How to Design a Multiple-Feedback Band-Pass Filter

A Multiple-Feedback Band-Pass filter is one of the Active Band-Pass filters of several designs. This design implements 3 Resistors, 2 Capacitors and 1 Op-Amp (operational amplifier). In this how to design section, we will discuss how to calculate the optimal value of those components.

That is, how you can optimize this design to your needs. There are 2 things that a designer must know or wants to implement while designing a Band-Pass filter.

  • The Center Frequency (F0)
  • The Bandwidth (BW) &
  • The Gain (A0)

The gain represents how much you want the desired signal to be amplified in the output. You can choose it 1 or 2 arbitrarily. Having known this parameter now you are ready to design the filter. The filter configuration looks like below.

band_pass_filter_design

Resistor R1 & Capacitor C1 forms low pass response and R2, C2 forms high pass response. But the calculation is not separate. Values of C1 & C2 are usually chosen as same (C) for simplicity of calculation. Let’s go to the calculation.

Calculation:

Let,

BW = Bandwidth
F0 = Center Frequency
A0 = Gain
C = C1 = C2 = 1nF (arbitrarily chosen)

Now,

Q = F0/BW

R1 = Q/ (2πF0CA0)

R2 = Q/ (πF0C)

R3 = Q/ {2πF0C(2Q²−A0)}

Then using these values build your circuit practically. In an FSK demodulator I have implemented this filter. Mark & Space frequencies were 950Hz & 750Hz. Here is an oscilloscope graph of one of the filter’s output vs. input.

band_pass_filter_design

Here, F0 = 750Hz; BW = 100Hz; A0 =2; C = 1nF. Upper one is input signal containing 2 different frequency and lower one is filter output. You can easily understand how much the filter attenuates the other (950) frequency and amplifies the center (750) frequency.

So, at last, before implementing this filter, the designer has to choose an Op-Amp which supports his desired operating frequency and reshape the component values to available components in the market.

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