Closing the loop deepens notches

  
Notch filters remove a single unwanted frequency from an input signal. They are also a vital component of pulse-shaping networks, such as time-averaging filters. You can tune a state-variable filter over a wide range by changing the time constants of its integrating amplifiers (References 1, 2, and 3). Textbooks focus on its high-pass, bandpass, and lowpass outputs, but they sometimes fail to note that subtracting the bandpass output from the input signal creates a notch filter.
Closing the loop deepens notches - schematic




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