, $$\displaystyle V_a $$ = final anode voltage.

• Deflection Factor ($G$):

  • Definition: Reciprocal of sensitivity (V/cm). $$\displaystyle G = 1/S $$.

[!TIP] Common Pitfall: Confusing $$\displaystyle V_a $$ (final anode) with $$\displaystyle V_d $$ (deflection plate voltage). Post-deflection acceleration uses high $$\displaystyle V_a $$ to boost speed after plates.

General Purpose CRO: Block Diagram & Applications

• Block Diagram:

  
  Vertical Amplifier → Delay Line → Deflection Plates
  
  Horizontal (Time Base) → Amplifier → Deflection Plates
  
  Trigger Circuit → Sweep Generator
  
  CRT & Power Supply
  
  

• Applications: Voltage/time display, frequency measurement (Lissajous), phase difference, waveform distortion analysis.

Dual-Beam vs Dual-Trace Oscilloscopes

Time Base Circuits

• Sweep Generator: Produces linear ramp voltage (sawtooth) for horizontal deflection.

• Synchronization: Trigger circuit forces sweep start at a specific point on input waveform → stable display.

• Effect on Accuracy:

  • Poor sync → drifting/rolling waveform.

  • Nonlinear sweep → distortion of time axis (e.g., curved edges on square waves).

Special Types

Sampling Oscilloscope (Multi-Input)

• Principle: Sample input signal at discrete intervals, reconstruct waveform from samples (effective for very high frequencies beyond direct amplifier bandwidth).

• Applications: GHz-range signal analysis, digital communications.

• Precautions:

  • Requires repetitive signals.

  • Aliasing if sampling rate < 2× signal frequency.

  • Sensitive to noise.

Wobbly Scope

• Construction: Modifies time base to sweep frequency slightly around a center value.

• Working: Used with a frequency-selective filter (e.g., wave analyzer). When sweep matches filter center frequency, a peak appears on screen → identifies signal frequency components.

Display Aspects

Graticules

• Types: Internal (etched on CRT), External (glass plate), Digital (stored in memory).

• Uses: Provide reference grid for voltage/time measurement.

Lissajous Patterns

• Formation: Apply sinusoidal signals to X and Y plates.

• Frequency Determination:

$$f_y = \frac{N_x}{N_y} f_x$$

where $$\displaystyle N_x $$ = horizontal tangencies, $$\displaystyle N_y $$ = vertical tangencies.

• [!TIP] Tangencies = points where pattern touches graticule lines. Always verify stability (ratio rational).

II. AC Bridges for Impedance Measurement

Bridge Fundamentals

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

• Sources of Errors:

  • Stray capacitance/inductance.

  • Frequency instability.

  • Non-ideal components (parasitic resistance in inductors, dielectric loss in caps).

• Mitigation:

  • Shielding, guarding, Wagner earth.

  • Use high-Q components.

  • Operate at optimal frequency.

• Q-Meter:

  • Circuit: Series resonant circuit with known $L$ and $C$, Q = $$\displaystyle \frac{V_C}{V_R} $$.

  • Working: Measure voltage across $C$ vs $R$ at resonance → Q-factor.

  • Applications: Measure Q of coils, inductance, capacitance.

• Loss Factor ($\tan\delta$) & Q-Factor:

  • $$\displaystyle \tan\delta = \frac{1}{Q} $$ for series model.

  • $$\displaystyle \tan\delta = \frac{R_s}{\omega L} = \omega C R_p $$ depending on model.

Maxwell Bridge

• Circuit: Measures unknown inductance $$\displaystyle L_x $$ with series resistance $$\displaystyle R_x $$.

  • Arms: $$\displaystyle Z_1 = R_1 $$, $$\displaystyle Z_2 = R_2 $$, $$\displaystyle Z_3 = C_1 $$ (standard), $$\displaystyle Z_4 = R_x + j\omega L_x $$.

