Why a Wireless Charger Is So Picky About Where the Phone Sits

Rand Simulation — Applications Engineering AI
Consumer Products · Ansys Maxwell · 8 min read

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The two modeled coils, sliding out of alignment. The pad's transmit coil (Tx) stays put; the phone's receive coil (Rx) slides sideways, and the readout tracks the solved Ansys Maxwell coupling k and the power the phone can still pick up. Aligned, the coils sit concentric and strongly linked; a half-inch off, the link has mostly collapsed. The gap is drawn slightly exaggerated so both coils read — the true coil-to-coil gap is 4 mm.

The short version: nudge your phone half an inch on a charging pad and it stops charging. We built the transmit and receive coils as the loosely-coupled air-cored transformer they really are and solved their magnetic coupling in Ansys Maxwell, sweeping lateral offset and gap. The coupling coefficient k falls from 0.73 aligned to 0.38 at 11 mm and 0.25 at 14 mm — but because the power a link can push scales with k², a half-inch nudge (12.7 mm) cuts the power the phone can pick up by roughly 80%. The twist: the link's best-case efficiency barely moves (96→89%), so the charger is not becoming inefficient — it is losing the operating point it was tuned for, and the control loop runs out of headroom trying to compensate. That compensation is also where the “my phone got warm charging crooked” heat actually comes from. And that steep falloff is exactly why alignment magnets exist.

Two Coils and One Number That Governs Everything

A wireless charger is a transformer with an air gap. A flat spiral “pancake” coil in the pad (the transmitter, Tx) drives an alternating magnetic field at the Qi operating frequency — we used 140 kHz; a matching coil in the phone (the receiver, Rx) picks up whatever fraction of that field links it and rectifies it to charge the battery. Unlike the iron-cored transformer in a wall adapter, the two coils are only loosely coupled by design, with nothing but air, plastic, and a few millimeters between them. The single number that governs the whole exchange is the coupling coefficient

k = M / √(L_tx·L_rx) (0 ≤ k ≤ 1),

where M is the mutual inductance between the coils and L_tx, L_rx are their self-inductances. There is no honest closed form for k of a real pancake coil with a ferrite shield at an arbitrary lateral offset — the textbook coaxial-loop formula only holds on the shared axis. So we let Maxwell compute the inductances directly from the solved magnetic field. We modeled a generic Qi-style pair — a 43 mm transmit coil and a 40 mm receive coil, ten litz turns each, each backed by a high-permeability MnZn ferrite tile that channels the flux, plus an aluminum plate standing in for the phone's metal back — and read a two-winding inductance matrix at each alignment.

Before trusting a single offset number, we checked the aligned case against physics we already know. The solved coupling at perfect alignment, k = 0.730, matches the classical coaxial-loop mutual-inductance formula's k = 0.733 to within 0.4% — even though the ferrite boosts the individual inductances about 2.1× above their air-core values. That is the strong physical check: ferrite lifts L and M together, so it barely moves k, and the solved coupling lands right on the closed form. Every solve converged to an energy error near 0.6% over twelve adaptive passes on roughly 40,000 tetrahedra.

How Fast It Falls Off

Here is the answer to the question the pad makes you ask every morning. Slide the phone sideways and the mutual inductance drops fast while the self-inductances barely change, so k falls steeply: 0.73 aligned, 0.67 at 4 mm, 0.52 at 8 mm, 0.38 at 11 mm, 0.25 at 14 mm. Coupling itself roughly halves at a half-inch offset. But k is not the thing you feel — delivered power is, and the power a loosely-coupled link can transfer scales with k² (more precisely, with M²). Square the falloff and it turns brutal: the power the phone can pick up drops to 68% at 6 mm, 51% at 8 mm, and just 28% at 11 mm. Interpolated to a literal half-inch, 12.7 mm, the phone is down to about 18% of the power it had when centered — an 80% loss for half an inch of travel. That squared law is the mathematical reason a small nudge feels like an on/off switch.

