Barkhausencriterium

The Barkhausen criterion is a principle used in the analysis and design of feedback oscillators. Named after the German physicist Heinrich Barkhausen, it was introduced in the early development of radio engineering to describe when a circuit can sustain self-oscillations.

Formally, consider a feedback loop with forward transfer A(jω) and feedback factor β(jω), giving the loop transfer function L(jω) = A(jω)β(jω). The Barkhausen criterion states that sustained oscillations occur at frequencies ω0 for which the loop gain has a magnitude of unity and a net phase shift of an integer multiple of 360 degrees: |L(jω0)| = 1 and ∠L(jω0) = 0° (mod 360°). The oscillation frequency is determined by the phase condition, while the required gain is determined by the magnitude condition.

In practice, the criterion serves as a necessary condition for the onset of oscillation and as a design guide. During startup, the loop gain often exceeds unity to overcome losses, after which nonlinearities in the circuit reduce the effective gain to unity to stabilize the amplitude. The Barkhausen criterion is widely applied to the analysis of electronic oscillators built with RC, LC, or crystal resonant networks, including Wien-bridge, Colpitts, Hartley, and similar configurations.

Limitations include that it is derived for linear models and does not by itself guarantee stability or determine the final amplitude. Real circuits may have multiple frequencies satisfying the condition, and amplitude stabilization depends on nonlinear behavior beyond the linear Barkhausen analysis.