Phasenquerfrequenz

Phasenquerfrequenz, often translated as phase crossover frequency, is a concept used in control system engineering and signal processing. It refers to the frequency at which the phase shift of a system's transfer function becomes -180 degrees, or pi radians. This specific frequency is significant because it marks a point where the system's output is exactly out of phase with its input.

In the context of a feedback control system, the phase crossover frequency is closely related to the system's stability. If the gain of the system at the phase crossover frequency is greater than 1 (or 0 dB), the system is likely to be unstable. This is because a signal at this frequency would be fed back to the input with a phase inversion and amplified, leading to oscillations that grow over time. Conversely, if the gain is less than 1 at this frequency, the system is generally considered stable.

The phase crossover frequency is typically determined from the Bode plot of the system's open-loop transfer function. The Bode plot graphically represents the magnitude and phase of the transfer function as a function of frequency. The frequency at which the phase plot crosses the -180 degree line is the phase crossover frequency. It is a key parameter used in stability analysis, alongside the gain crossover frequency, to assess the robustness and stability margins of a control system. Understanding and calculating this frequency is crucial for designing systems that behave predictably and avoid unwanted oscillations.