Line chart: coupling k and the receiver's power capability both falling with lateral offset, power falling much faster, with a marker at the half-inch point showing about 18 percent of aligned power — The money chart, straight from the converged solves. Coupling (blue) falls steeply with offset; the power the phone can pick up (red), which scales as M², falls far faster. At a half-inch nudge the receiver is down to roughly a fifth of its aligned power — the everyday “it just stopped charging.”

Lifting the phone off the pad does the same thing along the other axis. Holding the coils centered and opening the gap, k runs 0.86 at 2 mm, 0.73 at our nominal 4 mm, 0.61 at 6 mm, and 0.45 at 9 mm — which is why a thick case or a coin stuck to the back of the phone matters, and why the coils want to be as close as the plastic allows.

Two panels: coupling coefficient k versus lateral offset, and coupling coefficient k versus coil-to-coil gap, both falling monotonically — The two things you can do wrong. Left: slide the phone sideways. Right: lift it off the pad (a case, a bit of debris). Both drop the coupling monotonically; the sideways slide is the steeper sin because the field a coil throws sideways falls off faster than the field straight above it.

The Twist: The Link Never Gets Inefficient

You would expect all that lost power to show up as a collapsing efficiency. It does not. Feeding the solved inductances and the eddy-current winding resistance into the standard series–series resonant-link relations, the coils' quality factor comes out around Q ≈ 71 (litz wire keeps the resistance low), and the best-case link efficiency stays high across the whole sweep: 96% aligned, still 89% at the worst 14 mm offset. What collapses is the link's figure of merit U = k²·Q_tx·Q_rx, which falls about nine-fold — and U is what sets how much power the link can actually move at a matched operating point, not how efficiently it moves the last bit.

Chart showing maximum link efficiency staying between 96 and 89 percent while the figure of merit U falls about nine-fold on a log axis — Why “efficiency” is the wrong lens. The best achievable efficiency (green) barely moves because the coils are high-Q. The figure of merit U (blue, log scale), which governs how much power crosses at a fixed tuning, falls nine-fold. A perfectly re-tuned link would stay efficient at 11 mm — a real charger, tuned once for a centered phone, simply loses its match.

That is the honest resolution of the puzzle. Charging does not stop because the physics becomes lossy; it stops because a fixed charger, resonant-tuned and current-limited for a centered phone, falls off its operating point as the coupling drops. The received voltage sags, and the charger's control loop pushes more current to hold it — until it hits its limit and the receiver can no longer maintain the voltage its regulator needs. Then it gives up. We modeled the electromagnetic link, not that control loop, so we report the coupling and the power capability it sets, and name the loop as the thing that turns a steep curve into an abrupt cutoff.

Where the Wasted Power Goes — and Why It's Subtler Than It Sounds

The companion question was thermal: a badly-placed phone gets warm, so where does the heat land? We drove the transmit coil at a fixed, realistic current (1.4 A rms) and solved the eddy-current losses in the coils, ferrite, and aluminum shield, then fed those into an Icepak steady-state temperature solve. The result is a useful surprise, and it is worth stating plainly rather than forcing it to match the folklore. At a fixed drive current, the hardware barely warms differently when you misalign it. The peak temperature rise is 6.4 °C aligned and 6.0 °C at 11 mm — essentially flat, because most of the heat is the transmit coil's own resistive loss, which the geometry does not change. The aluminum shield's stray-current loss actually falls as the phone slides away, because less of the transmit field reaches it.

Two panels: solved per-object temperature rise nearly identical aligned versus offset, and transmit-coil heat rising sharply as one-over-k-squared when holding a fixed charge rate — Left: the solved Icepak temperature rise, aligned versus 11 mm offset — almost unchanged, because at a fixed drive the coil's own loss dominates. Right: the real reason a crooked phone warms up. To keep delivering the same charge rate as coupling falls, the drive current must rise, and coil heating scales as its square (∝ 1/k²) — about 3.6× more coil heat at a half-inch offset. That heat lives in the drive compensation, in the control loop we did not model.

