 The band pass filter allows frequencies to be passed between lower cut off frequency ( f_{L} ) and higher cut off frequency ( f_{H} ) whereas it reject all other frequencies below f_{L} and above f_{H.}
Where
f_{L} =
Lower cut off frequency
f_{H} = Higher cut off frequency
Classification of
band pass filter
The classification
of band pass filter is based on the value of quality factor / figure of merit.
( 1 ) Wide band
pass filter
 A filter is called as wide band pass filter, if its quality factor greater than 10.
Q > 10
 A wide band pass filter is obtained by cascading of high pass and low pass filter.
First order band
pass filter
 It is obtained by series connection of first order high pass filter and first order low pass filter.
Second order band
pass filter
 It is obtained by series connection of second order high pass filter and second order low pass filter.
Band pass
filter 
Cascading of
filter 
Rolling 

First order 
First order high pass filter 
First order low pass filter 
± 20 dB /
decade 
Second
order 
Second order
high pass filter 
Second order low
pass filter 
± 40 dB / decade 
Voltage gain
Voltage gain = A_{FT} ( f / f_{L}
) / √ [ 1 + ( f / f_{L} )^{2}] [ 1 + ( f / f_{H} )^{2}] Where A_{FT} = Total Passband gain f = Center frequency = √ ( f_{L}
× f_{H} ) f_{L} = Lower cut off frequency f_{H} = Higher cut off frequency 
( 2 ) Narrow band
pass filter
 A filter is called as narrow band pass filter, if its quality factor less than 10.
Q < 10
 In this filter, the OP – Amp is used in the inverting mode.
 It has multiple feedback path so it is called as multiple feedback filter.
 The narrow band pass filter is designed for specific value of center frequency ( f_{C} ) or bandwidth ( BW ).
Advantages of
multiple feedback
 Its center frequency f_{C} can be changed to new frequency f_{C}’ without changing gain or band width,
R_{2}’ = R_{2}
( f_{C} / f’_{C} )2
Where
f_{C} = Center frequency
Frequency Response of Narrow Band Pass Filter
The design of
circuit parameters is calculated as follows.
R_{1} = Q
/ 2πf_{C}A_{F}
R_{2} = Q
/ 2πf_{C} ( 2Q^{2} – A_{F} )
R_{3} = Q
/ πCf_{C}
Where
Passband gain A_{F} = R_{3 }/ 2R_{1}
Q = Quality Factor
The following condition must be satisfy A_{F} < 2Q^{2}
Importance of Q
factor
 Higher the value of Q factor, more selectivity or narrow bandwidth
Relation
between Q factor and center frequency Q
= f_{C} / Bandwidth = f_{C} / f_{H} – f_{L} 
The center frequency is given by f_{C} = √ ( f_{L}
× f_{H} ) Where f_{C} = Centre frequency
f_{L} = Lower cut off frequency
f_{H }= Higher cut off frequency 
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