UNIT 4: ELECTRONIC MEASUREMENTS AND INSTRUMENTATION

I. FUNDAMENTALS OF MEASUREMENT & INSTRUMENT CHARACTERISTICS

Static Characteristics

Accuracy is the closeness of agreement between a measured value and the true value. Precision is the repeatability or reproducibility of measurements (closeness among individual readings). A system can be precise but inaccurate (consistent error) or accurate but imprecise (scattered readings).

Resolution is the smallest change in input signal that produces a detectable change in output. For a digital instrument, it's the value of the least significant bit (LSB).

[!TIP] Exam Distinction: Accuracy → True value; Precision → Consistency among readings. High precision does NOT guarantee high accuracy.

Static Error ($$\displaystyle e_s $$) = Measured Value - True Value. Static Correction ($$\displaystyle c_s $$) = - $$\displaystyle e_s $$ (value to be added to measured value). Relative Error ($$\displaystyle \epsilon_r $$) = $$\displaystyle \frac{e_s}{\text{True Value}} $$. Percentage Relative Error ($$\displaystyle \%\epsilon_r $$) = $$\displaystyle \frac{e_s}{\text{True Value}} \times 100\% $$.

[!TIP] Common Pitfall: Relative error is a more meaningful quality indicator than absolute error for comparing instruments of different ranges.

Types of Errors:

1. Gross Errors: Human mistakes, reading errors.

2. Systematic Errors: Instrumental (calibration), environmental (temperature), observational.

3. Random Errors: Unpredictable fluctuations (noise).

Calibration is the process of comparing an instrument's output against a known standard to determine and correct its error. It's essential to minimize systematic errors and maintain accuracy over time.

Dynamic Characteristics & Response

Describes how an instrument responds to time-varying inputs. Key parameter is time constant (τ) for first-order systems.

Damping Ratio (ζ):

• Under-damped (ζ < 1): Oscillatory response before settling.

• Over-damped (ζ > 1): Slow, sluggish response without oscillation.

• Critically damped (ζ = 1): Fastest response without overshoot.

[!TIP] Why Slightly Under-damped? (JUN 2024, JUN 2023) It provides a faster time to first indication than critically damped, with a manageable, small overshoot. It's a trade-off between speed and stability.

Standard Test Inputs & Response:

1. Step Input: Sudden change. Tests speed of response, overshoot, settling time.

2. Ramp Input: Linear increase. Tests tracking ability, lag error.

3. Sine Input: Periodic. Tests frequency response (magnitude & phase).

4. Impulse Input: Very short pulse. Tests system's natural frequency and damping.

II. ANALOG & DIGITAL VOLTMETERS

DC Voltmeters

1. Chopper Type DC Voltmeter (JUN 2025)

• Principle: Converts DC input into an AC signal using a chopper (modulator), amplifies the AC signal with a high-gain AC amplifier (avoiding DC drift issues), then demodulates back to DC.

• Working: Input DC → Chopper (mechanical/electronic switch) → Modulated AC → High-gain AC Amplifier → Demodulator (detector) → Filtered DC Output → Meter.

• Advantage: High sensitivity and stability, as only AC amplification is used (no DC drift in amplifier).

2. Electrostatic Voltmeter (Attracted Plate Type) (JUN 2023 problem)

• Principle: Based on electrostatic force between two charged plates. Force $$\displaystyle F \propto V^2 $$.

• Construction: Fixed plate (guard ring) & movable plate. Applied voltage creates attraction, moving the plate against spring tension. Deflection is proportional to $$\displaystyle V^2 $$.

• Applications: High voltage measurement (kV range), high impedance circuits (very low loading effect).

AC Voltmeters

Types:

• Average-responding (with diode + capacitor filter): Rectifies AC, measures average value, calibrated to read RMS for sine waves only ($$\displaystyle V_{rms} = 1.11 \times V_{avg} $$ for sine).

