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 Forum index » DIY Hardware and Software » Developers' Corner
Tube Amp Models
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elektro80
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PostPosted: Wed Apr 30, 2008 6:25 am    Post subject: Reply with quote  Mark this post and the followings unread

Laughing

You have done some great work already. I´m not really into chuck at the moment ( no spare time ), but I´m sure your work will be of tremendous importance to the community.

As for real life applications of transformers and tubes, using DI/ line drivers inside modular synth patches will add something slightly magic and organic that is very hard to reproduce using traditional modules alone. It is a bit amazing that modules makers have mostly ignored this. I mean.. this is truly amazing! Shocked

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PostPosted: Wed Apr 30, 2008 9:44 am    Post subject: Reply with quote  Mark this post and the followings unread

I believe one simple way to model the transformer is to model saturation and not hysteresis. Although in some exaggerated plots the hysteresis seems huge, in practice it is actually very small, so that there is very little offset depending on whether the wave is going up or down.

If we accept that, then the simplest model would just be a Dyno in ChucK, or one could do a smoother piece-wise defined model with Gen7 just like I did with the tube model. So, really, just slapping in a Dyno will do the job (set on limiter of course). I'll give it a try in the model and see what happens.

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FreeElectrons



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PostPosted: Wed Apr 30, 2008 1:01 pm    Post subject: Reply with quote  Mark this post and the followings unread

Sorry to barge in on a good debate, but this thread caught my attention. I realize the end is intended to be an effects module. To that end I have a few comments I hope will be useful:

*) You cannot hear the distortion from a properly executed gain stage employing a single tube, like a triode as used here. If you can, then you are deliberately doing something wrong.

The exception is if you drive the tube into overload, something you'd normally do with a guitar amp to create their typical tone and distortions. Note that those amps usually employ pentodes in the over-drived output power stage, not triodes.

*) There is no practical high frequency limitation for tubes used for audio. The 3KHz low-pass filter in Inventor's model is completely arbitrary and has nothing to do with using a tube. For RC coupled gain stages you will frequently encounter a high frequency roll-off due to parasitic capacitances, but for triodes that frequency is usually around 80-100KHz. For pentodes it is about a factor of 10 higher still.

*) The mellow sound many tend to associate with tube amplifiers were mostly due to anything but the tubes used, in particular inferior output transformers, stone age speaker technology and frequently a wish to limit component count and thus cost in consumer electronics.

The hallmark of a good Hi-Fi tube amp, audiophile comments notwithstanding, is that they are simply a piece of wire with gain, flat in gain and phase across the audible spectrum before tonal corrections are applied. This was pretty close to what you got when building one of the classic Hi-Fi designs like the Mullard 5-10, dating to the mid-fifties, assuming you had a good output transformer. Those were never cheap.

Of course it is possible to artificially run tubes under conditions where they will create excessive and audible distortions but that is not 'what they sound like'. The effect of properly executed tube gain stages, even without feedback, is subtle at best. Not something you switch in circuit and go "Wow! Yeah!".

As for overdriving tubes into distortion, then I am aware of no successful attempt at numerically simulating the results of an inexpensive guitar amp. Hardly surprising once you start to consider all the factors involved in the transient phenomena of even a two-stage amplifier with transformer output. It cannot be impossible, of course, yet apparently the effort required doesn't match the potential economic rewards.

Frank.

Edit: Typo corrected. 7 -> 3KHz.

Last edited by FreeElectrons on Wed Apr 30, 2008 1:20 pm; edited 1 time in total
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DrJustice



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PostPosted: Wed Apr 30, 2008 1:09 pm    Post subject: Reply with quote  Mark this post and the followings unread

Hi FreeElectrons,

welcome to electro-music.com!

That's a heavy duty informative first posting - great! Very Happy

DJ
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FreeElectrons



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PostPosted: Wed Apr 30, 2008 1:52 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks DJ,

Might pop in from time to time, seeing that I apparently have interests in common with this nice community. Very Happy

Frank.
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DrJustice



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PostPosted: Wed Apr 30, 2008 2:07 pm    Post subject: Reply with quote  Mark this post and the followings unread

Inventor wrote:
I wrote up a web page on the tube amp model and how to derive your own model, it is here:

http://www.freedomodds.com/music/tube_amp.html

Thank you!
I've got no Chuck install here so I just changed the equation solver to C to have a look at the output for fun (some people don't know what real fun is Mr. Green).

