Maths Was Used To Create This PCB

Maths is everywhere, even though it may exist in the subconscious mind. That is what I personally discovered recently. I would like to share one example. And this example lead me to one maths term I called Math-lectronics.

I was going through some of the hardware projects done recently. The project called for the fabrication of printed circuit board (PCB). This board carries electrical current that does certain functions for a system. The board is consist of thin layer of copper glued onto a paper-based support. For functionality, the copper on the PCB is etched to a customised pattern that serves as path for electrical current to flow. I created one as shown below.



The diagram above is a mask that will be used to create the physical circuit board.

Looking at the pattern, I discovered that I had used, sub-consciously, maths to generate it. Why?

1) I need to come up with the physical dimension of the PCB to suit the housing.

2) I need to estimate the density of the components to be packed into the PCB.

3) I need to know the height of the highest component to be used.

4) I need to check the amount of current flowing through each individual copper track. The higher the electric current, the wider the track has to be. This is to offset the resistance of the copper.
Formula: Current = Voltage / Resistance where Resistance relates to length and (1/area).

5) I need to know the frequency of the current in each track. This may create cross-talk between the tracks if placed too closely to each others.

6) I need to decide the bending angle of the tracks to reduce noise within.

7) I need to determine the diameter of some holes to be drilled for component mounting.

8 ) I need to add up the currents for deciding the number of connectors I need.

The words bolded in the above considerations are related to maths, and was done sub-consciously by me.

Had I not learn maths, I would not be able to generate this copper pattern.
Do you think so? :)

Finally I would like to present the fabricate PCB using the pattern created.



So what is the term when maths and electronics merge? I call it Math-lectronics.

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