Creating a Bode plot by analyzing a transfer function

In summary, the conversation discusses the difficulty of constructing a Bode plot from a given transfer function due to the lack of a "jω" term in the numerator. The speaker is unsure how to rewrite the transfer function in the proper form and is seeking guidance. A helpful example is provided for reference.
  • #1
andrew.tkelly
2
0

Homework Statement



I am constructing a Bode plot from a given transfer function. I having trouble because I am unsure how to rewrite the transfer function in the proper form. What makes this transfer function particularly tricky for me, is that there is no "jω" in the numerator, just ω^2. In all the examples I've seen solved, they always use s = jω, and put the function in the proper form.


Homework Equations



H(jω) = (10ω^2) / [(jω + 10)(jω - 200)]


The Attempt at a Solution



Well, I know how to reduce the denominator values to their proper form, but not the numerator value...because there is no "j"... and no evidence of a j^2 because there is no negative sign in front.

Thank you for reading!
 
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  • #2
Suppose the transfer function was negative before the "jω" was squared...
 
  • #3
Moderator's note: thread moved to Engineering, Comp Sci, & Technology.

In the future, please post engineering homework problems in this forum.
 
  • #4
See example 3 of link below,

http://www1.mengr.tamu.edu/aparlos/MEEN651/E17.pdf [Broken]

the problem looks similar to yours.

Found via Google search "Bode plot from a given transfer function examples"

Good luck
 
Last edited by a moderator:
  • #5




Hi there, creating Bode plots by analyzing transfer functions can be a challenging task, especially when the transfer function is not in the standard form. In this case, the transfer function you are given is not in the standard form because it does not have a "jω" term in the numerator. However, this can be easily resolved by considering that "j" is simply the imaginary unit, and "ω" is the frequency variable. Therefore, you can rewrite the numerator as 10ω^2 = 10(jω)^2. This way, you can still use the standard form of the transfer function and proceed with constructing the Bode plot. I hope this helps. Good luck with your homework!
 

1. What is a transfer function and why is it important in creating a Bode plot?

A transfer function is a mathematical representation of the relationship between the input and output of a system. In the context of creating a Bode plot, the transfer function is used to analyze the stability and frequency response of a system. It allows us to understand how the system will respond to different input frequencies and helps us design and optimize the system for a desired output.

2. What is the process for creating a Bode plot using a transfer function?

The first step is to obtain the transfer function of the system, either through mathematical analysis or experimentation. Then, the transfer function is converted into its Bode form, which consists of a magnitude plot and a phase plot. The magnitude plot shows the gain of the system at different frequencies, while the phase plot shows the phase shift between the input and output signals. These plots are then combined to create the Bode plot.

3. How do I interpret the Bode plot to understand the behavior of the system?

The Bode plot is divided into two parts: the low-frequency region and the high-frequency region. In the low-frequency region, the magnitude plot shows the gain of the system, while the phase plot shows the phase shift. In the high-frequency region, the magnitude plot shows the roll-off of the system, while the phase plot shows the asymptotic phase shift. By analyzing these plots, we can determine the stability, bandwidth, and frequency response of the system.

4. Are there any limitations to using Bode plots in system analysis?

While Bode plots are a useful tool for understanding the behavior of a system, they have some limitations. Bode plots assume that the system is linear and time-invariant, which may not be true for all systems. They also do not take into account the effects of non-linearities and noise in the system. Additionally, Bode plots are only valid for systems with rational transfer functions.

5. Can I use Bode plots for systems with multiple inputs or outputs?

Yes, Bode plots can be used for systems with multiple inputs or outputs by analyzing each input-output pair separately. The transfer function for each input-output pair can be obtained and converted into its Bode form, and the resulting Bode plots can be superimposed to create a comprehensive plot for the entire system. This allows us to analyze the frequency response of each input-output pair and the overall behavior of the system.

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