comparatornon-linearoperational-amplifierschmitt-trigger
In order to solve a Schmitt trigger circuit implemented with an op-amp (or a comparator) connected in positive feedback, this wikipedia page uses the superposition theorem.
My question is : why can we use the superposition principle in this situation? Superposition is a property of linear system and this one is clearly nonlinear since positive feedback involves hysteresis and saturation…
Just plug those resistor values into the calculator you linked in your question and look what happens: -
The thresholds are switching between about 4.2 volts and 4.6 volts - that's the first thing - your input needs to be able to cross those boundaries for your circuit to switch.
Next, take a look at the LM358 data sheet and you'll see that input voltages are only valid between 0V and 3.5V (on a 5V supply) - don't expect this to do what you want when the input is above 3.5 volts.
Next take a look on the d-sheet to see what the output can do on a 5V rail, The d-sheet implies the highest output voltage that it can muster is typically 2V below the positive rail i.e. 3V.
My estimation is that your circuit is kind of working but maybe with the invalid 5V input in scenario 1, you get a weird inversion thing going on (it happens a lot on op-amps).
Welcome to the imperfect world of real op-amps!!
Try lowering thresholds to around 2V and 2.5V and see what happens when the input rises above 2.6V - I'd expect the output to swing down to 0V. When the input drops below 1.9V, I'd expect to see the output swing above 3V.
If you do that the amplifier will amplifiy its own output and the ouput will go high or low and stick there until a sufficiently low or high input is presented, which will make it go the other way (low or high).
In essence you will have created a schmitt trigger.
What the formulas don't show is that the solution for this amplifier configuration describes the metastable point,
Another limitation of those equations is that they don't represent the limited output voltage range of real amplifiers.
Best Answer
The Wiki article is using superposition correctly. It starts by assuming the output is in one state, then assuming the output remains in that state, calculates the comparator input with respect to the circuit input. It uses this relationship to determine the input level (producing zero volts at the comparator) to determine the trigger point at the specified state. It then does the same for the other state. What it does not do is to model the behavior of the circuit as a trigger point is passed - it only identifies what the trigger points are.