Filter Approximations: Overview of Butterworth, Chebyshev, Elliptic and Bessel Filter Approximation

In this video, five different types of filter approximations which are quite commonly used in the analog filter design have been discussed briefly.

What is Filter Approximation:
Ideal filters have brick wall type of frequency response. So, they have flat passband and monotonic stopband. And the transition from passband to stopband is very abrupt (vertical transition).
But in actual filter design, it is almost impossible to achieve frequency response like an ideal filter.
So, in filter design (particularly for higher order filter design), five different types of filter approximations are quite commonly used.

1. Butterworth Filter Approximation
2. Chebyshev Filter Approximation
3. Inverse Chebyshev (Chebyshev Type-II) Filter Approximation
4. Elliptic Filter Approximation
5. Bessel Filter Approximation

1. Butterworth Filter Approximation
This filter approximation is also known as the maximally flat response approximation as it provides the flat passband response.
It does not have any ripple in the stop band and the roll-off rate is 20n dB /decade. It is most often used in audio processing applications where flat passband response is necessary.

2. Chebyshev Filter

This filter has rippled passband and monotonic stopband, but the roll-off rate of this filter is faster than the Butterworth filter. It is also known as the equal ripple filter.

3. Inverse Chebyshev (Chebyshev Type -II) Filter Approximation

This filter has flat passband and rippled stop band, and the roll-off rate is same as the Chebyshev filter.

4. Elliptic filter approximation

This filter has rippled passband and stopband but it has fastest roll-off rate among all the filter approximations.
While it has very poor step response.

5. Bessel Filter Approximation

This filter has flat passband and monotonic stop band like Butterworth filter but the roll-off rate is slowest among all the filter approximations.

This filter has linear phase to frequency response, and hence very good step response.

Here are the timestamps for the different topics in the video:

0:48 What is Filter Approximation?

3:10 Butterworth Filter Approximation

4:04 Chebyshev Filter Approximation

5:13 Inverse Chebyshev Filter Approximation

6:07 Elliptic Filter Approximation

6:40 Bessel Filter Approximation

7:51 Comparision of different filter approximations

This video will be helpful to all students of science and engineering in understanding the concept of filter approximation and to get the overview of different filter approximations.

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Music Credit:

[shreyagokhale]

This video saved me in LIC viva, thanks a ton🥺🥺🥺🥺

[anand]

thank you so much..profs in iits should see this..this is how one should teach!

[Monotic-ji]

Aap ki her video to the point hoti hai thanks....

[MsSujoy]

Excellent.. And vocabulary used for explanation is very impressive... 💗💙💖💚💝💜💟

[usersn]

Thank you! Please make videos on Digital filters also.

[YashaswiniYashaswini-bu]

Ur voice is nice sir...tq for ur explanation 😊

[bdadavies]

Hi, great video, thanks so much. Do you have any idea which filter approximation would be best suited for an audio filter? Im trying to design my own bass filter for a sub woofer so planning on making both a low pass and high pass filter in parallel such that one outputs frequencies below 200MHz and the other frequencies above that.

[zuhalfirdaus]

Thank you very much sir, your explanation is easily understandable

[mathewselvam]

Nice presentation.Keep it up.Very useful information.Thanks.

[viveknepal]

Thank you so much for this amazing video

[prabhakardas]

sir can you provide 1 or 2 numericals regarding all the filters to understand the concept?

[ritik]

Can anyone tell me?? What is the meaning of roll off here??

[mnada]

So each type of these filters will have all kinds of high pass, low pass, band pass and band reject ? but sure the circuits will vary dapending on the kind implemented.

[radowanhossain]

Can you please give the transfer function derivation of second order high pass, low pass and band pass filter ?

[RATH]

Make video for elliptical inverse chebyshev bessel also

[youssefehab]

i do not understand the idea of approximations do we pick the approximation we want based on which thing we are interested in ?! or depends on the application itself i also do not get how can we measure the noise and for example if i am using a sensor and i designed the suitable filter for it will i but it before the input signal ???

[edufunmotivation]

Sir please provide the video on antenna

[sgvenigma]

Please sir can you upload video on Biquad filters

[SureshKumar-nkok]

Thank u sir, can I add different filter for low pass filter, which is best for vhf band with low capacitor used

[pradeepsharma]

Please tell me what is filter approximation, and why it is used