# Op Amp Active Notch Filter Circuit

### Op amp active notch filter circuits can be used to remove single frequencies or small bands of frequencies and are easy to design.

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Operational amplifiers provide an excellent way of making and designing notch filters. Op amp active notch filters are very effective whilst being easy to design and construct.

Notch filters can be used in a number of different applications where a particular frequency or band of frequencies needs to be removed. Often notich filers are fixed frequency, although it is possible to design some that have variable frequencies.

Fixed frequency notch filters find applications such as removing fixed frequency interference like mains hum, from audio circuits.

## Notch filter response

The ideal response for any notch filter would be a completely flat response over the usable range with the exception of the notch frequency. Here it would fall very fast providing a high level of attenuation that is able to remove the unwanted signal.

In reality, perfection is not achievable, but when using an operational amplifier circuit, high levels of attenuation and narrow notches can be achieved.

## Op amp active notch filter circuit

The diagram below shows an active notch filter circuit using a single op amp. The notch filter circuit is quite straightforward and the calculations for the component values are also easy to determine.

The active notch filter circuit is quite straightforward to design. It employs both negative and positive feedback around the operational amplifier chip and in this way it is able to provide a high degree of performance.

Calculation of the value for the circuit is very straightforward. The formula to calculate the resistor and capacitor values for the notch filter circuit is:

$R={R}_{3}={R}_{4}$

$C={C}_{1}={C}_{2}$

**Where:**

f_{notch} = centre frequency of the notch in Hertz

Π = 3.142

R and C are the values of the resistors and capacitors in Ω and Farads

## Notch filter design precautions

When building the active notch filter circuit, high tolerance components must be used to obtain the best performance. Typically they should be 1% or better. A notch depth of 45 dB can be obtained using 1% components, although in theory it is possible for the notch to be of the order of 60 dB using ideal components. R1 and R2 should be matched to within 0.5% or they may be trimmed using parallel resistors.

A further item to ensure the optimum operation of the circuit is to ensure that the source impedance is less than about 100 ohms. Additionally the load impedance should be greater than about 2 M Ohms.

The circuit is often used to remove unwanted hum from circuits. Values for a 50 Hz notch would be: C1, C2 = 47 nF, R1, R2 = 10 k, R3, R4 = 68 k.

## Op amp twin T notch filter circuit with variable Q

The twin T notch filter with variable Q is a simple circuit that can provide a good level of rejection at the notch frequency. It uses two operational amplifiers in the circuit, and the twin "T" section can be seen between the two operational amplifiers.

The variable Q function for the twin T active notch filter is provided by the potentiometer placed on the non-inverting input of the lower operational amplifier in the diagram.

Calculation of the value for the circuit is very straightforward. The formula is the same as that used for the passive version of the twin T notch filter.

**Where:**

f_{notch} = cut off frequency in Hertz

π = 3.142

R and C are the values of the resistors and capacitors as in the circuit

The notch filter circuit can be very useful, and the adjustment facility for the Q can also be very handy. The main drawback of the notch filter circuit is that as the level of Q is increased, the depth of the null reduces. Despite this the notch filter circuit can be successfully incorporated into many circuit applications.

The two op amp active notch filter circuits are very easy to design and use. Their performance is good enough for most applications, but if they need to be cascaded, then care must be taken to ensure they are on exactly the same frequency by using very close tolerance components for the frequency determining elements.

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