Projective capacitive field in 3D (along Z-axis)

[ricko_uk]

Hi,
with reference to the attached pictures representing a PCB with copper pads projecting/creating a capacitive field above the PCB (like in Q-touch capacitive sensing) and considering that two pads have always the same length but variable width and gap:

1) which projects the capacitive field lines further into space (Z-axis)?

2) within the same overall volume, which affects the most the Z-axis protrusion of the electric field lines, increasing the gap or increasing the pads widths? Do the field lines protrude further out into space (Z-axis) with larger pads width or larger pads gap?

3) how can I know/calculate how much further into space the field reaches for a given set of dimensions?

4) how can I calculate the capacitance for a given set of dimensions?

Thank you

[ricko_uk]

Any suggestions anybody?
Any feedback is much appreciated.
Thank you

[pwlps]

The greater the gap the greater the penetration on the z axis.  The pad width is less important as long as it is comparable or greater than the gap width, as most of the charge will be concentrated near the edges.  Therefore it is the gap width which is determinant for the z axis protrusion.  Very roughly I would say the gap width gives also an order of magnitude for the z-axis penetration of the electric field.

To calculate capacitance:
https://www.emisoftware.com/calculator/coplanar-capacitance/
But this is for long strip lines, I don't know if there are analytic solutions and formulas for short pads (otherwise you need a numerical solver). Anyway it can give you an order of magnitude.

[mag_therm]

Hi Ricko,
Lucky the QuickField is still booted up.
I was usually all magnetics  so it is a chance to use the QuickField electrostatic module (solving Poisson)
and learn a bit about it at the same time.

model is of your first plates, 55mm deep into page.

Copper Pads Er = 1, Air Er = 1, Universe is 690 mm radius at which E strength = 0
Substrate Er = 4 , substrate is 1 mm thick, spaced 1mm below copper pads for easy model.
There is a "blob" between and above the plates of plastic Er=4, just to get the local values shown.
PadPlus has charge of 0.001 Coulomb /metre^3
Padminus has charge of -0.001 Coulomb /metre^3
I think they might give a nasty shock?

Let me know if that meets your needs or if you need a sensor plate added or a grounded plate above  etc.
Do your pads have opposite charges as shown here?
I can update and add your 3rd option to the left side that is presently vacant.

Note , This is electrostatic , does not extend to frequency where radiation is significant.

[ricko_uk]

Thank you very much to both. And mag_therm, very much appreciated the simulation and the detailed explanation!!!

The pads in my original post were for simplification. What I am really trying to figure out is how far into space the electric field extends in a flat PCB coil and how they distribute (because every turn has a lower potential trace on one side and a higher potential trace on the other).

The track and gaps, since this afternoon, have been resized to 0.25mm track and 0.25mm gap. The coil is a single layer without planes nearby. The outside diameter is 77mm and 52 turns giving and inside diameter of around 25mm.

Would it be possible for you to run the same simulation for that coil and see the cross section of both electric field and magnetic field distribution?

Currents vary between 20mA and 500mA (when completed I can adjust them through a current source).

If too time consuming or complicated then no worries and thank you very much anyway for running the simulation in the first place. Much appreciated!!!

[mag_therm]

Well, I have been reading the Ferroxcube "Design of Planar Power Transformers" recently

I don't have any experience at all with planar transfomers on pcb layers, although did big ones with copper bus-bar secondaries. I was thinking about doing a pcb size design ,  in 2D  magnetic coupled to thermal.

How about I do that and put up the results?

I will select a core on the higher end of power and a frequency of 500 kHz.
It might be possible to do an approximate electrostatic too, not sure.

If anybody else  has experience with planar transformers I would be interested to hear before  starting.

[ricko_uk]

Thank you mag_therm, that'd be great and very much appreciated!!!