• Balance Equations:

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

• Merits: Direct reading of $$\displaystyle L_x $$ & $$\displaystyle R_x $$, independent of frequency if $$\displaystyle C_1 $$ non-inductive.

• Demerits: Requires precise $$\displaystyle C_1 $$, limited to moderate Q (1–10) because balance depends on $$\displaystyle R_1 $$ adjustment.

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

Schering Bridge

• For Capacitor Measurement:

  • Arms: $$\displaystyle Z_1 = R_1 $$, $$\displaystyle Z_2 = R_2 $$, $$\displaystyle Z_3 = C_1 $$ (standard), $$\displaystyle Z_4 = C_x $$ with loss (parallel $$\displaystyle R_p $$ or series $$\displaystyle R_s $$).

• Balance Equations (parallel model):

$$C_x = \frac{R_1}{R_2} C_1, \quad \tan\delta = \omega C_1 R_1$$

• High-Voltage Schering Bridge:

  • Special features: High-voltage capacitors for insulation testing, guarded electrodes to reduce stray capacitance, safety interlocks.

De Sauty's Bridge vs Schering Bridge

Wien Bridge

• Frequency Determination:

  • Arms: $$\displaystyle Z_1 = R_1 $$, $$\displaystyle Z_2 = R_2 $$, $$\displaystyle Z_3 = R_3 $$, $$\displaystyle Z_4 = C_3 $$ in series with $$\displaystyle C_4 $$? Actually standard Wien: $$\displaystyle Z_1 = R_1 $$, $$\displaystyle Z_2 = R_2 + 1/(j\omega C_2) $$, $$\displaystyle Z_3 = R_3 $$, $$\displaystyle Z_4 = 1/(j\omega C_4) $$.

  • Balance condition: $$\displaystyle \omega^2 = \frac{1}{R_1 R_2 C_1 C_2} $$ and $$\displaystyle R_2/R_1 = C_1/C_2 $$.

  • For equal components ($$\displaystyle R_1=R_2=R $$, $$\displaystyle C_1=C_2=C $$): $$\displaystyle f = \frac{1}{2\pi RC} $$.

• Wien Bridge Oscillator: Uses positive feedback through Wien network to generate sine waves.

Anderson Loop

• Basic Topology: Modified Maxwell bridge with a fixed capacitor in series with a variable resistor in one arm.

• Purpose: Extends measurement range for inductors with very low Q (e.g., iron-core coils). Avoids need for high $$\displaystyle R_1 $$ values in Maxwell bridge.

Overview: Selection of AC Bridges

III. Transducers

Transducer Fundamentals

• Primary vs Secondary:

  • Primary: Converts physical quantity to another intermediate form (e.g., Bourdon tube → pressure → displacement).

  • Secondary: Converts intermediate quantity to electrical output (e.g., LVDT → displacement → voltage).

  • Example: Thermocouple (primary: heat → Seebeck voltage; secondary: voltage amplifier).

• Input Characteristics:

  • Sensitivity: Output change per unit input.

  • Linearity: Deviation from straight-line input-output.

  • Hysteresis: Difference in output for increasing vs decreasing input.

  • Resolution: Smallest detectable input change.

  • Dynamic Response: Bandwidth, time constant.

Resistive Transducers

Strain Gauge

• Principle: Resistance $$\displaystyle R = \rho L/A $$. Strain $\epsilon$ changes $L$ and $A$ → $\Delta R$.

• Gauge Factor (GF):

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

where $\nu$ = Poisson’s ratio, last term = piezoresistive effect.

• Metal vs Semiconductor:

  | Property | Metal | Semiconductor | |----------|-------|---------------| | GF | 2–5 | 50–150 | | Temperature Sensitivity | Low | High (requires compensation) | | Nonlinearity | Low | Moderate |

• Instrumentation Amplifier Interface:

  • Use Wheatstone bridge (quarter/half/full bridge) to convert $\Delta R$ to $\Delta V$.

