text: so that after a trip around the loop the sine wave is the same amplitude. It can be seen intuitively that if the loop gain were greater than one, the amplitude of the sinusoidal signal would increase as it travels around the loop, resulting in a sine wave that grows exponentially with time, without bound.  If the loop gain were less than one, the signal would decrease around the loop, resulting in an exponentially decaying sine wave that decreases to zero.
  The sine wave at the end of the loop must be in phase with the wave at the beginning of the loop.  Since the sine wave is periodic and repeats every 2π radians, this means that the phase shift around the loop at the oscillation frequency ω0  must be zero or a multiple of 2π radians (360°)
  Equations (1) and (2) are called the Barkhausen stability criterion.  It is a necessary but not a sufficient criterion for oscillation, so there are some circuits which satisfy these equations that will not oscillate.  An equivalent condition often used instead of the Barkhausen condition is that the circuit's closed loop transfer function (the circuit's complex impedance at its output) have a pair of poles on the imaginary axis.