• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

second order harmonics

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.
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
 
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.
 
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
 
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.
 
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
 
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.
 
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
 
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.

http://www.diyaudio.com/forums/tube...-dual-triode-signal-enhancer-conditioner.html

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:
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.
 
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:
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.

There are plenty of audio DSP plug-ins that will create distortion. DSP-FX (quite an old plug-in that uses very little CPU) has something called the "Aural Activator" that gives a lot of control over the type (even - odd), the amount, and the order of the distortion. It's a great tool for learning what odd vs. even and high vs. low order distortion sounds like. But that's not what we're after here, at least not me. I've got VST plug-ins coming out the wazoo. I want the sound of real triodes. Unfortunately not many plug-ins can do that well IMHO. You would think it wouldn't be difficult.

To me 2nd order distortion changes the character of the sound in a pleasant way on certain instruments. It *is* harder to hear than more "unpleasant" types of distortion like high order odd harmonic distortion when present in equal amounts, but it certainly can be heard if present in adequate amounts. There are plenty of octave generators in the world of guitar effects processors and the octave can be heard, although admittedly it needs to be a lot louder than a note that's 3 times the fundamental to be clearly perceived.

I have a 300B SET tube power amp that I can get a lot of 2nd order out of. The sound is "rich and full" when I crank it up to create some distortion, even though it's being radically altered. I wouldn't want to be restricted to that sound, but it's nice on certain types of music on occasion. It's almost like 4 violins become 8 if cranked on certain classical pieces. Sounds great IMHO.
 
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.


It may not be a simple single factor that accounts for the marked difference in sound between a 6G6-A Bassman and the later AB-165 circuit. I've owned and played both for many years and they are certainly two very different animals. One of the key differences in the two is the use of a CF post 1st stage ax7 feeding the tone stack in the 6G6. This is absent in the AB-165. Again - it may not be that one thing that accounts for the big difference in sound, but coupled with the following observations from myself and others who've built studio recording preamp and line amp circuits using CF output stages it starts to suggest a certain sonic impression. Those observations include a certain blattiness or splatter when driven really hard into clipping. These adjectives also fit the bill for what you hear from the 6G6 Bassman when overdriven. So maybe there is something unique to the way that CF stages sound when overdriven. In a hi-fi amp with well defined and controlled signal levels I would expect there to be as you observed - no real audible difference. This makes sense as CF stages are noted for their very low distortion, and the type of clipping that seems to be associated with CFs would likely be far from what one would be seeking in a hi-fi amp.


I'm not sure why Fender chose to move away from the CF in the later Bassmans - it wasn't to save an extra tube. They leave a whole side of the 2nd ax7 unused! Perhaps they deemed the tone stack buffering and slight bit of extra gain available unnecessary.
 
^Could be. Fender's goal was mostly producing somewhat cheap but still decent quality clean amplifiers. The distortion from cranking up the amp was just a side product but they didn't really design for it until mid/late 1970's. ...at which point they fitted in ...guess what... A single stage of overdriven cathode follower with some wacky "blend" control between clean and distortion tone. The general opinion of those amps is that their distortion sounds downright horrible, though the asymmetric output of that distortion circuit introduces a wealth of 2nd order harmonic distortion. Just goes to show that all those flaunted harmonics don't really sound all that good in practice. On a contrary.

I don't know if the cathode follower in the generic Bassman/Marshall derivatives has any more "magic" than introducing harsher clipping to one half wave when driven hard enough. Basically the clipping turns from moderately soft and asymmetric to "semi-asymmetric" where the upper half wave is clipped somewhat softly and the bottom half wave is clipped harder. All in all, that's simply more distortion, which may as well be all what folks ultimately looked for.
 
Last edited:
Oh, forgot to mention: The Valve Wizard site oscilloscope captures do not tell the whole story of the circuit. Yes, a cathode follower stage directly coupled to common cathode voltage amp clips the postive half wave asymmetrically like that but only when rest of the cathode load is negligible, which it generally isn't in a generic Bassman/Marshall derivative guitar amp. A typical tonestack most commonly following the circuit represents about a 47k average additional load in parallel. This additional load will actually cause the cathode follower itself to clip -harshly- resulting also into clipping of the negative half wave and a more symmetric type of distortion. Ed Jahns realized this phenomenon of external load's effect to operation of a CF and used it when he designed that notorious distortion circuit for the Fender Super Twin's, but it was about a decade after classic Bassman/Marshall amps had made their debut.

