SCHMITT TRIGGER
The analysis is not difficult. It is, however, tedious. The , voltage divider sets the rough neighborhood of the trigger thresholds. controls the hysteresis of the switch (the difference between the ``turn on'' and ``turn off'' thresholds). The feedback resistor should be a factor 10-100 larger than the voltage divider resistors. Otherwise, it drags the thresholds apart.

1. Predict the ``turn on'' and ``turn off'' thresholds for k, k, k, and k. Rather than finding a general expression, it's fine to consider this particular case. For the analysis, assume a maximal output voltage swing of V. This actually varies with each op amp, but should not be far from the truth.

2. Build the circuit, using the resistance values given above. Measure the input thresholds of the trigger and compare with your prediction