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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)

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)

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)

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