Mitigating DNL and harmonic distortion errors

DNL (differential nonlinearity) causes uneven code widths and missing codes; harmonic distortion comes from INL (a curved transfer function), which turns a pure sine wave into a signal with harmonics. If the converter cannot be replaced, the errors can be reduced by the following measures.

1. Calibration with a correction table (lookup table)

Apply precision DC levels (or a slow ramp) to the converter, record the actual output code for each input, and store a correction value per code in ROM/flash. The processor then replaces each raw code by its corrected value. This removes the static INL and most DNL effects. For a DAC, the pre-distorted code is sent so that the output is correct.

2. Dithering

Add a small noise or triangular wave (about 1 LSB rms) to the analog input before the ADC. It randomises the quantisation error, so the DNL/INL errors are spread into the noise floor instead of appearing as harmonics. Subtract the dither digitally or average it out.

3. Oversampling and averaging

Sample faster than required (e.g. 4^n times) and average, or use a digital low-pass filter. It averages out DNL errors and improves the resolution by n bits (each 4x increase in sampling rate gives about 6 dB, or 1 bit).

4. Reduce the effective resolution

Use only the upper bits: discard 1-2 LSBs where DNL errors are present, or avoid the major carry transitions (for example near mid-scale).

5. Signal-level and frequency management

• Keep the input amplitude within the most linear part of the range (about 3-6 dB below full scale) to avoid clipping and nonlinear end regions.
• Use a lower signal frequency and an accurate sample-and-hold; slew-rate and aperture errors increase distortion at high frequency.

6. Filtering

• Use a low-pass anti-alias filter before the ADC and a reconstruction filter after the DAC.
• Remove known harmonics with digital notch/band-pass filters in software, or choose the signal frequency so that the harmonics fall outside the band of interest (coherent sampling).

7. Hardware care

A stable reference, good power supply decoupling, a short analog layout with separate analog and digital grounds, and temperature stabilisation reduce the other errors that add to distortion.

Calibration combined with dithering and oversampling normally brings the performance close to that of a good converter.