Hello,
- Is there somewhere a complete theoretic description of the typical application with all formulas? In the application notes I find a lot of formulas where measurements are used as an input.
The electromagnetic phenomena of the processes are described by Maxwell equations. Though they are simple by themselves, the solutions may be quite difficult to obtain. Often times, finite element simulations are the best approach.
- I want to know the requirements for my oscillator/crystal that needs to be connected to the chip
The error of the crystal will be directly reflected in the measurements error. I.e. if it's ±10%, your measurements will be ±10%.
1. I want to know Fcount with my design choices, but the application notes describe how to determine the output data rate, not how to determine Fcount (and if I assume they are the same, then the numbers are wrong)
Fcount = Freference*Integration time/3/Foscillation.
2. I want to know my proximity data for the design choices, such that I can determine the 'proximity data error' as a result of the error I can expect on my oscillator
I don't quite understand, what is the source of error? Proximity data will depend on many parameters, starting with the sensor parameters (R, L, C) as well as the Rp MIN/MAX settings. Also, LDC1000 has part-to-part variation of the proximity data - please keep this in mind.