Differences Between Magnetic Scales and Precision Code Discs: How to Select Magnetic Encoding Products

Author: AIC Engineering (骏材磁应用团队) | Material: | Industry:

Differences Between Magnetic Scales and Precision Code Discs:

How to Select Magnetic Encoding Products

Application Pain Points: The Positioning Accuracy Dilemma

Design engineers working on precision motion control—whether in CNC machine tools, semiconductor wafer handling, robotics, or high-speed packaging lines—face a fundamental selection challenge when specifying magnetic encoding components. The two dominant architectures, linear magnetic scales (magnetic grid scales) and rotary magnetic code discs (precision pole rings), serve overlapping yet distinct application envelopes, and the wrong choice can cascade into system-level problems.

Key pain points include:

• Resolution vs. speed trade-off: Finer pole pitches yield higher resolution but reduce maximum traversal speed before signal bandwidth is exceeded.
• Mounting tolerance sensitivity: Linear scales demand tight parallelism over long travel lengths; rotary discs require concentricity control relative to the sensor IC.
• Environmental robustness: Contamination from cutting fluids, ferrous dust, or thermal gradients degrades signal integrity differently for each architecture.
• Cost of field failure: In semiconductor or medical equipment, a single interpolation error can scrap a wafer or compromise patient safety—making signal-to-noise margin a critical design parameter, not a nice-to-have.

Understanding the first-principles physics behind each encoding topology is essential before selecting materials, pole geometry, and sensor matching.

Material and Architecture Comparison Table

What this means for your design: If your application demands sub-micron interpolated resolution over travel lengths exceeding 500 mm, rigid sintered scales with fine pole pitches (≤1 mm) are typically required. For rotary feedback in servo drives where compactness and shock resistance dominate, bonded NdFeB code discs with high pole counts offer the best volumetric efficiency.

First-Principles Derivation: Signal Generation and Resolution Limits

Fundamental Relationship: Spatial Harmonic Content

A magnetic encoder operates by detecting the periodic spatial variation of the magnetic field produced by alternating north-south poles. For a scale or disc with pole pitch ${\lambda }_p$ (the distance from one N-pole center to the next N-pole center), the dominant field component at the sensor plane can be expressed as:

where $B_1$ is the fundamental amplitude at the magnet surface, $g$ is the air gap between the magnet and the Hall/MR sensor, and $x$ is the linear (or arc-length) position coordinate.

What this means for your design: The exponential decay term $e^{-2\pi g/{\lambda }_p}$ is the single most critical factor governing signal strength. Halving the pole pitch while keeping the same air gap reduces the sensor-plane field amplitude by a factor of approximately $e^{-\pi }\approx 0.043$ (i.e., roughly 27 dB loss per halving). In practice, this means:

• A 2 mm pole pitch scale at 0.5 mm gap retains ~21% of surface field → adequate for standard Hall interpolation.
• A 1 mm pole pitch scale at the same 0.5 mm gap retains only ~4.3% → signal may fall below noise floor unless gap is tightened or sensor sensitivity is increased.

Tighter gaps increase mounting cost and vulnerability to mechanical contact. This is the fundamental physics constraint that forces designers to co-optimize pole pitch, gap, and sensor technology simultaneously.

Resolution After Interpolation

The achievable position resolution after electronic interpolation is:

where $N$ is the interpolation factor (typically 32× to 4096× depending on signal quality and ADC bit depth).

What this means for your design: A 2 mm pole pitch with 256× interpolation yields ~2 µm resolution—adequate for general CNC axes. Achieving 0.1 µm resolution requires either reducing pole pitch to 0.5 mm (with corresponding gap challenges) or pushing interpolation to 1024× or beyond, which demands extremely clean sinusoidal signals with total harmonic distortion (THD) below 1%. Harmonic distortion in the magnetization pattern directly limits usable interpolation depth, making magnetization quality a hidden cost driver.

