Electronic Measurements and Instrumentation (EC-302) - Unit 1 Short Notes

UNIT 1: ELECTRONIC MEASUREMENTS AND INSTRUMENTATION

I. FUNDAMENTALS OF MEASUREMENT & INSTRUMENT CHARACTERISTICS

Static Characteristics of Instruments

Define static characteristics as the performance parameters of an instrument when measuring constant (DC) or slowly varying signals.

[!TIP] Exam Focus: Accuracy vs. Precision is a very frequent 7-mark question. Use the target diagram (bullseye) to illustrate.

Errors in Measurement

Static Error (ε): $$\displaystyle \varepsilon = A_m - A_t $$ (Measured - True value)
Static Correction (C): $$\displaystyle C = A_t - A_m = -\varepsilon $$
Relative Error (δ): $$\displaystyle \delta = \frac{\varepsilon}{A_t} $$
Percentage Relative Error (%δ): $$\displaystyle \%\delta = \frac{\varepsilon}{A_t} \times 100\% $$

[!TIP] Common Pitfall: Relative error uses true value in denominator. If true value is unknown, use full-scale value for specification.

Dynamic Characteristics & Response

Relevant for time-varying inputs.

• Importance of Damping: An under-damped system oscillates before settling (fast response but overshoot). An over-damped system is slow without oscillation. Slightly under-damped is often preferred for fastest settling time without excessive overshoot.

• Time Constant (τ): Time for output to reach 63.2% of its final value for a step input. For a first-order system: $$\displaystyle \tau = RC $$ (electrical) or $$\displaystyle \frac{J}{D} $$ (mechanical).

• Bandwidth: Frequency range over which instrument response is within ±3dB (or 70.7%) of its mid-band value. $$\displaystyle \text{Bandwidth} \approx \frac{0.35}{\text{Rise Time}} $$.

II. ANALOG ELECTRONIC INSTRUMENTS: OSCILLOSCOPES

Cathode Ray Oscilloscope (CRO)

Block Diagram & Functional Description:

1. Vertical Amplifier: Amplifies input signal.

2. Horizontal Amplifier (Time Base): Generates sawtooth waveform for time-axis sweep.

3. Trigger Circuit: Synchronizes sweep with input signal for stable display.

4. Cathode Ray Tube (CRT): Displays waveform.

5. Power Supply: Provides high voltages (HV) and low voltages (LV).

CRT Construction & Operation:

• Internal Structure: Electron Gun (Cathode, Control Grid, Focusing & Accelerating Anodes) → Deflection Plates (Vertical & Horizontal) → Fluorescent Screen.

• Electrostatic Focusing: Adjustable focusing anode voltage creates an electrostatic lens to converge electron beam to a fine spot.

• Electrostatic Deflection: Voltage on vertical plates deflects beam up/down; horizontal plates deflect left/right.

• Graticules: Grid lines on CRT face for visual measurement of amplitude/time. Often internal (etched on glass) for accuracy.

Probes:

• Importance: Match impedance (typically 1MΩ || 20-50pF) to minimize circuit loading.

• 10:1 Probe: Uses a 9MΩ series resistor and compensation capacitor. Provides higher input impedance and lower capacitance, reducing loading. Must be compensated using the probe's adjustment capacitor to match the CRO's input capacitance.

Special Purpose & Advanced CROs

Applications of CRO:

• Voltage/time waveform display.

• Frequency & phase measurement (Lissajous figures).

• Timing & pulse measurements (rise time, width).

• Troubleshooting digital/logic circuits.

• Displaying output from sensors/transducers.

[!TIP] Exam Focus: Dual Beam vs. Dual Trace comparison and DSO block diagram are repeatedly asked.

III. AC BRIDGE CIRCUITS FOR IMPEDANCE MEASUREMENT

General Bridge Concepts

• Bridge Balance Condition: For a 4-arm bridge (ABCD), balance occurs when: $$\displaystyle Z_1 Z_3 = Z_2 Z_4 $$. No current flows through the detector (galvanometer).

• Bridge Sensitivity: Deflection per unit unbalance. Maximum sensitivity occurs when: Source impedance = Bridge impedance and Detector impedance = Bridge impedance at balance point.

