Last modified: December 2023

Orange, my internet provider in France will stop hosting webpages for its subscribers in September 2023. This site URL will then disappear and I invite you to bookmark the new one already online: http://powersimtof.com/Spice.htm. A redirection should be active until September 2024.

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News: my new book The Fast Track to Determining Transfer Functions of Linear Circuits is out and available for pre-orders on the publisher site. Thank you to Ken Coffman from Faraday Press who has worked with the materials I provided to assemble a 267-page book. The book can be seen as a crash course on fast analytical circuits techniques or FACTs and includes 7 chapters. Providing solid theoretical foundations and a refreshing look at transfer functions, the book will help students willing to speed-up ac analyses of linear circuits but also seasoned engineers facing circuits they would like to study without diving back into their university books. Unlike other books on the subject, I purposely slowed down the pace and took baby steps via numerous illustrations to show how to quickly and painlessly find transfer functions.

The four first chapters teach what a transfer function is and how to assemble it the right way, in a compact and readable format. Chapter 5, 6 and 7 respectively cover 1st-, 2nd- and 3rd-order transfer functions in comprehensively-documented examples, softly starting from the simplest ones to more complicated structures. The book is truly a manual for students looking for an easy but rigorous introduction to solving transfer functions swiftly and painlessly, going straight to the expected results in the fastest possible way. It will also be a good reference for young or seasoned engineers having to quickly determine a complex transfer function. The table of content is here. Chapters are organized as follows:

Chapter 1: this chapter starts smoothly by introducing poles and zeroes and how they link with time constants. In this chapter, the 6 possible transfer functions are introduced with the concept of low-entropy expressions which consists of writing expressions in the most compact and insightful way.

Chapter 2: learn how to turn the stimulus off and identify a pole or a zero in a few seconds, without writing a single line of algebra! Because this is the beauty of the methods: in many cases, you will be able to write the transfer function by inspecting the network, without resorting to equations.

Chapter 3: zeroes take place in the numerator of a transfer function. Learn how you can find where they hide in a circuit just by identifying transformed shunts or open-circuits. SPICE will help you check your results and it is an invaluable tool to check your progress.

Chapter 4: in this chapter, you will discover how it is possible to reuse the denominator time constants for finding the zeroes in the numerator. The generalized transfer function is very useful in complicated circuit where a null double injection is difficult to run.

Chapter 5: this chapter is entirely dedicated to 1st-order transfer functions with all steps detailed to determine input or output impedances, gains etc. 29 examples are fuly documented.

Chapter 6: we are now entering the worlds of 2nd-order network, featuring two energy-storing elements. Many examples detail how to handle these circuits, mostly analyzed with simple sketches. 25 examples are illustrated.

Chapter 7: in this last chapter, I have documented 10 examples of  3rd-order networks using FACTs. You'll be amazed how writing the transfer function of 3 cascaded RC networks only takes a few minutes!

As with the previous books, I will collect comments and findings from readers to gather them in the errata file.

The book is available from different channels. Stairway Press is the editor and they ship worldwide. Check-out their page below as the book is sold at a much better price than from on-line retailers!

Stairway Press

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After three long years of extensive work on this project, my new book entitled Transfer Functions of Switching Converters - Fast Analytical Techniques at Work with Small-Signal Analysis is available for purchase via the links given below.

The book starts with a smooth introduction to switching cells, going into the details of the first steps of linearization and small-signal modulation. You will then learn how the PWM switch model was derived and how to apply it to the basic structures operated in fixed switching frequency and various operating conditions like continuous and discontinuous modes in voltage- or current-mode control. The model is extended to other control schemes like quasi-resonance, constant on- and off-time converters, all with an associated small-signal version. The following chapters explore the founding structures like the buck, the boost and buck-boost cells, naturally covering their isolated versions like forward or flyback converters with many variations (push-pull, half- and full-bridge, phase-shift, interleave etc.). The last chapter deals with more complicated structures like Ćuk, Zeta, SEPIC and LLC.

The book represents an ideal companion for the young or seasoned engineer willing to study and stabilize her or his switching converter. Finally, BSEE, MSEE or Ph.D students will also find many useful descriptions and methods they can later apply during their studies or when facing their first industrial projects.

The book is printed in color and divided in five chapters with an appendix. The table of content is here.

 Chapter 1: you will find a guided introduction to small-signal modeling, why you need it and how to apply it. Once the foundations are laid out, the chapter explores the basic switching cells and determines their basic transfer characteristics like conversion ratios for isolated and non-isolated structures. Operating schemes like voltage- and current-mode control are detailed as well as quasi-resonance operation. The PWM switch model is then introduced and its small-signal model derived for future use in the subsequent chapters.

Chapter 2: this entire chapter is dedicated to the buck converter whose four transfer functions are determined for voltage- and current-mode controlled switching cells operated in the two conduction modes, CCM and DCM. Quasi-resonance is not forgotten as well as more exotic modes like COT and FOT or even the tapped version. Isolated versions are described such as push-pull, half- and full-bridge versions as well as active-clamp.

Chapter 3: the boost converter increases the input voltage and can be found in many applications like dc-dc and power factor correction circuits. The chapter starts with the dc-dc version and determines all the needed transfer functions as in the buck converter case. After the description of the tapped version, the boost operated in quasi-resonant current-mode version is also detailed. Finally, power factor correctors working in boundary control mode are described and operated in application examples.

Chapter 4: the buck-boost converter is well known when operated in its isolated version, the flyback converter. In this chapter, you will enjoy determining the four transfer functions of the buck-boost converter and extend the analysis to the flyback version. The popular quasi-resonant version is not forgotten and described in the book. Finally, single-stage converters are also popular and part of the descriptions.

