Oscilloscopes and Digital Instruments
CRO working, measuring amplitude, frequency and phase with Lissajous figures, probes, digital voltmeters and ADC types, frequency counters, Q-meter and transducers.
Modern measurement uses oscilloscopes and digital instruments. GATE asks about Lissajous patterns, ADC types and resolution.
Cathode ray oscilloscope (CRO) and DSO
- An electron beam (or, in a digital storage oscilloscope, a sampled display) shows voltage against time. The time base sweeps horizontally with a sawtooth; the trigger keeps the trace stable.
- Amplitude = divisions × volts/div; period = divisions × time/div.
- Probes: a 10:1 probe divides the signal by 10 and reduces loading; it must be compensated (adjustable capacitor) to avoid distorting square waves.
Lissajous figures
With signals on both X and Y plates:
- Frequency ratio: f_y/f_x = (number of horizontal tangencies)/(number of vertical tangencies).
- Phase difference of equal-frequency signals: sin φ = Y₀/Y_max (intercept on the Y axis divided by the maximum Y). A straight line → 0° or 180°; circle (equal amplitudes) → 90°.
Digital voltmeters and ADCs
| ADC type | Speed | Notes |
|---|---|---|
| Flash (parallel) | Fastest | Needs 2ⁿ − 1 comparators |
| Successive approximation | Fast | n clock cycles per conversion |
| Dual-slope integrating | Slow | Rejects noise (mains hum); used in DVMs |
| Counter (ramp) | Slow | Up to 2ⁿ clock cycles |
- Resolution of an n-bit converter = full scale/2ⁿ (or /(2ⁿ − 1)). A 3½-digit DVM shows up to 1999.
- Quantisation error is ±½ LSB.
Frequency and other measurements
- Frequency counter: counts cycles in a gate time; for low frequencies, measuring the period is more accurate.
- Q-meter: uses series resonance; Q = V_C/V_in.
- Transducers: strain gauges (gauge factor = (ΔR/R)/strain), thermocouples, RTDs, thermistors, LVDT (displacement), piezoelectric (dynamic force).
Worked example
An 8-bit ADC has a 5 V range.
- Resolution = 5/255 = 19.6 mV (using 2ⁿ − 1 steps).
Practice
A Lissajous figure has 3 horizontal tangencies and 2 vertical tangencies. If f_x = 100 Hz, what is f_y in Hz?
Show answer and explanation
Answer: 150f_y/f_x = 3/2, so f_y = 150 Hz.
An ellipse on a CRO cuts the Y axis at ±3 divisions and its maximum Y is ±6 divisions. What is the phase difference in degrees?
Show answer and explanation
Answer: 30sin φ = 3/6 = 0.5, so φ = 30°.
How many comparators does a 6-bit flash ADC need?
Show answer and explanation
Answer: 63A flash ADC needs 2ⁿ − 1 = 63 comparators.
A strain gauge of 120 Ω with gauge factor 2 is strained by 500 × 10⁻⁶. What is its change in resistance (Ω)?
Show answer and explanation
Answer: 0.12ΔR = GF × strain × R = 2 × 0.0005 × 120 = 0.12 Ω.