Square DTC-to-DTC Planar Coil Pair
Two flat square planar spirals (DTC) face each other across the gap. It is the flattest square arrangement in AirInduct Sim and, in the shared worked example, the topology with the highest coupling coefficient of all eight.
Worked example
Inputs. Transmitter: 5-turn square planar spiral (DTC), 2 mm pitch, turns at 50, 48, 46, 44, 42 mm half-side. Receiver: 5-turn square planar spiral (DTC), 2 mm pitch, turns at 50, 48, 46, 44, 42 mm half-side. 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 | 2.759 | 5.929 | 5.929 | 0.465 |
| 30 mm | 1.227 | 5.929 | 5.929 | 0.207 |
Going from 10 mm to 30 mm lowers k from 0.465 to 0.207, a 56% drop. Both values are the highest of the eight topologies at this geometry; the runner-up, circular DTC-to-DTC, reaches 0.461 and 0.197.
How it was computed. Both coils are five nested squares at a 2 mm pitch. The transmitter field is built segment by segment from finite-wire Biot–Savart terms; each receiver square integrates that field over its own area. k = M / √(L_tx · L_rx).
When it's the right choice
- Tablets, rectangular devices and flat industrial modules
- Designs where both PCBs carry the winding
- Pairings that must fit a square keep-out area
Spiral receiver vs wound receiver
Making the receiver a flat spiral as well gives the highest coupling coefficient of all eight topologies in the worked example, and AirInduct Sim shows why: with both sides as five-turn square spirals at 2 mm pitch, k reaches 0.465 at a 10 mm gap, against 0.396 for the DTC-to-Helmholtz pair with a wound receiver. Mutual inductance barely moves (2.76 µH versus 2.87 µH); the gain comes from the receiver’s self-inductance falling from 8.9 µH to 5.9 µH. At 30 mm the margin holds, 0.207 against 0.183. Higher k is not automatically better, though. Two printed spirals usually carry more series resistance per microhenry than wound copper, so the efficiency limit, which depends on k and on both coils’ quality factors, can still favour the wound receiver. Pick DTC-to-DTC for tablets, flat modules and any design where both windings are PCB traces; pick DTC-to-Helmholtz when the receiver has depth for a lower-loss wound coil.
Watch out for
- Two planar coils give the least misalignment tolerance of any topology here
- PCB-traced spirals have significant series resistance — confirm the loss budget, not just k
Neighbouring topologies
Square Helmholtz-to-DTC Coil Pair
Rectangular docks with PCB receivers. At the worked-example geometry: k = 0.403 at 10 mm.
Swap the receiver to HelmholtzSquare DTC-to-Helmholtz Coil Pair
Worktop panels, tool and robot docks. At the worked-example geometry: k = 0.396 at 10 mm.
Switch to a circular outlineCircular DTC-to-DTC Planar Coil Pair
Qi-style phone and watch charging. At the worked-example geometry: k = 0.461 at 10 mm.
All eight pairs side by side, with coupling at both gaps: coil topology comparison.
Check the numbers
Run the Square DTC-to-DTC Planar Coil Pair at your geometry
Frequently asked questions
Which coil topology gives the highest coupling coefficient?
For two 100 mm coils with five turns each at a 10 mm gap, square DTC-to-DTC does: k = 0.465, against 0.461 for circular DTC-to-DTC and 0.370 for the square Helmholtz pair. The ranking can change with turn count and pitch, so compare at your own geometry.
Does the highest k mean the highest efficiency?
No. The maximum link efficiency depends on the product k²·Q_tx·Q_rx. Printed square spirals often have lower Q than wound coils, so a pair with lower k can still win on efficiency once trace resistance is included.
What turn pitch should a square planar spiral use?
The worked example uses 2 mm. A tighter pitch keeps every turn near the outer edge, raising M, but narrows the trace and raises resistance. Sweep the pitch in AirInduct Sim and stop where the gain in k no longer pays for the extra loss.