Chapter 5: this final section deals with more complex higher-order converters like the Ćuk, SEPIC, Zeta and LLC. The analysis gains in complexity and the simulation examples help verifying the results analytically obtained. An LLC transfer function is proposed for the VCO-based control while the more recent current-mode version is also explored

Appendix A: this appendix can be seen as a crash course to let you discover the fast analytical circuits techniques and acquire a basic set of skills to understand how I derived all these transfer functions. Mastering the tool will require more efforts but the companion books given in the reference should let you strengthen your knowledge for a complete and firm acquisition of the method.

As with the previous books, I maintained an errata file you can download here.

The book is available from different channels. Stairway Press is the editor and they ship worldwide. Check-out their page as the book is often sold at a better price than from on-line retailers!

Stairway Press    Amazon (US)  Amazon (Canada)  Amazon (Germany)  Amazon (France)  Amazon  (Japan)  Amazon (UK)

Eddie Aho on his YouTube channel Kiss Analog published a video describing the book content. Merci Eddie!

You can read a review of the book published in How2Power and written by Dennis Feucht.

Free SIMPLIS Simulation Files: when writing this book on transfer functions, I have extensively used SIMPLIS to confim the results obtained with Mathcad and SPICE were correct. The many hours spent in simulating transfer functions of various converters lead me to aggregate all the circuits in ready-to-simulate templates which, for most of them, can work on the free demonstration version Elements. From simple dc-dc cells to more complex isolated converters operated in current- or voltage-mode control and controlled in fixed frequency, phase shift, COT, FOT and so on, you will find in these files converters that are fully compensated with an automated macro for computing type 2 or 3 compensation parameters. The description PDF is here while a ZIP of all the converters is here.

Mathcad calculation files: I have used many sheets to verify my calculations and illustrate the book examples. I have gathered 42 files described here and made them available for a small fee for company/professional individuals (150 USD or 140 Euros) and students/hobbyist (60 USD or 50 Euros). The files work with Mathcad 15 and include auto-toggling CCM/DCM compensation sheets for flyback and forward converters operated in current-mode. I will transfer the compressed file via a specific link to your address. Please write me to proceed, thank you.

 关于书籍(Transfer Functions of Switching Converters - Fast Analytical Techniques at Work with Small-Signal Analysis，中文版：开关变换器小信号建模-基于快速分析技术)中的Mathcad计算文件，我一共设计了书中的42个计算文档，并通过仿真进行了验证，同时提供给相关人员使用。对于工程师购买价格为120美元或100欧元，学生购买价格为60美元或50欧元，使用软件为Mathcad 15，包括各种控制模式，各种工作模式下的补偿计算表格，涵盖Buck: CM, VM, DCM/CCM, FOT, COT, QR Buck-derived: forward, tapped, push-pull, phase-shift full bridge，Boost: CM, VM, DCM/CCM, QR, PFC Buck-boost: CM, VM, DCM/CCM Buck-boost-derived: flyback, single-stage PFC SEPIC, Zeta, Cuk and LLC等各种电源变换器环路补偿计算表格 (图片)

如果您想购买Mathcad 15文件，请联系我的朋友Eric Wen-文天祥(eric.wen1984@qq.com)，他将指导您进转账汇款和文件资料发送等相关事宜。

谢谢，我希望你会喜欢这本新书！

I wish these models and files help you in your daily work whether you are a student, a beginner or a seasoned designer. Let me know if you have suggestions or comments, I'll be happy to discuss with you all.

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My previous book describes how to apply fast analytical circuits techniques (FACTs) when determining linear circuit transfer functions and is available from Wiley via numerous distributors. It is an excellent companion to my new one on transfer functions of switching converters. You will learn how to analyze simple to complex linear circuits by determining the circuit's time constants in different configurations. The idea is to split a complex circuit into small sketches and solve them independently. Then assemble the results to form the complete transfer function. The book is published by Wiley in the IEEE press imprint. Each chapter is offering 10 fully-documented problems so that you can check if you have acquired the skill. This book is currently being translated into French and should soon be available in that language. If you have contacts for publications in German, Italian or Spanish, I am open to suggestions. The French edition has been released in 2017 and the Chinese version is now available.

The front cover is shown below:

There are 5 chapters, gradually introducing you to the technique. The Table of Contents (TOC) is here.

Chapter 1: it is an introduction with generalities on time constants and transfer functions. You will learn how to determine the resistance driving a capacitor or an inductor by looking into the component's terminals. Through a refresh on classical theorems, you will see how you can simplify circuits analysis and smoothly enter the world of Fast Analytical Circuits Techniques (FACTs).

Chapter 2: this chapter starts with the definition of a linear system. What are the mathematical differences between a linear and a non-linear circuit. Time constants are introduced and linked to the forced and natural responses of a circuit in the time domain. Transfer functions are formely defined with various polynomial forms up to the order n. The 1st-order generalized tranfer function is given in this chapter.

Chapter 3: the Extra-Element Theorem (EET) is defined the way I understood it, with many simple drawings to teach how it was derived by Dr. Middlebrook. Null double injection is explained in this chapter with a method to verify your calculations using SPICE. Numerous simple passive and active circuits examples follow to show the power of this theorem. A simple variation of the theorem leads to the generalized transfer function of a 1st-order system, identical to that given in Chap. 2 but following a different path. Using this generalized form, you do not need to go through the null double injection and it amazingly simplifies the determination of transfer functions for any 1st-order networks.

Chapter 4: this chapter is entirely dedicated to passive or active 2nd-order circuits, built with op amps or transistors. The 2-EET is defined and a simple method is detailed to obtain transfer functions swiftly. Once the skill is acquired, you can determine some of the transfer functions without writing a single line of algebra!

