Skip to content

Analog to Digital Conversion Step-Through

Run the Analog to Digital Conversion Step-Through MicroSim Fullscreen
Edit in the p5.js Editor

About This MicroSim

Students routinely fold sampling and quantizing into one vague idea called "digitizing". They are two different losses with two different consequences, and this sim separates them into two independently adjustable controls applied to the same waveform.

Three stacked panels show the same signal three ways:

  1. The analog signal - smooth, continuous, infinitely detailed.
  2. Sampling - the same curve, but the converter only looks at it at these instants.
  3. Quantizing - each of those samples forced onto the nearest level below it, drawn as a stair-step against the quantization gridlines.

Stop on any sample and the panel gives you three numbers side by side: the exact analog value, the code it rounds to out of however many levels the bit depth allows, and the difference. Those three numbers are the explanation. A rolling table of the last eight samples shows the pattern of errors rather than one instance of it.

Two settings are there to make a point:

  • 2 bits gives four levels and a stair-step so absurdly coarse the idea becomes unmissable.
  • Step change with a low sample rate puts the event between two samples, and the sim reports the actual gap: the signal changed at 4.3 s, the last sample was at 4.00 s, the next was at 4.50 s, and nothing at all was recorded in between. Sampling loses time, not just value.

How to Use

  • Press Next sample and Previous sample to walk the cursor along. Play advances slowly; press it again to stop wherever you like.
  • Set Bits to 2 and look at panel 3. Then set it to 16 and look again.
  • Drag the Samples slider down to 5 or 6 and watch the stair-step lose the shape of the curve entirely.
  • Choose the step change waveform, drop the sample rate, and read the message in the panel. Change the sample rate and watch the reported gap change with it.
  • Try noisy signal: the noise is fixed, not re-rolled, so stepping back and forth gives the same value every time.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://iowerx.github.io/pi-env-monitor/sims/analog-to-digital-stepthrough/main.html"
        height="592px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

6-12

Duration

20-25 minutes

Bloom's Taxonomy Level

Understand (L2)

Prerequisites

  • Reading a value off a graph
  • Chapter 4 sections on what a sensor produces

Activities

  1. Exploration (6 min): Leave the waveform on slow sine. Change the bit depth from 2 to 16 one step at a time and describe in one sentence what changes and what does not.
  2. Guided practice (8 min): Set bits to 8 and step through ten samples. Copy the error column into your notes. Is the error ever zero? Is it ever positive? Explain why.
  3. Analysis (8 min): Switch to step change with 10 samples. Read the message. Now raise the sample rate until the gap around the event is under a tenth of a second. What did that cost you, in readings per second?

Assessment

  • Distinguishes a loss caused by sampling from a loss caused by quantizing.
  • Explains why quantization error is never positive with a floor-based converter.
  • States what raising the sample rate buys and what it costs.

References

  1. Wikipedia: Analog-to-digital converter
  2. Wikipedia: Nyquist-Shannon sampling theorem - how fast is fast enough.
  3. Wikipedia: Quantization (signal processing)
  4. Analog Devices, Data Conversion Handbook - the reference treatment of both losses.