Band Stop Filter:31 Facts That Most Beginner’s Don’t Know!

Band Stop Filer Definition

“Band reject filter is combined of low pass and high pass filter which eliminates frequencies or stop a particular band of frequencies.”

Band rejection is obtained by the parallel connection of a high pass section with a low pass section. Now, the general rule is that, the cutoff frequency should be higher than the cut-off frequency of the low-pass area.

There is another way to create it. If a multiple feedback system is incorporated with an adder, then that functions like the desired operation. It is called as notch.

The Frequency response of a bandstop filter is calculated by considering the frequency and gain.

The bandwidth is chosen through the lesser and greater cut-off frequency. Notch filter is used to remove the single frequency. From this frequency response, we can also obtain Passband ripple and stopband ripple.

                                 Pass Band Ripple= -20log₁₀(1-∂_p) dB

                                 Stop Band Ripple= -20log_1o(∂_s) dB

Where ∂_p= magnitude response of the passband filter

             ∂_s= magnitude response of the stopband filter

Why It is called band stop filter ?

Bandstop filter rejects a certain band of frequency and allows another frequency component of the primary signal. If the band of the frequency is narrow, the stopband filter is known as Notch Filter. The filter attenuates the specific band. The filter has several applications.

For example, a band-stop filter is designed to reject frequencies between 2.5 GHz to 3.5 GHz. The filter will allow frequency components lower than 2.5 GHz and above 3.5 GHz.  The filter will We will explore the filter in the below sections.

Passband and stopband of a filter

Before diving into a band-reject or bandpass details, let us understand what pass band and stop band means. A passband is the frequency bandwidth that is allowed by a filter. On the other hand, a stopband is the band of frequency which one filter hasn’t allowed to pass. For a bandstop filter, there are two passbands and one stopband.

What does a band-stop filter do?

As the name suggests, a band-stop filter simply ‘stops band.’ That means a band-stop filter resistor doesn’t allow a certain band of frequency to pass through the

What is a band-stop filter used for

When there is a need to attenuate a certain band of frequency and pass other frequency components, a band-stop filter is used. Bandstop filters are useful in various applications.

Band stop filter applications

Being a very important type of filter, bandstop filters has several applications. Let us find out some of the applications.

1. Medical Engineering: Bandstop filters are used in medical engineering. Like – in ECG machine. 60 Hz bandstop filters are used to remove the supply frequency from the output.
2. Audio Engineering: Bandstop filters have huge applications in audio engineering. They remove the unwanted spikes and noises from the score and provides a good quality of audio.
3. Telecommunication: Bandstop filters are used in telephonic connections to remove the internal noise from the lines.
4. Radio communication: Band rejects filters are widely used in radio stations to transmit a better audio quality.
5. Optical filters: Band-stop filters are used to block certain wavelengths of light in an optical communication system.
6. Digital Image Processing: Bandstop filters are also used in digital image processing to remove certain periodic noises.
7. Miscellaneous: Whenever there is a need to remove the noise of a certain frequency, a band-stop filter is used.

Band stop filter diagram

This article explains the bandstop filter with various circuit diagrams, block diagrams, and graphs. This article includes a block diagram, band reject-with op-amp, frequency response of band stop, passive circuits, bode plots.

Circuit diagram of band-stop filter

The bandstop filter can be designed in several ways. It can be active types (which has op-amp). It can be for passive kinds (without op-amp). Active types have several varieties, too as well as passive filters have different styles too. That is why there are several circuits available also. In this article, almost all possible courses are given below. Check out the needed one.

Band stop filter block diagram

The bandstop filter is a combination of both high pass filters as well as low pass filters and another amplification factor for the filter. The block diagram is given below.

Narrow band stop filter

If the freq. of the bandstop filter is narrowed than general, the filter is often known as a Notch filter(hyperlink) or narrow bandstop filter.

Simple band stop filter

Unlike notch filter or higher-order filters, the simple bandstop filter is a basic filter which attenuates certain band of frequency allowing other bands.