• True RMS-responding: Uses thermal or electronic conversion (e.g., square-law device, converter IC) to measure heating value directly. Reads RMS correctly for any waveform.

• Peak-responding: Uses a peak detector circuit. Holds peak value; may include a sample-and-hold.

Digital Voltmeters (DVM)

Principle: Convert analog voltage to digital code using an ADC and display numerically.

Digits & Resolution (JUN 2025, JUN 2023, DEC 2023):

• A 3½ digit DVM can display 3 full digits (0-9) and a ½ digit (usually 0 or 1).

• Resolution = $$\displaystyle \frac{1}{\text{Full Scale Range} \times 10^{\text{(number of full digits)}}} $$.

  • Example: 10V range on a 3½ digit DVM (3 full digits) → Resolution = $$\displaystyle \frac{1}{10V \times 10^3} = 1mV $$.

• Significance of ½ digit: It indicates the maximum possible first digit (over-range capability). A ½ digit can only be 0 or 1, so the maximum reading is 1999 counts (for a 3½ digit). It defines the counts or overflow point.

Sensitivity: Smallest change in input voltage that causes a one-count change in display. For a 3½ digit, 10V range: Sensitivity = 1mV.

Types of DVMs (ADCs)

1. Dual Slope Integrating Type ADC (DEC 2024)

• Block Diagram: Input → Integrator → Comparator → Control Logic → Counter & Clock → Digital Output.

• Working:

  • Phase 1 (Fixed time $$\displaystyle T_1 $$): Input voltage $$\displaystyle V_i $$ integrated. Output slope $$\displaystyle \propto V_i $$.

  • Phase 2 (Variable time $$\displaystyle T_2 $$): Reference voltage $$\displaystyle -V_{ref} $$ integrated. Output slope $$\displaystyle \propto -V_{ref} $$. Counter counts until integrator output returns to zero.

  • Result: $$\displaystyle T_2 \propto V_i $$. Digital output = Count in $$\displaystyle T_2 $$.

• Advantages: High noise rejection (integrates input), high accuracy, cost-effective.

2. Successive Approximation ADC (SAR) (JUN 2025, JUN 2023, NOV 2022)

• Block Diagram: Sample & Hold → Comparator → Successive Approximation Register (SAR) → DAC → Digital Output.

• Working: SAR starts with MSB=1, others=0. DAC output compared to input. If DAC < input, bit is retained; else, reset. Proceeds to next bit (MSB-1). n-bit conversion takes exactly n clock cycles.

• Conversion Time: $$\displaystyle T_{conv} = n \times T_{clock} $$.

3. Simultaneous (Flash) Type ADC (JUN 2024)

• Principle: Uses $$\displaystyle 2^n - 1 $$ comparators for n-bit conversion. Each comparator compares input with a reference from a resistor ladder.

• Conversion Logic: Priority encoder converts the highest-order active comparator's output to binary code.

• Advantage: Fastest conversion (propagation delay only).

• Disadvantage: Exponential increase in comparators with bits (cost, power).

4. Counter Type ADC (NOV 2022)

• Working: Simple up-counter drives a DAC. Comparator output controls counter clock enable. Counter increments until DAC output ≈ input. Slow (max $$\displaystyle 2^n $$ clock cycles).

Comparison of ADC Types (Clock Pulses Required):

III. CATHODE RAY OSCILLOSCOPE (CRO) & SPECIAL PURPOSE OSCILLOSCOPES

General Purpose CRO

Block Diagram:

[Vertical Amplifier] → [Delay Line] → [Horizontal Amplifier]

         ↑                      ↓

[Probe]      [Trigger Circuit]      [Time Base Generator (Sweep)]

         ↓                      ↑

[CRT (Display)] ← [Horizontal Deflection] ← [Sweep Signal]

CRT Construction:

1. Electron Gun: Cathode (heated emitter) → Control Grid (intensity control) → Focusing Anode (electrostatic/electromagnetic) → Accelerating Anode.

