How to Operate the Simulator
This virtual laboratory provides a dual-perspective view of electron beam electrodynamics. The left panel models the inner physical cutaway of a glass vacuum envelope Cathode Ray Tube (CRT), while the right panel renders the calibrated front panel 8×10 graticule display of a benchtop Cathode Ray Oscilloscope (CRO).
- Inspect Tube Stages: Use the camera presets (Entire CRO, Electron Gun, Deflection System, Phosphor Display) to zoom into specific subsystems. Hover the mouse cursor over any mechanical component to inspect its physical function and operating voltage.
- Regulate Electron Flow: In Tab 1, adjust the Filament Heater Temp to boil off electrons. Modify the Control Grid Bias (Vg) between 0 V and -110 V. When bias approaches -90 V (cutoff), note how thermal electrons crowd and form a static space-charge pool behind the aperture without streaming forward.
- Tune Focus & Acceleration: Shift the Focusing Anode (Vf) to achieve a sharp focal waist on the screen. Vary the Accelerating Anode (Va) to witness how higher kinetic energy increases beam stiffness, causing the vertical deflection amplitude to compress for identical input voltages.
- Select Waveforms & Modes: In Tab 3, choose between sinusoidal AC, pure DC, half-wave, full-wave, square, or triangular waveforms. In the Deflection Mode toolbar, isolate timebase-only (horizontal line), signal-only (vertical line), stationary spot, or both axes simultaneously.
- Calibrate Graticule Readings: In Tab 2, alter Y-Gain (Volts/Div) and Timebase (Time/Div). Adjust Phosphor Persistence to see lingering beam trails, and dial Graticule Illumination to balance grid visibility against ambient contrast.
Scientific Theory & Working Principles
1. Thermionic Emission & Space Charge Formation
The electron gun originates at an indirectly heated oxide-coated cathode sleeve (barium and strontium oxides on a nickel cylinder). When energized by an internal coiled tungsten filament at approximately 900 °C to 1050 °C, electrons absorb sufficient thermal energy to overcome the material work function (Phi ≈ 1.2 eV). In the presence of a strong negative potential on the surrounding Wehnelt cylinder (control grid), emitted electrons cannot escape into the forward field; instead, they accumulate in front of the emitting surface as a dense space-charge cloud, governed by the Richardson-Dushman and Child-Langmuir relationships.
2. Coaxial Electrostatic Cylindrical Lens
The beam passes through the drilled central pinhole of the Wehnelt cylinder into two or three coaxial cylindrical anodes. By maintaining the first focusing cylinder at an intermediate potential (e.g., +400 V to +600 V) while the pre-accelerating and accelerating cylinders are elevated to +1500 V to +3000 V, non-uniform curved electrostatic equipotential surfaces are established across the gap. The curved electric field components exert inward radial forces (Fr = -e · Er) that bend divergent electron trajectories back toward the central tube axis, converging the beam into a minimal waist diameter at the plane of the phosphor screen.
3. Orthogonal Electrostatic Deflection
The high-velocity, collimated beam travels into two orthogonal sets of metallic parallel plates:
- Y-Plates (Vertical Deflection): Positioned horizontally with an electric field oriented vertically. When an input voltage signal Vd is applied, electrons experience a vertical transverse electrostatic force Fy = e · Ey = e · (Vd / d), causing a parabolic trajectory while within the plate field and a straight drift trajectory thereafter.
- X-Plates (Horizontal Timebase Sweep): Positioned vertically with an electric field oriented horizontally. An internal sweep generator feeds a linear sawtooth voltage ramp (Vx proportional to t) to sweep the spot steadily from left to right, followed by a rapid flyback during which the grid is blanked off.
4. Phosphor Screen Luminescence
Upon reaching the front glass faceplate, energetic electrons collide with a thin polycrystalline inorganic phosphor layer (such as P31 zinc sulfide activated with copper, ZnS:Cu). The kinetic energy of each electron excites lattice electrons across the phosphor bandgap. As these excited states relax through recombination centers, visible photons (green, ~525 nm) are released via fluorescence (prompt emission within nanoseconds) and phosphorescence (delayed luminescence lasting tens of milliseconds). A grounded conductive graphite coating (Aquadag) coats the funnel interior to collect secondary electrons and prevent negative charge accumulation on the faceplate.
