Design guide
Encoder Disc Line Count, Interpolation and Resolution Explained
Counts per revolution = line count × ×4 (square wave) or × interpolation factor (sin/cos). A 2500-line disc gives 10,000 counts with ×4 decoding; a 2048-line sin/cos disc with ×1024 interpolation gives about 2.1 million (21-bit). Resolution is not accuracy.
Counts per revolution = line count × factor · Angular resolution = 360° ÷ counts per revolution
Square-wave output uses ×4 A/B edge multiplication; sin/cos output uses the interpolation factor of the readhead or chip.
| Line count | Signal | Factor | Counts / rev | Angular resolution |
|---|---|---|---|---|
| 1000 | Square wave | ×4 | 4,000 | 324″ (0.09°) |
| 2500 | Square wave | ×4 | 10,000 | 129.6″ |
| 5000 | Square wave | ×4 | 20,000 | 64.8″ |
| 2048 | Sin/cos | ×1024 | 2,097,152 (21-bit) | ≈ 0.62″ |
Line count and grating pitch
Grating pitch p = 2πr ÷ N
At a 20 mm reading radius, 2500 lines give a pitch of about 50 µm (≈ 25 µm line width at 1:1 duty cycle); 10,000 lines give only about 12.6 µm. Smaller pitches depend more on lithography quality and need tighter readhead-gap control.
Resolution is not accuracy
Resolution is the smallest step you can distinguish; accuracy is how far the reading is from the true angle. Accuracy is driven by graduation error, disc eccentricity and interpolation error. At R20 mm, 5 µm of eccentricity causes about 52″ of error — dozens of times the 0.62″ resolution in the last table row. See eccentricity error.
Sizing a line count in five steps
- Find the smallest angular step the system needs and convert it to counts per revolution.
- Choose the signal type: ×4 for square waves, or the interpolation factor your sin/cos chip supports.
- Line count = counts ÷ factor; round to a common value such as 1000, 1024, 2000, 2048, 2500 or 5000.
- Estimate the reading radius from the disc OD, calculate pitch and confirm the readhead supports it.
- Check allowable eccentricity and graduation error against your accuracy target and put them in the RFQ.