• Detectors: Galvanometer (DC/low-freq AC), Headphones/Amplifier (audio), Oscilloscope (high-freq).

Specific Bridges

1. Schering Bridge (For C & D - loss angle)

• Circuit: AB: R₁ (known), BC: C₂ (std. cap), CD: R₃ || C₃ (unknown Cₓ, Dₓ), DA: R₄ (std. res).

• Balance Equations:

$$ R_1 = R_4 \frac{C_3}{C_2} \quad \text{and} \quad C_x = C_2 \frac{R_4}{R_1} $$

$$ D_x = \omega C_3 R_3 \quad (\text{or } \tan \delta_x = \omega C_3 R_3) $$

• Applications: Cable testing, capacitor quality (dissipation factor), insulation testing.

2. Hay's Bridge (For L & C - high Q coils)

• Circuit: AB: R₁ (std.) in series with L₁ (std.), BC: R₂ (std.), CD: Rₓ in series with Cₓ (unknown), DA: R₄ (std.).

• Balance Equations (at ω):

$$ R_x = \frac{\omega^2 L_1^2 R_2}{R_4^2 + \omega^2 L_1^2} \quad \text{and} \quad C_x = \frac{R_4^2 + \omega^2 L_1^2}{\omega^2 L_1 (R_4^2 + \omega^2 L_1^2)} \approx \frac{R_4}{\omega^2 L_1} \text{ for high Q} $$

$$ L_x = \frac{R_2 R_4 C_x}{1 + \omega^2 C_x^2 R_2^2} \approx R_2 R_4 C_x \text{ for high Q} $$

• Applications: Measurement of inductance of coils with high Q factor.

3. Wien Bridge (For Frequency or C)

• Circuit: Two series arms (R, C) and two parallel arms (R, C). Balanced when:

$$ \omega^2 = \frac{1}{R_1 R_2 C_1 C_2} \quad \text{and} \quad \frac{C_2}{C_1} = \frac{R_4}{R_3} - 1 $$

For **frequency measurement** (R₁=R₂=R, C₁=C₂=C): $$\displaystyle \boxed{f = \frac{1}{2\pi RC}} $$

• Applications: Audio frequency oscillator (as feedback network), capacitance measurement, frequency measurement in audio range.

4. Maxwell's Inductance-Capacitance Bridge (For L & R)

• Circuit: AB: R₁ in series with L₁, BC: R₂, CD: Rₓ in series with Lₓ, DA: C₃ (std. cap).

• Balance Equations:

$$ L_x = R_1 R_2 C_3 \quad \text{and} \quad R_x = \frac{R_2}{R_1} R_1 = R_2 \frac{R_1}{R_1} \text{ (simplified)} $$

• Limitation for High Q Coils: Requires a very large standard capacitor (C₃) for high Lₓ, which is impractical. Also, R₃ (loss in unknown coil) appears in Rₓ expression, making separation difficult.

Q-Meter

• Principle: Uses a series resonant circuit (Lₓ, C, Rₓ) at known frequency. At resonance, reactive voltages cancel, and voltage across C is Q times the applied voltage.

• Impedance Measurement:

  • Series Connection: $$\displaystyle Q_s = \frac{X_s}{R_s} $$. Measures series resistance (Rₛ) and reactance (Xₛ).

  • Parallel Connection (more common):

$$ R_p = \frac{Q_m^2 + 1}{Q_s} R_s \approx Q_m^2 R_s \quad (\text{for high Q}) $$

$$ X_p \approx X_s \quad (\text{for high Q}) $$

$$ Q_p \approx Q_s \quad (\text{for high Q}) $$

    Where $$\displaystyle Q_m $$ is the **meter reading** (Q of the circuit including coil losses).

[!TIP] Exam Focus: Derivation for Schering and Hay's bridge balance conditions, and Q-meter parallel method expressions are very frequent.

