Please check the announcement in different languages (English, French, German, Japanese, Mandarin, Simplified Chinese, Korean and Spanish). Thanks to all my friends world-wide for their kind help! (Bernie, Werner, Ken-san, Kelvin, Patrick, W.S. and Juanito)

You can download the Table of Content here.

The book starts to explain loop control theory in a very basic approach, "with the hands" as we say in French. Then, the following chapters go deeper into the theory you need to know as a power supply engineer. There is some mathematical content but there are a lot of examples that show how to put the theory at work. This is a strength of the book to my opinion: it bridges theory that you have learned at school with what you will face in your engineering challenges. For instance, we all learned how to build a compensator with an op amp (I still have my class documents) but how do you apply that knowledge to a TL431, a Transconductance Amplifier or a Shunt Regulator? And what if you add an optocoupler? Throughout the pages, you will learn where phase margin comes from, how to select crossover frequency, how to efficiently compensate a control system and much more! I hope you will enjoy this new work that took me 3 years to write. As usual, almost all the equations were derived by myself with all the steps so that you can follow...and correct me if I am wrong!

**Chapter 1**: this chapter is an incomplete introduction to control systems. I have tried to gather the very basic things you need to know about control systems and I introduced some of the tools you will need in the following chapters. This chapter is for people who have no notion of control systems at all and want to understand how such a system works. No complex diagrams or difficult equations, a step-by-step introduction. Of course, experts reading this chapter will smile but, again, this brief introduction is not for them, they can jump to chapter 2 immediately : ) Please note that the entire Chapter 1 is offered for download by Artech on its website.

**Chapter 2**: now we start the discussion about serious stuff. I am showing how to properly write transfer functions. You will discover that a transfer function can be derived in different ways. One of them uses brute-force algebra. The result is analytically correct but when you look at the result, it is almost impossible to say if there is gain, if there are poles and zeros and where they are hide. Re-write the same function the proper way and all these information clearly appear in the equation. Knowing how to write transfer functions this way is the key to fast analytical techniques and so-called low-entropy expressions. Learn how to get the poles and zeros just by looking at the electrical schematic!

**Chapter 3**: in this chapter, I explain where phase and gain margins come from. At school, I was told that "you need to have at least 45 degrees of phase margin at crossover" and that was it! I never had a clue where this number was coming from and how to apply it. Learn how phase margin is linked to the quality factor of a second-order system. Check how to read these data on Bode but also on Nyquist plots. Learn what modulus and delay margins are. Understand the importance of output impedance and the way to shape it via the right crossover frequency.

**Chapter 4**: we now enter the world of compensation: how to shape the return path so that my control system be stable, fast and precise. PID configuration are explored and I reveal the link between coefficients and poles/zeros placement. Nothing new here, but this is done step by step so that you can follow the path. A few examples put the PID at work and show that in some cases where Bode says it will be stable, the system isn't. Learn why and how to properly compensate your product.

**Chapter 5**: this chapter covers compensators using operational amplifiers. You will find type 1, 2 and 3 structures, with and without optocouplers. You have all the equations, ready to use. I even re-wrote the k factor equations for those interested in the approach. All derivations steps are detailed and commented.

**Chapter 6**: transconductance amplifiers (OTAs) are popular among the IC designers community. They are easy to design and require less die area than they op amp cousins. However, the set of equations you have for op amps does not readily apply. I have re-derived all the design equations in this chapter. Even if you add an optocoupler, it is covered. Also, I explain why it is difficult to build a type 3 with an OTA and what are its limitations.

**Chapter 7**: the TL431 is the most popular elements found in todays power converters. Hosting a precise reference voltage and an open-collector op amp, it is a remarkably well-crafted device. Actually, op amp and reference make only one and the transistors arrangement was made by a genius designer! Check TL431 internals and learn how to use that component to build type 1, 2 and 3 compensators with an optocoupler.

**Chapter 8**: TOPSwitches from Power Integrations are very popular high-voltage switchers. Rather than hosting a voltage control input, these devices are sensitive to injected current as a means to control the duty ratio. Again, previous equations no longer fit and I have reworked them all for the classical compensator types.

**Chapter 9**: bench measurements are mandatory when you deal with control systems. It is important to verify that all hypothesis you made during the design phase lead to the expected phase and gain margins on the real prototype. And a prototype is a real piece of hardware, not a SIMPLIS simulation bench, please! In this chapter, I explain the theory behind closed-loop measurements and where to be careful for reliable measurements. Then follow 5 design examples, putting theory at work.

The book starts to explain loop control theory in a very basic approach, "with the hands" as we say in French. Then, the following chapters go deeper into the theory you need to know as a power supply engineer. There is some mathematical content but there are a lot of examples that show how to put the theory at work. This is a strength of the book to my opinion: it bridges theory that you have learned at school with what you will face in your engineering challenges. For instance, we all learned how to build a compensator with an op amp (I still have my class documents) but how do you apply that knowledge to a TL431, a Transconductance Amplifier or a Shunt Regulator? And what if you add an optocoupler? Throughout the pages, you will learn where phase margin comes from, how to select crossover frequency, how to efficiently compensate a control system and much more! I hope you will enjoy this new work that took me 3 years to write. As usual, almost all the equations were derived by myself with all the steps so that you can follow...and correct me if I am wrong!

There is no CDROM with that book but there are available simulation files that correspond to some of the book examples. These examples are simulated with Intusoft IsSpice and their demonstration version will certainly run a few of them. Didier Balocco was kind enough to translate some of these examples in LTspice. These are beta versions. If you have the time to translate the remaining examples, I will be glad to post them in this webpage.

Yes, I know it for fact, there will be errors and typos in the 1500 equations I derived in this book. The term derived is correct because I really worked almost all these equations myself. First, because doing so let me identify obstacles that I could teach you how to avoid them when you follow my steps. Second, copy/pasting equations or pulling them out of thin air is not my writing style as an engineer. I apologize in advance if you find errors, mistakes or typos in these mathematical expressions. Given their number and despite the care I put in chasing them, this is unavoidable. Please, let me know where these errors are and I will maintain an errata list (1st print, 2nd print), giving credits to people who found these mistakes. Merci d'avance ! (Thanks in advance).

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