Wireless power coil design: an end-to-end guide

What are the steps in designing a wireless power coil pair?

1. Write down the requirements: power, gap range, misalignment, size envelope and any standard.
2. Pick the frequency band, usually set by the standard or by regulations.
3. Choose a coil topology: wound or planar, circular or square, equal or unequal sizes.
4. Size the coils against the gap so the coupling coefficient k stays usable everywhere.
5. Choose turns to set the inductance and impedance level.
6. Estimate coil quality factor Q from the conductor and frequency.
7. Design the resonant compensation and check for frequency splitting.
8. Check the efficiency ceiling from k and Q.
9. Screen the magnetic field against exposure limits.
10. Prepare for fabrication, then build, measure and iterate.

The rest of this guide walks through each step with one running example, computed on this page with the same physics code as the free calculators. Each step links to a deeper article.

Which requirements should you fix first?

Gap and misalignment matter more than anything else, because they set the coupling and therefore almost every other number. Power level sets currents and voltages; the size envelope bounds the coils; and an interoperability standard, if one applies, fixes the frequency and often the transmitter design.

The running example is an illustrative accessory charger, not a design to any particular standard:

How do you choose the operating frequency?

If the product must interoperate, the standard decides: Qi typically operates at 87–205 kHz and its Magnetic Power Profile at 360 kHz, SAE J2954 at 85 kHz for vehicles, and AirFuel Resonant at 6.78 MHz (see wireless charging standards). For a proprietary link the trade-off is:

• Higher frequency raises the induced voltage ωMI and the coil Q for a given inductance, and shrinks capacitors. It also raises switching loss, skin and proximity loss, and sensitivity to self-resonance and parasitics, and it narrows the regulatory bands available.
• Lower frequency eases the power electronics and lets litz wire work well, at the cost of larger inductance and capacitance for the same power.

The example uses 125 kHz, inside the 87–205 kHz range in which Qi chargers typically operate. Check national rules for the band you choose; in the United States the FCC’s KDB 680106 describes how wireless power devices are authorised.

Which coil topology should you choose?

Three choices define the topology:

• Winding style. A wound coil, with all turns at one radius, packs the most inductance into its outline. A planar spiral, whose turns step inward, is flat and easy to print on a PCB but has less inductance per turn.
• Shape. Circular coils are rotationally symmetric, so misalignment in any direction has the same effect. Square or rectangular coils make better use of rectangular envelopes.
• Pairing. Equal transmitter and receiver sizes maximise peak k; a larger transmitter trades some peak k for a wider tolerance to misalignment.

The example uses two identical circular wound coils, the simplest case to compute and the one the calculators cover exactly.

How large should the coils be for the gap?

Coupling depends mainly on gap divided by coil size. With the 80 mm envelope, the largest circular coil has a radius of 40 mm. Using 1 mm wire and 10 turns, the coupling coefficient over the required range is:

k varies by a factor of about 2.5 across the gap range, and 10 mm of misalignment costs about 13 % at the nominal gap. That spread, not the nominal value, drives the compensation and control design. See coupling coefficient for how k behaves with distance and misalignment, and use the coupling coefficient calculator for other sizes.

How many turns do you need?

For compact windings self-inductance grows as N² and mutual inductance as N₁N₂, so turns change the impedance level but not k:

Pick N so the reactance matches the power electronics. Too few turns mean low voltage and high current for a given power; too many raise the capacitor voltage and the wire length, and push the coil towards self-resonance. The example keeps 10 turns: L = 18.11 µH, ωL = 14.2 Ω. For a planar spiral, use a planar inductance formula such as the expressions of Mohan et al., or compute the spiral turn by turn.

What coil Q can you expect?

Q = ωL/R depends on the AC resistance of the winding. For the example coil (2.51 m of 1 mm copper):

Proximity effect between adjacent turns adds further loss, so the real Q of a solid-wire coil will be lower than this bound. The example assumes Q = 100 for both coils, a value to confirm on an impedance analyser. Litz wire with strands well below the skin depth recovers much of the difference; Sullivan gives a method for choosing the strand count. WPT efficiency and kQ covers this in depth.

How do you design the compensation network?

Series–series (SS) compensation suits a link with a varying gap, because its capacitors depend only on the coil inductances:

The receiver load is set near the efficiency optimum R_L = R₂√(1 + U²) at the nominal gap, which gives R_L = 5.93 Ω (an AC-equivalent load seen by the coil, before the rectifier). Delivering 5 W then needs a primary current of 0.918 A RMS. The capacitor voltage is 13.1 V RMS (18.5 V peak), and the input resistance at resonance is 5.93 Ω.

The next check is frequency splitting. With this load the receiver’s loaded Q is ωL/R_L = 2.4. Scanning the input phase of the lossless link over 0.6–1.4·f₀ gives the zero-phase frequencies, together with the efficiency ceiling at Q = 100:

At the larger gaps the input is resistive only at 125 kHz. At the nominal gap and closer, the link is over-coupled for this load and extra zero-phase frequencies appear: bifurcation. A fixed-frequency controller at 125 kHz still works, but a controller that tracks zero phase could lock onto a side frequency, and the power delivered at fixed input voltage changes strongly with gap. The options are to accept and control it, to change the load or compensation (see compensation topologies, including LCC), or to reduce k at the closest gap. Size the capacitors with the compensation capacitor calculator.

How efficient will the link be?