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PostPosted: Wed Apr 30, 2008 2:37 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks for all the info, FreeElectrons! It's good what you said about not being able to hear a non-overdriven tube, because I have been tinkering with the implementation and now I cannot hear the difference! I thought I had done something wrong because all those harmonics went away, or most of them anyway. I decided that instead of faking the negative side of the waveform, I would bias it up and attenuate it by half, then run *that* signal thru the tube amp, and it seems to be working much better now.

The 3 kHz low-pass model is from the input stage capacitor and input stage resistors. The solution for it is here:

http://www.aikenamps.com/Equations.htm

But then again maybe I got the component values wrong and it's really a lot higher than 3 kHz! I've had to piece this all together with information from various sources so things like that can happen.

Also, DJ, I'm happy to hear you are having fun with the equation solver! I can see that whatever gets done here will be a community effort and not just my personal project, which I think is fantastic.

Folks, please feel free to critique my work in whatever way is constructive and makes it better in the long run. What we want is a good tube model and it will take input from several people to accomplish that.

On a progress update, I added the above mentioned biasing and a crude transformer model. I think I can hear the distortion kick in just when the input signal gets loud. I will make a demo recording so those without ChucK can hear it. Cooperation, community, coolness!

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PostPosted: Wed Apr 30, 2008 2:48 pm    Post subject: Reply with quote  Mark this post and the followings unread

Here is the test audio, complete with me explaining what's happening.

http://www.freedomodds.com/music/songs/Tube_Amp6.mp3

A little too much talk perhaps, but it is what it is, enjoy!

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PostPosted: Wed Apr 30, 2008 6:34 pm    Post subject: Reply with quote  Mark this post and the followings unread

FreeElectrons wrote:
Of course it is possible to artificially run tubes under conditions where they will create excessive and audible distortions but that is not 'what they sound like'. The effect of properly executed tube gain stages, even without feedback, is subtle at best. Not something you switch in circuit and go "Wow! Yeah!".

As for overdriving tubes into distortion, then I am aware of no successful attempt at numerically simulating the results of an inexpensive guitar amp. Hardly surprising once you start to consider all the factors involved in the transient phenomena of even a two-stage amplifier with transformer output. It cannot be impossible, of course, yet apparently the effort required doesn't match the potential economic rewards.


Actually, this is the only point where I don't necessarily agree with you, Frank, if I understand it right. As far as I know, people are intentionally driving their amps into saturation specifically to get that distortion effect. Isn't that what Jimmi Hendrix did with his guitar? I'm going for that effect here as well as normal linear modeling. Isn't that what all those amps do that are solid state but advertise a tube effect as a selling point? Correct me if I'm way out of line or something, but I want to rock, and I want that tube overdrive sound! Am I missing something here?

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elektro80
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PostPosted: Wed Apr 30, 2008 7:14 pm    Post subject: Reply with quote  Mark this post and the followings unread

No, you are doing fine. I guess Frank wanted to make a point here.
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PostPosted: Wed Apr 30, 2008 11:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

A good idea just occurred to me (don't they all seem good at first?): use an FFT / IFFT approach. If what we want is even harmonics, then why not simply insert even harmonics in the spectrum of the signal? That would be even better than tube saturation, because the tube saturation has a mix of even and odd harmonics, while our mathematically created signal would have only even ones. Would that be a super-tube or a stupor-tube?

I will have to code this up but right now I'm just reading up some more and relaxing - you can't code all the time, or I can't anyway! Keeping you posted...

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PostPosted: Thu May 01, 2008 2:04 am    Post subject: Reply with quote  Mark this post and the followings unread

elektro80 wrote:
No, you are doing fine. I guess Frank wanted to make a point here.

Yes, sorry about that. Reading my own reply I can understand the confusion. Please let me try that again... Embarassed

Normally, without driving a single class A tube gain stage into overload, you cannot - or should not be able to - hear the distortions created. If the control grid, g1, never ventures far away from the initial bias point, the actual level of waveform distortion produced is very low, assuming the amplifier stage is properly designed and operated.

