The digital oscilloscope
A 1 GS/s oscilloscope with 1000 points of memory, at 10 µs/div, samples at only 10 MS/s. A 10.1 MHz signal then appears as a clean 100 kHz sine wave that does not exist.
01From the beam to the memory
A digital storage oscilloscope (DSO) keeps the vertical channel of the analog scope —attenuator, amplifier, bandwidth— but instead of deflecting a beam, it digitizes the signal with a fast ADC and stores the samples in an acquisition memory. The trigger decides which part of that memory is displayed, and a processor builds the image, calculates measurements and stores the waveform. The advantage is enormous: you can see what happened before the trigger, capture a single event, measure automatically, calculate the FFT and decode serial buses.
The price is that there is now sampling, with all its consequences: the signal you see is a reconstruction from samples, and it may not resemble the real one.
02Sampling rate and memory
The maximum sampling rate appears in the specification, but the one actually used depends on the timebase, because the memory has to be enough to fill the ten divisions of the screen:
To reconstruct a sine wave properly, more than two samples per period are needed, according to the sampling theorem. Oscilloscopes interpolate between samples with the \( \sin(x)/x \) function and in practice need about 2.5 samples per period of the highest frequency; without interpolation, joining points with straight lines, about ten are needed. If the sampling rate falls below twice the signal frequency, an alias appears: a stable waveform, of lower frequency, that does not exist.
An oscilloscope with a 1 GS/s maximum. You choose the signal, the timebase and the memory length; the screen shows the real signal in gray and what the oscilloscope reconstructs from its samples, in green.
There are two defenses against aliasing: look first with the fastest timebase, to find out which frequencies the signal has, and use peak detect mode, which stores the maximum and minimum of each interval instead of one sample and does not let a glitch or a high frequency go by without showing it.
03Acquisition modes
| Mode | What it does | What for |
|---|---|---|
| Normal | One sample per interval | General use |
| Peak detect | Maximum and minimum of each interval, sampling at the maximum rate | Glitches and aliasing at slow timebases |
| High resolution | Averages the samples of each interval | Less noise and more effective bits on slow signals |
| Average | Averages several successive acquisitions | Reduces random noise by \( \sqrt{n} \), with repetitive signals |
| Segmented memory | Stores only the segments around each trigger | Widely spaced bursts, such as bus packets |
04Vertical resolution and bandwidth
Most oscilloscopes use 8-bit converters: 256 levels over the whole screen, about 32 per division. To avoid losing resolution, the signal has to fill almost the whole height: a signal that occupies one division is digitized with barely 5 bits. Recent models have 10 or 12 bits, useful for seeing small details on large signals, such as the ripple of a power supply.
The frequency response of a digital oscilloscope is usually steeper than that of an analog one, to make use of the sampling rate without letting aliases through. That is why the relationship between rise time and bandwidth is \( t_r \approx 0.4/BW \) to \( 0.45/BW \) instead of 0.35.
05Triggering, measurements and analysis
Digital triggering goes beyond the edge: it can wait for a pulse wider or narrower than a value, a pulse that did not reach the logic level (runt), a pattern on several channels or a frame with certain data on a serial bus. Automatic measurements —frequency, rise time, RMS value— are calculated on the samples, and their accuracy depends on there being enough samples per edge and on the calculation spanning a whole number of periods. The FFT turns the oscilloscope into a basic spectrum analyzer, with the limitation of its 8 bits.
06In the laboratory
With a 10 MHz generator, reduce the oscilloscope’s memory and lengthen the timebase until a low-frequency signal appears. Verify the apparent frequency with the formula and eliminate it with peak detect.
Measure a noisy 1 mV signal in normal mode and averaging 16 and 256 acquisitions. Estimate how much the noise drops.
Capture an I²C transaction, configure the decoding and trigger on a specific address.
07Common mistakes
- Trusting a stable waveform at a slow timebase. It may be an alias.
- Using a small signal on the screen. Bits of resolution are lost.
- Measuring a rise time with few samples per edge. Interpolation invents the shape.
- Leaving the memory at the minimum. It forces the sampling rate down at slow timebases.
08Self-assessment
At what rate does a 2 GS/s oscilloscope with 20,000 points sample at 50 µs/div?
\( 20\,000 / (10 \cdot 50\ \mu\text{s}) = 40 \) MS/s.
What apparent frequency does a 10.1 MHz sine wave sampled at 10 MS/s show?
100 kHz, the distance to the nearest multiple of the sampling rate.
How many quantization levels does a signal use that occupies two divisions with an 8-bit ADC and eight divisions?
About 64, the equivalent of 6 bits.
How much does random noise drop when averaging 100 acquisitions?
Tenfold: 20 dB.
09Further reading
- Tektronix. XYZs of Oscilloscopes. Tektronix, technical primer. Sampling, memory, acquisition modes and triggering in digital oscilloscopes.
- Keysight Technologies. Evaluating Oscilloscope Sample Rates vs. Sampling Fidelity. Application note 1587. How many samples per period are really needed, with measurements.
- Ian Hickman. Oscilloscopes: How to Use Them, How They Work. 5th ed., Newnes, 2001. Digital oscilloscopes compared with analog ones.