second order harmonics
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 21st April 2011, 08:38 PM #2 SY   On Hiatus     Join Date: Oct 2002 Location: Chicagoland It's important to understand one aspect of Fourier transforms- even harmonics correspond to waveform compression that is not symmetrical about the zero voltage point. That's irrespective of whether that compression looks roundish or sharper. Odd order distortions compress the waveform symmetrically, irrespective of whether that compression looks roundish or sharper. OK, practical approaches- small plate resistor, you can go as small as you like, subject to whatever minimum gain you need. Another approach is a bad cathode follower. RC couple to the grid, return the grid leak resistor to ground, then take signal off the cathode. For a first try, I'd use a 12AT7 with 250V on the plate and a 2k cathode resistor. That will be fairly extreme and swing 2V or so. __________________ "You tell me whar a man gits his corn pone, en I'll tell you what his 'pinions is."
 22nd April 2011, 12:02 AM #3 hoagje1   diyAudio Member   Join Date: Nov 2010 Post 2: Thanks for the reply. As in my first post, I will always try to number my posts and number my items of interest, so that members can just answer ex "post2, item 2" and not have to retype my text unless I have got it wrong. Paragraph 1 above explains why putting one driver+follower right after the next would be a no-go, since without an extra inverter between the two, the result would be symmetrical compression even if I could deal with the phase shift problem. That is what that second 180 degrees was there for. Thanks for the explanation. Clarifications before I go to the bench: I'm going to stick with the conventions at http://www.freewebs.com/valvewizard/accf.html for naming resistors and caps in the RC coupled cathode follower. The diagram there will help me with the second paragraph. Here is what I think you are advising. You can just say "yes," unless I've got it wrong. 1) Use Cin and Rg (RC couple to the grid and in this, case Rg to ground, not Rb) . 2) Rb + Rl = 2K (this is where I could foul things up if Rb alone is supposed to be 2K). On the other hand, you did say extreme. 3) Since we have put Cin (AC coupled) in the circuit I don't even have to think about bias or matching the 2 triodes. Thanks Hoagje1
 22nd April 2011, 01:24 PM #4 SY   On Hiatus     Join Date: Oct 2002 Location: Chicagoland Yes, Rb and Rl become a single 2k resistor. Since there's only one tube, I'm not sure what you mean about "matching." You'll get plenty of tone alteration. This implementation of cathode followers is the reason that audiophile urban legends about CFs and poor sound got started. But for deliberate manipulation, it'll work great. __________________ "You tell me whar a man gits his corn pone, en I'll tell you what his 'pinions is."
 22nd April 2011, 02:23 PM #5 hoagje1   diyAudio Member   Join Date: Nov 2010 I understand now that the follower is just one stage, but often guitar amp designers who have placed a directly coupled triode ("driver") or pentode just before the follower will call the whole package a cathode follower, and usually both stages are 1/2 12AX7, plate resistor 100K on the "driver" and cathode resistor 100K on the follower (hence my use of the word matched). Sometimes a pentode and triode in the same bottle like a 6AN8 is used. RC coupling is much less common. I'll try to adhere to the accurate terminology, but I'm just a simple guitar strummer. SY, you have answered a lot of questions and taught me a lot. Thanks. No need to reply to this. with regard to your signature: The ordinary modes of human thinking are magical, religious, social, and personal. We want our wishes to come true; we want the universe to care about us... For most people, wanting to know the cold truth about the world is way, way down the list. You've got the thinking part on the nose, and as for the behavior, it is just as ancient and tribal, which is why the cold truth DOES continue to confront us. Hoagje1
 22nd April 2011, 02:38 PM #6 SY   On Hiatus     Join Date: Oct 2002 Location: Chicagoland No problem- I've gotten so much from this community that the occasional time when I can give something back is small recompense. Me, I'm a guitar strummer as well, just a very mediocre one. The quote is from John Derbyshire, someone with whom I have a lot of strong disagreement and strong agreement. But he's always an entertaining and thoughtful writer. __________________ "You tell me whar a man gits his corn pone, en I'll tell you what his 'pinions is."
 22nd April 2011, 03:57 PM #7 jcx   diyAudio Member   Join Date: Feb 2003 Location: .. a problem with series distortion stages is that you get higher order distortion 2x high 2nd order distortion stages will give you a lot of 4th order distortion generally higher order distortions are considered much more objectionable in music reproduction I would investigate in software 1st - you can actually run a .wav clip thru a circuit simulator - not real time, but you can let the sim run as long as it takes to compute the processed .wav it make take ~10x time for a simple sim another issue is that 2nd harmonic distortion isn't readily audible - mostly masked by the fundmental and if your instrument produces even harmonics you may have to do massive damage to the waveshape to hear the difference
 22nd April 2011, 06:47 PM #8 sampleaccurate   diyAudio Member   Join Date: Mar 2010 Hyper 2nd Order Distortion This is my approach to generating even harmonic distortion of varying orders. It's a series triode even order distortion generator with adjustable drive and make up gain/attenuation. It uses op-amps to invert the signal between the triodes so each stage affects only one "side" of the waveform, and the triodes are biased so that they operate such that they run into cutoff before saturation so that only one side of the signal gets distorted and the distortion comes on gradually. A cathode follower is way too linear IMHO to be useful as a distortion generator for thickening/enhancing the sound of something like a guitar amp. The previous poster is correct in stating that cascaded stages of triodes (with the signal inverted before the second stage) will produce higher order (although still even) harmonics than a single stage. However, this can be useful during the recording process to artificially "brighten" a signal. In the device I built, either one stage can be driven hard for low order even harmonics, or both can be driven to brighten the sound. 12AX7 dual triode "Signal Enhancer/Conditioner" I would disagree that the 2nd harmonic isn't very audible - it really depends on the sound source and how much second harmonic is present to begin with. And there's nothing wrong with "mangling" the waveform. If it sounds better mangled than clean then by all means, mangle away I say. I'm speaking of individual instruments here - not the entire mix. Last edited by sampleaccurate; 22nd April 2011 at 06:51 PM.
 22nd April 2011, 07:15 PM #9 smoking-amp   diyAudio Member     Join Date: Dec 2001 Location: Hickory, NC If the signal is available in digital form at some point, then it is trivial to derive 2nd harmonic signals without IMD using the FiFoFFT described in Steins book on Digital Signal Processing. Just requires a subtraction, an addition and multiplication for each frequency bucket per time sample. Just requires a FiFo for signal storage (a stepped delay line essentially). This is way more efficient to calculate than standard FFTs. A lowly PIC processor can do it real time. __________________ For English, press 1, For an automated representative, press 2, To stay on the line forever, press 3, To self destruct, press 4, To start over, press 5
 22nd April 2011, 07:27 PM #10 cats squirrel   diyAudio Member   Join Date: Feb 2011 Location: Devon, UK 2nd harmonics, by definition, are always an octave above the fundamental, and therefore the same note, only an octave higher. This is difficut to hear. All musical instruments contain harmonics, and to my knowledge and experience, all contain the 2nd harmonic at least; some, like a sax, can go out to 32 harmonics! (that I have measured). What do you expect 2nd harmonic distortion to sound like? When you form an octave harmonic on a guitar (by touching the string at the twelfth fret) it sounds fine, well musically acceptable, at least. I suppose that's why it's called harmonic distortion and not unharmonic. The BBC, when building their LS5/x 'speakers noticed that anything below 30dB was not audible (down to a certainfrequency) suggesting that harmonic distortion below 30dB is inaudible. What they mean by 30dB is open to debate. Last edited by cats squirrel; 22nd April 2011 at 07:31 PM.

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