# Circuit Theory/Circuit Theory Introduction

## Who is This Book For?

This is designed for a first course in Circuit Analysis which is usually
accompanied by a set of labs. It is assumed that students are in a
Differential Equations class at the same time. Phasors are used to avoid
the Laplace transform of driving functions while maintaining a complex
impedance transform of the physical circuit that is identical in both.
1st and 2nd order differential equations can be solved using phasors and
calculus if the driving functions are sinusoidal. The sinusoidal is then
replaced by the more simple step function and then the convolution
integral is used to find an analytical solution to any driving function.
This leaves time for a more intuitive understanding of poles, zeros,
transfer functions, and Bode plot interpretation.

For those who have already had differential equations, the Laplace
transform equivalent will be presented as an alternative while focusing
on phasors and calculus.

This book will expect the reader to have a firm understanding of
Calculus specifically, and will not stop to explain the fundamental
topics in Calculus.

For information on Calculus, see the wikibook:
Calculus.

## What Will This Book Cover?

This book will cover linear circuits, and linear circuit elements.

The goal is to emphasize Kirchhoff and symbolic algebra
systems such as
MuPAD,
Mathematica or
Sage; at the expense of analysis methods such
as node,
mesh, and Norton
equivalent. A phasor/calculus based
approach starts at the very beginning and ends with the convolution
integral to handle all the various types of forcing functions.

The result is a linear analysis experience that is general in nature but
skips Laplace and Fourier transforms.

Kirchhoff\'s laws receive normal focus, but the other circuit
analysis/simplification techniques receive less than a normal attention.

The class ends with application of these concepts in Power Analysis,
Filters, Control systems.

The goal is set the ground work for a transition to the digital version
of these concepts from a firm basis in the physical world. The next
course would be one focused on modeling linear systems and analyzing
them digitally in preparation for a digital signal
(DSP) processing course.

## Where to Go From Here

-   For a technician version of this course which focuses on the
    practical rather than the idea, expertise rather than theory, and on
    algebra rather than calculus, see the
    **Electronics** wikibook.
-   Take **Ordinary Differential
    Equations** now that
    you have a practical reason to do so. This math class should ideally
    feel like an \"art\" class and be enjoyable.
-   To begin a course of study in Computer Engineering, see the
    **Digital Circuits** wikibook.
-   For a traditional \"next\" course, see the **Signals and
    Systems** wikibook. There should be
    an overlap with this wikibook.
-   The intended next course would have a name such as **A New Sequence
    in Signals and Linear
    Systems**
    or **Elements of Discrete Signal
    Analysis**.
