Ba depends on the primary voltage. Bdc depends of the DC current. Not sure what the nature of your argument is. The formulas are correct.
My argument is, Bdc has nothing to do with L, and the more turns, the higher Bdc, that is all for now, if you want me to elaborate on that I am there for you., Thank you.
Andre.
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Andre.
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Bdc depends of the L value. And the L value depends on the number of turns and permeability. For a fixed amount of turns, you can alter permeability, practically by influencing the airgap, so Bdc changes.
I know what L depens on, I know what the gap does. Bdc depends on the number of turns,it depends on the mu, and not on the L. Just tell me how Bdc depends on the L.
L with every thing unchaged depends on the frequency, Actually X depens on the frequency, L is only, because of the material of the core, with no core,
L will be constant for the range of frequencies, untill the losses, out of our discussion.
But never theless, tell me what will be the current in an inducter of Rdc=1 ohm and L=1H, exited with 1VDC compairing to 1VAC at f=1kHz.
50AE, you look like an experienced person, but some things are missing there. I am sorry, no offence. But you must know the differece between Bdc and Bac,
very important when you design a transformer.
L with every thing unchaged depends on the frequency, Actually X depens on the frequency, L is only, because of the material of the core, with no core,
L will be constant for the range of frequencies, untill the losses, out of our discussion.
But never theless, tell me what will be the current in an inducter of Rdc=1 ohm and L=1H, exited with 1VDC compairing to 1VAC at f=1kHz.
50AE, you look like an experienced person, but some things are missing there. I am sorry, no offence. But you must know the differece between Bdc and Bac,
very important when you design a transformer.
I don't see the point in your argument.
Bdc depends on the L from the formula practical point of view. And L depends of permeability.
Bdc and Bac have different formulas for calculation.
Both formulas work and that should do.
No offense taken.
Bdc depends on the L from the formula practical point of view. And L depends of permeability.
Bdc and Bac have different formulas for calculation.
Both formulas work and that should do.
No offense taken.
It's wrong. Inductance is a property and it is irrelevant if the current is DC or AC.
https://www.britannica.com/science/inductance
Bdc = (L x Idc) / (T x Afe) is just a practical forumla used for conveninece but it is correct.
The real magnetic field is: Hdc = [(0.4*pi*T)/lm]*Idc
and L= 0.4*pi*mu*(T^2)*(Afe/lm). This is the inducntace of an ideal cylidrical coil but it is valid with very good approximation for a transformer coil.
If I isolate (0.4*pi*T)/lm=L/(mu*T*Afe), I can write Hdc=(L*Idc)/(mu*T*Afe).
However B=mu*H, hence Bdc = (L x Idc) / (T x Afe).
When signal is applied, L is not perfectly constant and the aim of a good design is to avoid it decreases with signal.
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P.S.
The fact that inductance is only defined for a changing current is irrelevant from the practical point of view. The so-called DC inductance in the formula above is normally referred to a very small AC induction, typically 0.002 Tesla. That is how permeability as function of H for various air-gaps is measured and provided by core manufacturers.
The normal induction DC + AC varies from 0.4-0.6T (no signal) to 0.8-1.2 T, typically. That gives the scale of approximation.
The reason for the practical formula where Bdc is related to L has to do with amplifier design and basic requirements for the output transformer. The amplifier designer doesn't care about B, H or mu. He needs L, Idc, power rating....
The fact that inductance is only defined for a changing current is irrelevant from the practical point of view. The so-called DC inductance in the formula above is normally referred to a very small AC induction, typically 0.002 Tesla. That is how permeability as function of H for various air-gaps is measured and provided by core manufacturers.
The normal induction DC + AC varies from 0.4-0.6T (no signal) to 0.8-1.2 T, typically. That gives the scale of approximation.
The reason for the practical formula where Bdc is related to L has to do with amplifier design and basic requirements for the output transformer. The amplifier designer doesn't care about B, H or mu. He needs L, Idc, power rating....
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OK, yes I can see your point, inductance in the expression for Bdc calculation is only to make the calculation easier since it has number of turns and other staff inside of it. What I was trying to say is,
The inductance of itself has nothing to do with Bdc, only current (Idc), number of turns and permeability.
L is the property of the inductor, Bdc is not. L does not depend on the current, it exists with and without. Bdc does not exists only without Idc applied, so it depends on the Idc and some of the inductor’s properties such as number of turns and permeability of the core if it is there.
Though L also depends of those factors, it does not mean it has anything to do with Bdc.
L is used in the Bdc calculation just for convenience.
I am pretty sure, you guys know what I am trying to say.
