Electronic instruments: CRO and multimeter

In short

A cathode ray oscilloscope (CRO) draws a graph of voltage against time on a screen, so it shows *shape* - amplitude, period, rise time, distortion, phase and noise - while a multimeter gives a single steady number for voltage, current, resistance or continuity. Between them they handle almost every bench measurement in electronics, which is why both appear in every B.Sc practical syllabus, in the "Electronic Measurements and Instrumentation" paper of UGC-CBCS and AICTE curricula, and in GATE EC/IN and PSU questions on deflection sensitivity, dual-slope ADCs, loading error and probe loading. Interviewers at test-and-measurement, service and EMS companies (Keysight and Tektronix channel partners, Scientific/Aplab, Meco, HTC, Rishabh, Fluke India, plus Bharat Electronics, ISRO, DRDO labs and every electronics service centre) open with "how will you measure this?" and judge the answer on instrument choice, range, loading and safety. Calibration practice in India runs through NABL-accredited labs with traceability to CSIR-NPL, New Delhi, and safety through the IEC 61010 series - IS/IEC 61010-1 for the instrument, IEC 61010-2-030 for the measurement categories (CAT II-IV) of its inputs.

Explained

The cathode ray tube and electrostatic deflection

• CRT parts: electron gun (heater, cathode, control grid, focusing and accelerating anodes), two pairs of deflecting plates (Y = vertical, X = horizontal), and a phosphor-coated screen in an evacuated glass envelope.
• Electron gun: the heated oxide cathode emits electrons; the control grid (negative) sets beam current, hence intensity/brightness; the anodes form an electrostatic lens that focuses the beam, and astigmatism trims the spot to a round shape.
• Post-deflection acceleration (PDA): a high-voltage spiral near the screen accelerates electrons *after* deflection, giving brightness without losing sensitivity.
• Aquadag coating: a conducting graphite layer returns secondary electrons, preventing charge build-up on the screen.
• Phosphor and persistence: P31 (green) is standard for general use; long-persistence phosphors suit slow signals; persistence is the afterglow time.
• Deflection: a voltage on the Y-plates bends the beam in a parabola inside the plates and a straight line after it; deflection on screen is proportional to plate voltage and inversely proportional to accelerating voltage.
• Deflection sensitivity S = screen deflection per volt applied (mm/V); its reciprocal is the deflection factor (V/mm). Raising accelerating voltage brightens the trace but *reduces* sensitivity.
• Z-input (intensity modulation): an external signal fed to the grid blanks or brightens the trace - used for time markers.
• Graticule: the measuring grid (usually 8 vertical × 10 horizontal divisions), internal in better scopes to avoid parallax.

Block diagram and the time base

• Vertical channel: input coupling switch (AC / DC / GND) → attenuator (calibrated volts/div, usually 1-2-5 steps) → pre-amplifier → delay line → vertical output amplifier → Y-plates.
• Delay line holds the signal back by a few hundred nanoseconds so the sweep, started by the trigger, is already running when the leading edge arrives - without it the rising edge is lost.
• Horizontal channel: trigger circuit → sweep (time-base) generator producing a sawtooth → horizontal amplifier → X-plates. In X-Y mode the sweep is replaced by an external signal.
• Sweep action: the sawtooth's linear rise sweeps the spot left to right at a calibrated time/div; the fast flyback returns it, with the beam blanked during retrace.
• Sawtooth generation: a Miller integrator or bootstrap circuit charges a capacitor at constant current, giving a straight ramp; the slope sets the time/div.
• Free-running versus triggered sweep: a free-running (recurrent) sweep gives a stable picture only if its period is an exact multiple of the signal period; a triggered sweep starts each sweep at the same point on the waveform, so the trace stands still for any frequency.
• Trigger controls: *source* (internal channel, external, line/50 Hz), *level* (voltage at which firing occurs), *slope* (+/−), *mode* (auto gives a trace even with no signal; normal sweeps only on a trigger; single captures one event), and *hold-off*, which ignores triggers for a set time to stabilise complex waveforms.
• Calibrator output: a built-in 1 kHz square wave (typically 0.5-2 V peak-to-peak) for checking gain and compensating probes.
• Delayed sweep (main and delayed time base): magnifies a chosen part of a long waveform by starting a fast second sweep after a set delay.

