Bullard - Distortion: The Cause Of Harmonics And The Lie Of THD

By Dan P. Bullard
A book that explains the cause of harmonic distortion in electronic circuits.

Copyright Dan P. Bullard 2015
All rights reserved
No portion of this book may be reproduced without permission of the authorSend requests to dan@danbullard.com
ISBN-10:1511628456
ISBN-13:978-1511628457

DDC 537
Disclaimer
The author has made every effort to verify the information contained herein; however, errors may exist. Neither the author nor the publisher, CreateSpace, are responsible for damages arising from use of this information.
Cover art: A circuit board distorted using Graphic Converters Glass Block tool.
Acknowledgements

The author would like to thank Skip Davis and Kars Schaapman of Applicos Measurement and Control for sponsoring the video and providing the computer that made this book possible. Thanks also to Bob Metzler of Audio Precision for the original inspiration for this project, and Don Greer of Maxim Integrated Products for setting the standard high enough to make me fully explain my findings. A special thank-you to Dr. John Michael Williams and Norman Abbod MSEE for proofreading. Thanks to David Reynolds who is always happy to chat with me on mixed signal and DSP topics and helped keep me on track. Thank you to Brent David Cartwright who painstakingly reviewed the book and asked lots of questions, which thankfully I had answers for. Also, to my lovely wife April, for patiently listening to my theories and speculations, and putting up with my O-Dark-Thirty experiments.

My biggest thank-you goes out to Bruce Tibbetts of Teradyne, who inadvertently inspired me to dig so deeply into harmonics and their true cause.
For my wife, my children, and my grandchildren
False facts are highly injurious to the progress of science, for they often endure longCharles Darwin, The Descent Of Man IntroductionA Misunderstood PhenomenonPage 1
Chapter 1The Cause of HarmonicsPage 3
Chapter 2WaveformsPage 25
Chapter 3Distortion Signatures - ClippingPage 39
Chapter 4Distortion Signatures - CrossoverPage 63
The Lie Of THDPage 79
About the AuthorPage 85 Introduction Harmonics - A misunderstood phenomenon

Harmonics are the bane of most engineers. When stimulated by a sinusoid, a perfectly linear electronic circuit should output a sinusoid with no additional harmonic content. Everyone seems to know this, but the source of the harmonics in a non-perfect circuit seems to elude us. What causes the harmonics to form? What circuit faults causewhich harmonics? Can I forgive a non-linearity knowing that the harmonics created will not impact my application? If I see harmonics can I get a clue to the problem I face fromthe harmonic signature?

Most texts on the subject make generalizations that are not very helpful. In Audio Precisions 1992 book The Audio Measurement Handbook, which I skewered in my YouTube video Audio Quality and Total Harmonic Distortion 1 the statements are made that:

non-linearities which are not symmetrical around zero produce dominantly even harmonics and
non-linearities which are symmetrical around zero produce odd harmonics

Both of these statements are wrong (for different reasons), and my video proved this. Other books dealing with the topic are similarly flawed and vague, a bad combination for some poor soul working late into the night trying to figure out how to fix a high THD failure in his circuit.

This book will show you exactly how harmonics are created by non-linearities, which commonly found non-linearities create which harmonics, and how a harmonic signature can be interpreted to correctly assign blame to particular non-linearities allowing the user to spend his time wisely in identifying and fixing non-linearities in his circuit.

The information in this book was gleaned from experiments performed with an Excel spreadsheet that replicates the function of a sinusoid applied to a theoretical transfer function that can be manipulated at will, as well as years of working with real electronic circuits and various DSP based tools during my long career in electronics.

Throughout the book you will find links you can click on with your E-reader, which is one reason I published this as an E-book as well as a print book. If you are reading the print book, select hyperlinks are listed at the bottom of the page as footnotes (see below). Text is nice, but I have gone to a lot of trouble creating videos that can say more in a few seconds than hours of reading, so please take advantage of these links while reading this book. Throughout the book it is assumed that you have, at the very least, watched the video listed in the footnote below, for this video holds the key to this very interesting story of discoverythe story of how I figured out how harmonics are created.Join me now and prepare to be permanently changed by this journey.

1http://youtu.be/CHfeMGQC6WI A note on graphics

Virtually all of the figures in this book are one of two types. Time domain plots like the one below display waveforms, in which the X axis is in samples; usually 2048, and the Y axis is in volts; usually from -1V to +1V. The X axis labels are displayed so that the reader can compute angles or times to aid in comprehension of the material herein. The label Reordered TD Wave refers to the fact that I reorder 2 19 cycles into 1.

The other type of plot is a frequency domain, or spectral display, where the X axis is in spectral bin number and the Y axis is in dB, ranging from 0dB to -100 dB.
I used Dans Rules 3 to defy Nyquist and unfold the first order aliasing harmonics to create a spectrum of 2048 bins from my 2048 time domain samples. The X axis labels are displayed to help the reader count harmonics if desired. The fundamental frequency is always in bin 19, so, for example, the 4th harmonic would be in bin 4*19, or bin 76. The highest harmonic displayed is the 107th in bin 2033. Bins arecolor coded odd and even and the legend noting this is always displayed.

Both types of plots were created with Excel and are the result of purely mathematical waves being processed by Excel including the Fast Fourier Transform (FFT) from Microsofts optional Data Analysis Pack.

https://youtu.be/Gry57CQdik4 3 https://youtu.be/vJ8V8ipSZ50

When I posted the video Audio Quality and Total Harmonic Distortion on YouTube and shared it on LinkedIn I was almost instantly hammered by an ex-coworker from my days at Credence Systems Corporation who had recently gotten an MSEE degree. My sponsor of the video, Applicos Measurement and Control was a bit taken aback to say the least. Here was an experienced test engineer with a freshly minted MSEE degree challenging the video Applicos had paid me to make touting their product. This engineerinsisted that we take the video down because I had misunderstood the statements in the Audio Precision book which therefore invalidated the thrust of the video.