the Martin Logan CLX is a combination of a torroid for the midrange - high frequency range and an EI core of maybe 12 lbs in weight for the low end.
my Quad 63 EI core might weight 5 lbs. The same for my former Martin Logan Request ( although that only has to go down to 180 Hz). My acoustat Model one might be 10 pounds of EI core
The Dayton Wright Tranformer was designed to handle hundreds of watts without core saturation - (less distortion and dynamic compresion, especially in the low end). It was overdesigned but if you ever heard a pair ( or even better a double pair) of Dayton Wrights you heard a bottom end which matched the upper range for effortless reproduction with great detail and speed and very low dynamic compression. The speaker was designed to fully reproduce the low end by a combination of techniques - it,s size, the use of SF 6 gas to seal the speaker allowed it to run at higher voltages and because it was denser than air lowered the frequency at which the front and rear wavefronts cancelled AND had a transformer which could really handle high current low frequency reproduction.
my Quad 63 EI core might weight 5 lbs. The same for my former Martin Logan Request ( although that only has to go down to 180 Hz). My acoustat Model one might be 10 pounds of EI core
The Dayton Wright Tranformer was designed to handle hundreds of watts without core saturation - (less distortion and dynamic compresion, especially in the low end). It was overdesigned but if you ever heard a pair ( or even better a double pair) of Dayton Wrights you heard a bottom end which matched the upper range for effortless reproduction with great detail and speed and very low dynamic compression. The speaker was designed to fully reproduce the low end by a combination of techniques - it,s size, the use of SF 6 gas to seal the speaker allowed it to run at higher voltages and because it was denser than air lowered the frequency at which the front and rear wavefronts cancelled AND had a transformer which could really handle high current low frequency reproduction.
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A Quad esl-63 with a EI core is new for me. I had several at home and all had 2 (small) double c-cores inside.
Making an esl-transformer BIG is not always good. You get much winding capacity and the upper frequency range can be limited.
Important is to measure the frequency response and impedance, you don't want to low impedance for your amplifier (preferable not lower then 3 Ohm)
Making an esl-transformer BIG is not always good. You get much winding capacity and the upper frequency range can be limited.
Important is to measure the frequency response and impedance, you don't want to low impedance for your amplifier (preferable not lower then 3 Ohm)
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Take a look at section 3.6 (Step-up Transformer) of this project in order to give you an idea of a DIY transformer that could possibly give you the performance you are looking for in a single unit.
Do It Yourself - Electrostatic Speakers - Project: ESL-220-30 by Marc Schroeyers
You might be able to get the full details of the design build upon request as they are not displayed anymore openly on the website.
But the "As Finished" Specs are still there to see for all.
The primary inductance is stated as 47mh and a DCR of .65 ohms, then you can add your required secondary.
I have this full article that I had printed out from when it was still in its full format......somewhere.
This was the only fully detailed ESL transformer build that includes the theory that I have ever found, and, I always refer back to it every once in a while and each time I do I understand it more and more.
jer
Do It Yourself - Electrostatic Speakers - Project: ESL-220-30 by Marc Schroeyers
You might be able to get the full details of the design build upon request as they are not displayed anymore openly on the website.
But the "As Finished" Specs are still there to see for all.
The primary inductance is stated as 47mh and a DCR of .65 ohms, then you can add your required secondary.
I have this full article that I had printed out from when it was still in its full format......somewhere.
This was the only fully detailed ESL transformer build that includes the theory that I have ever found, and, I always refer back to it every once in a while and each time I do I understand it more and more.
jer
I found the following two different toroids
A) Dual 117/234 VAC primary, 50/60 Hz., Dual secondaries in parallel at 15VA 6V @ 2.5A, (12V CT @ 1.25A, in series)
B) Dual 117/234 VAC primary, 50/60 Hz., Dual secondaries in parallel at 80VA 6V @ 13.34A (12V CT @ 6.67A, in series)
How many of each of those above toroids would I need per panel? I guess i'm just trying to see how or if the higher current rating makes any difference with regards to playing down to 150Hz with ease.