Chapter 5: we enter 3rd-order circuits and above, using a generalized transfer function formula. Learn how you can determine op-amp based filters transfer functions by calculating time constants in various configurations. By breaking a complex circuit into smaller and simpler configurations, you can determine the transfer function of a complex circuit efficiently. By using SPICE in each step, you can verify your results and correct a mistake at any time in the derivation.

Google books offers a preview here. There is a book review here and PET published an excerpt here. How2Power also published another review in the July 2016 issue. The September 2016 IEEE newsletter has published a product news.

Each chapter ends with 10 fully documented examples/problems. All corresponding Mathcad files are available here. I maintain a list of identified typos here.

There are more than 70 fully solved examples of transfer functions from 1st to 4th order, active and passive. The complete list is here.

The book is announced on the below sites and the IEEE site also with separate download links.

Amazon (France) Wiley (UK)  Amazon (Germany) Amazon (US)  Amazon (Japan) Amazon (Italy) Amazon (UK) TMALL (China)

The French version has arrived! La version francaise est arrivee et est disponible chez Dunod depuis mars 2017. Voici l'avant-propos du livre decrivant son contenu. Amazon distribue le livre.

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Switch-Mode Power Supplies: SPICE Simulations and Practical Designs, second edition is now completed and the book has been sent to the printer. It took me a while to clean all typos, errors and bad drawings that you, readers friends, have been kind enough to report. The final listing for the 1st edition is posted here. So, what do we have in this second edition? Well, some chapters have been expanded, some simply cleaned up. Here we go for the detailed list:

Chapter 1: the complete derivation of all rms currents in CCM or in DCM for the power switch, the inductor, the diode and the input/output capacitors is now fully documented. All formulas have been tested and several Mathcad files will be available on the editor site to let you calculate these data depending on your design. Not only rms currents are calculated, but also the various time durations in DCM for instance. Convenient tables summarize constraints at the end of each subsection.

Chapter 2: on top of the classical PWM gain derivation, a feedforward small-signal block has now been described. The complete small-signal model of the PWM switch operated in current mode has been added and simulated. Duty ratio factories have been described to show how you can get the ac response of a DCM or a CCM current mode converter with a voltage-mode model by adding a single in-line equation to the existing model. Sub-harmonic instabilities are not predicted but low-frequency response for both modes perfectly agrees with that of higher order models. For those interested in small-signal modeling, I added an appendix in which I derive the ac response of a voltage-mode boost converter operated in DCM. You will see that despite previous SSA prediction, DCM converters are still second-order systems whose quality factor is simply much lower than in CCM.

Chapter 3: the compensator section has been expanded with OTA transfer functions for type 1 and 2. A complete TL431 bipolar-based model has now been included in this new edition

Chapter 4: some new SPICE blocks have been described and in particular, a corrected D flip-flop which is now more robust to forbidden input states.

Chapter 5: clean-up of the existing section mainly

Chapter 6: I have included a complete small-signal analysis of a BCM PFC stage when operated in current or voltage mode control. I also added a section letting you predict what the bulk minimum voltage will be when you have selected a normalized capacitor. This is important to know this bulk valley voltage as the converter will have to pass 100% of the power while in this input range.

Chapter 7: this chapter now includes a complete explanation of the over power phenomenon in flyback converters operated in CCM, DCM or in quasi-resonance (QR). Over power protection or OPP, is an important part of the flyback design. It is there to compensate the extra output power (hence current) a flyback converter will deliver when supplied from its highest input voltage. If no precautions are taken, risks of fire or destruction exist. This new section explains the origin of this output power runaway and how to compensate it. Small-signal has not been left aside and a small-signal model of the QR flyback converter in current mode is presented. A section showing how to account for the nonlinear variation of the Coss capacitor has been added as well as a simple laboratory circuit to check for transformer saturation.

Chapter 8: the complete transfer function of the active clamp forward converter operated in voltage mode has been added with step by step derivation as well as tests a against prototype response. Compensation details for a 30-A dc-dc are also offered. The coupled inductor small-signal response has also been revamped thanks to comments from a sharp reader.

There is no CDROM in this new edition, most of the files are available on line. They are here. Please note that I distribute another set of files which includes all the book examples plus the UC384x models with ready-made examples. The CADENCE OrCAD PSpice listing is here and you can write me to know the price of this library.

Mr. Jean-Marie Merienne has kindly translated the book's Mathcad files from version 15 to Mathcad Prime. You can download the PDF versions and the working files.

The book distributors

Amazon (France)    Amazon (US)    Amazon (Canada)    Amazon (Japan)    Amazon (Germany)   Amazon (UK)

Amazon (China)    Dang-Dang (China)

Comments, feedback and corrections: I keep a correction file in which I compile your findings and comments. The file is here and will be updated when needed.

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Designing Control Loops for Linear and Switching Power Supplies: a Tutorial Guide is now available for sale. This new book took me three years of work, every night. It first started in 2009, I wanted to write an exhaustive text on how to design compensators for power supplies. Operational amplifiers (op amps) were first on the list, but I then realized that there was many other types of active elements that could be used to perform this function: TL431, operational transconductance amplifiers (OTA) and shunt regulators like in the TOPSwitch (Power Integrations) series. If literature abounds on op amps, there are few documents on TL431, OTAs and TOPSwitches, but all scattered in application notes sometimes difficult to find. I have dedicated an entire chapter for each of them, even detailing TL431 internals. Of course, there are non-isolated and isolated versions with an optocoupler.

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.

Simulation files:

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.

Feedback

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).

