# Trouble interpreting Bode diagrams

• Gauss M.D.
In summary, the Bode plot is a graphical representation of the gain of a system as a function of frequency. It is a quick way to show features of the steady state response that EEs typically care the most about. However, it is just as theoretical as analysis of the poles and zeros of a complex function.
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?

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.

berkeman
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...)

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.

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.

LvW said:
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).

Here is a nice treatment of Bode plots. It also has a nice section on approximating the factors of large polynomials.

LvW said:
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.

Filip Larsen said:
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).

DaveE
LvW said:
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).

## 1. What is a Bode diagram?

A Bode diagram is a graphical representation of the frequency response of a system. It consists of two plots: the magnitude plot, which shows the amplitude of the output signal in relation to the input signal at different frequencies, and the phase plot, which shows the phase shift between the output and input signals at different frequencies.

## 2. How do I interpret a Bode diagram?

To interpret a Bode diagram, you need to understand the relationship between the input and output signals at different frequencies. In the magnitude plot, the higher the peak or dip, the more the system amplifies or attenuates the input signal at that frequency. In the phase plot, the horizontal line represents zero phase shift, and any deviation from this line indicates a phase shift between the input and output signals.

## 3. What causes difficulties in interpreting Bode diagrams?

Some of the common difficulties in interpreting Bode diagrams include not understanding the meaning of the plots, not being able to identify key features in the plots, and not having a clear understanding of the system being analyzed. It is also important to have a good understanding of the frequency domain and how different components in a system affect the frequency response.

## 4. How can I improve my ability to interpret Bode diagrams?

To improve your ability to interpret Bode diagrams, it is important to have a strong foundation in signal processing and frequency domain analysis. You can also practice by looking at different types of Bode diagrams and understanding how different components and systems affect the frequency response. Additionally, seeking guidance from a mentor or taking a course in signal processing can also help improve your skills in interpreting Bode diagrams.

## 5. Are there any limitations to Bode diagrams?

Yes, there are some limitations to Bode diagrams. They only show the frequency response of a system and do not provide information about the time domain behavior. Also, Bode diagrams assume linear systems and may not accurately represent the response of nonlinear systems. Additionally, Bode diagrams may not be suitable for analyzing systems with very high or low frequencies.

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