Notch filter- Theory, circuit design and Application

Notch filter

In this tutorial, we will learn about a special Band Stop Filter is known as a notch filter. Since notch filter is a special type band stop filter, so before discussing the notch filter we have to discuss some basics about band stop filter so that it will be easy to understand the complete concepts of the notch filter.

    Band Stop filter

    A Band reject or Band stop filter is a type of frequency selective circuit which has an exact opposite functionality to the Band Pass Filter. 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 elimination filter or band reject filter. Also, the attenuated frequency band is known as stopband.

    Band stop filter is formed by combining the Low pass and High pass filter in parallel connection through an amplifier circuit.
    Block diagram of Band stop filter is shown as below:
    block diagram of band stop filter

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

    active Band stop filter

    Unlike High pass and Low pass filter, Bandstop and bandpass filter 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 frequencies in between these cutoff frequencies are attenuated. So it has two passbands and one stop band. The characteristics of the Bandpass filter are shown below as.

    characteristics of Band pass filter

    Here FL is a cutoff frequency of low pass filter and FH is a cutoff frequency of 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 stop band of the notch filter is narrow so Notch Filter is also known as Narrow Band Stop filter. It is highly selective, high-Q, form of band stop filter which can be used to block a single or very small band of frequencies rather than whole bandwidth of different frequencies. It acts as a gain of one frequency component and attenuator for all the other frequencies.

    Notch filters by design have a very narrow stop band around their center frequency with the width of the notch being calculated by its selectivity Q in exactly the same way as resonance frequency peaks is calculated in RLC circuits.

    Notch Filter Frequency Response

    The ideal response of any 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 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 below figure as: 
    basic Twin-T Notch filter circuit

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

    The frequency at which this basic twin-T notch filter design offers maximum attenuation is called the “notch frequency”. So notch frequency is formulated as. 
    notch frequency
    For obtaining the high level of attenuation and narrow notch, an operational amplifier is used to design 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 a center notch frequency of 1kHz and a -3dB bandwidth of 100 Hz. Consider  0.1uF capacitors and calculate all the values of required components as explained in below steps.

    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 errors 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 equalizer, synthesizer and PA systems.
    • In telephone technology, Notch filters are used as the telephone line noise (harmonics) reducers and DSL internet services. It will help to eliminate the interference on the line which will reduce the DSL performance of internet service.
    • Also, the notch filters are widely used in the 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 makes it the best equipment. These are also used in some of the acoustic applications like mandolin, bass instrument amplifiers, etc.
    • It is also used in Optical communication technologies. The best example is in Raman spectroscopy. At the end of the optical fiber, there may be some interfering frequencies of light which make the distortions in the light beam of optical fiber. Then these distortions are eliminated by narrowband 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 are commonly used in our daily life.
    • These filters are also used in medical field applications,i.e., in biomedical instruments like EGC for removing line.

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