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 ,