The book distributors:

Amazon (France)    Amazon (US)   Wallmart (US)  Amazon (Canada)    Amazon (Japan)    Amazon (Germany)   Amazon (UK)    Barnes & Noble  

Amazon (China) Search JD (China)

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If you want to read my interview by EEWeb, please follow this link. I'm sure some of you will recognize the guy in the wall poster : )

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Switch-Mode Power Supplies: SPICE Simulations and Practical Designs was released in 2008. Another book on power electronics you say? Not really. In the technical literature, you either have books that are purely academicals and offer in-depth analysis of converters, unfortunately without the essential links to the market reality. You also have purely practical books that pull equations out of thin air without any theoretical grounds. This book bridges both approaches and will hopefully please the power electronics student and the design engineer, both looking for analytical explanations but also for practical solutions when facing customer demands. This book is really about power supplies designs, with SPICE as a design companion. It covers dc-dc but also ac-dc converters. By the way, the ac-dc conversion in offline converters is made by the diodes bridge and the capacitor, the downstream converter is always a dc-dc, isn't it?

Press release for the book announcement in French, English, German, Mandarin and Japanese!!

(Xie-xie to Patrick Wang and arigato gozaimasu to Iguchi-san!)

The book is now available in simplified Chinese and Korean. Thank you to Mr Zhangde Lu who translated the whole book in a record time! Mr Lu is a  teacher in Shaoxing university in China. The book is available from Publishing House China and Chinese links are posted below.

The book is organized in eight chapters covering the following subjects:

Chapter 1: this chapter starts with the basics of dc-dc conversion, step by step with linear regulators used to derive essential formulas such as closed-loop impedances or closed-loop input rejection. Then the classical buck, boost, buck-boost are analyzed in CCM/DCM and critical modes until an input filter is added. There, you will discover the effects of the filter insertion and learn how to compensate the converter while still attenuating the input noise (95 pages).

Chapter 2: small-signal modeling is really an important topic if you want to be serious about power supply designs. The chapter starts by showing what State Space Averaging is all about and how complicated it can be. Then, the PWM switch model is introduced and three new versions are derived: auto-toggling DCM/CCM voltage-mode and current-mode models, with sub harmonic prediction in CCM for the later. Of course, these models are large-signal ones and operate in dc, ac and transient analysis. Finally, a borderline model is derived, later used in PFC stages. This 100-page chapter really explains how these models were derived and how to use them for your studies (146 pages).

Chapter 3: loop control is always hard to understand for some new comers. I've strived to make things look simple, explaining how the k factor was derived and showing that, sometimes, it is not a panacea. I propose different equations to let you manually select the poles and zeros, crossing over at the exact desired frequency. Also, in most of the books, only op amps are used to illustrate compensation. In this book, I derived the transfer functions of TL431-based type 2 and 3 compensators and I showed how the optocoupler pole can affect the phase margin (100 pages).

Chapter 4: this is where you will learn how to build your basic subcircuit blocks and how to construct your new models, if necessary. For instance, how to model the error amp of the UC384X family. Understand the differences between syntaxes and learn how to write in-line equations. A section specifically details the derivation of a magnetic model, based on non-linear junctions. See how to wire generic PWM models in various configurations for the best simulation speed. Learn how to extract physical data from a transformer to later pass them to a subcircuit (66 pages).

Chapter 5: in this chapter, we cover the design of dc-dc converters, the classical structures, in both voltage-mode and current mode configurations. There are small-signal analysis and transient studies in all cases The front-end filter section is also analyzed with input ripple specification targets (84 pages).

Chapter 6: rectifying the sinusoidal mains is a section common to all ac-dc converters. After all, the diode bridge and the capacitor are the elements that really perform the ac to dc conversion. The downstream converter is still a dc-dc, no? This chapter covers the classical diode bridge configuration then further introduces passive power factor correction, quickly followed by active power factor correction. The most popular topologies are covered and there are several design examples. An extensive usage of the average models is made here, leading to extremely short simulation times (88 pages).

Chapter 7: it is time to describe the isolated buck-boost also called the flyback converter. This chapter covers a lot of techniques pertinent to the flyback converter, what is the leakage inductor role, how it affects the drain voltage excursion and how you can use its presence in active clamp versions etc. The design section contains useful tricks to limit the converter power capability at high line for instance or to compensate the leakage spike on the auxiliary winding. There are three design examples, among which a multi-output borderline converter using the new BCM average model, also described in the book (160 pages).

Chapter 8: the forward converter is widely used in ATX power supplies (the so-called silver box) where the 2-switch configuration excels in 250 to 400-W applications. The chapter explores the various reset methods and introduces you to multi-output configurations through mag amps, or synchronous rectifiers. A complete design example is proposed at the end of the book (129 pages).

CDROM: the CDROM found with the book contains some of the most popular demonstration versions of currently available simulation softwares. I strived to give away almost all the examples of the book in OrCAD/PSpice and ICAPS/IsSpice formats. Some of the distributed versions also feature examples kindly translated by the software editors themselves. This is the case for uCap, TINA, Multisim, B2 Spice, 5Spice. Other demos include Power 4-5-6, Transim and TopSpice. I updated the Excel file dedicated to the k-factor to which TL431-based configurations have been added.

Download the Table Of Content

Distributed libraries:

I purposely created specific application circuits that are not given away with the book. The library I am separately distributing includes the UC384X (UC3842/UC3843/UC3844/UC3845 SPICE models)  precisely modeled and implemented in a lot of application examples. The same applies for Power Factor Correction circuits, ready to go on several platforms. The library and application circuits are available in different formats that are Micro Cap, TINA, OrCAD and IsSpice. You can download an application listing to check what is inside these libraries - also available for TINA and  Micro Cap - OrCAD or IsSpice. Please drop me a line to my address: cbasso@wanadoo.fr ("SPICE library" as the subject ) to learn about this package and how to get it. I am currently setting up a distribution network for these files.

