3rd order Multiple Feedback Bandpass Filter Calculation

Center Freq
Q
Stagger factor
 
 Stage 1Stage 2Stage 3
Fc
C
R1
R2
R3
GBW required for opamps

Instructions

This Javascript program calculates component values for a 3rd order (3 stage) Multiple Feedback Bandpass filter. The schematic is shown below for one of the three cascaded stages.

The bandpass response is formed by staggering the center frequency of individual bandpass stages by a stagger factor a (that is, Fc1 = Fcenter / a, Fc2 = Fcenter, Fc3 = Fcenter * a). The Q value of the center stage (Fc2) is set at 1/2 that of the outer stages. Proper combinations of Q and a allow you to shape the response to have a flat passband and maintain steep slopes. See Figure 2.

For more informtion on 3rd order staggered bandpass filters, see Don Lancaster's "Active Filter Cookbook".

Limitations

  • Maximum practical Q for a single opamp MFB configuartion is about 10. Above this and the response becomes too sensitive to component tolerance.
  • The bandwidth requirement for the opamps in the MFB configuration is Gain Bandwidth Product >= 20*Q^2. A TL07x opamp can be used up to about 3500Hz. The GBW Required for opamps field shows the minimum gain-bandwidth product the opamp must have to support the current filter.
  • You can get around the Q and GBW limitations by using a State Variable Filter configuration for each of the individual stages. Q, Fcenter, and overall gain are individually tunable, Q can be much higher, and the GBW requirement is much lower. Disadvantage is that it requires three opamps per stage.

    • Operation

    Enter the desired Center frequency into the Center freq field and click Calculate. You can modify the chosen capacitors and click Calculate again to re-calculate the components with those capacitor values.

    To start a new filter set, click New.

    You can modify the Q or a values. These will not be erased when you start a New calculation.