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Original question:

Multiple feedback band pass filter

Multiple feedback band pass filter

Michele Bertoni1
Intellectual 340 points


Hi to all users!
I have some doubts designing bandpass filter: f0 = 1Hz, Q = 1.41421.

I fount this schematic:

Then I also found slightly different schematic (formulas are given from circuit #1 assuming R2 infinite):

  • QUESTION: both gains (if formulas are correct) are not affected by R2 so I can use R2 to trim frequency in first schematic (at fixed gain), while in second schematic if I trim frequency I also change gain. Except this, are there some reasons I should use second schematic instead first one?

In this discussion https://e2e.ti.com/support/amplifiers/f/14/t/354325?Multiple-feedback-band-pass-filter

it's reported slightly different gain formula for second circuit (as I found browsing all around), not talking about C1 and C2 values:

Q = 0,5 * (√R3/R1)

G = -2Q2.

GAIN = -0.5 R3/R1 = -2Q^2

I try to simulate circuit #2 (I have a board with these components):

C2 = 2200nF

C1 = 220nF

R3 = 470k

R1 = 82k

AMP = LT1012

I get different gain, so formula above is correct only when C1=C2. Why I always find C1=C2? Ok, it's more easy, but are there other reasons? I can't undertand why choose different values...

  • QUESTION: What about Q when C1 different than C2? Where can I find Q formula explicit for R1, R2, ?



Thanks.

  • 0
    Guru 140200 points

    Ciao Michele,

    C1 and C2 should usually be very precise and stable. Then it's simpler to buy one single cap type instead of two different ones. The other reason for keeping C1 and C2 equal is that the formulas heavily simplify:

    michele_bandpass.TSC

    Both circuits are normalized to a resonance frequency of 1kHz. A Q=1.414 is shown. The second circuit provides an additional signal attenuator of exemplary 20dB.

    Kai

  • 0
    TI__Guru**** 166196 points

    Hello Michele,

    Thevenin equivalent is an easy way to see the difference. The first schematic with R1 and R2 can be converted to just a R1' and VIN' like in the second schematic. 

    R1 equailent = R1 || R2 which is 1/(1/R1+1/R2)

    VIN equailent = VIN * R2 / (R1 + R2) , voltage divider rule

    R2 reduces gain and affects the resistance interacting with the filter caps.