This page is a section of Ultimate Electronics: Practical Circuit Design and Analysis, a free, online, interactive electronics textbook by Michael F. Robbins.

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If you want to design and analyze electronic systems, you have to learn about concepts at three levels:

  1. How the physics becomes math.
  2. How to solve the math.
  3. How to apply these techniques to design and understand practical systems.

This book aims to consider all three levels, but most importantly, to develop a coherent structure between them.

If you want a shallow overview of a single topic, check Wikipedia. If you want a deep overview of a single topic, check the academic literature. In contrast, we'll focus on teaching the counterintuitive part: how all these concepts overlap and interact to make electronics work.

About this Book

Ultimate Electronics: Practical Circuit Design and Analysis differs from other electronics texts in two ways:

  1. Distribution. It's free, it's online, and it's instantly accessible to anyone with a web browser.
  2. Interactivity. Where appropriate, it uses the CircuitLab electronics design software, providing a highly intuitive yet powerful circuit simulation environment.

For example, click this circuit:

When you click, the CircuitLab software opens in a new tab in your browser. You can run a simulation of the circuit pictured, and then you can modify the circuit and run it again.

While simulation can never replace the experience and intuition that one can gain from hands-on electronics experimentation, it's a handy tool to make learning electronics faster and easier.


This book is targeted toward an undergraduate-level university course in electronics analysis and design. At the time of writing, the CircuitLab software is in use within electronics courses at world-class universities around the globe. This book aims to provide educational content to make it easy for other institutions to add these new tools to their courses.

Increasingly, this topic is studied not just by electrical engineers, but also by engineers of all types, many scientists in various fields, and many computer scientists as well. A working knowledge of electronics is a powerful force multiplier in many fields of endeavor.

Individual learners, hobbyists, and enthusiasts studying on their own should also find this book to be a convenient tutorial and reference for their studies and projects.


Existing experience in calculus, linear algebra, differential equations, and classical physics (including thermodynamics, electricity, and magnetism) is recommended.

For online resources in these topics, we recommend these courses which provide excellent written lecture notes and/or video lectures:

Studying electronics will rapidly grow your intuition about these prerequisite topics, and vice-versa, so a concurrent course of study is encouraged.

About the Author

Michael F. Robbins holds the S.B. in Electrical Science and Engineering and the M.Eng. in Electrical Engineering and Computer Science degrees both from the Massachusetts Institute of Technology. Mike is the co-founder of CircuitLab, Inc. and developer of the CircuitLab circuit simulation software used by academic institutions, engineers, and hobbyists worldwide.

What's Next

In the next section, Schematics & Simulations Tutorial, we'll briefly introduce how to use the schematic capture and circuit simulation features built into this interactive book.

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