Band-pass filters

Passband characteristic:

W₁ ... Lower -3 dB frequency

W₂ ... Upper -3 dB frequency

DW = W₂ - W₁ ... Normalized bandwidth

W_m = W₂ W₁ = 1 ... Normalized centre frequency (Q = 1)

... Quality factor

 

Design of a band-pass filter

 

• Connection of a high-pass filter and low-pass filter in series

The simplest design

Used commonly in wide-band filter applications

• Cascaded filters

Different topologies and orders

Used for narrow-band filters

 

Second-order Band-pass Filter

General transfer function for a second -order band-pass filter:

• Multiple Feedback (MFB) Topology:

Corresponding transfer function:

By comparing the two preceding equations:

Centre frequency ...

 

Gain at f_m ...

 

Filter quality ...

 

Bandwidth ...

 

MFB band-pass topology allows to adjust Q, A_m, and f_m independently

R3 ... does not affect bandwidth and gain

     ... can be used to modify the centre frequency