Thanks 45 for the great lecture; we all can learn from this.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....
However, I am curious if you are in the theoretical stage still, or have you in the meantime also applied your knowledge in winding transformers?
I guess a few of us are curious what you accomplished, as this thread is about "showing your transformer work".
I have always said that I don't normally wind transformers. I have done it in the past but mostly design them and get them done. Often following the full process when I have something different in mind. My winder is my close friend. I have no reason to lie.
You can see a transformer of my design in Bartola website. The request was about getting a better frequency response than Lundahls with more or less the same specs regarding the rest....on a budget!
Considering that the transformer also had to support high voltage to be used with the 814 and 845, was delivered with real certification of insulation and, last but not least, Ale was more than satisfied I think it was quite successful.
Nice presentation, and what are Bac and Bdc according to your calculations?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....
Thank you,
Andre
Fair enough.I have always said that I don't normally wind transformers. I have done it in the past but mostly design them and get them done. Often following the full process when I have something different in mind. My winder is my close friend. I have no reason to lie.
You can see a transformer of my design in Bartola website. The request was about getting a better frequency response than Lundahls with more or less the same specs regarding the rest....on a budget!
Considering that the transformer also had to support high voltage to be used with the 814 and 845, was delivered with real certification of insulation and, last but not least, Ale was more than satisfied I think it was quite successful.
It's written. Total B is 0.8T approx. At 30Hz Bdc is a bit more than 0.4T and Bac a bit less (for 200V rms).
But that is just an example for calculations. The actual EI108 is in reality 3.7 cm and I would do the actual transformer on 3.7x4 cm cross- section. This would require more turns but they would be shorter. So copper loss would only be marginally higher but it would be more practical to apply the air-gap.
It could be 6P-5S scheme. Using 0.3 mm for the primary on could make 20 layers in total, 136 turns each and leaving 2 mm on each side of the standard coil former (that already has windows to bring the wires out). Divided in 6 primaries it would be 2+S+4+S+4+S+4+S+4+S+2 for 2720 primary turns.
The secondary for 8R would require 109 turns. The easiest and more straightforward would be 10 layers all in parallel, each secondary has 2 layers done with 0.355 mm wire. Between inner layers I would use 0.08 NOMEX and between P-S I would use 0.23 mm NOMEX. Both wires can be single layer insulation.
Air-gap for 60 mA and required inductance would be 0.18 mm (i.e. in practice 0.1mm spacer holding laminations tight). Effective mu will be around 440 with my M6 laminations.
So:
L = 26H (small signal like 3 Vrms at 50Hz)
Bmax= 0.8T at 30Hz
Bdc > 0.4T
Bac < 0.4 T for 200V RMS
Rprimary =140R
Rsecondary = 0.4R
Insertion loss with 300B = 0.57 dB
Leakage inductance = 4 mH
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@Zoran, I decide what is relevant what is not as I listen to the music. If I had to stick to standards I would not be using tube amps. Period. I don't listen to disco garbage, synthesized stuff and other noise like that. Only pipe organ and maybe one or two very rarely used instruments can go below 27.5 Hz. Only a few notes....that is the meaning of nothing.
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My current impression of your post content is your attempt of shedding some black light to output transformers in general. They aren't perfect, and each transformer designer decides what kind of compromises to make when building one.
@45, OK with winding scheme, but with 140R of primary DCR your transformer will never be better than mediocre.
In my experience, copper loss becomes a sound quality factor when primary DCR is much over 10% of tube Rp and total insertion loss exceeds 0.3 dB, especially when driving direct radiating loudspeakers. It would be less of an issue when driving horn loudspeakers with their superior acoustic damping.
So for 300B SE OPT, stay well under 100R for this parameter; it can easily be done with a bit more Afe without compromizing other parameters too much.
Optimizing SE transformers can actually not be done without taking the load (loudspeaker) into account.
Just my opinion and experience.
In my experience, copper loss becomes a sound quality factor when primary DCR is much over 10% of tube Rp and total insertion loss exceeds 0.3 dB, especially when driving direct radiating loudspeakers. It would be less of an issue when driving horn loudspeakers with their superior acoustic damping.