The tonestack will usually also skew the lower waveform portion so that it looks more like a "reverse shark fin" instead of plain square-wavish clipping. With a resistive load the clipping looks even harsher.

The following attachment from SPICE simulation of a typical gain stage + directly coupled cathode follower + tonestack combo illustrates what happens. Blue waveform is the circuit operating unloaded, green waveform is the circuit operating loaded by the tonestack's impedance. Signal takeoff points are the cathode follower's grid and cathode.

As mentioned earlier, I believe the sole magic of the cathode follower circuit simply comes from it generating more clipping overdrive than a circuit without one. Fender's and Marshall's engineers likely never thought it in the design process of their first amps that came with the circuit (because back then they were not trying to create a high-gain amp) but the countless cloners aiming for those classic overdrive tone surely must have done so since the difference it can make is obvious.
 

Attachments

  • cfc.gif
    cfc.gif
    6.3 KB · Views: 303
Last edited:
Just one more thing (couldn't edit it in due to time limit). The additional cathode load I'm talking about must be one that is capacitively coupled, that's the key attribute making a difference. Lower cathode loads will increase clipping of positive wave but when they become also capacitively coupled the cathode follower will also begin to clip the negative half wave.

Oh, judging by the scope captures and FFT transforms of signals coming from guitar amps using the classic gainstage + CF combo we can pretty much ignore all the talk about "pleasantness" of different types of harmonics and other yadda yadda like soft clipping. That ain't really happening. The distorted output is just downright "nasty" looking hard-clipped signal with plenty of both even and odd order harmonics, lots of high order ones too. That's what makes up the classic overdriven guitar tone a la Marshall. Just live with it.
 
Those are some interesting observations teemuk, particularly regarding the nature of the clipping when the CF is used in front of the tonestack. It would seem to confirm some of it's contribution to the 6G6 Bassman sound.


Oh, judging by the scope captures and FFT transforms of signals coming from guitar amps using the classic gainstage + CF combo we can pretty much ignore all the talk about "pleasantness" of different types of harmonics and other yadda yadda like soft clipping. That ain't really happening. The distorted output is just downright "nasty" looking hard-clipped signal with plenty of both even and odd order harmonics, lots of high order ones too. That's what makes up the classic overdriven guitar tone a la Marshall. Just live with it.


I would argue that when it comes to the case of the CF in a guitar amp you can pretty much ignore anything a scope or any other piece of analyzing equipment seems to be telling in regards to the nature of the overdrive in terms of the subjective evaluation of the end sound. Plug an instrument in, turn it on and play for 5 minutes and you know all you need to know. "Nasty" may be good for a guitar amp or it may be bad. True - whether it's "good" or "bad" will always be subjective but keep in mind the context. If you're listening to a 50W Marshall or Bassman in the room standing right near the cab it may likely be judged as harsh and nasty in a bad way, but this has more to do with general SPL levels pounding your ear drum than the nature of the clipping and harmonics structure. When recording with a mic, the sound you get onto the recorder tells the final story. The 6G6 has always left a sonic impression of fat and full to my ears.

For the hi-fi and recording amps the reliable opinions I've gleaned from others seem to point to "nasty" as being an undesirable thing. I have a preamp with CF output but I've yet to put it through the paces by overdriving it - it sounds so wonderful in the clean range. ;)
 
Wow, I'm just getting back to the thread after a weekend of 14 hour night shifts and I am very appreciative of the ideas supplied. Smoking-Amp, I've got time domain digital processors that I'm sure that I could do this with no problem, presets on the dials. But isn't the silliness of some guys like me who want to do it with a tube part of the whole tube thing? Of course we can't do it the easy way. We have to do it with a smoking-amp.

Sampleaccurate - please just send me that thing that you have built. Seriously, why don't you have to worry about phase shift slowly moving the peak you want to distort. You do have those 1uf coupling caps in there. What is the effect? This is something I need to learn, so please take your time with the reply. I would think that you would use cap values that put any phase shift outside the frequency band that you are inverting. And what is that thing that looks like a computer SMPS doing in there? I have a box of them that I am afraid to do anything with, especially inside of a chassis.

Thanks Everyone

Hoagje1
 
Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.