Scene from Killer Klowns From Outer Space

All About Circus

Published on March 8, 2020

Copyright © Dan P. Bullard

One of the things that I really enjoyed about my old pal from Credence, Bruce Tibbetts was his ability to craft crazy yet insightful names for things he didn't like. For example, he was not a fan of schematic capture tools from Mentor Graphics, so he called it Tormentor. Credence forced him to use Adobe Framemaker to write applications notes and other documents, since Credence was a Mac and Sun house and MS Word was not an option. Bruce wasn't a fan of Framemaker so it became Painmaker.

So after getting kicked off the website for being too bold and trying to show them how harmonics work, my mind started spinning. And as usual, at 3AM I awoke with an idea of melding AllAboutCircuits with one of my favorite dark sci-fi comedy/horror movies, Killer Klowns From Outer Space, because while they looked like a harmless electronics information clearinghouse and forum, it turns out they are committed to evil while denying free speech to anyone who challenges their fake knowledge. Rather than ranting about what they did to block me with this message;

I'll just show you the article I wrote for them that got me kicked off their site, mostly just so it doesn't go to waste, because I thought it was a pretty good article.


It was asked What creates harmonics here [I can't give you the link because I have been banned]. I answered it;

Harmonics are not produced when the current is disproportionate to the voltage. You don't see harmonics coming out of RLC circuits do you? That totally dispels this myth, but to answer your question (8 years later, sorry about that).

Harmonics are not really caused by distortion. Distortion causes a sine wave (distortion impacts all waves, but it's easier to talk here about sine waves) to be distorted, and a distorted wave cannot exist without harmonics. Harmonics create the distorted wave, not the other way around, as you can see here:

This is a Bullard Plot, invented by yours truly. In the foreground you see the distorted wave in black, and behind it you can see the harmonics that make it up. These harmonics and the phases they are in are extracted from an FFT of the wave shown in each frame. Starting at the top is the fundamental, harmonic #1, and you will notice that this wave (in blue because it's odd) changes very little over the span of this animation. Below that is the 2nd harmonic, in red because it's an even harmonic. Below that is the 3rd harmonic in blue because it's odd, and so on all the way down to the 36th harmonic. Got the color code?

OK, as the fixed size distortion makes its way from the positive peak to the zero crossing, you can see how the harmonics conspire to create the distortion in the black wave. Again, this distortion is always the same size in the transfer function but because as the distortion moves through the transfer function, it changes the area because of the way a sine wave works. A sine wave spends a lot of time at the peaks, and so when you distort just 4% of the transfer function, a very large portion of the peak gets distorted. But if you move it down, the peak is not impacted, and it just makes a smallish triangle in the wave. As the distortion moves downward, the triangle gets smaller and smaller, until at the zero crossing you have a hard time making out the distortion. I explain this in full detail in chapter 4 of my book Distortion. Now, with this graphic it's easy to see how the distortion is created by the harmonics, but strictly speaking, the distortion didn't make the harmonics.

Now, why do we color code the odd and even harmonics? All of this action happens on the positive peak of the sine wave, but why don't those distortions happen on the negative side? Think about it. Do you see that the even harmonics counter the odd harmonics in the right half of the wave, but the they accentuate the effects of the odd harmonics on the left side? Except for one frame. When the distortion hits the zero crossing, suddenly all the even harmonics go dead flat. Why? Because we are distorting both the upper half cycle and the lower half cycle exactly the same amount, with the same exact area, so we don't need the even harmonics, which serve only one purpose: They prevent the distortion from being duplicated on the opposite half cycle. But they don't actually go away, they are simply cancelled out by even harmonics in the exact opposite phase. Because of the way harmonics work, only four phases are allowed relative to a sine wave input. Watch the animation, you will see only four phases for each and every harmonic, no matter where the distortion occurs. 0°, 90°, 180° and 270°. That is a law, Bullard Laws of Harmonics #5. I discovered this law, so I claim it. Because the harmonics are stuck with only four phases, how do the harmonics create the plethora of waves that can be created by distortion? The only other axis of freedom is amplitude. Notice as the animation runs that some harmonics go dead flat, then come back to life as the distortion moves on to the next location along the transfer function. That's not an accident. The Harmonic Signature depends on the angle at which the sine wave impacts the distortion. That's Bullard Laws of Harmonics #2. As you can see with this spectrum, the "nulls" in the spectrum depend on the angle at which the sine wave impacts the distortion.

Now to answer your question: If you apply say, a 1 volt peak sine wave to a diode, what will impact the harmonics? Obviously the forward voltage will determine the angle at which the diode starts to conduct, and that will determine the harmonic signature.

I've written a bunch on my five laws of harmonics and most of them are accessible on LinkedIn. Find them at my website.


That was it, that article and the discussions the followed it got me kicked off. I know what you are thinking. I was rude to somebody. On the contrary, I just used the comments section to reply to people who dragged me over the coals over this article. One guy claimed that I was claiming to have invented harmonics;

"Harmonics have existed for thousands of years, all you did was make some squiggly lines." I never claimed to have invented harmonics. Did Darwin claim to invent Natural Selection four billion years ago? No, he simply described it, as did I with harmonics. Another fellow said this:

"I've got a textbook on power electronics that admitted that it's a waste of time to analyze a square wave as complete Fourier series and the turn ON/turn OFF ramps are what actually creates conductive, inductive, or radiated noise." I asked him for the name of the textbook, as I am constantly searching the web and the bookstores, library, etc. for statements that I can use to market my books. This is a beautiful quote, if it's true (or maybe he found the book's explanation indecipherable) I want to read that book and give it a scathing review on Amazon. That's one of my other hobbies. And no, I don't spend my life trashing other people's works, I give a lot of excellent reviews for books that deserve it. To quote the exchange between Malcolm and Badger on the short lived TV series Firefly;

Badger: I had a problem with your attitude is why. I felt you was... what's the word?

Jayne: Pretentious?

Badger: Exactly! You think you're better than other people!

Malcolm: Just the ones I'm better than.

Not everyone has the right answer, and the ones who have the wrong answer need to be called out for it. Maybe they'll come around, and maybe they won't. All I know is, the people who thought the Wright brothers were crazy would have persisted in saying that except that the Wrights had an ace up their sleeves: They had an airplane that could fly over the heads of the skeptics, and it's pretty hard to argue with that kind of proof. If only I had that kind of proof....