  • Instrumentation amp provides high gain, common-mode rejection.

RTD & Thermistor

• RTD (Resistance Temperature Detector):

  • Working: Pure metal (Pt, Ni) resistance increases linearly with $T$.

  • Applications: Industrial temperature (−200°C to 850°C), high accuracy.

• Thermistor:

  • Working: Semiconductor, resistance decreases exponentially with $T$ (NTC).

  • Applications: Limited range (−50°C to 150°C), high sensitivity, temperature compensation.

Inductive Transducer: LVDT

• Construction: Transformer with movable ferromagnetic core, primary winding center-tapped, two secondary windings series-opposed.

• Working Principle: Core displacement changes mutual inductance → differential voltage output.

• Input-Output Characteristics:

  • Linear region ≈ ± core travel.

  • Output voltage phase indicates direction (0° or 180°).

  • Null point when core centered.

• Advantages: Infinite resolution, no contact, robust.

• Limitations: Limited bandwidth (core inertia), requires AC excitation, sensitive to stray magnetic fields.

Piezoelectric Transducers

• Piezoelectric Effect:

  • Direct: Mechanical stress → charge generation.

  • Converse: Electric field → mechanical strain.

• Modes of Operation:

  • Transverse: Stress ⊥ polarization, charge on sides.

  • Longitudinal: Stress ∥ polarization, charge on ends.

  • Shear: Shear stress → charge on faces.

• Applications: Force, pressure, acceleration (seismographs), ultrasonic generation.

• Piezo Quartz Calculations:

  Given: dimensions $a \times b \times t$, charge sensitivity $d$ (C/N), Young’s modulus $Y$, permittivity $\epsilon$.

  • Strain $$\displaystyle \epsilon = \frac{\text{force}}{Y \times \text{cross-sectional area}} $$.

  • Charge $$\displaystyle Q = d \times \text{force} $$.

  • Voltage $$\displaystyle V = \frac{Q}{C} $$, $$\displaystyle C = \frac{\epsilon \times \text{area}}{t} $$.

Magnetic Transducers: Hall Effect

• Hall Voltage Generation:

$$V_H = \frac{I B}{n e t} = R_H \frac{I B}{t}$$

where $$\displaystyle R_H $$ = Hall coefficient, $t$ = thickness, $n$ = carrier density.

• Geometrical Correction Factor: Accounts for non-ideal sample shape (e.g., rectangular vs square). $$\displaystyle V_H^{\text{actual}} = k V_H^{\text{ideal}} $$.

Optical Transducers

• Why Photo-Diode for Low Light? Reverse bias widens depletion region → higher collection efficiency, lower capacitance → better signal-to-noise.

Thermoelectric Transducers: Thermocouple

• Seebeck Effect: Two dissimilar metals joined → temperature difference → voltage.

• Working Principle: Hot junction (measured $T$) vs cold junction (reference) → $V \propto \Delta T$.

• Materials:

  • Type K (Chromel-Alumel): wide range, robust.

  • Type T (Cu-Constantan): low temperature, corrosion resistant.

  • Type J (Fe-Constantan): reducing atmospheres.

• Applications: Industrial temperature (−200°C to 2300°C), gas turbines, ovens.

Transducer Interfacing: Digital Multiplexing

• Concept: Multiple transducers share a single ADC and data line via analog multiplexer (e.g., 16:1 MUX).

• Efficiency Improvement:

  • Reduces wiring complexity in industrial plants.

  • Lowers cost (fewer ADCs, signal conditioners).

  • Enables sequential sampling → data logger functionality.

  • [!TIP] Multiplexing adds switching noise; sample-and-hold circuits often needed per channel.

IV. Signal Generators and Wave Analyzers

Signal Generators

Function Generator

• Block Diagram:

  
  Frequency Control (VCF) → Sine Wave Generator (RC oscillator) 
  
    → Waveform Shaper (square/triangle) → Output Amplifier
  
  

• Sine Wave Production:

  • RC Oscillator (Wein bridge): Stable sine at audio frequencies.

