It turns out it is possible to normalize exactly the resonance gain of the second-order resonator tuned by a single coefficient . This is accomplished by placing the two zeros at , where is the radius of the complex-conjugate pole pair . The transfer function numerator becomes , yielding the total transfer function
Thus, the gain at resonance is for all resonance tunings .
Figure B.19 shows a family of amplitude responses for the constant resonance-gain two-pole, for various values of and . We see an excellent improvement in the regularity of the amplitude response as a function of tuning.
Peak Gain Versus Resonance Gain
Normalizing Two-Pole Filter Gain at Resonance