Here are the two toroids;
Hammond Mfg. - Toroid Power Transformer - (182 Series)
kind thanks,
Eddie
A) Dual 117/234 VAC primary, 50/60 Hz., Dual secondaries in parallel at 15VA 6V @ 2.5A, (12V CT @ 1.25A, in series)
B) Dual 117/234 VAC primary, 50/60 Hz., Dual secondaries in parallel at 80VA 6V @ 13.34A (12V CT @ 6.67A, in series)
How many of each of those above toroids would I need per panel? I guess i'm just trying to see how or if the higher current rating makes any difference with regards to playing down to 150Hz with ease.
Here are the two toroids;
Hammond Mfg. - Toroid Power Transformer - (182 Series)
kind thanks,
Eddie
Since you are operating them at a higher minimum frequency than what they were designed for then the VA rating will be much higher.
But the smaller transformer will have a smaller gauge of wire and would be more prone to burnout.
In your above example I would definitely go with the 80VA type.
But if you are talking about using 8 of them then it probably won't make a lot of difference as you would be able to handle 1.25Ax8= 12 amps of current.
But, Then again it may still be very marginal when you are operating them in to the 1 to 2 ohm range (close r to the saturation point and trying and to put more than 20Vrms in to the stack of cores!
Ohms law will tell you the exact figures.
And the only way too really find out is to get one and do an impedance curve test on one.
For your example of 150hz (Three times higher than 50hz) your VA rating of the core will be VA x 3 x 3= New VA.
Or 9 times more at 150hz than what the transformers original VA rating is at 50hz.
It still would take at least 8 of them to give you a good performance as they are still designed for 50hz however you would have a higher transformation ratio of 936/12=1:78 .
And, Your point of core saturation would be approximately 12*3=36Vrms at 150Hz.
Unless they are much more cheaper than the Antek's, you most likely won't be gaining or losing anything by using them and I do know that Hammond's transformers are not exactly cheap.
I have found that there is very very little useful information for an ESL to produce below about 240Hz or so.
This point is just below what most any male vocalist can produce.
jer
P.S. You have not yet stated what kind of amp that your are planning on driving these with as if it is a large amp capable of over 50Vrms then Maybe the 18V transformers would be a wiser chioce if you plan on going with the Hammond's.
This would also you give you your original target ratio (of 1:50) at 1:52 and a saturation point of 54Vrms at 150Hz.
As these are maximum rating calculations, if you are running anywhere near these values it will be quite loud if then panels are working up to par.
But the smaller transformer will have a smaller gauge of wire and would be more prone to burnout.
In your above example I would definitely go with the 80VA type.
But if you are talking about using 8 of them then it probably won't make a lot of difference as you would be able to handle 1.25Ax8= 12 amps of current.
But, Then again it may still be very marginal when you are operating them in to the 1 to 2 ohm range (close r to the saturation point and trying and to put more than 20Vrms in to the stack of cores!
Ohms law will tell you the exact figures.
And the only way too really find out is to get one and do an impedance curve test on one.
For your example of 150hz (Three times higher than 50hz) your VA rating of the core will be VA x 3 x 3= New VA.
Or 9 times more at 150hz than what the transformers original VA rating is at 50hz.
It still would take at least 8 of them to give you a good performance as they are still designed for 50hz however you would have a higher transformation ratio of 936/12=1:78 .
And, Your point of core saturation would be approximately 12*3=36Vrms at 150Hz.
Unless they are much more cheaper than the Antek's, you most likely won't be gaining or losing anything by using them and I do know that Hammond's transformers are not exactly cheap.
I have found that there is very very little useful information for an ESL to produce below about 240Hz or so.
This point is just below what most any male vocalist can produce.
jer
P.S. You have not yet stated what kind of amp that your are planning on driving these with as if it is a large amp capable of over 50Vrms then Maybe the 18V transformers would be a wiser chioce if you plan on going with the Hammond's.
This would also you give you your original target ratio (of 1:50) at 1:52 and a saturation point of 54Vrms at 150Hz.
As these are maximum rating calculations, if you are running anywhere near these values it will be quite loud if then panels are working up to par.
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the amp is the
VTA ST120 at 60watt per channel, below is the amp
tubes4hifi amplifier KITs page
it will have an active X-over at 150Hz. I've heard a pair of Monolith III's that were biamped with 50 per channel to the panels and 50 per channel to the woofers and it sounded great. So I'm certain that 60 per channel on the panels will be sufficient since I don't ever listen loud.
