I forgot this point:
In an operational amplifier, you need to feed back a negative signal to
reduce the gain, so you control it
to works inside the analog voltage range you want. The way to do that is
just return part of the output
signal to the negative input, normally done with a resistor divider
network.

Using an operational amplifier you can build a true logic gate just
fixing the negative input to half point of the Vcc, so whenever the
positive input is higher, even micro volts, will trigger the output to a
high positive level, below that the same to a strong negative output.
As the gain of an average op-amp is in the thousands units, it works
that way.

The CMOS logic gates (and others) works like that, the "internal
negative input" is buried at half Vcc or so,
then the positive input triggers around that voltage. To make it works
as an analog device, you need to feed
back the negative output to reduce the gain to a level where the output
follows the input in such manner you do with an operational amplifier.

As you don't have access to the "internal negative input" pin (it
doesn't exist), the way is feedback the negative output to the positive
input, but it will oscillate, so this is why they use 1 Mega Ohm
resistor, so the input impedance can kill the oscillation, not the
feedback.

Yes, try to reduce the input impedance, using a pot below 10k Ohms to
find the trigger point. Use a large
coupling capacitor, since small ones will helps the "oscillator"...
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Wagner Lipnharski - UST Research Inc. - Orlando, Florida
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