Magnetoresistive Sensors (AMR/GMR/TMR)
Theory: three ways a field changes resistance
Overview
I'm choosing a sensor to measure motor rotor angle. Hall, AMR, GMR, TMR — too many options. What's the difference?
Hall elements generate a voltage in a field; the other three are magnetoresistive elements whose resistance changes. A larger resistance change means larger output — AMR a few percent, GMR around 10%, TMR over 100%. Bigger isn't automatically better, though: range, temperature behaviour, noise and cost all differ, so start from the field magnitude you need to measure.
Three types
| Type | Mechanism | Typical MR ratio | Typical uses |
|---|---|---|---|
| AMR | Resistance depends on angle between magnetisation and current | a few % | Electronic compasses, angle sensors |
| GMR | Scattering depends on whether magnetic layers are aligned | around 10% | Automotive speed sensors, earlier read heads |
| TMR | Tunnelling probability through a thin insulator changes | over 100% | Modern read heads, high-sensitivity sensors |
MR ratio and bridge output
Output of a full bridge in which two elements increase and two decrease with field. $V_b$ is the bias voltage and $B_k$ half the linear field range. For small MR the output approximates $V_b\,\mathrm{MR}\,b/2$, but for large MR, as with TMR, the $2+\mathrm{MR}$ denominator matters.
The discovery that drove hard-disk capacity
GMR was discovered independently in 1988 by Fert in France and Grünberg in Germany, leading to the 2007 Nobel Prize in Physics: stacking magnetic and non-magnetic layers just a few nanometres thick produced large resistance changes. From around 1997 it was used in hard-disk read heads, letting them read the weak fields of tiny magnetic domains and rapidly raising recording density. It was later replaced by TMR heads with even larger changes, and both are now widely used in sensors.
Worked examples
Example 1: full-bridge output
Illustrative parameters for comparison. Output at the edge of the linear range (b = 1) and sensitivity for a 5 V full bridge:
| Type | MR ratio | Linear range B_k | Full-scale output | Sensitivity | Output at Earth field 0.05 mT |
|---|---|---|---|---|---|
| AMR | 2.5% | 1 mT | 61.7 mV | 61.7 mV/mT | 3.1 mV |
| GMR | 10% | 5 mT | 238 mV | 47.6 mV/mT | 2.4 mV |
| TMR | 100% | 5 mT | 1.67 V | 333 mV/mT | 16.7 mV |
GMR has four times AMR's MR ratio but lower sensitivity.
Because this example assumes GMR's linear range is five times AMR's. Sensitivity is set by MR ratio divided by range, so elements that cover a wider range give less output per mT. For weak fields like the Earth's, choose AMR or TMR; for magnets of a few mT, choose wide-range GMR or TMR. Size the choice to the field you need to measure. TMR's large output also reduces the relative impact of amplifier noise.
Example 2: field for current sensing
| Current | At 2 mm | At 5 mm |
|---|---|---|
| 1 A | 0.10 mT | 0.04 mT |
| 10 A | 1.0 mT | 0.40 mT |
| 50 A | 5.0 mT | 2.0 mT |
An AMR with a 1 mT linear range placed 2 mm from the conductor saturates at 10 A. To measure up to 50 A, move it to 5 mm or more or choose a wider-range element. On real boards conductors have finite width and neighbouring conductors add their fields, so confirm the field at the element with a magnetic analysis.
Example 3: why a bridge
Taking permalloy's temperature coefficient of resistance as about 0.3%/K, a single element changes 0.3% per kelvin and 3% for 10 K. The AMR signal is only about 1.25% per side, so temperature swamps the field signal. In a bridge with all four elements at the same temperature, thermal changes cancel and only the field-induced change reaches the output.
Analysis and design cautions
Cautions
- Saturation and hysteresis: exposure to a strong field can disturb magnetisation and shift the output. AMR sensors use set/reset pulses to restore it.
- Stray fields: nearby motors, magnets and conductors add their fields; cancel them with differential layouts or shielding.
- Sensitive axis: magnetoresistive elements respond to a specific in-plane direction, often different from a Hall element's, so placement errors are common.
- Modelling: elements are tiny, so magnetic analyses usually compute the field at the element location and convert to output using the characteristic curve.
“The compass goes wrong in the car”
A smartphone's electronic compass measures the Earth's field (about 0.05 mT) with AMR or TMR elements to find heading, yet it can go wrong in a car mount. The mount's magnet and the car body's steel add fields as large as or larger than the Earth's. When the phone asks you to wave it in a figure eight, it is rotating the device to identify and subtract the constant surrounding field. The weaker the field a sensor measures, the more its accuracy depends on estimating the surroundings.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Choosing by MR ratio alone | Range mismatch, saturation | Choose by field magnitude |
| Using a single element | Output drifts with temperature | Use a bridge |
| Ignoring conductor spacing | Current sensor saturates | Check with B = μ₀I/(2πr) |
| Ignoring stray fields | Offset errors | Differential layout, calibration |
| Wrong sensitive axis | Almost no output | Check the datasheet axis |
I'd like to try bridge and Hall calculations myself.
Try the Wheatstone bridge calculator for bridge output and the Hall effect simulator for the Hall effect. Compare other magnetic sensors in Hall effect sensors, fluxgate magnetometers, magnetic encoders and eddy current sensors.
Related Topics
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