Notch Filter- Theory, Circuit design and Application

A notch filter is nothing but a narrow band stop filter. If the stop band of Band stop filter is very narrow and highly attenuated over a few hertz, then that special type of band stop filter is known as Notch Filter.

Notch filter is a special type of Band Stop filter used by electrical and electronics engineers. In this article, We will discuss in detail the complete concepts about Notch Filter. But before that, we should discuss some basics of the Bandstop filter to understand the complete concepts of the Notch filter in an easy way.

Band Stop filter

A band stop filter is a type of frequency selective circuit that has an exact opposite functionality to the bandpass filter. As the name itself indicates that it will stop or attenuate a particular band or range of frequencies. Since it eliminates frequencies so it is also known as Band reject filter or band elimination filter. Also, that attenuated frequency band is known as a stopband of the filter.

Band stop filter is formed by combining the low pass and high pass filters in parallel connection through an amplifier circuit. The block diagram of the Band-stop filter is shown below:

Block diagram of band-stop filter

Whereas the circuit diagram of an active Bandstop filter is shown as:

Active Band stop filter

Unlike high pass and low pass filter, band-stop, and band-pass filters have two cutoff frequencies. It will pass above or below a particular range of frequencies whose cutoff frequencies are defined by the components used in the circuit. Any frequency in between these cut-off frequencies is attenuated. So it has two pass-bands and one stop-band. The characteristics of the band-pass filter are shown below:

Characteristics of band-pass filter

Here FL is the cut-off frequency of the low-pass filter and FH is the cut-off frequency of the high-pass filter. So the center frequency of band-stop filter will be:

Notch Filter Theory

A Notch filter is nothing but a narrow band-stop filter. If the stop-band of band-stop filter is very narrow and highly attenuated over a few hertz, then that special type of band-stop filter is known as Notch filter.

Since the stopband of Notch filter is narrow up to a few Hz so the Notch filter is also known as Narrow band stop filter in some cases. It is a highly selective (High Q value) form of band-stop filter which can be used to block a single or very small band of frequencies rather than the whole bandwidth of different frequencies. It acts as a gain for one frequency component and an attenuator for all other frequencies.

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Notch filter by design has a very narrow stopband around their center frequency. The width of the notch is being calculated by its selectivity Q in exactly the same way as the resonance frequency peak is calculated in the RLC circuit.

Notch Filter Frequency Response

The ideal response of notch filter would be a completely flat response over the usable range with the exception of notch frequency as shown in the figure below.

Notch Filter Frequency Response

Practically perfection is very tuff to achieve. But by using the operational amplifier circuit, a high level of attenuation and narrow notch can be achieved.

Notch Filter Circuit

The most common Notch filter design is the twin-T notch filter network. In its basic form, the twin-T is also called a parallel-T configuration. It consists of two RC branches in the form of two tee sections connected in parallel.

The basic twin-T Notch filter circuit is shown in the figure below as: 

basic Twin-T Notch filter circuit

The upper T-configuration of resistor 2R and capacitor 2C form the low pass filter section, whereas the lower T-configuration of resistor R and capacitor C form the high pass filter section of the design.

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The frequency at which this basic twin-T notch filter design offers maximum attenuation is called Notch frequency. So notch frequency is formulated as:

For obtaining a high level of attenuation and narrow notch, an operational amplifier is used to design a single Op-Amp twin-T notch filter circuit. The single Op-Amp twin-T notch filter circuit is shown in the below figure as:

single Op-Amp Twin-T Notch filter circuit

Notch Filter Design

For designing a two Op-Amp narrow band RC notch filter with center notch frequency of 1kHz and 3-dB bandwidth of 100 Hz. Consider the 0.1uF capacitor and calculate all the values of the required components as explained in the below steps.

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Step 1: Calculate the value of R for the given capacitance of 0.1uF.

Step 2: Calculate the value of Q.

Step 3: Calculate the value of feedback fraction K.

Step 4: Calculate the value of R3 and R4.

Step 5: Finally Calculate the value of notch depth in dB as:

Hence after using these values in the circuit we can design the Notch filter as:

Notch filter design

Notch Filter Applications

In different technologies, Notch filters are used in different ways.

• In communication electronics, the signal is distorted due to some harmonics (Noise) which makes the original signal to interfere with noise signal which leads to error in the output. Thus notch filters are used to eliminate these unwanted frequencies of harmonics.

• These filters are used by musicians in high-quality audio applications such as graphic equalizers, synthesizers, and PA systems.

• In telephone technology, Notch filters are also used as the telephone line noise (Harmonics) reducer and DSL performance of internet service.

• Also the notch filters are widely used in electric guitar amplifiers. Actually, the electric guitar produces a ‘hum’ at 60 Hz frequency. Then this filter is used to reduce that ‘hum’ by rejecting 60 Hz in order to amplify the signal produced by the guitar amplifier and make it the best equipment. These are also used in acoustic applications like Mandolin, Bass instrument amplifiers, etc.

• It is also used in Optical communication technologies. The best example is Raman Spectroscopy. At the end of optical fiber, there may be some interfering frequencies of light that make the distortions in the light beam of optical fiber. Then these distortions are eliminated by the narrow band-stop filters.

• In image and signal processing, these filters are highly preferred to eliminate noise.

• It is also used to reduce the static on the radio, which is commonly used in our daily life.

• These filters are also used in medical field applications, i.e., in biomedical instruments like ECG for removing lines.

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