Barkhausen stability criterion

It cannot be applied directly to active elements with negative resistance like tunnel diode oscillators.

In the real world, it is impossible to balance on the imaginary axis; small errors will cause the poles to be either slightly to the right or left, resulting in infinite growth or decreasing to zero, respectively.

Thus, in practice a steady-state oscillator is a non-linear circuit; the poles are manipulated to be slightly to the right, and a nonlinearity is introduced that reduces the loop gain when the output is high.

[6] Barkhausen's original "formula for self-excitation", intended for determining the oscillation frequencies of the feedback loop, involved an equality sign: |βA| = 1.

At the time conditionally-stable nonlinear systems were poorly understood; it was widely believed that this gave the boundary between stability (|βA| < 1) and instability (|βA| ≥ 1), and this erroneous version found its way into the literature.