Thus, without overload, you shouldn't be able to hear the mainly even order distortion products produced. I have a DIY stereo headphone amplifier using two triodes for each channel, no overall feedback. While I know it must be producing some distortion, it is inaudible to me. Indeed, the amplifier seems not to be there at all, save for the increase in output level.

Of course it is possible to design a gain stage such that noticeable distortion occurs: Zero grid bias is a classic, and so is choosing a tube type unsuitable for audio amplification. But for this purpose doing either must be considered bad engineering, as none of these are the source of the classic guitar amp distortions.

Worse still, then pretty much every guitar amp worthy of the name runs in push-pull, driver stage included. This largely cancels any even order distortion products. You won't ever get complete cancellation as perfect balance is not going to happen when using tubes.

But the conclusion is still there: Any nonlinearities in the semi-linear transfer characteristics of the tubes are not the source of the distortions in a guitar amp. Ie. the 3/2rd power law is a wild goose chase. You can probably crank the parameters until audible waveform distortion occurs, yet that is not the source of guitar amp distortion.

What you should be looking for are non-linearities arising from running the tubes outside their normal linear operating range, Ie. close to current cutoff and driving the grid positive or nearly so. Also circuit configuration plays a large role, combined with actual component values like DC blocking capacitor values.

Frank.
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PostPosted: Thu May 01, 2008 2:17 am    Post subject: Reply with quote  Mark this post and the followings unread

Forgot to mention: Seems like you must have made a calculation error, Inventor, as the formulas presented looks correct.

The high pass cut-off frequency is governed by the anode resistor of the driving stage combined with the grid input capacitance of the driven stage. For a typical triode used for audio, a 12AU7 / ECC82, the voltage amplification is about 10 and the Cag is 2pf, plus another 2pF or so from Cgk.

So the total Miller multiplied input capacitance would in this case be 2 + 2* (1+10) = 24pF. If the anode resistor of the preceding stage is, say, 100K, then the high pass cut-off frequency would be:

F(-3dB) = 1/(2 * Pi * 100K * 24E-12) = 66KHz.

Frank.
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PostPosted: Thu May 01, 2008 3:15 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks, that clears it up Frank. Yes, I used the wrong capacitance in the calculation, I got Ci mixed up with Cin - should know better. I'll be looking into the overdriven tube amp and also using a pentode in the output stage. Glad you chimed in, you bring up some relevant points that are important for me to know about in doing this. Cheers.
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PostPosted: Fri May 02, 2008 4:03 am    Post subject: Reply with quote  Mark this post and the followings unread

Just thought I'd mention the following site as a good quick-visit if you don't have much time on your hands. The author quickly describes why we use pentodes instead of triodes and then presents some linear mode analysis (non-overdrive).

http://www.angelfire.com/electronic/funwithtubes/Basics_05_Multigrid.html

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Blue Hell
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PostPosted: Fri May 02, 2008 4:47 am    Post subject: Reply with quote  Mark this post and the followings unread

How about http://www.osti.gov/bridge/product.biblio.jsp?osti_id=522278 - a non linear tetrode model.
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PostPosted: Fri May 02, 2008 5:36 am    Post subject: Reply with quote  Mark this post and the followings unread

Blue Hell wrote:
How about http://www.osti.gov/bridge/product.biblio.jsp?osti_id=522278 - a non linear tetrode model.


Wow, that's a good one! All those current sources and diodes, each a transcendental function, would require a multi-variable optimization algorithm to solve, but it's worth doing and I can code those up. I'll read further, I'm in an information gathering mode right now...

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PostPosted: Fri May 02, 2008 6:45 am    Post subject: Reply with quote  Mark this post and the followings unread

You did see http://lib.tkk.fi/Diss/2008/isbn9789512292431/ already I think? There seems to be quite some overlap with your work.
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PostPosted: Fri May 02, 2008 8:09 am    Post subject: Reply with quote  Mark this post and the followings unread

Blue Hell wrote:
You did see http://lib.tkk.fi/Diss/2008/isbn9789512292431/ already I think? There seems to be quite some overlap with your work.


