Okay, I just took the opportunity to read this "Dan Bullard's Law of Harmonics."
Several comments:
1. Unlike someone like Isaac Newton, Dan Bullard has neither the stature nor
acceptance nor technical and scientific underpinnings (at least in his article
get to call what he writes as a Law of Anything.
2. I have no idea what Bullard does for a living, but it's clear that he suffers
from a fundamental misunderstanding of the topic.
For example, he claims:
"Look at that! Odd harmonics galore! Why? most people believe that harmonics
come from discontinuities in voltage, in fact, discontinuities can be created by
discontinuites in time too."
I'm sorry, but this is so much BS and gobbledygook.
I can create harmonic distortion simply by LINEARLY summing the right collection
of completely LINEAR sine functions. Indeed, I can duplicate Bullards sample
slew-limited waveform PRECISELY this way. And not one of those sine functions
is slew-limited. I say so, Fourier says so.
Further, if you have a signal who's first derivative wrt time is non-zero (i.e. it changes
from moment to moment, a discontinuity in time MUST cause a discontinuity in
amplitude. Bullard cannot arbitrarily treat time and amplitude as independent
phenomenon.
3. He states:
"while most people believe..."
You want to risk life and limb by waving that red flag in front of me, do so at your
at your own peril. How on earth do you know what "most people believe?" Statements
like this are the height of high-end audio ignorance and BS.
4. He states:
"this is exactly why we don't have people looking at o'scopes to verify waveform quality"
Really? Is he kidding? I stopped using an oscilloscope for such probably 50+ years ago.
How many people in the real world actually do this?
5. He states:
"the invention of the FFT by Cooley and Tukey is such a watershed event in human history.
It allows us to deduce signal quality very, very quickly (hence the name FAST Fourier
Transform).
This stands out like a sore thumb set on fire then doused with radium in an attempt
to smother the flames.
The Cooley/Tukey alorithm is but one of amny mathematically equivalent transforms
that are computationally efficient in one way or another.
It is NOT "very very" quicker per say, it is computationally efficient ONLY WHEN THE
THE DATA SET IS EXACTLY A POWER OF TWO SAMPLES LONG (more on this below).
And, come on, it's a "watershed event in human history". Really? as significant as say,
Newton's law of gravity? Einstein's theory of general relativity (which under relativistic
situation, where Neton falls apart, bive FAR more accurate results)? Quantum mechanics
(which, after all, does allow us to have this exchange)? Penicillin? Calculus? The internet?
6. He states:
"the Even harmonics (red) are likely due to the fact that my poor sine wave gets one cycle
to run through the "filter" of my slew rate restriction."
Sorry, no. It is as likely due to the the distinct possibly that even though the number of
points passed to the FFT is, indeed, 2018 samples long, the entire waveform does not
complete in it's entirety in that 2048 second. In other words, you're looking at the
discontinuity at the end of the data. In yet other words, you may well have failed
to obey your own rules about ttime discontinuities. Had you roperly windows the data,
those harmonics wouldn't be there. The error thus is not the "filter" whatever that means,
but sloppy technique.
"The DC offset (bin zero) is a clue t what is going on."
It is indeed: it screams "bad, sloppy technique" to me: if my hypotheses above is correct,
the resulting waveform he generated MUST have an offset because the date set does not
integrate to 0 within the FFT bin size.
7. Lastly, his claims suffer the same problem as Obe...s original post: it utterly fails to address
his claims in the light if ACTUAL real-world data. Though it is difficult to read the actual
scale of his graphs, he claims he simulated a slew rate of, to quote him, "6V/ms."
Does he REALLY mean 6V/mS? If so, that mean 0.006 V/us and in all of my career, I have
NEVER ONCE encoutered such a preposterously slow slew rate (unless done deliberately as
an opamp based integrator.
The excercise I did earler whowed clearly that you meed a minimum of
an opamp with a minimum slew-rate spec of 0.387 V/us. That's 387 V/ms,
using Bullard's odd notation. If course, if you could ever hope to find such
a demonstrably lousy part and it could fit, the CD player would sound like sh*t.
But we can't, we won't, and Bullard's law is a load of crap.
So there.
> [ rare insert from the mod: if you are asked a direct question and you
> avoid answering it, I am inclined to think you are trying to troll.
> -- dsr the last remaining moderator ]
Yeah, you're probably right. But the bait was too large, too juicy and too attractive
to ignore.