# 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.