Circular DTC-to-DTC Planar Coil Pair
Two flat circular planar spirals (DTC) face each other across the gap. It is the pad-to-phone geometry behind most Qi-style chargers, and in AirInduct Sim it gives the highest coupling coefficient of the four circular topologies.
Worked example
Inputs. Transmitter: 5-turn circular planar spiral (DTC), 2 mm pitch, turns at 50, 48, 46, 44, 42 mm radius. Receiver: 5-turn circular planar spiral (DTC), 2 mm pitch, turns at 50, 48, 46, 44, 42 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 | 2.264 | 4.912 | 4.912 | 0.461 |
| 30 mm | 0.967 | 4.912 | 4.912 | 0.197 |
Going from 10 mm to 30 mm lowers k from 0.461 to 0.197, a 57% drop. M is the lowest of the circular four, yet k is the highest (0.461), because both spirals have the low 4.9 µH self-inductance.
How it was computed. Both coils are five concentric circular turns at a 2 mm pitch. The transmitter field is a sum of elliptic-integral loop fields, and each receiver turn integrates that field over its own disc. k = M / √(L_tx · L_rx).
When it's the right choice
- Qi-style pads, phones, earbud cases and smartwatches
- Products where both windings must be flat, printed or flex-circuit traces
- Designs placed by hand at any rotation rather than aligned mechanically
Circular vs square planar spirals
Changing only the outline from circular to square, with the same 50 mm half-dimension, five turns and 2 mm pitch, lifts both mutual inductance and coupling, and AirInduct Sim shows by how much: M rises from 2.26 µH to 2.76 µH and k from 0.461 to 0.465 at a 10 mm gap. At 30 mm the square pair still leads, 0.207 against 0.197. The square spirals enclose more area per turn, which raises self-inductance as well as mutual inductance, so k moves far less than M does. Pick the circular spiral pair when the product is round or placed at any rotation — a phone on a pad, a watch on a puck — because the coupling of two coaxial circles does not depend on how the device is turned about the axis. Pick the square spiral pair when a rectangular PCB or battery outline sets the keep-out area and you would rather fill the corners with copper than leave them empty.
Watch out for
- Two planar coils make the pair especially sensitive to lateral offset
- The solver models air-core coils; commercial pads usually add a ferrite sheet, which raises L and k and needs an FEM tool to capture
Neighbouring topologies
Circular Helmholtz-to-DTC Coil Pair
Thin tags, implants, smart cards. At the worked-example geometry: k = 0.389 at 10 mm.
Swap the receiver to HelmholtzCircular DTC-to-Helmholtz Coil Pair
Earbud, stylus and wearable pads. At the worked-example geometry: k = 0.390 at 10 mm.
Switch to a square outlineSquare DTC-to-DTC Planar Coil Pair
Tablets, flat modules, PCB-to-PCB links. At the worked-example geometry: k = 0.465 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-DTC Planar Coil Pair at your geometry
Frequently asked questions
Is circular DTC-to-DTC the same geometry as a Qi charger?
The coil layout is: two flat spirals face to face. AirInduct Sim models them as air-core windings, which isolates the coil geometry. Shipped Qi pads add ferrite shielding that raises inductance and coupling; to model that layer, use a FEM tool after settling the winding here.
Why does a spiral-to-spiral pair have higher k than a wound Helmholtz pair?
Coupling is k = M / √(L_tx·L_rx). The spirals lose a little M (2.26 µH versus 2.69 µH for the wound circular pair at 10 mm) but lose far more self-inductance (4.91 µH versus 7.36 µH), so k rises from 0.366 to 0.461.
Should I fill the centre of a circular planar spiral with turns?
Usually not. Inner turns enclose little area, so they add resistance faster than they add mutual inductance. Sweep the turn count in the simulator and watch where M stops climbing for your gap.