Triggering, acquisition & time base

In a simplified real-time acquisition model, the analog front end first delivers a conditioned voltage to an ADC. The ADC samples at rate f_s, so adjacent sample times are separated by

If N samples are retained in one waveform record, the approximate record duration is

These are acquisition quantities. They do not by themselves define the analog bandwidth of the front end.

Analog bandwidth describes how the continuous-time front end attenuates signal content before digitization. Sample rate describes how densely that conditioned waveform is digitized in time.

A high sample rate cannot restore frequency content already attenuated by an insufficient analog front end. Conversely, a wide-band analog front end followed by too-low sampling can alias the passed content.

For an ideally band-limited signal with highest frequency component f_max, unique reconstruction requires

This is a mathematical lower bound for the ideal sampling theorem. It does not say that two samples per cycle are visually or numerically sufficient for every oscilloscope measurement.

Waveforms with fast edges contain harmonics above their repetition frequency, interpolation has finite implementation limits, noise exists, and measurement objectives may require many samples across an edge. Practical oscilloscope guidance therefore often recommends sample rates comfortably above twice the analog bandwidth or signal bandwidth.

The required margin is a measurement-design choice, not a new theorem.

Samples of a sinusoid cannot distinguish frequencies that differ by integer multiples of f_s. An alias can appear at

for an integer k chosen so the apparent frequency falls in the sampled baseband.

Example: sampling a 9 MHz sinusoid at 10 MS/s can produce samples consistent with a 1 MHz apparent sinusoid because

A stable-looking trace can therefore be wrong. Stability on the display is not evidence that the sample rate is adequate.

From

a required time window and sample rate immediately determine the minimum memory.

If you need to observe 20 ms while retaining 100 MS/s,

With only 200 kpoints available, the instrument must either shorten the captured time or reduce the effective sample rate. Real scopes may change one or both automatically when time-base settings change.

If the display has n horizontal divisions and the scale is t_div seconds/division, the visible span is roughly

The instrument then chooses or constrains sample rate, record length and acquisition architecture according to its hardware and settings. Therefore two scopes can show the same time/div while using different f_s or N.

Always read the actual sample rate/record length when quantitative fidelity matters instead of inferring them from the grid alone.

For an edge trigger, define a trigger source x(t), threshold V_T, and slope sign. A rising-edge event occurs when x crosses the threshold upward:

The acquisition/display system then places t_T at a chosen horizontal reference position. Repeated records aligned to equivalent events produce a stable-looking periodic waveform.

Nothing has been fed back into the DUT. Triggering organizes acquisitions around an observed condition.

If the threshold lies in noise or multiple crossings exist, trigger time can jitter between records and the display can look unstable even when the underlying waveform is periodic.

Digital scopes can continuously fill acquisition memory while waiting for a trigger. Once the event occurs, part of the stored samples before t_T can be retained together with samples after it.

This makes it possible to see what led to a fault, glitch or threshold crossing.

The horizontal trigger position therefore allocates memory/time around an event; it is not merely a cosmetic screen marker.

Exact timeout, re-arm and UI behavior are instrument-specific. The universal idea is whether records are accepted without a qualifying event, repeatedly accepted on events, or stopped after one event.

Single acquisition is especially useful for one-off transients when combined with adequate pre-trigger memory and a correct trigger condition.

For a reproducible capture, record at least: analog bandwidth/limit settings, f_s, N, total time span, vertical scale, probe factor, trigger source/type/level/slope, trigger position and acquisition mode.

1. At 2 GS/s, what is the sample interval?
2. At 500 MS/s with N=2 Mpoints, what record duration is available?
3. You need 50 ms at 200 MS/s. What minimum N is required?
4. A 19 MHz sinusoid is sampled at 20 MS/s. Give the simplest low-frequency alias.
5. Why does f_s>2f_signal not guarantee faithful measurement of a 1 MHz square wave?
6. What three quantities define a basic rising-edge trigger?
7. Why can a noisy threshold produce horizontal jitter?
8. What is the conceptual purpose of pre-trigger memory?

Chapter 04 will add the signal source. Generator amplitude settings are not independent of load impedance: the source’s Thévenin resistance and the selected amplitude convention determine what voltage actually appears at the DUT.