2. Deflection System: Electrostatic (plates) for most CROs. Electromagnetic (yokes) for TV/monitors.

3. Fluorescent Screen: Converts electron beam energy to visible light (phosphor).

Electrostatic Focusing & Deflection:

• Focusing: Voltage on focusing anode creates electrostatic field that converges electron beam to a fine spot.

• Deflection: Voltage on Y-plates moves beam vertically; voltage on X-plates moves beam horizontally.

Probes (DEC 2023):

• Importance: Isolate CRO from circuit, minimize loading (capacitance/resistance), protect CRO.

• Types: 1:1 (direct), 10:1 (most common).

• 10:1 Probe Circuit: Series resistor (9MΩ) in probe, parallel capacitor (compensation capacitor) matches scope input capacitance (≈20pF). Creates 10:1 voltage divider, reduces loading.

Graticules (DEC 2023): Grid lines on CRT face for measurement. Typically 1cm x 1cm grid with finer subdivisions (e.g., 0.2cm).

Special Purpose CROs

1. Dual Beam vs. Dual Trace CRO (DEC 2023, DEC 2024)

2. Dual Trace CRO Operation (JUN 2025, NOV 2022)

• Chopping Mode: Fast electronic switch (≈1MHz) alternately connects channel A and B to vertical amplifier. Suitable for low-frequency signals.

• Alternate Mode: Sweep completes for channel A, then for channel B. Suitable for high-frequency signals.

• Circuit: Electronic switch (e.g., FETs) controlled by gate signal from time base.

3. Sampling Oscilloscope (DEC 2024, NOV 2022)

• Principle: For very high-frequency signals (>1GHz) beyond direct amplifier bandwidth. Takes one sample per trigger from successive cycles, builds up waveform slowly.

• Circuit: Sample-and-hold circuit, strobe pulse (very narrow, synchronized to input), storage (e.g., CRT with long-persistence phosphor or digital memory). Effective bandwidth determined by sampling rate, not amplifier.

4. Digital Storage Oscilloscope (DSO) (JUN 2025, DEC 2024)

• Block Diagram: Probe → Vertical Amplifier & ADC → Memory (FIFO/Block) → Microprocessor/Controller → Display (LCD). Trigger circuit controls sampling start.

• Working: Analog signal sampled at high rate, digitized, stored in memory. Digital signal processing (FFT, measurements) possible. Waveform can be stored/recalled indefinitely.

Applications of CRO:

• Voltage/time waveform display.

• Frequency & phase measurement (using Lissajous patterns).

• Timing measurements (rise time, pulse width).

• Debugging digital circuits (logic analyzer mode).

• Displaying characteristics (e.g., transistor curves with curve tracer).

IV. BRIDGE CIRCUITS FOR IMPEDANCE MEASUREMENT

AC Bridges - General

Balance Condition: $$\displaystyle Z_1 Z_4 = Z_2 Z_3 $$ (product of opposite arms). In polar form: $$\displaystyle |Z_1||Z_4| = |Z_2||Z_3| $$ and $$\displaystyle \angle Z_1 + \angle Z_4 = \angle Z_2 + \angle Z_3 $$. Bridge Sensitivity: Deflection of detector (e.g., galvanometer) per unit change in unknown parameter. Maximum sensitivity occurs when bridge is balanced and detector impedance is matched to bridge arms. For a detector with resistance $$\displaystyle R_g $$, sensitivity max when $$\displaystyle R_g = \sqrt{R_2 R_3} $$ (for simple resistive bridges).

Detectors for AC Bridges:

• Tuned phones: For audio frequency, sensitive at resonance.

• VTVM (Vacuum Tube Voltmeter): Broadband, sensitive.

• CRO: Visual, wide frequency range.

Specific Bridges

1. Wien Bridge (JUN 2024, DEC 2024)

• Use: Frequency measurement in audio range (20Hz-20kHz), also used in RC oscillators.

