Signal quality
Sin/Cos Encoder Disc Interpolation Error: 4 Signal Metrics to Check
Interpolation error comes from four signal flaws: DC offset (1 cycle per period, ≈ ε rad), amplitude mismatch (2 cycles, ≈ δ/2), phase deviation from 90° (2 cycles, ≈ φ/2) and harmonics (3rd harmonic → 4 cycles). On a 2048-line disc, 1 % offset ≈ 1.0″.
A sin/cos readhead outputs two signals 90° apart; the interpolator computes phase and divides each period into hundreds or thousands of steps. Ideal signals have equal amplitude, no DC offset, exact quadrature and pure sine shape. Any deviation creates a periodic error inside every signal period.
1. The four metrics
| Metric | Error cycles per signal period | Error amplitude (small deviations, electrical angle) |
|---|---|---|
| DC offset (relative ε) | 1 | ≈ ε rad |
| Amplitude mismatch (relative δ) | 2 | ≈ δ/2 rad |
| Phase deviation from 90° (φ) | 2 | ≈ φ/2 rad |
| Third harmonic | 4 | Grows with harmonic content |
2. Worked example: 2048 lines
One period = 360° ÷ 2048 ≈ 632.8″; 1 rad electrical ≈ 632.8″ ÷ 2π ≈ 100.7″.
- 1 % DC offset → ≈ 0.01 rad ≈ 1.0″
- 2 % amplitude mismatch → ≈ 0.01 rad ≈ 1.0″
- 1° phase error (≈ 0.0175 rad) → ≈ 0.0087 rad ≈ 0.9″
Higher interpolation factors make these errors more visible. Many interpolation chips auto-correct gain and offset, but the disc’s pattern quality remains the foundation.
3. Disc-side factors
- Duty cycle and edge quality — how close the waveform is to a sine; drives harmonics
- Pitch uniformity — graduation error over the revolution
- Optical density or reflectance contrast — amplitude and SNR; see reflectance contrast
- Eccentricity — once-per-revolution error and amplitude modulation
- Disc-to-readhead gap and tilt — amplitude and channel matching
4. Check with a Lissajous figure
Feed sin and cos into an oscilloscope in XY mode and rotate the disc. A perfect circle is ideal. Center offset = DC offset; horizontal/vertical ellipse = amplitude mismatch; tilted ellipse = phase error; polygonal outline = harmonics. Record amplitude, offset, phase and harmonic content for acceptance.
In your RFQ, state the number of signal periods, readhead or interpolation chip model, and any duty-cycle and edge-quality requirements. See custom encoder discs.