Cathode ray oscilloscope and digital storage oscilloscope

Why it matters

A meter gives one number; an oscilloscope shows the whole waveform — its shape, rise time, distortion, glitches and timing relative to other signals. Fault-finding in power electronics, drives and digital circuits depends on it. Knowing its bandwidth, probe and sampling limits is what separates a correct measurement from a pretty but misleading trace.

Key ideas

Cathode-ray tube (CRT).

• The electron gun (heated cathode, control grid for intensity, focusing and accelerating anodes) produces a narrow beam accelerated through a potential Ea.
• Vertical (Y) and horizontal (X) electrostatic deflection plates bend the beam.
• It strikes a phosphor screen, which glows; persistence depends on the phosphor.
• The deflection on the screen is proportional to the plate voltage and inversely proportional to Ea. A high Ea gives a bright trace but low sensitivity, which is why post-deflection acceleration is used.

Block diagram of an analogue CRO.

• Vertical system: input coupling (AC/DC/GND), calibrated attenuator (V/div), vertical amplifier, and a delay line so the leading edge of a signal that triggers the sweep is still visible.
• Horizontal system: a time base generating a linear sawtooth sweep (time/div), with fast flyback and the beam blanked during retrace.
• Trigger circuit: starts each sweep at the same point on the waveform (level and slope chosen by the user), so repeated sweeps overlay and the trace is stable. Modes: auto, normal, single.
• X–Y mode: the time base is switched off and a second signal drives the X plates — used for Lissajous patterns and characteristic curves.
• Dual trace: one gun switched between two channels. Alternate mode (one full sweep per channel) suits fast sweeps; chop mode (switching rapidly within each sweep) suits slow sweeps.

Bandwidth and rise time. The vertical amplifier behaves roughly as a first-order low-pass system. Its −3 dB bandwidth and rise time are linked by tr ≈ 0.35/BW. A displayed rise time is the root-sum-square of the signal's and the scope's (and the probe's). Rule of thumb: choose a scope whose rise time is at least 3–5 times faster than the signal's.

Probes. A 10:1 passive probe has a 9 MΩ series resistor shunted by an adjustable capacitor. With the scope input (1 MΩ ∥ Cin) it forms a divider that is frequency-independent only when Rp·Cp = Rin·Cin. Adjust it with the scope's square-wave calibrator: an over-compensated probe shows overshoot on the edges, an under-compensated one shows rounded edges. A 10:1 probe raises input resistance to 10 MΩ and reduces loading capacitance, at the cost of a tenth of the signal.

Digital storage oscilloscope (DSO).

• The input is conditioned, sampled and digitised by a fast ADC (commonly 8-bit, higher on some models), stored in acquisition memory, and processed for an LCD display.
• Sample rate must comfortably exceed twice the highest frequency (Nyquist); in practice 2.5–5 times the bandwidth for real-time sampling. Too low a rate causes aliasing — a false, lower-frequency waveform.
• Record length (memory depth) × sample interval = time window captured. For a fixed memory, slowing the time base forces a lower sample rate.
• Advantages: storage of single-shot events, pre-trigger viewing (what happened before the trigger), automatic measurements, maths and FFT, averaging to reduce noise, export to a PC. Equivalent-time sampling reconstructs fast repetitive signals from samples taken on successive cycles.
• Limitations: vertical resolution limited by ADC bits, possible aliasing, display update rate (dead time can miss rare glitches).

Formulas

D = L·l·Vd / (2·d·Ea) ; S = D/Vd = L·l / (2·d·Ea) ; G = 1/S D = deflection on screen (m); L = distance from centre of plates to screen (m); l = plate length (m); d = plate spacing (m); Vd = deflecting voltage (V); Ea = accelerating voltage (V); S = deflection sensitivity (m/V); G = deflection factor (V/m).

v = √(2·e·Ea / m) (beam velocity; e/m = 1.759 × 10¹¹ C/kg)

tr ≈ 0.35 / BW ; tr,displayed = √(tr,signal² + tr,scope² + tr,probe²) tr in s; BW in Hz.

Rp·Cp = Rin·Cin (probe compensation)

fs > 2·fmax (Nyquist) ; Time window = record length / fs fs = sample rate (samples/s).

Worked examples

Example 1 — CRT deflection sensitivity. A CRT has Ea = 2000 V, deflection plates 2 cm long and 5 mm apart, and the screen 25 cm from the centre of the plates. Find the deflection sensitivity and the plate voltage for a 2 cm deflection.

1. S = L·l/(2·d·Ea) = 0.25 × 0.02 / (2 × 0.005 × 2000) = 0.005/20 = 2.5 × 10⁻⁴ m/V.
2. S = 0.25 mm/V; G = 4 V/mm.
3. Vd = D/S = 0.02 / 2.5 × 10⁻⁴ = 80 V.

Answer: S = 0.25 mm/V; 80 V gives a 2 cm deflection.

Example 2 — bandwidth, probe and sampling (GATE level). (a) A 50 MHz oscilloscope displays a pulse whose true rise time is 10 ns. What rise time is shown? (b) The scope input is 1 MΩ ∥ 20 pF. Find the compensating capacitor for a 10:1 probe with a 9 MΩ series resistor. (c) A DSO with 10 000-point memory is set to 1 ms/div across 10 divisions. What is the sample rate, and the highest frequency it can show without aliasing?

1. (a) tr,scope = 0.35/50 × 10⁶ = 7 ns; displayed = √(10² + 7²) = √149 = 12.2 ns.
2. (b) Cp = Rin·Cin/Rp = 10⁶ × 20 × 10⁻¹²/9 × 10⁶ = 2.22 pF.
3. (c) Window = 10 × 1 ms = 10 ms; fs = 10 000/0.01 = 1 MS/s; Nyquist limit = 500 kHz (in practice keep signals well below this).

Answer: (a) 12.2 ns (22 % slow); (b) 2.22 pF; (c) 1 MS/s, below 500 kHz.

Common mistakes

• Forgetting the factor 2 in the deflection formula or using the plate-to-screen distance from the plate edge instead of the plate centre.
• Thinking a 100 MHz scope shows a 100 MHz sine wave at full amplitude — at the −3 dB point it shows 70.7 %.
• Leaving a probe uncompensated; square waves look tilted or rounded and amplitudes are wrong.
• Forgetting the 10:1 probe factor when reading V/div.
• Trusting a DSO trace without checking the sample rate — an aliased waveform looks perfectly stable.
• Using chop mode at fast sweep speeds (the trace breaks up) or alternate mode at slow speeds (flicker).

For GATE IN

Expect NAT questions on CRT deflection sensitivity, bandwidth–rise-time relations, cascaded rise times, probe compensation, and DSO sample rate, record length and aliasing. MCQs test trigger functions, delay lines, alternate versus chop, and DSO features such as pre-trigger. Practise reading voltage and time from a described display (divisions × V/div or time/div).

Quick check

1. A scope has a 20 MHz bandwidth. Its rise time?
2. A sine wave spans 4.6 divisions peak to peak with the scope input at 2 V/div and a 10:1 probe (scope not set to correct for it). Peak voltage at the probe tip?
3. A 1 MHz sine wave is sampled at 1.2 MS/s. What frequency appears?
4. What does the delay line in the vertical channel do? Answers: 1. 17.5 ns; 2. 4.6 × 2 × 10 = 92 V peak to peak, i.e. 46 V peak; 3. 0.2 MHz (200 kHz alias); 4. delays the signal so the start of the triggering edge is displayed.