# [015] Buck Converter with Voltage-Mode Control

### Introduction

In this article, Dr. Ridley discusses the problems in comprehending supposedly-simple power electronics circuits. A free piece of analysis software, the first in a series of six, is provided to readers of this column to help them with their power supply design and analysis.

### Modeling Power Supplies

The power electronics field is supposedly simple. We have circuits with maybe half a dozen major components in the power stage, and perhaps 20 more parts in the control loop. We use time-tested techniques like breadboards, oscilloscopes, and frequency response analyzers to measure quantities that we are supposed to be able to predict easily with either simulation or design equations.

Despite the apparent simplicity of the field, it rapidly becomes a bewildering place when you design your first products. There are countless books, references, papers and application notes which try to shed some light on the topics that are involved in design.

In teaching power supply design courses for the last 20 years, I constantly face challenges in presenting material that is up-to-date, accurate, interesting, and most importantly, of immediate practical use in the workplace. Engineers attending the courses are expected to immediately increase their productivity at work, and they do. One of the ways that practicality is kept to the forefront of training is by not getting weighed down with excessive equations.

When presenting courses and showing some of the waveforms or transfer functions of converters, I am constantly asked – do you have the equation for that? Some equations are in the notes I present, but most are in the design software that goes with the courses. Of course I have the design equations, but something has always prevented me from writing them all out. First, they are in the form of software equations, and it is a lot of work to extract them from their native format. But, secondly, I do not believe it would do a service to the engineering community to just provide the equations.

It is a strange fact that for the simple set of the three main converters, the buck, boost, and buck-boost (or flyback) there is no single publication that summarizes all of the design and analysis equations in a single place. It has been on my list of things to do for some time now to generate a complete set of equations and publish them as a poster for the basic converters operating in CCM and DCM, and with voltage-mode and current-mode control.

Texas Instruments once provided a wall chart which made some progress toward this, but it had omissions, out-of-date models, or did not cover all of the functions needed by a designer. It is still quite useful if you can find one.

### Too Many Equations

I have come to realize that the ultimate set of equations in a concise printed reference won’t happen, and finally last week I was able to put my finger on why. Christophe Basso has just published an update to his Switch-Mode Power Supply book [1] which is highly recommended as a reference to all those involved in power supply design. In this book, he has a thorough review of multiple different modeling techniques over the years, and he presents summaries, including many of the equations needed for design.

There are, in total, over 1300 equations in this book just to cover the basics of operation of our “supposedly simple” converters. Basso’s book is very much a practical volume and the equations in there are necessary to understand this field properly. When you have been in this field for a long time, there is a tendency to forget how much background is really needed to be an effective designer. At some point in your career, you need to go through these equations and understand where they come from, and how they impact your circuit. However, at other times, you want to get to the results as quickly as possible because you are subject to an aggressive schedule.

Fortunately, you don’t have to digest all the equations before you can design a converter. The big advantage of Basso’s book is that it provides Spice models on a CD so you can immediately get to work on your power supply. Understanding the equations can come later.

If you include other advanced aspects of power supplies – resistances that are frequency dependent and nonlinear, multi-output supplies, the intricacies of switching and high frequency snubber networks – the number of equations goes up by an order of magnitude. In fact, it’s worse than that, since many of the expressions for quantities become implicit equations that cannot be solved in a closed form.

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