Laplace Transform and Analysis in the s-Domain

Please answer BOTH of the questions.

Answer Discussion

This week’s Discussion asks you to consider the benefits of the Laplace transforms and transfer functions toward simplifying the analysis of time-based circuits to discuss the following:

Discuss what is meant by poles and zeros of a transfer      function.

How does the determination of each help in understanding the      response of a circuit?

Some key points to think about when discussing this topic are:

The poles and zeros of transfer functions allow for a      determination of the relative stability circuits. Stability refers to      whether the output of a circuit can be easily controlled with predictable      limits for a given range of inputs. Thus, a stable circuit has a bounded      output for bounded inputs.

If you utilize any other sources or the internet to support      your post, please be sure to site your source as specified in the      references below in the “Cite your Sources” section.

1. .

Classmate Responses (Reply to these two please)

1. Keenan Davis 

Zeros are the frequency value that makes the numerator equal to zero, while poles are the frequency value that makes the denominator equal to zero in a transfer function. The way that the poles and zeros can be determined is by finding the s value that will cause either the numerator or denominator to be equal to zero, depending if you’re looking for the zeros or the poles of the function. 

Determining the zeros and poles of a system can determine the stability of the system, how well it will perform, and its response. As the s value of the numerator approaches a zero, the numerator of the transfer function itself also approaches 0. However, as the s value of the denominator approaches a pole, the value of the transfer function approaches infinity.

Control Systems/poles and zeros. Wikibooks, open books for an open world. (n.d.). Retrieved March 20, 2022, from https://en.wikibooks.org/wiki/Control_Systems/Poles_and_Zeros#:~:text=Poles%20and%20Zeros%20of%20a,how%20well%20the%20system%20performs.

Colin Heckman 

• Poles are where the transfer function becomes infinitely large, while zeros are where the transfer function becomes zero. On the s plane, poles and zeros are plotted as real by imaginary (real on the horizontal and imaginary on the vertical). Poles and zeros are essential to converting complex transfer functions into simple algebra. The example on page 475 of our textbook is a perfect example. First, the KVL equation for V in terms of iL is formulated. Secondly, the laplace transform is found using the function pairs discussed earlier in the chapter. Then, the laplace transform is simplified using the poles and zeros. Lastly, the simplified function can be converted to the inverse laplace transform and solved. The inverse laplace transform is also solved through simple algebra just as the calculations for the poles and zeros.