# Notch Filters

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A notch filter is a type of band-stop filter designed to attenuate heavily at a specific frequency and pass all other signals. They are frequently used to eliminate some known, but unwanted component from a signal, for example eliminating 50Hz mains artefacts from a signal of interest that spans mains frequency.

The classic passive notch filter is the twin-T filter as shown in Figure 1a. With ideal components the attenuation of this filter rises to a peak at fc = 1/(2 R C). This occurs because at the critical frequency the circuit effectively sums two signals that are 180° out of phase.

The Q of this filter is limited to 0.25, meaning it has a relatively gentle characteristic, attenuating signals either side of the centre frequency considerably as shown in the simulation in Figure 2a. The maximum attenuation is  about -12dB. We can improve the Q of the notch by using the active circuit shown in Figure 1b. This allows us to set the Q anywhere from 0.25 to (theoretically) infinity by adjusting the ratio of R1 and R2. Figure 2b shows the improvement this makes – the notch is narrower and deeper.

While it is possible to tune the Q of the twin-T filter, it is very difficult to tune the frequency since we need to simultaneously change three resistors (or capacitors) while keeping the ratio of their values constant. A better alternative is the circuit shown in Figure 3a, sometimes called the bridged differentiator. The notch frequency is given by the equation fc = 1/[2πC(3 R1 R2)].  Matching of components is important for good performance.

The results in Figure 4a shows that this filter achieves a much deeper notch, although the Q is relatively low. Just like the twin-T filter, an active version of the bridged differentiator (Figure 3b) can provide adjustable Q and a narrower notch at the expense of notch depth, as illustrated in Figure 4b.

If we are aiming for the narrowest possible notch, you can use the relatively obscure Bainter notch filter shown in Figure 5. This is much more complex but has the advantage of allowing the us to set the Q independent of the frequency by manipulating the gain of the op amp stages. Determining the component values is more involved than for the preceding filters, so I suggest you refer to the Analog Devices “Mini Tutorial” MT-203 for more details if you want to use this design.

Figure 6 shows the simulation results for two different configurations. On the left is a version with a passband gain and Q of unity for comparison with the previous examples. Here you can see a very narrow notch with about -25dB of attenuation. Increasing the gain (and therefore Q) of the circuit to 20 results in a very narrow and relatively deep notch (Figure 6b).

Be warned that the simulations use ideal components. In practice, for any of these circuits you will need to select components with care as tolerance, temperature drift and mismatching will all result in less-than optimal outcomes.

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