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# Damping Factor (or ratio) of a nth Order System

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## Damping Factor (or ratio) of a nth Order System

(OP)
Hi,

I have a query regarding the Damping Ratio of a system. With a 2nd order system the damping ratio, denoted by zeta ζ, is obtained from the denominator of the transfer function, but how do you find and define the damping ratio from a higher order transfer function, please?
Especially, considering that each pole in the system has a damping ratio, which is the overall damping ratio of the system or closed loop system?

Any help would be really appreciated.

Thanks

### RE: Damping Factor (or ratio) of a nth Order System

As you said, damping factors are associated with poles, not systems.

First-order poles (and you can count second-order overdamped and critically-damped systems as systems having two first order poles) have a damping factor of 1.

Second-order underdamped (i.e., complex) poles have damping factors between 0 and 1.

Second-order undamped poles have a damping factor of 0.

Systems that have more than two poles will have a damping factor associated with each pole.

The dominant pole or poles will have the associated damping factor dominate the system behavior.

xnuke
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### RE: Damping Factor (or ratio) of a nth Order System

(OP)
Thanks for the explanation, xnuke.

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