I had not seen that one yet - it does use almost exactly the same triode circuit. There are unfortunately no equations or circuit analysis presented. The author does present a great state-of-the-art discussion and cites many excellent references for us to follow though! He mentions the paper that I got those first equations from, and the method from, really. Keep 'em comin' folks, we're getting there - slowly but surely!

Code:
                   Q
        ______    /|\
       (_     Z.(o\_)=="#
       __Z        / \
ejm97 |()|        \  \
      |__|        ~   ~

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PostPosted: Fri May 02, 2008 8:50 am    Post subject: Reply with quote  Mark this post and the followings unread

Here's another good one. It very clearly and simply describes the basic functionality of tubes, working from the diode on up. I'm still reading it now and it seems to be an excellent introduction, providing the reader with an "intuitive" understanding of tube operation - a good link.

http://web.telia.com/~u85920178/begin/tube0.htm

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PostPosted: Fri May 02, 2008 1:30 pm    Post subject: Reply with quote  Mark this post and the followings unread

You know what occurs to me, after studying these tube amps for what, three or four days, is a design for a low-cost, high reliability tube amp. Inspired by the Z.VEX amp for $450, the proposed amplifier would address the cost and reliability problems associated with tube amplifiers in a creative way.

If I understand tube amp operation, we get the warm saturation with even harmonics from overdriving the power output pentode and using purposely poor performing magnetics and discretes. Each amplifier has typically three stages of tubes, the preamp, the amp, and the speaker driver. What if we overdrove the center (2nd) amp at low power and replaced the output tube with a large enough model that it could run in linear mode? Either that or use solid-state preamp and speaker driver, requiring just the one tube to get the desired distortion.

I imagine if I did that, I'd have an ultra-reliable "tube" amplifier with all the desired distortion and low cost plus enhanced reliability. I am tempted to take the idea further and do an initial design sketch of that one! But I'll wait to hear what someone else has to say about it.

In the mean time, I'm still researching pentodes... I think I'll code up an FFT "signal warmer" tonight... we'll see...

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PostPosted: Fri May 02, 2008 3:20 pm    Post subject: Reply with quote  Mark this post and the followings unread

Inventor wrote:
Wow, that's a good one!

...
Quote:
"Curves derived from Thomson's published data (with estimates at low anode voltage)."


(Page 5 down below.)

Who says guitar amps are unreliable as they are? Tubes were pretty decently reliable until the DIY people started simulating them like semiconductor circuitry - and believed their simulations.

Frank.
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PostPosted: Fri May 02, 2008 3:47 pm    Post subject: Reply with quote  Mark this post and the followings unread

I have made some nice progress on the Fourier - based signal warmer, and it makes a good sound. Attached you will find the mp3 file of a sinusoid with second thru sixth harmonics added. The harmonics decay as (phi - 1) * previous harmonic, where phi is the Golden Ratio, or about 1.6. Also the harmonics ramp up from zero amplitude to full amplitude over the course of ten seconds, which is repeated 3 times. Call me krazy, but you can really hear the "warmth" of the sound. Just look for the transitions from full effect to none and you'll hear it. Maybe one of the effects that we could have would be a "signal warmer" like this one? Interesting result anyway.


Tube_FFT_Warmer.mp3
 Description:
Three cycles, 10 seconds each, of harmonics increasingly added to a sinosc - feel the "warmth"!

Download
 Filename:  Tube_FFT_Warmer.mp3
 Filesize:  469.79 KB
 Downloaded:  312 Time(s)


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PostPosted: Fri May 02, 2008 4:15 pm    Post subject: Reply with quote  Mark this post and the followings unread

Sorry, I posted too early on that sound file, I looked at the waveform in audacity and it is not as expected... gotta fix the program now. Pardon the mix-up! I jumped the gun on that one...
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PostPosted: Fri May 02, 2008 4:20 pm    Post subject: Reply with quote  Mark this post and the followings unread

FreeElectrons wrote:
Who says guitar amps are unreliable as they are? Tubes were pretty decently reliable until the DIY people started simulating them like semiconductor circuitry - and believed their simulations.

Frank.


Interesting, I did not know that tubes were reliable. I have no experience in that area, so I wouldn't know. I had always heard that people were frequently taking tubes down to the tube tester at the store and checking for bad tubes. Maybe that is not the case, just how reliable are tubes anyway?

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