So why does a misaligned phone genuinely feel warm? Because a real charger does not hold the drive fixed — it cranks the current up to fight the falling coupling and keep the charge going. Coil heating scales as the square of that current, so holding the same charge rate through the collapsing link would take on the order of 3.6× more heat in the coil at a half-inch offset, and more still beyond that. The warming is real, but it is a symptom of the compensation, not of the geometry — the misalignment does not dump more heat into the phone so much as it forces the charger to work far harder to deliver the same watts. That distinction is exactly the kind of thing a field solve makes visible and intuition gets backwards.

Why Alignment Magnets Became a Thing

Put the two findings together and the design decision writes itself. Coupling collapses within a few millimeters of offset; delivered power, scaling as its square, collapses faster; and the only way to keep a fixed charger on its operating point is to keep the coils centered. You cannot ask the user to place a phone within a couple of millimeters by eye every time. So manufacturers stopped asking: they ringed the coils with permanent magnets (the MagSafe-style ring) that mechanically snap the phone onto the axis, guaranteeing the aligned end of every curve in this study. The magnets are not there for convenience — they are there because the coupling falloff we measured is that unforgiving. We did not simulate the magnet ring's holding force here; that is a separate magnetostatic force problem. But the reason it exists is the curve on this page.

Honest scope. This is a physics demonstration on a self-authored, brand-free generic Qi-style coil pair — a 43 mm transmit and 40 mm receive pancake coil, ten litz turns each, MnZn ferrite tiles (linear μ_r = 2000), and a 70 × 68 mm aluminum shield plate — not any specific product, and no specific phone's watts or charge time. The coupling k, mutual and self inductances are solved directly in Ansys Maxwell (3-D magnetostatic, two-winding inductance matrix), swept over seven lateral offsets and four gaps; every solve converged to about 0.6% energy error over twelve adaptive passes (≈ 40,000 tetrahedra each, 397,000 across the coupling sweep, 4 cores). The aligned coupling matches the closed-form coaxial-loop value to 0.4%, and each coil's self-inductance tracks the Wheeler planar-spiral formula. Delivered power and efficiency are derived, not solved directly: we run the solved two-port (L, M from magnetostatic; winding R from a 140 kHz eddy-current solve) through the standard series–series resonant-link relations (η_max = U/(1+√(1+U))², U = k²Q_txQ_rx); every input is a Maxwell number, only the well-known link algebra is applied. We do not model the power electronics — the transmit inverter, the receive rectifier and regulator, Qi's closed-loop power control, or foreign-object detection — so the abrupt real-world cutoff is attributed to that control loop, not claimed from a solved converter. Litz wire is idealized as stranded (no intra-strand skin loss, correct at these frequencies); the ferrite uses a linear permeability with a representative loss, not a datasheet Steinmetz fit; the thermal companion is a steady-state bounding ΔT at a fixed drive with simplified open-air convection, not a warm-up curve or exact case temperatures. The “3.6× more coil heat” figure is the k² scaling of holding a fixed charge rate, an interpretation of the solved coupling, not a solved converter result. The alignment magnet is explained as the consequence of the measured falloff, not simulated. The animated hero renders the true solved geometry; the intended field-linkage animation degraded because the headless magnetic-field grid export returned a near-uniform plane, so the hero shows the recognizable coils with the solved coupling annotated instead.

Designing a coil, a motor, or any magnetic link that has to hold its coupling across real tolerances? The number that decides whether it works — how much flux one winding actually links into another as geometry shifts — is a field quantity with no shortcut, and it is exactly what a low-frequency field solve prices before you wind copper. We run magnetics and coupled electromagnetic–thermal studies in Ansys Maxwell, geometry through validated results. Rand Simulation — innovation through insight.