How To Hand Draw Bode Plots
Rules for Constructing Bode Diagrams
This certificate will hash out how to actually draw Bode diagrams. Information technology consists mostly of examples.
one. Rewrite the transfer role in proper form.
A transfer function is normally of the form:
As discussed in the previous document, we would similar to rewrite this so the lowest order term in the numerator and denominator are both unity.
Some examples will clarify:
Example 1
Note that the terminal result has the lowest (nada) order power of numerator and denominator polynomial equal to unity.
Example two
Note that in this instance, the lowest power in the numerator was 1.
Instance 3
In this instance the denominator was already factored. In cases like this, each factored term needs to accept unity as the lowest society power of southward (nil in this example).
2. Split the transfer office into its constituent parts.
The side by side stride is to dissever up the function into its constituent parts. At that place are 7 types of parts:
- A abiding
- Poles at the origin
- Zeros at the origin
- Existent Poles
- Real Zeros
- Complex cohabit poles
- Complex conjugate zeros
We can use the examples above to demonstrate again.
Example ane
This office has
- a abiding of 6,
- a zip at s=-ten,
- and complex conjugate poles at the roots of southtwo+3s+50.
The circuitous conjugate poles are at southward=-ane.5 ± j6.9 (where j=sqrt(-1)). A more mutual (and useful for our purposes) manner to express this is to use the standard notation for a second order polynomial
In this instance
Instance 2
This function has
- a constant of 3,
- a nix at the origin,
- and complex conjugate poles at the roots of due south2+3s+50, in other words
Example 3
This function has
- a constant of 2,
- a zero at s=-10, and
- poles at south=-3 and s=-50.
3. Draw the Bode diagram for each role.
The rules for drawing the Bode diagram for each part are summarized on a separate page. Examples of each are given later.
4. Describe the overall Bode diagram by calculation upwards the results from footstep three.
After the individual terms are drawn, information technology is a elementary affair to add them together. See examples, below.
Examples: Draw Bode Diagrams for the following transfer functions
These examples are compiled on the adjacent page.
Example 4
Repeated poles, a zero at the origin, and a negative constant
Total Solution
References
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Source: https://lpsa.swarthmore.edu/Bode/BodeRules.html
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