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Old 21st April 2011, 07:07 PM   #1
hoagje1 is offline hoagje1  United States
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Default second order harmonics

Greetings from Tacoma,

My interest in DC coupling is that the cathode follower has always had the reputation for "warming" up a guitar amp. I explained things poorly in a previous post, so SY (and anyone else reading this), the link, http://www.freewebs.com/valvewizard1/dccf.htm will repair the damage -- at least a look at the second graph and scope tracings. You don't have to know much about Fourier transforms to see that odd order harmonics would be filling up square wave clipping, and more even order harmonics "round" the sine wave. So this is the mythical goal.

Well, I built my 2A3 SE amp and cathode follower in the preamp, and I can't hear the difference. I couldn't hear it in my Bassman either, which is probably why Leo dumped it. So this is the mythical but inaudible reality.

Unless I am dissuaded here, I have decided that my next project should be to put several "cathode followers" as shown in the link above, in series. I have no training in electronics, but it seems logical that 1) all of the followers would need to round up the same half of the wave, so there will have to be 180 (inverter) +180 (driver) degrees of phase inversion between each cathode follower and 2) there can be no phase shift from a blocking cap/grid resistor. There isn't much to look at on the web. 1) Are these assumptions correct?

I made an inquiry in another thread, but I was too far off the subject being discused there. SY (moderator) made the very helpful suggestion, "For high 2nd harmonics, just run a normal common cathode stage with a small plate resistor. For example, using a 30k plate resistor in a 12AX7 stage will give you lower gain (maybe 30) and very high second harmonic." This is great. I'm looking for a sound that is so exaggerated that I will ultimately back off on it. 2) How far can I reduce the plate resistor, since I don't need any gain? 3) The audio lexicon is very subjective ("clinical," "round," "balanced," "blahblah,), but for the sake of a benchmark, what does "very high second harmonic" mean, 5%, 10%, 12%, and when am I going to start to hear it?

Practically speaking this is not at all subjective. When I fret a note on the guitar neck then create a node (with fundamental still sounding) I can create chime that is musical and audible to all, smooth -- no Alvin and the chipmunks, probably no subharmonics. This is where I want to go, analog, tube. Unfortunately, this is a one-note-at a time technique, not a way to play a song.

I would still like a choice of ways to DC couple several stages. RDH, 4th ed. has a cool little circuit, Fig 12.49, with a gas glow tube ?biasing? the grid of the next stage (as opposed to a blocking cap which would cause phase shift). The text says it is noisy. There must be other ways of doing this, although much of what I have read about bipolar, balanced circuits (for bias) says that they have their own odd-order harmonic problems.

ANY other ideas will be greatly appreciated, as only this one method of achieving my goal has occurred to me (tube types and component values appreciated).

Pretend that you are explaining things to a young child if you have advice. Thanks, SY, for getting me started and clarifying just how far I can go with your technique.

Hoagje1
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Old 21st April 2011, 07:38 PM   #2
SY is offline SY  United States
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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.
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Old 21st April 2011, 11:02 PM   #3
hoagje1 is offline hoagje1  United States
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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

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Old 22nd April 2011, 12:24 PM   #4
SY is offline SY  United States
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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.
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Old 22nd April 2011, 01:23 PM   #5
hoagje1 is offline hoagje1  United States
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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.

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Old 22nd April 2011, 01:38 PM   #6
SY is offline SY  United States
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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.
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Old 22nd April 2011, 02:57 PM   #7
jcx is offline jcx  United States
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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
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Old 22nd April 2011, 05:47 PM   #8
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Default 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 05:51 PM.
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Old 22nd April 2011, 06:15 PM   #9
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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.
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Old 22nd April 2011, 06:27 PM   #10
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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 06:31 PM.
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