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Using transfer functions for calculations

For combinations of transfer functions simple rules for determining the resulting transfer function can be derived. The combinations are of the type that transfer function blocks are connected. In making any transfer function block connection it is assumed that the connection does not load the block to which the connection is being made.

a)
Series connection

From the diagram in Figure 3.4 it follows that

   
   
   

The total transfer function of this series connection is

(3.13)

Figure 3.4: Series connection of two transfer functions

b)
Parallel connection

For the output of both functions it follows from Figure 3.5 that

   
   

The output of the total system is

   

and from this the transfer function of a parallel connection is

(3.14)

Figure 3.5: Parallel connection of two transfer functions

c)
Feedback loop

From Figure 3.6 the output is

   

Since

   

one obtains

   

and from this

   

The total transfer function of the feedback loop is

(3.15)

Figure 3.6: Feedback using two elements

As the output of is fed back via to the input, this is called feedback. One has to distinguish between a positive feedback for positive adding of and a negative feedback for negative adding of .

Example 3.6.1   For the special case of being a pure amplifier with a high gain , one obtains for negative feedback

   

The entire technique of operational amplifiers is based on this principle. In a feedback loop for which is an amplifier with then an element can be used to realise any transfer function within certain limits.

Interactive Questions 3.3   Test your basic knowledge about transfer functions

Interactive Questions 3.4   Test your knowledge about transfer functions and stability

Interactive Questions 3.5   Test your knowledge about transfer functions and electrical circuits

Interactive Questions 3.6   Test your knowledge about transfer functions and electrical elements

Interactive Questions 3.7   Test your knowledge about simple combinations of transfer functions

Interactive Questions 3.8   Test your knowledge about complicated combinations of transfer functions

Interactive Questions 3.9   Test your knowledge about transfer functions with dead time



Next: Frequency Response Up: Transfer functions Previous: Poles and zeros of   Contents
Christian Schmid 2005-05-09