Mathematical Foundations & Formulas
Quantitative analysis of the electron beam and oscilloscope graticule relies on fundamental classical electrodynamics. All calculations avoid raw formatting symbols:
Kinetic Energy: Ek = e · Va = 0.5 · m_e · v²
Velocity: v = √((2 · e · Va) / m_e)
where e = 1.6022 × 10⁻¹⁹ C, m_e = 9.1094 × 10⁻³¹ kg, Va = accelerating anode potential.
Formula 2 (Transit Time Through Deflection Plates):
Transit Time: t_p = l / v = l · √(m_e / (2 · e · Va))
where l = axial plate length.
Formula 3 (Total Screen Deflection):
Transverse Displacement: D = (l · L · Vd) / (2 · d · Va)
where L = drift distance from plate center to screen, d = plate separation distance, Vd = applied deflection voltage.
Formula 4 (Deflection Sensitivity & Factor):
Deflection Sensitivity: S = D / Vd = (l · L) / (2 · d · Va) [units: mm/V or cm/V]
Deflection Factor: G = 1 / S = (2 · d · Va) / (l · L) [units: V/cm]
Formula 5 (Oscilloscope Voltage & Time Readings):
Peak-to-Peak Voltage: V_pp = (Vertical Peak-to-Peak Divisions) × (Y-Gain in Volts/Div)
Signal Amplitude: V_0 = V_pp / 2
RMS Voltage (Sine Wave): V_rms = V_0 / √2 = 0.7071 · V_0
Wave Period: T = (Horizontal Divisions per Cycle) × (Timebase Setting in Time/Div)
Frequency: f = 1 / T
Real-World Engineering & Industrial Applications
The electrodynamic architecture modeled in this laboratory formed the cornerstone of 20th-century electronics and remains vital in high-energy physics:
- Analog Oscilloscopes (Testing & Telecommunications): For over six decades, analog oscilloscopes provided real-time hardware signal tracing with zero digitization lag, making them indispensable for radar pulse inspection, RF oscillator alignment, and audio amplifier harmonic analysis.
- Medical Diagnostic Electrocardiography (ECG & Vectorcardiograms): Dual-axis CRO screens historically traced the cardiac vector loop directly by routing lead signals to the X and Y axes simultaneously (Lissajous figures), immediately exposing bundle branch blocks and myocardial infarctions.
- Aviation & Naval Plan Position Indicator (PPI) Radar: Marine and air-traffic radar systems employed rotating deflection yokes and long-persistence phosphors (P7 cascade) to paint revolving radial sweeps, maintaining clear echoes of aircraft and coastlines between antenna revolutions.
- Particle Accelerators & Synchrotrons: Modern particle accelerators utilize advanced electrostatic and magnetic deflection chambers operating on identical Lorentz-force deflection formulas to steer relativistic electron bunches into beamlines for macromolecular crystallography and medical isotope production.
Practice Problems & Diagnostic Tasks
Test your quantitative comprehension of electron acceleration, deflection physics, and graticule signal interpretation with the five exercises below:
A sinusoidal AC signal is fed into the Y-input of a CRO. The Y-gain control is set to 5.0 V/div. On the graticule, the peak-to-peak vertical trace occupies exactly 6.4 vertical divisions. Calculate:
a) The peak-to-peak voltage (V_pp).
b) The peak amplitude (V_0).
c) The root-mean-square voltage (V_rms).
An unknown audio frequency generator is connected to a CRO with the timebase calibrated to 0.50 ms/div. Two complete full cycles of the displayed waveform span a horizontal distance of 8.0 divisions. Determine:
a) The time period (T) of one complete cycle.
b) The fundamental frequency (f) of the signal.
The accelerating anode potential of a laboratory CRT is set to Va = 2500 V. Given that electron charge e = 1.602 × 10⁻¹⁹ C and electron rest mass m_e = 9.109 × 10⁻³¹ kg:
a) Calculate the kinetic energy acquired by each electron in joules.
b) Compute the forward axial velocity (v) of the electrons as they emerge from the anode.
c) Express this velocity as a percentage of the speed of light (c = 3.00 × 10⁸ m/s) and confirm whether non-relativistic mechanics is valid.
