This should be true if ferromagnetic materials were linear and isotropic, i.e. hysteresis-less.
B = μ H
With μ=constant
I must remind you that μ is the rank 2 permeability tensor such that
Bi = μij Hj
And even worse, permeability tensor is also function of frequency and magnetic field... even for super-duper modern magnetic materials...
I agree that the expression shown on post#139 is an antiquity, but it was written to show the resistance dependence of THD.
Modern M6 GOSS @ 20 Hz, 40 Ω source and -40 dBu signal level exhibits about 0.5% THD, and it is not negligible, isn't it?
[Glen Ballou - Handbook for Sound Engineers - 4th Edition - page 284]
Anyway, a coreless transformer (e.g. vacuum) will show THD due to winding resistance, which can easily seen in LTSpice simulations.
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I built PP amp without global feedback 3 years ago or so, and even complete amp (with transformer) have not showed so high THD until power reached about 25% of nominal. I discarded measurement data, as far as I remember it was about 0.2% - 0.3% (for the entire setup).
Have no idea where author of this book took these awful numbers, probably simply copied from 195x - 196x literature, or miscalculated something.
Then try to measure at a lower frequency, where the magnetic field is stronger.
PP OPTs are not the best to work without global feedback by the way.
4th edition is from 2008 and chapter 11 was written by Bill Whitlock (Jensen Transformers).
In 50's or 60's they did not refer to M6 grade but 6% silicon-steel AFAIK.
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Transformer harmonic distortion is highest at low frequencies, and increases with driver's impedance. In real life tube OPT with grain-oriented steel laminations, 20 Hz THD may be as high as 5-10%, even if transformer is very large and operated well below saturation. For a small transformer operating close to saturation, 20 Hz THD may be 60-80%.
Maybe, maybe not, as
Bac(max) = (Uac x 10⁸) / (√2 π fo S Np)
Bac is inversely proportional to frequency, so I agree that at lower frequency distortion will increase, but your numbers seems a bit arbitrary as there are so many variables: SE, PP, core material (lots of GOSS grades), core geometry (C-core, EI, toroid,...), wire resistance, chosen winding scheme...
Not necessarily a bigger core gives less distortion, as I said before an ideal linear isotropic (hysteresis-less) core will follow constitutive relation
B = μ H
With μ=constant, so we need that magnetic permeability will be quite constant along the hysteresis loop, this implies a very thin closed curve (sometimes a very thin ellipse) hence hysteresis losses must be very low, as they are expressed in W/Kg, a bigger core will have greater losses and hence more distortion.
Transformer design is a big set of compromises.
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Again, it depends on the core, for a gapped core (SE OPT) μ can be quite constant along the whole hysteresis loop, about two orders of magnitude smaller but quite constant, even at Bac=0 (Single ended magic)
A lower μ does not means necessarily higher distortion.
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The nonlinearity of the hysteresis loop distorts only the magnetizing current. If the inductance is large or very large and at the same time the resistance of the lamps is low, or very low, then no matter what form this magnetizing current will be, even if it is a triangular shape. The main thing is that it will be insignificant in size. This is very well explained in his article James Moir, GA 3 \ 1994 (part 2). Moreover, it beautifully showed that the reduced load resistance together with the low internal resistance of the lamps further reduces the distortion. Therefore, in tetrodes and UL, it is possible to obtain distortions even lower than in triodes. And he also stressed that it is not worthwhile to get involved in reducing induction, since in this case the permeability and inductance of the primary winding decreases. The dependence of the third harmonic is shown: K3 = R / wL All this is already true even for steel magnetic cores. In modern amorphous materials whose permeability is much higher, the hysteresis loop is even and the loss is much smaller the picture is radically even better. In general, in the amplifier, in fact, a larger contribution to the distortion is made by the lamps themselves and not by the transformers that have been properly made.
http://www.vestnikara.spb.ru/vestn/n3/moir17.gif
http://www.vestnikara.spb.ru/vestn/n3/moir.htm
http://www.vestnikara.spb.ru/vestn/n3/moir17.gif
http://www.vestnikara.spb.ru/vestn/n3/moir.htm
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I need time to answer to the different questions; I am coming back soon with some other tests and info.
