How To Draw Bode Plot By Hand
Rules for Constructing Bode Diagrams
This certificate will discuss how to actually depict Bode diagrams. It consists mostly of examples.
1. Rewrite the transfer function in proper form.
A transfer function is normally of the class:
As discussed in the previous certificate, nosotros would like to rewrite this so the lowest club term in the numerator and denominator are both unity.
Some examples volition clarify:
Instance 1
Note that the terminal upshot has the lowest (cypher) lodge power of numerator and denominator polynomial equal to unity.
Case 2
Note that in this example, the everyman ability in the numerator was 1.
Instance 3
In this example the denominator was already factored. In cases like this, each factored term needs to have unity every bit the lowest club ability of southward (nix in this case).
ii. Separate the transfer function into its constituent parts.
The next stride is to split up the role into its constituent parts. In that location are seven types of parts:
- A abiding
- Poles at the origin
- Zeros at the origin
- Real Poles
- Real Zeros
- Circuitous conjugate poles
- Circuitous conjugate zeros
Nosotros can use the examples above to demonstrate once more.
Example 1
This office has
- a constant of 6,
- a zero at s=-10,
- and complex conjugate poles at the roots of s2+3s+50.
The complex cohabit poles are at due south=-1.5 ± j6.9 (where j=sqrt(-1)). A more common (and useful for our purposes) fashion to limited this is to utilise the standard notation for a 2nd order polynomial
In this instance
Example 2
This role has
- a constant of 3,
- a zero at the origin,
- and complex cohabit poles at the roots of southward2+3s+50, in other words
Example three
This office has
- a constant of two,
- a null at s=-ten, and
- poles at s=-three and s=-50.
iii. Draw the Bode diagram for each function.
The rules for cartoon the Bode diagram for each part are summarized on a split page. Examples of each are given subsequently.
four. Draw the overall Bode diagram past calculation up the results from pace three.
Afterwards the individual terms are drawn, information technology is a uncomplicated thing to add them together. See examples, below.
Examples: Depict Bode Diagrams for the following transfer functions
These examples are compiled on the next page.
Case four
Repeated poles, a aught at the origin, and a negative constant
Full Solution
References
Supervene upon
Source: https://lpsa.swarthmore.edu/Bode/BodeRules.html
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