Oscilloscopes and Time/Frequency Measurement – GATE Exam Quick Notes

Cathode Ray Oscilloscope (CRO)

CRO - Basic Principle

  • Electron beam deflected by electric field

  • X-axis: Time base (horizontal deflection)

  • Y-axis: Signal amplitude (vertical deflection)

  • Phosphor screen displays waveform

  • Persistence of vision creates continuous display

  • Deflection factor: \(D = \frac{V_d}{V_s}\) (V/cm)

CRO - Block Diagram Components

  • Electron Gun: Cathode, control grid, focusing anode

  • Deflection System: Vertical and horizontal plates

  • Phosphor Screen: Converts electron energy to light

  • Vertical Amplifier: Amplifies input signal

  • Horizontal Amplifier: Time base generator

  • Power Supply: High voltage for CRT operation

  • Graticule: Calibrated scale for measurements

CRO - Electron Gun

  • Cathode: Emits electrons when heated (thermionic emission)

  • Control Grid: Controls electron beam intensity (brightness)

  • Pre-accelerating Anode: Accelerates electrons (A1)

  • Focusing Anode: Focuses electron beam (A2)

  • Accelerating Anode: Final acceleration 1000-4000V (A3)

  • Aquadag coating: Provides uniform potential

CRO - Deflection System

  • Vertical Deflection: Y-plates, signal amplitude

  • Horizontal Deflection: X-plates, time base

  • Electrostatic Deflection: Used in CRO

  • Magnetic Deflection: Used in TV tubes

  • Deflection sensitivity: \(S = \dfrac{l \cdot L}{2 \cdot d \cdot V_a}\)

  • Deflection factor: \(G = \frac{1}{S}\) (V/cm)

CRO - Phosphor Screen Properties

  • Phosphor types: P1 (green), P2 (blue-green), P7 (blue)

  • Persistence: Time for brightness to decay to 10%

  • Short persistence: Fast transients (P2)

  • Long persistence: Slow phenomena (P7)

  • Luminescence: Light emission during electron bombardment

  • Phosphorescence: Light emission after excitation stops

Digital Storage Oscilloscope (DSO)

DSO - Advantages over CRO

  • Storage and recall capability

  • Digital processing and analysis

  • Automatic measurements

  • Computer interface (USB, Ethernet)

  • Better accuracy and stability

  • No phosphor burning

  • Portable and lightweight

  • Pre-trigger capture capability

DSO - Block Diagram

  • Input Attenuator: Signal conditioning

  • Sample and Hold: Captures instantaneous values

  • ADC: Analog to Digital Converter (8-12 bits)

  • Memory: Stores digital samples (acquisition memory)

  • Microprocessor: Controls operations

  • Display: LCD/LED screen

  • Trigger circuit: Digital triggering

DSO - Sampling Techniques

  • Real-time Sampling: High sampling rate (single-shot)

  • Equivalent-time Sampling: For repetitive signals

  • Random Sampling: For non-repetitive signals

  • Nyquist Theorem: \(f_s \geq 2f_{max}\)

  • Aliasing: Sampling rate too low, causes false frequencies

  • Interpolation: Sin(x)/x or linear reconstruction

DSO - Memory and Acquisition

  • Record length: Number of samples stored

  • Memory depth: Total storage capacity

  • Acquisition modes: Sample, Peak detect, Average

  • Waveform math: Add, subtract, multiply, FFT

  • Persistence display: Overlapping waveforms

  • Zoom function: Time base expansion

Time Measurements

Time Period Measurement

  • Time between two identical points on waveform

  • \(T = \dfrac{\text{No. of divisions} \times \text{Time/division}}{1}\)

  • Frequency: \(f = \dfrac{1}{T}\)

  • Phase difference: \(\phi = \dfrac{\Delta t}{T} \times 360^{\circ}\)

  • Rise time: 10% to 90% of final value

  • Fall time: 90% to 10% of final value

  • Propagation delay: Signal travel time

Time Base Generator

  • Provides horizontal deflection voltage

  • Sawtooth waveform for linear sweep

  • Triggered sweep for stable display

  • Time/division control (1 sec/div to 1 ns/div)