• Circuit: Series RC ($$\displaystyle R_1, C_1 $$) in one arm, parallel RC ($$\displaystyle R_2, C_2 $$) in adjacent arm. Other two arms are pure resistors ($$\displaystyle R_3, R_4 $$).

• Balance Equations:

$$R_4 = \frac{R_1}{R_2} R_3 \quad \text{and} \quad C_4 = \frac{C_1 R_2}{R_1}$$

For **frequency measurement**, set $$\displaystyle R_1 = R_2 = R $$, $$\displaystyle C_1 = C_2 = C $$. Then balance occurs when:

$$f = \frac{1}{2\pi RC}$$

At balance, detector shows null.

2. Schering Bridge (JUN 2025, JUN 2024, DEC 2023)

• Use: Measurement of unknown capacitance and dissipation factor (tan δ) of capacitors and insulators.

• Circuit: Unknown $$\displaystyle C_x $$ (with loss $$\displaystyle R_x $$) in one arm. Known capacitor $$\displaystyle C_3 $$ in adjacent arm. Two resistors $$\displaystyle R_1, R_2 $$ (or $$\displaystyle R_1, R_2, C_2 $$) in other arms.

• Balance Equations:

$$C_x = \frac{C_3 R_1}{R_2}, \quad R_x = \frac{C_2 R_2}{C_3}$$

Dissipation factor $$\displaystyle \tan \delta = \frac{1}{\omega R_x C_x} = \omega C_2 R_2 $$.

• Operation: Adjust $$\displaystyle R_1 $$ and $$\displaystyle C_2 $$ (or $$\displaystyle R_2 $$) for null.

3. Hay's Bridge (JUN 2025, DEC 2024, JUN 2023)

• Use: Measurement of inductance with high Q factor (Q > 10).

• Circuit: Unknown $$\displaystyle L_x $$ (with series resistance $$\displaystyle R_x $$) in one arm. Known capacitor $$\displaystyle C_4 $$ in adjacent arm. Resistors $$\displaystyle R_1, R_2, R_3 $$ in other arms.

• Balance Equations:

$$L_x = \frac{R_2 R_3}{2\pi f C_4 R_1}, \quad R_x = \frac{R_2 R_3}{R_1}$$

*Note:* $$\displaystyle R_1 $$ is the series resistance of the inductor arm. Bridge gives **series equivalent** of coil.

4. Maxwell's Inductance Capacitance Bridge (DEC 2023)

• Use: Measurement of inductance (medium Q).

• Limitation for High Q Coils: Balance condition involves $$\displaystyle R_2 $$ (known resistor) and $$\displaystyle R_4 $$ (variable standard resistor). For high Q ($$\displaystyle \omega L_x \gg R_x $$), $$\displaystyle R_4 $$ becomes very large and difficult to obtain accurately.

Q-Meter

Principle: Series resonant circuit. At resonance, $$\displaystyle X_L = X_C $$, voltage across capacitor $$\displaystyle V_C = Q \times V_{source} $$. By measuring $$\displaystyle V_C $$ (with voltmeter calibrated in Q), Q-factor is found. Circuit: Coil under test $$\displaystyle L_x $$ with $$\displaystyle R_x $$ in series with a known capacitor $C$ and a source $$\displaystyle V_{source} $$. Voltmeter across $C$.

Impedance Measurement by Q-Meter:

1. Q Measurement: Adjust $C$ to resonance (max $$\displaystyle V_C $$), read Q.

2. Inductance $$\displaystyle L_x $$: From resonance frequency $$\displaystyle f_0 = \frac{1}{2\pi \sqrt{L_x C}} $$.

3. Effective Resistance $$\displaystyle R_x $$: $$\displaystyle R_x = \frac{2\pi f_0 L_x}{Q} $$.

"Parallel-connection" Method (JUN 2024, NOV 2022):

• Coil is connected in parallel with a known capacitor $$\displaystyle C_n $$ and a small known resistor $$\displaystyle R_n $$.

