text: In general, the phase shift of the feedback network increases with increasing frequency so there are only a few discrete frequencies (often only one) which satisfy the second equation. If the amplifier gain   is high enough that the loop gain is unity (or greater, see Startup section) at one of these frequencies, the circuit will oscillate at that frequency. Many amplifiers such as common-emitter transistor circuits are "inverting", meaning that their output voltage decreases when their input increases.  In these the amplifier provides 180° phase shift, so the circuit will oscillate at the frequency at which the feedback network provides the other 180° phase shift.
  At frequencies well below the poles of the amplifying device, the amplifier will act as a pure gain , but if the oscillation frequency  is near the amplifier's cutoff frequency , within , the active device can no longer be considered a 'pure gain', and it will contribute some phase shift to the loop.
  An alternate mathematical stability test sometimes used instead of the Barkhausen criterion is the Nyquist stability criterion.  This has a wider applicability than the Barkhausen, so it can identify some of the circuits which pass the Barkhausen criterion but do not oscillate.