Band stop filter using op-amp

Active bandstop filters are designed using operational amplifiers. Op-amp is one of the most important devices in making a filter. In passive filters, as there is no op-amp, there is no amplification. Thus, using the op-amp as a circuit element gives amplification.

Bandstop filter circuit using op-amp

This filter consists of a high-pass filter, a low-pass filter, and a summing amplifier to summation the lpf and hpf’s o/p, The circuit is shown below.

Band pass filter vs Band stop filter

There are fundamental differences between bandpass and bandstop filter.

The main principle of a bandpass filter is that it allows a certain band of frequency. At the same time, the main tenet of the bandstop filter is that it blocks a certain band of frequency.

Let us take an example to demonstrate. Let us say there is a lower cutoff frequency of _Flow and a higher cutoff frequency _high. Now, for a bandpass filter, the frequency in between the lower cutoff and higher cutoff will only pass, and other components below the _Flow and above the f_high will not pass.

Now, for a band-stop filter, the frequency band lower _Flow, and above f_high will pass. But the band in between the frequency limit will not pass.

Band stop filter vs notch filter

A notch filter is one type of bandstop filter. The main difference between them is that a notch filter attenuates a narrower band of frequency than a bandstop filter. In other words, bandstop filters have a wider band of frequency to attenuate.

Band stop filter RLC circuit

The band stop filter can be designed using basic components like resistor, capacitor, and inductor. There are two ways of developing the filter – 1. RLC parallel band-reject filter or Parallel resonant band-reject filter, & 2. RLC series resonant band-reject filter. As we are using passive elements, so both the filters will be of passive types.

Parallel RLC band stop filter

As mentioned earlier, a bandstop filter can be designed with basic components like – resistor, capacitor, and inductor. There are two ways of developing the circuits. The methods are discussed below.

Parallel RLC band stop filter 

A Parallel RLC bandstop filter is a tank circuit. It also works fine as a frequency attenuator as the tank circuit is providing a lot of impedance. The below image shows the circuit diagram of a parallel rlc bandstop filter.

The parallel resonant band stop filter 

The parallel resonant bandstop filter is also known as the parallel rlc bandstop filter. The details of the circuit and filter are given previously.

Series resonant bandstop filter 

The main instruments for this filter are – capacitor and inductor. As the name suggests, the inductor and capacitor are kept in series. This part is the filter. At resonance, the circuit can attenuate certain frequencies before reaching the load. The below image shows the circuit diagram of the series resonant circuit.

Passive bandstop filter circuit 

The passive bandstop filter is made of passive components, such as – resistor, inductor, and capacitor etc. Previously given circuits are an example of such filters. These filters do not have any operational amplifiers. Thus, there is no amplification process. A passive band stop filter consists of both passive hpf and passive lpf.

Active band stop filter

Unlike passive bandstop filters, active band-reject filters come with active components. The most important active part is the operational amplifier which also introduces amplification. Circuit using op-amp or the functional bandstop filter diagrams are given previously in this article.

Active bandstop filter design 

Let us design a band stop filter. The center frequency will be 2 KHz.  The bandwidth will be -3 dB of 200 Hz. Take capacitor value as one uF.

So, f_N = 2000 Hz, BW = 200 Hz, C = 1 uF.

At first calculate the R. R = 1 / 4πf_N C,

R = 39.78 ohm.

The Quality factor: Q = f_N / BW = 2000/200 = 10

The value of feedback function: K = 1 – (1/ 4Q)

Or, K = 1 – (1/40)

Or, K = 0.975

Let us find out the value of resistors.

K = R4 / (R3 + R4)

The R4 value is assumed as 20 kΩ.

R3 comes as: R3 = R4 – 0.975 R4 = 20000 – 0.975 * 20000 = 500 Ω

The notch depth is: 1/Q = 1/10 = 0.1

The depth in decibel comes as: 20log (0.1) = -20 db.