Multi-trace, Lissajous figures and probes

• Dual trace: one gun, one vertical amplifier shared by an electronic switch - ALT mode draws CH1 on one sweep and CH2 on the next (best at high sweep speeds), CHOP mode switches rapidly between them within one sweep (best at slow speeds). Dual beam uses two guns and is genuinely simultaneous.
• Display modes: CH1, CH2, dual, ADD (CH1+CH2), and INVERT on CH2 to get a difference.
• X-Y mode and Lissajous figures: two sine waves on X and Y produce a closed pattern that gives their frequency ratio from tangency counts and their phase difference from the ellipse's intercepts. A straight line at 45° means equal frequency and 0° phase; a circle means equal frequency, equal amplitude and 90°.
• Probes: a 1× probe passes the signal but loads the circuit with cable capacitance; a 10× (×10) passive probe uses a 9 MΩ series resistor with the scope's 1 MΩ input to divide by 10, raising input impedance to 10 MΩ and cutting capacitance to about 10-15 pF. Multiply all voltage readings by 10 unless the scope auto-senses the probe.
• Probe compensation: adjust the probe's trimmer on the 1 kHz calibrator until the square wave is flat - overshoot means over-compensation, rounded corners under-compensation.
• Keep ground leads short: their inductance causes ringing on fast edges. Never connect a mains-referenced scope ground to a live point - use a differential probe or an isolated scope.
• Other probes: current probes (Hall/clamp), high-voltage probes, 50 Ω passive and active FET probes.

Analog versus digital storage oscilloscope (DSO)

• DSO chain: attenuator → amplifier → sample-and-hold + ADC (usually 8-bit, flash type) → acquisition memory → microprocessor → LCD display.
• Key DSO specifications: analogue bandwidth (the −3 dB point), sample rate (GSa/s), memory depth (record length), vertical resolution (8-bit = 256 levels; 10/12-bit on newer scopes), and number of channels. An MSO adds digital/logic channels.
• Rules of thumb: bandwidth ≥ 3-5 times the highest signal frequency (≥ 5 times the clock for digital work); sample rate ≥ 2× bandwidth by Nyquist, but 4-10× in practice for good reconstruction.
• Aliasing: under-sampling makes a high-frequency signal appear as a low-frequency one. Peak-detect mode and checking the trace at a faster time base expose it.
• Acquisition modes: *sample* (normal), *peak detect* (catches narrow glitches), *average* (reduces random noise, needs a repetitive signal), *hi-res* (over-samples and averages adjacent points), *envelope*, and *roll* for very slow signals.
• DSO advantages: stores and recalls waveforms, captures single-shot and pre-trigger events, automatic measurements (Vpp, RMS, frequency, rise time, duty cycle), cursors, FFT, maths, USB/LAN export, pass/fail masks.
• Analog CRO advantages: real-time display with no aliasing or processing artefacts, finer intensity grading of a repetitive trace, low cost - still common in college labs; the trade-off is no storage and no automatic measurement.

The analog multimeter (VOM)

• Movement: a PMMC (D'Arsonval) meter - a coil on a pivot in a radial magnetic field, deflection proportional to average current, with a spring for restoring torque and air or eddy-current damping. Scale is linear for DC.
• DC voltmeter: a series multiplier resistance extends the range; higher range needs a larger multiplier.
• DC ammeter: a shunt resistance in parallel with the movement carries most of the current.
• AC ranges (rectifier type): a bridge or half-wave rectifier feeds the PMMC, which responds to the average value; the scale is calibrated in RMS for a sine wave using the form factor 1.11. Readings on square, triangular or distorted waveforms are therefore wrong.
• Ohmmeter: an internal cell drives current through the unknown resistance; the scale is non-linear and reversed (zero ohms at full deflection). In a series ohmmeter, the resistance that gives half-scale deflection equals the instrument's internal resistance. "Zero-adjust" compensates for cell ageing.
• Sensitivity = 1/(full-scale deflection current), in Ω/V - the single most important analog-meter figure. A 50 µA movement gives 20 kΩ/V; a 1 mA movement only 1 kΩ/V.
• Input resistance on a range = sensitivity × range, so the same meter loads a circuit differently on each range.
• Loading effect: the voltmeter draws current and pulls the reading down, badly in high-impedance circuits. This is the classic exam error source.
• Accuracy classes of analogue indicating instruments (class 0.1 to class 5, expressed as a percentage of full scale) follow the IS 1248 series; so a class-2 meter on a 100 V range can be off by 2 V anywhere on the scale - which is why you read in the upper two-thirds of the scale.

