Sensitivity, dynamic range and bandwidth pull against each other. A sensor is a choice of corner, not a wish-list — and in this toy model the three weights sum to one fixed design budget. (Real hardware moves the whole triangle, not just the point inside it — see Explain.)
The question: why can't one detector be exquisitely sensitive, cover a huge dynamic range, and respond at high bandwidth all at once? Drag the handle P above and watch the three weights — they always add to 100%. Push toward one corner and the other two collapse: that is the proof you can't max all three.
Got a feel for it? Step to 2 · Notice →
…
The thing to notice: every weight you pour into one corner is drained straight out of the other two. The full seven-magnetometer comparison — the evidence for the exercise — is in the table below the triangle.
Wherever P sits, the three weights sum to one. Slide P toward the Bandwidth corner and watch Sensitivity and Dynamic range drain away in lock-step. Why is the total conserved — why can't a clever design just buy back the corners it spent?
The three corners draw on the same physical pool: a finite count of quanta (photons, atoms, spins) read out in a finite time. Spend that pool on resolving a tiny change and you have used up the headroom for a large one (range) and the speed of repeated reads (bandwidth). You can move the allocation — that is engineering — but you cannot create more total without changing the hardware (more atoms, longer integration, lower temperature), which moves the whole triangle, not P inside it. Real sensors are points pinned to a corner because their physics already chose the split for them.
Put the three corners at vertices vS, vD, vB. Any point P inside the triangle has a unique barycentric coordinate P = wSvS + wDvD + wBvB with wS + wD + wB = 1 and every w ≥ 0. Each weight is the relative area of the sub-triangle opposite that corner (divide P-to-edge distance by the triangle's height). At a vertex one weight is 1 and the others are 0 — the visual proof you cannot max all three. The constraint Σw = 1 is the conserved quantity: the readout's percentages are just 100·w.
Same shape elsewhere on the hub:
You need to detect a 10 nT magnetic field at 1 kHz. Drag P into the red target zone near the bandwidth corner — see how much sensitivity and range you spend to get there. Then read the seven-magnetometer table below the triangle, pick two candidates, and decide between them.
Fill the judgement (Claim · Evidence · Assumption · Limitation · Decision):
| Claim | (which technology, in one line) |
| Evidence | where each sits on sensitivity / range / bandwidth for the 10 nT @ 1 kHz target |
| Assumption | what about the task you're taking for granted (field strength stable? single-shot? environment?) |
| Limitation | which corner your choice gives up — and whether that matters here |
| Decision | your pick, and what would change it |
What good looks like:
Logbook (one entry): Tried · Stuck (where/how long) · Hub resource used · Changed my mind because… · Still unclear.
The dots highlighted in the triangle above are these seven (greyed dots are non-magnetometers, for scale). • Sensitivity — smallest field you can resolve (noise floor). • Dynamic range — smallest to largest before it saturates. • Bandwidth — how fast a change you can follow.
| Technology | Sensitivity (noise floor) | Dynamic range | Bandwidth | Best corner |
|---|---|---|---|---|
| ● Hall probe | ~0.1–1 µT/√Hz | mT – tens of T | DC – MHz | range |
| ● MR · magnetoresistive (AMR/GMR/TMR) | ~0.1–10 nT/√Hz | nT – mT | DC – MHz | bandwidth |
| ● Coil · search / induction coil | ~fT–pT/√Hz (rises at low f) | wide | AC only, ~Hz – MHz | bandwidth |
| ● FGM · fluxgate | ~5–10 pT/√Hz | ±~100 µT (Earth field) | DC – ~1 kHz | range |
| ● NV · NV-diamond | ~1 pT – nT/√Hz | µT – T (vector) | DC – MHz+ | bandwidth |
| ● SQUID | ~1–10 fT/√Hz | wide (flux-locked loop) | DC – kHz+ | sensitivity |
| ● OPM · SERF / optically-pumped | ~1–15 fT/√Hz | small (near-zero field) | DC – ~100–200 Hz | sensitivity |
Order-of-magnitude, after Bennett et al., Sensors 21, 5568 (2021) (open: arXiv:2106.15843); the conventional sensors after Lenz & Edelstein, IEEE Sens. J. 6, 631 (2006). Abbreviations & how each one works: the reference list below.
For 10 nT @ 1 kHz: 10 nT is a large field, so sensitivity is not the binding constraint — only the Hall probe (µT floor) is too coarse to see it. 1 kHz bandwidth is: it rules out SERF/OPM (fades by ~200 Hz) and strains the fluxgate. Which room-temperature rows actually clear 1 kHz with field to spare? Deciding that is the Connect step (4).
The seven graph/table labels: Hall Hall probe · MR magnetoresistive (AMR / GMR / TMR = anisotropic / giant / tunnelling) · Coil search / induction coil · FGM fluxgate magnetometer · NV nitrogen-vacancy (centre in diamond) · SQUID superconducting quantum interference device · OPM optically-pumped magnetometer. Also: SERF spin-exchange-relaxation-free · ODMR optically-detected magnetic resonance · /√Hz per-root-hertz (amplitude noise density) · T tesla (1 T = 10⁹ nT).
It governs sensors at every scale — the clock buys 10¹⁸ sensitivity by surrendering range and speed:
| Sensor | Sensitivity | Dynamic range | Bandwidth | Corner |
|---|---|---|---|---|
| Human eye (dark-adapted rod) | ≈ a single photon | ~10⁶ (with adaptation) | ~10–60 Hz | sensitive & wide, but slow |
| Smartphone MEMS accelerometer | ~10⁻³ m/s² | 0 – 80 m/s² (≈ ±8 g) | < 100 Hz | wide & fast, modest sensitivity |
| Trapped-ion optical clock | ~1 part in 10¹⁸ | one transition ± few MHz | ~1 reading / hour | ultimate sensitivity, narrow & slow |
From the 2025 Sensing I notes.