Thank you,
Andre
The inductance of itself has nothing to do with Bdc, only current (Idc), number of turns and permeability.
L is the property of the inductor, Bdc is not. L does not depend on the current, it exists with and without. Bdc does not exists only without Idc applied, so it depends on the Idc and some of the inductor’s properties such as number of turns and permeability of the core if it is there.
Though L also depends of those factors, it does not mean it has anything to do with Bdc.
L is used in the Bdc calculation just for convenience.
I am pretty sure, you guys know what I am trying to say.
Thank you,
Andre
L does depends on the amount of current unfortunately. Only in theory it does not. Finding the correct air-gap minimizes change in L. This happens because the permeability is not constant ( B=B(H) is not really linear) and a change in Idc, for a given air-gap, will result in slightly different L when any signal is applied. Even if the air-gap is optimal. Moreover L depends on the AC voltage as well because permeability is not constant again.
In first approximation L is considered constant and because it's a property it can be used a parameter in the practical transformer equation. With no signal and DC current only the inductor is ideally a short-circuit but that is consequence of reactance 2*pi*f*L being zero. L is always defined and f=0.
Don't try to reroute me and yourself, How do you measure L when F=0, I wonder. You seem to be quite educated, watch what you are saying.
In my posts I did not touch anything concerning Bac, that is a different subject, has nothing to do with Bdc, so if you still have something to
argue about, lets stay within.
Bdc has changed not because L has changed, but because something else has been changed that made the L to change, so L is not the primary
player in the Bdc behavior.
I am not rerouting anything, it's a definition. You think so probably because you are confused. There is no frequency in the inductance formula for the coil so it is defined for f=0. The electromotive force defined as L*di/dt is zero because di/dt=0 and it means that it does not oppose the passage of DC current (f=0). It's zero reactance for DC current.
The fact that L will not be truly constant depends on the fact that permeability is not a just a number but is a tensor.
Besides you were arguing about the fact that if one changes the number of turns that does not reflect the change in Bdc if it is written in the form L*Idc/(T*Afe) which is wrong. It does because the overall dependence on number of turns remains the SAME as L is proportional to T^2.
The fact that L will not be truly constant depends on the fact that permeability is not a just a number but is a tensor.
Besides you were arguing about the fact that if one changes the number of turns that does not reflect the change in Bdc if it is written in the form L*Idc/(T*Afe) which is wrong. It does because the overall dependence on number of turns remains the SAME as L is proportional to T^2.
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let us rename this thread to "Magnetics and Inductance for Transformers" theory and practice discussions....
I did not say that, I said L of itself has no meening for DC in whichever form it is, I said that in the posted expression for Bdc, L is included only for the practical purpouse sinse L has Nsqr(number of turns). I don't want to continue the discussion, we are going circles there. For those who understand what I am trying to say, it is abvious.
Thank you.
AndreK, you wrote:
The more turns the higher Bdc is still happening if the expression is (L*dc)/(T*Afe). That's what matters. It is not about rewriting the theory of electromagnetism and such expression has not been created on purpose for this thread....
If one defines:
Bac = Vpri / (4.44 x Afe x T x f)
Bdc = (L x Idc) / (T x Afe)
then can write that B=Bac+Bdc= Vpri / (4.44 x Afe x T x f) + (L x Idc) / (T x Afe)
from this T = [1/(B*Afe)] * [(Vpri/(4.44*f) + L*Idc]
So I have the number of turns expressed in terms of applied core cross-section, total induction, primary voltage, DC current, frequency and inductance. That is the only meaning: practical formula expressed in terms of practical parameters, getting rid of permeability.
you created a circle with a pointless comment. No one is associating a meaning with anything. That's just you.
The more turns the higher Bdc is still happening if the expression is (L*dc)/(T*Afe). That's what matters. It is not about rewriting the theory of electromagnetism and such expression has not been created on purpose for this thread....
If one defines:
Bac = Vpri / (4.44 x Afe x T x f)
Bdc = (L x Idc) / (T x Afe)
then can write that B=Bac+Bdc= Vpri / (4.44 x Afe x T x f) + (L x Idc) / (T x Afe)
from this T = [1/(B*Afe)] * [(Vpri/(4.44*f) + L*Idc]
So I have the number of turns expressed in terms of applied core cross-section, total induction, primary voltage, DC current, frequency and inductance. That is the only meaning: practical formula expressed in terms of practical parameters, getting rid of permeability.
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At this point let's make the formula even more practical with actual units and factors. Then how to use it efficiently with a simplified example.