  • Sweep rates: \(1 \mathrm{sec/div}\) to \(1 \mathrm{\mu s/div}\)

  • External trigger capability

  • Delayed sweep: Magnified time base

Triggering

  • Auto Trigger: Automatic triggering

  • Normal Trigger: Manual trigger level

  • Single Trigger: One-shot display

  • Edge Trigger: Rising/falling edge

  • Level Trigger: Specific voltage level

  • Slope: Positive or negative

  • Trigger holdoff: Prevents multiple triggers

Frequency Measurements

Direct Frequency Measurement

  • Using time period: \(f = \dfrac{1}{T}\)

  • Count cycles in known time

  • Electronic counter method

  • Gate time selection important

  • Accuracy depends on crystal oscillator

  • Resolution: \(\Delta f = \dfrac{1}{\text{Gate time}}\)

  • Prescaler: For high frequency division

Lissajous Patterns

  • X-Y mode operation

  • Two sinusoidal signals applied

  • Frequency ratio determination

  • \(\dfrac{f_x}{f_y} = \dfrac{\text{Vertical\ tangencies}}{\text{Horizontal\ tangencies}}\)

  • Phase difference measurement: \(\sin \phi = \frac{a}{b}\)

  • Stable patterns for integer ratios

  • Circle: Same frequency, 90° phase difference

Frequency Counter

  • Input Signal Conditioning: Amplification, filtering

  • Schmitt Trigger: Converts to digital pulses

  • Gate Circuit: Controls counting time

  • Counter: Counts pulses (BCD counters)

  • Display: Shows frequency value (7-segment)

  • Time Base: Crystal oscillator reference (10 MHz)

  • Decade dividers: Generate gate times

Oscilloscope Specifications

Key Specifications

  • Bandwidth: Maximum frequency response (-3dB point)

  • Rise Time: \(t_r = \dfrac{0.35}{BW}\) (10-90% rise time)

  • Sensitivity: Minimum detectable signal (mV/div)

  • Accuracy: Measurement precision (±2% typical)

  • Input Impedance: Typically \(1~\mathrm{M \Omega} || 20~\mathrm{pF}\)

  • Sampling Rate: For DSO (MSa/s, GSa/s)

  • Vertical resolution: ADC bits (8-12 bits)

Probes and Accessories

  • 1:1 Probe: Direct connection, low frequency

  • 10:1 Probe: Reduces loading, high frequency

  • 100:1 Probe: High voltage measurements

  • Current Probes: Measure current without breaking circuit

  • Differential Probes: Common mode rejection

  • Probe Compensation: Square wave calibration (1 kHz)

  • Probe loading: \(R_{probe} || C_{probe}\)

Advanced Measurements

Pulse Measurements

  • Pulse width: Time between 50% points

  • Duty cycle: \(D = \frac{t_{on}}{T} \times 100\%\)

  • Rise time: 10% to 90% of amplitude

  • Fall time: 90% to 10% of amplitude

  • Overshoot: Percentage above final value

  • Undershoot: Percentage below final value

  • Preshoot: Distortion before main pulse

AC Measurements

  • Peak-to-peak voltage: \(V_{pp}\)

  • RMS value: \(V_{rms} = \frac{V_{pp}}{2\sqrt{2}}\) (sine wave)

  • Average value: \(V_{avg} = \frac{2V_{peak}}{\pi}\) (sine wave)

  • Crest factor: \(CF = \frac{V_{peak}}{V_{rms}}\)

  • Form factor: \(FF = \frac{V_{rms}}{V_{avg}}\)

  • Distortion factor: THD measurement

Digital Signal Analysis

  • Logic states: High/Low levels

  • Setup time: Data stable before clock edge

  • Hold time: Data stable after clock edge

  • Propagation delay: Input to output delay

  • Timing violations: Setup/hold violations

  • Eye diagram: Data quality assessment

  • Jitter measurement: Timing variations

Specialized Oscilloscopes

Mixed Signal Oscilloscope (MSO)

