Notch Filter Design: 37 Interesting Facts To Know


In this article, we will discuss different techniques of notch filter design. Let’s see what are the points of discussions for this article.

Points of Discussion

  1. What is notch filter?
  2. how to build a notch filter
  3. notch filter eq || notch filter equation
  4. notch filter ic
  5. notch filter q factor
  6. notch filter frequency
  7. notch filter example
  8. Notch filter design || rlc notch filter design || how to design a notch filter
  9. tunable notch filter
  10. tunable notch filter design
  11. digital notch filter
  12. digital notch filter design
  13. dsp notch filter
  14. design of notch filter in dsp
  15. fir notch filter
  16. fir notch filter design
  17. iir notch filter || digital iir notch filter
  18. iir notch filter design
  19. active notch filter design || analog notch filter design || notch filter derivation
  20. lc notch filter design
  21. notch filter using op amp || notch filter circuit using op amp
  22. 60hz notch filter
  23. 60 hz notch filter design
  24. rf notch filter design
  25. programmable notch filter
  26. notch filter code
  27. fm broadcast notch filter
  28. audio notch filter
  29. audio notch filter design || audio notch filter circuit || fm notch filter circuit
  30. audio notch filter schematic
  31. biquad notch filter
  32. 532 nm notch filter
  33. harmonic notch filter
  34. notch filter design tool
  35. betaflight notch filter
  36. notch filter transfer function derivation
  37. notch filter for ecg signal

What is notch filter?

A notch filter is generally a modified form of the Band Reject or Band Stop filter. The main objective of these filters is to stop or prohibit a certain range of frequencies from appearing in the output. For example, a Band Stop filter having a narrow stopband is called a notch filter.

Let us take an example. Suppose a Notch filter is designed to stop frequency between 100kHz to 110kHz. So, it will pass every signal below the 100kHz range and give any signal higher than 110kHz but will prevent any signal in between the 100kHz to 110 kHz.

how to build a notch filter

The building of a notch filter is quite easy. There are three main steps in building a notch filter. The steps are – 1. Note down the requirement perfectly, 2. Understand the need and design the notch filter (Designing a notch filter is written below), 3. Check with the expectation. (If perfect, then use, if not re-design the filter).

notch filter eq || notch filter equation

Some of the important equations of notch filter are given below.

  • The HF cut-off of the LPF: fL = 1 / ( 2 * RLP * CLP * π)
  • The LF cut-off of the HPF: fH = 1 / ( 2 * RHP * CHP * π)
  • The quality factor of the notch filter:  Q = fr / Band Width

notch filter ic

There are several Integrated Circuit available in the market which implement a notch filter. There are many advantages of using IC over conventional circuits. One of the most popular normal notch filter IC is LTC1059. The PIN diagram of the IC is given below.

PIN diagram of LTC 1059

notch filter q factor

The q factor of a notch filter is the same as the q of a notch. Q or Quality Factor of a Notch filter is given by the following equation: Centre Frequency/Bandwidth. Q is the measurement of the selectivity of the filter. It also gives an idea of sharpness of the depth.

The center frequency is the Notch Frequency, and it is the center frequency of the passband.

notch filter frequency

The frequency of the notch filter is referred to as the frequency of the stopband. This is because the narrow band’s frequency is what the notch filter rejects. Therefore, the frequency is also the identity of the notch filter.  

notch filter example

There are several examples of notch filters. There are numbers of types also. Every types has sub topics as well as many examples. Digital notch filters, analog notch filters, optical notch filters, FM notch filters, audio notch filters, helical notch filters, tunable notch filters, 50hz notch filters, and 60 Hz 2.4 GHz notch filters. Some of the examples are based on their specifications. Like – 532 nm notch filter. It is a optical filter te blocking wavelength is specified with the name.

Notch filter design || rlc notch filter design || how to design a notch filter

Let us design a notch filter from scratch. First, let us create an RLC type filter(notch) to eliminate the band of 45 kHz to 50 kHz. Say, the inductance is L = 30 mH.

So, the given datas are: fL = 45 kHz, fH = 50 kHz, l = 30 mH = 0.03 H

The resonant frequency will be: fr = fH – (BW/2)

The BW is Bandwidth and BW = 50 – 45 = 5kHz.

Or, fr = 50 *103 – ((5 * 103)/2)

Or, fr = 50000 – 2500

Or, fr = 47.5 * 103

So, the Resonant frequency is 47.5 kHz.

