I’m sure others have linked to Technology Connections’ video on the subject below, but there are two general ways it works:
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There is a humidity sensor in the microwave that will sense when food is done. In the case of popcorn, it senses when there’s a burst of steam inside when the bag inflates enough to open the vent, and then given how long that took it calculates how big the bag of popcorn is and thus how long to keep running the microwave for. The other sensor cook buttons look for trends in humidity that have to do with other foods. The microwave will likely indicate that it has this feature with the word “Sensor” or similar branding on the control panel, and when you press the Popcorn button, it just starts running because it can figure out everything it needs to know for itself.
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Small, cheap microwaves probably just use a timer. If it asks you if the bag of popcorn is small, medium or large at the beginning, it’s just a timer and you should just go with the instructions on the bag instead.
A peak detector that resets a timer is within the realm of possibility, maybe combine it with the moisture sensor so that you start listening for the pops to slow down after you detect the burst of steam.
Want to go half on the patent?