Capacitive sensors: mutual capacitance

[MyNameIsNeo]

Hi folks,

I'm playing around with capacitive sensors (mutual capacitance sensors) and interested in computing/approximating the capacitance between the sensor lines. Mutual capacitance sensors usually consist of two lines/conductors that intersect. Obviously, one can model this is a parallel plate capacitor. However, I would be interested in doing this more accurately.

I attached a sketch to illustrate the problem. One can see the two conductors that intersect (for now, the angle of the intersection shall be 90 degrees). In between, let's assume there is air or some other dielectric material. The red area shows the parallel plate of the "parallel plate capacitor". From my understanding, the orange and yellow area should also contribute to the capacitance and this is exactly the part I cannot understand/model. For the model, let's simply assume that the two conductors have infinite length (bold arrow on the top conductor shall indicate that it does not end)

Please note, that for mutual capacitance sensors, there is always one transmitting line, and one or more receiving lines. Hence, they are call TX-electrode, whereas the other ones are named RX-electrode.

I did study computer science and had some courses in EE, too. But I guess this is a little too advanced which is why I'm asking here for your support. In particular, I would like to know:

a) How to compute the complete capacitance
b) Which models/possible solutions exist on how to compute it (is there a significant difference?))
c) How things change when, e.g., a shielding is on top and/or bottom (probably "blocks" the field lines somehow)

Ideally, your explanation is easy to follow for a non-EE/physics student ;-)

https://www.physicsforums.com/attachments/conductor_intersection-png.76696/?temp_hash=33ae8af28afb2c8cbec51caad716c2e6

 

[mfb]

You can simulate it to get an approximation - for a given potential difference, iteratively solve the Poisson equation, then determine the electric field strength at the surface of the conductors, calculate the charge and divide it by the given potential difference. Or find a software package that does those steps for you for every geometry you want to study.