Discussion Forum

Good day! For the past few days I've started using COMSOL to do some simple (?) electrostatics calculations in a system of a meander inductor coupled to a (piece of) coplanar waveguide. All of them superconducting metals on top of a silicon substrate in air. There are three capacitances of interest: the capacitance of the inductor Cinductor, of the waveguide Cwaveguide, and their coupling Ccoupling. Getting the capacitances to ground of the individual elements has been fine if modeled in isolation, but extracting coupling capacitancen(especially because they are an order of magnitude or 2 smaller than the capacitances to ground?) has been troublesome. I've attached my model and I'll explain what I'm trying to do, to make the situation clear.

What am I doing? Ground plane at 0V, inductor at 1V and waveguide at 0V. We then run electrostatics, and calculate the total charges on each surface with surface integration over es.Nd. If I am not mistaken, the charges should then directly give Cinductor and Ccoupling, the one I am strugling with.

However, the issue is that the total charges do not add up to zero. Instead, if I run the above numbers, what I get is -5.2810^-15 charges on the waveguide, 1.5610^-14 on the inductor, and -1.8310^-14 on the ground. The sum of this is -7.9510^-15, which is not only nonzero (there will always be errors I imagine), but on the order of the charges I am interested in themselves. So this is my problem; how do I get this error in charge conservation to go down?

What I've tried is making the mesh finer and finer, but I am running into the limits of my 16gb of RAM it seems. I dont' think this structure is all that crazy, so perhaps there is some trick I am not thinking about, or a simplification I dont' see. Would anyone be able to assist and give a hint as to how I can improve the above?

Kind regards

Note: in an attempt to remove a name I uploaded the file twice; I don't see how to remove the other one. They are identical.