# How to Draw a Bode Plot from a Given Transfer Function with a Zero at s=1

• Jon Trausti
In summary, the speaker is given a transfer function and needs to draw a Bode plot from it. They are unsure how to handle the zero at s = 1 and ask for advice. They are not looking for a solution, just clarification on how to approach the problem. They are informed that the zero will have the same amplitude spectrum as a zero in the left-half plane and should be handled like any other zero. However, there may be a difference in the phase spectrum. The speaker thanks the other person for their help.
Jon Trausti

## Homework Statement

Hi,

I'm given a transfer function, and am suppose to draw Bode plot from it.

H(s) = ( 2000s (s - 1) ) / (s + 2000)^2

I'm wondering what to do for the zero at s = 1? Should I just solve this normally, as every example we have done and every example I've seen uses simple zeros/poles (with "+" in the middle, and positive number.

So any idea? :)

p.s. I'm not looking for solution, I'm just little puzzled by the minus

Jon Trausti said:
I'm wondering what to do for the zero at s = 1?
It'll have the same amplitude spectrum as a zero in the left-half plane, so just go about it like you normally would. There's a significant difference in its phase spectrum, however, if you need to include it.

ok, great thank you!

## 1. How do I plot a Bode plot from a given transfer function with a zero at s=1?

To plot a Bode plot from a given transfer function, you will need to first find the magnitude and phase of the transfer function at different frequencies. Then, you can plot these values on a logarithmic scale for frequency and a linear scale for magnitude and phase. Make sure to label your axes and include a legend to indicate which curve represents the magnitude and which represents the phase.

## 2. What is a Bode plot and why is it useful?

A Bode plot is a graphical representation of the frequency response of a system. It shows the magnitude and phase of the system's output as a function of frequency. Bode plots are useful because they allow us to easily analyze and understand the behavior of a system, particularly in terms of its stability and frequency response.

## 3. How do I find the magnitude and phase of a transfer function at a specific frequency?

To find the magnitude and phase of a transfer function at a specific frequency, you will need to plug in that frequency value into the transfer function and solve for the magnitude and phase. This can be done using algebraic manipulation or by using a calculator or software.

## 4. How do I interpret the magnitude and phase of a Bode plot?

The magnitude of a Bode plot represents the ratio of the output amplitude to the input amplitude, expressed in decibels. A higher magnitude indicates a larger output compared to the input, and a lower magnitude indicates a smaller output. The phase of a Bode plot represents the delay between the output and input signals, expressed in degrees. A phase of 0 degrees means the output is in phase with the input, while a phase of 180 degrees means the output is completely out of phase with the input.

## 5. Can I use a Bode plot to determine the stability of a system?

Yes, Bode plots are commonly used to determine the stability of a system. Specifically, the phase plot can indicate if a system is stable, marginally stable, or unstable. A phase margin of greater than 0 degrees indicates stability, while a phase margin of less than 0 degrees indicates instability. Additionally, a Bode plot can also show the frequency at which the system's gain crosses 0 dB, known as the gain crossover frequency, which can also be used to determine stability.

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