Active band-reject filter analysis

Thread Starter

Let_07

Joined Mar 16, 2017
5
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
 

joeyd999

Joined Jun 6, 2011
5,237
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
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.
 

Thread Starter

Let_07

Joined Mar 16, 2017
5
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:

ltspice.png

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 :/
 

crutschow

Joined Mar 14, 2008
34,285
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.

upload_2017-3-16_12-33-51.png
 

Attachments

Last edited:

Thread Starter

Let_07

Joined Mar 16, 2017
5
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.

View attachment 122594
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.
 

joeyd999

Joined Jun 6, 2011
5,237
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.
 

joeyd999

Joined Jun 6, 2011
5,237
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.
 

Thread Starter

Let_07

Joined Mar 16, 2017
5
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.
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.
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 :D 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!
 

crutschow

Joined Mar 14, 2008
34,285
ts 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.
As noted in my simulation, the Twin-T center frequency if 1 / (4πRC).
What else do you want to calculate?
 

Thread Starter

Let_07

Joined Mar 16, 2017
5
As noted in my simulation, the Twin-T center frequency if 1 / (4πRC).
What else do you want to calculate?
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?
 

crutschow

Joined Mar 14, 2008
34,285
But for example, is there any way to get the value of Q factor?
Here's a reference that shows the calculation of the Q factor.
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?
It simplifies the equations and makes the response basically symmetrical around the notch frequency.
 

crutschow

Joined Mar 14, 2008
34,285
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.
 

Attachments

Top