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 B.20 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.B.21, for which the pole radii have been reduced to .
Constant Peak-Gain Resonator
Constant Resonance Gain