# Circle Fitting

This is a common method of extracting mode shape vectors from a set of frequency response functions. It is based upon the principle that a plot of the out of phase, or imaginary component versus the in-phase, or real component will trace a circular arc for each resonance. The method uses single degree of freedom technology and has been extended to include the analysis of real and complex modes. Circle properties are estimated using a least squares circle fitting algorithm.

The modal coefficient is determined by the diameter of the circle and the phase by its location relative to the imaginary axis.

For a real mode, it should be either completely above or completely below the imaginary axis.

**See also: **Modal Analysis, Nyquist Plot.

**Subjects: ** Noise & Vibration