Bode Plots: Plotting Homework Statement

[tandoorichicken]

Homework Statement

I have to plot some data for a lab writeup. It's based on the frequency response of fluid catheter-transducer systems. Part of this writeup includes making Bode plots for the gain and phase shift. I know how to plot my data; the problem that I am having is that I want to try to fit a trendline that closely follows the data, but I don't know how to do this.

1) What is the function (as in x/y) for a theoretical Bode plot for a second-order system?
2) Is this the right way to go about this or is there a better way?

Any insight would be much appreciated.

 

[berkeman]

Do you know what the gain and phase shift are for 2nd order lowpass, highpass, bandpass and notch filters? Start by understanding what these four types of filters have for their 2nd order responses, and I think you'll see what your options are.

 

[piercas]

I understand your struggle with plotting and fitting data for your lab writeup. Bode plots are commonly used to analyze and visualize the frequency response of systems, and it is important to accurately represent the data in order to draw meaningful conclusions.

To answer your first question, the theoretical Bode plot for a second-order system can be represented by the following function:

H(jω) = K/(1+jω/ω_n)^2

Where H(jω) is the transfer function, K is the system gain, ω is the frequency, and ω_n is the natural frequency of the system.

Regarding your second question, there are a few ways you can approach fitting a trendline to your data. One method is to manually adjust the parameters of the theoretical Bode plot function to best fit your data. Another option is to use software or programming tools that can automatically fit a trendline to your data. Whichever method you choose, it is important to consider the limitations and assumptions of the theoretical function and make sure it accurately represents your data.

In conclusion, there are different ways to fit a trendline to your Bode plot data, and it is important to carefully consider the best approach for your specific situation. I hope this helps with your lab writeup and wish you success in your research.

 

[piercas]

Hello,

Bode plots are a useful tool for analyzing the frequency response of systems, and it sounds like you are on the right track with your lab writeup. To answer your first question, the function for a theoretical Bode plot of a second-order system is a combination of two functions: a low-pass filter and a high-pass filter. The low-pass filter function is 1/(1+ω^2/ωn^2), where ω is the frequency and ωn is the natural frequency of the system. The high-pass filter function is ωn^2/(1+ω^2/ωn^2). When plotted on a log-log scale, these two functions result in a characteristic "S" shape for the Bode plot.

As for fitting a trendline to your data, it can be helpful to first plot your data on a log-log scale to see if it follows a similar shape as the theoretical Bode plot. If it does, then you can try to fit a trendline that best fits the data points. However, keep in mind that in some cases, the data may not perfectly match the theoretical function due to experimental errors or other factors. In these cases, it may be more appropriate to use a curve fitting tool or software to find the best-fit function for your data.

In terms of whether there is a better way to approach this, it really depends on the specific goals and requirements of your lab writeup. If you are simply trying to analyze the frequency response of the system and make a qualitative comparison between your data and the theoretical Bode plot, then fitting a trendline may be sufficient. However, if you need to make more accurate quantitative measurements, it may be worth considering using a curve fitting tool or consulting with your instructor for guidance.

I hope this helps and good luck with your lab writeup!