Coupling coefficient of coils

Hi there,

Are there any formulas that give the coupling coefficient between 2 coils based on the distance of separation and other such parameters? I need to calculate the coupling coefficient for the single turn coil ( of say diameter 20cm) and flat spiral coil ( say Inner dia = 10cm, Outer diameter =20cm) and coupling coefficient between 2 flat spirals of the above mentioned configuration.

Thanks in advance.

https://www.wa4dsy.net/filter/filterdesign.html
May have some coil calculators but I think you need to use ferrite to concentrate the EM field for coupling and want to use tapped coils in auto transformer to stepup coupler to stepdown to improve impedance matching for free space coupling. Consider 1 turn as primary on sender and 1 turn secondary on receiver of ferrite bar coil .

At least the spiral coil geometry is sufficient complex to suggest usage of an EM tool. FastHenry from fastfieldsolvers.com is a simple free tool for AC magnetic problems that can do it.

Thanks for the reply. Using EM solvers is the only way to find coupling/mutual inductance between coils of different geometries? Also, I find that EM solvers are used for designing inductors in PCB which have very small geometries. Is it accurate enough to simulate coils of the sizes I mentioned?

@Sunnyskyguy: I cannot use a ferrite core. I have to use an air core coil. That is one of the requirement.

Assuming a sufficient low frequency, e.g. a few 10 MHz for the shown geometry, the analysis can be restricted to AC magnetic, not considering the coupling between electric and magnetic field. If you also ignore skin effect and eddy currents, the problem reduces to an magnetostatic one. Then the coupling can be calculated by integrating Biot-Savarts law. This is almost easy for circular loops of axisymmetric arrangement and less convenient for spiral coils.

EM solvers also models skin and proximity effect as well as eddy currents. Coils of extreme geometries, where the current has to be carried by a very small part of the conductor area give possibly inaccurate results at high Q. But apart from this point, there's no problem with large or small structures. Small structure analysis are more accurate because skin depth spans a larger part of the structure.

Very poor efficiency with your choices. Why the restrictions?
How much power do you need to transfer?
What separation values?