I am still waiting for a demonstration or plausible argument that air-cored transformers or inductors are noticeably non-linear at typical audio frequencies and typical audio powers. Of course, we know that no physical system is perfectly linear so to say so is unremarkable. We also know that some physical systems are sufficiently linear that for all reasonable engineering purposes we can regard them as linear. So what, exactly, are we arguing about?
All I have gleaned so far is that someone appeared to say (in another thread?) that an air-cored transformer can be non-linear and someone else asked him to back this up with facts. Such facts have not yet appeared. So was the original statement false and to be retracted, or misunderstood and to be clarified, or true and to be supported with facts?
All I have gleaned so far is that someone appeared to say (in another thread?) that an air-cored transformer can be non-linear and someone else asked him to back this up with facts. Such facts have not yet appeared. So was the original statement false and to be retracted, or misunderstood and to be clarified, or true and to be supported with facts?
Then you might wait forever. Non one said that and actually air-core transformers are do exist at all for typical audio power. Even for a fraction of 1 watt. The point was just about running simulations for a system that has some sort of non-linearity. So it's a useless argument and you are just starting a new flame.
I can concede you that my Tarzan-English is challenging and my memory at my age is not (never was) optimal, but as far as I know I never said that.
Not even read my original statement… snake oil hunter…
I did not mention an air-cored transformer, to live in Fantasyland we need to make it well, with a proper vacuum core.
Nonlinear losses in transformers are sources for nonlinearities.
1) Transformer core
In another thread I did prove to you that ferromagnetic materials are nonlinear and anisotropic and hence they show hysteresis.
I suppose that we must agree on that nonlinear and anisotropic nature of magnetic materials is a source of transformer nonlinearity, because the constitutive relation
B = μ H
Is not a straight line due to μ, the magnetic permeability, is a tensor.
2) Transformer winding
i) Capacitance
In the same mentioned thread I did prove to you that dielectric materials are also nonlinear and anisotropic and hence they show hysteresis too.
High quality capacitors, e.g. polypropylene with tan (δ) ∼ 10⁻⁴ clearly show hysteresis at about 70 VRMS.
High quality transformer insulators (e.g. Nomex) show about an order of magnitude higher dissipation factor, i.e. tan (δ) ∼ 10⁻³ and primary to secondary voltage is very often greater than 70 VRMS, and then they must clearly show hysteresis.
It follows that distributed capacitance is another source for transformer nonlinearity because the constitutive relation
D = ε E
Is not a straight line due to ε, the dielectric permittivity, is a tensor.
ii) Leakage inductance
To derive the equation for leakage inductance you must evaluate the leakage magnetic field along the hysteresis loop, it is a wasted energy too, then losses due to leakage inductance are nonlinear too and they also increase transformer nonlinearity.
iii) Winding resistance
Very often, an OPT is connected to a valve, valves are nonlinear and the current flowing in a valve irremediably contains harmonics, and we say that that current is nonlinear.
A nonlinear current flowing through a linear resistance produces a nonlinear voltage.
Even neglecting nonlinearities from (1), (2.i), and (2.ii) an increase on winding resistance will produce an increase in transformer THD.
Maybe you never run an LTSpice simulation?
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I didn't start this thread. I am merely seeking clarification about what this thread is about. It is obvious that an air-core transformer will be linear. It is obvious that an iron-cored transformer will be somewhat nonlinear. Neither need a new thread saying so.45 said:
OK, so this thread is not about air-cored transformers. The thread title is misleading.popilin said:
Nonlinearities are sources of nonlinearities.
Of course.
Hysteresis and loss are not the same thing. Losses can be linear, so non-zero DF does not imply hysteresis.
That is valve nonlinearity, not transformer nonlinearity.
OK, should the thread title be about vacuum core transformers? Are you saying that vaccum core transformers are nonlinear, or querying why LTspice allegedly suggests that they are? Winding resistance is linear (to a very good approximation) so is not a source of nonlinearity.
I realise that by getting into a discussion with popilin it is sadly likely that very soon he will remind me why he normally sits in my ignore list. I hope I am proved wrong this time.
It's about simulations and how to see the same effect without introducing a model in LTSpice for the magnetic cores. It's so obvious...if one knows where is coming from!!!
The fact there is another thread is not your business and anyway you are questioning moderators choice.
It has been proved that copper losses are nonlinear.
Pcu = I1² sin² (ω t + φ1) Rp + ∑ Ih² sin² (h ω t + φh) Rp, h = 2, 3, … , ∞
Hysteresis losses are nonlinear, that is the point; and non-zero dissipation factor DOES imply hysteresis.