  • Integrator: Convert square wave → triangle.

  • Comparator: Convert triangle → square.

• Voltage-Controlled Frequency (VCF): Input voltage changes RC time constant or varactor capacitance.

Sweep Generator

• Fixed-Frequency: Outputs single frequency (e.g., crystal oscillator).

• Sweep-Frequency: Output frequency varies linearly/logarithmically with time → used for frequency response analysis (Bode plots).

Beat Frequency Oscillator (BFO)

• Principle: Two close frequencies $$\displaystyle f_1 $$ and $$\displaystyle f_2 $$ mixed → difference frequency $$\displaystyle |f_1 - f_2| $$ in audio range.

• Working: One variable-frequency oscillator + one fixed oscillator → mixer → low-pass filter → audio beat signal. Used in radio direction finding, signal detection.

Wave Analyzers

Frequency Selective Wave Analyzer

• Operation: Tuned filters (LC or crystal) select one frequency at a time → detector → meter.

• Limitations: Narrow bandwidth, slow scanning, limited sensitivity.

Heterodyne Wave Analyzer

• Operation:

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

  2. Fixed IF filter (e.g., 455 kHz) selects one sideband.

  3. Detect and display.

• Comparison:

  | Feature | Frequency Selective | Heterodyne | |---------|---------------------|------------| | Sensitivity | Low (limited by filter Q) | High (due to IF amplification) | | Selectivity | Moderate (filter bandwidth) | High (narrow IF filter) | | Frequency Range | Audio to RF | Wide (RF to microwave) | | Speed | Slow (tuning) | Fast (LO sweeps) |

Spectrum Analyzer

• Block Diagram:

  
  Input → Attenuator → Mixer (with swept LO) → IF Filter/Amplifier → Detector → Display (X: frequency, Y: amplitude)
  
  

• Importance: Visualizes harmonic content, interference, signal integrity.

• Applications: EMI testing, communication system analysis, distortion measurement.

Total Harmonic Distortion (THD)

• Definition: Ratio of RMS voltage of all harmonics to RMS fundamental voltage.

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

• Significance: Quantifies waveform purity. Critical in audio, power systems, and signal generation.

V. Digital Measurement Instruments

Digital Voltmeter (DVM)

• Advantages: High accuracy, noise immunity, easy reading, auto-ranging, data output.

• Types & Working Principles:

  | Type | Principle | Speed | Accuracy | Noise Rejection | |------|-----------|-------|----------|-----------------| | Ramp (Integrating) | Measure time to charge capacitor to input voltage | Medium | Medium | Poor | | Successive Approximation | Binary search with DAC → fast conversion | Fast | Good | Moderate | | Dual Slope Integrating | Integrate input for fixed time, de-integrate with reference → measure de-integration time | Slow | Very High | Excellent (rejects 50/60 Hz noise) |

• Comparison: Dual Slope vs Successive Approximation:

  • Dual slope: Better accuracy & noise rejection (averaging), slower.

  • Successive approximation: Faster, moderate accuracy, sensitive to noise.

• Resolution:

  • For $n$-digit meter: Resolution = $$\displaystyle \frac{1}{10^n} $$ of full scale.

  • 3½ digit: Max count = 1999 → resolution = 0.05% of full scale.

    • On 10V range: 1 LSB = 10V / 1999 ≈ 1 mV.

    • On 1V range: 1 LSB = 1V / 1999 ≈ 0.5 mV.

  • Display Examples (3½ digit, 10V max):

    • 11.52V → Overrange (blanks or shows "1").

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

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

Digital Frequency Meter

• Block Diagram:

  
  Input → Conditioning ( Schmitt trigger) → Gate (controlled by time base) → Counter → Display
  
  Time Base (crystal oscillator) → Gate Control
  
  

• Operation: Count input pulses during precise gate interval (e.g., 1 s) → frequency = count / gate time.