• Expressions:

$$R_p = \frac{R_n Q^2}{Q^2 + 1}, \quad X_p = \frac{R_n Q}{\sqrt{Q^2 + 1}}, \quad Q = \frac{X_p}{R_p}$$

Where $$\displaystyle R_p, X_p $$ are the parallel equivalent resistance and reactance of the coil.

V. TRANSDUCERS

Introduction

Transducer: A device that converts a physical quantity (non-electrical) into an electrical signal (or vice versa). Classification (JUN 2025, DEC 2023):

• Active/Primary: Self-generating (e.g., Thermocouple, Piezoelectric).

• Passive/Secondary: Requires external power (e.g., Strain gauge, LVDT, Thermistor).

• Analog/Digital.

• Input/Output: Displacement, force, temperature, light → Electrical.

Electromagnetic Transducers

LVDT - Linear Variable Differential Transformer (DEC 2024, JUN 2024, JUN 2023)

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

• Working: AC excitation to primary. Core position determines coupling to secondaries.

  • Null Position: EMFs in secondaries equal & opposite → $$\displaystyle V_{out}=0 $$.

  • Displacement Right/Left: EMFs unequal → $$\displaystyle V_{out} \neq 0 $$. Phase indicates direction.

• Output vs Displacement: Linear over small range around null. Infinite resolution theoretically.

• Advantages: Non-contact, infinite resolution, rugged, linear.

Piezoelectric Transducers (DEC 2024)

• Principle: Piezoelectric effect (direct): Certain crystals (Quartz, Rochelle salt, PZT) generate charge on surfaces when mechanically stressed.

• Modes of Operation:

  • Thickness Mode: Stress applied perpendicular to faces (common).

  • Length Mode: Stress along length.

  • Shear Mode: Stress tangential.

• Equivalent Circuit: Charge source $q$ in parallel with capacitor $$\displaystyle C_p $$ (crystal capacitance) and resistor $$\displaystyle R_p $$ (leakage).

• Applications: Accelerometers (mass on crystal → force ∝ acceleration), pressure sensors, microphones, buzzers.

• Definitions:

  • Binders: Crystals that generate charge when compressed (e.g., Quartz).

  • Twisters: Crystals that generate charge when twisted (shear mode).

Optical Transducers (DEC 2023, JUN 2024)

Photodiode (DEC 2024, NOV 2022):

• Construction: PN junction with transparent window.

• Working (Reverse Bias): Photocurrent ∝ light intensity. Fast response.

• Phototransistor: Photodiode base current controls transistor current → higher gain, slower.

Thermal Transducers

Thermistor (JUN 2024, NOV 2022):

• Definition: Temperature-sensitive resistor (semiconductor). NTC (Negative Temp Coeff) most common: Resistance ↓ with Temp ↑.

• Importance: High sensitivity (large ΔR/ΔT), small size, low cost.

• Advantages: High sensitivity, fast response (small size), low cost.

• Disadvantages: Non-linear, self-heating, limited temperature range.

• Applications: Temperature measurement/compensation, inrush current limiter, temperature compensation in bridges.

Thermocouple (JUN 2025):

• Principle: Seebeck effect: Two dissimilar metals joined at two junctions produce a voltage proportional to temperature difference between junctions.

• Cold Junction Compensation: Reference junction must be at known temperature (often 0°C ice bath or electronic compensation).

Bolometer (NOV 2022):

• Principle: Absorption of radiation (IR, microwave) causes heating → change in resistance of a material (e.g., thermistor or thin metal film).

• Use: Power measurement, radiation detection.

Display & Output Transducers

1. LED - Light Emitting Diode (JUN 2025)

• Principle: Electroluminescence. Forward biased PN junction, electrons & holes recombine in active region, emitting light (color depends on bandgap).

• Construction: PN junction, often with epoxy lens.