But I would like to say that this post from GUNFU is very important and is the real world!!!!
On other my thread:
http://www.diyaudio.com/forums/tubes-valves/308607-p-p-el34-kt120.html
there is written this; please read also the test in attach we done at Audioreview magazine in the lab, on this amps.
Another thing; in NOT TRUE that the pp aren't fine to work without feedback. There some consideration to do.
For this I will send other interesting tests.
But I would like to say that this post from GUNFU is very important and is the real world!!!!
On other my thread:
http://www.diyaudio.com/forums/tubes-valves/308607-p-p-el34-kt120.html
there is written this; please read also the test in attach we done at Audioreview magazine in the lab, on this amps.
Another thing; in NOT TRUE that the pp aren't fine to work without feedback. There some consideration to do.
For this I will send other interesting tests.
At the expense of selecting wires for winding the output transformers.
If once again carefully read the mentor James Moir then the conclusion on the distortions is simple. It is necessary to have a large inductance, high frequency and low resistance of the generator in the replacement circuit. We can not change the frequency, because the frequency range is set by a sound signal. We can only affect inductance and resistance. Inductance depends on the applied magnetic material and the number of turns, here everything is also understandable. The more permeability and more turns, the greater the inductance. It remains to understand the resistance. And it, as written by the old mentor, depends on the internal resistance, the tubes, the reduced load resistance and alas the resistance of the wires. And in fact, even from the losses in the magnetic circuit! But in this case, we have already chosen the best material, for example, amorphous alloy or HI-B steel, and the size of the magnetic circuit has already been determined, and accordingly we can no longer greatly affect these losses, perhaps, since we can also optimize the shape or design of the magnetic circuit.
The resistance of the Litz wire at low frequencies is likely to be higher than that of a single wire of the same cross section. And at high frequencies the signal power itself may not be as significant as at low frequencies. My opinion is the best wire, taking into account the loss reduction is one wire made of silver. And the magnetic circuit with the lowest losses is a nanocrystalline alloy or HI-B.
If once again carefully read the mentor James Moir then the conclusion on the distortions is simple. It is necessary to have a large inductance, high frequency and low resistance of the generator in the replacement circuit. We can not change the frequency, because the frequency range is set by a sound signal. We can only affect inductance and resistance. Inductance depends on the applied magnetic material and the number of turns, here everything is also understandable. The more permeability and more turns, the greater the inductance. It remains to understand the resistance. And it, as written by the old mentor, depends on the internal resistance, the tubes, the reduced load resistance and alas the resistance of the wires. And in fact, even from the losses in the magnetic circuit! But in this case, we have already chosen the best material, for example, amorphous alloy or HI-B steel, and the size of the magnetic circuit has already been determined, and accordingly we can no longer greatly affect these losses, perhaps, since we can also optimize the shape or design of the magnetic circuit.
The resistance of the Litz wire at low frequencies is likely to be higher than that of a single wire of the same cross section. And at high frequencies the signal power itself may not be as significant as at low frequencies. My opinion is the best wire, taking into account the loss reduction is one wire made of silver. And the magnetic circuit with the lowest losses is a nanocrystalline alloy or HI-B.
That is true however you don't do the secondary with a large solid core wire usually otherwise bye bye high frequency good performance. Skin effect and proximity effect will kill it as the AC resistance will increase much quicker. As the secondary, for low AC resistance, is usually made with smaller size solid core wire with multiple windings in series-parallel I can assure that the resultant resistance is not simply given by the series-parallel combination of the windings resistances. It depends on how this is done. One has to add contact resistance which might not be negligible when one is looking after smallish sub-ohm values for the secondary. So it is not as simple as that.
The condition for minimum copper loss is half winding volume for the primary and half for the seconday. No escape!
If you use large size solid core wire, copper or silver it doesn't make significant difference, AC resistance will increase quickly well within the audio band (it also depends on other factors, namely the winding gemotry). In fact one can often see many DIY amplifiers that simply do not achieve the rated power above 2-3 KHz with the same distortion as 1KHz. Actually at 10KHz THD is 2-3 times higher already for 1W output.....!!! But the latter one is also a consequence of poor balance in PP amps.
