I made a battery management system using one attiny per cell, communicating via I2C (using capacitors as a cheap way to shift voltage levels between the cells.). Each attiny has an external 100kOhm resistor to keep its capacitor at the correct offset. For the total bus, this means the effective pull-up is all of them in parallel (with 16 cells that's 6.25kOhm). Despite its high number of devices and high pull up resistance, it works fine (already for ~half a year). However it "only" runs in standard 100kHz mode and has long pauses between communications to let the connection capacitors settle to the correct voltage again.
Once i discovered I2C extender chips i stopped worrying about all this bus capacitance stuff. Those things are amazing. Just add them to yoir circuit and you can communicate over long diatances with no problem.
You can still lower the frequency to for instance 10Hz and add a huge amount of capacitance, right? It might not be a display on the other end, but a temperature sensor read every 10 minutes. It sounds like a fun project to make the master measure the rise time and configure the speed automatically.
If you measured the inductance of the following: SCL to GND, SDA to GND, and SCL to SDA, using an LCR meter would that correspond well to your calculations? SCL to SDA would measure unwanted coupling between the two, but curious about your thoughts on the other two measurements
Practically speaking, I don't think you could measure signal to GND with an LCR (without a fixture anyway.) And if you tried to measure signal to signal, you'd just end up measuring the effective capacitance (since these aren't DC signals). Regardless, I would expect the inductive effects to cause crosstalk while the capacitive effects will contribute to the (slower) rise times. Another way I first thought of your question is these are not DC signals and we're talking about impedance. By measuring (or calculating) the capacitance, we also account for the inductance. Maybe that needs more thought.
kind of seems like devices (like the oled screens) should have enough resistance to take care of themselves and their own built-in capacitance and then the "system" pcb's should have space for more.
Mh, maybe someone can correct me: I would like to trigger taps on capacitive touch screen (similar to a touch screen on your phone). I took the tip of a stylus, and soldered a long cable to it. The length of the cable alone already triggers on some screens enough capacitance; registering constantly as a touch. So I assume, I need to put enough „power“ in to the cable from my side, so it matches the screen... Would pull up resistors, knowledge about impedance etc in this video help in solving this scenario? Just need some pointers into what direction I should search learn - it is a learning project. Thx