While the constant resonance-gain filter is very well behaved, it is
not ideal, because, while the resonance gain is perfectly
normalized, the peak gain is not. The amplitude-response peak
does not occur exactly at the resonance frequencies
except for the special cases
, ,
and . At other resonance frequencies, the peak due to one pole
is shifted by the presence of the other pole.
When is close to 1, the shifting can be negligible, but in more
damped resonators, e.g., when , there can be a significant
difference between the gain at resonance and the true peak gain.

Figure 10.21 shows a family of amplitude responses for the
constant resonance-gain two-pole, for various values of and
. We see that while the gain at resonance is exactly the same
in all cases, the actual peak gain varies somewhat, especially
near dc and when the two poles come closest together. A more
pronounced variation in peak gain can be seen in
Fig.10.22, for which the pole radii have been reduced
to .

Figure:Frequency response overlays for the
constant resonance-gain two-pole filter
,
for and 10 values of
uniformly spaced from 0 to . The 5th case is
plotted using thicker lines.

Figure:
Frequency response overlays for the
constant resonance-gain two-pole filter
, for and
10 values of uniformly spaced from 0 to . The 5th
case is plotted using thicker lines. Note the more pronounced
variation in peak gain (the resonance gain does not vary).