Transfer Functions


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:



    is equivalent to


  3. Parallel:




    is equivalent to:


  5. Positive Feedback:



    is equivalent to:


  7. Negative Feedback:

is equivalent to

Additional Rules:

  1. Summing Junctions



  3. 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 ( 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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