7
Notes Legend
The notes for this course are organized into specific sections. You are responsible on
assignments and exams for sections with a blue background title and star, as below:
The following is a list of section types that you will encounter:
Pre-Reading
–
You should read these sections before the lecture whenever possible;
they will make the lecture much easier to understand and more useful to you. It will
be assumed that you have read these before coming to class.
Lecture Notes
–
These include copies of any circuit diagrams and other graphs to
save you time (and provide tidy notes). Space to complete all examples is included;
simply copy from the board into your notes.
In-Class Break
–
Bored in class? Can‟t stay awake during that
Friday afternoon (or
Tuesday evening) lecture? Read one of these for a quick change of pace, and maybe
an interesting fact or bit of practical knowledge you can use later!
Real-World Example
–
A detailed example from the real-world relevant to the
material just covered. This course has the potential to be one of the most practical
courses you take; hopefully these will give you some interesting ideas about how to
apply the course content.
Project
–
These sections outline detailed, real-world projects which you can build
and use at home.
Practice Problems
–
A number of practice problems will be included at the end of
every chapter. Problems for which solutions are provided are clearly marked.
Tip
–
Small but relevant bits of information about the course or related topics.

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8
Chapter 1
Frequency Domain
Analysis

9
What is the Laplace Transform?
As you may have seen in previous courses, such as ECE110 or control systems courses, the
Laplace Transform is a type of integral transform
–
a linear operator which is most useful
in electronics for converting a time-domain
signal,
,
, to a complex or frequency-
domain signal,
.
The formal mathematical definition of the Laplace Transform is given for a function,
,
where
, as the following:
{ } ∫
While the Laplace Transform of any time-domain function can theoretically be calculated
directly using the above formula, we will see that it is much simpler in most cases to
instead use tables and properties of the transform.
Why do I need to learn this?
The main use of the Laplace Transform is to allow us to work in the frequency domain for
circuit analysis. This is beneficial for a number of reasons. First, the basic math behind
determinin
g a circuit‟s response to an arbitrary signal
may be significantly less complex
when using the frequency domain. This is seen in the graphic from the start of the chapter:
Pre-Reading:
Introduction to Laplace

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10
In the time domain, we have some signal,
, for which we can to determine the output of
a circuit,
. For the time-domain system, the effect of the system is represented by the
function,
. To determine the output of the system, one must apply convolution in the
time domain:
∫

- Spring '17