**A CHAOTIC ELECTRONIC CIRCUITS PRIMER**

## This is a tutorial website for people who want to learn the basics of “chaos” and experiment with electronic circuits that exhibit what are called “chaotic” responses. The meaning of the terms “chaos” and “chaotic” will be explained in detail on the following pages.

## For now, keep in mind that “chaos” is a phenomenon that occurs in a wide variety of the things that comprise our universe.

# WHY USE ELECTRONIC CIRCUITS?

## While many different kinds of systems in nature can be chaotic, this website focuses on chaotic electronic circuits. This is because chaotic electronic circuits demonstrate all the important aspects of chaos theory and are, in most cases, the easiest chaotic systems to simulate and/or construct.

## People investigating non-electrical chaotic systems often create an electrical “analog” of the system they want to study. An “analog” is a system that in certain important ways mimics another system that, otherwise, is totally different. An electrical analog of a chaotic biological system, for example, usually is much easier to work with and is much easier to modify than is the actual biological system itself.

# WHAT BACKGROUND IS NEEDED TO LEARN ABOUT CHAOS?

## A modest college level background in science and electronics will be helpful in learning about chaos, but is not absolutely necessary. Even advanced high school students can benefit from this website. The main requirement is a desire to LEARN.

**I will include only enough “theory” to give people a basic understanding of fundamental chaos principles. These principles apply to all chaotic systems, not only to chaotic electronic circuits. A knowledge of mathematics through ordinary differential equations will be helpful, but is not necessary. **

# MORE HELP IS AVAILABLE.

**References and links to published materials which have more detailed explanations are provided. ****However, only those references that I believe are clearly written have been included. I also have included references and links to other websites having material which complements that which is on this website. **

**To get the maximum benefit from the material I have included, I strongly recommend that you read all the pages in sequence. As is the case with most science topics, more than one reading of this material is recommended.**

# WHAT WILL YOU LEARN AND WHY SHOULD YOU LEARN IT?

## In addition to learning the fundamentals of chaos, you will learn how to simulate on the computer electronic circuits that have chaotic responses.

## A free but very sophisticated program called LTspice will be used to do the simulations. The program is easy to learn and it’s FREE!

## In addition, you will learn that it’s also easy and fun to build the actual electronic circuits using common, inexpensive circuit components. You don’t have to be some kind of weird geek to do it.

## The responses of these chaotic circuits are fascinating to see and they demonstrate many of the principles of chaos. More importantly, chaos is an extremely interesting topic to study. It is an important aspect of the world we live in.

#### (Click on the images to enlarge them.)

**After following the discussion on this website, you will understand the basics of chaos and will be able to generate “strange attractors” at home like the ones shown above. Strange attractors are characteristic of all chaotic systems and are incredibly fascinating to observe. **

**The precise strange attractor that is produced, however, depends on the circuit being simulated and the component values used. **

**I used the LTspice circuit simulation software to obtain these displays. You, too, will find out how easy it is to do this.**

# WHO AM I?

**My name is Jim and I have studied, prac-ticed, and taught electrical engineering for over 50 years. I am now retired and investigate chaotic electronic circuits as a hobby. I hope that you find chaos and chaotic electronic circuits to be as interesting as I do. **

**PLEASE NOTE: I have tried to check and recheck what I have written for errors. However, there is no guarantee that there are no remaining inadvertent errors in what I have provided on these pages. If there are any errors, I apologize. **

**The links provided to other websites all worked at the time when I published this website. Sometimes, others change their websites and, thus, invalidate the links. I have no control over this.**

### CORRECTIONS AND CONSTRUCTIVE COMMENTS CAN BE MADE BY EMAIL TO:

### administrator@chaotic-circuits.com