Band stop filter transfer function

The transfer function of a device refers to a mathematical function that provides output for every input. The transfer function of a band-stop filter is given below.

The second-order band-stop filter transfer function

The transfer function expression for the second-order band-stop filter transfer function is given below.

 Band stop filter graph

The phase response stands for the phase output of the bandstop filter, bottom one represented the phase response.

Credit: Inductiveload, Band-Reject Filter Response, marked as public domain, more details on Wikimedia Commons

Band stop filter bandwidth 

The bandwidth of the bandstop filter depends on the requirement. The band-width is the range of freq. in which the filter will attenuate. In general, the bandwidth is referred to as the specification of a filter.

The impulse response of band-stop filter

Bandstop or band-reject filter can be designed digitally. There are two types of digital band-reject filters, They are – Infinite Impulse Response(IIR) and Finite Impulse Response(FIR). FIR method is more popular.

There are two design methods of FIR filter. They are also known as non-recursive filters. The methods are – 1. Window method & 2. Weighted-Chebyshev method.

Sallen key band stop filter

Low pass filters allow the lower frequency components of a filter and reject the higher frequency components. So, for the low pass filter, the stopband is the high-frequency component.

Sallen key is another topology of designing filters. The bandstop filter can also be created using the topology.  Sallen key topology is designed using operational amplifiers for creating higher-order filters. Thus, we can understand this topology is for active filters. 

Basic Sallen Key topology comes with one non-inverting op-amp and two resisters. It creates a Voltage Control Voltage Source or VCVS circuit. The circuit provides high input impedance and low output impedance which useful for filter analogy.

This Sallen Key topology also provides good stability of the system, which is highly suggested. The circuit is also very simple. They are connected one after another to achieve the higher-order filters. The circuit diagram of the band-reject filter using Sallen key topology is given below.

Band stop filter formula

There are some important equations for designing a band stop filter. Using these equations, we can find out important parameters. But one of the values of the parameter should be supplied as it is needed to design the filter.

The Normal Frequency Equation:

The Lower Frequency Cut-off:

The Higher Frequency Cutoff:

Here, the R_L is lower resistance, and R_H is higher resistance.

• The center frequency:

• The bandwidth: f_BW = f_H – f_L

• The Q Factor of the filter: Q = f_C/f_BW

Band stop filter example

The bandstop filter is an important concept that has several applications. That is why there are several examples as well. There is a band stop filter for blocking certain frequencies. Like – 2.4 GHz Band Stop filter. There is a band-reject filter for blocking narrower frequency bands, like the Notch filter, which has several applications. Audio bandstop filters, optical band-reject filters, digital-analog filters are some of its examples.

60 Hz band stop filter

From the filter’s name, we can understand that this bandstop filter is designed for attenuate frequency bands of 60 Hz. Now, the question comes why the 60 Hz band reject filter is so popular. It is because, in the USA, their supply frequency is 60 Hz. So, in most cases, when there is an interference of the supply frequency with the working signal, a 60 Hz bandstop filter is used to remove the frequency band from the output.

Band stop filter bode plot

At first, let us understand what the abode plot means. Abode plot refers to the graph of the frequency response of a device. The freq. response of the band-reject filter is presented below.

Credit: Michael Frey, Passive Band-stop filter Bode Plot, marked as public domain, more details on Wikimedia Commons

Cutoff frequency of band-stop filter

The cutoff frequency of a band-reject filter refers to the frequency of the band to be attenuated. There are formulas for lower frequency cutoff and higher frequency cutoff.

The lower cutoff frequency: f_L = 1 / 2π R_L C

The higher cutoff frequency: f_H = 1 / 2π R_H C

Band stop filter image processing

The bandstop filter is used in image processing. There are some different kinds of noises. The noises are repetitive. They have certain frequencies. A band-stop filter omits such noises. At first, the frequency is matched with the noise frequency. Then the bandstop filter removes the noises and makes the image a better one.

