Butterworth Filter : Design of Low Pass and High Pass Filters

In this video, the design of higher order Butterworth Low pass and High pass filter has been discussed.
In this video, you will learn how to design Butterworth Low pass and High pass filters using the resistors, capacitors and active components like an Op-Amp.

Butterworth Filter Design:

For second Order Butterworth Filter design, the value of Quality factor (Q) in the transfer function should be equal to 0.707.
In this video, the Butterworth filter design using Sallen Key Filter Topology has been discussed.

By cascading the second order filters, higher order filters can be designed. (During the higher order filter design, the Q of each second order filter may be higher or lesser than 0.707, so that at the cut-off frequency the amplitude is 0.707 times the maximum value.)

The link for the derivation of the transfer function of the sallen key filter topology.


The timestamps for the different topics is given below:

1:16 Transfer function of Second Order Low Pass Filter

3:42 Criteria for Second-Order Butterworth Filter Design (Q= 0.707)

6:16 Sallen Key Filter Topology

11:44 Third Order Butterworth Filter Design Example

14:09 Butterworth High Pass Filter Design

This video will be helpful to all the students of science and engineering in learning, how to design the higher order Butterworth Low pass and High Pass filters.

Follow me on YouTube:

Follow me on Facebook:

Follow me on Instagram:

Music Credit:

[ALLABOUTELECTRONICS]

The link for the derivation of the transfer function for the sallen key filter topology.

[noweare]

really good explaination. Now I know why I cant get the gain I was trying to get out of my filter. Thanks Boss!

[shazadali]

Dude... like thank you so much I was lost until I heard that beautiful voice shower me with knowledge.

Thank you so much, this helps me so much in my ee2320 class!

[varunnagpal]

Remark at at 6:07: For 2nd order
If Q = 1/sqrt(2) then filter type is butteworth (no ripples in passband) and
if Q > 1/sqrt(2) then filter type is chebyshev (ripples in passband)

[김민보-mr]

Thank you. The process of deriving formulas and drawing conclusions for higher-order filter design is very interesting

[L.Becker]

Hi, I found a mistake in your video, at 2:51 you can not simply calculate the transfer function by multiplying the functions from the two RC lowpass filters, because the first transfer function changes when you connect a load. You can't just use a normal voltage divider there. You have to calculate the transfer function again using Kirchhoff which adds an extra term, however, it does't change much of the final result. When setting R1 = R2 = R and C1 = C2 = C the new transfer function simply has a 3 instead of a 2 as a factor at 5:29 .

[noweare]

There's a lot of math and I watched the video a couple of times to understand. This can all be simplified to a) using sallen-key topology b) Using Fc = 1/(2x PI x R x C) choose Fc, C and solver for R c) Keeping the gain between 1 and 2.5

[amitghosh]

I think i am half done by seeing this video, all i required now is to watch it again.

[ashwinmurali]

2:46 bro the second low pass portion will draw some current from the first one, you cannot simply multiply the transfer function of individual filters In such case. Proper nodal analysis will give you the correct transfer function.

[chitrareddychitra]

Thank you for excellent explaination A small suggestion form my side ... It is good if subtitles r placed little bit low we couldn't see equations clearly

[thirstymente]

Sir can u please explain how the frequency shifts by cascading? i.e. Wnc=Wc*√(2^(1/n)-1)

[NowshinAlam]

Can you explain why exactly the terms in the denominator of transfer function are what they are? Like how exactly do we know that 1/R1R2C1C2 in the equation was wc^2, the term with s was equal Wc/Q and so on?
Are these found from observation? Do we make the assumptions first and then find out from the equation that the gain from transfer function for w = wc becomes equal Q?

[shashwattripathi]

at first you told that for butterworth filter, we need small q-factor. Then you said we need positive feedback to get large q-factor. So isn't it contrary?

[kaursingh]

SIR -PRAY SUGGEST BOOK WITH MANY SOLVED EXAMPLES -THANK U SIR FOR EXCELENT LECTURE

[mr.amp]

I am gonna put this on my breadboard.... Wanna see how well it works

[l.jenipharjeni]

please explain the digital electronics and microprrocessor & microcontroller and DSP

[muratownuk]

thank you for posting these videos! Good knowledge refresher!

[pedrohenriquevalentimsanto]

This video Helped me a lot. Thanks mate! Keep up with the great work.

[mnada]

4:20
Do you mean cut off frequency gets shifted because of loading effect ? And from where the w_nc is derived ?

[MasterMindmars]

Very good
Is it not possible to cascade 4 operationals with gain 1 and without the R3 and R4 to adjust the gain, connecting the output directly to the negative input ?