• Applications: Indicator lamps, 7-segment displays, IR emitters, traffic lights.

2. LCD - Liquid Crystal Display (JUN 2025, DEC 2024, DEC 2023)

• Working Principle: Liquid crystals (nematic) twist polarized light. Twisted Nematic (TN) type: Alignment layers at 90°. Without field, crystals twist light 90° → light passes through second polarizer (bright). With field, crystals align → no twist → light blocked (dark).

• Types: TN, STN (Super Twisted Nematic), TFT (Active Matrix).

• Advantages: Low power consumption, no self-emission (good for battery), wide viewing angle (TFT), no geometric distortion.

• Disadvantages: Slow response (ms), limited temperature range, needs backlight (passive), viewing angle dependent (TN).

Classification of Display Devices:

• LED: Active (emits light), high brightness, fast, high power.

• LCD: Passive (modulates light), low power, needs backlight, slower.

VI. SIGNAL GENERATORS & WAVEFORM GENERATORS

Sweep Frequency Generator (AF/RC Oscillator) (JUN 2025, DEC 2023)

• Block Diagram: RC Oscillator (Wein Bridge or Phase Shift) → Voltage-Controlled Oscillator (VCO) or Variable RC → Sweep Circuit (ramp generator) → Output Amplifier & Attenuator.

• Working Principle: Generates a sinusoidal output whose frequency varies smoothly and continuously over a specified range (e.g., 20Hz-20kHz). Sweep rate controlled by a ramp voltage applied to VCO or by mechanically varying RC components.

• Applications: Frequency response testing of amplifiers/filters, Bode plotter.

Pulse/Function Generators (DEC 2024)

• Pulse Wave Generator Block Diagram: Time Base (ramp/step) → Voltage-Controlled Switch → Multivibrator (monostable/astable) → Pulse Shaping → Output Amplifier.

• Working: A ramp or step voltage controls the switching point of a multivibrator, determining pulse width and repetition rate. Can generate square waves, pulses with variable duty cycle.

VII. DIGITAL-TO-ANALOG CONVERTERS (DAC)

Weighted Resistor DAC (DEC 2023, NOV 2022)

• Circuit (4-bit): Digital inputs $$\displaystyle D_3...D_0 $$ control switches to resistors $R, 2R, 4R, 8R$ (weighted). All resistors connect to summing junction of op-amp.

• Output Voltage Equation:

$$V_o = -\frac{V_{ref}}{R} \left( \frac{D_3}{2} + \frac{D_2}{4} + \frac{D_1}{8} + \frac{D_0}{16} \right) R$$

Simplifies to: $$\displaystyle V_o = -V_{ref} \left( \frac{D_3}{2} + \frac{D_2}{4} + \frac{D_1}{8} + \frac{D_0}{16} \right) $$

• Transfer Characteristic: Staircase. Step size (LSB) = $$\displaystyle \frac{V_{ref}}{2^n} $$.

• Disadvantage: Requires precision resistors with exact binary ratios (hard for high bits).

R-2R Ladder DAC (JUN 2025, DEC 2024, JUN 2024, NOV 2022)

• Circuit (4-bit): Ladder of R and 2R resistors. Each bit controls a switch to either $$\displaystyle V_{ref} $$ or ground at a ladder node.

• Working Principle: Uses Thevenin equivalence. Each bit sees equivalent resistance of 2R looking into the ladder, simplifying analysis.

• Output Voltage (for n-bit, $$\displaystyle V_{ref} $$ positive for '1'):

$$V_o = V_{ref} \left( \frac{D_{n-1}}{2} + \frac{D_{n-2}}{4} + ... + \frac{D_0}{2^n} \right)$$

• Advantage: Only two resistor values (R and 2R) needed, easy to fabricate with good matching.

• Calculation Example (DEC 2024):

  • Step size (LSB) = $$\displaystyle \frac{V_{ref}}{2^n} = \frac{5V}{16} = 0.3125V $$.