Band stop filter pole-zero plot

A band-reject filter can be designed using two zeros placed at ±jω₀. These types of designs don’t have a unity gain at zero frequency. A notch filter can be developed by putting two poles close to the zeros.

Bandstop filter using op-amp 741

As mentioned earlier, band-reject filters can be designed using operational amplifiers. That is known as creating active band-reject filters. The band-reject filters consist of both low pass and high pass filters. Both these filters require operational amplifiers to design. Op-amp 741 is used here. Another summing op-amp is also necessary to sum the outputs of the previous filters and provide amplification. Op-amp 741 can be used in all those cases.

Band stop notch filter

A bandstop notch filter is just a special type of band-reject filter. Bandstop notch filter has a narrower bandwidth than usual band-reject filters. To know more about the notch filter, check out my article on Notch filter.

Band stop vs. Bandpass filter

 The name of both the filters explains the difference between them. Here band means the range of frequency. Bandpass filter allows the specific band to pass through the filter and attenuates other components. At the same time, band-reject filters attenuate the particular band of frequency while it will enable other parts.

Characteristics of band stop filter

The bandstop filter has several characteristics. Some of them are listed below.

1. It has two passbands and one stopband.
2. It comes with a combination of lpf and a hpf.
3. If the bandstop filter has a narrow bandwidth, it is a notch filter that has great depth.
4. Bandstop filters are also known as band-reject filters as it ‘rejects’ the specified band.

Constant k band stop filter

Constant k filter is another topology of designing a filter. It is quite a simple topology, but it has a shortcoming. Here, the ‘k’ is referred to as the impedance level of the filter. It is also known as the nominal impedance. The terminating resistance is also considered as ‘k’ ohms (R_k² = k²). The bandstop filter using constant k topology is shown below.

Design Procedure: At first, the center frequency, the bandwidth, and the intended characteristic impedance should be specified. Then follow the steps.

1. Calculate C₂ using w_H -w_L = R_kC₂w₀²/2.
2. Calculate L₂ using L₂ = 1/w₀²C₂.
3. Calculate L₁ using L₁ = k²C₂, as L₁/C₂= k².
4. Calculate C₁ using C1 = 1/w₀²L₁.

FIR band stop filter

FIR or Finite Impulse Response Filter is a digital bandstop filter. The formula for an FIR bandstop filter is given below.

N signifies the dimension of the filter. F1 and F0 are the cut off freq and Fs is the sampling freq.

lC band stop filter

A passive band-reject filter can be designed with an LC circuit. The working of the LC filter is quite simple. Inductors come with a reactance as well as capacitors also come with capacitive reactance. Now an increase in the frequency causes the decrease in capacitive reactance and increase in inductive reactance. This is the primary principle behind LC bandstop filter.

Notch band stop filter

As mentioned earlier, the notch bandstop filter is a normal bandstop filter that has a narrower bandwidth. It has several applications as it has great depth and performance than a band-reject filter. To know more about notch band-reject filters, check here. <link>.

Optical band stop filter

Optical band-reject filters block a certain wavelength of light and allow other components to pass. Just like normal band-reject filters, an optical filter rejects a certain wavelength. For example, there is a 532nm optical bandstop filter. Now, it will block the light, which has a wavelength of 532 nanometers.

RC band stop filter

The bandstop filter can also be designed using resistance and capacitors. Such band-reject filters are known as RC band top Filter. The circuit is shown below. It is a first-order filter. The resistors and capacitors are connected in parallel at first; then, they are connected in series. The frequency components are trapped in between them.

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RF band stop filter

The bandstop filter has several applications in Radio Frequency Domain. For example, during the measurement of non-linearities of a power amplifier. Also, when radio signals are transmitted from stations, band-reject filters are used to remove interfering noises.

