What is the inductance between two points of a ground plane ?

There are many discussions about PCB track inductance, via inductance, but what about ground plane inductance ?

Of course, an inductance which is a local constant is defined between two points and the result should depend on the plane size. So, let's define a 1 x 1 cm2 plane with two access 1.8 mm appart at the center. The access are 0.2 x 0.4 mm2 and sit above 35 um thick ground plane.

Any guess what the inductance can be ?

And, by the way, what is the series resistance between the two points ?

No easy answer. One solution is running a finite elements simulation with a solver like EZMod3D to get an answer. Cover picture shows how voltage distributes inside the ground plane.

Finally, the answers are:

Ssimulated series resistance is 3.67E-4 ohms

Simulated series inductance is 0.42 nH

When it comes to deal with large dI/dt values, estimating all the parasitic inductances is mandatory, and ground plane inductance cannot be neglected.

Finite elements analysis with solvers such as EZMod3D is one convenient solution to get results before "etching the copper", saving money and time to market.