---
title: "Digital Oscilloscope Interactive Lab | Sandbox Physics"
description: "When can a stable waveform be an illusion created by sampling? A stable trace can still be an alias."
canonical_url: "https://sandboxphysics.com/labs/digital-oscilloscope/"
language: "en"
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  zh-CN: "https://sandboxphysics.com/zh/labs/digital-oscilloscope/"
last_modified: "2026-10-29"
---

IN12 · A stable trace can be an alias

# Digital Oscilloscope

**When can a stable waveform be an illusion created by sampling?** A stable trace can still be an alias. Different signals can pass through the same sampled values, and a trigger can align those values repeatedly. Check the sampling rate and analog bandwidth, then measure the stored samples; a smooth connecting line cannot restore changes that were never recorded.

Capture pulses and two-tone signals through a probe, analog bandwidth and ADC. Compare raw samples with their linear display and measure the same record.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A simulated real-time, single-channel DC-coupled instrument uses a unity-gain buffered probe with a one-megaohm input, resistive source loading and a settled single-pole analog front end. Probe capacitance, cable delay, reflections and nonlinear electronics are omitted. A signed round-to-nearest ADC includes declared gain, offset, bounded noise and optional aperture jitter. Digital edge triggering uses acquired codes with a two-code rearm band; normal mode retains the preceding record on failure, while auto mode captures after a three-record-length timeout. Calibration reads known DC levels and a one-second clock gate. Automatic measurements use acquired codes and their saved calibration. Source and filtered curves are separate simulation references; no equivalent-time acquisition or commercial scope is reproduced.

### What did the sampling clock actually keep?

Saved simulated record · raw ADC acquisition

$t/\mathrm{ms}$ $V/\mathrm V$

ADC points and linear display Probe input · model reference Filtered input · model reference

Gold and violet are separate simulation references; turquoise is acquired data. Drag the pink marker to preview a new digital trigger; keeping a capture freezes its samples and standards.

Reopen a kept record

Raw codes, clock and calibration provenance

First and last samples of the shown acquisition

| Sample | ADC code | $t/\mathrm{ms}$ | $V/\mathrm V$ | Overload |
| --- | --- | --- | --- | --- |

Exports retain every code, nominal timestamp, overload mask, trigger index/fraction, range, known-reference observations, version and seed. Realized jitter times are simulation provenance, not measured timestamps.

Physics tutorial

## Read the samples before trusting the line

**Background** A probe delivers a voltage to an analog input. The ADC stores one code at each clock tick, and a digital trigger chooses which part of that stream becomes a record.

**Why it matters** A crisp, repeatable picture is useful only when you know which changes the instrument could capture.

Start with the essentials

- **Focus question**: How can a stable slow wave come from a much faster input?
- **One-sentence intuition**: Trigger alignment stabilizes a record; sampling and analog bandwidth determine what information reached it.

### Core mathematical model

#### A declared single-pole analog input

$$
H(f)=\frac{1}{1+\mathrm i f/B},\qquad t_{10\text{–}90}=\frac{\ln9}{2\pi B}
$$

The rise-time relation is exact for a settled ideal step through this chosen one-pole filter. A finite pulse and sample-derived levels can give a different measured edge time.

#### Voltage and time come from saved standards

$$
V_n=V_{\rm ref}\frac{c_n-\bar c_0}{\bar c_{\rm ref}-\bar c_0},\qquad \Delta t=\frac{T_g f_{\rm cal}}{N_g f_s}
$$

Known DC levels set volts per code. A one-second reference gate and its observed tick count calibrate the common clock. Aperture jitter is not measured by that gate.

#### Two frequencies can have the same samples

$$
\sin\!\left(2\pi\frac{1100n}{1000}\right)=\sin\!\left(2\pi\frac{100n}{1000}\right)
$$

This equality describes ideal instantaneous samples before filtering. The full instrument also changes amplitude and phase in its analog front end.

### Common difficulties

#### A smooth line is not extra data

**Typical misconception** If the connecting line looks smooth, the missing fast motion has been recovered.

**Better mental model** Linear interpolation passes through the stored samples and adds no independent observations between them.

#### Peak values can be clipped

**Typical misconception** The largest displayed sample always gives the input peak.

**Better mental model** An overload mask marks samples outside ADC code range. A clipped peak is only a lower bound; clipped edge times are withheld.

### Run the experiment

1. 01

   #### Compare an edge with its samples

   Choose An edge stands still, then use Edge zoom below the apparatus.

   **What to observe:** The teal dots and linear display share one acquired record. Its measured rise comes from the stored 10 and 90 percent crossings.

2. 02

   #### Change the sampling clock

   Choose Fast becomes slow and compare the gold input reference with the turquoise record.

   **What to observe:** The input is faster than the clock can distinguish. Its stable apparent period describes the sampled trace.

3. 03

   #### Miss the trigger condition

   Raise the trigger level above the signal, then compare normal and auto trigger mode in the advanced controls.

   **What to observe:** Normal mode retains the prior capture. Auto mode keeps actual samples after its timeout, marked as untriggered.

Physical conclusion

Keep the ADC codes, range and trigger with each reading, and treat the input curve as a separate reference.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Where does the slow wave on an oscilloscope come from?**](https://sandboxphysics.com/stories/instruments/digital-oscilloscope/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)