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. The attenuation of such an open-loop notch filter is limited by how well the components match; typically, it's approximately 40 dB. Figure 1 shows a standard state-variable filter with an amplifier, IC₄, added to invert the bandpass output. You can implement a notch filter by adding a further amplifier to sum the input signal and the output of IC₄.

An alternative is to move the input to R₉ and to take the notch output from the output of IC₄. Closing the loop around the notch filter makes the depth of the notch depend only on the gain of the integrating amplifiers. Replacing R₅ and R₆ by differential-input, current-output multipliers (for example, the Harris HA2547) creates the tunable notch filter in Figure 2. The time constants T₁ and T₂ are the products of the values of the integrating capacitors and the multipliers' transimpedances. In Figure 1 and Figure 2, R₃ controls the width of the notch.

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