DC Errors — Data Conversion

Along the way

1
Four textbook errors. Offset: nonzero at zero. Gain: slope ≠ 1. INL: smooth leftover after the best-fit line. DNL: each step vs exactly 1 LSB.
2
Two-point calibration kills offset and gain. Measure zero and full scale, solve slope/intercept. That is why datasheets split “offset/gain” (always calibratable) from “INL” (the leftover).
3
INL is the residual bow. Zero offset and gain — the middle plot still bows. That leftover after the best-fit line is what the INL spec bounds.
4
DNL = −1 LSB is a missing code. That step’s width went to zero. INL is the running sum of DNL — that is where the name comes from.
5
This page is a 5-bit cartoon on a 5 V box. Real 12- and 16-bit INL is a few millivolts — invisible on a transfer plot. We exaggerate so you can see the shapes. ADC Tools does the real units.

Temperature and supply drift of the same errors, and INL shape (bow vs S-curve vs MSB kink) as a debug clue.

Next: more parts planned (references, anti-aliasing, architecture). Back to the series hub.

Transfer, then the datasheet plots

Top: 5-bit staircase on a 5 V box · middle: INL vs code · bottom: DNL vs code (red line = missing)

Offset (mV) Gain error (%) INL bow (LSB) DNL wobble (LSB)

Ideal 1:1 Actual staircase INL DNL

Transfer · 5-bit · 5 V · offset shifts · gain tilts · INL bows · DNL changes step width

INL vs code · leftover after the best-fit line · Y is fixed ±6.5 LSB (not zoomed to the bow)

DNL vs code · step width − 1 LSB · rose line = missing code

Offset—

Gain—

Peak INL—

Worst DNL—

Missing code—

\[ v_{\mathrm{out}} = (1+\varepsilon_g)\,v_{\mathrm{in}} + V_{\mathrm{os}} + \mathrm{INL}(v_{\mathrm{in}}) \]

\[ \mathrm{DNL}_k = \dfrac{\Delta v_k}{\mathrm{LSB}} - 1 \]

→ —

\[ \mathrm{INL} \approx \sum \mathrm{DNL}\quad\text{(plus a smooth bow)} \]

→ —

5-bit, 5 V on purpose — a 12-bit LSB is 1.2 mV and would vanish on this plot. Offset and gain still calibrate out (two points). INL and a missing code do not.

Try it: “Offset-heavy” is a parallel shift. Zero offset and gain — the rose INL bow stays. Drag DNL to 1.0 — the midscale bar hits −1 LSB (missing code) and that stair disappears.

Deep link: put real datasheet offset/gain/INL/DNL numbers into the ADC Tools calculator to see the total error budget in LSBs and volts.

Analog Intuition

DC errors — offset, gain, INL, DNL

Transfer, then the datasheet plots