The digital multimeter (DMM)

• Chain: input protection and attenuator → signal conditioner (AC-to-DC converter, current shunt, or constant-current source for resistance) → ADC → counter/latch → 7-segment or LCD display.
• ADC types: dual-slope integrating is the classic DMM converter - it integrates the input for a fixed time, then de-integrates with a reference, so the reading is independent of R and C drift; integrating over a multiple of 20 ms rejects 50 Hz mains hum (good NMRR), which matters in India. Successive-approximation is faster; sigma-delta is used in modern high-resolution meters.
• Digits and counts: a 3½-digit meter displays 0 to 1999 (2000 counts), 3¾-digit 3999, 4½-digit 19999. Resolution = range / counts; on a 2 V range a 3½-digit meter resolves 1 mV.
• Accuracy specification is quoted as ±(% of reading + number of counts/digits) - never as a plain percentage. Resolution is not accuracy.
• Average-responding versus true-RMS: a cheap DMM rectifies and averages, then scales by 1.11, so it mis-reads any non-sinusoidal waveform (phase-cut dimmers, VFD outputs, SMPS currents). A true-RMS meter computes the real RMS value and is specified up to a maximum crest factor; "true RMS AC" meters are AC-coupled and ignore the DC component, while "AC+DC" meters include it.
• Other functions: continuity buzzer, diode test (shows forward drop), capacitance, frequency, duty cycle, hFE, temperature with a K-type thermocouple, non-contact voltage detect, min/max/hold, relative mode.
• Current measurement: the meter goes in series and has burden voltage (the drop across its shunt), which disturbs low-voltage circuits; current inputs are fuse-protected, and a clamp meter measures AC current without breaking the circuit (Hall-effect clamps also read DC).
• Low-resistance work: two-wire measurement includes lead resistance, so milliohm work uses four-wire (Kelvin) connections.
• Safety and standards: DMMs for mains work carry a measurement category with a voltage - defined since 2010 in IEC 61010-2-030, the test-and-measurement part of the IS/IEC 61010 safety series; the old CAT I is now marked O (circuits not connected to mains) - CAT II for socket-outlet circuits, CAT III for distribution boards, CAT IV for the service entrance. Use the matching category and keep probes with finger guards; instruments used in trade come under the Legal Metrology Act, 2009, and periodic calibration in industry is done by NABL-accredited labs traceable to CSIR-NPL.

Key points

• CRO - plots voltage (Y) against time (X); it is a voltage-measuring instrument with very high input impedance (typically 1 MΩ ∥ ~20 pF).
• Deflection sensitivity - screen deflection per volt on the plates; rises with plate length and screen distance, falls with plate spacing and accelerating voltage.
• Delay line - lets you see the triggering edge itself by delaying the signal relative to the sweep.
• Triggered sweep - locks the trace by starting every sweep at the same level and slope; the real cure for a drifting display.
• Blanking - the beam is switched off during flyback so the retrace is invisible.
• ALT vs CHOP - alternate sweeps for fast signals, chopping for slow signals.
• Lissajous figure - X-Y pattern giving frequency ratio from tangencies and phase from intercepts.
• 10× probe - raises input impedance to 10 MΩ and cuts capacitive loading, at the cost of 10× signal attenuation; must be compensated on the 1 kHz calibrator.
• Bandwidth and rise time - related by tr ≈ 0.35/BW for a single-pole response; choose BW at least 3-5× the signal frequency.
• Aliasing - a DSO artefact of sampling below the Nyquist rate; an analog CRO cannot alias.
• Memory depth - with sample rate, fixes how long a record you can capture at full resolution.
• Sensitivity (Ω/V) - the analog multimeter's figure of merit = 1/I(fsd); input resistance = Ω/V × range.
• Loading error - a low-impedance voltmeter across a high-impedance node reads low; a 10 MΩ DMM makes it negligible in most electronics.
• Multiplier and shunt - series resistance extends voltage range, parallel resistance extends current range.
• Series ohmmeter - half-scale deflection resistance equals the meter's internal resistance; scale is non-linear and reversed.
• Dual-slope ADC - integrating converter giving drift immunity and 50 Hz noise rejection; the standard DMM core.
• Counts, not digits - resolution = range/counts; accuracy = ±(% reading + counts).
• True RMS - needed for all non-sinusoidal waveforms; average-responding meters are calibrated only for sine waves.
• CAT rating - the IEC 61010-2-030 measurement category (O, CAT II-IV) defines the transient energy the meter can survive; match it to the installation point.

Formulas and examples

Example 1 - Reading a waveform off the screen. A sine wave with a ×10 probe occupies 6.0 vertical divisions peak-to-peak at 0.5 V/div, and one cycle spans 4.0 horizontal divisions at 0.2 ms/div.

