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Log-Log plots (x_0 vs w) why slopes are -1 and -2 when system goes infinity in first and second syms 1

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jimmi975

jimmi975

Student
Apr 13, 2022
11
1st_order_tirrfn.png
2nd_order_qvu4dk.png
1st_order_kutxw2.png
Log-Log plots (x_0 vs w) why slopes are -1 and -2 when the system goes to infinity in first and second-order systems respectively.
 
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Both system equations and plots are provided in the attached files
 
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well, log is just used as a scale here, the main question is why the slopes are -1 and -2?
challange_ygmfhi.png
 
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the slope is -1 and -2 for first and second-order systems respectively?
 
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first_ord_limhd2.png



this is what I can explain regarding first-order dynamics and the difference between this and second order is just the damping ratio is involved in the second-order characteristic equation and the highest degree is 2 and the plot you get for frequency response of the log-log plot of x vs w is already given in above pictures.
 
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I think as the ratio is constant for the change in vertical vs change in horizontal for 1 st order dynamics thus, we get a 1 slope, and the reason it's negative is the inverse relation between w and x.
 
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You are not showing the final part.

What is the equation for a line?

How does that look like the logarithm of the equation of the transfer function? What assumptions do you need to make?

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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I don't think I have an equation that you ask for, but the above image might help.
 
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that is the general equation, we can have any value of taw in there. As in this image, the taw is RC, but the main idea is no matter what is the taw, the plots will remain the same at a steady state. with the slope of -1 for 1st order systems.
rc_pnipkz.png
 
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Well, if we put infinity instead of taw, the characteristic eq goes to infinity and the TF goes to 0.
 
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I cant see what A-line(Asymptotes) has to do with slope?
 
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