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‘~ --- - Session 2648

Laplace and Z-Transform Analysis and Design Using Matlab

Harold L. Broberg Indiana University - Purdue University, Fort Wayne

I. INTRODUCTION The Electrical Engineering Technology (EET) curriculum at IPFW requires an understanding of Laplace and z-transforms and their use in circuit analysis and design. This is emphasized in junior level courses [1, 2] which focus on analog and digital circuits and systems. Senior level electives, including courses in automatic control systems and digital filters [3, 4] build on this knowledge. The computer program used in these courses must enable students to easily calculate and plot time and frequency responses using Laplace and z-transform equations. The program must also be easily programmable, allow simple conversion between domains, and enable students to mathematically predictor verify Pspice circuit simulations. It must also be useable in as many courses as possible, for continuity, and be widely used in industry.

The Professional version of Matlab meets these requirements at a relatively low cost for a networked version. It also has many available Toolboxes, and a simple programming language. Simulink (a graphical simulation tool), the Control System Toolbox, and the Signal Processing Toolbox were also purchased with Matlab and are used extensively in these courses. The Fuzzy Logic Toolbox, another of the many available toolboxes, is used in another senior level course. The networked version of Matlab, with these toolboxes, is also used by Mechanical Engineering Technology and Electrical Engineering students, and these departments shared the cost of the software. The Matlab “notebook”, which comes with the professional version of Matlab, was used for this document. This “notebook” enables the user to embed Matlab programs, solutions, and graphs into a Microsoft Word 6.0 document and is an excellent tool for instructors.

A linear algebra course is not required in EET, but students are familiar with many of the basic concepts by their junior year. This familiarity, along with the primarily vector (or list) characteristics of most Matlab commands enable students to learn to use the vector/matrix based format with little difficulty. Matlab is powerful, has an extensive help facility, and is useful for introducing and using mathematical methods in continuous and discrete circuit analysis, control systems, and filters. It has an extensive system simulation capability, using the optional Simulink, and its power and graphical capabilities are appreciated by students. The examples described below focus on time and frequency response using the Laplace and z-domain and use a small subset of the Matlab commands. The Bookware Companion series [5] contains many excellent Matlab applications.

II. LAPLACE CIRCUIT ANALYSIS AND DESIGN The use of Matlab to augment Pspice for the mathematical portions of circuit analysis was well received by the students. Student use of Matlab provides a better understanding of the mathematics involved

1 The MathWorks, Inc. 24 Prime Park Way, Natick, MA 01760

$iiia 1996 ASEE Annual Conference Proceedings ) ‘..+,~yy’: .

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Broberg, H. L. (1996, June), Laplace And Z Transform Analysis And Design Using Matlab Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6159