With U = k√(Q₁Q₂) the coil-to-coil efficiency ceiling is η_max = U²/(1 + √(1 + U²))². At the nominal gap, k = 0.417 and Q = 100 give U = 41.7 and η_max = 95.3 %; the table above shows how it changes across the gap range. These are ceilings for the coils alone. Inverter switching, rectifier conduction, capacitor ESR and any ferrite or nearby metal reduce the end-to-end figure, so treat η_max as an upper bound and a way to compare geometries.

How do you check magnetic field exposure?

The ICNIRP 2010 general-public reference level from 3 kHz to 10 MHz is 27 µT; above 100 kHz the ICNIRP 2020 thermal limits apply as well, and IEEE C95.1-2019 is the other widely used reference. At the 5 W operating point the transmitter carries 0.918 A RMS, giving an on-axis field of 144 µT at the coil centre, falling to 27 µT about 57.4 mm above the coil plane (coil alone, in air).

In use, the receiver and device sit in the region of strong field, which is normal. What matters is the field where people can be, averaged as the guidelines require, and in the final product with its enclosure, ferrite and shielding. Compliance follows dedicated assessment methods such as IEC/IEEE 63184. The standards and exposure limits article gives the numbers and sources.

What matters when you fabricate the coils?

• Conductor. At 125 kHz the copper skin depth is 0.187 mm, so litz wire with finer strands, or several parallel thinner conductors, cuts AC loss. At MHz frequencies, solid or plated conductors and wide traces are more practical.
• PCB spirals. Trace width, copper weight and spacing set resistance and inter-turn capacitance. Multiple layers can be paralleled to lower resistance or connected in series to raise inductance.
• Ferrite and shielding. A ferrite sheet behind the coil raises L and k and contains the field; a metal plate behind it lowers both and adds eddy-current loss. Either change requires re-tuning, and neither is in an air-core model.
• Capacitors. Use low-loss dielectrics rated for the resonant voltage and current, and allow for tolerance and temperature drift in the tuning.

How do you verify the prototype?

1. Measure each coil’s inductance and Q at the operating frequency with an impedance analyser or LCR meter.
2. Measure k by the open/short method: k = √(1 − L_sc/L_oc), at several gaps and offsets across the range.
3. Tune the capacitors to the measured inductances, then sweep frequency at low power to find the zero-phase points.
4. Measure efficiency and coil and capacitor temperatures at full power across the gap and misalignment range.
5. Measure the field around the finished product for the exposure assessment.

If the measured k differs from the air-core model by more than the measurement uncertainty, look for nearby metal, ferrite or a winding that differs from its drawing; Biot–Savart vs FEM explains which effects the closed-form model leaves out.

References

1. G. A. Covic and J. T. Boys, “Inductive power transfer,” Proceedings of the IEEE 101(6), 1276–1289 (2013). doi.org/10.1109/JPROC.2013.2244536
2. C.-S. Wang, G. A. Covic and O. H. Stielau, “Power transfer capability and bifurcation phenomena of loosely coupled inductive power transfer systems,” IEEE Trans. Industrial Electronics 51(1), 148–157 (2004). doi.org/10.1109/TIE.2003.822038
3. W. Zhang and C. C. Mi, “Compensation topologies of high-power wireless power transfer systems,” IEEE Trans. Vehicular Technology 65(6), 4768–4778 (2016). doi.org/10.1109/TVT.2015.2454292
4. M. Zargham and P. G. Gulak, “Maximum achievable efficiency in near-field coupled power-transfer systems,” IEEE Trans. Biomedical Circuits and Systems 6(3), 228–245 (2012). doi.org/10.1109/TBCAS.2011.2174794
5. C. R. Sullivan, “Optimal choice for number of strands in a litz-wire transformer winding,” IEEE Trans. Power Electronics 14(2), 283–291 (1999). doi.org/10.1109/63.750181
6. S. S. Mohan, M. del Mar Hershenson, S. P. Boyd and T. H. Lee, “Simple accurate expressions for planar spiral inductances,” IEEE J. Solid-State Circuits 34(10), 1419–1424 (1999). doi.org/10.1109/4.792620
7. F. W. Grover, Inductance Calculations: Working Formulas and Tables, Van Nostrand (1946); Dover reprint (2004), ISBN 978-0-486-49577-4. openlibrary.org/isbn/9780486495774
8. Wireless Power Consortium, “Qi Specification version 1.3: Introduction” (PDF), operating frequency and power profiles. www.wirelesspowerconsortium.com/media/cd4ljryt/qi-v13-introduction.pdf
9. SAE International, J2954_202408, “Wireless Power Transfer for Light-Duty Plug-in/Electric Vehicles and Alignment Methodology” (2024). saemobilus.sae.org/standards/j2954_202408-wireless-power-transfer-light-duty-plug-electric-vehicles-alignment-methodology
10. ICNIRP, “Guidelines for limiting exposure to time-varying electric and magnetic fields (1 Hz to 100 kHz),” Health Physics 99(6), 818–836 (2010). doi.org/10.1097/HP.0b013e3181f06c86
11. ICNIRP, “Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz),” Health Physics 118(5), 483–524 (2020). doi.org/10.1097/HP.0000000000001210
12. IEEE Std C95.1-2019, IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 Hz to 300 GHz (2019). doi.org/10.1109/IEEESTD.2019.8859679
13. IEC/IEEE 63184:2025, Assessment methods of the human exposure to electric and magnetic fields from wireless power transfer systems (3 kHz to 30 MHz). Supersedes IEC PAS 63184:2021. standards.ieee.org/ieee/63184/10156/
14. U.S. FCC Office of Engineering and Technology, KDB 680106, “Wireless Power Transfer” (updated October 2023). apps.fcc.gov/oetcf/kdb/forms/FTSSearchResultPage.cfm?switch=P&id=41701