A CRT has deflection plates of length l = 3.0 cm separated by a distance d = 1.0 cm. The axial distance from the center of the plates to the phosphor screen is L = 20.0 cm.
a) If Va = 1200 V, calculate the deflection sensitivity (S) in mm/V.
b) What is the screen displacement (D) when a potential difference of Vd = 36.0 V is applied across the plates?
c) If the operator increases Va from 1200 V to 2400 V while keeping Vd constant, explain quantitatively what happens to the deflection D.
A technician suspects that the horizontal timebase sweep circuit of an oscilloscope has suffered a total component failure.
a) What visual pattern will appear on the phosphor screen if an AC sinusoidal signal is applied to the Y-input while the timebase sweep generator is completely dead?
b) How could the technician verify that the vertical deflection amplifier is still functioning correctly using only the front panel controls?
c) If the Wehnelt cylinder bias is accidentally shorted to -120 V, what will happen to the screen trace regardless of the input signals, and why?
Click to Reveal Solutions and Step-by-Step Proofs
Solution to Task 1:
a) Peak-to-peak voltage: V_pp = (divisions) × (Y-Gain) = 6.4 div × 5.0 V/div = 32.0 V.
b) Peak amplitude: V_0 = V_pp / 2 = 32.0 V / 2 = 16.0 V.
c) Root-mean-square voltage for a pure sine wave: V_rms = V_0 / √2 = 16.0 V / 1.4142 = 11.31 V.
Solution to Task 2:
a) Two full cycles occupy 8.0 divisions, meaning one complete cycle occupies: 8.0 div / 2 = 4.0 divisions per cycle.
Period: T = 4.0 div × 0.50 ms/div = 2.0 ms = 2.0 × 10⁻³ s.
b) Frequency: f = 1 / T = 1 / (2.0 × 10⁻³ s) = 500 Hz.
Solution to Task 3:
a) Kinetic Energy: Ek = e · Va = (1.602 × 10⁻¹⁹ C) × (2500 V) = 4.005 × 10⁻¹⁶ J.
b) Velocity: v = √((2 · Ek) / m_e) = √((2 × 4.005 × 10⁻¹⁶ J) / (9.109 × 10⁻³¹ kg)) = √(8.793 × 10¹⁴) = 2.965 × 10⁷ m/s.
c) Percentage of speed of light: (2.965 × 10⁷ m/s / 3.00 × 10⁸ m/s) × 100% = 9.88% of c. Since v is below 10% of c, relativistic mass increase is under 0.5%, fully justifying classical Newtonian mechanics.
Solution to Task 4:
a) Deflection Sensitivity: S = (l · L) / (2 · d · Va).
Converting all units to meters: l = 0.03 m, L = 0.20 m, d = 0.01 m, Va = 1200 V.
S = (0.03 × 0.20) / (2 × 0.01 × 1200) = 0.006 / 24 = 0.00025 m/V = 0.25 mm/V.
b) Deflection displacement: D = S · Vd = 0.25 mm/V × 36.0 V = 9.0 mm (0.90 cm).
c) Since S is inversely proportional to Va, doubling Va from 1200 V to 2400 V halves the deflection sensitivity from 0.25 mm/V to 0.125 mm/V. Consequently, the screen displacement drops by exactly 50% to 4.5 mm. Higher electron momentum creates a stiffer beam that deflects less.
Solution to Task 5:
a) With no horizontal sweep voltage, the electron beam cannot travel across the screen. The Y-plates will oscillate the beam purely vertically along the central axis, displaying a single vertical line whose total height equals the peak-to-peak voltage.
b) The technician can adjust the Y-Gain or Y-Position control. If changing Y-Gain expands or shrinks the vertical line length proportionally, and adjusting Y-Position moves the line up and down, the vertical amplifier is proven to be operational.
c) A grid bias of -120 V exceeds the tube's cutoff threshold (approximately -90 V). The electrostatic potential well formed by the Wehnelt cylinder will completely repel all thermionic electrons back into the cathode space charge cloud. The beam current drops to 0 µA, resulting in a completely dark, blank screen with no trace visible.