# Bode plot with given transfer function

• gfd43tg
In summary: So, if you have a gain of 20dB and you want to calculate the phase angle for a frequency of 500Hz, simply plug in 20 for gain and 500 for frequency and solve for phase angle. In summary, the student is having problems drawing bode plots. The professor retracted his statement that everything should be standard form with (ω/ω_c), so the student is now confused. The student has the right idea when describing the plot as being "OK until you get to w=2, then a -20dB/decade fall from w=2 to w=10 is still OK, but then for some reason you give it a +40dB/decade rise when it should be just +
gfd43tg
Gold Member

## The Attempt at a Solution

Hello,

I am having serious problems being able to draw bode plots. At first the professor said to put everything into standard form with an (ω/ω_c)...and then there is also a table in the textbook with standard forms that don't all include an ω_c, and he retracted his statement. So now I am just so confused how to draw these things.

I am working on the first transfer function in the image, and with two poles at 50 and 100, I'm not sure how to represent that.

#### Attachments

• 9.1.png
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Here is what I have for my magnitude plot

I don't see anything in this table that looks like this transfer function anyway, leaving me even more confused

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• 9.1 attempt 1.jpg
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Your Bode gain plot needs help. But you have the right idea.

It's OK (flat) until you get to w=2, then a -20dB/decade fall from w=2 to w=10 is still OK, but then for some reason you give it a +40dB/decade rise when it should be just +20 dB. So make that correction and try again to finish the plot.

I would recommend you get some semi-log paper. It will make things much easier

rude man said:
Your Bode gain plot needs help. But you have the right idea.

It's OK (flat) until you get to w=2, then a -20dB/decade fall from w=2 to w=10 is still OK, but then for some reason you give it a +40dB/decade rise when it should be just +20 dB. So make that correction and try again to finish the plot.

To add to what Rude man said the slope is a running total

Should the paper be log scale on horizontal axis and linear on vertical axis? I found a website that I can print semi log paper, thanks for the suggestion

Maylis said:
Should the paper be log scale on horizontal axis and linear on vertical axis? I found a website that I can print semi log paper, thanks for the suggestion

The gain and frequency are both logrithmic if referring to gain. If referring to dB, then only the horizontal is logrithmic.

Keep in mind that your transfer function will give you the exact gain and phase angle for any value of omega. So if you ever get confused, start plugging in your limits for 0 and infinity to see where your gain sits. Then plug in other values of interest, the break frequencys for sure. If there is an "s" in your transfer function, simply substiture "jω" for "s" and solve for that frequency. You will always get a vector with magnitude (gain) and an angle (phase).

If you plug in 0, 2, 10, 50 and 100 and infinity for omega, you can never miss.

And if you are "guessing" with the zeros and poles...at least you can back check your guess.

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## 1. What is a Bode plot?

A Bode plot is a graphical representation of the frequency response of a system. It shows the magnitude and phase response of a system as a function of frequency.

## 2. How is a Bode plot created?

A Bode plot is created by plotting the magnitude and phase response of a transfer function on a logarithmic scale. The frequency is plotted on the x-axis and the magnitude and phase are plotted on the y-axis.

## 3. What is the purpose of a Bode plot?

The purpose of a Bode plot is to provide insight into the stability and performance of a system. It can help identify the dominant poles and zeros of a transfer function, which can affect the system's behavior.

## 4. What information can be obtained from a Bode plot?

A Bode plot can provide information such as the frequency at which the system's response peaks, the gain margin and phase margin, and the overall frequency response of the system.

## 5. How can a Bode plot be used in system design?

Bode plots can be used in system design to analyze and optimize the performance of a system. By observing the behavior of the system at different frequencies, engineers can make adjustments to improve stability and meet design specifications.

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