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ExamplesHow the Piecewise Linear Plots are Made
This document will discuss how to actually draw Bode diagrams. It consists mostly of examples.
A transfer function is normally of the form:
As discussed in the previous document, we would like to rewrite this so the lowest order term in the numerator and denominator are both unity.
Some examples will clarify:
Note that the final result has the lowest (zero) order power of numerator and denominator polynomial equal to unity.
Note that in this example, the lowest power in the numerator was 1.
In this example the denominator was already factored. In cases like this, each factored term needs to have unity as the lowest order power of s (zero in this case).
The next step is to split up the function into its constituent parts. There are seven types of parts:
A constant
Poles at the origin
Zeros at the origin
Real Poles
Real Zeros
Complex conjugate poles
Complex conjugate zeros
We can use the examples above to demonstrate again.
This function has
a constant of 6,
a zero at s=-10,
and complex conjugate poles at the roots of s2+3s+50.
The complex conjugate poles are at s=-1.5 ± j6.9 (where j=sqrt(-1)). A more common (and useful for our purposes) way to express this is to use the standard notation for a second order polynomial
In this case
This function has
a constant of 3,
a zero at the origin,
and complex conjugate poles at the roots of s2+3s+50, in other words
This function has
a constant of 2,
a zero at s=-10, and
poles at s=-3 and s=-50.
The rules for drawing the Bode diagram for each part are summarized on a separate page. Examples of each are given later.
After the individual terms are drawn, it is a simple matter to add them together. See examples, below.
© Copyright 2005-2007
Erik Cheever This page may be freely used for educational
purposes.
Erik Cheever Department of Engineering Swarthmore College