IV. TRANSDUCERS & SENSORS

Classification of Transducers

1. By Input/Output: Electrical ↔ Non-Electrical (e.g., Strain Gauge, Thermocouple).

2. By Operating Principle: Active (self-generating, e.g., Piezo) vs. Passive (externally powered, e.g., Potentiometer).

3. By Output Type: Analog vs. Digital.

4. By Application: Displacement, Pressure, Temperature, etc.

Resistive Transducers

• Potentiometer: Resistive element + sliding contact. Measures linear/angular displacement. Advantage: Simple, low cost. Disadvantage: Loading, wear.

• Strain Gauge: Resistance changes with strain (ΔR/R = GF × ε). Bonded type (metallic foil on insulator). Used in load cells, pressure transducers.

• Thermistor: Semiconductor with high negative temperature coefficient (NTC). High sensitivity, small size, but non-linear. Used in temperature measurement/compensation.

Inductive & Capacitive Transducers

• LVDT (Linear Variable Differential Transformer):

  • Construction: Primary winding (center-tapped), two secondary windings (series-opposite), moveable ferromagnetic core.

  • Principle: Core displacement changes mutual inductance between primary and secondaries.

  • Operation: AC excitation on primary. When core is centered, $$\displaystyle V_{s1} = V_{s2} $$, $$\displaystyle V_{out} = 0 $$. Core displaced → phase & amplitude of secondary voltages differ → differential output.

  • Displacement Detection:

    • Magnitude: $$\displaystyle |V_{out}| \propto \text{displacement} $$.

    • Direction: Phase of $$\displaystyle V_{out} $$ relative to excitation (0° or 180°) indicates direction.

  • Advantages: Infinite resolution, frictionless, robust, linear over wide range.

Piezoelectric Transducers

• Working Principle: Piezoelectric Effect (e.g., Quartz, PZT). Mechanical stress → surface charge (voltage). Converse effect: Voltage → strain.

• Modes of Operation:

  • Binder (Longitudinal): Stress applied parallel to polarized axis. Charge on faces perpendicular to stress.

  • Twister (Shear): Stress applied perpendicular to polarized axis. Charge on faces parallel to stress.

• Piezoelectric vs. Piezoresistive: Piezoelectric generates charge/voltage (dynamic, AC). Piezoresistive changes resistance (e.g., semiconductor strain gauge, static possible).

Optical Transducers

• Photodiode: Reverse-biased p-n junction. Photocurrent $$\displaystyle I_{ph} \propto $$ light intensity. Fast response.

• Phototransistor: Photodiode + transistor gain. Higher sensitivity than photodiode, slower.

Other Special Transducers

• Thermocouple: Seebeck effect – junction of two dissimilar metals generates EMF proportional to temperature difference.

• LED as Transducer: Forward-biased LED emits light proportional to current. Used as light source in optical sensors.

• Accelerometer: Measures acceleration. Often uses mass-spring system with LVDT or piezoelectric crystal.

• Bolometer: Measures incident radiation power by measuring temperature rise of a blackened strip (change in resistance).

V. DIGITAL INSTRUMENTS: A/D & D/A CONVERSION

Digital Voltmeter (DVM)

• Digits Concept: n½ digits means:

  • Full digits: 0-9.

  • ½ digit: Can display 0 or 1 only.

  • Example: 3½ digits → Max reading = 1999 (not 3999). 5½ digits → Max reading = 19999.

  • Significance of ½ digit: Allows display of leading "1" for full-scale readings, improving resolution without increasing digit count.

• Resolution: Smallest change in voltage that can be detected. For an N-bit DVM with range V:

$$ \text{Resolution} = \frac{V}{2^N - 1} \approx \frac{V}{2^N} $$

• Sensitivity: Minimum input voltage required to produce a full-scale output (often same as resolution for ideal DVM).

Digital-to-Analog Converters (DAC)

1. Weighted Resistor DAC

• Circuit: Binary-weighted resistors (R, 2R, 4R...) from switch array to op-amp summing junction.

