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I'm having trouble understanding how to infer from the transfer function amplitude how to draw the bode plot. i.e given the following transfer function:

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Is the amplitude is the slope of the graph? when I'm looking at the analysis of the amplitude I can't relate what's written in the table to what I'm seeing

enter image description here

What are the physical meaning of the amplitude and the phase shift? I understood that the amplitude gives me the intensity of the signal, but that doesn't mean much to me either. can anyone please give me a practical example to how is this information used in planning and designing a system?

Thank you.

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    \$\begingroup\$ You are asking for a book to be written. FYI. There is useful information in your table that you might take to heart, though. If \$\omega\$ is very much smaller than \$\omega_{_0}\$ then you are in one fixed situation. If \$\omega\$ is very much larger than \$\omega_{_0}\$ then you are in another fixed situation. In between, there is variation that is interesting. Just a note. 1st order filters are pretty easy. But 2nd order are worth the time to study. 3rd order and beyond are too complex for most folks, so they usually try and break them into combinations of 1st order and 2nd order. \$\endgroup\$ – jonk Dec 9 '19 at 6:46
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This is a very broad question indeed.

For a practical high level example. Think of a black box with a filter inside, you can input a sine wave with 1V amplitude then you sweep the frequency of that sine wave from 1-500 Hz. In your case you will start to see an attenuation in the 1V at around 10 Hz (That's your -3dB) where the signal has lost half its power. If you keep going up in frequency you will see a higher and higher attenuation (Low pass filter).

You could also see an increase in amplitude doing the same sweep if you had a high pass filter.

As for the phase shift, that is the shift in the input vs the output in terms of voltage gain (Vout/Vin -> which is your transfer function in this case) - I've mainly used the phase plot to determine stability when working with control systems Lecture. I don't know if this answers your questions, but there are loads of material regarding this, I will suggest you take your time and read this paper.

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  • \$\begingroup\$ Another note is to see what happens to inductors and capacitors as you go WAY up in frequency. They become shorts/open and changes your circuitry completely. Look at the impedance formula for both components, and try to observe the impedance when you set the frequency to 0 and 10,000,000 \$\endgroup\$ – Sorenp Dec 9 '19 at 9:08
  • \$\begingroup\$ thank you very much for the reading material! I'll try to simulate your suggestions in simulink and look at the results \$\endgroup\$ – E. Ginzburg Dec 12 '19 at 12:47

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