Square DTC → Helmholtz
A flat square planar-spiral transmitter driving a multi-turn square receiver. A practical pairing when the transmitter is a panel and the receiver can afford depth.
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
- Panel or surface-integrated transmitters under a worktop or shelf
- Receivers with room to wind turns vertically
- Industrial docking where the receiver is a fixed, engineered part
Watch out for
- Receiver depth buys coupling only while turns stay close to the transmitter plane
- Check current density in the innermost transmitter turns, which carry the same current over a shorter path
Run your geometry.
How is mutual inductance calculated for a square DTC to Helmholtz pair?
AirInduct evaluates the Neumann double integral between every transmitter turn and every receiver turn, then sums the contributions. Square turns are integrated segment by segment along each of the four straight sides, using the closed-form Biot–Savart result for a finite straight conductor. 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.