There are couples of methods to create a band-pass filter such as cascaded band-pass filter, multiple-feedback band-pass filter, state variable band-pass filter, biquad band-pass filter etc. The process of designing a cascaded band-pass filter was explained in the earlier tutorial How to Design Active Band Pass Filter - Cascaded HPF and LPF Band Pass Filter. Here the process of designing a multiple-feedback band-pass filter is explained with online calculator to calculate the component values.
The multiple-feedback band-pass filter circuit diagram is shown below.
The above multiple feedback band-pass filter circuit has two feedback, the path from output via R2 back to input and the path from output via C1 back to the input. That is why it is referred as multiple-feedback. The circuit has both low pass filter and high pass filter. The capacitor C1 and resistor R1 forms the LPF while the capacitor C2 and R2 forms the HPF.
The frequency response graph of a band-pass filter is shown below.
The center frequency \(f_{0}\) of the band-pass filter can be expressed as,
\[f_{c}= \frac{1}{2 \pi \sqrt{(R_{1} || R_{3}) R_{2}C_{1} C_{2}} }\]
because as viewed from capacitor C1 feedback R1 is parallel with R3.
Lets take C=C1=C2 then,
\[f_{c}= \frac{1}{2 \pi C } \sqrt{\frac{R_{1} + R_{3}}{R_{1} R_{2} R_{3}}}\]
The Quality factor or Q-factor is,
Without derivation, the value of the three resistors R1,R2 and R3 are as follows,
\[R_{1}= \frac{Q}{2 \pi f_{0} C A_{0}}\]
\[R_{2}= \frac{Q}{\pi f_{0} C}\]
\[R_{3}= \frac{Q}{2 \pi f_{0} C (2Q^2 - A_{0})}\]
Solving for gain \(A_{0}\) at center frequency using relation for R1 and R2 we get,
\[A_{0}= \frac{R_{2}}{2 R_{1}}\]
Online Calculator for Multiple-Feedback Band-Pass Filter
Multi-Feedback Band-Pass Filter Design Example
Consider the design of a multi-feedback BPF with center frequency at 1KHz and bandwidth of 1KHz. Let the maximum gain of the filter which occurs at the center frequency be 1.5. Let us select value of the capacitor C1 and C2 of 0.01uF. Then using the above online multi-feedback band pass filter calculator we get,
Q = 1, R1 = 10.62KOhm, R2 = 31.85KOhm, R3 = 31.85KOhm
Let us use LM324 operational amplifier. The circuit diagram of multiple feedback BPF designed with calculated values is shown below,
- How to design Active Filters- Low Pass Filter & High Pass Filter
Hello what would be the transfer function of this amplifier?
i have not calculated the transfer function of this filter. but, transfer function is basically Vout/Vin and to calculate this ratio, current and voltages at the different junction and branches have to calculated in term of Vin and Vout.
if c1 != c2, how to calculate this..?
what do you want to calculate? the cutoff frequency when c1!=c2 is provided you can use that to determine the component values.