The Design of a Tunable Notch Filter with Variable Q

In electro-mechanical servo systems one often encounters undesired resonances which contribute to the system instability. One method used to combat such a resonance is to place a notch filter in the feedback loop to reduce gain at the resonance frequency, while allowing frequencies outside the notch to pass without appreciable phase shift or attenuation. The notch filter described in this paper is particularly useful in this application since it can be tuned to the resonant frequency while in the circuit, the Q can be adjusted to cover the resonance, and the notch attenuation can be adjusted for essentially zero transmission at the center frequency. The filter is of simple design and easily constructed. The most critical restriction is that the operational amplifiers used in the circuit be stable at unity gain. However, this is not particularly difficult to realize.