## 25/07/2021

### Band Pass Filter

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 ( fL ) and higher cut off frequency ( fH ) whereas it reject all other frequencies below fL and above fH.

Where

fL = Lower cut off frequency

fH = 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 ( fC ) or bandwidth ( BW ).

• Its center frequency fC can be changed to new frequency fC’ without changing gain or band width,

R2’ = R2 ( fC / f’C )2

Where

fC = Center frequency

Frequency Response of Narrow Band Pass Filter

The design of circuit parameters is calculated as follows.

R1 = Q / 2πfCAF

R2 = Q / 2πfC ( 2Q2 – AF )

R3 = Q / πCfC

Where

Passband gain AF = R3 / 2R1

Q = Quality Factor

The following condition must be satisfy AF < 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

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