I also have participated to the development of a more comprehensive library file with AEi Systems. There are currently more than 200 PWM IC models in this file and you can obtain a detailed quotation and information via this link.

So what?

Yes, I know, there is place for more and there are subjects that I did not cover. However, this last book took me three years to finish and I felt I was writing a new never ending story... : ) I therefore kept interesting stuff for a next edition, in a few years from now. For instance, I will show where the phase margin value come from and how to analytically link the crossover frequency and the phase margin to the converter output impedance.

Feedback

Please, forgive me in advance in case you find errors, mistakes or typos, despite all the efforts in trapping them, there might still be some left, even further to thorough corrections ran by numerous reviewers. I have maintained a list of collected remarks, with credits to authors that have found them! The corrections file for the first edition is here, compiling all errors and mistakes previously published.

Reviews

The US IEEE Power Electronic Society has reviewed my book and published its comments in the PELS April newsletter.

A review from Design/Analysis Consultants, Inc. where the book is recommended!

An excerpt has been published online in Power Management Design line.

The book appears in the "Best Power Supply Design Books" directory in SMPSTech webpage

Dr. Yan-Fei Liu from Queen's University (Canada) published a review in the Canadian section of IEEE.

The book was one of the best sales for technical books at ISSCC Conference 2009. Read this excerpt.

The book distributors:

Amazon (France)    Amazon (US)    Amazon (Canada)    Amazon (Japan)    Amazon (Germany)   Amazon (UK)    Barnes & Noble  

DangDang (China)    Amazon (China)  Infibeam (India) FriendsOfBooks (India)  Fishpond (New-Zealand)    Fishpond (Australia)   

There are several reviews you can read in the Amazon US website to learn about the book acceptance by engineers.

Presentations and papers to download

Ohmpilot ac-to-ac converter: I have recently installed a 3-kW solar generator in my garden and I wanted to store the surplus of energy elsewhere than in a battery. I have found the Ohmpilot from Fronius was a cool solution to implement. It basically adjusts the ac voltage applied to a boiler resistance from 0 to 230 V rms in relationship to the excess of energy. Unlike triac-based dimmers, the inverter implements an ac-to-ac buck converter that I simulate in the PPT. And it works well as the graphs in the end of the document show. The French version is here.

Loop compensation for the NCP1680: in this short document, I show how I did simulate the digital compensator found in the NCP1680 and NCP1681 totem-pole PFCs.

Introduction to Loop Control with TL431: this is a seminar I presented in a 2015 Asian tour and I found it worth posting for new comers.

Compensating a buck converter with a type 3 OTA: I have often seen application notes in which an OTA was compensated like if it was an op-amp: stay away from this option and learn how to properly build a type 3 with an OTA provided you understand where the limit is.

Dc-shift compensation of a DAB converter: further to the seminar I proposed about the DAB converter, I realized that the insertion of a dc-block capacitor can be costly and impractical in many cases. Especially in bidrectional converters where two capacitors are needed. The method I have simulated is the analogue implementation of a digital approach described in this paper.

PCIM 2023 - I was presenting a poster on Thursday the 11th of May in Nuremberg and this is the presentation I built. It described the implementation of a 500-W LLC digitally controlled with an STM32G4. The loop combines a cheap analogue front-end integrator built around a TL431 and an optocoupler to which a pole-zero pair coded in C is added in the non-isolated side.

Type 3 compensator for the TL494: Some people still use the TL494 PWM controlller which is well suited for push-pull applications considering its two complementary outputs. Unfortunately, the two on-board op-amps are ORed in such a way that you need to wire them in a non-inverting configuration for regulation purposes. As I could not find design equations for a type 3 in this mode, I derived a transfer function and applied it to a buck converter.

Transfer Function of a CLLC Converter: This is a good example showing how the fast analytical circuits techniques or FACTs can help determine the transfer function of a 4th-order system painlessly without writing a single line of algebra.

Introduction to the DAB: This introductory seminar offers an overview of the dual-active bridge converter or DAB and explores the stress endured by the switches and the output capacitor.

Writing Guidelines: Proper writing is part of engineering excellence and there are rules you must obey when you work on presentation materials or write an article. This guide has been written by my late friend and former colleague Chuck Mullet. It will teach you how important it is to insert a space between the number and the unit (3 A, 2 kW and not 3A or 2kW) or write ac-dc or dc-dc converters (all lowercased, with a dash and not a slash). Something I also underlined in my document on presentation skills.

Seminars List: This is the list with clickable links of all the seminars I built with an abstract so that you can choose one knowingly.

I took the above picture in Lise and Larry Meares's house, back in 2004. Dr. David Middlebrook is seating left, then his wife Val and Larry in the back. I remember Dr. Middlebrook as a kind person, always open to explain things with the soft voice he had. At that time, David and Larry worked together to adapt the general feedback theorem (GFT) to ICAPS, the simulation suite of Intusoft. I value these moments of complicity around a good meal and friendly discussions with people I was fortunate to meet. 

Introduction to Power Factor Correction: This short seminar gives an overview on power factor correction, where it comes from and what are the currently-available solutions. Many examples with simulation results are proposed in this document.

Control Methods of LLC Converter: This 90-mn seminar offers an introduction to LLC converters without entering into design details. Then the document reviews some modern control techniques like charge control or current-mode control.

Introduction to Switching Power Supplies: This is a new 90-mn seminar I recently built for new comers to the switching world. The document smoothly starts with linear regulators and then goes through the basic switching cells and their isolated derivatives.