T= 10^8* [1/(B*Afe)] * [(Vpri/(4.44*f) + L*Idc]
with the operative condition that L*Idc > Vpri/4.44*f and B is significantly less than saturation induction.
where:
B is expressed in Gauss (1 Tesla = 10000 Gauss)
Afe is expressed in square cm
Vpri is expressed in Volt
f is expressed in Hertz
L is expressed in Henry
Idc is expressed in Ampere
I want a 5K/8R, 300B SE output transformer to deliver 8W at 30Hz with low distortion and I have a core EI108 with 3.8cm x 5cm cross-section.
What does it mean low distortion? It means that at low frequency it does not deviate much respect to 1KHz. To achieve this at the low frequency under consideration (30Hz) the inductive reactance needs to be much higher than the equivalent resistance.
Here the simplification is that I am not going to consider the DC resistance of the windings and the core is already assigned. So the equivalent resistance is just the tube's plate resistance in parallel with the nominal primary reflected impedance.
For 8W into 5K the max peak current is 56.6 mA. Let's make it 60 mA. From the WE datasheet, with anode voltage of 400V, anode current of 60 mA (for -87V bias), 5K I get 8.3W @ 3% THD. Moreover, the plate resistance in such conditions is 750R. Then the equivalent resistance Req is:
Req=750//5000 ohms = 652 ohms
The inductive reactance is X= 2*pi*f*L and I want X/Req=10 or more. For such ratio equal to 10 at 30Hz, I need L=(10*Req)/(2*pi*f)=24.5H.
N.B.
I am considering a factor of 10 because the 300B is a very favourable case, thanks to its plate low plate resistance and high ratio between load impedance and plate resistance. In many other cases, achieving a factor of 6 is already a fair challenge....
8W into 5K means 200Vrms.
What Bmax at 30Hz? Looking at manufacturers data, permeability of EI lamination is normally max around 8000 Gauss (0.8T). I pick this one as Bmax = Bdc+ Bac at 30Hz. This leaves some freedom to re-adjust other parameters and will also ensure that it won't saturate down to 20Hz. First condition satisfied.
Second check:
L*Idc = 24.5* 0.06=1.47
V/4.44*f=1.5
L*Idc < V/4.44*f 🙁 👎
Need a bit more inductance or operate at higher anode current. L>25H is the minimum to satisfy the condition that Bdc>Bac with 60 mA although 24.5H could be just fine as distortion is not zero and the anode current at max output might be some 5-10% higher. But let's stay with 60mA and try to try get, say, 26H minimum.
Finally Afe for EI laminations is 0.95*cross-section = 3.8x5*0.95=18.05 cm^2
Then I will need: T=2120 turns.
Does this sound reasonable? It does and actually will result in fairly low copper loss.
This is the first step. Then find the correct air-gap, find out the inductance and if it doesn't match the minimum requirement make some adjustments or adjust something else like Idc if more convenient. Then evaluate geometry with resultant capacitance and leakage inductance for high frequency performance, multiple secondaries etc...
Just to say that, instead of worrying about definitions there's so much more stuff to evaluate yet....
T= 10^8* [1/(B*Afe)] * [(Vpri/(4.44*f) + L*Idc]
with the operative condition that L*Idc > Vpri/4.44*f and B is significantly less than saturation induction.
where:
B is expressed in Gauss (1 Tesla = 10000 Gauss)
Afe is expressed in square cm
Vpri is expressed in Volt
f is expressed in Hertz
L is expressed in Henry
Idc is expressed in Ampere
I want a 5K/8R, 300B SE output transformer to deliver 8W at 30Hz with low distortion and I have a core EI108 with 3.8cm x 5cm cross-section.
What does it mean low distortion? It means that at low frequency it does not deviate much respect to 1KHz. To achieve this at the low frequency under consideration (30Hz) the inductive reactance needs to be much higher than the equivalent resistance.
Here the simplification is that I am not going to consider the DC resistance of the windings and the core is already assigned. So the equivalent resistance is just the tube's plate resistance in parallel with the nominal primary reflected impedance.
For 8W into 5K the max peak current is 56.6 mA. Let's make it 60 mA. From the WE datasheet, with anode voltage of 400V, anode current of 60 mA (for -87V bias), 5K I get 8.3W @ 3% THD. Moreover, the plate resistance in such conditions is 750R. Then the equivalent resistance Req is:
Req=750//5000 ohms = 652 ohms
The inductive reactance is X= 2*pi*f*L and I want X/Req=10 or more. For such ratio equal to 10 at 30Hz, I need L=(10*Req)/(2*pi*f)=24.5H.
N.B.
I am considering a factor of 10 because the 300B is a very favourable case, thanks to its plate low plate resistance and high ratio between load impedance and plate resistance. In many other cases, achieving a factor of 6 is already a fair challenge....
