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Just a small correction: It is the LOOP GAIN which must be "1"-

Yes, the correct name should be LOOP GAIN.

Closed loop gain and open loop gain are usually used to describe the transfer function of feedback amplifier or feedback control system.

By the way, it is sometimes not easy to find the mathematical equation of the oscillator loop gain, so I tried the simplest example below, but I think it is too difficult to derive manually for more complicated situation.

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