  • Combines analog and digital channels

  • Typically 2-4 analog + 16 digital channels

  • Synchronized sampling of both domains

  • Protocol analysis capability

  • Logic analyzer functionality

  • Trigger on digital patterns

  • Applications: Microcontroller debugging

Sampling Oscilloscope

  • Very high bandwidth (>50 GHz)

  • Sequential sampling technique

  • Requires repetitive signals

  • Lower real-time sampling rate

  • Equivalent time sampling: Builds waveform over multiple cycles

  • Applications: High-speed digital, RF signals

  • Limitation: Cannot capture single-shot events

PC-Based Oscilloscope

  • USB/PCI/Ethernet interface

  • Uses computer display and processing

  • Cost-effective solution

  • Software-based analysis

  • Advantages: Portability, upgradability

  • Disadvantages: Limited real-time performance

  • Applications: Education, field service

Measurement Errors and Limitations

Oscilloscope Loading Effects

  • Input impedance: \(R_{in} || C_{in}\)

  • Loading error: Due to finite input impedance

  • Frequency response: Affected by input capacitance

  • Probe compensation: Minimizes loading

  • High impedance rule: \(R_{source} << R_{input}\)

  • Bandwidth limitation: Signal distortion

Common Measurement Errors

  • Bandwidth limitation: Signal distortion

  • Probe loading: Circuit modification

  • Ground loops: Noise pickup

  • Trigger jitter: Unstable display

  • Quantization noise: ADC limitation (DSO)

  • Aliasing: Insufficient sampling rate

  • Interpolation errors: Waveform reconstruction

Applications and Measurements

Common Measurements

  • Voltage: Peak, RMS, average values

  • Time: Period, frequency, phase

  • Waveform Analysis: Shape, distortion

  • Transient Response: Step response

  • Pulse Measurements: Width, duty cycle

  • Frequency Response: Bode plots

  • Harmonic analysis: FFT spectrum

Special Applications

  • Digital Signal Analysis: Logic states, timing

  • Modulation Analysis: AM, FM, PM

  • Power Measurements: VI products, power factor

  • Spectrum Analysis: FFT capability

  • Protocol Analysis: Serial communication (SPI, I2C)

  • Automotive: CAN, LIN bus analysis

  • EMI/EMC testing: Electromagnetic compatibility

GATE Specific Topics

CRO Mathematical Relations

  • Deflection sensitivity: \(S = \frac{l \cdot L}{2 \cdot d \cdot V_a}\)

  • Deflection factor: \(G = \frac{1}{S}\)

  • Bandwidth-rise time: \(BW = \frac{0.35}{t_r}\)

  • Sampling theorem: \(f_s \geq 2f_{max}\)

  • Phase from Lissajous: \(\sin \phi = \frac{a}{b}\)

  • Resolution: \(\Delta f = \frac{1}{\text{Gate time}}\)

GATE Important Points

  • CRO vs DSO comparison

  • Sampling theorem and aliasing

  • Probe compensation necessity

  • Bandwidth-rise time relationship

  • Lissajous pattern analysis

  • Triggering modes and applications

  • Time base generator operation

  • Frequency measurement methods

  • Loading effects and probe selection

Common GATE Questions

  • Deflection sensitivity calculations

  • Probe attenuation effects

  • Sampling rate requirements

  • Frequency ratio from Lissajous patterns

  • Rise time from bandwidth

  • Phase measurement techniques

  • Counter gate time selection

  • Oscilloscope loading effects

  • Aliasing frequency calculation

Numerical Problem Types

  • Given bandwidth, find rise time

  • Calculate deflection sensitivity

  • Determine sampling rate to avoid aliasing

  • Phase difference from time delay

  • Frequency resolution from gate time

  • Probe compensation calculations

  • Loading effect on measurement

  • Lissajous pattern frequency ratio

Summary

  • Oscilloscopes: Essential measurement instruments

  • CRO: Analog, real-time display

  • DSO: Digital, storage capability

  • Time measurement: Period, frequency, phase

  • Frequency measurement: Direct and indirect methods

  • Proper probe selection crucial

  • Understanding specifications important

  • Loading effects must be considered