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Laplace Transforms, Part 4: Frequency and Phase Analysis

COURSE NO: E03-036
Laplace Transforms, Part 4: Frequency and Phase Analysis
Course Highlights

This online engineering PDH course begins the work of determining the magnitude and phase response of a circuit modeled by Laplace transforms, using Bode's technique.  While a stand-alone module, it is the fourth in series of modules designed to develop working expertise in the use of transforms in the design and analysis of any circuit that must be modeled using differential/integral equations. Working familiarity with and knowledge of Calculus and basic transforms is assumed.


In general, the purpose of the Laplace Transform is to transform ordinary differential equations (ODEs) into algebraic equations, which makes it easier to solve ODEs. However, the Laplace Transform gives one more than that: it also does provide qualitative information on the solution of the ODEs. The Laplace Transform is a generalized Fourier Transform, since it allows one to obtain transforms of functions that have no Fourier Transforms.


This 3 PDH online course is particularly applicable to electronic/electrical engineering enterprises.  However, any discipline that depends upon differential equations as a model basis for physical systems will benefit from this course.

Learning Objectives

This PE continuing education course is intended to provide you with the following specific knowledge and skills:

  • Learning how to develop the equations necessary to determine magnitude response as a function of frequency;
  • Learning how to develop the equations necessary to determine phase response as a function of frequency;
  • Recognizing the filter type from its transfer function;
  • Understanding the significance of component values on frequency response;
  • Developing the skills necessary to create magnitude and phase plots as a function of frequency.
  • Extending the student's knowledge base sufficiently wide to master the skills required to determine the circuit's output at any frequency.
Course Document

In this professional engineering CEU course, you need to review the course document titled, “Laplace Transforms, Part 4: Frequency and Phase Analysis", by Tom Bertenshaw.

To view, print and study the course document, please click on the following link(s):
Laplace Transforms, Part 4: Frequency and Phase Analysis
Course Quiz

Once you complete your course review, you need to take a multiple-choice quiz consisting of thirty (30) questions to earn 3 PDH credits. The quiz will be based entirely on the material contained in this course document.

The minimum passing score is 70%. There is no time limit on the quiz, and you can take it multiple times until you pass at no additional cost.
Certificate of Completion

Upon successful completion of the quiz, print your Certificate of Completion instantly. (Note: if you are paying by check or money order, you will be able to print it after we receive your payment.) For your convenience, we will also email it to you. Please note that you can log in to your account at any time to access and print your Certificate of Completion.

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