Bode Plot Examples

Several examples of the construction of Bode Plots are included in this file.  Click on the transfer function in the table below to jump to that example.

Examples  (Click on Transfer Function)
1



(a real pole)
2



(real poles and zeros)
3



(pole at origin)
4


(repeated real poles,
negative constant)
5


(complex conj.
poles)
6

(multiple poles at
origin, complex
conj zeros)
7



(time delay)

 


Bode Plot: Example 1

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.  

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 0 polynomial, the denominator is order 1.

 

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 2 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The overall asymptotic plot is the translucent pink line, the exact response is the black line.  

Bode Plot



Bode Plot: Example 2

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.  

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 1 polynomial, the denominator is order 2.

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 4 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The overall asymptotic plot is the translucent pink line, the exact response is the black line.  

Bode Plot



Bode Plot: Example 3

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.  

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 1 polynomial, the denominator is order 2.

 

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 4 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The overall asymptotic plot is the translucent pink line, the exact response is the black line.  

Bode Plot



Bode Plot: Example 4

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.  

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 1 polynomial, the denominator is order 3.

 

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 4 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The overall asymptotic plot is the translucent pink line, the exact response is the black line.  

Bode Plot



Bode Plot: Example 5

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 1 polynomial, the denominator is order 2.

 

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 4 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The exact response is the black line.  

Bode Plot



Bode Plot: Example 6

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.  

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 2 polynomial, the denominator is order 3.

 

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 4 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The exact response is the black line.  

Bode Plot


Bode Plot: Example 7

Draw the Bode Diagram for the transfer function:

This is the same as "Example 1," but has a 0.01 second time delay.  We have not seen a time delay before this, but we can easily handle it as we would any other constituent part of the transfer function. The magnitude and phase of a time delay are described here.

Step 1: Rewrite the transfer function in proper form.  

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 0 polynomial, the denominator is order 1.

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 3 components:

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The exact response is the black line.  

 



References

© Copyright 2005-2013 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College