This shows the (simplified) internals of a 555 timer chip. As in the last example, it is doing a square wave.
A voltage divider sets the inputs of the two op-amps (used as comparators). The upper op-amp compares the trigger input to 1/3 the supply voltage. The lower op-amp compares the threshold input to 2/3 the supply voltage.
A timing interval starts when the trigger input goes low enough to trigger the upper op-amp. That sets the flip-flop, causing the output to go high. The 555 waits for the threshold input to trigger the lower op-amp. As the capacitor charges, the threshold input slowly rises until it reaches the required level. Then, the op-amp resets the flip-flop, bringing the output low. The flip-flop's inverted output also provides current to the base of the transistor on the bottom, which discharges the capacitor through the discharge input.
When the capacitor is discharged enough so that the upper op-amp is triggered again, a new timing interval begins.
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