The history of the Barkhausen Stability Criterion is an
unfortunate one. In 1921, during his study of feedback
oscillators, Barkhausen developed a ``formula for self-
where K is an amplifier gain factor and F(jw)is the
frequency dependence of the feedback loop. This equation
was originally intended for the determination of the
oscillation frequency for use in radio transmitters.
However, before conditionally-stable nonlinear systems were
understood, it was widely believed that only a single value
of K separated stable and unstable regions of behavior.
Thus, Barkhausen's Criterion was incorrectly used as a
stability criterion, especially in the German literature
A criterion used to determine the stability of an oscillator
circuit which states that, if the circuit is seen as a loop
consisting of an amplifier with gain A and a linear circuit
whose gain β(jω) depends on frequency ω, then the loop will
oscillate with a perfect sine wave at some frequency ω0 if
at that frequency Aβ(jω0) = 1 exactly, that is, if the
magnitude of Aβ(jω0) is exactly 1 and its phase is 0° or 360°.