All About Circuits Forum Twin T Bandpass Filter transfer function's derivation
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#1
01-18-2009, 10:09 AM
 Lieta Junior Member Join Date: Jan 2009 Posts: 12
Twin T Bandpass Filter transfer function's derivation

Hi, guys.
Could somebody help me out with the subject? I've searched the net, but didn't find anything useful.
#2
01-18-2009, 10:15 AM
 bertus Administrator Join Date: Apr 2008 Location: Amsterdam,Holland (GMT + 1) Posts: 12,264

Hello,

Take a look at the PDF in the link.
http://www.drp.fmph.uniba.sk/ESM/twin.pdf

Greetings,
Bertus
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#3
01-18-2009, 10:18 AM
 mik3 Senior Member Join Date: Feb 2008 Location: Cyprus, but now in UK (GMT+0) Posts: 4,846 Blog Entries: 9

Assume an ideal op amp so you can say that the voltage on the non-inverting terminal (V2) equals the voltage on the inverting terminal (V1). The voltage are measured with respect to ground. First find the transfer function (relationship) between Vin and V2. Then find the transfer function between Vo and V1. Finally, because V1=V2, substitute V1 with the equation relating V2 with Vin to get the transfer function between Vo and Vin.
#4
01-18-2009, 10:38 AM
 hgmjr Super Moderator Join Date: Jan 2005 Location: Tennessee, USA (GMT-6) Posts: 9,030 Blog Entries: 11

Quote:
 Originally Posted by Lieta Hi, guys. Could somebody help me out with the subject? I've searched the net, but didn't find anything useful. Link to circuit: http://www-k.ext.ti.com/SRVS/Data/ti...s/spttbphq.gif

hgmjr
#5
01-18-2009, 02:53 PM
 The Electrician Senior Member Join Date: Oct 2007 Posts: 1,744

Quote:
Judging from the subject line, I think he wants you to produce one of those lovely detailed transfer function derivations that you do so well. :-)

But, he hasn't shown any of his own work yet.
#6
05-01-2009, 05:49 PM
 Lieta Junior Member Join Date: Jan 2009 Posts: 12

Thanks, bertus, for the document. The twin-T filter without an op-amp is a band-stop filter (see fig. 4).
Denote
Vout - output of whle circuit.
Vin_pas - input of passive twin-T filter
V(-) - input of inverting input of op-amp.
V(+) - input of non-inverting input of op-amp
Vin - input of the whole circuit
Vin_pas = V(-) = V (+) = Vin*k, where k = R5/(R4+R5).
Vout/Vin_pas - band-stop filter transfer funct. and because Vin_pas = Vin*k,
Vout/Vin also band-stop filter transfer funct., but actually the circuit if band-pass filter. How to take an op-amp into account? Where am I wrong?
#7
05-02-2009, 01:44 AM
 The Electrician Senior Member Join Date: Oct 2007 Posts: 1,744

Are you still interested in deriving the overall transfer function for the opamp plus twin-T feedback network?

Are you required to use any particular method to derive it, or can you use any method you like?

This thread is several months old, so I thought I would ask if your interest level is still high.
#8
05-02-2009, 09:18 AM
 Lieta Junior Member Join Date: Jan 2009 Posts: 12

I'm still very interested in deriving the overall transfer function for the opamp plus twin-T feedback network. Any method is fine.
#9
05-02-2009, 11:43 AM
 The Electrician Senior Member Join Date: Oct 2007 Posts: 1,744

You said "How to take an op-amp into account?". Does this mean that you don't want to make the usual assumption that the opamp is ideal, with infinite gain?
#10
05-02-2009, 11:48 AM
 Lieta Junior Member Join Date: Jan 2009 Posts: 12

No, assume op-amp as ideal. I ment how to derive transfer function for whole circuit, including op-amp, because without op-amp it's a notch filter, but with it it's band pass filter.

 Tags bandpass, derivation, filter, function, transfer, twin

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