Notch filter is insensitive to component tolerances

By John Guy, Maxim Integrated Products, Sunnyvale, CA -- 3/2/2000

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.

Two allpass filter stages, IC_1A and IC_1B , 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)

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