Notch filter is insensitive to component tolerances
Many approaches for creating notch filters, which reject a narrow band of frequencies and pass all others, are unsatisfactory because they allow the component tolerances to interact. The circuit in Figure 1a overcomes this limitation and enables easy calculation of the component values for a desired notch frequency.
Figure 1 Summing VIN with the output of IC1’s phase-shifting allpass filter results in a notch response (a). Operating the circuit with 5% values for R1 and R2 and 10% values for C1 and C2 produces a notch frequency of approximately 99 Hz (b).
Two allpass filter stages, IC1A and IC1B , create a dc-accurate, 180° phase shift at the cutoff frequency. Each op amp in IC1 includes gain resistors that match to within 0.1%. This tight tolerance eliminates the need for trimming in most applications. Summing this phase-shifted signal with the input produces a cancellation that produces the notch.
At low frequencies for which the impedance of C2 is negligible, the circuit forms a voltage follower and produces no phase inversion. For high frequencies, however, this capacitor acts as a short circuit that causes the amplifier to act as a unity-gain inverter with the associated 180° phase shift. Phase behavior for the resulting allpass filter is identical to that of a single RC pole and produces 90° of phase shift at the resonant frequency, which is equal to 1/2pR1 C1 and 1/2pR2 C2 .
R1 , R2 , C1 , and C2 affect only the notch frequency and not its depth. Conversely, the integrated resistors in IC1 affect only the depth of the notch and not its frequency. If you require a highly accurate notch frequency, specify R1 , R2 , C1 , and C2 accordingly or simply trim one of the two resistors. IC2 is a precision differential amplifier that the circuit uses as a matched summing amplifier. Note that the inverting input is left unconnected.
Figure 1b shows the circuit's performance with 5% resistors and 20% capacitors, all unmatched. To produce a deeper notch, you can trim the circuit by adding a 100W resistor in series with Pin 3 of IC2 . You can also add a 200W potentiometer in series with Pin 1 of IC2 and adjust this potentiometer for maximum rejection at the desired frequency. (DI #2492)