I'm having trouble seeing where THD distortion/harmonics could come from in SPICE Ideal coupled inductors, resistors, sources...
how are you implementing a nonlinear element for air core?
Skin and Proximity effects seem to be very well linearly modeled
Ordinary Magnetoresistance? - I would like to see numbers for nonlinear effect in room temp, ordinary audio cable/wiring or xfmr
if there is measurable Ordinary Magnetoresistance/Geometric nonlinear term then wouldn't Litz for all windings reduce it?
I can see below that Sh is a multiplicative factor - no core nonlinear term = no Ra nonlinearity from this equation
how are you implementing a nonlinear element for air core?
Skin and Proximity effects seem to be very well linearly modeled
Ordinary Magnetoresistance? - I would like to see numbers for nonlinear effect in room temp, ordinary audio cable/wiring or xfmr
if there is measurable Ordinary Magnetoresistance/Geometric nonlinear term then wouldn't Litz for all windings reduce it?
I can see below that Sh is a multiplicative factor - no core nonlinear term = no Ra nonlinearity from this equation
The active power transmitted to a load is a function of the fundamental component I1 of the current. When the current drawn by the load contains harmonics, the rms value of the current, Irms, is greater than the fundamental I1.
THD = √[(Irms / I1)² - 1]
No need a nonlinear anisotropic core to have harmonics, with a valve is enough.
The harmonic currents cause an increase in copper losses, even ignoring skin effect.
Conclusion: Copper losses in OPT are nonlinear and hence an increase in winding resistance causes an increase in THD.
An air core is linear, no need to implement a nonlinear element for it.
So what
I cannot see your point; to see magnetoresistance in copper you must lower the temperature to about 4 ºK, or increase the magnetic field to about 100 KGauss at room temperature for a tiny increase of about 14% in its resistance, and that would be a really crazy idea.
Maybe you are referring to proximity effect and I am so dumb to not realize that, if so, we already seen on post#41 that for copper @ 100 KHz skin depth is
δ ≈ 0.21 mm
Proximity effect has the same cure as leakage inductance, i.e. winding interleaving, then, for properly made transformers both effects are irrelevant in audio.
If you take the trouble to read again, the equation gives the harmonic distortion directly, so no need for any nonlinear term, this role is already covered by Sh, nonlinear and anisotropic behavior (aka hysteresis) was reduced to a simple coefficient.
Vh/Vf = [(Sh x 10⁹ lm Ra) / (8 π² Np² S f)] [1 - (Ra/4 Zf)]
The function
f(Ra) = Ra [1 - (Ra/4 Zf)]
Is not a straight line by the way, some people call this non-linear…
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typically EE like to model useful sized, but clearly delimited circuit elements - say a transformer and understand its subcomponent(s) model linearity/nonlinearity, range of application
then when you appear to say a air core transformer is nonlinear:
"Anyway, a coreless transformer (e.g. vacuum) will show THD due to winding resistance, which can easily seen in LTSpice simulations."
by my reading you are making a statement about the transformer
that its transfer function when operated with Ideal, linear sources and RLC is nonlinear
not that its linear response to external circuit generated nonlinear I from nonlinear drive or loads shows up across its linear model sub components like (very linear) Rpri and "will show THD due to winding resistance"
to an EE that would be just restating that a nonlinear current through a linear R gives a nonlinear V - in your words "so what"
then when you appear to say a air core transformer is nonlinear:
"Anyway, a coreless transformer (e.g. vacuum) will show THD due to winding resistance, which can easily seen in LTSpice simulations."
by my reading you are making a statement about the transformer
that its transfer function when operated with Ideal, linear sources and RLC is nonlinear
not that its linear response to external circuit generated nonlinear I from nonlinear drive or loads shows up across its linear model sub components like (very linear) Rpri and "will show THD due to winding resistance"
to an EE that would be just restating that a nonlinear current through a linear R gives a nonlinear V - in your words "so what"
Please accept my apologies for my Tarzan-English, so often I want to say something and the language does not help...
Also my ignorance in electronics plays a not less important role, I know that a RLC is nonlinear, but the power valve was more at hand...