Twin-t band stop filter

It is another method of implementing a higher-order filter and provide great depth and accuracy in performance. That is why this method is popular for notch filters. The twin t filter is made of two T networks, there is an RCR circuit, and another is the CRC network

Mathematical Expression for a Band Stop Filter:

Band Reject Filter can also be obtained by using the multiple -feedback bandpass filter with an adder. A notch filter is created using a circuit which eliminates the output of a bandpass filter from the unmodified signal.

Characteristics of a Band Reject Filter:

• A band-stop filter works a frequency remover which is not within a specific range, reason it is called a rejection filter.
• A band-stop filter passes frequencies of a particular bandwidth with maximum attenuation.
• Different types of band-stop filters produce a maximum rate of roll-off rate for a given order and flat frequency response in the passband.

Applications of a Band Stop Filter:

• An active Band Pass filter is used in the public addressing system and speakers for enhancing the quality.
• A bandstop filter is also used in telecommunication technology as a noise reducer from different channels.
• BSF is used in radio signals to remove static on the radio devices for better and clear communications.
• Besides radios and amplification, this filter is also used in many other electronic devices to decrease a specific range of frequencies, known as ‘noise.’
• In the medical field, BSF is used in making many useful devices like ECG machines, etc.
• It also plays a vital role in image processing.

What is a Notch filter?

Notch filters find applications when there is a need to attenuate the undesirable frequencies while passing the necessary frequencies.

Advantages & Disadvantages of a band stop filter:

A bandstop filter attenuates the frequencies that are below the cut off range, so key advantage of using this filter is, it eliminates the external and unwanted noise or signals as well as gives us a stable output.

On the other hand, due to some certain limitations a band stop filter does not function properly under sustainable conditions. The parallel arrangement between the high pass and low pass filter my vary about the change of frequencies.

Frequently Asked Questions :

What is the Q factor or ‘Quality Factor’?

Q is given by the ratio between the resonant frequency to the bandwidth. It is an important parameter and it helps us to calculate the selectivity.

The higher the value Q, the more selective is the filter, i.e., narrower is the bandwidth.

How do a Band stop filter work?

A band stop or band reject filter always cuts or rejects frequencies that are not within a certain range, as the name implies. Besides this, it also gives easy passage to the frequencies to pass which are not in the range. These types of filters are often termed as ‘Band Elimination Filters’.

How to design a Band Reject Filter?

To make a Band Stop/reject filter we always need a Low Pass Filter(LPF) & a High Pass Filter(HPF). Therefore we combine them and  make a ‘parallel’ connection with both the filters to create a band reject filter.

What does a Notch Filter do?

Notch Filter is also band reject filter. They can be used to fix frequency noise sources which are from the line frequency within a certain limit. Notch filter is also used to remove resonances from a system. Like a Low pass filter, notch filter creates less phase lag in a control loop.

Find out the differences between between a band reject filter & a notch filter?

A band reject filter or band stop filter is a filter that carries or passes the frequencies without altering and attenuates them in a specific range to low level. This is the opposite of a band pass filter.

On other hand, a notch filter is a bandstop filter which has a narrow stop band and has good high ‘Quality factor’(Q-factor).

What is Ideal Filter & Real Filter?

Sometimes, for the reason of simplification, we often use the active filters to approximate ways. We upgrade them into an ideal and theoretical model, which is called ‘Ideal Filter.’

The use of these standards is insufficient, leading to errors; then, the filter should be treated based on accurate real behaviour, For example, the Real filters.

The characteristics of an ideal filter are:

• The response transits between zones in a sudden way.
• It does not create any distortion when the signal passes through the transit zone.
• The pass of the signal causes no loss.

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Sudipta Roy

Hi, I am Sudipta Roy. I have done B. Tech in Electronics. I am an electronics enthusiast and am currently devoted to the field of Electronics and Communications. I have a keen interest in exploring modern technologies such as AI & Machine Learning. My writings are devoted to providing accurate and updated data to all learners. Helping someone in gaining knowledge gives me immense pleasure.
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