  • Input 0111 (binary 7): $$\displaystyle V_o = 5 \times (0 + \frac{1}{4} + \frac{1}{8} + \frac{1}{16}) = 5 \times 0.4375 = 2.1875V $$.

  • Input 1111 (binary 15): $$\displaystyle V_o = 5 \times (0.5+0.25+0.125+0.0625) = 5 \times 0.9375 = 4.6875V $$.

VIII. ANALOG-TO-DIGITAL CONVERTERS (ADC)

Successive Approximation ADC (SAR) (JUN 2025, JUN 2023, NOV 2022)

• Block Diagram: Sample & Hold → Comparator → SAR (Logic) → DAC → Digital Output.

• Detailed Operation:

  1. Sample input $$\displaystyle V_i $$ (S/H holds).

  2. SAR sets MSB=1, others=0. DAC gives $$\displaystyle V_{DAC} = V_{ref}/2 $$.

  3. Compare $$\displaystyle V_{DAC} $$ with $$\displaystyle V_i $$.

     • If $$\displaystyle V_{DAC} < V_i $$: Keep MSB=1.

     • If $$\displaystyle V_{DAC} > V_i $$: Reset MSB=0.

  4. Set next bit (MSB-1) to 1, repeat comparison.

  5. Continue for all n bits.

• Conversion Time: $$\displaystyle T_{conv} = n \times T_{clock} $$ (fixed, predictable).

Dual Slope (Integrating) ADC (DEC 2024)

• Block Diagram: Input → Switch (to $$\displaystyle V_i $$ or $$\displaystyle -V_{ref} $$) → Integrator → Comparator → Control Logic → Counter & Clock.

• Operation:

  • Phase 1 ($$\displaystyle T_1 $$ fixed): Integrate $$\displaystyle V_i $$ → output slope $$\displaystyle \propto V_i $$.

  • Phase 2 ($$\displaystyle T_2 $$ variable): Integrate $$\displaystyle -V_{ref} $$ → output slope $$\displaystyle \propto -V_{ref} $$. Counter counts until integrator output returns to zero.

  • Digital Output: Count in $$\displaystyle T_2 $$ ∝ $$\displaystyle V_i $$.

• Advantages: Excellent noise rejection (integrates input), high accuracy, independent of clock frequency accuracy (only needs stable $$\displaystyle T_1 $$ and $$\displaystyle V_{ref} $$).

Flash (Simultaneous) ADC (JUN 2024)

• Principle: $$\displaystyle 2^n - 1 $$ comparators, each with reference from resistor ladder ($$\displaystyle V_{ref}/2^n $$ steps).

• Conversion Logic: Comparator outputs fed to priority encoder. Highest-order '1' output determines digital code.

• Comparison: Fastest (propagation delay only), but complexity grows exponentially with bits. Used for very high-speed applications (video, radar).

Counter Type ADC (NOV 2022)

• Simple: Up-counter drives DAC. Comparator enables counter clock until $$\displaystyle V_{DAC} \ge V_i $$.

• Conversion Time: Up to $$\displaystyle 2^n $$ clock cycles (worst case). Slow but simple.

Resolution of ADC (DEC 2023)

• Definition: Smallest change in input voltage that changes output code by 1 LSB.

• Formula: $$\displaystyle \text{Resolution} = \frac{V_{FS}}{2^n} $$ or $$\displaystyle \frac{V_{FS}}{2^n - 1} $$ (for bipolar).

• Example (DEC 2023): 5-bit ADC, range 10V.

  • Resolution = $$\displaystyle \frac{10V}{2^5} = \frac{10}{32} = 0.3125V $$.

  • Range for MSB (bit 4): 5V to 10V (since MSB weight = $$\displaystyle V_{FS}/2 $$).

  • % Error in conversion: Ideally ½ LSB max error = $$\displaystyle \frac{0.5 \times 0.3125}{10} \times 100\% = 1.5625\% $$.