Op Amp Notch Filter Circuit

- the circuit, calculations and design considerations for a single op amp notch filter and a twin T notch filter using an operational amplifier.

Operational amplifiers can be used to make notch filter circuits. Here we show two, a standard notch filter circuit, and another for a twin T notch filter circuit.

A notch filter is used to remove a particular frequency, having a notch where signals are rejected. Often they are fixed frequency, but some are able to tune the notch frequency.

Having a fixed frequency, this operational amplifier, op amp, notch filter circuit may 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.

The response of a notch filter showing the flat response way from the notch and the attenuation around the notch frequency
Notch filter response

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 notch filter circuit

The diagram below shows a 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.

Diagram of a notch filter circuit showing the arrangement using four resistors and two capacitors
Op amp notch filter circuit

The 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:

The formula to calculate the values for the  op amp notch filter circuit where Fnotch = 1 / (2 Π R C)

Where:
    fnotch = 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

When building the 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 notch filter is provided by the potentiometer placed on the non-inverting input of the lower operational amplifier in the diagram.

Diagram of a op amp notch filter using a twin T configuration and two chips
Op amp twin T notch filter circuit with variable Q

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.

The formula to calculate the values for the  op amp notch filter using a twin T configuration providing variable Q

Where:
  fc = 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.

Notch filter circuits

The two op amp notch filter circuits are very easy to use and provide a good level of performance without being excessively complicated. They are a useful tool in the armoury of the analogue development engineer.

By Ian Poole


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