Simulating with SIMPLIS: This seminar offers an introduction to the simulation of switching converters using SIMPLIS, a piece-wise linear simulation engine offering lightning-quick simulation time which can extract the small-signal ac response from any switching circuits. I used this program extensively in my last book on transfer functions. For those interested by the subject of simulation, this seminar from Vicor is well documented.

Starting with Elements: Elements is the free demonstration version from SIMPLIS and lets you simulate many circuits including isolated switching converters. You can also download the version including notes where you can read the comments going along with the slides. A good companion for my last book on transfer functions!

The TL431 in Switching Converters: I built this seminar for an Asian tour back in 2009 and it describes how to use a TL431 in the classical compensators types like 1, 2 and 3.

SPICE Predicts Differential Conducted EMI: I remember publishing this article in EDN, in 1997. I was describing how you could use a SPICE simulator to predict the conducted noise signature of your switching converter and see how the filter could be accordingly designed. The on-line version does not print pictures which is a problem. You can find the PDF version with pictures here.

APEC 2021, 3-hour professional seminar held on line, C. Basso: this new seminar focuses on loop compensation using analogue and digital compensators. It starts with compensation strategies built around an op-amp and later extended to a TL431. The PID is explored and in particular saturation effects. Finally, the remaining presentation offers a smooth introduction to the digital world and shows how to implement digital filters starting from a Laplace expression. Oh, by the way, it is my last presentation with ON Semi as the company recently fired me as part of a cost-reduction program - Hasta la Vista, Cisco Kid!

Compensators in SIMPLIS: look at these types 1, 2 and 3 with automated compensation values around op-amps or a TL431 for the type 2 and an optocoupler. I have recently updated the examples with type 2 and 3 implemented in a digital way in SIMetrix or SIMPLIS. A digital PID is also there and all these compensators automatically compute the digital and analogue coefficients to meet the design criteria.

Measuring the loop gain from the output impedance, C. Basso: this is an attempt I've recently tried first by looking at the theory but, unfortunately, I did not find the time to pursue my experiments. These papers from Ridley and Gunma University can be consulted for more practical aspects. This method is not a substitute to regular stability measurements and can even lead to wrong results if probing is incorrectly done.

The impact of the current loop crossover on CM instability, C. Basso: read how the small phase margin in the inner current loop brings instability in a current-mode-controlled power supply. I have also detailed how the feedforward gains of Ridley's models were determined here.

A small-signal model of the RPM buck, C. Basso: the constant-on-time (COT) converter keeps a constant on-time while the off-time is adjusted for regulation purposes. In current-mode control, the inductor valley current is set by the control voltage. A variant has been patented in 2009 which allows a dynamic adjustment of the on-time when a transient occurs. This is the ramp pulse modulation (RPM) concept and I have determined its transfer function in this PPT using the PWM switch model.

Importing SIMPLIS plots in Mathcad, C. Basso: this file teaches you how to import ac data obtained with SIMPLIS into a Mathcad file for response comparisons. The examples are here. Thank you to Simon Tian for showing this.

A multiplier with SIMPLIS, C. Basso: you cannot dynamically multiply variables in SIMPLIS without resorting to a log-based circuit. Nothing complicated once you have the subcircuit.

A 6th-order transfer function with FACTs, C. Basso: I show in this PPT how to derive the transfer function of a 6th-order Bessel filter made of cascaded cells. The Mathcad sheet is in the ZIP file.

A 5th-order transfer function with FACTs, C. Basso: I show in this PPT how to derive the transfer function of a 5th-order filter made of cascaded RC cells. The Mathcad sheet is in the ZIP file.

Over power Protection in the forward converter, C. Basso: this document details how a forward converter can possibly deliver more power at low line than in high-line conditions. The associated Mathcad 15 file is here.

APEC 2019, 3-hour professional seminar held in Anaheim, CA, C. Basso: this seminar describes the modeling of buck converters operated in different control schemes with the four transfer functions of the CCM buck converter presented as examples. SPICE, SIMPLIS and, finally, bench experiments are shown along the examples to confirm theory matches reality. I have purposely built demonstration boards showing how experimental results agree well with the simulations if you properly characterize some of the components. The audience was between 100-150 people and I was really happy to see you all again. Thank you for attending this session and see you next year in New-Orleans!

Switching-Converter Dynamic Analysis with Fast Analytical Techniques, C. Basso: this document is a quick introduction to the fast analytical circuits techniques or FACTs and apply them to a DCM-operated SEPIC. It was published in the IEEE Power Electronics Magazine from September 2017.

The video of my tour in China, in 2018: it was a great experience, coached by the friends of 21DianYuan, I gave speeches in four big cities in China, starting with Beijing, Xi'an, Shanghai and Shenzhen across a 10-day tour. Very pleasant experience and many readers I was happy to chat with. I signed many copies of my books as the below pictures show.

APEC 2018, 3-hour professional seminar held in San Antonio, TX, C. Basso: this seminar describes how to obtain the control-to-output transfer function of a converter using small-signal analysis, average model SPICE simulations, SIMPLIS and, finally, bench experiments. I have purposely built demonstration boards showing how experimental results match well with the simulations if you properly characterize some of the components. I used the FACTs to determine the transfer function of the boost converter in voltage-mode control. The audience was between 100-150 people (statistical data here) and I was really happy to see you all again. Thank you for attending this session and see you next year!

FACTs applied to a type-3 compensator, C. Basso: this document details how to derive the transfer function of the type 3 compensator when the open-loop gain AOL is involved. The Mathcad sheet is here.

Current mode simulations with VM-PWM switch, C. Basso: this document shows how you can re-use the original voltage-mode PWM switch model and by adding a simple resonating capacitor, turn it into a current-mode model able to predict sub-harmonic oscillations in CCM with dc and transient capabilities. It uses the models ported to LTSpice by Didier Balocco (see several lines below for download) and builds on experiments kindly done by Mark Dimattina. The LTSpice files are here.