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On the account, application of Litz wire or many conductors connected in parallel in the secondary winding instead of one wire, I agree, here the effect will take place. Regarding the primary winding, the question is very controversial. Everyone says a lot about the resistance in the wires and no one about the losses in the magnetic circuit, but they are still equal to each other and sometimes even more in large magnetic circuits on the M6 than in the wires. Because of this, the bad results described by you can appear above 2-3 kHz, and not because of the wires.
Using local feedbacks from the cathode windings, UL, or feeding a feedback signal separately from each anode of the shielded lamp to the driver cathode, and actually to the first grid of this same output lamp. This, given the reduced load resistance, makes it possible to create the lowest equivalent generator impedance much lower than in triodes. And the use of a silver wire can in fact only be justified in these three schemes, and not in triodes, as one well-known Japanese-English firm advertises.
Using local feedbacks from the cathode windings, UL, or feeding a feedback signal separately from each anode of the shielded lamp to the driver cathode, and actually to the first grid of this same output lamp. This, given the reduced load resistance, makes it possible to create the lowest equivalent generator impedance much lower than in triodes. And the use of a silver wire can in fact only be justified in these three schemes, and not in triodes, as one well-known Japanese-English firm advertises.
I doubt very much about the THD a 2-3KHz is due to the losses in the core. At that frequency the AC induction is very small and so the core losses...
The increase in THD also happens with cathode fb or Schade plate-to-grid feedback with perfectly AC balanced output stage and is due to the transformer that simply can't cope with higher power as the freqeuncy goes up. This doesn't happen, or it is minimal to be more realistic, if the transformer is done right. However that means at 99% the secondary has to be done with multiple windings in series-parallel. If one doesn't want to do that and use a "single" wire then Litz wire is the solution.
The increase in THD also happens with cathode fb or Schade plate-to-grid feedback with perfectly AC balanced output stage and is due to the transformer that simply can't cope with higher power as the freqeuncy goes up. This doesn't happen, or it is minimal to be more realistic, if the transformer is done right. However that means at 99% the secondary has to be done with multiple windings in series-parallel. If one doesn't want to do that and use a "single" wire then Litz wire is the solution.
Comparison of the frequency characteristics of M6 and amorphous alloys shows that the permeability of steels with increasing frequency falls sharply, and this I am an indirect sign of the growth of losses compared with amorphous alloys in which the permeability graph is linear over a very wide frequency range.
Probably, the use of the Litz wire in the primary winding will also be justified only in these three circuits, and not in triodes. And then, if you use magnetic circuits with low losses from a nanocrystalline alloy or HI-B, but not in a cheap M6.
Probably, the use of the Litz wire in the primary winding will also be justified only in these three circuits, and not in triodes. And then, if you use magnetic circuits with low losses from a nanocrystalline alloy or HI-B, but not in a cheap M6.
That is not an opinion! It depends on the proximity effect, skin effect, material, sinze and -last but not least- gemometry of the winding. It can be calculated. There is no magic number valid for all transformers....
If you tell a specific core and transformer you want to make (i.e. impedance, power and all the usual stuff) I will tell you the number. I won't tell you how I calculated it. Sorry...you might look for that in the books.
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The most important factor on HF is the leakage inductance, its reduction is achieved by alternating the primary and secondary windings. Also, the alternation of the primary winding with the secondary winding in the transformers reduces the proximity effect.
"Losses in windings due to proximity effect"
Dr. Ray ridley
Ridley R.?????? ? ???????? ?????????? ??????? ????????
"Losses in windings due to proximity effect"
Dr. Ray ridley
Ridley R.?????? ? ???????? ?????????? ??????? ????????
Yup, very true... in mains power transformers connected to a zero impedance source....
Output power transformers do work in a different form.
Paradoxically proximity effect and leakage inductance both have the same cure: winding interleaving.
We must repeat over and over again that using Litzendraht wire in audio transformers do more harm than good...
Most of us do not understand Russian language BTW.
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