Ada Audits the ADC Numbers
Ada checks resolution, range use, aliasing, and the noise floor behind the ADC example
ADA · CALCULATION AUDIT
Ada Audits the ADC Numbers
An ADC is a physics contract: the voltage step, sample clock, and anti-alias boundary decide whether firmware receives evidence or a polished false pattern.
The chapter’s worked example puts a temperature sensor that outputs 10 mV per 1 degree C onto a 12-bit ADC with a 3.3 V reference and 4096 possible codes, with the conditioned signal spanning 0.1 V to 1.75 V. The chapter claims this gives “enough amplitude detail for many temperature tasks” without yet proving the sample rate or calibration are sound. This audit asks the question that worked example invites: how many degrees does one ADC code actually represent, and how much of the converter’s 4096-code range does this sensor use?
Companion to the chapter Sampling and Aliasing — every number here comes from that chapter.
1. The 12-bit voltage step is small enough for the chapter's temperature scale
The worked example uses a 3.3 V reference and 4096 possible codes:
With the stated 10 mV per 1 degree C sensor scale, one code is 0.806 / 10 = 0.0806 degree C. The ideal half-LSB uncertainty is 0.806 / 2 = 0.403 mV, or 0.0403 degree C before real noise and calibration error are included.
2. Range use is reviewable, not a guess
The conditioned output spans from 0.1 V to 1.75 V:
That is exactly half of a 4096-code converter, which matches the chapter note that the design uses useful but not perfect code coverage.
3. Sampling math explains the alias warnings
For a useful signal up to 40 Hz, the mathematical lower boundary is more than 2 × 40 = 80 samples/s; real filters need margin above that. If unwanted frequencies reach the ADC, the fold calculation shows the false result:
| Check | Arithmetic shown | Audit result |
| 90 Hz interference at 100 SPS | round(90 / 100) = 1; |90 - 100·1| | 10 Hz alias |
| 1200 Hz component at 1000 SPS | round(1200 / 1000) = 1; |1200 - 1000·1| | 200 Hz alias |
| Ideal 12-bit SNR | 6.02 × 12 + 1.76 | 74.0 dB before real-world losses |
What the audit buys you: amplitude resolution, sample rate, and noise floor are separate gates. A 12-bit ADC can resolve the temperature example while still producing false evidence if the analog path lets high-frequency content fold into the sampled band.
Every number above is taken from this chapter's own worked example and re-derived step by step.