# Dither experiment results and evidence The examples cover PN gain tracking, isolated error mechanisms, joint identification, fixed-point three-PN HDC, and architecture-specific observation controls. Their equations and reproduction commands ship in [DITHER_GUIDE.md](../../python/src/adctoolbox/examples/11_calibration/DITHER_GUIDE.md). The public `DitherGainTracker`, `apply_dither_gain` and `DitherHDCTracker` reuse the gain and HDC algorithms measured here. ## Measured HDC result The historical joint HDC run uses a three-PN peak of 0.2, a 13-bit backend and 28-bit signed arithmetic with 24 fractional bits. Gain, cubic nonlinearity, one-tap memory and a two-cell DAC mismatch are present together. The main run uses three seeds, 2^27 samples per case and a simultaneous parameter step; the additional constant-parameter run uses seed 404 and 2^30 samples. | Single-tone correction | Main SNDR / SFDR (dB) | Additional long-run SNDR / SFDR (dB) | |---|---:|---:| | Uncalibrated, nominal probe removed | 33.33 / 39.99 | 33.32 / 39.98 | | Fixed point, 2^20-sample window | 51.04 / 61.33 | 50.85 / 61.58 | | Fixed point, 2^24 / 2^28-sample window | 55.76 / 66.18 | 56.93 / 67.12 | | Floating point, same long windows | 55.76 / 66.18 | 56.93 / 67.12 | | True parameters, same cubic approximate inverse | 56.79 / 66.49 | 56.79 / 66.49 | | True parameters, exact (Newton) inverse, evaluation only | 74.36 / 106.29 | 74.36 / 106.26 | Metrics use coherent 32768-point FFTs and averages over the last quarter of each record; the main column also averages three seeds. These results support longer averaging at unchanged Dither amplitude. They do not establish general convergence or a bound on all inputs. The final device has k/g of about -0.235, so the cubic approximate inverse caps SNDR near 57 dB even with true parameters, about 17 dB below the exact inverse. That gap comes from the inverse order, not from noise or estimation. The spectral metrics therefore do not show parameter convergence: with 2^24-sample windows the cubic coefficient's relative RMSE over the last quarter was 11.81%, 14.60% and 2.54% for the three seeds (gain 0.38%, 0.54% and 0.17%), so two seeds exceed the registered 10% band while mean SNDR stays within about 1 dB of the true-parameter cubic inverse. The single-seed 2^28-window run reached 1.50% cubic and 0.084% gain error. Each update uses one window only; the public `DitherHDCTracker` therefore defaults to 2^24-sample windows, and shorter windows trade accuracy for tracking speed. The main sine/two-tone runs have no overloads, but their minimum backend headroom is only 0.005647 / 0.011304 of full-scale amplitude. DC and low-frequency inputs with peak 0.8 can overload. The corresponding DC 0.78 control has positive headroom; this is a range check, not a full spectral qualification. The 2^28-window resource model uses six sample-rate multipliers, one shared slow multiplier, five 56-bit correlation accumulators, one serial divider and 1456 register bits including accumulator state. This is an arithmetic budget, not synthesis/PPA evidence. Full assumptions and register accounting are in [HDC_FIXED.md](../../python/src/adctoolbox/examples/11_calibration/HDC_FIXED.md). ## Physical and statistical limits - The [model basis](hdc-model-basis.md) and [state/phase derivation](hdc-physical-state-and-phases.md) come with executable algebra checks. The fixed-feedback capacitor connection supports the static charge equation; the one-tap memory model is conditional and PN need not observe every physical memory state. - Finite-record correlation variance, quantization-correlated bias and gain/cubic estimator coupling are distinct. Increasing a window cannot remove every systematic bias. Small-signal diagnostics include offset and amplitude sweeps and continued-update versus frozen-coefficient controls. - The cross-architecture controls have separate assumptions: held-sample paired SAR conversions, a known analog probe slope for TI timing, and transfer-aware subtraction for Delta-sigma. A shared PN distribution does not make their identification mechanisms interchangeable. ## Detailed evidence archive > **External archive.** The reports below live in a contributor's fork > (`chenzc24/ADCToolbox`), not in this repository. They are not maintained here > and stay reachable only while that fork keeps the pinned commit. The runnable > source of truth is `python/src/adctoolbox/examples/11_calibration/`; rerun > its scripts to regenerate the evidence. Detailed CSV/JSON outputs, trajectories, figures and dated reports are retained on [`codex/dither-evidence-20261102`](https://github.com/chenzc24/ADCToolbox/tree/codex/dither-evidence-20261102). The links below pin the complete snapshot to commit `daa4e4a28425265b94a5dc97c182e37da7b8d4c3`, so later branch changes cannot alter the cited evidence. Large generated outputs are not stored in this repository. | Evidence | Archived report | |---|---| | Gain tracking and isolated mechanisms | [Gain](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-10-31-dither-background.md), [mechanisms](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-01-dither-coverage.md) | | Joint model and convergence diagnostics | [Joint](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-01-joint-dither.md), [convergence](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-01-joint-convergence.md) | | HDC spectra, headroom, parameters and resources | [Fixed-point HDC](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-02-hdc-fixed.md) | | Offset/amplitude scans and correlation controls | [Small signal](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-02-hdc-small-signal.md), [correlation](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-02-hdc-correlation.md) | | Pipeline, SAR, TI and Delta-sigma controls | [Architectures](https://github.com/chenzc24/ADCToolbox/blob/daa4e4a28425265b94a5dc97c182e37da7b8d4c3/docs/experiments/2026-11-02-pn-architectures.md) | Reports link to their data and original configuration/source SHA-256 records. The archived full runs predate the current code: the frozen gain-fit helper has since changed, and the HDC tracker now holds only the mismatch coefficient when that estimate is unobservable or out of range, instead of rejecting the whole update. Their source hashes identify the archived files, not every file in the current tree. Current checks are recorded in [Dither validation](dither-validation.md).