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 .

                   

INVERTING OPERATIONAL AMPLIFIER

 INVERTING OPERATION AMPLIFIER

                                                  

To understanding Inverting operational amplifier , then you have to first understand the concept of Virtual Ground .

Now in this blog article we will go to learn about virtual ground in simple and precisely. This virtual ground concept is only , applicable when we are providing the negative feedback to this operational amplifier (Op-amp) , or we can say in other words this virtual ground concept is only valid when we providing negative feedback to this operational amplifier .

              Now , here for a given (op-amp) the open loop gain of this (op-amp) is 10 raise to the power 6 . And we know the output (o/p) voltage (Vout) of (op-amp) is given as A multiply with differential input voltage .

                                              

             This is the input voltage between these inverting and the non-inverting input terminals . Now , here let's we consider that through this negative feedback , we are controlling the output (o/p) voltage of this (op-amp) in a such a way that , the output voltage is always less than the saturation voltage. Or in other words we can say that we are operating this (op-amp) in a linear region . 

           So , let consider that the output (o/p) voltage is ten volt (10 v) . So, we can say that 10 v is equals to the 10 raise to the power 6 multiply with this differential input voltage . Or we can say that in other words that the differential input voltage is equal to 10 micro volts . 

           Now , here this differential input voltage is nothing , but the differential between this inverting and the non-inverting input terminals . So , we can write this differential input voltage as a (V plus minus V minus) ( V+ -V- ) this is equals to 10 micro volt . 

          Now , here this 10 micro volt is very very small signal and we can almost neglect it . So , we can write this (V plus minus V minus) (V+ - V-) as approximately equal to zero volts or we can say that in other words that Vplus , that is equal to Vminus .

           It means that the inverting and the Non-inverting input (I/P) terminals are at the same potential or we can say that in other words that there is virtually short between this inverting and non-inverting input (I/P) terminals .

             Now here , the term we use virtual it means that , these two terminals are not actually short circuited , but they are virtually short circuited . So, whatever voltage that appear at one terminal , the exact and same voltage will appear at another terminal . 

            So , now in this configuration , this Non-inverting input terminal is grounded . So, we can say that Vplus that is equals to zero (0) . So, accordingly to this result , Vminus should be equals to zero (0) . It means that this terminal is not actually grounded , but it will act like as a virtual ground . 

            So , this negative feedback will ensure that the difference between this inverting and the Non-inverting input (I/P) is very very small or we can say that in another words that it is almost negligible .

           And because of that , we can consider these both input (I/P) terminal at the same potential . So , this concept is known as the virtual ground concept .

          So , now let use this concept , if virtual ground and let's derive the expression between this Vout and Vin .

           And let's say that node is , node X . And let's say that the current , that is flowing through this resistor Rf is If . We had seen that the (Op-amp) has very high input (I/P) impedance or if we assume the ideal (Op-amp) is infinite . It means that no current is entering into this (Op-amp) or we can say that in other words that current ( I ) that is equal to zero (0) .

                                                  

So , as you can see here , just by changing the value of this ( Rf ) and ( R1 ) we can control the gain of this (Op-amp) . And we can use this (Op-amp) as a amplifier .

         Now , here the negative sign indicates that the output voltage is 180 degree out of phase with respect to input voltage .

          So , let's say that , if we have applied the sinusoidal signal at the input , then at the output we will get the amplified sinusoidal signal , which is having a 180 degree phase with respect to the input signal .

           And that is why this configuration of the (Op-amp) is known as the inverting configuration . Because the output (O/P) will be get inverted with respect to input (I/P) voltage .

Wide band pass filter

 Wide band pass filter

Ans. The wide band pass filter is formed by cascading high-pass section and low-pass section . 

Look here , the wide band pass filter is made by two order , First is high-pass filter and second is low-pass filter . So when we combine or we can say that cascading first order high-pass section and first order low-pass section is called as or we can say that known as wide band pass filter ( WBPF ) .

                                                             

  Here , question is arises , that how we can conclude first order high-pass section ? 

For concluding first order high-pass section is that , at non-inverting terminal in input ( I/P ) section of non-inverting terminal capacitor is placed . And with capacitor , resistor is connected in parallel that , combination is proved that this is first order high-pass section .

   And also question arises is that , how we can conclude first order low pass section ? 

For concluding first order low-pass section is that , at non-inverting terminal in input ( I/P ) section of non-inverting terminal Resistor is placed , and with resistor , capacitor is connected in parallel that combination is proved that , this is first order low-pass section .

In this , the product is plus and minus + or - 20 db ( decibel ) per decade . In which condition ? , when the first order low pass and high pass section cascade with each other .

  As like as , if we talk about second order high-pass section and second order low-pass section , the product is plus or minus + or - 40 db ( decibel ) per decade . In which condition ? , When the second order low-pass section and high pass section  cascade or we can say that combine with each other .

If we see the frequency response of wide band pass filter . Here , wide band pass filter has two cut off frequency . First is ( fH ) and second is ( fL ) . 

Whereas , ( fH ) stands for or we can say that it shows the high cut off frequency and ( fL ) stands for or we can say that it show low cut off frequency . 

In both of these cut off frequency ( fH ) is always greater than ( fL ) . In other words we can say that high cut off frequency is always greater than low cut off frequency. 

In wide band pass filter , if we talk about Q-factor or we can say that quality factor . It is denoted by capital Q .

Because of Q-factor we can show that wide band pass filter and narrow band pass filter. When Q-factor is less than 10 i.e.  Q < 10 than it shows wide band pass filter , and Q-factor is greater than 10 i.e.  Q > 10 , than it shows narrow band pass filter .

                                                             

                                                        

In wide band pass filter , if we see the relation between the Q , 3dB bandwidth and the center frequency fc is given by  

                                Q = fc / Bw

                          i.e. Q = fc / fH-fL

In wide band pass filter our, frequency response is given by in the above graph . Here in this graph fL is low cut off frequency and fH is represents high cut off frequency , and 0.707 is the gain magnitude .

In between high cut off frequency and low cut off frequency there is pass band is exist . Where as AFT is a total pass band gain .

At fL point low cut off frequency, there is plus +20 dB per decade is present . And if we move towards fL to fH , it means that if we move low cut off frequency to high cut off frequency +20 dB is constant for some given of time and after it goes minus -20 dB per decade -20 dB/decade at point high cut off frequency ( fH ) .

From fL to fH there is pass band is there and from outside of these fL and fH there is stop band is present .

And one thing always remember that fH is always greater than fL or we can say that high cut off frequency is always greater than low cut off frequency .

And after all of these , there is another point is center frequency . Center frequency is arises in between both fH and fL and it is denoted by ( fc ) .

                i.e.     fc = √ fH .fL

And , if we talk about gain of high pass low pass filter than it is given as ,