NOTE: A 3rd edition is scheduled for March 2012 (please see the update at the bottom of this page). The parts of the current 2nd edition from 1989 that deal with digital electronics are quite outdated, so if you are interested in this, you should wait for the 3rd edition to arrive. If, however, you are mainly interested in analog electronics and you do not have much patience, you might want to order the 2nd edition (or to grab it in your local library) right now.
For many electronics engineers, physicists and advanced electronics hobbyists, The Art of Electronics (sometimes just abbreviated to AoE) is their favorite book on electronics.
The approach of this book is quite unique. It tries to get away with an absolute minimum of mathematics. Rather than deriving lots of complicated formulas, it tries to build an intuitive understanding of electronics in the reader. Many people love it passionately - for this intuitive approach as well as for the entertaining style in which it is written. Besides trying to bring an intuitive understanding of electronics to you, the book offers an incredible amount of tips and tricks that you will need to make your circuits work in the real world.
However, the fact that the book is easy on the math, does in no way mean that it is an easy book in general. In fact, there are quite a lot of people - individual students, but also professors who have tried to teach a course using this book - who think that the book is too difficult for someone who is new to electronics. There is even a minority of people who have much experience and do not like the special approach of the book (but I have never heard any serious person question the competence of the authors). I personally am firmly in the camp of those who love it passionately, but I already knew a bit about electronics before I discovered the book.
So my advice is this: If you are sure that you will spend a significant part of your career designing electronics, and especially analog electronics, you should buy this book (but see the note about the 3rd edition at the top of this page). Even if you are new to electronics - if you find that the book is too hard to understand for you now, try reading it again after a few months. If, however, you are mainly interested in a book that will teach you the theory that you will need to pass your exams (and you are not sure if you really want to spend much time building actual circuits) other books like Sedra/Smith may be more useful to you.
The book contains several exercises, but no solutions. A very nice feature are the Bad Circuits examples, that show circuits that will NOT work. Looking at these circuits and finding the error is great fun and will tell you whether you have really mastered the relevant concepts. Unfortunately there are no solutions for the Bad Circuits either. However, there is a thread in the Electrical Engineering Forum of Physics Forums with a discussion of some of the Bad Circuits. You have to register there if you want to view the pictures. By the way, if you have difficulties understanding any parts of the book, this forum is an excellent place to ask, lots of the regular posters there know and love it. You might want to look at what I have written about the Physics Forums before you register.
Here is the list of content of the book with some comments:
Chapter 1 Foundations
Chapter 2 Transistors
Chapter 3 Field-Effect Transistors
Chapter 4 Feedback and Operational Amplifiers
Chapter 5 Active Filters and Oscillators
Chapter 6 Voltage Regulators and Power Circuits
Chapter 7 Precision Circuits and Low Noise Techniques
Chapter 8 Digital Electronics
Chapter 9 Digital Meets Analog
Chapter 10 Microcomputers
Chapter 11 Microprocessors
Chapter 12 Electronic Construction Techniques
Chapter 13 High Frequency and High Speed Techniques
Chapter 14 Low Power Design
Chapter 15 Measurement and Signal Processing
Chapter 1 provides an introduction to the basics like voltage and current and basic passive components. There is very little theory, but the most important concepts like Thevenin's equivalent circuit are clearly explained. However, you should alreday know about calculus and complex numbers if you want to understand the short discussion of capacitors and inductors in the time and frequency domain.
Chapters 2 and 3 teach you how to analyze and design transistor circuits, like the rest of the book with a minimum amount of math and a lot of very insightful explanations. If you are eager to build your own circuits as soon as possible, you might want to jump ahead to chapter 4 - designing circuits is much easier and more fun with op amps than with transistors (Of course, for a real in-depth understanding of the op amp, you will have to return and look at the humble transistor again one day...)
Chapter 4 is one of the best introductions to Operational Amplifiers I have ever seen. If you have read and mastered the 2 Golden Rules, understanding the following paragraphs with all kinds of exciting circuits that can be built with Op Amps becomes very easy. This chapter also contains an exhaustive discussion of the most important parameters of real Op Amps, and how you have to take them into account if you want to design really great circuits. But do not spend too much time with the tables where all kinds of Op Amps with their parameters are listed. Remember that the tables were compiled over 20 years ago, so some of the Op Amps listed may not be available anymore. The same is true for most of the other tables in the book.
Chapters 5 to 7 build on the knowledge of Op Amps and transistors to introduce you to many interesting applications and to teach you how to select Op Amps (and other components) to build precision circuits. Most of this material is still very relevant today. Chapter 7 is very interesting even if you do not have to build circuits of ultra precision. Section 7.11 (Origins and kinds of noise) and the following sections provide a very readable introduction to noise. You should study them carefully if you want to make sure that your signals do not get lost. The same goes for section 7.23 on Interference.
Large parts of chapter 8 are outdated (but of course the introduction to combinational and sequential logic is still valid). The same is true for most parts of chapters 10 and 11, especially the in-depth discussion of the 68008 microprocessor (the 680XX was a great microprocessor family in the 1980s and 90s, but is mainly of historical interest today).
Some of the construction techniques in chapter 12 are still interesting, but what is missing are simulation techniques. The book contains a short section (not even one page) on analog modeling tools where PSpice is mentioned, but even this section is hidden in the High Frequencies and High Speed Techniques chapter.
The parts of chapter 15 that cover the different kinds of sensors for temperature, light, strain and displacement are still relevant today. The same is true for the techniques to measure frequency and period, or for the tricks to recover a small signal from the noise.
You should also take a look at some recommendations for other books on practical analog electronics.
UPDATE ( 01 / 24 / 2012 ): Sadly, the schedule for the 3rd edition of The Art of Electronics has slipped. This post quotes a mail by Winfield Hill in which he explains the current state of the book and says that it "should be out by late 2012 or early 2013”. Considering the history of delays of the 3rd edition, I think that early 2013 is more probable, and I would not be surprised at all if it will be much later. It seems obvious that both authors would rather delay the 3rd edition even further than to rush their work and deliver a book of lower quality. Anyway, as soon as I learn of a new schedule I will add it here.
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