# Circuit Theory

Most of electrical engineering was invented by 1925, reduced to practice by 1935, and mathematically analyzed and scientifically understood by 1945. So what makes this book different? Symbolic computation programs such as MATLAB, MuPAD, and Mathematica eliminate calculators and time consuming math. Cloud computing at sites like Circuit Lab make simulation possible on a cell phone. This leaves room for more material to be covered at greater depth.

**This Course**

The 1st and 2nd order differential equations can be solved with Euler's equation (phasors) and calculus. This solution technique is compared with Laplace transforms. The course builds on Kirchhoff's laws to write differential equations using transfer functions. The particular solution reduces to a final condition if sources are replaced with a unit step function. All that needs to be calculated is the homogeneous step response. Then response to any complex voltage or current source can then be found through the convolution integral.

**Requirements**

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. This book shows where Laplace transforms provide an alternative solution, but only in a few examples in parallel with phasor solutions.

*This book is not nearly completed, and could still use a lot of work. People with knowledge of the subject are encouraged to contribute.*

**Print Version:** Print Version ( ) (discuss)

**Warning:**The print version is over 90 pages long, as of 2 August, 2006.

**Cover Page:** Cover Page

**All Pages:** All Pages

## Contents

### Introduction[edit]

### Circuit Basics[edit]

- Terminology
- Variables and Units
- Circuit Basics
- Resistors
- Negative Resistance
- Capacitors
- Inductors
- Power supplies
- Terminal Relations

### Transistors[edit]

### Circuit Analysis[edit]

### Steady State Response[edit]

- Sinusoidal Sources
- Phasors
- Power
- Maximum Power Transfer
- Phasor Examples
- Power Factor Mitigation
- Complex Frequency
- Complex Frequency Examples

### Circuit Analysis Tips and Tricks[edit]

#### Impedance, Node, Mesh[edit]

#### Source Transformation[edit]

- Dangling Resistors
- Shorted Resistors
- Open Puzzles
- One Port Devices
- Source Injection
- Thevenin
- Norton
- Circuit Simulation
- Bridge Circuit Example
- Review Problem

#### Tips and Tricks[edit]

### Transient Response[edit]

- Transients
- Initial Conditions
- Exponential Time Constants
- First Order Initially Excited
- First Order Source Excitement
- First Order Initial and Source
- Second Order Initially Excited
- Second Order Source Excitement
- Convolution Integral
- More Examples