what is the default amplitude value of the input signal when matlab gives the frequency response with fuction bode ?

As far as I know, Frequency response is measured like this : we give sinusoidal signals which have different frequencies but the same amplitude values as input to the system,then we measure the output signal, which is also a sinusoidal with the same frequency but a decrease in amplitude value and also a delay in phase. what I want to know is what is the default amplitude value of the input sinusoidal signal when I analysis a model with the function "bode"? Can that value be changed and how to change it? where can I find clues on this question. thanks!

Answer 1

[Jonathan LeSage]

Good question! The magnitude Bode plot depicts only the relative gain between two signals. Likewise, the phase plot gives you the relative phase difference between input and output. If you provide a known system (e.g. G(s) = 1/(s+1)) for the bode function, you already know the relative gain and phase differences. For a given input, you can find the output magnitude directly.

What you are describing is referred to as swept-sine testing which is one potential method to determine the Bode plot (and identify G(s)) for a particular system. You could equally generate the Bode plot using an impulse hammer response or a white noise input. If you want to learn more, here is a link to some material that discusses and contrasts the different methods:

• http://www.utwente.nl/ctw/wa/web_dev/old/lectures/113170/notes/notes.pdf

As far as your original question is concerned, the documentation for the bode function provides information on all possible inputs and changes you can make. You can find the documentation here:

• http://www.mathworks.com/help/ident/ref/bode.html

Hope this helps clarify things up!

[Matthew Crema]

Good answer. I would add that for a "linear" system like the one Jonathan provides as an example, the bode plot should be exactly the same regardless of the amplitude of the sinusoids, because you normalize (divide) by this amplitude when generating the plot.

And as Jonathan says, given the bode plot, you can determine the amplitude of the output for ANY input (by multiplication).