I would like to find a toroidal transformer that won't require me to use eight of them per speaker. What would the specs be of a toroidal that would only require me to use one or two toroids per speaker? Hammond has a very large selection of X-formers so it seems to me that they should have one that can get the job done with only one or two per speaker...right?
tks,
Eddie
VTA ST120 at 60watt per channel, below is the amp
tubes4hifi amplifier KITs page
it will have an active X-over at 150Hz. I've heard a pair of Monolith III's that were biamped with 50 per channel to the panels and 50 per channel to the woofers and it sounded great. So I'm certain that 60 per channel on the panels will be sufficient since I don't ever listen loud.
I would like to find a toroidal transformer that won't require me to use eight of them per speaker. What would the specs be of a toroidal that would only require me to use one or two toroids per speaker? Hammond has a very large selection of X-formers so it seems to me that they should have one that can get the job done with only one or two per speaker...right?
tks,
Eddie
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Okay, that changes things a bit since your amp won't produce much more than 22Vrms.
Is there any particular reason you want a 1:50 ratio?
I would definitely consider a higher ratio.
it won't matter what transformer you get as the 117v windings turns count are all the same for any particular size category.
All of the 25watt series of cores are the same regardless of the LV winding voltage spec.
As is all of the 50 watt cores are all the same, but not the same as the 25's.
The same goes for the 100watt series of cores.
You can take any one of these cores and add your own LV winding to customize your ratio as long as you follow the same rules I have been explaining.
As I have done here,
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-3.html#post2129471
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-2.html#post2103369
The calculations are very straight forward.
Here is some more info,
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design.html#post2096503
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-3.html#post2115394
You may even get by with charlie's original set up but using a 6v winding with a 1:78 or so ratio.
But would still limit you to 180hz as your lowest frequency.
Getting to lower Frequency's is the issue here, not to mention that the impedance of the transformer is quite low in this range as well, most typically below 2 ohm as well!!
Unless you use a higher voltage rated LV winding and more cores to make up the difference of a lower ratio per core.
I show this with charts for a unloaded Antek AN(AS)-1206 in this post (note the second chart),
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-6.html#post3404300
A 7.5V winding would get you to 150Hz at 1:62.4 ratio using 2 or 4 cores with 4 cores giving you the best performance as already discussed.
I was calculating for a much bigger amp and is how I came up with 8 cores using 15V types.
But Antek only makes a 7V type with a 10 watt rating.
These may actually work for you with a 1:66.85 ratio but it is not advisable should you decide to later use a bigger amplifier.
You would also be limited to 157Hz as your lowest frequency as well using the 7V type.
This is not an issue though if you are operating well under your amplifiers maximum power output of 22Vrms.
In this post I show the results of when the core is going into saturation and how I came up with my data in the charts I made for the cores that I have been using in which have a VA rating of 210watts.
But it really makes no difference of there VA rating as all of the cores I have test have the same results (only a different number of actual turns are on them is all) as per core size when it came to saturation levels and input voltage levels,
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-5.html#post2194027
jer
Is there any particular reason you want a 1:50 ratio?
I would definitely consider a higher ratio.
it won't matter what transformer you get as the 117v windings turns count are all the same for any particular size category.
All of the 25watt series of cores are the same regardless of the LV winding voltage spec.
As is all of the 50 watt cores are all the same, but not the same as the 25's.
The same goes for the 100watt series of cores.
You can take any one of these cores and add your own LV winding to customize your ratio as long as you follow the same rules I have been explaining.
As I have done here,
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-3.html#post2129471
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-2.html#post2103369
The calculations are very straight forward.
Here is some more info,
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design.html#post2096503
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-3.html#post2115394
You may even get by with charlie's original set up but using a 6v winding with a 1:78 or so ratio.
But would still limit you to 180hz as your lowest frequency.
Getting to lower Frequency's is the issue here, not to mention that the impedance of the transformer is quite low in this range as well, most typically below 2 ohm as well!!
Unless you use a higher voltage rated LV winding and more cores to make up the difference of a lower ratio per core.
