🔋Wireless Charging & Cooktop Simulator - Mutual Inductance, Coupling, Efficiency

How to use Wireless charging & induction cooktops

1. 1On Coil coupling, pick a preset or set the radii, turns and spacing, then drag the receive coil and watch k change
2. 2On Resonant link efficiency, set frequency, Q values and load to see the efficiency curve and the frequency split
3. 3On Qi phone charger, drag the phone to compare coupling and efficiency aligned and offset
4. 4On Induction cooktop, choose the pan material, frequency, diameter and thickness to see skin depth and heating power

FAQ

Why does wireless charging only work over such short distances?

It relies on near-field magnetic coupling. Beyond about one coil radius the transmit field falls roughly as 1/d³, and the coupling coefficient k drops just as fast. A Qi coil is only about 4 cm across: a few millimetres apart k is 0.3–0.6, and at 2 cm there is little left. Going further needs bigger coils, or high-Q resonance so that a small k still gives decent efficiency.

How can resonance be efficient when k is tiny?

With series-series compensation the coil reactance is cancelled and efficiency depends only on the figure of merit U = k√(Q₁Q₂). The maximum efficiency is η = U²/(1+√(1+U²))². For k = 0.05 and Q₁ = Q₂ = 300, U = 15 and efficiency is still above 87%. That needs the load matched to R₂√(1+U²); the tool shows how efficiency falls when it is not.

What is frequency splitting?

When two resonators tuned to the same frequency are coupled strongly (k above roughly 1/Q), the system gets two new natural frequencies near f₀/√(1±k). Load power versus frequency changes from one peak to two, and the original f₀ becomes a dip. So a charger fixed at f₀ delivers less power when the coils are too close, unless it tracks frequency or adapts the load.

Why can’t induction hobs heat aluminium or copper pans?

Heating power is proportional to the surface resistance R_s = √(πfμρ). Iron has high permeability and fairly high resistivity, so at 25 kHz its skin depth is under 0.1 mm and R_s is large. Aluminium and copper are non-magnetic with low resistivity, so their R_s is only a few percent of iron’s: they barely warm at the same current, and the coil sees too small a load for the inverter to match. Matching iron would take hundreds of times the frequency, which is why only special all-metal hobs handle them.

How accurate are the inductance calculations?

Coaxial single-turn mutual inductance uses the closed form with complete elliptic integrals K and E, accurate to floating point. Offset and tilt use the Neumann formula integrated numerically over 160×160 segments, which agrees with the closed form to well under 1%. Multi-turn coils are treated as wound at a single radius and self-inductance uses μ₀a[ln(8a/r)−2], so real flat spiral coils will differ somewhat. Treat the results as estimates for learning and early design.