So for 300B SE OPT, stay well under 100R for this parameter; it can easily be done with a bit more Afe without compromizing other parameters too much.
Optimizing SE transformers can actually not be done without taking the load (loudspeaker) into account.
Just my opinion and experience.
@daanve, in my experience you are wrong. The best recipe for a good transformer is always a good balance of ALL parameters. Considering that it would be a "budget" transformer it's pretty good. FR will extend to 40KHz easily. Optimizing one parameter at expense of the others is a bad idea.
Then you are confusing an example of how to use a practical equation with a "best" solution. Although EI cores cannot achieve the same copper loss as C cores, my normal one would be EI120 40x50 for 12-13W @ 30Hz and lower copper loss. Already posted other times.....
Then you are confusing an example of how to use a practical equation with a "best" solution. Although EI cores cannot achieve the same copper loss as C cores, my normal one would be EI120 40x50 for 12-13W @ 30Hz and lower copper loss. Already posted other times.....
I was referring to you 3,7 x 4 cm core cross section which makes it a "budget" transformer already; that is different from a good transformer with a good balance of ALL parameters. A really good 300B SE OPT needs more than 3,7 x 4 cm of Afe, period. I guess you agree when your normal transformer would be EI120 40x50. We know about c-cores but that's not the subject here.
Really? Then show me how you make a budget transformer with EI core, same specification for power rating, inductance and frequency response better than that. Let's see how DC resistance shrinks and what happens to the rest. Design a transformer with numbers, NOT OPINIONS.
I already know the answer. You are not capable. And if you are not capable, don't continue to highjack this thread with your petulancy, please.
The bigger transformer with EI 120 is not on budget. It also has vertical sectioning and multiple secondary impedance always using all turns.
I already know the answer. You are not capable. And if you are not capable, don't continue to highjack this thread with your petulancy, please.
The bigger transformer with EI 120 is not on budget. It also has vertical sectioning and multiple secondary impedance always using all turns.
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What exactly is "budget"? I would not even think of using EI core, because a c-core of comparable size might cost just a few dimes more and will make you a better transformer. For me, a budget transformer has acceptable parameters for minimal cost. 140R Primary DCR and 0.57 dB insertion loss are not acceptable parameters for me, so I would not wind one like that.
And why do you stay in EI territory, also for your "non budget" transformers? When your winder does not have access to c-cores let me know....I'd be pleased to send you some HiB c-cores from my remaining stock for no more than cost price.
What are premium brands like Tango, Hashimoto, Monolith Magnetics, Lundahl, Tamura missing when they insist to use c-cores exclusively for their non budget transformers (Hashimoto and Tango (U-808) have some budget EI transformers)??
And why do you stay in EI territory, also for your "non budget" transformers? When your winder does not have access to c-cores let me know....I'd be pleased to send you some HiB c-cores from my remaining stock for no more than cost price.
What are premium brands like Tango, Hashimoto, Monolith Magnetics, Lundahl, Tamura missing when they insist to use c-cores exclusively for their non budget transformers (Hashimoto and Tango (U-808) have some budget EI transformers)??
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The Tango U808 with EI core has 210R primary DC resistance at 5K and 21H, is a VERY NICE transformer displaying near PERFECT 20KHz square waves that you C-core transformers can only dream (or prove otherwise) and is not budget by any standard, except if one lives in Japan. Please stop with your nonsense based on nothing.
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What language? Do you realize that EVERY thread talking about transformers you keep saying always the same stuff even if it is not relevant?
I asked you to show with numbers or kindly stop hijacking the thread. You can't do it. Q.E.D. Now you should just stop because I don't care about your opinion. I don't need your advice because I have a number of Japanese transformers of different kind, including PSU transformers not just OPTs.....plus Lundahls, NP Acoustic etc....
I asked you to show with numbers or kindly stop hijacking the thread. You can't do it. Q.E.D. Now you should just stop because I don't care about your opinion. I don't need your advice because I have a number of Japanese transformers of different kind, including PSU transformers not just OPTs.....plus Lundahls, NP Acoustic etc....
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