I show this with charts for a unloaded Antek AN(AS)-1206 in this post (note the second chart),
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-6.html#post3404300
A 7.5V winding would get you to 150Hz at 1:62.4 ratio using 2 or 4 cores with 4 cores giving you the best performance as already discussed.
I was calculating for a much bigger amp and is how I came up with 8 cores using 15V types.
But Antek only makes a 7V type with a 10 watt rating.
These may actually work for you with a 1:66.85 ratio but it is not advisable should you decide to later use a bigger amplifier.
You would also be limited to 157Hz as your lowest frequency as well using the 7V type.
This is not an issue though if you are operating well under your amplifiers maximum power output of 22Vrms.
In this post I show the results of when the core is going into saturation and how I came up with my data in the charts I made for the cores that I have been using in which have a VA rating of 210watts.
But it really makes no difference of there VA rating as all of the cores I have test have the same results (only a different number of actual turns are on them is all) as per core size when it came to saturation levels and input voltage levels,
http://www.diyaudio.com/forums/planars-exotics/161485-step-up-transformer-design-5.html#post2194027
jer
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I just checked out the amp.
The very low impedance that the transformers cause at such a low frequency is all the reason enough to use many cores with a higher voltage rated LV winding.
I will try to get my Impedance measuring rig set back up and see what Antek's 100watt core that I have shows for some higher rate LV winding's produce as an impedance in the frequency range you desire.
I just got some smaller chipamp's that I was planning to use to drive transformer primary's in my test jig rather than my big ole' crown in my test jig.
I would hate to see you cook the OPT's due to such a low impedance.
jer
The very low impedance that the transformers cause at such a low frequency is all the reason enough to use many cores with a higher voltage rated LV winding.
I will try to get my Impedance measuring rig set back up and see what Antek's 100watt core that I have shows for some higher rate LV winding's produce as an impedance in the frequency range you desire.
I just got some smaller chipamp's that I was planning to use to drive transformer primary's in my test jig rather than my big ole' crown in my test jig.
I would hate to see you cook the OPT's due to such a low impedance.
jer
what does "LV" stand for?
The reason I'm going to make it be a 1:50 ratio is because that is what Martin Logan uses on the Monolith III along with 3,200v to 3,400v on the diaphragm.
I measured the capacitance of my Monolith III panels today and both panels are dead steady at 2.30nF.
So if I recall, I read somewhere that that number can be used in a formula to somehow determine the design of the step up transformers.
The reason I'm going to make it be a 1:50 ratio is because that is what Martin Logan uses on the Monolith III along with 3,200v to 3,400v on the diaphragm.
I measured the capacitance of my Monolith III panels today and both panels are dead steady at 2.30nF.
So if I recall, I read somewhere that that number can be used in a formula to somehow determine the design of the step up transformers.
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1- I use LV for "Low Voltage" winding as not to confuse any one with primary and secondary since we are using them in reverse.
HV winding typically meaning the 115V to 120V winding that would normally be called the primary but in our case is now the secondary winding.
2- 1:50, Okay that is understandable having a slightly higher ratio will do no harm and will increase the sensitivity some.
This is especially good when using a lower power amplifier as long as you don't go to high with the ratio this also lowers the resulting impedance.
2.3nf or .0023uf is about what I expected from a panel of that size.
The formula is Xc / Ratio^2= Reflected impedance and I use this online calculator to find Xc,
Electronics 2000 | Reactance Calculator
The theoretical impedance with a 1:50 ratio at 20Khz would be 3460ohms(Xc) / (50 * 50) Ratio squared = 1.384 ohms.
BUT, This figure will actually be lower than this because you have to add the transformer capacitance as well.
Let us just say that transformers capacitance is as high as 1600pf total, as they can range from 400pf to as much as 1200pf or more (for some) per core.
Now your total capacitance is ESLpf + TRANSFORMERpf = Total Xc of 2040 ohms.
Now your reflected impedance with a 1:50 ratio at 20Khz now becomes 2040/ (50*50)= .816 ohms at 20Khz!!
This is not so much of a problem since dipole panels have a rising frequency response of +10db per decade and when EQ'ed properly the signal can/will be some -20db lower at 20Khz than the level will be at 200hz.