APEC 2017, 3-hour professional seminar held in Tampa, FL, C. Basso: this presentation focuses on interactions between an EMI filter and a switching converter. Fast Analytical Circuits Techniques are at work here and they truly simplify the analysis. I was happy to see some known faces again and hope the new ones enjoyed the show. 108 people were registered for this seminar. The seminar slides are here and the statistic here. Thank you all!

Op amp interaction with Type 2, C. Basso: this Mathcad 15 file shows the impact of the op amp open-loop gain and its two low- and high-frequency poles in a type 2 compensator. It is usually not a problem for low crossover frequencies but as soon as you need gain and phase boost at values at or beyond 10 kHz, the GBW product matters. The PDF is here.

APEC 2016, 3-hour professional seminar held in Long Beach, CA, C. Basso: this presentation introduces you to Fast Analytical Circuits Techniques which let you derive transfer functions in a quick manner and sometimes without writing a single line of algebra. The method is at work with two switching converters, the buck and the buck-boost in voltage mode. The seminar went well and I thank you all in the audience! Statistics of this seminar are here.

Small-signal response of QR flyback with multiple valley switching, C. Basso: this paper studies the dynamic response of a current-mode flyback converter operated in boundary mode and switching in different valleys.

Leakage inductance effects in the flyback converter, C. Basso: this 3-part article originally published in How2Power.com describes how the leakage inductance affects the conversion ratio of a flyback converter by truncating the duty ratio. Power dissipation via the clamping network also damps the control-to-output response as modeled through a new average circuit.

Zeta converter with the PWM switch, C. Basso: this short PPT shows how you can wire the PWM switch model to simulate the control-to-output response of a Zeta converter.

APEC 2015, 3-hour professional seminar held in Charlotte, NC, C. Basso: this presentation capitalizes on what has been discussed during previous seminars and bridges theory with practical results. For instance, what is the impact of an op amp slew-rate and GBW product on phase margin for instance? How to ensure clean start-up sequences on isolated dc-dc converters? These are among the few topics I tackled during the session. Again, thank you all for attending! Statistics about this seminar are here.

Small Signal Modeling of the Boost Converter Operated in CM, C. Basso: this seminar shows how to derive the control-to-output transfer function of the boost converter operated in peak current mode control.

Active Clamp Forward in Current Mode, C. Basso: this short PPT shows the ac simulation results I was able to obtain with my voltage-mode model to which a duty ratio factory was added. Results are not far from what Simplis predicts.

Duty Ratio Factory Modeling in a CCM CM Buck Converter, C. Basso: this presentation shows how to independently model the control voltage Vc to duty ratio D block in a current mode converter. The presentation shows that by using a voltage mode stage to which a separately-modeled Vc-to-D is added, you obtain the complete control-to-output transfer function of the CCM CM buck converter.

APEC 2014, 3-hour professional seminar held in Fort Worth, TX, C. Basso: this presentation shows the PWM switch models at work in various converter structures. Fixed switching frequency in voltage and current mode is described but borderline conduction mode is also demonstrated. This presentation also introduces the small-signal model of the active clamp forward converter operated in voltage mode control. The model is then compared to bench measurements. The audience peaked to 150 people during the show, thank you all for attending! Statistics are here.

Presentation skills, C. Basso: I have been teaching and speaking in front of an audience for a while now. My first speech, which goes back 20 years, was a complete disaster: trembling voice, shaky legs and so on. I made the obvious mistakes untrained people do and with time, I started to improve by learning from professionals. I also took several presentation skills classes (Decker training was excellent) and I improved over years. At least I hope I did : ) For those who need to present, I compiled most of the mistakes you must avoid to make your speech efficient and credible. I have one in French as well.

Small-signal analysis of the fixed current mode variable frequency flyback converter, C. Basso: this presentation teaches you how to derive the transfer function of a flyback converter operated in constant peak current while switching frequency is controlled. This technique is now widely used in converters implementing frequency foldback in light-load conditions.

APEC 2013, 3-hour professional seminar held in Long Beach, CA, C. Basso: this presentation teaches step by step how to derive large and small-signal models of switching converters. The presentation starts by showing how to linearize non-linear equations and then describes models for voltage-mode and current-mode CCM/DCM converters. It extensively makes usage of the PWM switch model. A model of a QR flyback model is also presented. Merci to my friend Chris Warin for kindly taking the below pictures!

Introduction by Mrs Chen, chairman of the conference    Agenda of what I am about to present                                    There we go, the audience peaked to 200 people which is very rewarding, thank you all!

Genuine type 2 compensator with the TL431, C. Basso: this short document shows you that a real type 2 built with a TL431 and involving two lanes is not wired as a type 2 with an op amp: a single capacitor is enough across the TL431. Adding an extra RC is useless.

APEC 2012, 3-hour professional seminar held in Orlando, FL, C. Basso: this presentation teaches you some less known aspects of loop control theory applied to switching and linear converters. Things like delay margins, modulus margin or how a PID converts to a type 3 compensator. They were in this new seminar entitled "The Dark Side of Loop Control Theory". The seminar statistics are here.

This is me, together with Franki Poon from the PowerEsim website!

APEC 2011, 3-hour professional seminar held in Fort Worth, TX, C. Basso: this presentation teaches you the untaught aspects of the flyback converter. Things like Over Power Protection (OPP) or Quasi-Resonant small-signal compensation are rarely included in seminars. They were in this one, entitled "The Dark Side of Flyback Converters".

These are the covered subjects in the 3-hour time. The RHPZ presence in both CCM and DCM was explained to the students.

