Trouble interpreting Bode diagrams

[Gauss M.D.]

Trying to get my head around frequency response and Bode plots, but I'm having trouble interpreting what's going on. The bode plot of a function is expressing what would happen to my function if I multiply it with sin(ωt), right?

To get a better feel for it, I asked Matlab to give me the Bode plot of 1/(s^2+1), ie sin(t). Shouldn't I be getting a graph of the different amplitude ratios for sin(t)*sin(ωt)?

But according to Matlab, the amplitude ratio approaches infinity at ω = 1. I don't get it. Can anyone explain what I'm not getting?

 

[anorlunda]

The bode plot gives you the gain of the system as a function of frequency. It is like making a sweep of all frequencies. A perfect oscillator can oscillate with zero input. Therefore, the gain appears to be infinite at that frequency.

 

[LvW]

You want a BODE plot of 1/(s^2+1).
Do you know the meaning of the parameter "s"?
In this case, "s" is nothing else than an abbreviation for "jw"="j*2Pi*f" with "f" being the frequency which is varied over a large region.
When you evaluate the given complex function by hand, you must discriminate between "magnitude" of this function and the varying phase of this function (between input and output of the corresponding device that has this transfer function).
And that`s what the BODE diagram shows: The magnitude as well as the phase as a function of a running frequency.
(Oscillators have nothing to do with your question...)

 

[Filip Larsen]

A more practical way to understand the relationship between the transfer function and its corresponding frequency response (Bode plot) is to look at the zeros and poles. Try search for "bode plot zeros poles guide" for some good descriptions on this.

 

[LvW]

I rather think, that analyzing the poles and zeros of a complex function are a more theoretical way for interpreting the frequency response. This is because poles and zeros are calculated with "s" being a complex frequency (s=sigma + j*omega), which is a pure mathematical (in reality non-existing) expression.

 

[DaveE]

I rather think, that analyzing the poles and zeros of a complex function are a more theoretical way for interpreting the frequency response. This is because poles and zeros are calculated with "s" being a complex frequency (s=sigma + j*omega), which is a pure mathematical (in reality non-existing) expression.

Perhaps. The Bode plot is popular because it is a graphical representation of what you would typically measure in the lab. Likewise it is a quick way to show features of the steady state response that EEs typically care the most about. So, basically it is popular because it is a very practical tool.
Given that caveat that Bode plots are only concerned with the steady state response, they are just as theoretical. If you are familiar with them you can easily see poles, zeros, gain, and Q (or damping).

 

[DaveE]

Here is a nice treatment of Bode plots. It also has a nice section on approximating the factors of large polynomials.
http://ecee.colorado.edu/~ecen4228/hw/hw6/bode_erickson.pdf

 

[Filip Larsen]

I rather think, that analyzing the poles and zeros of a complex function are a more theoretical way for interpreting the frequency response.

Just to clear any misunderstanding, I was hinting it as a practical tool to go in the opposite direction as what you say. That is, given a transfer function and no frequency response, then one can fairly easy gain insight into what the frequency response will look like by examining the zeros and poles for that transfer function. Of course, for an arbitrary transfer function you would then first have to convert it to a fraction which requires some math.

In the present case, the transfer function only has a single pole so the frequency response is straight forward to describe.

 

[LvW]

Just to clear any misunderstanding, I was hinting it as a practical tool to go in the opposite direction as what you say. That is, given a transfer function and no frequency response, then one can fairly easy gain insight into what the frequency response will look like by examining the zeros and poles for that transfer function.

OK and yes - I agree.
However, this requires some knowledge how poles an zeros of the compex function are represented in the BODE diagram (using the frequency w instead of "s").
Example: A "pole" does not mean "infinite" but indicates a corner frequency (change of the asymptotic line for the magnitude).

 

[Filip Larsen]

A "pole" does not mean "infinite" but indicates a corner frequency (change of the asymptotic line for the magnitude)

Hence my reference to the "rules of zeros and poles", like what this guide seems to cover in some detail (I haven't used that guide myself; my references on this topic are all 20+ years old and sitting on my shelf).