Now, we know that resonant frequency can be written as –

fr = 1 / [2 * pi * (LC)1/2]

or, 47.5 * 103 = 1 / (1.088 * C1/2)

or, C = 374.41 pico-Henry

So the Quality factor will be = fr / BW = 47500/5000 = 9.5

Again, Q = wr L / R

Or. R = wrL/Q = 2 * pi * f * L/Q

Or, R = 8.95 kilo-ohm

So for the notch filter, R = 8.95 kilo-ohm, L = 30 mH, C = 374.41 pico-farad.

tunable notch filter

Tunable notch-filters are such narrowband filters where we can manually get the high rejection from a particular frequency and comparatively lower attenuation from other frequency signals. There are several tunable notch-filters available in the market, like – EM-7843. Tunable filters can be of another type. If the Q factor of a notch filter is tuneable that filter can also be termed as tuneable notch filter.

tunable notch filter design

The design of the Tuneable notch filter is not so simple. It requires a lot of calculation and concept. But the creation of a digital tuneable notch filter is somewhat easy. The design should be made such that one can change the centre frequency easily.

digital notch filter

Digital notch filters refer to the FIR Notch-filter and IIR Notch-Filter. FIR and IIR both have their advantages in different conditions and are used as per the requirement. They are termed digital because they are designed digitally.

digital notch filter design

Digital notch filters have two types of design techniques. They are – Infinite Impulse Response Notch Filter (IIR), Finite Impulse Response Notch Filter (FIR). We have discussed both the filter details below.

dsp notch filter

 DSP stands for Digital Signal Processing. The notch filters used in the digital processing of signals are termed DSP notch filters. Therefore, it is fairly understandable that only digital filters are used as DSP notch filters. The FIR, IIR notch filters are an example of these kinds of filters.

design of notch filter in dsp

Digital notch filters have two types of design techniques. They are – Infinite Impulse Response Notch Filter(IIR), Finite Impulse Response Notch Filter. We have discussed both the filter details below.

fir notch filter

FIR filters stand for Finite Impulse Response filter. FIR filters generally come with lots of stability, which made them famous. When the stability of the system is more necessary, then these types of filters are used.

fir notch filter design

There are several methods of designing an FIR notch-filter, like – frequency sampling and computer optimization. Analytical methods, Semi-Analytical methods, second-order IIR filter prototypes are some other processes of preparing the same. Bernstein polynomials are also used in creating the FIR type digital notch filters.

iir notch filter || digital iir notch filter

IIR stands for Infinite Impulse Response. This is also a digital filter like an FIR filter. IIR filters generally come with an efficient approximation for a very low order requirement. These types of filters are required when the linearity of phases is not that much important.

iir notch filter design

IIR notch filters are designed in two major parts. At first, an analog notch filter is designed with the required specifications, and then the analog filter is transformed into a Digital IIR filter using inverse transformation.

active notch filter design || analog notch filter design || notch filter derivation

Let us design a notch-filter from scratch. First, let us create an RLC type filter(notch) to eliminate the band of 55 kHz to 60 kHz. Say, the inductance is L = 30 mH.

So, the given datas are: fL = 55 kHz, fH = 60 kHz, l = 30 mH = 0.03 H

The resonant frequency will be: fr = fH – (BW/2)

The BW is Bandwidth and BW = 60 – 55 = 5kHz.

Or, fr = 60 *103 – ((5 * 103)/2)

Or, fr = 60000 – 2500

Or, fr = 57.5 * 103

So, the Resonant frequency is 57.5 kHz.

Now, we know that resonant frequency can be written as –

fr = 1 / [2 * pi * (LC)1/2]

or, 57.5 * 103 = 1 / (1.088 * C1/2)

or, C = 255 .51 pico-Henry

So the Quality factor will be = fr / BW = 57500/5000 = 11.5

Again, Q = wr L / R

Or. R = wrL/Q = 2 * pi * f * L/Q

Or, R = 7.39 kilo-ohm

So for the notch-filter, R = 7.39 kilo-ohm, L = 30 mH, C = 255.51 pico-farad.

lc notch filter design

As we can interpret from the name of the filter, the LC Notch-filter is designed using only inductors and capacitors. The design method of an LC notch-filter is quite simple. At first, one inductor and once capacitor is kept at parallel connection. Then another combo of inductor and capacitor is kept in series connection. The circuit diagram is as follows.

LC circuit for notch-filter

The output impedance comes as:

The transfer function is:

The cut-off frequencies are –

notch filter using op amp || notch filter circuit using op amp

Notch filters are realized using operational amplifiers. At first, both the high pass and low pass filters are created using operational amplifiers. Then their outputs are summed up using another operational amplifier to get the outcome. The circuit diagram given in the article depicts a notch filter using op-amps.

60hz notch filter

A 60 Hz notch filter can reject a 60 Hz signal by keeping the power of the movement almost intact. A notch filter is used because it will accurately attenuate the frequency band. A 60 Hz notch filter has demand in the USA because the power supply in households has a frequency of 60 HZ.

60 hz notch filter design

As we know, any notch filter is designed with a high pass filter and a low pass filter. An additional op-amp is needed to add up the output of both the filters. Typically, the Q comes as 6 for a 60 Hz filter. The given equation can determine the notch frequency.

