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 (F
_{0}) - The Bandwidth (BW) &
- The Gain (A
_{0})

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.

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

F_{0} = Center Frequency

A_{0} = Gain

C = C1 = C2 = 1nF (arbitrarily chosen)

Now,

**Q = F _{0}/BW**

**R1 = Q/ (2πF _{0}CA_{0})**

**R2 = Q/ (πF _{0}C)**

**R3 = Q/ {2πF _{0}C(2Q²−A_{0})}**

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**.

Here, F_{0} = 750Hz; BW = 100Hz; A_{0} =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.