Narrow Band Pass Filter

 Narrow Band Pass Filter

Ans. 

                                                  

                                                  

Here , in this topic we are going to learn Narrow Band Pass Filter ( NBPF ) . So , the Narrow Band Pass Filter is also known by the other name called as or we can say that known as multiple feedback filter .

             So , question arises here , why we called or known by the name " multiple feedback filter " .

              Because this Narrow Band Pass Filter has two feedback path , Hence it is called by the name is multiple feedback path .

               In this Narrow Band Pass Filter , there is only one active component is taken in use is operational amplifier ( Op-amp ) in place of two active ( Op-amp ) .

                   This Narrow Band Pass Filter is work only in inverting configuration or we can say that in another words that inverting mode .

                 The Narrow Band Pass Filter or we can say that multiple feedback filter is design for particular or specifically for value of center frequency  ( fc ) , Q which is called as quality factor and Bandwidth .

                   So , we know that in Band Pass Filter there is two cut-off frequency , which is 

1) High cut-off frequency , which is denoted by ( fH ) .

2) Low cut-off frequency , which is denoted by ( fL ) .

          And here we also know that , High cut-off frequency is always greater than low cut-off frequency that is , fH > fL .

           The Q-factor , which is known as 

quality factor is greater than 10 that is ,Q >10

          Now here , if we see the relation between Q-factor , 3db bandwidth and the centre frequency ( fc ) is given by , 

                        Q = fc / BW

                         But   Band-width = fH - fL

             i.e.      Q = fc / fH - fL

       The center frequency is as , fc = √ fH . fL

Where as , 

Q = quality factor

fL = Low cut-off frequency 

fH = High cut-off frequency

BW= Band-width

fc = center frequency

So , Here in this Narrow Band Pass Filter there is two capacitor is there .

One capacitor C1 at the inverting input of the terminal and second capacitor C2 at the inverting terminal for feedback .

       So in this circuit , for specific calculation C1 = C2 = C it means that the capacitor C1 and C2 is both equal to C .

         So , in this circuit what is the value of Resistor (R1) , (R2) and (R3)

              R1 = Q / 2 .pi.fc.C.AF

              R2 = Q / 2 .pi.fc.C (2Q square - AF)

              R3 = Q / 2 .pi.fc.C

   This is required for calculation purpose .

               Gain is denoted by AF

Here , AF is the gain at the center frequency ( fc ) . The center frequency gain shows the 

                AF = R3 / 2R1

   The gain must be satisfied the following condition i.e. therefore ,

                      AF < 2Q square   , it means that gain must be less than 2 times quality factor square .

 

    If we see , the frequency response of the Narrow Band Pass Filter , so the frequency response draw in between frequency and gain .

                                        

                                                

So , here in this frequency response graph show that , ( fL ) show low cut-off frequency and ( fH ) show high cut-off frequency .  So in both low cut-off frequency and high cut-off frequency there is narrow band pass filter's bandwidth is exist .

             Here , in this center frequency ( fc ) , we can change with new frequency ( f'c ) without changing the gain or bandwidth by changing the R2 to R'2 so like that .

                  If we change the value of Resistor R2 with any value R'2 so it is given as ,

               R'2 = R2 ( fc / f'c ) whole square

In this way we can change the center frequency with new center frequency .