• 3-bit Transfer Characteristic:

  | Digital Input (D₂D₁D₀) | Analog Output $$\displaystyle V_o $$ (for R-2R) | | :--- | :--- | | 000 | 0 | | 001 | $$\displaystyle -\frac{V_{ref}}{8} $$ | | 010 | $$\displaystyle -\frac{V_{ref}}{4} $$ | | 011 | $$\displaystyle -\frac{3V_{ref}}{8} $$ | | 100 | $$\displaystyle -\frac{V_{ref}}{2} $$ | | 101 | $$\displaystyle -\frac{5V_{ref}}{8} $$ | | 110 | $$\displaystyle -\frac{3V_{ref}}{4} $$ | | 111 | $$\displaystyle -\frac{7V_{ref}}{8} $$ |

  Step Size (LSB): $$\displaystyle \Delta V = \frac{V_{ref}}{2^N} $$

2. R-2R Ladder DAC

• Circuit: Uses only two resistor values (R & 2R). Each bit drives a 2R resistor to a ladder network.

• Operation: Each bit switch connects either to V_ref or GND. The ladder presents Thevenin equivalent resistance of 2R to the op-amp.

• Output Formula: $$\displaystyle V_o = -\frac{V_{ref}}{2^N} (D_{N-1}2^{N-1} + ... + D_1 2^1 + D_0 2^0) $$

• Advantage over Weighted Resistor: Only two precise resistor values needed, easier for high bits.

Analog-to-Digital Converters (ADC)

[!TIP] Exam Focus: SAR operation (binary search), Dual-Slope working (integration phases), and R-2R ladder problems (step size, output) are very common.

VI. SIGNAL GENERATORS & DISPLAY DEVICES

Signal Generators

• Sweep Frequency Generator:

  • Block Diagram: Voltage-Controlled Oscillator (VCO) + Sweep Control Circuit (ramp generator) + Output Amplifier.

  • Working: Ramp voltage from sweep circuit controls VCO frequency, generating a continuous frequency sweep (e.g., 10Hz-1MHz). Used with spectrum analyzers or to test filter response.

• Pulse Wave Generator:

  • Block Diagram: Astable Multivibrator (or crystal oscillator) + Monostable (for pulse width) + Buffer/Amplifier.

  • Working: Multivibrator generates clock. Monostable triggered by clock produces pulse of fixed width. Repetition rate set by clock frequency.

Display Devices

1. LED (Light Emitting Diode)

• Construction: p-n junction (GaAs, GaP). Forward biased.

• Working: Electron-hole recombination → light emission (color depends on semiconductor bandgap).

• Advantages: Bright, low voltage, fast response, long life.

• Disadvantages: Power consumption, limited viewing angle, temperature sensitive.

2. LCD (Liquid Crystal Display)

• Construction: Liquid crystal layer between polarizers & transparent electrodes. Twisted Nematic (TN) type common.

• Working: No voltage → LC twists light 90° → passes through second polarizer (bright). Voltage applied → LC untwists → blocks light (dark). Requires backlight (transmissive) or reflective layer.

• Advantages: Very low power, good for battery devices, no glare.

• Disadvantages: Slow response (ms), temperature limited, requires external light source.

Classification: Segment Displays (7-seg, 16-seg), Dot Matrix Displays, Bar Graph Displays.

VII. MISCELLANEOUS & INTEGRATED TOPICS

Chopper Type DC Voltmeter

• Working Principle: Converts DC input to AC using a chopper (mechanical or electronic switch), then amplifies with a high-gain AC amplifier (good stability, low drift), and finally demodulates back to DC.

• Circuit: DC input → Chopper (modulates to AC) → AC Amplifier (high gain, stable) → Demodulator/Filter → DC output.

• Advantage: Eliminates DC drift and 1/f noise of amplifiers. Used for very low DC voltage measurement (μV, nV).

Comparison: Digital vs. Analog Instruments

Importance of Calibration

• Process: Comparing instrument output with a known standard and applying correction factors.

• Purpose: To minimize systematic errors, ensure traceability to national/international standards (NPL, NIST), maintain accuracy over time (due to drift, aging, environmental changes).

• Frequency: Depends on instrument stability, required accuracy, and usage. Critical for quality control, certification labs.

[!TIP] Exam Focus: Be prepared for short notes on any topic from the blueprint (e.g., Accelerometer, Bolometer, Binary adder). Structure: 1-line definition → Principle → Construction/Working → Applications/Advantages.