In this article, detail study of classification of band pass filter, first order band pass filter, second order band pass filter, wide band pass filter, narrow band pass filter is given.

Band Pass Filter

• 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 = AFT ( f / fL ) / √ [ 1 + ( f / fL )2] [ 1 + ( f / fH )2] Where AFT = Total Passband gain f = Center frequency = √ ( fL × fH ) fL = Lower cut off frequency fH = 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,

       R₂’ = R₂ ( 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.

R₁ = Q / 2πf_CA_F

R₂ = Q / 2πf_C ( 2Q² – A_F )

R₃ = Q / πCf_C

Where

Passband gain A_F = R₃ / 2R₁

Q = Quality Factor

The following condition must be satisfy A_F < 2Q²

Importance of Q factor

• Higher the value of Q factor, more selectivity or narrow bandwidth 

Relation between Q factor and center frequency Q = fC / Bandwidth     = fC / fH – fL

The center frequency is given by             fC = √ ( fL × fH ) Where fC = Centre frequency            fL = Lower cut off frequency            fH = Higher cut off frequency

 

You may also like :

Low pass Butterworth Filter

High pass Butterworth Filter

What is mobility?

What do you understand by Variable Frequency Drive?