Peavy and output transormer saturation

[Mike Sulzer]

Peavy has discussed the effects of output transformer saturation here and there, for example: http://peavey.com/monitor/pvpapers/Chapter7.pdf. I think what he writes is not correct, but perhaps I am missing something and someone could tell me what it is.

Here is why I think transformer saturation cannot be the big deal he makes of it:

A relatively simple discussion here: Practical Considerations - Transformers : Transformers - Electronics Textbook shows (in the section on core saturation) that saturation is a frequency dependent thing. For example, if you design an amplifier so that the OT just saturates at 80 Hz at the maximum possible ac voltage across the primary (assume push-pull so there is no dc) then it does not saturate at 160 Hz. So for guitar we have two cases:

1. Single note playing. If the fundamental of the note has a lot of power and is low enough in frequency, then saturation can occur. But there is some frequency above which there is no saturation.

2. Playing chords. We have a wide range of frequencies present at once. Thus the power at the low frequencies at which saturation might occur is too low to cause saturation, the total power summed all frequencies being limited, of course.

So this statement

"A little known aspect of output transformers is that their frequency response tends to drop off rapidly at both the high and the low frequency EXTREMES as the signal level approaches “saturation” of the core. This is a “dynamic process” which means that it is CONSTANTLY CHANGING with the frequency and amplitude of the driving signal supplied by the valves.In normal operation, frequency response is usually reasonably flat, but as the signal approaches saturation (maximum output) the extreme ends of the transformer’s bandpass tend to drop considerably, but in a “dynamicfashion” (meaning that the transformer’s “bandpass characteristics” are CONSTANTLY CHANGING!). "

seems to have no basis in the real world. That is, the concept of the signal level approaching saturation makes no sense, unless severely qualified to the point that this dynamic filtering does not happen as he says it does.

[nickb]

I expect the statement derives from considering that the permeability is not constant, falling as the H field increases. Therefore, so the argument goes, at lower fluxes the inductance is bigger and so the low end is better and the highs are reduced, in other words the whole band moves down. At very low fluxes the permeability becomes small again so moving the bandwidth higher.

Looking at it in a time domain way, with low frequency big signal swings the effect is to round the tops of the waveform as the core saturates.

The big question is whether the volt-seconds for a particular transformer ever gets big enough to make the effect very audible. The specs available on current transformers are rather incomplete.

[J M Fahey]

I guess there might be *a little* of that going on.
And that using a very undersized transformer, low frequencies present will modulate high frequencies, that would be audible.
Mid/high frequencies would do nothing by themselves.

And in a ClassA single ended OT (think Champ) , even if undersized, DC would be the main and fixed component, all else pale besides it ... even low frequencies.

What low frequency can compete with DC?

[Mike Sulzer]

I expect the statement derives from considering that the permeability is not constant, falling as the H field increases. Therefore, so the argument goes, at lower fluxes the inductance is bigger and so the low end is better and the highs are reduced, in other words the whole band moves down. At very low fluxes the permeability becomes small again so moving the bandwidth higher.

Looking at it in a time domain way, with low frequency big signal swings the effect is to round the tops of the waveform as the core saturates.

The big question is whether the volt-seconds for a particular transformer ever gets big enough to make the effect very audible. The specs available on current transformers are rather incomplete.

Yes, saturation is approached somewhat gradually, with permeability falling to that of free space at full saturation. But this only happens at low frequencies. The argument, as in the second link, is that it takes a certain rate of change of flux to support the voltage across the primary. For lower frequencies, the rate of change occurs for a longer time, and therefore the flux (the integral over time of the change in flux) must get bigger. Thus what you mentioned only happens at low frequencies because the flux can only approach the limit when the frequency is low.

Also, he is claiming that you lose both lows and highs as the flux goes up. Actually, the high end is not affected by saturation. Transformers lose high frequencies because of leakage flux, a different problem.

So I think a significant part of his transtube circuitry is based on a misunderstanding of how transformers work.

[nickb]

Yes, saturation is approached somewhat gradually, with permeability falling to that of free space at full saturation. But this only happens at low frequencies. The argument, as in the second link, is that it takes a certain rate of change of flux to support the voltage across the primary. For lower frequencies, the rate of change occurs for a longer time, and therefore the flux (the integral over time of the change in flux) must get bigger. Thus what you mentioned only happens at low frequencies because the flux can only approach the limit when the frequency is low.

Also, he is claiming that you lose both lows and highs as the flux goes up. Actually, the high end is not affected by saturation. Transformers lose high frequencies because of leakage flux, a different problem.

So I think a significant part of his transtube circuitry is based on a misunderstanding of how transformers work.

Yes, agreed. Only the low end is affected (only for the single note case).

