Lesson 40 – Laplace II: Pole-Zero Diagrams and the Inverse Laplace. (Sections 9-3, 9-4 and 9-5) (CLOs 9-1 and 9-2) There is a lot to cover in this lesson and depending on how much emphasis you want to place on classical expansion of transforms it may take part of the next lesson to cover this material. Begin this lecture by introducing the s-plane. Write a general Laplace function, factor the numerator and denominator into factors like ( s–a )( s+b ) etc. and ask them what values of “ s ” in the numerator will make it go to zero. Similarly, what values of “ s ” that will make the denominator go to zero and hence force the function towards infinity. We call these factors zeros and poles. We can infer a lot of information about our function by knowing these values and their location on the s-plane. Visually we plot the zeros as a small circle o and the pole as a small x . There is one o or x for each value of “s”. Show some examples including imaginary and complex poles. Students grasp how to plot poles and
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