Digital Tachometer

• Working Principle:

  • Optical (reflective mark on rotating shaft → photodiode pulses).

  • Magnetic (Hall sensor on gear teeth).

  • Pulse count over time → RPM = $$\displaystyle \frac{60 \times \text{count}}{\text{pulses per rev} \times \text{gate time}} $$.

Digital pH Meter

• Working Principle:

  • pH Electrode: Glass membrane potential $E \propto \text{pH}$ (Nernst equation: $$\displaystyle E = E_0 - 0.059\,\text{pH} $$ at 25°C).

  • Circuit: High-impedance amplifier → ADC → digital display.

  • Calibration: With buffer solutions (pH 4, 7, 10).

VI. Instrumentation Interfaces and Data Systems

Communication Interfaces

[!TIP] GPIB is parallel with hardware handshaking → reliable for lab; USB/Ethernet are serial with software protocols → flexible for distributed systems.

Data Systems

• Data Logger:

  • Standalone, battery-powered, stores data internally (SD card).

  • Low cost, portable, limited processing.

  • Used for field monitoring (temperature, humidity over days).

• Data Acquisition System (DAS):

  • Connected to PC, real-time processing, high channel count.

  • Includes signal conditioning, ADC, software for analysis/display.

  • Used for lab experiments, process control, real-time monitoring.

VII. Display Devices

LED (Light Emitting Diode)

• Construction: p-n junction, forward biased → electron-hole recombination → light.

• Working: Electroluminescence. Color depends on semiconductor bandgap.

• Applications: Digital readouts, indicators, matrix displays.

LCD (Liquid Crystal Display)

• Theory: Liquid crystals twist polarized light. Voltage untwists → blocks light.

• Twisted Nematic (TN): Common type. No voltage → 90° twist → light passes. Voltage → alignment → blocks light.

• Advantages over LED:

  • Lower power (reflective types).

  • No glare, wider viewing angle (IPS).

  • Cheaper for large displays.

  • No radiation (vs CRT).

Other Display Technologies

VIII. Recording Instruments

X-Y Recorders

Analog X-Y Recorder

• Working Principle: Two inputs (X, Y) control deflection of pen on paper via servo motors.

• Circuit Diagram:

  
  X Input → Error Amplifier → Servo Motor → X-Deflection
  
  Y Input → Error Amplifier → Servo Motor → Y-Deflection
  
  (Feedback from pen position)
  
  

• Applications: Plot transfer functions (Bode plots), stress-strain curves, P-H diagrams.

Digital X-Y Recorder

• Comparison with Analog:

  | Feature | Analog | Digital | |---------|--------|---------| | Recording | Continuous pen trace | Sampled points or raster scan | | Accuracy | Limited by servo linearity, friction | High (ADC + memory) | | Speed | Limited by pen inertia | Fast (memory buffer) | | Storage | Paper only | Digital files, repeatable | | Cost | Low | Higher |

General Comparison: Analog vs Digital Recorders

IX. Specialized Topics and Safety

Wagener's Earthing Device

• Purpose: Safety in CROs. Prevents high voltage (final anode, ~2–10 kV) from appearing on external connectors (vertical/horizontal inputs) if internal insulation fails.

• Construction: Capacitive coupling between input shield and earth via a safety capacitor. AC signals pass, DC/high voltage blocked to ground.

Storage Factor

• Relevance in Bridges: Storage factor $$\displaystyle Q = \frac{\omega L}{R} $$ (for inductor) or $$\displaystyle Q = \frac{1}{\omega C R} $$ (for capacitor). Determines bridge balance difficulty.

  • Maxwell Bridge: Best for $Q \approx 1–10$. Too high Q → $$\displaystyle R_1 $$ becomes impractically large; too low Q → balance insensitive.

  • Anderson Bridge: Extends to lower Q values.

  • Schering Bridge: Used for capacitors with low $\tan\delta$ (high Q).