I note he says

"Because modern output transformers are usually welldesigned, most people don’t realize that they have
such a profound effect on the frequency response of
amplifiers."

So, he is actually saying that you can't hear it (with modern transformers) I guess.

It's also not clear that the transtube series modulate both the high and lows from the text. I guess I'll have to look at a schematic to find out.

Afterthought edit: I think for a guitar ( i.e. not bass) the lows tend to be a small part of the total output the effect may never be significant in practice.

[Mike Sulzer]

I guess there might be *a little* of that going on.
And that using a very undersized transformer, low frequencies present will modulate high frequencies, that would be audible.
Mid/high frequencies would do nothing by themselves.

And in a ClassA single ended OT (think Champ) , even if undersized, DC would be the main and fixed component, all else pale besides it ... even low frequencies.

What low frequency can compete with DC?

Yes very undersized, indeed! It would only put out a small fraction of rated power at 80 Hz, power varying as the square of voltage or current.

DC is the worst case for sure, and so the single ended amp pays a severe penalty. But mostly they are so low power that maybe it is not too much of an issue. I think anyone who wanted too make an 80 watt single ended tube amp would probably abandon the project before completion!

[R.G.]

It's a mismash of techno... um, stuff.

A transformer works by producing a *changing* magnetic field in the iron by pumping the primary. The secondary can only respond to a *changing* magnetic field. This is the fundamental reason you can't transform DC. No change, no transforming.

If you pump the primary of a transformer with an AC signal, the primary responds as though it's an inductor. That's because it is. This pumping establishes a changing magnetic field in the transformer. The intensity of the field is proportional to NI, the number of turns and the current, and *in an inductor only* that is proportional to the applied voltage times time, because V = L di/dt, and so di = Vdt/L. That's your volt-time number you hear about. You can figure current by integrating that to get the change in current (and NI, since N is fixed) as I = V*deltaT/L.

The flux density in the iron is then proportional to both the volt-time integral and the NI peak. And the flux density in the iron saturates in a soggy, soft, folding-over way.

There is a great deal of misinformation about what happens when a transformer saturates. Saturation is the condition where all the magnetic domains in the core that can be magnetically aligned have been aligned. While there are specialized materials where this happens suddenly, at a razor's edge point, those materials are not used for output transformers. For OTs, you come on saturation gradually. In fact, saturation isn't an event - it happens so gradually that you have to make an arbitrary definition about where it is. Saturation is the gradual reduction in the ability of the iron to latch onto and "shunt" any magnetic field through itself.

Iron and other ferromagnetic materials "conduct" M-fields better than free space. If there's an M-field around it would rather "flow through" the iron than free space, so it will bend itself over into the iron. The iron is a lower energy path, and the field wants to be there. But as more and more threads of magnetic flux enter the iron, it gets crowded. That's saturation. The iron is less of a better "conductor" of M-field than free space, so some of the flux stays out, until at really, really saturation, the iron's no better at sucking in more M-field than free space.

As a consequence, *the higher the field inside the iron, the more leakage OUTSIDE the iron happens*. This is the origin of the high frequency response being modulated by the low frequency content. At high frequencies, the ability of the iron to keep M-field inside is damaged by the instantaneous M-field, much of which is determined by the low frequency content.

So yeah, high and low frequency response is modulated, but it's not in any simple way. It's all full of integrals and time dependent differential equations. The low frequency approach to soggy, soft saturation si matched by higher leakage because the core can't soak up so much of the incoming M-field and it's not as effectively coupled to any secondaries that exist because it's not coupled to the primary/core.

Things also get more complex when you consider secondaries. The field equations work out that pumping a primary with an AC voltage sets up some M-field, which is determined by the volt-time and the current, and we interconnect those as "inductance", that being the relationship of current that flows for an applied voltage and frequency. The voltage, frequency, and inductance set up some value of changing M-field. Secondaries suck some of that energy out, lowering the M-field. The lower-M-field energy is instantly replaced from the primary, so it looks like the energy is flowing through the transformer, but actually the secondary is poisoning the core's ability to resist incoming current by sucking current out.

As you can tell, this gets deep enough for chest waders really quickly. Peavey is probably forced to dumb this down for the audience if he understands it.

[Mike Sulzer]

Yes, agreed. Only the low end is affected.

I note he says

"Because modern output transformers are usually welldesigned, most people don’t realize that they have
such a profound effect on the frequency response of
amplifiers."

So, he is actually saying that you can't hear it (with modern transformers) I guess.

It's also not clear that the transtube series modulate both the high and lows from the text. I guess I'll have to look at a schematic to find out.

I think he is saying that you cannot hear it with a modern transformer designed for "hifi", but since tube amps use much smaller transformers, it is an audible effect.


