An encoder datasheet lists accuracy, resolution, and repeatability as performance parameters. The values are often very different from each other, a 24-bit encoder (sub-arc-second resolution) may have an accuracy of only ±0.01° (36 arc-seconds).
Understanding why requires examining what each parameter measures, how each is tested, and what mechanical and electrical phenomena limit each one.
Correct encoder selection requires specifying all three independently against the application requirements.
Resolution: The Smallest Detectable Increment
Resolution is the smallest angular increment that the encoder output can distinguish. It is determined by the combination of the grating pitch and the interpolation factor applied to the sinusoidal output signal.
How Resolution Is Determined
For an optical encoder with a 20 µm grating pitch:
- The raw sensor output is a sinusoidal signal with a period of 20 µm.
- Interpolation electronics compute the arctangent of the sin/cos ratio, subdividing the period into smaller angular increments.
- At ×100 interpolation, each 20 µm period produces 100 output counts: effective resolution = 0.2 µm.
- For a rotary scale with 256 lines on a 100 mm circumference: line pitch = ~391 µm; with ×100 interpolation → 3.91 µm effective resolution → approximately 0.0016° per count.
Resolution expressed in bits: For a 360° full turn absolute encoder:
- 14-bit resolution: 2¹⁴ = 16,384 counts → 0.022° per count.
- 20-bit resolution: 2²⁰ = 1,048,576 counts → 0.000344° per count.
- 26-bit resolution: 2²⁶ = 67,108,864 counts → 0.0000054° per count.
High bit-count resolution does not mean high accuracy. Interpolation error, grating uniformity, and mechanical factors limit the usable accuracy to a fraction of the theoretical resolution.
Incremental Resolution (ABZ Output)
For incremental encoders with ABZ quadrature output, resolution is expressed in pulses per revolution (PPR) or lines per revolution. With ×4 quadrature counting (counting all four edges of the A and B channel transitions), the effective counts per revolution equals 4 × PPR.
Accuracy: The Maximum Position Error
Accuracy is the maximum deviation between the true angular position and the encoder’s reported position, measured over the full 360° range. It is the most critical parameter for positioning applications.
What Limits Accuracy
Accuracy is limited by a combination of:
Grating uniformity (periodic error): Variations in the line pitch of the scale produce systematic position errors that repeat at the scale periodicity. For glass scales (chrome on glass), grating uniformity is better than for metal tape (laser-etched) scales.
Interpolation error: The arctan interpolation assumes a perfect sine wave. Harmonic distortion in the actual sensor output introduces systematic errors within each grating period. The magnitude of interpolation error depends on signal quality.
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Scale eccentricity: For rotary applications, any misalignment between the disc center and the axis of rotation produces a once-per-revolution sinusoidal error. This is often the dominant error term in real installations.
Thermal effects: Differential thermal expansion between the scale material and the mounting structure introduces a temperature-dependent systematic error.
Bearing runout: Bearings have a finite radial runout that produces a once-per-revolution error identical to eccentricity.
Accuracy Classes in Practice
| Technology | Typical Accuracy Class |
|---|---|
| Interferential optical, glass scale | ±2 arc-seconds (±0.00056°) |
| High-accuracy capacitive | ±0.001° (±3.6 arc-seconds) |
| Inductive angle encoder | ±19 arc-seconds (±0.0053°) |
| Magnetic encoder (standard) | ±0.05° to ±0.1° |
These values represent fully assembled, correctly mounted encoders. Installation errors (particularly eccentricity) add to the inherent accuracy of the encoder. For a 50 mm radius scale, 10 µm eccentricity adds ~0.011° of error.
Integral vs. Differential Accuracy
Some datasheets distinguish:
- Integral accuracy (absolute): Maximum deviation from true position over any position in the full 360° range. Dominated by scale uniformity and eccentricity errors.
- Differential accuracy (edge-to-edge): Maximum deviation from the expected angular increment between adjacent grating lines. Dominated by interpolation error and periodic error. The CT scanner encoder specification of < 0.02° edge-to-edge with < 0.1° absolute integral accuracy is an example of this distinction.
Repeatability: The Variability of Repeated Measurements
Repeatability measures how consistently the encoder reports the same position when the axis returns to the same physical location multiple times.
Repeatability vs. Accuracy
An encoder can have excellent repeatability but poor absolute accuracy, if a systematic error is present (e.g., a grating defect at a specific position), the encoder will report the same wrong value each time it passes that position. Repeatability measures variability; accuracy measures systematic error.
Repeatability is the relevant parameter for:
- Closed-loop position control: The servo drive uses the encoder to maintain a commanded position. If the encoder repeatably reports the same value at the same position, the closed-loop system holds that position precisely, regardless of the absolute accuracy error.
- Relative positioning: Moves from point A to point B and back to point A rely on the encoder to complete the return with the same count, repeatability.
What Limits Repeatability
Repeatability is limited by:
- Electrical noise: Random noise on the sin/cos signal produces random variation in the computed position. This is the fundamental floor of repeatability, typically less than ±1 count at the encoder’s native resolution.
- Mechanical hysteresis: Bearing friction and compliance cause the axis to approach a position from slightly different physical angles depending on the direction of approach. The encoder accurately reports this physical difference, but it manifests as an apparent position error.
- Thermal noise: Low-frequency thermal fluctuations in the electronics produce slow drift in the position output that affects long-term repeatability.
For well-designed optical and capacitive encoders, repeatability is typically 1–2 orders of magnitude better than accuracy. A ±5 arc-second accuracy encoder may achieve ±0.1 arc-second repeatability.
Practical Specification Workflow
When specifying an encoder for a rotary application:
Step 1: Determine the accuracy requirement
What is the maximum tolerable position error at any angle? This defines the required accuracy class. Account for installation error (eccentricity, tilt) that will add to the encoder’s inherent accuracy.
Step 2: Determine the resolution requirement
What is the minimum position increment the controller must respond to? This defines the minimum resolution. The rule of thumb: resolution should be at least 10× better than the required accuracy to ensure the accuracy budget is not consumed by quantization error.
Step 3: Determine the repeatability requirement
What is the tolerable variation when returning to a commanded position? In most closed-loop servo applications, repeatability is more critical than absolute accuracy.
Step 4: Verify thermal margin
Does the accuracy specification hold over the operating temperature range? Magnetic encoders degrade with temperature more than optical or capacitive designs.
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