Plus the components of the Crossover section, DC resistances of the transformers primary and such also adds resistance to the total as well.
But since you want to get down to 150Hz this imposes some issues as well as I have shown in the charts in the link of post #27.
In that chart the impedance shown at 150hz is about 2 Ohms for one single core and when you added another core with the LV winding in Parallel the impedance on that end of the scale also drops to 1/2 or 1 ohm.
If you were add two more cores to double the ratio again the impedance at 150hz drops in 1/2 again and now your impedance is .5 ohms at 150Hz!!
8 cores would surely bring this as low as .25 ohms at 150Hz!!!!
This is for a 6V LV winding.
This is the reason I had refered to use many cores with a higher rated LV winding such as 15V and 8 cores, besides the core saturation issues with using a 6v LV winding.
Every time you double the amount of turns this increases the windings inductance value by 4.
Raising the inductance value by 4 for also increases the inductive reactance by 4 as well, this raises the low frequency impedance of the transformer by 4 as well.
Going from a 6V winding to a 15V LV winding will raise the LV windings impedance of for a single core approximately 6.25 times if my math is correct.
Hence 15V/6V( representing the turns difference between the two winding) squared=Xlohms*6.25 .
Another words a 15v winding will have 6.25 times a higher impedance than a 6V winding will.
By the time you have say 8x15V cores the impedance will be something like, 2ohms(for a 6v winding)*6.25/8= 1.56 ohms at 150Hz not very far from the original 2ohms for a single core, but with the capability of not saturating at 45v input at 150Hz.
Since you only require half of that amount of drive voltage it is possible to get away with only using 4 cores with with all of the HV windings in series, But the trade off in increasing the transformers total capacitance as well.
This drops the high frequency impedance as I have explained earlier.
The issue here is that the added total capacitance with the leakage inductance can put the transformers resonate frequency in to the audio range.
Adding a small amount of resistance to the primary side is the technique used to dampen this resonance.
The trade off of putting the HV windings in series lowers the leakage inductance by a factor of 4 per core as turns*2=L*4 and Leakage Inductance is L*1/4 but it doubles the capacitance per core at the same 0time.
This may not be so good when you are talking about a tube amp that can't deliver the large amounts of currents that a large SS amp can.
Again, This is considering the maximum levels of operation.
I have no issues of driving my panels at a normal listening levels using my 50 to 80 watt SS amp unless I decide to crank it up a bit with my projected impedance of .5 to .8 ohms at 20khz.
But for my little panel setup, my panels are only 35pf to 50pf and the transformer dominates the overall impedance and accounts for 90% of the power usage because of it.
90% of the power is wasted in the transformer itself as heat!!
This is how I discovered using 4 cores rather than two gave me better performance.
Not in SQ, But in how much power the amp has to produce for a given SPL using the two configurations.
There is just no way around this as we are stuck with the parameters that Power Toroid Transformers are designed for.
Unless, You design and build one just for ESL's.
I will go over that in my next post as I was finally able to take what I have learned and apply it to an example that doesn't look so bad, last night.
Anyhow,
Leakage inductance and winding inductance are not the same thing but they are related as far as the number of turns the winding has.
The leakage inductance for each core is multiplied by the number of cores to get the total, since they are connected in series, and share no mutual magnetic flux between the cores.
It is a lot to understand I know and it took me nearly 3 years to finally understand it to the point of where I am now and being able to explain it.
At low frequency's the ESL's reactance is very very high, and, has little to no effect on the impedance at the lowest frequency's and it is the Transformers primary inductance that determines the impedance at this point.
jer
HV winding typically meaning the 115V to 120V winding that would normally be called the primary but in our case is now the secondary winding.
2- 1:50, Okay that is understandable having a slightly higher ratio will do no harm and will increase the sensitivity some.
This is especially good when using a lower power amplifier as long as you don't go to high with the ratio this also lowers the resulting impedance.
2.3nf or .0023uf is about what I expected from a panel of that size.
The formula is Xc / Ratio^2= Reflected impedance and I use this online calculator to find Xc,
Electronics 2000 | Reactance Calculator
The theoretical impedance with a 1:50 ratio at 20Khz would be 3460ohms(Xc) / (50 * 50) Ratio squared = 1.384 ohms.
