Fluxgate Magnetometer
Principle: reading the asymmetry of saturation
Overview
I heard satellites and geomagnetic observatories use fluxgates rather than Hall sensors. What's so different?
It comes down to how small the field is. The Earth's field is a few tens of microtesla, and you want to track changes of a few nanotesla down to 0.1 nT, stably, for years. A fluxgate deliberately drives a soft magnetic core into saturation with AC and reads the external field from the asymmetry of that saturation. Its zero point hardly drifts with temperature, and it excels at weak, low-frequency fields.
Where the second harmonic comes from
A common arrangement drives two cores (or the two halves of a ring core) in opposite directions and picks up the change in their total flux with a coil around both. Approximating the magnetisation curve with a saturating function gives:
With no external field the two fluxes cancel and the pickup sees nothing. With an external field one core saturates earlier and the other later, producing the same difference every half cycle — which appears as a component at twice the drive frequency.
How many A/m is the Earth's field?
The permalloy or amorphous alloys used in fluxgate cores approach saturation at a few to a few tens of A/m. So the Earth's field itself is comparable to the core's saturating field and can exceed the range where it counts as “small”. That leads to the linearity issue in the next section.
From hunting submarines to exploring space
The fluxgate principle was known from the 1930s, but it was developed rapidly during the Second World War, when aircraft used it to detect the tiny disturbances submarines cause in the Earth's field. After the war it spread to geological and mineral surveys, and from the late 1950s it flew on satellites and planetary probes, underpinning observations of the magnetospheres of the Earth and other planets. Decades later it is still the standard sensor for magnetic measurements in space.
Worked example: linearity with a simple model
Second harmonic versus external field
Using the model above with $H_k = 10$ A/m and drive amplitude $H_{exc} = 100$ A/m (ten times $H_k$), one period was computed at 4096 points and the second-harmonic amplitude extracted. Values are relative to $H_{ext} = 1$ A/m.
| External field $H_{ext}$ | Second harmonic | Deviation from linear |
|---|---|---|
| 1 A/m | 1.000 | 0 % |
| 5 A/m | 4.994 | −0.1 % |
| 10 A/m | 9.949 | −0.5 % |
| 20 A/m | 19.58 | −2.1 % |
| 40 A/m (about the Earth's field) | 36.53 | −8.7 % |
At Earth-field levels it reads almost 9% low. How can that possibly resolve nanotesla?
That's why real fluxgates run closed loop. When a second harmonic is detected, current is driven through a separate feedback coil until the harmonic is nulled, cancelling the external field. The core then always works near zero field, the linearity problem disappears, and the reading comes from the current needed for cancellation. Linearity and stability are then set by the feedback coil's geometry and the accuracy of the current measurement.
Drive amplitude and sensitivity
| Drive amplitude | Sensitivity (1 at $H_{exc} = 10H_k$) |
|---|---|
| 0.5 $H_k$ | 0.84 |
| 1.5 $H_k$ | 3.05 |
| 3 $H_k$ | 2.82 |
| 10 $H_k$ | 1.00 |
| 30 $H_k$ | 0.34 |
In this simple hysteresis-free model, sensitivity peaks at drive amplitudes of about 1.5–3 times the saturating field and falls when the core is overdriven, because the saturation transitions become brief. In practice cores are often driven several times harder than that to erase magnetic memory (zero-point shifts left by earlier exposure) and reduce noise. The drive level is a trade-off between sensitivity, noise and zero-point stability, not sensitivity alone.
Analysis and design points
Modelling in field simulation
- Nonlinear transient analysis is required: saturation is the working principle, so a linear frequency-domain analysis cannot produce the second harmonic. Include the nonlinear B-H curve, solve several drive periods in time, and Fourier-analyse the pickup voltage.
- Time step: saturation transitions occupy a small fraction of the period, so use at least several hundred steps per period or the harmonic amplitudes will be off.
- Asymmetry errors: a slight mismatch between the two cores or windings produces a second harmonic even with zero external field, which appears as an offset. Sensitivity studies with geometric tolerances as parameters are useful.
- Nearby magnetic materials: steel brackets or housings distort the field and, once magnetised, add offset. Keep the sensor surroundings non-magnetic and check the effect in the analysis.
Comparison with other magnetic sensors
| Sensor | Strength | Weakness |
|---|---|---|
| Fluxgate | Weak low-frequency fields (geomagnetism, space, NDT) | Power, size, bandwidth |
| Hall-effect sensors | Moderate to strong fields including DC; current sensing | Zero-point drift and noise |
| magnetoresistive sensors | Small and sensitive; angle and position sensing | Characteristics change in strong fields |
| search coils | AC fields and flux changes | Cannot measure DC |
When the reading changes although nothing moved
In precise fluxgate measurements the reading sometimes drifts although neither the sensor nor its surroundings moved. Common causes are temperature-driven changes in the feedback coil's dimensions and fields from DC currents in nearby equipment. A single car passing tens of metres away can change the reading by several to tens of nanotesla. That is why observatories sit far from towns; in the lab, recording cable routing and power-supply positions makes such drifts much easier to trace.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Using a linear frequency-domain analysis | No second harmonic appears | Nonlinear B-H with transient analysis |
| Measuring a wide range open loop | Output deviates from linear at large fields | Use feedback to null the field |
| Time step too coarse | Harmonic amplitudes are off | Several hundred steps per period or more |
| Assuming perfect symmetry of cores and windings | Offset cannot be estimated | Run tolerance sensitivity studies |
| Ignoring nearby iron | Distortion and offset | Use non-magnetic parts and check in the analysis |
I'd like to see for myself how saturation of the magnetisation curve matters.
Change the saturation and hysteresis shape in the magnetic hysteresis simulator or the magnetic materials B-H curve simulator to see how the core behaves at different drive amplitudes. How the pickup coil voltage arises can be checked with the Faraday's law simulator.
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators