Q of a Complex Resonator

The simplest case is a *complex one-pole resonator* having its
single pole at
:

The maximum gain is readily found to be ,

Next, we need to find the 3dB-bandwidth. Without loss of generality, we can set , since bandwidth is not changed for a complex one-pole resonator by a vertical translation along the axis. (Consider the graphical method for calculating amplitude response from poles and zeros.) It is now easy to see that the -3dB points of a ``dc resonance are at :

We have thus found that the of a complex one-pole resonator with pole at is given by

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