In this link (http://peavey.com/monitor/pvpapers/Chapter3.pdf), he seems to imply that the effect is at all frequencies. He does not say that it is limited to low frequencies, and he does say that high frequency response is cut down with saturation. Yes, a look at the circuit would be useful.

[R.G.]

As I noted, the water gets deep, because high frequency response is cut by the instantaneous saturation level modulating the leakage inductance. It's a side effect similar to those used in magnetic amplifiers. So if you had a just-into-saturation 80Hz signal and a 1kHz signal, the 1kHz signal would be somewhat lessened by the saturation peaks of the 80Hz tone, giving you 160Hz intermodulation of the 1kHz signal.

Hifi OTs generally handle this by running the peak flux density way, way lower than any nominal saturation to keep the distortion numbers of the transformer itself down. So yeah, in a hifi transformer, the flux density peaks may be so low as to keep this from happening noticeably.

[Mike Sulzer]

That is very interesting; you have explained how enough power at low frequencies to saturate can reduce high frequencies more than, say middle frequencies. But does this happen in a real guitar signal? I think it does not because the fraction of low frequency frequency energy in a chord containing a wide range of frequencies is not very high, and thus does not saturate significantly. For sure using the bridge pickup, the harmonics in the open E string alone have significantly more power than the fundamental. Add in the other strings and the fraction gets much smaller. The neck pickup must have more low frequencies, but I would have to make some measurements to see how much.

It's a mismash of techno... um, stuff.

A transformer works by producing a *changing* magnetic field in the iron by pumping the primary. The secondary can only respond to a *changing* magnetic field. This is the fundamental reason you can't transform DC. No change, no transforming.

If you pump the primary of a transformer with an AC signal, the primary responds as though it's an inductor. That's because it is. This pumping establishes a changing magnetic field in the transformer. The intensity of the field is proportional to NI, the number of turns and the current, and *in an inductor only* that is proportional to the applied voltage times time, because V = L di/dt, and so di = Vdt/L. That's your volt-time number you hear about. You can figure current by integrating that to get the change in current (and NI, since N is fixed) as I = V*deltaT/L.

The flux density in the iron is then proportional to both the volt-time integral and the NI peak. And the flux density in the iron saturates in a soggy, soft, folding-over way.

There is a great deal of misinformation about what happens when a transformer saturates. Saturation is the condition where all the magnetic domains in the core that can be magnetically aligned have been aligned. While there are specialized materials where this happens suddenly, at a razor's edge point, those materials are not used for output transformers. For OTs, you come on saturation gradually. In fact, saturation isn't an event - it happens so gradually that you have to make an arbitrary definition about where it is. Saturation is the gradual reduction in the ability of the iron to latch onto and "shunt" any magnetic field through itself.

Iron and other ferromagnetic materials "conduct" M-fields better than free space. If there's an M-field around it would rather "flow through" the iron than free space, so it will bend itself over into the iron. The iron is a lower energy path, and the field wants to be there. But as more and more threads of magnetic flux enter the iron, it gets crowded. That's saturation. The iron is less of a better "conductor" of M-field than free space, so some of the flux stays out, until at really, really saturation, the iron's no better at sucking in more M-field than free space.

As a consequence, *the higher the field inside the iron, the more leakage OUTSIDE the iron happens*. This is the origin of the high frequency response being modulated by the low frequency content. At high frequencies, the ability of the iron to keep M-field inside is damaged by the instantaneous M-field, much of which is determined by the low frequency content.

So yeah, high and low frequency response is modulated, but it's not in any simple way. It's all full of integrals and time dependent differential equations. The low frequency approach to soggy, soft saturation si matched by higher leakage because the core can't soak up so much of the incoming M-field and it's not as effectively coupled to any secondaries that exist because it's not coupled to the primary/core.

Things also get more complex when you consider secondaries. The field equations work out that pumping a primary with an AC voltage sets up some M-field, which is determined by the volt-time and the current, and we interconnect those as "inductance", that being the relationship of current that flows for an applied voltage and frequency. The voltage, frequency, and inductance set up some value of changing M-field. Secondaries suck some of that energy out, lowering the M-field. The lower-M-field energy is instantly replaced from the primary, so it looks like the energy is flowing through the transformer, but actually the secondary is poisoning the core's ability to resist incoming current by sucking current out.

As you can tell, this gets deep enough for chest waders really quickly. Peavey is probably forced to dumb this down for the audience if he understands it.

[Mike Sulzer]

As I noted, the water gets deep, because high frequency response is cut by the instantaneous saturation level modulating the leakage inductance. It's a side effect similar to those used in magnetic amplifiers. So if you had a just-into-saturation 80Hz signal and a 1kHz signal, the 1kHz signal would be somewhat lessened by the saturation peaks of the 80Hz tone, giving you 160Hz intermodulation of the 1kHz signal.

