# Band-Pass Active Filter

A band-pass filter has a pass-band between two cut-off frequencies

*f*(lower cut-off frequency) and_{ce}*f*_{cu}_{ }(upper cut-off frequency) such that*f*>_{cu}*f*_{cl}_{. }Any input frequency outside this pass-band is attenuated.# Bandwidth (BW)

The range of frequency between

*f*_{CL}_{ }and*f*is called the bandwidth._{CU}The bandwidth is not exactly centered on the resonant frequency (

*f*)._{r}If

*f*_{CU}_{ }and*f*are known, the resonant frequency can be found from,_{CL}*f*=

_{r}**Band pass filter characteristics**

# Quality Factor (Q)

It is defined as the ratio of resonant frequency to bandwidth, i.e.,

*Q*=*Q*is a measure of the selectivity. Higher the value of

*Q*, the more selective is the filter, i.e., narrower is the bandwidth.

# Types of Band-Pass Filters

**Wide Band-Pass Filter**wide-band filter has a bandwidth that is two or more times the resonant frequency; i.e.,*Q*â‰¤ 0.5.**Narrow Band-Pass Filter**A narrow band filter has a quality factor,*Q*> 0.5.