# Active band-reject filter analysis

Discussion in 'General Electronics Chat' started by Let_07, Mar 16, 2017.

1. ### Let_07 Thread Starter New Member

Mar 16, 2017
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Hello

Recently I've been trying to analyse an active band-reject filter in order to make some simulations but so far I didn't have success.

The filter looks like this:

Considering a capacitor of 1uF, how can I calculate the rest of the components having a low-cut frequency of about 20KHz and high-cut frequency of about 30KHz? Or better say central frequency of 25KHz

Also I would like to have no gain, just to simply cut between those frequencies and be able to "mess" with the Q factor... However I'm really struggling to have the correct formulas. I know it might look easy but I'm not very experienced in this and I would like your help

Thank you

2. ### crutschow Expert

Mar 14, 2008
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It is not particular easy to analyze that circuit.
Here's a reference on active bandstop filters.

3. ### Nykolas Active Member

Aug 27, 2013
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It seems to me this is a band-pass, not band-reject filter. The gain is varied by changing the values of R1/R2. E

Aug 1, 2013
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5. ### joeyd999 AAC Fanatic!

Jun 6, 2011
4,013
5,594
The "loop gain" is determined by Q, which is a function of R1 and R2.

The overall gain is attenuated by voltage divider R3 and R4.

Here's a spreadsheet I designed for designing 4th order circuits.

Edit: Sorry, slightly different topology.

6. ### Let_07 Thread Starter New Member

Mar 16, 2017
5
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Thank you for the answers. I'll try to analyze some of the files sent.

Regarding this being a band-pass filter, I did some simulations on LTSpice and obtained the following results:

So it seems to work as a band-reject. Before I was doing some research on internet and bandpass filters look similar except that there are no resistors R3 and R4... (I'm not saying you are wrong, just providing the information I got from my research)

So, I basically have a band reject filter, I just don't know how to tune it correctly expect from "throwing" random values at the simulation and hope for it to work, which is not really ideal solution :/

7. ### joeyd999 AAC Fanatic!

Jun 6, 2011
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You are correct. That accounts for the difference in topology I noticed.

Sorry, I don't have a spreadsheet for that.

8. ### crutschow Expert

Mar 14, 2008
20,501
5,809
Perhaps a notch filter would better do what you want.
Below is the LTspice simulation of a Twin-T active notch filter with adjustable Q.
The output is shown for U1 Q-control pot settings of 10%, 50% and 95%.

Note that for good response with high Q values at a notch frequency of 25kHz, the gain-bandwidth of the op amp should be at least 10MHz.

The calculations can be found here.

• ###### Filter - Twin T.asc
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Last edited: Mar 16, 2017
9. ### Let_07 Thread Starter New Member

Mar 16, 2017
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Thank you. Actually I was reading about the notch filters but they seem too "narrow" for what I wanted... However I put a Q control very low and it kind of worked in the end...

Now I just have one problem, its there any way where I can make this calculations on my own? I mean, without using the calculator of the website? There is some transfer function there but still I don't see how I can calculate the values of resistors/capacitors.

10. ### joeyd999 AAC Fanatic!

Jun 6, 2011
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You've intrigued me with this circuit. I've never seen it before and I've searched far and wide trying to find an online example -- to no avail. I've only had time to do about half of the analysis. Maybe this weekend I'll be able to complete it and share my results with you.

11. ### joeyd999 AAC Fanatic!

Jun 6, 2011
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FYI, the top half of the circuit is a standard MFBF. The difference is in the lower half at the non-inverting input. I assume the attenuation network is designed to exactly cancel at the center frequency. Neat design, if it works.

12. ### Let_07 Thread Starter New Member

Mar 16, 2017
5
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To be honest I'm looking for some example of this circuit for ages, but for some reason Internet doesn't want to sharei it with me I can only find the schematics of the circuit and that's it. I find similar circuits, but not that one.
That's why I asked for help.

That would be nice, if somehow you manage to analyze it fully just write me something!

13. ### crutschow Expert

Mar 14, 2008
20,501
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As noted in my simulation, the Twin-T center frequency if 1 / (4πRC).
What else do you want to calculate?

14. ### Let_07 Thread Starter New Member

Mar 16, 2017
5
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I'm just trying to understand from where the calculations come from. About the center frequency I got it. But for example, is there any way to get the value of Q factor? In my case it is important because I need to analyze this Q factor and have the calculations would be nice. I mean, I know how to calculate this factor if I have already values for bandwidth, etc. But not when I have a scheme of the circuit on a paper.

Also, from what I found everything tells that R1 and R2 are just 2xR3, as well C3 is equal to 2xC1/C2, but I can't find any explanation for this. Is there any?

15. ### crutschow Expert

Mar 14, 2008
20,501
5,809
Here's a reference that shows the calculation of the Q factor.
It simplifies the equations and makes the response basically symmetrical around the notch frequency.

Oct 9, 2007
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17. ### Bordodynov Well-Known Member

May 20, 2015
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crutschow.
Beside I appeared the problems with your symbol POT.sym. There is symbol In my library with such name, but several another.

18. ### crutschow Expert

Mar 14, 2008
20,501
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Attached are the two LTspice files I use for the potentiometer.
The .sub file goes in the sub directory and the .asy file goes in the desired symbol directory.

File size:
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• ###### pot.sub
File size:
193 bytes
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