Calculating the bulk capacitor parameters in an offline converter, C. Basso: this paper updates the current book content by improving the formulas used to derive the bulk capacitor value in a front-end rectifying section. Nothing spectacular here but I realized that these results could help the design community to calculate the right value.

APEC 2010, 3-hour professional seminar held in Palm Springs, CA, C. Basso: this presentation teaches you how to design compensators based on TL431, op amps or OTAs. This seminar associated with that of 2009 represent the subject of my new book on loop control.

This is me, teaching how to derive the full analysis equations for a type 2 compensator with an op amp. There were more than 100 students in the room.

An average model for the phase shifted converter, C. Basso: this document shows how I built an auto-toggling average model for the phase shifted converter. The model exists in IsSpice but also in PSpice. Both average and generic cycle-by-cycle models are available in ready-to-use templates describing a 12-V/25-A power converter. They are part of the distributed library files.

APEC 2009, 3-hour professional seminar held in Washington DC, C. Basso: this presentation teaches you where phase margin and crossover frequency come from and guides through the stabilization process of a dc-dc converter.

I am on the left, on the ON Semiconductor booth at APEC 2009. The other fellow is my friend Larry Jenck.

Dealing with low-current optocouplers, C. Basso: this is an article I wrote in 2009 that describes how an optocoupler works and why you should always characterize its inherent pole. A method is offered to extract it quickly through a simple test fixture.

The TL431 in loop control, C. Basso: the TL431 is never studied as a part of the compensator in control theory  books.  However, this is a market reality, op amps are rarely used! Go through this new series of articles and learn how the TL431 works and how you can use it in a variety of configurations.

Selecting the cross-over frequency in relationship to the converter output impedance, C. Basso: this paper teaches how the cross-over frequency affects the output impedance of the converter you want to stabilize.

The link between the open-loop phase margin and the closed-loop quality factor, C. Basso: this paper explains the relationship between the open-loop phase margin you select and the resulting transient response you can obtain.

The PWM switch operated in Borderline Conduction, current-mode, C. Basso: this paper shows how to get the small-signal model of a flyback converter operated in the so-called quasi-resonant mode.

The RHPZ, a two-way control path, C. Basso: the Right-Half-Plane-Zero plagues the flyback or the boost converters operated in CCM. This paper explores the origins of the RHPZ.

Stability Analysis in multiple loop systems, S. Conseil, N. Cyr, C. Basso: a TL431 combines a fast and a slow lane. How to measure the total loop gain combining both lanes is the object of this paper.

"The PWM switch in transitioning models": this document was presented in PCIM 2005 and covers the history of SPICE models.

"The PWM switch concept...", PCIM 2005: this is the paper published in the PCIM proceedings.

"Quasi-Resonant SPICE model eases loop design", PCIM 2003: this model uses CoPEC approach to model a QR controller. There are two associated models, in PSpice and IsSpice.

"the forward converter small-signal gains": a short PowerPoint which shows how my new models match calculations in both VM and CM for a forward converter.

Analysis of Current-Mode Controlled PWM Converters Using the Model of the Current-Controlled PWM Switch: this paper from Vatche Vorperian was published in 1990 and is difficult to find.

New models to download

PWM Switch LTspice: Mark Dimattina offers a way to implement the PWM CM version in LTspice. Thank you for sharing your models Mark. The documentation is here.

PWM Switch LTspice: Byron Rogers kindly shares his PWM Switch model also intended to be simulated in LTspice.

TL431 models discussion: an interesting discussion on the TL431 and the performance of several available models.

New LTspice models: Didier Balocco has come up with a new series of LTspice circuits implementing the PWM Switch model in voltage and current modes. There are plenty of examples plus a quick installation guide. The files are here. Merci Didier !

LTspice models: Charles Denton has been kind enough to translate the PWM switch models in LTspice. Yes, it is obvious, you need a good book to understand how to use them... ;-)

It has been reported that parameter "K" could be mixed by LTspice with the Boltzman constant. To avoid this, please change "K" into "Kf" and it should work. Kindly pointed out by Dennis in March 2015.

VerilogA models: the PWM switch model working in VerilogA, nicely translated by Nico Cyr formerly with ON Semi.

VerilogA models: the PWM switch model working in VerilogA, a new model contributed by Rainer Krenzke from Dialog Semiconductor.

Flyback current-mode automated calculation spreadsheet: this is a new automated software which calculates the TL431 elements to stabilize of a flyback converter operated in peak current mode control. The software includes mode transition, sub harmonic poles and optocoupler pole contribution. Check it out!

Switch Mode Power Supply Cookbook - download files

SPICE editors links

Intusoft - OrCAD - TINA - PSIM - SIMPLIS - Electronic Workbench - MicroCap - TopSpice - 5Spice - Beigebag - NL5

SPICE sites and power supply sites:

Biricha : numerous videos from Dr.Ali Shirsavar of Biricha Digital talking about power supplies design

YouSPICE : a community for electronic design and simulation.

PowerEsim : if you want to design your power supply online, this is the link to follow.

How2Power : The newsletter to sign-up for if you are in power electronics. The site is maintained by David Morrison, former PET editor.

AEi Systems: a consulting engineering firm on SPICE modeling and worst-case analysis

Design/Analysis Consultants: a consulting firm specialized in worst-case analysis and design robustness

Power Electronics links with papers to download

Texas-Instruments / Unitrode Seminars

Delta Electronics Triangle Park

Colorado Edu: you can download papers published by Dragan Maksimovic and Robert Erickson (click on the tabs to access PDFs).

Ben-Gurion University

Dr Middlebrook documents related to his Design-Oriented Analysis course

Queens Power Group Publications

My previous books

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