Electronic – How to calculate rise times for a push pull GPIO with load with hand calculations

There are a couple of unclear things in your schematic, which should be taken care of:

1. I assume that U0 is the output voltage which you want to measure with a high-ohmic oscilloscope. The way you depicted it, U0 is a 0 V voltage source which will defeat any functionality of your circuit.
2. The depicted circuit cannot work as a limiter. U0 is a full-swing output. I think you're confusing the terms limiter and limiting amplifier. This circuit is a limiting amplifier (at least the way you use it), to be more specific it's a common emitter stage.
3. To finally answer your question about the rise time: The main problem with this circuit is that it is not properly biased. You need to define the operating point of this common emitter stage so that the output voltage is in the middle between the rails for a 0V input signal.

I hope it helps! :)

The question was answered, but the answer seems to have disappeared. The problem stemmed from using a buffered inverter, along with implementing the circuit on a breadboard. Switching to an unbuffered inverter and implementing on perfboard fixed the waveform.