Circular DTC-to-Helmholtz Coil Pair
A flat circular planar-spiral (DTC) transmitter drives a wound multi-turn circular receiver. This is the familiar consumer layout: a flush pad underneath, a wound coil inside the earbud case, stylus or wearable.
Worked example
Inputs. Transmitter: 5-turn circular planar spiral (DTC), 2 mm pitch, turns at 50, 48, 46, 44, 42 mm radius. Receiver: 5 co-located circular turns at 50 mm radius. Coaxial, no lateral offset, 1 A at 6.78 MHz, air gaps of 10 mm and 30 mm.
| Air gap | M (µH) | L_tx (µH) | L_rx (µH) | k |
|---|---|---|---|---|
| 10 mm | 2.384 | 4.912 | 7.615 | 0.390 |
| 30 mm | 1.052 | 4.912 | 7.615 | 0.172 |
Going from 10 mm to 30 mm lowers k from 0.390 to 0.172, a 56% drop. The 4.9 µH pad is the lower-inductance side here, which keeps transmitter voltage modest for a given drive current — useful when the pad runs from a low-voltage USB supply.
When it's the right choice
- Earbud, stylus and wearable charging pads
- Transmitters that must sit flush under a desk, tray or console surface
- Retrofits onto an existing flat charging surface
Wound receiver vs spiral receiver
Keeping the flat spiral transmitter but swapping the wound receiver for a second spiral raises the coupling coefficient, and AirInduct Sim quantifies the gain: k climbs from 0.390 to 0.461 at a 10 mm gap and from 0.172 to 0.197 at 30 mm. The reason is not more shared flux — mutual inductance actually falls slightly, from 2.38 µH to 2.26 µH — but the lower self-inductance of the spiral receiver, whose inner turns enclose less area. Because k divides M by the square root of both self-inductances, trimming L_rx from 7.6 µH to 4.9 µH outweighs the small loss in M. So why keep a wound receiver at all? Its co-radial turns all sit at the full radius where linkage is strongest, so it delivers slightly more induced voltage per ampere of pad current and suits a device with some depth. Choose this DTC-to-Helmholtz pair for earbud cases, styluses and wearables with a wound coil; choose DTC-to-DTC when both sides must be flat PCB traces.
Watch out for
- Coupling falls off sharply with vertical gap — check k at your real enclosure thickness, not at contact
- Lateral misalignment is the dominant real-world failure mode; sweep it before committing
Neighbouring topologies
Circular Helmholtz Coil Pair
Calibration, teaching, benchmarking. At the worked-example geometry: k = 0.366 at 10 mm.
Swap the receiver to DTCCircular DTC-to-DTC Planar Coil Pair
Qi-style phone and watch charging. At the worked-example geometry: k = 0.461 at 10 mm.
Switch to a square outlineSquare DTC-to-Helmholtz Coil Pair
Worktop panels, tool and robot docks. At the worked-example geometry: k = 0.396 at 10 mm.
All eight pairs side by side, with coupling at both gaps: coil topology comparison.
Check the numbers
Run the Circular DTC-to-Helmholtz Coil Pair at your geometry
Frequently asked questions
Why is a spiral pad with a wound receiver so common in consumer charging?
The pad has to be flat to sit under a surface, while small devices such as earbud cases often have a few millimetres of depth for a wound coil. At 50 mm and a 10 mm gap this pair reaches k = 0.390 in AirInduct Sim, comparable to a matched wound pair, without a bulky transmitter.
Why does a five-turn spiral have less inductance than five wound turns?
In a DTC spiral each turn steps inward by the pitch, so the inner turns enclose less area and link less of each other’s flux. With a 2 mm pitch the five-turn spiral gives 4.91 µH against 7.62 µH for five co-radial turns at 50 mm.
What gap should I simulate for a charging pad?
The real distance between the copper planes: pad cover, device back and any air or adhesive layers. For this pair, k is 0.390 at 10 mm but 0.172 at 30 mm, so a few millimetres of enclosure changes the design noticeably.