Resonant inductive coupling links a transmitter and receiver coil through a shared oscillating magnetic field. Efficiency depends on how tightly the coils are magnetically coupled (which falls off fast with distance and misalignment) and how closely both are tuned to the same resonant frequency.
k = k₀ / (1 + (d/d₀)³) · cos(θ_misalign)
η = k²Q² / (1 + k²Q² + (Δf/f₀·Q)²)
P_out = P_in · η
- Coil distance — separation between transmitter and receiver; coupling drops roughly with the cube of distance.
- Frequency detuning — how far the receiver's resonant frequency drifts from the transmitter's; even a few percent mismatch sharply cuts efficiency at high Q.
- Coil misalignment — angular tilt between coil axes; misaligned coils couple less of the magnetic flux.
- Load resistance — receiver-side load; affects how much of the coupled power is actually extracted versus circulating.
This is the same physics behind Qi wireless phone chargers, wireless EV charging pads, and implanted medical-device power links — all use tuned resonant coils rather than direct electrical contact.