ELEC 320, Fall 1998
Prof. Rich Kozick

## Homework 21

Date Assigned: Monday, November 30, 1998
Date Due: Friday, December 4, 1998

1. Quiz 5 is take-home and is due on Wednesday, December 2 at 9:00 AM.

2. Lab Projects: All students will present and/or demonstrate their lab projects on Tuesday, December 8, from 8:00 AM to 11:00 AM. More details about the presentations and lab reports are available on the Web at
http://www.eg.bucknell.edu/~kozick/elec32098/lab.html

3. Reading: Please read Chapter 7 on the Laplace transform. Sections 7.1 - 7.3 describe the forward and inverse Laplace transform operations. Section 7.4 describes the application of the Laplace transform to solving differential equations. Since you have done this in MATH 212, we will mention it only briefly in this course. The concept of the transfer function in Section 7.5 is very important. If you have notes on the Laplace transform from previous courses (MATH 212 and/or ELEC 220), you might want to find and review those notes.

If we have time, we will show how the Laplace transform is an important tool for designing higher-order analog filters. Sections 8.4 and 8.5 discuss frequency response and Bode plots. Section 8.6 discusses analog filters from the point of view of the "s-plane".

4. Please submit solutions to the following inverse Laplace transform problems on December 4.

Problem 7.9, parts a, b, c, d, f, and g.

For each problem, perform the partial fraction expansion analytically, and then check your results using MATLAB. Click here for notes on using MATLAB for partial fraction expansion.

*** REVISION: USE MATLAB ONLY, AND YOU DO NOT HAVE TO SUBMIT SOLUTIONS. ***

5. Check out the "Exploring the s-Plane" demonstration at
http://www2.ece.jhu.edu/wjr/
Notice how the locations of the transfer function "poles" of a linear, time-invariant system affect how the system responds to a unit step input signal. Your observations should agree with our discussion in class about the relation between the s-plane and time signals. Nothing needs to be handed in for this exercise.

Thank you.