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