• V_pp = 6.0 × 0.5 × 10 = 30 V; V_peak = 15 V; V_rms = 30/(2 × 1.4142) = 10.6 V.
• T = 4.0 × 0.2 ms = 0.8 ms → f = 1/0.0008 = 1,250 Hz (1.25 kHz).
• If the probe factor were forgotten, the answer would be 3 V - a tenth of the truth.

Example 2 - Deflection sensitivity of a CRT. Plate length l = 2 cm, separation d = 0.5 cm, plate-centre-to-screen L = 20 cm, accelerating voltage V_a = 2,000 V.

• S = (0.20 × 0.02)/(2 × 0.005 × 2,000) = 0.004/20 = 2 × 10⁻⁴ m/V = 0.2 mm/V.
• Deflection factor = 1/S = 5,000 V/m = 5 V/mm.
• A 30 V peak-to-peak signal applied directly to the plates gives 30 × 0.2 = 6 mm of deflection - which is why a vertical amplifier is essential.
• Doubling V_a to 4,000 V halves S to 0.1 mm/V.

Example 3 - Analog voltmeter design and its loading error. A 50 µA, 2 kΩ PMMC movement is used on a 10 V DC range.

• Sensitivity = 1/50 µA = 20 kΩ/V; total resistance needed = 20 kΩ × 10 = 200 kΩ; multiplier R_s = 200 − 2 = 198 kΩ.
• Now measure the mid-point of a divider: 10 V source with two 100 kΩ resistors; the true voltage is 5.00 V (Thevenin source resistance 50 kΩ).
• With the 200 kΩ meter across the lower resistor: 100 k ∥ 200 k = 66.67 kΩ; reading = 10 × 66.67/(100 + 66.67) = 4.00 V → error = −20%.
• With a 10 MΩ DMM: 100 k ∥ 10 M = 99.01 kΩ; reading = 10 × 99.01/(100 + 99.01) = 4.975 V → error = −0.5%.

Example 4 - Bandwidth and rise time. A 20 MHz CRO measures a pulse edge as 40 ns.

• Scope rise time = 0.35/(20 × 10⁶) = 17.5 ns.
• True signal rise time = √(40² − 17.5²) = √(1,600 − 306.25) = √1,293.75 = 36 ns.
• The instrument has added about 11% to the reading; a 100 MHz scope (t_r = 3.5 ns) would read 36.1 ns, essentially correct.

Example 5 - DMM resolution and accuracy. A 3½-digit DMM (2000 counts, reading up to 1999) specified ±(0.5% of reading + 2 counts) reads 1.234 V on the 2 V range.

• Resolution = 2 V/2000 = 1 mV (the last displayed digit).
• Error = 0.005 × 1.234 + 2 × 0.001 = 0.00617 + 0.002 = ±0.0082 V.
• Result = 1.234 V ± 0.008 V, i.e. between 1.226 V and 1.242 V. Quoting "1.234 V" as exact is wrong.

Example 6 - Lissajous phase and frequency. An ellipse has y-intercept y₁ = 2.0 div and maximum vertical deflection y₂ = 4.0 div → sin φ = 0.5 → φ = 30°. A pattern with 3 tangencies to a horizontal line and 2 to a vertical line gives f_v/f_h = 3/2, so a 1 kHz horizontal input implies 1.5 kHz on the vertical.

Where it is used

• Electronics service and repair: multimeter for supply rails, continuity, fuses and diode checks; CRO/DSO for ripple on SMPS outputs, oscillator and clock activity, horizontal/vertical drive in displays - the core skill of TV, inverter, UPS and appliance technicians and of authorised service franchises.
• EMS and PCB test lines: incoming power-rail checks, ripple and noise measurement, signal-integrity and timing checks on prototypes in companies such as Dixon, Syrma SGS, Kaynes, Bharat FIH and captive plants in Noida, Pune, Hosur, Sriperumbudur and Bengaluru.
• Embedded and R&D bench: DSO with an MSO option to debug UART, SPI and I2C traffic, PWM duty cycle, ADC settling and interrupt latency; FFT for noise and EMI pre-screening.
• Power and instrumentation plants: true-RMS DMMs and clamp meters on VFD and inverter circuits where waveforms are non-sinusoidal; 4-20 mA loop checks in process instrumentation; CAT III/IV meters for panel work.
• Telecom, broadcast and defence labs: Bharat Electronics, ISRO centres, DRDO labs and railway signalling workshops use calibrated scopes and multimeters with NABL-traceable certificates and fixed recalibration intervals.
• Academic and NSQF/ITI training: CRO experiments on Lissajous figures, phase measurement, rectifier and amplifier waveforms, and multimeter experiments on loading error and ohmmeter scales are standard B.Sc, polytechnic and ITI practicals, and standard viva material.