8W into 5K means 200Vrms.
What Bmax at 30Hz? Looking at manufacturers data, permeability of EI lamination is normally max around 8000 Gauss (0.8T). I pick this one as Bmax = Bdc+ Bac at 30Hz. This leaves some freedom to re-adjust other parameters and will also ensure that it won't saturate down to 20Hz. First condition satisfied.
Second check:
L*Idc = 24.5* 0.06=1.47
V/4.44*f=1.5
L*Idc < V/4.44*f 🙁 👎
Need a bit more inductance or operate at higher anode current. L>25H is the minimum to satisfy the condition that Bdc>Bac with 60 mA although 24.5H could be just fine as distortion is not zero and the anode current at max output might be some 5-10% higher. But let's stay with 60mA and try to try get, say, 26H minimum.
Finally Afe for EI laminations is 0.95*cross-section = 3.8x5*0.95=18.05 cm^2
Then I will need: T=2120 turns.
Does this sound reasonable? It does and actually will result in fairly low copper loss.
This is the first step. Then find the correct air-gap, find out the inductance and if it doesn't match the minimum requirement make some adjustments or adjust something else like Idc if more convenient. Then evaluate geometry with resultant capacitance and leakage inductance for high frequency performance, multiple secondaries etc...
Just to say that, instead of worrying about definitions there's so much more stuff to evaluate yet....
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This is, forgive me i dont want be offansive, main mistake to consider Lprim value.
the working shape of reactive load is elipse. Not the line as is for static calculations on the anode curves graph.
It is then to line only in central part of the BW.
At low F it is dominant inductive component, at the high end it is capacitive component.
If the insuficiant L is used the elipse will tend more to the circle.
In that case when aproaching X axes, will deform the shape badly. That is distortion in sound, cutting out the -db, AND phase...
And it is getting worse with magnetisation inclouded...
This coud be simulated.
.
So first task is to determine the elipse shape, directly in function of Lprim, to be undistorted and represent whole elipse.
comparing the results in transfer and phase.
.
I will show some examples hoew it is look like
Non offense taken. If you start wandering about ellpises you will never make a transformer and probably will never make SE an amplifier....but reality tells a different story because with musical signal below 40Hz there is already very little, at 30Hz even less and at 20Hz often there is nothing at all. And hopefully it's not about using full power all the time.
A factor of 10 is normally considered to be "much bigger than" and it's enough to get started. Try to get X/Req=10 for 2.5K transformer for 2A3 and see how much harder it gets without doing something odd like using oversized core or making a lot more turns and accepting propostrous copper loss etc. There is no escape, the lower the frequency the more distortion you will get below a certain frequency. If this is limit is 40Hz or 35 Hz or 30Hz won't be a real problem.
All the evaluations I made above are for getting started. The hard part is the rest, starting from the fact that winding the actual trnasformer in the best possible way is not as easy as it looks and requires quite some effort and time.
A factor of 10 is normally considered to be "much bigger than" and it's enough to get started. Try to get X/Req=10 for 2.5K transformer for 2A3 and see how much harder it gets without doing something odd like using oversized core or making a lot more turns and accepting propostrous copper loss etc. There is no escape, the lower the frequency the more distortion you will get below a certain frequency. If this is limit is 40Hz or 35 Hz or 30Hz won't be a real problem.
All the evaluations I made above are for getting started. The hard part is the rest, starting from the fact that winding the actual trnasformer in the best possible way is not as easy as it looks and requires quite some effort and time.
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It is about the phase degradation and distortion not only in cut out the BW. And Yes we have in the a lot informations below 30Hz...
Oversized core crossection is not the top solution. Because what we actually need is more space for the windings and isolation.
We dont need extra core area. But that is come to the standard window dimensions for power transformers. Which are not suitable for audio aplications by the dimmensions nor by the magnetizaton chrs... 🙁
And with increasing the only iron area there wil be dis-ballans in copper losses and iron losses... 🙁
Ideally should be close to each other...
.
Oversized core crossection is not the top solution. Because what we actually need is more space for the windings and isolation.
We dont need extra core area. But that is come to the standard window dimensions for power transformers. Which are not suitable for audio aplications by the dimmensions nor by the magnetizaton chrs... 🙁
And with increasing the only iron area there wil be dis-ballans in copper losses and iron losses... 🙁
Ideally should be close to each other...
.
I think we speak a different language. No idea what music you are talking about with lots of information below 30Hz. Maybe you talk about "musical tendencies" with low frequency massage. In that case I don't think a tube amp is a good solution at all. Waste of money and time.