Drive the transfer function of the following filter "Sallee-Key second order fme, and put It in...

Question

Drive the transfer function of the following filter "Sallee-Key second order fme, and put It in standard form. (Show each step of derivation)

David · Accepted Answer

Sol: 
        Let 
1 2 3,   V V and V be the node voltage at point A, B and C respectively. In this 
case, we will use the node voltage method to derive the transfer function. 
Assuming zero initial conditions for each capacitor and using the Laplace 
Transform approach, we write the three KCL equations relating voltage at nodes 
A, B, and C;
   At node 1;
 
 
 
   
   
1 1 2
1
2
1
2
1
1 2
1 2
2 0
1 1
2
1
2
2 1
2 1                  ................  (1),
in
in
in
in
in
V V s V V
sCV
R R
V sV
V sC
R R R R
V sVsCR
V
R R R
V sCR V V s
V sCR V s V
 
  
 
    
 
 
  
 
  
  
 
        At node 2;
 
 
 
2 1
2 3
1
2 3
1
2 3
2 1 3
1 2 3
0
1
1
1
1            ........... (2),
V V
sC V V
R
V
V sC sCV
R R
VsCR
V sCV
R R
V sCR V sCRV
V V sCR sCRV

  
 
   
 
 
  
 
  
  
 
At node 3;
    
  
   
   
     
   
 
3
3 3 2
3 2
3 2
3 2
2
3
0
2
2 2
2
1 2
2
2 1 2
2
      ...

Drive the transfer function of the following filter "Sallee-Key second order fme, and put It in standard form. (Show each step of derivation)

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment