Presets
Playback
Disk, speed and electronics
Four edges per slot give a four times finer step than the slot count. The decoder must sample faster than the edges arrive, and the disk run-out limits the accuracy no matter how many slots it has.
Model checks
The science
What is modelled
A rotating disk with N slots modulates two photodiode signals that are a quarter slot pitch apart, so channel A follows sin(N theta) and B follows cos(N theta). A comparator with hysteresis turns them into digital A and B, and a transition table counts up or down at each of the four edges per slot. Speed is estimated either by counting edges in a gate or by timing the interval between edges.
Equations
- Light signals
A = 0.5 + 0.45 sin(N (theta + e sin(2 theta + 0.37))), B with cos;e = run-out / 112 mm. - Counts per turn
4 N; step360 / (4 N)degrees. - Sampling must be well above the edge rate
4 N n / 60. - Count method error
d_theta / T_gate; period method errorw / (x - 1) - w,x = d_theta f_clk / w. - Crossover speed
d_theta sqrt(f_clk / T_gate).
Checks run in the page
- Four counts per slot, in both directions.
- Position error bounded by run-out plus one count.
- Swapped channels reverse the count; a blocked arc loses it.
- Both speed estimators against their quantisation bounds.
Honest simplifications
A single-turn kinematic model at constant speed: no motor, no load and no control loop (the 3D page has those), no index pulse, a perfectly round disk apart from the eccentricity term, white Gaussian photodiode noise, an ideal comparator and decoder clock, and a fixed 112 mm pitch radius. A teaching model, not an encoder datasheet.
What to try
- Press Fast shaft, slow sampling and watch invalid transitions appear; then press Fast shaft, fast sampling.
- Press Channels swapped to see the count run backwards.
- Raise the run-out and see the position error bound grow while the step stays the same.