WPT efficiency calculator, from k and Q.
Maximum link efficiency, the figure of merit U = k√(Q1Q2), the optimal load and the coupling you need — with η plotted against k.
WPT efficiency calculator
- Maximum link efficiency η_max
- 81.9 %
- Figure of merit U = k√(Q₁Q₂)
- 10
- Optimal load R_L / R₂ (series secondary)
- 10.05= √(1 + U²)
- k needed for 90 %
- 0.1897
Coil-to-coil efficiency with ideal resonant compensation and an optimally matched load; excludes inverter and rectifier losses. Q = ωL/R of each unloaded coil.
What is the maximum efficiency of a wireless power link?
The maximum efficiency of a wireless power link is η_max = k²Q1Q2 / (1 + √(1 + k²Q1Q2))², set entirely by the coupling coefficient k and the quality factors Q1 and Q2 of the two coils. Engineers usually summarise this with the figure of merit U = k√(Q1Q2): a link with U = 10 can reach about 82 % coil-to-coil efficiency, U = 30 about 94 %, and U = 100 about 98 %. This explains why loosely coupled resonant systems still work — a small k can be offset by high-Q coils. This calculator returns η_max, U, the load-to-coil resistance ratio that achieves it, and the coupling needed to hit a target efficiency, with a chart of efficiency against k on a log scale. It assumes ideal resonant compensation and excludes inverter and rectifier losses, so treat it as an upper bound. AirInduct Sim computes k and the coil losses behind Q from real geometry in its full simulator.
How it's calculated
This is the coil-to-coil efficiency of a two-coil link with both sides resonant and the load chosen to maximise efficiency. For a series-tuned receiver with coil resistance R₂ the optimum load is:
Inverting the efficiency formula gives the coupling needed for a target η:
- Q₁ = ωL₁/R₁ and Q₂ = ωL₂/R₂ are the unloaded quality factors at the operating frequency.
- Excludes inverter, capacitor ESR, rectifier and DC–DC losses: an upper bound.
- We checked the formula and the optimal load by brute-force sweeping R_L in an SS circuit model; both match to four significant figures.
- Get k from coil geometry with the coupling coefficient calculator.
Worked example
How efficiency responds to coupling and coil quality:
| k = 0.05, Q₁ = Q₂ = 100 | U = 5, η_max = 67.2 %, R_L/R₂ = 5.1 |
|---|---|
| k = 0.1, Q₁ = Q₂ = 100 | U = 10, η_max = 81.9 %, R_L/R₂ = 10 |
| k = 0.2, Q₁ = Q₂ = 100 | U = 20, η_max = 90.5 %, R_L/R₂ = 20 |
| k = 0.1, Q₁ = Q₂ = 300 | U = 30, η_max = 93.6 %, R_L/R₂ = 30 |
With Q = 100 coils, 90 % efficiency needs k ≥ 0.19. Tripling both Q factors does the same job as tripling k: the last row reaches the same U as k = 0.3 with Q = 100.
When you need the full simulator
This calculator is free to use and answers one question at a time. The full AirInduct Sim simulator takes the same physics further:
- k from your actual coil geometry, gap and misalignment rather than an estimate.
- Coil resistance and Q from Litz-wire AC-resistance and skin/proximity-loss models.
- Full efficiency through the matching network, inverter and rectifier, swept over load.
- Thermal analysis of the coils at the operating current.
More free calculators
- Mutual inductance calculatorM between two circular or square coils from turns, size, axial gap and lateral offset — or from k, L1 and L2.
- Coupling coefficient calculatork from coil geometry (with both self-inductances) or from L1, L2 and M, plus a k-versus-gap curve.
- Helmholtz coil calculatorCentre field, required current and optimal spacing for circular and square Helmholtz pairs, with axial uniformity.
- Square Helmholtz coil calculatorSquare pairs at the 0.5445·a spacing: centre field, current for a target field and the uniform region.
- WPT compensation capacitor calculatorSeries–series and series–parallel resonant capacitors from L1, L2, M and frequency, with capacitor voltage stress.
Frequently asked questions
What is the figure of merit U in wireless power transfer?
U = k√(Q1Q2) combines coupling and coil quality into one number that alone fixes the best achievable coil-to-coil efficiency. Doubling k has the same effect as quadrupling the product Q1Q2. Values of U above about 10 are needed for efficiencies above 80 %.
How can I increase the efficiency of my WPT link?
Raise k or raise Q. k increases with larger coils relative to the gap, better alignment and ferrite shielding. Q = ωL/R increases with lower AC resistance — Litz wire at kHz frequencies, thicker conductors or plated copper at MHz — and, up to the point where AC losses take over, with higher frequency. Then make sure the load is matched to the optimum ratio the calculator reports.
Is this the efficiency of the whole charger?
No. It is the coil-to-coil (link) efficiency with ideal capacitors and an optimally matched load. A complete system also loses power in the inverter, the compensation capacitors, the rectifier and any DC–DC stage, so system efficiency is lower. It is a useful upper bound for comparing coil designs.
Does the maximum efficiency depend on SS or SP compensation?
The maximum coil-to-coil efficiency η_max is the same for the common topologies once each is tuned and its load is optimally matched; what changes is the load value that achieves it. For a series-tuned receiver the optimum is R_L = R2·√(1 + U²). Use the compensation capacitor calculator to size the tank.