Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


Damping Ratio

Damping ratio $ \zeta \isdeftext 1/(2Q)$ is defined to conveniently divide the underdamped, critically damped, and overdamped conditions at unity for a second-order system.

The damping ratio $ \zeta$ (zeta) is defined by

$\displaystyle \zeta \isdefs \frac{1}{2Q} \eqsp \frac{\alpha}{\omega_0}
$

where $ Q$ is defined above in Eq.(E.8) as the peak frequency divided by the peak bandwidth, and $ \alpha$ and $ \omega_0$ are defined above in Eq.(E.7).

As shown in Eq.(E.9), a damping factor of 1 is critically damped, while a damping factor less than 1 is underdamped, and $ \zeta>1$ is overdamped.


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2018-04-13 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA