Emulating negative feedback/presence/transformer saturation?

[SeanCostello]

Hi all:

Earlier today, I took a break from working to play through my late SF Princeton Reverb. I was comparing the sound of the amp with volume at 2.5 (as loud as I can get w/o distortion), in conjunction with the TS-808 side of a Jekyll&Hyde pedal, versus turning the amp volume up past 7 and not using the TS-808. The basic distortion sound of the two settings was similar, although I had to greatly reduce the bass tone control on the amp when I turned the gain up to get nice sounding distortion. The main difference: The pure amp distortion had a much less raspy high end. If I picked quietly, it was a beautiful clean sound, with plenty of highs in the signal. Hitting the strings hard produced a nice distortion, with the high end somehow rolled off. The TS-808 at amp volume 2.5 definitely had a much scratchier high end.

So...what is going on here? Am I hearing output transformer saturation in action? I know that saturated output transformers have an output response with less highs and lows present. How does this work with negative feedback?

And, just to make things more complicated, how does this work with a presence control?

It would be cool to emulate this in a pedal. The tricky part is that most emulations try to approximate filtering and nonlinearities as separate blocks. In this situation, the nonlinearities of the power amp/output transformer/speaker reactance probably aren't best approximated by a series combination of filtering and nonlinearites, but rather as a filter with embedded nonlinearites.

Any thoughts? What sort of nonlinear/filter combo allows me to roll off the lows AND highs as clipping increases?

Thanks,

Sean Costello

[Mark Hammer]

Traditional presence controls were intended to clean up the sound, actually.  They work by providing negative feedback that effectively cancels out those components of the output signal going to the power tube section that might generate "unwanted" harmonic content on the other side of the transformer.  So, presence controls are essentially wired up opposite to how one may think:  more presence = less of that regulatory feedback.  Essentially, turning up the presence allows the power section and transformer to do what it "wants" to do; much like letting teenagers loose with a credit card.

The reason why the amp will sound different than your pedal is twofold.  First, most presence controls are selective in what they feed back.  It is rare (if ever) one sees a feedback path that is full bandwidth.  Typically, the feedback is restricted to upper mids and highs.  Second, what is fed back in negative fashion in an amp is the added harmonic content produced by the power tubes and transformer, which are somewhat different than what is produced by diodes and op-amps.

I've been prodding people for a while to experiment with output transformers and negative feedback in those various tube-to-FET amp emulations, such that they start to become more like full amps rather than simply front-end emulations.  Whether that is even feasible is another matter, though.  The sorts of inter-stage and output transformers available in that power range may well be unsuited to the task, or may require more drive than is normally provided to do the requested task.

[R.G.]

You may also be seeing the consequence of the magnetic nature of the iron.

I recently found and bought a mint-condition book, Allegheny-Ludlum Steel Corporation's 150 page book on Electrical Steel Characteristics.
Yes, I'm crazy. 

But it explained some things that had not been clear to me about transformer iron before, and one of those was the loss of both bass and treble in output transformers at high inductions - that meaning "bigger signal levels".

Transformer iron gets successively worse as a transformer material as frequency goes up. Eddy current losses eat progressively more of the signal as frequency goes up, and it does it by changing the loading on the output tubes on a moment by moment basis. This starts at as low as 1kHz, so at higher harmonics it can be pretty bad.

This is NOT saturation. Your ability to saturate iron is highly limited as frequency increases, because a given quantity of iron takes a certain volt-second integral to saturate. Higher frequencies lessens time, so the volt-ability goes up, and you're limited to the power supply at hand. You can't saturate the iron at anything from moderate frequencies on up in a guitar amp. Mother Nature says so. But you do lose treble.

[SeanCostello]

I recently found and bought a mint-condition book, Allegheny-Ludlum Steel Corporation's 150 page book on Electrical Steel Characteristics.
Yes, I'm crazy. 

I don't even want to talk about how much I have spent on DSP books over the years. The big difference is that DSP books are really only useful going back to 1975 (with an exception made for Max Mathew's book from 1969), while a tube book from the 1940's is still useful for analog stuff.

But it explained some things that had not been clear to me about transformer iron before, and one of those was the loss of both bass and treble in output transformers at high inductions - that meaning "bigger signal levels".

Transformer iron gets successively worse as a transformer material as frequency goes up. Eddy current losses eat progressively more of the signal as frequency goes up, and it does it by changing the loading on the output tubes on a moment by moment basis. This starts at as low as 1kHz, so at higher harmonics it can be pretty bad.

This is NOT saturation. Your ability to saturate iron is highly limited as frequency increases, because a given quantity of iron takes a certain volt-second integral to saturate. Higher frequencies lessens time, so the volt-ability goes up, and you're limited to the power supply at hand. You can't saturate the iron at anything from moderate frequencies on up in a guitar amp. Mother Nature says so. But you do lose treble.

OK, this is a bit confusing - not your explanation, just the subject. So, my understanding of what you said is the following:

- The loss of high frequencies (and low frequencies) is not a result of saturation. The frequency loss is level dependent, and changes on a moment-by-moment basis.
- Saturation requires a certain "volt-second" interval. This implies a nonlinearity with memory.

My questions about this:

- Is the level-dependent loss of high frequencies essentially linear? In other words, does the process introduce harmonics of a given input signal?
- How is the time-constant determined with saturation? Is it symmetrical, or is there different attack/decay constants?

Feel free to point me towards any literature on the subject that would be relevant. I have access to a largish University library system, so I can look things up there. I am not sure how far back IEEE has digitized their papers, but the library should still have many of the older books, as well as journal articles in hardcopy form.

Thanks,

Sean Costello

[SeanCostello]

I should clarify one of my questions, which turns it into another question:

A level-dependent filtering is probably not nonlinear. What I am wondering is, does it generate noticable harmonics? If not, I would presume that there is a time constant that is affecting things, similar to a compressor limiter. If there is a time constant...where does it come from?

Again, the answer to my questions might be "read x, y, and z, and come back in 6 months when you kind of understand the texts." I am used to this - I am finally digesting some material from 10 years ago. My brain has a pretty large time constant...

Sean Costello

[R.G.]

OK, this is a bit confusing - not your explanation, just the subject. So, my understanding of what you said is the following:
- The loss of high frequencies (and low frequencies) is not a result of saturation. The frequency loss is level dependent, and changes on a moment-by-moment basis.
- Saturation requires a certain "volt-second" interval. This implies a nonlinearity with memory.

Not so much memory as path-sensitivity. The culprit is the BH curve of the iron and the eddy current losses. Where you are on the BH curve of an iron core is the result of the entire history of the piece of iron since it was last seriously demagnitized or heated above its Curie temp. Excitations less than sat-to-sat work on minor loops, the slope (permeability) of which is always less than the slope of the theoretical major loop. In point of fact, the minor loops are the reality, and the major BH loops are the abstraction, being only the locus of the ends of the minor loops as you vary the minor loops from -Sat to +Sat. It is the exception rather than the rule that a core ever follows the major loop we're all introduced to.

The exact position in the BH plane at any instant is the (nonlinear!) sum of the DC excitation in Ampere-turns or Oerstads forcing a flux density through the permeability and air gaps, and the volt-second driven AC excursions around the DC operating point. So as frequency rises, the number of volts which a specific winding can stand goes up.

However, the number of times the minor BH loop is traversed goes up too; you go around that loop once per cycle. And the area of the minor loop is expressed as core loss heating and separately as eddy current losses in the purely electrical effects in the core iron.

A pentode in particular is a power-limited driver for the transformer. So while the output tubes can deliver X power into the transformer + load, the transformer eats ever more of the power as core losses. You fight the eddy current losses by making the electrical domains smaller with thinner and thinner lams and finally iron powder or ferrites, and the BH loop losses by keeping the flux density excursions small with lots of turns.

- Is the level-dependent loss of high frequencies essentially linear? In other words, does the process introduce harmonics of a given input signal?

As I understand it, it's just a loss of power, essentially resistive. Remember that signals aren't sines, so the actual BH loops that are being traversed are anything but simple little loops. There are back-and-forth wiggles and subloops within subloops. What does generate harmonics is when you get one end pushed into the saturation area. I think that is what I like about amall SE tube outputs. For full output, one end is always knocking on saturation, and big bass signal push small treble signals riding on them into the saturation end of things. Then one side of even the treble signal is over in the soft, starting-to-sat region. For P-P, you're always coming back to almost 0 until the bass signal pokes you into saturation on  both ends at the same time.

- How is the time-constant determined with saturation? Is it symmetrical, or is there different attack/decay constants?

The only time constant I can think of that happens with the sex life of the magnetic domain is the time for the domain to realign. That's tiny. Much more important is what's happening with the DC bias point and the bass signals moving the center of the high frequency loop around.

Feel free to point me towards any literature on the subject that would be relevant. I have access to a largish University library system, so I can look things up there. I am not sure how far back IEEE has digitized their papers, but the library should still have many of the older books, as well as journal articles in hardcopy form.

I would if I knew any. I've never seen the description you just got anywhere else. In fact, some of it just occurred to me as I typed. 

If you're really going to try to DSP model transformer effects, we probably should talk off line. I may be able to scan and send you some stuff or explain it better.

[R.G.]

A level-dependent filtering is probably not nonlinear. What I am wondering is, does it generate noticable harmonics? If not, I would presume that there is a time constant that is affecting things, similar to a compressor limiter. If there is a time constant...where does it come from?

I don't think that it generates harmonics.

The time constant, as such, is only the time needed to move the minor loop into the edges of saturation. And that is the RL of the main circuit.

Ah. OK, better answer: the time constant is that of the grosser level circuit, the driving voltage and source impedance, and the inductance of the core. If I have a high frequency minor loop of 0.1 Bsat my highs are traversing, that loop moves within the theoretical major BH curve as driven by DC (Oerstad/Ampere-turn) excitation and the Volt-second excitation of the flux density. The time constant is whatever is available to move the minor loop on the major one - that being the volt-seconds of the lower frequency forcing signal.

It ramps toward + sat or - sat at a speed determined by the available volts, and of course the static stuff: core materials, number of turns, air gap, etc.

Every do a pulse inductance test? You hook up an inductor to ground and apply a voltage-source pulse to it, while watching voltage across it and current through it. You vary the pulse duty cycle from 0 up towards 100%. The current executes a neat ramp of di/dt = V/L. As you increase the duty cycle, the ramp reaches a point where it turns upwards and heads for the sky. That's the edge of saturation, where the incremental inductance is falling off and so the current gets big. The primary inductance of a transformer is what keeps the excitation OUT of the core and available for the secondary to sip from.

[frank_p]

Hi Sean,
ok, this does not really answer all your questions, but it's just to put some discussions that had been made "at work".

My experience with FETs, small transformers and a variable feeback loop (going in // with the OT, and no master volume at the end of "the preamp") is that:
- The OT does not have big influence on the tone: you can put R-C filter
- The OT have a big influence on tone if magnetised.
- The OT have to be VERY SMALL to be saturated (with audio small signal FETs): even is saturation occurs, it does not change the sound that much.
- The feeback loop have an influence on "tone" and on the "shape" of the distortion: Vary it's presence and it's frequency transmission capability and you can have a vast domain to play in.

Have some look there where Mark and R.G. gave me some explications:
http://www.diystompboxes.com/smfforum/index.php?topic=65824.0
http://www.diystompboxes.com/smfforum/index.php?topic=65915.0

[SeanCostello]

Thanks for all of your responses, even if some of them are WAY over my head. I asked for it!

I had some thoughts on what I was hearing with my Princeton Reverb, based on a diagram of an output section frequency response with and without negative feedback in a Kevin O' Connor book:

- The frequency response of a small output transfomer, in the "linear" realm of operation, w/o negative feedback, is a bandpass filter.
- By adding negative feedback to the output section, the frequency response becomes "flatter," in that the peak of the bandpass is flattened out. This produces a more hi-fi response, with clear highs.
- When the power tubes are driven into saturation, the negative feedback no longer has the "flattening" effect on the frequency response, since the negative feedback is limited.
- Therefore, power tube saturation has more of a bandpass frequency response, with less high frequencies than would otherwise be available.

Does the above description ring true to you brainy types? The reasons why this would be a useful model:

- The transformer can be modeled as a linear filter, and still have the useful effect.
- The nonlinearities can be modeled separately from the filter.

As far as DSP modeling of this, I'm not going to tackle it anytime soon. Bandlimited distortion is problematic enough in a digital system. Adding negative feedback creates its own problems, since feedback in a digital system produces an implicit delay of at least one sample. If I just used the nonlinearitiy->bandpass->negative feedback model, I would be creating some weird highpass filtering that would not be present in the analog model.  A possible solution would be to embed nonlinearities within a higher order filter, as found with many of the Moog models. I created a Big Muff model like this once, where a polynomial approximation to tanh() was placed after the summing junction in a one-pole filter, similar to the transistor clipping stages in the Big Muff with the diodes and capacitor working together.

My thoughts were that this type of circuit would be useful to creating analog stomp boxes with a more "tube-like" response. The exact nonlinearity shape of tubes would not be modeled, so much as the dynamic behavior found, as the output of the above loop would be a form of level-dependent filtering. It would require a fairly symmetrical clipping function (back-to-back diodes going to ground would work), a bandpass filter, and buffered negative feedback from the output of the filter to the input of the clipping function, with the output of the system taken from the bandpass filter. To emulate the Princeton Reverb and other blackface/silverface Fenders, no presence controls would be used. An RC filter could be added to the feedback path to create the presence found in the 5f6-A and most Marshalls.

Again, any thoughts on whether this would emulate the effects I am hearing are welcomed. Feel free to school me.

Sean Costello

[morcey2]

One component you're forgetting is the speaker.  In a cranked amp, the speaker will color the sound quite a bit and add it's own distortion IF it isn't rated significantly higher than the output power of the amp.  The other thing the speaker adds at higher volume is a 'push-back' effect on the transformer when the speaker is returning to center from a long excursion or incursion.  If the speaker can handle lots more power than the amp will put out, it will add less of it's own sound.  If it's an alnico, it will compress quite a bit before break-up, much more than a ceramic-magnet speaker - everything else being equal.  Alnico's are very bright (usually) until they're pushed where they start to roll off the highs. 

If you're princeton has the original 10" speaker or something similar, you were probably pushing it pretty hard even though they're rated for about 25 watts. 

The whole package is very interesting.  Were you using the TS as a clean boost, or as a distortion box?  I firmly believe that there is a 'feel' with the whole Power Tube/OT/Speaker saturation that will be very hard to emulate with a DSP, or even with a FET emulation.  I'm convinced that the speaker response and the interaction between the speaker and OT will be the hardest to nail down. 

Matt.

[frank_p]

I'm convinced that the speaker response and the interaction between the speaker and OT will be the hardest to nail down. 

Even harder would be the the non-linear behavior-deformation of the materials (ex: cardboard cone) in the speaker.

[SeanCostello]

If you're princeton has the original 10" speaker or something similar, you were probably pushing it pretty hard even though they're rated for about 25 watts. 

Yeah, it is the original "Fender Special Design" ceramic speaker. I had considered getting a Weber, but maybe I will hold off for now.

The whole package is very interesting.  Were you using the TS as a clean boost, or as a distortion box? 

At low PR volumes, the Jekyll (TS-808) was running as a distortion box, all knobs at noon. At the maxed out amp volume, the Jekyll was bypassed.

Now I wonder how much speaker distortion there was. It is entirely possible that the high frequencies were pushed into saturation by the low frequencies, even when I had the bass control rolled down to a low value (Vol 10, Treble 7.5, Bass 3). In the digital realm, it is usually assumed that nonlinearities generate harmonics, so it is weird to encounter nonlinearities that reduce the high frequency content. Of course, the standard digital synthesis uses a sine wavetable to shape a sawtooth wave into a sine wave, which is an extreme example of a nonlinearitiy reducing harmonic content.

Sean Costello

[SeanCostello]

I'm still thinking about this idea. My current questions:

- Is there a simpler way of viewing this type of bandpass filter with amplitude-limited negative feedback? Is this something that can be expressed with a single op-amp stage, a cap, a few resistors, and some diodes? I'm just now getting back into analog, so forgive my ignorance.

- Is it possible I am just hearing the effect of the low frequencies pushing the high frequencies out of the way? I turned down the lows, but it still might be enough to have the highs riding on top of the lows.

- Does speaker distortion have some special characteristic that can be expressed via some nice equations...that I won't understand?

Thanks,

Sean Costello

[frank_p]

- Is there a simpler way of viewing this type of bandpass filter with amplitude-limited negative feedback? Is this something that can be expressed with a single op-amp stage, a cap, a few resistors, and some diodes? I'm just now getting back into analog, so forgive my ignorance.

I still don't know for saturation and leakage,  I suppose for the rest it would be feasible...  my 0.02$ :
Others would be more in position to respond to that.

Bold = R.G.

« but it's hard to eliminate it with feedback because the leakage inductance is effectively in series with the OT primary and to an extent "hides" the transformer from the output tubes. »

Is this a Zen koan on which I can meditate more to have Illumination?

« The original article on the McIntosh transformer/amplifier made a big deal of this. »

Is it written in Pali language or it is accessible?

- Is it possible I am just hearing the effect of the low frequencies pushing the high frequencies out of the way? I turned down the lows, but it still might be enough to have the highs riding on top of the lows.

For the same (absolute) amplitude we hear the highs more easily.
EX:

Ref: http://www.engr.uky.edu/~donohue/audio/fsear.html

That is why we can mask a signal with noise (ex: white noise) ---perceptive masking--

Look at some graphs on this site:
http://www.santafevisions.com/csf/html/lectures/007_hearing_II.htm
EX:

The more you get close to threshold of hearing, the more the effect is clear.
BUT: in the other sense also: the more the mean volume is high, the less this effect will be there (the ear becomes more linear).
So bass signal may become more perceptible (compared to the highs).

- Does speaker distortion have some special characteristic that can be expressed via some nice equations...that I won't understand?

It depend on what you call distortion:
For the firsts modes of vibration (of the cone at reasonable amplitudes), it is very possible, but still it's hard maths (and the results may be 50% off the real thing even with good measures).
For higher amplitudes and higher frequency: Nearly impossible with equations : Too much dependant variables: we now use finite elements analysis.
These are equations they are used on and on in a software until a convergent solution is attained.
An example: considering the cone only (at "breakup"- there are different degree of breakup considering the design of the loudspeaker):



Ref.:http://www.vibroacoustics.co.uk/audio/fsacbens.htm

But:
You have to keep in mind also: fluid(air)-structure(cone/basket/etc.) interractions.

[Caferacernoc]

"- The frequency response of a small output transfomer, in the "linear" realm of operation, w/o negative feedback, is a bandpass filter.
- By adding negative feedback to the output section, the frequency response becomes "flatter," in that the peak of the bandpass is flattened out. This produces a more hi-fi response, with clear highs.
- When the power tubes are driven into saturation, the negative feedback no longer has the "flattening" effect on the frequency response, since the negative feedback is limited.
- Therefore, power tube saturation has more of a bandpass frequency response, with less high frequencies than would otherwise be available.

Does the above description ring true to you brainy types? The reasons why this would be a useful model:"



I think this is a huge reason tube power amp distortion sounds different than preamps and pedals. As you dig in you get that bandpass effect so instead of getting more fizzy you get that thick midrange oomph. Clapton's RHYTHM tone on Cream's Disreali Gears is a great example.
IMHO the effect is so cool, and the reason I love cranked amps, it's amazing it wasn't designed that way on purpose.

[Caferacernoc]

I also think people overlook the fact that power amp clipping occurs after the tone stack. Most tone stacks result in a mid dip even with the tone controls flat so the power amp clipping is receiving a signal with a mid dip. This is completely different than what occurs in the typical stomp box. A tube screamer, for example, has a bass cut before the clipping followed by a treble cut after the clipping.

[frank_p]

"- The frequency response of a small output transfomer, in the "linear" realm of operation, w/o negative feedback, is a bandpass filter.
- By adding negative feedback to the output section, the frequency response becomes "flatter," in that the peak of the bandpass is flattened out. This produces a more hi-fi response, with clear highs.
- When the power tubes are driven into saturation, the negative feedback no longer has the "flattening" effect on the frequency response, since the negative feedback is limited.
- Therefore, power tube saturation has more of a bandpass frequency response, with less high frequencies than would otherwise be available.

Does the above description ring true to you brainy types?

You are (probably) right.
But be carefull not insulting anybody.  Here it is a tradition to not harm and to give what you are willing to give (For what I understand).
I am half the brain I used to be...
There is no reason to hurt anybody.
I surely appreciate your response; but not the pointing you are doing about brainy types: (Who ever they are, I appreciate their response even if they would not be qualified as such)...   
Here, everybody is accepted when they are polite and civil.  (Well that is what I understood, (and what I repent for, in all the wrong replies I gave: "especially for Brett")).

Brainy, nerds, pretenders, straights, rockers, defenders, historians, hobbyists, professionals, engineers, neophytes, tone lovers, collectionners, wannabees , etc., etc, etc., are all wellcommed here.

But don't isolate anybody in any corner.
Especially if you want to talk.

I speak for myself (that is sure), but what I understand for consideration of others: act nice and gentle to them: because those "brains" are willing to give advices.

So you are also, it seems...
There are no trophy that will be given ( am I right ?)

Excuses, I am a very sensitive person...   
F.H.P.

[petemoore]

  All I can to is try to explain what I imagine.
  Pressure levels go way up and down on the cone whenever it is at either excursion limit [or near it], and when it is in the center of travel.
  This also relates to loads going up and down between the coil and the transformer.
  And these things being interactive, also the cabinet can make a big difference in these things, a small enclosed cavity behind the speaker for instance, compared to open back or even a reflex design.
  To make a digital model of all these interactions I would guess is possible [I just watched simulated earth get hit by a simulated comet...looked good enough...]. But to reproduce it 'actually' in real-time is...something to work on I guess, that or something electronic/digital with this capability which I'm as yet unaware of.
  Weight, inertia, damping, resonances, loads which are influenced by and influence these things...a lot to think about when factoring in say A-440.
  There'd be like a zillion calculations to do in a second, how many of them are actually important to the sound ?
  A whole new world out there, and like it's predecessors, subject to opinion, pre-concieved notions [I wonder how much of that I just demonstrated] conjecture, facts and real world results....as percieved and interpreted by humans.

[frank_p]

  Pressure levels go way up and down on the cone whenever it is at either excursion limit [or near it], and when it is in the center of travel.
  This also relates to loads going up and down between the coil and the transformer.
  And these things being interactive, also the cabinet can make a big difference in these things, a small enclosed cavity behind the speaker for instance, compared to open back or even a reflex design.
  To make a digital model of all these interactions I would guess is possible [I just watched simulated earth get hit by a simulated comet...looked good enough...]. But to reproduce it 'actually' in real-time is...something to work on I guess, that or something electronic/digital with this capability which I'm as yet unaware of.
  Weight, inertia, damping, resonances, loads which are influenced by and influence these things...a lot to think about when factoring in say A-440.
  There'd be like a zillion calculations to do in a second, how many of them are actually important to the sound ?
  A whole new world out there, and like it's predecessors, subject to opinion, pre-concieved notions [I wonder how much of that I just demonstrated] conjecture, facts and real world results....as percieved and interpreted by humans.

That is all true Pete.
But nobody are willing to put equations to point to a little "road".
Then there could be some "adjustments" to be made.
But now we are in the world of words to describe physical (electrical-mechanical) properties that points out to an other world that is tone that we perceive. (...)

Cafe Ra-Cernoc was right in his description of what we perceive.

And you are right in what you say about preconceptions.
But there we are talking and we have no scientific "references" to tie a rope and "surf" around it.
Talking could go on and on...

If we take the problem on an electrical-mechanical point of view, it could be more easy (erhm...) but now we are philosophising (in the pejorative sense of the word) --- (and including myself).

All we can do is read about theory about negative feedback going over the transformer and power stage considering the mechanical implications ( mass, rigidity, dampening of the speaker affecting the transformer (and the electromagnetically columned) and the power section (and vice's)...

Oouff...

I wonder if speaker maker tune their loudspeaker as I tune an acoustic guitar tabletop...
And then they (I) are dealing only with the mechanical point of view. Not how electrical-mechanical influences are interacting together (!).

F.Y.P.  Yours !