Interview questions

• Q: Why is a delay line used in the vertical channel of a CRO? A: The trigger circuit and sweep generator take a few hundred nanoseconds to start; the delay line holds the signal back by the same amount so the triggering edge is on screen instead of being lost.
• Q: What decides a CRO's deflection sensitivity, and how does accelerating voltage affect it? A: Sensitivity = L·l/(2·d·V_a) - it increases with plate length and screen distance and decreases with plate spacing and accelerating voltage, so a brighter trace means lower sensitivity.
• Q: Why is a 10× probe preferred even though it attenuates the signal? A: It raises input impedance to about 10 MΩ and drops input capacitance to 10-15 pF, so it loads the circuit far less and distorts fast edges far less; the lost amplitude is recovered by the volts/div setting.
• Q: How do you compensate a probe and why? A: Feed the scope's 1 kHz calibrator square wave and adjust the probe trimmer until the top is flat - overshoot means over-compensation, rounded corners under-compensation; uncompensated probes misreport amplitude and rise time.
• Q: Difference between ALT and CHOP modes? A: ALT draws each channel on alternate sweeps and suits fast time bases; CHOP switches between channels within one sweep and suits slow time bases where ALT would flicker.
• Q: What is aliasing and can an analog CRO alias? A: Aliasing is a sampled high-frequency signal appearing as a lower frequency when f_s < 2 f_max; a purely analog CRO does not sample, so it cannot alias.
• Q: A 20 MHz scope shows a 40 ns edge - is the signal really that slow? A: No; the scope's own rise time is 0.35/20 MHz = 17.5 ns, so the true edge is √(40² − 17.5²) ≈ 36 ns.
• Q: What does "20 kΩ/V" on an analog multimeter mean? A: Its movement needs 50 µA for full-scale deflection, so on any range the input resistance is 20 kΩ times the range value - 200 kΩ on the 10 V range.
• Q: Why does an analog voltmeter read low in a high-impedance circuit? A: Its finite input resistance appears in parallel with the circuit and draws current, reducing the voltage it is trying to measure - the loading effect; use a 10 MΩ DMM or a FET-input meter instead.
• Q: Why is an ohmmeter scale non-linear and reversed? A: The current through the movement varies as E/(R_internal + R_unknown), a hyperbolic relation, and zero resistance gives maximum current, so zero ohms sits at full deflection.
• Q: Why is a dual-slope ADC used in DMMs? A: Charging and discharging through the same R and C cancels component drift, and integrating over a multiple of the mains period (20 ms in India) rejects 50 Hz interference.
• Q: When must you insist on a true-RMS multimeter? A: For any non-sinusoidal waveform - phase-controlled dimmers, VFD and inverter outputs, SMPS input currents - because an average-responding meter is calibrated with the 1.11 sine form factor and will read wrong.
• Q: What is burden voltage and why does it matter? A: It is the voltage dropped across the meter's internal shunt when measuring current in series; in low-voltage circuits it reduces the current you are trying to measure.
• Q: What does CAT III 600 V on a multimeter mean? A: Under the IEC 61010 series (measurement categories in IEC 61010-2-030) the meter can withstand the transient energy expected in fixed distribution installations up to 600 V to earth; using a CAT II meter there is a safety violation, not just an accuracy issue.

Common mistakes

• Forgetting the ×10 probe factor, or forgetting that peak-to-peak divisions must be divided by 2√2 to get the RMS value of a sine wave.
• Reading amplitude with the input left on AC coupling when a DC level or offset matters, or leaving the vertical position off-centre so the waveform clips.
• Measuring frequency by counting cycles on screen instead of measuring one period and taking its reciprocal, or using a CRO's calibrated time base when a frequency counter is far more accurate.
• Confusing resolution with accuracy on a DMM, and quoting the last digit as if it were exact.
• Connecting a multimeter in parallel while it is on a current range (a direct short through the shunt - it blows the fuse) or in series on a voltage range.
• Leaving an analog voltmeter on a low range in a high-impedance circuit and trusting the loaded reading, or measuring resistance with the component still powered and in-circuit.
• Measuring a distorted or chopped AC waveform with an average-responding meter and reporting it as the true RMS value.
• Using the oscilloscope's earthed ground clip on a live or floating mains node instead of a differential probe - the usual cause of blown probes, tripped RCDs and shocks.
• Over-compensating or ignoring probe compensation, then blaming the circuit for overshoot and ringing.
• Zero-adjusting an analog ohmmeter once and never again as the internal cell ages, or omitting the "zero ohms" check between ranges.

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