Design Parameter Recommendations

Linear Magnetic Scales

• Pole pitch selection: 2.0 mm for general industrial (resolution ≥ 1 µm achievable with 512× interpolation); 1.0 mm for precision applications requiring sub-micron performance.
• Air gap specification: Target 0.3–0.5 mm for 2 mm pitch; 0.15–0.25 mm for 1 mm pitch. Include ±0.05 mm tolerance budget for thermal expansion and mechanical deflection.
• Scale length tolerance: For scales exceeding 1 m, specify cumulative pitch error ≤ ±5 µm/m for precision grades.
• Harmonic distortion: Request THD specification from the magnetization source; target < 2% for interpolation factors above 128×. Magnetostatic FEA validation of the pole geometry prior to tooling commitment can identify harmonic issues early—AIC Engineering provides this type of magnetization pattern simulation and verification as part of custom scale and code-disc development.

Rotary Magnetic Code Discs

• Pole count selection: 32–64 poles for standard servo feedback (electrical cycle = mechanical rotation / pole pairs); higher pole counts (128–256) for direct-drive torque motors requiring fine commutation resolution.
• Concentricity: Specify ≤ 10 µm radial runout for pole counts above 64; this directly impacts once-per-revolution error.
• Magnetization uniformity: Peak-to-peak amplitude variation across all poles should be < 3% to maintain interpolation accuracy. For high pole-count rings (≥128 poles), multi-pole magnetization fixtures must be designed with tight angular indexing; pole-to-pole amplitude and phase uniformity should be confirmed via scanning Hall probe characterization before production release.

Custom magnetic encoder components—both linear scales and multi-pole rotary rings—require careful co-design between the magnetization pattern, magnet material grade, and the sensor IC's input range. Magnetization pattern verification using scanning Hall probe measurements can ensure harmonic content and amplitude uniformity meet the interpolation requirements before volume production. When evaluating rotary code discs, matching the Hall sensor's linear operating range to the disc's field amplitude at the specified gap avoids saturation or insufficient signal margin.

Engineering Action Checklist

1. Verify signal amplitude at worst-case gap: Using the exponential decay relationship, calculate the minimum expected $B_z$ at your maximum operating air gap (including thermal expansion and mounting tolerance stack-up). Confirm this exceeds your sensor IC's minimum input threshold by at least 6 dB margin.
2. Characterize harmonic distortion of candidate components: Request or measure the spatial harmonic spectrum (at least through the 5th harmonic) of any magnetic scale or code disc under evaluation. Cross-reference against your interpolation ASIC's THD requirement. A "Magnetic Design Review Checklist" document can structure this verification step alongside gap, temperature, and lifetime criteria.
3. Perform thermal derating analysis: Confirm that the magnet material's temperature coefficient of Br (typically −0.11%/°C for NdFeB, −0.18%/°C for ferrite) does not reduce signal below threshold at maximum operating temperature. For applications above 100 °C, evaluate SmCo-based or high-coercivity NdFeB bonded compounds.
4. Validate mounting tolerance budget with prototype measurement: Before committing to production tooling, measure actual installed gap variation and concentricity (for rotary) or parallelism (for linear) using a calibrated fixture. Compare measured signal quality metrics against the design specification to confirm adequate margin exists for volume manufacturing variation. Where in-house scanning Hall probe capability is unavailable, engaging a specialist such as AIC Engineering for magnetization uniformity mapping can de-risk the transition from prototype to volume.

References

1. E. Ramsden, Hall-Effect Sensors: Theory and Application, 2nd ed., Elsevier,
2. R. S. Popovic, Hall Effect Devices, 2nd ed., Institute of Physics Publishing,
3. P. Campbell, Permanent Magnet Materials and Their Application, Cambridge University Press,
4. iC-Haus GmbH, "Interpolation of Sine/Cosine Signals from Magnetic Encoders," Application Note,
5. Renishaw plc, "Magnetic Encoder Design Guide," Technical White Paper,
6. J. M. D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, 2010, Ch. 13 (Permanent Magnet Applications).