ALP is the low pass filter’s output when the frequency of the filter is the same as the desired output frequency, whereas AHP is the output for the high pass filter. In general, the

value is one. So, the notch frequency comes as output frequency, which is 60 Hz.

The following expression can also determine the output frequency:

As we can observe, the output frequency is dependent on the RF. So, changing the value of Rf will change the notch frequency.

rf notch filter design

Designing an RF filter is a very complicated process. It needs a skilled engineer as accuracy is an important parameter for these kind of filters. The design process of an RF notch filter is given below.

  1. Specify the Response: In his stage, all the required parameter value is specified. Parameters like – Response, cut-off point, etc. are needed to be set.
  2. Frequency Normalization: The frequencies are converted to match the standard tables and charts.
  3. Calculation of Ripple: In this stage, the concept of a notch filter is used. To create an RF notch filter, which can reject only one frequency from a certain frequency band, the ripple value should be considered a high priority. The higher the ripple value tolerance limit, the more selective the filter becomes.
  4. Matching the attenuating curves.
  5. Calculation of element values.
  6. Scaling of normalized values.

programmable notch filter

The most popular filter used nowadays is the Programmable filter. Programmable filters are easy to maintain, easy to work with. Programmable notch filters are no exception. We can control the Q value as well as the natural frequency by just changing the clock frequency.

notch filter code

The notch filter code to design a notch filter in MATLAB is given below. Writing any one of them with the right specifications will provide you a notch filter.

Code for designing a notch-filter in MATLAB simulator.

fm broadcast notch filter

Almost in every major city, there is a high possibility that one can receive the radio frequency from the FM radio stations. The FM broadcast notch filter will provide a 30db attenuation for the FM signals in the range of 88 to 108 MHz.

audio notch filter

A notch filter is an important instrument for audio engineering. Generally, some unwanted frequency components get mixed up in the original audio. To remove or eliminate such frequency, an audio notch filter is used.

audio notch filter design || audio notch filter circuit || fm notch filter circuit

The following circuit is an example of audio and fm notch design. Carefully observe the resistance and capacitor values before starting the design. The formula for centre frequency is also given.

Notch Filter Design
Audio notch-filter design circuit

audio notch filter schematic

The audio notch filter has quite a simple design. The schematic can be drawn easily for the current condition by following the standard procedures.

biquad notch filter

A biquad filter is a digital filter. More specifically, it is an IIR filter that has two poles and two zeros. The ‘Biquad’ is an abbreviation from the term – Bi-quadratic. Notch filters can also be designed using the topology. The transfer function for the filter comes as:

532 nm notch filter

532 nm notch filter is a variety of optical notch filters. The specification of the filter is 532 nm, that means the optical notch is able to block the light component having wavelength of 532 nanometre. It is one of the most popular optical notch filter. There are other specifications like 785 nm.

harmonic notch filter

A harmonic notch filter is a special type of notch filter, which has applications in several fields. The filter follows the following transfer function.

H(z)=12(1+A(z))

notch filter design tool

There is a different kind of tools available in the market for designing the notch filter digitally. Many types of digital filters can be created using such devices. It would be best if you assigned the frequency value only. One of the favourite tools is produced by Texas Instruments.

betaflight notch filter

Betaflight is a flight control software where multi-rotor crafts are controlled. As a part of the process, notch filters are also designed and tuned in the software.

notch filter transfer function derivation

The following expression gives the transfer function of a notch filter –

Here, wz refers to the Zero-Circular Frequency, whereas wp refers to the pole-circular frequency. Finally, q means the Quality Factor of the notch filter.

Q is given by – fr / Bandwidth.

If the ωp = ωz, it is a standard notch type.

If the ωp > ωz, it is a high pass notch type.

If the ωz < ωp, it is a low pass notch type.

notch filter for ecg signal

ECG or Electrocardiograph is a very important process of diagnosis in medical sciences. Several filters are used to display the output data produced by the machine. Without the filters, it is quite impossible to read the values.

There are three kinds of filters used in an ECG reading. They are – high pass filter, low pass filter, and notch filter. High pass filter filters out high-frequency components, whereas low pass filters do the same for common frequency components. The notch filters filter out a certain given range of frequency.

Especially the supplied frequency of the AC interferes with the ECG readings. Notch filter removes such interference. For North America, the supply frequency is 60 Hz, so a 60 Hz notch filter is used. In India and other countries where the supply frequency is 50 Hz, a 50 Hz notch filter is used.

Sudipta Roy

I am an electronics enthusiast and currently devoted towards the field of Electronics and Communications. I have a keen interest in exploring modern technologies such as AI & Machine Learning . My writings are devoted towards providing accurate and updated data to all learners. Helping someone in gaining knowledge gives me immense pleasure. Let's connect through LinkedIn - https://www.linkedin.com/in/sr-sudipta/

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