BUT, This figure will actually be lower than this because you have to add the transformer capacitance as well.
Let us just say that transformers capacitance is as high as 1600pf total, as they can range from 400pf to as much as 1200pf or more (for some) per core.
Now your total capacitance is ESLpf + TRANSFORMERpf = Total Xc of 2040 ohms.
Now your reflected impedance with a 1:50 ratio at 20Khz now becomes 2040/ (50*50)= .816 ohms at 20Khz!!
This is not so much of a problem since dipole panels have a rising frequency response of +10db per decade and when EQ'ed properly the signal can/will be some -20db lower at 20Khz than the level will be at 200hz.
Plus the components of the Crossover section, DC resistances of the transformers primary and such also adds resistance to the total as well.
But since you want to get down to 150Hz this imposes some issues as well as I have shown in the charts in the link of post #27.
In that chart the impedance shown at 150hz is about 2 Ohms for one single core and when you added another core with the LV winding in Parallel the impedance on that end of the scale also drops to 1/2 or 1 ohm.
If you were add two more cores to double the ratio again the impedance at 150hz drops in 1/2 again and now your impedance is .5 ohms at 150Hz!!
8 cores would surely bring this as low as .25 ohms at 150Hz!!!!
This is for a 6V LV winding.
This is the reason I had refered to use many cores with a higher rated LV winding such as 15V and 8 cores, besides the core saturation issues with using a 6v LV winding.
Every time you double the amount of turns this increases the windings inductance value by 4.
Raising the inductance value by 4 for also increases the inductive reactance by 4 as well, this raises the low frequency impedance of the transformer by 4 as well.
Going from a 6V winding to a 15V LV winding will raise the LV windings impedance of for a single core approximately 6.25 times if my math is correct.
Hence 15V/6V( representing the turns difference between the two winding) squared=Xlohms*6.25 .
Another words a 15v winding will have 6.25 times a higher impedance than a 6V winding will.
By the time you have say 8x15V cores the impedance will be something like, 2ohms(for a 6v winding)*6.25/8= 1.56 ohms at 150Hz not very far from the original 2ohms for a single core, but with the capability of not saturating at 45v input at 150Hz.
Since you only require half of that amount of drive voltage it is possible to get away with only using 4 cores with with all of the HV windings in series, But the trade off in increasing the transformers total capacitance as well.
This drops the high frequency impedance as I have explained earlier.
The issue here is that the added total capacitance with the leakage inductance can put the transformers resonate frequency in to the audio range.
Adding a small amount of resistance to the primary side is the technique used to dampen this resonance.
The trade off of putting the HV windings in series lowers the leakage inductance by a factor of 4 per core as turns*2=L*4 and Leakage Inductance is L*1/4 but it doubles the capacitance per core at the same 0time.
This may not be so good when you are talking about a tube amp that can't deliver the large amounts of currents that a large SS amp can.
Again, This is considering the maximum levels of operation.
I have no issues of driving my panels at a normal listening levels using my 50 to 80 watt SS amp unless I decide to crank it up a bit with my projected impedance of .5 to .8 ohms at 20khz.
But for my little panel setup, my panels are only 35pf to 50pf and the transformer dominates the overall impedance and accounts for 90% of the power usage because of it.
90% of the power is wasted in the transformer itself as heat!!
This is how I discovered using 4 cores rather than two gave me better performance.
Not in SQ, But in how much power the amp has to produce for a given SPL using the two configurations.
There is just no way around this as we are stuck with the parameters that Power Toroid Transformers are designed for.
Unless, You design and build one just for ESL's.
I will go over that in my next post as I was finally able to take what I have learned and apply it to an example that doesn't look so bad, last night.
Anyhow,
Leakage inductance and winding inductance are not the same thing but they are related as far as the number of turns the winding has.
The leakage inductance for each core is multiplied by the number of cores to get the total, since they are connected in series, and share no mutual magnetic flux between the cores.
It is a lot to understand I know and it took me nearly 3 years to finally understand it to the point of where I am now and being able to explain it.
At low frequency's the ESL's reactance is very very high, and, has little to no effect on the impedance at the lowest frequency's and it is the Transformers primary inductance that determines the impedance at this point.
jer
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