Hifi OTs generally handle this by running the peak flux density way, way lower than any nominal saturation to keep the distortion numbers of the transformer itself down. So yeah, in a hifi transformer, the flux density peaks may be so low as to keep this from happening noticeably.

But in a hifi signal you have everything, and so you can have a very large fraction of low frequencies for a short time which would then crush the higher frequencies with an undersized transformer. I do not see how this can happen in a guitar signal. Only a single string (say open E6) can make any significant relative amount of bass, and most of the effect there is harmonic distortion (which you have for various reasons), not intermod.

[Mike Sulzer]

Here are four plots of guitar spectra. If the amp can put out an 80 Hz sine wave with nearly the rated power, then it appears that the relative power at about 80 Hz in these signals is too small to cause significant saturation.

E6openBridge.pdf
E6openNeck.pdf
EmChordBridge.pdf
EmChordNeck.pdf

[Gregg]

I'm not as good in theory as some here but my experience with running tests on different amps and OTs is it's almost impossible to drive an OT into saturation even at 50-60Hz (sine wave). Very rarely I've observed a slightly "broken" and/or "tilted" sine wave hinting to initial saturation and those were really small OT's. The saturation is also audible - the OT will start buzzing at low frequencies like 40 or 30Hz (when amp output is connected to a dummy load).

[R.G.]

That is very interesting; you have explained how enough power at low frequencies to saturate can reduce high frequencies more than, say middle frequencies. But does this happen in a real guitar signal? I think it does not because the fraction of low frequency frequency energy in a chord containing a wide range of frequencies is not very high, and thus does not saturate significantly.

I didn't indicate one way or the other in my "how trannies work" polemic, only that there is a mechanism there.

Signals, by definition, vary. So there is some combination of highs and lows and other stuff that can cause modulation of the highs by the lows through saturation for every possible transformer, which also vary - a lot.

There's a lot of internet supposition that "guitar amp output transformers" or "guitar signals" are a coherent whole. They are, very much, not so. Given that, can the subject effect happen? Absolutely, yes. Does it happen? Absolutely yes, for some values of amplifier, signal and whatever OT has been buckled in there. Does it happen rarely, some, much of the time, most of the time, or nearly always? Probably the most accurate answer is "some of the above".

I personally think it's very rare, which is why my personal opinion of the Peavey article is that it's plausible-sounding techno-pap. But there are a few glittery grains down there in the mush. So for the case:

But in a hifi signal you have everything, and so you can have a very large fraction of low frequencies for a short time which would then crush the higher frequencies with an undersized transformer. I do not see how this can happen in a guitar signal. Only a single string (say open E6) can make any significant relative amount of bass, and most of the effect there is harmonic distortion (which you have for various reasons), not intermod.

The issue of what is a low frequency depends on the OT being driven and the voltage it's being driven with. There are two terms in the flux density equation - volts and time. If you have a lot of volts, time can get short. If you have very low frequencies, you can use low volts and still get to saturation. The other issue is the core and windings. Saturation is what happens when all the magnetic domains are aligned. It's a volume effect. A smaller chunk of iron, smaller core area and shorter magnetic path, can be driven to saturation more easily, as it takes less energy to fill it up. So for the same volt*time product, smaller iron will saturate sooner.

What I'm getting at is that it's not strictly possible to say that 80Hz, 160Hz, or 1kHz is "low frequency"; it's only low in comparison to the volt-time ability of the core. You could probably put the OT of an AC15 on a Marshal Major output stage and saturate it with the high E string. But on average, yeah, I'm with you. Doesn't happen hardly ever.

But all that being said, again, I'd have to say that the confluence of the amp designers doing their job fairly well is what makes "typical" amps not saturate for "typical" values of guitar signal, and average values of "typical".

And that's really what is at the bottom - whether the guy who spec'd the OT bought one that has enough core area and high enough primary inductance not to get into the soggy beginnings of saturation for his target market of guitars. Mostly they do, and so it's likely to be very rare that you see this issue in a real-world guitar amp - and hence the Peavey article is a lot of sound and fury, and we know what that means.

I find that I have to work hard to keep a straight face when an amp builder explains to me why his OTs are so absolutely superior. The stories are really fun.

[loudthud]

When a guitar amp is overdriven, new frequencies are created that were not present in the signal that came from the guitar, or they were are such low levels that they were ignored. Some of these frequencies are below the the audio spectrum, they are artifacts of pick transients, note envelopes and asymmetrical clipping. Some of this was discussed here: http://music-electronics-forum.com/t37023/

Could these very low frequencies nudge the OT towards saturation in a way that causes compression of audible signals?