Question for people with general circuitry knowledge

I love this question!  I've been learning some of this in my Digital and Analog Communications class.

This is a perfect example of what is called the Gibbs phenomenon.  It's what happens when a square wave is passed through a low-pass filter.

In the above picture, we see the waveforms of two low-pass filters.  Any signal that falls underneath the large peak at the center of the graph is allowed through.  Ideally, no other wave component is allowed to pass, that is all waves that fall outside the central peak are filtered out.  However, you can see where the low-pass filter still exists outside the main filtering frequency.  Higher frequencies that we want filtered out are still slipping past, generating the diminishing sine wave you see at the top and bottom of the square wave.  As we make the low-pass filter narrower, the Gibbs phenomenon also gets smaller, but can never be made to disappear.

Basically, it's a technical limitation and a fact of life that really has no effect on you unless for some bizarre reason you need a completely clean square wave.

You can also see the Gibbs phenomenon in your DMG square wave there.  Notice how the wave seems to extend beyond it's logical point and ripples ever so slightly before settling back down into the primary wave?  The DMG square wave appears to be on a very narrow low-pass filter, resulting in a very small Gibbs phenomenon.

EDIT: additionally, the Gibbs phenomenon can be seen in the generation of square waves themselves.  You can generate a square wave by combining multiple sine waves together, with the result being a square wave exhibiting the Gibbs phenomenon.  The greater the number of harmonics (the number of sine waves you are combining), the smaller the Gibbs phenomenon.  If you want, I can try to teach you the math, but I'm afraid I barely understand it myself.

Last edited by scienceguy8 (Feb 23, 2010 4:46 pm)

Or like you posted so you can show off

Awesome thread!  Thanks Scienceguy for the info.

I have a limited understanding of the math and physics involved but I've seen this waveform in some of my DIY stuff.  That kind of falloff does look like some kind of capacitor discharge at or near the output or something to do with load at the output, maybe even the speaker is bringing it down.  They're calling it Low Frequency Roll off.

Maybe changing the speaker would change the wavform, that's an interesting idea...

Some links that might shed some light:
http://www.machrone.net/mt/archives/202 … phs_a.html
http://commons.wikimedia.org/wiki/File: … charge.svg
Figure 10 @ http://www.eal.gr/english_language.htm
http://users.tpg.com.au/users/ldbutler/Waveforms.htm
http://ap.com/kb/show/187
http://diyaudioprojects.com/Tubes/6T9-Tube-Amp-Kit/

I think Low Frequency Roll Off is a great name for an album, hehe.

Last edited by droffset (Feb 24, 2010 8:57 pm)

Ahhh, impedance. I haven't considered this. Unfortunately I remember next to nothing about it, I'll have to read up. Thanks for the tip!

Good summary here

Last edited by µB (Feb 24, 2010 9:51 pm)

Short discussion of the above on IRC, kudos to abrasive for explaining:

<uB> so the shape of the waveform would change with frequency
<abrasive> the exponential decay curve should stay the same
<uB> absolute or relative to the duty cycle?
<abrasive> absolute
<abrasive> its time constant will be set by physical components
<abrasive> i expect that is the DC blocking capacitor
<abrasive> -> high pass filter
<abrasive> so the fast edges are preserved
<abrasive> but the bits that should be flat are not
<uB> cool, I wasn't too far off then
<uB> thanks!
<abrasive> headphone/other loading on the output will change things, how much and in what way depends on the dmg output arrangement.
<uB> there are some ciruits to dynamicaly adjust this, right?
<abrasive> to adjust the loading you present to the DMG?
<uB> welllll, the output impedance
<abrasive> that's... complicated.
<abrasive> you can adjust the input impedance of whatever you plug into the dmg easily enough
<uB> I'm not trying to mod anything, I just needed the details for some pet project of mine :)
<abrasive> a headphone amplifier typically has high impedance (10kOhm and up)
<abrasive> you can then put resistors across the dmg output to reduce the impedance seen by the DMG
<abrasive> and the output waveforms will change.
<uB> hm, you could bass it up that way
<abrasive> this is part of the reason for pro sound mods - you bypass the output HPF, and get better bass
<abrasive> but since there's also no amplifier you can't drive low impedance (headphone) loads with a prosound out.
<abrasive> i think the DMG internals go audio out -> amplifier -> HPF -> jack
<uB> shouldn't there be a LPF that causes the gibbs effects on the waveform, too?
<abrasive> inherent in the circuitry
<abrasive> parasitic effects
<uB> ah
<Scotty> why isn't the audio amp first in the cirsuit
<abrasive> the HPF blocks DC out from the amp