Circular DTC → Helmholtz
A flat circular planar-spiral transmitter driving a multi-turn circular receiver. This is the common consumer arrangement: a pad underneath, a wound receiver in the device.
The simulator computes the field from the Biot–Savart law and the mutual inductance from the Neumann double integral, then reports the coupling coefficient k for the geometry you enter. Nothing is meshed and nothing is fitted, so the result is reproducible to the digit.
Use it for
- Phone, earbud and wearable charging pads
- Any design where the transmitter must sit flush under a surface
- Retrofits onto an existing flat charging surface
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
Run your geometry.
How is mutual inductance calculated for a circular DTC to Helmholtz pair?
AirInduct evaluates the Neumann double integral between every transmitter turn and every receiver turn, then sums the contributions. Circular turns are evaluated with complete elliptic integrals (K and E), which is why the circular cases are the fastest and the most numerically exact in the solver. Because this is a closed-form evaluation rather than a meshed field solve, the same geometry always returns the same number and there is no discretisation error to tune away.
What coupling coefficient should I expect from this topology?
There is no single figure — k depends on the radii, turn counts, separation and alignment you choose, and it falls off steeply with distance. That is precisely why this page links to the simulator rather than quoting a number: enter your geometry and read k directly. As a rough orientation, closely spaced pairs of similar size can reach k above 0.5, while a gap comparable to the coil radius typically drops k below 0.1.
Do I need to install anything?
No. The solver runs from the browser and the free tier covers individual research and coursework use. Desktop and mobile builds run the identical kernels if you prefer a local install.
Is this accurate enough to replace a full-wave FEM tool?
For inductive WPT in the magnetostatic regime — coils small relative to a wavelength, no dominant ferrite or lossy material in the field volume — the closed-form result is exact, not approximate. If your design depends on shielding, ferrite loading, strong proximity effects in litz bundles, or radiative behaviour, a full-wave or FEM tool is the right instrument and we will tell you so.