Another misunderstanding, I did not want to say that primary resistance is nonlinear, losses are, and you said it better than me.
So we can say that we almost agree! Cheers for that!
Also my ignorance in electronics plays a not less important role, I know that a RLC is nonlinear, but the power valve was more at hand...
Another misunderstanding, I did not want to say that primary resistance is nonlinear, losses are, and you said it better than me.
So we can say that we almost agree! Cheers for that!
Is this going to be one of those threads where, having proved that the original statement X was false, the one who said it then denies saying it and said that he said something else - namely Y? It is then shown that Y implies X - so then he denies saying Y, or attempts to prove that under certain extremely rare circumstances Y does not imply X. Or it is shown that Y is unremarkable, so why state it in a way which implies something else?
I have been in threads like this. They rarely end well.
I have been in threads like this. They rarely end well.
Still not seeing how a linear element generates non-linear losses. The reasoning appears to be linear losses to a distorted input is equivalent non-linear losses to a linear input.
Skin and proximity effects have been covered above, the only trivial effect remaining is the self-heating effect, just like for drivers, but that's something rather well understood and having a diminishing effect at higher frequencies.
If you go really, really very deep, the vacuum itself (or space-time continuum or aether, call it what you like) is non-linear: a strong field, be it magnetic or electric holds energy, and this energy affects the local constants: permeability and permittivity, at least in theory.
But to observe the practical effects of such a theory, you would need immense field strength, on the par with neutron stars, and extremely sensitive instruments, not just your ordinary THD-meter capable of resolving 1ppm.
Note that even without heating, the relationship between the applied electric field for a conductor like copper and the charge displacement is very slightly non-linear: Ohm's law is an approximation, but a very, very good one.
Nothing to worry about.....
If you go really, really very deep, the vacuum itself (or space-time continuum or aether, call it what you like) is non-linear: a strong field, be it magnetic or electric holds energy, and this energy affects the local constants: permeability and permittivity, at least in theory.
But to observe the practical effects of such a theory, you would need immense field strength, on the par with neutron stars, and extremely sensitive instruments, not just your ordinary THD-meter capable of resolving 1ppm.
Note that even without heating, the relationship between the applied electric field for a conductor like copper and the charge displacement is very slightly non-linear: Ohm's law is an approximation, but a very, very good one.
Nothing to worry about.....
It's the magnetic core the non-linear element that generates non-linear distortion. However as THD is also directly proportional to series resistance Ra it is obvious that for everything else being the same the higher Ra the higher THD.
If the core is linear Sh will be zero, hence no non-linear distortion I guess....having not read the article. However there is the tube that is non-linear too.
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No. You didn't get it! He said that one doesn't need to implement the real model of transformer in TSpice but just consider the valve because the valve generates distortion itself and that's the non-linear element.
Let’s suppose that fundamental current is sinusoidal
I (t) = I1 sin (ω t + φ1)
Copper loss
Pcu = [I (t)]² Rp = I1² sin²(ω t + φ1) Rp
Let’s consider now the fundamental and the harmonics
I (t) = I1 sin (ω t + φ1) + ∑ Ih sin (h ω t + φh), h = 2, 3, … , ∞
Copper loss
Pcu = [I1 sin (ω t + φ1) + ∑ Ih sin (h ω t + φh)]² Rp
Your point is really very good; I did not want to go so far, but all for audio transformers!
Quantum vacuum seems to be nonlinear and anisotropic; hence a “vacuum core” will also show hysteresis.
Nevertheless the fundamental constants is a very complex topic, if vacuum permeability and permittivity would change we would have some issues with the speed of light and Relativity.
Even on the scope of classical electrodynamics, so far I did ignore dielectric anisotropy and nonlinearity, another source of hysteresis and losses, worsened due to high voltage and hence high electric fields in transformers.
I did also ignore leakage inductance, another source of losses and nonlinearity.
I do not want to be party pooper, but so far a linear transformer is just an idealization.
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What is this? A kind of generic post? Your participation would be good for the discussion, so please stop to throw tomatoes and join to the thread.
No problem, my join to the forum on 2010 was a bit traumatic because of him, not the first discussion though...
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