Transfer Functions
 
 

Definition:

The relationship from an input signal, u, to an output signal, y, in the Laplace transform domain.

  1. Equation form: L[y] = G(s) L[u]
  2. Block Diagram form:


Block Diagram Equivalence:

  1. Series:

    2.  



     



    is equivalent to
     



     


  2. Parallel:

    3.  

     


     



    is equivalent to:
     



     


  3. Positive Feedback:

    4.  



     


    is equivalent to:
     


     


  4. Negative Feedback:


is equivalent to



Additional Rules:

  1. Summing Junctions

    2.  



     



  2. For the transfer functions of multiple inputs: u1, u2, etc., to output y, use superposition. That is, for the transfer function of u1 to y, disregard the effects u2, u3 etc.


Example 1:
 



 




is equivalent to:
 
 


 


This page is maintained by Tomas B. Co (tbco@mtu.edu). Last revised 1/19/1999.
     Tomas B. Co
     Associate Professor
     Department of Chemical Engineering
     Michigan Technological University
     1400 Townsend Avenue
     Houghton, MI 49931-1295

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