To write constitutive relation without using tensors
D = ε(ω) E
We need a different model for ε(ω), as far as I know, the cool and easiest way is
ε(ω) = ε’(ω) + i ε’’(ω)
Then, dissipation factor, can be written as
tan (δ) = ε"(ω) / ε'(ω)
Then, we can write
ε(ω) = ∣ε(ω)∣ [ cos (δ) + i sin (δ) ]
On condition of taking the real part, we also can write
E = Eo exp (- i ω t) = Eo [ cos (ω t) - i sin (ω t) ]
Then
D = Re [ε(ω) E ] = ∣ε(ω)∣ Eo cos (ω t - δ)
E = Eo cos (ω t)
On the plane E D, those are parametric equations of a differentiable closed curve, in this case an ellipse, so was proved hysteresis.
Call it as you want, if it makes you happy.
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Please popilin, save us your formulas; virtually nobody is checking them!
When you want to simulate air core inductors/transformers, IMO it's enough to regard them being linear.
Your sim is probably right for 99,9%.
Most likely there are other parameters distorting the sim more than air core inductors/transformers happening to be a tiny bit less linear than linear.
This is another redundant thread; there seem to be a lot of redundant threads over the last weeks...
When you want to simulate air core inductors/transformers, IMO it's enough to regard them being linear.
Your sim is probably right for 99,9%.
Most likely there are other parameters distorting the sim more than air core inductors/transformers happening to be a tiny bit less linear than linear.
This is another redundant thread; there seem to be a lot of redundant threads over the last weeks...
I'm glad you said that, I thought it was just me! I've been getting bored and disillusioned...perhaps it's the time of year...most people having better things to do and those that haven't, getting cranky
If we read Radiotron carefully we can see that there are two important step about distortion in OT trafo ( par. 5.3)
Mr. Popillin wrote a formula by Partdridge and if consider it correct we can see that as divider there is f =frequency.
The final formula is:
Vh/Vf = 5.54 x Sh x l x Ra (= Rp tubes+Rwinding// Rload ) / Nsquare x A x F
Sh distortion coefficent of the magnetic, l lenght of the magnetic path,
The Ra mentioned is the parallel of Rp+ R of winding with the RL on the primary,that is much different to say that is is only the resistive part of winding.
Nsquare is the ratio of trafo, A area of the core, F frequency
The consideration is correct until the frequency is low, as WELL described in Radiotron.
In fact at page 217 of 5.3 there is a little chapter regarding only the distortion at high frequncy where the parasitc are dominant with the non linearity of tube.
No mention about R of windings.
In fact on the formula increasing the F until infinity the distortion goes to zero (theoretically of course)
Walter
Mr. Popillin wrote a formula by Partdridge and if consider it correct we can see that as divider there is f =frequency.
The final formula is:
Vh/Vf = 5.54 x Sh x l x Ra (= Rp tubes+Rwinding// Rload ) / Nsquare x A x F
Sh distortion coefficent of the magnetic, l lenght of the magnetic path,
The Ra mentioned is the parallel of Rp+ R of winding with the RL on the primary,that is much different to say that is is only the resistive part of winding.
Nsquare is the ratio of trafo, A area of the core, F frequency
The consideration is correct until the frequency is low, as WELL described in Radiotron.
In fact at page 217 of 5.3 there is a little chapter regarding only the distortion at high frequncy where the parasitc are dominant with the non linearity of tube.
No mention about R of windings.
In fact on the formula increasing the F until infinity the distortion goes to zero (theoretically of course)
Walter
My point is that I did not start this discussion, whether in this thread or some other thread, hence I should not be accused of starting something when I am merely seeking to discover what this thread is actually about.45 said:
If by this strange statement you mean that power (whether loss or otherwise) is proportional to a second-order term then that is of course true, but in itself it is not a form of nonlinearity. To get nonlinearity you have to show that some other parameter, assumed linear, is affected by power. The usual one is the effect of temperature on resistance, but that only does anything noticeable at low frequencies. In any case it is known.popilin said:
Adding a resistor in series or parallel with a capacitor has the same effect as DF, but the resultant network does not show hysteresis.
Calling valve nonlinearity 'valve nonlinearity' and calling transformer nonlinearity 'transformer nonlinearity' makes me very happy. Maybe I am peculiar, but I like things to be called what they are - not what something else is.
If someone else can discover what this thread is about then they may be able to contribute to it, but I am now out.
This discussion originated from the thread on litz wire. As it had become a bit off topic some messages were cut and used to start this thread. I didn't think it was so off topic to start a separate thread as the orginal one didn't have much say anymore. I also think that it would not go on like this as the intial misunderstanding was cleared in few posts and didn't need a new thread. But that was the moderators decision and I don't have problems with it.
Your first post doesn't look like a question of someone who wants to know what this is about. The tone is not certainly that. So you can't expect a friendly response. I was referring to this. Good that you call yourself out now.
All capacitors have hysteresis and it comes form dielectric absorption. I did upload real hysteresis curves for some types of capacitors some time ago.....
DF represents leakage and the other parasitic elements. Leakage anyway is non-linear with applied voltage too, although manufactureses only give one number representing a typical self-discharge time constant.
ok guys, enough is enough....- Status
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