Formulas for Bridged T filter including Q and Bandwidth

[garybdmd]

Hi all, I'm posting because I couldn't find equations for Q and bandwidth for Bridged T filters, so I made a formula to estimate it and I'd like any comments/suggestions I can get.

The formula for Q and bandwidth are estimates only, but quick and easy.  Here is a summary of everything
I found.  If you'd like to see how I came up with the formulas it you can check out what I did.  I know its just an estimate but a lot easier than trying to use the inverse of the transfer function.

https://sites.google.com/site/garydavenportelectronics/home/bridgedtnotchfilter


     -------C1-----
     |            |
in --|            |--- out
     |            |
     --R1------R2--
          |
          C2
          |
         ///

                        1
center frequency = ------------------
                   2pisqrt(R1R2C1C2)

                   1 + R2/R1
notch depth= --------------------
               1 + R2/R1 + C2/C1

                        1          1   
bandwidth estimate = -------  -  -------
                    2piR2C1      2piR1C2

                 sqrt(c2/c1)
Q estimate =   -------------
                (c2/c1)-1

db loss at center freq = 10 log (notch depth)

I would appreciate any critiques/suggestions about this because its quite complicated.

[GibsonGM]

Hi Gary, welcome to the forum!

Yes, it is quite complicated  

You may well be right with the formulas, didn't go thru them.   For daily design, why not try some free software? In Duncan's tone stack calculator, you can modify the Big Muff tilt control to simulate a Bridged T for you!   

You can then get a visual, rather than mathematical, representation of what you're dealing with.    IMO, much easier than running the numbers!    Altho that is very respectable, of course.  I just find that I get more out of the thing by being able to access the info quickly (more time building/trying than calculating).  So, I'd have made a spreadsheet or VB program to do this anyway, lol.

PRR will likely come along and give you more info on the formulae - I'm looking forward to that, actually!  But for general 'what's it gonna go', I'd recommend going the TSC route...

http://www.muzique.com/lab/notch.htm

Don't forget to set R2 to 10M to 'remove' it from the circuit (it becomes transparent at those high amounts of resistance). 

[garcho]

check it nice

http://www.geofex.com/article_folders/eqs/paramet.htm